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THE PURCHASING POWER OF MONEY

THE MACMILLAN COMPANY'
NEW YORK • BOSTON • CHICAGO
SAN FRANCISCO

MACMILLAN & CO.,

L im it e d

LONDON • BOMBAY • CALCUTTA
MELBOURNE

TH E MACMILLAN CO. OF CANADA, L m

TORONTO

THE PURCHASING POWER
OF MONEY
ITS DETERMINATION
AND RELATION TO CREDIT
INTEREST AND CRISES

IRVING FISHER
rilO FESSO It o r PO LITIC AL e c o n o m y i n t a l e

U NIVERSITY

ASSISTED B T

HARRY G. BROWN
INSTRUCTOR IN PO LITIC AL ECONOMY IN YA L E U NIVERSITY

N E W AN D REVISED EDITION

Ifcfa fgfltfe
THE MACMILLAN COMPANY
1920

COPYM OHT,

1911,

Bt THE MACMILLAN COMPANY*
Set up and electrotvped. Published March, 19x1.

Ncttooofc $ r « *
J. S. Cashing Co.— Berwick <fc Smith Co.
Norwood, Mass., TJ.SJL

Co
THE

M E M O R Y OP

S IM O N N E W C O M B
G R EAT SCIENTIST, IN SP IR IN G

F R IE N D ,

PION EER IN TH E S T U D Y
OP
“ SO CIETAR Y C IR C U L A T IO N ”

PREFACE TO THE FIRST EDITION
T h e purpose of this book is to set forth the principles
determining the purchasing power of money and to
apply those principles to the study of historical changes
in that purchasing power, including in particular the
recent change in “ the cost of living,” which has aroused
world-wide discussion.
If the principles here advocated are correct, the pur
chasing power of money — or its reciprocal, the level of
prices — depends exclusively on five definite factors:
(1) the volume of money in circulation; (2) its velocity
of circulation; (3) the volume of bank deposits subject
to check; (4) its velocity; and (5) the volume of trade.
Each of these five magnitudes is extremely definite, and
their relation to the purchasing power of money is defi
nitely expressed by an “ equation of exchange.” In my
opinion, the branch of economics which treats of these
five regulators of purchasing power ought to be recog
nized and ultimately will be recognized as an exact
science, capable of precise formulation, demonstration,
and statistical verification.
The main contentions of this book are at bottom simply
a restatement and amplification of the old “ quantity
theory ” of money. With certain corrections in the usual
statements of that theory, it may still be called funda
mentally sound. What has long been needed is a candid
reexamination and revision of that venerable theory rather
than its repudiation.
Yet in the voluminous literature on money, there seems
to be very little that approaches accurate formulation and

vii

via

PREFACE TO THE FIRST EDITION

rigorous demonstration, — whether theoretical or statis
tical.
In making this attempt at reconstruction, I have the
satisfaction of finding myself for once a conservative
rather than a radical in economic theory. It has seemed
to me a scandal that academic economists have, through
outside clamor, been led into disagreements over the
fundamental propositions concerning money. This is due
to the confusion in which the subject has been thrown
by reason of the political controversies with which it has
become entangled.
As some one has said, it would seem that even the
theorems of Euclid would be challenged and doubted
if they should be appealed to by one political party as
against another. At any rate, since the “ quantity
theory ” has become the subject of political dispute, it
has lost prestige and has even come to be regarded by
many as an exploded fallacy. The attempts by pro
moters of unsound money to make' an improper use of the
quantity theory — as in the first Bryan campaign — led
many sound money men to the utter repudiation of the
quantity theory. The consequence has been that, espe
cially in America, the quantity theory needs to be rein
troduced into general knowledge.
Besides aiming to set forth the principles affecting the
purchasing power of money, this book aims to illustrate
and verify those principles by historical facts and statis
tics. In particular, the recent rise in prices is examined
in detail and traced to its several causes.
The study of the principles and facts concerning the
purchasing power of money is of far more than academic
interest. Such questions affect the welfare of every in
habitant of the civilized world. At each turn of the tide
of prices, millions of persons are benefited and other
millions are injured.

PREFACE TO THE FIRST EDITION

For a hundred years the world has been suffering from
periodic changes in the level of prices, producing alter
nate crises and depressions of trade. Only by knowledge,
both of the principles and of the facts involved, can such
fluctuations in future be prevented or mitigated, and only
by such knowledge can the losses which they entail be
avoided or reduced. It is not too much to say that the
evils of a variable monetary standard are among the most
serious economic evils with which civilization has to deal;
and the practical problem of finding a solution of the dif
ficulty is of international extent and importance. I have
proposed, very tentatively, a remedy for the evils of mon
etary instability. But the time is not yet ripe for the
acceptance of any working plan. What is at present most
needed is a clear and general public understanding of
principles and facts.
Toward such an end this book aims to contribute : —
1. A reconstruction of the quantity theory.
2. A discussion of the best form of index number.
3. Some mechanical methods of representing visually
the determination of the level of prices.
4. A practical method of estimating the velocity of
circulation of money.
5. The ascertainment statistically of the bank deposits
in the United States which are subject to check, as distinct
from “ individual deposits,” as usually published.
.6. An improved statistical evaluation of the volume
of trade, as well as of the remaining elements in the
equation of exchange.
7.
A thorough statistical verification of the (recon
structed) quantity theory of money.
As it is quite impossible to do justice to some of these
subjects without the use of mathematics, these have been
freely introduced, but have been relegated, so far as

PREFACE TO THE FIRST EDITION

possible, to Appendices. This plan, which is in accord
ance with that previously adopted in The Nature of Cap
ital and Income and The Rate of Interest, leaves the text
almost wholly nonmathematical.
Most of the statistical results review and confirm the
conclusions of Professor Kemmerer in his valuable Money
and Credit Instruments in their Relation to Greneral Prices,
which appeared while the present book was in course
of construction. I am greatly indebted to Professor
Kemmerer for reading the entire manuscript and for
much valuable criticism throughout.
My thanks are due to Professor F. Y. Edgeworth of
All Souls’ College, Oxford, and to Professor A. W. Flux
of Manchester for kindly looking through the manuscript
of the Appendix on index numbers and for suggestions
and criticisms.
To Dr. A. Piatt Andrew, now Assistant Secretary of
the Treasury, my thanks are due for his kindness, as
Special Assistant to the National Monetary Commission,
in putting the resources of that Commission at my dis
posal, and in working out, from the records of the office
of the Comptroller of the Currency, the volume of deposits
subject to check at various dates in the past. For cooper
ation in carrying out these same calculations, I am like
wise indebted to Mr. Lawrence O. Murray, Comptroller
of the Currency. These valuable figures are the first of
their kind.
To Mr. Gilpin of the New York Clearing House, my
thanks are due for his kindness in furnishing various
figures asked for and cited specifically in the text.
To Mr. Richard M. Hurd, President of the Lawyers
Mortgage’ Co., I am indebted for reading parts of the
manuscript and for valuable criticism.
To Mr. John O. Perrin, President of the American
National Bank of Indianapolis, I am indebted for statistics

PREFACE TO THE FIRST EDITION

of the “ activity” of bank accounts in his bank, and for
similar figures I am indebted to the officers of the National
New Haven Bank and the City Bank of New Haven. ^
My thanks are due to the Economic Journal for permis
sion to use unaltered some parts of my article on “ The
Mechanics of Bimetallism,” which first appeared in that
journal in 1894.
My thanks are due to the Journal of the Royal Statistical
Society for similar permission with reference to my article
on “ A Practical Method for estimating the Velocity of
Circulation of Money,” which appeared in December,
1909.
A number of my students have rendered valuable
service in gathering and coordinating statistics. I would
especially mention Mr. Seimin Inaoka, Mr. Morgan Porter,
Mr. N. S. Fineberg, Mr. W. E. Lagerquist, now in
structor at Cornell University, Messrs. G. S. and L. A.
Dole, Dr. John Bauer, now assistant professor at Cornell
University, Dr. John Kerr Towles, now instructor at the
University of Illinois, Dr. A. S. Field, now instructor at
Dartmouth College, Mr. A. G. Boesel, Mr. W. F. Hickernell, Mr. Yasuyiro Hayakawa, Mr. Chester A. Phillips,
and Mr. R. N. Griswold. Mr. Griswold performed the
lengthy calculations involved in ascertaining an index
of the volume of trade.
There are two persons to whom I am more indebted
than to any others. These are my brother, Mr. Her
bert W. Fisher, and my colleague, Dr. Harry G. Brown.
To my brother my thanks are due for a most searching
criticism of the whole book from the standpoint of peda
gogical exposition, and to Mr. Brown for general criticism
and suggestions as well as for detailed work throughout.
In recognition of Mr. Brown’s assistance, I have placed
his name on the title-page.
IRVING FISHER.
Y

ale

U n iv e r s it y ,

February, 1911.

PREFACE TO THE SECOND EDITION

second edition is a reprint of the first with the fol
lowing changes: —
1. Correction of occasional misprints.
2. Addition of data for 1910, 1911, and 1912, in the
tables on pages 304, 317, and the diagram between pages
306 and 307.
3. A change in Figure 1 (page 13) to make it conform
to the facts for 1912.
4. Changes in the table on page 147 with accompany
ing text to make the data correspond to the facts for 1912.
5. The insertion of an addendum on pages 492-493,
giving the revised figures for deposits subject to check as
calculated by Professor Wesley Clair Mitchell.
6. An appendix to the second edition (page 494 ff.) on
“ standardizing the dollar.”
For corrections of misprints and various helpful criti
cisms of the first edition I am under great obligations to a
number of friends and correspondents and particularly to
Major W. E. McKechnie, of the Indian Medical Service,
Etawah, United Provinces, India; Professor Warren M,
Persons, Colorado College, Colorado Springs, Colo.; Mr.
J. M. Keynes, Editor, Economic Journal, Kings College,
Cambridge; Carl Snyder, author,New York City; James
Bonar, Deputy Master of the Royal Mint, Ottawa, Canada;
Professor Allyn A. Young, Washington University, St.
Louis, Mo.; Professor Stephen Bauer, Director, Interna
tional Office of Labor Legislation, Basle, Switzerland;
Professor Wesley Clair Mitchell, New York City; Pro
fessor O. M. W. Sprague, Harvard University.
xii
T he

PREFACE TO THE SECOND EDITION

x iii

I have endeavored to avoid disturbing the plates of the
first edition more than was absolutely necessary. Other
wise I should have been glad to incorporate some changes
to make use of some valuable but general criticisms. In
particular I should have liked to modify somewhat the
statement of the theory of crises in Chapter IV and in
Chapter XI to make use of the helpful criticism of Miss
Minnie Throop England, of the University of Nebraska,
in The Quarterly Journal of Economics, November, 1912;
also to meet a criticism of Mr. Keynes’ to the effect
that, while my book shows that the changes in the quantity
of money do affect the price level, it does not show how
they do so. To those who feel the need of a more defi
nite picture of how the price level is affected by a change
in the quantity of money I refer the reader to my Ele
mentary Principles of Economics, pages 242-247, and to
other writers on this subject, particularly Cairns.

IRVING FISHER.

SUGGESTIONS TO READERS
1. 'The general reader will be chiefly interested in
Chapters I-VIII.
2. The cursory reader will find the gist of the book in
Chapter II.
3. Objectors to the quantity theory will find their theo
retical and statistical objections discussed in Chapters
VIII and XII respectively.
4. Students of financial history should read Chapter XII.
5. Currency reformers should read Chapter XIII.
6. The appendices are addressed mainly (though not
exclusively) to mathematical economists, for whom the chief
interest will probably lie with the Appendix to Chapter
X, on Index Numbers, (which should be read as a whole,)
and § 6 of the Appendix to Chapter XII, on the Method
of Determining Velocity of Circulation.
7. The remainder of the Appendix to Chapter XII is
supplied chiefly in order that statistical critics may be en
abled to verify the processes described in the text.
8. Chapter X and its Appendix are of chief interest to
students of index numbers, a subject as fascinating to some
as it is dry to others.
9. The analytical table of contents, the index, and the
running page headings have been constructed with espe
cial reference to the varying needs of different classes of
readers.
The book is, however, designed to constitute a complete
whole, and it is hoped that as many as possible of those
who approach it irom special viewpoints may, in the end,
read it all.
xiv

SUMMARY OF CONTENTS
CH APTER

II.

PAGI

P r im a r y D

e f i n i t i o n s ................................................................... ...........

t io n o f E x ch a n g e ”
III.

I nflu ence

IV .

is t u r b a n c e
d u r in g

VI.
VII.
VIII.

................................................................... 8 .
C urrency

e p o s it

therefore

P u r c h a s in g P o w e r o f M o n e t a s r e l a t e d t o t h e “ E qu a

P u r c h a s in g P o

E q u a t io n

and

T r a n s it io n P e

I n d ir e c t I n f l u e n c e s

I n d ir e c t I n f l u e n c e s (

I nfluence

Q u a n t it y

P u r c h a s in g P o w e r

P ow er

and

T he D

X
XL

S t a t is t ic a l V

e r if ic a t io n .

General H

Xn.

S t a t is t ic a l V

e r if ic a t io n .

XIII.

T he P ro blem

o f m a k in g

of
he

P r ic e s

P u r c h a s in g P o
est

m akes

w e r

I n d ex N um bers

90
112

O th er F actors

E ach Oth er

IX.

is p e r s io n

P u r c h a s in g P o w e r

M oney

P ow er

........................................................ 65

Continued)

M o n e t a r y S ystem s

and

............................................. 33

P u r c h a s in g

u r c h a s in g

E q u a t io n

th e

w er

r io d s

I nflu ence

necessary

149

Index

....................................................................1 84
P u r c h a s in g P o w e r

ecent

is t o r ic a l

ears

P u r c h a s in g P o w e r

e v ie w

276

Stable

319

m ore

198
234

•

Chapter

II •
III
V
V I .
VI I
VIII
X

• • • •
349
• • • • • .
367
...........................................................370
• • • • • • «
372
• • • • • • • •
376
•
.
.......................................... 379
.
♦
•
•
•
•
*
.
385

C hapter

XII

•

p p e n d ix t o

Chapter

p p e n d ix to

Chapter

p p e n d ix

Chapter

p p e n d ix

Chapter

p p e n d ix to

Chapter

p p e n d ix t o

Chapter

p p e n d ix

•

430

ANALYTICAL TABLE OF CONTENTS
CHAPTER I
P r im a r y D

e f in it io n s
PAG E

•
.
§ 1. Wealth and e x c h a n g e ..........................................
§ 2. Exchangeable g o o d s ............................................................ 4
§ 3. Circulation of money against goods .
.
.
.
.
.
CHAPTER II
P

u r c h a s in g

P ow er

M oney

■

as related

to th e

q u a t io n

E xchange

§ 1.
§ 2.
§ 3.
§ 4.
§ 5.

The various circulating media . a .
•
•
.
The equation of exchange arithmetically expressed
The equation of exchange mechanically expressed
The equation of exchange algebraically expressed
Conclusion and illustrations
.
.
.
.
.
.

•

•
*

8
14
21
24
28

CHAPTER III
I nflu ence

e p o s it

C urrency

o n t iie

E q u a t io n

AND TH EREFORE ON PU RC H ASIN G P O W E R

§ 1.
§ 2.
§ 3.
§ 4.
§ 5.
§ 6.

The mystery of circulating c r e d i t ...................................
The basis of circulating credit .
•
.
•
.
Banking limitations..........................................
The revised equation of e x c h a n g e ...................................
Deposit currency normally proportioned to money •
Summary.............................................................................

.
.
.
.
.

40
42
47
49
53

CHAPTER IV
D

is t u r b a n c e

E q u a t io n
T

§ 1.
§ 2.
§ S.
§ 4.

and

r a n s it io n

u r c h a s in g

P ow er

d u r in g

P e r io d s

Tardiness of interest adjustment to price movements
.
•
IIow a rise of prices generates a further rise . .
. .
Extent of disturbances in e q u a tio n ................................... 6 1
How a rise of prices culminates in a crisis
.
.
.
.

xvii

65
68
64

XV111

ANALYTICAL TABLE OF CONTENTS
PAG*

§ 5. Completion of the credit cycle.......................................... . 6 7
§ 6. Summary...................................................................
.
.

CHAPTER V
I n d ir e c t I n f l u e n c e s

u r c h a s in g

P ow eb

.§ 1. Influence of conditions of production and consumption on
trade and therefore on prices
.
74
§ 2. Influence of conditions connecting producers and consumers
on trade and therefore on prices.......................................... 77
§ 3. Influence of individual habits on velocities of circulation and
therefore on p r i c e s .......................................................... 79
§ 4. Influence of systems of payment on velocities of circulation
and therefore on p r i c e s .................................................. 83
§ 5. Influence of general causes on velocities of circulation and
therefore on p r i c e s ...........................................................87
§ 6. Influences on the volume of deposits subject to check and
therefore on p r i c e s .......................................... .
. 88

CHAPTER

I n d ir e c t I n f l u e n c e s (

Continued)

§ 1. Influence of foreign trade on the quantity of money and there
fore on p r i c e s ...................................................................90
§ 2. Influence of melting and minting on the quantity of money
and therefore on p r i c e s .................................................. 96
§ 3. Influence of the production and consumption of money metals
on the quantity of money and therefore on prices
•
.
99
§ 4. Mechanical illustration of these influences
.
.
•
. 104

CHAPTER VII
I n f l u e n c e o f M o n e t a r y S y s te m s o n P u r c h a s in g P ow er

§ 1. Gresham’ s L a w ................................................................... 112
§ 2. Cases \fhen bimetallism fails immediately
. .
.
.
....115
§ 3. Cases when bimetallism fails after production overtakes con
sumption
............................................................................121
§ 4. The limping standard ; the gold-exchange standard
.
. 127
§ 5. Bimetallism in France
.
.
.
.
.
.
.
.
132

ANALYTICAL TABLE OF CONTENTS

x ix
FAGE

§ 6.
§ 7.
§ 8.
§ 9.

Lessons of French e x p e r i m e n t .......................................... 135
The limping standard in I n d i a .......................................... 138
The limping standard in the United States
.
.
.
.
140
General description of system in the United States.
•
. 143

CHAPTER VIII
I n f l u e n c e o f Q u a n t i t y o f M o n e y a n d O t h e r F a c t o r s on
P u r c h a s in g P o w e r a n d o n E a c h O t h e r

§ 1. The equation of exchange implies no causal sequence .
.
149
§ 2. Effects of a change in money ( M ). Quantity theory in causal
s e n s e ....................................................................................151
§ 3. Quantity theory not strictly true during transition periods . 159
§ 4. Effects of a change in deposits (JT) relatively to money ( I f )
162
§ 5. Effects of changes in velocities of circulation ( Y and V 1)
. 164
§ 6. Effects of changes in volume of trade (the Q's)
.
.
. 165
§ 7. Can the price level be regarded as cause as well as effect ?
. 169
§ 8. Distinction between causation of individual prices and the
price l e v e l ........................................................................... 174
§ 9. S u m m a r y ........................................................................... 181
CHAPTER IX
T

is f e r s i o n o f

P r ic e s
P

m ak es necessary a n

u r c h a s in g

Index

Pow er

§ 1. Some prices cannot respond readily to price movements.
. 184
§ 2. Consequently other prices must over-respond .
.
.
.
190
§ 3. Transformation of the right side of the equation of exchange
from 'LpQ to P T ...................................................................194
§4. S u m m a r y ..................................
.
.
.
.
196
CHAPTER X
T h e B e s t I n d e x N u m b ers o f P u r c h a s in g P ow er

§ 1.
§ 2.
§ 3.
§ 4.
§ 5.
§ 6.

Forms of index n u m b e r s .................................................. 198
Various purposes of index numbers
;
.
204
An index number as a standard of deferred payments .
. 208
Deferred payments based on total exchanges .
.
.
.
217
Practical r e s t r i c t i o n s ........................................................... 225
Summary...........................................................
.
. 231

ANALYTICAL TABLE OF CONTENTS
CHAPTER X I
Statistical V erification, General Historical R eview

§ 1.
§ 2.
§ 3.
§ 4.
§ 6.
* § 6.
•§ 7.
§ 8.
§ 9.
§ 10.
§ 11.
§ 12.
§ 13.
§ 14.
§ 15.
§ 16.
§ 17.
§ 18.

PAG*
234
The last thousand y e a r s .......................................... ........
The last four c e n tu r ie s ...........................................................237
The nineteenth century
238
Its five price movements .
.......................................... 240
Retrospect
.
.
.
.
.
.
.
.
.
.
246
Outlook .
.
.
.
.
.
.
.
.
.
.
248
Paper m o n e y ...................................
.
.
.
.
260
Paper money in P r a n c e ...........................................................252
Paper money in England1...........................................................253
Paper money in A ustria...........................................................255
Early American paper money.................................................. 256
The “ greenbacks” ................................................................... 258
Confidence in the green b a ck .................................................. 261
Confederate paper money
.
.
.
.
.
.
.
263
Deposit currency and crises .
265
Particular c r i s e s .................................. •
.
.
.
267
Velocity of deposits and crises
.
.
.
.
.
.
270
Summary..........................................
274

§ 1.
§ 2.
§3.
§ 4.
§ 5.
§ 6.
§ 7.
§ 8.
§ 9.
§ 10.
§ 11.

CHAPTER X n
Statistical V erification. R ecent Y ears
Professor Kemmerer’s statistics, 1879-1908 . .
. .
276
New estimates for M and Jf7, 1896-1909
.
.
.
.
280
New estimates for M’ V7and F ', 1896-1909 .
.
.
.
282
New estimates for M V and V , 1896-1909
. .
.
.
285
Estimates for T and P, 1896-1909 ..........................................
290
P directly and indirectly calculated
.
.
.
.
.
292
Correcting discrepancies...........................................................298
The final r e s u l t s ................................................................... 304
The comparative importance of price-raising causes
.
. 307
Influence of antecedent causes such as tariffs, etc. .
.
.311
Results and by-products of Chapter XI I .
.
.
.
.
315

CHAPTER XHI
T he Problem of making P urchasing P ower more Stable
§ 1. The problem of monetary r e f o r m ..........................................319
§ 2. Bimetallism as a s o l u t i o n .................................................. 323
§ 3. Other proposed solutions.................................. ........
328
§ 4. The tabular s t a n d a r d ...........................................................332
§ 6. The writer’s proposal
.
.
•
•
•
•
•
.
337
§ 6. Summary and conclusion..................................................
348

APPENDICES
A ppendix to Chapter II
PAG*

§ 1 (to Ch. II, § 3). The concept of an average .
.
.
.
(to Ch. II, § 6). The concept of velocity of circulation .
.
(to Ch. II, § 6). “ Arrays” of p ’s, Q’s, and p Q’s .
(to Ch. II, § 6). “ Arrays” of e’s, m’s, and 7 ’s
(to Ch. II, § 6). The coin-transfer concept of velocity and the
concept of time of t u r n o v e i ..................................................
§ 6 (to Ch. II, § 5). Algebraic demonstration of equation of ex
change
....................................................................................
§ 7 (to Ch. II, § 5). P must be a specific form of average in order
to vary directly as M and V and inversely as the § ’s, .
.

349
352
355
358
362
364
364

A ppendix to Chapter III
§ 1 (to Ch. Ill, § 2). “ Arrays” of k's and r’s
367
§ 2 (to Ch. Ill, § 4). Algebraic demonstration of equation of ex
change including deposit c u r r e n c y .......................................... 368
A ppendix to Chapter V
§ 1 (to Ch. V, § 6).

Effect of time credit on equation of exchange

370

A ppendix to Chapter YI
§ 1 (to Ch. VI, § 1). Modification of equation of exchange required
by international trade
.
.
. " .................................. 372
A ppendix to Chapter YII
§ 1 (to Ch. VII, § 2). Money substitutes unlike other substitutes . 376
§ 2 (to Ch. VII, § 2). Limits for ratios within which bimetallism
is possible .................................................................................... 378
A ppendix to Chapter VIII
§ 1 (to Ch. VIII, § 6).
§ 2 (to Ch. VIII, § 8).

Statistics of turnover at Yale University .
Four types of commodities contrasted
xxi

379
382

APPENDICES

x x ii

p p e n d ix t o

Ch apter

X
FJL6K

§ 1. Each form of index number for prices implies a correlative
index number for q u a n t i t i e s ...................................................385
§ 2. Index numbers for prices occur in arithmetical pairs as also
do index numbers for quantities.................................................. 390
§ 3. General meanings of p *s and Q’s ...........................................392
§ 4. Review of 44 formulae, heading table columns
.
#
. 393
• § 5. Review of 8 tests, heading table r o w s .................................. 400
■ § 6. The interior of the table; column 11 in particular .
.
. 408
§ 7. The 44 formulae c o m p a r e d ................................................... 418
§ 8. Reasons for preferring the median practically
.
.
. 425
§ 9. Summary.....................................................................................428
A ppendix to Chapter XII
§1
§2
§3
§4

(to Ch. XII, § 1). Professor Kemmerer’s calculations .
. 430
(to Ch. XII, § 2). Method of calculating M .
.
. 432
(to Ch. XII, § 2). Method of calculating M* .
.
.
. 434
(to Ch. XII, § 3). Method of calculating W V 1 for 1890 and
1909 ............................................................................................ ..441
§ 5 (to Ch. XII, § 3). Method of calculating M V* for 1897-1908 440
§ 6 (to Ch. XII, § 4). General practical formula for calculating V 448
§ 7 (to Ch. XII, § 4). Application of formula to calculations of
V for 1896 and 1909 ................................................................... ..460
§ 8 (to Ch. XII, § 4). Interpolating Values of V for 1897-1908 . 477
§ 9 (to Ch. XII, § 5). Method of calculating T .
478
§ 10 (to Ch. XII, § 6). Method of calculating P .
486
§ 11 (to Ch. XII, § 7). Mutual adjustments of calculated values
of M, J/7, F, F , P, T
...........................................................488
§12 (to Ch. XII, § 8). Credit and cash transactions. Comparison
with Kinley’s estimates.................................................................491
§ 13 (to whole Ch.). Addendum to second edition
.
.
. 492
Appendix on “ Standardizing the Dollar.”
..................................494

ADDENDUM
(In this revised edition figures for 1910-1912 are given on pages 304,317.
See also page 492.)

Data have just become available by which to bring down
through 1910 the statistics of Chapter XII. The results
are as follows:
M a g n it u d e s in t h e E q u a t io n o p E x c h a n g e f o r

Jf'

1910*

j / r + j r r ' PT

As first calculated

1.64 7.24 21 62.8 103.7 397

416

412

As finally adjusted

1.64 7.23 21 52.7 104.0 399

415

The table shows that the figures, as first calculated,
conform admirably to the equation of exchange. The
adjustment needed, to produce perfect conformity, in only
one case reaches the half of one per cent I
From the adjusted figures we may calculate the per
centages of cash and check transactions (M V^JiTT+W V1
and
These are 8% and 92%,
which may be added to the table on page 317. The
ratio of deposits to money (J f'/J f) is 4.4, which shows
*
The above figures may be inserted by the reader in the tables on
pages 280, 281, 284, 285, 290, 292, 293, 304. The methods of deriving
the figures are in general the same as those explained in the Appendix to
Chapter XII. The antecedent figures on which the above table depends
may be inserted by the reader as follows:
M. On page 432 add (to the bottom of columns 1-8 incl.) in tlie table
the following: 1910, 3.42, 3.42, .32, 1.41, 3.3%, 1.46, 1.64.
MK It is not necessary to complete the table on page 435, as the
Comptroller’s Report for 1910 (p. 64) gives for the first time deposits
subject to check (7.82 billions). To this 7.82, however, three corrections
are needed: (1) subtract .29 for 44savings accounts ” improperly included
(estimated for me by the Comptroller’s Office at half of the figure in note
<z, lower table, p. 64, Comptr. R p t.); (2) subtract .54 as 44exchanges
for clearing house” ( = J times those for national banks); (3) add .25
xxiii

x x iv

ADDENDUM

a great increase over 1909. The disproportionate growth
of deposits relatively to money and the excessive velocity
of circulation (52.7) of deposits, substantially equal to the
unprecedented figure for 1909, are disquieting symptoms
and serve only to confirm the forebodings in the text.
For aid in working out the figures in this addendum I
am. indebted to three of my students, Mr. H. A.iW .
Duckert, Mr. J. M. Shortliffe, and Mr. M. G. Hastings,
as the Comptroller’s Office estimate, for me, of unreported deposits sub
ject to check. By applying these corrections we obtain 7.24.
V. I have simply taken 21 as a safe approximate estimate on the basis
of the previous statistics of V (p. 478) and its assumed relation to V f.
M f V 1 and V f. Add to columns 1-7 of table on page 448 the following:
1910, 97.3, 68.4, 429.3, .89 (by extrapolation, an unsafe guide), 382, 62.8.
P. This is obtained (on the principles of the table on page 487) from
the index number 131.6 of wholesale prices for 1910 (kindly supplied in
advance of publication by the Bureau of Labor) and the average price
96.2 of stocks as given by the Commercial and Financial Chronicle, both
being compared with the respective figures for 1909, viz. 126.5 and 97.5.
They are combined by “ weighting ” the wholesale prices 10 and the stock
prices 1 and reducing the results so that the average for 1909 shall be 100.
T. This is obtained: (a) by continuing columns 1-5 of the table on
page 479 by inserting: 1910, 160, 113,162,164; (the extension of column
2 for 1910 is made by means of somewhat more complete data than
those enumerated on pages 480-482) ; (b) by combining the result, 164,
obtained for column 5 with the figures for railway cars handled. These
were 19.8 millions for 1909 and 22.3 for 1910. Column 5 being weighted
10 and the car figures 1, we get as indices of trade: for 1909, 1718, and
for 1910, 1763, showing an increase of 2.6%, which, applied to the
(corrected) estimate of the absolute trade of 1909, viz. 387 billions, gives
397 as the absolute trade in 1910.
(The opportunity is here taken to correct an inadvertence on pp. 480 ff.
It should have been there stated that, of the 41 categories mentioned,
some are alternative and not independent items, viz. those having the
same names and differing only in the number of cities; also that the dates
given do not imply that the items opposite are in all cases used for all
the intervening time, but only for such periods as the items were actually
available.)
It is noticeable that the changes in business in 1910 as compared with
1909 are somewhat irregular; the sales of stocks have declined; exports
and imports (both of them) have declined about 10%.

THE PURCHASING POWER OF MONEY

THE PURCHASING POWER OP MONEY
CHAPTER 1 1
PRIMARY DEFINITIONS

§1
In order to make clear the relation which the topic
treated in this book bears to the general subject of
economics, some primary definitions are necessary.
In the first place, economics itself may be defined as •
the science of wealth, and wealth may be defined as
material objects owned by human beings. Of wealth,
therefore, there are two essential attributes: material
ity and appropriation. For it is not all material things
that are included under wealth, but only such as have
been appropriated. Wealth does not include the sun,
moon, and other heavenly bodies, nor even all parts
of the surface of this planet, but only such parts as
have been appropriated to the use of mankind. It
is, then, appropriated parts of the earth’s surface and
the appropriated objects upon it which constitute
wealth.
For.. convenience, wealth may be classified under
three heads: real estate, commodities, and human
beings. Real estate includes the surface of the earth
and the other wealth attached thereto — improvements
such as buildings, fences, drains, railways, street im1 This chapter is mainly a condensation of Chapters I and II of
the author’s Nature of Capital and Income, New York (Macmillan),
1906..

THE PURCHASING POWER OF MONEY

[C h a p .

provements, and so on. Commodities include all mova
ble wealth (except man himself), whether raw materials
or finished products. There is one particular variety
of commodity — a certain finished product — which
is of especial importance in the subject of which this
book treats; namely, money.. Any commodity to be
called “ money ” must be generally acceptable in exchange,
and any commodity generally acceptable in exchange
should be called money. The best example of a money
commodity is found to-day in gold coins.
Of all wealth, man himself is a species. Like his
horses or his cattle, he is himself a material object, and
like them, he is owned; for if slave, he is owned by
another, and if free, by himself.1
But though human beings may be considered as
wealth, human qualities, such as skill, intelligence, and
inventiveness, are not wealth. Just as the hardness
of steel is hot wealth, but merely a quality of one par
ticular kind of wealth,— hard steel, — so the skill of a
workman is not wealth, but merely a quality of another
particular kind of wealth— skilled workman. Similarly,
intelligence is not wealth, but an intelligent man is
wealth.
Since materiality is one of the two essential attributes
of wealth, any article of wealth may be measured in
physical units. Land is measured in acres; coal, in
tons; milk, in quarts; and wheat, in bushels.- There
fore, for estimating the quantities of different articles
of wealth, all the various physical units of measurement
1 If we wish to include only slaves as wealth and not free men,
we shall have to amend our definition of wealth so as to read:
Wealth consists of material objects owned by human beings and
external to the owner. For the purpose of this book it makes no
practical difference whether this narrower meaning or the broader
one be employed.

S ec. 1]

PRIMARY DEFINITIONS

may be employed: linear measure, square measure,
cubic measure, and measure by weight.
Whenever any species of wealth is measured in its
physical units, a first step is taken toward the measure
ment of that mysterious magnitude called “ value.”
Sometimes value is Iboked upon as a psychical and some
times as a physical phenomenon. But, although the
determination of value always involves .a psychical
process— judgment — yet the terms in which the re
sults are expressed and measured are physical.
It is desirable, for the sake of clearness, to lead up
to the concept of value by means of three preliminary
concepts; namely, transfer, exchange, and price.
A transfer of wealth is a change in its ownership.
An exchange consists of two mutual and voluntarytransfers, each in consideration of the other.
When a certain quantity of one kind of wealth is
exchanged for a certain quantity of another kind, we
may divide one of the two quantities by the other,
and obtain the price of the latter. For instance, if
two dollars of gold are exchanged for three bushels of
wheat, the price of the wheat in gold is two thirds of a
dollar per bushel; and. the price of the gold in wheat
is one and a half bushels per dollar. It is to be noticed
that these are ratios of two physical quantities, the units
for measuring which are quite different from each other.
One commodity is measured in bushels, or units of
volume of wheat, the other in dollars, or units of weight
of gold. In general, a price of any species of wealth is
merely the ratio of two physical quantities, in whatever
way each may originally be measured.
This brings us, at last, to the concept of value. The
value of any item of wealth is its price multiplied by its
quantity. Thus, if half a dollar per bushel is the price

THE PURCHASING POWER OF MONEY

[C hap . 1

of wheat, the value of a hundred bushels of wheat is
fifty dollars.

§2
Hitherto we have confined our discussion to some
of the consequences of the first prerequisite of wealth —
that it must be material. We turn now to the second
prerequisite, namely, that it must be owned. To own.
wealth is simply to have the right to benefit by it
that is, the right to enjoy its services or benefits/ Thus
the owner of a loaf of bread has the right to benefit bj
it by eating it, by selling it, or by otherwise disposing
of it. The man who owns a house has the right to
benefit by enjoying its shelter, by selling it, or by rent
ing it. This right, the right to or in the benefits of
wealth— or more briefly, the right to or in the wealth it
self — is called a “ property right ” or simply “ property.”
If things were always owned in fee simple, i.e. if there
were no division of ownership,— no partnership rights,
no shares, and no stock companies, — there would be
little practical need to distinguish property from wealth;
and as a matter of fact, in the rough popular usage, any
article of wealth, and especially real estate, is often
inaccurately called a “ piece of property.” But the
ownership of wealth is frequently divided; and this
fact necessitates a careful distinction between the thing
owned and the rights of the owners. Thus, a railroad
is wealth. Its shares and bonded debt are rights to
this wealth. Each owner of shares or bonds has the
right to a fractional part of the benefits from the railway.
The total of these rights comprises the complete owner
ship of, or property in, the railway.
Like wealth, property rights also may be meas
ured ; but in units of a different character. The units

S ec. 2]

PRIMARY DEFINITIONS

of property are not physical, but consist of abstract
rights to the benefits of wealth. If a man has twentyfive shares in a certain railway company, the measure
ment of his property is twenty-five units just as truly
as though he had twenty-five bushels of wheat. What
he has is twenty-five rights of a specific sort.
There exist various units of property for measuring
property, as there are various units of wealth for meas
uring wealth; and to property may be applied pre
cisely the same concepts of transfer, exchange, price,
and value which are applied to wealth.
Besides the distinction between wealth and property
rights, another distinction should here be noted. This is
the distinction between property rights and certificates
of those rights. The former are the rights to use wealth,
the latter are merely the written evidence of those rights.
Thus, the right to receive dividends from a railroad
is property, but the written paper evidencing that
right is a stock certificate. The right to a railway
trip is a property right, the ticket evidencing that
right is a certificate of property. The promise of
a bank is a property right; the bank note on
which that promise is engraved is a certificate of
property.
Any property right which is generally acceptable in
exchange may be called “ money.” Its printed evi
dence is also called money. Hence there arise three
meanings of the term money, viz. its meaning in the
sense of wealth; its meaning in the sense of property; 1
and its meaning in the sense of written evidence.
From the standpoint of economic analysis the prop
erty sense is the most important.
1
Cf. Menger, Ilandworterbuch der Staatswissenschaften, Jena
(Fischer), Vol. IV, 1900, Article, “ Geld,” pp. 69-71.

THE PtmCHASING POWER OF MONET

[C h a p .

What we have been speaking of as property is the right
to the services, uses, or benefits of wealth. By benefits
of wealth is meant the desirable events which occur by
means of wealth. Like wealth and property, benefits
also may be measured, but in units of a still different
character. Benefits are reckoned either'" by time,” — as
the services of a gardener or of a dwelling house; or
“ by the piece,” — as the use of a plow or a telephone.
And just as the concepts of transfer, exchange, price,
and value apply to wealth and property, so do they
apply to benefits.
The uses (benefits) of wealth, with which we have been
dealing, should be distinguished from the utility of
wealth. The one means desirable events, the other,
the desirability of those events. The one is usually
outside of the mind, the other always inside.
Whenever we speak of rights to benefits, the benefits
referred to are future benefits. The owner of a house
owns the right to use it from the present instant on
ward. Its past use has perished and is no longer sub
ject to ownership.
The term “ goods” will be used in this book simply as
a convenient collective term to include wealth, properly,
and benefits. The transfer, exchange, price, and value of
goods take on innumerable forms. Under price alone,
as thus fully applied to goods, fall rent, wages, rates
of interest, prices in terms of money, and prices in
terms of other goods. But we shall be chiefly con
cerned in this book with prices of goods in terms of
money.
§3
' Little has yet been said as to the relation of wealth,
property and benefits to time. A certain quantity
of goods may be either a quantity existing at a partic

S ec. 3]

PRIMARY DEFINITIONS

ular instant of time or a quantity produced, consumed,
transported, or exchanged during a period of time.
The first quantity is a stock, or fund, of goods; the
second is a flow, or stream, of goods. The amount of
wheat in a flour mill on any definite date is a stock of
wheat, while the monthly or weekly amounts which
come in or go out constitute a flow of wheat. The
amount of mined coal existing in the United States at
any given moment is a stock of mined coal; the weekly
amount mined is a flow of coal.
There are many applications of this distinction; for
instance, to capital and income. A stock of goods,
whether wealth or property, existing at an instant of
time is called capital. A flow of benefits from such
capital during a period- of time is called “ income.” In
come, therefore, is one important kind of economic flow.
Besides income, economic flows are of three chief classes,
representing respectively changes of condition (such
as production or consumption), changes of position (such
as transportation, exportation, and importation), and
changes of ownership, which we have already called
“ transfers.” Trade is a flow of transfers. Whether for
eign or domestic, it is simply the exchange of a stream of
transferred rights in goods for an equivalent stream
of transferred money or money substitutes. The second
of these two streams is called the “ circulation” of money.
The equation between the two is called the “ equation
of exchange ” ; and it is this equation that constitutes
the subject matter of the present book.

CHAPTER II
’ PURCHASING POWER OF MONEY AS RELATED TO THE
EQUATION OF EXCHANGE
/

§ i
W e define -money as what is generally acceptable in
exchange for goods.1 The facility with which it may
thus be exchanged, or its general acceptability, is its
distinguishing characteristic. The general acceptability
may be reenforced by law, the money thus becoming
what is known as “ legal tender” ; but such reenforce
ment is not essential. All that is necessary in order that
any good may be money is that general acceptability
attach to it. On the frontier, without any legal sanc
tion, money is sometimes gold dust or gold nuggets.
In the Colony of Virginia it was tobacco. Among the
Indians in New England it was wampum. “ In German
New Guinea the bent tusks of a boar are used as money.
In California red birds’ heads have been used in the
same way.” 2 Stone money and shell money are so used
in Melanesia.3 “ In Burmah Chinese gambling counters
are used as money. Guttapercha tokens issued by
1 For discussions on the definition of money, see A. Piatt An
drew, “ What ought to bo called M oney” in Quarterly Journal of
Economics, Vol. X I I I ; Jevons, Money and the Mechanism of Ex
change, London (Kegan Paul) and New York (Appleton), 1896;
Palgrave, Dictionary of Political Economy; Walker, Money, and
other treatises and textbooks.
2 Sumner, Folkways, Boston (Ginn), 1907, p. 147.
8 Ibid., p. 150.

Sec. 1]

THE EQUATION OF EXCHANGE

street car companies in South America are said to be
used in the same way.” 1 Not many years ago in a
town in New York state, similar tokens got into local
circulation until their issue was forbidden by the United
States government. In Mexico large cacao beans
of relatively, poor quality were used as money, and on
the west coast of Africa little mats were used.2 The
list could be extended indefinitely. But whatever the
substance of such a commodity, it is general exchange
ability which makes it money.
On the other hand, even what is macje legal tender
may, by general usage, be deprived of its practical char
acter as money. During the Civil War the govern
ment attempted to circulate fifty-dollar notes, bearing
interest at 7.3 per cent, so that the interest amounted
to the very easily computed amount of a cent a day.
The notes, however, failed to circulate. In spite of the
attempt to make their exchange easy, people preferred
to keep them for the sake of the interest.3 Money
never bears interest except in the sense of creating con
venience in the process of exchange. This convenience
is the special service of money and offsets the apparent
loss of interest involved in keeping it in one’s pocket
instead of investing.
There are various degrees of exchangeability which
must be transcended before we arrive at real money.
Of all.kinds of goods, perhaps the least exchangeable
is real estate. Only in case some person happens to be
found who wants it, can a piece of real estate be traded.
A mortgage on real estate is one degree more exchange
able. Yet even a mortgage is less exchangeable than a
well-known and safe corporation security; and a cor1 Sumner, Folkways, p. 148.
2 Ibid.
* See Jovons, Money and the Mechanism of Exchange, p. 245.

THE PURCHASING POWER OF MONEY

[C h a p .

poration security is less exchangeable than a government
bond. In fact persons not infrequently buy govern
ment bonds as merely temporary investments, intending
to sell them again as soon as permanent investments
yielding better interest are obtainable. One degree
more exchangeable than a government bond is a bill
of exchange; one degree more exchangeable than a bill
of exchange is a sight draft; while a check is almost
as exchangeable as money itself. Yet no one of these
is really money for none of them is “ generally accept
able.”
If we confine our attention to present and normal
conditions, and to those means of exchange which either
are money or most nearly approximate it, we shall
find that money itself belongs to a general class of
property rights which we may call “ currency ” or
“ circulating media.” Currency includes any type of
property right which, whether generally acceptable or
not, does actually, for its chief purpose and use, serve
as a means of exchange.
Circulating media are of two chief classes: (1) money;
(2) bank deposits, which will be treated fully in the next
chapter. By means of checks, bank deposits serve as
a means of payment in exchange for other goods. A
check is the “ certificate” or evidence of the transfer
of bank deposits. It is acceptable to the payee only
by his consent. It would not be generally accepted by
strangers. Yet by checks, bank deposits even more
than money do actually serve as a medium of exchange.
Practically speaking, money and bank deposits subject
to check are the only circulating media. If post-office
orders and telegraphic transfer are to be included, they
may be regarded as certificates of transfer of special
deposits, the post office or telegraph company serving

S ec. 1]

THE EQUATION OP EXCHANGE

the purpose, for these special transactions, of a bank of
deposit.
But while a bank deposit transferable by check is
included as circulating media, it is not money. A
bank note, on the other hand, is both circulating
medium and money. Between these two lies the final
line of distinction between what is money and what
is not. < True, the line is delicately drawn, especially
when we come to such checks as cashier’s checks or
certified checks, for the latter are almost identical with
bank notes. Each is a demand liability on a bank,
and each confers on the holder the right to draw money.
Yet while a note is generally acceptable in exchange, a
check is specially acceptable only, i.e. only by the con
sent of the payee. Real money rights are what a payee
accepts without question, because he is induced to do
so either by “ legal tender” laws or by a well-established
custom.1
Of real money there are two kinds: primary and
fiduciary. Money is called “ primary” if it is a commod
ity which has just as much value in some use other than
mpney as it has in monetary use. Primary money has
its full value independently of any other wealth. Fidu
ciary money, on the other hand, is money the value
of which depends partly or wholly on the confidence
that the owner can exchange it for other goods, e.g. for
primary money at a bank or government office, or at any
rate for discharge of debts or purchase of goods of mer
chants. The chief example of primary money is gold
coin; the chief example of fiduciary money is bank
notes. The qualities of primary money which make for
exchangeability are numerous. The most important
1 See Francis Walker, Money, Trade, and Industry, New York
(Holt), 1879, Chapter I.

THE PURCHASING POWER OF MONET

[Chap. II

are portability, durability, and divisibility.1 The chief
quality of fiduciary money which makes it exchangeable
is its redeemability in primary money, or else its im
posed character of legal tender.
Bank notes and all other fiduciary money, as well as
bank deposits, circulate by certificates often called
“ tokens.” “ Token coins” are included in this de
scription. The value of these tokens, apart from the
rights they convey, is small. Thus the value of a silver
dollar, as wealth, is only about forty cents; that is all
that the actual silver in it is worth. Its value as prop
erty, however, is one hundred cents; for its holder has
a legal right to use it in paying a debt to that amount,
and a customary right to so use it in payment for
goods. Likewise, the property value of a fifty-cent
piece, a quarter, a ten-cent piece, a five-cent piece, or
a one-cent piece is considerably greater than its value
as wealth. The value of a paper dollar as wealth — for
instance, a silver certificate — is almost nothing. It is
worth just its value as paper, and no more. But its
value as property is a hundred cents, that is, the equiva
lent of one gold dollar. It represents to that extent a
claim of the holder on the wealth of the community.
Figure 1 indicates the classification of all circulating
media in the United States. It shows that the total
amount of circulating media is about 8£ billions, of
which about 7 billions are bank deposits subject to
check, and 1J billions, money; and that of this 1}
billions of money, 1 billion is fiduciary money and only
about \ a billion, primary money.
In the present chapter we shall exclude the consider
ation of bank deposits or check circulation and confine
our attention to the circulation of money, primary
1 See Jevons, Money and the Mechanism of Exchange, Chapter V.

Sec. 1]

t h e EQUATION OF EXCHANGE

and fiduciary. In the United States, the only primary
money is gold coin. The fiduciary money includes
(1) token coins, viz. silver dollars, fractional silver,
and minor coins (“ nickels” and cents); (2) paper
money, viz. (a) certifi
cates for gold and sil
ver, and (b) promissory
notes, whether of the
D e p o s it s s u b j e c t
United States govern
ment ("greenbacks” ),
TO CHECK
or of the National
banks.
Q i
Checks aside, we F id u c ia r y
m oney
B il l io n s
may classify exchanges Primary! ^
into three groups: the M oney
exchange s of goods bSS-n
against goods, or bar
Fig. 1.
ter; the exchange of
money against money, or changing money; and the
exchange of money against goods, or purchase and sale.
Only the last-named species of exchange makes up what
we call the “ circulation” of money. The circulation
of money signifies, therefore, the aggregate amount of
its transfers against goods. All money held for circula
tion, i.e. all money, except what is in the banks and
United States government’s vaults, is called “ money in
circulation.”
The chief object of this book is to explain the causes
determining the- purchasing power of money. The
purchasing power of money is indicated by the quan
tities of other goods which a given quantity of money
will buy. The lower we find the prices of goods, the
larger the quantities that can be bought by a given
amount of money, and therefore the higher the purchas

THE PURCHASING POWER OF MONEY

[C h a p .

ing power of money. The higher we find the prices
of goods, the smaller the quantities that can be bought
by a given amount of money, and therefore the lower
the purchasing power of money. In short, the purchas
ing power of money is the reciprocal of the level of
prices; so that the study of the purchasing power of
money is identical with the study of price levels.
§2
. Overlooking the influence of deposit currency, or
checks, the price level may be said to depend on only
three sets of causes: (1) the quantity of money in circu
lation; (2) its “ efficiency” or velocity of circulation (or
the average number of times a year money is exchanged
for goods); and (3) the volume of trade (or amount of
goods bought by money). The so-called “ quantity
theory,” 1i.e. that prices vary proportionately to money,
has often been incorrectly formulated, but (overlooking
checks) the theory is correct in the sense that the level
of prices varies directly with the quantity of money in
circulation, provided the velocity of circulation of that
money and the volume of trade which it is obliged to
perform are not changed.
The quantity theory has been one of the most bitterly
contested theories in economics, largely because the
recognition of its truth or falsity affected powerful
1 This theory, though often crudely formulated, has been accepted
by Locke, Hume, Adam Smith, Ricardo, Mill, Walker, Marshall,
Hadley, Fetter, Kemmerer and most writers on the subject. The
Roman Julius Paulus, about 200 a . d . , stated his belief that the
value of money depends on its quantity. See Zuckerkandl, Theorie
den Preises; Kemmerer, Money and Credit Instruments in their
Relation to General Prices, New York (Holt), 1909. It is true
that many writers still oppose the quantity theory. See especially,
Laughlin, Principles of Money, New York (Scribner), 1903.

Sec. 21

THE EQUATION OF EXCHANGE

interests in commerce and politics. It has been main
tained — and the assertion is scarcely an exaggeration
— that the theorems of Euclid would be bitterly con
troverted if financial or political interests were in
volved.
The quantity theory has, unfortunately, been made
the basis of arguments for unsound currency schemes.
It has been invoked in behalf of irredeemable paper
money and of national free coinage of silver at the ratio
of 16 to 1. As a consequence, not a few “ sound money
men,” believing that a theory used to support such
vagaries must be wrong, and fearing the political effects
of its propagation, have drifted into the position of
opposing, not only the unsound propaganda, but also
the sound principles by which its advocates sought
to bolster it up.1 These attacks upon the quantity
theory have been rendered easy by the imperfect com
prehension of it on the part of those who have thus
invoked it in a bad cause.
Personally, I believe that few mental attitudes are
more pernicious, and in the end more disastrous, than
those which would uphold sound practice by denying
sound principles because some thinkers make unsound
application of those principles. At any rate, in scien
tific, study there is no choice but to find and state the
unvarnished truth.
The quantity theory will be made more clear by the
equation of exchange, which is now to be explained.
, The equation of exchange is a statement, in math
1 See Scott, 4‘ It has been a most fruitful source of false doctrines
regarding monetary matters, and is constantly and successfully
employed in defense of harmful legislation and as a means of pre
venting needed monetary reforms.”
Money and Banking9 New
York, 1903, p. 68.

THE PURCHASING POWER OF MONEY

[Chap.

ematical forfn, of the total transactions effected in a
certain period in a given community. It is obtained
simply by adding together the equations of exchange for
all individual transactions. Suppose, for instance, that
a person buys 10 pounds of sugar at 7 cents per pound.
This is an exchange transaction, in which 10 pounds of
sugar have been regarded as equal to 70 cents, and this
fact may be expressed thus: 70 cents = 10 pounds of
sugar multiplied by 7 cents a pound. Every other sale
and purchase may be expressed similarly, and by adding
them all together we get the equation of exchange for
a certain period in a given community. During this
same period, however, the same money may serve,
and usually does serve, for several transactions. For
that reason the money side of the equation is of
course greater than the total amount of money in cir
culation.
The equation of exchange relates to all the purchases
made by money in a certain community during a cer
tain time. We shall continue to ignore checks or any
circulating medium not money. We shall also ignore
foreign trade and thus restrict ourselves to trade within
a hypothetical community. Later we shall reinclude
these factors, proceeding by a series of approximations
through successive hypothetical conditions to the actual
conditions which prevail to-day. We must, of course,
not forget that the conclusions expressed in each suc
cessive approximation are true solely on the particular
hypothesis assumed.
The equation of exchange is simply the sum of the
equations involved in all individual exchanges in a year.
In each sale and purchase, the money and goods ex
changed are ipso facto equivalent; for instance, the
money paid for sugar is equivalent to the sugar bought.

Sec. 2]

THE EQUATION OF EXCHANGE

And in the grand total of all exchanges for a year, the
total money paid is equal in value to the total value
of the goods bought. The equation thus has a money
side and a goods side. The money side is the total
money paid, and may be considered as the product of
the quantity of money multiplied by its rapidity of
circulation. The goods side is made up of the products
of quantities of goods exchanged multiplied by their
respective prices.
The important magnitude, called the velocity of cir
culation, or rapidity of turnover, is simply the quotient
obtained by dividing the total money payments for
goods in the course of a year by the average amount
of money in circulation by which those payments are
effected. This velocity of circulation for an entire com
munity is a sort of average of the rates of turnover of
money for different persons. Each person has his own
rate of turnover which he can readily calculate by di
viding the amount of money he expends per year by
the average amount he carries.
Let us begin with the money side. If the number of
dollars in a country is 5,000,000, and their velocity of
circulation is twenty times per year, then the total
amount of money changing hands (for goods) per year
is 5,000,000 times twenty, or $100,000,000. This is the
money side of the equation of exchange.
Since the money side of the equation is 8100,000,000,
the goods side must be the same. For if $100,000,000
has been spent for goods in the course of the year, then
$100,000,000 worth of goods must have been sold in
that year. In order to avoid the necessity of writing
out the quantities and prices of the innumerable va
rieties of goods which are actually exchanged, let us
assume for the present that there are only three kinds

THE PURCHASING POWER OF MONEY

[C h a p .

of goods, — bread, coal, and cloth; and that the sales
are: —
200,000,000 loaves of bread at $ .10 a loaf,
10.000.000 tons of coal at
5.00 a ton, and
30.000.000 yards of cloth at
1.00 a yard.

The value of these transactions is evidently $100,000,000, i.e. $20,000,000 worth of bread plus $50,000,000
worth of coal plus $30,000,000 worth of. cloth. The
equation of exchange therefore (remember that the
money side consisted of $5,000,000 exchanged 20 times)
is as follows: —
$5,000,000 X 20 times a year
= 200,000,000 loaves X S .10 a loaf
+ 10,000,000 tons X 5.00 a ton
+ 30,000,000 yards X 1.00 a yard.

This equation contains on the money side two magni
tudes, viz. (1) the quantity of money and (2) its
velocity of circulation; and on the goods side two
groups of magnitudes in two columns, viz. (1) the
quantities of goods exchanged (loaves, tons, yards),
and (2) the prices of these goods. The equation shows
that these four sets of magnitudes are mutually related.
Because this equation must be fulfilled, the prices must
bear a relation to the three other sets of magnitudes, —
quantity of money, rapidity of circulation, and quan
tities of goods exchanged. Consequently, these prices
must, as a whole, vary proportionally with the quantity
of money and with its velocity of circulation, and in
versely with the quantities of goods exchanged.
Suppose, for instance, that the quantity of money
were doubled, while its velocity of circulation and the
quantities of goods exchanged remained the same.
Then it would be quite impossible for prices to
remain unchanged. The money side would now be

Sec. 2]

THE EQUATION OP EXCHANGE

$10,000,000 X 20 times a year or $200,000,000; whereas,
if prices should not change, the goods would remain
$100,000,000, and the equation would be violated.
Since exchanges, individually and collectively, always
involve an equivalent quid pro quo, the two sides must
be equal. Not only must purchases and sales be equal
in amount— since every article bought by one person
is necessarily sold by another— but the total value of
goods sold must equal the total amount of money
exchanged. Therefore, under the given conditions,
prices'must change in such a way as to raise the goods
side from $100,000,000 to $200,000,000. This doubling
may be accomplished by an even or uneven rise in
prices, but some sort of a rise of prices there must be.
If the prices rise evenly, they will evidently all be exactly
doubled, so that the equation will read: —
$10,000,000 X 20 times a year
= 200,000,000 loaves X $ .20 per loaf
*
+ 10,000,000 tons X 10.00 per ton
+ 30,000,000 yards X
2.00 per yard.

If the prices rise unevenly, the doubling must evidently
be brought about by compensation; if some prices rise
by less than double, others must rise by enough more
than double to exactly compensate.
But whether all prices increase uniformly, each being
exactly doubled, or some prices increase more and some
less (so as still to double the total money value of the
goods purchased), the prices are doubled on the average.1
This proposition is usually expressed by saying that the
"general level of prices” is raised twofold. From the
mere fact, therefore, that the money spent for goods
1 This does not mean, of course, that their simple arithmetical
average is exactly doubled. For definition of an average or “ mean”
in general, see § 1 of Appendix to (this) Chapter II.

THE PURCHASING POWER OF MONEY

[C h a p .

must equal the quantities of those goods multiplied by
their prices, it follows that the level of prices must rise
or fall according to changes in the quantity of money,
unless there are changes in its velocity of circulation or
in the quantities of goods exchanged.
If changes in the quantity of money affect prices, so
will changes in the other factors — quantities of goods
and velocity of circulation — affect prices, and in a
very similar manner. Thus a doubling in the velocity
of circulation of money will double the level of prices,
provided the quantity of money in circulation and the
quantities of goods exchanged for money remain as be
fore. The equation will become: —
$5,000,000 X 40 times a year
= 200,000,000 loaves X $ .20 a loaf
+ 10,000,000 tons X 10.00 a ton
+ 30,000,000 yards X
2.00 a yard,

or else the equation will assume a form in which some
of the prices will more than double, and others less than
double by enough to preserve the same total value of
the sales.
Again, a doubling in the quantities of goods exchanged
will not double, but halve, the height of the price level,
■provided the quantity of money and its velocity of
circulation remain the same. Under these circum
stances the equation will become: —
$5,000,000 X 20 times a year
= 400,000,000 loaves X $ .05 a loaf
+ 20,000,000 tons X 2.50 a ton
+ 60,000,000 yards X
.50 a yard,

or else it will assume a form in which some of the prices
are more than halved, and others less than halved,
so as to preserve the equation.

S ec. 3]

THE EQUATION OF EXCHANGE

Finally, if there is a simultaneous change in two or
all of the three influences, i.e. quantity of money,
velocity of circulation, and quantities of goods ex
changed, the price level will be a compound or resultant
of these various influences. If, for example, the quan
tity of money is doubled, and its velocity of circulation
is halved, while the quantity of goods exchanged remains
constant, the price level will be undisturbed. Like
wise, it will be undisturbed if the quantity of money is
doubled and the quantity of goods is doubled, while
the velocity of circulation remains the same. To double
the quantity of money, therefore, is not always to double
prices. We must distinctly recognize that the quantity
of money is only one of three factors, all equally impor
tant in determining the price level.

§ 3
The equation of exchange has now been expressed by
an arithmetical illustration. It may be also represented
visually, by a mechanical illustration. Such a repre
sentation is embodied in Figure 2. This represents a

mechanical balance in equilibrium, the two sides of which
symbolize respectively the money side and the goods
side of the equation of exchange. The weight at the
left, symbolized by a purse, represents the money in
circulation; the “ arm” or distance from the fulcrum
at which this weight (purse) is hung represents the

THE PURCHASING POWER OP MONEY

[C hap. II

efficiency of this money, or its velocity of circulation.
On the right side are three weights, — bread, coal, and
cloth, symbolized respectively by a loaf, a coal scuttle,
and a roll of cloth. The arm, or distance of each from
the fulcrum, represents its price. In order that the lever
arms at the right may not be inordinately long, we have
found it convenient to reduce the unit of measure of
coal from tons to hundredweights, and that of cloth
from yards to feet, and consequently to enlarge corre
spondingly the numbers of units (the measure of coal
changing from 10,000,000 tons to 200,000,000 hundred
weights, and that of the cloth from 30,000,000 yards to
90,000,000 feet). The price of coal in the new unit per
hundredweight becomes 25 cents per hundredweight,
and that of cloth in feet becomes 33J cents per foot.
We all know that, when a balance is in equilibrium,
the tendency to turn in one direction equals the tend
ency to turn in the other. Each weight produces on
its side a tendency to turn, measured by the product of
the weight by its arm. The weight on the left produces,
on that side, a tendency measured by 5,000,000 x 20;
while the weights on the right make a combined opposite
tendency measured by 200,000,000 x .10+200,000,000 x
.25 + 90,000,000 x .33J. The equality of these opposite
tendencies represents the equation of exchange.
An increase in the weights or arms on one side re
quires, in order to preserve equilibrium, a proportional
increase in the weights or arms on the other side. This
simple and familiar principle, applied to the symbolism
here adopted, means that if, for instance, the velocity
of circulation (left arm) remains the same, and if the
trade (weights at the right) remains the same, then any
increase of the purse at the left will require a lengthen
ing of one or more of the arms at the right, represent

S e c . 3]

THE EQUATION OF EXCHANGE

ing prices. If these prices increase uniformly, they will
increase in the same ratio as the increase in money; if
they do not increase uniformly, some will increase more
and some less than this ratio, maintaining an average.
Likewise it is evident that if the arm at the left
lengthens, and if the purse and the various weights on
the right remain the same, there must be an increase in
the arms at the right.
Again, if there is an increase in weights at the right,
and if the left arm and the purse remain the same, there
must be a shortening of right arms.
In general, a change in one of the four sets of mag
nitudes must be accompanied by such a change or
changes in one or more of the other three as shall main
tain equilibrium.
As we are interested in the average change in prices
rather than in the prices individually, we may simplify
this mechanical representation by hanging all the righthand weights at one average point, so that the arm shall
represent the average prices. This arm is a “ weighted
average” of the three original arms, the weights being
literally the weights hanging at the right.
This averaging of prices is represented in Figure 3,
which visualizes the fact that the average price of goods

(right arm) varies directly with the quantity of money
(left weight), and directly with its velocity of circulation

THE PURCHASING POWER OF MONEY

[C h a p .

(left arm), and inversely with the volume of trade (right
weight).
§4
We now come to the strict algebraic statement of
the equation of exchange. An algebraic statement is
usually a good safeguard against loose reasoning ;
and loose reasoning is chiefly responsible for the sus
picion under which economic theories have frequently
fallen. If it is worth while in geometry to demonstrate
carefully, at the start, propositions which are almost
self-evident, it is a hundredfold more worth while to
demonstrate with care the propositions relating to
price levels, which are less self-evident; which, indeed,
while confidently assumed by many, are contemptuously
rejected by others.
Let us denote the total circulation of money, i.e. the ■
amount of money expended for goods in a given com
munity during a given year, by E (expenditure); and
the average amount of money in circulation in the com
munity during the year by M (money). M will be
the simple arithmetical average of the amounts of money
existing at successive instants separated from each
other by equal intervals of time indefinitely small.
If we divide the year’s expenditures, E, by the average
amount of money, M, we shall obtain what is called
the average rate of turnover of money in its exchange
E
for goods, — , that is, the velocity of circulation of
money.1 This velocity may be denoted by V, so that
E
= V; then E may be expressed as MV. In
words: the total circulation of money in the sense of
1 For discussion of the concept of velocity of circulation, see
§ § 2, 4, 5 of Appendix to (this) Chapter II.

S ec. 4]

THE EQUATION OF EXCHANGE

money expended is equal to the total money in circu
lation multiplied by its velocity of circulation or turn
over. E or MV, therefore, expresses the money side of
the equation of exchange. Turning to the goods side
of the equation, we have to deal with the prices of
goods exchanged and quantities of goods exchanged.
The average1 price of sale of any particular good,
such as bread, purchased in the given community
during the given year, may be represented by p
(price); and the total quantity of it purchased, by Q
(quantity); likewise the average price of another
good (say coal) may be represented by p' and the
total quantity of it exchanged, by Q'; the average
price and the total quantity of a third good (say cloth)
may be represented by p" and Q" respectively; and so
on, for all other goods exchanged, however numerous.
The equation of exchange may evidently be expressed
as follows: 2—
M V = pQ

+ P'(y
+ v"Q "
+ etc.

‘ This is an average weighted according to the quantities pur
chased on various occasions throughout the period and country
considered. See § 3 of Appendix to (this) Chapter II.
*
An algebraic statement of tho equation of exchange was made
by Simon Newcomb in his able but little appreciated Principles
of Political Economy, Now York (Harper), 1885, p. 346. It is also
expressed by Edgeworth, “ Report on Monetary Standard.” Report
of the British Association for the Advancement'of Science, 1887, p.
293, and by President Hadloy, Economics, New York (Putnam),
1896, p. 197. See also Irving Fisher, “ Tho RGlo of Capital in Eco
nomic Theory,” Economic Journal, December, 1899, pp. 515-1)21,
and E. W . Kemmerer, Money and Credit Instruments in their Rela
tion to General Prices, New York (Holt), 1907, p. 13. While thus
only recently given mathematical expressioh, the quantity theory
has long been understood as a relationship among the several fac-

THE PURCHASING POWER OF MONEY

[C h ap .

The right-hand side of this equation is the sum of
terms of the form pQ — a price multiplied by a quantity
bought. It is customary in mathematics to abbreviate
such a sum of terms (all of which are of the same form)
by using “ 2 ” as a symbol of summation. This symbol
does not signify a magnitude as do the symbols M, V,
p, Q, etc. It signifies merely the operation of addition
and should be read “ the sum of terms of the following
type.” The equation of exchange may therefore be
written:—
M Y = SpQ.

That is, the magnitudes E, M, V, the p’s and the Q’s
relate to the entire community and an entire year; but
they are based on and related to corresponding magni
tudes for the individual persons of which the community
is composed and for the individual moments of time
of which the year is composed.1
The algebraic derivation of this equation is, of course,
essentially the same as the arithmetical derivation
previously given. It consists simply in adding together
the equations for all individual purchases urithin the
community during the year.2
By means of this equation, MY = 'ZpQ, the three
theorems set forth earlier in this chapter may be now
expressed as follows: —
(1)
If V and the Q’s remain invariable while M varies
in any ratio, the money side of the equation will vary
tors: amount of money, rapidity of circulation, and amount of trade.
See Mill, Principles of Political Economy, Book III, Chapter V III,
§ 3. Ricardo probably deserves chief credit for launching: the theory.
1For the relations subsisting between these magnitudes (as
relating to' the whole community and the whole year), and the
corresponding elementary magnitudes relating to each individual
and each moment, see § 4 of the Appendix to (this) Chapter II.
2 See § 6 of Appendix to (this) Chapter II.

Sec. 4]

THE EQUATION OP EXCHANGE

in the same ratio and therefore its equal, the goods side,
must vary in that same ratio also; consequently, either
the p’s will all vary in that ratio or else some p’s will
vary more than in that ratio and others enough less to
compensate and maintain the same average.1
(2) If M and the Q’s remain invariable'while V varies
in any ratio, the money side of the equation will vary
in the same ratio, and therefore its equal, the goods
side, must vary in that ratio also; consequently, the
p’s will all vary in the same ratio or else some will vary
more and others enough less to compensate.
(3) If M and V remain invariable, the money side
and the goods side will remain invariable; consequently,
if the Q’s all vary in a given ratio, either the p’s must
all vary in the inverse ratio or else some of them will
vary more and others enough less to compensate.
We may, if we wish, further simplify the right side
by writing it in the form PT where P is a weighted
average of all the p’s, and T is the sum of all the Q’s.
P then represents in one magnitude the level of prices,
and T represents in one magnitude the volume of trade.
This simplification is the algebraic interpretation of
the mechanical illustration given in Figure 3, where all
the goods, instead of being hung separately, as in
Figure 2, were combined and hung at an average point
representing their average price.
We have derived the equation of exchange, MV =
%PQ, by adding together, for the right side, the sums
expended by different persons. But the same reasoning
would have derived an equation of exchange by taking
the sums received by different persons. The results of
l For the nature of the average here involved and for th§ aver
ages involved in the other two following cases, see § 7 of Appendix
to (this) Chapter II.

THE PURCHASING POWER OF MONEY

[C h a p .

the two methods will harmonize if the community has
no foreign trade; for, apart from foreign trade, what is
expended by one person in the community is necessarily
received by some other person in that community.
If we wish to extend the reasoning so as to apply
to foreign trade, we shall have two equations of ex
change, one based on money expended and the other
on money received or accepted by members of the com
munity. These will always be approximately equal and
may or may not be exactly equal within a country ac
cording to the “ balance of trade” between that coun
try and others. The right side of the equation based
on expenditures will include, in addition to the domes
tic quantities already represented there, the quantities
of goods imported and their prices, but not those ex
ported; while the reverse will be true of the equation
based on receipts.

§ 5
This completes our statement of the equation of
exchange, except for the element of check payments,
which is reserved for the next chapter. We have seen
that the equation of exchange has as its ultimate basis
the elementary equations of exchange pertaining to given
persons and given moments, in other words, the equa
tions pertaining to individual transactions. Such ele
mentary equations mean that the money paid in any
transaction is the equivalent of the goods bought at
the price of sale. From this secure and obvious premise
is derived the equation of exchange MV = SpQ, each
element in-which is a sum or an average of the like
elementary elements for different individuals and differ
ent moments, thus comprising all the purchases in the
community during the year. Finally, from this equa

Sec. 5]

THE EQUATION OF EXCHANGE

tion we see that prices vary directly as M and V, and
inversely as the Q’s, provided in each case only one of
these three sets of magnitudes varies, and the other two
remain unchanged. Whether to change one of the
three necessarily disturbs the others is a question re
served for a later chapter. Those who object to the
equation of exchange as a mere truism are asked to
defer judgment until they have read Chapter VIII.
To recapitulate, we find then that, under the con
ditions assumed, the price level varies (1) directly as the
quantity of money in circulation (M), (2) directly as
the velocity of its circulation (F), (3) inversely as the
volume of trade done by it (T). The first of these
three relations is worth emphasis. It constitutes the
“ quantity theory of money.”
So important is this principle, and so bitterly con
tested has it been, that we shall illustrate it further.
As already indicated, by “ the quantity of money” is
meant the number of dollars (or other given monetary
units) in circulation. This number may be changed
in several ways, of which the following three are naost
important. Their statement will serve to bring home
to us the conclusions we have reached and to reveal the
fundamental peculiarity of money on which they rest.
As a first illustration, let us suppose the government
to double the denominations of all money; that is, let
us suppose that what has been hitherto a half dollar is
henceforth called a dollar, and that what has hitherto
been a dollar is henceforth called two dollars. Evi
dently the number of “ dollars” in circulation will then
be doubled; and the price level, measured in terms
of the new “ dollars,” will be double what it would
otherwise be. Every one will pay out the same coins
as though no such law were passed. But he will, in

THE PURCHASING POWER OF MONEY

[C h a p .

each case, be paying twice as many “ dollars.” Fol
example, if $3 formerly had to be paid for a pair of
shoes, the price of this same pair of shoes will now
become $6. Thus we see how the nominal quantity of
money affects price levels.
A second illustration is found in a debased currency.
Suppose a government cuts each dollar in two, coining
the halves into new “ dollars” ; and, recalling all paper
notes, replaces them with double the original number —
two hew notes for each old one of the same denomination.
In short, suppose money not only to be renamed, as in
the first illustration, but also reissued; prices in the de
based coinage will again be doubled just as in the first
illustration. The subdivision and recoinage is an im
material circumstance, unless it be carried so far as
to make counting difficult and thus to interfere with
the convenience of money. Wherever a dollar had
been paid before debasement, two dollars — i.e. two
of the old halves coined into two of the new dollars —
will now be paid instead.
In the first illustration, the increase in quantity was
simply nominal, being brought about by renaming
coins. In the second illustration, besides renaming, the
further fact of recoining is introduced. In the first
case the number of actual pieces of money of each kind
was unchanged, but their denominations were doubled.
In the second case, the number of pieces is also doubled
by splitting each coin and reminting it into two coins,
each of the same nominal denomination as the original
whole of which it is the half, and by similarly redoubling
the paper money.
For a third illustration, suppose that, instead of
doubling the number of dollai’s by splitting them in
two and recoining the halves, the government duplicates

S ec. 5]

THE EQUATION OF EXCHANGE

each piece of money in existence and presents the du
plicate to the possessor of the original.1 (We must in
this case suppose, further, that there is some effectual
bar to prevent the melting or exporting of money.
Otherwise the quantity of money in circulation will
not be doubled: much of the increase will escape.) If
the quantity of money is thus doubled, prices will also
be doubled just as truly as in the second illustration, in
which there were exactly the same denominations. The
only difference between the second and the third
illustrations will be in the size and weight of the coins.
The weights of the individual coins, instead of being
reduced, will remain unchanged; but their number
will be doubled. This doubling of coins must have the
same effect as the 50 per cent debasement, i.e. it must
have the effect of doubling prices.
The force of the third illustration becomes even more
evident if, in accordance with Ricardo’s presentation,2
we pass baqk by means of a seigniorage from the third
illustration to the second. That is, after duplicating
all money, let the government abstract half of each coin,
thereby reducing the weight to that of the debased
coinage in the second illustration, and removing the
only point of distinction between the two. This
"seigniorage” abstracted will not affect the value of the
coins, so long as their number remains unchanged.
In short, the quantity theory asserts that (provided
velocity of circulation and volume of trade are un
changed) if we increase the number of dollars, whether
1 Cf. J. S. Mill, Principles of Political Economy, Book III, Chap
ter V III, § 2. Ricardo in his reply to Bosanquet uses an illus
tration similar in principle though slightly different in form. See
IPor/cs, 2d ed., London (Murray), 1852, p. 34G.
1 Works, 2d ed., London (Murray), 1852, pp. 346 and 347
(reply to Bosanquet, Chapter V I ) ; see also pp. 213 a*id 214.

THE PURCHASING POWER OP MONEY

[C h a p .

by renaming coins, or by debasing coins, or by increasing
coinage, or by any other means, prices will be increased
in the same proportion. It is the number, and not
the weight, that is essential. This fact needs great
emphasis. It is a fact which differentiates money
from all other goods and explains the peculiar manner in
which its purchasing power is related to other goods.
Sugar, for instance, has a specific desirability dependent
on its quantity in pounds. Money has no such quality.
The value of sugar depends on its actual quantity. If
the quantity of sugar is changed from 1,000,000 pounds
to 1,000,000 hundredweight, it does not follow that a
hundredweight will have the value previously possessed
by a pound. But if money in circulation is changed
from 1,000,000 units of one weight to 1,000,000 units
of another weight, the value of each unit will remain
unchanged.
The quantity theory of money thus rests, ultimately,
upon the fundamental peculiarity which money alone of
all goods possesses, — the fact that it has no power to
satisfy human wants except a power to purchase things
which do have such power.1
1 Cf. G. F. Knapp, Staatliche Theorie des Geldes, Leipzig, 1905;
L. von Bortkiewicz, “ Die geldtheoretischen und die wahrungspolitischen Consequenzen des ‘ Nominalismus,, ” Jahrbuch fur Gesetzgebung, Verwaltung und Volkswirtschaft, October, 1906; Bertrand
Nogaro, “ U experience bimStalliste du X I X siSele et la th£orio
g6n£rale de la monnaie,” Revue d’Economie politique, 1908.

CHAPTER III
INFLUENCE OF DEPOSIT CURRENCY ON THE EQUATION
AND THEREFORE ON PURCHASING POWER

§ 1
We are now ready to explain the nature of bank
deposit currency, or circulating credit. Credit, in
general, is the claim of a creditor against a debtor.
Bank deposits subject to check are the claims of the
creditors of a bank against the bank, by virtue of which
they may, on demand, draw by check specified sums
of money from the bank. Since no other kind of bank
deposits will be considered by us, we shall usually
refer to “ bank deposits subject to check” simply as
“ bank deposits.” They are also called “ circulating
credit.” Bank checks, as we have seen, are merely
certificates of rights to draw, i.e. to transfer bank de
posits. The checks themselves are not the currency;
the bank deposits which they represent are the currency.
It is in the connection with the transfer of bank
deposits that there arises that so-called “ mystery of
banking” called “ circulating credit.” Many persons,
including some economists, have supposed that credit
is a'special 'form of wealth which may be created
out of whole cloth, as it were, by a bank. Others have
maintained that credit has no foundation in actual
wealth at all, but is a kind of unreal and inflated bubble
with a precarious, if not wholly illegitimate, existence.
As a matter of fact, bank deposits are as easy to under
stand as bank notes, and what is said in this chapter
D

THE PURCHASING POWER OF MONET

[C h a p .

Ill

of bank deposits may in substance be taken as true
also of bank notes. The chief difference is a formal one,
the notes circulating from hand to hand, while the
deposit currency circulates only by means of special
orders called “ checks.”
To understand the real nature of bank deposits, let
us imagine a hypothetical institution, — a kind of
primitive bank existing mainly for the sake of deposits
and the safe keeping of actual money. The original
bank of Amsterdam was somewhat like the bank we
are now imagining. In such a bank a number of people
deposit $100,000 in gold, each accepting a receipt for the
amount of his deposit. If this bank should issue a
“ capital account,” or statement, it would show $100,000
in its vaults and $100,000 owed to depositors, as fol
lows : —
Assets

Liabilities

G o l d ............................ $100,000 | Due depositors

$100,000

The right-hand side of the statement is, of course,
made up of smaller amounts owed to individual de
positors. Assuming that there is owed to A, $10,000,
to B, $10,000, and to all others $80,000, we may m ite
the bank statement as follows: —
Assets

Liabilities

G o l d ............................ §100,000

§100,000

Due depositor A . .
Due depositor B . .
Due other depositors

$10,000
10,000
80,000

$100,000

Now assume that A wishes to pay B $1000. A could
go to the bank with B, present certificates or checks
for $1000, obtain the gold, and hand it over to B, who
might then redeposit it in the same bank, merely hand-

DEPOSIT CURRENCY

ing it back through the cashier’s window and taking a
new certificate in his own name. Instead, however,
of both A and B visiting the bank and handling the
money, A might simply give B a check for §1000. The
transfer in either case would mean that A ’s holding in
the bank was reduced from §10,000 to $9000, and that
B’s was increased from $10,000 to $11,000. The state
ment would then read: —
Assets

Liabilities

G o l d ............................ $100,000

$100,000

Due depositor A . .
Due depositor B . .
Due other depositors

9,000
11,000
80,000

S100,000

Thus the certificates, or checks, would circulate in
place of cash among the various depositors in the bank.
What really changes ownership, or “ circulates,” in
such cases is the right to draw money. The check is
merely the evidence of this right and of the transfer of
this right from one person to another.
In the case under consideration, the bank would be con
d u c t e d at a loss. It Avould be giving the time and labor
of its clerical force for the accommodation of its deposi
tors, without getting anything in return. But such a
hypothetical bank would soon find — much as did the
bank of Amsterdam1— that it could “ make money” by
lending at interest some of the gold on deposit. This
could not offend the depositors; for they do not expect
or desire to get back the identical gold they de
posited. What they want is simply to be able at any
time to obtain the same amount of gold. Since, then,
1 See Dunbar’s Theory and History of Banking, 2d ed., edited
by O. M . W . Sprague, New York and London (G. P. Putnam’s
Sons), 1901, pp. 113-116.

THE PURCHASING POWER OF MONEY

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their arrangement with the bank calls for the payment,
not of any particular gold, but merely of a definite
amount, and that but occasionally, the bank finds it
self free to lend out part of the gold that otherwise
would lie idle in its vaults. To keep it idle would be
a great and needless waste of opportunity.
.Let us suppose, then, that the bank decides to loan
out half its cash. This is usually done in exchange for
promissory notes of the borrowers. Now a loan is
really an exchange of money for a promissory note
which the lender — in this case the bank — receives
in place of the gold. Let us suppose that so-called
borrowers actually draw out $50,000 of gold. The
bank thereby exchanges money for promises, and its
books will then read: —

Ossete
Gold reserve. . . .
Promissory notes . .

Liabilities
$50,000
50,000

§100,000

Due depositor A . .
Due depositor B . .
Due other depositors.

§ 9,000
11,000
80,000
S100,000

It will be noted that now the gold in the bank is
only $50,000, while the total deposits are still
$100,000. In other words, the depositors now have
more “ money on deposit” than the bank has in its
vaults ! But, as will be shown, this form of expression
involves a popular fallacy in the word “ money.”
Something good is behind each loan, but not necessarily
money.
Next, suppose that the borrowers become, in a sense,
depositors also, by redepositing the $50,000 of cash
which they borrowed, in return for the right to draw out
the same sum on demand. In other words, suppose

S ec. 1]

DEPOSIT CURRENCY

that after borrowing $50,000 from the bank, they lend
it back to the bank. The bank’s assets will thus be
enlarged by $50,000, and its obligations (or credit
extended) will be equally enlarged; and the balance
sheet will become: —
Assets
Gold reserve
. .
Promissory notes .

Liabilities

. $100,000
.

50,000

Due depositor A .
Due depositor B .

.
.

Due old depositors .
Due new depositors,
i.e. the borrowers.
$150,000

$ 9,000

11,000
80,000
50,000
$150,000

What happened in this case was the following: Gold
was borrowed in exchange for a promissory note and
then handed back in exchange for a right to draw.
Thus the gold really did not budge; but the bank
received a promissory note and the depositor a right to
draw. Evidently, therefore, the same result would have
followed if each borrower had merely handed in his prom
issory note and received, in exchange, a right to draw.
As this operation most frequently puzzles the beginner
in the study of banking, we repeat the tables repre
senting the conditions before and after these “ loans,”
i.e. these exchanges of promissory notes for present
rights to draw.1
1
In the ultimate analysis, and outside of its function of insuring
credit, a bank is really an intermediary between borrowers and
lenders. It is by virtue of bringing borrowers and ultimate lenders
together and providing the former with a supply of loans which

would not otherwise exist, that a bank simultaneously tends to
lower the rate of interest and increase the supply of credit cur
rency. See paper by Harry G. Brown, in the Quarterly Journal of
Economics, August, 1910, on “ Commercial Banking and the Bate of

Interest.”

THE PURCHASING POWER OF MONET iChap. I l l

B efore th e L oans

Assets
Gold reserve

Liabilities
.

§100,000 | Due depositors

$100,000

$150,000

A fter th e L oans

Gold reserve. . . .
Promissory notes . .

$100,000
50,000

Due depositors

Clearly, therefore, the intermediation of the money in
this case is a needless complication, though it may help
to a theoretical understanding of the resultant shifting
of rights and liabilities. Thus the bank may receive
deposits of gold or deposits of promises. In exchange
for the promises it may give, or lend, either a right
to draw, or gold, — the same that was deposited by
another customer. Even when the borrower has
only a promise, by fiction he is still held to have de
posited money; and like the original cash depositors, he
is given the right to make out checks. The total value
of rights to draw, in whichever way arising, is termed
“ deposits.” Banks more often lend rights to draw (or
deposit rights) than actual cash, partly because of the
greater convenience to borrowers, and partly because
the banks wish to keep their cash reserves large, in order
to meet large or unexpected demands. It is true that
if a bank loans money, part of the money so loaned will
be redeposited by the persons to whom the borrowers
pay it in the course of business; but it will not neces
sarily be redeposited in the same bank. Hence the
average banker prefers that the borrower should not
withdraw actual cash.
Besides lending deposit rights, banks may also lend
their own notes, called “ bank notes.”
And the
principle governing bank notes is the same as the prin

S ec. 1]

DEPOSIT CURRENCY

ciple governing deposit rights. The holder simply gets
a pocketful of bank notes instead of a bank account.
In either case the bank must be always ready to pay
the holder — to “ redeem its notes” — as well as pay
its depositors, on demand, and in either case the bank
exchanges a promise for a promise. In the case of the
note, the bank has exchanged its bank note for a cus
tomer’s promissory note. The bank note carries no
interest, but is payable on demand. The customer’s
note bears interest, but is payable only at a definite
date.
Assuming that the bank issues $50,000 of notes, the
balance sheet will now become: —

Assets
Gold reserve.
Loans . . .

$100,000
100,000

$200,000

Liabilities
Due depositors .
Due note holders.

.
.

5150.000
50,000
5200.000

We repeat that by means of credit the deposits (and
notes) of a bank may exceed its cash. There would
be nothing mysterious or obscure about this fact, nor
about credit in general, if people could be induced not
to think of banking operations as money operations.
To so represent them is metaphorical and misleading.
They are no more money operations than they are
real estate transactions. A bank depositor, A, has not
ordinarily “ deposited money” ; and whether he has
or not, he certainly cannot properly say that he “ has
money in the bank.” What he does have is the bank’s
promise to pay money on demand. The bank owes him
money. When a private person owes money, the
creditor never thinks of saying that he has it on deposit
in the debtor’s pocket.

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§2
It cannot be too strongly emphasized that, in any
balance sheet, the value of the liabilities rests on that
of the assets. The deposits of a bank are no excep
tion. We must not be misled by the fact that the
cash assets may be less than the deposits. When
the uninitiated first learn that the number of dol
lars which note holders and depositors have the right
to draw out of a bank exceeds the number of dollars
in the bank, they are apt to jump to the conclusion
that there is nothing behind the notes or deposit liabil
ities. Yet behind all these obligations there is always,
in the case of a solvent bank, full value; if not actual
dollars, at any rate dollars’ worth of property. By no
jugglery can the liabilities exceed the assets except in
insolvency, and even in that case only nominally,
for the true value of the liabilities (“ bad debts” ) will
only equal the true value of the assets behind them.
These assets, as already indicated, are largely the
notes of merchants, although, so far as the theory of
banking is concerned, they might be any property
whatever. If they consisted in the ownership of real
estate or other wealth in “ fee simple,” so that the
tangible wealth which property always represents
were clearly evident, all mystery would disappear.
But the effect would not be different. Instead of
taking grain, machines, or steel ingots on deposit, in
exchange for the sums lent, banks prefer to take interestbearing notes of corporations and individuals who own,
directly or indirectly, grain, machines, and steel ingots:
and by the banking laws the banks are even compelled
to take the notes instead of the ingots. The bank
finds itself with liabilities which exceed its cash assets;

Sec. 2]

DEPOSIT CURRENCY

but in either case the excess of liabilities is balanced by
the possession of other assets than cash. These other
assets of the bank are usually liabilities of business
men. These liabilities are in turn supported by the
assets of the business men. If we continue to follow
up the ultimate basis of the bank’s liabilities we shall
find it in the visible tangible wealth of the world.
This ultimate basis of the entire credit structure is
kept out of sight, but the basis exists. Indeed, we may
say that banking, in a sense, causes this visible, tangible
wealth to circulate. If the acres of a landowner or
the iron stoves of a stove dealer cannot circulate in
literally the same way that gold dollars circulate, yet
the landowner or stove dealer may give to the bank a
note on which the banker may base bank notes or de
posits ; and these bank notes and deposits will circulate
like gold dollars. Through banking, he who possesses
wealth difficult to exchange can create a circulating
medium. He has only to give to a bank his note — for
which, of course, his property is liable— get in return the
right to draw, and lo ! his comparatively unexchange
able wealth becomes liquid currency. To put it crudely,
banking is a device for coining into dollars land, stoves,
and other wealth not otherwise generally exchangeable.
It is interesting to observe that the formation of
the great modern “ trusts” has given a considerable
impetus to deposit currency; for the securities of large
corporations are more easily used as. “ collateral se
curity” for bank loans than the stocks and bonds of
small corporations or than partnership rights.
We began by regarding a bank as substantially a
cooperative enterprise, run for the convenience and at
the expense of its depositors. But, as soon as it reaches
the point of lending money to X, Y, and Z, on time,

THE PURCHASING POWER OP MONEY

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while itself owing money on demand, it assumes
toward X, Y, and Z and its cash depositors risks which
the depositors would be unwilling to assume. To
meet this situation, the responsibility and expense of
running the bank are taken by a third class of people —
stockholders — who are willing to assume the aug
mented risk for the sake of the chance of profit. Stock
holders, in order to guarantee the depositors against loss,
put in some cash of their own. Their contract is, in
effect, to make good any loss to depositors. Let us sup
pose that the stockholders put in $50,000, viz. S40,000
in cash and §10,000 in the purchase of a bank building.
The accounts now stand:—
Assets

Liabilities

C a s h ............................5140,000
L o a n s ............................
100,000
B u ild in g ......................
10,000

Due depositors . . §150,000
Due note holders . .
50,000
Due stockholders
.
50,000

§250,000

The accounts as they now stand include the chief fea
tures of an ordinary modem bank, — a so-called “ bank
of deposit, issue, and discount.”
§ 3
We have seen that the assets must be adequate to meet
the liabilities. We now wish to point out that the form
of the assets must be such as will insure meeting the lia
bilities promptly. Since the business of a bank is to fur
nish quickly available property (cash or credit) in place
of the “ slower” property of its depositors, it fails of its
purpose when it is caught with insufficient cash. ’ Yet
it “ makes money ” partly by tying up its quick property,
i.e. lending it out where it is less accessible. Its prob

Sec. 3]

DEPOSIT CURRENCY

lem in policy is to tie up enough to increase its prop
erty, but not to tie up so much as to get tied up itself.
So far as anything has yet been said to the contrary,
a bank might increase indefinitely its loans in relation
to its cash or in relation to its capital. If this were
so, deposit currency could be indefinitely inflated.
There are limits, however, imposed by prudence and
sound economic policy, on both these processes. In
solvency and insufficiency of cash must both be avoided.
Insolvency is that condition which threatens when loans
are extended with insufficient capital. Insufficiency
of cash is that condition which threatens when loans
are extended unduly relatively to cash. Insolvency
is reached when assets no longer cover liabilities (to
others than stockholders), so that the bank is unable
to pay its debts. Insufficiency of cash is reached when,
although the bank’s total assets are fully equal to its
liabilities, the actual cash on hand is insufficient to
meet the needs of the instant, and the bank is unable
to pay its debts on demand.
The less the ratio of the value of the stockholders’
interests to the value of liabilities to others, the greater
•is the risk of insolvency; the risk of insufficiency of
cash is the greater, the less the ratio of the cash to the
demand liabilities. In other words, the leading safe
guard against insolvency lies in a large capital and sur
plus, but the leading safeguard against insufficiency of
cash lies in a large cash reserve. Insolvency proper
may befall any business enterprise; insufficiency of
cash relates especially to banks in their function of
redeeming notes and deposits.
Let us illustrate insufficiency of cash. In our bank’s
accounts as we left them, there was a reserve of §140,000
of cash, and $200,000 of demand liabilities (deposits

THE PURCHASING POWER OF MONEY

[C h a p .

Ill

and notes). The managers of the bank may think
this reserve of §140,000 unnecessarily large or the loans
unnecessarily small. They may then extend their loans
(extended to customers in the form of cash, notes or
deposit accounts) until the cash reserve is reduced,
say to §40,000, and the liabilities due depositors and note
holders increased to $300,000. If, under these cir
cumstances, some depositor or note holder demands
$50,000 cash, immediate payment will be impossible.
It is true that the assets still equal the liabilities. There
is full value behind the $50,000 demanded; but the
understanding was that depositors and note holders
should be paid in money and on demand. Were this
not a stipulation of the deposit contract, the bank
might pay the claims thus made upon it by transfer
ring to its creditors the promissory notes due it from
its debtors; or it might ask the customers to wait until
it could turn these securities into cash.1
Since a bank cannot follow either of these plans, it
tries, where insufficiency of cash impends, to forestall this
condition by “ calling in” some of its loans, or if none
can be called in, by selling some of its securities or other
property for cash. But it happens unfortunately that
there is a limit to the amount of cash which a bank
can suddenly realize. No bank could escape failure if
a large percentage of its note holders and depositors
should simultaneously demand cash payment.2 The
paradox of a panic is well expressed by the case of
the man who inquired of his bank whether it had cash
available for paying the amount of his deposit, saying,
“ If you can pay me, I don’t want it; but if you can’t,
1 See Irving Fisher, The Nature of Capital and Income, Chapter V.
2 Cf. Ricardo, Works, 2d ed., London (Murray), 1852, p. 217
(Principles of Political Economy and Taxation, Chapter X X V II).

S e c . 3]

DEPOSIT CURRENCY

I do.” Such was the situation in 1907 in Wall Street.
All the depositors at one time wanted to be sure their
money' ‘ was there. ” Yet it never is there all at one time.
Since, then, insufficiency of cash is so troublesome
a condition, — so difficult to escape when it has arrived,
and so difficult to forestall when it begins to ap
proach, — a bank must so regulate its loans and note
issues as to keep on hand a sufficient cash reserve, and
thus prevent insufficiency of cash from even threaten
ing. It can regulate the reserve by alternately selling
securities for cash and loaning cash on securities. The
more the loans in proportion to the cash on hand,
the greater the profits, but the greater the danger also.
In the long run a bank maintains its necessary reserve
by means of adjusting the interest rate charged for
loans. If it has few loans and a reserve large enough to
support loans of much greater volume, it will endeavor
to extend its loans by lowering the rate of interest.
If its loans are large and it fears too great demands
on the reserve, it will restrict the loans by a high interest
charge. Thus, by alternately raising and lowering in
terest, a bank keeps its loans within the sum which the
reserve can support, but endeavors to keep them (for
the sake of profit) as high as the reserve will support.
If the sums owed to individual depositors are large,
relatively to the total liabilities, the reserve should be
proportionately large, since the action of a small num
ber of depositors can deplete it rapidly..1 Similarly, the
reserves should be larger against fluctuating deposits
(as of stock brokers) or those known to be temporary.2
1Victor Morawetz, The Banking and Currency Problem in the
United Slates, Now York (Tho North American Review Publish
ing Co.), 1909, pp. 36 and 37. Also Kemmerer, Money and Prices,
1909, p. 80.
*2 Ibid.

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The reserve in a large city of great bank activity needs
to be greater in proportion to its demand liabilities than
in a small town with infrequent banking transactions.
Experience dictates differently the average size of
deposit accounts for different banks according to the
general character and amount of their business. For
every bank there is a normal ratio, and hence for a
whole community there is also a normal ratio — an
average of the ratios for the different banks. No
absolute numerical rule can be given. Arbitrary rules
are often imposed by law. National banks in the
United States, for instance, are required to keep a re
serve for their deposits, varying according as they are
or are not situated in certain cities designated by law
as “ reserve” cities, i.e. cities where national banks
hold deposits of banks elsewhere. These reserves are
all in defense of deposits. In defense of notes, on
the other hand, no cash reserve is required, — that is,
of national banks. True, the same economic princi
ples apply to both bank notes and deposits, but the law
treats them differently. The government itself chooses
to undertake to redeem the national bank notes on
demand.
The state banks are subject to varying restrictions.1
Thus the requirement as to the ratio of reserve to de
posits varies from 12J per cent to 22\ per cent, being
usually between 15 per cent and 20 per cent. Of the
reserve, the part which must be cash varies from 10 per
cent (of the reserve) to 50 per cent, being usually 40
per cent.
Such legal regulation of banking reserves, however,
1 “ Digest of State Banking Statutes,” in Reports of the National
Monetary Commission, 61st Congress, 2d Session Senate Document,
No. 353.

S e c . 4]

DEPOSIT CURRENCY

is not a necessary development of banking. In Can
ada, the law makes the notes practically coordinate
with the deposits. Indeed, banking may exist with
out government regulations at all. “ George Smith’s
money ” furnishes an illustration. George Smith, Alex
ander Mitchell and others established in 1839 an
Insurance Company which, though forbidden to exer
cise “ banking privileges,” issued certificates of deposit
payable to bearer, and these certificates were actually
circulated like bank notes.1
§4
The study of banking operations, then, discloses two
species of currency: one, bank notes, belonging to
the category of money; and the other, deposits, be
longing outside of that category, but constituting an
excellent substitute. Referring these to the larger
category of goods, we have a threefold classification
of goods: first, money; second, deposit currency, or
simply deposits ; and third, all other goods. And by
the use of these, there are six possible types of ex
change : —
(1) Money against money,
(2) Deposits against deposits,
(3) Goods against goods,
(4) Money against deposits,
‘
(5). Money against goods,
(6) Deposits against goods.
For our purpose, only the last two types of exchange
are important, for these constitute the circulation oj
currency. As regards the other four, the first and third
have been previously explained as “ money changing”
and “ barter” respectively. The second and fourth
1 See Horace White, Money and Banking

THE PURCHASING POWER OF MONEY

[C h a p . I ll

are banking transactions: the second being such as
the selling of drafts for checks, or the mutual cancel
lation of bank clearings; and the fourth being such
operations as the depositing or the withdrawing of
money, by depositing cash or cashing checks.
The analysis of the balance sheets of banks has pre
pared us for the inclusion of bank deposits or circulating
credit in the equation of exchange. We shall still use
M to express the quantity of actual money, and V to
express the velocity of its circulation. Similarly, we
shall now use M' to express the total deposits subject
to transfer by check; and V' to express the average
velocity of circulation. The total value of purchases
in a year is therefore no longer to be measured by M V,
but by MV + M'V'. The equation of exchange, there
fore, becomes: —

MV + M'V' = IpQ = P7V
Let us again represent the equation of exchange by
means of a mechanical picture. In Figure 4, trade,

F ig .

as before, is represented on the right by the weight of
a miscellaneous assortment of goods; and their average
price by the distance to the right from the fulcrum, or
1 The equation of exchange is also stated by Keramerer, Money
and Credit Instruments in their Relation to General Prices, so as to
include bank credit, although in a somewhat different way. That
credit acts on prices in the same manner as money is by no means
a newly established principle. See, for example, Mill, Principles o]
Political Economy, Book III, Chapter X II, §§ 1, 2.

Sec. 5]

DEPOSIT CURRENCY

the length of the arm on which this weight hangs.
Again at the left, money (M ) is represented by a weight
in the form of a purse, and its velocity of circulation (F)
by its arm; but now we have a new weight at the left,
in the form of a bank book, to represent the bank de
posits (M '). The velocity of circulation (F') of these
bank deposits is represented by its distance from the
fulcrum or the arm at which the book hangs.
This mechanism makes clear the fact that the average
price (right arm) increases with the increase of money or
bank deposits and with the velocities of their circulation,
and decreases with the increase in the volume of trade.
Recurring to the left side of the equation of exchange,
or MV + M'V', we see that in a community without
bank deposits the left side of the equation reduces
simply to MV, the formula used in Chapter I I ; for
in such a community the term “ M'V'” vanishes. The
introduction of M' tends to raise prices. That is, the
hanging of the bank book on the left requires a lengthen
ing of the arm at the right.
Just as E was used to denote the total circulation
of money, MV, so we may now use E' to denote the
total circulation of deposits, M'V'.
Like E, M, and F, so also E', M', and V' are sums
and averages of corresponding .magnitudes pertaining
to different parts of the year, or different persons.1

§ 5
With the extension of the equation of monetary
circulation to include deposit circulation, the influence
1 Tho mathematical analysis of E\ M \ and V' in terms of
“ arrays” of e"s, m"s, and v” s, etc., is precisely parallel to that of
E y M , and F, given in tho Appendix to Chapter II. See also §§ 1
and 2 of Appendix to (this) Chapter III.
E

THE PURCHASING POWER OF MONEY

[C h a p .

Ill

exerted by the quantity of money on general prices
becomes less direct; and the process of tracing this
influence becomes more difficult and complicated. It
has even been argued that this interposition of circulating
credit breaks whatever connection there may be be
tween prices and the quantity of money.1 This would
be true if circulating credit were independent of money.
But the fact is that the quantity of circulating credit, M',
tends to hold a definite relation to M, the quantity of
money in circulation; that is, deposits are normally
a more or less definite multiple of money.
Two facts normally give deposits a more or less
definite ratio to money. The first has been already
explained, viz. that bank reserves are kept in a more
or less definite ratio to bank deposits. The second
is that individuals, firms, and corporations preserve
more or less definite ratios between their cash trans
actions and their check transactions, and also between
their money and deposit balances.2 These ratios are
determined by motives of individual convenience and
habit. In general, business firms use money for wage
payments, and for small miscellaneous transactions
included under the term “ petty cash” ; while for
settlements with each other they usually prefer
checks. These preferences are so strong that we
could not imagine them overridden except .tempora
1 An almost opposite view is that of Laughlin that normal credit
cannot affect prices because it is not an offer of standard money and
cannot affect the value of the standard which alone determines general
prices. See the Principles of Money, New York (Scribner), 1903, p. 97.
Both views are inconsistent with that upheld in this book.
2 This fact is apparently overlooked by Laughlin when he argues
that there is not “ any reason for limiting the amount of the deposit
currency, or the assumption of an absolute scarcity of specie re
serves.”
See Principles of Money1 p. 127.

S e c . 5]

DEPOSIT CURRENCY

rily and to a small degree. A business firm would
hardly pay car fares with checks and liquidate its
large liabilities with cash. Each person strikes an
equilibrium between his use of the two methods of
payment, and does not greatly disturb it except for
short periods of time. He keeps his stock of money
or his bank balance in constant adjustment to the
payments he makes in money or by check. Whenever
his stock of money becomes relatively small and his
bank balance relatively large, he cashes a check. In
the opposite event, he deposits cash. In this way
he is constantly converting one of the two media of
exchange into the other. A private individual usually
feeds his purse from his bank account; a retail com
mercial firm usually feeds its bank account from its
till. The bank acts as intermediary for both.
In a given community the quantitative relation of
deposit currency1 to money is determined by several
considerations of convenience. In the first place, the
more highly developed the business of a community,
the more prevalent the use of checks. Where business
is conducted on a large scale, merchants habitually
transact their larger operations with each other by
means of checks, and their smaller ones by means of
cash. Again, the more concentrated the population,
the more prevalent the use of checks. In cities it is
more convenient both for the payer and the payee to
make large payments by check; whereas, in the coun
try, trips to a bank are too expensive in time and effort
to be convenient, and therefore more money is used
in proportion to the amount of business done.2 Again,
1 The convenient expression “ deposit currency” is used by
Laughlin, The Principles of Money, p. 118.
2 See Kinloy’s “ Credit Instruments/1 Report of the National

THE PURCHASING POWER OF MONEY

[C h ap .

Ill

the wealthier the members of the community, the more
largely will they use checks. Laborers seldom use
them; but capitalists, professional and salaried men
use them habitually, for personal as well as business
transactions.
There is, then, a relation of convenience and custom
between check and cash circulation, and a more or less
stable ratio between the deposit balance of the average
man or corporation and the stock of money kept in
pocket or till. This fact, as applied to the country
as a whole, means that by convenience a rough ratio
is fixed between M and M'. If that ratio is disturbed
temporarily, there will come into play a tendency to
restore it. Individuals will deposit surplus cash, or
they will cash surplus deposits.
Hence, both money in circulation (as shown
above) and money in reserve (as shown previously)
tend to keep in a fixed ratio to deposits. It follows
that the two must be in a fixed ratio to each
other.
It further follows that any change in M, the quantity
of money in circulation, requiring as it normally does
a proportional change in M', the volume of bank de
posits subject to check, will result in an exactly pro
portional change in the general level of prices except,
of course, so far as this effect be interfered with by
concomitant changes in the 7 ’s or the Q’s. The
truth of this proposition is evident from the equation
MV + M'Y' = 2pQ; for if, say, M and M' are
doubled, while V and V' remain the same, the left
side of the'equation is doubled and therefore the right
side must be doubled also. But if the Q’s remain
Monetary Commission, Senate Document, 399, 61st Congress, 2d

Session, 1910, p. 188.

Sec .6]

DEPOSIT CURRENCY

unchanged, then evidently all the p’s must be doubled,
or else if some are less than doubled, others must be
enough more than doubled to compensate.
§6
The contents of this chapter may be formulated in
a few simple propositions: —
(1) Banks supply two kinds of currency, viz. bank
notes — which are money; and bank deposits (or
rights to draw) — which are not money.
(2) A bank check is merely a certificate of a right
to draw.
(3) Behind the claims of depositors and note holders
stand, not simply the cash reserve,- but all the assets of
the bank.
(4) Deposit banking is a device by which wealth,
incapable of direct circulation, may be made the basis
of the circulation of rights to draw.
(5) The basis of such circulating rights to draw or
deposits must consist in part of actual money, and it
should consist in part also of quick assets readily ex
changeable for money.
(6) Six sorts of exchange exist among the three classes
of goods, money, deposits, and other goods. Of these
six sorts of exchange, the most important for our pres
ent purposes are the exchanges of money and deposits
against goods.
(7) The equation of money circulation extended so
as to include bank deposits reads thus: —

MV + M'V' = SpQ or PT.
(8) There tends to be a normal ratio of bank deposits
(M') to the quantity of money (M) ; because business

THE PURCHASING POWER OF MONEY

[C h a p . I l l

convenience dictates that the available currency shall
be apportioned between deposits and money in a cer
tain more or less definite, even though elastic, ratio.
(9)
The inclusion of deposit currency does not nor
mally disturb the quantitative relation between money
and prices.

CHAPTER IV
DISTURBANCE OF EQUATION AND OF PURCHASING POWER
DURING TRANSITION PERIODS

§
In the last chapter it was shown that the quantity
of bank deposits normally maintains a definite ratio
to the quantity of money in circulation and to the
amount of bank reserves. As long as this normal
relation holds, the existence of bank deposits merely
magnifies the effect on the level of prices produced by
the quantity of money in circulation and does not in
the least distort that effect. Moreover, changes in
velocity or trade will have the same effect on prices,
whether bank deposits are included or not.
But during periods of transition this relation between
money (M) and deposits (M1) is by no means rigid.
We are now ready to study these periods of transition.
The change which constitutes a transition may be
a change in the quantity of money, or in any other factor
of the equation of exchange, or in all. Usually all are
involved, but the chief factor which we shall select for
study (together with its effect on the other factors)
is quantity of money. If the quantity of money
were suddenly doubled, the effect of the change would
not be the same at first as later. The ultimate effect
is, as we have seen, to double prices; but before this
happens, the prices oscillate up and down. In this
chapter we shall consider the temporary effects during

THE PURCHASING POWER OF MONEY

[C h a p .

the period of transition separately from the permanent
or ultimate effects which were considered in the last
chapter. These permanent or ultimate effects follow
after a new equilibrium is established, — if, indeed,
such a condition as equilibrium may be said ever to
be established. What we are concerned with in this
chapter is the temporary effects, i.e. those in the tran
sition period.
The transition periods may be characterized either by
rising prices or by falling prices. Rising prices must
be clearly distinguished from high prices, and falling from
low. With stationary levels, high or low, we have in
this chapter nothing to do. Our concern is with ris
ing or falling prices. Rising prices mark the transition
between a low and a high level of prices, just as a hill
marks the transition between flat lowlands and flat
highlands.
Since the study of these acclivities and declivities
is bound up with that of the adjustment of interest
rates, our first task is to present a brief statement
regarding the effects of rising and falling prices1 on
the rate of interest. Indeed, the chief object of this
chapter is to show that the peculiar behavior of the
rate of interest during transition periods is largely
responsible for the crises and depressions in which price
movements end.
It must be borne in mind that although business loans
are made in the form of money, yet whenever a man
borrows money, he does not do this in order to hoard
the money, but to purchase goods with it. To all
intents and purposes, therefore, when A borrows one
hundred dollars from B in order to purchase, say, one
1 For a fuller statement, see Irving Fisher, The Rate of Interest,
New York (Macmillan), 1907, Chapters V, X IV .

TRANSITION PERIODS

S e c . 1]

hundred units of a given commodity at one dollar per
unit, it may be said that B is virtually lending A one
hundred units of that commodity. And if at the end
of a year A returns one hundred dollars to B, but the
price of the commodity has meanwhile advanced, then B
has lost a fraction of the purchasing power originally
loaned to A. For even though A should happen to
return to B the identical coins in which the loan was
made, these coins represent somewhat less than the
original quantity of purchasable commodities. Bear
ing this in mind in our investigation of interest rates,
let us suppose that prices are rising at the rate of 3 per
cent each year. It is plain that the man who lends $100
at the beginning of the year must, in order to get 5 per
cent interest in purchasing power, receive back both
$103 (then the equivalent of the $100 lent) plus 5 per
cent of this, or a total of $108.15. That is, in order to
get 5 per cent interest in actual 'purchasing power, he
must receive a little more than 8 per cent interest in
money. The 3 per cent rise of prices thus ought to add
approximately 3 per cent to the rate of interest. Rising
prices, therefore, in order that the relations between
creditor and debtor shall be the same during the rise
as before and after, require higher money interest than
stationary prices require.
Not only will lenders require, but borrowers can afford
to pay higher interest in terms of money; and to some
extent competition will gradually force them to do so.1
Yet we are so accustomed in our business dealings to
consider money as the one thing stable, — to think of
a “ dollar as a dollar” regardless of the passage of time,
that we reluctantly yield to this process of readjustment,
thus rendering it very slow and imperfect. When prices
1 Rate of Interest, Chapter X IV .

THE PURCHASING POWER OF MONEY

[C hap . IV

are rising at the rate of 3 per cent a year, and the nor
mal rate of interest— i.e. the rate which would exist were
prices stationary— is 5 per cent, the actual rate, though
it ought (in order to make up for the rising prices) to
be 8.15 per cent, will not ordinarily reach that figure;
but it may reach, say, 6 per cent, and later, 7 per cent.
This inadequacy and tardiness of adjustment are fostered,
moreover, by law and custom, which arbitrarily tend to
keep down the rate of interest.
A similar inadequacy of adjustment is observed when
prices are falling. Suppose that, by the end of a year,
$97 will buy as much as $100 at the beginning. In that
case the lender, in order to get back a purchasing power
equivalent to his principal and 5 per cent interest,
should get, not $105, but only $97 + 5 per cent of $97
or $101.85. Thus the rate of interest in money should
in this case be 1.85 per cent, or less than 2 per cent,
instead of the original 5 per cent. In other words, the
3 per cent fall of prices should reduce the rate of interest
by approximately 3 per cent. But as a matter of fact,
such a perfect adjustment is seldom reached, and money
interest keeps far above 2 per cent for a considerable
time.1
§ 2
We are now ready to study temporary or transitional
changes in the factors of our equation of exchange. Let
us begin by assuming a slight initial disturbance, such
as would be produced, for instance, by an increase in the
quantity of gold. This, through the equation of ex
change, will cause a rise in prices. As prices rise,
profits of business men, measured in money, will rise
also, even if the costs of business were to rise in the same

1 Rate of Interest, loc. ext.

S ec. 2]

TRANSITION PERIODS

proportion. Thus, if a man who sold $10,000 of goods
at a cost of $6000, thus clearing $4000, could get double
prices at double cost, his profit would be double also,
being $20,000 — $12,000, which is $8000. Of course
such a rise of prices would be purely nominal, as it
would merely keep pace with the rise in price level.
The business man would gain no advantage, for his
larger money profits would buy no more than his former
smaller money profits bought before. But, as a matter
of fact, the business man’s profits will rise more than this
because the rate of interest he has to pay will not ad
just itself immediately. Among his costs is interest,
and this cost will not, at first, rise. Thus the profits will
rise faster than prices. Consequently, he will find him
self making greater profits than usual, and be en
couraged to expand his business by increasing his bor
rowings. These borrowings are mostly in the form of
short-time loans from banks; and, as we have seen,
short-time loans engender deposits. As is well known,
the correspondence between loans and deposits is re
markably exact.1 Therefore, deposit currency (M ') will
increase, but this extension of deposit currency tends
further to raise the general level of prices, just as the in
crease of gold raised it in the first place.2 Hence prices,
which were already outstripping the rate of interest,
tend to outstrip it still further, enabling borrowers,
1 See J. Pease Norton, Statistical Studies in the New York Money
Market (Macmillan), 1902, chart at end.
2 Soe article by Knut Wicksell in the Jahrbucher fur NationalSkonomie, 1897 (Band 68), pp. 228-243, entitled “ Der Bankzins als
Regulator dor Warenpreiso.” This article, while not dealing di
rectly with credit cycles as related to panics, points out the con
nection between tho rate of interest on bank loans and changes
in tho level of prices due to the resulting expansion and contraction
of such loans.

THE PURCHASING POWER OF MONEY

[C h a p .

who were already increasing their profits, to increase
them still further. More loans are demanded, and
although nominal interest may be forced up some
what, still it keeps lagging below the normal level.
Yet nominally the rate of interest has increased;
and hence the lenders, too, including banks, are led to
become more enterprising. Beguiled by the higher
nominal rates into the belief that fairly high interest
is being realized, they extend their loans, and with the
resulting expansion of bank loans, deposit currency
(M'), already expanded, expands still more. Also, if
prices are rising, the money value of collateral may be
greater, making it easier for borrowers to get large
credit.1 Hence prices rise still further.2 This sequence
of events may be briefly stated as follows: —
1. Prices rise (whatever the first cause may be; but
we have chosen for illustration an increase in the amount
of gold).
2. The rate of interest rises, but not sufficiently.
3. Enterprisers (to use Professor Fetter’s term), en
couraged by large profits, expand their loans.
4. Deposit currency (M') expands relatively to
money (M).
5. Prices continue to rise, that is, phenomenon No. 1
is repeated. Then No. 2 is repeated, and so on.
In other words, a slight initial rise of prices sets in
motion a train of events which tends to repeat itself.
Rise of prices generates rise of prices, and continues
to do so as long as the interest rate lags behind its normal
figure.
1 See Kinley, Money, New York (Macmillan), 1904, p. 223.
2 See Wicksell, op. cit.

S e c . 3]

TRANSITION PERIODS

§3
The expansion of deposit currency indicated in this
cumulative movement abnormally increases the ratio of
M' to M. This is evident if the rise of prices begins in
a change in some element or elements in the equation
other than the quantity of money; for if M remains
constant and M ' increases, the ratio M' to M must in
crease also. If M increases in any ratio, M' will increase
in a greater ratio. If it increased only in the same ratio,
prices would increase in that ratio (assuming velocities
and quantities unchanged); and if prices increased in
that ratio, loans (which being made to buy goods must
be adjusted to the prices of goods) would have to be
increased in that ratio in order to secure merely the
same goods as before. But enterprisers, wishing to
profit by the lag in interest, would extend the loans
beyond this old or original point. Therefore, deposits
based on loans would increase in a greater ratio. That
is, the ratio M' to M would increase. In other words,
during the period while M is increasing, M' increases
still faster, thus disturbing the normal ratio between
these two forms of currency.
This, however, is not the only disturbance caused by
the increase in M. There are disturbances in the Q’s (or
in other words T) in V, and in V'. These will be taken
up in order. Trade (the Q’s) will be stimulated by the
easy terms for loans. This effect is always observed
during rising prices, and people note approvingly that
“ business is good” and “ times are booming.” Such
statements represent the point of view of the ordinary
business man who is an “ enterpriser-borrower.” They
do not represent the sentiments of the creditor, the
salaried man, or the laborer, most of whom are silent but

THE PURCHASING POWER OP MONEY

[C h a p .

long-suffering, — paying higher prices, but not getting
proportionally higher incomes.
The first cause of the unhealthy increase in trade lies
in the fact that prices, like interest, lag behind their
full adjustment and have to be pushed up, so to speak,
by increased purchases. This is especially true in cases
where the original impetus came from an increase in
money. The surplus money is first expended at nearly
the old price level, but its continued expenditure grad
ually raises prices. In the meantime the volume of
purchases will be somewhat greater than it would have
been had prices risen more promptly. In fact, from the
point of view of those who are selling goods, it is the
possibilitjr of a greater volume of sales at the old prices
which gives encouragement to an increase of prices.
Seeing that they can find purchasers for more goods
than before at the previously prevailing prices, or for as
many goods as before at higher prices, they will charge
these higher prices.
But the amount of trade is dependent, almost en
tirely, on other things than the quantity of currency,
so that an increase of currency cannot, even temporarily,
very greatly increase trade. In ordinarily good times
practically the whole community is engaged in labor, pro
ducing, transporting, and exchanging goods. The in
crease of currency of a “ boom” period cannot, of itself,
increase the population, extend invention, or increase
the efficiency of labor. These factors pretty definitely
limit the amount of trade which can be reasonably
carried on. So, although the gains of the enterpriserborrower may exert a psychological stimulus on trade,
though a few unemployed may be employed, and some
others in a few lines induced to work overtime, and al
though there may be some additional buying and selling

S e c . 3]

TRANSITION PERIODS

which is speculative, yet almost the entire effect of an
increase of deposits must be seen in a change of
prices. Normally the entire effect would so express
itself, but transitionally there will be also some increase
in the Q’s.
We next observe that the rise in prices — fall in
the purchasing power of money — will accelerate the
circulation of money. We all hasten to get rid of any
commodity which, like ripe fruit, is spoiling on our
hands.1 Money is no exception; when it is depreciat
ing, holders will get rid of it as fast as possible. As
they view it, their motive is to buy goods which appre
ciate in terms of money in order to profit by the rise in
their value. The inevitable result is that these goods
rise in price still further. The series of changes, then,
initiated by rising prices, expressed more fully than
before, is as follows: —
1. Prices rise.
2. Velocities of circulation ( V and V') increase;
the rate of interest rises, but not sufficiently.
3. Profits increase, loans expand, and the Q’s in
crease.
4. Deposit currency (M') expands relatively to
money (M).
5. Prices continue to rise; that is, phenomenon
No. 1 is repeated. Then No. 2 is repeated, and so on.
It will be noticed that these changes now involve all
x For statistical proof, see Pierre des Essars, Journal de la Societe
The figures relate only
to velocity of bank deposits. N o corresponding figures for velocity
of circulation of money exist. Pierre des Essars has shown that
in European banks V' reaches a maximum in crisis years almost
without fail. The same I find true in this country as shown by
the ratio of clearings to deposits in Now York, Boston, and Phila
delphia.
de Slatistique de Paris, April, 1895, p. 143.

THE PURCHASING POWER OF MONEY

[C h a p .

the magnitudes in the equation of exchange. They are
temporary changes, pertaining only to the transition
period. They are like temporary increases in power and
readjustments in an automobile climbing a hill.
§ 4
Evidently the expansion coming from this cycle of
causes cannot proceed forever. It must ultimately
spend itself. The check upon its continued operation
lies in the rate of interest. It was the tardiness of the
rise in interest that was responsible for the abnormal
condition. But the rise in interest, though belated, is
progressive, and, as soon as it overtakes the rate of
rise in prices, the whole situation is changed. If prices
are rising at the rate of 2 per cent per annum, the boom
will continue only until interest becomes 2 per cent
higher. It then offsets the rate of rise in prices. The
banks are forced in self-defense to raise interest be
cause they cannot stand so abnormal an expansion
of loans relatively to reserves. As soon as the interest
rate becomes adjusted, borrowers can no longer hope
to make great profits, and the demand for loans ceases
to expand.
There are also other forces placing a limitation on
further expansion of deposit currency and introducing
a tendency to contraction. Not only is the amount
of deposit currency limited both by law and by prudence
to a certain maximum multiple of the amount of bank
reserves; but bank reserves are themselves limited by
the amount of money available for use as reserves.
Further, with the rise of interest, the value of certain
collateral securities, such as bonds, on the basis of
which loans are made, begins to fall. Such securities,
being worth the discounted value of fixed sums, fall

S ec. 4]

TRANSITION PERIODS

as interest rises; and therefore they cannot be used as
collateral for loans as large as before. This check to
loans is, as previously explained, a cheek to deposits
also.
With the rise of interest, those who have counted
on renewing their loans at the former rates and for the
former amounts are unable to do so. It follows that
some of them are destined to fail. The failure (or
prospect of failure) of firms that have borrowed heavily
from banks induces fear on the part of many depositors
that the banks will not be able to realize on these loans.
Hence the banks themselves fall under suspicion, and for
this reason depositors demand cash. Then occur “ runs
on the banks/’ which deplete the bank reserves at the
very moment they are most needed.1 Being short of
reserves, the banks have to curtail thei:1 loans. It is
then that the rate of interest rises to a / o,nic figure.
Those enterprisers who are caught must have currency2
to liquidate their obligations, and to get it are willing
to pay high interest. Some of them are destined to
become bankrupt, and, with their failure, the demand
for loans is correspondingly reduced. This culmination
of an upward price movement is what is called a crisis,3—
a condition characterized by bankruptcies, and the bank
1 A part of tho theory of crises here presented is similarly ex
plained in a paper by Harry G. Brown, Yale Review, August, 1910,
entitled “ Typical Commercial Crises versus a M oney Panic.”
* Irving Fisher, Rale of Interest, pp. 325, 326.
3
This is tho definition of a crisis given by Juglar and the his
tory of crises which ho gives in dotail corresponds to the descrip
tion.
See Juglar, Des Crises Commerciales cl de leur retour
piriodique en France cn Angleterre ct aux lilals-Unis. 2d ed.,
Paris (Guillaumin), 1889, pp. 4 and 5. See also translation of part
dealing with tho United States, by Do Courcoy W . Thom, A Brief
History of Panics in the United States, New York (Putnam), 1893,
PP. 7-10.

THE PURCHASING POWER OF MONEY

[C h a p .

ruptcies being due to a lack of cash when it is most
needed.
It is generally recognized that the collapse of bank
credit brought about by loss of confidence is the essential
fact of every crisis, be the cause of the loss of confidence
what it may. What is not generally recognized, and
what it is desired in this chapter to emphasize, is that
this loss of confidence (in the typical commercial crisis
here described) is a consequence of a belated adjustment
in the interest rate.
It is not our purpose here to discuss nonmonetary
causes of crises, further than to say that the/monetary
causes are the most important when taken in connection
with the maladjustments in the rate of interest. The
other factors often emphasized are merely effects of
this maladjustment. “ Overconsumption” and “ over
investment ” are cases in point. The reason many people
spend more than they can afford is that they are relying
on the dollar as a stable unit when as a matter of fact
its purchasing power is rapidly falling. The bond
holder, for instance, is beguiled into trenching on his
capital. He never dreams that he ought to lay by a
sinldng fund because the decrease in purchasing power
of money is reducing the real value of his principal.
Again, the stockholder and enterpriser generally •are
beguiled by a vain reliance on the stability of the rate
of interest, and so they overinvest. It is true that for
a time they are gaining what the bondholder is losing
and are therefore justified in both spending and in
vesting more than if prices were not rising; and at
first they prosper. But sooner or later the rate of
interest rises above what they had reckoned on, and they
awake to the fact that they have embarked on enterprises
which cannot pay these high rates.

S ec. 5]

TRANSITION PERIODS

Then a curious thing happens: borrowers, unablo
to get easy loans, blame the high rate of interest for
conditions which were really due to the fact that the
previous rate of interest was not high enough. Had
the previous rate been high enough, the borrowers
never would have overinvested.

§5
The contraction of loans and deposits is accompanied
by a decrease in velocities, and these conspire to pre
vent a further rise of prices and tend toward a fall.
The crest of the wave is reached and a reaction sets in.
Since prices have stopped rising, the rate of interest,
which has risen to compensate the rise of prices, should
fall again. But just as at first it was slow to rise, so
now it is slow to fall. In fact, it tends for a time to
rise still further.
The mistakes of the past of overborrowing compel
the unfortunate victims of these mistakes to borrow
still further to protect their solvency. It is this special
abnormality which marks the period as a “ crisis.”
Loans are wanted to continue old debts or to pay these
debts by creating new ones. They are not wanted
because of new investments but because of obligations
connected with old (and ill-fated) investments. The
problem is how to get extricated from the meshes of
past commitments. It is the problem of liquidation.
Even when interest begins to fall, it falls slowly, and
failures continue to occur. Borrowers now find that
interest, though nominally low, is still hard to meet.
Especially do they find this true in the case of contracts
made just before prices ceased rising or just before they
began to fall. The rate of interest in these cases is
agreed upon before the change in conditions takes place.

THE PURCHASING POWER OP MONEY

[C h a p .

There will, in consequence, be little if any adjustment
in lowering nominal interest. Because interest is hard
to pay, failures continue to occur. There comes to be
a greater hesitation in lending on any but the best
security, and a hesitation to borrow save when the
prospects of success are the greatest. Bank loans tend
to' be low, and consequently deposits (M') are reduced.
The contraction of deposit currency makes prices fall
still more. Those who have borrowed for the purpose
of buying stocks of goods now find they cannot sell
them for enough even to pay back what they have
borrowed. Owing to this tardiness of the interest rate
in falling to a lower and a normal level, the sequence
of events is now the opposite of what it was before: —
1. Prices fall.
2. The rate of interest falls, but not sufficiently.
3. Enterpriser-borrowers, discouraged by small profits,
contract their borrowings.
4. Deposit currency (Mr) contracts relatively to
money (M).
5. Prices continue to fall; that is, phenomenon
No. 1 is repeated. Then No. 2 is repeated, and so on.
Thus a fall of prices generates a further fall of prices.
The cycle evidently repeats itself as long as the rate
of interest lags behind. The man who loses most is
the business man in debt. He is the typical business
man, and he now complains that “ business is bad.”
There is a “ depression of trade.”
During this depression, velocities (7 and V') are
abnormally low. People are less hasty to spend money
or checks when the dollars they represent are rising
in purchasing power. The Q’s (or quantities in trade)
decline because (1) the initiators of trade — the enter
priser-borrowers — are discouraged; (2) the inertia of

S ec. 5]

TRANSITION PERIODS

high prices can be overcome only by a falling off of
expenditures; (3) trade against money which alone the
Q’s represent gives way somewhat to barter. For a
time there is not enough money to do the business
which has to be done at existing prices, for these prices
are still high and will not immediately adjust them
selves to the sudden contraction. When such a ' ‘ money
famine” exists, there is no way of doing all the business
except by eking out money transactions with barter.
But while recourse to barter eases the first fall of prices,
the inconvenience of barter immediately begins to
operate as an additional force tending to reduce prices
by inducing sellers to sell at a sacrifice if only money
can be secured and barter avoided; although this ef
fect is partly neutralized for a time by a decrease in
the amount of business which people will attempt
under such adverse conditions. A statement includ
ing these factors is : —
1. Prices fall.
2. Velocities of circulation (V and V') fall; the rate
of interest falls, but not sufficiently.
3. Profits decrease; loans and the Q’s decrease.
4. Deposit currency (ikP) contracts relatively to
money (M ).
Prices continue to fall; that is, phenomenon No. 1
is repeated. Then No. 2 is repeated, and so on.
The contraction brought about by this cycle of causes
becomes self-limiting as soon as the rate of interest
overtakes the rate of fall in prices. After a time,
normal conditions begin to return. The weakest
producers have been forced out, or have at least been
prevented from expanding their business by increased
loans. The strongest firms are left to build up a new
credit structure. The continuous fall of prices has

THE PURCHASING POWER OP .MONEY

[C h a p .

made it impossible for most borrowers to pay the old
high rates of interest; the demand for loans diminishes,
and interest falls to a point such that borrowers can
at last pay it. Borrowers again become willing to take
ventures; failures decrease in number; bank loans
cease to decrease; prices cease to fall; borrowing
and carrying on business become profitable; loans are
again demanded; prices again begin to rise, and there
occurs a repetition of the upward movement already
described.
We have considered the rise, culmination, fall, and
recovery of prices. These changes are abnormal
oscillations, due to some initial disturbance. The up
ward and downward movements taken together con
stitute a complete credit cycle, which resembles the
forward and backward movements of a pendulum.1
In most cases the time occupied by the swing of the
commercial pendulum to and fro is about ten years.
While the pendulum is continually seeking a stable
position, practically there is almost always some oc
currence to prevent perfect equilibrium. Oscillations
are set up which, though tending to be self-corrective,
are continually perpetuated by fresh disturbances.
Any cause which disturbs equilibrium will suffice to
set up oscillations. One of the most common of such
causes is an increase in the quantity of money.2 An
other is a shock to business confidence (affecting enter
prise, loans, and deposits). A third is short crops,
affecting the Q’s. A fourth is invention.
The factors in the equation of exchange are there
1 For a mathematical treatment of this analogy, see Pareto,
Cours d'economie 'politique, Lausanne, 1897, pp. 282-284.

*2 Such would seem to be the explanation of the panic of 1907.
Cf. Irving Fisher, Rate of Interest, p. 336.

S e c . 5]

TRANSITION PERIODS

fore continually seeking normal adjustment. A ship
in a calm sea will “ pitch” only a few times before
coming to rest, but in a high sea the pitching never
ceases. While continually seeking equilibrium, the
ship continually encounters causes which accentuate
the oscillation. The factors seeking mutual adjustment
are money in circulation, deposits, their velocities, the
Q’s and the p’s. These magnitudes must always be
linked together by the equation MV + M'V' = 2pQ.
This represents the mechanism of exchange. But in
order to conform to such a relation the displacement
of any one part of the mechanism spreads its effects
during the transition period over all parts. Since
periods of transition are the rule and those of equi
librium the exception, the mechanism of exchange is
almost always in a dynamic rather than a static con
dition.
It must not be assumed that every credit cycle is so
marked as to produce artificially excessive business ac
tivity at one time and “ hard times” at another. The
rhythm may be more or less extreme in the width of its
fluctuations. If banks are conservative in making loans
during the periods of rising prices, and the expansion of
credit currency is therefore limited, the rise of prices is
likewise limited, and the succeeding fall is apt to be less
and to take place more gradually. If there were a bet
ter appreciation of the meaning of changes in the price
level and an endeavor to balance these changes by ad
justment in the rate of interest, the oscillations might
be very greatly mitigated. It is the lagging behind
of the rate of interest which allows the oscillations to
reach so great proportions. On this point Marshall
well says: “ The cause of alternating periods of in
flation and depression of commercial activity . . . is

THE PURCHASING POWER OF MONEY

[C h a p .

intimately connected with those variations in the real
rate of interest which are caused by changes in the
purchasing power of money. For when prices are
likely to rise, people rush to borrow money and buy
goods, and thus help prices to rise; business is inflated,
and is managed recklessly and wastefully; those working
on borrowed capital pay back less real value than they
borrowed, and enrich themselves at the expense of
the community. When afterwards credit is shaken
and prices begin to fall, every one wants to get rid of
commodities which are falling in value and to get hold
of money which is rapidly rising; this makes prices
fall all the faster, and the further fall makes credit
shrink even more, and thus for a long time prices fall
because prices have fallen.” 1
A somewhat different sort of cycle is the seasonal
fluctuation which occurs annually. Such fluctuations,
for the most part, are due, not to the departure from a
state of equilibrium, but rather to a continuous adjust
ment to conditions, which, though changing, are normal
and expected. As the autumn periods of harvesting and
crop moving approach, there is a tendency toward a
lower level of prices, followed after the passing of this
period and the approach of winter by a rise of prices.
§ 6
In the present chapter we have analyzed the phe
nomena characteristic of periods of transition. We
have found that one such “ boom” period leads to a
reaction, and that the action and reaction complete a
cycle of “ prosperity” and “ depression.”
It has been seen that rising prices tend towards a
1 Marshall, Principles of Economics, 5th ed., London (Macmillan),
1907, Vol. I, p. 594.

Sec. 6]

TRANSITION PERIODS

higher nominal interest, and falling prices tend towards a
lower, but that in general the adjustment is incomplete.
With any initial rise of prices comes an expansion of loans,
owing to the fact that interest does not at once adjust
itself. This produces profits for the enterpriser-borrower, and his demand for loans further extends de
posit currency. This extension still further raises
prices, a result accentuated by a rise in velocities though
somewhat mitigated by an increase in trade. When
interest has become adjusted to rising prices, and loans
and deposits have reached the limit set for them by the
bank reserves and other conditions, the fact that prices
no longer are rising necessitates a new adjustment.
Those whose business has been unduly extended now
find the high rates of interest oppressive. Failures
result, constituting a commercial crisis. A reaction sets
in ; a reverse movement is initiated. A fall of prices,
once begun, tends to bp accelerated for reasons exactly
corresponding to those which operate in the opposite
situation.

CHAPTER V
INDIRECT INFLUENCES ON PURCHASING POWER
§

T h u s far we have considered the level of prices as
affected by the volume of trade, by the velocities of
circulation of money and of deposits, and by the quan
tities of money and of deposits. These are the only
influences which can directly affect the level of prices.
Any other influences on prices must act through these
five. There are myriads of such influences (outside of
the equation of exchange) that affect prices through
these five. It is our purpose in this chapter to note
the chief among them, excepting those that affect the
volume of money (M ) ; the latter will be examined in
the two following chapters.
We shall first consider the outside influences that
affect the volume of trade and, through it, the price
level. The conditions which determine the extent of
trade are numerous and technical. The most important
may be classified as follows: —
1. Conditions affecting 'producers.
(a) Geographical differences in natural resources.
(b) The division of labor.
(c) Knowledge of the technique of production.
(d) The accumulation of capital.
2. Conditions affecting consumers.
(a) The extent and variety of human wants.'

S e c . 1]

INDIRECT INFLUENCES

3. Conditions connecting 'producers and consumers.
(a) Facilities for transportation.
(b) Relative freedom of trade.
(c) Character of monetary and banking systems.
(d) Business confidence.
1 (a). It is evident that if all localities were exactly
alike in their natural resources and in their compara
tive costs of production little or no trade would be set
up between them. It is equally true that the greater
the difference in the costs of production of different arti
cles in different localities, the more likely is there to be
trade between them and the greater the amount of that
trade. Primitive trade had its raison d’etre in the fact
that the regions of this earth are unlike in their prod
ucts. The traders were travelers between distant coun
tries. Changes in commercial geography still produce
changes in the distribution and volume of trade. The
exhaustion of gold and silver mines in Nevada and of
lumber in Michigan have tended to reduce the volume
of trade of these regions, both external and internal.
Contrariwise, cattle raising in Texas, the production of
coal in Pennsylvania, of oranges in Florida, and of ap
ples in Oregon have increased the volume of trade for
these communities respectively.
1 (6). Equally obvious is the influence of the division
of labor. Division of labor is based in part on differences
in comparative costs or efforts as between men, — cor
responding to geographic differences as between coun
tries. These two, combined, lead to local differentia
tion of labor, making, for example, the town of Sheffield
famous for cutlery, Dresden for china, Venice for glass,
Paterson for silks, and Pittsburg for steel.
1 (c). Besides local and personal differentiation, the
state of knowledge of production will affect trade.

THE PURCHASING POWER OF MONEY

[C h a p .

The mines of Africa and Australia were left unworked
for centuries by ignorant natives but were opened by
white men possessing a knowledge of metallurgy. Vast
coal fields in China await development, largely for lack
of knowledge of how to extract and market the coal.
Egypt awaits the advent of scientific agriculture, to
usher in trade expansion. Nowadays, trade schools
in Germany,' England, and the United States are in
creasing and diffusing knowledge of productive tech
nique.
1 (d). But knowledge, to be of use, must be applied;
and its application usually requires the aid of capital.
The greater and the more productive the stock or capital
in any community, the more goods it can put into the
currents of trade. A mill will make a town a center
of trade. Docks, elevators, warehouses and railway
terminals help to transform a harbor into a port of
commerce.
Since increase in trade tends to decrease the general
level of prices, anything which tends to increase trade
likewise tends to decrease the general level of prices.
We conclude, therefore, that among the causes tending
to decrease prices are increasing geographical or personal
specialization, improved productive technique, and the
accumulation of capital. The history of commerce
shows that all these causes have been increasingly
operative during a long period including the last century.
Consequently, there has been a constant tendency, from
these sources at least, for prices to fall.
2 (a). Turning to the consumers’ side, it is evident
that their wants change from time to time. This is
true even of so-called natural wants, but more con
spicuously true of acquired or artificial wants.
Wants are, as it were, the mainsprings of economic

S ec . 2]

INDIRECT INFLUENCES

activity which in the last analysis keep the economic
world in motion. The desire to have clothes as fine as
the clothes of others, or finer, or different, leads to the
multiplicity of silks, satins, laces, etc.; and the same
principle applies to furniture, amusements, books, works
of art, and every other means of gratification.
The increase of wants, by leading to an increase in
trade, tends to lower the price level. Historically,
during recent times through invention, education, and
the emulation coming from increased contact in centers
of population, there has been a great intensification and
diversification of human wants and therefore increased
trade. Consequently, there has been from these causes
a tendency of prices to fall.

§2
3 (a). Anything which facilitates intercourse tends
to increase trade. Anything that interferes with inter
course tends to decrease trade. First of all, there are
the mechanical facilities for transport. As Macaulay
said, with the exception of the alphabet and the printing
press, no set of inventions has tended to alter civilization
so much as those which abridge distance, — such as
the railway, the steamship, the telephone, the tele
graph, and that conveyer of information and advertise
ments, the newspaper. These all tend, therefore, to
decrease prices.
3 (b). Trade barriers are not only physical but legal.
A tariff between countries has the same influence in
decreasing trade as a chain of mountains. The freer
the trade, the more of it there will be. In France,
many communities have a local tariff (octroi) which
tends to interfere with local trade. In the United States
trade is free within the country itself, but between the

THE PURCHASING POWER OF MONEY

[Chap. V

United States and other countries there is a high pro
tective tariff. The very fact of increasing facilities
for transportation, lowering or removing physical
barriers, has stimulated nations and communities to
erect legal barriers in their place. Tariffs not only
tend to decrease the frequency of exchanges, but to the
extent that they prevent international or interlocal
division of labor and make countries more alike as well
as less productive, they also tend to decrease the
amounts of goods which can be exchanged. The ulti
mate effect is thus to raise prices.
3 (c). The development of efficient monetary and
banking systems tends to increase trade. There have
been times in the history of the world when money was
in so uncertain a state that people hesitated to make
many trade contracts because of the lack of knowledge
of what would be required of them when the contract
should be fulfilled. In the same way, when people
cannot depend on the good faith or stability of banks,
they will hesitate to use deposits and checks.
3 (d). Confidence, not only in banks in particular,
but in business in general, is truly said to be “ the
soul of trade.” Without this confidence there can
not be a great volume of contracts. Anything that
tends to increase this confidence tends to increase
trade. In South America there are many places wait
ing to be developed simply because capitalists do not
feel any security in contracts there. They are fearful
that by hook or by crook the fruit of any investments
they may make will be taken from them.
We see,'then, that prices will tend to fall through
increase in trade, which may in turn be brought about
by improved transportation, by increased freedom of
trade, by improved monetary and banking systems,

S ec. 3]

INDIRECT INFLUENCES

and by business confidence. Historically, during recent
years, all of these causes have tended to grow in power,
except freedom of trade. Tariff barriers, however, have
only partly offset the removal of physical barriers. The
net effect has been a progressive lowering of trade re
strictions, and therefore the tendency, so far as this
group of causes goes, has been for prices to fall.
§3
Having examined those causes outside the equation
which affect the volume of trade, our next task is to
consider the outside causes that affect the velocities
of circulation of money and of deposits. For the most
part, the causes affecting one of these velocities affect
the other also. These causes may be classified as
follows: —
1. Habits of the individual.
(a) As to thrift and hoarding.
(b) As to book credit.
(c) As to the use of checks.
2. Systems of payments in the community.
(а) As to frequency of receipts and of disburse
ments.
(б) As to regularity of receipts and disbursements.
(c) As to correspondence between times and
amounts of receipts and disbursements.
3. General Causes.
(а) Density of population.
(б) Rapidity of transportation.
1 (a). Taking these up in order, we may first con
sider what influence thrift has on the velocity of cir
culation. Velocity of circulation of money is the same
thing as its rate of turnover It is found by dividing
the total payments effected by money in a year by the

THE PURCHASING POWER OF MONEY

[C h a p .

amount of money in circulation in that year. It de
pends upon the rates of turnover of the individuals
who compose the society. This velocity of circula
tion or rapidity of turnover of money is the greater
for each individual the more he spends, with a given
average amount of cash on hand; or the less average
cash he keeps, with a given yearly expenditure.
The velocity of circulation of a spendthrift may be
presumed to be greater than the average.1 He is al
ways apt to be “ short” of funds, — to have a small
average balance on hand. But his thrifty neighbor
takes care to provide himself with cash enough to meet
all contingencies. The latter tends to hoard and lay
by his money, and will, therefore, have a slower velocity
of circulation. When, as used to be the custom in
France, people put money away in stockings and kept
it there for months, the velocity of circulation must
have been extremely slow. The same principle applies
to deposits. In a certain university town the banks
often refuse to take deposits from students of spend
ing habits because the average balances of the latter
are so low ; or insist on a special stipulation that the
balance shall never fall below S100.
Hoarded money is sometimes said to be withdrawn
from circulation. But this is only another way of say
ing that hoarding tends to decrease the velocity of
circulation.
A man who is thrifty is usually, to some extent, a
hoarder either of money2 or of bank deposits. Laborers
who save usually keep their savings in the form of
1 Cf. Jevons, Money and the Mechanism of Exchange, New York
(Appleton), 1896, p. 336.
2 Cf. Harrison H. Brace, Gold Production and Future Prices,
New York (Bankers’ Publishing Co.), 1910, p. 122.

S e c . 3]

INDIRECT INFLUENCES

money until enough is accumulated to be deposited
in a savings bank. Those who have bank accounts
will likewise accumulate considerable deposits when
preparing to make an investment. Banks whose de
positors are “ rapidly making money” and periodi
cally investing the same, have, it is said, less active
accounts than banks whose depositors “ live up to their
incomes.”
1 (6). The habit of “ charging,” i.e. using book
credit, tends to increase the velocity of circulation of
money, because the man who gets things “ charged”
does not need to keep on hand as much money as he
would if he made all payments in cash. A man who
pays cash daily needs to keep cash for daily contin
gencies. The system of cash payments, unlike the
system of book credit, requires that money shall be
kept on hand in advance of purchases. Evidently, if
money must be provided in advance, it must be pro
vided in larger quantities than when merely required
to liquidate past debts. This is true for two reasons:
First, in advance of purchases, there is always uncer
tainty as to when money will be needed and how much,
while after bills are incurred, the exact sum needed
is known. Secondly, and as a consequence of the first
circumstance, money held in advance must be held
a longer time than money received after a use for it
has been contracted for. In short, to keep money in
advance requires (a) a larger margin for unforeseen
contingencies and (6) a longer period before being dis
bursed during which the money is idle. In the system
of cash payments, a man must keep money idle in
advance lest he be caught in the embarrassing position
of lacking it when he most needs it. With book credit,
he knows that even if he should be caught without a

THE PURCHASING POWER OF MONEY

[C h a p .

cent in his pocket, he can still get supplies on credit.
These he can pay for when money comes to hand.
Moreover, this money need not lie long in his pocket.
Immediately it is received, there is a use awaiting it to
pay debts accumulated. Now, to shorten the period
of waiting evidently decreases the average balance
carried, even if in the end the same sums are received
and disbursed. For instance, a laborer receiving and
spending $7 a week, if he cannot “ charge,” must make
his week’s wages last through the week. If he spends
$1 a day, his weekly cycle must show on successive
days at least as much as $7, $6, §5, $-1, S3, $2, and
$1, at which time another 57 comes in. This makes
an average of at least $4. But if he can charge every
thing and then wait until pay day to meet the resulting
obligations, he need keep nothing through the week,
paying out his §7 when it comes in. His weekly cycle
need show no higher balances than $7, SO, SO, SO, SO,
SO, SO, the average of which is only SI.
Through book credit, therefore, the average amount
of money or bank deposits which each person must keep
at hand to meet a given expenditure is made less. This
means that the rate of turnover is increased; for if
people spend the same amounts as before, but keep
smaller amounts on hand, the quotient of the amount
spent divided by the amount on hand must increase.
But we have seen that to increase the rate of turn
over will tend to increase the price level. Therefore,
book credit tends to increase the price 1 level. More
over, a community can to some extent cover the relative
scarcity of money of a period when business is large
1 This indirect effect on the price level must not be confused with
the direct effect sometimes claimed. See § 1 of Appendix to (this)
Chapter V.

S e c . 4]

INDIRECT INFLUENCES

with the relative surplus of a period when fewer de
mands are made on its supply of money. Otherwise,
to maintain the same general level of prices, there would
have to be considerably more money when business
was large; and this money, unless it were some form
of elastic bank currency which could be canceled and
retired, would lie idle during those seasons when busi
ness was slack.
In short, book credit economizes money (M) even
though it may not economize money 'payments (E)
and therefore increases the velocity of circulation
of money (E/M).
1 (c). The habit of using checks rather than money
will also affect the velocity of circulation; because a
depositor’s surplus money will immediately be put
into the bank in return for a right to draw by check.
Banks thus offer an outlet for any surplus pocket
money or surplus till money, and tend to prevent
the existence of idle hoards. In like manner surplus
deposits may be converted into cash — that is, ex
changed for cash — as desired. In short, those who
make use both of cash and deposits have the opportunity,
by adjusting the two, to prevent either from being idle.
We see, then, that three habits — spendthrift habits,
the habit of charging, and the habit of using checks —
all tend to raise the level of prices through their effects
on the velocity of circulation of money, or of deposits.
It is believed that these habits (except probably the
first) have been increasing rapidly during modern times.

§4
2 (a). The more frequently money or checks are
received and disbursed, the shorter is the average in
terval between the receipt and the expenditure of money

THE PURCHASING POWER OF MONEY

[C h a p .

or checks and the more rapid is the velocity of circula
tion.
This may best be seen from an example. A change
from monthly to weekly wage payments tends to
increase the velocity of circulation of money. If a
laborer is paid weekly S7 and reduces this evenly each
day, ending each week empty-handed, his average cash,
as we have seen, would be a little over half of S7 or
about §4. This makes his turnover nearly twice a
week. Under monthly payments the laborer who
receives and spends an average of $1 a day will have
to spread the $30 more or less evenly over the follow
ing 30 days. If, at the next__pay_ day, he comes out
empty-handed, his average'money during the month
has been about §15. This makes his turnover about
twice a month. Thus the rate of turnover is more
rapid under weekly than under monthly "payments.
The same result would hold if we assumed that,
instead of ending the cycle empty-handed, he ended
it with a given fraction — say half — of his wages
unspent. Under weekly payments, he would begin
with §10.50, and end with §3.50, averaging about §7.
Under monthly payments he would thus begin with an
average of §45, and end with §15, averaging about §30.
In the former case his average velocity of circulation
would be once a week and in the latter once a month.
The turnover will thus still be about four times as
rapid under weekly as under monthly payment.
Thus if the distribution of expenditure over the two
cycles should have exactly the same “ time shape” 1
(distribution in time), weekly payments would ac1 Compare Adolphe Landry, “ La Rapidity de la Circulation
Monfitaire,” Extrait de La Revue d’Economie politique, FSvrier,
1905.

S e c . 4]

INDIRECT INFLUENCES

celerate the velocity of circulation in the same ratio
which a month bears to a week. As a matter of his
tory, however, it is not likely that the substitution
of weekly payments for monthly payments has in
creased the rapidity of circulation of money among
workingmen fourfold, because the change in another
element, book credit, would be likely to cause a some
what compensatory decrease. Book credit is less
likely to be used under weekly than under monthly
payments. Where this book-credit habit or habit
of “ charging” is prevalent, the great bulk of money
is spent on pay day. It is probable that the substitu
tion of weekly for monthly payments, when it has
taken place, has enabled many workingmen, who
formerly found it necessary to trade on credit, to make
their own payments in cash, thus tending to decrease
the velocity of turnover of money.
Frequency of disbursements evidently has an effect
similar to the effect of frequency of receipts; i.e. it
tends to accelerate the velocity of turnover, or cir
culation.
2 (6). Regularity of payment also facilitates, the turn
over. When the workingman can be fairly certain
of both his receipts and expenditures, he can, by close
calculation, adjust them so precisely as safely to end
each payment cycle with an empty pocket. This
habit is extremely common among certain classes of
city laborers. On the other hand, if the receipts and
expenditures are irregular, either in amount or in time,
prudence requires the worker to keep a larger sum on
hand, to insure against mishaps.1 Even when fore
known with certainty, irregular receipts require a
larger average sum to be kept on hand. This state-

1 Compare Landry, ibid.

THE PURCHASING POWER OF MONEY

[C h a p . V

ment holds, at least, if we assume that th&frequency
of payments per year is the same as in the case of
regular payments, and that the “ time shape” of ex
penditures between receipts is also the same. Thus,
suppose that a workman spends at the rate of SI a
day and receives at the average rate of SI a day. The
average amount that he will require to keep on hand
will be less if his receipts occur once every fortnight
than if they occur at intervals of three weeks and one
week respectively in alternation. For, supposing he
tries to come out empty-handed just before each pay
ment, in the former case he will evidently need an aver
age sum each fortnight of $7; but in the latter case, he
will need for the first period of three weeks, or twentyone days, $10.50, and in the second period $3.50,
the average of which — remembering that the S10.50
applies for three weeks and the $3.50 for one week —
will be $8.75. We may, ’therefore, conclude that reg
ularity, both of receipts and of payments, tends to
increase velocity of circulation.
2 (c). Next, consider the synchronizing of receipts
and disbursements, i.e. making payments at the same
intervals as obtaining receipts. Where payments such
as rent, interest, insurance and taxes occur at periods
irrespective of the times of receipts of money, it is
often necessary to accumulate money or deposits in
advance, thus increasing the average on hand, with
drawing money from use for a time, and decreasing
the velocity of circulation. This result may, however,
be obviated if the individual is willing and able to
borrow in order to meet his tax or other special ex
pense, repaying the loan later at his convenience.
This is one of the ways in which banking, as already
explained, through loans and deposits, serves the con

INDIRECT INFLUENCES

S e c . 5]

venience of the public and increases the velocity of
circulation of money and deposits. Similarly book
credit may obviate the inconveniences arising from
the disharmony between the times of receipt and dis
bursement; for we have already seen that it is a great
convenience to the spender of money or of deposits,
if dealers to whom he is in debt will allow him to
postpone payment until he has received his money
or his bank deposit. This arrangement obviates the
necessity of keeping much money or deposits on hand,
and therefore increases their velocity of circulation.
We conclude, then, that synchronizing and regu
larity of payment, no less than frequency of payment,
have tended to increase prices by increasing velocity
of circulation.
§5
3 (a). The more densely populated a locality, the
more rapid will be the velocity of circulation.1
There is definite evidence that this is true of bank
deposits. The following figures2 give the velocities of
circulation of deposits in ten cities, arranged in order
of size: —
Paris
Berlin
Brussels
Madrid
Rome

116 "
161 ✓
123
14
43

Lisbon
Indianapolis
New Haven
Athens
Santa Barbara

29
30
16
4
1

Madrid is the only city seriously out of its order in
respect to velocity of circulation.
1 This is pointed out by Kinley, Money, New York (Macmillan),
1904, p. 150.
JTheso figures are the medians of those of Pierre des Essars for
Europoan banks (Journal de la Sociele de Slatislique de Paris, April,
1895) supplemented by data secured by me from a few American
banks.

THE PURCHASING POWER OF MONEY

[C h a p . V

3 (&). Again, the more extensive and the speedier the
transportation in general, the more rapid the circulation
of money.1 Anything which makes it easier to pass
money from one person to another will tend to increase
the velocity of circulation. Railways have this effect.
The telegraph has increased the velocity of circulation of
deposits, since these can now be transferred thousands of
miles in a few minutes. Mail and express, by facilitat
ing the transmission of bank deposits and money, have
likewise tended to increase their velocity of circulation.
We conclude, then, that density of population and
rapidity of transportation have tended to increase
prices by increasing velocities. Historically this con
centration of population in cities has been an im
portant factor in raising prices in the United States.
Ordinarily, the velocity of circulation of money and
the velocity of circulation of deposits will be similarly
influenced by similar causes. In time of panics,
however, if the confidence of depositors is shaken,
the tendency is for deposits to be withdrawn while
money is hoarded. Hence, for a time, the two velocities
may change in opposite directions, although there are
no good statistics for verifying this supposition.
§6
Lastly, the chief specific outside influences on the
volume of deposits subject to check are:—
(1) The system of banking and the habits of the
people in utilizing that system.
(2) The habit of charging.
1. It goes without saying that a banking system must
1 Cf. Jevons, Money and the Mechanism of Exchange, Now York
(Appleton), 1896, p. 33G; also Kinley, Money, Now York (M ac
millan), 1904, pp. 156 and 157.

S ec. 6]

INDIRECT INFLUENCES

be devised and developed before it can be used. The
invention of banking has made deposit currency pos
sible, and its adoption has undoubtedly led to a great
increase in deposits and consequent rise of prices.
Even in the last decade the extension in the United
States of deposit banking has been an exceedingly
powerful influence in that direction. In Europe de
posit banking is still in its infancy.
2.
“ Charging” is often a preliminary to payment
by check, rather than by cash. If a customer did not
have his obligations “ charged,” he would pay in money
and not by check.1 The ultimate effect of this practice,
therefore, is to increase the ratio of check payments to
cash payments (E' to E) and the ratio of deposits to
money carried (ill' to M), and therefore to increase
the amount of credit currency which a given quantity
of money can sustain.
This effect, the substitution of checks for cash pay
ments, is probably by far the most important effect
of “ charging,” and exerts a powerful influence toward
raising prices.
1 Andrew, “ Credit and tho Value of M oney.” Reprint from Papert
and Proceedings of the Seventeenth Annual Meeting American Economic
Association, December, 1904, p. 10.

CHAPTER VI
in d ir e c t in flu e n c e s

(continued)

§1
We have now considered those influences outside the
equation of exchange which affect the volume of trade
(the Q’s), the velocities of circulation of money and
deposits (F and V'), and the amount of deposits (ilF).
We have reserved for separate treatment in this chapter
and the following the outside influences that affect the
quantity of money (M).
The chief of these may be classified as follows: —
1. Influences operating through the exportation and
importation of money.
2. Influences operating through the melting or mint
ing of money.
3. Influences operating through the production and
consumption of money metals.
4. Influences of monetary and banking systems, to be
treated in the next chapter.
The first to be considered is the influence of foreign
trade. Hitherto we have confined our studies of price
levels to an isolated community, having no trade re
lation with other communities. In the modern world,
however, no such community exists, and it is important
to observe that international trade gives present-day
problems of money and of the price level an interna
tional character. If all countries had their irredeem
able paper money, and had no money acceptable
elsewhere, there could be no international adjustment

Sec. 1]

INDIRECT INFLUENCES CONTINUED

of monetary matters. Price levels in different countries
would have no intimate connection. Indeed, to some
extent the connection is actually broken between exist
ing countries which have different metallic standards,
— for example, between a gold-basis and a silver-basis
country, — although through their nonmonetary uses
the two metals are still somewhat bound together.
But where two or more nations trading with each
other use the same standard, there is a tendency for the
price levels of each to influence profoundly the price
levels of the other.
The price level in a small country like Switzerland
depends largely upon the price level in other countries.
Gold, which is the primary or full weight money in
most civilized nations, is constantly travelling from one
country or community to another. When a single
small country is under consideration, it is therefore
preferable to say that the quantity of money in that
country is determined by the universal price level,
rather than to say that its level of prices is determined
by the quantity of money within its borders. An
individual country bears the same relation to the world
that a lagoon bears to the ocean. The level of the
ocean depends, of course, upon the quantity of water
in it. But when we speak of the lagoon, we reverse the
statement, and say that the quantity of water in it
depends upon the level of the ocean. As the tide in
the outside ocean rises and falls, the quantity of water
in the lagoon will adjust itself accordingly.
To simplify the problem of the distribution of money
among different communities, we shall, for the time
being, ignore the fact that money consists ordinarily
of a material capable of nonmonetary uses and may
be melted or minted.

THE PURCHASING POWER OP MONEY

[C h a p .

Let us, then, consider the causes that determine the
quantity of money in a state like Connecticut. If the
level of prices in Connecticut temporarily falls below
that of the surrounding states, Rhode Island, Massa
chusetts, and New York, the effect is to cause an export
of money from these states to Connecticut, because
people will buy goods wherever they are cheapest and
sell them wherever they are dearest. With its low
prices, Connecticut becomes a good place to buy from,
but a poor place to sell in. But if outsiders buy of
Connecticut, they will have to bring money to buy
with. There will, therefore, be a tendency for money
to flow to Connecticut until the level of prices there
rises to a level which will arrest the influx. If, on the
other hand, prices in Connecticut are higher than in
surrounding states, it becomes a good place to sell to and
a poor place to buy from. But if outsiders sell to Con
necticut, they will receive money in exchange. There
is then a tendency for money to flow out of Connecticut
until the level of prices in Connecticut is lower.
But it must not be inferred that the prices of various
articles or even the general level of prices will become
precisely the same in different countries. Distance,
ignorance as to where the best markets are to be found,
tariffs, and costs of transportation help to maintain
price differences. The native products of each region
tend to be cheaper in that region. They are exported
as long as the excess of prices abroad is enough to more
than cover the cost of transportation. Practically, a
commodity will not be exported at a price which would
not at least be equal to the price in the country of origin,
plus the freight. Many commodities are shipped only
one way. Thus, wheat is shipped from the United
States to England, but not from England to the United

S ec. 1]

INDIRECT INFLUENCES CONTINUED

States. It tends to be cheaper in the United States.
Large exportations raise its price in America toward the
price in England, but it will usually keep below that
price by the cost of transportation. Other commodities
that are cheap to transport will be sent in either direc
tion, according to market conditions.
But, although international and interlocal trade will
never bring about exact uniformity of price levels, it
will, to the extent that it exists, produce an adjustment
of these levels toward uniformity by regulating in the
manner already described the distribution of money.
If one commodity enters into international trade, it
alone will suffice, though slowly, to act as a regulator
of money distribution; for in return for that com
modity, money may flow and, as the price level rises
or falls, the quantity of that commodity sold may
be correspondingly adjusted. In ordinary intercourse
between nations, even when a deliberate attempt is
made to interfere with it by protective tariffs, there
will always be a large number of commodities thus
acting as outlets and inlets. And since the quantity
of money itself affects prices for all sorts of commodi
ties, the regulative effect of international trade applies,
not simply to the commodities which enter into that
trade, but to all others as well. It follows that now
adays international and interlocal trade is constantly
regulating price levels throughout the world.
We must not leave this subject without emphasizing
thp effects of a tariff on the purchasing power of money.
When a country adopts a tariff, the tendency is for the
level of prices to rise. A tariff obviously raises the
prices of the “ protected” goods. But it does more
than that, — it tends also to raise the prices of goods
in general. Thus, the tariff first causes a decrease

THE PURCHASING POWER OF MONEY

[Chap.

in imports. Though in the long run this decrease in
imports will lead to a corresponding decrease in exports,
yet at first there will be no such adjustment. The
foreigner will, for a time, continue to buy from the pro
tected country almost as much as before. This will
result temporarily in an excess of that country’s exports
over its imports, or a so-called “ favorable” balance of
trade, and a consequent inflow of money. This inflow
will eventually raise the prices, not alone of protected
goods, but of other goods as well. The rise will con
tinue till it reaches a point high enough to put a stop
to the “ favorable” balance of trade.
Although the “ favorable balance” of trade created
by a tariff is temporary, it leaves behind a permanent
increase of money and of prices. The tariff wall is a
sort of dam, causing an elevation in the prices of the
goods impounded behind it.
This fact is sometimes overlooked in the theory of
international trade as commonly set forth. Emphasis
is laid instead on the fact that in the last analysis the
trade is of goods for goods, not of money for goods, and
that a tariff on imports reduces, not only imports, but
exports also,— that it merely interrupts temporarily the
virtual barter between nations. The effect of a tax on
imports is likened to that of a tax on exports. But in
respect to effects on price levels a tax on imports and a
tax on exports are diametrically opposed. If we place
our tax on exports, we first interfere with exports. The
imports are not checked until money has flowed out
and has reduced the general price level enough to de
stroy the “ unfavorable” balance of trade first created.
We conclude that the general purchasing power of
money is reduced by a tariff and that it would be in
creased by a tax on exports.

S ec. 1]

INDIRECT INFLUENCES CONTINUED

This is, perhaps, the chief reason why a protective
tariff seems to many a cause of prosperity. It furnishes
a temporary stimulus, not only to protected industries,
but to trade in general, which is really simply the stimu
lus of money inflation.
Our present interest in international trade, however,
is mainly directed to its effects on international price
levels. Except for the export or import of money to
adjust the price levels, international trade is at bottom
merely an interchange of goods. Where the price level
is not concerned, the money value of the goods sold by a
country will exactly equal the value of those bought.
Only when there is a difference in these values, or a
"balance of trade,” will there be any flow of money
and consequently any tendency to modify the price
level.1
We have shown how the international and interlocal
equilibrium of prices may be disturbed by differential
changes in the quantity of money alone. It may also
be disturbed by differential changes in the volume
of bank deposits; or in the velocity of circulation of
money; or in the velocity of circulation of bank de
posits ; or in the volume of trade. But whatever may
be the source of the difference in price levels, equilibrium
will eventually be restored through an international or
interlocal redistribution of money and goods brought
about by international and interlocal trade. Other
elements in the equation of exchange than money and
commodities cannot be transported from one place to
another.
Except for transitional effects, then, international
differences of price levels produce changes only in one
1 For mathematical statcmont, see § 1 of Appendix to (this)
Chapter VI.

THE PURCHASING POWER OF MONEY

[C h a p . V l

of the elements in the equation of exchange, — the
volume of money. Practically, of course, transition
periods may be incessant or chronic. It seldom happens
that a nation has no balance of trade. For decades Ori
ental nations took silver from Occidental nations even
when silver was, under the bimetallic regime, at a stable
ratio with gold. In Europe there was a consequent
long-continued tendency for prices to fall, and in Asia
a tendency to rise, with all the other transitional effects
involved.

§2
We have seen how M in the equation of exchange
is affected by the import or export of money. Con
sidered with reference to the M in any one of the coun
tries concerned, the M ’s in all the others are “ outside
influences.”
Proceeding now one step farther, we must consider
those influences on M that are not only outside of the
equation of exchange for a particular country, but out
side those for the whole world. Besides the monetary
inflow and outflow through import and export, there
is an inflow and outflow through minting and melting.
In other words, not only do the stocks of money in the
world connect with each other like interconnecting
bodies of water, but they connect in the same way with
the outside stock of bullion. In the modern world one
of the precious metals, such as gold, usually plays the
part of primary money, and this metal has two uses,—
a monetary use and a commodity use. That is to say,
gold is not only a money material, but a commodity as
well. In their character of commodities, the precious
metals are raw materials for jewelry, works of art, and
other products into which they may be wrought. It is

Sec. 2]

INDIRECT INFLUENCES CONTINUED

in this unmanufactured or raw state that they are
called bullion.
Gold money may be changed into gold bullion, and
vice versa. In fact, both changes are going on con
stantly, for if the value of gold as compared with other
commodities is greater in the one use than in the other,
gold will immediately flow toward whichever use is
more profitable, and the market price of gold bullion
will determine the direction of the flow. Since 100
ounces of gold, $ fine, can be transformed into S1860,
the market value of so much gold bullion, ^ fine, must
tend to be $1860. If it costs nothing to have bullion
coined into money, and nothing to melt money into
bullion, there will be an automatic flux and reflux from
money to bullion and from bullion to money that will
prevent the price of bullion from varying greatly. On
the one hand, if the price of gold bullion is greater than
the money which could be minted from it, no matter
how slight the difference may be, the users of gold who
require bullion — notably jewelers — will save this
difference by melting gold coin into bullion. Con
trariwise, if the price of bullion is less than the value
of gold coin, the owners of bullion will save the differ
ence by taking bullion to the mint and having it coined
into gold dollars, instead of selling it in the bullion
market. The effect of melting coin, on the one hand,
is to decrease the amount of gold money and increase
the amount of gold bullion, thereby lowering the value
of gold as bullion and raising the value of gold as money;
thereby lowering the price level and restoring the equal
ity between bullion and money. The effect of minting
bullion into coin is, by the opposite process, to bring the
value of gold as coin and the value of gold as bullion
again into equilibrium. In practice, the balance is

THE PURCHASING POWER OF MONEY

[C h a p . VI

probably1 maintained chiefly by turning newly mined
gold into the one or the other use according to the mar
ket. By thus feeding the two reservoirs according to
their respective needs there is saved the necessity of any
great amount of interflow between money and the arts.
Where a charge — called “ seigniorage ” — is made for
changing bullion into coin, or where the process in
volves expense or delay, the flow of bullion into currency
will be to that extent impeded. But under a modem
system of free coinage and with modem methods of
metallurgy, both melting and minting may be performed
so inexpensively and so quickly that there is practically
no cost or delay involved. In fact, there are few in
stances of more exact price adjustment than the ad
justment between gold bullion and gold coin. It
follows that the quantity of money, and therefore its
purchasing power, is directly dependent on that of gold
bullion.
The stability of the price of gold bullion expressed in
gold coin causes confusion in the minds of many people,
giving them the erroneous impression that there is no
change in the value of money. Indeed, this stability has
often been cited to show that gold is a stable standard
of value. Dealers in objects made of gold seem to
misunderstand the significance of the fact that an ounce
of gold always costs about $18.60 in the United States
or £3 17s. 10|d. in England. This means nothing
more than the fact that gold in one form and meas
ured in one way will always bear a constant ratio to
gold in another form and measured in another way.
An ounce'of gold bullion is worth a fixed number of gold
dollars, for the same reason that a pound sterling of
1 Cf. De Launay, The World’s Gold, New York (Putnam), 1908,
pp. 179-183.

Sec. 3]

INDIRECT INFLUENCES CONTINUED

gold is worth a fixed number of gold dollars, or that a
gold eagle is worth a fixed number of gold dollars.
Except, then, for extremely slight and temporary
fluctuations, gold bullion and gold money must always
have the same value. Therefore, in the following dis
cussion respecting the more considerable fluctuations
affecting both, we shall speak of these values inter
changeably as “ the value of gold.”
§ 3
The stock of bullion is not th e. ultimate outside
influence on the quantity of money. As the stock of
bullion and the stock of money influence each other,
so the total stock of both is influenced by production
and consumption. The production of gold consists of
the output of the mines, which constantly tends to add
to the existing stocks both of bullion and coin. The
consumption of gold consists of the use of bullion in
the arts by being wrought up into jewelry, gilding, etc.,
and of losses by abrasion, shipwreck, etc. If we con
sider the amount of gold coin and bullion as contained
in a reservoir, production would be the inflow from
the mines, and consumption the outflow to the arts
and by destruction and loss. To the inflow from the
mines should be added the reinflow from forms of art
into which gold had previously been wrought, but
which have grown obsolete. This is illustrated by
the business of producing gold bullion by burning
gold picture frames.
We shall consider first the inflow or production,
and afterward the outflow or consumption. The reg^ ulator of the inflow (which practically means the
production of gold from the mines) is its estimated
“ marginal cost of production.”

100

THE PURCHASING POWER OF MONEY

[C h a p .

Mining is a hazardous business and estimates are
subject to great error. But however erroneous the
estimated cost, it exerts a regulatory power over pro
duction. Wherever the estimated cost of producing
a dollar of gold is less than the existing value of a dollar
in gold, it will normally be produced. Wherever the
cost of production exceeds the existing value of a dollar,
gold will normally not be produced. In the former
case the production of gold is profitable; in the latter
it is unprofitable. There will be an intermediate .or
neutral point at which normally profitable production
ceases and unprofitable production begins, a point at
which the cost of producing S100 will be exactly SI 00.
The cost at this point is called the marginal cost of
production. At the richest mines, the cost of produc
tion is extremely small. From this low standard the
cost gradually rises at other mines, until the marginal
mine is reached, at which the cost will normally be
equal to the value of the product. In fact, there
exists a marginal point of production, not only as
among different mines, but for each mine individually.
The fact that cost tends in general to increase with
increased product is due to the fact that gold is an
extractive industry. It is subject to the law of increas
ing cost, or, as it is often expressed, "the law of decreas
ing returns.” If a mine is only moderately worked, the
cost of production per ounce of gold will be less than
if it is worked at more nearly its full capacity, and
there will always be a rate of working such that the
cost per ounce of any extension in that rate of working
will make the extension barely profitable. It will pay
to extend production to the point where the additional
return is just equal to the consequent additional cost,
but no further. The mine operator may unintention

Sec. 3]

INDIRECT INFLUENCES CONTINUED

101

ally or temporarily overshoot the mark or fall within
it, but such errors will only stimulate him to correct
them; and gold production will always tend toward
an equilibrium in which the marginal cost of produc
tion will (when interest is added) be equal to the
value of the product.
This holds true in whatever way cost of production
is measured, whether in terms of gold itself, or in
terms of some other commodity such as wheat, or of
commodities in general, or of any supposed “ absolute”
standard of value. In gold-standard countries gold
miners do actually reckon the cost of producing gold
in terms of gold. From their standpoint it is a need
less complication to translate the cost of production
and the value of the product into some other standard
than gold. They are interested in the relation between
the two, and this relation will not be affected by the
standard.
To translate the cost and value from gold money
into wheat, it is only necessary to divide both cost
and value by the price of wheat in gold money.
Such a change in the method of expressing both
cost and value will not affect their relation to each
other.
To illustrate how the producer of gold measures
everything in terms of gold, suppose that the price
level rises. Assuming that the rise of prices applies
to wages, machinery, fuel, and the other expenses of
producing gold, he will then have to pay more dollars
for wages, machinery, fuel, etc., while the prices ob
tained for liis product (expressed in those same dol
lars) will, as always, remain unchanged. Conversely,
a fall in the level will lower his cost of production
(measured in dollars), while the price of his product

102

THE PURCHASING POWER OF MONEY

[C h a p .

will still remain the same.1 Thus we have a constant
number expressing the price of gold product and a
variable number expressing its cost of production.
If we express the same phenomena, not in terms of
gold, but in terms of wheat, or rather, let us say, in
terms of goods in general, we shall have the opposite
conditions. When prices rise, the purchasing power of
money falls, and this purchasing power is the value of
the product expressed in terms of goods in general.
If the mining costs change with the general price move
ment, there will not occur any change in the cost of
producing gold relatively to goods. There will, however,
be a change in the value of the gold product. That
is, we shall then have a variable number expressing the
price of the gold product and a constant number ex
pressing its cost of production.
Thus the comparison between price and cost of
production is the same, whether we use gold or other
commodities as our criterion. In the one view—
i.e. when prices are measured in gold— a rise of prices
means a rise in the gold miner’s cost of production;
in the other view — i.e. when prices are measured
in other goods — the same rise in prices means a fall in
the price (purchasing power) of his product. In either
view he will be discouraged. He will look at his troubles
in the former light, i.e. as a rise in the cost of produc
tion ; but we shall find it more useful to look at them
in the latter, i.e. as a fall in the purchasing power of
the product. In either case the comparison is between
the cost of the production of gold and the purchasing
power of gold. If this purchasing power is above the
cost of production in any particular mine, it will pay
1 Cf. Mill, Principles o} Political Economy, Book III, Chapter
IX , § 2.

Sec. 3]

INDIRECT INFLUENCES CONTINUED

103

to work that mine. If the purchasing power of gold
is lower than the cost of production of any particular
mine, it will not pay to work that mine. Thus the
production of gold increases or decreases with an in
crease or decrease in the purchasing power of gold.
So much for the inflow of gold and the conditions
regulating it. We turn next to outflow or consumption
of gold. This has two forms, viz. consumption in the
arts and consumption for monetary purposes.
First we consider its consumption in the arts. If
objects made of gold are cheap — that is, if the prices
of other objects are relatively high — then the relative
cheapness of the gold objects will lead to an increase in
their use and consumption. Expressing the matter in
terms of money prices, when prices of everything else
are higher and people’s incomes are likewise higher,
while gold watches and gold ornaments generally re
main at their old prices, people will use and consume
more gold watches and ornaments.
These are instances of the consumption of gold in the
form of commodities. The consumption and loss of gold
as coin is a matter of abrasion, of loss by shipwreck
and other accidents. It changes with the changes in
the amount of gold in use and in its rapidity of ex
change. The outlets from this reservoir represent the
consumption of gold coins by loss. Just as production
is regulated by marginal cost of what is produced, so is
consumption regulated by marginal utility of what is
consumed. This is not the place to enter into a dis
cussion of the essential symmetry between these two
marginal magnitudes, a symmetry often lost sight of
because cost is usually measured objectively and util
ity subjectively. Both are measurable in either way.
The subjective method is the more fundamental, but

104

THE PURCHASING POWER OP MONEY

[C h a p .

takes us farther away from our present discussion than
is necessary or profitable.
We see then that the consumption of gold is stimu
lated by a fall in the value (purchasing power) of gold,
while the production of gold is decreased. The pur
chasing power of money, being thus played upon by
the opposing forces of production and consumption,
is driven up or down as the case may be.1
§4
In any complete picture of the forces determining
the purchasing power of money we need to keep prom
inently in view three groups of factors: (1) the
production or the “ inflow” of gold (i.e. from the mines);
(2) the consumption or “ outflow” (into the arts and
by destruction and loss); and (3) the “ stock” or
reservoir of gold (whether coin or bullion) which
receives the inflow and suffers the outflow. The re
lations among these three sets of magnitudes can be
set forth by means of a mechanical illustration, given
in Figure 5. This represents two connected reservoirs
of liquid, Gband Gm. The contents of the first reservoir
represent the stock of gold bullion, and the contents
of the second the stock of gold money. Since purchas1 The theory here presented, that the value of gold bullion
and the cost of production of gold affect prices by way of the
quantity of money, is the one which economists have generally
held. A different view is represented by Laughlin, who says, “ the
quantity of money used as the actual media of exchange no more
determines price than the entries of deeds and conveyances in
the county records determine the prices of tho land whose sale is
stated in the papers recorded,” and that “ price is an exchange
relation between goods and tho standard money commodity, whether
that money commodity be used as a medium of exchange or not.”
See The Principles of Money , New York (Scribner), 1903, pp. 317
and 318.

S ec. 4]

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105

ing power increases with scarcity, the distance from
the top of the cisterns, 00, to the surface of the liquid,
is taken to represent the purchasing power of gold over
other goods. A lowering of the level of the liquid
indicates an increase in the purchasing power of money,
since we measure this purchasing power downward
from the line 00 to the surface of the liquid. We shall
not attempt to represent other forms of currency ex
plicitly in the diagram. We have seen that normally
the quantities of other currency are proportional to

the quantity of primary money, which we are supposing
to be gold. Therefore, the variation in the purchasing
power of this primary money may be taken as rep
resentative of the variation of all the currency. We
shall now explain the shapes of these cisterns. The
shape of the cistern Gmmust be such as will make the
distance of the liquid surface below 00 decrease with
an increase of the liquid, in exactly the same way as
the purchasing power of gold decreases ivith an increase
in its quantity. That is, as the quantity of liquid in
0m doubles, the distance of the surface from the line

106

THE PURCHASING POWER OF MONEY

[C hap.

00 should decrease by one half. In a similar manner
the shape of the gold bullion cistern must be such as
will make the distance of the liquid surface below 00
decrease with an increase of the liquid in the same way
as the value of gold bullion decreases with an increase
of the stock of gold bullion. The shapes of the two
cisterns need not, and ordinarily will not, be the same,
for we can scarcely suppose that halving the purchas
ing power of gold will always exactly double the amount
of bullion in existence.
Both reservoirs have inlets and outlets. Let us
consider these in connection with the bullion reservoir
(<?(,). Here each inlet represents a particular-mine
supplying bullion, and each outlet represents a partic
ular use in the arts consuming gold bullion. Each
mine and each use has its own distance from 00.
There are, therefore, three sets of distances from 0 0 :
the inlet distances, the outlet distances, and the liquidsurface distance. Each inlet distance represents the
cost of production for each mine, measured in goods;
each outlet distance represents the value of gold in
some particular use, likewise measured in goods. The
surface distance, as we have already explained, repre
sents the value of bullion, likewise measured in goods,
— in other words, its purchasing power.
It is evident that among these three sets of levels
there will be discrepancies. These discrepancies serve
to interpret the relative state of things as between
bullion and the various flows — in and out. If an
inlet at a given moment be above the surface level,
i.e. at a less distance from 00, the interpretation is
that the cost of production is less than the purchasing
power of the bullion. Hence the mine owner will turn
on his spigot and keep it on until, perchance, the sur*

S ec. 4]

INDIRECT INFLUENCES CONTINUED

107

face level rises to the level of his mine, — i.e. until
the surface distance from 00 is as small as the inlet
distance, — i.e. until the purchasing power of bullion
is as small as the cost of production. At this point
there is no longer any profit in mining. So much for
inlets; now let us consider the outlets. If an outlet
at a given moment be below the surface level, — i.e.
at a greater distance from 00, — the interpretation is
that the value of gold in that particular use is greater
than the purchasing power of bullion. Hence gold
bullion will flow into these uses where its worth is
greater than as bullion. That is, it will flow out of all
outlets below the surface in the reservoir.
It is evident, therefore, that at any given moment,
only the inlets above the surface level, and only the
outlets below it, will be called into operation. As the
surface rises, therefore, more outlets will be brought
into use, but fewer inlets. That is to say, the less the
purchasing power of gold as bullion, the more it will
be used in the arts, but the less profitable it will be for
the mines to produce it, and the smaller will be the
output of the mines. As the surface falls, more inlets
will come into use and fewer outlets.
We turn now to the money reservoir (Gm). The fact
that gold has the same value either as bullion or as
coin, because of the interflow between them, is in
terpreted in the diagram by connecting the bullion
and coin reservoirs, in consequence of which both will
(like water) have the same level. The surface of the
liquid in both reservoirs will be the same distance be
low the line 00, and this distance represents the value
of gold or its purchasing power. Should the inflow
at any time exceed the outflow, the result will neces
sarily be-an increase in the stock of gold in existence.

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THE PURCHASING POWER OF MONEY

[C h a p .

This will tend to decrease the purchasing power or
value of gold. But as soon as the surface rises, fewer
inlets and more outlets will operate. That is, the
excessive inflow or production on the one hand will
decrease, and the deficient outflow or consumption on
the other hand will increase, checking the inequality
between the outflow and inflow. If, on the other hand,
the outflow should temporarily be greater than the in
flow, the reservoir will tend to subside. The purchas
ing power will increase; thus the excessive outflow
will be checked, and the deficient inflow stimulated, —
restoring equilibrium. The exact point of equilibrium
may seldom or never be realized, but as in the case
of a pendulum swinging back and forth through a posi
tion of equilibrium, there will always be a tendency to
seek it.
It need scarcely be said that our mechanical diagram
is intended merely to give a picture of some of the chief
variables involved in the problem under discussion.
It does not of itself constitute an argument, or add
any new element; nor should one pretend that it in
cludes explicitly all the factors which need to be con
sidered. But it does enable us to grasp the chief
factors involved in determining the purchasing power
of money. It enables us to observe and trace the
following important variations and their effects: —
First, if there be an increased production of gold —
due, let us suppose, to the discovery of new mines or
improved methods of working old ones — this may be
represented by an increase in the number or size of the
inlets into' the Gb reservoir. The result will evidently
be an increase of “ inflow” into the bullion reservoir,
and from that into the currency reservoir, a consequent
gradual filling up of both, and therefore a decrease in

S e c . 4]

INDIRECT INFLUENCES CONTINUED

109

the purchasing power of money. This process will be
checked finally by the increase in consumption. And
when production and consumption become equal, an
equilibrium will be established. An exhaustion of gold
mines obviously operates in exactly the reverse manner.
Secondly, if there be an increase in the consumption
of gold — as through some change of fashion — it
may be represented by an increase in the number or
size of the outlets of Gb. The result will be a draining
out of the bullion reservoir, and consequently a de
creased amount in the currency reservoir: hence an
increase in the purchasing power of gold, which in
crease will be checked finally by an increase in the out
put of the mines as well as by a decrease in consump
tion. When the increased production and the decreased
consumption become equal, equilibrium will again be
reached.
If the connection between the currency reservoir
and the bullion reservoir is closed by a valve, that
is, if the mints are closed so that gold cannot flow
from bullion into money (although it can flow in the
reverse direction), then the purchasing power of the
gold as money may become greater than its value as
bullion. Any increase in the production of gold will
then tend only to fill the bullion reservoir and decrease
the distance of the surface from the line 00, i.e. lower
the value, of gold bullion. The surface of the liquid
in the money reservoir will not be brought nearer 00.
It may even by gradual loss be lowered farther away.
In other words, the purchasing power of money will
by such a valve be made entirely independent of the
value of the bullion out of which it was first made.
An illustration of this principle is found in the history
of the silver currency in India. After long discussion the

110

THE PURCHASING POWER OF MONET

[C hap. V I

mints of India were closed to silver in 1893. Previous
to that time the value of coined silver had followed
closely the value of silver bullion, but the closure
produced an immediate divergence between the two.
The rupee has remained independent of silver ever since;
and during the first six years — until 1899 — it was
independent of gold also. Its present relation to the
latter metal will be discussed in the next chapter.
We have now discussed all but one of the outside in
fluences upon the equation of exchange. That one is
the character of the monetary and banking system
which affects the quantity of money and deposits.
This we reserve for special discussion in the following
chapter. Meanwhile, it is also noteworthy that al
most all of the influences affecting either the quantity
or the velocities of circulation have been and are pre
dominantly in the direction of higher prices. Almost
the only opposing influence is the increased volume
of trade; but this is partly neutralized by increased
velocities due to the increased trade itself. We may
here point out that some of those influences discussed
in this and the preceding chapter operate in more than
one way. Consider, for instance, technical knowledge
and invention, which affect the equation of exchange
by increasing trade. So far as these increase trade,
the tendency is to decrease prices; but so far as they
develop metallurgy and the other arts which increase
the production and easy transportation of the precious
metals, they tend to increase prices. So far as they
make the transportation and transfer of money and
deposits quicker, they also tend to increase prices.
So far as they lead to the development of the art of
banking, they likewise tend to increase prices, both by
increasing deposit currency (AT) and by increasing the

S e c . 4]

INDIRECT INFLUENCES CONTINUED

111

velocity of circulation both of money and deposits.
So far as they lead to the concentration of population
in cities, they tend to increase prices by accelerating
circulation.
Finally, so far as per capita trade is increased through
this or any other cause, there is a tendency to decrease
prices. What the net effect of the development of the
arts may be during any given period will depend on the
predominant direction in which the arts are developed.

CHAPTER VII
INFLUENCE OF MONETARY SYSTEMS ON PURCHASING
POWER

§1
T h u s far we have considered the influences that de
termine the purchasing power of money when the money
in circulation is all of one kind. The illustration given
in the previous chapter shows how the money mecha
nism operates when a single metal is used. We have
now to consider the monetary systems in which more
than one kind of money is used.
One of the first difficulties in the early history of
money was that of keeping two (or more) metals in
circulation. One of the two would become cheaper than
the other, and the cheaper would drive out the dearer.
This tendency was observed by Nicolas Oresme,
afterwards Count Bishop of Lisieux, in a report to
Charles V of France, about 1366, and by Copernicus
about 1526 in a report or treatise mitten for Sigismund I, King of Poland.1 Macleod in his Elements
of Political Economy, published in 1857,2 before he had
become aware of the earlier formulations of Oresme
and Copernicus,3 gave the name “ Gresham’s Law” to
this tendency, in honor of Sir Thomas Gresham, who
stated the principle in the middle of the sixteenth cen1 Henry Dunning Macleod, The History of Economics, New York
(Putnam), 1890, pp. 37 and 38.
2 P. 477.
* Macleod, The History of Economics, pp. 38 and 39.

112

Sec. 1]

INFLUENCE OF MONETARY SYSTEMS

113

tury. The tendency seems in fact, to have been rec
ognized even among the ancient Greeks, being men
tioned in the “ Frogs” of Aristophanes: 1—
“ For your old and standard pieces valued and approved and tried,
Here among the Grecian nations and in all the world beside,
Recognized in every realm for trusty stamp and pure assay,
Are rejected and abandoned for the trash of yesterday,
For a vile, adulterate issue, drossy, counterfeit, and base
Which the traffic of the City passes current in their place.”

Gresham’s or Oresme’s Law is ordinarily stated in
the form, “ Bad money drives out good money,” for
it was usually observed that the badly worn, defaced,
light-weight, “ clipped,” “ sweated,” and otherwise de
teriorated money tended to drive out the full-weight,
freshly minted coins. This formulation, however, is
not accurate. It is not true that “ bad” coins, e.g.
worn, bent, defaced, or even clipped coins, will drive
out other money just because of their worn, bent, de
faced, or clipped condition. Accurately stated, the
Law is simply this: Cheap money will drive out dear
money. The reason the cheaper of two moneys always
prevails is that the choice of the use of money rests
chiefly with the man who gives it in exchange, not
with the man who receives it. When any one has
the choice of paying his debts in either of two moneys,
motives of economy will prompt him to use the
cheaper. If the initiative and choice lay principally
with the person who receives, instead of the person who
pays the money, the opposite would hold true. The
dearer or “ good” money would then drive out the
cheaper or “ bad” money.
What then becomes of the dearer money ? It may
1893-898, Frero’s translation.

114

THE PURCHASING POWER OF MONEY

[C h a p . V H

be hoarded, or go into the melting pot, or go abroad,—
hoarded and melted from motives of economy, and
sent abroad because, where foreign trade is involved, it
is the foreigner who receives the money, rather than
ourselves who give it, who dictates what kind of money
shall be accepted. He will take only the best, because
our legal-tender laws do not bind him.
The better money might conceivably be used in ex
change at a premium, i.e. at its bullion value; but the
difficulties of arranging payments in it, which would
be satisfactory to both parties, are such that in practice
it is never so used in large quantities. In fact, the force
of Gresham’s Law is so great that it will even sacrifice
the convenience of a whole nation. For instance, in
Italy fifteen years ago the overissue of paper money
drove not only gold across the Alps, but also silver
and copper. These could circulate in Southern France
at a par with corresponding coins there because France
and Italy belonged to the Latin Union. Consequently,
for a time there was very little small change left, below
the denomination of 5 lire notes. Customers at retail
stores often found it impossible to make their pur
chases because they lacked the small denominations
necessary, and because the storekeeper lacked the same
small denominations, and could not make change. To
meet the difficulty, 30,000,000 of 1 lire notes were
issued, and these were so much in demand that dealers
paid a premium for them.
Gresham’s Law applies not only to two rival moneys
of the same metal; it applies to all moneys that cir
culate concurrently. Until “ milling” the edges of
coins was invented and a “ limit of tolerance” of the
mint (deviation from the standard weight) was adopted,
much embarrassment was felt in commerce from tho

Sec. 2]

INFLUENCE OF MONETARY SYSTEMS

115

fact that the clipping and debasing of coin was a com
mon practice. Nowadays, however, any coin which has
been so “ sweated” or clipped as to reduce its weight
appreciably ceases to be legal tender, and being com
monly rejected by those to whom it is offered ceases
to be money. Within the customary1 or legal limits of
tolerance, however — that is, as long as the cheaper
money retains the “ money” power — it will drive
out the dearer.

§2
The obvious effect of Gresham’s Law is to decrease
the purchasing power of money at every opportunity.
The history of the world’s currencies is largely a record
of money debasements, often at the behest of the
sovereign. Our chief purpose now, in considering
Gresham’s Law, is to formulate more fully the causes
determining the purchasing power of money under
monetary systems subject to the operation of Gresham’s
Law. The first application is to bimetallism.
In order to understand fully the influence of any
monetary system on the purchasing power of money,
we must first understand how the system works.2 It
has been denied that bimetallism ever did work or can
be made to work, because the cheaper metal will drive
out the dearer. Our first task is to show, quite irrespec
tive of its desirability, that bimetallism can and does
“ work” under certain circumstances, but not under
others. To make clear when it will work and when it
will not work, we shall continue to employ the mechani1 Sometimes custom is less strict than law. For instance, in
California worn gold coin below the mint limit of tolerance con
tinues to circulate. It is called “ bank gold.”
2 Irving Fisher, “ Tho Mechanics of Bimetallism,” (British)
Economic Journal, September, 1894, pp. 527-536.

116

THE PURCHASING POWER OF MONEY

[C h a p . VII

cal illustration1of the last chapter, in which the amount
of gold bullion is represented by the contents of res
ervoir Gb (Figs. 6, 7). Here, as before, we represent
the purchasing power or value of gold by the distance
of the water level below the zero level, 00. In the
last chapter, our figure represented only one metal,
gold, and represented that metal in two reservoirs, — the
bullion reservoir and the coin reservoir. We shall now,
one step at a time, elaborate that figure. First, as in
Figure 6 a, we add a reservoir for silver bullion (St,), a

reservoir of somewhat different shape and size from
Gb. This reservoir may be used to show the relation
1
In its present application it is somewhat like a s y m b o lis m
suggested by Jevons in his Money and the Mechanism of Exchange.
New York (Appleton), 1896, p. 140.

S ec. 2]

INFLUENCE OF MONETARY SYSTEMS

117

between the value or purchasing power of silver and
its quantity in the arts and as bullion. Here, then,
are three reservoirs. At first the silver one is entirely
isolated; but after a while we shall connect it with
the middle one. For the present, let us suppose that
the middle one, which contains money, is entirely filled
with gold money only (Fig. 6 a), no silver being yet
used as money. In other words, the monetary system
is the same as that discussed in the last chapter. The
only change we have introduced is to add to the pic
ture another reservoir (Sb), entirely detached, showing
the quantity and value of silver bullion.
We next suppose a pipe opened at the right, connect
ing Sb with the money reservoir; that is, we introduce
bimetallism. Under bimetallism, governments open
their mints to the free coinage of both metals at a fixed
ratio, i.e. a fixed ratio between the said metals. For
instance, if a silver dollar contains 16 grains of silver
for every grain of gold in a gold dollar, the ratio is said
to be 16 to 1. Under this system, the debtor has the
option, unless otherwise bound by his contract, of mak
ing payment either in gold or in silver money. These,
in fact, are the two requisites of complete bimetallism,
viz. (1) the free and unlimited coinage of both metals at
a fixed ratio, and (2) the unlimited legal tender of each
metal at that ratio.1 These new conditions are repre
sented in Figure 6 b (and later, Fig. 7 b), where a pipe gives
silver an entrance into the money or central reservoir.2
1 Tlio possibility of government’s fixing any ratio between gold
and silver to which tho market ratio will conform has been so bitterly
disputed that in addition to tho positive argument contained in the
text, a negative criticism of wliat are believed to be the chief fal
lacies underlying these disputes is inserted in § 1 of the Appendix
to. (this) Chapter VII.
2 Of courso a unit of water represents gold and silver at their

118

THE PURCHASING POWER OF MONEY

[C h a p .

VII

What we are about to represent is not the relations
between mines, bullion, and arts, but the relations be
tween bullion (two kinds) and coins. We may, there
fore, disregard for the present all inlets and outlets
except the connections between the bullion reservoirs
and coin reservoir.
Now in these reservoirs the surface distances below
00 represent, as we have said, purchasing power
of gold and silver. But each unit of silver (say each
drop of silver water, whether as money or as bullion)
contains sixteen times as many grains as each unit of
gold (say each drop of gold water, whether as money
or as bullion). That is, a unit of water represents a
dollar of gold or a dollar of silver. All we wish to
represent is the relative purchasing power of corre
sponding units.
The waters representing gold and silver money are
separated by a movable film /. In Figure 6 a this film
is at the extreme right; in Figure 6 b, at the extreme
left; in Figure 7 a, again at the right; and in Figure 7 b,
midway. The a figures represent conditions before
the mints are opened to silver. The b figures repre
sent conditions after they have been opened and Gres
ham’s Law has operated. If, just previous to the in
troduction of bimetallism, the silver level in Sb is below
the gold level in Gb the statute introducing bimetallism
will be inoperative, i.e. the silver bullion will not flow
uphill, as it were, into the money reservoir; but if, as
in Figure 6 a or in 7 a, the silver level is higher, then as
coining weights.
If the bimetallic ratio is 16 to 1, the cisterns
must be so constructed that a cubic inch of water shall represent
an ounce of gold or 16 ounces of silver and that the number of
inches separating the surfaces of liquid from 0 0 shall represent the
marginal utility of an ounce of gold and of 16 ounces of silver,
respectively.

S e c . 2]

INFLUENCE OF MONETARY SYSTEMS

119

soon as the mints are open to silver, it will flow into
circulation. Being at first cheaper than gold, it will
push out the gold money through the left tube (i.e. by
melting) into the bullion market. This expulsion of
gold may be complete, as shown in Figure 6 b, or only
partial, as shown in Figure 7 b. The expulsion will

continue just as long as there is a premium on gold;
that is, as long as the silver level in the bullion reservoir
is above the gold level in the money reservoir; i.e. as
long as silver bullion is cheaper than gold money.
Let mm, as shown in Figure 6 a, be the mean level;
that is, a level such that the volume x above it equals
the combined vacant volumes y and z below it. This
line, mm, remains the mean level, whatever may be the

120

THE PURCHASING POWER OF MONEY

[C h a p .

VII

distribution of the contents among the three reservoirs.
As soon as the connecting pipe is inserted, silver will
flow into the money reservoir and, in accordance with
Gresham’s Law, will displace gold.
Here we have to distinguish two cases: (1) when the
silver x above the mean line, mm, exceeds the total con
tents of the money reservoir below this line; (2) when x
is less than said lower contents. In the first case, it
is evident that silver will sweep gold wholly out of
circulation, as shown in Figure 6 b, where the film has
moved from the extreme right to the extreme left.
The contents of silver in the bullion reservoir are less
than before, and the contents of gold in the bullion
reservoir greater than before.
But this redistribution is only the first effect of open
ing the mints to silver. The balance between produc
tion and consumption has been upset both for gold
and for silver. The increased value of silver (lowered
level in Sb) has stimulated production, bringing into
operation silver mines (uncovered inlets at right);
and, on the other hand, the decreased value of gold
(raised level in Gb) has discouraged gold production,
shutting off gold mines (covered inlets at left). Like
alterations are effected in the outflows, i.e. the con
sumption, waste, and absorption of each metal.
The result is that the levels resulting from the
first redistribution will not necessarily be permanent.
They may recede toward their original respective
levels, and under all ordinary conditions will do so.
But in any case, — and this is the point to be em
phasized, — they cannot return entirely to those levels.
Such a supposition would be untenable, as the follow
ing reasoning shows. Suppose, for the moment, that
silver should return to its original level. Then the

Sec. 3]

INFLUENCE OF MONETARY SYSTEMS

121

silver inflow (production) would also return to its origi
nal rate dependent on that level, but the silver outflow
(consumption, waste, etc.) would be greater than
originally. The consumption in the arts would be the
same; but the waste and absorption of silver money
constitute an additional drain. Therefore, consump
tion (equal to production before) will now exceed pro
duction, and the high original level cannot be main
tained. The conclusion follows that, whatever the new
level of permanent equilibrium, it lies below the old.
The same argument, mutatis mutandis, proves that for
gold the new level of permanent equilibrium lies above
the old. The gap between the two original levels has
therefore been reduced. Even though bimetallism has
failed to bring about a concurrent circulation of both
metals and a parity of values at the given coinage
ratio, it has resulted in reducing the value of the dearer
metal (gold) and increasing that of the cheaper (silver).
This effect of mutual approach will be referred to in
discussing the second case which follows.
§3
So much for the first case, where x is larger than the
contents of the money reservoir below mm. In the
second case, x is supposed to be smaller than the con
tents of the money reservoir below the line mm; that
is, there is not enough silver to push all the gold out
of circulation. Under these circumstances, disregard
ing for the moment any change in production or
consumption, the opening of the pipe — the opening
of the mints to silver — will bring the whole system
of liquids to the common level mm. In other words,
the premium on gold bullion will disappear (Fig. 7 b),
and its purchasing power and the. purchasing power

122

THE PURCHASING POWER OF MONEY

[C h a p .

VII

of silver bullion will be a mean between their original
purchasing powers, this mean being the distance of the
mean line, mm, below 00. In other words, bimetallism
in this case succeeds; that is, it will establish and
maintain an equality for a time between the gold and
silver dollars in the money reservoir.
But the equilibrium which we have just found is a
mere equalization of levels produced by a redistribution
of the existing stocks of gold and silver among the
various reservoirs. It will be disturbed as soon as
these stocks are disturbed. A permanent equilibrium
requires that the stocks shall remain the same, — re
quires, in other words, an equality between production
and consumption for each metal. After the inrush of
silver from the silver bullion to the money reser
voir, it is evident that the production and consump
tion of gold need no longer be equal to each other,
nor need the production and consumption of silver
be equal to each other. The same stimulation of sil
ver production and discouragement of gold production
will occur that occurred in the case considered in the
last section. The result may be that silver will, in
the end, entirely displace gold; or again it may fail to
do so.
There may be, then, two possibilities. One possibility
is obvious, namely, that gold may be completely driven
out, the result being the same as already represented in
the lower part of Figure 6. In the second possibility,
gold will not be pushed out.
The reality of this second possibility will be clear if
we attempt first to deny it. Suppose, therefore, that the
film / be at the extreme left, and permanent equilib
rium finally established. In the illustrative mechanism
the gold level will be lower than before, and the silver

Sec. 3]

INFLUENCE OF MONETARY SYSTEMS

123

level higher. How much lower and higher depends
evidently on technical conditions of the production and
consumption corresponding to the situation. It is of
course not inconceivable that the gold level may be so
much lower and the silver level so much higher as to
make their relative positions reversed, i.e. to make
the gold level higher than the silver level. But in this
event it is quite impossible that the film / should be
at the left. Gold, now being the cheaper, would flow
into circulation and displace silver. Under the con
ditions we are now imagining, the film cannot stay
at either extreme. If it is at the right, silver will be
cheaper than gold and will move it leftward; if it
is at the left, gold will be cheaper than silver and
will move it rightward. Under these circumstances,
evidently, equilibrium must lie between these extremes,
as in Figure 7 b. The conditions of production and con
sumption under which bimetallism can succeed are
therefore (1) that under silver monometallism a gold
dollar would in equilibrium be cheaper than a silver
dollar, and (2) that under gold monometallism silver
would be cheaper than gold. A bimetallic level, there
fore, when bimetallism is feasible, must always lie
between the levels which the two metals would have
assumed under gold monometallism, gold being currency
and silver not, and for the same reasons it must lie
between the levels which the two metals would have
under silver monometallism, silver being currency and
gold not.1 In all our reasoning we have supposed a
given legal ratio between the two metals. But bimetal
lism, impossible at one ratio, is always possible at
1 But it does not necessarily lie between the level of the currency
under gold monometallism and its level under silver mono
metallism.

124

THE PURCHASING POWER OF MONEY

[C h a p . V II

another. There will always be two limiting ratios be
tween which bimetallism is possible.1
It is easy to show that the two limiting ratios for a
single nation are narrower than for a combination of
nations, since the currency reservoir is, for one nation,
smaller than for many, while the arts reservoirs are
virtually larger by the amount of the monometallic
currencies of the remaining nations. When bimetallism
has broken down at one ratio, it can always be set in
operation again at another, but the transition requires
a depreciation of the currency. The only way of re
introducing the metal which has passed out of the
currency reservoir is by lowering the amount of it in
the monetary unit, — unless the still more drastic
measure is adopted of raising the coinage weight of
money already in circulation.
It should also be pointed out that two nations can
not both maintain bimetallism at two different ratios
unless the difference is less than the cost of shipment.
One of the two nations would lose the metal which it
undervalued and find itself on a monometallic basis.
A few additional observations may now be stated.
The temporary and normal equilibriums which have
been considered separately are in fact quite distinctly
separated in time. The time of redistributing existing
stocks of metal, according to a newly enacted law,
depends on the rapidity of transportation, melting, and
minting, and would be measured in months or weeks.
Normal equilibrium, however, depends on the slow
working of changes in the rates of production and
consumption, and would be measured in years. The
normal equilibrium, if once established, is permanent so
long as the conditions of production and consumption
1 See § 2 of Appendix to (this) Chapter V II.

Sec. 3]

INFLUENCE OF MONETARY SYSTEMS

125

do not change. Slight alterations of these conditions —■
the exhaustion of mines, the discovery of new leads,
etc. — will cause slight variations in the proportions of
gold and silver money, that is, in the position of the
film /. The oscillations of this film (and not of the
price ratio as in the case of two unconnected com
modities) reflect these changing conditions. But, in
all probability, this film will sooner or later reach one
of its limits. The probable time for such an event is,
however, very long. The gold currency of the world
is, roughly speaking, perhaps $5,000,000,000; the annual
production of silver, reckoning at its present market
price, is roughly about $100,000,000. Supposing a
system of international bimetallism at, say, 36 to 1 to
be initially in normal equilibrium, consider the effect
of an enormous increase in the silver production, say
a half, or $50,000,000. Then a hundred years would
be required to push out gold without taking into account
the fact that, as the pushing proceeds, the excess of
production over consumption steadily declines. If
this excess dwindles uniformly from $50,000,000 to zero,
the period would be double, or two hundred years.
When we add to these considerations the fact that,
while the stimulus to the production of one metal acts
quickly, the ensuing check to the production of the
other acts more slowly, owing to the fixity of the “ sunk”
capital, and that, therefore, the volume of the currency
is greater at the end than at the beginning; also the
fact that the currency reservoir is itself constantly
expanding; and finally the fact that fluctuations of
production are likely to be in either direction, and for
either metal, we may be tolerably confident that, if
initially successful with the film near the middle 'position,
international bimetallism would continue successful

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THE PURCHASING POWER OP MONEY

[C h a p . VII

for many generations. The initial success depends,
as has been seen, upon the ratio enacted.
It is to be observed that bimetallism can never avoid
a slight premium. On the contrary, it is this difference
of level which supplies the force which compells change
from one point of equilibrium to another.1
In a series of years, the bimetallic level remains
intermediate between the changing levels which the
two metals would separately follow. Bimetallism
spreads the effect of any single fluctuation over the
combined gold and silver markets.2 The steadying
power of bimetallism depends on the breadths of the res
ervoirs, and not on the position of the film /. It remains
in full force, no matter what may be the proportions
1 As long as the premium lasts, the cheaper metal m il doubtless
circulate somewhat faster, and the dearer somewhat more slowly,
than when there is no premium. This may, if desired, be repre
sented by conceiving the thickness of the currency reservoir to
decrease on the one side of / and increase on the other, making one
metal “ go farther” (cover more area in the diagram) than normally,
and hasten the motion of / to the equilibrium point. Sluggishness
(increase of thickness), of which “ hoarding” is the chief application,
is referred to below.
2 To represent the steadying effect on a single fluctuation, we
observe that under bimetallism the three reservoirs act as one.
Therefore, compared with monometallism, the fluctuations are
diminished in tho inverse ratio of the liquid surfaces over which
the fluctuations spread. Thus, if the combined breadths of the
two left reservoirs at water level are two thirds of the combined
breadths of the three, an influx of gold which, if distributed only
over the two reservoirs, would make a layer an inch in depth,
would, over the three, have a depth of two thirds of an inch. Like
wise the right reservoir being one third the aggregate width, an
inch fluctuation of silver, when merely merchandise, would be
reduced to one third of an inch, when connection is maintained
with the money reservoir. The breadths of tho reservoir, which
here play the important rdle, are the rate of increase of commodity
relative to decrease of marginal utility. The law of inverse breadth
applies with exactness only to static, or short-time readjustments.

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of gold and silver money, and is as great when only
one nation is bimetallic as when the whole world adopts
the system. Even if only Switzerland had a system
of bimetallism in successful operation, it would, until
its breakdown, keep together and equalize the currencies
of the whole world, wherever either gold or silver was
standard. In fact, the world would have all the benefits
of bimetallism enjoyed by Switzerland without its evils
and dangers. This international function would cease
abruptly as soon as the system of bimetallism should
fail.
It should be pointed out that the equalizing effect
maintained is relative only. It is conceivable that one
metal would be steadier alone than when joined to the
other. In a later chapter we shall consider the extent
to which this equalization is an advantage. Here
we confine ourselves to showing merely the mechanical
operation of the bimetallic system.1
§4
Bimetallism is to-day a subject of historical interest
only. It is no longer practiced; but its former prev
alence has left behind it in many countries, including
France and the United States, a monetary system
which is sometimes called the “ limping” standard.
Such a system comes about when, in a system of
bimetallism, before either metal can wholly expel the
other, the mint is closed to the cheaper of them, but the
coinage that has been accomplished up to date is not
recalled. Suppose silver to be the metal thus excluded,
as in France and the United States. Any money
! Cf. Leonard Darwin, Bimelallismy London (Murray), 1897, 341
p p .; Bertrand Nogaro, “ L yexperience bimetalliste,” Revue d’economic
politique, 1908.

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THE PURCHASING POWER OF MONEY

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already coined in that metal and in circulation is kept
in circulation at par with gold. This parity may con
tinue even if limited additional amounts of silver be
coined from time to time. There will then result a
difference in value between silver bullion and silver coin,
the silver coin being overvalued. This situation is
represented in Figure 8. Here the pipe connection
between the money reservoir and the silver-bullion

reservoir has been, as it were, cut off, or, let us say,
stopped by a valve which refuses passage of silver from
the bullion reservoir to the money reservoir but not
the reverse (for no law ever can prevent the melting
down of silver coins into bullion). Newly mined silver
cannot now become money, and thus lower the pur
chasing power of the money.
On the other hand, new supplies of gold continue to
affect the value of currency, as before, — the value, not
only of the gold, but also of the concurrently circulating
overvalued silver. If more gold should flow into the
money reservoir, it would raise the currency level.
Should this level ever become higher than the level
of the silver bullion reservoir, silver would flow from
the money reservoir into the bullion reservoir; for the

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INFLUENCE OF MONETARY SYSTEMS

129

passage in that direction (i.e. melting) is still free.
So long, however, as the currency level is below the
silver level, i.e. so long as the coined silver is worth
more than the uncoined, there will be no flow of silver
in either direction. The legal prohibition prevents
the flow in one direction, and the laws of relative levels
prevent its flow in the other.
In the case just discussed, the value of the coined
silver will be equal to the value of gold at the legal ratio.
Precisely the same principle applies in the case of any
money, the coined value of which is greater than the
value of its constituent material. Take the case, for
instance, of paper money. So long as it has the dis
tinctive characteristic of money,— general acceptability
at its legal value, — and is limited in quantity, its value
will ordinarily be equal to that of its legal equivalent
in gold. If its quantity increases indefinitely, it will
gradually push out all the gold and entirely fill the
money reservoir, just as silver would do under bimetal
lism if produced in sufficiently large amounts. Like
wise, credit money and credit in the form of bank
deposits would have this effect. To the extent that
they are used, they lessen the demand for gold, decrease
its value as money, and cause more of it to go into
the arts or to other countries.
So long as the quantity of silver or other token
money, e.g. paper money, is too small to displace gold
completely, gold will continue in circulation. The value
of the other money in this case cannot fall below that
of gold. For if it should, it would, by Gresham’s Law,
displace gold, which we have supposed it is not of suffi
cient quantity to do. The parity between silver coin
and gold under the “ limping” standard is, therefore,
not necessarily dependent on any redeemability in gold,

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THE PURCHASING POWER OF MONEY

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but may result merely from limitation in the amount of
silver coin. Such limitation is usually sufficient to
maintain parity despite irredeemability. This is not
always true, however; for if the people should lose con
fidence in some form of irredeemable paper or token
money, even though it were not overissued, it would de
preciate and be nearly as cheap in money form as it is in
the raw state. A man is willing to accept money at its
face value so long as he has confidence that every one
else is ready to do the same. But it is possible, for
instance, for a mere fear of overissue to destroy this
confidence. The payee, who, under ordinary circum
stances, submits patiently to whatever money is cus
tomary or legal tender, may then take a hand and
insist on “ contracting out” of the offending standard.1
That is, he may insist on making all his future con
tracts in terms of the better metal, — gold, for instance,
— and thus contribute to the further downfall of the
depreciated paper.
Irredeemable paper money, then, like our irredeemable
silver dollars, may circulate at par with other money,
if limited in quantity and not too unpopular. If it
is gradually increased in amount, such irredeemable
1 In the mechanical interpretation, since the law would now be
inoperative, the film would no longer yield to pressure from the
right, and an appreciable difference of level on its two sides would
ensue. Such a mechanism would illustrate the concurrent cir
culation of two metals at independent valuations, but experience
shows that such a condition is too full of inconveniences to be
maintained long. The silver will be progressively tabooed, that is,
its velocity of circulation will gradually decrease. This, as we
have seen, may bo figured by supposing the currency reservoir (on
the right of the film only) to be thickened, thus bringing the film
to the right. If the silver is completely tabooed, the film will be
completely to the right, and there will be gold monometallism.
The monetary result of such discrimination against silver is thus
the appreciation of gold.

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131

money may expel all metallic money and be left in
undisputed possession of the field.
But though such a result — a condition of irredeem
able paper money as the sole currency — is possible, it
has seldom if ever proved desirable. Unless safeguarded,
irredeemability is a constant temptation to abuse, and
this fact alone causes business distrust and discourages
long-time contracts and enterprises. Irredeemable
paper money has almost invariably proved a curse to
the country employing it. While, therefore, redeemability is not absolutely essential to produce parity of
value with the primary money, practically it is a wise
precaution. The lack of redeemability of silver dollars
in the United States is one of the chief defects in our
unsatisfactory monetary system, and a continuing
danger.
It is possible to have various degrees of redeemability.
One of the most interesting systems of partial redeem
ability is the system now known as the gold-exchange
standard, by which countries, not themselves on a strict
gold basis, nevertheless maintain substantial parity with
gold through the foreign exchanges. By this system the
government or its agent, while not redeeming its cur
rency in gold, redeems it in orders on gold abroad.
That is, the government sells bills of exchange on Lon
don or New York at a stated price. The currency which
it thus receives, and in a sense redeems, it keeps out of
circulation until the price of foreign exchange falls (i.e.
until the demand for redemption ceases).
The gold-exchange standard may be regarded as a
kind of limping standard with the added feature of
partial redemption.
•This added feature, however, greatly modifies the
nature of the limping standard. The limping standard

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THE PURCHASING POWER OP MONEY

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V II

■A

without the gold-exchange attachment may at any time
break down, if the silver (or whatever else the over
valued money may be) should become so redundant,
relatively to trade, as completely to displace gold. As
soon as all gold is driven abroad, parity with gold ceases.
But with the gold-exchange system this catastrophe is
avoided. In fact, with this system it is not necessary to
have gold in circulation at any time. The willingness of
the government to sell foreign exchange at a fixed price,
and to lock up the silver it receives thereby, takes that
much currency out of circulation just as effectively as
though the equivalent of gold had been exported. So
long as the government is willing and able to maintain
the price of bills of exchange with a gold country, it,
ipso facto, maintains approximate parity with gold.1
§5
We have now to illustrate, by historical examples, the
principles just explained. The first and most important
case is that of France. The ratio of 15& to 1 was
adopted by France in 1785 and continued by the law
of 1803. The history of France and the Latin Union
during the period from 1785, and especially from 1803,
to 1873 is instructive. It affords a practical illustration
of the theory that when conditions are favorable, gold
and silver can be kept tied together for a considerable
period by means of bimetallism. During this period
the public was ordinarily unconscious of any disparity
of value, and only observed the changes from the rela
tive predominance of gold to the relative predominance
of silver in the currency and vice versa. In the whole
sale bullion market, it is true, there were slight varia1 Cf. Charles A. Conant, “ The Gold Exchange Standard,” Economio Journal, June, 1909, pp. 190-200.

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INFLUENCE OF MONETARY SYSTEMS

133

tions from the ratio of 15% to 1. But such variations
simply supplied the force to restore equilibrium.
From 1803 until about 1850 the tendency was for
silver to displace gold. In our mechanical terms there
was, for the most part, an inflow on the right-hand side
of the money reservoir, and the film was gradually
pressed leftward. The statistics for the movements
of gold and silver are not given separately and continu
ously before 1830. But from 1830 to 1847, inclusive,
there was a net export of gold of 73,000,000 francs,
although five of the years showed an import, making
an average export of over 4,000,000 francs a year.1
From 1830 until 1851 there was a net importation of
silver in every year, amounting to a total for the period
of 2,297,000,000 francs or an average of over 104,000,000
francs a year.2 The statistics for silver are taken to
1851 because after that year the movement for silver
was reversed, while for gold the inward flow began
with 1848. Silver was displacing gold and filling up
the currency reservoir. Nevertheless, the reservoir
was expanding so fast, that is, trade was increasing, that
there was no increase of prices, but rather a decrease.
By 1850, the film had practically reached its limit.
Bimetallism would have broken down and resulted in
silver monometallism then and there, except for the
fact that, as though to save the day, gold had just been
discovered in California. The consequence of the new
and increased gold production was a reverse movement,
an inflow of gold into the French currency and an out
flow of silver. From 1848 to 1870, inclusive, the net
importation of gold amounted to 5,153,000,000 francs
or over 224,000,000 francs a year, while the net exporta1 W . A. Shaw, The History of the Currency, 3d ed., London
(Clement Wilson), 1899, p. 183.
2 Ibid., p. 184.

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THE PURCHASING POWER OF MONEY

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VII

tion of silver from 1852 to 1864, inclusive, amounted to
1.726.000.000 francs or nearly 133,000,000 francs a year.1
Gold was displacing silver and filling the currency. It
seemed probable that France would be entirely
drained of her silver currency and come to a gold basis.
France formed with Belgium, Italy, and Switzerland
in 1865, and Greece in 1868, the Latin Monetary Union.
The amount of silver in the subsidiary coins was re
duced, but the standard silver coins were kept at the old
ratio with gold. But the new gold mines were gradu
ally exhausted, while silver production increased, with
the consequence that there was again a reversal of
the movement. From 1871 to 1873, inclusive, the
exportation of gold netted 375,000,000 francs, or an
average of 125,000,000 francs a year, while from 1865
to 1873, inclusive, the net importation of silver was
860.000.000 francs, or over 94,000,000 francs a year.
Thus, even before the gold began to flow out, in 1871,
silver had begun to flow in, i.e. in 1865. Silver grad
ually pushed gold out of circulation and, had not France
and the other countries of the Latin Union successively
suspended the free coinage of silver in 1873-1878, they
would have found themselves on a silver, instead of a
gold, basis. It has been claimed by bimetallists that
this action in demonetizing silver was itself the cause of
the breakdown. The truth is, that the breakdown
was the cause of demonetization, although demonetiza
tion, by keeping back silver from circulation and keeping
gold in circulation, did operate to widen the breach
already made.
The film, in other words, was close to the left limit, and
the currency reservoir was filled for the most part with
1W. A. Shaw, The History of the Currency, 3d ed., London
(Clement W ilson), 1899, pp. 183 and 184.

Sec .

INFLUENCE OF MONETARY SYSTEMS

135

silver. The Latin Union might conceivably have main
tained bimetallism longer if other countries had joined
with them. But it had to absorb, not only much of
the silver provided by the mines, but also a considerable
amount which had previously formed part of the mon
etary stock of Germany and which, at the adoption of
the gold standard by that country following the FrancoPrussian War, was thrown on the market. That is,
not only silver mines, but countries demonetizing silver,
dumped silver on the Latin Union. Add to this the
movement toward the gold standard in Scandinavia
and the United States, and it becomes evident that the
obstacles were many for a union comprising so few, and
mostly unimportant, states.
The parity with gold of the silver remaining in circu
lation in the Latin Union is now preserved on the prin
ciples explained earlier in the chapter, viz. by limiting
its quantity, as well as by making it full legal tender
and receivable for public dues.

§6
It is strange that the lessons of the French and other
experiments do not seem to be generally understood
either by monometallists or bimetallists. For instance,
uncompromising monometallists have pointed to the
variation in the value of gold and silver during the three
quarters of a century as disproving the possibility of
maintaining a legal ratio. They might as well point to
the ripples on a pond or the slight gradient of a river,
as disproving the fact that water seeks a level. These
ripples are really evidence of the process of seeking a
level and are trifling as compared with those which in
all .probability would have taken place had there not
been a legal ratio. The diagram and tables used in

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THE PURCHASING POWER OF MONEY

[C h a p . V ll

Shaw’s History of the Currency and the similar diagram
here given show that during the period of inflowing
silver, 1803 to 1850, in spite of the great increase in
the quantity of silver, the ratio was changed from 15J
to 1 by at most only .75 points or'slightly over 4.8 per
cent in any year, and the average departure was only
.29 points or 1.9 per cent. Moreover, the greater part of
the deviation is explainable by the seigniorage charge
then in force in France.1 During the succeeding period
from 1851 to 1870, characterized largely by an inflow of
gold, the maximum departure (in the opposite direction)
was .31 points or 2 per cent, with an average departure
of .14 points or .9 per cent, while during the succeeding
period of inflowing silver and outflowing gold, from
1871 to 1873, the ratio rose above 15| to 1 by a maxi
mum of .42 points or 2.7 per cent and an average of
.21 points or 1.4 per cent. Contrast .these figures with
those since 1873.2 The maximum departure from the
ratio of 15J to 1 since 1873 is 23.65 points, or 152.6
percent, and the average departure 10.4 points, or 67.1
per cent.3 The history of the ratio is shown in Figure 9.
On the other hand, bimetallists have often failed to
see that this experiment illustrates the limits as well
as the possibilities of bimetallism. In 1850 bimetallism
had almost broken down in France and would have been
succeeded by silver monometallism had not the in
creased production of gold reversed the flow. In 1865,
1 Cf. J. F. Johnson, Money and Currency, Boston (Ginn) 1905,
p. 227.
2 Although France did not entirely suspend tho coinage of the
silver five-franc pieces until 187G, yet limitation began with 1874.
See W. A. Shaw, The History of the Currency, pp. 194, 196.
3 These figures are compiled from data given in W . A. Shaw,
The History of the Currency, p. 159, and Reports of the Director of the
Mint.

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INFLUENCE OF MONETARY SYSTEMS

137

gold had largely driven out silver. By 1873, gold had
again largely disappeared, and it seems evident that it
would have disappeared entirely had not the suspension
of the free coinage of silver followed. A continuance

of bimetallism at a ratio of 15i to 1 by France and the
Latin Union alone would doubtless have been im
possible. Yet the attempt, though a failure, would have
kept the ratio nearer 15| to 1 than it actually has been;

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THE PURCHASING POWER OF MONEY

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for the Union would have furnished a large market for
silver. Possibly bimetallism could have been main
tained longer, despite increased silver production, had
not several other countries adopted the gold standard
in these critical years. This fact helped to flood the
countries of the Latin Union with silver and drain them
of their gold. These countries were suffering all the
expense and trouble of maintaining the ratio between
gold and silver, while other countries were reaping most
of the benefits. Herein lies one of the weaknesses of
bimetallism as a practical political proposition, — each
country prefers that some other country or countries
should be the ones to adopt it. There is little prospect,
therefore, in the future, of any single country taking the
initiative, and still less of any international agreement.

§7
The system now in use in France is also employed
in many other countries which, like France, have been
forced to adopt it or else become silver-standard coun
tries. After the rupture of the bimetallic tie, which
until 1873 linked all gold and silver countries together,
the commercial world broke into two parts, gold-stand
ard countries and silver-standard countries; and many
desiring to join the ranks of the former, but in danger of
being thrust among the latter, saved themselves by
closing their mints to silver and thereby adopting the
limping standard. One of these countries was British
India.
The case of India is interesting because it never was
a bimetallic country, and at the time of the adoption
of the present system, in which gold is the standard,
no gold was in circulation. The mints were closed to
silver in June, 1893, and the legal ratio put the rupee

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INFLUENCE OF MONETARY SYSTEMS

139

at 16d. At first, to the great discomfiture of those
who had advocated the new system, this value was
not maintained. But failure at first was to be ex
pected because no gold was in circulation, and un
suspected coined stores of silver existed to swell the
circulation in spite of the closure of the mints. More
over, the government accepted from banks and others
considerable amounts of silver which had been shipped
to India before the closing of the mints, and coined it,
and a considerable amount was withdrawn from the
government reserve and put into circulation. The
value of the rupee fell by 1895 to as low as 13d. But
even from the first the value of the rupee kept above
the value of its contained silver. If it fell as compared
with the then appreciating gold, it rose as compared
with the value of silver bullion. Surely this may be
held to show that the value of money has some relation
to its quantity, apart altogether from the quantity and
the value of the constituent material. Furthermore,
the value of the rupee rose gradually, even in rela
tion to the gold standard, from 13d. in 1895 to 15J in
1898 and to 16d., the legal par, by 1899, where it has
since remained. As the Indian government has, during
the last decade, paid out rupees for gold on demand, at
this rate, the value of the rupee cannot go appreciably
higher. Should it do so, gold would be presented for
rupees, more rupees would have to be issued, and this
would continue until their value had fallen to 16d. per
rupee.1
The system of India is virtually the gold-exchange
standard described in § 4. The same system is now in
1 For a brief history and discussion of the Indian experience,
see E. W . Kemmerer, Money and Credit Instruments in their Rela
tion to Prices, pp. 36-39.

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THE PURCHASING POWER OP MONEY

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V II

successful operation in the Philippines, in Mexico, and
in Panama.1 It withstood a severe test in India when,
in 1908, the trade balance was “ adverse ” and required
the sale of over £8,000,000 of bills on London be
fore the Indian currency was sufficiently contracted to
stem the tide.

§8
Among the nations which now have the limping
standard is the United States. In 1792, Congress
adopted complete bimetallism. Full legal-tender qual
ity was given to both gold and silver coins; both were
to be coined freely and without limit at the ratio of
15 ounces of silver to 1 of gold.
This soon came to be below the market ratio as
affected by conditions abroad and especially in France.
In consequence, gold tended to leave the country. It is
impossible to state with exactness how soon this move
ment began, but Professor Laughlin sets it as early as
1810 and concludes that by 1818 little gold was in cir
culation.2 America, although nominally a bimetallic
country, became actually a silver country.
Influenced partly by the desire to bring gold back
into circulation, and partly also, perhaps, by the sup
posed discoveries of gold in the South, Congress passed
acts in 1834 and 1837 establishing the ratio of “ 16 to
1 See Charles A. Conant, “ The Gold Exchange Standard in the
Light of Experience/’ Economic Journal, June, 1909, pp. 190-200;
Hanna, Conant, and Jenks, Report on the Introduction of the Gold Ex
change Standard into China, the Philippine Islands, Panama, and
other Silver-using Countries and on the Stability of Exchange, Wash*?
ington (Government Printing Office), 1904; Kemmerer, “ Estab
lishment of the Gold Exchange Standard in the Philippines,”
Quarterly Journal of Economics, August, 1905, pp. 600-605.
2 The History of Bimetallism in the United States', New York
(D. Appleton and Company), 1901, 4th ed., p. 29.

Sec.

INFLUENCE OF MONETARY SYSTEMS

141

1,” — or, more exactly, 16.002 to 1 in 1834 and 15.998
to 1 in 1837. Whereas silver money had been over
valued by the previous laws, by these new laws gold
was overvalued. That is, the commercial ratio con
tinued to be near 15| to 1, while the monetary ratio
was slightly greater. This remained the case up to
1850; consequently, in accordance with Gresham’s
Law, gold money, now the cheaper, drove out silver
money, and the United States became a gold-standard
country. In 1853, to prevent the exportation of our
subsidiary silver coins, their weight was reduced.
The United States continued to be a gold-using
country until the period of the Civil War, during which
“ greenbacks,” or United States notes, were issued in
considerable excess. Again Gresham’s Law came into
operation. Gold was in turn driven from the currency,
and the United States came to a paper standard.1
For some years after the close of the war the country
remained on a paper standard, little gold being in
circulation except on the Pacific coast, and not much
silver anywhere.
In 1873 Congress passed a law (called by bimetallists
the “ Crime of ’73” ) by which the standard silver dollar
was entirely omitted from the list of authorized coins.
Of course this could not have had any immediate
effect on the value of gold and silver, because the coun
try was at the time on a paper basis. But when specie
payments (i.e. gold and silver payments) were resumed
in 1879, this repeal of the free coinage of silver brought
the country to a gold standard, not to a silver one.
1 See especially Wesley Clair Mitchell, History of the Greenbacks,
Chicago (The University of Chicago Press), 1903; also his Gold,
Prices, and Wages under the Greenback Standard, Berkeley, California
(University of California Press), 1908.

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THE PURCHASING POWER OF MONEY

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Had it not been for the law of 1873, the United States,
when it returned in 1879 to a metallic basis, would have
been a silver country with a standard considerably
below the gold standard it actually reached. Our
monetary problems would then have been very different
from what they actually became.
But in returning to a gold basis we reintroduced
the silver dollar in a minor role. Although the free
coinage of silver was not resumed, the advocates of
silver, through the “ Bland-Allison A ct” of 1878 and
the “ Sherman A ct” of 1890, which replaced it, succeeded
in pledging the government to the purchase of large,
but' not unlimited, amounts of silver and the coinage
of a large, but not unlimited, number of silver dollars.
The Bland-Allison Act required the Secretary of the
Treasury to purchase every month from $2,000,000 to
$4,000,000 worth of silver and to coin it into standard
silver dollars. The Sherman Act required the pur
chase every month of 4,500,000 ounces of silver.
Under these acts 554,000,000 silver dollars were
coined, although less than 20 per cent of them have
ever been in actual circulation. Silver certificates
redeemable in silver dollars on demand, and, for a time
treasury notes, have circulated in the place of this
immense mass of silver. The silver dollars (and there
fore the silver certificates) maintain their value on
a parity with gold primarily because they are limited
in amount. If any question were raised as to their
parity with gold, the treasury would probably offer to
specifically redeem them in gold. No law directly
provides for the redemption of silver in gold, but
it is made the duty’ of the Secretary of the Treasury
to take such measures as will maintain its parity
with gold.

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143

In 1893 the Sherman Act was repealed, and in 1900
a law was passed specifically declaring that the United
States shall be on a gold basis.
§9
The system of the limping standard, now obtaining
in the United States, logically forms a connecting link
between complete bimetallism and those “ composite”
systems by which any number of different kinds of
money may be simultaneously kept in circulation. The
manner in which most modern civilized states have
solved the problem of concurrent circulation has been
to use gold as a standard, and to use silver, nickel, and
copper chiefly as subsidiary money, limited in quantity,
with, in most cases, limited amounts of paper money,
the latter being usually redeemable. The possible
variations of this composite system are unlimited.
In the United States at present we have a system
which is very complicated and objectionable in many
of its features — especially (as we shall presently see)
in its lack of elasticity. Gold is the standard and is
freely coined. A limited number of silver dollars,
worth, moneywise, more than double their value bullionwise, are a heritage of former bimetallic laws long
since rendered inoperative by the paper money of the
Civil War and expressly repealed in 1873. The two
attempts of 1878 and 1890 to return halfway to bi
metallism by the purchase of silver — attempts dis
continued in 1893 — have greatly swollen the volume
of coined silver. The attempt to force silver dollars
into circulation was not acceptable to the business
world, and Congress therefore issued instead the two
forms of paper mentioned. The chief form is the
“ silver certificate.” For each silver certificate a silver

144

THE PURCHASING POWER OF MONEY

[C h a p .

VII

dollar is kept in the vaults of the United States gov
ernment.
The absurdity of the situation consists in the fiction
that somehow the silver keeps paper at par with gold.
The paper would keep its parity with gold just as well
if there were no silver. A silver dollar as silver is worth
less than a gold dollar just as truly as a paper dollar,
as paper, is worth less than a gold dollar. The fact
that the silver is worth more than the paper will not
avail in the least to make the paper worth a whole
dollar so long as the silver is not itself worth a whole
dollar. A pillar which reaches only halfway to the
ceiling cannot hold the ceiling up any more than a
pillar an inch high.
The paper representatives of silver would continue
to circulate as well as they do now, even if the “ silver
behind them” were nonexistent, although the absurdity
of the situation would then be so apparent that they
would probably be retired. Whether the half billion
dollars of new currency, which came into circulation
with the Bland and Sherman Acts, are of silver, over
valued to the extent of 50 per cent, or of paper, over
valued to the extent of 100 per cent, does not really
affect the principle of the limping standard which keeps
silver dollars at par with gold. The idle silver in the
treasury vaults represents mere waste, a subsidy given
by the government to encourage silver mining. Its
only real effect to-day is to mislead the public into
the belief that in some way it keeps or helps to keep
silver certificates at par with gold;1 whereas they are
kept at par by the limitation on its amount. The
1 Seager, in his Introduction to Economics, 3d ed., New York (Holt),
1908, p. 317, urges that the government should attempt gradually
to dispose of this silver and substitute an equal valuo of gold.

S ec. 9]

INFLUENCE OF MONETARY SYSTEMS

145

silver and its paper representatives cannot fall below
par without displacing gold, and they cannot displace
gold because there are not enough of them.
Another and equally useless anomaly is the existing
volume of “ greenbacks.” These are United States
government notes. Under the law of 1875, the green
backs were by 1879 retired in sufficient numbers to
restore parity with gold; but by a counterlaw of 1878,
347,000,000 of them were kept in circulation and are
in circulation now. As soon as redeemed, they must
be reissued; they cannot be retired. They are a fixed
ingredient in our money pot pourri, neither expansive
nor shrinkable. They have been kept at par with gold
because: (1) they are limited in amount; (2) they are
redeemable in gold on demand; (3) they are receivable
for taxes and are legal tender. But it is absurd to
redeem but not retire — in fact, almost a contradiction
in terms. This absurdity has at times seriously embar
rassed the government.
The next feature of our currency to be considered
is the bank note. Although the National Bank acts
wiped out the old, ill-assorted state bank notes, they tied
the new notes up with the war debt, and they have re
mained so tied ever since, in spite of the fact that the
advantages of the connection have long been terminated
and the disadvantages have grown acute. National
bank notes cannot legally be issued in excess of the
government debt, however urgent the need for them;
nor can the government pay its debt without thereby
compelling national banks to cancel their notes.
One of the curious anomalies of the situation is that
the prices of United States bonds are so high, and
therefore the rate of interest returned on these bonds so
low that there is actually less inducement to issue bank

146

THE PURCHASING POWER OF MONEY

[Chap .

VII

notes in regions where the rate of interest is high, as in
the West, than in regions where it is low, as in the East.
The result is an inelastic currency which, instead of
adjusting itself to the seasonal fluctuations in trade,
and thus mitigating the ensuing variations in the price
level, remains a hard and solid mass to which the other
elements in the equation of exchange must adapt
themselves.1
The remaining features of our currency system, such
as fractional and minor coins, adjusted to public
demand, are satisfactory. The gold and currency
certificates of deposit are scarcely independent features,
as they are simply government receipts for public con
venience representing the deposit of gold or greenbacks.
The status in the United States July 1, 1912, is
represented in the table on the opposite page taken
from Comptrollers’ Reports and Treasurers’ Reports.
We see here a currency system in which gold, the
basis of it all, enters as between one third and one half
the circulation outside of the Treasury and banks and
a little over half the money in banks used as reserves
for deposits (and for bank notes, though these are also
guaranteed by the government). The remaining money
in circulation consists almost wholly of inelastic and
almost constant elements. - Consequently, a change in
the quantity of gold in circulation will not cause a pro
portional change in the quantity of all money in circu
lation, but only about one third as much. Since,
however, almost all the money can be used as bank
reserves, even national bank notes being so used by
state banks and trust companies, the proportionate
1 The Aldrich-Vreeland Act of 1908 has not changed this situa
tion. However helpful it may be in mitigating the evils of crises, it
does not give elasticity of tho currency in ordinary times.

Sec. 9]

147

INFLUENCE OF MONETARY SYSTEMS

relations between money in circulation, money in re
serves, and bank deposits will hold true approximately
as the normal condition of affairs. The legal require
ments as to reserves strengthen the tendency to pre
serve such a relationship.
M

oney

the

In U.S. Treasury .
In banks . . . .
Outside both . . .
Total

. . . .

o ld

n it e d

S il v e r

2641 2 6 4
8012 2175
7523 323
1817

566

States

(in Millions)
S u b s id ia r y
a n d M in o r

U .S .
N o tes

B ank
N o tes

9
253
85

40
108
597

26
38
107

365
1417
1864

347

.745

171

3646

otal

C o in s

In the United States, then, we have a currency sys
tem in which, as has been observed, the only really
adjustable money is gold. As gold requires time for
minting or transportation, the adjustment is slow and
clumsy as compared with the prompt issue or retirement
of bank notes practiced in other countries. The seasonal
changes in the purchasing power of money, as well as
the changes connected with crises and credit cycles, are
1 “ Free ” gold (i.e. exclusive of gold held in Treasury for gold
certificates held by the public).
2 Including 563 millions of gold certificates for which gold was
on deposit in the United States government vaults.
8 Including 380 millions of gold certificates for which gold was
on deposit in the United States government vaults.
4 “ F ree” (i.e. exclusive of silver held in the Treasury for silver
certificates held by the public).
5 Including 194 millions of silver certificates for which silver was
on deposit in the United States government vaults.
. 8 Including 275 millions of silver certificates for which silver was
on deposit in the United States government vaults.

148

THE PURCHASING POWER OF MONEY

[C h a p .

V II

therefore greatly and needlessly aggravated. As this
second edition goes to press, there seems a likelihood
that Congress may at last enact legislation designed to
remedy this condition.

CHAPTER VIII
INFLUENCE OF QUANTITY OF MONEY AND OTHER FAC
TORS ON PURCHASING POWER AND ON EACH OTHER

§1
T h e chief purpose of the foregoing chapters is
to set forth the causes determining the purchasing
power of money. This purchasing power has been
studied as the effect of five, and only five, groups of
causes. The five groups are money, deposits, their veloc
ities of circulation, and the volume of trade. These
and their effects, prices, we saw to be connected
by an equation called the equation of exchange,
MV + M'V' = 2pQ. The five causes, in turn, we found
to be themselves effects of antecedent causes lying en
tirely outside of the equation of exchange, as follows:
the volume of trade will be increased, and therefore
the price level correspondingly decreased by the dif
ferentiation of human wants; by diversification of in
dustry; and by facilitation of transportation. The
velocities of circulation will be increased, and there
fore also the price level increased by improvident
habits; by the use of book credit; and by rapid trans
portation. The quantity of money will be increased,
and therefore the price level increased correspondingly
by the import and minting of money, and, anteced
ently, by the mining of the money metal; by the
introduction of another and initially cheaper money
metal through bimetallism; and by the issue of bank

149

150

THE PURCHASING POWER OF MONEY

[C h a p .

VIII

notes and other paper money. The quantity of de
posits will be increased, and therefore the price level
increased by extension of the banking system and by
the use of book credit. The reverse causes produce, of
course, reverse effects.
Thus, behind the five sets of causes which alone
affect the purchasing power of money, we find over a
dozen antecedent causes. If we chose to pursue the
inquiry to still remoter stages, the number of causes
would be found to increase at each stage in much the
same way as the number of one’s ancestors increases
with each generation into the past. In the last analysis
myriads of factors play upon the purchasing power of
money; but it would be neither feasible nor profitable
to catalogue them. The value of our analysis consists
rather in simplifying the problem by setting forth
clearly the five proximate causes through which all
others whatsoever must operate. At the close of our
study, as at the beginning, stands forth the equation of
exchange as the great determinant of the purchasing
power of money. With its aid we see that normally the
quantity of deposit currency varies directly with the
quantity of money, and that therefore the introduction
of deposits does not disturb the relations we found to
hold true before. That is, it is still true that (1) prices
vary directly as the quantity of money, provided the
volume of trade and the velocities of circulation remain
unchanged; (2) that prices vary directly as the veloci
ties of circulation (if these velocities vary together),
provided the quantity of money and the volume of
trade remain unchanged; and (3) that prices vary
inversely as the volume of trade, provided the quantity
of money — and therefore deposits — and their ve
locities remain unchanged.

Sec. 2]

QUANTITY THEORY

151

§2
It is proposed in this chapter to inquire how far these
propositions are really causal propositions. We shall
study in detail the influence of each of the six magni
tudes on each of the other five. This study will afford
answers to the objections which have often been raised
to the quantity theory of money.
To set forth all the facts and possibilities as to causa
tion we need to study the effects of varying, one at a
time, the various magnitudes in the equation of ex
change. We shall in each case distinguish between the
effects during transition periods and the ultimate or
normal effects after the transition periods are finished.
For simplicity we shall in each case consider the normal
or ultimate effects first and afterward the abnormal or
transitional effects.
Since almost all of the possible effects of changes in
the elements of the equation of exchange have been
already set forth in previous chapters, our task in this
chapter is chiefly one of review and rearrangement.
Our first question therefore is: given (say) a doubling
of the quantity of money in circulation (M), what are
the normal or ultimate effects on the other magnitudes
in the equation of exchange, viz.: M', V, V', the p’s
and the Q’s ?
We have seen, in Chapter III, that normally the effect
of doubling money in circulation (M ) is to double
deposits (M ') because under any given conditions of
industry and civilization deposits tend to hold a fixed or
normal ratio to money in circulation. Hence the ulti
mate effect of a doubling in M is the same as that of dou
bling both M and Mf. We propose next to show that this
doubling of M and M' does not normally change V, V' or

152

THE PURCHASING POWER OP MONEY

[C h a p .

V IH

the Q’s, but only the p’s. The equation of exchange of
itself does not affirm or deny these propositions.
For aught the equation of exchange itself tells us,
the quantities of money and deposits might even vary
inversely as their respective velocities of circulation.
Were this true, an increase in the quantity of money
would exhaust all its effects in reducing the velocity of
circulation, and could not produce any effect on prices.
If the opponents of the “ quantity theory” could establish
such a relationship, they would have proven their case
despite the equation of exchange. But they have not
even attempted to prove such a proposition. As a
matter of fact, the velocities of circulation of money
and of deposits depend, as we have seen, on technical
conditions and bear no discoverable relation to the
quantity of money in circulation. Velocity of circula
tion is the average rate of “ turnover,” and depends on
countless individual rates of turnover. These, as we
have seen, depend on individual habits. Each person
regulates his turnover to suit his convenience. A
given rate of turnover for any person implies a given
time of turnover — that is, an average length of time a
dollar remains in his hands. He adjusts this time of
turnover by adjusting his average quantity of pocket
money, or till money, to suit his expenditures. He
will try to avoid carrying too little lest, on occasion,
he be unduly embarrassed; and on the other hand
to avoid encumbrance, waste of interest, and risk
of robbery, he will avoid carrying too much. Each
man’s adjustment is, of course, somewhat rough, and
dependent largely on the accident of the moment;
but, in the long run and for a large number of people,
the average rate of turnover, or what amounts to
the same thing, the average time money remains in

Sec. 2]

QUANTITY THEORY

163

the same hands, will be very closely determined. It
will depend on density of population, commercial cus
toms, rapidity of transport, and other technical condi
tions, but not on the quantity of money and deposits
nor on the.price.level. These may change without any
effect on velocity. If the quantities of money and de- .<
posits are doubled, there is nothing, so far as velocity of
circulation is concerned, to prevent the price level from
doubling. On the contrary, doubling money, deposits,
and prices would necessarily leave velocity quite un
changed. Each individual would need to spend more
money for the same goods, and to keep more on hand.
The ratio of money expended to money on hand would
not vary. If the number of dollars in circulation and
in deposit should be doubled and a dollar should come
to have only half its former purchasing power, the
change would imply merely that twice as many dollars
as before were expended by each person and twice as
many kept on hand. The ratio of expenditure to stock
on hand would be unaffected.
If it be objected that this assumes that with the
doubling in M and M' there would be also a doubling
of prices, we may meet the objection by putting the
argument in a slightly different form. Suppose, for a
moment, that a doubling in the currency in circulation
should not at once raise prices, but should halve the..velocities instead; such a result would evidently upset for
each individual the adjustment which he had made of
cash on hand. Prices being unchanged, he now has
double the amount of money and deposits which his
convenience had taught him to keep on hand. He will
then try to get rid of the surplus money and deposits by
buying goods. But as somebody else must be found to
take the money off his hands, its mere transfer will not

154

THE PURCHASING POWER OF MONEY

[C h a p .

VIII

diminish the amount in the community. It will sim
ply increase somebody else’s surplus. Everybody has
money on his hands beyond what experience and con
venience have shown to be necessary. Everybody will
want to exchange this relatively useless extra money
for goods, and the desire so to do must surely drive up
the price of goods. No one can deny that the effect of
every one’s desiring to spend more money will be to
raise prices. Obviously this tendency will continue
until there is found another adjustment of quantities
to expenditures, and the F ’s are the same as originally.
That is, if there is no change in the quantities sold
(the Q's), the only possible effect of doubling M and M'
will be a doubling of the p’s ; for we have just seen that
the 7 ’s cannot be permanently reduced without causing
people to have surplus money and deposits, and there
cannot be surplus money and deposits without a desire
to spend it, and there cannot be a desire to spend it
without a rise in prices. In short, the only way to get rid
of a plethora of money is to raise prices to correspond.
So far as the surplus deposits are concerned, there
might seem to be a way of getting rid of them by can
celing bank loans, but this would reduce the normal
ratio which M' bears to M, which we have seen tends
to be maintained.
We come back to the conclusion that the velocity of
circulation either of money or deposits is independent
of the quantity of money or of deposits. No reason has
been, or, so far as is apparent, can be assigned, to show
why the velocity of circulation of money, or deposits,
should be different, when the quantity of money, or
deposits, is great, from what it is when the quantity
is small.
There still remains one seeming way of escape from

S ec. 2]

QUANTITY THEORY

155

the conclusion that the sole effect of an increase in the
quantity of money in circulation will be to increase
prices. It may be claimed — in fact it has been claimed
— that such an increase results in an increased volume
of trade. We now proceed to show that (except during
transition periods) the volume of trade, like the velocity
of circulation of money, is independent of the quantity
of money. An inflation of the currency cannot increase A'
the product of farms and factories, nor the speed of
freight trains or ships. The stream of business depends
on natural resources and technical conditions, not on
the quantity of money. The whole machinery of pro
duction, transportation, and sale is a matter of physical
capacities and technique, none of which depend on the
quantity of money. The only way in which the quan
tities of trade appear to be affected by the quantity of
money is by influencing trades accessory to the creation
of money and to the money metal. An increase of gold
money will, as has been noted, bring with it an increase
in the trade in gold objects. It will also bring about
an increase in the sales of gold mining machinery, in
gold miners’ services, in assaying apparatus and labor.
These changes may entail changes in associated trades.
Thus if more gold ornaments are sold, fewer silver orna
ments and diamonds may be sold. Again the issue of
paper money may affect the paper and printing trades,
the employment of bank and government clerks, etc.
In fact, there is no end to the minute changes in the Q’s
which the changes mentioned, and others, might bring
about. But from a practical or statistical point of view
they amount to nothing, for they could not add to nor
subtract one tenth of 1 per cent from the general aggre
gate of trade. Only a very few Q’s would be appre
ciably affected, and those few very, insignificant. Prob-

156

THE PURCHASING POWER OP -MONEY

[C h a p .

V III

ably no one will deny this, but some objectors might
claim that, though technique of production and trade de
termine most of these things, nevertheless the Q’s — the
actual quantities of goods exchangedfor money and deposit
currency — might conceivably vary according as barter
is or is not resorted to. If barter were as convenient
as sale-and-purchase, this contention would have force.
There would then be little need of distinguishing be
tween money as the generally acceptable medium of ex
change and other property as not generally acceptable.
If all property were equally acceptable, all property
would be equally money; or if there were many kinds of
property nearly as exchangeable as money, resort to
barter would be so easy that some of the goods sold for
money could be almost equally well bartered for some
thing else. But as long as there were any preference
at all for the use of money, resort to barter would be
reluctantly made and as a temporary expedient only.
We have seen this when studying transition periods.
Under normal conditions and in the long run only a
negligible fraction of modern trade can be done through
barter. We conclude, therefore, that a change in the
quantity of money will not appreciably affect the quanti
ties of goods sold for money.
Since, then, a doubling in the quantity of money:
(1) will normally double deposits subject to check in the
same ratio, and (2) will not appreciably affect either the
velocity of circulation of money or of deposits or the vol
ume of trade, it follows necessarily and mathematically
that the level of prices must double. While, therefore,
the equation of exchange, of itself, asserts no causal
relations between quantity of money and price level,
any more than it asserts a causal relation between any
other two factors, yet, when we take into account con

S e c . 2]

QUANTITY THEORY

157

ditions known quite apart from that equation, viz.,
that a change in M produces a proportional change in
M', and no changes in V, V', or the Q’s, there is no pos
sible escape from the conclusion that a change in the
quantity of money (M) must normally cause a propor
tional change in the price level (the p’s).
One of the objectors to the quantity theory attempts
to dispose of the equation of exchange as stated by
Newcomb, by calling it a mere truism. While the
equation of exchange is, if we choose, a mere “ truism,”
based on the equivalence, in all purchases, of the money
or checks expended, on the one hand, and what they
buy, on the other, yet in view of supplementary
knowledge as to the relation of M to M', and the nonrelation of M to V, V', and the Q's, this equation is
the means of demonstrating the fact that normally
the p’s vary directly as M, that is, demonstrating the
quantity theory. “ Truisms” should never be neg
lected. The greatest generalizations of physical science,
such as that forces are proportional to mass and ac
celeration, are truisms, but, when duly supplemented
by specific data, these truisms are the most fruitful
sources of useful mechanical knowledge. To throw
away contemptuously the equation of exchange because
it is so obviously true is to neglect the chance to formu
late for economic science some of the most important
and exact laws of which it is capable.
We may now restate, then, in what causal sense the
quantity theory is true. It is true in the sense that one
of the normal effects of an increase in the quantity of money
is an exactly proportional increase in the general level of
prices.1
1Cf. Albert Aupetit, Essai sur la tMoric gtnirale de la monnaiet
Paris (Guillaumin), 1901.

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THE PURCHASING POWER OF MONEY

[C h a p .

V III

To deny this conclusion requires a denial of one
or more of the following premises upon which it
rests: —
(1) The equation of exchange, MV + M'V' —
(2) An increase of M normally causes a proportional
increase of M'.
(3) An increase of M does not normally affect V, V',
or the Q’s.
If these three premises be granted, the conclusion
must be granted. If any of the premises be denied, the
objector must show wherein the fallacy lies. Premise
(1) has been justified in Chapter II and Chapter III,
and mathematically demonstrated in the Appendices to
Chapters II and III. Premise (2) has been shown to
be true in Chapter III and premise (3) in the present
chapter.
So much pains has been taken to establish these prem
ises and to emphasize the results of the reasoning based
on them because it seems nothing less than a scandal
in Economic Science that there should be any ground
for dispute on so fundamental a proposition.
The quantity theory as thus stated does not claim
that while money is increased in quantity, other causes
may not affect M', V, V', and the Q’s, and thus aggra
vate or neutralize the effect of M on the p’s. But these
are not the effects of M on the p’s. So far as M by
itself is concerned, its effect on the p’s is strictly propor
tional.
The importance and reality of this proposition are not
diminished in the least by the fact that these other
causes do not historically remain quiescent and allow
the effect on the p’s of an increase in M to be seen alone.
The effects of M are blended with the effects of changes
in the other factors in the equation of exchange just as

S e c . 3]

QUANTITY THEORY

159

the effects of gravity upon a falling body are blended
with the effects of the resistance of the atmosphere.
Finally, it should be noted that, in accordance with
principles previously explained, no great increase of
money (M) in any one country or locality can occur
without spreading to other countries or localities. As
soon as local prices have risen enough to make it profit
able to sell at the high prices in that place and buy at
the low prices elsewhere, money will be exported. The
production of gold in Colorado and Alaska first results
in higher prices in Colorado and Alaska, then in send
ing gold to other sections of the United States, then in
higher prices throughout the United States, then in
export abroad, and finally in higher prices throughout
the gold-using world.
§3
We have emphasized the fact that the strictly pro
portional effect on prices of an increase in M is only the
normal or ultimate effect after transition periods are
over. The proposition that prices vary with money
holds true only in comparing two imaginary periods for
each of which prices are stationary or are moving alike
upward or downward and at the same rate.
As to the periods of transition, we have seen that an
increase in M produces effects not only on the p’s, but
on all the magnitudes in the equation of exchange. We
saw in Chapter IV on transition periods that it increases
M' not only in its normal ratio to M, but often, tem
porarily, beyond that ratio. We saw that it also
quickened V and V' temporarily.
As previously noted, while V and V' usually move in
sympathy, they may move in opposite directions when
a panic decreases confidence in bank deposits. Then
people pay out deposits as rapidly as possible and

1 60

THE PURCHASING POWER OP MONEY

[C h a p .

VIII

money as slowly as possible — the last-named tendency
being called hoarding.
We saw also that an increase of M during a period of
rising prices stimulated the Q’ s. Finally we saw that a
reduction in M caused the reverse effects of those above
set forth, decreasing V and V', decreasing M' not abso
lutely only, but in relation to M, and decreasing the Q’s
partly because of the disinclination to sell at low money
prices which are believed to be but temporary, partly
because of a slight substitution of barter for sales; for if
M should be very suddenly reduced, some way would
have to be found to keep trade going, and barter would
be temporarily resorted to in spite of its inconvenience.
This would bring some relief, but its inconvenience
would lead sellers to demand money whenever possible,
and prospective buyers to supply themselves there
with. The great pressure to secure money would en
hance its value — that is, would lower the prices of
other things. This resultant fall of prices would make
the currency more adequate to do the business required,
and make less barter necessary. The fall would proceed
until the abnormal pressure, due to the inconvenience
of barter, had ceased. Practically, however, in the
world of to-day, even such temporary resort to barter is
trifling. The convenience of exchange by money is
so much greater than the convenience of barter, that
the price adjustment would be made almost at once. If
barter needs to be seriously considered as a relief from
money stringency, we shall be doing it full justice if
we picture it as a safety-valve, working against a
resistance so great as almost never to come into opera
tion and then only for brief transition intervals. For all
practical purposes and all normal cases, we may assume
that money and checks are necessities for modern trade.

Sec. 3]

QUANTITY THEORY

161

The peculiar effects during transition periods are
analogous to the peculiar effects in starting or stopping
a train of cars. Normally the caboose keeps exact
pace with the locomotive, but when the train is starting
or stopping this relationship is modified by the gradual
transmission of effects through the intervening cars.
Any special shock to one car is similarly transmitted
to all the others and to the locomotive.
We have seen, for instance, that a sudden change in
the quantity of money and deposits will temporarily
affect their velocities of circulation and the volume of
trade. Reversely, seasonal changes in the volume of
trade will affect the velocities of circulation, and even,
if the currency system is elastic, the quantity of money
and deposits. In brisk seasons, as when “ money is
needed to move the crops, ” the velocity of circulation
is evidently greater than in dull seasons. Money is
kept idle at one time to be used at another, and such
seasonal variations in velocity reduce materially the
variations which otherwise would be necessary in the
price level. In a similar way seasonal variations in the
price level are reduced by the alternate expansion and
contraction of an elastic bank currency. In this case
temporarily, and to an extent limited by the amount of
legal tender currency, money or deposits or both may
be said to adapt themselves to the amount of trade.
In these two ways, then, both the rise and fall of prices
are mitigated.1 Therefore the “ quantity theory ” will
not hold true strictly and absolutely during transition
periods.
1 Cf. Hildebrand, Theorie des Geldes, Chapter X I, who, though
seemingly unconscious of its bearing on the velocity of circulation,
calls attention to the difference between two communities having
the same expenditures, but one having a uniform trade and the
other a trade “ bunched” in certain seasons — say the crop seasons.
M

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We have finished our sketch of the effects of M, and
now proceed to the other magnitudes.
§4
As to deposits (M ‘'), this magnitude is always depend
ent on M. Deposits are payable on demand in money.
They require bank reserves of money, and there must
be some relation between the amount of money in cir
culation (M ), the amount of reserves ( a1) , and the
amount of deposits (M'). Normally we have seen that
the three remain in given ratios to each other. But
what is a normal ratio at one state of industry and civi
lization may not be normal at another. Changes in
population, commerce, habits of business men, and
banking facilities and laws may produce great changes
in this ratio. Statistically, as will be shown in Chapter
XII, the ratio M'/M has changed from 3.1 to 4.1 in
fourteen years.
Since M' is normally dependent on M, we need not
ask what are the effects of an increase of M'; for these
effects have been included under the effects of M. But,
since the ratio of M' to M may change, we do need to
ask what are the effects of this change.
Suppose, as has actually been the case in recent years,
that the ratio of M' to M increases in the United States.
If the magnitudes in the equations of exchange in
other countries with which the United States is con
nected by trade are constant, the ultimate^ effect on M
is to make it less than what it would otherwise have
been, by increasing the exports of gold from the United
States or reducing the imports. In no other way can
the price level of the United States be prevented from
rising above that of other nations in which we have
assumed this level and the other magnitudes in the

Sec. 4]

QUANTITY THEORY

163

equation of exchange to be quiescent. While the ulti
mate effect then is to increase the volume of circulating
media, this increase is spread over the whole world.
Although the extension of banking is purely local, its
effects are international. In fact, not only will there
be a redistribution of gold money over all gold coun
tries, but there will be a tendency to melt coin into
bullion for use in the arts.
The remaining effects are the same as those of an
increase in M which have already been studied. That
is, there will be no (ultimate) appreciable effect on F,
V', or the Q’s, but only on the p’s, and these will rise,
relatively to what they would otherwise have been,
throughout the world. In foreign countries the normal
effect will be proportional to the increase of money in
circulation which they have acquired through the dis
placement of gold in the United States. In the United
States the effect will not be proportional to the in
crease in M', since M has moved in the opposite direc
tion. It will be proportional to the increase in M + M'
if V and V are equal, and less than in that proportionif V is less than V', as is the actual fact.
In any case the effect on prices is extremely small,
being spread over the whole commercial world. Taking
the world as a whole, the ultimate effect is, as we have
seen, to raise world prices slightly and to melt some
coin. The only appreciable ultimate effect of increas
ing the ratio of M' to M in one country is to expel
money from that country into others. All of these
effects are exactly the same as those of increasing the
issue of bank notes, so long as they continue redeem
able in gold or other exportable money. An issue
beyond this point results in isolating the issuing coun
try and therefore in rapidly raising prices there in-

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VIII

stead of spreading the effect over other countries.
This is what happened in the United States during the
Civil War.
As to transitional effects, it is evident that, before
the expulsion of gold from the United States, there must
be an appreciable rise in prices there, of which traders
will then take advantage by selling in the United States,
shipping away money, and buying abroad. During the
period of rising prices all the other temporary effects
peculiar to such a period, effects which have been
described at length elsewhere, will be in evidence.
Exactly opposite effects of course follow a decrease of
M' relatively to M.
§5
We come next to the effects of changes in velocities
(V and V'). These effects are closely similar to those
just described. The ultimate effects are on prices,
and not on quantity of money or volume of trade.
But a change in the velocity of circulation of money in
any country, connected by international trade with
other countries, will cause an opposite change in the
quantity of money in circulation in that country.
There will be a redistribution of money among the
countries of the world and of money metal as between
money and the arts.
The normal effect, then, of increasing V or V' in any
'country is to decrease M by export, to decrease M'
proportionally, and to raise prices (p’s) slightly through
out the world. There is no reason to believe that there
will, normally, be any effects on the volume of trade.
It is quite possible that a change in one of the two
velocities will cause a corresponding change in the
other, or, at any rate, that most of the causes which
increase one will increase the other. Increased density

S e c . 5]

QUANTITY THEORY

165

of population, for instance, in all probability quickens
the flow both of money and checks. Unfortunately,
however, we have not sufficient empirical knowledge of
the two sorts of velocity to assert, with confidence, any
relations between them
During transition periods the effects of changes in
velocities are doubtless the same as the effects of in
creased currency.

§6
Our next question is as to the effects of a general
increase or decrease in the Q’s, i.e. in the volume of
trade.
An increase of the volume of trade in any one country,
say the United States, ultimately increases the money
in circulation (M). In no other way could there be
avoided a depression in the price level in the United
States as compared with foreign, countries. The in
crease in M brings about a proportionate increase in
M'. Besides this effect, the increase in trade undoubt
edly has some effect in modifying the habits of the
community with regard to the proportion of check and
cash transactions, and so tends somewhat to increase
M' relatively to M ; as a country grows more commercial
the need for the use of checks is more strongly felt.1
As to effects on velocity of circulation, we may
distinguish three cases. The first is where the change
in volume of trade corresponds to a change in popula1
This is very far from asserting as Laughlin does that “ The
limit to the increase in legitimate credit operations is always ex
pansible with the increase in the actual movement of goods” ; see
the Principles of Money, New York (Scribner), 1903, p. 82. We
have seen, in Chapter IV, that deposit currency is proportional to
the amount of m oney; a change in trade may indirectly, i.e. by
changing the habits of the community, influence the proportion,
but, except for transition periods, it cannot influence it directly.

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THE PURCHASING POWER

OP MONEY

[C hap. VIII

tion, as when there is an increase in trade from the set
tling of new lands, without any greater concentration in
previously settled areas, and without any change in the
per capita trade or in the distribution of trade among
the elements of the population. Under such conditions
no reason has been assigned, nor apparently can be as
signed, to show why the velocity of circulation of money
should be other for a condition in which the volume of
trade is large than for a condition in which it is small.
The second case is where the increase in volume of
trade corresponds to an increased density of population,
but no change in per capita trade. In this ease, the closer
settlement may facilitate somewhat greater velocity.
The third case is where the change in the volume of
trade does affect the per capita trade or the distribution
of trade in the population.
There are then several ways in which the velocity of
circulation may conceivably be affected. First, any
change in trade, implying a change in methods of
transportation of goods, will imply a change in meth
ods of transportation of money; quick transportation
means usually more rapid circulation.
Secondly, a changed distribution of trade will alter
the relative expenditures of different persons. If their
rates of turnover are different, a change in their ex
penditures will clearly alter the relative importance or
weighting of these rates in the general average, thus
changing that average without necessarily changing
the individual rates of turnover. For instance, an
increased trade in the southern states, where the veloc
ity of circulation of money is presumably slow, would
tend to lower the average velocity in the United States,
simply by giving more weight to the velocity in the
slower portions of the country.

Sec. 6]

QUANTITY THEORY

167

Thirdly, a change in individual expenditures, when
due to a real change in the quantity of goods purchased,
may cause a change in individual velocities. It seems
to be a fact that, at a given price level, the greater a
man’s expenditures the more rapid his turnover; that
is, the rich have a higher rate of turnover than the
poor. They spend money faster, not only absolutely
but relatively to the money they keep on hand. Statis
tics collected at Yale University of a number of cases of
individual turnover show this clearly.1 In other words,
the man who spends much, though he needs to carry
more money than the man who spends little, does not
need to carry as much in proportion to his expenditure.
This is what we should expect; since, in general, the
larger any operation, the more economically it can be
managed. Professor Edgeworth2 has shown that the
same rule holds in banking. When two banks are con
solidated, the reserve needed is less than the sum of the
two previous reserves.
We may therefore infer that, if a nation grows richer
per capita, the velocity of circulation of money will
increase. This proposition, of course, has no reference
to nominal increase of expenditure. As we have seen,
a doubling of all prices and incomes would not affect
anybody’s rate of turnover of money. Each person
would need to make exactly twice the expenditure for
the same actual result and to keep on hand exactly
twice the money in order to meet the same contingencies
in the same way. The determinant of velocity is real
expenditure, not nominal. But a person’s real expendi
ture is only another name for his volume of trade. We
1 See § 1 of Appendix to (this) Chapter V III.
2 “ Mathematical Theory of Banking/!- Journal of the Royal Sta*
tistical Society, March, 1888.

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[C h a p .

VIII

conclude, therefore, that a change in the volume of
trade, when it affects the per capita trade, affects ve
locity of circulation as well.
-■
.
We find then that an increase in trade, unlike an
increase in currency (M and M') or velocities (F and F')
has other effects than simply on prices — effects, in
fact, of increasing magnitudes on the opposite side of
the equation, F and F', and (though only indirectly by
affecting business convenience and habit) M' relatively
to M. If these effects increase the left side as much as
the increase in trade itself (the Q’s) directly increases
the right side, the effect on prices will be nil. If the
effect on the left side exceeds that on the right, prices
will rise. Only provided the effect on the left side is
less than the increase in trade will prices fall, and then
not proportionately to the increase in trade.
In a former chapter, it was shown that a change in
trade, provided currency (M and M') and velocities
(F and V') remained the same, produced an inverse
change in prices. But now we find that the proviso is
inconsistent with the premise; currency and velocities
can remain the same only by the clumsy hypothesis
that the various other causes affecting them shall be
so changed as exactly to neutralize the increase in trade.
If these various other causes remain the same, then
currency and velocities will not remain the same.
This is the first instance in our study where we have
found that normally, i.e. apart from temporary or
transitional effects, we reach different results by assum
ing causes to vary one at a time, than by assuming the
algebraic factors in the equation to vary one at a time.
The “ quantity theory” still holds true — that prices
(p’s) vary with money (M) — when we assume that
other causes remain the same, as well as when we assumed

Sec. 7]

QUANTITY THEORY

169

merely that other algebraic factors remain the same;
and all the other theorems stated algebraically were
found to hold causationally, excepting only the theorem
as to variation in trade. While the main purpose of
this chapter is to justify the “ quantity theory” as
expressing a causal as well as an algebraic relation, it is
important to point out that causal and algebraic theo
rems are not always identical.
As to the transitional effects of a change in the
volume of trade, these depend mainly on one of the
two possible directions in which prices move. If
they move upward, the transitional effects are similar
to those we are already familiar with for periods of
rising prices; if downward, they are’ similar to those
incident to such a movement.
§7
We have now studied the effects of variations in
each of the factors in the equation of exchange (save
one) on the other factors. We have found that in
each case except in the case of trade (the Q’s) the
ultimate effect was on prices (the p’s). The only
group of factors which we have not yet studied as cause
are the prices (p’s) themselves. Hitherto they have
been regarded solely as effects of the other factors.
But the objectors to the quantity theory have main
tained that prices should be regarded as causes rather
than as effects. Our next problem, therefore, is to ex
amine and criticize this proposition.
So far as I can discover, except to a limited extent
during transition periods, or during a passing season (e.g.
the fall), there is no truth whatever in the idea that the
Price level is an independent cause of changes in any of
the other magnitudes M, M', V, 'V', or the Q’s. To

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THE PURCHASING POWER OP MONET

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VIII

show the untenability of such an idea let us grant for
the sake of argument that — in some other way than
as the effect of changes in M, M', V, V', and the Q’s —
the prices in (say) the United States are changed to
(say) double their original level, and let us see what
effect this cause will produce on the other magnitudes
in the equation.
It is clear that the equality between the money side
and the goods side must be maintained somehow, and
that if the prices are raised the quantity of money or
the quantity of deposits or their velocities must be
raised, or else the volume of business must be reduced.
But examination will show that none of these solutions
is tenable.
The quantity of money cannot be increased. No
money will come from abroad, for we have seen that
a place with high prices drives money away. The
consequence of the elevation of prices in the United
States will be that traders will sell in the United States
where prices are high, and take the proceeds in money
and buy abroad where prices are low. It will be as
difficult to make money flow into a country with high
prices as to make water run up hill.
For similar reasons money will not come in via the
mint. Since bullion and gold coin originally had the
same value relatively to goods, after the supposed dou
bling of prices, gold coin has lost half its purchasing
power. No one will take bullion to the mint when he
thereby loses half its value. On the contrary, as we saw
in a previous chapter, the result of high prices is to make
men melt coin.
Finally, the high prices will not stimulate mining,
but on the contrary they will discourage it, nor will
high prices discourage consumption of gold, but on the

S e c . 7]

QUANTITY THEORY

171

contrary they will stimulate it. These tendencies have
all been studied in detail. Every principle we have
found regulating the distribution of money among
nations (the distribution of money metal as between
money and the arts or the production and consumption
of metals) works exactly opposite to what would be
necessary in order to bring money to fit prices instead
of prices to fit money.
It is equally absurd to expect high prices to increase
the quantity of deposits (M'). We have seen that
the effect would be to diminish the quantity of money
in circulation (M ) ; but this money is the basis of the
deposit currency (Mr), and the shrinkage of the first
will entail the shrinkage of the second. The reduction
of M and M' will not tend to favor, but on the con
trary will tend to pull down the high' prices we have
arbitrarily assumed.
The appeal to the velocities (V and V') is no more
satisfactory. These have already been adjusted to
suit individual convenience. To double them might
not be a physical possibility, and would certainly be
a great inconvenience.
There is left the forlorn hope that the high prices will
diminish trade (the Q’s). But if all prices including
the prices of services are doubled, there is no reason
why trade should be reduced. Since the average person
will not only pay, but also receive high prices, it is
evident that the high prices he gets will exactly make
him able to stand the high prices he pays without
having to reduce his purchases.
'
We conclude that the hypothesis of a doubled price
level acting as an independent cause controlling the
other factors in the equation of exchange and uncon
trolled by them is untenable. Any attempt to maintain

17 2

THE PURCHASING POWER OP MONEY

[C h a p .

VIII

artificially high prices must result, as we have seen, not
in adjusting the other elements in the equation of ex
change to suit these high prices, but on the contrary
in arousing their antagonism. Gold will go abroad
and into the melting pot, will be produced less and
consumed more until its scarcity as money will pull
down the prices. The price level is normally the one
absolutely passive element in the equation of exchange.
It is controlled solely by the other elements and the
causes antecedent to them, but exerts no control over
them.
But though it is a fallacy to think that the price level
in any community can, in the long run, affect the
money in that community, it is true that the price level
in one community may affect the money in another
community. This proposition has been repeatedly
made use of in our discussion, and should be clearly
distinguished from the fallacy above mentioned. The
price level in an outside community is an influence
outside the equation of exchange of that community,
and operates by affecting its money in circulation and
not by directly affecting its price level. The price level
outside of New York City, for instance, affects the
price level in New York City only via changes in the
money in New York City. Within New York City
it is the money which influences the price level, and not
the price level which influences the money. The price
level is effect and not cause. Moreover, although the
price level outside of New York is a proximate cause
of changes of money in New York, that price level in
turn is cause only in a secondary sense, being itself an
effect of the other factors in the equation of exchange
outside of New York City. For the world as a whole
the price level is not even a secondary cause, but solely

S ec, 7]

QUANTITY THEORY

173

an effect — of the world’s money, deposits, velocities,
and trade.
We have seen that high prices in any place do not
cause an increase of the money supply there; for money
flows away from such a place. In the same way high
prices at any time do not cause an increase of money
at that time; for money, so to speak, flows away from
that time. Thus if the price level is high in January as
compared with the] rest of the year, bank notes will not
tend to be issued in large quantities then. On the con
trary, people will seek to avoid paying money at the
high prices and wait till prices are lower. When that
time comes they may need more currency; bank notes
and deposits may then expand to meet the excessive
demands for loans which may ensue. Thus currency
expands when prices are low and contracts when prices
are high, and such expansion and contraction tend to
lower the high prices and raise the low prices, thus work
ing toward mutual equality. We see then that, so far from
its being true that high prices cause increased supply of
money, it is true that money avoids the place and time
of high prices and seeks the place and time of low
prices, thereby mitigating the inequality of price levels.
What has been said presupposes that purchasers have
the option to change the place and time of their pur
chases. To the extent that their freedom to choose
their market place or time is interfered with, the cor
rective adjustment of the quantity of money is pre
vented. The anomalous time of a panic may even be
characterized by necessity to meet old contracts which
afford no choice of deferring the payment. There may
then be a “ money famine ” and a feverish demand for
emergency currency needed to liquidate outstanding
contracts which would never have been entered into if

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THE PURCHASING POWER OP MONEY

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VIII

the situation had been foreseen. That such anomalous
conditions do not negative the general thesis that prices
are the effect and not the cause of currency (including
deposit currency) is shown statistically by Minnie
Throop England.1

§8
Were it not for the fanatical refusal of some econo
mists to admit that the price level is in ultimate anal
ysis effect and not cause, we should not be at so great
pains to prove it beyond cavil. It is due our science
to demonstrate its truths. The obligation to do this
carries with it the obligation to explain if possible why
so obvious a truth has not been fully accepted.
One reason has already been cited, the fear to give
aid and comfort to the enemies of all sound economists,
— the unsound money men. Another may now
receive attention, viz. the fallacious idea that the
price level cannot be determined by other factors in
the equation of exchange because it is already deter
mined by other' causes, usually alluded to as “ supply
and demand.” This vague phrase has covered multi
tudes of sins of slothful analysts in economics. Those
who place such implicit reliance on the competency of
supply and demand to fix prices, irrespective of the
quantity of money, deposits, velocity, and trade, will
have their confidence rudely shaken if they will follow
the reasoning as to price causation of separate articles.
They will find that there are always just one too few
equations to determine the unknown quantities in
volved.2 The equation of exchange is needed in each
1 “ Statistical inquiry into the influence of credit upon the level
of prices,” University Studies (University of Nebraska), January,
1907, pp. 41-83.
8 Cf. Irving Fisher, “ Mathematical Investigations in the Theory

Sec. 8J

QUANTITY THEORY

175

case to supplement the equations of supply and
demand.
It would take us too far afield to insert here a com
plete statement of price-determining principles. But
the compatibility of the equation of exchange with
the equations which have to deal with prices individu
ally may be brought home to the reader sufficiently for
our present purposes by emphasizing the distinction
between (1) individual prices relatively to each other
and (2) the price level. The equation of exchange de
termines the latter (the price level) only, and the latter
only is the subject of this book. It will not help, but
only hinder the reader to mix with the discussion of
price levels the principles determining individual prices
relatively to each other. It is amazing how tenaciously
many people cling to the mistaken idea that an indi
vidual price, though expressed in money, may be deter
mined wholly without reference to money. Others,
more open-minded but almost equally confused, see the
necessity of including the quantity of money among the
causes determining prices, but in the careless spirit of
eclecticism simply jumble it in with a miscellaneous
collection of influences affecting prices, with no regard
for their mutual relations. It should be clearly recog
nized that price levels must be studied independently of
individual 'prices.
The legitimacy of separating the study of price levels
from that of prices will be clearly recognized, when it is
seen that individual prices cannot be fully determined
by supply and demand, money cost of production, etc.,
without surreptitiously introducing the price level
itself. We'can -scarcely overemphasize the fact that
and Value of Prices,” Transactions of the Connecticut Academy oj
Arts and Sciences, Vol. IX , 1892, p. 62.

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VIII

the “ supply and demand” or the “ cost of production”
of goods in terms of money do not and cannot com
pletely determine prices. Each phrase, fully expressed,
already implies money. There is always hidden some
where the assumption of a general price level. Yet
writers, like David A. Wells,1 have seriously sought
the explanation of a general change in price levels in the
individual price changes of various commodities con
sidered separately. Much of their reasoning goes no
farther than to explain one price in terms of other
prices. If we attempt to explain the money price of
a finished product in terms of the money prices of its
raw materials and other money costs of prices of pro
duction, it is clear that we merely shift the problem.
We have still to explain these antecedent prices. In
elementary textbooks much emphasis is laid on the
fact that “ demand” and “ supply” are incomplete
designations and that to give them meaning it is neces
sary to add to each the phrase “ at a price.” But
emphasis also needs to be laid on the fact that “ demand
at a price” and “ supply at a price” are still incom
plete designations, and that to give them meaning it
is necessary to add “ at a price level.” The demand
for sugar is not only relative to the price of sugar, but
also to the general level of other things. Not only
is the demand for sugar at ten cents a pound greater
than the demand at twenty cents a pound (at a given
level of prices of other things), but the demand at
twenty cents at a high level of prices is greater than the
demand at twenty cents at a low level of prices. In
fact if the price level is doubled, the demand at twenty
cents a pound will be as great as the demand was before
1 Recent Economic Changes, New York (Appleton), 1890, Chap
ter

rv.

S ec. 8)

QUANTITY THEORY

177

at ten cents a pound, assuming that the doubling applies
likewise to wages and incomes generally. The signifi
cance of a dollar lies in what it will buy; and the equiv
alence between sugar and dollars is at bottom an equiv
alence between sugar and what dollars will buy. A
change in the amount of what dollars will buy is as
important as a change in the amount of sugar. The
price of sugar in dollars depends partly on sugar and
partly on dollars, — that is, on what dollars will buy
—•that is, on the price level. Therefore, beneath the
price of sugar in particular there lies, as one of the bases
of that particular price, the general level of prices. We
have more need to study the price level preparatory
to a study of the price of sugar than to study the price
of sugar preparatory to a study of the price level.
We cannot explain the level of the sea by the height
of its individual waves; rather must we explain in
part the position of these waves by the general level
of the sea. Each “ supply curve” or “ demand curve”
rests upon the unconscious assumption of a price level
already existing. Although the curves relate to a com
modity, they relate to it only as compared with money.
A price is a ratio of exchange between the commodity
and money. The money side of each exchange must
never be forgotten nor the fact that money already
stands in the mind of the purchaser for a general pur
chasing power. Although every buyer and seller who
bids or offers a price for a particular commodity tacitly
assumes a given purchasing power of the money bid or
offered, he is usually as unconscious of so doing as the
spectator of a picture is unconscious of the fact that he
is using the backgroundj?f_the picture against which to
measure’ the figures in the foreground. As a conse
quence, if the general level changes, the supply and
N

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THE PURCHASING POWER OF MONEY

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VIII

demand curves for the particular commodity considered
will change accordingly. If the purchasing power of
the dollar is reduced to half its former amount, these
curves will be doubled in height; for each person will
give or take double the former money for a given
quantity of the commodity. If, through special causes
affecting a special commodity, the supply and demand
curves of that commodity and their intersection are
raised or lowered, then the supply and demand curves
of some other goods must change in the reverse direc
tion. That is, if one commodity rises in price (without
any change in the quantity of it or of other things
bought and sold, and without any change in the volume
of circulating medium or in the velocity of circulation),
then other commodities must fall in price. The in
creased money expended for this commodity will be
taken from other purchases. In other words, the waves
in the sea of prices have troughs. This can be seen from
the equation of exchange. If we suppose the quantity
of money and its velocity of circulation to remain
unaltered, the left side of the equation remains the
same, and therefore the right side must remain unal
tered also. Consequently, any increase in one of its
many terms, due to an increase of any individual price,
must occur at the expense of the remaining terms.
It is, of course, true that a decrease in the price of any
particular commodity will usually be accompanied
by an increase in the amount of it exchanged, so that
the product of the two may not decrease and may even
increase if the amount exchanged increases sufficiently.
In this case, since the right side of our equation re
mains the same, the effect of the increase in some
terms will necessarily be a decrease in others; and the
remaining terms of the right side must decrease to some

S ec. 8]

QUANTITY THEORY

179

extent. The effect may be a general or even a universal
lowering of prices. Even in this case the reduction in
the price level has no direct connection with the reduc
tion in the price of the particular commodity, but is
due to the increase in the amount of it exchanged.1
The reactionary effect of the price of one commodity
on the prices of other commodities must never be lost
sight of. Much confusion will be escaped if we give
up any attempt to reason directly from individual
prices. Improvements in production will affect price
levels simply as they affect the volume of business
transacted. Any rational study of the influence of
improvements in methods of production upon the level
of prices should, therefore, fix attention, first, on the
resulting volume of trade, and should aim to discover
whether this, in turn, carries prices upwards or downw,ards.
[One of the supposed causes of high prices to-day,
much under discussion at the present time, is that of
industrial and labor combinations. From what has
been said, it must be evident that, other things remain
ing equal, trusts cannot affect the general level of prices
through manipulating special commodities except as
they change the amounts sold. If prices for one com
modity are changed without a change in the number
of sales, the effect on the price level will be neutralized
by compensatory changes in other prices. If trade
unions seek to raise prices of labor while trusts raise
prices of commodities, the general level of everything
may rise or fall; but it can rise only by a general
decrease in the quantities of commodities, labor, etc.,
sold, or by an increase of currency, or by an increase in
velocities of circulation. ; If there is neither an increase
1For further discussion, see § 2 of Appendix to (this) Chapter V III.

180

THE PURCHASING POWER OF MONEY

[C h a p .

V III

nor decrease in volume of business, and if the quantity
and velocity of circulation of money and its substitutes
remain unchanged, the price level cannot change.
Changes in some parts of the price level may occur only
at the expense of opposite changes in other parts.
We have seen that the price level is not determined
by individual prices, but that, on the contrary, any
individual price presupposes a price level. We have
seen that the complete and only explanation of a price
level is to be sought in factors of the equation of ex
change and whatever antecedent causes affect those
factors. The terms “ demand” and “ supply,” used in
reference to particular prices, have no significance what
ever in explaining a rise or fall of price levels. In con
sidering the influence affecting individual prices we say
that an increase in supply lowers prices, but an increase
in demand raises them. But in considering the influ
ences affecting price levels we enter upon an entirely
different set of concepts, and must not confuse the prop
osition that an increase in the trade (the Q’s) tends to
lower the price level, with the proposition that an in
crease in supply tends to lower an individual price.
Trade (the Q’s) is not supply — in fact is no more to
be associated with supply than with demand. The Q’s
are the quantities finally sold by those who supply, and
bought by those who demand.
We may here state a paradox which will serve to
bring out clearly the distinction between the causation
of individual prices relatively to each other and the
causation of the general level of prices. The paradox
is that although an increased demand for any individual
commodity results in a greater consumption at a higher
price, yet-an increased general demand for goods will
result in a greater trade (the Q’s) at lower prices.

S e c . 9]

QUANTITY THEORY

181

We cannot, therefore, reason directly from particular
to general prices; we can reason only indirectly by refer
ence to the effects on quantities. Sometimes the rise
in an individual price raises and at other times lowers
the general price level.1 To draw a physical parallel
let us suppose that a thousand piles have been driven
in a quicksand and that the owner wishes to raise their
level a foot. He gets hoisting apparatus and planting
it on the piles pulls one of them up a foot. He then
pulls up another and continues until he has pulled up
each of the thousand. But if every time he has pulled
one up a foot he has pushed down 999 over
of a
foot, when he has finished, he will find his thousand
piles lower than when he began. Each time a pile has
risen, the average level of all has fallen.
The proposition that a general increase in demand,
resulting in an increase in trade, tends to decrease and
and not to increase the general level of prices, may be
regarded as a sort of pons asinorum to test one’s knowl
edge of the fundamental distinction between those
influences affecting the general price level and those
affecting the rise and fall of a particular price with re*
spect to that level.
§9
We have seen that the various factors represented in
the equation of exchange do not stand on the same
causal footing. Prices are the passive element and their
general level must conform to the other factors. The
causal propositions we have found to be true normally,
i-e. after transitions are completed, are in brief as
follows: —
1. An increase in the quantity of money (M) tends
1For further discussion, see § 2 of Appendix to (this) Chapter
VIII.

182

THE PURCHASING POWER OF MONEY

[C h a p .

VIII

to increase deposits (M1) proportionally, and the increase
in these two (M and M') tends to increase prices pro
portionally.
2. An increase in the quantity of money in one
country tends to spread to others using the same money
metal, and to the arts, as soon as the price levels or the
relative value of money and bullion differ enough to
make export or melting of the money metal profitable
and to raise slightly world prices.
3. An increase in deposits (.M') compared with money
(M ) tends likewise to displace and melt coin, and to
raise world prices.
4. An increase in velocities tends to produce similar
effects.
5. An increase in the volume of trade (the Q’s) tends,
not only to decrease prices, but also to increase velocities
and deposits relatively to money and through them to
neutralize partly or wholly the said decrease in prices.
6. The price level is the effect and cannot be the cause
of change in the other factors.
7. Innumerable causes outside the equation of ex
change may affect M, M', V, V', and the Q’s and through
them affect the p’s. Among these outside causes are
the price levels in surrounding countries.
8. The causation of individual prices can only explain
prices as compared among themselves. It cannot ex
plain the general level of prices as compared with money9. Some of the foregoing propositions are subject
to slight modification during transition periods. It is
then true, for instance, that an increase in the quantity
of money (M) besides having the effects above men
tioned will change temporarily the ratio of M' to M and
disturb temporarily V, V', and the Q’s, making a credit
cycle.

S ec. 9]

QUANTITY THEORY

183

In general, then, our conclusion as to causes and
effects is that normally the price level (the p’s) is the
effect of all the other factors in the equation of exchange
(M, M', V, V', and the Q’s ) ; that among these other
factors, deposits (M’) are chiefly the effect of money,
given the normal ratio of M' to M ; that this ratio is
partly the effect of trade ( the Q’s ) ; that V and V’ are
also partly the effects of the Q’s ; and that all of the
magnitudes, M, M', V, V', and the Q’s are the effects of
antecedent causes outside the equation of exchange, ad
infinitum.
The main conclusion is that we find nothing to inter
fere with the truth of the quantity theory that variations
in money (M) produce normally proportional changes
in prices.

CHAPTER IX
THE DISPERSION OF PRICES MAKES NECESSARY AN
INDEX OF PURCHASING POWER

§1
W e have found that the general level of prices is
determined by the other magnitudes in the equation of
exchange. But we have not hitherto defined exactly
what a “ general lever’ may mean. There was no need
of such a definition so long as we assumed, as we have
usually done hitherto, that all prices move in perfect
unison. But practically prices never do move in per
fect unison. Their dispersion would render impossible
the statistical study of general price movements were
there no practical method of indicating the general
movement. A simple figure indicating the general
trend of thousands of prices is a great statistical con
venience. It also simplifies our equation of exchange
by converting the right side, which now consists of
thousands of terms, into a single simple term. <
Such an indication is called an “ index number” of
the price level. Its reciprocal indicates, of course, the
purchasing power of money.
The present chapter will, then, treat of the dispersion
of prices, the next chapter of index numbers which this
dispersion renders a practical necessity, and the two
following chapters of the practical statistical use of index
numbers.
The chief conclusion of our previous study is that an
increase of money, other things equal, causes a pro-

184

Sec. 1J

DISPERSION OF PRICES

185

portional increase in the level of prices. In other words,
the p’s in the sum 2pQ tend to rise in proportion
to the increase in money. It was noted, however, that
the adjustment is not necessarily uniform, and that
if some p’s do not rise as much as in this proportion,
others must rise more. In this connection, we observe
that some prices cannot adjust themselves at once,
and some not at all. This latter is true, for instance,
of prices fixed by contract. A price so fixed cannot
be affected by any change coming into operation be
tween the date of the contract and that of its fulfillment.
Even in the absence of explicit contracts, prices may be
kept from adjustment by implied understandings and
by the mere inertia of custom. Besides these restric
tions on the free movement of prices, there are often
legal restrictions; as, for example, when railroads are
prohibited from charging over two cents per passenger
per mile, or when street railways are limited to five-cent
or three-cent fares.
Whatever the causes of nonadjustment, the result is
that the prices which do change will have to change in
a greater ratio than would be the case were there no
prices which do not change. Just as an obstruction
put across one half of a stream causes an increase in
current in the other half, so any deficiency in the move
ment of some prices must cause an excess in the move
ment of others.
In order to picture to ourselves what are the classes
of prices which rise or fall, we must survey the entire
field of prices. Prices, measured as we are accustomed
to measure them, in terms of money, are the ratios of
exchange between other goods and money. The
term “ goods,” as previously explained, is a collective
term comprising all wealth, property, and services,

186

THE PURCHASING POWER OF MONEY

[C h a p .

these being the magnitudes designated in sales. The
chief subclasses under these three groups, which occur
in actual sales, may be indicated as follows: —
Wealth

Property

Services

Real estate
Commodities
Stocks
Bonds
Mortgages
Private notes
Time bills of exchange
Of rented real estate
Of rented commodities
Of hired workers
Of some or all these agencies combined.

The prices of these various classes of goods cannot
all move up and down in perfect unison. Some are far
more easily adjustable than others. Only by extremely
violent hypotheses could we imagine perfect adjust
ability in all. The order of adjustability from the least
to the most adjustable may be roughly indicated as
follows:1—
1. Contract prices of properties and services, espe
cially where the contracts are for a long time; these in
clude bonds, mortgage notes, use of real estate by leases.
2. Contract prices of properties and services, where
the contracts are for a shorter time; these include
bills of exchange, use of rented real estate and com
modities, services of workmen, etc.
1 Cf. Jevons’s admirable “ Classification of Incomes according as
they suffer from Depreciation,” Investigations in Currency and
Finance, London (Macmillan), 1884, p. 80, and after. See also The
Gold Supply and Prosperity, edited by Byron W . Holt, New York
(The M oody Corporation), 1907, especially the Conclusion or
Summary by the editor, beginning on page 193.

Sec. 1]

DISPERSION OP PRICES

187

3. Prices of commodities made of the money metal.
4. Prices of substitutes for said commodities.
5. Prices fixed by law, as court fees, postage, tolls,
use of public utilities, salaries, etc.
6. Prices fixed by custom, as medical fees, teachers’
salaries, etc., and to some extent wages.
7. Prices of real estate.
8. Prices of most commodities at retail.
9. Prices of most commodities at wholesale.
10. Prices of stocks.
Take, for instance, bonds and mortgages. In order
that the prices of these may be perfectly adjustable, we
should have to suppose, not only that there were no
restraint from custom or law, but that the contracts
were perfectly readjusted to each new price level.
We should have to suppose, for instance, that after
the price level had doubled in height, because cur
rency had doubled, there would be a S2000 bond
wherever there had been a $1000 bond. This, obvi
ously, is not the case. The holder of a $1000 bond
can receive at its maturity only $1000, besides in
terest payments in the interim. If, meanwhile, the
price level doubles, he will receive no more. It is
true that a change of price level will, in time, change
the volume of new loans. A merchant, to lay in a
given stock of goods, will need to borrow a larger
sum if prices are high than if they are low. Per
sonal notes and bills .of exchange will be drawn for
double the amount which would have obtained had
the price level not doubled. Similarly, a corporation
issuing bonds for new projects may have to issue a
larger amount. But obligations outstanding when the
price levels change cannot be thus adjusted; their
prices can vary only slightly during the interim be

188

THE PURCHASING POWER OF MONEY

[C h a p .

tween issue and maturity. The fact that their face
value is expressed in money sets very definite limits
to their prices.1 If, because of a doubling in the quan
tity of money, the value and profits of a railroad
measured in money were doubled, the bondholder could
not, on that account, realize more money for his bond.
The value of the bond is not greatly affected by the
valuation and profits of the railroad, so long as these
are sufficient to guarantee the bond. The bond is an
agreement to pay stated sums at stated times. It repre
sents a limited money value carved out of the road.
The only ways in which the money price of a bond or
salable debt can vary at all are by variations in the
rate of money interest and by changes in the degree of
certainty of payment. Only so far as these features are
affected by the changes in the volume of money will
the value of bonds be affected. We have seen, for in
stance, that inflation, while it is taking place, raises
interest.2 It therefore lowers the price of bonds during
the transition period.3 Again if violent changes in the
price level increase or decrease the number of bank
ruptcies, they thereby affect the degree of certainty of
payment, and consequently affect the value of bonds.
But these ways of affecting prices of such securities ex
pressed in money are of less account than the ordinary
effect of inflation or contraction on price levels, and of
a different character.
1 See article by Walter S. Logan on the “ Duty of Gold,” in The
Gold Supply and Prosperity, edited by Byron W . Holt, New York
(The M oody Corporation), 1907, p. 10G. See also Ricardo, “ Essay
on the High Price of Bullion,” JForfcs, 2d ed., London (Murray),
1852, p. 287.
2 Supra, Chapter IV, § 1.
3
See article by Robert Goodbody, “ More Gold means Higher
‘ Time* Money and Lower Bond Prices,” in The Gold Supply and
Prosperity, edited by Byron W . Holt, New York (The M oody
Corporation) 1907, p. 163 and after.

S ec. 1]

DISPERSION OP PRICES

189

The chief peculiarity of these forms of property lies,
then, in the fact that they are expressed in terms of
money and therefore are compelled to keep in certain
peculiar relations to money. Being based on contracts,
the money terms of which during a given period must
not be changed, they are not free to be influenced in
the same ways as other property. The existence of
such contracts constitutes one of the chief arguments
for a system of currency such that the uncertainties
of its purchasing power are a minimum. An uncertain
monetary standard disarranges contracts and discour
ages their formation.
The longer the contract, the larger the nonadjusta
bility. A fifty-year bond usually means a relative fixity
of price for half a century. Only at the end of that
time, if prices have risen, can bonds, issued de novo
for the means of purchasing goods, be correspondingly
more numerous or of correspondingly larger denomi
nations. A 30-days’ bill of exchange, on the other
hand, while it cannot change much in price, is can
celed at the end of a month. The relative fixity of
price is, therefore, of shorter duration.
A special class of goods, the prices of which cannot
fluctuate greatly with other prices, are those special
commodities which consist largely of the money metal.
Thus, in a country employing a gold standard, the
prices of gold for dentistry, of gold rings and ornaments,
gold watches, gold-rimmed spectacles, gilded picture
frames, etc., instead of varying in proportion to other
prices, always vary in a smaller proportion. The
range of variation is the narrower, the more predomi
nantly the price of the article depends upon the gold
as one of its raw materials.
From the fact that gold-made articles are thus more

190

THE PURCHASING POWER OF MONEY

[Chap. IX

or less securely tied in value to the gold standard, it
follows also that the prices of substitutes for such
articles will tend to vary less than prices in general.
These substitutes will include silver watches, ornaments
of silver, and various other forms of jewelry, whether
containing gold or not. It is a fundamental principle
of relative prices that the prices of substitutes will move
in sympathy. In the case of perfect substitutes, the
prices must always be equal or must bear a fixed ratio
to each other.1
The remaining items in our list require little comment.
The imperfect adjustability of prices fixed bylaw and
custom and the perfect adjustability of wholesale prices
of commodities and prices of stocks are familiar to all.

§2
The fact that wages, salaries, the price of gold in non
monetary forms, etc., and especially the prices of bonded
securities, cannot change in proportion to monetary
fluctuations, means, then, that the prices of other things,
such as commodities in general and stocks, must change
much more than in proportion. This supersensitiveness
to the influence of the volume of currency (or its velocity
of circulation or the volume of business) applies in a
maximum degree to stocks. Were a railroad to double
in money value, the result would be, since the money
value of the bonds could not increase appreciably, that
the money value of the stock would more than double.
Stocks are shares in physical wealth the value of which,
in money, can fluctuate. Since the money price of
bonds is relatively inflexible, that of stocks will fluctuate
1 See Irving Fisher, “ Mathematical Investigations in the Theory
of Value and Prices,” Transactions of the Connecticut Academy oj
Arts and Sciences, 1892, p. 66 and after.

S ec. 2]

DISPERSION OF PRICES

191

more than the price of the physical wealth as a whole.
The reason is that these securities not only feel the
general movement which all adjustable elements feel,
but must also conform to a special adjustment to make
up for the rigid nonadjustability of the bonds associated
with them.
To illustrate, let us suppose the right side of the
equation of exchange to consist of the following ele
ments:—
Miscellaneous adjustable elements such as commodi
ties, having a value o f .......................................... $ 95,000,000
Five thousand shares of stock at $1000 per share,
making a value o f ...............................................
5,000,000
K ve thousand bonds on the same underlying wealth
at $1000 each, making a value o f .....................
5,000,000
Miscellaneous nonadjustable elements such as other
bonds, notes, government salaries, government
fees, dentists’ gold, etc., having a value of . . .
20,000,000
$ 125,000,000

Let us suppose that, with no change in the velocities of
currency circulation or in the volume of business, there
is an increase’of 40 per cent in the quantities of currency.
Then, the total value of goods exchanged will have
to increase from $125,000,000 to §175,000,000. Let
us assume that the last two items are absolutely non
adjustable; then none of the increase of $50,000,000
can occur through any change in these items, which will
remain at $5,000,000 and $20,000,000, respectively, or
$25,000,000 in all. Consequently, the first two items
must rise by the whole of the $50,000,000, that is, from
$100,000,000 to $150,000,000 or 50 per cent. To dis
tribute this increase of $50,000,000 over the first two
or adjustable items, let us assume that the total $10,000,000 worth of actual wealth, which consists half of

192

THE PURCHASING POWER OF MONEY

[C h a p .

stocks and half of bonds, will rise in the same ratio
as the $95,000,000 worth of adjustable elements rise.
Now the whole (comprising all three items) evidently
rises from $105,000,000 to $155,000,000, making an in
crease of 47.6 per cent. This, therefore, is the common
percentage which we are to assume applies equally to
the first item and the combination of the second and
third. Applied to the former it makes an increase from
$95,000,000 to $140,200,000. Applied to the latter it
makes an increase from $10,000,000 to $14,800,000.
But since half of the property consists of bonds and ,
cannot increase, the whole of the increase, $4,800,000,
must belong to the stock alone. This will, therefore,
rise from $5,000,000, to $9,800,000, a rise of 96 per
cent. The four items then change as follows: —
First item — from ,$95,000,000 to $140,200,000, or
47.6 per cent.
Second item — from $5,000,000 to $9,800,000, or
96 per cent.
Third item and fourth item — no change.
All items combined — from $125,000,000 to $175,000,000, or 40 per cent.
Besides the dispersion of price changes produced by
the fact that some prices respond more readily than
others to changes in the factors determining price levels,
M, M', V, V', and the Q’s, a further dispersion is pro
duced by the fact that the special forces of supply and
demand are playing on each individual price, and caus
ing relative variations among them. Although these
forces do not, as we have before emphasized, neces
sarily affect the general price level, they do affect the
number and extent of individual divergencies above and
below that general level. Each individual price will
have a fluctuation of its own.

Sec. 2]

DISPERSION OP PRICES

193

Among the special factors working through supply
and demand, changes in the rate of interest should be
particularly mentioned. Whether or not due to monetary
changes, a movement of interest will tend to make the
prices of different things vary in different directions or
to different extents. The prices of all goods, the bene
fits of which accrue in the remote future, depend on the
rate of interest. The standard example is that of bonds
and other securities. Another good example is that of
real estate. In the case of farm lands yielding a con
stant rental, a reduction of interest causes an increase
of value in the inverse ratio. If interest falls from 5
per cent to 4 per cent, the value will increase in the ratio
4 to 5. If the benefits or services are not constant each
year, but are massed together in the remote future, the
price may be still sensitive to a change in the rate of
interest. In the case of land used for forest growing
from which the trees are to be cut in half a century,
the value will be extremely sensitive. A fall in interest
from 5 per cent to 4 per cent will cause a rise of the
value of the land, in the ratio not of 4 to 5, but nearly
of 4 to 7.1 On the other hand, mining land or quarries
with a limited life will be less sensitive. The same
is true of dwellings, machinery, fixtures, and other
durable but not indestructible instruments, and so on
down the scale until we reach perishable and transient
commodities, such as food and clothing, which are only
indirectly affected by changes in the rate of interest.
It is evident, therefore, that prices must constantly
change relatively to each other, whatever happens to their
1 From figures showing yield of forest of white pine in New
Hampshire, New Hampshire Forestry Commission Report, 1905-1906,
P. 246. See F. R. Fairchild, “ Taxation of Timberland,” Report of
the National Conservation Commission, 60th Congress, 2d Session,
Senate Document 676, vol. II, p. 624.

194

THE PURCHASING POWER OF MONEY

[C h a p .

general level. It would be as idle to expect a uniform
movement in prices as to expect a uniform movement
for all bees in a swarm. On the other hand, it would
be as idle to deny the existence of a general move
ment of prices because they do not all move alike, as
to deny a general movement of a swarm of bees because
the individual bees have different movements.
§3
Corresponding to changes in an individual price there
will be changes in the quantity of the given commodity
which is exchanged at that price. In other words, as
each p changes, the Q connected with it will change also;
this, because usually any influence affecting the price
of a commodity will also affect the consumption of it.
Changes in supply or demand or both make changes in
the quantity exchanged. Otherwise expressed, the
point of intersection of the supply and demand curve
may move laterally as well as vertically.
This changing of the Q’s introduces a new complica
tion. We have in many of our previous discussions
been assuming, as was admissible theoretically, that
all the Q’s remain unchanged while we investigate
the changes in the p’s due to changes in the currency or
in velocities of circulation. But practically we can
never get an opportunity to study such a case. Again,
in order to show the effect of a change in “ the volume of
business” upon the price level, we supposed a case in
which all the Q’s were uniformly changed. Such a
supposition is not only impossible to carry out in prac
tice, but is difficult to conceive even in theory; because,
as we have just seen, each Q is associated with a p. In
showing the effect of a change in the volume of business
upon the level of prices we cannot assume that all the

Sec. 3]

DISPERSION OP PRICES

195

Q’s change uniformly in one direction and all the p’s
uniformly in the other. If the first set change uni
formly, the second cannot change uniformly. A dou
bling in the quantities of all commodities sold, or (what
is almost the same thing), a doubling of the quantities
consumed, would change their relative desirabilities
and therefore their relative prices. To double the
quantity of salt might make its marginal desirability
zero, while to double the quantity of roses might scarcely
lower their marginal desirability at all.1
We see, therefore, that it is well-nigh useless to speak
of uniform changes in prices (p’s) or of uniform changes
in quantities exchanged (Q’s). In place of positing
such uniform changes, we must noW proceed to the
problem of developing some convenient method of
tracing these two groups of changes. We must formu
late two magnitudes, the price level and the volume of
trade. This problem is especially difficult because, in
measuring changes in the price level, we shall need
to use the quantities (Q’s) in some way as weights in
our process of averaging; and we now find, not only
that the prices whose average we seek are extremely
variable, but that the weights by which we attempt to
construct the average are variable also.
It is desired, then, in the equation of exchange, to
convert the right side, SpQ, into a form PT where T
measures the volume of trade, and P is an “ index
number” expressing the price level at which this trade
is carried on. These magnitudes — price level (P)
and volume of trade (T) — need now to be more pre
cisely formulated. Especially does P become hence
forth the focal point in our study.
1 Cf. Jevons, Theory of Political Economy, London (Macmillan),
1888, pp. 155-156.

196

THE PURCHASING POWER OF MONEY

[C h a p .

As explained in the next chapter, there are an in
definite number of ways of conceiving and forming
index numbers of prices and volume of trade. We shall
here mention only the simplest. T may be conceived as
the sum of all the Q’s, and P as the average of all the p’s.
This method is practically useful only provided suitable
units of measure are selected. It must be remembered
that the various Q’s are measured in different units.
Coal is sold by the ton, sugar by the pound, wheat by
the bushel, etc. If we now add together these tons,
pounds, bushels, etc., and call this grand total so many
“ units” of commodity, we shall have a very arbitrary
summation. It will make a difference, for instance,
whether we measure coal by tons or hundredweights.
The system becomes less arbitrary if we use, as the unit
for measuring any goods, not the unit in which it is
commonly sold, but the amount which constitutes a
“ dollar’s worth” at some particular year called the base
year. Then every price, in the base year, is one dollar,
and therefore the average of all prices in that year is
also one dollar. For any other year the average price
(i.e. the average of the prices of the newly chosen units
which in the base year were worth a dollar) will be the
index number representing the price level, while the
number of such units will be the volume of trade.
The equation of exchange now assumes the form

MV + M'V' = PT
and its right member is the product of the index number
(P) of prices multiplied by the volume of trade ( T).
§4
In this chapter we have seen that prices do not, and
in fact cannot, move in perfect unison. The reasons

Sec. 4]

DISPERSION OP PRICES

197

for dispersion are principally three: (1) Many prices
are restrained by previous contract, by legal prohibition,
or by force of custom. (2) Some prices are intimately
related to the money metal. (3) Each individual price
is subject to special variation under the influence of its
particular supply and demand. There exists, however,
a compensation in price movements in the sense that the
failure of one set of prices to respond to any influence
on the price level will necessitate a correspondingly
greater change in other prices.
The quantities sold likewise vary, and their variations
are bound up with those of prices.
In order to express in one figure the general movement
of prices, an index number (P) is constructed; and
in order to express in one figure the general movement of
trade, an index of trade ( T) is constructed. The nature
of these indices will form the subject of the next chapter.

CHAPTER X
THE BEST INDEX NUMBERS OF PURCHASING POWER

§1
In the previous chapter the necessity for an index
number (P) was shown and a particular form of index
number was suggested. This form of index number
had been shown in Chapter II and its appendix to meet
certain conditions (of proportionality of price level to
quantity of money, etc.) required by the equation of
exchange, MV+M'V'=PT. In the present chapter,
this index number will be compared with others and
the general purposes of index numbers discussed, in
cluding purposes having little direct concern with the
equation of exchange.
Index numbers may be compared in respect to (1)
form, under which term are included methods of weight
ing and of determining the “ base” prices; (2) the
selection of elements to be included. In this section
we shall consider the question of form.
The number of possible forms of index numbers is
infinite. They differ enormously in complexity, in ease
of calculation, and in conformity to various other tests.
A few of the simplest may here be mentioned. Their
discussion will be brief and will in many cases be dog
matic. Full proofs and discussions are contained in
the mathematical appendix.1
If in 1900 the average price per pound of sugar was
6 cents, and in 1910 it was 8 cents, the ratio of the price
1 See Appendix to (this) Chapter X , § § 1-8, where 44 types of
index numbers are compared.

198

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THE BEST INDEX NUMBERS

199

in 1910 to that in 1900 must have been £ or 133-J- per
cent. If, in the same period, the average price of coal
per ton had changed from $4 to $6, the corresponding
ratio for coal must have been £ or 150 per cent. If the
price of a given grade of cloth, on the other hand, fell
from 10 cents to 8 cents a yard, the ratio for cloth must
have been & or 80 per cent. P is an average of all
these three price ratios and other price ratios, that is,
an average of 133J per cent, 150 per cent, 80 per cent,
etc. The simple arithmetical average of these three
ratios specified would be 133f|-% + 150%+80% ^or 121
O

per cent. The simple geometric average would be
^133^x150x80, or 117 per cent.
These are examples of simple or unweighted averages.
Since, however, weighted averages have many advan
tages in theory and some advantages in practice, we
shall proceed to consider them.
There are innumerable methods of weighting1 and of
averaging. None of them is perfectly satisfactory
from a theoretical standpoint. We must choose what
seems to be best from a practical standpoint. The
effect of changed volume of currency or changed veloc
ity of circulation on the whole series of prices is complex,
and cannot, even in theory, be compressed into one
figure representing all price changes, any more than a
1 For discussions of different ways tliat have been proposed,
see Walsh, The Measurement of General Exchange Value, New York
and London (Macmillan), 1901; Edgeworth, “ Report on Best
Mothods of Ascertaining and Measuring Variations in the Value of
the Monetary Standard ” ; Report of the British Association for the
Advancement of Science for 1887, pp. 247-301; ditto for 1888, pp.
181-209; ditto for 1889, pp. 133-164. Nitti, La misura delle variazioni di valore della moneta, Turin, 624 p p .; also the Appendix to
(this) Chapter X .

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THE PURCHASING POWER OF MONEY

[Chap.

lens can be constructed which will focus in one point
all the rays of light reaching it from a given point.
But, although in the science of optics we learn that a
perfect lens is theoretically impossible, nevertheless, for
all practical purposes lenses may be constructed so
nearly perfect that it is well worth while to study and
construct them. So, also, while it seems theoretically
impossible to devise an index number, P, which shall
satisfy all of the tests we should like to impose,1 it is,
nevertheless, possible to construct index numbers which
satisfy these tests so well for practical purposes that we
may profitably devote serious attention to the study
and construction of index numbers.
The index number mentioned in Chapter IX may be
constructed by the following process: Suppose that the
year 1910 is the period to be considered in our equation
of exchange MV + M'V' =
= PT. We select
another year (say 1900) and call it the “ base ” year.
This means that the prices of 1910 are to be expressed
as a percentage of the prices of the equation of exchange
for 1900.
Next we obtain an expression for trade (or T).
As shown in the appendix to this chapter, every form
of index number, P, for prices implies a correlative
form of index for trade, T, and vice versa. It is con
venient to select T first. We observe that trade (or T)
is not the value of transactions measured at the actu al
prices of the year 1910, for this value is PT or SpQ,
1
Cf. Mill, Political Economy, Book III, Chapter X V ; Sidgwick,
Principles of Political Economy, Book I, Chapter I I ; “ Report of
Committee on Value of Monetary Standard,” Report of the British
Association for the Advancement of Science, 1887; Wesley C. Mitchell»
Gold, Prices, and Wages under the Greenback Standard, Berkeley, 1908
(University of California Press), p. 19;
Chapter X .

and Appendix to (this)

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THE BEST INDEX NUMBERS

201

that is, the entire right side of the equation. Trade
( T) by itself must be divorced from the price level ( P ) ;
it may be conceived as the value which the total trans
actions would have had if the actual quantities sold had
been sold at the base prices. It is thus the sum of a
number of terms, each term being the product of the
quantity, or Q, pertaining to 1910 and the price, or p,
pertaining to the base year 1900. Algebraically it is
PqQ + p'oQ' + p"oQ" + etc., or, more briefly, %>o<2, where
the prices of 1910 are expressed simply as p, p', p",
etc., and those of the base year, 1900, are expressed
as Po, P'o, P"o, etc.
Having defined this ideal value (T), we now define
P as the ratio of the real value of transactions in 1910
(SpQ) to that ideal (2poQ). More fully expressed, P is
the ratio of a real value (the value of the trade of
1910 at the prices of 1910) to an ideal value (the value
of the trade of 1910 at the prices of 1900). This ratio
is really a weighted arithmetical average of price ratios.1
The foregoing method is simple both in conception and
in mathematical expression,2 and appears to furnish,
theoretically at least, the best form of P, or index num
ber of prices. The particular form of P (viz.
-*•
~PoQ) which we have just described is, then, associated
with and dependent on a particular form of T (viz.
^ PoQ). Tm ay be called an index number of trade, and
We may say that, the particular form of T (viz. 2p„Q)
is the best form of index or barometer of trade.
Another method of conceiving the same form of
index number of prices is that mentioned at the close of
1 Seo Appendix to (this) Chapter X for a table and discussion
forty-four sample types of index numbers.
2 It is formula 11 of the large table in the Appendix to (this)
Chapter X .

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THE PURCHASING POWER OF MONEY

[C h a p .

the preceding chapter, as follows: Conceive each kind
of goods to be measured in a new physical unit — viz.
the amount which was worth one dollar in the base
year (1900) — and let us use this unit for each other year
(as 1910). Thus instead of a pound as the unit for
sugar we take as the unit whatever amount of sugar was
a dollar’s worth in 1900. Hence the price of sugar in
the base year, 1900, was SI, as of course was the price
of everything else. If, now, the price of sugar in any
other year (as 1910) is $1.25 in terms of the new unit
(viz. the amount which was a dollar’s worth in 1900),
we. know that the price has risen 25 per cent. In this
way P may be defined simply as an average price instead
of as an average price ratio and T as the total number
of the new units of goods sold of all kinds. The right
side of the equation is now simply the product of the
total number of units sold, multiplied by their average
price.
The two definitions of P which have been given (viz.
the ratio of real to ideal values, and the average price in
1910 of all goods when measured in dollar’s worth of
1900) are interchangeable; and both definitions of T
(ideal values of transactions in 1910 at prices of 1900, and
total number of units sold in 1910, the units being
each a dollar’s worth in 1900) are interchangeable.
There are other ways of defining P and T without chang
ing their meanings. Thus “ P is the weighted arith
metical average of the ratios of prices of goods in 1910
to those of 1900, wh'fen these ratios are weighted accord
ing to.the values of the goods exchanged in 1910 reck
oned at the prices of 1900.” Whichever of these defi
nitions we prefer, the system of index numbers is the
same and has advantages over most other systems.
Above all, it enables us to say without qualification that

Sec. 1]

THE BEST INDEX NUMBERS

203

if the quantities sold remain unchanged, so that T will
remain unchanged, P will vary directly as the left side
of the equation of exchange.1
We choose, then, as one of the best index numbers of
prices, the average price of the goods sold, those goods
being measured in units worth a dollar in the base year;
in other words, the ratio of the value of sales at actual
prices to the value of the same sales if made at base
prices; in still other words, the weighted arithmetical
average of all price ratios, each ratio being weighted
according to the values sold, reckoned at base prices.
We have still to consider the selection of the base. It
makes a difference to the above index numbers, not
only absolutely, but also relatively, whether the base
year is, for instance, 1900 or 1860.
Excepting Jevons’s index numbers, which were
geometric averages, there are few index numbers which
are not vitiated in some degree by having a base remote
from the years for which comparisons are most needed.
As Professor Marshall has maintained and as Professor
Flux has emphasized, the best base for any year seems
to be the previous year.
Instead, then, of employing a fixed base year for which
all prices are called 100 per cent and in terms of which all
other prices are expressed in percentages, each year
may be taken as the base for the succeeding year.
Thus we obtain a chain of index numbers, each num
ber being connected with the preceding year instead of
with a common base year.
The great advantage of this chain system is that it
yields its best comparison for the cases in which com
parison is most used and needed. Each year we are inter1 See Appondix to Chapter II and the Appendix to (this) Chap-

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THE PURCHASING POWER OF MONET

[C h a p .

ested in Sauerbeck’s index number in order to compare
it with the number of the preceding year, and only to a
less extent with other years. The number, however, as
actually constructed, affords something quite different.
It gives us, as its best or most accurate comparison,
the ratio between the current year and the years 18671877. This comparison is of little or no interest to
any one. What all users of these statistics actually do
is to compare two comparisons. The index numbers for
1909 and 1910 (each calculated in terms of 1867-1877)
are compared with each other. But direct comparison
between 1909 and 1910 would give a different and more
valuable result. To use a common base is like compar
ing the relative heights of two men by measuring the
height of each above the floor, instead of putting them
back to back and directly measuring the difference of
level between the tops of their heads. The direct com
parison is more accurate, although in the case of the
men’s heights both methods would theoretically agree.
In the case of price levels, unfortunately, few index
numbers will even theoretically give consistent results
when the base is shifted; 1 and those few will fail to
meet other equally important tests.
It may be said that the cardinal virtue of the suc
cessive base or chain system is the facility it affords for
the introduction of new commodities, the dropping out
of obsolete commodities, and the continual readjustment
of the system of weighting to new conditions. A fixed
base system soon gets behind the times in every sense
of the word.

§2

Our next question is : What prices should be selected
in constructing an index number ? The answer to this
1 See Appendix to (this) Chapter X , § 5, test 7.

Sec. 2]

THE BEST INDEX NUMBERS

205

question largely depends on the purpose of the index
number. Hitherto we have considered only one purpose
of an index number, viz. to best meet the requirements
of the equation of exchange. But index numbers may
be used for many other purposes, of which the two
chief are to measure capital and to measure income.
Each of the three purposes mentioned (viz. exchange,
capital, and income) may be subclassified according as
the comparison desired is between places or times. Thus
index numbers may be used for comparisons between
places with respect to their exchange of goods, their
capital, or their income. When, for instance, the British
Board of Trade1 tries to compare the cost of living in
various towns of England, Germany, and the United
States the comparison is with reference to the prices of
living (or income) of the working classes.
We thus have at least six large classes of purposes
for which index numbers may be used, viz. to compare
the prices, in different places, of the goods exchanged; of
the capital goods; and of the income goods; and of the
same three groups of goods at different times.
In each of the six cases, prices of goods and quantities
of goods will be associated with each other, and an index
number (P) for one will imply an index number (T) for
the other (we here use T in the general sense of an index
of quantities of goods whether they are exchanged goods,
as hitherto, or capital goods, or income goods).
Evidently there will be a great difference in the selection
of the prices to be compared according to which of the
six comparisions we wish to make. Suppose, for in
stance, that we wish to measure changes in the general
1 See Report (to Parliament) of an Enquiry by the Board of Trade
into Working Class Rents, Housing and Retail Prices, London
(Darling), 1908, 1909.

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THE PURCHASING POWER OF MONEY

IC h a p .

level of prices of capital goods,1— railways, ships, real
estate, etc., — and also to measure the relative changes
in the amounts of those goods. The prices of some kinds
of capital may have increased, and of others decreased,
and some may have increased at different rates from
others. How shall we measure the general change in
prices of capital goods ? Again, the quantity of some
kinds of capital, as railroads, may have increased faster
than that of other lands, as sailing ships. Still other
kinds of capital may have decreased. How shall it be
determined whether capital in general has increased, and
how much ? These two problems (of prices of capital
and quantities of capital) may be said to consist in
measuring the average change in the price of the same
quantity of capital, and the average change of quantity
of capital taken at the same prices.
For either index (since only capital is under considera
tion, and not income or other designated goods, whether
stocks or flows), the index numbers should relate, not
to general prices and quantities, but only to prices and
quantities of capital goods. Thus, the prices and quan
tities of all labor services should be omitted. The use
of capital and the rents paid for that use, such as the
rent paid for house shelter, should be omitted. Only
capital instruments, and not the services yielded by
these, should be included. We may obtain the price
index first and then obtain a quantity index by dividing
the value of capital in any year by the price index, or we
may proceed in the reverse direction.2 In making index
numbers of prices of capital and quantities of capital, we
1 This has been suggested by Nicholson, Journal of the Royal
Statistical Society, March, 1887.
2 Giffen, in his Growth of Capital, London (Bell & Sons), 1899,
pp. 50-54, makes correction for price changes although without
attempting to construct a special index number for capital.

Sec. 2]

THE BEST INDEX NUMBERS

207

naturally select for our list articles which are important
as capital, and weight them accordingly.
To determine this general change in prices of capital,
we should weight each ratio by the value of the partic
ular capital to which that ratio relates. In this case
each ratio should be weighted, not according to the
annual sales, but according to the existing capital.
Obviously, the difference between these two modes of
weighting may be great. Thus, real estate forms a
large part of all existing capital, but sales of real estate
are a relatively unimportant part of all sales. Food
products, on the other hand, contribute little to capital
and much to exchange. Consequently, prices and quan
tities of food products would not figure in capital index
numbers, but would figure largely in the index numbers
relating to the equation of exchange.
Again, suppose the purpose of the index numbers of
prices is to measure the quantities and prices of income,
not of elements of capital. In this case the list of
articles and their weights will be quite different from
those in a capital index.
If the income of workingmen is under consideration,
we have to deal with index numbers for prices of those
goods entering into workingmen’s budgets, and with
index numbers of the quantities of such goods. The
first will show the cost of living of the workingman,
or the purchasing power of a workingman’s dollar;
the second will show what is called his “ real wages”
or “ consumption.” In this case the aim is to compare,
not stocks existing at two points of time, but flows
through two periods of time. One way to obtain an
index of real wages is to correct the nominal or money
Wages by using the index number of prices of goods
for which wages are spent. Thus, if money wages for

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THE PURCHASING POWER OF MONEY

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1908 were twice those for 1900, but money prices of the
necessaries and comforts of life had also doubled, real
wages would be unchanged.
Evidently the index numbers used in the case of
quantities and prices of workmen’s living are not the
same as those used in the case of capital. Goods should
have each an importance in the index number, depend
ent upon its importance in workingmen’s budgets.
The goods in this case are flows, while in the case of
capital the goods considered were stocks. In compar
ing capital, the index numbers must relate to capital;
and in comparing income, the index numbers must
relate to income.
§3
Perhaps the most important purpose of index num
bers is to serve as a basis of loan contracts.1 It is
1
An early attempt to construct a series of index numbers ex
pressing the general change in prices was made by Sir George
Shuckburgh Evelyn, Bart., F.R.S. and A.S. in 1798 in an article
entitled “ An Account of Some Endeavors to Ascertain a Standard
of Weight and Measure,” in the Philosophical Transactions of the
Royal Society of London, Vol. L X X X V III, pp. 133-182, inclusive.
Bishop William Fleetwood in 1707 in Chronicon Preciosum, an
Account of English Money , the Price of Corn and Other Commodities
for the Last Six Hundred Years, raises and discusses the question
whether the holder of a fellowship founded between 1440 and 14G0
and open only to persons having an estate of less value than £5 a
year may rightly swear that he has less than that, if he has £6, the
value of money, however, having meanwhile greatly depreciated.
The idea of using an index number or tabular standard of money
value was later put forth by Joseph Lowe, The Present State of Eng
land in regard to Agriculture and Finance, London, 1822 (see pp.
261-291, Appendix, pp. 89-101), and afterwards by G. Poulett
Scrope, Principles of Political Economy . . . applied to the Present
State of Britain, London, 1833, pp. 405-408, although, as we have
seen, the idea of an index number itself antedated them. See Correa
Moylan Walsh, The Measurement of General Exchange Value, New
York and London (Macmillan), 1901; Bibliography, p. 555.

Sec. 3]

THE BEST INDEX NUMBERS

209

desirable to determine the particular form and weighting
best suited to this purpose as well as the best selection
of prices to be included.
An index number which serves the purpose of measur
ing the appreciation or depreciation of loan contracts —
or what is called “ deferred payments ” — evidently be
longs to the time rather than the place group of com
parisons. But to which if any of the three sub-groups
(exchange, capital, or income) it most properly belongs
is not at first clear. But, before considering this ques
tion and as a preliminary to finding the best index
number for contracts between borrower and lender, we
must arrive at some opinion as to what is the ideal
basis for loan contracts.
In the first place, it should be pointed out that
though there is a gain and loss there is not necessarily
any “ injustice” wrought because of a change in the
level of prices. Thus, if a man borrows $1000, con
tracting to pay it back with $40 additional as interest
at the end of five years, and meanwhile prices unex
pectedly double, he is a decided gainer. Though he
has to pay, to be sure, the same number of dollars, he
needs to sell only about half as much of his stock of
goods as he expected. He pays back, in the princi
pal, only half of the real purchasing power borrowed.
The lender, on the other hand, is a loser by the change.
Yet the contract was perfectly fair. Each party
knew or should have known that the price level might
change, and took the risk. There was no fraud any
more than when wheat has been ordered for future
delivery at a certain price and the market unexpectedly
turns; or when an insurance company loses a “ risk”
prematurely.
Indeed, for a government to attempt by legislation

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THE PURCHASING POWER OF MONEY

[C h a p .

to deprive the gainer of his profit would itself be in
general unfair.1 To protect themselves from losses
the risk of which they took upon themselves, the losing
parties cannot justly betake themselves to legislation
after the making of contracts.
The unfairness of so doing becomes the more manifest,
when it is considered that, if the change in price level
is at all expected, there is apt to be some compensation
by means of an adjustment in the rate of interest.2
If the price level is rising, the nominal rate of interest
will probably be a little higher, compensating the
lender somewhat for the loss of part value in his prin
cipal; while, if the price level is falling, the borrower
is likely to be partly compensated for his loss by a
lower nominal rate of interest. It is not right that
either side should use its influence with government
to impair the obligations of contracts already made.3
It is, however, sound public policy to lessen in advance
the risk element, as rapidly as may be, so that future
contracts may be made by all parties on the most cer
tain basis possible. In the problem of time contracts
between borrowers and lenders, the ideal is that neither
debtor nor creditor should be worse off from having
been deceived by unforeseen changes. Experience
shows that the rate of interest will seldom adjust itself
perfectly to changes in price level, because these changes
are only in part foreseen. The aim should be to make
the currency as certain or dependable as possible.
Practically speaking, this means that it shall be as
nearly constant as possible.
1 Cf. Irving Fisher, “ Appreciation and Interest,” Part 3, Publica
tions of the American Economic Association, 1896.
2 Rate of Interest, Chapter X IV .
3 Appreciation and Interest, Part 3, § 4.

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THE BEST INDEX NUMBERS

211

In an ideal standard of value, the index number of
prices would continually register 100 per cent.1 But
as long as an absolutely stable currency does not exist,
and cannot be had, the index number is itself a possible
standard for long-time contracts. It is called the
“ tabular standard,” as it depends on a table of prices.
Thus, if a man borrows $1000 when the index number
is 100, he might agree to pay back, not the same dollars,
but the same general purchasing power, with interest.
If, at the time of repayment, the index number had gone
to 150, the principal of the debt would be understood
to be $1500, since this represents the same purchasing
power that was borrowed. If, on the other hand, the
level of prices had fallen to 80, the principal would
automatically become $800. Thus, both parties would
be protected against fluctuations in the value of money.
The same correction would apply to the interest pay
ments, each of which would be adjusted according to
the index number relating to the time of payment.
We are now ready to consider the question of what
are the goods the prices of which should be included in
an index number to serve the purposes of measuring
changes in loan contracts.
1
It has been argued that an ideal standard ought to be such
as to keep constant not objective, but subjective, prices, so that a
debt would be ropaid in a given amount of “ labor” or “ utility.”
But, aside from the practical difficulties of measuring such subjec
tive magnitudes — which are insuperable and therefore render their
discussion purely academic — there are even more serious theo
retical objections because of the fact that the standard would in
crease with some persons and decrease with others as they grow
poorer or richer and that these changes are anticipated in making
loan contracts — in fact, are tho instigating causes of such contracts.
See § 4 infra and Irving Fisher, “ Appreciation and Interest,”
Chapter X II, § 2, Publications of the American Economic Association, 1896.

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THE PURCHASING POWER OF MONEY

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If all goods kept the same ratios of prices among
themselves, it would make no difference whether a
loan contract were made in terms of one index number or
another or even whether it were made in terms of wheat,
tons of coal, or pounds of sugar. But because prices
do not vary in the same, but in different proportions, an
index number measuring the general level of prices is
necessary. If repayment is made in equivalent pur
chasing power (plus interest), over one kind of goods,
this may be either more or less than equivalent purchas
ing power over other kinds. Hence, one party or the
other is a loser according to the kind of goods he handles
as a producer or prefers to use as a consumer. Even
if each contracting party could arrange to receive or pay
back purchasing power over an amount of goods of the
kinds which most concerned him, equivalent to what he
lent or borrowed, with interest, the speculative element
resulting in gain or loss to one or the other, though de
creased, would not be entirely removed.1
Suppose, for example, that a lender receives back
purchasing power over an amount of goods of the kinds
he wished to use, equivalent to what he lent plus in
terest.2 Suppose also that, during the period of the
loan, these goods appreciate relatively to others.
Then the lender really gains, since he can now get more
of other goods in exchange for those it was his original
purpose to use, — a course which he may now be
tempted to take while otherwise he would not. To the
borrower, however, the appreciation of the goods on
1 Cf. Kinley, Money , New York (Macmillan), 1904, p. 267.
2 The argument of the remainder of this section is substantially
the same as that in a paper by Harry G. Brown, in the Quarterly
Journal of Economics, August, 1909, entitled, “ A Problem in De
ferred Payments and the Tabular Standard.”

Sec. 3]

THE BEST INDEX NUMBERS

213

the basis of which repayment is made, relatively to the
goods he is engaged in producing, might be regarded
as causing him loss. The same purchasing power over
the goods, on the basis of which he is to make pay
ment, means in such a case, a greater purchasing power
over the goods he is engaged in producing.
It is clear that no one kind of goods is a fair stand
ard. An index number intended to serve as a standard
for deferred payments must have a broad basis.
Were all borrowers and all lenders interested merely
as consumers — lenders denying themselves in immedi
ate consumption in order to lend, with the idea of con
suming more on repayment, and borrowers planning to
consume more immediately with the intention of later
consuming less — an exactly satisfactory index number
for each individual would seem impossible. The goods
which interested a lender in any given case might not be
those of most importance to the borrower. Only a
rough average could be struck and an index number
found to be used by all parties in their contracts. Such
an average would-doubtless be one in which each price
ratio would be weighted according to the total con
sumption of the goods to which it related, — the total
consumption of all borrowers and all lenders in the
country considered.
The case is even more complicated, however; for many
borrowers and lenders are interested less in consumption
than in investment.1 The choice is as much between
lending and other investing as between lending and con
suming. Similarly, the borrower may borrow to invest
as well as to consume and may raise the money for repay
ment by curtailing investment rather than by curtailing
consumption. Borrowers and lenders, in other words,
1 Cf. Kemmerer, Quarterly Journal of Economics, August, 1909.

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THE PURCHASING POWER OF MONEY

[C h a p .

maybe more interested in purchasing factories, railroads,
land, durable houses, etc., which yield services during
a long future, than in purchasing more or better food,
shelter and entertainments, which yield immediate
satisfactions. To base our index number for time con
tracts solely on services and immediately consumable
goods would therefore be illogical. Though the prac
tical differences may amount to little, yet, in theory at
least, they are important.
Let us suppose each price ratio to be weighted by
the value (at standard prices) of the services of quickly
consumable goods enjoyed during a given period, pur
chases of durable capital being omitted. Suppose also
that before the time of repayment arrives the rate
of interest has risen. With higher interest, the value
of land, railroads, and other durable capital will be lower
because the value depends on future earnings or future
services, and these are now discounted at a higher rate.1
The borrower, in paying back an equal purchasing
power over consumable goods and services, is pay
ing back a much higher purchasing power over such
things as land, houses, and factories — a much higher
purchasing power over future income — than he bor
rowed. The lender is receiving back, therefore, a larger
purchasing power over these durable items of capital
than he loaned, though not a larger purchasing power
(except for the interest) over immediately consumable
goods and services. He gets back no more control over
present income, but he gets a purchasing power over
a greater amount of deferred income. Had he invested
1 For a discussion of tlie effect of a change in the rate of interest
on prices, see Irving Fisher, Nature of Capital and Income, New
York (Macmillan), 1906, p. 227, and Rate of Interest, New York
(Macmillan), 1907, pp. 226 and 227.

Sec. 3]

THE BEST INDEX NUMBERS

215

in land at the start, instead of lending, the rise of interest
would have left him with the same amount of land, but
a less value. As it is, he gets back a purchasing power
over a greater amount and the same value of land. An
accident has made the lender better off than he ex
pected, and better off than he would have been had he
invested instead of loaning.
If, on the other hand, the rate of interest should fall,
the borrower will be benefited, and the lender injured.
The value of land and of any other property, the income
of which extends far into the future, would rise in
comparison with the value of food, shelter, and so on.
The value of a house is the discounted value of its
future rent or service in affording shelter. The rate
of interest having fallen, the value of the house will be
higher, in comparison with the yearly rental value,
than before. To repay the same amount of purchasing
power over shelter as was borrowed is to repay less than
the same amount of purchasing power over houses.
The borrower is benefited to the extent that he has to
curtail investments to repay, since he repays a less
investing power although as great a spending power.
He need not, therefore, curtail his investments in land
and machinery quite so much as he otherwise would
have to do. The lender, on the other hand, is in the
same degree injured. If he wishes to invest in durable
capital, such as an office building, a mine, or shares in
a railroad, he cannot purchase as much of these with
•the returned principal as he could have purchased with
the same principal at the time of the loan. Had he
foreseen the fall in interest, he might have refused to
make the loan and invested instead. He would then
have had, in place of interest on a loan, a return on his
investment and a larger amount of capital on which

216

THE PURCHASING POWER OF MONEY

[C h a p .

to realize future income. The effect of the fall in in
terest would then have been, not to decrease the re
turns on his investment, but to increase the capitalized
value of the investment.
It appears, then, that while an index number based
on services and the less durable commodities may be
adapted to time contracts between a borrower intend
ing to indulge in immediate consumption, and a lender
intending to postpone consumption until the repay
ment of the loan, such an index number is not entirely
suited to contracts one or both parties to which are
interested in more permanent investment.
Instead, therefore, of basing our index number on
consumable goods and services enjoyed during a period,
we ought rather to base it partly on these and partly on
the amount of durable capital. Each borrower and
each lender may wish to make a different distribution
in time of his income stream.1 One man, that he may
have a large income in the future, wants to invest;
another, that he may enjoy a large income soon, does
not want to invest. One lender is,^therefore, interested
in getting back as much durable capital as he lent;
another lender is interested in receiving as great pur
chasing power over services and consumable goods
as he lent.
Now different persons, with different intentions as
to the spending of their money, nevertheless make
loan contracts with each other. Even if a separate
index number, specially weighted, could be used for
each couple, such a standard would not be equally
fitted to both parties. Yet the same debt cannot be
paid in two different standards. Therefore, absolute
equalization is out of the question. We can mitigate

1 Rate of Interest, pp. 121-125.

Sec. 4]

THE BEST INDEX NUMBERS

217

the evils of a fluctuating money standard, but we cannot
entirely remove the element of speculation from time
contracts.
Although different persons and different classes
might establish different standards for special contracts,
yet for the great mass of business contracts involving
postponed payments, a single series of index numbers
including articles used and purchased by all classes,
and including also services, would probably be found
advisable. This index number would be best suited
to contracts between different classes, between in
dividuals of differing habits of consumption, and to fix
the money payments on bonds which are securities
sold to the public in general.
Without attempting to construct index numbers
which particular persons and classes might sometimes
wish to take as standard, we shall merely inquire re
garding the formation of such a general index number.
It must, as has been pointed out, include all goods and
services. But in what proportion shall these be
weighted? How shall we decide how much weight
should be given, in forming the index, to the stock of
durable capital and how much weight to the flow of
goods and services through a period of time, — the flow
to individuals, which mirrors consumption ? The two
things are incommensurable. Shall we count the rail
ways of the country as equally important with a month’s
consumption of sugar, or with a year’s?
§4
To cut these Gordian knots, perhaps the best and
most practical scheme is that which has been used in
the explanation of the P in our equation of exchange,
an index number in which every article and service

218

THE PURCHASING POWER OF MONEY

[C h a p .

is weighted according to the value of it exchanged at
base prices in the year whose level of prices it is desired
to find.1 By this means, goods bought for immediate
consumption are included in the weighting, as are also
all durable capital goods exchanged during the period
covered by the index number. What is repaid in con
tracts so measured is the same general -purchasing
power. This includes purchasing power over every
thing purchased and purchasable, including real estate,
securities, labor, other services, such as the services
rendered by corporations, and commodities.
There has been much discussion as to the propriety
of the inclusion of services of human beings, or so-called
“ labor.” In one way the question solves itself, since
the inclusion or exclusion on the basis of piece work will
make little or no difference to the results.
It is well known that we may measure wages either
“ by the piece ” or by “ time.” In either case they enter
into and affect the general index number expressing
the price level, but the influence is different in the
two cases. If we take hours of labor as the basis and
measure the wages paid by the hour or b3r the day,
then we are likely to find that, during a period of
improvement in the arts, money wages are rising while
the prices of goods are falling, or that money wages are
rising faster than the prices of goods, or are falling more
slowly. But if we measure wages by the piece, we shall
find less inconsistency of results. If goods increase
faster than currency, so that prices tend to fall, piece
1 The same conclusion as to the best standard for deferred pay
ments is reached by Professor H. S. Foxwell by a somewhat differ
ent line of reasoning. See remarks of Professor F. Y. Edgeworth
(as Secretary of the Committee on Variations of the Monetary
Standard). Report of the British Association for the Advancement
of Science, for 1889, pp. 134-139.

Sec. 4]

THE BEST INDEX NUMBERS

219

wages will tend to fall, on the average, in very much
the same proportion. As improvements in machinery
make the output per hour of labor, i.e. the piece work,
increase, the price per piece may decrease.
The two methods of measurement giving these differ
ent results for price indexes make opposite differences
in the volume of trade. The volume of piece work
increases with progress in invention faster than the
volume of time work.
In considering the index number as a standard for
deferred payments, the desirability of assuming piece
wages to change like commodity prices is based largely
on the difficulty and consequent impracticability of
including wages on a time basis. On the piece-wage
basis, changes in money prices of other goods furnish
an approximate measure of changes in money prices
of labor.
Those who make time contracts on the basis of
such an index number know that they will pay back,
or receive back, purchasing power over the same
quantities of goods, the purchasing power over which
they borrowed or lent. This form of index number is
an objective standard of goods.
If an index number were to be constructed from time
wages alone (not including goods at all), debtors would
pay back and creditors receive an equivalent purchas
ing power over hours of labor. When the time wages
and prices of goods are both included, the problem is
how much weight to give to each. Kemmerer weights
wages 3 per cent out of a total of 100 per cent. Its
influence, therefore, would in any case not be felt
greatly, while, if we take piece wages, it will not be felt
at all; that is, it will not greatly matter whether
Wages are included or not. Since practically we have

220

THE PURCHASING POWER OF MONEY

[C h a p .

no statistics of relative piece wages, and few good
statistics for time wages, we may, in general, as well
omit wages altogether.
This procedure has another advantage. In an index
number intended to serve as a basis for deferred pay
ments for wage earners, it is clear that wages should
be excluded. A wage earner does not judge his pur
chasing power on the basis of how much labor he can
buy.1
In this connection it may be well to call attention
to another standard of purchasing power of money
which has sometimes been suggested for adjusting
contracts. This is the utility standard. According
to this, each person would be expected to receive or
pay back marginal utility equivalent to what he had
lent or borrowed. But the marginal utility of the
same goods is different for different persons and different
for the same person at different periods of his life.
Hence, no such standard could be practically applied.
A price is an objective datum, susceptible of measure
ment, and the same for all men. Marginal utilities,
on the other hand, not only are impossible to meas
ure, but are unequal and vary unequally among in
dividuals. The purchasing power of money in the
objective sense is, therefore, an ascertainable magnitude
with a meaning common to all men. It is of course true
that marginal utility of money is a fundamental magni
tude and that it depends in part on the purchasing
power of money. But it depends also on each man’s
income. The marginal utilities of money will vary
directly with the purchasing power of money if all
prices and all money incomes change in the same ratio, or
1 Cf. Edgeworth, in Palgrave’s Dictionary of Political Economy,
“ Index Numbers.”

Sec. 4]

THE BEST INDEX NUMBERS

221

(roughly at least) if incomes change in the ratio of the
average price change. Ideally, this fixed ratio between
marginal utilities and purchasing power should hold
true when the quantity of money varies (assuming that
deposits vary equally and that velocities of circulation
and volume of trade remain unchanged) after transi
tion periods are over. Practically, however, all these
elements vary, and vary unequally. Money incomes
sometimes increase faster, often more slowly, than
prices. The result is that changes in the purchasing
power of money do not correspond to changes in mar
ginal utilities of money.
Society may become more prosperous, or it may be
come less so, during the time a contract has to run.
This fact, it may be thought, should influence the re
lation of the amount repaid to the amount borrowed.
It has been claimed that the benefits of progress
should be equably distributed between borrowers and
lenders.1
But while loan contracts are made with reference to
marginal utilities, it is here contended that corrections
in a monetary standard not only cannot, but should not,
include variations in the subjective value of money
due to changes in incomes, but should be confined to
variations in objective purchasing power. At any rate,
to obtain a measure of objective purchasing power is
1
See, for example, paper by Professor J. B. Clark, “ The Gold
Standard in Recent Theory,” Political Science Quarterly, Septem
ber, 1895. Comparo with this “ The Standard of Deferred Pay
ments,” by Professor Edward A. Ross, Annals of the American
Academy of Political and Social Science, November, 1892 ; Lucius S.
Merriam, “ Tho Theory of Final Utility in its Relation to M oney
and tho Standard of Deferred Payments,” ibid., January, 1893; Pro
fessor Frank Fetter, “ Tho Exploitation of Theories of Value in the
Discussion of the Standard of Deferred Payments,” ibid., M ay, 1895.

222

THE PURCHASING POWER OF MONEY

[C h a p .

a step which may properly be taken by itself before
any step more ambitious is considered. The search for
a standard of deferred payments which shall auto
matically provide for the just distribution of the “ ben
efits of progress ” seems as fatuous a quest as the search
for the philosopher’s stone. Since we cannot measure
utility statistically, we cannot measure the corrections
in utility required to redistribute the “ benefits of prog
ress.” In the absence of statistical measurement, any
practicable correction is out of the question. The
“ utility standard” is therefore impracticable, even if
the theory of such a standard were tenable.
Somewhat similar theories of a perfect standard of
deferred payments are based on the idea that a dollar
should require always the same amount of labor to pro
duce it. In one sense, since marginal utility and mar
ginal effort are normally equal, the labor standard is
identical with the marginal utility standard. But in
whatever sense “ labor ” is defined, it is an elusive mag
nitude, quite impracticable as a measurable basis for
statistics of purchasing power. Seemingly labor may
be measured in terms of time and, on such a basis, “ a
day’s labor ” has been suggested as a proper unit for
measuring deferred payments. But even “ a day’s
labor” is not a sufficiently definite unit in which to
measure with any considerable degree of accuracy the
•purchasing power of money. Days’ labor differ in
hours, in intensity, and disagreeability of effort as well
as in the quality of labor performed — whether it be
manual, mental, etc. A magnitude which offers so
many theoretical difficulties in measurement can never
serve as a practical standard of deferred payments.
We see then that the attempt to set up a utility
or labor standard is too ambitious to be practica

Sec. 4]

THE BEST INDEX NUMBERS

223

ble.1 We should content ourselves with securing the
maximum attainable improvement in the standard of
deferred payments, without attempting to secure an
ideal distribution of “ the benefits of progress.”
It will also simplify our problem if we remember that
our ideal is not primarily constancy of ;the dollar but
rather dependability. Fluctuations which can be fore
seen and allowed for are not evils. Each man may
presumably be depended on to allow for changes in his
own fortunes, utility, and labor, and perhaps even to a
large extent on the general effects of invention and prog
ress. At any rate he should not expect the monetary
unit to insure him against every wind that blows.
The manner in which each person allows for such
future changes as he can foresee is by adjusting the
size of loans he makes or takes and the rate of interest
thereon. If the average income is rising, the borrower
can afford to repay more and the lender should receive
more; while, if the average income is falling, the
amount paid should be less. The fact is that such are
the tendencies where the rise or fall of average income
is foreseen. If the average income is rising, the lender
will be less anxious to deplete his present income, which
is relatively meager, in order to increase his future in
come, which he sees will probably be larger anyway.
Thus, increasing prosperity (by which is meant, not
great prosperity, but growing prosperity) tends to re
strict the supply of loans. At the same time, it tends to
increase the demand and so raise interest. Conversely,
a decreasing average income will tend to lower interest.2
1 Cf. Charles A. Conant, The Principles of Money and Banking,
Vol. II, Chapter VII.
2 Rate of Interest, pp. 95-98 and 304-306. This position is taken
by Correa M oylan Walsh, The Fundamental Problem in Monetary
Science, New York (Macmillan), 1903, p'. 345, footnote.

224

THE PURCHASING POWER OF MONEY

[C h a p .

All this follows only in case the rise or fall of incomes
is foreseen. If not foreseen, it can exercise no influence
of importance on the interest rate. To the extent
that such changes come unexpectedly after loan con
tracts have been entered into which take no account
of them, — to that extent loan contracts are speculative.
If incomes fall, the lender has gained relatively to the
borrower, because he has realized a higher interest than
he could have realized had the change been foreseen.
The chief burden of the change falls on the borrower.
If incomes experience an unexpected rise, the relative
positions are reversed; the whole gain goes to the
borrower. The normal effect of continuous extension
of income is to raise the rate of interest.
Our present problem, however, is not to safeguard
the interests of debtors and creditors against all pos
sible elements of change, but only against those ele
ments which are purely monetary. Industrial changes
are in a class by themselves, and contracting parties
must be trusted to work out their own salvation. We
are merely concerned in providing them with a stable
or reliable monetary standard. A secure monetary
standard cannot guarantee against earthquake' nor in
sure the equable distribution of prosperity. It can,
however, mitigate the losses now suffered from changes
in the relation of money to other goods.
Statistics of nominal or money interest rates and
virtual or commodity interest rates prove that the
latter fluctuate much more than the former.1 The
effects of this lack of compensation are evil. In the
first place, the situation interferes with the normal dis
tribution of wealth and income. If the level of prices
is rising, since nominal interest does not for a con1 Rate of Interest, Chapter X IV .

Sec. 5]

THE BEST INDEX NUMBERS

225

siderable time rise enough to compensate, the lender
gets back a less amount of wealth or services than he
might reasonably have expected. Creditors lose and
debtors gain. It should be noted also that all persons
with relatively fixed money salaries lose by this rise
of prices. When the level of prices falls, on the other
hand, creditors and persons with relatively fixed in
comes gain at the expense of debtors. The distribu
tion of wealth is changed in either case from purely
monetary causes, and the change can be averted by
making the standard of deferred payments more stable.

§5
We are brought back again, therefore, to the conclusion
that on the whole the best index number for the purpose
of a standard of deferred payments in business is the
same index number which we found the best to indicate
the changes in prices of all business done; — in other
words, it is the P on the right side of the equation of
exchange.1
It is, of course, utterly impossible to secure data for
all exchanges, nor would this be advisable. Only
articles which are standardized, and only those the use
of which remains through many years, are available
and important enough to include. These specifica
tions exclude real estate, and to some extent wages,
retail prices, and securities, thus leaving practically
nothing but wholesale prices of commodities to be in
cluded in the list of goods, the prices of which are to be
1

This is really the same conclusion as that reached by Walsh,

The Fundamental Problem in Monetary Science, in which, after a

thorough and critical review of tho literature of the subject, the
author concludes that the Irind of stability desirable in the standard
of deferred payment is “ stability of exchange value.”

226

THE PURCHASING POWER OF MONEY

[C h a p .

compounded into an index number. These restrictions,
however, are not as important as might be supposed.
The total real estate transactions of New York City
(Manhattan and the Bronx) in 1909 (an active year)
measured by assessed valuations (probably
of the
market valuation) amounted to only 8620,000,000.
This is utterly insignificant if compared only with the
104 billions of bank clearings in New York City. Yet
real estate transactions probably constitute a higher
percentage of total transactions in New York than in
the United States.1 In the United States we feel safe,
therefore, in saying that they amount only to a fraction
of 1 per cent of the total transactions. As to exchanges
in securities, Kemmerer estimates, on the basis of the
transactions of the New York Stock Exchange, that
about 8 per cent of the total transactions of the coun
try consist in the transfer of securities.2 As already
stated, he also estimates that wages amount to about
3 per cent.3 As to the comparative importance of
retail as compared with wholesale prices, we have
some figures of Professor Kinley, of the Monetary
Commission.4 On this basis, and because wholesale
and retail prices roughly correspond in their move
1At any rate the impression is strong that real estate ’is more
“ active” in New York than in most other cities, because of the
rapid change in the character of sites on account of the narrowness
of Manhattan Island and tho consequent acceleration of growth
in one direction (northward) and that, in general, cities have more
trade in real estate than the country, not only absolutely, but relalively to other trade.
2 Money and Prices, 2d ed., New York (Holt), 1909, p. 138.
J Ibid., p. 138.
4 Credit Instruments, 1910, 61st Congress, 2d Session, Senate Docu
ment 399, pp. 69, 73, 134, 136, would indicate that wholesale trade
requires something like twice as much exchange work as retail
trade.

Sec. 5]

THE BEST INDEX NUMBERS

227

ments,1 we may omit retail prices altogether. It is true
that retail prices usually lag behind wholesale prices; but
part of the lagging is more apparent than real. Expert
testimony of those who have collected such statistics
shows that when, as at present, prices are rising rapidly,
retailers obviate the necessity of confronting their
customers with too frequent and rapid increases in
prices by quoting the same prices and substituting in
ferior grades or, in some instances, smaller loaves or
packages.
It is true that wholesale transactions constitute
a minority of all transactions, perhaps only a fifth.2
Nevertheless, wholesale prices are more typical than
any other.
They are to a large extent typical of producers’
prices which precede them, and of retail prices which
succeed them. They are typical of many large and
often nondescript groups which go to make up the total
transactions, such as are classed together in Kinley’s
Report to the Monetary Commission under the head
“ other deposits,” including hotel charges, fees of pro
fessional men, etc., as well as wages. Among items of
which wholesale prices may not be very typical are
the transactions in securities (speculative and other),
railway and other transportation charges, and insurance.
Latterly, prices of stock securities have advanced faster
than wholesale prices, while transportation and insur
ance charges have not advanced as fast. The attempts
1 Tho studies of tho Bureau of Labor in retail prices seem to show
a general sympathy in movement between retail or wholesale prices,
as indeed might be expected.
2 See, in Report of National Monetary Commission on Credit
Instruments, the figures of aggregate sums deposited in banks by
wholesale merchants and others. While these do not afford an ex
act comparison, they aid in making a rougli guess.

228

THE PURCHASING POWER OF MONEY

[C h ap .

of Kemmerer and myself (Chapter X II) to combine in
one average wholesale prices and prices of stocks and
wages yield results differing only slightly from those
based on wholesale prices. From a practical stand
point, wholesale prices of commodities are the only
prices which are yet sufficiently standardized, and the
use of the goods sufficiently stable through a long
period of time, to make them serviceable for general
use.
Not only may we consider that wholesale prices
roughly represent all prices, but we may, with even more
.confidence, confine our statistics for wholesale prices
to a relatively small number. Edgeworth and others
have shown, both practically and theoretically, that
a large number of articles is needless and may even
be detrimental. The 22 commodities employed by
“ The Economist” afford an index number of con
siderable value; the 45 of Sauerbeck have given us a
standard of great value; and the 200 and more com
modities used in the Aldrich Report and the bulle
tins of the Bureau of Labor are certainly numerous
enough, if not too numerous, to give a most accurate
index number of prices.
The recommendations of the Committee of the
British Association for the Advancement of Science
were that the index number should include six groups,
comprehending twenty-seven classes of articles, and
that the prices should be weighted in round numbers
representing approximately the relative expenditures
of the community in these objects. The groups and
classes with weighting were as follows: 1—
1 See Report of the Committee in Report of the British Associa
tion for the Advancement of Science, for 1888, p. 186.

Sec. 5]

THE BEST INDEX NUMBERS

Breadstuff's (wheat 5, barley 5, oats 5, potatoes, rice, etc., 5) .
Meat and dairy (meat 10, fish 21, cheese, butter, milk, 7 i) . .
Luxuries (sugar 21, tea 21, beer 9, spirits 21, wine 1, tobacco

229
. 20
. 20

2 i ) ........................................................................................20
Clothing (cotton 21, wool 25, silk 21, leather 2 2 ) .......................... 10
Minerals (coal 1 0 , iron 5, copper 21, lead, zinc, tin, etc., 2 i ) . . 2 0
Miscellaneous (timber 3, petroleum 1, indigo 1, flax and linseed
3, palm oil 1, caoutchouc 1 ) ....................................... 10

This report was made after very thorough considera
tion by a remarkably competent committee consisting
of Mr. S. Bourne, Professor F. Y. Edgeworth (Sec.),
Professor H. S. Foxwell, Mr. Robert Giffen, Professor
Alfred Marshall, Mr. J. B. Martin, Professor J. S.
Nicholson, Mr. R. H. Inglis Palgrave, and Professor
H. Sedgwick. The report also gives the precise techni
cal description of the articles the price quotations of
which are to be used (the iron, for instance, being
“ Scotch pig iron” ), and also the price list or other source
for price quotations (the wheat, for instance, being the
“ Gazette Average” ).
With slight modifications this recommendation of
the British Committee could be made to apply to
American figures. In America we have had a number
of index numbers of wholesale prices, the most im
portant being (1) those of Roland P. Falkner in the
Aldrich Senate Report, covering a period from 1840
to 1891, in which, beginning with 1860, there were 223
commodities included, the results being given in two
Ways, viz., weighted, the weightingbeing arranged accord
ing to relative expenditures on these articles or their
congeners used by workmen, and also unweighted;
(2) those of the United States Labor Bureau for 251 to
261 commodities beginning with 1890, and now, it is
understood, to be published every year; (3) Dun’s

230

THE PURCHASING POWER OP MuNEY

[C h a p .

index numbers from 1860 to 1906 continued recently
for Gibson by Dr. J. P. Norton; and (4) Bradstreet’s
index numbers since 1895 for 96 commodities.
We need not go into detailed criticism of these index
numbers. On the whole they seem to include too many
commodities, while they all employ the objectionable
fixed-base system. It would be a great advantage if we
could fix upon a system in America which would be not
only authoritative, but would give out its results at
least yearly and promptly.
For practical purposes the median is one of the best
index numbers. It may be computed in a small fraction
of the time required for computing the more theoret
ically accurate index numbers, and it meets many of
the tests of a good index number remarkably well.
It also has the advantage of easily exhibiting (by means
of the “ quartiles” ) the tendency to dispersion of prices
(from each year as a base to the next) on either side
of the median. The median should be weighted in
round numbers analogously to the weighting already dis
cussed for the more theoretically perfect index numbers.1
The median of a series of numbers is a number such
that there are as many numbers above as below it in
the series. If the number of terms in the series is odd,
the median is the middle term of the series of numbers
arranged in the order of magnitude. If the number of
terms is even, the median falls between two terms. If
these are equal, the median is identical with them both;
if they are unequal, the median lies between them and
may then be taken as their simple arithmetical, geo
metric, or any other average. Practically the two
middle terms are almost inevitably so close together
that it would make no appreciable difference what
1 See Appendix to (this) Chapter X , § 8.

S ec. 6]

231

THE BEST INDEX NUMBERS

method of averaging the two middle terms is adopted.
The method of weighting the terms from which a
median is computed consists in counting each term the
number of times indicated by its weight. To illustrate
these statements, it is evident that the median of the
numbers 3, 4, 4, 5, 6, 6, 7, arranged in order of magni
tude is 5; and the median of 3, 4, 4, 5, 6, 6 is 4J.
If the weights to be attached to these latter numbers are
for
for
for
for
for
for

number
number
number
number
number
number

3
4
4
5
6
6

weight
weight
weight
weight
weight
weight

1
2
3
4
2
1

the median is then found from the following: —
Series

............................................. 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6

The weights b e i n g .......................

of which the median is 5. The arithmetical averages
corresponding to the three medians mentioned (5, 4J
and 5) are 5., 4.67 and 4.69 respectively.
Practically it is not necessary to arrange the terms
in exact order of size. Terms easily recognized as low
can readily be paired off against those easily recognized
as high and only the remaining few central terms need
be arranged in exact order. The terms near the middle
being usually almost or quite equal, make the selection
of the median extremely easy.
In order to use the median for an index number of
prices, we first arrange our 'price ratios and then select
the median ratio.
§ 6
In this chapter we have aimed to show that an excel
lent form of index number of prices is the ratio of real

232

THE PURCHASING POWER OF MONEY

[C h a p .

values to ideal values at base prices; and that the ele
ments entering into the construction of index numbers
differ according to the different purposes for which they
are desired. If the purpose is to measure capital, the
prices of services should not be included, but only the
prices of the different articles of wealth existing at any
point of time. If the purpose is to obtain means to
measure real wages, only those things should be in
cluded which workingmen buy; and they should be
included according to the values bought during a given
period, these values being measured at standard prices.
The question of justice between borrower and lender,
where the purpose is to fix on the best index number as
a standard for deferred payments, was also considered.
It was seen to be not an infringement of justice that one
man should gain from another on account of fluctuations
in the money standard; for the contract is a free one
in which normally each should assume whatever risk
there may be of loss for the sake of whatever chance
there may be of gain. It was maintained, also, that
it would be wrong for the government deliberately to
take his gain away from a person who had assumed a
risk of loss in the first place. Nevertheless, it was urged
that a means by which contracts made in the future
could be made less speculative, is desirable.
It was urged that it is no part of the function of an
index number of general prices to guard against rising
and falling real income. The function of such an index
number is to measure the change in the level of prices,
in order that, in contracts involving deferred payments,
there shall be no element of risk so far as money is con
cerned. Without the index number as a standard, such
contracts are quite highly speculative. The adjustment
of the rate of interest compensates to some extent, but

Sec. 6]

THE BEST INDEX NUMBERS

233

not nearly enough, for the fluctuations in the value of
money. These fluctuations influence the distribution
of wealth among persons and classes, and bring about
crises and business depressions. It is desirable that
some basis for time contracts should be fixed upon,
which will remedy these evils. It is believed that an
index number expressing the price level entering into
the equation of exchange might be adopted as such
a basis. The ideal set forth is that neither debtor
nor creditor should be the worse off by being deceived
through changes in the level of prices of goods bought
and sold. Some system is to be sought, therefore, by
which the actual results of the contract should closely
approximate the expected results in nearly all cases.
It was shown that different persons and different
classes might be interested in having for their time con
tracts index numbers somewhat differently constructed,
because different persons are interested in consuming
different kinds of commodities and because they desire
to invest larger or smaller proportions of their earnings.
But for general purposes, as the best compromise to
fit the needs of different classes, what was suggested
Was an index number based on the prices of all goods
exchanged during a given period. It was pointed out,
however, that the different forms of index numbers
which had gained reputation lead to practically the
same results.
Finally, it was shown that for rough and ready com
putations the median has advantages over all other
forms of index numbers.

CHAPTER X I
STATISTICAL VERIFICATION.

GENERAL HISTORICAL

REVIEW

§ 1
S i n c e both the level of prices and the quantity of
money in circulation cannot in practice be perfectly
measured, and since the level of prices depends upon
other factors besides the quantity of money, — viz.
the quantity of circulating credit, the velocities of cir
culation of that credit and of money, and the volume of
business, — it would be absurd to expect any exact
correspondence between variations in the quantity of
circulating money and variations in the price level;
and it is likewise absurd to state, as some have stated,
that the absence of exact statistical correspondence
proves the absence of any influence of quantity of money
on price level. Nevertheless, when the volume of money
changes greatly and quickly, the effect on prices from
this cause is usually so great as to make itself manifest.
The general trend of prices has usually been upward,
as Figure 101 shows. According to the diagram prices
are now about five times as high as a thousand years
ago and are from two to three times as high as in the
period between 1200 and 1500 a .d .2 Beginning with
the last-named date, or shortly after the discovery of
America, prices have almost steadily risen.
1 This diagram shows the changes in price level according to the
separate estimates of D ’Avenel, Hanauer, and Leber as given in
Aupetit’s Essai sur la theorie generate de la monnaie, Paris (Guillaumin), 1901, p. 245.
2 These figures are found by supplementing those of D ’Avenel,
Hanauer, and Leber by those of Jevons and Sauerbeck in tho
19th century. W ithout such supplementing the rise is still more,
being tenfold in a thousand years and four to six times since
1200-1500.

234

S ec. 1]

235

STATISTICAL VERIFICATION

The discovery of America was followed in 1519 by
the invasion of Mexico under Cortez and, twenty years
later, by Pizarro’s conquest of Peru. From these
conquests and the consequent development of New
World mining of precious metals, dates the tremendous
production of gold, and especially of silver, during the
sixteenth century. From the discovery of America
until the after effects of its discovery began to be felt,
200
j

>60
160
Mq

IOC

□AVENE.L.
---------- HANAUER
-------- -LEBER.

6C
40
So

—
—

I
1/\ , r
i \ I
\\ i \ l
7
L
4
7
—

Ov
X

0
400

aso

ISOO

OOO

IAOO

1300

1600

1700

\
f \

1600

)/\
\

1900

F ig . 10.

or, to be exact, through the year 1544, the average
annual output of gold was less than five million dollars,
and of silver about the same.1 The rich mines of Potosi
1 These and the following figures are from “ The W orld’s Pro
duction of Gold and Silver from 1493-1905,” J. D. Magee, Journal
of Political Economy, January, 1910, p. 50 ff. Mr. Magee’s figures
to 1885 are based on Soetbeer’s, and since that date, on the Reports
of the Director of the United States Mint. For Soetbeer’s figures,
see Adolf Soetbeer, Edelmctall-Produktion und Werthverhaltniss
zmschen Gold und Silber seit der Entdeckung Amerika's bis zur
Gegenwart, Gotha (Justus Perthes), 1879, p. 107. These figures
and others to follow are given also in the same author’s Materialien

and are quotod, and their significance discussed, in L. L. Price,

236

THE PURCHASING POWER OF MONEY

[C h a p .

in Bolivia were discovered in 1546. From 1545 to 1560
the annual production of silver averaged eighteen mil
lions, which was over fourfold the previous rate. The
product of gold also increased, though slightly. The
rates of production for both metals rose steadily (with
slight interruption, 1811-1840) up to the present time.
These new world mines began to pour their product
into Europe: first into Spain, the chief owner of the
mines, then, by trade, into the Netherlands and other
parts of Europe, and then into the Orient — that great
“ sink of silver.” Accordingly, as Cliffe Leslie1 has
shown,, prices rose first in Spain, then in the Nether
lands, and then in other regions.
But, though the new supplies of the precious metals
distributed themselves very gradually through Europe,
and the rise of prices was consequently in some regions
delayed, there can be no doubt that they rose or that
the rise was great. The rise between the discovery of
America and the beginning of the nineteenth century
was several hundred per cent. This rise was simul
taneous with an increase of the stock of the precious
metals, because production outran consumption.
Although the total production of the precious metals
continued to increase until 1810, the ratio of the yearly
production to the existing stock became gradually less.
Corresponding to this slackening of production, and
presumably because of it, prices did not continue to rise
at the same rapid rate as at first. Furthermore, with
the development of trade with the East, more and more
of the new supplies found their way thither. The
most rapid rise occurred during the sixteenth century.
Money and its Relation to Prices, London (Sonnenscliein), 1900,
New York (Scribner’s), p. 82 fT.
1 Essays in Political Economy, 2d ed., No. 19.

S e c . 2]

237

STATISTICAL VERIFICATION

§ 2
The stock of money metals at any time in any country
is evidently the difference between the total product and
the sum of the consumption and the net export. Jacob1
has estimated roughly the stock in Europe at various
dates. The following table compares the estimated me
tallic stocks in Europe with the estimated price levels:—
M o n e y a n d P r ic e s

Estimated Product, Consumption, and Stock of Precious Metals in
Europe, expressed in Millions of Dollars, and Price Levels2

D ate

1500 . . . .
1600 . . . .

P roduct

C o n s u m p t io n
and E xport

670

290

1640

740

1700 . . . .
4280

3880

13,000

8960

1800 . . . .
1900 . . . .

Stock

P r ic e s

170

550

1450

1850

100

5890

125 (?)

1 William Jacob, F.R.S., An Historical Inquiry into the Produc
tion and Consumption of the Precious Metals, 2 vols., London (Mur
ray) 1831; Vol. II, p. 03. Seo also Price, Money and its Relation
to Prices, p. 78.
2 The estimates of the product and stock are those of Jacob and
Soetbeer (op. cit.) and Del Mar, History of the Precious Metals,
New York (Cambridge Encyclopaedia Co.), 1902, p. 449. The price
levels (except that for 1900) are the averages of those of Vicomte
D ’Avenel, Histoirc Economiquc de la Propriete des Salaires et des
Denrees, Vol. I, pp. 27 and 32, Leber and Hanauer (see A. Aupetit,
Essai sur la tlitorie gSntrale de la monnaie, Paris (Guillaumin), 1901,
p. 245), the threo estimates being each reduced to 100 per cent for
the last quarter of the eighteenth century, or rather 1770-1790.
The figure for each century year is taken as the average of the
figures given by the three authorities for the preceding and succeed
ing quarter century. Tho figure for 1900 is given as 125 as a com-

238

THE PURCHASING POWER OF MONEY

[C h a p .

With the enormous increase in the quantity of the
precious metals, small wonder if prices have risen !
We see that there has been a general increase (1) in the
stock of money metals, and (2) in the price level, and
that the greatest increase of each was in the sixteenth
century. We find also that the prices did not increase
as fast as the quantity of money. This relative slow
ness on the part of prices was to be expected, because of
the increased volume of business. This, we know, must
have come with increased population and with progress
in the arts — especially the arts of trade — and with
development in transportation. As to changes in the
velocity of circulation of money we know absolutely
nothing.
§3
During the last century the price movements have
been more carefully recorded and show many ups and
downs. The most complete statistics (those of Sauer
beck) are for England. They are represented in Figure
l l . 1 As is well known, English prices were inflated by
promise between widely conflicting results. Leber, Hanauer, and
D ’Avenel agree fairly well and D ’Avenel (writing in 1890 to 1894)
finds (p. 32) the “ present” price level in France to bo double what it
was for 1776-1790, which would make the required figure 200. The
figures for England, however, of Jevons for 1782 to 1818, Investi
gations in Currency and Finance, London (Macmillan), 1884, p. 144,
combined with those of Sauerbeck from 1818 to the present, Course
of Average Prices in England, London (King), 1908, indicate an actual
fall of prices, the figure for 1900 being on the above basis from 75
to 80. The English figures are so much more complete than the
continental figures of D ’Avenel, Leber, and Hanauer, that they are
given more weight, and 125 seems a fair rough average for Europe.
But the wide discrepancies between the various figures make this,
or any other figure which might be chosen, extremely uncertain.
1
The figures are taken from various numbers of the Journal of
the Royal Statistical Society. For many years Sauerbeck has pub
lished yearly his index number in the March issue of this journal.

S e c . 3]

STATISTICAL VERIFICATION

239

the issue of irredeemable paper during the Napoleonic
wars. This period of the paper standard extended
from 1801 to 1820. But prices in paper were only
slightly higher than prices in gold, and the chief price

17*0 was 1700 1799 IBOO

F ig . 11.

movements (except in a few years) were but slightly
affected by the existence of a paper standard. The
main periods of price movements in England since
1789 may be stated as follows: —
Prices
Prices
Prices
Prices
Prices

rose
fell
rose
fell
rose

1789-1809, stock increasing.
1809-1849, stock stationary.
1849-1873, stock increasing.
1873-1896, stock increasing slightly.
1896-present, stock increasing.

In each case is cited the movement in the stock of
money metals in Europe as given in the table of Del Mar.1
The only period which does not, at first glance, agree
with what we might expect if our theory of price levels
1
History of the Precious Metals, p. 449. The data given by Del
Mar are based on the estimates of King, Humbolt, Jacob, Tooke,
Newmarch, McCulloch, and himself.
The dates correspond ap
proximately with the ends of the periods of price movements as
above given. The following figures summarize those of Del Mar
as to stock (expressed in billions of dollars): —
1776
1808
1838
1850

1.4
1.9
1.3

2.0

1870.
1876.
1893.
1896.

3.6
3.7
3.7
4.5

240

THE PURCHASING POWER OF MONEY

[C h a p .

in relation to money is correct, is the period 1873-1896.
Of the other four periods, three are periods of rising
prices and increasing stocks. The fourth is a period of
a stationary stock; and since the volume of trade un
doubtedly increased, a fall of prices was naturally to
be expected.
The exceptional period 1873-1896 — a period of
falling prices — is probably to be accounted for by the
increasing volume of trade and the successive demone
tization of silver by various countries.
The foregoing parallelism between monetary stocks
and prices is somewhat remarkable in view of the in
completeness of the data.1 In the table there are lack
ing, not only exact statistics as to the volume of trade
and all statistics whatever of velocity of circulation,
but also statistics of the volume of bank notes, govern
ment notes, and deposit currency. We know, however,
that modern banking, which had scarcely developed at
all before the French Revolution, developed rapidly
throughout the nineteenth century. It is also known
that banking and deposit currency developed more
rapidly during the third period in the table (1849-1873)
than during the fourth (1873-1896),2 which fact con
tributes somewhat to explain the contrast between the
price movements of these two periods.
§4
We may, therefore, summarize the course of price
movements during the nineteenth century by the fol
lowing probable statements: —
1. Between 1789 and 1809 prices rose rapidly, the
1Cf. Albert Aupetit /E ssa i sur la theorie generate de la monnaiet
Paris (Guillaumin), 1901, pp. 271-285.
2 See Mulhall, Dictionary of Statistics, article on ‘.‘ Banks.!!

Sec. 4]

STATISTICAL VERIFICATION

241

index numbers of Jevons moving from 85 to 157 when
prices are expressed in the gold standard, or 161 when
expressed in paper.1 That is, prices practically doubled
in twenty years. This rise was due to the increased
stock of gold and silver, which in turn was due to their
large production during this period as compared with
the periods before and after. The production of silver
was especially great.2 The Napoleonic wars with their
destruction of wealth and interference with trade prob
ably exercised some influence in the same direction.3
2. Between 1809 and 1849 prices fell. The fall was
measured byJevonsasafall from 157, gold (or 161, paper),
to 64. That is, in forty years prices were reduced to
less than half, or, to be more exact, to two fifths. This
fall in prices was presumably due to the lull in the pro
duction of the precious metals, which prevented the
aggregate stock from keeping pace with the volume of
business. Indeed, the aggregate stock remained station
ary while the volume of business increased. Even the
development of bank currency was insufficient to offset
the continued increase in the volume of business. It is
interesting to observe that this period of falling prices
was interrupted by a temporary rise after 1833, which
Jevons was at a loss to account for, but which was ap
parently due to the inflow of Russian gold after the
discoveries of gold in Siberia in 1830.4
3. Between 1849 and 1873 (although with two nota
ble interruptions) prices rose. They rose, according
1Jevons, Investigations in Currency and Finance, London (Mac
millan), 1884, p. 144.
2 See Magee, ‘ ‘ W orld’s Production of Gold and Silver "Journal
of Political Economy, January, 1910, pp. 54, 56.
3 See Harrison H. Brace, Gold Production and Future Prices,
New York (Bankers’ Publishing Co.) 1910, pp. 16 and 17.
4 Price, Money and its Relation to Prices, p. 112.

242

THE PURCHASING POWER OP MONEY

[C h a p .

to Jevons’s figures supplemented by Sauerbeck’s,1 from
64 to 86, and according to Sauerbeck’s alone, from 74
to 111. That is, in 24 years prices increased, according
to one calculation, by one third; according to another,
by one half. This rise was presumably in consequence
of the gold inflation following the famous California gold
discoveries in 1849 and Australian discoveries in 1851
and 1852. The simultaneous rapid development of
banking contributed to the same result in spite of the
continued increase in trade.
4.
Between 1873 and 1896 prices fell. This fall was
presumably due to the slackening in the production of
gold; to the adoption of the gold standard by nations
previously on a silver basis, and the consequent with
drawal of gold by these new users from the old; to the
arrest of the expansion of silver money consequent on
the closure of mints to silver; to the slackening in the
growth of banking; and to the ever present growth of
trade.2
During the long fall of prices from 1873 to 1896, coun
try after country adopted the gold standard. We have
already seen that Germany adopted the gold standard
1 This rise is found by adding to Jevons’s table, which ends in
1865, a fictitious figure (86) for 1873, calculated to be in the ratio
to the 1865 figure (78), which Sauerbeck’s figure for 1873 (111)
bears to his figure for 1865 (101).
2 It is not that the left-hand side of the equation did not increase,
but that it did not increase so fast as trade; therefore prices fell.
Laughlin seems to think he is overthrowing M ill’s position that
credit acts like money on prices (an increase of credit raising prices,
other things equal), by appealing to the fact of an enormous growth
of deposit currency in this period which had not raised prices nor
prevented their fall. But if trade increased even faster (and Laugh
lin himself asserts an increase of trade, though he denies that it is a
satisfactory answer), then a fall of prices was not opposed to, but
entirely consistent with, M ill’s theory. See Laughlin, The Principles
of Money , New York (Scribner), 1903, pp. 319 and 320.

S ec. 4]

STATISTICAL VERIFICATION

243

in 1871-1873, thus helping to render impossible the
maintenance of bimetallism by the Latin Union. The
Scandinavian monetary union adopted the gold stand
ard in 1873. Between that date and 1878 the countries
of the Latin Union suspended the free coinage of silver
and came practically to a gold basis. In the United
States the legislation of 1873 signified that with re
sumption (which took place in 1879), the country would
come to a gold basis, although no considerable amount
of silver, except for small change, had been coined here
for several decades previously. The Netherlands virtu
ally adopted the gold standard in 1875-1876, Egypt in
1885, Austria in 1892, India in 1893, Chili in 1895,
Venezuela and Costa Rica in 1896, Russia, Japan, and
Peru in 1897, Ecuador in 1899, and Mexico in 1905. In
fact, most countries of importance have now definitely
adopted the gold standard.
The preceding figures apply only to gold countries.
But in 1873 gold and silver countries, as it were, fell
asunder. It is interesting, therefore, to inquire whether
the movement of prices in gold countries was parallel
or antithetical to that in silver countries. As might be
expected, we find it antithetical. The demonetization
of silver in gold countries made a greater amount of that
metal available for silver countries. Accordingly, we
find that prices rose in India from 107 in 1873 to 140 in
1896,1in Japan from 104 in 1873 to 133 in 1896,2 and in
1 F. J. Atkinson, “ Silver Prices in India,” Journal of the Royal
The figures for 1893, 1894,
1895, and 1896 wore lowered by the closure of the Indian mint to
silver in 1893.
2 The figures, from 1873 to 1893 are from Japanese Monetary
Reports, 1895, translated for mo by Mr. Sakata of Yale University.
Tho figures for 1894, 1895, 1896 were also from official Japanese
sources provided by Japanese students.
Statistical Society, March, 1897, p. 92.

244

THE PURCHASING POWER OF MONEY

[C h a p .

China from 100 in 1874 to 109 in 1893.1 These figures,
although not as reliable and representative as the figures
for gold countries, agree in indicating a rise of prices.
The amount of rise is differently indicated, ranging
roughly from 10 per cent to 35 per cent. The following
table shows the contrast between the gold and silver
countries as between 1873-1876 and 1890-1893, the
last year being that of the closure of the Indian mint to
silver.2
P r ic e s in G o ld a n d S il v e r C o u n t r ie s *

G o ld

1873-1876
1890-1893

...................................................
...................................................

100
78

S ilver

100
117

We see that gold prices fell a little more than 20 per
cent and that silver prices rose a little less than 20 per
cent.4
If some way had been contrived by which gold and
silver could have been kept together (say by world-wide
1 From tho Japanese Report mentioned in the above note.
2 The figures for prices in India are, of course, too meager and
local to be of as great value as the corresponding index numbers for
Europe and America. Cf. figures cited by J. Barr Robertson’t.
article (1903), Report of Commission on International Exchange, 58th
Congress, 2d Session, H. R. Document 144, Washington, 1903.
pp. 357-378.
3 Irving Fisher, “ Prices in Silver Countries,” Yale Review, May,
1897, p. 79. The index numbers for gold countries are based on
those of Sauerbeck for England, Soetbeer, Heintz, and Conrad for
Germany, and Falkner (Aldrich Report) for the United States.
Those for silver countries are from Atkinson for India and the
Report of the Japanese Currency Commission above referred to.
4 W e may remark in passing that this divergence between the
two sets of prices is somewhat more than the divergence between
gold and silver themselves.

S ec. 4]

STATISTICAL VERIFICATION

245

bimetallism), prices would not have fallen so much in
gold countries, or risen so much (if at all) in silver coun
tries, but would probably have fallen in gold countries
slightly — probably about 10 per cent up to 1890-1893
and more up to 1896. This is because the stocks of
specie in silver countries were less than half those in gold
countries1 (including those with the “ limping stand
ard ” from left-over silver); so that had there been a
transfer of a given amount of silver from the silver
Orient to the gold Occident, this would have affected
Oriental prices about twice as much as Occidental.
The transition of India from the silver to the gold
side has left about nine tenths2 of the specie (gold and
overvalued silver) in the gold column. In other words,
the world is now practically on a gold basis. The result
has been to make Indian prices move in sympathy with
European prices,3 instead of in opposition.
5.
From 1896 to the present, prices have been rising
because of the extraordinary rise in gold production and
the consequent increase in money media of all kinds.
The gold of South Africa combined with the gold from
the rich mines of Cripple Creek and other parts of the
Rocky Mountain Plateau, and reenforced by gold from
the Klondike, caused, and is still causing, a repetition
of the phenomenon of half a century ago.
That there has been a distinct rise in prices is evident
from the figures of all index numbers. Those of The
Economist, Sauerbeck, Dun, the Labor Bureau Reports,
and Bradstreet are given on the following page.
1 See Muhleman, Monetary Systems of the World, New York
(Nieoll), 1897, p. 177.
2 See Muhleman, ibid.
3 See J. B. Robertson, “ Variations in Indian Price Levels since
1861 expressed in Index Numbers,” Department of Commerce and
Industry (Government of India).

THE PURCHASING POWER OF MONEY

246

1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
.
.
.
.
:
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.

Economist

1950
1890
• 1918
2145
2126
1948
2003
2197
2136
2342
2499
2310
2197
2373

A m e r ic a n

E n g l is h

Close of Dec.

[C h a p .

Sauerbeck

Dun

Labor Bureau

Bradstreet

61
62
64
68
75
70
69
69
70
72
77
80
73
74

74
72
77
85
91
91
102
99
97
98
105

90
90
93
102
111
109
113
114
113
116
123
130
123
127

59
61
66
72
79
76
79
79
79
81
84
89
80
85

The high points of 1900 and 1907, as compared with
the low level of 1896, must be regarded as at least partly
due to expansion of credit. The fairest comparison (to
eliminate the effects of undue changes in credit) is per
haps that of the years 1896, 1903, and 1909. That the
rise of prices has been world wide is evidenced not only
by index numbers, which are only available for a limited
number of countries, but by general impressions of con
sumers and by special reports and investigations.1
The period 1896-1909 for the United States will be
studied in more detail in the following chapter.
§5
It will be seen that the history of prices has in sub
stance been the history of a race between the increase in
media of exchange (M and M') and the increase in
trade ( T), while (we assume) the velocities of circulation
xSee Report of the Select Committee on Wages and Prices of Commodities, Senate Report 912, 61st Congress, 2d Session, 1910.

Sec. 5]

STATISTICAL VERIFICATION

247

were changing in a much less degree. Knowing little of
the variations in the development of trade, we may ten
tatively assume a steady growth, and pay chief atten
tion to the variations of circulating media. Sometimes
the circulating media shot ahead of trade and then prices
rose. This was undoubtedly the case in the periods
numbered 1,3, and 5 of the five periods just considered.
Sometimes, on the other hand, circulating media lagged
behind trade and then prices fell. This must have
been the case in the periods numbered 2 and 4.
It is important to emphasize at this point a fact
mentioned in a previous chapter; namely, that the
breakdown of bimetallism and the consequent division
of the world into a gold section and a silver section
have made each section more sensitive than before to
fluctuations in the production of the precious metals.
The present flood of gold can spread itself only over
the gold section of the world, and not over the whole
world as was virtually the case with the Californian gold
immediately after 1849. At that time gold displaced
silver in bimetallic France and sent it to the Orient.
In this way the Orient afforded relief for bimetallic
countries by draining off silver and making room for
gold; and the bimetallic countries thereby afforded
relief to gold countries also.
Since 1873, therefore, the gold reservoir of Europe
and America has been separated from the silver reser
voir of the East, with the consequence that the Euro
pean and American reservoir level has been made more
sensitive to either a scarcity or a superabundance of
gold. The result has been to aggravate both the fall of
prices from 1873 to 1896 and the present rise, although
the later effect is mitigated by the previous extension
of the gold standard.

248

THE PURCHASING POWER OF MONEY

[C h a p .

§6
The outlook for the future is apparently toward a
continued rise of prices due to a continued increase in
the gold supply. To-day almost as much gold is pro
duced every year as was produced in the whole of the
16th century.
The most careful review of present gold-mining con
ditions shows that we may expect a continuance of gold
inflation for a generation or more. “ For at least
thirty years we may count on an output of gold higher
than, or at least comparable to, that of the last few
years.” 1 This gold will come from the United States,
Alaska, Mexico, the Transvaal, and other parts of
Africa and Australia, and later from Colombia, Bolivia,
Chili, the Ural Province, Siberia, and Korea. It must
be remembered that it is the stock of gold and not the
annual production which influences the price level;
and that the stock will probably continue to increase
for many years after the production has begun to
decline, — as long, in fact, as production keeps above
consumption.
A lake continues to rise long after the freshet which
feeds it has reached its maximum. So the stock of
gold will continue to increase long after the annual
production of gold has stopped increasing. Whether
or not prices will continue to rise depends on whether
the increase in gold and the circulating media based
on gold continues to exceed the growth of trade. It is
the relation of gold to trade that chiefly affects prices.
Even if the stock of gold should increase for many years,
prices may not rise; for trade may increase still faster.
1 L. de Launay, The World’s Gold, English translation, New York
(Putnam), 1908, p. 227.

Sec. 6]

STATISTICAL VERIFICATION

249

If the annual additions of gold to the total stock remain
constant and consequently the stock continually in
creases, the ratio between the constant annual addi
tion and the increasing stock will evidently decrease,
and the increase in stock will count for less and less in
raising prices.1
It is difficult to predict the future growth of trade and
therefore impossible to say for how long gold expansion
will keep ahead of trade expansion. That for many
years, however, gold will outrun trade seems probable,
for the reason that there is no immediate prospect of
a reduction in the percentage growth of the gold stock,
nor of an increase in the percentage growth of trade.
Not only do mining engineers report untold workable
deposits in outlying regions (for instance a full billion
of dollars in one region of Colombia alone), but any
long look ahead must reckon with possible and probable
cheapening of gold extraction. The cyanide process
has made low grade ores pay. If we let imagination
run a little ahead of our times, we may expect similar
improvements in the future whereby still lower grades
may be worked or possibly the sea compelled to give
up its gold. Like the surface of the continents, the
waters of the sea contain many thousand times as much
gold as all the gold thus far extracted in the whole
history of the world. It is to be hoped that the knowl
edge of how to get this hidden treasure may not be
secured. To whatever extent inventors and gold
miners might be enriched thereby, scarcely a worse
economic calamity can be imagined than the resulting
*
Cf. Xenons, . Investigations in Currency and Finance, London
(Macmillan), 1884, pp. 64, 65, 66; also Harrison H. Brace, Gold
Production and Future Prices, New York (Bankers’ Publishing Co.),
1910, p. 113,

250

THE PURCHASING POWER OF MONEY

[C h a p .

depreciation. It may be, however, that only by such a
calamity can the nations of the world be aroused to the
necessity of getting rid of metallic standards altogether.
§7
We have briefly summarized the history of price
movements since the discovery of America and shown
their relation to the stock of the precious metals. But,
as we have emphasized in previous chapters, the pre
cious metals do not include all forms of circulating
media. Paper money and bank deposits have come
during the nineteenth century to occupy very important
places in currency systems.
We shall not attempt any complete review of the
effects of paper money on prices. The best that can
be done is to mention briefly the most striking cases of
paper money inflation and contraction. These are all
cases of irredeemable paper money. When paper
money is redeemable, its possible increase is restricted
by that fact and, what is more important, the effects of
the increase are dissipated over so large an area as to
have little perceptible effect on prices. This dissipa
tion takes place through the export of specie from the
country in which the paper issues occur. Though
the paper cannot be itself exported, it can displace
gold or silver, which amounts to the same thing so far
as spreading out the effect on prices is concerned.
But when the paper is irredeemable, after specie has
been expelled from circulation (whether by export,
melting, or hoarding in anticipation of disaster) there
is no such spreading-out effect. The effects on prices
are then entirely local and therefore greatly magnified.1
1 See Ricardo, Essay on the “ High Price of Bullion,” Worksx
2d ed., London (Murray), 1852, p. 278.

Sec. 7]

STATISTICAL VERIFICATION

251

The consequence is that the most striking examples
of price inflation are cases of irredeemable paper money.
The rise of prices is often still further aggravated by
the gradual substitution of other and better money
or resort to barter, which further restricts the sphere
in which the paper is used and within that sphere makes
it the more redundant. Where the paper money is
looked upon with disfavor, for whatever reason —
whether because its promised redemption has been
indefinitely postponed, or simply because of the bare
fact that it is depreciating, or because of any other
consideration — its sphere of use is restricted.1 Credi
tors and tradesmen avoid taking it if they can, by
“ contracting out” in advance; by barter; by fixing
a double set of prices, one in paper and the other in
some other money; and by outright refusal. In the
end it may happen that the paper ceases to be used at
all. In that case its value depreciates indefinitely and
therefore prices (so far as still expressed in terms of
paper) rise indefinitely.
Whatever the situation, the equation of exchange
continues to hold true though its significance becomes
of less importance, because T, instead of comprising
practically all trade, comes to mean only that disappear
ing portion of trade still transacted by means of paper
money.
The value of irredeemable paper money is, therefore,
extremely precarious. If once it starts depreciating —
from whatever cause — it is likely to depreciate further,
not simply because of the ever present temptation to
further issue, but also because of a growing public
1 See Francis A. Walker, Money , New York (Holt), 1878, p. 199.
Cf. Joseph French Johnson, Money and Currency, Boston (Ginn),
1906, p. 269.

252

THE PURCHASING POWER OF MONEY

[C h a p .

sentiment against it which sooner or later restricts its
use.1 In many cases the irredeemable paper money
continues to be used with sufficient acceptability to give
it a virtual monopoly as a medium of exchange.
Although theoretically irredeemable paper money
may be the cheapest and most easily regulated form
of currency, and although, in some cases, it has remained
a stable currency for a considerable period, the lesson
of history is emphatically that irredeemable paper
money results in monetary manipulation, business dis
trust, a speculative condition of trade, and all the evils
which flow from these conditions.
§8
One of the early paper-money schemes was that of
John Law, who established a bank of issue in France
in 1716. Two years later (December 4,1718), the bank
was taken over by the Crown. Soon shrewd traders
were acquiring specie for notes and exporting the
specie secretly, although exportation of specie was illegal.
May 27, 1720, only four years after its establishment,
the bank stopped payment of specie. By November of
the very same year the paper had fallen to one tenth of
its par value, and after this it became utterly worthless.
The case of the assignats of the French Revolution is
classic.2 It was in December, 1789, that the first issue,
four hundred million francs, was ordered, based osten
sibly on the landed property of the nation. The notes
were issued in April, 1790, and bore 3 per cent interest.
According to the original plan, all of the assignats received
1 Cf. the mention of this influence on depreciation in the Bullion
Report, III.
2 For the following facts, see Andrew D. White, Paper Money
Inflation in France, Economic Tracts, N o. V II, No. 3 of Series, 1882.

S ec. 8J

STATISTICAL VERIFICATION

253

in payment for land were to be burned. But original
plans seem never to be carried out with respect to paper
money. Instead, a hundred millions were reissued in
the form of small notes. Prices began to rise. In
June of the year 1791, six hundred millions more were
issued. Depreciation to the extent of 8 to 10 per cent
immediately followed. Specie was rapidly disappear
ing. Another three hundred millions of francs were
ordered in December, 1791. By February, the assig
nats were over 30 per cent below par. In April, 1792,
came a decree for the issue of three hundred millions
more, and in July for the same amount additional.
Most prices were very high, but wages seem to have
still remained at the level of 1788. By December 14
of 1792, thirty-four hundred million francs had been
issued in assignats, of which six hundred millions had
been burned, leaving twenty-eight hundred millions in
circulation. Laws were enacted to fix maximum prices,
but were evaded. By 1796, forty-five billion francs had
been issued, of which thirty-six billions were in circula
tion. In February of that year the gold louis, of 25
francs, was worth 7200 francs in assignats; and the
assignats were worth
of par. A new kind of paper
money, the mandats, was next issued, but soon fell to
5 per cent of its nominal value. In the end the twentyfive hundred million mandats and the thirty-six billion
assignats were repudiated and became entirely worth
less.
§9
England’s experience with irredeemable paper money
was more temperate. Under the stress of the Napole
onic .wars, the Bank of England suspended cash pay
ments in 1797. This nullified the force which auto
matically limited overissue. The bank resumed cash

254

THE PURCHASING POWER OF MONEY

[C h a p .

payments in 1821. During much of the intervening
period of paper money, prices in paper were very high.
The following table of Jevons shows the relative prices
in notes and specie from 1801 to 1820:1—
Y

ear

1 8 0 1 .....................................
1802 .....................................
1803 .....................................
1804 .....................................
1805 ....................................
1806 .....................................
1807 ....................................
1808 .....................................
1809 .....................................
1 8 1 0 .....................................
1 8 1 1 .....................................
1 8 1 2 .....................................
1 8 1 3 .....................................
1 8 1 4 .....................................
1 8 1 5 .....................................
1816 ' .....................................
1 8 1 7 .....................................
1 8 1 8 .....................................
1 8 1 9 .....................................
1820 .....................................

G o ld S t a n d a r d

P a p e r St an d ar d

140
110
125
119
132
130
129
145
157
142
136
121
115
114
109
91
117]
132
112
103

153
119
128
122
136
133
132
149
161
164
147
148
149
153
132
109
120
135
117
106

The causes of the rise of prices were discussed in
the famous Bullion Report. The general conclusion
reached was that a “ rise of the market price of gold
above its mint price will take place,” if the local cur
rency of any particular country, “ being no longer con
vertible into gold, should at any time be issued to excess.
That excess cannot be exported to other countries, and,
not being convertible into specie, it is not necessarily
returned upon those who issued it; it remains in the
channel of circulation, and is gradually absorbed by
1 Investigations in Currency and Finance, London (Macmillan),
1884, p. 144.

S ec . 10]

STATISTICAL VERIFICATION

255

increasing the prices of all commodities. An increase
in the quantity of the local currency of a particular
country will raise prices in that country exactly in the
same manner as an increase in the general supply of pre
cious metals raises prices all over the world. By means
of the increase of quantity, the value of a given portion
of that circulating medium, in exchange for other com
modities, is lowered. In other words, the money prices
of all other commodities are raised — that of bullion
with the rest.” This is an excellent statement of the
philosophy of irredeemable paper money when that
money is sufficiently within bounds to remain in general
use. No mention is made of partial or complete aban
donment of use because of worthlessness. The reason
is doubtless that in England the paper money never
reached this pass, as it undoubtedly did in many in
stances in France, Austria, America, and elsewhere.

§10
Austrian experience with paper money is instructive.1
Like so many of the European banks, that of Austria
was used by the government as an instrumentality for
obtaining loans. This was done by allowing the bank
to issue large sums in notes. The wars with Napoleon
demanded supplies, and during these wars the issue was
largely increased. In 1796 the note issue was 47,000,000
gulden; in 1800 it was 200,000,000; in 1806, it was
449,000,000. The notes were much below par. In
1810 the bank notes fell successively to \ and about
tVof par. In 1811 a proclamation openly valued them
at one fifth of their nominal value and decreed their
exchange at this rate for redemption notes, called the
1 See W. G. Sumner, History of American Currency, New York
(Holt). 1874, Chapter III.

256

THE PURCHASING POWER OF MONEY

[C h a p .

Viennese legal tender, which became the Austrian
legal-tender currency. But even these new issues soon
fell to
of their face value (May, 1812) and
of their
face value (June, 1812), while the bank notes were at
1690 to 100 in silver. New issues were added under a
different name until, in 1816, the amount of paper
money was over 638,000,000, with prices, of course,
tremendously inflated. In 1816 was founded the Aus
trian national bank, which was intended to draw in the
paper money. From time to time thereafter the amount
of paper circulation was reduced, but not without occa
sional relapses. At the present time Austria has no
paper money which is not at par.
§11

Many of the American colonies had experience with
paper money. In fact, one of the grievances against
England was the parliamentary prohibition of paper
money issues ! In practically all cases 1there was over
issue and depreciation. This was true, for example, in
Massachusetts, where paper money was issued to pay
the expenses of the expeditions against Canada,2 and
in Rhode Island,3 which suffered more, perhaps, from
paper money than any of the others. Following are
figures for Rhode Island taken from the account book
of Thomas Hazard (the entries and memoranda ex
tending from 1750 to 1785), which show the height and
variability of prices.4
1 Pennsylvania seems to have been an exception.
2 W. G. Sumner, History of American Currency, Chapter I.
3 Ibid.
4 Rowland Hazard, Sundry prices taken from Ye Account Book
of Thomas Hazard, son of Robt. Wakefield, R.I. (Times Print),
1892.

STATISTICAL VERIFICATION

Sec. 11]

1755.

H a y £20 p e r L o a d

C o rn p e r B u sh el

B u tter per P ound

25 s.
50 s.
100 s.

1751
1758
1762

1751
1760

W ool per P ound

7 s.
16 s.

P otatoes p e r B u sh el

8
12
28
32

1752
1756
1759
1768

257

s.
s.
s.
s.

1750
1753
1774

............................ 10 s.
............................ 20 s.
............................ 35 s.

We had also during the Revolution a national expe
rience with Continental paper money which gave rise
to the derogatory phrase, still current, “ not worth a
continental.” Depreciation began almost from the
moment of issue (1775), and finally the money was
recognized by Congress itself to have reached
of the
nominal value.1 All prices, of course, were tremen
dously high. Even the new tenor paper given for the
old emissions at the rate of a dollar for forty2 declined
rapidly in value. A bushel of wheat was worth, at
one time, seventy-five dollars, coffee four dollars a
pound, and sugar three dollars a pound.3 It is inter
esting to observe that, in this case, the depreciation
seems to have been accentuated far beyond what mere
overissue tended to produce, by a distrust of the money
and a refusal to receive it in trade. Several classes were
disinclined to receive it to begin with, and as confidence
waned, the number who were unwilling to receive it
increased. Barter frequently took the place of trade
with money.'4
The depreciation was doubtless much greater because
1 See Albert S. Bolles, Financial History of the United Stales,
Vol. I, from 1774 to 1789, Now York (Appleton), 1879, p. 135.
* Ibid., pp. 137 and 138.
J Ibid., p. 141.
* Ibid., Chapter IX .
8

258

THE PURCHASING POWER OF MONEY

[C h a p .

, the paper money of various colonies helped to overflow
the circulation, competing with the congressional money
and limiting its sphere of circulation.

§12
The effects were so disastrous that, in the Constitu
tion of the United States, a provision was incorporated
prohibiting any state from issuing “ bills of credit.”
But, during the Civil War, the temptation again came
to resort to this easy way of securing means of pay
ment ; and the federal government itself issued United
States notes or “ greenbacks.” The banks had already
suspended specie payments so that gold was at a slight
premium in bank paper.1
These greenbacks were issued from time to time dur
ing the war with resulting depreciation as their quantity
increased, — a depreciation greater or less also accord
ing as failure or success of the Union armies affected
confidence in the paper money. The amounts issued
were: $150,000,000 by the act of February 25, 1862;
§150,000,000 by act of July 11, 1862; §150,000,000
authorized by acts of January 17 and March 3, 1863.
Besides the greenbacks (issued in denominations in no
case under a dollar), there was some issue of fractional
currency and of interest-bearing notes running for a
brief period, both of which were also made legal tender.2
The rise in prices is shown by the following table :3—
1 Davis Rich Dewey, Financial History of the United States, Nev/
York (Longmans), 3d ed., § 29.
2 For a brief account of the greenbacks, see Dewey, Financial
History of the United States, Chapter X II.
The most complete
account is found in Wesley Clair Mitchell, A History of the Green
backs, Chicago (University of Chicago Press), 1903.
3 Aldrich Senate Report on Wholesale Prices and Wages, 52d
Congress, 2d Session, table 24, p. 93.

SEC. 12]

STATISTICAL VERIFICATION

I n d e x N u m b e r s o f P r ic e s d u r in g

In d e x N os.

1 P r i c e op
Y

1861
1863
1865
1867
1869
1871
1873
1875
1877
1879

.
.
.

.
.

.
.
.

100
144
163
138
136
112
114
115
105
100

G r e e n b a c k D e p r e c ia t io n

N o r t h e r n P r ic e s

(1860 = 100)

Falkner*

'G o l d 1 in
G reen backs

eah

259

In Gold*

In Paper4

94
91
107
123
112
123
115
115
107
95

94
132
232
166
152
136
129
129
114
95

Dun5
in Paper

Mitchell*
Median
in Paper

89
150
169
164
143
132
124
117
95
85

96
134
158
150
158
130
130
121
100
85

It has been asserted that the rise of prices during the
greenback depreciation was not due to the quantity
of the greenbacks, but to the public distrust of green
backs. The truth is probably that it was due to both.
Distrust was evident and restricted the sphere of
greenbacks very materially. California and, in fact,
all the region west of the Rocky Mountains, made
strenuous efforts to prevent the circulation of green
backs, — efforts which were largely successful. And
naturally the greenbacks could not circulate in the
South. These restrictions alone would confine their
circulation to a population of about 20 millions out of a
total population in 1860 of 31 millions, that is, to less
1Average of quotations in January, April, July, October, from
Wesley Clair Mitchell, Gold Prices and Wages under the Greenback
Standard, Berkeley (University Press), March, 1908.
2 Weighted’ arithmetical average of articles comprising 68.60 per
cent of total expenditure.
3 Aldrich Report, p. 100.
1 Ibid., p. 93.
* From Wesley Clair Mitchell, ibid., p. 59.

260

THE PURCHASING POWER OF MONEY

[C hap . X I

than two thirds of the entire population. Therefore
the volume of trade for which the greenbacks were used
must have been greatly reduced. The total circulating
currency during the war is not known with certainty;
but the best estimates of the various forms of circu
lating media are those compiled by Mitchell.1 Though
he modestly warns the reader against any attempt to
cast up sums, his results may be considered as at least
of some value. The totals, omitting money in the
Treasury and interest-bearing forms, which were known
to have only a very sluggish circulation, we find to be
as follows: —
R ough ly

Y ear

1860
1861
1862
1863
1864
1865
1866

.. . .
.
.
.
.
.
.

.
.
.
.
.
.

C ir c u l a
L o y a l St a t e s

e s t im a t e d

t io n i n

433
490
360
677
708
774
759

P r ic e s o f a l l A r t i c l e s a v e r
aged
ACCORDING TO IMPOR
TANCE, co m p risin g 6S.G0
or
T o t a l E x p e n d it u r e

100
94
104
132
172
232
188

Considering the unreliability of the figures for cur
rency 4and the lack of data as to the other magnitudes in
the equation of exchange, there is here a rough corre
spondence between the volume of the currency and the
level of prices.
1Wesley C. Mitchell, History of the Greenbacks, Chicago (Uni
versity of Chicago Press), 1903, p. 179.
2 Mitchell, ibid., p. 179.
3 Aldrich, Report on Wholesale Prices.
AThe great reduction in 1862, for instance, is due to the assump
tion that practically all gold was withdrawn from circulation ex
cept in California. A more reasonable assumption would seem to
be that it was only partially withdrawn. Much of it may have

S ec. 13]

STATISTICAL VERIFICATION

261

§13
It is necessary to remember that the confidence with
which we have to deal is not primarily confidence in
redemption, but confidence in the paper money,— its
purchasing power. This confidence may rest on ex
pectation of redemption or on other conditions, particu
larly the expectation of further inflation or contraction.
The explanation of the value of the greenbacks appears
to me to be in brief as follows: —
The Redemption Act of 1875 announced the intention
of our government to redeem the greenbacks on and af
ter January 1, 1879. Each greenback being thus kept
equal to the discounted value of a full dollar due Jan
uary 1,1879, they rose steadily toward par as that date
approached. Some of them were withdrawn from cir
culation to be held for the rise. The value of a green
back dollar could not be much less than this discounted
value of the gold dollar promised in 1879; otherwise
speculators might withdraw the greenbacks wholly.
This would pay them well provided they were certain
that the government’s promise would be fulfilled. On
the other hand, the value of greenbacks could not, with
paper money redundant for trade, be greater than said
discounted value, because in that case speculators
would return it all to the circulation, the prospective
rise being “ too small to repay the interest” lost in
carrying it. Thus speculation acted as a regulator of
the quantity of money.
been hoarded in coin form preparatory to export or melting. If
so, it probably circulated to some extent. “ Hoarding” means a
longer retention in the same hands, but not necessarily failure to
be exchanged at all. Gold was a valuable form of bank “ reserve”
at this time. While not paid out in meeting demand obligations,
it was a very quick asset and could be quickly realized upon.

262

THE PURCHASING POWER OF MONEY

[C h a p .

Thus the rise in value of the greenbacks, like other com
ing events, cast its shadow before. It was “ discounted
in advance.” It is quite true that confidence in redemp
tion was here the ultimate cause of the appreciation of
the paper money; but the readjustments caused by
this confidence include a reduction in the quantity of
the money in circulation. Without such readjustment
the appreciation would be impossible, as the equation of
exchange plainly shows. We should note, however, that
if the price of the currency were already sufficiently high,
the prospect of future redemption would not further
raise it. It might happen that the value of the currency
was already above the discounted par value promised
at the time set for redemption. In such a case there
need not be any speculation or any immediate rise in
value until the date of redemption drew near enough
to make itself felt. On the other hand, when, during
the war, the government announced a further issue of
a paper currency already depreciated, the public antici
pated its further depreciation by releasing such hoards
and stocks as were available; in other words, by accel
erating the circulation of money. Each man hastened
to spend his money before an expected rise of price,
and his very action hastened that rise.
Announcements of federal defeats in the war acted
in the same way, being signals that further issues of
greenbacks might be required; while announcement
of victories acted in the opposite way, being like signals
of probable redemption.
When appreciation is anticipated, there is a tendency
among owners of money to hoard or hold it back, and,
among owners of goods, to sell them speedily; the result
being to decrease prices by reducing the velocity of circu
lation and increasing the volume of trade. When, on the

S e c . 14]

STATISTICAL VERIFICATION

263

contrary, depreciation is anticipated, there is a tendency
among owners of money to spend it speedily and among
owners of goods to hold them for a rise, the result being
to raise prices by increasing the velocity of circulation
and decreasing the volume of trade. In other words,
the expectation of a future rise or fall of prices causes
an immediate rise or fall of prices.
These anticipations respond so promptly to every
sign or rumor that superficial observers have regarded
the rise and fall of the greenbacks as related directly
and solely to expected redemption and as having no
relation to quantity. These observers overlook the real
mechanism at work; they fail to see that these effects,
though quick, are slight and limited. They are the
simple adjustments of transition periods described in
Chapter IV. It would be a grave mistake to reason,
because the losses at Chickamauga caused greenbacks
to fall 4 per cent in a single day, that their value had
no relation to their volume. This fall indicated a slight
acceleration in the velocity of circulation, and a slight
retardation in the volume of trade; but, under ordinary
circumstances, it is only slightly that the velocity of
circulation can thus be accelerated; while to make
trade stagnate long or completely would require a
cataclysm.
§ 14
In the South it is “ impossible to state even approx
imately how many Confederate treasury notes were
outstanding at any time.” 1 Professor Schwab has,
however, given the value of gold in Confederate cur
rency and index numbers of prices in the South. He
concludes:2—'
1J. C. Schwab, Confederate States of America, 1861-1865, New
York (Scribner), 1901, p. 165.
2 Ibid., pp. 167-169.

264

THE PURCHASING POWER OF MONEY

[C h a p .

“ This movement of the gold premium corresponds
roughly with the amount of government notes out
standing in each period. The relatively rapid increase
in the issue of notes after August, 1862, during the last
months of 1863, and again 'during the last months of
the war, is reflected in the rapid increase of the gold
premium at those three times. When the amount of
outstanding notes remained stationary at the beginning
of 1863, there was a somewhat slower advance of the
gold premium during those months; while the shrink
ing of the outstanding notes during the first half of 1864
is distinctly reflected in a temporary decline of the
premium.
“ In the North during the Civil War the course of gold
premium only remotely suggested the amount of notes
outstanding at any time. The premium rose most
rapidly, or, in other words, the notes sank in value most
rapidly, at the beginning of 1863, recovering again
during the second quarter of that year, declining after
August, 1863, to their lowest point in the summer of
1864, and rising again during the last months of the
war.1 The value of the ‘ greenback’ was much more
a barometer of popular feeling as to the eventual out
come of the war than a gauge of their amount in cir
culation, for the latter did not materially increase after
July, 1863, and certainly not after July, 1864. In fact,
the gold value of the' federal ‘ greenback ’ ran closely
parallel with the gold value of the federal bonds during
the war. This is also true of the confederate bonds and
treasury notes. These two sets of parallel fluctuations
were evidently caused by the changing credit of the two
governments concerned.
1 J. C. Schwab, Confederate States of America, 1861-1865, New
York (Scribner), 1901, table on p. 167.

S ec. 15]

STATISTICAL VERIFICATION

265

“ A general index number for either section, based
both on a simple and a weighted average, can be con
structed. The lines plotted to indicate these two sets
of figures do not run parallel, but converge and diverge
during different periods of the war, converging at those
times when events in the military, the political, or the
financial field discouraged the South, and correspond
ingly encouraged the North in the general belief that
the war was approaching an end; diverging at those
times when,federal reverses, or similar events in other
than the military field, raised the hopes of the South,
and led to belief on both sides that the war would be
protracted.” 1
We thus see that redundancy of issue produces a
rise of prices, not only because of increased quantity, but
because of decreased confidence,2 which affects the
sphere of use of the money and therefore the volume
of trade performed by the money, and accelerates its
velocity.
§ 15
We have given historical instances of the effects on
prices of changes in the precious metals and in paper
money.
There remain to be considered historical instances
of the effects on prices of changes in deposit currency.
The price movements due to changes in deposit currency
usually include those culminations called crises and de
pressions.
The economic history of the last century has been
1 J. C. Schwab, ibid., p. 179.
2 Cf. Wesley Clair Mitchell, History of the Greenbacks, pp. 208 and
210. Also Francis A. Walker, Political Economy, 3d ed.,New York
(Holt), 1888, p. 164.

266

THE PURCHASING POWER OF MONEY

[C h a p .

characterized by a succession of crises. Juglar in his de
scription of the conditions preceding crises mentions the
signs of great prosperity, the enterprise and the specula
tion of all kinds, the rising prices, the demand for labor,
the rising wages, the ambition to become at once rich,
the increasing luxury, and the excessive expenditure.1
A crisis is, as Juglar in fact defines it, an arrest of
the rise of prices. At higher prices than those already
reached purchasers cannot be found. Those who had
purchased, hoping to sell again for profit, cannot dis
pose of their goods.2
Our previous analysis has shown us that, before a
crisis, while prices are ascending, there is a great in
crease in bank deposits; and that these, being a cir
culating medium, accelerate the rise.
It has been pointed out that, with trade international,
the rise of prices, resulting from expansion of deposits,
is also international. Even if, in some of the countries,
deposits should not expand, a rise of the price level
would nevertheless occur. The expansion of deposits
even in one country of considerable size would, by
tending to raise prices there, cause the export of gold.
Thus, in other countries the supply of money would
increase and prices rise also. This would tend to stim
ulate expansion of deposits in these other countries and
bring about a further rise. Even, therefore, if credit
1 Clement Juglar, Des Crises Commerdales 'et de leur Retour
Periodique en France, en Angleterre et aux Etats-Unis, 2 ed., Paris
(Guillaumin), 1889, pp. 4 and 5. See also translation of same deal
ing with United States, by Do Courey W . Thom, A Brief History
of Panics in the United Stales, New York (Putnam), 1893, pp. 7-10.
Juglar is mistaken in adding that interest rates fall during rising
prices. The facts show that they rise, though not sufficiently to
check the excessive lending. See Irving Fisher, The Rate of Interest,
Chapter X IV .
2Juglar, ibid., p. 14.

S ec. 16]

STATISTICAL VERIFICATION

267

expansion did not begin at the same time in all the prin
cipal commercial countries, the beginning of it in one
country would be quickly communicated to others.
For the same reason the arrest of rising prices and the
beginning of falling prices would occur at about the
same time in most of the principal countries. As a
matter of fact this is what we find to be the case. Juglar
has made out a table showing the crises in England,
France, and the United States from 1800 to 1882.1
With the addition of the dates of later crises the table
is as follows: —
F rance

E ngland

1804
1810
1813-1814
1818
1825
1830
1836-1839
1847
1857
1864
1873
1882
1889-1890

1803
1810
1815
1818
1825
1830
1836-1839
1847
1857
1864-1866
1873
1882
1890-1891

1907

U n it e d S t a t e s

1814
1818
1826
1837-1839
1848
1857
1864
1873
1884
1890-1891
1893
1907

§ 16
A study of Juglar’s or Thom’s tables will show that,
in general, bank note circulation and bank deposit cir
culation increase before a crisis and reach a maximum
at the time of the crisis. Index numbers of prices show
the same general trend.
1 Juglar, ibid., charts at end; Thom’s translation, p. 19, brings the
table to 1891.

268

THE PURCHASING POWER OF MONEY

[C hap. X I

Thus,1 for the United States, the crisis of 1837-1839
shows that circulation of state banks increased each year
from 61 millions in 1830 to 149 in 1837 and fell to 116
in the next year; that individual deposits rose each year
from 55 millions in 1830 to 127 in 1837 and fell to 84 the
next year; that from 1844 to 1848, the date of the next
crisis, circulation rose from 75 millions to 128, falling
back to 114 the next year, and that the deposits rose
from 84 millions to 103, falling back to 91; that from
1851 to 1857, the date of the next crisis, circulation rose
from 155 millions to 214, falling the next year to 155, and
that the deposits rose from 128 millions to 230, falling
the next year to 185. These facts— that prices and de
posits rose, culminated, and fell together in reference to
the crises of 1837, 1846, and 1857 — are confirmed by
figures for per capita circulation and deposits given by
Sumner.2 These show the characteristic sharp check to
expansion in the crisis years, mild in the mild crisis of
1846 and pronounced in the more pronounced crises of
1837 and 1857. Corresponding phenomena occurred
at the next crisis, 1863-1864. After this time, the chief
statistics are for national banks, and these show simi
lar results. Thus, from 1868 to 1873, national bank
circulation rose from 295 millions to 341 and then fell,
while in the same period deposits rose from 532 mil
lions to 656 and then fell. Similar, though less marked,
movements occurred in the milder crises of 1884 and
1890, which is the last included in Thom’s tables. The
crisis of 1893 was exceptional and largely confined to
the United States, being chiefly due to the fear as to the
1 See Thom, tables following p. 18.
2 History of Banking in the United States, Vol. I of History of Bank
ing in all Nations, New York (Journal of Commerce), 1896, p. 456.
The figures are taken from 37th Congress, 3d Session, 5 Ex., 210.

Sec. 16]

STATISTICAL VERIFICATION

269

stability of the gold standard without much reference
to currency and deposit expansion.1 Whereas in the
typical speculative cycle the ratio of deposits to re
serves gradually increases until it reaches a maximum
just before the crisis, as it did in 1873,1884, and 1907,
this did not happen in 1893. It is true that the deposits
of national banks were larger in 1892 than in 1890 or
1891, but they were no larger relatively to reserves,
though possibly this fact is to be accounted for by an in
crease of reserves following the slight crisis of 1890-1891.
It is true, also, that the ratio of the deposits of national
banks to reserves was high in 1893, but this was due, not
to an expansion of deposits, for deposits decreased during
that year, but to the runs on the banks and consequent
depletion of their reserves.2 The crisis of 1907, on the
other hand, was, like that of 1857, typically a crisis of
currency expansion. The facts in reference to this crisis
will be discussed more fully in the following chapter.
In France the same tendency of circulation and de
posits to reach a maximum at or about a crisis and recede
immediately afterward is illustrated fairly well,3 es
pecially for deposits.
1 Lauek, Causes of the Panic of 1893, Boston (Houghton, Mifflin),
1907, p. 118. O. M . W. Sprague, in “ History of Crises under the
National Banking System,” National Monetary Commission Report,
Senate Document 538 (61st Congress, 2d Session), points out that
m the runs on banks there was no special demand for gold, and is
inclined to think that the influence of the currency expansion has
been exaggerated.
2For a statistical comparison of this with typical crises, see
article by Harry G. Brown, “ Typical Commercial Crises versus a
Money Panic,’ ' Yale Review, August, 1910.
3Juglar, op. cit.f tables following p. 339 and charts at end.
Juglar calls the crisis of 1873 in France political rather than com
mercial. The statistics of circulation and deposits and their velocity
of circulation (as shown by Pierre des Essars), however, reach a
maximum in 1873 and recede immediately after.

270

THE PURCHASING POWER OP MONEY

[C hap. X I

For the Bank of England we find the same general
correspondence between crises, circulation, and private
deposits.1
§17
Not only do money and deposit currency (M and M')
rise regularly to a maximum at the time of a crisis, but
their velocity of circulation, so far as statistics indicate,
goes through the same cycle. Pierre des Essars has
demonstrated this beyond peradventure, so far as
velocity of circulation of deposits is concerned.2
For the United States we have scarcely any statistics
of velocity of circulation of deposits, but those for two
New Haven banks and for an Indianapolis bank, which
I have secured for the last few years, show a maximum
in the crisis year 1907.
After a crisis, a decrease occurs in M, M', V, and V'.
Bank reserves are increased, and this causes a decrease
in M.
Since, then, currency and velocity both increase
before a crisis, reach a maximum at the crisis, and fall
after the crisis, it is small wonder that prices follow the
same course. That they do is the real meaning of a
crisis. In fact, as we have seen, Juglar defines a crisis
as an arrest of a rise of prices. The index numbers of
prices show the rise, maximum, and slump for almost
every crisis year for which price statistics exist.3
1 Juglar, op. cit., tables following p. 291.
2 “ La vitesse de la circulation,” Journal de la Societe de Statistique
de Paris, April, 1895, p. 148. From 1810 to 1892 in Franco, taking
the thirteen crisis years and the twelve years of “ liquidation,” Des
Essars finds that, without exception, the velocity of circulation of
deposits at the bank of France is a maximum in the crisis years
and a minimum in the years of liquidation.
3 The detailed figures will be seen in the Appendix to the next
chapter (Chapter X II).

S ec. 17]

STATISTICAL VERIFICATION

271

113
228
144
279
160
315
145 / 323
132
294

113.2
.7
114.0
5.3
120.0
6.6
127.9 -1 .7
125.7 --

4.2
4.3
5.7
6.4
4.4

Virtual4 Interest

Money Interest4 New
York Price, m. Twoname 60-day Paper

5.0
5.8
6.2
6.2
5.1

Per Cent5 Rise of
Prices during Year.

658
649
651
692
849

Pi
.2

Index* Number of
Prices, P. (Jan.)

3.31
3.78
4.06
4.32
4.38

Clearings2 (billions)

Ratio1 of Deposits of
National Banks to Re
serves

1904 .
1905 .
1906 .
1907 .
1908 .

Reserves1 of National
Banks (millions)

Year

Deposits1 of National
Banks (billions)

The following figures are designed to present a picture
of the crisis of 1907 in the United States as illustrating
the culmination of a typical credit cycle: —

3.5
- 1 .0
- 0 .9
8.1

We notice, in the first column, a steady and rapid
crease in the deposits of national banks up to, and
cluding, the crisis year. Though deposits for 1908
not decrease, yet they remain almost stationary

in
in
do
as

1 Tho figures for deposits and reserves of national banks are
those given in the Reports of the Comptroller of the Currency, and
represent the condition of the banks at their third report to the
Comptroller (generally about July 1) of each year. The ratio
column explains itself.
2 Tho figures for clearings are taken from the Financial Review
for 1910, p. 33. Those for M 'V ' are constructed from the figures
for clearings by a method explained in § 5 of Appendix to Chapter
X II.
3 Tho index numbers of prices are those of tho Bureau of Labor
(Bulletin 81, March, 1909), and relate to January of each year in
question. The next column, therefore, headed “ Per cent rise of
prices during year” indicates the rise from January of the year in
question to January of the next.
4 The figures for interest rates are taken from the Appendix of
The Rate of Interest, p. 418, brought through 1908 by computations
from the Financial Review. Tho per cent rise of prices is subtracted
from money interest to got virtual interest.

272

THE PURCHASING POWER OF MONEY

[C h a p .

compared with those of the previous year. The second
column, that for reserves, shows, as we should expect,
a large increase in the year after the crisis, the banks
having fortified themselves against the decrease of busi
ness confidence. We find, then (third column), an in
crease in the ratio of deposits to reserves, the highest
ratio being reached in 1906 and 1907, not because re
serves were depleted, — on the contrary, they were
expanding, — but because deposits were expanding
still more rapidly. If the theory presented in Chapter
IV is correct, it is precisely this high ratio of deposits to
reserves, brought about by failure of interest to rise
with rise of prices, which forced the banks to raise their
rates of discount and so check further expansion of
credit. Then came the crisis and the short succeeding
depression. The next column, headed “ clearings,” is
indicative of the volume of check transactions, the circu
lation of deposit currency. As a fairly constant pro
portion of checks is settled through the various clearing
houses of the country, clearings may fairly be regarded
as somewhat of a criterion of M'V'. The fifth column
is derived from the fourth and from other data, and
is intended as an estimate of M'V'. These two col
umns increase through 1906, but (since they relate to
the whole year and not to a point in the middle of the
year) begin to show the effects of the credit slump in the
fall of 1907, so that their growth is arrested somewhat
in that year, and still more in the year after. We
should expect to find, then, a rise of prices reaching a
maximum with 1907 and falling in 1908, and this we do
find in column six. Column seven shows the per cent
rise during each year. Thus, for January, 1904, the
index number or P is 113.2, and for January, 1905, it
is 114.0. The rise, therefore, is a little less than 1 per

S e c . 17]

STATISTICAL VERIFICATION

273

cent. The minus sign signifies a fall. The eighth col
umn is for rates of interest and indicates, as we should
expect, a rise, culminating in 1907. Virtual interest —
that is, the interest in terms of commodities — was ex-'
ceedingly low during the years immediately preceding
1907, because prices were rising so fast. This is shown
in column nine, where the nominal interest (measured
in money) is corrected by the rise or fall of prices to
give interest as measured in actual purchasing power.
With the culmination of the cycle in 1907 and the re
sultant fall of prices, we find virtual interest suddenly
becomes very high. No wonder that borrowing enter
prisers often found it hard to make both ends meet.
The facts as to credit cycles, then, completely con
firm the analysis already given in previous chapters
and indicate that prices rise and fall with cycles of
currency and velocity. For the benefit of those who
doubt whether the expansion of deposit currency raises
prices, or whether the rise of prices creates deposit cur
rency, it may be added that facts, as well as theory,
show that the former relationship is the true one (al
though temporarily, as during 1904-1907, there exists
a reaction of prices on deposits). Miss England has
shown, for instance, that loans and deposits expand be
fore prices rise, and that, though prices often fall before
loans and deposits shrink, this anomalous order of
events is explainable by the revival of trade following
a crisis.1
No attempt has been made in this chapter to review
all the phenomena or even all the typical phenomena
of crises. We are not here concerned with crises
1 Minnio Throop England, “ Statistical Inquiry into the Influence
of Credit upon the Level of Prices,” University Studies (University
of Nebraska), 1907.

274

THE PURCHASING POWER OF HONEY

[C h a p .

except in relation to currency. Our concern is with
the magnitudes entering the equation of exchange, es
pecially M, M', and V', for these are the immediate
elements the variations in which affect the price level
and cause it to rise and fall.
§ 18
This chapter has been devoted to an historical study
of changes in the quantity of currency and of the effects
of these changes on prices. We have seen that, on the
whole, increases in the amount of money have tended
to raise prices from century to century during the last
thousand years, and especially since the discovery of
America. The changes in the last century, or more
exactly, from 1789 to 1909, have been considered in
somewhat more detail, covering five periods of alter
nately rising and falling prices. We have seen evidence
to connect these price movements with changes in the
quantity of money and in the volume of business. The
periods 1789-1809, 1849-1873, and 1896-1909 were
periods of rising prices and large increases of the money
supply. In the period 1809-1849 prices fell presumably
because of a falling off in gold and silver production and
a continuing increase of business; while between 1873
and 1896, although the world’s stock of precious metals
was increasing slowly, prices in gold countries fell,
because in addition to the increasing volume of business
there was a stampede of nations to adopt the gold stand
ard and demonetize or limit the coinage of silver.
We have observed the recent continual increase of
gold production and found reasons for the tentative
prediction that the gold production of the future would
continue excessive and probably cause the present rise
of prices to continue for some time in the future.

Sec. 18]

STATISTICAL VERIFICATION

275

We have described some of the chief examples of paper
money inflation and shown that the records for circula
tion and price changes bear out in a general way the
principles set forth in previous chapters. The paper
money experiences of France during the French Revolu
tion, of England during the Napoleonic wars, of Austria,
the American colonies, the United States, and the Con
federacy have been briefly reviewed. We have noted
that in these cases, as in others, prices depended on the
quantity of money, its velocity, and the volume of busi
ness. We have seen that the apparent exceptions
due to lack of confidence in paper money are not
really exceptions, because lack of confidence works it
self out through the magnitudes in the equation of ex
change. Distrust increases the velocity of circulation,
and decreases the trade performed by the money. We
have shown that the general effect of irredeemable paper
money issues, which are almost always in large quanti
ties, despite pledges to the contrary, has been to raise
prices.
Finally, our study of deposit circulation and crises
has afforded further illustration. Preceding a typical
crisis, there is, in general, a tendency for deposits to
increase and also for their velocity of circulation to in
crease, while prices tend to rise. Following the crisis
comes a decrease in bank deposits and their velocity of
circulation, an increase in bank reserves, with a corre
sponding tendency to diminish money in circulation, and
a fall of prices. In the years of the principal crises
these took place simultaneously in different countries.

CHAPTER X II
STATISTICS OF RECENT YEARS

§1
T h e last chapter was devoted to a brief sketch of price
movements and their causes, in so far as the scanty data
available make even a tentative interpretation possible.
From this telescopic view of the past we turn to a micro
scopic view of the present. We shall confine it to a
study of the events of the last three decades in the
United States. In the study of the last chapter we
found the facts of history to be in accord with the a
priori principles already set forth in the equation of
exchange. But these facts of history were too general
and vague to constitute a quantitative fulfillment of the
equation of exchange. We shall find, however, much
fuller data in the last few decades. We shall see that
the equation of exchange, which has already been
proved a priori, may also be verified by actual statistics
— within at least the limit of error to which the statis
tics are liable.
A good beginning of such a study is afforded by the
pioneer work of Professor Kemmerer, already often re
ferred to. He has estimated1 roughly the chief magni
tudes of the equation of exchange and found that these
conform in a general way to the conditions which the
equation of exchange imposes. For each year, begin1
Money and Credit Instruments in their Relation to General Prices,
New York (Holt), 1909, Book II.
276

S e c . 1]

STATISTICS OF RECENT YEARS

277

ning with 1879 (the year of resumption of the gold stand*
ard), and ending with 1908, he has estimated the total
monetary and check circulation (what we have called
MV and M'V') and the volume of trade (T), and from
these has calculated 1 what the price level ought to
be as determined by these factors, i.e.
This calculated magnitude, which Professor Kemmerer
calls the “ relative circulation of money,” he then com
pares with the actual figures for price levels as given in
statistics of index numbers.
Professor Kemmerer’s calculation is, I believe, the
first serious attempt ever made to test statistically the
so-called “ quantity theory ” of money. The results
show a correspondence which is very surprising when
we consider the exceedingly rough and fragmentary
character of the data employed.
Most other writers who have attempted to test the
quantity theory statistically seem to have been ani
mated by a desire not to give it a fair test, but to
disprove it. They have carefully avoided taking ac
count of any factors except money and prices. It is
not to be wondered at that they find little statistical
correlation between these two factors.2 The virtue
of Professor Kemmerer’s work consists in giving due
attention to factors other than money.
The chief error in his investigation is the assumption
of 47 as the velocity of circulation of money. The true
value, as we shall see, is nearer 18 to 20. But the volume
1 For the details of Professor Kemmerer’s calculations the reader
is referred to his book. A very brief summary and criticism are
given in § 1 of the Appendix to (this) Chapter X II.
2 See e.g. Miss S. M . Hardy, “ The Quantity of Money and
Prices, 1860-1891. An Inductive Study.” Journal of Political
Economy, Vol. 3, pp. 145-168.

278

THE PURCHASING POWER OF MONET

[C h a p .

X II

of money payments, even with Kemmerer’s exaggerated
figure for velocity, is so small when compared with
check payments, that this weakness does not greatly
affect his final comparisons. At my request, Professor
Kemmerer has recalculated his curves on the basis of
18 instead of 47 as the velocity of circulation of money.
The results are given in Fig. 12. If these are com
pared with those contained in Professor Kemmerer’s
book, there will be seen to be little difference.
It is
interesting to observe that when minute comparison is

made the selection of 18 as the estimate of velocity
gives a slightly better agreement between the two
curves than does 47.
The “ coefficient of correlation” between Professor
Kemmerer’s results for P, as directly shown by statis
tics and as indirectly calculated from the other factors
in the equation of exchange, is found, by Professor
Persons 1 of Dartmouth, to be only .23 (or 23 per cent
of perfect correlation), with a probable error of .13.
As Professor Persons says, this is a very low degree of
correlation.
1 “ Quantity Theory as tested by Kemmerer,” Quarterly Journal
of Economics, February, 1908, p. 287.

Sec. 1]

STATISTICS OF RECENT YEARS

279

But Persons’s method of testing agreement by means
of a coefficient of correlation is not really applicable to
two curves representing magnitudes changing in time.
For it practically ignores a most essential factor, their
order in time. A year-to-year comparison is better.
If we consider the curves of prices and of “ relative cir
culation,” 1we see at a glance that almost every succes
sive change in direction in the one curve is matched by a
corresponding change in direction in the other. In fact,
out of 28 such possible coincidences, we find the actual
number to be 16 cases of agreement in the changes of
direction, 9 cases of disagreement, and 3 cases of a
neutral kind {i.e. cases which showed no change of
direction in one of the two curves).
The above figures relate to the curves in Professor
Kemmerer’s book. The later curves employing 18
instead of 47 for money-velocity show about the same
results, there being 16 cases of agreement, 8 cases of dis
agreement, and 4 cases of a neutral kind. The corre
spondence here between prices and “ relative circulation ”
is very slightly greater than before. In both sets of dia
grams the agreements are not only much more numerous
but much more pronounced than the disagreements.
Finally, some of the disagreements seem to be really
agreements, disguised by being shifted forward one year.
Thus, the inflections of 1899, 1900, 1901, for “ relative
circulation,” although all counted as cases of disagree
ment, are strikingly similar respectively to the inflec
tions of 1900, 1901, 1902, for “ general prices.” From
the fact that the statistics are partly for calendar and
partly for fiscal years, such one-year shifting of corre
spondence is to be expected, as Professor Kemmerer
points out.
1Kommerer, op. c i t p. 149.

280

THE PURCHASING POWER OF MONEY

[C h a p .

X II

§2
I shall now attempt to make as precise statistical
estimates of the magnitudes in the equation of exchange
for the years 1896-1909 as the data available will allow.
This period — 1896-1909 — is selected chiefly because
its two end years afford the only known data making
possible an estimate of velocity of circulation of money
and of bank deposits.
The magnitudes will be considered in the order
M, M', V', V, T, P. For each the figures to be used
are new.
M. The following table gives the estimated amount of
money in circulation in the United States. By this
we mean the total amount of money (coin and paper)
outside of the federal treasury and outside the banks
of deposit and discount (national, state, private and
trust companies). The treasury stock is excluded be
cause it is a hoard which does not become adjusted
to needs of payment in the sense — or at any rate in the
degree — that the stocks in merchants’ tills and in
people’s pockets become adjusted. The bank reserves
are excluded because, as we have shown, they are used
for banking operations, not commercial purchases.
E stim a ted M o n e t in C i r c u l a t i o n in t h e U n ite d S t a t e s (M )
(in B i l l i o n s op D o l l a r s )

1896
1897
1898
1899
1900
1901
1902

.
.
.
.
.
.
.

....................... 87
....................... 88
....................... 96
. . . . 1.03
. . . . 1.17
. . . . 1.22
. . . . 1.26

1903
1904
1905
1906
1907
1908
1909

...........................1.38
.......................... 1.37
.......................... 1.45
.......................... 1.59
.......................... 1.63
.......................... 1.63
.......................... 1.63

This table is based on the official estimate of money
in the United States, which includes money in banks and

S ec. 2]

281

STATISTICS OP RECENT YEARS

in the federal treasury. These official figures are then
corrected by means of recent revisions of the estimates
of the gold in the United States, and by deducting the
money in the federal treasury and the estimate of money
in banks reporting and unreporting.1 The results differ
somewhat from the official figures for so-called "money
in circulation,” the chief reason for the discrepancy being
that these official figures include money in banks. The
figures here given are probably nearly correct; the prob
able error may, I believe, be assumed to be within 2 or
3 per cent.
The table shows that, during the space of thirteen
years between 1896 and 1909, the money in circulation
has nearly doubled and that its increase has been almost
uninterrupted.
M'. The following figures for M' are estimates of
individual deposits, subject to check.
I n d iv id u a l D e p o s its s u b je c t t o C h e c k (AT ) 2 (in B i l l i o n s op
D o lla r s )

1896
1897
1898
1899
1900
1901
1902

.
.
.
.
.
.
.

2.68
2.80
3.19
3.90
4.40
5.13
5.43

1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
.

5.70
5.80
6.54
6.84
7.13
6.60
6.75

These figures are based on the official figures for "in
dividual deposits,” but are much less than these, owing
to the fact that the official figures include deposits in
savings banks and other deposits not subject to check,
as well as to several other minor causes. The estimates
here given constitute the first attempt to give a series
. * For details as to the construction of the table, see § 2 of Ap
pendix to (this) Chapter X II.
s For the method of estimating these figures see § 3 of Appendix
to (this) Chapter X II.

282

THE PURCHASING POWER OF MONEY

[C h a p .

X II

of figures for the bank deposits subject to check in the
United States. It was made possible through the kind
cooperation of the National Monetary Commission
and its expert, Mr. A. Piatt Andrew.1
These figures give, therefore, the actual deposit cur
rency of the United States. They show an enormous
growth of bank deposit currency. In the space of
thirteen years (between the beginning and the end of the
table) it has nearly trebled. Moreover, each year shows
an advance over the preceding year, excepting only the
year 1908 following the crisis of 1907.
§ 3
Haviiig found M and M', the circulating media, we
next proceed to ascertain V and V’, their velocity of cir
culation. We shall find it convenient to consider the
latter first.
The velocity of circulation of bank deposits is found
by dividing respectively the total check circulation
(M'V') by the bank deposits (M'). The divisor, M',
has already been found. As to the dividend, M'V', this
is practically the total checks drawn in a year, for we
may reasonably assume that, on the average, each check
circulates against goods once and but once.2
For two years, 1896 and 1909, thanks to the efforts of
Professor Kinley of the University of Illinois, we have
voluminous and unique data collected originally for the
purpose of calculating the ratio of money-transactions
to check-transactions in the United States, i.e. the ratio
of MV to M’ V’ . We shall see that these data, in con
junction with other official statistics, are sufficient for
something more important than computing this ratio;
1 For details see § 3 of Appendix to (this) Chapter X II.
1 Cf. Kemmerer, op. c i t p. 114.

S ec. 3]

STATISTICS OF RECENT YEARS

283

for they enable us to calculate with a tolerable degree
of exactness the magnitudes V andF' for both the years
mentioned. We shall find incidentally that, with the
aid of these magnitudes, it is possible to work out more
exactly than in the investigations above mentioned the
very magnitude for which these investigations were
undertaken, viz. the ratio of money-transactions to
credit-transactions.
We need first to estimate M'V'.
M'V'. Professor Kinley’s special investigation of
1896 indicates that on “ the settling day nearest July 1,
1896,” the value of the checks deposited was about
$468,000,000. If we could assume that this day was an
average day for the year, we should need, in order to
obtain the total year’s deposits of checks, simply to
multiply this by the number of settling days in 1896,
which was 305.1 But it happens that July 1 is an excep
tionally heavy day in the deposit of checks. Making
allowance for this fact, as indicated by the clearings of
the New York clearing house, we conclude that the
total year’s deposits of checks in 1896 was about 97 bil
lions, with a probable error of some 5 or 6 per cent.2
Similar calculations for 1909 make the total check trans
actions of that year 364 billions.3 We have thus the
value of the total check circulation {M'V') in the two
years 1896 and 1909, and find them to be 97 and 364
billions respectively, indicating a prodigious growth in
thirteen years. We have still to interpolate figures for
intervening years. For the period between these two
years, we have, unfortunately, no such data as those of
1 This multiplication gives $143,000,000,000, which figure is used
by-Professor Kemmerer (op. cit., pp. 110-111).
2 Tho method of reaching this result is described in § 4 of Appen
dix to (this) Chapter X II.
* See § 4 of Appendix to (this) Chapter X II.

284

THE PURCHASING POWER OF MONEY

[C h a p .

X II

Professor Kinley for 1896 and 1909. However, we can
find an excellent barometer in the clearing house trans
actions,— a barometer dependent partly on the clearings
in New York City, but more on those outside of New
York City. It is well recognized that, although the
clearings in New York deserve an exceedingly large
representation, their relative importance in the total
clearings is exaggerated.1
On the question, therefore, “ What relative impor
tance should be given respectively to clearings in New
York and to the outside clearings in order to get the best
barometer of the check transactions for the entire coun
try ?” we conclude that, if the outside clearings be
multiplied by five and the result added to the New York
clearings, we shall have a good barometer of check
transactions for the United States.2
By means of this barometer of check transactions,
consisting of New York clearings plus five times the out
side clearings, and our knowledge of the actual check
transactions of 1896 and 1909, we may easily derive
from the “ barometer” an estimate of the actual check
transactions. The result is as follows: —
E s tim a te d C h e c k T r a n s a c t i o n s { M ' V ) (in B i l l i o n s op
D o l l a r s ) 1896-19093

1896
1897
1898
1899
1900
1901
1902

.
.
.
.
.
.
.

97
106
127
166
165
208
222

1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
..

.
.
.
.
.
.
.

..................... 223
..................... 233
..................... 282
..................... 320
..................... 320
..................... 300
..................... 364

1 See e.g. the remarks on these clearings in Financial Review for
1910, p. 33, and in Babson’s Business Barometers (Wellesley Hills,
Mass.), 1910, p. 188.
* See § 5 of Appendix to (this) Chapter X II.
J See § 5 of Appendix to (this) Chapter X II.

Sec . 4]

285

STATISTICS OF RECENT YEARS

The probable error of the figures between 1896 and 1909
may be set at some 5 to 10 per cent.
V'. Having obtained estimates of M'V' and having
previously obtained estimates of M', it is easy, by simple
division, to obtain V . The results are as follows: —
E stim ated V e l o c i t y (V') o f C i r c u la t io n , b y C h eck s, o f D e
p o s its S u b je c t t o C h e ck

1896 . . .
1897 . . .
1898 . . .
1899 . . .
1900 . . .
1901 . . .
1902 . . .

.
.
.
.
.
.
.

36
38
40
43
37
41
41

1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
.

39
40
43
47
45
46
54

The probable error in these figures may be set at some 5
to 10 per cent, being least for 1896 and 1909 and greatest
midway between.
We note that the velocity of circulation has increased
50 per cent in thirteen years and that it has been sub
ject to great variations from year to year. In 1899 and
1906 it reached maxima, immediately preceding crises.
These results correspond to those of Pierre des Essars
for the rates of turnover of deposits in continental
banks already noted, except that he usually finds the
maximum in the crisis year itself rather than the year
before. It is to be noted that the figure for 1909 is
much the highest in the table. Whether it portends an
approaching crisis, time will determine.
§4

MV. Our next quest is for the velocity of circular
tion of money. The calculation of the velocity of circu
lation of money presents great difficulties, — difficulties
which, in fact, have usually been considered insurmount

286

THE PURCHASING POWER OP HONEY

[C h a p .

X II

able. This opinion was well expressed by Jevons,1
who wrote:
“ I have never met with any attempt to determine in any coun
try the average rapidity of circulation, nor have I been able to
think of any means whatever of approaching the investigation of
the question, except in the inverse way. If we know the amount of
exchanges effected, and the quantity of currency used, we might
get by division the average number of times the currency is turned
over; but the data, as already stated, are quite wanting.”

As we shall see, however, data now exist, capable of
revealing the “ amount of exchanges effected,” or, MV.
In fact, this is equal to the total money deposited
in banks, plus the total money-wages paid, plus a small
miscellaneous item. From MV and M it is of course
easy to obtain V by division.
The formula for obtaining MV is as simple as it may
at first seem mysterious. The chief peculiarity of the
method which this formula represents, and the feature
which adapts it to practical use, is that it utilizes bank
records and other ascertainable statistics as a means of
discovering the total value of money transactions. The
method is based on the idea that money in circulation
and money in banks are not two independent reservoirs,
but are constantly flowing from one into the other, and
that the entrance and exit of money at banks, being a
matter of record, may be made to reveal its circulation
outside.
It is obvious how the bank-record would be read, were
it true that every dollar withdrawn from banks cir
culated once and only once before being redeposited.
Under these circumstances the annual flow of monetary
circulation would exactly equal the annual withdrawal
1 Money and the.'Mechanism of Exchange (London), p. 336.

Sec. 4]

STATISTICS OP RECENT YEARS

287

from banks prior to circulation, as well as the annual
deposits in banks subsequent to circulation.
Since we have a record of the first and last steps of
the three, viz. the withdrawals and the deposits, we
possess the means of knowing the intermediate step,
the exchange of money for goods. The ordinary circula
tion of money, — excluding cases where it changes
hands more than once between withdrawal and rede
posit, — is equal to the money-flow through banks.
The complete facts, however, are not so simple, for
the reason that money withdrawn from banks is often
circulated more than once. Yet the complications
involved follow definite laws. They do not destroy the
value of the bank record, but merely make it somewhat
more difficult to read. We propose to show (1) that in
actual fact much money circulates out of bank only once,
as in the hypothetical case just mentioned; (2) that when
it is paid for wages, it usually circulates twice; and (3)
that only rarely does it circulate three or more times
before completing its circuit back to the banks.
This statement means that, like checks, money circu
lates in general only once outside of banks; but that
when it passes through the hands of non-depositors
(which practically means wage-earners) it circulates
once more, thus adding the volume of wage payments to
the volume of ordinary money circulation, which, as we
have seen, is equal to the flow of money through banks.
We falsely picture the circulation of money in modern
society when we allow ourselves to think of it as consist
ing of a perpetual succession of transfers from person to
person. Were it such a succession, it would be, as Jevons
said, beyond the reach of statistics. But we may
form a truer picture by thinking of banks as the home
of money, and the circulation of money as a temporary

288

THE PURCHASING POWER OF MONEY

[C h a p .

X II

excursion from that home. If this description be true,
the circulation of money is not very different from the
circulation of checks. Each performs one transaction
or, at most, a few transactions, outside of the bank, and
then returns home to report its circuit.
As is shown in the Appendix, the total money de
posited in banks in 1896 amounted to nearly 10 billions of
dollars,1 and the total expenditures of non-depositors
to nearly 6 billions, of which 4§ billions constituted
the expenditures of wage-earners; the remaining item
in the formula for circulation amounted to less than
1 billion, making about 16 billions for the total cir
culation.
For 1909 the corresponding figures are: money de
posited, 21 billions; expenditures of non-depositors, 13
billions; and the remaining item about 1 billion, making
35 billions in all.
The following table summarizes these results in bil
lions of dollars:2—

1st term (money deposited in banks)
. . .
2d term (expenditure of “ non-depositors ” ) .
Remaining i t e m ...............................................
T otal

..............................................................

1896

1909

106116 +

21
13
1
35

1 For a fuller account of the method of estimating the velocity
of circulation of money and its statistical application, see § 6 of the
Appendix to (this) Chapter X II, which consists, with revisions and
additions, of an article of mine published in December, 1909, in
the Journal of the Royal Statistical Society on “ A New Method of
estimating the Velocity of Circulation of M oney.” The additions
incorporated in the Appendix (§§ 7, 8) include the statistical de
tails of the calculations for the United States.
2 For details as to the figures in this table, see § 7 of Appendix
to (this) Chapter X II.

Sec. 4]

STATISTICS OF RECENT YEARS

289

V. In order to obtain the velocity of circulation, the
total circulation, MV (16 billions for 1896, or to be more
exact, 16.2 billions), must be divided by the amount of
money, M, circulating in 1896. This amount is estimated
at $870,000,000. Hence the velocity is 16,200,000,000
870,000,000 = 18.6, or about 19 times a year. In other
words, money was held on the average about 365 -s-19,
which amounts to 19 or 20 days. If I have made as
full allowance for error as I believe has been made, the
error in this estimate does not exceed two or three days.
For 1909 the velocity of circulation is estimated as the
total circulation (35.1 billions) divided by the money in
circulation (1.63 billions), which is 21.5+; that is, about
22 times a year, or once in 17 days. We conclude that
the velocity of circulation of money in 1896 and the
velocity in 1909 were about 19 and 22 times respec
tively, with a probable error judged to be about 2 in
1896 and not much more than 1 in 1909.
These results would assign money a slower circulation
than most of the estimates or guesses which have been
made. We must remember, however, that such persons
as economists, who are most apt to think about the circu
lation of money, have a rapid turnover. They are usu
ally city dwellers and the comparatively well to do, who,
as we know, do not keep their cash inactive long,
laborers, especially thrifty laborers and laborers paid
monthly, will keep cash on hand for several weeks with
out spending it. Farmers and others living in sparsely
settled districts will even keep it for months. Probably
the velocity of circulation of money differs widely
among different classes and different localities.
We may now compare the years 1896 and 1909 in
respect to money in circulation, deposit currency, their
velocities, and their total circulation as follows: —
u

290

THE PURCHASING POWER OF MONEY

(1)
1896
1909

(2)

(3)

(4)

(5)

(6)

.87
1.63

2.68
6.75

19
22

36
54

16
35

[C h a p .

X II

(8)

(7)

M 'V ' M V + M 'V '

97
364

113
399

Our next task is to interpolate estimates for V between
19 in 1896 and 22 in 1909. The results are given in the
following table: —
E stimates

1896
1897
1898
1899
1900
1901
1902

19
19
20
■ 22
, 20
22
22

.
.
.
.
.
.

V , 1896

19091
21
21
22
22
21
20
22

1903
1904
1905
1906
1907
1908
1909

§ 5
We have now finished our statistical review of the
magnitudes M, M', V, V on the left side of the equation
of exchange, and have remaining only the two magni
tudes P, T, on the right side of the equation.
First we shall consider T. The results of our calcula
tions are given in the following table, which expresses
the volume of trade in billions of dollars as reckoned at
the prices of 1909:—
E stim ated V olume

T rade (in B illion s

1896
1897
1898
1899
1900
1901
1902

.
.
.
.
.
.
.

,.
,.
.
,.
,.
.
,.

.
.
.
.
.
.
.

209
239
260
273
275
311
304

D ollars

P rices

1909)
1903
1904
1905
1906
1907
1908
1909

................................335
................................324
................................378
................................39G
................................412
................................381
................................399

1 For the method of calculating this table see § 8 of Appendix
to (this) Chapter X II.

Sec. 5]

STATISTICS OF RECENT YEARS

291

The tabic is constructed by averaging the index num
bers of the quantities (not the values) of trade in various
lines. The figures representing trade are based on data
for 44 articles of internal commerce, 23 articles of im
port and 25 of export, sales of stocks, railroad freight
carried, and letters through the post office. The final
figures are so adjusted that the figure for 1909 shall be
399; namely, the actual money value of transactions in
that year as worked out on the other side of the equa
tion (i.e. MV + M'V'). Relatively to each other, the
numbers for T are independent of the other side of the
equation.1
P. The only remaining factor in the equation of ex
change is the index number of prices, P. Theoretically
this could be calculated from the other five magnitudes
already evaluated, provided all our previous calculations
could be depended upon for absolute accuracy. But
there are possible errors in all the magnitudes M, M',
V, V', T, and such errors, should they exist, would be
registered cumulatively in P. It is important, therefore,
to check such an indirectly calculated value of P by
directly calculated statistics. By so doing we are able
to compare the P directly calculated and the P in
directly calculated. In like manner, we might, if desired,
compare the directly and indirectly calculated values
of M, M', V, V', and T. We shall confine ourselves to
comparing the two values of P, since it is P which, as
we have seen, is really dependent on the five other fac
tors in the equation of exchange. The values of P (in
cluding prices of commodities, securities, and labor),
directly calculated in terms of the figures for 1909, as
100 per cent, are as follows: —
1 For tho exact method (necessarily laborious) of constructing this
table see § 9 of tho Appendix to (this) Chapter X II.

292

THE PURCHASING POWER OP MONEY

I n de x N umbers

1896
1897
1898
1899
1900
1901
1902

.
.
.
.
.
.
.

63
64
66
74
80
84
89

[C h a p .

XII

G en e r al P rices

1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
.

. . . .
.
.
.
.

.
.
.
.

87
96
97
92
100

This table is based on the figures of the Bureau of
Labor for wholesale prices. It differs slightly from the
Bureau of Labor figures owing to the fact that we here
include prices of securities and wages.1
It remains to compare these actual statistics for P
with P as computed indirectly from the other magni
tudes in the equation of exchange. This calculation
and comparison will be given in the following section.

§6
We have now calculated independently the six magni
tudes of the equation of exchange for the fourteen years
1896-1909. But, as already stated, we know that these
six magnitudes are mutually related through the equa
tion of exchange. The question arises whether the
magnitudes as calculated will actually fulfill approxi
mately the equation of exchange.
One way of testing this question is that adopted by
Professor Kemmerer; namely, to compare the statis
tics for any one factor (say P ), as above directly calcu
lated, with what it would be as indirectly calculated
from the five other magnitudes in the equation of ex
change. The following table shows the value of P as
obtained in these two ways: —
1 For the method of constructing this table see § 10 of Appendix
to (this) Chapter X II.

Sec.

293

STATISTICS OF RECENT YEARS
I n d e x N u m b e r s o f P r ic e s a s C a l c u l a t e d

D irectly
(P)

Indirectly
^ F + M '7 'j

1896

.........................................................

1897

.........................................................

1898

.........................................................

1899

.........................................................

1900

.........................................................

1 9 0 1 .........................................................
1902
.........................................................

1903

.........................................................

1904

.........................................................

1905

.........................................................

1906

.........................................................

1907

.........................................................

1908

........................................................

1909

.........................................................

100

The agreement between the two sets of figures is
visualized in Figure 13.
The two values as shown by the upper and lower

F jq . 13.

294

THE PURCHASING POWER OF MONEY

[Chap.

XII

curves agree with each other remarkably well.1 The
closeness of their agreement may be expressed in several
ways. One way is to count the agreements and dis
agreements in their changes of direction or inflections.
Out of 12 inflections in each curve the two agree six
times, disagree three times, and are neutral three times.
Another method is that employed by Professor Pearson.
This method consists in calculating what Professor
Pearson calls a “ correlation coefficient.” It shows an
agreement of 97 per cent of perfection as compared
with 23 per cent which Professor Persons of Dart
mouth found for Professor Kemmerer’s figures2 for
1879-1901. But, as already stated, a coefficient of cor
relation for successive data is apt to be misleading. If,
in the case of Professor Kemmerer’s figures, the coeffi
cient .23 was an understatement of the parallelism
between his curves, the coefficient .97 overstates the
parallelism between mine. This overstatement is
always likely to result when both of the curves to be
compared rapidly ascend or descend.3
The proper method of applying a coefficient of cor
relation to successive data appears to be to calculate
1 The intermediate curve will be explained later.
2 “ Quantity Theory as tested by Kemmerer,” Quarterly Journal
of Economics, 1907-1908, p. 287.
3 E.g. Persons finds a coefficient of .98 for the correlation between
Kemmerer’s figures for bank reserves and money in circulation
inclusive of bank reserves, although the two magnitudes do not show
any very great agreement between fluctuations in successive years,
but only a general agreement in tho fact that both ascend rapidly.
The coefficient for Professor Kemmerer’s figures for P will be much
higher, if instead of taking the period beginning with 1879, which
includes many years in which prices do not greatly change, we take
the period beginning at the same time as my own figures begin, viz.
1896. The correlation coefficient for Kemmerer’s figures 1896-1908
is 83 per cent, which is far higher than that obtained by Persons for
the period beginning in 1879.

S ec. 6]

STATISTICS OF RECENT YEARS

295

the coefficient, not for the raw figures, but for their
successive year-to-year ratios. In other words, we
tabulate and compare the ratios of each year’s P to the
MV + M'V'
preceding year’s P and of each year’s ------ ^ -------- to
the preceding year’s

^ ‘

If the two sets of

ratios should rise or fall together, the curves would show a
close parallelism or agreement in their successive changes
of direction. As a matter of fact, the results of this
method show a coefficient of correlation of 57 per cent
(or .57 ± .10, where .10 is the probable error). This
figure, 57 per cent, is a moderately high coefficient of
correlation.1 We may conclude, therefore, that the
“ quantity theory” is statistically verified to a high
degree of correlation.2
It is to be emphasized that the coefficients of correla
tion as just given compare the price level with what it
should be according to the statistics of the five magni
tudes on which, by the so-called quantity theory, it is
dependent. The correlation would be less if instead of
these five magnitudes only one were taken. Thus the
coefficient of correlation for 1896-1909 as between
money, M, and prices, P, by the year-to-year-ratio
1 For instance, no one would deny that the length and breadth
of nuts are highly correlated. The coefficient of their correlation is
57 per cent. The height of a man and the breadth of his face are
correlated to tho extent of 35 per cent.
2 Incidentally we may here compare the relative degree of corre
lation of Professor Kemmerer’s figures and of my own. For this
purpose we take the period 1896-1908, which is the longest period
common to both investigations. For these years tho coefficient for
my figures is 54 per cent (or .54 ± .11) as against 37 per cent (or
•37 ± ’ .14) for Kemmerer’s. These are by the method of year-toyear ratios. B y the method of raw figures my correlation is 95 per
cent and Kemmerer’s, 83 per cent.

296

THE PURCHASING POWER OF MONEY

[C hap. X I I

method is 43 per cent (or .43±.13).1 Even this is a
moderately high degree of correlation.
If the opponents of the “ quantity theory” who at
tempt to disprove any relation between money and
prices by pointing out the lack of statistical correspond
ence between the two mean merely that other factors
besides money, M',V, V', T, change from time to time
and that therefore the level of prices does not in actual
fact vary exactly with the quantity of money, their
contention is sound. But the proposition involved is of
as little scientific consequence as the proposition that
the pressure of the atmosphere does not vary from day
to day in exact proportion to its density. We know
that, temperature being constant, the pressure of a gas
varies directly as its density; but that, as a matter of
fact, temperature seldom is constant. Any critic of
Boyle’s law who should attempt to dispute its validity
on such a ground, however, would merely betray his
ignorance of the real meaning of a scientific law; and if
he should seriously attempt to “ disprove it statistically”
by plotting daily curves of barometric pressure and
atmospheric density, he would subject himself to scien
tific ridicule.
If any one has ever really imagined that the price level
depends solely on the quantity of money, he should
certainly be corrected. But the really important
matter is that students of economics should appreciate
the existence of a law of direct proportion between quan
tity of money and price level — a law as real, as im
portant, and as fundamental in the economic theory of
money, as Boyle’s law of direct proportion between
density and pressure is real, is important, and is funda1 B y the (misleading) direct comparison between M and P tho
coefficient of correlation for 1896-1909 is 97 per cent.

Sec. 6]

STATISTICS OF RECENT YEARS

297

mental in the physical theory of gases. I believe that
the frequent failure to realize the existence of this law is
due largely to the lack of any clear conception of the
magnitudes involved. M and P seem to be the only
magnitudes which some students really understand.
M', V, V’, T are seldom discussed or even mentioned.
But not until the subject is put on a statistical basis, —
in figures which measure actual deposit currency, ve
locities of circulation, and volume of trade, — will these
magnitudes be recognized as having a real existence and
significance.
But, to a candid mind, the quantity theory, in the
sense in which we have taken it, ought to .appear suffi
ciently secure without such checking. Its best proof
must always be a priori, not in the sense which applies
to the proof of abstract mathematical propositions, but
in the sense which applies to the proof of Boyle’s law.
Thus, it is known by induction that the pressure of a
confined gas is caused by the bombardment of its mole
cules on the containing walls. It is likewise known by
induction that the pressure must be proportional to
the frequency of impact, provided the velocities of
the molecules are constant. Finally, it is known that
frequency of impact must be proportional to the num
ber of molecules, i.e. the density of the gas, and that
constancy of velocity implies constancy of tempera
ture. Therefore, it follows that, temperature being
constant, pressure is proportional to density. Thus,
from knowledge gained inductively of the individual
pressures of the molecules which compose the gas,
we may reason out deductively the general pressure
of a gas.
Analogously, from knowledge gained inductively of
individual exchanges — molecules as it were — which

298

THE PURCHASING POWER OF MONEY

[Chap.

XII

compose society’s exchange, we may reason out deduc
tively the general equation of exchange.
Fortunately, just as Boyle’s law has been established
both deductively and inductively, we may now assert
that the equation of exchange has been sufficiently
established both deductively and inductively.
As previously remarked, to establish the equation of
exchange is not completely to establish the quantity
theory of money, for the equation does not reveal which
factors are causes and which effects. But this ques
tion has been answered in Chapter VIII.
§ 7
To those who have faith in the a 'priori proof of
the equation of exchange the real significance of the
remarkable agreement in our statistical results should
be understood as a confirmation, not of the equation
by the figures, but of the figures by the equation.
There are discrepancies in our inductive verification;
but these are all well within the limit of errors of meas
urement. The discrepancies prove that slight errors
exist among the figures; otherwise, they would conform
exactly to the relation prescribed by the equation of
exchange.
Our next task is to examine the discrepancies and lo
cate, so far as possible, the errors involved. The degree
of total mutual discrepancy between the independently
calculated magnitudes is best expressed by the degree
of inequality between the calculated values of MV +
M'V' and PT, which should be equal. That is, PT
divided by MV + M'V' should always be unity. Ac
tual division gives the figures in the column headed
“ original” in the following table. The other column
will be explained presently.

Sec. 7]

299

STATISTICS OF RECENT YEARS

R atio

(1)

1896 .....................................
1897 .....................................
1898 .....................................
1899 .....................................
1900 .....................................
1 9 0 1 .....................................
1902 .....................................
1903 .....................................
1904 .....................................
1905 .....................................
1906 .....................................
1907 .....................................
1908 .....................................
1909 .....................................

M V + M ' Y'

C alcu lated

O b ig in a l

R educed

(2 )

(3)

1.17
1.24
1.18
1.06
1.17
1.11
1.08
1.16
1.06
1.09
1.08
1.13
1.05
1.00

1.06
1.13
1.07
.95
1.06
1.00
.97
1.05
.95
.98
.97
1.02
.94
.89

The figures in column (2) show that the calculated
values of PT are always larger than the calculated
values of MV + M'V’, the excess varying from 24
per cent to 0 and averaging 11 per cent.
But these discrepancies between PT and MV + M'V'
can be substantially diminished merely by changing the
base for measuring prices. This base we have thus far
taken as the price level of 1909. But as the index num
bers have only a relative significance, we are free to
choose any other set of numbers so long as they maintain
the same relative magnitudes. In. accordance with this
prerogative we choose to reduce all the numbers for P
by 11 per cent, this being the average of the original
discrepancies. The result will be to decrease PT by 11
Per cent and to change the series of discrepancies from
those shown in column (2) to (approximately) those
shown in column (3). These numbers vary from 13 per
cent above to 11 per cent below unity. These errors

300

THE PURCHASING POWER OF MONEY

[C h a p .

X II

are very small — far smaller in fact than might have
been expected in view of the incomplete and unreliable
character of some of our data.
The question remains, Where shall we place the blame
for the errors which the small existing discrepancies
indicate? Is the fault with M, M\ V, V', P, or T1

How shall we correct our calculated figures ? We may
conclude on general principles that the smallest correc
tions are the most likely to be right. The smallest cor
rections imply a mutual adjustment between the six
factors, each adjustment being in the direction which
will diminish the existing discrepancy. In this way
each factor, as calculated, is regarded as having some
value, and is given some influence in correcting the

Sec. 71

STATISTICS OF RECENT TEARS

301

others; so that any one factor requires extremely little
change. The changes made in the various factors are
made in proportion to their assumed relative liability to
error.
The results are shown in Figures 14, 15, 16, and the
previous Figure 13, each of which relates to one of the
factors in the equation of exchange as originally calcu
lated and as finally adjusted (dotted lines). When they

F iu . 15.

are all thus adjusted, they conform exactly to the equa
tion of exchange.1
In Figure 14 we see that the alterations made in the
figures for M and M' are so trifling as to be almost negli
gible, being usually much less than 1 per cent. The al
terations in V and V', which are shown in Figure 15,
though somewhat greater, are also small, being usually
1 For tho method of adjustment, see § 11 of Appendix to (this)
Chapter X II.

302

THE PURCHASING POWER OF MONEY

[C h a p .

X II

less than 2 per cent. The alterations in T, as shown in
Figure 16, though still greater than the preceding, are
nevertheless so small and uniform as to preserve an
almost perfect parallelism between the original and the
altered curve. The differences rarely exceed 10 per cent.
The alterations in P are shown in the previous Figure
13, the upper curve representing the original and the

dotted, or middle, curve representing the altered fig
ures for P. Here also an extremely close parallelism
between the original and the altered curves is evident.
The differences rarely exceed 3 per cent.
Certainly the most exacting of critics could not ask
for any greater consistency of results and conformity
to the theory of the equation of exchange than these
statistics show. The corrections which have been found
necessary to bring the six figures as first calculated into
perfect agreement are smaller than the probable error

Sec.

STATISTICS OP RECENT YEARS

303

in those figures themselves. I had — quite antecedently
to any knowledge of how closely the final results would
harmonize — assigned certain rough estimates of the
probable errors. These are noted in the Appendix. The
probable error of M is adjudged to be 2 or 3 per cent; of
M', 2 or 3 per cent; of V, 5 to 10 per cent; of V', 5 to
10 per cent; of P, 5 to 10 per cent; and of IT, 5 to 10 per
cent. In other words, our statistical data were regarded
as only rough or approximate ; yet the final “ doctor
ing” needed to make them agree with each other was, as
has been seen, seldom over 2 per cent, being less than 1 par
cent for M and Mr; less than 2 per cent for V and V'; less
than 3 per cent for P; and less than 4 per cent for T. We
conclude then that the figures fit each other better than
might be expected from their known lack of precision.
The corrections which we have assigned to the va
rious factors are so insignificant that it would be haz
ardous to attempt to explain them specifically. The
errors which they presumably represent might be due
to numerous sources, such as the varying ingredient in
the New York clearing house transactions of bank trans
fers as distinct from ordinary check transactions; or
such as errors or defects in the statistics of trade in grain,
etc.; or such as an over or underestimate of the devia
tion from normal of the particular days in 1896 and 1909
on which the statistics of deposits made in banks were
gathered; or such as over or underestimates of the un
reported deposits, or over or underestimates of the gold
in the United States, or over or underestimates of wages
and of other numerous minor though often conjectural
elements in our calculations.
•The sources of error just mentioned were named
in the order of their probable importance. It is, per
haps, significant that the greatest discrepancies are in

304

THE PURCHASING POWER OF MONEY

[C h a p .

X II

the years 1896-1898, whose data for T were most defect
ive, and in 1900, 1903, and 1907, which were years of
crises or of impending crises.

§8
After making the above named mutual adjustments
among the six magnitudes in the equation of exchange,
we reach the following figures, constituting our final
table of values for M, M', V, V', P, and T; they are the
figures plotted in the dotted curves above given: —
F i n a l l y A d ju s t e d V a lu e s o f
E xch an ge

1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

(a s t o

.88
.90
.97
1.03
1.18
1.22
1.25
1.39
1.36
1.45
1.58
1.63
1.62
1.61
1.69
1.64
1.71

2.71
2.86
3.22
3.88
4.44
5.13
5.40
5.73
5.77
6.54
6.81
7.13
6.57
6.68
7.23
7.78
8.17

18.8
19.9
20.2
21.5
20.4
21.8
21.6
20.9
20.4
21.6
21.5
21.3
19.7
21.1
21.
21.
22.

36.6
39.4
40.6
42.0
38.3
40.6
40.5
39.7
39.6
42.7
46.3
45.3
44.8
52.8
52.7
49.9
53.4

E le m e n ts

E q u a tio n o f

1 9 1 0 -1 9 1 2 , s e e p . 4 9 2 )

60.3
60.4
63.2
71.6
76.5
80.5
85.7
82.6
82.6
87.7
93.2
93.2
90.3
100.0
104.0
102.2
105.3

M 'V '

M V + M 'V f
&
PT

191
215
237
259
253
291
287
310
310
355
375
384
361
387
399
413
450

16
18
2022
24
27
27
29
28
31+
34
35
32
34
34
34
38

99
112
131 —
163
170
208
219
227
228
279+
315
323
294
353
381
388
436

115
130
150
185
194
235
246
256
256
311
349
358
326
387
415
422
474

This table, combining as it does the virtues of all the
independent calculations of M, M', V, V', P, T, with
the corrections of each necessary to make it conform to
the others, may be considered to give the best available
data concerning these magnitudes.
These figures, or the dotted curves in the preceding
diagram, show that money in circulation (M) has nearly

S ec. 8]

STATISTICS OF RECENT YEARS

305

doubled in thirteen years; that its velocity of circular
tion (F) has increased only 10 per cent; that the de
posit currency has nearly tripled and its velocity of
circulation (V') has increased 50 per cent; that the
volume of trade has doubled; and that prices have risen
two thirds.
These results are not surprising, but are, I believe, just
such as we might expect. Nevertheless, almost all are
new. The figures for money in circulation (M) are not
greatly different from those given in official documents
and used by Professor Kemmerer. Likewise the figures
for index numbers of prices are based chiefly on, and are
very similar to, the index numbers for wholesale prices
of the United States Labor Bureau. The statistics for
volume of trade are constructed entirely anew and differ
somewhat from Kemmerer’s, which were their only pre
cursors. The statistics for deposits subject to check
(M') are here published for the first time. The statis
tics of velocities of circulation of bank deposits (V') are
the first statistics of their kind, excepting the statistics
for the activity of bank accounts of European banks.
Finally the statistics of velocity of circulation of money
(F) are the first of their kind.
With these data we are able to form a fairly correct
statistical picture of the circulatory system in the United
States. According to the records of 1909, the money in
actual circulation (M) is 1.6 billions of dollars or $18 per
capita (much less than the official figure given for circu
lation, $35); its velocity of circulation (F) is twenty-one
times a year; the deposit currency (M ') is 6.7 billions or
$74 per capita — fourfold that of money; its velocity of
circulation ( V'), 53 times a year — two and a half
times that of money; the total circulation of, or pay
ments by, money {MV), 34 billions a year; the circula

306

THE PURCHASING POWER OF MONEY

[C h a p .

X II

tion of deposits subject to check or payments by check
(M'V'), 353 billions — ten times as much or nearly a
billion a day. This makes a grand total for business
done at present prices (MV + M'V' or PT) of 387 bil
lions, or more than a billion a day. The size of this
aggregate will probably astonish most readers. In the
absence of actual statistics we have heretofore little real
ized the colossal proportions of our trade. Probably few
persons outside of statisticians would have imagined
that our import and export trade, which has filled so
large a place in our political vision, sinks into utter insig
nificance as compared with the internal trade of the
country. The total exports and imports amount only
to a paltry 3 billions as compared with a total national
trade of 387 billions.
We are now ready to represent the entire set of figures
given in the last table by means of the mechanical illus
tration adopted in previous chapters. This is done in
Figure 17, which shows at a glance the course of all the
six magnitudes for fourteen years, making 84 statistical
figures in all. This mechanical picture visualizes the
increase in prices (lengthening in right arm) which has
been going on during these fourteen years, and at the
same time exhibits the changes in all the five factors on
which that increase of prices depends. All of the six
magnitudes represented are, of course, the corrected ones,
so as to exactly harmonize with each other and make
the two sides of the scales balance.
The steady
growth of the money in circulation is shown in the in
crease in the size of the hanging purse; the similar but
more rapid growth of deposits subject to check is shown
by the increase in the size of the bank book; the lesser
growth in the velocities of these two media of exchange is
shown by the lengthening of the two arms at the left

The weight f # t syrritolizing a purse, represents M , the money in circulation in the United States (i. e. all
money outside

of the U. S. Treasury and the banks).

It is usually between one and two billions.

The leverage of this purse, or its distance from the fulcrum, represents V , the velocity of circulation of money.
Money usually turns over about twenty times a year.
symbolizing a bank, book, represents M , the bank deposits against which checks are drawn

The weight

three to eight billions).
(usually from
The leverage of this bank book represents V J.th e velocity of circulation (“activity”) of these deposits.

The deposits

are usually turned over from forty to fifty times a year.

The weight

symbolizing a grocer's tray, represents T , the volume of trade expressed in “ units,” each

“ unit” being the

quantity which could be purchased for $1 in 1909.

The leverage of this tray represents P .th e index, number of prices measured as a percentage of the prices of 1909.

1897

i|in i m iq n m m q i i i'n m n i n i'fi n n n n |iiin i m|ri

U
nm
iM
nm
nm
nm
niuiiH
T
T
'ntT
pTr^nTm
iiniiiniii^lniM
irnm
iim
nrr-ijp

-4 0

le o

ioo

i||in i )i n i|ilii| iiii| iiH|i i i i|i i i i |i in iii n | iiii; T iiiMi i i ; i ; i n j

i|ii i||ii i i |P

1903

1904.

w
«rV
e,

310

^ fiitiTifiM ii n i iiiiiiiMi|iiii|i i ii|iii i |iii i|iiii|iin|i iM|iii i p ii>|»i|iir»i in y ^T'M||i, ii|,Hni||i riiirT’'nTr

H ii

1111 i n

i n i |]T

1906

HTT- ^ ^ n|ii"|Mrirrni[" " |im^M"|" i|^nti|"rr]riTrnK)i" ii|ii^j^i|!|'in^|
^ ii|TrninTi|" i^ nT:T|Tir^ iH'T^ ~^.

19*07

i111t11111r111 :11iiini
>

TTTTJTTTT]

r11II11!1111111l|IllIJMII]U!I[II111H
111'H
TT]fn I!I!Il|,M
l[;T17-

TIB.

^ILUON

lo " 'l" ' '|lo "',rrTf0 ''"';lo "l"2lo "l"3lo "'"X ...... .........................gg^g

rr^^i|lii'|i"i|'HT[iHTiiT|r[nrrH
Tii;HniH'M
jiin|iin[nr'|mi|^ii|iiii)iiii|'■n|iinrn'j in
1912

F ig .

17.

Sec. 9]

STATISTICS OF RECENT YEARS

307

of the fulcrum. These four factors have all conspired
to increase prices. The only cause resisting the rise is
the growth of trade, which is shown by the increasing
size of the hanging tray at the right and which has
tended to reduce prices.
We have here a complete quantitative picture of the
causes affecting the price level during the last fourteen
years, or, at any rate, of all the -proximate causes;
for, as we have noted, back of the five proximate causes
lie innumerable antecedent causes.
What then, in brief, are the facts of history ? They
are that prices have increased by about two thirds be
tween 1896 and 1909, that this has been in spite of a
doubling in the volume of trade, and because of (1) a
doubling of money, (2) a tripling of deposits, and (3
and 4) slight increases in the velocities of circulation.
§9
There has been much discussion as to the most im
portant causes which have increased prices during re
cent years. It is, therefore, interesting to compare the
four proximate causes which, as we have seen, have alone
tended to increase prices in the period 1896-1909. Per
haps the simplest and best method is to compare the
actual rise of prices with what it would have been if
any one cause of that rise had been absent. That is,
we test the importance of any price-raising factor by
answering the question, What difference does it make
to prices whether that factor is present or absent?
We shall find that the growth of money is by far the most
important cause. The growth of deposits is less impor
tant than appears at first glance. The growth of deposits
would have to be regarded as the most important cause
if deposits could be considered as independent of money.

308

THE PURCHASING POWER OF-MONEY

[C h a p .

X II

But they are not independent. We have seen that,
normally, deposits rise or fall with money in circulation.
Therefore, if deposits had increased just as fast as money
and no faster, we should ascribe the whole increase to
money alone. In that case no part of the rise of prices
would be ascribable to any increase in deposits; for
there would have been no increase except what was due
to the increase in money. The increase of deposits
subject to check can be considered independently of the
increase of money only in so far as the deposits have
increased relatively to money. We have seen that mere
increase of money would of itself normally cause a pro
portionate increase of deposits; only the disproportion
ate increase of deposits should therefore be considered
apart from the increase in money as a cause of rising
prices. Therefore the true method of considering de
posits as a separate cause appears to be to reckon them
M'
relatively to money. That is, not M', but
is
the magnitude to be considered.1
We may therefore consider as the only causes tending
to raise prices during the period 1896-1909, the follow
ing four: —
(1) The increase in money in circulation, i.e. the in
crease in M.
(2) The increase in relative deposits, i.e. the increase
. M'
ln ")T
Mr*
(3) The increase in the velocity of circulation of
money, i.e. the increase in V.
(4) The increase in the velocity of circulation of de
posits, i.e. the increase in V'.
1 See § 1 of Appendix to Chapter III, where this magnitude (rela
tive deposits) is treated and represented by the letter k.

Sec. 9]

STATISTICS OF RECENT YEARS

309

The fifth factor determining the price level, viz.
the factor T has, as we have seen, tended to lower
prices.
We shall now proceed to note what would be the sepa
rate effects on prices of these four price-raising causes
and of the one price-depressing cause.
We wish, then, to know what the price level would
have been in 1909 under the following five conditions : —
(1) If the money in circulation (M ) had not grown
at all since 1896,
M'
(2) If the relative deposits — had not grown at all
since 1896,
(3) If the velocity of circulation of money (V) had
not grown at all since 1896,
(4) If the velocity of circulation of deposits (F') had
not grown at all since 1896,
(5) If the volume of trade ( T) had not grown at all
since 1896,
assuming in each case that all the other four factors
had grown in exactly the way they did grow. We have
taken the actual price level in 1909 as 100 per cent and
shall continue to do so, expressing on this basis what
the price level would have been under each of the five
hypotheses above named. We reach the following
results: 1—
1 Tho calculations needed are obvious and simple. They consist
of substituting, for all tho factors but one in the right side of the
equation P

M V + M ’V
T

, the statistics already
T

obtained for 1909, and for that one factor remaining, the figure for
1896. This one factor remaining is, for the first hypothesis, M ;
for the second, M ' / M ; for the, third, V ; the fourth, V ' ; and the
fifth T,

310

THE PURCHASING POWER OF MONEY

[C h a p . X I I

Were it not for the growth of
(1) Money (M ), the price level of 1909 would have
been 55 instead of 100;
(2) Relative deposits (j^ > the price level of 1909
would have been 77 instead of 100;
(3) Velocity of circulation of money (F), the price
level of 1909 would have been 99 instead of 100;
(4) Velocity of circulation of deposits (V'), the price
level of 1909 would have been 72 instead of 100;
(5) Volume of trade ( T), the price level of 1909 would
have'been 206 instead of 100.
In other words, were it not for the growth of
(1) Money (M), prices would have been 45 per cent
lower;
(2) Relative deposits

prices would have been

23 per cent lower;
(3) Velocity of money (F), prices would have been 1
per cent lower;
(4) Velocity of deposits (V'), prices would have been
28 per cent lower.
(5) Volume of trade ( T), prices would have been 106
per cent higher.
The four price-raising causes may, therefore, be
arranged in the following order of relative impor
tance : —
Except for the growth of V, prices would have been
1 per cent lower than they were.
M'
Except for the growth of
prices would have been
23 per cent lower than they were.
Except for the growth of V', prices would have been
28 per cent lower than they were.

Sec. 10]

STATISTICS OP RECENT YEARS

311

Except for the growth of M, prices would have been
45 per cent lower than they were.
We conclude, therefore, that the growth of the velocity
of circulation of money was a negligible factor in raising
prices; that the relative growth of deposits and their
velocity were large factors; and that the growth of
money was the largest. The importance of the growth
of money as a price-raising factor was, according to the
above figures, almost exactly double that of relative
deposits and a little over 50 per cent greater than that
of their velocity of circulation.
§10
But the full effect of the increase in the quantity of
money is really greater even than these figures indicate;
for we have not included the effect of the overflow of
money abroad, caused by the great increase in Ameri
can bank deposits. Evidently this overflow must be
taken into account; for the other three price-raising
factors, by crowding out money and usurping its place,
have given themselves an exaggerated appearance of
importance. In other words, there has been a greater
increase in money than appears from the United States
figures by the amount which has overflowed into foreign
lands. The United States is only a small part of the
world’s market, and its price level is largely determined
by the world’s price level. Whatever raises prices in
one country tends to raise prices in all countries, and in
the last analysis the only correct way to measure the
relative importance of price-raising causes is to consider
the world as a whole. If the statistics we have worked
out for the United States were typical of the world,
the resulting estimate of the relative importance of the
four price-raising causes would be true of the world.

312

THE PURCHASING POWER OF MONEY

[C h a p .

XII

But there is strong reason to believe that the growth of
deposits and of their velocity played 'a far greater
part in raising prices in the United States than anywhere
else. The reason is that banking is in its infancy in
France and most other countries. It is so unimportant
that even if its rate of growth there were prodigious, it
would still be a relatively insignificant price-raising
factor. We may therefore be certain, humanly speak
ing, that outside of the United States the increase of
prices is even more largely due to the growth of money
(gold) than in the United States.
We conclude, therefore, with much confidence, that
the increase in the world’s gold is chiefly responsible for
the increase in the world’s prices. What has been said
probably explains why, in the last three years, there has
been no actual increase in the quantity of money in cir
culation in the United States. It has been crowded out
or prevented from increasing by the excessively great
increase of our deposits and of their velocity of circula
tion.
But besides the world movements of prices there are
special local movements as well. Anything which in
terferes with trade, like a tariff, tends to make the rise
of prices unequal. There remains, therefore, the ques
tion of such special influences on the American price
level as the tariff, — working out its effects through M.
As we have seen in a previous chapter, the effect of en
acting a protective tariff is to raise the price level of
the “ protected” country by creating temporarily a
“ favorable” balance of trade and thus stimulating im
ports of the money metal and discouraging its export.
This effect ceases as soon as the price level at home has
been elevated enough, relatively to the price levels abroad,
to restore the equilibrium of trade and stop the relative

Sec . 10]

STATISTICS OF RECENT TEARS

313

accumulation of gold in the protected country. There
after the tariff ceases to affect the price level,
except as it interferes with trade and thereby prevents
the price level at home from adjusting itself to the price
levels abroad. This interfering effect may be in either
direction; that is, the price level at home will be ren
dered more independent of foreign price levels than it
would be if trade were free. The tariff merely isolates
the protected country.
During the period under investigation, (1896-1909,
there have been two changes in the tariff, that of 1897,
and the more recent law of 1909. The first represented
an advance over the rates of 1894. This law of 1897
must have tended, therefore, somewhat to restrict im
ports and to raise prices. So far as our prices have
risen faster [than prices have risen in other countries,
like England, in the period here considered, it seems
fair to attribute a part of this additional rise to our
tariff system.
We come finally to the tariff of 1909. This act is
so recent as scarcely yet to have had much perceptible
influence, even if that influence be assumed to have
begun as soon as the act was planned, early in 1909.
There has waged a bitter political controversy over the
question whether it was a revision upward or downward.
The best unbiased opinion seems to be that it was
slightly upward but was chiefly a mere rearrangement
by which some duties were raised and others lowered.
These conclusions of Professor Taussig, Professor Willis,
and others are based on an intensive study of the tariff
schedules.
A review of the statistics of the equation of exchange is
entirely consistent with these conclusions. This consist
ency may not be evident at first glance. On the con

314

THE PURCHASING POWER OF MONEY

[C h a p .

X II

trary, those who claim that duties have been greatly
increased might point to the fact that since the tariff
American prices have risen faster than English prices j1
while those who claim that the revision was distinctly
downward might point to the increase in our imports of
commodities, and the increase in our exports of gold.
But these seemingly discordant facts are reconcilable.
American statistics show that there has been an enor
mous expansion in bank deposits and in their velocity
of circulation in 1909 as compared with 1908. This
would naturally have the effect of raising American
prices, displacing gold, and checking the increase of
money in circulation in the United States, which would
otherwise occur, and correspondingly of encouraging the
import of commodities. The facts agree precisely with
these known tendencies. Prices in the United States have
risen more than in England, the increase in the quantity
of money in circulation has been checked, the export of
gold and the import of commodities have been increased.
Thus we may explain all the facts without assuming
the tariff as a disturbing element.2
It would take us too far afield to discuss all the other
factors which have been held more or less responsible for
the increase in prices. We have already made it clear
1 Beyond 1909 only American figures are available. Those in
the Bulletin of the United States Bureau of Labor show an uninter
rupted rise in prices from Jamiary, 1909, to March, 1910. Between
these dates the index numbers for wholesale pricos rose from 124.0
to 133.8. For a good English-American comparison, see Report of the
(Mass.) Commission on the Cost of Living. Boston, 1910, pp. 26, 56.
2 But, although we cannot justly convict the tariff of raising our
price level in recent years, it is of course true that a reduction in the
tariff would tend powerfully to reduce that level; for, as we have seen,
a tariff wall acts like a dam in keeping up the high level accumulated
by the original imposition of duties.

Sec. 11]

STATISTICS

RECENT YEARS

315

that none of these could influence prices except by in
creasing the quantity of money in circulation, the rela
tive deposits, or their velocities, or by decreasing trade.
As trade has increased greatly, the last possibility may
be ignored.
As to the causes which have increased money and de
posits and their velocities, the most important seem to
be the following: —
(1) The chief cause of the increase of money has been the
increase in gold mining. Bank notes have only slightly
more than kept pace with other money in circulation.
(2) The chief causes of the relative increase in
bank deposits seem to have been those which
have extended banking especially in the South.
The recent banking laws, encouraging the establish
ment of small banks, may have had some part in this
extension.
(3) The chief cause of the increase of velocity of cir
culation, especially of bank deposits, seems to have been
the concentration of population in cities. We have
seen that the larger the town the greater the velocity of
circulation of bank deposits.
§ 11
Throughout this book we have aimed at explaining
the general purchasing power of money, not its purchas
ing power over any particular goods or class of goods.
The problem of the rise in “ the cost of living ” is partly
a general problem of the purchasing power of money,
and partly a special problem of the prices of food, cloth
ing and other costs of “ living.”
With the special
problem we have here nothing to do. But it so hap
pens that the special changes in the cost of living are
very small as compared with the general change in

316

THE PURCHASING POWER OP MONEY

[C h a p .

X II

prices. At any rate this is true of the wholesale prices
of food. The index number of food rose between Jan
uary, 1909, and March, 1910, from 122.6 to 130.9, while
general wholesale prices rose from 124.0 to 133.8; that
is, the special prices of food rose about evenly with the
general rising tide of prices. So far as there was any
difference it was such that the special prices rose slightly
less than general prices. The “ general prices” here
referred to are only wholesale prices and do not include
prices of labor and securities; but the inclusion of these
elements, judging from the statistics as already given
up to 1909, and market reports since that date, would
not materially change the result.
We conclude that the “ rise in the cost of living ” is
no special movement of food prices nor, presumably, of
other particular prices, but is merely a part of the gen
eral movement of prices. The cost of living is swept
along with the general rising tide of prices of all sorts.
It indicates little or no special change in the supply
or demand of special classes of goods, but simply
reflects the fall in the general purchasing power of
money.
These remarks apply not simply to the
months beginning w th January, 1909, but back to
1908. Back of 1908 food prices move somewhat ir
regularly as compared with general prices, but on the
whole maintain an approximately even pace from 1897
to 1909.
The following table gives some interesting by-prod
ucts of our study for the period 1896-1909.
We note from column (2) that deposits (M') have
grown, not only absolutely, but relatively to money
(M), changing, from a little over threefold to a little
over fourfold the money in circulation. The figure for
the panic year, 1907, was the highest but one, and

S ec. 11]

317

STATISTICS OF RECENT YEARS

the drop in the succeeding year was the largest drop
in the table.
Column (3) shows the “ virtual” velocity of money,
based on the idea that the total work of exchange, even
that performed by checks, is really the work, indirectly,
of money. It is simply the quotient of the total ex
change work done, divided by the total money in circula
tion and in banks.
(1)

1896 ..........................
1897 ..........................
1898 ..........................
1899 ..........................
1900 ..........................
1 9 0 1 ..........................
1902 ..........................
1903 ..........................
1 9 0 4 ..........................
1905 ..........................
1906 ..........................
1907 ..........................
1908 ..........................
1909 ..........................
1910 (seo p . 492) . .
1911 “ “
“
• •
1912 “ “
“
• •

(2)

(3)

(4)

(5)

M'
M

V ir tu al
V e l o c it y

'MV
M V +M 'V '

M 'V
M V + M 'V '

80
84
89
103
99
114
115
113
107
125
132
129
107
124
134
131
144

.14
.14
.13
.12
.12
.11
.11
.11
.11
.10
.10
.10
.10
.09
.08
.08
.08

.86
.86
.87
.88
.88
.89
.89
.89
.89
.90
.90
.90
.90
.91
.92
.92
.92

3.1
3.2
3.3
3.8
3.6
4.2
4.3
4.1
4.2
4.5
4.3
4.4
4.0
4.1
4.4
4.7
4.8

•

We note that this virtual velocity of circulation of
money, or its efficiency in providing for exchanges, has
grown about 50 per cent. Its growth has been inter
rupted by occasional slumps, but all of these were trifling
excepting that following the crisis of 1907.
The fourth and fifth columns give the solution of the
much mooted question of the relative importance of
check transactions (M'V') and money transactions

318

THE PURCHASING POWER OF MONEY

[C h a p .

X II

(MV), — a question to which many w r ite r s , including
Professor Kinley, have given much attention. We find
that in 1896 about 14 per cent of the business in the
United States was performed by money and in 1909
about 9 per cent. In other words, checks performed in
1896 about 86 per cent of the total exchange work, and
in 1909 about 91 per cent.1
These figures appear to afford the first fairly precise
determination of the relative importance of check and
money transactions. They confirm the belief2 that the
relative part played by checks in the country’s trans
actions has substantially increased. The prevailing im
pression that they constitute nine tenths of all transac
tions is also seen to be correct.
1 For discussion of these figures, see § 12 of the Appendix to (this)
Chapter X II, where comparison is made with Professor Kinley’s
results.
2 See e.g. Cannon on Clearing Houses among the Reports of the
Monetary Commission, 1910.

CHAPTER X III
'

THE PROBLEM OP MAKING PURCHASING POWER MORE
STABLE

§1
W e have seen that the purchasing power of money
(or its reciprocal, the level of prices) depends exclu
sively on five factors, viz.: the quantity of money in cir
culation, its velocity of circulation, the quantity of
deposits subject to check, its velocity, and the volume
of trade. Each of these five magnitudes depends on
numerous antecedent causes, but they do not depend
on each other except that: —
(1) Deposits subject to check depend on money in
circulation, the two normally varying in unison.
(2) The velocities of circulation of money and deposits
tend to increase with an increase in the volume of trade.
(3) Any two or more of the five factors may be in
directly related by virtue of being dependent on a com
mon cause or causes. Thus, the same invention may
cause an increase in both velocities, or in both money
and trade, or in both deposits and their velocity. To
take an historical case, we know that the growing
density of population has operated to increase all of
the five factors.
(4) During transition periods certain temporary dis
turbances or oscillations occur in all six magnitudes, the
extremes of which are crises and depressions. Normally,
the price level is an effect and not a cause in the equation

319

320

THE PURCHASING POWER OF MONEY

[C h a p .

X I II

of exchange; but during such transition periods its
fluctuations temporarily react on the other five factors,
and especially on deposits. A rise will thus temporarily
generate a further rise, while a fall temporarily operates
in the opposite direction.
The price level, then, is the result of the five great
causes mentioned, normally varying directly with the
quantity of money (and with deposits which normally
vary in unison with the quantity of money), provided
that the velocities of circulation and the volume of
trade remain unchanged, and that there be a given
state of development of deposit banking. This is one
of the chief propositions concerning the level of prices
or its reciprocal, the purchasing power of money. It
constitutes the so-called quantity theory of money.
The qualifying adverb "normally” is inserted in the
formulation in order to provide for the transitional
periods or credit cycles. Practically, this proposition is
an exact law of proportion, as exact and as fundamental
in economic science as the exact law of proportion be
tween pressure and density of gases in physics, assum
ing temperature to remain the same. It is, of course*
true that, in practice, velocities and trade seldom re
main unchanged, just as it seldom happens that tem
perature remains unchanged. But the tendency repre
sented in the quantity theory remains true, whatever
happens to the other elements involved, just as the
tendency represented in the density theory remains true
whatever happens to temperature. ’ Only those who fail
to grasp the significance of what a scientific law really
is can fail to see the significance and importance of the
quantitative law of money. A scientific law is not a
formulation of statistics or of history. It is a formula
tion of what holds true under given conditions. Sta

Sec. 1]

THE PRICE LEVEL CONTROLLABLE ?

321

tistics and history can be used to illustrate and verify
laws only by making suitable allowances for changed
conditions. It is by making such allowances that we
have pursued our study of the last ten centuries in the
rough and of the last decade and a half in detail. In
each case we found the facts in accord with the princi
ples previously formulated.
From a practical point of view the most serious prob
lem revealed by this historical and statistical study is
the problem of stability and dependability in the pur
chasing power of money. We find that this purchasing
power is subject to wide variations in two ways: (1) It
oscillates up and down with the transitional periods
constituting credit cycles; and (2) it is likely to suffer
secular variations in either direction according to the
incidents of industrial changes. The first transition is
connected with the banking system; the second depends
largely upon the money metal.
One method of mitigating both of these evils is the
increase of knowledge as to prospective price levels.
As we have seen, the real evils of changing price levels
do not lie in these changes per se, but in the fact that
they usually take us unawares. It has been shown that
to be forewarned is to be forearmed, and that a fore
known change in price levels might be so taken into
account in the rate of interest as to neutralize its evils.
While we cannot expect our knowledge of the future
ever to become so perfect as to reach this ideal, viz.
compensations for every price fluctuation by corre
sponding adjustments in the rate of interest — never
theless every increase in our knowledge carries us a
little nearer that remote ideal. Fortunately, such in
crease in knowledge is now going on rapidly. The edi
tors of trade journals to-day scan the economic horizon

322

THE PURCHASING POWER OF MONEY

[C h a p .

X III

as weather predictors scan the physical horizon; and
every indication of a change in the economic weather
is noted and commented upon. Within the past year a
certain firm has instituted a statistical service to supply
bankers, brokers, and merchants with records, or “ busi
ness barometers,” and forecasts based thereon, with the
avowed object of preventing panics. Yet it is probably ■
in regard to the fundamental mechanism by which such
forecasts are based that there is the greatest need of a
wider diffusion of knowledge. The range of the ordi
nary business man’s theoretical knowledge is extremely
narrow. He is even apt to be suspicious of such
knowledge, if not to hold it in contempt. The conse
quences of this narrowness are often disastrous, as, for
instance, when, in pursuance of the advice of New York
business men, Secretary Chase issued the greenbacks, or
when the ill-advised legislation to close the Gold Room
was enacted. And it is not altogether in unusual pre
dicaments such as those brought by the Civil War that
the business man’s limitations in knowledge react in
juriously upon him. Every day he is hampered by a
lack of understanding of the principles regulating the
purchasing power of money; and in proportion as he
fails to understand these principles he is apt to fail in
predictions. The prejudice of business men against
the variability of, and especially against a rise of the
rate of interest, probably stands in the way of prompt
adjustment in that rate and helps to aggravate the far
more harmful variability in the level of prices and its
reciprocal, the purchasing power of ’money. The busi
ness man has, in fact, never regarded it as a part of
the preparation for his work to understand the broad
principles affecting money and interest. He has rather
assumed that his province was confined to accumu

Sec. 2]

THE PRICE LEVEL CONTROLLABLE?

323

lating a technical acquaintance with the nature of the
goods he handles. The sugar merchant informs him
self as to sugar, the grain merchant as to grain, the
real estate trader as to real estate. It scarcely occurs
to any of them that he needs a knowledge as to gold;
yet every bargain into which he enters depends for
one of its two terms on gold. I cannot but believe
that the diffusion among business men of the fuller
knowledge of the equation of exchange, of the relation
of money to deposits, of credit cycles and of interest,
which the future is sure to bring, will pay rich returns
in mitigating the evils of crises and depressions which
now take them so often unawares.

§2
But while there is much to be hoped for from a greater
foreknowledge of price changes, a lessening of the price
changes themselves would be still more desirable. Va
rious preventives of price changes have been proposed.
We shall first consider those which are more particularly
applicable to secular price changes, and afterward con
sider those more particularly applicable to the price
changes involved in credit cycles. The secular price
changes are, as we have seen, chiefly due to changes in
money and in trade. There has been for centuries, and
promises to be for centuries to come, a race between
money and trade. On the results of that race depends to
some extent the fate of every business man. The com
mercial world has become more and more committed to
the gold standard through a series of historical events
having little if any connection with the fitness of that or
any other metal to serve as a stable standard. So far as
the question of monetary stability is concerned, it is
not too much to say that we have hit upon the gold

324

THE PURCHASING POWER OP MONEY

[C h a p .

X III

standard by accident just as we hit on the present rail
way gauge by the accident of previous custom as to
road carriages; and just as we hit upon the decimal
notation by the accident of having had ten fingers, and
quite without reference to the question of numerical
convenience in which other systems of numeration
would be superior. Now that we have adopted a gold
standard, it is almost as difficult to substitute another
as it would be to establish the Russian railway gauge
or the duodecimal system of numeration. And the
fact that the question of a monetary standard’ is to
day so much an international question makes it all
the more difficult. Yet, as Professor Shaler, the geol
ogist, has said, “ It seems likely that we shall, within
a few decades, contrive some other means of measur
ing values than by the ancient device of balancing
them against a substance of which the supply is ex
cessive.” 1
I shall not attempt to offer any immediate solution
of this great world problem of finding a substitute
for gold. Before a substitute for gold can be found,
there must be much investigation and education of
the public. The object here is to call attention to
the necessity for this investigation and education,
to examine such solutions as have been already pro
posed and, very tentatively, to make a suggestion which
may possibly be acted upon at some future time,
when, through the diffusion of knowledge, better statis
tics, and better government, the time shall become
ripe.
One suggestion has been to readopt bimetallism. This
has already been discussed in Chapter VII. We were
then concerned, however, chiefly with the, “ mechanics
1 Man and the Earth, New York (DulBeld), 1906, p. 62.

S ec.

IS THE PRICE LEVEL CONTROLLABLE ?

325

of bimetallism” and not its influence on price levels.
We have now to note the claim of advocates of a
bimetallic standard that such a standard would tend
to steady prices.1 As we have seen, by connecting the
currencies of both gold and silver countries, bimet
allism, as long as it continues in working order, has
the effect of spreading any variation of one particular
metal over the combined area of gold, silver, and bime
tallic countries. If variations occur simultaneously in
both metals, they may be in opposite directions, and
neutralize each other more or less completely; while,
even if they happen to be in the same direction, the
combined effect on the whole world united under bi
metallism would be no greater than on the two halves
of the world under silver and gold monometallism re
spectively. Even if bimetallism did not enlarge the
monetary area, it might reduce monetary fluctuations.
Thus a world-wide gold standard might prove more
variable than bimetallism.2 But if the amount of one
metal used in coinage increases faster or more slowly
than business, while the amount of the other maintains
a constant ratio to business, then the use of the two
metals results in less steadiness than would result from
the less variable of the two, though in somewhat more
steadiness than would result from the use of the more
variable.
Two variable metals joined through bimetallism
may be likened to two tipsy men locking arms. To
gether they walk somewhat more steadily than apart,
although if one happens to be much more sober
1 Seo Jevons, Investigations in Currency and Finance, London
(Macmillan),' 1884, pp. 331-333.
* Cf. F. Y. Edgeworth, “ Thoughts on Monetary Reform,’’
(British) Economic Journal, September, 1895, p. 449.

326

THE PURCHASING POWER OF MONEY

iChaf.

XIII

than the other, his own gait may be made worse by
the union.1
The table in the footnote shows that in the seven
teenth and nineteenth centuries the two metals were
about equally unsteady. In the eighteenth century
gold was the more steady. During the first half of the
nineteenth century silver was the more steady, while
for 1851-1890 gold was the more steady. Since then,
silver has been the more steady. On the whole, there
is not much to choose between the behaviors of the two.
Bimetallism, then, even could it be maintained, would
offer but an indifferent remedy for the variations in the
price level, and, moreover, there is always the objection
previously noted that the system may break down.
We then saw that whatever the ratio at which both
metals are to circulate, one metal is likely, sometime, to
be produced in such abundance as completely to fill
the money reservoir, driving the other metal altogether
out of circulation. Such a result may be long in com
ing, but eventually it is practically sure to come.
1 The variabilities of gold and silver production have been calcu
lated by one of my students, Mr. Morgan Porter. He finds the
following mean percentage variations from the mean productions for
each period named: —
G o ld

S il v e r

1601-1701
1701-1800
1801-1900

5 periods of 20 years e a c h ........................
5 periods of 20 years e a c h ........................
5 periods of 20 years e a c h ........................

%
7.8
15.6
69.0

%
7.7
27.4
67.0

1801-1850
1851-1885
1886-1890
1891-1895
1896-1900
1901-1905

5
7
5
5
5
5

52.4
8.1
5.9
13.3
12.3
10.7

22.3
40.8
10.5
6.3
3.4
1.9

periods
periods
periods
periods
periods
periods

of
of
of
of
of
of

10 years e a c h ........................
5 years e a c h ........................
1 year e a c h ........................
1 year e a c h ........................
1 year e a c h ........................
1 year e a c h ........................

Sec. 2]

IS THE PRICE LEVEL CONTROLLABLE?

327

A more important objection remains to be noted.
Since bimetallism, as usually proposed, would greatly
overvalue one of the two metals, the first great effect
of its adoption might be not to steady prices but to
disrupt them and upset the relation of debtor and
creditor. While the great overvaluation of one metal
is not a necessary feature of bimetallism, it has always
been the feature which has made it politically popular.
Thus, the bimetallism advocated in the United States
during the last twenty or thirty years has been a bimet
allism which would grossly overvalue silver. It pro
posed that 16 ounces of -silver should circulate as the
equivalent of an ounce of gold, when during much of
this time it really required 30 or 35 ounces of silver to
be equivalent to one of gold. Such an overvaluation
of silver would mean that silver would be imported
from Mexico, India, China, and other silver countries,
as well as mined in larger quantities and coined in the
United States, thus depreciating the currency both
greatly and suddenly. The proposal was well satirized
by a cartoon in the “ free silver” campaign of 1896
representing the United States as a ship sailing over
Niagara Falls in order to reach smooth sailing below
the falls, — if only it survive the shock of the fall!
Bimetallism is the only scheme of steadying the
monetary standard which has ever secured political
momentum; and even its popularity lay far less in its
potency for ultimately steadying than in its potency
for immediately unsteadying the standard. We now
pass on to consider schemes which have never reached
the stage of practical proposals, but are still wholly
academic. ••
The first is polymetallism, a generalization of bimet
allism. The theory of bimetallism contemplates the

328

THE PURCHASING POWER OP MONEY

[C hap . X I I I

circulation side by side of two metals; that of poly
metallism looks to the contemporaneous circulation of
more than two. So long as several metals could be
maintained in circulation together, the price level might
fluctuate less than if one metal only were used. But
all of the theoretical objections against bimetallism
apply also against polymetallism. One metal would
eventually drive all the others out of a country, or,—
if polymetallism were international, — into the arts.
§3
Recognizing the force of the arguments against bi
metallism (and polymetallism), Professor Marshall has
suggested as a substitute a system which has been called
symmetallism. Under this scheme — symmetallism —
two (or more) metals would be joined together physically
in the same coin or in “ linked bars.” Evidently any
ratio could be used, and neither metal could push the
other out of circulation. The value of the composite
coin would be the sum of the values of its two constit
uents, and the fluctuations in its value would be the
mean of the fluctuations of its constituents.1
Many other schemes for combining metals have been
suggested. Among them are the “ joint-metallisms” of
Stokes and Hertzka, which are kinds of bimetallism at
a variable instead of at a fixed ratio. Another, advo
cated by Walras,2 is the gold standard with a “ silver
regulator,” which is simply the limping standard such
as now prevails in the United States, France, or India
1 See F. Y. Edgeworth, “ Thoughts on Monetary Reform,”
(British) Economic Journal, September, 1895, p. 448.
2“ Monnaie d’or avee billon d’argent regulateur,” Revue de droit
international, December, 1884; reprinted in Etudes d'Economic
'politique appliquce, Lausanne (Rouge), 1898, pp. 3-19.

Sec. 3]

IS THE PRICE LEVEL CONTROLLABLE ?

329

except that the quantity of silver in circulation, instead
of being fixed, would be systematically manipulated by
the government in such a manner as,to keep prices
steady. But these, like symmetallism and bimetallism,
offer a remedy which at best is only partial. For in
stance, in Walras’s scheme, in order to maintain prices,
the amount of silver might need to be reduced to zero
— after which no further regulation would be possible;
or it might need to be increased so far as to expel all
gold, after which the system would be no longer a gold
standard, but would become an inconvertible silver
standard. Worst of all, every one of these proposed
remedies would be subject to the danger of unwise or
dishonest political manipulation.
It is true that the level of prices might be kept almost
absolutely stable merely by honest government regula
tion of the money supply with that specific purpose in
view. One seemingly simple way by which this might
be attempted would be by the issue of inconvertible
paper money in quantities so proportioned to increase
of business that the total amount of currency in circu
lation, multiplied by its rapidity, would have the same
relation to the total business at one time as at any
other time. If the confidence of citizens were pre
served, and this relation were kept, the problem would
need no further solution.
But sad experience teaches that irredeemable paper
money, while theoretically capable of steadying prices,
is apt in practice to be so manipulated as to pro
duce instability. In nearly every country there exists a
party, consisting of debtors and debtor-like classes,
which favors depreciation. A movement is therefore
at any time possible, tending to pervert any scheme for
maintaining stability into a scheme for simple inflation.

330

THE PURCHASING POWER OF MONEY

[C h a p .

XIII

As soon as any particular government controls a paper
currency bearing no relation to gold or silver, excuses
for its over-issue are to be feared.
Even if, in times of peace, these persistent pleas for
inflation could be resisted, it is doubtful if they could
be resisted in time of war. In time of war many
plausible defenses can be given, notably the need of
government supplies. The history of our own country
in this respect is not reassuring. It is natural, there
fore, that such schemes should have gotten in bad
odor. Indeed, their odor has been so bad that many
have impulsively concluded that the “ quantity theory”
which has been appealed to as making possible govern
ment manipulation of prices must be fundamentally
unsound. Experience has shown, however, that the
evil feared need not always be realized.
Another method by means of which government could
theoretically keep the price level more stable is by
confining the primary money to a precious metal, say
gold, and regulating the quantity of this metal in the
currency by means of a system of seigniorage. Thus,
as the supply of gold from the mines increased, and
gold tended to depreciate in value, the value of gold
coin could be kept up by making a continuously higher
charge for coinage, in the shape of seigniorage. This
charge would become higher as gold bullion became
cheaper, in such proportion as to keep the currency in
the same relation with the volume of business, and thus
to keep the level of prices stable. If, later, the annual
production of gold should become very small, and gold,
in consequence, should begin to appreciate in value,
stability might be maintained by a reversal of this
policy, i.e. by gradually reducing the seigniorage so
as to prevent appreciation of the currency. There

Sec. 3]

IS THE PRICE LEVEL CONTROLLABLE ?

331

would, however, be a limit to the power to regulate in
this direction similar to the limit we noted in the case
of Walras’s scheme. The seigniorage could never be
reduced to less than zero. Money can never be ma
terially cheaper than the metal composing it, since the
slightest tendency in this direction will result in coin
being exported or melted into bullion. In a period of
rising prices, regulation would be easy; in a period of
falling prices, regulation might be quite impossible.1
Another plan is a convertible paper currency, the
paper to be redeemable on demand, — not in any re
quired weight or coin of gold, but in a required pur
chasing power thereof. Under such a plan, the paper
money would be redeemed by as much gold as would
have the required purchasing power. Thus, the amount
of gold obtainable for a paper dollar would vary in
versely with its purchasing power per ounce as com
pared with commodities, the total purchasing power
of the dollar being always the same. The fact that a
paper dollar would always be redeemable in terms of
purchasing power would theoretically keep the level of
prices invariable. The supply of money in circulation
would regulate itself automatically. Should money
tend to increase fast enough to impair its purchasing
power, the notes would be presented for redemption
in gold; for under the arrangement assumed, the gold
1 For tho effect of the legal prohibition of exportation see Kemmerer, Money and Credit Instruments in their Relation to General
Prices, 2d Edition, New York (Holt), 1909, p. 39 n. Cf. Kemmerer,
“ Tho Establishment of tho Gold Exchange Standard in tho Philip
pines,” in tho Quarterly Journal of Economics. Vol. X IX , G00-605
(August, 1905) ; Second Annual Report of the Chief of the Division
of- Currency; etc., 14, 15, 2 1 -2 8 ; and “ A Gold Standard for tho
Straits,” II, in tho Political Science Quarterly. Vol. X X I , p. 665-677
(December, 1906).

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which would be given would always have the same
purchasing power. Should the money tend to become
scarce and thus to appreciate, the amount of gold hav
ing unchanged purchasing power would be exchanged
for the notes.
It is true that this scheme, like a simple paper-money
scheme, would be liable to abuse, — but it would have
two practical advantages. Having a metallic basis, it
would inspire more confidence than a pure paper-money
plan, while it would offer less excuse for abuse and less
chance to delude the public. Every change in the
weight of the gold dollar would be definitely measurable,
and would have to be justified to the public. A reduc
tion in weight not fully explained by a fall in prices
would be a clear confession of depreciation.
§4
The next plan to be considered is that advocated by
Professor Marshall and the Committee of the British
Association.1 It is, in essence, the revival of the tabu
lar standard proposed and discussed by Lowe,2 Scrope,3
Jevons,4 and others; a standard which is relatively in
dependent of special legislation. This involves the
passing of a law — first merely permissive — by which
contracts could be expressed in terms of an index num
ber. Such a law would not be necessary, but it might
serve to draw attention to the index method. The
1 See Report of the British Association for the Advancement of
Science, 1890, p. 488, containing a draft of a proposed Act of Par
liament for this purpose.
2 Present State of England in regard to Agriculture, Trade, and
Finance. London, 1622.
3 Principles of Political Economy, London, 1833, p. 406.
4 Investigations in Currency and Finance, London (Macmillan),
1884, p. 122 ; also Money and the Mechanism of Exchange, London,
(Kegan, Paul), 1893, Ch. X X V .

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THE PRICE LEVEL CONTROLLABLE ?

333

money of the country would continue to be used as a
medium of exchange and as a measure of value, but
not as a standard for all deferred payments. The
standard of deferred payments, when advantage was
( taken of the law, would be the index number of general
prices; and contracts involving deferred payment could,
when desired, call for the exchange of a given purchas
ing power, or of an amount of money varying directly
with the index number. To facilitate such a change,
it might be well for the government to inaugurate an
authorized system of index numbers, but government
action would not have to go farther than this, or in
deed, necessarily, so far. The aim would no longer be
to keep the level of prices absolutely stable. Gold or sil
ver or both would furnish the primary money, and their
value would consequently fluctuate with that of the con
stituent metal or metals. But the contracts based on
index numbers would not be affected because made
in terms of the index number. Doubtless the plan
would encounter much opposition,1 but it would ap
peal strongly to certain classes.2 For instance, those
“ living on their incomes” would like to be guaranteed
a stable purchasing power. A widow, or a trustee,
or other long-time investor, would prefer to buy bonds
which guaranteed a regular yearly purchasing power over
subsistence, rather than those which merely promised a
given sum of money of uncertain value. A few prece
dents already exist, suggestive, at least, of what the new
system would be. In England, the “ tithe averages”
have been made to vary with the value of grain, so that
the tithe was in effect so much grain, not so much money;
. . 1 Cf. Francis Walker, Money , New York (Holt), 1891, pp. 157-163.
2 See Joseph French Johnson, Money and Currency, Boston
(Ginn), 1906, p. 175.

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THE PURCHASING POWER OF MONEY

[Chap.

XIII

also the Scotch fiars prices have existed for more than
two centuries for similar purposes, establishing the price
of grain on the basis of which rents contracted in grain
should be paid in money.1
As has been already indicated, government action
looking to this result need not necessarily b e 1taken.
The beginnings of such a plan for “ a tabular standard
of value” could be made at any time by private con
tracting parties, some index number already in vogue,
such as Sauerbeck’s or the Bureau of Labor’s, being
used as a standard. Should the results of such experi
ments, on the whole, satisfy the contracting parties,
others might follow their lead. At first contracts
would be interpreted as having been made in terms
of money except when otherwise provided. A specific
proviso would therefore be required in contracts made in
terms of the index number. If the latter form of con
tract should become more general, however, legislation
could be passed, making the index number the standard
in all cases, except where specifically provided that
payment should be based on a different standard.
It is to be noted that such a custom, however general
it might become, would not do away with the desir
ability of having an elastic currency to respond to
seasonal variations of business. Seasonable readjust
ments of wages, for instance, and of many other prices,
are difficult. Custom tends to establish standards hold
ing through successive seasons. Since there is more
business at some seasons than others, there will be an
element of strain unless there is also an expansion of
credit. An elastic banking system, facilitating creditexpansion, would, therefore, remain a desideratum.
1 See Edgeworth, Reports of the British Association for the Ad
vancement of Science for 1888, p. 182.

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IS THE PRICE LEVEL CONTROLLABLE ?

335

The system of making contracts in terms of the price
level is not intended directly to prevent fluctuations
in price level. Its purpose is rather to prevent these
fluctuations from introducing a speculative element into
business. But an incidental result of the system would
be that fluctuations in the level of prices would be less
than before, because credit cycles would no longer be
stimulated. The alternate abnormal encouragement
and discouragement of loans would cease. Hence, credit
fluctuations would become less, and the level of prices
would be comparatively unaffected by them.1 Even if
panics should occur, accompanied by sharp falls of prices,
they would not be as severe as now. At present, loans
must be liquidated in terms of a given amount of money,
though that money may buy more (or less) at the time
of liquidation than when the loan was contracted, and
though the borrower must dispose of more (or less) com
modities to raise the given amount. He is compelled to
pay, when prices have fallen, on the same basis in terms
of money, and a much higher value in terms of goods,
than when prices ranged higher. Hence failure often
results, credit currency contracts still further because
of the general distrust, and depression becomes more
severe. With payment in terms of purchasing power,
the situation would be altogether different. Falling
prices would neither injure borrowers nor benefit lenders.
On the whole, the “ tabular standard” seems to have
real merit.2 Certainly there could be no material harm
in trying a “ permissive” law. But the tabular standard
is subject to serious if not fatal objections: One is the
1 See Jevons, Money and the Mechanism of Exchange, London

(Kogan Paul), 1893, p. 333.
2See J. Allen Smith, “ The Multiple Money Standard/1 Annals o)
the American Academy of Political and Social Science. March, 1896.

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THE PURCHASING POWER OF MONEY

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X III

fact that it would involve the trouble of translating
money into the tabular standard and would therefore
fail to attract the public sufficiently to warrant its com
plete adoption by any government. Another objection
is that its halfway adoption would really aggravate
many of the evils it sought to correct, and therefore
discourage, rather than encourage, its further extension.
Even were the system adopted in its complete form for
any one country, it would have the disadvantage of
isolating that country commercially, and thus reintro
ducing the inconveniences of an uncertain rate of inter
national exchange. An analogous inconvenience would
arise by its partial adoption in any one country. Busi
ness men naturally and properly prefer a uniform system
of accounts to two systems warring with each other.
They would complain of such a double system of ac
counts in exactly the same way, and on exactly the same
grounds, as they have always complained of the double
system of accounts involved in international trade be
tween gold and silver countries. A business man’s
profits constitute a narrow margin between receipts and
expenses. If receipts and expenses could both be reck
oned in the tabular standard, his profits would be more
stable than if both were reckoned in money. But if he
should pay some of his expenses, such as interest and
wages, on a tabular basis, while his receipts remained
on the gold basis, his profits would fluctuate far more
than if both sides, or all items of the accounts, were in
gold. In fact, his expected profits would often turn into
losses by a slight deviation between the two standards,
in precisely the same way as the importer or exporter of
goods between China and the United States may have
his profits wiped out by a slight variation in the ex
change. In either case, he would prefer to have the

Sec. 5]

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337

same standard on both sides of the account, even if this
standard fluctuated, rather than have two standards,
only one of which fluctuated; for his profits depend
more on the parallelism between the two sides of his ac
count than on the stability of either. It was to escape
the evils from having two standards that, after lengthy
debate and experiment, the present gold-exchange stand
ard was adopted in India, the Philippines, Mexico,
Straits Settlement, Siam, and Panama.
§5
The mention of the gold-exchange standard brings
us to the proposal which is here tentatively suggested, —
a proposal which, it is believed, may one day be found
both practicable and advisable. This plan involves a
combination of the tabular standard with the principles
of the gold-exchange standard.
We have already described briefly the gold-exchange
standard, and given references to other and fuller
sources of information. While the gold-exchange stand
ard purports to be a system of redemption, or partial
redemption in gold of the native coin, yet as a matter
of fact, no gold is necessarily required in the country
itself where the system is in operation. Thus, the
Philippine government does not offer gold for silver
pesos, even when gold is wanted for export to New
York. Instead, it keeps a reserve of gold in New
York, and “ redeems” the Filipino’s pesos in merely a
draft upon this gold. As this draft may be forwarded
to New York, it serves the purpose of gold redemption
for export. The price of the sale includes a premium
on exchange corresponding to the usual excess above
the “ gold point” ; that is, the government charges the
Filipino the equivalent of freight, insurance, and other
expenses on gold to New York.

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THE PURCHASING POWER OF MONEY

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XIII

It will be evident that the gold-exchange system is
only nominally a redemption system. In actual fact,
it is a system of manipulating the silver currency in such
a manner as to prevent its value from diverging from
par with gold by more than the usual premiums on
exchange between gold countries. This manipulation
consists in contracting the currency when the rate of
exchange reaches a certain point above par, and ex
panding the currency when it reaches a certain point
below par. The contraction of the currency is secured
by selling foreign bills of exchange and locking up the
currency received therefor, while the expansion of the
currency is secured by releasing this currency to circula
tion, or, if necessary, by coining more currency.
The successful operation of the system is not only
compatible with, but actually requires, an overvalua
tion of the metallic content of the silver currency. In
fact, in the Philippines it was found necessary to reduce
the silver pesos from 374 grains to 247 grains, to prevent
their disappearance. Without a margin between the
coin-value and the bullion-value of the peso, the power
to regulate its circulation would exist only in one direc
tion— contraction; with such a margin, the power
exists to expand as well as to contract.
After once becoming familiar, the system would
operate just as successfully if the weight of the silver
coins were still further reduced, or, in fact, if a paper
currency were substituted instead. It will be seen,
therefore, that at bottom the gold-exchange standard is
practically the same standard as that which is now in
operation for paper currency in Austria. In that
country the paper is really irredeemable, but is kept
at par by the sale of exchange on London.
The plan by which the bullion content of the coins

Sec. 5]

IS THE PRICE LEVEL CONTROLLABLE?

339

is kept below their value as coins not only prevents
melting and exportation, and the consequent loss of
control of their quantity and value, but also has the
advantage of economy. The reduction of the weight
of the pesos was, in fact, used as a means of defraying
the expense of maintaining the gold reserve and the
other expenses of inaugurating and operating the
system in the Philippines.
The gold-exchange standard was at first regarded
with great suspicion, and its advocates scarcely dared
claim for it any better virtue than that of a practical
makeshift, affording, as it did, a means of easy transi
tion from the previously existing system to the gold
standard, without shock, or introducing an unfamiliar
coinage.
But the results have been so satisfactory that it
may well be asked whether those who devised the
gold-exchange standard did not build better than they
knew. While the system bears a close, though some
what superficial, resemblance to a fiat money system,
it has now little or none of the odium or suspicion
attached to it which we associate with that name.
So simple are the duties of maintaining the goldexchange par, and so unfailingly has the system been
faithfully executed, that even those who at first most
strenuously opposed it seem now inclined to trust it
implicitly. There is, indeed, no reason why, under
almost any conceivable circumstances, there should be
even the fear of this system being abused.
Now that there has been actually constituted a new
form of governmental machinery, which can be as fully
trusted to perform its functions of regulation as the
mint, there seems to be no reason why the system
should not be extended. It is well known that the par of

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THE PURCHASING POWER OF MONEY

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XIII

exchange which has been adopted for the gold-exchange
standard is quite arbitrary, and it must be evident that
this par could be changed. The par of exchange be
tween the English and Indian system is lGci. per rupee.
This par could be easily changed to 15d. or 17d., and
gradually changed further in either direction. By such
changes of the gold par of exchange, the currency of
those countries now having a gold-exchange standard
could, if desired, be kept at par with a tabular stand
ard. Thus, when it is found practicable to measure
by index numbers the exact shifting of the gold stand
ard, a corresponding shifting of the par of exchange or
price of rupees in gold could be effected.
As the system is now operated, the coinage is manip
ulated to keep it at par with gold, that is, to follow the
fluctuations of the gold standard wherever they may
lead. We have, therefore, the spectacle of India, and
other countries formerly having a silver standard, now
clinging to the skirts, as it were, of the gold standard
countries, and following that erratic standard whereever it may lead them, although it is within their power,
by exactly the same machinery, to keep their course
steady.
I would not, however, for a moment suggest that these
countries should give up their par of exchange with gold
standard countries. Although much might be said in
favor of such a course, it would, to a large extent, be a
step backward by again restoring the uncertainties of
international exchange which have been mentioned.
What is needed is to induce the entire civilized world
to do what is now within the power of the gold-exchange
countries to do, viz. to keep pace with a tabular stand
ard. It is a little anomalous that these gold-exchange
standard countries now have a power to regulate their

Sec. 5]

IS THE PRICE LEVEL CONTROLLABLE ?

341

price level, which is not possessed by the gold standard
countries themselves. The latter are, by their present
system, kept absolutely at the mercy of the accidents
of gold mining and metallurgy, while the former can
keep or change the par of exchange with gold countries
at will.
But evidently the gold countries could do precisely
what the silver countries have done, namely, inaugu
rate the system of a gold-exchange standard by closing
their mints to gold, reducing, if need be, the weight of
gold coins (although with the depreciation now going
on in gold, this would probably not be necessary),
and operating an exchange standard system in pre
cisely the same way that the Philippines and the other
countries mentioned now operate their gold-exchange
system.
To make this clear we shall suppose, at first, that one
country, say Austria, would continue on the gold stand
ard while England, Germany, France, the United States,
and the other chief countries of the world should close
their mints to the free coinage of gold. They could
then maintain a gold-exchange standard with a (vary
ing) par of exchange with Austria. By suitably chang
ing the par of exchange from time to time, the whole
commercial world, excepting Austria, could then keep
the purchasing power of money stable, instead of allow
ing it to fluctuate with gold. The same relation which
India now bears toward England would then be held
by both India and England toward Austria. But
it would not even be necessary that one country like
Austria should hold aloof in commercial isolation. The
system, when put in operation, should include all the
countries concerned and sufficiently interested to enter
into a treaty agreement. Instead of sacrificing its own

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THE PURCHASING POWER OF MONEY

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X III

interests by serving as a gold standard country in
terms of which all the other countries of the world
should in common adjust their pars of exchange,
Austria could itself adjust its currency by buying and
selling gold. In other words, precisely the same prin
ciples which regulate the currency of India or the
Philippines, by buying and selling exchange on gold
abroad, could be operated more directly through buying
and selling gold itself at home. Austria might be a
good country in which to do this, because it has long
operated substantially this system, and by it kept its
irredeemable paper money at a fixed par with gold.
Should suitable treaty arrangements be effected,
Austria might maintain a par, not with a fixed weight
of gold, but with such a weight of gold as should have a
fixed purchasing power, and could do this by buying
and selling gold at these adjusted prices, selling gold
bullion for gulden to contract the currency, and buying
gold bullion for gulden to expand the currency. All
other countries could maintain their par with Austria,
or each other, by the methods by which now India
maintains its par with England, or, if they chose, by
exactly the same process as proposed for Austria. In
fact, it is evident that the method of maintaining par
by selling exchange on other countries, and by exchang
ing currency directly for some commodity, such as
gold, are at bottom much the same thing.
In order that such an international system should
work, we might imagine three separate functions:
( 1) the function of maintaining an exchange par with
the Austrian gulden to be performed by Foreign Ex
change Offices exactly as at present in the Philippines
under the gold-exchange system; (2) the similar func
tion of regulating the currency in at least one country,

S ec. 5]

IS THE PRICE LEVEL CONTROLLABLE?

343

say Austria, by a Bureau of Currency Regulation
through buying or selling gold, at the option of the
public, at an official price, changing from time to time
according to the decisions of the Statistical Office about
to be mentioned; (3) the function of fixing this official
price of gold according to the price level. An inter
national Statistical Office at, say, The Hague, could be
established to do this in a purely clerical manner; its
duties would consist in ascertaining the index number
of prices in the usual way and then dividing the
market price of gold by that number.
For instance, if, a year after'the system was started,
it were found by the Statistical Office that prices had
risen one per cent, this Office would, in order to neutral
ize the rise, issue an official declaration to the Bureau
of Currency Regulation fixing the official price of gold
at substantially one per cent lower than the ruling
market price. At this cheap price the public will buy
gold bullion of the government and surrender currency
in return. Therefore the currency will be contracted
and general prices will fall until no more gold is called
for, or until there is declared a new official gold price.
Should the next official gold price be set above the
market price, the government would become a buyer
of gold and would thus reissue some of the currency
previously called in, or if need be, issue new currency.
The plan, as above outlined, fixes a single price of gold
at which the government must be ready either to buy
or sell. There would be practical advantages, however,
in fixing a pair of prices differing slightly from each
other, the higher for selling and the lower for buying.
The device pf a pair of prices was proposed by Ricardo.1
1Proposals for an Economical and Secure Currency, 2d Edition,
London (Murray), 1816, p. 26.

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X I II

It is also employed, as we have seen, in the gold-exchange
standard to simulate the “ gold-points.” The Austrian
paper currency, although usually called irredeemable, is
kept at par with gold by a similar arrangement under
which the Austro-Hungarian bank stands ready to buy
gold at k. 3, 2781 per kilo and to sell gold-exchange on
London at a slightly higher rate.
It will be seen that the plan here proposed requires
no revolution of the world’s currencies. It requires lit
tle more than to assemble, into one working whole,
operations already existing separately, viz. ( 1) cal
culating Index Numbers as done at present by our
Bureau of Labor; (2) buying and selling exchange, as
done at present by the Philippine Government; (3)
buying and selling gold, as done at present in Austria;
(4) periodically readjusting the gold pars as was done
at least once when the present system was inaugurated
in India, the Philippines, Panama and Mexico. The
readjustment of par is the only feature which could be
called new, and this should not be condemned as caus
ing fluctuations in values; for its only object is to prevent
the fluctuations from which we now suffer. Neither
this periodic readjustment nor any other feature of the
plan would require changes in the circulating medium.
Each nation would continue to use its old familiar cur
rency, whether gold, silver, or paper. The ordinary
man would be unaware of any change.
The cost of maintaining the gold-exchange system has
been slight and the cost of maintaining the system here
proposed, whatever it might be, could be as nothing
compared with the benefits it would render the entire
civilized world.
1See L. V. Mises, “ The foreign exchange policy of the AustroHungarian Bank,” Economic Journal, June, 1909, p. 201.

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IS THE PRICE LEVEL CONTROLLABLE ?

345

One incidental benefit which could easily be secured
would be the oft-proposed readjustment of relative
values of various coins; for the first adjustment of pars
would naturally make the sovereign equivalent to five
dollars, the ruble to fifty cents, the Japanese yen to
fifty cents, the Dutch florin to forty cents, the mark
to twenty-five cents, the franc to twenty cents, the
Austrian crown to twenty cents, and the Portuguese
crown to ten cents.
The plan as above outlined contemplates the regu
lation of the world’s currencies by buying and selling
gold; but of course silver or any other commodity
could be used instead. The less variable the commod
ity relatively to commodities in general, the less would
be the readjustments needed and the less active the
buying or selling of that commodity by the govern
ment.
The objections which could be urged against this sys
tem are doubtless many, but they do not seem to be as
serious as the objections which have already been urged
against the adoption of the gold-exchange standard,
and which have been satisfactorily answered by the
course of events. In fact, there would seem to be no
greater danger in trusting Austria, under treaty agree
ment, to maintain her gulden at an ideal par with com
modities in accordance with an index number, than to
trust her, as at present, to maintain stable exchange
with London, or than to trust the Indian, Mexican,
Panama or Philippine governments to maintain their
overvalued silver at par with gold. The functions in
volved are clerical; the acts required are specific. De
partures from a strict compliance with the law or treaty
would be instantly recognized, and would bring upon
the culprit wrath and punishment proportionate to the

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XIII

international gravity of the offense. The plan does not
require and would not permit any experimental dosing
of the circulation dependent on the judgment of an
official. The official who regulates does so merely by
buying and selling at specific prices fixed by others;
and he must buy or sell at the pleasure of the public.
He would have no more choice than a broker who is
ordered to buy or sell at prices specified by his custom
ers, or than his prototype, the present official in the
Philippines, who now buys or sells foreign exchange.
The danger of abuse or fraud in the Statistical Office,
the work of which is based on published market prices
and is necessarily done in the light of day, would seem
negligible.
Not only would the scheme seem to be entirely free
from the possibility of mismanagement by individual
officials, but it would seem also to be fully safeguarded
against the danger of inflationistic legislation. No in
dividual nation could inflate the currency without
withdrawing from the international arrangement and
isolating itself accordingly, while it is quite inconceiv
able that all the civilized nations of the world should
voluntarily and simultaneously commit the folly of
inflationistic legislation.
But, before any control of the price level be
undertaken, the public must learn to realize its neces
sity. So long as the rank and file even of business
men fail to realize that they are daily gambling in
changes in the value of money, a fact of which they
are blissfully unaware, they will exert no demand for
preventing those changes. They are the parties whose
interests are chiefly involved, and the first essential
step in the reform process is that they shall be made
to comprehend the benefits of a stable purchasing

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THE PRICE LEVEL CONTROLLABLE?

347

power.1 Until this time arrives, any political proposals
will be premature.

§6
At the beginning of this chapter we reviewed the
principles determining the purchasing power of money
and the practical problems involved. We then consid
ered the possible methods of avoiding the evils of varia
bility in purchasing power. Among these, one of the
most feasible and important was found to be an increase
of knowledge, — both specific knowledge of conditions
and general knowledge of principles. Next, the claims
of bimetallism and polymetallism as means of maintain
ing a stable level of prices were considered. It was seen
that there was no guarantee of keeping two or more
metals in circulation indefinitely at an agreed ratio, and
it was pointed out that, even could this be done, the
gain in stability of prices would be likely to be incon
siderable. The latter objection was brought also
against symmetallism— the proposal to have more
1A recent popular pamphlet by A. C. Lake, Currency Reform the
Paramount Issue, Memphis (28 N. Front St.), Tenn., proposes to
stop the free coinage of gold. As I write, other evidences of the
spread beyond academic circles of the idea that gold is an unstable
standard come to hand. The rapid rise in the cost of living has of
course thrust the subject on the attention of the magazine and news
paper press. Mr. Edison, in a recent interview, predicts the further
downfall of gold, through the discovery, — sure to be made sooner
or later, — of cheap methods of extracting immense quantities of gold
from some Southern clays. He asks the pertinent question : “ Is it
not absurd to have, as our standard of values, a substance, the only
real use of which is to gild picture frames and fill teeth ? ” Mr.
Carnegie, in his last gift of ten millions of dollars to the Carnegie
Institution of Washington, stipulates that a certain part of the in
come shall bo set aside as a sinking fund against “ the diminishing
purchasing power of money.” This is significant as one of the first
cases in which a business man has taken cognizance, in a practical
way, of the instability of gold.

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X III

than one precious metal in each standard coin — as
well as against joint metallism, etc.
Several methods were next considered by which a
government might regulate the quantity of money rel
atively to business so as to keep the level of prices con
stant. One such method was to make inconvertible
paper the standard money, and to regulate its quantity.
Another was to regulate the supply of metallic money
by a varying seigniorage charge. Still another was to
issue paper money, redeemable on demand, not in fixed
amounts of the basic precious metal, but in varying
amounts, so calculated as to keep the level of prices
unvarying. Lastly was considered the proposal of the
writer, — to adopt the gold-exchange standard combined
with a tabular standard.
It was suggested that the first step in this needed
reform would be to persuade the public, and especially
the business public, to study the problem of monetary
stability and to realize that, at present, contracts in
money are as truly speculative as the selling of futures,
— are, in fact, merely a subdivision of future-selling.
The necessary education once under way, it will then
be time to consider schemes for regulating the purchas
ing power of money in the light of public and economic
conditions of the time. All this, however, is in the
future. For the present there seems nothing to do
but to state the problem and the principles of its
solution in the hope that what is now an academic
question may, in due course, become a burning issue.

For a fuller explanation of the above described plan
to “ standardize the dollar,” the reader is referred to
pages 494 ff.

APPENDIX TO CHAPTER II
§ 1 (t o C h a p t e r II, § 3)

The Concept of an Average
The subject of averages or means is so important — both
theoretically and practically — and so little upon it is readily
available for economic readers that a short statement of its
fundamental principles may be fitly inserted here.1
There are numerous kinds of averages or means. Among
them are the arithmetical, geometrical, and harmonical; and
of each of these there are many different varieties. The
simple arithmetical mean of a specific series of terms is found
by adding the terms together and dividing by their number.
Thus, suppose it is desired to find a mean of 2 and 8 . It is
evidently

~ = 5. This is, as a matter of fact, the

mean most commonly employed.
The simple geometrical mean is obtained by multiplying all
the terms together and extracting that root of the product
which corresponds to the number of terms. Thus, the geo
metrical mean of 2 and 8 is V 2 X 8 or 4.
The simple harmonical mean of any number of terms is
the reciprocal of the arithmetical average of their reciprocals.
For 2 and 8 it is 7 -7 -7 or
2

The weighted arithmetical mean is a modification of the
simple arithmetical mean. Suppose it is desired to find the
mean height of two groups of trees, one tall, the other short.
1For discussion of certain statistical averages, see Dr. Franz
Zizek, Die Slatistischen Miltelwerte, Leipzig (Duncker & Humblofc),
1908, in which (p. 2) will bo found further references.
349

350

THE PURCHASING POWER OF MONEY

[A p p e n d .

The tall group is 8 yards high, the short, 2. The simple
arithmetical mean as we have seen is 5. But this mean treats
both groups as of equal importance. Let us suppose that
there are twenty of the two-yard trees and ten of the eightyard trees, and let us seek a mean of the two heights, such
as will give equal importance to each tree. This will give
the short group of twenty trees twice the importance of the
tall group of ten trees. We shall be giving equal importance
to each tree if we take the simple arithmetical mean of the
thirty trees. But this simple mean of thirty trees will be a
weighted mean of the two groups of trees. It is to be found
by adding their heights together (twenty heights of two
yards plus ten of eight) and dividing by the number of trees
(20 +10).

That is, the mean height is

^ ^= ^

and this (considered as an average of the two groups instead
of that of the thirty trees) is said to be the weighted arith
metical mean of 2 and 8, the 2 being weighted twenty times,
and the 8, ten times. The weighted mean of the two groups
means the simple mean of the thirty trees. In other words
when we “ weight ” the various terms averaged, we no longer
count these terms once each, but we count one term as though
it were (say) twenty, and another as though it were (say)
ten and the number of times we count a term is its “ weight.”
In the same way we may define the weighted geometrical
and weighted harmonical means. Taking the same example
of the trees, we find the results to be respectively 220•810

or3.175and^ m | 1|)W or 2}.
30
The same results would have been obtained in each case
if, instead of the weights 20 and 10, we had taken, as weights,
2 and 1.
Since there are so many different kinds of means, the ques
tion arises, What is the meaning of an average or mean in gen
eral ? We answer : Any mean of a series of terms must be
obtainable from them by a mathematical rule such that,

S e c . 1]

APPENDIX TO CHAPTER II

351

when applied to a series of identical terms, it will make their
mean identical with each of them. Any rule of averaging is
admissible which is consistent with this condition (that the
average of identical terms must be identical with each).
We know that the simple arithmetical mean A , of a, 6, and c
is A —5L+A+5. it is easy to see that this formula meets
the required test. Substituting A for each of the three
magnitudes a, 6, and c in
, we obtain ^ ^ -4 + 4.,
u
O
which is evidently equal to A ; thus the test is satisfied.
Again; let G be the geometrical mean of a, 6, and c ; so
that G='V/a6c. This formula also conforms to the defini
tion of a mean because G= 'VGGG.
Similarly, the harmonical average (which we may call H)
of a, byand c is H= -— -— -• This also conforms, because

a
H=

1
1
1 . 1 ,1

b c
3

H+ H+ H
3
For a weighted arithmetical average Awof a, 6, c, the
weights being (3, y, we have the formula Aw=
0 y ~9
which conforms to our test, since evidently

A _ ftAW~f~ftAw-j- yAyrf_
U+ /3+ y
By applying this general rule, we can make at will in
numerable kinds of averages. It is only necessary to write
any formula twice, once using the terms to be averaged
and once using, instead, the required average, and then
equate the two. Thus, let us take the complicated formula

(a + a*+ Ka?)(b+-^)
-------------- 3- = -----— • This may be employed to obtain a
c + V&c

352

THE PURCHASING POWER OF MONEY

[A p p e n d .

new species of average (a) of a, b, and c, simply by equating

(x + x2+ Kx?)fx +
it with the similar form -------------- 0-7=------- - • That x as
x + -Vz2
determined by this equation will conform to our definition of
an average is evident, since substituting x for a, 6, and c,
the equation becomes a truism, showing that the proposed
new average of the identical terms x is x.
A special case of the definition, requiring particular men
tion, is that in which two or more means (not necessarily of
the same kind) are related to one another. In order that
A should be a mean of ai, 02, a3, •••when we know that B is
a mean of 61, b2) 63, ••• it is only necessary to have a deter
mining formula such that if d\= a2= a3 ••• and at the same
time &i = 62 = &3 ••• (each of which by hypothesis must be
equal to B)} then A shall also be equal to each of the magni
tudes ai, (h, dz, etc. Many examples of pairs of means like
A and B will be given in Chapter X (on the construction of
index numbers). The following is a simple example : —
Let nAB = aj)i + a2b2 + ajbz H— and let B be the arithmeti
cal mean = ——
^ + _-_^ ^n ^e;ng
nuinber of terms).
n
Then A is a (new) sort of mean of ah a2, a3; for, substituting
A for ai, a2, dz, ••• and B for 61, b2y 63, in the equation nAB
= ai&i -}----, the equation is satisfied.
§ 2

(t o

C h apter

II, § 5 )

The Concept of Velocity of Circulation
The velocity of circulation of money has been defined as a
ratio of the money expended to the average money on hand,
that is, as a rate of turnover. A rate of turnover differs from
the popular concept of velocity. The latter regards velocity
as the average number of times money changes hands from
one person to another; whereas, the concept we have em
ployed treats velocity as the average number of coins which

Sec. 2]

APPENDIX TO CHAPTER II

35 3

pass through one man’s hands, divided by the average amount
held by him. The difference between the two concepts is
very similar to that between two methods of obtaining the
velocity of a railway train. One method is to follow the
train for a certain number of miles, and note how long a time
it takes to travel those miles. The other is to stand on a
certain spot beside the track and note the time consumed by
a given length of train in passing that spot. Following the
train from place to place is like following a coin from person
to person, while watching the train pass one point is like ob
serving the rate of turnover of one person’s purse. We may
distinguish the two methods as the “ coin-transfer ” method
and the “ person-turnover ” method. Both methods, if cor
rectly employed, yield the same result. But in the coin-trans
fer method, an important distinction is usually overlooked,
the distinction between the gross and net circulation of money. /
What is desired is the rate at which money is used for pur
chasing goods, not for “ making change.” The result is the
difference between the number of times each piece changes
hands against goods, and the number of times it changes
hands with goods. If a $10 bill is transferred in purchase of
goods and $2 is given back “ in change,” the actual money
expended for goods is measured, not by 812, the gross trans
fer of money, nor yet by $10 , the gross amount transferred
against goods, but by 88, the net amount paid for goods.
If it is desired, in the coin-transfer method, to learn the
average velocity of circulation of two pieces of money, such
as a dollar and a ten-cent piece, we must not only find the
net rate of turnover of each coin, but also take account of
the discrepancy between the buying efficiencies of the two
coins. Let it be assumed that during the year the dollar is
passed 115 times against goods and 15 times with goods, so
that its net velocity of circulation is 115 —15 or 100 . If we
suppose the velocity of the ten-cent piece to be 290 —90 or
200, the average velocity of the two must somehow take
account of the different values of different denominations.
A dollar is the equivalent of ten dimes. Its rapidity of cir2

354

THE PURCHASING POWER OF MONEY

[A p p e n d .

culation should therefore be “ weighted” tenfold in order
to get the real average, that is, the average of the service
performed by the two. The net rate of circulation of 100'
for the dollar is equivalent to a net velocity of circulation
of 100 for each and every one of ten dimes. It follows that
the average velocity of the two coins is — X 100 + 200^ ^
result much closer to the velocity of the dollar than to that
of the dime. With these two safeguards against error ap
plied to the coin-transfer method, it is easy to see that the
coin-transfer method will yield the same results as the person-turnover method.1
There is yet another magnitude which should be considered
in connection with the velocity of monetary circulation.
This may be called the average time of turnover, i.e. the
average amount of time consumed by all the given money,„
in being turned over once. This is the “ reciprocal” of
velocity. If money changes hands twenty times in a year,
it turns over, on the average, once in
of a year, or once in
somewhat over 18 days. This is its average time of turnover.
If the average velocity of circulation or rate of turnover is
forty times a year, then the average time of turnover is of
a year or about 9 days. Or, instead of considering all the
given money directly, let us come at it through a component
part of it. If a man having, on the average, $10 in his
pocket every day, expends on the average SI a day, he evi
dently turns over XV of his money each day. Since to turn
over TV of his average stock each day is to turn over the
whole of it 36£ times a year or once in 10 days, the time of
turnover will be 10 days. If the man under consideration
had a pocketbook arranged with a series of ten one dollar
bills, and every day, as one was taken from the top to be
expended, another were added at the bottom, evidently any
and every bill would remain in his hands just ten days
traveling from the bottom to the top of the pile.
1 For mathematical statement, see § 5 of this Appendix.

Sec. 3]

355

APPENDIX TO CHAPTER II
§ 3 (t o

C hapter

II,

§ 5)

“ Arrays ” of p’s, Q’s, and pQ’s
Let us assume that the year is divided into an indefinite
number of periods, or moments, and distinguish the prices
and quantities relating to those successive periods by the
subscripts 1, 2, 3, etc., at the left; and that we are dealing
with a community of an indefinite number of persons, dis
tinguished likewise by subscripts at the right. Thus the
quantity of a particular kind of goods purchased by individ
ual No. 1 in moment No. 3 is represented by 3gi and the price
of the sale by 3pi. The entire system of quantities and prices
is represented by the two following “ arrays.”
P eriods

P e rio d s
P ersons
2

3 ...

101

201

301* ••

1(72

2 (72

3^2—

1(73

2(73

3 0 3 -..

Total

3 ...

lPl

2 Pi

3 P l‘ . .

1P2

2 P2

3 i? 2 ...

IPs

2 PZ

zPz—

Pi
P2
P3

Average

P-

Qi
Q2
Qi

A verage

P ersons

T o ta l

We have just stated the meaning of the letters inside these
arrays. Those outside are as follows: Qi is the total quantity
bought by person 1 and is the sum (1*71 + 2(71 + 3(71 + •••) of all
quantities purchased by him in all the different periods of time.
Like definitions apply to Q2, Qz, etc. iQ is the total quantity
purchased in moment 1 and is the sum (1(71 + 1(72 + 1(73 + •••)
of all quantities purchased in that moment by all the differ
ent persons. Like definitions apply to 2Q, 3Q, —• Finally
Q is (as already employed in the text) the grand total of quan
tities bought by all persons in all periods of time. Evidently,
Q = iQ + 2Q +3Q +
= Q1 +

62 +

Q 3+

•••
•••

~ 1(71 + 2(71 + etc. + 1(72 + 2(72 + etc. ••• + etc.

356

THE PURCHASING POWER OF MONEY

[A p p e n d .

Like definitions apply to the letters outside the p array, but
the relations to the letters inside are here averages instead of
sums. We may best derive the form of these averages from
a third or intermediate array for pQ indicating the money
values of the purchases.
This last named array is
P eriods
T otal

P ersons
1

lPl 101

2i?1201

3P 1301

Pi Q 1

1P2 102

2P-2 202

2P2 302

lP 3 103

2P3 203

ZP3 303

Ps Q 2
Po Q 3

zP z Q

p Q

Total

1P 1 Q

2P 2 Q

In this array the same relations must evidently hold as in
the Q array. That is, pQ, the entire sum spent on the given
commodity by all persons in the community during all periods
of the year, must be equal to (1) the sum of the column above
it, (2) the sum of the row at its left, and (3) the sum of the
interior terms of the array. In other words, it must be equal
to (1) the sum of the total yearly amounts spent by the many
different persons, (2) the sum of the total amounts spent in
the community at the many different periods of the year, and
(3) the sum of the purchases of all the individuals in all the
periods.
The nature of the p array is now determined by the Q and
the pQ arrays. It must namely be such as to permit the
summation just described for the pQ array. That is, each of
the average prices (such as pi) must conform to the type of
formula: —
Pi Qi = iPi iQi + 2P12<?i+ •••* that is
Vl = igu gi + ggLagi^....

= iVnQi + 2Vi2qi+
lgl + 201+ •••

S e c . 3]

APPENDIX TO CHAPTER II

357

Hence, p is a weighted average of ipi, 2P1, etc., the weights
being igi, 2qi, etc. That is, the average price paid by person
No. 1 is the weighted arithmetical average of the prices paid
by him at different moments through the year, the weights
being the quantities bought. The same principle obtains for
all other persons.
Similarly, the average price, 1p} may be shown to be
i<7i + iP2 1(72+ ••• .
1Q (= i(?i + 1^2 + •••)
That is, the average price in period No. 1 is the weighted
arithmetical average of all prices paid by different per
sons at moment No. 1, the weights being the quantities
bought by each. The same principles obtain at all other
moments.
Finally, the average price, p, in the lower right corner of
the p array, is either p =

~j"
^ — - (that is, p is a
Q ( = Qi + ^2 H— )
weighted arithmetical average of pi, p2, etc., the weights
being Qh Q2, etc.); or (using the row instead of column), p is
the like weighted arithmetical average of ip} 2p, etc., the
weights being 1Q, 2Q, etc.; or lastly, either of these two ex
pressions for p, combined with the preceding expression for
Pi, P2, etc., or with that for ip, 2p, etc., may be used to show
that p is a weighted arithmetical average of all the p’s
within the array, the weights being the corresponding q’s. In
short, the price of each commodity for the year is its aver
age at all times and for all purchases in the year weighted
according to the quantities bought.
This principle covers the method of averaging prices in
different localities. Thus the average price of sugar in 1909
in the United States is the weighted arithmetical average of
all prices of sales by all individuals throughout the United
States, and at all moments throughout the year, the weights
being the quantities bought. Thus, if there are large local
or temporal variations in price, it is important to give chief
weight to the largest purchases.

358

THE PURCHASING POWER OF MONEY

[A p p e n d .

What has been said as to Q and p arrays relates only to
one commodity. But the same principles apply to each com
modity yielding separate arrays corresponding to each of the
total quantities, Q, Q', Q", etc., as well as corresponding to
each of the average prices, p, pf, p", etc.
§4

(t o C h a p t e r

II, § 5)

“ Arrays ” of e’s, m7s, and V’s
In the preceding section we have seen that there exists an
“ array ” of p’s, pQ’s and Q’s for each commodity. These
relate to the right side of the equation of exchange. Similar
arrays relate to the left side.
If, as before, we assume a community of any number of
persons, distinguished respectively by subscripts at the right,
and if we divide the year into moments, distinguished by
subscripts at the left, we may designate the amount of money
expended in the first moment by the first person as 161, the
average amount of money he has on hand at that moment
as iWi and his velocity of circulation at that moment (reck
oned at its rate per year) as {V\. The expenditure in the
moment being ieh that moment’s rate per annum is \Uii^i,
there being n moments in the year, so that the velocity of
circulation or rate of turnover per annum, 1 F1, is n— • A
lWi
similar notation may be used to express the amounts ex
pended and held and the velocity of circulation for each
member of the community during each moment of the
year as shown in the following three “ arrays ” (inside the
lines).
In the first table, E\ at the right of the first line is the
sum expended by the first person, being the sum of i£i,
20i, 3^1, •••in the first line representing the amounts expended
by him at successive moments during the year. Likewise,
I?2 is the sum expended by the second person during the
year, and E$ is the sum expended by the third, iE at the foot
of the first column is the amount expended by all persons in

Sec. 4]

APPENDIX TO CHAPTER II

359

the first moment; that is, it is the sum of all the amounts
in the column above i t ; 2E is likewise the amount expended
by all persons in the second moment; ZE, the amount ex
pended in the third, etc. Finally, E, in the lower right-hand
corner, is, as employed in the text, the grand total expended
by all persons in all moments of the year. Evidently E can
be obtained by adding the row to the left of it, or by adding
the column above it. It is also the sum of all the elements
inside the lines, i.e. E = 2iJ5 = 3Z?i = 2iei.
A

mount

E xpended

M oney

P e r so n s

T otal

8 •••

H and

P e r io d s

P e r io d s
P e r so n s

verage

3 -

1^1

261

3^1 •••

1W 1

2? n i

3?71l •••

xe2

2<?2

302

Ei
e2

l? ft 2

2*^2

3*712 “ •

103

2^3

303 “ •

1™ 3

2WI3

3*713

mi
m2
m3

E •••

Total

3m -

Total

iE 2E

e l o c it y

iM 2m

C ir c u l a t io n

P eriods
A verage

P ersons

II
ta

— = Vi

303
-rr
11---- = s Vz

^=V z

n^ r = * v

3m2

zmz
3E

7712

w
II

Average

fesTfei
n

1T27

103
rr
n ---- = 1 Vs

ie'2
1m2

— = Fi

n^
3^1L = sF l
302
-TTn-----— zV2

a* fa

^ -----=— 1
n

£
Cl
II

n — = 1 F1
imi

«1
wl S«

In the second table, M in the lower right corner is a sum
of the average amounts held by the different members of

360

THE PURCHASING POWER OF MONEY

[A p p e n d .

the community during the year, i.e. it is the sum of the
elements in the column above it, mi, m2, m3, etc., each of
which is by hypothesis a simple average of the row to its
left.
Or, again, M is a simple average of the row to its left, 1M,
2M, 3M, etc., the average amounts of money in the com
munity, in the successive moments of the year, each of which
averages is in turn the sum of the column above it, i.e.

M = 2 mi = —— . Thus M is both the sum of averages and
n
the average of sums. That the two are equal follows by
expressing both in terms of the elementary quantities mi
by means of the equations
= mi+*ni + *n i+ 'V et
n
and the equations 1M = imi + 17112 + 1 mz -J----. It is, of course^
easy also to express M directly in terms of imi, etc., within
the table. Thus expressed, it is -

•.
n
The third table (that for velocities) is derived from the
other two. As just explained, 1 V1 is the velocity of circula
tion (considered as a per annum rate) for the first person in
the community in the first moment.
There remain to be shown the relations of the elements in
the V table.
Evidently,
v =—
M
—FJi + E2+ •••
?Ui +

77lo +

•••

^ mi7i + m272+ —
mi+m2+ •••

(jj

Form (1 ) shows that V is a weighted average of the yearly
velocities of the different persons, the velocity of each person
being for the entire year and weighted according to his aver
age amount of money on hand.

Sec. 4]

APPENDIX TO CHAPTER II

3 61

Following an analogous but slightly different sequence, we
have

n
i2? + 2Z?+
XM + 2 M + •••

xM+ 2M + __
1

iF + 2flf2F +•••
M + 2M + —

(2)

Form (2) shows that F is also the weighted average of the
yearly velocities of the successive moments into which the
year is divided, the velocity of each moment being for the
entire community and weighted according to its average
amount of money then in circulation.
Thus form (1) gives F in terms of the column above it,
while form (2) gives F in terms of the row at its left. A
formula similar to (1) may be constructed to express each of
the magnitudes iF, 2F , zV, etc., in terms of the column
above it, while a formula similar to (2) may be constructed
to express each of the magnitudes Fi, F2, F3, etc., in terms
of the row at its left. That is, the velocity in the entire
community at any particular moment is a specific form of
average of the velocities of different persons at that moment;
and the velocity for the entire year of any particular person
is a specific form of average of the velocities at different
moments for that person.
Finally, F may be expressed, not only as an average of its

362

THE PURCHASING POWER OF MONEY

[A p p e n d .

column and row as in formula (1) and (2), but also as an
average of the magnitudes in the interior of the table. This
last result may be obtained in several ways, of which the
most direct may briefly be expressed as follows: We know
that E is the sum of the interior of the first or E table, that
is, E = Siei; and that M is equal to - Sirai. Hence, we have

SironFi
SiWi
That is, V is the weighted arithmetical average of the yearly
velocities pertaining to different persons in different mo
ments, each velocity being weighted by the amount of money
on hand in that instance. The mathematical reader will
perceive that an alternative treatment would derive the re
sult in terms of an harmonic average.
§5

(to C h a p t e r

II, § 5)

The Coin-transfer Concept of Velocity and the Concept of
Time of Turnover
We now turn to the coin-transfer concept of velocity of
circulation. To show what kind of an average V is of the
velocity of circulation of individual coins, or rather of in
dividual pieces of money in general, let us denote the values
of the individual pieces of money circulating in the commu
nity by the letters a, 6, c, d, etc., and let us denote the net ve
locity of circulation of these (the number of times exchanged

Sec. 5]

APPENDIX TO CHAPTER II

3 63

against goods minus the number of times exchanged with
goods or “ in change ” ) by h, i, j , k, respectively, etc. Then
E, the total amount expended, is denoted by ha + ib + jc +
Jcd+ •••; and the amount of money, M, in the community
is a + b + c + d.
Hence
^ ^ ha + ib + jc+ k $ + - .
M
a + b + c + d+ •••
jp

That is, — is a weighted average of the net velocities of cir
culation of the different pieces of money, the velocity of each
E
piece being weighted according to its denomination. But —
is also F, which we have already seen is the velocity of circu
lation in the person-turnover sense.
It is clear, therefore, that the coin-transfer method of aver
aging is the same in results as the person-turnover method,
if all the pieces of money in the community are included.
Finally, we come to the concept of “ time of turnover.”
If velocity of circulation is represented as F, then ~ repre
sents the time of turnover. Similarly, the reciprocals of iF,
Vi, Vs,
1 V1 , iV2, •••, 2Vx, ••*, are corresponding times
of turnover. Using W for the reciprocal of V and applying
the appropriate subscripts, we may write an array of W’s
analogous to the previous array of F's, and we may show
that W is an average of Wi, W2, or of JF, 2W, ••• or of 1W1,
lW2,-,2Wl9
But these averages are all harmonic averages. To see this,
we need only remember that V has already been analyzed1
as a weighted average of the elementary F’s, and that W has
been defined as the reciprocal of F. That is, W is the re
ciprocal of this weighted average of elementary F;s. But
the elementary IF;s are reciprocals of the elementary F's.
In other words, W is the reciprocal of the weighted arith
metical average of the reciprocals of elementary IF's. This
2F,

1 In § 4 of this Appendix.

364

THE PURCHASING POWER OF MONEY

[A p p e n d .

makes W, by definition, a weighted harmonic average of
these elementary magnitudes.
§ 6 (to C h a p t e r I I , § 5)

Algebraic Demonstration of Equation of Exchange
It is clear that the equation of exchange, MV = 2pQ, is
derived from elementary equations expressing the equiva
lence of purchase money and goods bought. The money
expended by any particular person at any particular mo
ment is, by the very concept of price, equal to the quanti
ties of all commodities bought in that moment by that
person multiplied by the prices, i.e.
iei = ipi 1S1 + ip 'i ig'i + ip "i ig"i + —.

From this equation and others like it, for every person in
the community and for every moment in the year, simply
by adding them together, we obtain, for the left side of the
equation, the sum of the e’s which we call E ; and for the
right side the sum of all the pq’s. We have already seen in
the text how the left side, E, may be converted (by multiply
ing and dividing by M) into MV, and we have also just seen
(§ 3 of this Appendix) how the sum of all the terms relating to
each particular commodity represented on the right side may
be converted (by similar simple algebraic operations) into one
term of the form pQ so that the whole sum becomes 2pQ.
The final result is, therefore, MV = 2pQ. This reasoning
constitutes, therefore, a demonstration of the truth of this
formula, based on the simple elementary truth that in every
exchange the money expended equals the quantity bought
multiplied by the price of sale.
§ 7

(to C h a p t e r II, § 5)

P must be a Specific Form of Average in order to vary
directly as M andI! V and inversely as the Q’s
Let us assume that V and the Q’s remain invariable while
M changes to Mo and p, p', p", etc., to po, p'o, p"o, etc.

Sec.

365

APPENDIX TO CHAPTER II

(The subscripts “ 0 ” refer to a year called the base year
other than the original year.) We have for the two years
respectively the two equations: —

MV = pQ + p 'Q '+ MqV = poQ+ vfoQf + •••
whence by division, we obtain

p Q + p '< y + - f e ) >,l3+ f e ) l’,,Q' +
poQ + p'oQf + •■•*
PoQ + p'oQ" —

•"

The last expression is evidently a weighted arithmetical
average of (&),

\Po/ \P o J

etc., the weights being p0Q, p'0Q

etc. We conclude that, if the velocity of circulation and the
quantities of goods exchanged remain unaltered, while the
quantity of money is altered in a given ratio, then prices will
change in this same ratio “ on the average,” the average
being exactly defined as a weighted arithmetical average, in
which the weights are the values of goods sold, reckoned at
the prices of the base year. The ratio may evidently also be
written: —
M = pQ + v’Q ' + ~ ^
1

PoQ +p/oQH—

PoQ

p'oQ ' •••
vQ+v'Q’ + '-u

~ (g > e + (^ > -a -+ -

P Q +P 'Q '+which is a weighted harmonic average of

Vo . V o

etc., in

which the weights are vQ> v'Q!\ e^cv that H
values, n°t
in the base year, but the other year.
If M and the Q’s remain invariable, while V changes from

v to Vh evidently the ratio ~ will be expressed by preVi
cisely the same formulae as above.

366

THE PURCHASING POWER OF MONEY

[A p p e n d .

If the Q’s remain invariable, while M and V both change,
evidently thte ratio

will be expressed by the same

formulae.
Again the same formulae apply if M and V remain invari
able while the Q’s all vary in a given ratio, or if the Q’s all
vary in a given ratio in combination with any variation in
M or V or both. In short, the formulae apply perfectly in all
cases of variation, except when the Q’s vary relatively to each
other.
These formulae, it should be noted, are those later discussed
as the formulae numbered ( 11) in the large table of formulae
in the Appendix to Chapter X.

APPENDIX TO CHAPTER III
§

(to C h a pter

III, § 2)

“ Arrays” of k’s andr’s
( Mf\
Let k be the ratio of deposits to money in circulation!— 1
which, on the average, the public prefers to keep; k will then
be derivable from the like ratios for the different persons
and business firms in the community in the successive mo
ments of the year, and we may, therefore, form an array on
the analogy of previous arrays, of the form: —
Pebiods
A verage

P ersons
2

l& i

2&1

1&2

2&2

Average

Each letter outside the array is a weighted arithmetical aver
age either of the row to its left or of the column above it.
k (in the lower right corner) also is both of these as well as
the weighted arithmetical average of all the elements inside
the lines (the weights being in all cases the amounts of money
in circulation, which are the denominators of the ratios repre
sented in* the arrays). The same proportions hold true if
“ harmonic” be substituted for “ arithmetic” (provided the
weights be changed from the denominators to the numerators

367

368

THE PURCHASING POWER OF MONEY

[A p p en d .

Ill

of the ratios, viz. the deposits). These theorems can be easily
proved analogously to those in § 7 of the Appendix to Chapter
M*
II, remembering that k -----M
Similarly, we may let r stand for the average ratio, for the
year, of the reserves of all banks (/x) to their deposits (M').
This ratio ^r, or

is resolvable into an array expressing

the ratios for different banks at different moments, viz.: —
P ekiods
P ersons *

A verage
l

in
i r2

sri
2**2

Average

Here each element outside the lines is a weighted arithmetic
(or harmonic) average of the terms in the row to its left or
the column above it, while r is both of these as well as a
weighted arithmetic (or harmonic) average of all the terms
inside, the weights being (for the arithmetic^ average) the
deposits in each case or (for the harmonic average) the
money in each case. The total currency of the community
is fi+M +M ', although only M + M' is actually in circulation.
§ 2 (t o C h a p te r

III, § 4)

Algebraic Demonstration of Equation of Exchange Including
Deposit Currency
The money expended for goods by individual 1 at moment
1 is and his check expenditure is ie\. His total expendi
ture for goods by money and checks is, therefore, iei + \e\ =
ipn<zi + ip'iig'i+ —.

Sec. 2]

APPENDIX TO CHAPTER III

369

By adding together all such equations for all persons in
the community and all moments of the year, we obtain the
equation
E + E' = 5pQ
which becomes
MV + M'V' = 2pQ
since, by definition, V = ^ and V' = 7 —
M
M'

APPENDIX TO CHAPTER V
§ 1 (t o C h a p te r

V, § 5)

Effect of Time Credit on Equation of Exchange
It is important to note that, though the system of book
credit has a great influence on prices indirectly, it does not
enter into the equation of exchange like circulation or bank
credit. We may properly include in the discussion with
book credit, those cases of credit where the record of the
debt is not simply on the books of one of the two parties, but
in which an explicit record exists in the form of a promissory
note given by the purchaser to the seller. In either case,
goods are bought by a promise to pay at a later time; in
the one case, the promise is explicit; in the other, implied.
Such an exchange of goods against a later payment may
be resolved into two successive exchanges. The first occurs
at the start when the credit is given for the goods. The pur
chaser then buys goods in exchange for a promise to pay.
The second exchange occurs at the close of the transac
tion, when the debt is liquidated. The original purchaser
may then be said to buy back his book credit or promissory
note with money. Unlike bank credit, then, time credit
does not directly save the use of money. Its immediate effect
is simply to postpone1 that use, since, to eventually extin
guish the credit, as much money or checks must be expended
as though cash were paid in the first instance. Dr. Andrew,
now Assistant Secretary of the Treasury, points out that if
time credit is being contracted faster than it is being ex1 See A. Piatt Andrew, “ Credit and the Value of M oney,” Pro
ceedings Seventeenth Annual Meeting, American Economic Associa
tion, December, 1904.

370

Sec. 1]

APPENDIX TO CHAPTER V

371

tinguished, prices tend to become higher, but that as soon as
the paying of these debts becomes as rapid as the making of
them, prices will fall back to their old level.1 The excess of
credit contracted over credit extinguished acts just as does
so much money or bank deposits offered for goods.
In order to show how these considerations as to book credit
affect the equation of exchange, let us denote the creation of
all book credits and other time loans by the letter E", and
their extinguishment by the letter E'". The left side of our
equation of exchange — or the total of money payments,
check payments, and book charges and promissory notes
for goods bought in the course of the year — will now be
MV + M'V' + E "; and the right side, including the value
of (1) goods bought and (2) debts maturing and extin
guished during the year by payment of money or check,
will be represented by
+ E'Transposing for con
venience E the equation of exchange may now be written
MV + M'V' + En —E'" = 2pQ. Since En will be approxi
mately equal to E,n, these equal and opposite terms nearly
cancel, i.e. E" —Ef" becomes zero, and the equation virtually
becomes again MV + M'V' = SpQ.
Before leaving the subject it may be noted that book credit
tends to increase prices by creating offsetting debts and thus
diminishing the volume of trade which must be done by money
or checks. Thus, the farmer buys on account at the village
store, occasionally selling farm produce there, also on account.
The account is balanced at long intervals when the difference
only is paid in money.2 And, of course, as pointed out in the
text of this chapter, book credit tends also to increase
velocity.3
1Andrew, loc. cit.

* Ibid, p. 10.

3 Chapter V, § 4.

APPENDIX TO CHAPTER VI
§ 1 (t o C h a p t e r

VI, § 1)

Modification of Equation of Exchange required by Inter
national Trade
•We have already seen that there are two equations of ex
change, one for purchases, and the other for sales. In a closed
community, these two are necessarily identical, for every
purchase by one member of the community is a sale by an
other member. But in a community with international trade
they will be slightly different. The equation of exchange as
developed in this book relates to the expenditure of money
for the purchase of goods, and not to the receipt of money
for the sale of goods. This equation of exchange at its last
stage of elaboration was

MV + M’V’ + E" - E’" = 2pQ
where the letters have the meanings previously given to them,
E" relating to the debts contracted in the given period in
book accounts and promissory notes used in purchase of
goods, and E,n relating to the extinguishment of such debts
during the same period. Since MV was developed from E}
and M'V' from Er, this equation may be written as follows: —

E + E' + E " - E '" = 5pbQb
where the letters E on the money side of the equations are
used to indicate that the money is expended money and the
subscripts b on the goods side are used to indicate that the
goods are goods bought; likewise, if the letter R is used to in
dicate received money, and the subscript s to indicate that the

372

Sec. 1J

APPENDIX TO CHAPTER VI

373

goods are goods sold, the following equation expresses the re
ceipt of money, etc., in exchange for the sale of goods: —
R + R' + R " - R ' " = $PsQs.

If there is no external trade, the several magnitudes in these
two equations mil-evidently be identical on each side. If
external trade exists, each equation may be resolved into an
equation in which are distinguished the home trade and the
outside trade. Thus, for the first equation, relating to ex
penditures, the E, E', etc., may be replaced by H + 0, H' + O',
etc., where the H’s relate to the purchases at home and the
O's to money 'spent outward. On the other side of the equa
tion the 'SpbQb may be replaced by ^phQh+ 2 p * Q * where the
subscripts h relate to the goods purchased at home and the
subscripts i to those coming inward. The equation will then
become: —

(H + H' + R” - H” ') + (0 + 0' + 0" ~ O'")
= %phQh+ SptQi
which, for brevity, we may write 2£T+ 20 = 'SphQh+ ^PtQu
Similarly, the second equation, relating to sales, may be
written: —

'ZH+ 'ZI = %phQh+ 'ZpoQo.

That is, the net sum of the receipts at home (of money, bank
credit, and book credit) plus the sum of payments for goods
coming inward, is equal to the sum of the value of the goods
sold at home plus the value of those sent out of the country.
The last two equations, one relating to purchases and the
other to sales, may be added together so as to give in a com
mon equation the total trade in which the given community
is concerned, that is, the total sales and purchases within
itself and the sales and purchases with respect to the outside
World. The combined equation will be: —
2

20 +

27 =

2 2 phQh +

ZpoQo-

Here the internal trade is counted twice, because every trans
action occurs both as a sale and as a purchase. This expresses

374

THE PURCHASING POWER OF MONEY

[A p p e n d .

the equation of exchange for the total trade (domestic and
foreign) in which the country under consideration engages.
If, instead of adding, we subtract one equation from the
other, we obtain the following: —
20 —27 = %PiQi —2poQo
which is the equation of the balance of trade in its most
general form, taking account, as it does, of credit as well as
of money. The flow of money, as to or from a nation, depends
upon this last equation.
The right-hand side of the penultimate equation, depends
.on three sets of prices,— the home prices (the pn s), the prices
of goods which come into the country (the pi s), and the
prices of goods which go out (the po’s).
If, for instance, thep/^s are extremely high, the consequence
will be a stimulus to goods coming in (Qt) and a discouragement
to goods going'out (Q0), thus tending to make the right side of
the last equation large and, therefore, also increasing the left
side. In other words, there will be a so-called unfavorable
balance of trade and a tendency for media of payments to go
out rather than to come in; that is, there will be an outflow of
money (indicated by 0), or a transfer of bank credit to foreigners
(O'), or a charging on the books of the foreigners (0"), or a less
ening of the liquidations of previous book accounts (O'") ; or
else there will be opposite changes in 7,7', 7", 7'"; or finally,
a combination of both tendencies, while temporarily there
will be fluctuations between these various magnitudes. In
the long run and in the last analysis, the changes will relate
largely to the actual export and import of money, that is,
will concern the unprimed magnitudes 0 and 7.
For a large country like the United States, the outside
trade is so small, compared with the internal trade, as to be
negligible. As we shall see in Chapter XII, the foreign
trade of the United States is only a fraction of one per cent
of the internal trade. And, because the export and import
sides of the various magnitudes (O's, 7's, QoS and Q{’s)

S e c . 1]

APPENDIX TO CHAPTER VI

375

nearly cancel each other, the net balance remaining on either
side of the equation of exchange seldom amounts to more
than one eighth of one per cent of the internal trade of the
United States.
Almost equally insignificant is the difference, E" — E
between debts annually contracted and liquidated, if we may
judge from estimates of that indebtedness, such as Holmes’s.
We are at any rate safe in saying that the corrections to our
equation of exchange which have been discussed in this and
the previous section are needless complications so far as the
United States s concerned. We may therefore consider the
equation MV + M'V' =
as practically a precise form of
the equation.

APPENDIX TO CHAPTER VII
§

(to C h a p t e r

VII, § 2)

Money Substitutes Unlike Other Substitutes
Much reasoning has been based upon the assumption "that
the price determination of two commodities used as money
is analogous to that of any other two commodities. It is
clear, however, that two forms of money differ from a random
pair of commodities in being substitutes.1 Two substitutes
proper"are regarded by the consumer as a single commodity.
This lumping together of the two commodities reduces the
number of demand conditions, but does not introduce any
indeterminateness into the problem because the missing
conditions are at once supplied by a fixed ratio of substitution.
Thus, if ten pounds of cane sugar serve the same purpose as
eleven pounds of beet-root sugar, their fixed ratio of substitu
tion is ten to eleven; or if a bushel of India wheat can replace
a bushel of Dakota wheat, the substitution ratio is unity.
In these cases, the fixed ratio is based on the relative capaci
ties of the two commodities to fill a common need, and is
quite antecedent to their prices. Ten pounds of cane sugar
can replace eleven pounds of beet-root sugar so long as human
taste marks no other ratio. India and Dakota wheat have
the same desirability or utility because they have the same
relation to man’s tastes. No change of market conditions,
1 Substitutes merely in the sense of Gresham’s Law that the
cheaper will be substituted for the dearer. It does not deny that
the metals are differently preferred for different monetary uses.
We cannot compare gold and silver to independent commodities as
“ copper and wheat,*1 or “ beef and shoes/* but only to some other
pair of substitutes, or quasi substitutes, such as iron and steel,
cotton and wool, oats and maize, molasses and sorghum, cane and
beet-root sugar, India and Dakota wheat.

Sec. 1]

APPENDIX TO CHAPTER VII

377

no change of price, could make a consumer regard one bushel
of India wheat as equivalent to two of Dakota. The sub
stitution ratio is fixed by nature, and in turn fixes the price
ratio.
In the single case of money, however, there is no fixed
ratio of substitution. In one age, ten ounces of silver may
circulate as the equivalent of one of gold; in another, twenty
ounces. No human taste or need will interfere. We have
here to deal, not with relative sweetening power, nor relative
nourishing power, nor with any other capacity to satisfy
wants — no capacity inherent in the metals and independent
of their prices. We have instead to deal only with relative
;purchasing power. We do not reckon a utility in the metal
itself, but in the commodities it will buy. We assign their
respective desirabilities or utilities to the sugars or the wheats
before we know their prices, but we must first inquire the
relative circulating value of gold and silver before we can
know at what ratio we ourselves prize them. To us the ratio
of substitution is identically the price ratio and therefore can
have no influence in fixing that ratio. The case of two forms
of money is unique. They are substitutes, but have no natural
ratio of substitution, dependent on consumed preferences.
The foregoing considerations are emphasized for the reason
that they are overlooked by those writers who imagine that a
fixed legal ratio is merely superimposed upon a system of
supply and demand already determinate, and who seek to
prove thereby that such a ratio is foredoomed to failure. This
is the monometallist’s favorite analogy. It is unsound,
though its unsoundness does not necessarily involve the unsoundness of the monometallist’s general conclusions. Gold
and silver or any other two commodities which serve the
purposes of money are not analogous to two ordinary and
unrelated articles and are not completely analogous even to
two substitutes, because, for two forms of money, there is no
consumer’s natural ratio of substitution. There seems,
therefore, room for an artificial ratio. We shall see, however,
that there are limits beyond which an artificial ratio will fail.

378

THE PURCHASING POWER OF MONEY

§ 2 (t o

C h apter

[A p p e n d .

VII

VII, § 2)

Limits for Ratios within which Bimetallism is Possible
A change of ratio is represented by a reconstruction of our
reservoirs in new units, but we can, without the trouble
of such a transformation, exhibit on the mechanism as it
stands the limiting ratios between which bimetallism is pos
sible. Suppose the film in Figure 76 to be forced, firstly to
its extreme right limit, and secondly to its extreme left, and
in each case permanent equilibrium to be attained. In the
one case there is a premium on gold, in the other, a premium
on silver. These premiums mark the divergences from the
given ratio which are possible without destroying bimetallism.
Thus suppose the legal ratio and that for which the mecha
nism is constructed is 32 of silver to 1 of gold and that, when
the film is moved to the left limit, the level of gold will be be
low 00 a distance f as great as the silver level, while at the
right limit it will be -£. Then the ratio 32 to 1 can be varied
between the factors | of 32 to 1 and f of 32 to 1 and bimetal
lism would succeed at any ratio between 32 X -J to 1 and
32 X f to 1, i.e. between 28 to 1 and 40 to 1. A ratio below
28 to 1, such as the famous 16 to 1, would ultimately convert
gold monometallism into silver monometallism, but would
be inoperative in the opposite direction. A ratio above 40
to 1, such as 50 to 1, would ultimately convert silver mono
metallism into gold monometallism. A ratio between the
two extremes would result in neither sort of monometallism
but in bimetallism. The statistical determination of these
limits is, of course, a problem which cannot with present
knowledge be solved. The figures 28 and 40 are not intended
as guesses, but purely as illustrations.

APPENDIX TO CHAPTER VIII
§ 1 (t o C h a p t e r

VIII, § 6)

Statistics of Turnover at Yale University
The rate of turnover of money varies with the amount of
money expended at a given level of prices. In other words, it
varies with the volume of trade of the individual. The statis
tics of turnover among Yale students form two series, the
first or earlier showing an average velocity or rate of turn
over of 34 per year, the second or later, of 66. The differ
ence is probably due in part to the higher expenditure of the
second group of students, although it is probably chiefly ac
counted for by the fact that the first series were not ac
curate. Each student in the first series was simply asked
to estimate roughly his annual cash expenditure and the
average cash on hand. The quotient of the first divided by
the second showed his rate of turnover. Estimates were
received from 128 men. The average annual expenditure in
cash was $514 and the average cash on hand, 815, yielding
the quotient 34 times a year as the average rate of turnover.
These estimates, being usually little more than guesses, may
have been wide of the mark. In order to obtain a more
exact estimate the second series was undertaken. The plan
was adopted of asking volunteers to keep an exact account
for one month of the daily cash expenditures and balances
at the beginning and end of each day. It was found from
these statistics that for the 113 individuals who contributed
these new data, the average annual rate of expenditure was
8660 and an average cash on hand was almost exactly 810,
giving the quotient 66 times a year. The rougher estimates,
the average of which was 34, have so little weight compared
.with the accurate records, the average of which was 66, that
we may place the general average at 60, the nearest round
number below 66. Besides the two student series, returns

379

380

THE PURCHASING POWER OF MONEY

[A p p e n d .

V III

were received from five other persons. One was a stenogra
pher who, during a month, spent at the rate of $435 a year
and had an average cash balance of $7.86, making her turn
over rate 55 times a year. Another was a young librarian
whose cash expenditures, kept carefully for six months,
showed a rate of $854 a year and whose average cash bal
ance was $10.41, making a rate of 82 times a year. A third
was a lawyer who made a practice of paying all bills in cash,
and as these amounted to some $4000 a year, he carried in his
pocket an average cash balance estimated at $175. This
figure he regarded as correct within $15. His velocity of
circulation, on the basis of 4000 divided by 175, shows 23
times a year. The other two cases were of professors. The
first, from careful records, found that he turned over his cash
37 times a year and turned over his bank account 52 times a
year. The second roughly estimated his rate of cash turnover
at 175 and of bank deposits at 25.
Of the total 246 persons whose records were collected, only
116 had kept careful accounts. Of these 116, all except three
were students. The reason for believing that the lower veloc
ity of the first series is not wholly accounted for by its being
erroneously estimated, but is partly due to the smaller ex
penditures of that group, is based on the fact that we find a
distinct relation between amount of expenditure and rate of
turnover within each group. Thus, if we separate the 113
students who gave careful returns into two groups, one,
those who spend less than $50 a month and the other those
who spend $50 and over, we find the following figures: —

No.

op
C ases

A verage
A nnual
R ate of
E xpendi

A verage
C ash
B alance

V el . of
C ircu
lation

ture

Expending less than $600 a
y e a r .....................................
Expending $600 and over a
y e a r .....................................

$ 367

$ 8.60

1175

12.70

Sec. 1]

APPENDIX TO CHAPTER VIII

381

Here we see that the richer men averaged about three times
as great an expenditure as the poorer, but carried only 50
per cent more cash on hand. In consequence, the velocity
of the richer was 93 as against 43 for the poorer, or more than
double. The progressive relation between expenditure and
rate of turnover may be seen by arranging the 113 cases into
five groups according to expenditure.
N o. OF
C ases

Expending less than $300 a year . .
Expending over $300 and under $600
a y e a r ...................................................
Expending over $600 and under $900
a y e a r ...................................................
Expending over $900 and under $1200
a year ...................................................
Expending over $1200 a year . . .

A verage
E xpendi

V el . op
C ircu

ture

lation

179

450

781

10
12

1012
1936

96
137

The number of cases is small, but the results are uniformly
consistent. They show that velocity and expenditure are
directly correlated. Even the other series (of rough esti
mates) show the same general relation. Taking the same
classifications for expenditure, we find that the velocities are
22, 30, 44, 88, 32. Here the only exception is the last figure,
which, as it is the average of only five individuals, is an ex
ception of little importance. We conclude, therefore, with
at least a moderate degree of confidence, that for a given
price level, the greater the expenditure the higher the rate of
turnover. In other words, persons who spend money faster
absolutely than others also spend it faster relatively to the
amount kept on hand. The amount kept on hand by the
rich, though larger absolutely than that kept on hand by
the poor, is smaller relatively to the expenditure.
This law of increasing velocity with increasing expenditure
agrees with the general fact that the larger the scale of any
business operation, the greater the economy. Small stores
have to keep a larger stock relatively to their business than

382

THE PURCHASING POWER OF MONEY

[A p p e n d .

V III

larger stores. Likewise, small banks have to keep a larger
reserve in proportion to business transacted. Professor
Edgeworth has shown a mathematical basis for the fact that
the larger the bank, the smaller relatively the reserve needed.
Hence, we need not be surprised to find that the small pur
chaser finds it well to keep on hand a relatively larger stock
of money than the large purchaser.
The data are too meager to state any exact quantitative
relation between velocity and expenditure. They show that
velocity increases as expenditure increases. But beyond
this we cannot safely go. The data seem to point to the
•conclusion, however, that the velocity increases in a smaller
ratio than expenditure.
§2

(to C h a p t e r

VIII, § 8)

Four Types of Commodities Contrasted
Let us assume four sorts of commodities which we may,
for convenience, designate as wine, sugar, beef, and salt.
We shall suppose that a reduction in the respective prices
of these will have in each case a different effect on the sale.
Accordingly we shall witness four possible effects on the
general price level, following a reduction in the price of the
four commodities respectively.
First, wine. This is assumed to be a commodity of such a
sort that a reduction in its price will be accompanied by a
more than proportionate increase in its sale. Thus the total
amount of money expended for wine will be increased. This
leaves a less amount with which to buy other commodities.
In consequence, the prices of these other commodities, as well
as of the wine itself, must fall.
Next, as to sugar. This is assumed to be such a commodity
that a reduction in its price will be accompanied by an
exactly proportionate increase in sales; so that the total
money expended upon sugar will be unchanged. Under these
circumstances the amount of money to be expended in ex-

Sec. 2]

APPENDIX TO CHAPTER VIII

38 3

change for other things will be neither increased nor de
creased, and other prices will remain unchanged; but the
general level of prices, including that of sugar itself, will be
slightly lowered because the fall of one commodity, when
others do not change, must produce some decrease in the
average.
Third, as to beef. This typifies what is called a “ neces
sary.” We assume that a reduction in its price will be ac
companied by an increase N
in consumption, but not sufficient
to absorb all the money that was previously spent for it.
The total expenditure for beef will thus be reduced, and in
consequence there will be set free a certain amount of money
to be expended for other goods, the prices of which will,
therefore, in general, rise slightly. The net effect, however,
will be an infinitesimal fall of general prices, including beef;
for to the slight extent that there has been an increase of
the total of goods sold by reason of the increase in the sales
of beef, without any increase in the total amount of money spent,
there must be a fall in the average prices.1
Lastly, as to salt. This is assumed to be an “ absolute
necessary,” so that a reduction in its price will not affect the
amount sold. The result will be that the general price level
will be unaffected, the fall in the price of salt being exactly
offset by a compensatory rise in other prices, and the total
volume of trade remaining unchanged.
We see then that the degree of fall in price level due to
the fall in a single price may be great or small or nothing at
all, according to circumstances.
In all of the four foregoing illustrations, it was assumed
that the fall in the individual price originated in a change in
the supply curve or schedule. If the fall in price originates .
1
The mathematical necessity of this result can bo seen from the
formula) in the Appendix to Chapter X , where the right side of the
equation of exchange is transformed into the product of two factors,
tko volume’ of trade ( T) and the price level (Z3). If their product
remains the same, an increase in the volume of trade, however small,
must cause a decrease in the price level.

384

THE PURCHASING POWER OF MONEY

[A p p e n d .

V III

in a change in the demand curve or schedule, there will in
general be a rise in other prices and in the general price
level, for, there being less of the particular commodity bought
and that at a less price, there will be less spent upon it and
therefore more on other commodities, the price of which will
be higher and, as the reduction in the amount bought of the
particular commodity will, in general, imply a reduction in
the total volume of trade, the general price level will be
raised.1
*See Irving Fisher, “ Mathematical Investigations in the Theory
of Value and Prices,” Transactions oj the Connecticut Academy of
' Arts and Sciences, 1892, p. 51.

APPENDIX TO CHAPTER X

§ 1. Each Farm of Index Number for Prices implies a Cor*•
relative Form of Index Number for Quantities
We have seen that the number of possible forms of aver
ages is infinite. Since an index number, as Pi, is an average,
it follows that there exists an infinite number of possible
forms of index numbers. Forty-four of the simplest and
most important forms are given in the table which follows.
In this table the subscript “ 1 ” relates to any specified year
called for convenience “ year 1,” while the subscript “ 0 ”
likewise relates to “ year 0,” called the “ base” year. The
headings of the columns in the table give the formula for
the index number, Pi, for the year 1 relatively to the base
year 0. By substituting “ 2 ” for “ 1,” each formula could
be made to refer to a second year, 2, considered relatively to
the base year 0. Likewise, substituting “ 3,” “ 4,” etc., for
“ 1,” we have an entire series of index numbers, Pi, P2, P3,
f*4, etc., for different years, all relative to the same base year
0. Since the formula) are all alike and differ only in sub
scripts, it is unnecessary to waste space by expressing P2,
ft, etc., in the headings. Consequently, in each column
heading, only the formula for Pi is expressed.
Also to save space, the column headings omit the formulae
for Ti, etc., correlative to those for Pi. Each form of price
index, Ph applicable to the equation of exchange, implies a
correlative trade index, T\, such that the product of the two
is equal to SpiQi, the right side of the equation of exchange.

PXTX= 2piQh

Since

it follows that T\ =

*1
Hence, given a particular formula for Pi, we have a result
ant and particular formula for T\. For instance, if Pi is-a
2c

385

386

THE PURCHASING POWER OF MONET

simple arithmetic average of

[A p p e n d .

/
//
^(n)
2^, 2 * •••2 *
Po P o P o
p(%

i.e. if

Pi = i 2— (formula 3 of the table), where n is the numn p0
ber of commodities of which the price ratios are included,
then the correlative formula for Ti will evidently be

m _ SpiQi _ SpiQi
1
A 221*
^ Po
Again, if Pi is the geometric average \ Si •2_L. TL± ... 2 ^
^Po P o P o p%
(formula 7 of the table), then T\ has the correlative form
SpiQi
w/p i.p Lmmm
^Po p'o
Conversely any particular formula for T\ implies a correl
ative particular formula for Pi. For, since

PiT^ZpiQi,
it follows that
p _ SpiQi
1
Ti *
By means of this equation, if we have given any particu
lar formula for Ti, we may obtain a resultant particular
formula for Pi.
The examples already given of Pi (the arithmetical and geo
metric average) illustrate how to obtain the correlative formula
for Ti. If we work backward from these somewhat compli
cated formulae for Ti, we may in turn derive as the correla
tive formulae for Pi the arithmetic and geometric averages.
As a third example illustrating the derivation of the
formula for Pi from a given formula for T\, let T\ be
defined as 2p0Qi; then
P - 2PiQi
1
Ti
SpoQi
(Formula 11 of the table.)

Sec. 1]

APPENDIX TO CHAPTER X

387

We may consider, then, that each column heading, though
stating only the formula for Pi, implies also a corresponding
formula for T\; that is, Pi and Ti occur in correlative pairs.
Pi and Ti are such that if one of them (say Pi) is given
independently of the equation, ^piQi = P1 T1 , the other is
then defined by means of that equation.
The two magnitudes Pi and Ti are not, however, abso
lutely symmetrical. There is this important distinction
between them: that, while Pi is an abstract number, Ti is
concrete, being expressible in dollars and cents.
It thus appears that, although the p’s and Q’s enter sym
metrically into the expression SpiQi, yet, when this expression
is replaced by PiTh the first factor, Pi, represents the p’s in
a somewhat different manner from that in which the second
factor, Ti, represents the Q’s. Pi is a pure number, an aver
age of pure numbers— the ratios the p’s bear to the base
prices, po’s, whereas Th being -

>is a concrete number,
Pi
being a value found by dividing the value 5piQi by the
pure number Pi.
Thus, while the p’s and Q’s occur symmetrically in the
original formula SpiQi, the process by which we convert
SpiQi into P1 T1 treats them asymmetrically. But evidently
we can reverse the asymmetry in their treatment; for, in
stead of putting SpiQi equal to P1 T1 , we may put it equal to
AiQi, in which Qi is now a quantity index, that is, an average
of the ratios which the Qi’s bear to the Qo’s or base quanti
ties (i.e. an average of ~
”m
\ anc* ^i, being
\
Qo Q o Q o /
therefore
is the “ aggregate price,” that is, the value
Qi
found by dividing the value SpiQi by the pure number Qi.
Here, if the form of Qi is given independently of the equa
tion SpiQi = AiQi, the form of Axis defined by means of this
equation, and conversely.
Thus we may convert
into either PiTi or A\Qi. In
the first, the p’s are represented by a ratio, Pi ; in the second,

388

THE PURCHASING POWER OF MONEY

[A p p e n d .

by a value, Ai; in the first, the Q’s are represented by a value,
Ti; in the second, by a ratio, Qi. The asymmetry of each of
the two formulse PiTi and A\Q\ is the reverse of the other.
Finally we may, if we wish, treat both the p’s and Q!s
alike by putting SpiQi equal to (2p0Q0)Pi()i, where Pi and Qi
are, both of them, index numbers for the pi’s and Qi's
respectively. That is (as we shall prove), Pi and Qi are

averages respectively of price ratios like

and of quantity
Vo
ratios like — • The equation 2piQi = (2p0Q0)Pi@i may be
Qo
said to define either one of the two averages (Pi and Qi) in
terms of the other. One or the other must be defined irre
spective of the equation.
Thus there are three ways of resolving SpiQi, as follows
SpiQi = PiTi = AiQi = (3poQo)P1 Q1 •
The third form becomes, dividing the equation through by
SpoQo,
12# = p 1<?1.
a)
^PoQo
We wish now to prove that if either Pi or Qi is first de
termined in any way conformably to the definition of an
average, leaving the other to be determined by the above
equation, then the latter also necessarily conforms to the
definition of an average. We have to prove that if Qi is
O Qr
taken as an average of
then the correlative exQo Q o
pression for Pi derived from (1), viz.: —
SpiQi

SpiQi
^PoQo

t> _ ^PoQo __

P i — qT '
is an average of

Qo’ Wo )

(2)

it is, therefore, only necessary to
Po p o

show (in accordance with the most general definition of an

Sec. 1]

APPENDIX TO CHAPTER X

389

average as given in the Appendix to Chapter II) that ex
pression (2) shall be equal to k when
& = 2J = . . . = &
Po Po
(and when at the same time
Q \ — ~ tj \

Qi _

Qo Q'o

We therefore suppose that
2i = ?£ = .'•. = h,

so that
and also that
so that
Then
Now, since

Po po
Pi = kpo; p\ = Jcp'0; •••;
—=
= •••= k',
Qo y o
Qi = k'Qa; Q\ = k'Q\;
SpiQi = 2(7cp0X k'Qo) = kk' ZpoQo.
7T = 7T = •••= &',
yo yo

it follows that (^Av.
^r, •••') = 7c'
\
y#
/
by the definition of an average.
Hence the expression (2) may now be written
kk' SpoQo
SpoQo
k'
which is evidently equal to k.
Therefore expression (2) is, by definition, an average of
j/ ” *

same reasonin£ we may show conversely
SpiQi

that

____ SpoQo____
( Av. 21, 2lt..A
\

Pa Po

is a true average of —,
Qo Q o

We conclude that if either

390

THE PURCHASING POWER OF MONEY

[A p p e n d .

is an average of the p or
SpoQo
Q ratios respectively, then the other is also an average re
spectively of the Q or p ratios.

Pi or Oi in the formula Pi(?i =

§ 2. Index Numbers for Prices occur in Antithetical Pairs as
also do Index Numbers for Quantities
We have seen that, given any special form of average for
Pi, there results therefrom a correlative form for Qi and vice

versa. Thus if Pi is the simple arithmetical average - 2
n po
SpiQi
then Oi is

■° . Again, if we start with Qi as the simple

n
arithmetical average i 2 then we discover in its correlate
n Qo
SpiQi
anew formula for Pi, viz. -- ■
■
In this way any given
1
n Qo
formula for Pi leads to another formula for Pi which may be
called its antithesis. This second formula for Pi is identical
in form with the formula for Qi correlative to the first for
mula for Pi, differing merely in the fact that the pi’s and Qi’s
are interchanged.
The four forms and their relations are best seen by placing
them in a square, as in the following example :—
2?Pi
2piQi

Pi = —^
n

antithetical to
S^i

correlative to
SpiQi

Qi = ~
n po

Isa

Pi =

n Qo

correlative to
x-Qi
antithetical to

& = — -•

Sec. 2]

APPENDIX TO CHAPTER X

391

The pair of formulse in the left vertical column express
correlative formulse, one for Pi and the other for Q\. The
formula diagonally opposite each of these has the p’s and
Q’s interchanged. The right pair thus formed are evidently
also correlates of each other and each is the antithesis of that
in the same horizontal line at its left. Since any formula
for P1involves an antithetical formula for Pi, we have here
a means of devising new formula? from old and also of noting
certain unsuspected relationships between formulas already
in use.
In the table of index numbers for Pi which follows, the
antithetical formulse are in each case placed side by side
and joined by a bracket. The two together represent, in
each case, the upper half of a square like the above. The
omitted lower half, giving the correlative forms for Qh can
be readily supplied in every case; but, to save space, each
column heading in the table only includes the formula for
Pi, omitting its correlate for Qi as well as the corresponding
formulse for T\ and A\. The formula for Qi is, as above
explained, easily written by interchanging p’s and Q’s in the
formula given in the neighboring (antithetical) columns;
that for Ti is found by dividing SpiQi by Px; that for Ai by
dividing SpiQi by Qu Practically Pi and Ai serve the same
purpose, namely, that of indicating price changes; likewise
Qi and T\ serve the same purpose, namely, that of indicating
quantity changes. For any series of years the numbers for
Pi and for Ai will be proportional, the only difference being
that Pi is expressed in percentages, the figure for the base year
being 100 per cent, whereas Ai is expressed in dollars, the fig
ure for the base year being the actual exchanges 2p0Qo in
that year. Likewise Qi and Ti differ merely as percentage
and dollar measurements, the base figure being 100 per cent
and SpoQo dollars respectively.

392

THE PURCHASING POWER OF MONEY

[A p p e n d .

§ 3. General Meanings of p’s and Q’s
We may here pause to point out that the whole present
discussion relates purely to the form of an index number of
p’s and Q’s without reference to the meaning to be assigned
to these p's and Q’s. These meanings may be far wider
than simply the prices and quantities in the equation of
exchange. For example, an index number of prices may be
constructed with reference to the purchasing power of a
workman's wages. In this case, the same formula as be
fore, 'SpiQi, may be employed, but the terms have different
meanings. The p’s now relate to the prices of goods enter
ing into the workmen's budgets, and the Q’s to the quantities
of workmen's goods entering into their consumption. In this
case, the price index, P, indicates the price level of work
men's consumption, and the index, T, means an index for
workmen's real-wages. Any special form of price index now
implies a correlative special form of real-wages index.
Again, if we are studying statistics of capital such as in
Giffen's Growth of Capital, we have
as the value of capi
tal, the p’s being the prices of different forms of capital and
the Q's, their quantities. For every special form of price
index number, P, representing the price level of capital,
there will be a correlative special index of capital showing
the real “ growth of capital” as distinct from its mere money
value. Such an index seems seldom to have been employed.1
Yet it is evidently advisable to distinguish between an ap
parent increase of capital due to inflated prices and a real
increase, as would be shown by such an index as here
suggested.
1 See GifFen, Growth of Capital, London (George Bell and Sons),
1889, pp. 50-54, where allowance is made for changes in the price
level. Index numbers of the Econo?nist, of Sauerbeck, and of
Soetbeer are cited. Professor J. S. Nicholson has advocated such
a capital-standard in the Journal of the Royal Statistical Associationt
March, 1887, pp. 152 ff. This method is discussed by Edgeworth,
Report of the British Associationt 1887, p. 276.

Sec. 3]

APPENDIX TO CHAPTER X

39 3

We see, therefore, that wherever prices and quantities are
united, we have the requisite conditions for constructing
correlative pairs of index numbers, one index in each pair
relating to prices, and the other to quantities.
We shall, however, for convenience, continue to employ
the magnitude T, rather than Q, and to refer to it as a
" trade” index.
§4. Review of 44 Formulas, heading the Table Columns
We shall now briefly review the formulae of the table of
selected index numbers. Each even-numbered formula is
best regarded as derivable from the odd-numbered formula
at its left as its antithesis. The odd formulae are those con
structed directly for the p’s without reference to any average
for the Q’s; the even are constructed indirectly by refer
ence to some average first assumed for the Q’s. The latter
are what Walsh had in mind under the name of “.double
weighting.”
Formula (1) is simply the ratio of the sums of prices. It
may also be considered as the ratio of the averages of prices
in the two years considered, as is evident by writing it, —

*Ei
SB
n

, where n is the number of commodities employed.

This formula was used by Dutot in 1738,1and has been
used recently by Bradstreet,2 who applied it practically.
Although it is a ratio of average prices, it may also be
thrown into the form of a weighted arithmetical average of
the price ratios,

2Li etc., as the following transforPo

Po p o

mation shows: —
1 See Walsli, Measurement of General Exchange Value, New York
(Macmillan), 1901, pp. 534, 553.
1 Bradstreet's Journal from 1895.

394

THE PURCHASING POWER OF MONEY

[A p p e n d .

Spi =zpi + p'i + p” i+ —
p<>+ p,o+ p,/o+ *•*

2po

Po + p'o + p "o +

—

The formula in this last form is evidently the weighted arith
metical average of the ratios in parenthesis, the weights be
ing the prices p0} p'o, p"o, ••• of the year 0. A change in
the units of quantity for the various goods would change
these prices; thus a change from ounces to pounds would
multiply the number expressing price by sixteen. Such a
change in any price, such as po, would entirely change the
relative importance of the “ weights,” po, p'o, etc. Conse
quently this system of weighting is, as Walsh says, quite
accidental or haphazard.1
The same formula is also a harmonic average, as the follow
ing transformations show: —
Spi = pi +

2p0

p /i +

Po + p'o +

—

Pi + P'i +

—

pi + p'i + —
The last expression is evidently the reciprocal of a weighted
arithmetical average of the price ratios in parenthesis. But
these price ratios are the reciprocals of

(p7^)’ (p77^)' etC#

In other words, the formula is the reciprocal of a weighted
1 Walsh, op. cit., pp. 81 and 82.

Sec. 4]

39 5

APPENDIX TO CHAPTER X

arithmetical average of the reciprocals of the ratios

etc.

It is therefore the weighted harmonic average of these ratios
Pi
etc., the weights being pi, pi , etc., or the prices of the
year 1.
In short, formula ( 1) is both an arithmetical and a har
monic average of

2 J, etc., the weights being, in the first
Vo Vo
case, the terms of the denominator, and in the second, those
of the numerator.
We have vseen that formula (1) in the table, although
primarily a ratio of averages of prices, may be also con
sidered as an average of ratios of prices with arbitrary
weighting.
Conversely we may, if we choose, regard every average of
ratios as a ratio of averages by assuming arbitrary units for
measuring commodities. It is evident that, if the unit of
measure is increased in any ratio, the number expressing
the price is decreased in the inverse ratio. If, therefore, we
change the unit of measure of a commodity the price of
which is at first expressed by pi by dividing by the ratio p0,

this price becomes 2^. Thus 2imay be considered to be a
Po

price as well as a price ratio. Hence an average of —,

£77!,

Po P o p 0

etc., may be regarded as an average of prices. The new
units, instead of being pounds, yards, etc., are dollars-worth-inthe-base-year. With these units, the price in the base year is
unity, for dividing the price, p0j in the original units by the
factor po, we obtain unity.
Hereafter, however, we shall treat all index numbers as
averages of price ratios.
It is interesting to note that the antithesis of Dutot’s or
Bradstreet’s formula (No. 2), found by dividing the frac
tion

*PoQo

by the correlative formula for Qi, viz.,

*Qo

turns

396

THE PURCHASING POWER OF MONEY

[A p p e n d .

out to be that advocated by Drobisch,1 and earlier by Sir
Rawson-Rawson.2
Formula (3)3 is evidently the familiar simple arithmetical
average,—

Formula (4), the antithesis of formula (3), gives, as the
average price ratio, the ratio of total values 3piQi / 'SpoQo
corrected for change in the Q’s by division by the arith
metical average ratio of the Q’s.
Hereafter the even-numbered formulae, being antitheses of
the preceding odd formulie, will be passed over unless there
is, in any case, special reason for mention.
1 See M . W . Drobisch, “ Ueber Mittelgrossen und die Anwendbarkeit derselben auf die Berechnung des Steigens und Sinkens des
Geldwerthes ” (Berichte uber die Verhandlungen der Koniglich sticksischen Gesellschaft der Wissenschaften zu Leipsig; Mathematischphysische Classe, Band X X II I, 1871, pp. 25-48).
Also “ Ueber die
Berechnung der Veranderungen der Waarenpreise und des Geldwerthes” (Jahrbucher fur National-oekonomie und Statistik, 1871,
Band X V I, pp. 143-156) ; and “ Ueber einige Einwiirfe gegen die in
diesen Jahrbiichern veroffentlichte neue Methode, die Verander
ungen der Waarenpreise und des Geldwerthes zu bereehnen”
(ibid., 1871, Band X V I, pp. 416-427). See also Walsh, op. cit
pp. 97-99, where the method is explained.
2 See Edgeworth, Report of the British Association for the Ad
vancement of Science, 1889, p. 152. Sir Rawson-Rawson’s sug
gestion, as developed by Edgeworth, was to divide the Vtilue of
exports (or imports) by the tonnage of exports (or imports) and
consider the result as an index number of prices of exports (or im
ports). The suggestion was made not for any theoretical virtues,
but because of the practical ease of computation. Edgeworth
compares the results of Rawson’s rough and ready method with the
more exact method of Giffen by actual figures for 1886 compared
with 1885, and finds substantial agreement.
3 For a statement of the history of this formula from Carli to the
present, see Walsh, op. cit., p. 534.

Sec. 4]

APPENDIX TO CHAPTER X

397

Formulae (5), (7)1, and (9)2 are respectively the simple
harmonic, simple geometric, and simple median averages.
We note that the antithesis of (7), viz. (8), is one proposed by
Nicholson and Walsh.3
Formula (ll)4resembles Bradstreet’s, except that the in
troduction of the Q’s as multipliers prevents the weighting
from being arbitrary; for the weights p0Qi, etc., unlike the
weights po, etc., are uninfluenced by a change in the units
of measurement for commodities. Whether an article be
measured in pounds or ounces will not affect the value of a
given amount of it. The following transformations show
that the formula is a weighted arithmetic mean : —
SpiQi
2p0Qi

PiQi + p'jQ'i + —
PoQi + p/oQ/i + •••

PoQi + p,oQ/i + •••
The last expression is evidently a weighted arithmetic
average of the price ratios in the parentheses, the weights
being p0Qh p'0Q'i, etc., i.e. the values of the quantities in the
year 1reckoned at the prices of year 0.
But the same formula is also a harmonic average, as may
be seen by transforming the denominator instead of the
numerator as was done for formula (1). It is a weighted
harmonic average, the weights being piQi, p\Q'i, etc., or the
values in the year 1.
In short, formula (11) or
is, like formula (1), both a
*PoQi
weighted arithmetical and a weighted harmonic average of
1 See Jevons, Investigations in Currency and Financey London
(Macmillan), 1884 ; Edgeworth, Reports British Association, 1887,8,
9; Walsh, op. cit.j pp. 22911.
2 See Edgeworth, Reports British Association, 1887, 8, 9, esp.
1888, pp. 206 ff.
3 Walsh, op. cit., p. 548.
4 For Formuloo 11 and 12 there exists a large literature.
Walsh, op. cit., esp. pp. 191 ff., and pp. 539 ff.

Sea

398

THE PURCHASING POWER OF MONEY

Po V o V o

[A p p e n d .

>etc., but the weights are different in the two

cases.
(11) has the interesting property that its antithesis (12) is
of the same form except that the subscripts for Q are now 0
in place of 1. Similar reasoning shows that this formula (12)
is also both an arithmetical and an harmonic average, weighted
according to the terms in its denominator and numerator
respectively.
These two formulae, (11) and (12), seem to be the favorites
among writers on Index Numbers. Since the shortcomings
of one are, in some cases, not shortcomings of the other, there
have been many attempts to combine them into some com
posite. No. (13),1 for instance, is their simple arithmetical
average. The antithesis of (13), viz. (14), turns out to be the
simple harmonic average of (11) and (12). Number (15) is the
simple geometric average of (11) and (12). This formula (15)
has the distinction of being identical with its own antithesis
(16). Numbers (17), (19), (21), and (23) are other attempts
at combining (11) and (12), not by averaging them, as was
the case with (13) and (15), but by averaging their coefficients,
viz., Qi and Qo, Q\, and Q'0, etc. Two antitheses of these,
namely (18) and (22), turn out to be formulae proposed by
Walsh, and a third (24) to be one proposed by Julius Lehr.2
We have seen that the formulae (11) and (12) considered
as arithmetical averages have for weights
PoQi, p'oQ'i, p"oQ"i> etc., for No.
and
VoQo, p'oQ'o, v"oQ"o, etc., for No.
We next use weights
ViQh v'lQ'h p"iQ"i> etc., for No.
and
piQo, p'iQ'o, p "iQ "o , etc., for No.

(11),
(12).
(25),
(27),

1 For references to literature concerning this and many others
among the remaining formulae of the table (col. 13-44), see Walsh,
op. cit.
2Beitrage zur Statistik der Preise, Frankfurt-a.-M, 1885 (p. 11 and
pp. 37-42 for the method). The method is explained in Walsh,
Measurement of General Ezchange-Value, pp. 386-388.

Sec. 4J

399

APPENDIX TO CHAPTER X

thus completing the four permutations of the subscripts, 01,
00, 11, 10. Number (29) represents a weighted arithmetical
average in which the weights are derived from other con
siderations than the product of the prices and quantities of
the base year (1). An instance is the method employed in
some of the tables in the “ Aldrich Report,” 1 the weights
being the percentage of consumption of various kinds in
workingmen’s budgets without reference to the base year or
any other particular year.
Numbers (31) and (33) are weighted harmonic means in
which the weights instead of being

PiQh etc., as in (11),
piQo, etc., as in (12),
p0Qh etc., for (31), '
poQo, etc., for (33),

or
are
and

thus completing for harmonic averages the same permuta
tions of subscripts as before for arithmetical averages. We
see then that the odd formulae (11) to (33) inclusive are
merely arithmetical averages or harmonic averages of

Vo
etc., or else averages or mixtures of such averages.
Numbers (35), (37), (39), (41) are various forms of
weighted geometric averages of those price ratios, the
weights being
PiQu etc., for (35).
poQo, etc., for (37).
piQo, etc., for (39).
PoQi, etc., for (41).
Number (43) is the ratio of the weighted geometric aver
age of the prices in years 1 and 0, the weights being piQi, etc.,
for year 1 and poQo, etc., for year 0.
1 Report on Wholesale Prices, Senate Report
52d

Congress,

1893.

1394, 2 d

Session

400

THE PURCHASING POWER OF MONEY

[A p p e n d .

It will be seen that all of the 44 formulas selected for the
table are based on a few simple principles of averaging.
Most are arithmetic, harmonic, or geometric averages or
their combinations. Needless to say, numerous other and
more complicated forms might be constructed.
§ 5. Review of Eight Tests, heading the Table Rows
Having reviewed the headings of the vertical columns of
the table, we have next to note the headings of the horizon
tal rows. These headings are the eight tests of index* num
bers. The first six tests are arranged in pairs, the odd being
expressed in terms of prices and the even in terms of
quantities.
T h e E ig h t T ests f o r a G ood I n d e x N u m b e r

The eight tests are intended to include all the tests which
have been hitherto applied in the study of index numbers
and some others. They are:
1. Test of proportionality, as to prices.
2. Test of proportionality, as to trade.
3. Test of determinateness, as to prices.
4. Test of determinateness, as to trade.
5. Test of withdrawal or entry, as to prices.
6. Test of withdrawal or entry, as to trade.
7. Test by shifting base, both as to prices and as to trade.
8. Test by shifting unit of measurement, both as to prices
and as to trade.
We shall first define each of these tests in general terms
and then proceed to illustrate them by actual applications.
1.
Test of proportionality as to prices. A formula for the
price index should be such that the price index will agree
with all individual price ratios when these all agree with
each other. Thus, if in 1910 the price of everything is 10 per
cent higher than in 1909, the index number should register
10 per cent higher.

Sec. 5]

APPENDIX TO CHAPTER X

401

2. Test of 'proportionality as to trade. Likewise the cor
relative formula for the trade index should be such that the
trade index will agree with all individual trade ratios when
these all agree with each other.
3. Test of determinateness as to prices. A price index should
not be rendered zero, infinity, or indeterminate by an individ
ual price becoming zero. Thus, if any commodity should in
1910 be a glut on the market, becoming a “ free good,” that
fact ought not to render the index number for 1910 zero.
4. Test of determinateness as to trade. The correlative trade
index should not be rendered zero, infinity, or indeterminate
by an individual quantity becoming zero. Thus, if any com
modity should go completely out of use in 1910 so that its
quantity exchanged becomes zero, that fact ought not to
render the trade index for 1910 indeterminate;
5. Test of withdrawal or entry as to prices. A price index
should be unaffected by the withdrawal or entry of a price
ratio agreeing with the index. Thus, if the price index of a
certain number of goods, not including sugar, should be 105
in 1910 as compared with 1900, and the price of sugar itself
should be 105 in 1910 as compared with 1900, then the in
clusion of sugar in the calculation of the index number ought
not to change the index from 105.
6. Test of withdrawal or entry as to trade. The correlative
trade index should be unaffected by the withdrawal or entry
of a quantity ratio agreeing with the index.
7. Test by changing base. The ratios between various price
indexes (and therefore also, as we shall see, the ratios between
the correlative trade indexes) should be unaffected by revers
ing or changing the base. Thus, if the index number for 1910
is twice that for 1900, when calculated on the basis of 1860,
it should remain twice, when calculated on the basis of 1870.
8. Test by changing unit of measurement. The ratios be
tween various price indexes (and therefore also, as we shall
see, the ratios between the correlative trade indexes) should
be unaffected by changing any unit of measurement. Thus,
if the index number for 1910 is twice that for 1900 when coal
2 d

402

THE PURCHASING POWER OP MONEY

[A p p e n d .

is measured by the ton, it should remain twice, when coal is
measured by the pound.
The statements of tests 7 and 8 are expressed in each case
both as to prices and quantities; in these cases it was im
plied that what holds true of price indexes holds true also of
trade indexes, and vice versa. To show this reciprocal rela
tion for test 7 (base shifting), let the price index for year 1
in terms of year 0 be designated by Pi, o instead of by Pi as
heretofore, in order that the base year may be specifically
designated, and let us compare years 1 and 2 by using first
year 0 as a base and then (say) year 8. If the base-shifting
test is fulfilled for the P’s, i.e. if

we are to prove
P2 , 0 P2 , 8
that the corresponding relation is also true for the IT’s, viz.
that
T\y 0 _ Ti, 8 ,

? 2, 0 T23 8
We know that

(1)
(2)
(3)
(4)

Divide (1) by (2) and (3) by (4). The quotients are

and
Comparing the right sides of these equations, we find that
the 112 ” ratios are identical in the two cases, and we know
that the P ratios are equal by hypothesis. Consequently

Sec. 5]

APPENDIX TO CHAPTER X

403

the entire right sides of the two equations, and therefore
the left sides, are also equal, and this is what was to be
proved. The converse reasoning is also evident.
Like the base-shifting test, the unit-shifting test, No. 8,
cannot apply to prices without applying also to quantities,
and vice verm. To show this we employ the equation T —
Evidently the numerator of the right side of this
equation is unaffected by a change of unit. For instance,
if coal should be measured in ounces instead of tons, thus
greatly increasing the number (say Q) representing its quan
tity, the value (pQ) will not be disturbed, since the number
(p) representing the price will be correspondingly diminished.
Consequently, if the denominator (P) meets the correspond
ing test, i.e. is likewise unaffected by a change in unit, the
quotient (T) must be unaffected. That is, if the unit-shift
ing test is met for P, it must be met for T. As the con
verse reasoning also applies, the proposition is proved.
As will have been noted, the first six tests are expressed
alternately in terms of 'prices and in terms of quantities.
We now wish to point out that those expressed in terms of
prices have a significance for quantities also, and that those
expressed in terms of quantities have a significance for prices
as well. That is, all the tests have significance both as to
prices and as to quantities.
To emphasize this fact, which is important, let us note the
price significance of each test. Since the price significance
of tests 1, 3, 5, 7, 8 is evidently expressed in the statement
of the test, we have left merely to express the price signifi
cance of tests 2, 4, 6.
Test 2 tells us that if all the trade ratios agree, their index
should agree with them; that is,

Qi _ Q'i _ Q"_\_____ *

404

THE PURCHASING POWER OF MONEY

[A p p e n d .

The question now before us is, assuming this condition to hold
as to the Q’s, what condition holds true as to the p’s. The
answer evidently is:—
SpiQi
Pi = Tx = SpiQi ^ T i = fcSpiQa
P2

^^2^2

'%p2Q2

^PlQl

[obtained by substituting kQ2for Qi, kQf2for Qi, etc., and kT2
for 7M
=
.
J
2P2Q2 MQ'i
The last form is derived from the next to the last by multi
plying both numerator and denominator by k and then sub
stituting Qi for kQ2, Q'i for 7cQ'2, etc.
f
p
The resulting two formulse for •
— express test No. 2 in
P2
terms of the conditions to which prices must conform.
These formulse will be recognized as those discussed in § 7
of the Appendix to Chapter II, the significance of which was
there explained. It was there shown that a change in M, or
a change in F, or a uniform change in all the Q’s, or any
combination of these changes will, through the equation of
exchange, affect the price level in the manner expressed by
the formula:—
P i = ^piQ i = Q2
^p-zQi SpiQ*

Spi

Thus the equation of exchange itself prescribes test No. 2;
for the fundamental theorems which the equation of ex
change has taught us are that prices vary directly as M and
as the V’s and inversely as the Q’s; and the only forms of
index numbers which will faithfully reflect these changes, i.e.
will vary directly with M and inversely with the Q’s (assum
ing that all Q’s vary in unison), are those forms of index
numbers which conform to test No. 2. Any other form of in
dex number, when M (and M') increased 50 per cent and there
was no change in V’s or Q’s, might register a rise of 49 per cent

Sec. 5]

APPENDIX TO CHAPTER X

405

or 51 per cent. That is, no other forms of index numbers will
enable us to say that when the quantity of money changes, the
velocity of circulation and the Q’s remaining the same, the
index number of prices will vary proportionately. No other
forms will enable us to state the corresponding theorem
as to the effect of a change in velocity or of a (uniform)
change in the Q’s. But these theorems are fundamental. The
very concept of an index number is that it shall replace the
divergent individual variations and enable us to state of its
proportionate changes the same theorems which hold true
when prices all change alike.
Test No. 2 is therefore of such fundamental importance
that we may profitably pause a moment to restate it in
words. To be concrete, let us suppose two years, 1900 and
1910. Let us assume that the quantity of' every kind of
goods sold in 1910 is (say) exactly double the quantity sold
in 1900. Then the only proper ndex number showing
the level of prices in 1910 (year 1) as compared with the
level of prices in 1900 (year 0) is

the ra^° the total
Zpotyi
value of the goods sold in 1910 to what that value would
have been at the prices of 1900; or, what amounts to the
same thing, it is

2p0Qo

the ratio of what the total value of

the goods sold in 1900 would have been at the prices of 1910
to what it actually was at the prices of 1900.
Of the 44 formulae in the table, only the following reduce
to the required formula when the Q’s change uniformly:
(2) of Drobisch, (4), (6), (8), (10), (11), (28), (30), (34), (38),
(40). All these are even-numbered except formula 11.
Several others will reduce to the required formula, provided
one of the years compared is the base year.
The formulae of the tables which fail to meet test 2 at all
would not even allow us to say of MV+M'V'=PT that if
all the Q’s remain the same, T will remain constant and
P will vary as the other side of the equation. For these
formulae T fails as a true index of the Q’s, and its error

406

THE PURCHASING POWER OF MONEY

[A p p e n d . X

in one direction implies a corresponding error in P in the
opposite direction.
Test 2 seems therefore in some respects the most important
of all ‘the eight tests for prices; although primarily it was
not stated in terms of prices, but in terms of quantities. It
is the only test which indicates the kind of weighting re
quired. It completely prescribes the conditions which,
while permitting any individual changes in prices, however
divergent, enable us to say that a change in M or the two
F’s or in all the Q’s in a given ratio will affect prices “ on
the average ” in that same ratio (directly, of course, for the
ATs and V’s and inversely, for the Q’s).
Test 2 in fact points out the true form of the index num
ber of prices as prescribed by the equation of exchange under
all possible circumstances except when the Q’s vary in un
equal proportions. It also points to the proper weights
required. These weights may be said to depend either on
the Qi’s or on the Qo’s, interchangeably. The formula sug
gested by the Qi*s is formula 11; that suggested by the Qo?s
is formula 12. Either will be perfectly satisfactory when the
Qi’s and Qo’s are proportional, while when they are not, their
discrepancy is negligible. When the Q’s vary unequally,
however, there seems to be no perfectly satisfactory formula.
Under these circumstances the two systems of weights —
one in terms of Qis, the other in terms of Qo’s — conflict
with each other. But the conflict has been shown by Edgeworth 1 to be slight. In fact, the weights are of much less
importance in determining an index number of prices than
the prices themselves.
The discussion of test 2 will be resumed later when in § 7
we come to compare the various forms of index numbers.
1 Report of the British Association for the Advancement of Science
for 1887, pp. 288-292 and for 1888, pp. 197-198, 200, 202, 203, 206.
Edgeworth shows in the case specified by him that an “ error” in the
weights only makes an “ error” one twentieth as great in the re
sultant index number, while an “ error” in the prices themselves
makes an “ error” in the resultant index number one fourth or fifth
as great.

T e sts A lg e b r a ic a lly S ta te d
T W O Y E A R S COMPARED

S p e c ia l C

407

APPENDIX TO CHAPTER X

S ec . 5]

ase

w hen

SU B STIT U T E “ 0 ”

one

fo r
TO

th e

PRICES
the

tw o

years

base

year

Tiie T e st Hequibes t e a t
(as t o p ’ s)
(as to <>’s)

e .

P i^ P iQ i
P,

~PiQ*

2 p 1(21 “ 2p ,(?i

P1 and P 2 determinate

p t — 0 or
Test 3,
Determinateness P j » 0, etc.

and not zero nor In
finity

as t o p ’ s

Test 2,
Qi
Proportionality as 3
to 4 ’s

p - t

5 -*
and T, determinate
and not zero nor
infinity

I 1!
o o

Px and P j determinate Tx and T9 determinate
and not zero nor in
finity

as to Q's

and not
infinity

T't

zero

nor

2p \ Q \ .P t

P ',
r*
^P'iQ'i ‘ P ,
(Primes signify that
(Primes signify p it

entry as to p ’ s

Pv Pi>

Qt are

excluded; absence of
primes signifies they
are included.)
P 'i
-P'iQ'i . Tt
P ' r ^ P Y / 2 ‘ T%

(Primes and their
absence signify as
above.)

Base changed from
oo Pi» 8
Test 7,
“ 0 ” to “ 8 ” chang Px» o P a- s
By changing base
ing:

Pt> Qh Qt are ex
cluded ; absence of
primes signifies they
are included.)

TLl T’,

(Primes a n d their
absence signify as
above.)

7i»
Pji o

Pi» o to Px» 8
A* o to P *8

0t o

o to Tx, 3
<2x and pi changed in
Test 8,
§ unchanged
inverse ratio
By changing units
*i
of measurement.

any
TH E

ojld?
rj aj
vrl/T

P'»

Test 6,
By withdrawal or «»
entry as to <2’s

(F O R

<>|<S

Test 1,
Proportionality as Pi
to p ’s

Test 5,
By withdrawal or

C ase

TRADE.

FOR “ 2 . ” )

G iven

Test 4,
Determinateness

G en era l
AN D

T
~ unchanged

408

THE PURCHASING POWER OF. MONEY

[A p p e n d .

As to test 4, this states that if an individual quantity be
comes zero this fact should not render the quantity or tradeindex zero, infinity, or indeterminate. But according as the
index does or does not become zero, infinity, or indetermi
nate, will the price index become or not become infinity, zero,
or indeterminate respectively. This is clear from the rela
tion Pi = —

- • Hence test 4 possesses a significance as to

prices similar to that which it possesses as to quantities.
The price significance of test 6 is more complex and of no
apparent importance. Its statement is included in the ex
planatory table on page 407. In the preceding table of
44 index numbers the “ score” for test 6 is bracketed to
indicate that it has no important price significance, and is
to be omitted in the totals.
Mutatis mutandis, each of the tests expressed in terms of
prices (tests 1, 3, 5) has a significance as to quantities also.
The preceding explanatory table exhibits in algebraic terms
both hypothesis and conclusion for each of the eight tests
with respect both to prices and quantities.
§6. The Interior of the Table; Column 11 in Particular
We have reviewed briefly the headings of the table, includ
ing both those of the vertical columns and those of the hori
zontal rows. Their relations to each other are contained in
the interior of the table. The object of the table is to show
the degree of conformity of the 44 various formulae for P
(and their correlates for T) to the eight tests. In spite of
all the mathematical ingenuity spent by many writers in
devising index numbers, no known formula and apparently
no possible formula will meet all eight of the tests.
For each test we note three possible degrees of conformity.
It may be fulfilled by any particular formula in three de
grees of conformity or nonconformity: (1) completely, (2)
partially, or (3) not at all. These three degrees are indicated
in the table which follows, by the numbers 1, -J-, 0 respec

S ec. 6]

APPENDIX TO CHAPTER X

40 9

tively. A test is completely fulfilled by index numbers for
any two years whatever (as year 1 and year 2). A test is
'partially fulfilled if it is fulfilled by index numbers for two
years, one of which is the base year (year 0). Thus the
former relates to the general case, the latter to a particular
case. Since the general includes the special, if the test is
fulfilled in general it is fulfilled in particular; the converse
is not necessarily true. But if the test is not fulfilled in the
particular case, it is not fulfilled in general; the converse of
this proposition is not necessarily true. In short, an affirma
tive answer to the question of complete conformity carries
with it an affirmative answer to the question of partial
conformity; and a negative answer to the question of par
tial conformity carries with it a negative answer to the
question of complete conformity. These two rules save
much labor in working out the figures in the table.
Our next task is to illustrate the eight tests by applying
them to a particular formula for Pi and the correlative
formula for
We select for this illustration the pair of
formulae numbered (11) in the table, namely Pi = |j£iQi
2 PoQi

and Ti = 2p0Qi, and we seek to know how far this pair of
formulse conform to the eight tests.
Test 1. Proportionality as to prices. — We shall begin with
“ the particular case ” where one of the two years compared
is the base year. In concrete terms, this test means that,
if all prices for the year 1 are any given number of times
(k times) the prices for the base year 0, then the index num
ber for the year 1 (in terms of the year 0) should be the
same number k.
The test is best expressed in algebraic language as follows:—
If
i.e. if

Pi = p\ = p"i _ ...
Po P f 0 p" 0
Pi =

kpo; p'i = kpf0; p " i = fcp"o•••,fcbeing

the given constant price ratio, then also should

410

THE PURCHASING POWER OP MONEY

[A p p e n d .

that is (since Po = 1),
Pi = k.
It is easy to apply this test to our given pair of formulae.
; T\ = 2p0Qi.

The formulae for year 1 are Pi =
The formulae for year 0 are
It is evident that

P0=

ZpoQo

(= 1 );

= 2p0Qo.

Pi = M - 1= PlQl t P'lQ' — v

—(^Pq)Qi + fe>'o)Q/i + •••_ HvoQi + p'qQ'i + ••*)
2p0Qi
2p0Qi
= fcSpoQi _ 7
2p0Qi
Therefore test 1 is fulfilled for the particular case when
one of the years is the base year.
But, as we have noted, it does not follow that the test is
fulfilled in general. For “ the general case” of any two
years the test may be thus stated: If the price of each good
for the year 1 is k times the price of the same good for the
year 2, then the index number for the year 1 (in terms of
the year 0) should also be k times the index number for the
year 2 (in terms of the year 0). That this may be true,
the test requires, for the general case, that if
£1 = ^ = 2 ^ = ... =*,

i.e. if

P2 P'2 P'f2
pi = kp2, p\ = kpf2, pni = kp"2 etc.,
p

— = k.
P2
This general test, however, will not be fulfilled, as may be
seen from the following: —
SpiQi

then must

Sec. 6]

APPENDIX TO CHAPTER X

411

In order that this last expression should reduce to k, it
is evident that

would have to be equal to
But
SpoQi
2p0Q2
this cannot be assumed to be always true. If this equality
should happen to hold true for any particular value of (say)
Q2, it would evidently be disturbed by the slightest deviation
from that value. If, for instance, Q2 should vary, the left
side,

of the supposed equality would be unaffected, but
SpoQi
the first term in the numerator and the first term in the
denominator of the right side would vary. Consequently the
right fraction

2p0Q2

would be affected, except when the ratio

of the first term, ^ 77, happened to be equal to
in
2W 2
^W 2
which case by a well-known principle of proportion (the
principle of “ composition and division ” ) the size of the
terms p2Q2and p0Q2would be immaterial.
The first test, therefore, is fulfilled for the particular case
where one of the two years compared is the base year, but is
not fulfilled in general. Therefore, following our convention,
we assign to formula 11 the number £ as representing its
degree of conformity to test 2.
T e s t 2. Proportionality as to trade. This test, stated for
the general case, is: If the quantities of all goods sold in the
year 1 is &times the quantities of the corresponding goods
sold in the year 2, the index number of trade for the year
1 (in terms of the year 0) should also be k times the index
number for the year 2 ( n terms of the year 0).
That is if
l h a t l s ’ lf

0^1 - ... —b

Q2 “ Q '2 ~ Q "2 ”
rp

then should

■
—= k.
r2

We shall find that this test is fulfilled'in the general case,
and therefore also in the particular case.

412

THE PURCHASING POWER OF MONEY

[A p p e n d .

which was to have been proved. Therefore test 2 is com
pletely fulfilled, and the formula is therefore assigned the
full credit, “ 1,” in the table.
T e st 3. Determinateness as to prices. This test is also
completely fulfilled.
If, in the formula for Pi, namely
some but not all
2poQi
of the prices, as ph or one of the quantities, as Qh should
become zero, it is clear that the above expression would still
be determinate, and lie between zero and infinity. It will
merely happen that some of the numerous terms in the
numerator will vanish, but all the other terms will remain.
p
Since the same reasoning applies to P2, it follows that -=?
1
must also be determinate, being the quotient of two finite,
non-zero, and determinate numbers. Thus test 3 is com
pletely fulfilled.
T est 4. Determinateness as to trade. The fourth test is
analogous to the third, and states that the trade index num
ber must not be rendered indeterminate, zero, or infinity
simply because some price or prices should become zero.
The formula for Ti is always

♦ Since, as neither the
Pi
numerator nor the denominator of this fraction becomes
zero, infinity, or indeterminate by the vanishing of some but
not all of the p’s or Q’s, the quotient must likewise be non
zero, finite, and determinate. Thus, test 4 is completely
fulfilled.1
1 It might seem that the simple tests of determinateness would bo
fulfilled by any formula whatever, but such is not the case. (If it
were, the total “ score ” given in the last column opposite test 4
would bo 44 instead of 31.) Thus the simple geometrical average
(formula 7) will not conform to test 3 of determinateness as to
prices. The simple geometrical average for “ n ” commodities is
.... Evidently if pi becomes 0, the value of the entire

* po p o

S e c . 6]

A P P E N D IX

CHAPTER

413

T e st 5. Withdrawal or entry as to prices. Suppose that
there are 100 specified commodities. If the general price
level of one year s k times that of another, and if any good,
the price of which in the one year is k times that in the
other, be withdrawn from the 100 commodities, leaving 99,
then the ratio of the price levels of the two years should
remain unchanged.
This is a difficult test to meet, and the formula under dis
cussion meets it only partially, that is, when one of the two
years compared is the base year.

where k is a given ratio,

SpoQi

and if also

= fc, then we are
= h, where

to prove that
V o Q 'i

of course
while
so that

2p'iQ'i=

p\Q\-hpr,iQf\’\m
m
** ,

SpiQi = PiQi+ p'iQ'i+ p"iQ"i ■+— ;
’ Sp'iQ'i = ZpiQi —piQi.

Now we know that,
since

then
And, since

*PoQi

= k, it follows by the principle of pro-

expression becomes 0. If, therefore, we should depend on the geo
metric mean for ascertaining price levels, the temporary plethora of
any commodity, to the extent of making its price vanish for a single
moment, would cause the index number representing the entire price
level for that moment to fall to 0. A form of average which in an
oxtreme case is so absurd will approach absurdity before the ex
treme is reached. Thus the geometrical average is unduly affected
hy prices which aro low, oven if not actually zero.

414

THE PURCHASING POWER OF MONEY

[A p p e n d .

portion (“ composition and division ”) that
2p0Qi ~ P0Q1
that is,

i ^rxr = ^ which was to have been proved,
oQ o

If the missing commodity is'reentered, the ratio will
evidently be undisturbed, so the rule works both ways, i.e.
for entry as well as for withdrawal. Therefore, test five is
fulfilled for the particular case.
• When, however, we consider the general case for price
ratios of two years neither of which is the base year, the test
will not be fulfilled.
That is, if

SpoQz
and if also

then

Z p 2
2p'0Q'2

will not in general be equal to h.

For, if this expression should happen to be equal to h in any
particular instance, a slight change in any base year price,
such as p'o, would disturb the equality, unless the variation
in p'o should affect the denominators of both numerator and
denominator of the last expression in the same proportion.
^7)' Of *
This would mean that the ratio t; fir}- would be unaffected
0Q 2
by a change in p'o, which in turn would assume (by the prin
ciple of “ composition and division ”) that

p'oQ'i~l Sp'oQ'i
p'oQ’i ’Zp'oQ'z

Sec. 6]

APPENDIX TO CHAPTER X

415

This is not necessarily true, as it is evidently easy to assume
values for (say) Q'i which would render it untrue. Thus, a
doubling of Q\ would double the left side but not the right.
Therefore test five is only partially met by our formula.
This is therefore to be credited only with %as its degree of
conformity to test 5.
T e s t 6. Withdrawal or entry as to trade. If the index
numbers for trade are in a given ratio, the inclusion or ex
clusion of a given good, the quantities of which are in the
same ratio, ought not to disturb that ratio. This test is
completely fulfilled by our formula.
The test requires that if
and if
then should

~ =/b,

Ti __ SpoQi __ 7
m
n2
Ti ~ SP0Q
St/qQ'i __6

Sp'oQ'a *

This test is fulfilled; for from

P0Q2

by the principles of proportion (i.e. by “ composition and

which was to have been proved.
T e s t 7. Changing the base. This test 7 is not fulfilled
by our formula even in the particular case. The particular
case means here the case of reversing the base, as between
(say) year 1 and year 0.

416

THE PURCHASING POWER OF MONEY

[A p p e n d .

In order not to alter and thereby confuse the notation
we shall have to use the subscript 0, which indicated
the original base year, to indicate that same year, even
when, for the moment, it is not considered as the base
year; and likewise we shall use the subscript 1 to indicate
the year 1, even when it is, for the moment, taken as the
base year.
By the formula which we are testing, the price index ratio
for year 1 compared to year 0 as the base is

By
•ZpoQi
analogy it is clear that the price index ratio for year 0, com

pared with year 1 considered as the base, is

If these

two expressions are reciprocals of each other, then
should be equal to
That this is not necessarily true is evident, since there is
no necessary relation between the
and the Qi’s. If the
equation should accidentally hold true for a particular set of
and Qi’s, the change, even in the smallest degree, of a ,
single letter, say
or
would evidently disturb the rela
tion. Therefore the test is not fulfilled even for the par
ticular case of reversing the base as between two years, and
the formula must therefore be assigned a “ 0 ” or complete
failure to conform to test 7.
T e s t 8. Changing units of measurement. If the unit for
indicating the price, say of coal, should be changed from
a ton to a pound, the index number ought not to be
affected thereby. We shall find that this test is met by
formula (11).
Evidently a change of unit, say from a ton to a pound,
applied to any particular goods (the prices of which are
Pu P'h P " it the corresponding quantities being Qi, Q'i, Q"i)
will magnify all the Q’s 2000 times, but, on the other hand,
will reduce all the p’s in the reciprocal ratio Gnnnr)* Con
sequently, the products piQi, p'iQ'i, p"iQ"i, will be unaffected.

Qo’s

Qo Qi,

Sec. 6]

APPENDIX TO CHAPTER X

417

Hence the sum of such products constituting the n um erator
and denominator of the right side of the equation
SpiQi

P i _ 2p0Qi
P2 -PiQ i
SpoQa
will likewise be unaffected. Therefore the ratio of the index
numbers ~ will be unaffected. Hence the test is completely
fulfilled.1
1 It might seem that every index number would conform to this
Unit-shifting test. It is true of 40 formulae out of the 44. Yet the
index number which is perhaps the simplest of all, Bradstreet’s,
P 1 = — -1, fails to conform.

*po

It is evident that if there is a change in the unit of any one com
modity, such as that whose prices are pi, and po, both the numerator
and denominator will be affected, but not in the same proportion,
except when it happens that
po

2p0*

Consequently, the index number is dependent upon the
Measurement. Such an index number is entirely arbitrary, and by
sufficient manipulation of the units of measurement could be made
to favor any particular commodity. The larger the unit of any
particular commodity employed, the higher the price for it which
enters into tho formula, and the more that commodity tends to
affect the result.
Bradstreet uses 96 commodities in common use, all of which are
measured by tho pound. The result is that silver, for instance,
dominates over iron, entering at several dollars a pound instead of
a few cents. If radium, which recently cost 88,000,000 an ounce, were
included, it would absolutely dominate tho group, and we would
reach tho absurd result that since radium has fallen to hundreds of
thousands instead of millions of dollars an ounce, the general price
level must have fallen several fold in spite of the general impression
of rising prices !• An index number of this kind is fitly called by
Walsh one of accidental or haphazard weighting.
2 E

418

THE PURCHASING POWER OF MONEY

[A p p en d .

§ 7. The J+J± Formulce Compared
We have gone through the reasoning by which the con
formity of one pair (Pi =

; T\ = SpoQi) out of the

44 pairs of index numbers of prices and trade, given in the
table, are tested and graded with respect to the eight tests.
The table contains for the remaining 43 formulae the results
of similar reasoning. This reasoning is here omitted to save
space. The mathematical reader who chooses can verify the
results as tabulated. He can also prove the relationship by
which it follows that the figure in any column for the odd
tests corresponds to that in the neighboring antithetical col
umn for the even tests. In consequence of this relationship
the sum of any column for the odd tests equals the sum in
the antithetical column for the even tests. In fact, the table
is full of correspondences and relationships of many kinds.
The footings give us a means of comparing the merits of
the various index numbers. These footings are intended to
express, so far as may be, the fitness of the formulae to serve
as index numbers for price levels. Consequently the score
for test 6 should be omitted from the footing, as test 6 has
no value in regard to prices. (If it be desired to compare the
scores of the correlative index numbers for quantities or
trade, the score of test 6 will be included, but that of test 5
should then be omitted.)
Thus a perfect score would be seven. The highest score in
the table is 5J-, the lowest, 2.
It would, of course, be absurd to compare the merits of
index numbers merely by their “ score” in the table. This
score is more or less arbitrary, and it treats all seven tests as
equally important. Yet it affords at least some insight into
the comparative characteristics of the 44 formulae. It is
noteworthy that, in general, the simplest formulae have high
scores and the most complicated have low scores. Thus
formulae 1 (Dutot), 7 (simple geometric), 9 (median), 11 and
12 (Scrope)’ have scores of 5 and 5J-. The only others as

(2 )

T est

2Pi(?i
2<?t

T est

Statem ent of

Test

N um ber

liradstreet

Drobisch
RawsonRawson

(G)

2—
Po
n

(7)

(8)

UO)

»9)
Median
value
of

Simple
Geometric

ZPxQi
'ZPoQ*
n
S <?o

N ame

(5)
Simple
Harmonic

Simple
Arithmetic

TA BLE OF IN D E X NUMBERS OF PRICES AND TIIEIR
1
CONFORMITY TO CERTAIN TESTS

<3)

s p ig i
ZPoQo
” IZl J i J ..
\ P o V o "

P 'o “

-P iQ t
'S'PqQo
Median
value
of
&
Qo

Carli
Evelyn
Economist
Sauerbeck
Soetheer

Jevons
Westergaard

Nicholson
Walsh

Six,.
Vo

Edgeworth

Kll\

(12)

Wghtd. arith. *
(wghts. denom.)
or wghtd.
harmon.
(wghts. num.)

(13)

(14)

(15>

(16)

(17)

(18)

(20)

(1»)

(21)

ZPiQo
2 p 0<?0

Geometric

Scrope
Sidgwick
Sauerbeck
Giffen

^■PoVi

ZpoQp
2 .

ZPoVo
ZPiQo

ZpoQt
XPxQt

Sp xQ,

'S.PiQo

Edgeworth
Marshall

(27)

(28)

^P\Q\
ZPoQo

\Q\

s(& ± £ s)< ? .

( 20)

The odd formulie are other weighted arithmetical averages

^V\Q\

Sidgwick
Drobisch

(25)

(24)

(23)

Mixtures of same two formulas

Average o f two preceding averages (11 and 12)

5Po<?o
ZPiQi
2 P qQi

( 22 )

Walsh

(\QiA Q)J

ZPoQo

^ VPoPiQo

s( i h >
\pl

^ P o P iQ t

p j

Scrope
and .
Walsh

g ( P iQ i+ P * Q o \

Plt +
\ P
+ Po
'
{P xQ i+ P oQ o\ „
-v 'P iT F r )r°

* /PtV l+PoQ o\s,
Qi+Qo ) Ql
K / P lQ l+ P o Q o \s*

Q i+ Q o

) Qo

SPiQi
ZPtQa
^PxQi

I.ehr

itfO)

(32)

(33)

(34)

(3u)

The odd formulae are other weighted harmonic means

Arith.
(constant
weights)

vvJ

(31)

S;>tQt
2/>oQo
0
± P iQa._

~PoQ»

(30)

(37,

ZPxQi
S;?oQo
SPoQo

(3!»

(38)

The odd formula* are weighted geometric averages

S p.Q i
S/>oQ»

*PxQx
-PuQo

SPxQo

Palgrave

(42)

(41)

(40)

AVeighted geometric averages

zpiQ »
spoQi

Walsh

(2ii)

AVeiglited geometric averages

<PoQt

W )

Pifh

~P\Q\
ZPtfia
ZPlQo

(43)

(44)

Weighted geometric averages

SpiQt I PxQx
M pi
J>-uQ oi

2 >iQo

-P i Q t
T

otal

-P iQ ij PiQ]
_ \ Q i

\]>»

-PuQol PuQ0
\Qo

Young
Falkner
Dun

F o rk ’ s

A p rice in d ex should agree with the
p r ic e ra(io8 if these all agree with
each other.1

184

For Q's

A trade ind ex should agree with the
trade ratios if these all agree with
each other.*

184

For p ’ s

A p r ic e in d ex (consequently also
the correlative trade index) should
not be rendered zero, infinity, or
indeterminate by an ind ividual
p rice becoming zero.

For (>’ s

A trade in d ex (consequently also
the correlative price index) should
not be rendered zero, infinity, or
indeterminate by an in d ivid u a l
quantity becoming zero.

For p ’ s

A p rice in d ex should be unaffected
by the withdrawal or entry o f a
p r ic e ratio agreeing with the
index.

For <>’ 8

A trade index should be unaffected
by the withdrawal or entry o f a
trade ra tio agreeing with the
index.*

For p ’s and
for Q'a

The ratios between various p rice
indexes (and therefore those be
tween the trade indexes) should
be unaffected by reversing or shift
ing the base.

By changing unit For p ’ s and
for <2’ s
of measurement

The ratios between various p r ic e
ind exes (and therefore those be
tween the trade ind exes) should
be unaffected by changing any unit
o f measurement.

Proportionality

Determinateness

Dy withdrawal or
entry

By changing
base

Total “ score” out o f possible perfect score o f 7 (test 6 being omitted)
for index number of prices.
Consequently the correlative trade index should be equal to the ratio
of the values of the trade in the two years compared, these values
being reckoned at the prices of one of those two years.
Consequently the correlative price index should be equal to the ratio
o f the values of the trade in the two years compared, these valnes
being reckoned for the quantities o f one of those two years.
•The figures In this row are In parenthesis to signify that it has no
p r ic e significance. (See § 5, pp. 407, 408.)

(0)

(i)

(0)

(1 )

(0)

(1)

(0)

(i)

(0 )

(4)

(0)

(i)

(0)

134
(0)

(0)

(4)

(0)'

(4)

( 0)

(4)

(0)

(4)

(0)

(4)

(0)

(i)

(0)

(i)

(0)

(4)

(0)

(4)

(0)

(4)

(0)

(1)

(0)

4**

(0)

(134
12

40
4b

* In case o f •withdrawal^ the test is fulfilled only provided (if the number o f terms is
first odd) that the median term is also equal to the median o f the two neighboring terms,
or (if the number o f terms is first even) provided the two middle terms are equal Practi
cally these conditions are fulfilled, at least approximately, in all ordinary circumstances.
In case o f entry no such reservations are necessary.
** Provided number o f terms is odd. I f number o f terms is even, test Is fulfilled only
provided we take geom etric mean o f adjacent middle terms as median.

IC G

Sec. 7]

419

APPENDIX TO CHAPTER X

high as 5 are “ mixtures” of formulae 11 and 12. The simple
arithmetical (3) and simple harmonic (5) have a score of 4,
which is fairly high. The more complicated forms which
have fairly high scores are in several cases “ mixtures,”
averages, or antitheses of simple formulae 11 and 12.
The above comparisons treat all the other seven tests as
of equal importance. But they are not of equal importance.
Since opinions might differ as to the exact relative impor
tance of the various tests, we shall not attempt to “ weight”
them. Nor will this be necessary in order to decide the
question of most importance to us, viz., which of the 44
index numbers meet the tests most completely. Tests 3 and
4 are probably of little practical importance as compared
with the remaining tests. Test 2, on the other hand, may be
accorded chief importance, for reasons given in section 5 of
this Appendix and in Chapter II. In order to select the
best index numbers of prices, therefore, let us first rule out
of the competition all the 18 formulae which have “ 0” for
test 2. We have left the following formulae classified into
two groups.
(Omitting test 6), score for formulae which do not com
pletely fail on test 2,
Form u la

c o m p l e t e l y f u l f il l i n g

T e st 2

Formulso

Score

2
4

4
3
3
4

28
30
34
38

41
5
4
3
3
3

F o rm ulae

p a r t i a l l y f u l f il l i n g

Formula)

13
14
15
16
17
18

20
21

24
26
32
36
42

T e st 2

Score

51
4
4
41
41
5
41
4
5
41
4
31

2i
21

420

THE PURCHASING POWER OF MONEY

[A p p en d .

If, next, we rule out of the competition from among those
which completely meet test 2, all except those which have
scores of 4£ or above, we have left only formulae num
bers 10 and 11. Among the formulse which only partially
meet test 2 we may eliminate all which fail to exceed 4%in
total score; for, although those which reach 4£ tie formula
10, yet when all tests are counted as of equal importance,
they are inferior in not completely meeting the most impor
tant test — test 2. Putting the matter in another way, we
may say that if test 2 should be weighted more heavily than
the other tests, the scores of those formulse half meeting that
test which now tie formulse wholly meeting that test would
fail to do so and would therefore drop out of competition
with formulse 10 and 11 in the first column.
Eliminating therefore from the second column all formula
with scores of 44 or less, we have as the only rivals of formulse
10 and 11, formulse 12, 17, and 21, having scores of 5J-, 5, and
5 respectively. Our best formula, therefore, should be found
among numbers 10, 11, 12, 17, 21. We shall therefore exam
ine with particular care these five surviving competitors.
These all conform to tests 3, 4, and 8. Comparing them
in other respects, we find: —

Test
Test
Test
Test

1
2
5
7

............................
............................
.............................
.............................

T o t a l .......................

0
1
0
i

i
1
i
0

1
i
1
0

i
*

i
i
i
J

__— ■—

Tests 17 and 21 have scores identical in every instance, and
may therefore be said to be tied.
Comparing tests 11 with 17 (or 21), we see that 11 excels
in respect to the important test 2, and 17 in test 7. As test
2 is regarded as of more importance than test 7, we may

Sec. 7]

APPENDIX TO CHAPTER X

421

safely give the preference to formula 11 over 17 (or 21).
We therefore now strike out 17 and 21 from the competition.
We have left formulae 10,11, 12; comparing 10 and 11, we
note that 10 excels in test 7, while 11 excels in tests 1 and 5.
If we maybe allowed here to exercise a comparative judgment,
we shall say that the superiority in the one test 7 is more than
offset by superiority in the two tests, 1 and 5. We therefore
eliminate formula 10.
We now have left only the two formulae, 11 and 12. There
is not much to choose between them. While 12 has the higher
score when all tests are counted as of equal importance, 11
excels in the most important test 2, and we are therefore in
clined to give it the preference.
According to our judgment, therefore, test 11 emerges as
the winner in the score contest. It has also the advantage
of being among the very simplest formulae and of having as
its correlative formula for T the simplest of all formulae for T,
viz. Tj = SpbQj.
In nonmathematical language, the pair of formulae 11
mean that the level of prices in any year is found by dividing
the total value of the quantities sold in that year by what that
value would have been at base prices, and that the trade index
in any year is simply the value of the quantities sold in that
year reckoned at base prices.
Applying formula 11 to the equation of exchange," we
have —
MV + M'V' = $piQi
(1)
= PiTi
(2)

We wish now to emphasize once more the virtues of this
formula 11 in respect to test 2. The equation of exchange,
stated above, is intended to show how prices are affected by
changes in M, M', V, V' or the Q’s. It is evident from the
original form (1) of this equation that a proportional change
in the M and M' (if the F’s and Q’s remain unchanged) will

422

THE PURCHASING POWER OF MONE1

lAppend. X

affect all the p /s in exactly the same ratio, or else raise some
prices more and others enough less than this ratio to com
pensate in the sense that the equation of exchange will be
preserved. In some sense, therefore, the general level of prices
varies exactly with M and M\ Form (3) enables us to ex
press this proportionality by formulating the price level as
the fraction

This varies directly with the ill’s.
2VoQx
In precisely the same way we are enabled to state that a
uniform change in the two 7's, or any change in the left side
of the equation as a whole, will affect prices in precisely the
same ratio (the Qi’s being assumed constant). We may also
say that a uniform change in the Qi’s will affect Ti in exactly
the same ratio, and Pi in exactly the inverse ratio (assuming
the left side of the equation to be unchanged). In fact, if
we use formula 11 to express the average price ratio, we are
able to state in all cases (so long only as the QiS change in
unison or not at all) that prices rise or fall “ on the average”
directly as the left side of the equation, and inversely as the
Qi’s.
As noted, these are the basic theorems for which the equa
tion of exchange stands. We w’ould naturally like to remove
the restriction as to the Qi’s changing uniformly. We should
consider an index number perfect (so far as needed in the
equation of exchange) if we could assert of it the same
theorem of proportion as above, without the restriction as to
the Qi’s changing uniformly, so that we might substitute an
average change in the Q’s in place of a uniform change. No
such index is found in the table, and no such index seems
possible. Practically this conclusion does not greatly mat
ter, for we are interested in prices far more than in quantities,
the latter being chiefly important as supplying weights for
the price indexes. As wTe have already noted, Edgeworth
has shown that considerable variation in weighting is ol
comparatively little practical importance.
The chief use of index numbers is to compare successive
years, not years remotely distant from each other. We arc

Sec. 7]

APPENDIX TO CHAPTER X

423

not so much interested in comparing the prices of 1909 and
1910 each with those of 1873 as we are in comparing them with
each other. In fact, the chief use of 1873 as a base year is to
enable us to compare any other two years with each other.
But only a few index numbers which afford a true comparison
between any year and another year as the base will give a
true comparison between any two years, each in terms of a
third year as the base. These few index numbers are those
which completely meet the base-shifting test 7.1 In the table
the only formulse which come up to this requirement are for
mulae numbered 1, 2, 7, 8, 43, 44, to all of which there are
serious objections on other grounds. Formulse 1 and 2 are
very arbitrary, having “ haphazard weighting” ; formulse 43
and 44 have the lowest scores in the table; formula 7 has no
system of weighting; and formula 8 becomes zero if a single
quantity, as Q, should disappear from a year's sales.
The question therefore arises, why should wre, as has usually
been done, construct our index numbers with reference to a
fixed base in terms of which we indirectly compare two given
years? Why not make the comparison directly? The in
direct comparison introduces an error in all cases except of
those formulae which conform to test 7. In these cases the
indirect comparison cannot, of course, give any better result
than the direct comparison, while in all other cases the direct
comparison is better.
It seems, therefore, advisable to compare each year with
the next, or, in other words, to make each year the base year
for the next. Such a procedure has been recommended by
Marshall, Edgeworth, and Flux.2 It largely meets the diffi*That this test is the most difficult one to meet is shown by the
fact that the total “ score” as given in the last column opposite test
7 is the lowest in that column, being only 12 out of a possible 44;
the next most difficult test to meet is test 5 (or 6), opposite which
the total “ score ” is 13 J.
The easiost test to meet is test 8, opposite which the total is 40
°ut of 44 ; the next easiost is test 3 (and 4) with 31 out of 44.
2“ Modes of constructing Index Numbers,” Quarterly Journal oj
Economics, August, 1907, pp. 613-631.

424

THE PURCHASING POWER OF MONEY

[A p p e n d .

culty of non-uniform changes in the Q’s, for any inequalities
for successive years are relatively small.
Such successive index numbers, each on the basis of 100
per cent for the previous year, will, if multiplied together,
give a chain of index numbers showing the fluctuations from
year to year, like any ordinary series, but much more suitable
for comparison of neighboring years.
Let us now reexamine the comparative merits of index
numbers on the supposition that they are to be used only for
successive years, that is, for comparison between each year
and the previous year as a base. In this case we do not need
to distinguish between a “ partial” and a “ complete” ful
fillment of the tests. We may therefore now substitute “ 1 ”
for every “ 1.” Omitting, as before, all formulae which fail
to meet test 2, we have the following results: —
F ormula

Sco u t:

4
3
3
4
4\
G
G
5
5
G
G
7
G
G

4
G
8
10
11
12
13
14
15
1G
17
18
19

F o rm u la

20
21
22
24
2G
23
30
32
34
3G
3S
40
42

S core

5
7
6

5
4
4
3
3
3
3
3
3
3

We note that formulae 11 and 12 have scores of Geach, while
their average 15 (and 1G) and their mixture IS and also 22
have the same score, but that formulae 17 and 21, which are
mixtures of 11 and 12, have perfect scores, 7. Each of these
two formula? uses as weights the average of the weights used
in formula* 11 and 12. Theoretically, therefore, we find two
formula? which fit all tests perfectly so far as year-to-year
comparisons of prices are concerned.

S ec. 8]

APPENDIX TO CHAPTER X

425

Where, therefore, great accuracy is desired and there exist
abundant funds to provide for the laborious computations
necessary, we may recommend the use of formula 17 or 21.
This presupposes that statistics are available for the Q’s,
which is not usually the case.
Thus far our conclusions therefore are (1) that theoretically
formula 11 is the best when each year is expressed in terms of
a common base; (2) that (also theoretically) formulse 17 and
21 are slightly superior when each year is expressed in terms
of the preceding year as base, and that these two meet all
tests for year-to-year comparisons.
§ 8. Reasons for preferring the Median for Practical Purposes
Practically, however, there is little if any advantage in 17
and 21 over 11 (or 12, which in the case of year-to-year com
parisons amounts to the same thing) because (1) weighting
is of little importance; (2) the more perfect weighting con
tained in formulae 17 and 21 will seldom differ materially
from that of 11 and 12, for any gain of precision would prob
ably be less than the errors in measurement of the Q’s, which
are never exactly known; (3) the systems of 17 and 21 are
practically far more laborious. In the end we must be guided
largely by practical considerations except where the great
labor and expense of computation may be disregarded. If
in a practical spirit we examine the merits of the various
formulse, we shall, I believe, reject all formulse except 9 and
11, and come to the conclusion that the best index number is
the weighted median. It has no rival in ease of computation.
The score of the median in the table (formula 9) is high,
although it fails in test 2. Excepting this test it meets,
partially or wholly, every other test. It therefore possesses
some merit even on the theoretical side.
In passing, we may mention a feature of medians, although
I am disposed to regard it as a fault. Edgeworth empha
sized the fact that price dispersion upward always or usually
exceeds the price dispersion downward. There is no limit to

426

THE PURCHASING POWER OF MONEY

[A p p e n d .

the former, but the latter is limited by zero. Statistical tests
show clearly this asymmetry of dispersion.1 From this fact
it has been argued that the best average should be one from
which large deviations above it count no more than small
deviations below it. This condition, whether good or ill,
is not met by arithmetical averages, but is met by the geo
metric average and by the median2 which, in fact, usu
ally closely follows the geometric average. Edgeworth also
argues that the median is superior when the variabilities of
the various elements averaged are widely different.3
Edgeworth concludes that “ in the present state of our
knowledge, and for the purposes on hand, the median is the
proper formula.” 4
As to methods of weighting, theoretical discussion with
reference to test 2 shows that the weighting should be made
on the basis of values sold in one or the other of the years
compared.
It is easy to show that a system of weighting the median
by given weights, that is, by counting each price ratio, not only
1 See Edgeworth, “ First Report on Monetary Standard,” Report
of the British Association for the Advancement of Science, 1887, pp*
284-855.
2 Edgeworth, ibid., pp. 284-286. From the standpoint, however,
of the relation of prices to the currency, a large upward variation
should count more than a small downward variation ; for it requires
more currency. In fact, as we have already seen, the arithmetical
average complained of is precisely the average needed to fit into tho
equation of exchange. See § 6 of Appendix to Chapter II and § V
of this Appendix. As to the asymmetry of price dispersion, see
Mitchell, Gold, Prices, and Wages under the Greenback StandardI
Berkeley (University of California Press), 1908, and reviews of samo
by Edgeworth, Journal of the Royal Economic Society, December,
1908, pp. 578-582; and H. G. Brown, Yale Review, M ay, 1909,
pp. 99r 101.
* Edgeworth, Report, etc., 1887, p. 291, and “ On the Choice of
Means/* Philosophical Magazine, September, 1887; see also Report
of the British Association for the Advancement of Science, 1889, pp.
156-161, and Journal of the Royal Statistical Society, June, 1888.
4 Ibid., p. 191.

Sec. 8]

APPENDIX TO CHAPTER X

427

once but a certain number of times (that number being the
Weight) will not affect the relative fulfillments of the tests as
met by the simple median 9, which is the only median in the
table. Edgeworth has shown that for all practical purposes
a very rough system of weighting will suffice.1 Whether the
weighting be according to the values p0Q0, etc., or piQi, etc.,
or VoQb etc., or piQo, etc., is usually of no practical importance
whatever. If, then, we subordinate theoretical to practical
considerations, the proper procedure would seem to be to
select certain constants consisting of simple integers, and as
near as may be to the values dealt with in the years consid
ered. These weights need not be changed every year, but
should be changed when the values (piQi) change very greatly.
If it be desired to have a quantity or trade-index number
(Qi, or Ti) as well as a price-index number (Pi), we may like
wise select as the form for Qi the median. In other words,
the indexes for p’s and Q’s are best selected independently of
each other. It is true we thereby abandon any absolute mu
tual consistency between the two, but we are now speaking
of practical, not theoretical, considerations.
One of the great practical advantages of the median is its
Use in conjunction with “ quartiles” or “ deciles” to portray
dispersion as well as averages. This method of showing dis
persion about a mean is both easier to calculate, and capable
of more detail, if detail be desired, than the method of Karl
Pearson of the “ Standard Deviation” about an arithmetical
mean.
The final practical conclusion, therefore, is that the weighted
median serves the purposes of a practical barometer of prices,
and also of quantities as well as, if not better than, formulae
theoretically superior.
In spite, however, of the peculiar simplicity and ease of
1 Seo Report of the British Association for the Advancement of
Science, 1888, pp. 208-211. Edgowortli compares various means
for 21 articles in 1885 and 1873, one being that recommended by the
committee of which ho was a member, and above referred to in tho
text of Chapter X , § 5.

428

THE PURCHASING POWER OF MONEY

[A p p e n d .

computation which characterizes the median, and in spite of
Edgeworth's strong indorsement, it remains still almost
totally unused, if not unknown. Wesley C. Mitchell1 has
used the median for price indexes more extensively than any
one else. Professor Davis R. Dewey has used them for wages
in his special Census report on that subject.
§ 9. Summary
The conclusions of this Appendix may be briefly stated as
follows: —
1. Any sum of products of twro factors each, such as 2pQ,
may be converted into any one of three forms: ( 1) PT, in
which P is an average of the ratios of the p's to some base
po's, and T is the quotient

; (2) AQ7in which Q is an

average of the ratios of the Q’s to some base Qo’s, and A is the
2;vQ
quotient - q - ; (3) PQ2p0Q0.
2. Of the foregoing three formulae only the last is symmetri
cal in the sense that the p's and Q’s are treated alike.
3. P and T (or P and Q) are said to be correlative, and any
particular formula for either implies a particular correlative
formula for the other.
4.- Two correlative formulse for P and Q are, in general,
quite unlike each other. If like formulse be constructed for
P and Q, the correlate of Q constitutes a new formula for Pf
1 Gold, Prices, and Wages under the Greenback Standard, Publica
tions of the University of California. Mitchell’s use of deciles,
however, is of small value, as he employs a common base, 1860, so
that his figures for each subsequent year give the dispersion of that
year relatively to 1860. There is practically no use in knowing the
dispersion of prices in 1909 or 1910 as compared with 1860, and this
knowledge throws no light on whether prices change uniformly or
disperse widely from 1909 to 1910. What is needed is a knowledge
of price dispersion from year to year, and this can readily bo in
dicated by drawing three radiating lines from 1909 to 1910, the
central one to show the movement of the median, and the other two
to show the movements of the two neighboring quartiles.

Sec. 9]

APPENDIX TO CHAPTER X

42 9

said to be antithetical to the original formula for P, and
vice versa.
5. There are an indefinite number of formulae for P, of
which 44 are given in the table; and there are at least 8
important tests to which each formula may conform in one
of three degrees (1) wholly, or for the ratio of Pi to P2, each
being relative to a third year as a base; (2) partially, or for
the ratio Pi to unity; and (3) not at all.
6. The eight tests are of proportionality as to prices or
quantities (1 and 2); determinateness as to prices or quan
tities (3 and 4) ; withdrawal or entry as to prices and quanti
ties (5 and 6); changing base as to prices and quantities (7) ;
and changing units as to prices and quantities (8).
7. The tests arrange themselves in pairs, one of each pair
relating to the p’s in the same manner as the other is related
to the Q’s; but each test has significance both with respect
to the p’s and the Q’s.
8. The formulse arrange themselves in antithetical pairs.
9. Of any four neighboring compartments in the table,
relating to two correlative rows (tests) and two antithetical
columns (formulse), the diagonals will have the same “ scores.”
10. No known form of index number P conforms perfectly
to all the eight tests when a common base year is employed,
but several conform well, the best being formula No. l l , ^ 1^1*
■ZpoQi
11. But if we are content with year-to-year comparisons,
renouncing comparisons in terms of a third year, there are
two formula? which conform perfectly, viz. formulse 17 and 21.
12. Practically, however, formula 11 is superior to 17 or
21, and formula 9 (median) — when properly “ weighted” —
is superior to 11.
13. For practical purposes, therefore, unless the expense and
labor of computation can be disregarded, the median (with
its two neighboring quartiles) is recommended, with a simple
system of weights (whole numbers) based on expenditures,
and changing from time to time for the sake of making better
year-to-year comparisons.

APPENDIX TO CHAPTER XII
§

1 (t o

C hapter

XII, § 1)

Professor Kemmerer’s Calculations

Professor Kemmerer (Money and Prices, p. 99) estimates
the money in circulation (M) by deducting from the money
in the United States, as estimated by the Comptroller of the
Currency, two items, viz. the money in the United States
treasury and that in banks (reported and estimated). He
then estimates the velocity of circulation of money as 47
times a year, and assumes, in the absence of any data by which
to estimate its variations, that it remains constant. He
arrives at the figure 47 as follows: The amount of check
transactions he first estimates for 1896, at 143 billions (p. 111).
This estimate is based on figures taken from Kinley’s investi
gation, made through the Comptroller of the Currency in
1896. Referring to Kinley’s estimate that check transactions
are at least three times money transactions, he takes one
third of 143 billions, or 47.7 billions, as the amount of money
transactions. Estimating the amount of money in circula
tion at 1.025 billions for 1896, he divides 47.7 by 1.025
and obtains (p. 114) 47 times a year as the velocity of circu
lation of money. This figure, as we shall see, is probably
nearly three times too large, the error arising from the fact that
Professor Kemmerer does not accept the opinion expressed
by Professor Kinley that his (Kinley’s) estimate for the per
centage of check circulation in 1896 was a “ safe minimum,”
but expressed the contrary opinion that it was rather a safe
maximum. We shall give reasons for believing that Kinley
was quite right in concluding that the estimate of check trans
actions at three fourths of total transactions was a “ safe
minimum.” The calculations which we shall presently offer
prove nine tenths rather than three fourths to be the probable
figure.
Professor Kemmerer, as already indicated, estimates check

430

Sec. 1]

APPENDIX TO CHAPTER XII

431

transactions (what we have called MrVr) at 143 billions in
1896. For other years than 1896, there being no corre
sponding data, he estimates check transactions by assuming
that bank clearings are always 35 per cent thereof (p. 118).
He makes no attempt to estimate Mf (bank deposits) and F'
(their velocity) separately. The volume of trade (J7) Pro
fessor Kemmerer estimates relatively {i.e. he estimates what
We have called Q in the Appendix to Chapter X). This is
confessedly one of the roughest parts of all his estimates.
He seeks to get as many indicators as possible of the growth
of trade (p. 130), without much regard to their suitability.
His indicators are fifteen in number, viz. population, foreign
tonnage entered and cleared, exports and imports of mer
chandise (values), revenues of Post Office Department, gross
earnings from operation of railroads in the United States,
freight carried by railroads, receipts of Western Union Tele
graph Company, consumption of pig iron, bituminous coal,
wheat, corn, cotton, wool, wines and liquors, and market
value of reported sales on New York Stock Exchange. Rep
resenting each- of these sets of figures by index numbers, he
takes their simple average as the index number of trade for
each year in question.
Of course, as Professor Kemmerer well realized, many of
these figures are open to more or less serious objections.
Population is a poor index of trade when trade per capita is
changing. Values are inappropriate unless the prices are
supposed constant, which cannot be the case for exports and
unports, railroad earnings, or stocks, and can be only par
tially the case for post office revenues and telegraph receipts.
Having thus computed for 1879-1908 the various elements
theoretically determining price levels (viz. il/F +il/'F ' and
T), Professor Kemmerer uses these to calculate an index
number of prices. The index number thus calculated from
the other magnitudes in the equation of exchange, he calls
the “ relative circulation.” He then compares the figures
for relative ciroulation (virtually from the formula P =
{MV -f M'V') -f- T) with the actual statistics of price levels.

432

THE PURCHASING POWER OF MONEY

[A p p e n d .

X II

These directly calculated index numbers of prices he takes
as an average of index numbers of wholesale prices (Com
mon's figures and those of the Bureau of Labor, p. 137),
wages (those of reports of Bureau of Labor, p. 137), and of
the Industrial Commission), and prices of railroad stocks (In
dustrial Commission and Wall Street Journal), weighting
them as follows: wages, 3 per cent; stocks, 8 per cent;
wholesale commodities, 89 per cent.
The two sets of figures — “ relative circulation” and “ gen
eral prices” — presented visually by curves (p. 149), show
a general agreement.
§2

(t o C h a p t e r

XII, § 2)

M ethod of Calculating M

The estimates for M , or money in circulation in the United
States, are based on the reports of Comptroller of the Cur
rency. The calculations are shown in the following table: —

1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909

.
.
.
.
.
.
.
.
.
.
.
.
.
.

1.80
1.91
2.07
2.19
2.34
2.48
2.56
2.68
2.80
2.88
3.07
3.12
3.38
3.41

4
*y
OOH
1.74
1.83
1.94
2.09
2.25
2.37
2.45
2.59
2.68
2.77
2.97
3.12
3.38
3.41

03
S3
Z 5*
-«
P
w2

(5)
aj
M
§
£H
W
M
«
HO
&«M
O
Sc

SB
Ke u
OOH
g o---<

.29
.27
.24
.29
.28
.31
.31
.32
.28
.29
.33
.34
.34
.30

.53
.63
.69
.72
.75
.79
.84
.85
.98
.99
1.01
1.11
1.36
1.44

s.4 %
8.4%
7.7%
6.7%
6.4%
5.4%
5.3%
5.2%
4.5%
3.9%
3.4%
4.2%
3.8%
2.8%

.58
.68
.74
.77
.80
.84
.88
.89
1.03
1.03
1.05
1.15
1.41
1.48

(4)

.87
.88
.96
1.03
1.17
1.22
1.26
1.38
1.37
1.45
1.59
1.63
1.63
1.63

i (3>

Yeah

(3)

Money in Circu
lation EXCLUDING -S'
(4) AND (7) from “

Monet in U. S.
(Official)

( 1)

Unreforted as
Estimated Per
Cent of Reported S
Money in Banks

M o n e y in t h e U n it e d S t a t e s , e t c . (in B il l io n s o p D o l l a r s )

Sec. 2]

APPENDIX TO CHAPTER XII

433

Column (2) gives the money in the United States in the middle
of each calendar year according to the official estimates of the
director of the mint. In 1907 these official estimates were
corrected by subtracting an estimated error of S135,000,000
from the gold believed to be in the United States, this cor
rection being made in view of the investigations of Maurice
L* Muhleman. The mint corrections were made, however,
only for the ends of calendar years.1 In order to make the
corrections apply to the middle of a given calendar year, the
corrected figures for gold in the United States at the begin
ning and end of it were averaged. The average thus obtained
was assumed to be the corrected figure for gold at the middle
of the year. This corrected figure was then compared with the
official figure for gold for the middle of the year and the differ
ence assumed to be the correction for that date. This correc
tion was then deducted from the figures for money in the
United States given in column (2) above. We thus obtain the
figures in column (3). Mr. Muhleman has made independent
corrections for the middles of the years 1896-1900 inclusive.
These are slightly smaller than those calculated from the mint
figures as given above, the differences being in successive
years, .05, .03, .00, .03, .05. Columns (4) and (5) of our table
give the money in the federal treasury and the money re
ported in banks as stated in the annual reports of the Comp
troller of the Currency. Column (6) gives the estimated per
centage not reported. This estimate is found by assuming
that the unreported reserves bear the same ratio to thereported reserves as unreported deposits bear to reported de
posits, the latter ratios being calculated from the table given
m the next section (§ 3) of this Appendix.
This estimated percentage being calculated and the correc
tion found by it being added to the money in reporting banks,
(column 5), we get the .total estimated money in banks,
(column 7). Column (8) is then found by subtracting from tho
corrected money in the United States (as given in column 3),
1Seo Report of the Director of the Mint, 1907, p. 87.

434

THE PURCHASING POWER OF MONEY

[A p p e n d .

X II

the sum of the money in treasury (column 4), and estimated
money in banks (column 7). These estimates of money in
nonreporting banks are of course subject to some error; but
even a 50 per cent error in the largest of them would not
affect the last column much more than 2 per cent. A more
important possible source of error is in column (2), which de
pends upon hypothetical estimates of gold in the United
States. Mr. Muhleman writes me that in his opinion the
corrections made by the Mint Bureau are not adequate.
The corrections as made by that Bureau and here adopted
affect several of the figures in column (8) by as much as 10
per cent. The errors in these corrections would presumably
be much smaller than this. There are few other sources of
error and, taking all things into account, it seems likely that
the results are in general trustworthy — subject to a prob
able error of perhaps 2 or 3 per cent. This is fair accuracy
as ordinary statistics go.
§3

(t o C h a p t e r

XII, § 2)

Method of Calculating M '

The calculations for obtaining M', or individual deposits
subject to check, are shown in the table on page 49.
The figures of column (2) are those of “ Individual Depos
its” taken from the annual reports of the Comptroller of the
Currency (see Report for 1909, pp. 64-66). For the years
1896-1899 correction is made for deposits of trust companies
and savings banks misclassified as individual deposits. Prior
to 1900 many banks included such deposits of bankers as
individual deposits. They should be deducted because such
deposits in one bank by other banks are not generally used
for commercial purchases, but for banking operations. These
deposits, to be deducted from column (2), are given in col
umn (3).
The figures in cloumn (3) are estimates based on the fact
that the deposits of savings banks and trust companies in
national banks are (whenever comparison is possible, viz.

Sec. 3]

435

APPENDIX TO CHAPTER X II

1900-190S) found to be approximately equal to the deposits
of state banks in national banks. As the state bank figures
are available for 1896-1899, they are taken in lieu of the
missing trust and savings figures. Since the original edition
of this book was printed, consultation with the Comptroller
has convinced the writer that these corrections are too large
and that it would have been better to have omitted them
altogether. They are retained, however, in order not to
necessitate numerous changes in the plates. Fortunately,
as will be seen on page 492, the net error thus retained is
very small.
C h e ck

(in Billions of Dollars)

.
.
.
.
.
.
.
.
.
.
.
.
.
.

4.95
5.10
5.69
6.77
7.24
8.46
9.10
9.55
10.00
11.35
12.22
13.10
12.78
14.01

1.91
1.94
2.07
2.23
2.45
2.60
2.75
2.93
3.0(5
3.26
3.48
3.69
3.66
3.91

.11
.11
.16
.27
.18
.36
.36
.25
.23
.36
.40
.33
.29
.38

SH
Y

ffl
s o

I p

-S
§o
E o
£ H
S S
o
o

^
a

S 3 !

3.17
3.25
3.63
4.38
5.06
5.96
6.47
6.87
7.16
8.17
8.75
9.63
9.30
10.11

85
86
88
89
87
86
84
83
81
80
78
74
71
67

o
w

.40
.41
.42
.44
.45
.46
.48
.50
.45
.44
.41
.55
.49
.39

(8)

(7) X (8)
I n d ivid ua l D eposits
S ubject to C heck

S a v in g s

^
S a v in g s
N at. B ks.
and
in

C os.
B ks.

isclassified
D e
posits
of T rust

.16
.21
.25
.33

E x c h a n g e s tor
C le a r in g H o u s e

.
.
.
.
.
.
.
.
.
.
.
.
.
.

D eposits
B anks

.
.
.
.
.
.
.
.
.
.
.
.
.
.

(7)

§«

E stimated U n r e ported
D eposits

1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909

ear

I n d ivid ua l

eposits

(1)

I ndividual D eposits , S ubject

2.68
2.80
3.19
3.90
4.40
5.13
5.43
5.70
5.80
6.54
6.84
7.13
6.60
6.75

After deducting the correction of column (3), our next
step is to add the correction of column (4), the estimated
deposits unreported.
The figures for nonreporting banks to: 1900 and 1902-1909

436

THE PURCHASING POWER OF MONEY

[A p p e n d .

X II

are the official estimates of the Comptroller of the Currency.
(Those for 1900 and 1902 are entered in the Comptroller's
tables under the rubric “ reporting capital only” instead of
“ nonreporting,” but I am assured by the Comptroller's
office that this is a distinction without a difference.) The
figure for 1901 is interpolated between those of 1900 and 1902.
The figure for 1896 is estimated by the aid of two assumptions.
The first assumption is that the unreported deposits in that
year should be larger relatively to all deposits than was the
case in 1903, as the table shows that the farther back we go
the larger is the percentage of missing deposits. This con
sideration indicates that the correction exceeds .28. The
second assumption is that the correction should be less
absolutely than in later years; because the total deposits were
then much less than later; and because the official figures
in column (4), viz. those for 1900 and 1902-1909 show, as we
proceed backward in time, that there is a slight tendency for
them to grow less in absolute amount. (The chief exception
is for 1909, when the special investigation of April 28 reached
an unusual degree of accuracy.) This consideration would
make the correction less than .50. Therefore, betwreen .28
and .50 we select .40 as a rough mean. The error involved is
not likely to affect the final column more than 3 or 4 per
cent. The corrections for 1897-1899 are interpolated.
Column (5) gives a correction to be subtracted, viz. the
deposits in savings banks. These deposits, by the nature
of the case, are not used as a circulating medium, but are
nevertheless included in the official “ individual deposits”
of column (2). The item for 1909 as here given includes,
besides the reported figures, an additional item of .20 (i.e.
$200,000,000), being the savings accounts of the state
banks of Illinois. The inclusion of this Illinois item is
simply in order to make the figures for 1909 comparable
with those of the preceding years in which the same item
had always been included (see Comptroller's Report, 1909,
pp. 43-44).
Column (6) contains another, though small, subtractive

Sec. 3]

APPENDIX TO CHAPTER XII

437

correction, viz. the “ exchanges for clearing house.” In
general, these exchanges represent checks which have been
deposited by the persons receiving them but which have not
yet reached the home bank and been charged against the per
sons who drew them. Any one (except a sharper or a
blunderer) will, as soon as he has drawn a check, deduct the
amount of it (say $100) from his deposit balance and refrain
from drawing against it again. Such a person— say Smith
— regards the $100 as transferred to his drawee — say Jones
—' and no more Smith's than money would be which he had
paid out. But it takes time before the bank on which Smith
draws knows of this transfer of Smith’s deposits to Jones.
In the meantime the bank books still include this $100 among
Smith's deposits. The total figure for deposits is not dis
turbed by the inclusion of the $100 in Smith's account pro
vided it is not included in Jones's account also. But wrhen
Jones deposits the check in his bank, this (Jones's) bank adds
$100 to Jones's account before Smith’s bank can deduct it from
Smith’s account. That is, the $100 is temporarily counted as
both Smith's and Jones's. If both sides of this transfer were
recorded at the same time, there would be no double counting.
But until the check reaches Smith's bank the only record of
the deduction which should be made from Smith's account is
in the “ exchanges for clearing house" which, accordingly, wre
ttiust deduct in our statistics.
These figures, however, have to be estimated. Only for
April 28, 1909, are they given for all banks, the figures being
those of the special Report of the Monetary Commission al
ready referred to. Of this amount, four fifths are of national
banks; and as national banks report annually their exchanges
Against clearing houses, we assume that the total each year
^ five fourths of that reported by the national banks (see
Comptroller's Report, 1908, pp. 514-522). The whole correc
tion is so small that any error in this assumed ratio is quite
negligible in the final result.
Column (7) is derived by applying to column (2) the above
Mentioned corrections,— deduction of items in column (3),

438

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

addition of those of column (4), deduction of column (5), and
deduction of column (6).
But even yet we have not reached the desired item,—deposit
currency, or deposits subject to check. The net individual
deposits which we have estimated include, not only current
accounts, but deposits on certificate and other deposits which
are considered investments rather than media of exchange.
The first published attempt to give the true deposits subject to
check is that of the National Monetary Commission. In their
valuable special Report as of April 28,1909, constructed through
the Comptroller of the Currency, the checkable deposits are
given as 6.94 billions.1 This 6.94 is subject to an addition
for “ nonreporting banks” and a deduction for “ exchange
against clearing house.” The unreported deposits of all
kinds are estimated for 1909 in the table at .39, of which, by
proportion, only

of .39 or .19, is probably checkable.

The .38 exchanges against clearing houses must be assumed to
be almost wholly against deposits subject to check. The net
corrected figure is therefore 6.94 + .19 — .38 or 6.75 billions
as the checkable deposits in 1909. These constitute about
67 per cent of the “ net individual deposits ” of column (7).
This figure* for checkable deposits in 1909 is found at the
bottom of column (9) in the table. As it is only 67 per cent
of the net individual deposits, and as it could not be assumed
that the same ratio obtained for other years,’I was unwilling
to guess at the deposits subject to check for these other years
without further light. Accordingly I wrote to Mr. A. Piatt
Andrew, then Director of the Mint, and asked him whether,
in his capacity as advisor to the Monetary Commission, he
could not have a search made among the Comptroller's rec
ords for 1896 and a few other years in order to obtain the
1 See Senate Document, 225, 61st Congress, 2d Session, Special
Report from Banks of the United States, April 28, 1909, p. 261; also
Report of Comptroller of the Currency, 1909, p. 835. The figures are
exclusive of Hawaii, Porto Rico, and the Philippines, although tho
sum thus excluded is scarcely appreciable.

Sec. 3]

APPENDIX TO CHAPTER X II

439

corresponding ratio for such years. Through his kindness
and that of the Commission and Comptroller, in acceding to
my request, it has been made possible to work out the corre
sponding ratio for 1896 as 85 per cent; for 1899 as 89 per cent;
and for 1906 as 78 per cent.
* Mr. Andrew gives 4.97 billions as the total (uncorrected)
deposits of all banks as of July 14, 1896. This figure is
slightly more complete than what I had already used from the
Comptroller’s Report (viz. 4.95), doubtless because, for this
particular inquiry, a larger number of banks were included
than had originally been used in the Comptroller’s tables.
Mr. Andrew gives the checkable deposits as 2.59 billions.
This figure is subject to two corrections: one to account for
unreporting banks, and one to account for exchanges for clearmg house. We have estimated the deposits of nonreporting
banks at .40; and, since Mr. Andrew has discovered in such
banks .02 more total deposits (4.97) than the Comptroller
reported, we must assume that there are .02 less unreported
deposits in his figures than in the Comptroller’s. This would
make the estimated unreported deposits for Andrew’s figures
*38 instead of .40 which we assumed for the Comptroller’s.
The part of this ascribable to the deposits subject to check
(2.59) is

X .38 or .20. This is the first (and additive)
4.97
correction. The second (and subtractive) correction is the
exchanges for clearing house, viz. .11. The final corrected
figure is therefore 2.59 + .20 — .11 or 2.68. The ratio of
this to the “ net deposits” is

^ or 85 per cent.

Tor 1899, Andrew’s figures for total net deposits are 4.38 and
for checkable deposits 4.09. His figures for total deposits
(7.07) are .30 completer than those of the Comptroller em
ployed in the first column of the above table, and thus reduce
the estimate for nonreporting banks applicable to Andrew’s
figures from .44 to .14, of which ^55 X .14 or .08 are ascrib7.07
able to the deposits subject to check. The correction con*

440

THE PURCHASING POWER OP MONEY

[A p p e n d .

X II

sisting of exchanges for clearing house is .27. The figures
for checkable deposits are therefore 4.09 + .08 — .27 or
3.90, which is 89 per cent of the “ net deposits” (4.38).
For 1906 Andrew’s figures for total net deposits are 8.75
and for checkable deposits, 6.90. His figures for total
deposits (12.37) are less complete than those of the Comp
troller, thus increasing the estimate for unreporting banks
applicable to his figures from .41 to .61, of which —^ X .61
12.3 /
or .34 are ascribable to the deposits subject to check. The
exchanges for clearing house were .40. The figures for check
able deposits are therefore 6.90 + .34 — .40 or 6.84, which is
78 per cent of the “ net deposits” 8.75). We thus have
figures for column (9) and column (8) for the years 1896,
1899, 1906, 1909.
If now, for intervening years, we interpolate evenly between
these percentage figures for the years 1896, 1899, 1906, 1909,
we shall have column (8) of the preceding table.
Column (9) may next be formed for the remaining years
by applying the percentages in column (8) to the net indi
vidual deposits in column (7). Thus the table is made com
plete.
The results are of course subject to a probable error which,
however, is believed to be only some 2 or 3 per cent for
the years 1896, 1899, 1906, 1909, and perhaps double as
much for years midway in the intervals between these four
years.
It seems strange, since so much has been said of the relative
importance of check and money circulation, that no attempt
has previously been made to estimate or record the volume of
the currency which circulates by check. This currency and
its circulation are of many times the statistical importance of
money and its circulation. Our wonder is the greater when
we consider that “ deposits subject to check” have been regu
larly reported by individual banks to the Comptroller of
the Currency. The published figures began in the ’60’s to
omit this category and lump all “ individual deposits” to

Sec. 4]

APPENDIX TO CHAPTER X II

441

gether, and subsequent reports have simply followed the prec
edent thus established. The present Comptroller states that
he intends, hereafter, to separate the item of deposits subject
to check; so that we may hope from now on to have annual
returns of the checkable deposits. We shall then know each
year the magnitude of that item in our circulatory medium
which, as we shall see, does nine tenths of the exchange
Work of the country.
§ 4 (t o C h a p t e r

XII, § 3 )

Method of Calculating M 'V r for 1896 and 1909

According to the Comptroller's Report for 1896, the total
sum (money and checks) deposited in all reporting banks on
the settling day nearest July 1,1896, was 303 millions. Pro
fessor Kemmerer's allowance for nonreporting banks (op. tit.,
pp. 110-111) brings the figures up to 506 millions. The pro
portion of checks found in all deposits reported was 92.5 per
cent, which, if applied to the estimated 506 millions of total
deposits, will give 468 millions as the total checks deposited
one day. But July 1, being a first day of the month,
Would show exceptionally large deposits. In order to de
termine how much allowance to make for this fact, I have
obtained, through the kindness of Mr. Gilpin of the New
York clearing house, the figures for the New York clearings of
July 2, 1896. July 2 was selected because the checks depos
ited in New York July 1 would appear in the clearing house
statistics of July 2. The clearings for July 2 amounted to
157 millions, while the daily average for 1896 was only 95
pillions or 60 per cent as much. Thus, the excessive clearlngs of July 2 have to be corrected by multiplying by .60 in
order to reach a true average for the year. It is perhaps fair
to assume that the deposits made on July 1 in New York
require substantially the same correction. If we could as
sume that the abnormality of the day's deposits in the rest
of the country were exactly like that of New York, requiring
the same correction factor (.60), then this correction factor

442

THE PURCHASING POWER OF MONEY

[A p p e n d .

XIl

would apply to the whole country. But this assumption we
cannot make. Doubtless .60 is too small an estimate of the
true multiplier for the whole country outside of New York.
The departure from the average was probably somewhat less
than in New York City.
That this is the case appears likely for various reasons.
In the first place New York is more sensitive to the varia
tions in business activity than the country generally. Con
sistently with this view, we find that the percentage fluctua
tion in clearings from year to year is much greater in NeW
York than in the rest of the country. By comparing each
year with the next, we find this to be true of all except five of
the twenty-seven years from 1883 to 1909 1inclusive.
Again, the quarterly and semiannual dividends would cut a
larger figure in a financial center like New York than in other
places, in many of which few or no dividends are received.
Finally, in large cities like New York, checks are deposited
more systematically and promptly, so that a fuller proportion
of the first-of-the-month checks received on July 1 would be
deposited on that day than in a smaller community. In the
smaller community these checks straggle along to banks
through several days after being received, thus tending to
even up the daily flow and in particular to diminish the excess
on and about July 1. W e conclude that .60 is a minimum
estimate for our multiplier for 1896.
Having obtained .60 as a minimum estimate, we next
proceed to ascertain a maximum estimate. We may be
reasonably sure that deposits outside of New York are so far
subject to the influence of quarterly dividends, first-of-themonth payments, etc., that the volume of checks deposited
outside of New York must to some extent exceed the average
in 1896. We need to know to what extent we are safe in
assuming that this outside volume of checks deposited on the
day chosen exceeded the average. We can best reach such a
1 See Financial Review (the Annual of the Commercial and
Financial Chronicle), 1906, p. 2G and 1910, p. 33.

Sec. 4]

APPENDIX TO CHAPTER X II

443

safe estimate by means of some data on clearing houses in the
Finance Report for 1896 (p. 493, Comptroller’s Report).
It is there shown that on July 1, or “ the settling day nearest
July l ” 66 out of the 78 clearing houses of the country had
§228,000,000 of clearings. We are safe in assuming that the
country’s total clearings on that day were larger than this, be
cause the returns as given include only 66 out of the 78 clear
ing houses of the country; and that on the following day they
were larger still,1because it was then that occurred the bulk of
the heavy July 1 deposits of checks. If the $228,000,000 clear
ings on July 1, 1896, were representative for each day of
1896, we could, simply by multiplying by the number of
settling days of 1896, 305 days, find the total clearings of the
country. But the result of this multiplication is 67.1 bil
lions, whereas the actual clearings of the country for 1896
were only 51.2 billions. This is conclusive evidence that the
clearings on July 1, and presumably still more those of July 2,
exceeded the daily average and need to be reduced at least in
the ratio ~ or .76.
67.1
Hence the true correction factor must lie between .60 and
•76. Splitting the difference we have .68 as an estimate which
cannot be far from the correct figures on either side; espe
cially as .60 and .76 are so very safe or extreme limits. Fig
ures very near either of them are improbable. The probable
error is simply set at 5 or 6 per cent.
We turn now to similar calculations for 1909. At my
request Professor Weston of the University of Illinois,
through the kindness of Professor Kinley, has used sub
stantially the same method for estimating the check circula1 Convincing proof that the clearings on July 2 exceeded those
on July 1 is afforded by the fact that whereas the New York state
clearings for July 1,1896, were $140,000,000, as given in the Comp
troller’s Report for 1896 (p. 494), the New York City clearings
alone on July 2 were $157,000,000.
For New York City the clearings, as M r. Gilpin of the New York
clearing house has informed mo, were far larger on July 2, 1896,
than on July 1, the two figures being 157 and 138 millions respectively.

444

THE PURCHASING POWER OF MONEY

[A p p e n d .

X ll

tion of 1909 based on Kinley’s investigation1of that year for
March 16. Professor Weston estimates the total check de
posits of March 16, 1909, at 1.02 billions. This is below the
daily average. A proof of this is found in the clearings of the
New York clearing house on March 17, which reflect the de
posits made in New York banks on the previous day; these
were 268 millions, which was not representative of the year,
as the average daily clearings were much greater, being 342
millions, or 28 per cent greater than those of March 17.
1.28 is therefore the correction multiplier we would apply if
we could trust New York clearings to be a faithful barometer
for the whole country. But since, as we have seen, New
York is especially sensitive to speculative and other varia
tions in banking operations, and as a part is usually more
variable than the whole, it is reasonable to assume that the
abnormality we find in New York of the deposits on March
16 exaggerates the abnormality of that day for the country
at large, and that the correction multiplier should be less
than 1.28. In order to set a safe lower limit, we may see
what figure would result from the extreme assumption that
outside of New York the day’s deposits on March 16, 1909,
were exactly the same as the daily average for the year.
We can make a fairly good estimate of the resulting correc
tion factor from the table on page 59.
This table is constructed from data taken from Kinley’s
report to the Monetary Commission on Credit Instruments
(pp. 182, 186) together with the estimated corrections for the
whole country’s check deposits made by Professor Weston.
The figure for deposits in New York City is given for March
16, 1909. Deducting these figures from those estimated by
Weston for the entire country, we have the deposits (786)
outside New York. But the daily average in New York has
been shown to be probably 28 per cent higher, or 306. These
figures, added to those for deposits outside New York (786),
1 Kinley, The Use of Credit Instruments in Payments in the United
States, National Monetary Commission, 61st Congress, 2d Session,
Doc. No. 399, 1910.

Sec. 4]

445

APPENDIX TO CHAPTER XII

give the daily average for the entire country, on the assump
tion that only New York City was abnormal on the day se
lected. The result (1092), compared with the actual deposits
on the day selected (1025), shows the correction factor on the
assumption that only New York was abnormal. This factor
is 1.07. This furnishes a lower limit for the correction factor
we are seeking.
C h e c k s D e p o s it e d

( in M il l io n s )

(1)

March 16, 1909 ........................................
Daily average if New York were alone
a b n o r m a l........................................
Ratio average to actual =

(2)

(3)

(4)

N e w Y ork
C it y

O u t s id e
N e w Y ork
C it y

T o tal
U .S .

239

786

1025

306

786

1092

- 1.07

Splitting the difference between our extreme limits, 1.07
and 1.28, we get, as our estimate of the correction factors,
1-17 in 1909 as compared with .08 for 1896. The range of
possible error on either side is about 10 for 1909 and 8 for
1896. As the limits are all very extreme, the probable error
must be much less — perhaps half as much. We may judge
that the correction factors, .68 and 1.17, are probably correct
within 5 or 6 per cent.
We conclude, then, that the 468 millions estimated as the
actual check deposits made on July 1, 1896, must be multi
plied by .68 in order to obtain the estimated average daily
deposits in 1896. The result is 318 millions; which, multi
plied by the 305 (settling days), gives 97.0 billions as our esti
mate for the check transactions in the United States for the
year 1896.
Likewise, multiplying the estimated volume of actual
check transactions in the United States on March 16, 1909
(viz. 1025 millions), by the correction factor, 1.17, we obtain

446

THE PURCHASING POWER OF MONEY

[A p p e n d .

X II

1.20 billions as the estimated daily average check deposits
and transactions. Multiplying this by 303 (the number of
clearing days of the New York clearing house and presumably
the average number of banking days in the country), we
obtain 364 billions as our estimate of the check transactions
in the United States in 1909.

§5

(to C h a p t e r

XII, § 3)

M'V' for 1897-1908
Although New York clearings constitute two thirds of all
clearings for the country, it cannot be imagined that the
check transactions in and about New York form two thirds
of the check transactions of the United States. We have
already seen that the reported check deposits in New York
on March 16, 1909, amounted to 239 millions. This figure,
being for New York, is probably nearly complete and indi
cates, as we have seen, an estimated average for the daily
deposits in New York City in 1909 of 306 millions. This
gives 306 X 303 or 93 billions for New York City, for the
entire year. Our estimate for the entire country was 364
billions, leaving 271 billions outside of New York City. Let
us compare these estimated figures for checks deposited with
the figures for clearings. The New York clearings in 1909
amounted to 104 billions and those outside New York, to
62 billions.
The New York clearings (104) thus exceed the New York
check deposits (93), probably because the clearings on ac
count of outside banks include clearings representing bank
ing transactions as distinguished from commercial trans
actions, since New York City is the chief central reserve
93
city. The New York City deposits were thus only ^
M ethod of Calculating

or about 90 per cent of the New York clearings. Outside of
New York, on the other hand, the deposits far exceeded the
clearings, being in the ratio 271
— ■or 4.4. These ratios between

Sec. 5J

APPENDIX TO CHAPTER X II

447

check transactions and clearings, viz. .90 for New York and
4.4 for “ outside,” would indicate that the published figures
for clearings should be weighted in the ratio of 4.4 to .9 or
about 5 to 1. That is, on the basis of 1909 figures, five times
the outside clearings plus once the New York clearings should
be a good barometer of check transactions.
Of 1896, unfortunately, we lack the figures for New York
City deposits. We have, however, figures for the deposits
in New York state in both 1896 and ,1909; and a study of
these figures indicates that the ratio of weighting for 1896
should be something over 3 to 1. Not to put too fine a point
upon it, we shall use the weighting 5 to 1 for all the years.
The difference in the results between this system of 5 to 1 and
& system of 3 to 1, or any intermediate system, will be small,
but 5 to 1 is chosen because (1) the data for 1896 on which the
number 3 is based are less certain than those for 1909, and
(2) the New York clearings are not as good a representative
of New York deposits as the outside clearings are of outside
deposits; the New York clearings being somewhat vitiated by
an element extraneous to New York and especially by the
banking transactions connected with adjustments of bank
reserves. We prefer, therefore, to give as much weight as
possible to the “ outside” clearings.
Having obtained our “ barometer” of check transactions,
viz. New York clearings plus five times outside clearings, we
merely need to multiply this by the proper ratio in order to
obtain the check transactions themselves. Absolute knowl
edge of this ratio of check transactions to the barometer
exists only for 1896 and 1909, in which years we know
the check transactions as well as the barometer. These ra
tios are .69 and .88. But we cannot err greatly in assuming
that the intermediate years have intermediate ratios, varying
regularly each year. The result is the following table: —

448

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

C l e a r in g s a s B a r o m e t e r o f C h e c k T r a n s a c t io n s

(2)

(1)

(3)

N e w Y ork
C l e a r in g s

Y eah

(4)

O u t s id e
B aro m eter
C l e a r in g s (2) -f 5 X (3)

(5)

(6) M 'V '

R a t io o f
C heck
T rans

C heck
T ran s
a c t io n s

a c t io n t o

B arom eter

1896
1897
1898
1899
1900
1901
1902
1903
1904
• 1905
1906
1907
1908
1909

.
.
.
.
.
.
.
.
.
.
.
.
.
.

28.9
33.4
42.0
60.8
52.6
79.4
76.3
66.0
68.6
93.8
104.7
87.2
79.3
103.6

22.4
23.8
26.9
33.3
33.4
39.0
41.7
43.2
43.9
50.0
55.2
57.8
53.1
62.0

140.9
152.4
176.5
227.3
219.6
274.4
284.8
282.0
288.1
343.8
380.7
376.2
344.8
413.6

.69
.70
.72
.73
.75
.76
.78
.79
.81
.82
.84
.85
.87
.88

(4) X (5)

97
106
127
166
165
208
222
223
233
282
320
320
300
364

(7) V '
V e l o c it t
OF ClRCU.
o f D e
p o sits ( V ')

(O)-i-M'

36.2
37.9
39.8
42.6
37.5
40.6
40.9
39.1
40.2
43.1
46.8
44.9
45.5
53.9

As already indicated, only the first and last figures in column
(5) are independently calculated, the rest being interpolated.
The other figures in the table explain themselves. The last
column gives the very important magnitude which we have
called the velocity of circulation of bank deposits subject to
check, or the “ activity ” of checkable accounts. The probable
errors of the last column are believed to range between about
5 and 10 per cent.
§ 6 (to C h a p te r

XII, §

General Practical Formula for Calculating V
I. An Approximate Formula

For the purpose of tracing the circulation of money, and
measuring it by bank records, we may classify the persons
who use money in purchase of goods into three groups: —
1. Commercial depositors, i.e. all engaged in business —
firms, companies, and others — who have bank deposits
mainly or wholly apart from personal accounts.
2. All other depositors, chiefly private persons.

S ec . 6]

APPENDIX TO CHAPTER X II

449

3. All who, like most wage earners, are not depositors at all.
These three classes we shall distinguish as “ Commercial
depositors,” “ Other depositors,” and “ Nondepositors,”
or C, 0, and N. The money in the possession of “ Commer
cial depositors ” we shall call “ till money,” and the rest
“ pocket money.”
The three groups necessarily include all in the community
who circulate money. By circulating money is meant ex
pending it in exchange, not for some other circulating medium,
as checks, but for goods.
The nature of these three groups of people must now occupy
our attention. In countries advanced in the.art of banking,
“ Commercial depositors” include practically all business
establishments, and little else; “ Other depositors” include
most persons in the professional and salaried classes and pro
prietors, and little else; while the class of “ Nondepositors”
is almost coterminous with wage earners.
It is true that these characterizations of the three classes
are not quite complete. “ Commercial depositors,” for in
stance, do not include some small business dealers, like street
Vendors, for these usually have no bank accounts. But the
number of such is comparatively small in comparison with
the number of business men or corporations who do have ac
counts, and, what is more to the point, the business they do is
still smaller. It follows that the money they handle is negli
gible. In the United States, at least, excepting those rural
parts of the South and a few other places where the money
expenditures are very small, the custom of having bank
accounts is practically universal among business men, firms,
and corporations.
To keep a bank account is, in fact, a practical necessity of
business. Without such an account a business man practi
cally deprives himself of three of the most essential aids in
modem business: the use of circulating credit; the use of
remittance by mail; and the use of time credit.
Unless a dealer is obliged to pay “ spot cash” or prefers
to do so — and such cases are both few in number and insignif*
2a

450

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

icant in the amounts of money involved — he will almost in
variably find it easier to make payment by check. More
over, the very fact that most other business men use banking
facilities creates in his mind the desire to have an account
himself, both because he dislikes to appear “ different,” and
because, when others pay him by checks, he finds it necessary
to cash these checks, — a procedure which is always more
trouble than to deposit them.
Cash payments are especially inconvenient when business
is done at a distance. Remitting money by post, express, or
personal delivery is troublesome, risky, and expensive as
compared with posting a letter containing a check. Even
a post-office money order is a clumsy and expensive substi
tute, and its use proclaims the user an insignificant financial
factor.
Again, a business man without a bank account cannot usu
ally obtain time credit, either from dealers or from banks.
In the United States a bank likes to lend only to its own de
positors. A business man who asks for a bank loan usually
meets with the request to open an account. If he should seek
a loan from another dealer, as for instance, his supply house,
the absence of a bank account would arouse suspicions as to
his business standing, and might lead to a refusal.
These facts, confirmed by observation and inquiry, have
led to the belief that practically all business transactions in
the United States, certainly over 99 per cent (measured, not
by their number, but by their aggregate size), make some use
of bank accounts. Even in localities where there are no banks,
traders usually like to have a bank account in the nearest
town, in order to facilitate their dealings as purchasers.
We conclude, therefore, that the category of “ Commercial
depositors” coincides for all practical purposes with the cate
gory of business establishments.
“ Other depositors” include most proprietors, professional,
and salaried persons. Almost no wage earners are included,
and almost no business establishments or business men in a
business capacity. When a single individual conducts a busi

Sec. 6]

APPENDIX TO CHAPTER X II

451

ness, he usually separates carefully his business self from
his personal self. John Smith, the individual, and the John
Smith Shop are distinct. The pocket money of the one and
the till money of the other are not often confused. Where
payments of money are made from one to the other, the trans
action is regarded as of the same nature as the payments be
tween the shop and any other person. Originally, and under
primitive conditions, it is of course true that no such distinc
tion was observed, and even to-day the differentiation is
sometimes unmarked, e.g. in the case of hucksters, peddlers,
fruit-stand dealers, and small country shopkeepers. But,
as we have seen, these persons are not usually depositors
anyway. Moreover, their number is small; and since by the
nature of the case the money they handle is also small, their
classification is, for practical purposes, a matter of indifference.
It is true that occasional cases exist of ordinary business men
who have the exclusive ownership of a business and do not
take care to separate clearly their business and their personal
accounts. Yet we may, in such cases, perform the separation
in thought. When such a person withdraws money from his
till and puts it in his pocket, we may say his business self has
paid his personal self some dividends of the business. Like
wise, his checks drawn are usually distinguishable as between
his business or his personal expenses, even though he him
self fails to keep two separate bank accounts. But such cases
are rare and unimportant, because modern business of size is
usually conducted by partnerships and corporations, where a
strict separation of accounts is necessary to safeguard con
flicting interests.
So much for the line of demarcation between “ Other de
positors” and “ Commercial depositors.” As to the line
separating “ Other depositors” and “ Nondepositors,” it
should be observed that, although “ Other depositors” in
clude most proprietors and professional and salaried persons,
yet some proprietors and professional men, especially in rural
communities; and some salaried persons, chiefly small clerks,
are “ Nondepositors.”

452

THE PURCHASING POWER OF MONET

[A p p e n d .

XII

Finally, “ Nondepositors” consist chiefly of those who are
classed in statistics as wage earners. While there are some
wage earners who are depositors,1 they are rare; and while
there are some “ Nondepositors” who are not wage earners,
especially (as just indicated) the agricultural proprietors
(farmers) and small clerks, the amount of money circulated
by them is small in comparison with the total circulation.
While the line separating wages and salaries is not definitely
marked in theory, it is usually easily recognized in practice.
Children under, say, twelve years need not be included in
any of the three categories, as they are not handlers of money;
at least, not to a sufficient degree to have any appreciable in.fluence on the total circulation.
We may now picture concretely the main currents of the
monetary flow, including the circulation of money in ex
change for goods. Figure 18 illustrates the three principal
types.
The corners of the triangle, C, 0 and N, represent the three
groups of “ Commercial depositors,” “ Other depositors,”
and “ Nondepositors,” and the B’s represent banks. The
arrows represent the flow of money from each of these four
categories to the others. Thus B0represents the annual with
drawals from banks by “ Other depositors,” Oc the spending
of this withdrawn money by “ Other depositors” among
“ Commercial depositors,” and Cb the return of the money
from the “ Commercial depositiors” to the banks. This
circuit (B0OcCh) of three links is very common. A second
type of circuit is represented by a chain of four arrows
{B0OnNcCb). It is illustrated by private depositors draw
ing money (B0), and paying wages (0n) to servants who in
turn spend the money (Nc) among tradesmen who finally
deposit it (C6). A third type of circuit, also fourfold, is
represented by the arrows BcCnNcCb. It is illustrated by
commercial firms cashing their checks at banks (Bc) for pay
1 The term “ depositors,” as here used, does not, of course, in
clude savings bank depositors. A savings bank is not a true bank
of deposit, providing circulating credit.

S e c * 6]

APPENDIX TO CHAPTER X II

453

rolls, with the cash so obtained paying wages (Cn) to work
men who spend it (Nc) among other tradesmen who redeposit
it in banks (Ch). These three types are not the only ones, but
they are so much more important than any others that they
merit our undivided attention before a completer study is
undertaken. Figure 18 has been constructed for the purpose
of exhibiting them uncomplicated by other details.

It will be noted that not all of the flows described are ex
amples of the circulation of money. As already indicated,
money may be said to circulate only when it passes in ex
change for goods. Its entrance into and exit from banks is a
flow, but not a circulation against goods. In the diagram
the horizontal arrows represent such mere banking operations,
not true circulation. On the other hand, the arrows along the
sides of the triangle represent actual circulation. The dia
gram shows four such arrows, representing the four chief
types of circulation: Oc payments of money from “ Other

454

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

depositors” to “ Commercial depositors” in the purchase of
goods; 0n payments from “ Other depositors” to “ Nondepositors,” as when a housewife pays wages; Cn payments
from “ Commercial depositors” to “ Nondepositors,” as
when a firm pays wages; and Nc payments from “ Non
depositors” to “ Commercial depositors,” as when a wage
earner buys goods of a merchant.
These four types of circulation of money occur in the three
circuits already described, being sandwiched between the flows
from and to the banks. The first, 0C) is contained within
the circuit B0OcCb, and, since no “ Nondepositors” inter
vene, represents money changing hands once between its with
drawal from bank and its re-deposit there. The remaining
types {0n, Cn, and Ne) are contained within the two other
circuits (.B0OnNcCb and BcCnNcCb), and, owing to the fact
that “ Nondepositors” intervene, represent money circulat
ing twice between withdrawal and re-deposit.
In short, one of the three circuits (B0OcCh) shows money
circulating once out of bank. Both the others pass through
N, and show money circulating twice out of bank. The
diagram, then, represents all circulating money as springing
from and returning to the banks; all of it as circulating at
least once in the interim; and that portion handled by “ Non
depositors” as circulating once in addition. Therefore, the
total circulation exceeds the total flow from and to banks
by the amount flowing through “ Nondepositors.” In other
words, the total circulation in the diagram is simply the sum
of the annual money flowing from and to banks and the
money handled by “ Nondepositors.” The quotient of this
sum divided by the amount of money in circulation will give
approximately the velocity of circulation of money.
II. The Complete Formula

We have, however, still to consider the correction to be
made for the less important forms of monetary circulation
excluded from Figure 18.

S e c . 6]

APPENDIX TO CHAPTER X II

455

In order to estimate the degree of accuracy of the first
approximation just made for the circulation of money, we
need to compare this approximation with a complete formula
framed to include all possible transfers of money against
goods.1 There are nine possible kinds of transfers, three
being respectively within each one of the three groups C, 0,
and N, and six being between each pair of these three, in either
direction.
The exchanges possible within a class are (1) those between
one “ Commercial depositor” and another “ Commercial
depositor” ; (2) those between one “ Other depositor” and
another; and (3) those between one “ Nondepositor” and
another. The transfers possible between classes are (4
and 5) those between “ Commercial depositors” and “ Other
depositors” in either direction; (6 and 7) those between
* Other depositors ” and “ Nondepositors ” in either direction;
and (8 and 9) those between “ Nondepositors” and “ Com
mercial depositors” in either direction. Thus there are
three intraclass kinds and six interclass kinds of transfers of
money against goods.
Figure 19 gives a complete picture of all these nine flows
of money in exchange for goods; that is, of the entire “ cir
culation of money.” The nine flows are represented in the
diagram by the nine arrows about the triangle, six being along
the three sides of the triangle and representing interclass
circulation, and three (c, o, and n) at the corners to represent
mtraclass circulation. The remaining six arrows on the hori
zontal lines represent, of course, mere banking operations.
The total circulation or monetary flow (F) in exchange for
1 That is, all transfers within the community considered. If it
is desired to include as part of a community’s circulation tlie sums
sp orted or imported in foreign trade, tlieso may most conveniently
he added at the end. But oven if they bo included, they will bo of
trifling significance, partly because foreign trade is usually very
small compared with domestic, and partly because money is so little
used in foreign trade, especially if we exclude bullion from the
category of money.

456

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

goods is, therefore, the sum of the magnitudes represented
by these nine arrows, viz.
F = Oc+ Co + Nc+ Cn+ On+ N0 + c + o + n.

(1)

This is an exact formula for the circulation of money. We
shall now compare it with the inexact first approximation,

namely, “ money deposited plus expenditures of ‘ Nondeposi
tors. 1” This comparison will express the error of the first
approximation, and will suggest a method of transforming the
exact formula (1) into a shape more suitable for statistical
application. First, we need to express algebraically the
first approximation. This may easily be done by inspect
ing Figure 19. The total money deposited is C*-f-Oj +
N6, while the total expenditure of “ Nondepositors” is
Nc + N0. The sum of these two expressions we shall call Ff*
It is: —
F' = Cb+ Ob+ N L+ Nc+ N0,

(2)

Sec. 6]

APPENDIX TO CHAPTER X II

457

which is, therefore, the algebraic expression for the first ap
proximation.
To obtain the difference, F — F', between the exact and the
approximate formula, we subtract (2) from (1), canceling Ne
and N0and placing the negative terms first. We thus obtain
for a remainder (r) the following: —

rs=-.F~~Ff——Cb—Ob—iV$+0<.+ C^+Cn+On+c+o+w. (3)
That the value of F — F' is small may be seen clearly by
transforming (3). We shall transform it by means of another
equation (1) given below. In order to derive this new equa
tion (4), we shall need to make a digression. This new equa
tion is merely a special application of the general principle
that the net outflow (i.e. outflow minus inflow) from the con
tents of any reservoir must equal the net decrease in its con
tents during the same time, or (algebraically expressed) that
the net outflow (positive or negative) plus the net increase
in contents (negative or positive) must be zero. We may
apply this principle to any reservoir or store of money, but
shall here find it most helpful to apply it to the reservoir of
money contained among the “ Commercial depositors” and
Nondepositors” taken together as one group. Let us desig
nate the combination of these two as the “ CN group.” The
total outflow indicated in the diagram from this “ CN group”
is evidently Cb + C0 + Nb+ N0, and the total inflow Be +
Oc + Bn + On. Hence, the net outflow, so far as the diagram
shows usf is: —
Cb+ CQ+ Nb+ N0- B e- O e- B n- O n.

This, plus the net outflow not shown in the diagram, is the
true net outflow. Since the diagram was constructed to show
°nly flows against goods (monetary circulation), and flows to
°r from banks, we have still to take account of money flow
ing in the community in exchange for something else than
goods, and that flowing without any exchange at all, as well
as any net outflow outside of the community.
We have thus to take account of three undiagramed flows.

458

THE PURCHASING POWER OF MONEY

[A p p e n d .

XIl

The first is the net outflow of money from the “ CN group ” to
the “ 0 group,” which, though in exchange, is not in exchange
for goods. This means simply cashed checks, for, according
to the classification we are here using, “ goods” are taken to
include anything exchangeable, not either money or checks.
Our first correction is, therefore, the net outflow of money from
the “ CN group” for cashing checks, i.e. the difference be
tween the checks cashed by the “ CN group” for the “ 0
group ” and those cashed in the opposite direction.
It will be understood that wre have nothing to do here with
the cashing of checks at banks, for this is included in the dia
gram (B0) Bn, and Bc). Moreover, we have nothing to do
here with cashing of checks within the 11CN group,” as when
a storekeeper cashes a check presented by a “ Nondepositor."
We have only to do with the net outflow for cashed checks
from CN to 0. This net outflow (which may be positive,
negative, or zero) we shall designate by the letter a, to stand
for “ accommodation” checks.
For the second correction, we have to designate the net out
flow of money given away by the “ CN group” in gifts, taxes,
thefts, etc., for which no specific goods are received in return.
This net outflow may be designated by g.
We have, thirdly and lastly, the net outflow of money with
respect to the “ CN group” outside of the community, i.e. the
net amount of money which is lost to the country by export,
fire, shipwreck, melting, etc., in excess of that imported,
minted, etc. This net outflow may be designated by e, to
stand for “ external” outflow. Adding the net undiagramed
outflow (a + g + e) to the net diagramed outflow, we have,
for the total net outflow,
C&+ C0+ Nb+ N0 — Bc — Oc — Bn — On+ a + g + e.
Now, on the reservoir principle already explained, the alge
braic sum of this net outflow from the “ CN group” and the
net increase of the money in that group must be zero. That
is, representing this net increase by i, we have
0 = Cb+ C0+ Nb+ N0—Bc—Oc—Bn—0n+ a + g + e + i. (4)

Sec. 6]

APPENDIX TO CHAPTER X II

459

We now place this new equation (4) under the old equation (3),
giving the value of r = F —Frin the following manner: —
r = — (C&) — Ob — (Nb)

+ (0c) + Co + Cn + (On)4+ c + o + n

(Cb) + C0+ W>) + No —Bc — (Oc) —Bn

— (0;») + a + 0 + e + i .

Adding and canceling the terms of (3) and (4) indicated in
parentheses, and rearranging the remaining terms, we have
r = F — Ff = {C0 + Cn— jBc) + (Co + iVo — Ob) + (c + o
+ n) + {a + g + e) + i —Bn.
(3)'
The letters are grouped in parentheses forming six terms,
arranged, as far as can be judged, in the order of descending
importance.
By using the expression just obtained for r, the complete
formula (1) for the circulation of money may now be put in a
form suitable for statistical application. Since r = F — F',
then F = F' + r. Substituting for Ff and r the expression
already given in equations (2) and (3)', we have, as a trans
formation of (1),
F = Ff + r

= (Cb+ Ob+ Nb) + (Nc + N0)
+ (C0 + Cn—Bc) + (C0 + N0 — 0 b) + (c + o + n) + (a + g
+ e) + i —Bn
(1)'
= (1) all money deposited
+ (2) money expenditures of “ Nondepositors ”
+ (3) C’s money expenditures from tills (i.e. money expendi
tures in excess of money withdrawn from bank)
+ (4) O’s money receipts pocketed (i.e. money receipts in
excess of money deposited in bank)
+ (5) intraclass monetary circulation
+
CN’s undiagramed net outflow of money
+ (7) CN’s net increase of money on hand
(8) N1s withdrawals of money from bank.

(G)

This is a complete and universal formula for the circu
lation of money in any community. Its first two terms

460

THE PURCHASING POWER OF MONEY

[A p p e n d .

XIl

constitute the first approximation, and the other six
terms constitute r, which may be called the “ remainder
term.”
The first and second terms are by far the most important.
The last three terms — sixth, seventh and eighth — are
doubtless quite negligible under all circumstances actually
met with. I am also reasonably confident that, in the United
States, the 3d, 4th, and 5th terms amount to less than 10 per
cent of the total and probably less than 5 per cent. There
fore, the complete omission of all except the first two terms
would still give us a fairly good figure for the total F; for
any one familiar with the inaccuracies of statistics knows
that 5 or 10 per cent is a small error, especially for a
magnitude which has hitherto eluded any attempt at meas
urement.
We may, therefore, distinguish three successive stages in our
approximations. The first approximation comprises only
the first two terms, viz. money deposited plus expenditures
of “ Nondepositors” ; the second includes, in addition, terms
(3), (4), and (5), viz. till-paid money expenditures of C, pock
eted money receipts of 0, and intraclass circulation; while
the third is rendered absolutely complete by including terms
(6)> (7), and (8), none of which has practical importance.
The complete formula is presented in the hope of arousing
discussion and investigation which will disclose in particular
to what extent it may be applied in countries where data
exist for the first two terms, viz. money deposited and expend
itures of “ Nondepositors.” The former is to a large extent
a matter of daily record in most civilized countries, and the
latter consists chiefly of wages, a magnitude which has for
long been a favorite subject for statistical estimate.
§ 7 (t o C h a p t e r

XII, § 4 )

Application of Formula to Calculation of V for 189G and 1909

We shall now exemplify the use of our formula by means of
actual figures for the United States. The Report of the

Sec. 7]

APPENDIX TO CHAPTER XII

46 1

Comptroller of the Currency for 1896, already referred to,
and the special report of the National Monetary Commission
for 1909, give a basis for estimating the first term (Cb + Ob +
Nb), the annual money deposited in banks in those years.
Both reports were made under the direction of Professor
David Kinley of the University of Illinois. We shall consider
first the figures for 1896. The total money deposited in
banks on the settling day nearest July 1,1896, was 7.4 per cent
of the total deposits of all lands. This total for all reporting
banks was 303 millions, of which 7.4 per cent would make
§22,400,000. It was made up of over 816,200,000 from 3474
national banks, and the remainder from 2056 other banks.
There were, all together, according to the Comptroller’s Re
port, about 13,000 banks in the country at that time. On the
basis of these figures, the Comptroller attempts to estimate
the (retail) deposits of all kinds for all these 13,000 banks,
assuming that the average deposit was the same as for the
country banks replying. This average was S2375 for
banks in places of 12,000 inhabitants or less. Applying
this average to the unreporting banks, we would increase
the retail deposits (which were §26,500,000) by an addi
tional §17,800,000.
If we assume the same ratio of increase for the total money
deposits, the sum of 22.4 millions would be increased by 15.0
millions, making a total of 37.4 millions, as the amount of
money deposited in banks on the settling day nearest July 1,
1896. This figure represents at least a rough approximation
to the inflow of cash into, and, therefore, also the outflow of
cash from, the banks of the country. Multiplying by 305
settling days for the year, we obtain 11.4 billions as the
total annual amounts deposited. The figures, being for the
settling day nearest the first of July, are probably above
the daily average for the year. Thus 11.4 is an upper limit
rather than an estimate. Later we shall also set a lower
limit.
The preceding figures relate to the year 1896. Similar
calculations for 1909 have been made by Professor David

462

THE PURCHASING POWER OF MONEY

[A p p e n d .

X II

Kinley1with the assistance of Professor Weston. The re
sulting figure for money deposited in 1909 is 19.1 billions.2
But if it is necessary to adjust the figures for deposits of
checks in 1896 and 1909 because the days selected are excep
tional (see § 4 of this Appendix), it is also necessary to
adjust the figures for the deposits of money. On July 1,1896,
many June bills must have been paid by cash as well as by
check and on March 16, 1909, the middle of a month, there
must have been slackness of settlements by cash as well as
by check. Consequently, like the total deposits of checks,
the total deposits of money made on July 1,1896, were in all
probability above the daily average for 1896, and on March
16, 1909, they were below the daily average for 1909. In
other words, without adjustment for the abnormality of the
days selected, the figure expressing monetary circulation for
1896 would be too large, and that for 1909, too small. That
is, without such adjustment our calculations merely set an
upper limit in 1896 and a lower limit in 1909.
But we may easily set the opposite limits. We may be
reasonably sure that deviations .from the average are less
for money deposits than for check deposits. It cannot be
expected that daily money deposits fluctuate as greatly as
1 See “ Note on Professor Fisher’s Formula for Estimated Velocity
of Circulation of M oney.” Publications American Statistical Associationj March, 1910. The calculations are based on data taken from
Professor Kinley’s valuable monograph on “ Credit Instruments,”
61st Congress, 2d Session, Doc. No. 399 in Reports of National
Monetary Commission.

2 Professor Kinley gives 18.3. The difference is due to the fact
that Professor Kinley, while estimating the daily deposits as 62.9
millions, calls this in round numbers 60 millions. It seems prefer
able to use the estimate as it stands and make any allowances for
errors at the end rather than the beginning. Professor Kinley also
takes 305 settling days for the year, this being the number used by
Professor Kemmerer for 1896. But Mr. Gilpin of the New York
clearing house tells me that the clearing house business days, though
305 in 1896, were 303 in 1909. I have therefore used 303 as the
number of settling days in 1909. The product 62.9 millions, times
303, is 19.1 billions.

S e c . 7]

APPENDIX TO CHAPTER XII

463

daily check deposits. Practically all check payments are in
fluenced by the periodicity in receipts of checks by the de
positors (as of their salary, interest, or dividend checks), or by
the periodicity of credit extended to them (as of the trades
men who render them monthly bills). While the fluctuations
to which money payments are subject are more or less similar,
they are much less in extent for two reasons: First, the pay
ment or credit cycles which influence the fluctuations of
money deposits are usually shorter than those which influence
the fluctuations of check deposits; the wage earner usually
gets his money weekly as against the salaried man who re
ceives his check monthly, or the stockholder who receives
his dividends quarterly. Secondly, unlike check payments,
many, if not most, money payments have no payment or credit
cycle. There is no credit cycle in what are called “ cash”
Payments, for they imply that no credit is given.. The receipts
at “ cash stores,” the smaller receipts at all stores, the receipts
°f tramway, railway, and steamship offices, the receipts at
theaters and many miscellaneous establishments are almost
wholly on a cash basis and result in daily and fairly steady
money deposits made by these establishments. These are
facts of every-day experience and are confirmed by inquiry of
bankers, who state that their money deposits are far steadier
day by day than their check deposits. Confirmatory and
conclusive evidence is also obtainable from Kinley’s investi
gation in the Comptroller’s Report for 1896 (p. 95). If check
and money deposits were to fluctuate in perfect sympathy
With each other, the percentage of the total which consists of
checks would remain constant. But if, as we shall endeavor
to show, the excess or abnormality of check deposits on July 1
ls greater than the excess or abnormality of money deposits
°n that date, then we ought to find that the percentage of
check deposits is greater on July 1 than usual. The figures
the Comptroller’s Report indicate that this is the case.
They show that the percentage of checks received (unfortu
nately not quite synonymous with “ deposits”) was on
September 17, 1890, 91.0 per cent and on July 1 of the same

464

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

year, 92.5 per cent, or 1£ per cent higher. Again, com
paring July 1,1896, with the nearest available date for another
season of the year, namely, September 15, 1892, we find the
figures to be as follows: for September 15, 1892, check re
ceipts, 90.6 per cent; for July 1, 1896, check deposits, 92.5
per cent, or 1.9 per cent higher. The excess would have been
still greater if both the figures were for receipts instead of one
of them being for deposits; for, as the Comptroller says, the
inclusion of other receipts than deposits tends to exaggerate
the percentage of checks. That July 1 has a far larger pro
portion of checks than June 30 is indicated by the figures for
retail deposits for June 30,1894, and July 1, 1896, the former
being 58.5 per cent and the latter 67.6 per cent, or 9.1 per
cent higher. We should be cautious, however, in drawing any
quantitative conclusion from this difference, since the investi
gations for 1891 and 1896 were conducted somewhat differ
ently. But the difference, as we find it, harmonizes with all
the facts at hand. Similar confirmation may be drawn from
the absence of any contrast between the figures for June 30
and September 17,1881, as compared with the’sharp contrast
already noted between July 1 and September 17, 1890. The
credit receipts in 1881 on June 30 and September 17 were
91.77 per cent and 91.85 per cent, respectively, which figures
are substantially equal, while, as above noted, for July 1 and
September 17, 1890, we find a difference of 1-J- per cent.
We feel, therefore, safe in concluding that check deposits
are subject to greater fluctuations or abnormalities than
money deposits. Consequently the deposits of money on
July 1, 1896, while they may have exceeded the daily aver
age, were probably not so far above the daily average as
were the deposits of checks; also on March 16, 1909, the
deposits of money were probably not so far below the
average daily deposits of money as were the deposits of
checks.
Now, if this were not true, — if the money deposits fluctu
ated exactly parallel with check deposits, — we should need to
assume the same correction-factors for money as for checks,

Sec. 7]

APPENDIX TO CHAPTER XII

465

viz. .68 in 1896 and 1.17 in 1909, with the results given in
column (1) of the following table: —
E s t im a t e d M

(1)

(2)
M

oney D e
p o s it e d o n D a y
Selected

(In M

1896 .
1909 .

.
.

il l io n s )

37.4
62.9

(3)

oney

e p o s it s o f

(4)

s s u m in g C o r
A s s u m in g D a y r e c t io n F a c t o r s
a n A v e r a g e O n e e q u a l t o th ose
( I n B il l io n s )
fo r C h eck
•.De p o s i t s

ear

(5)

11.4
19.1

7.8
22.3

M ean betw een
T w o P r e c e d in g
C olum ns

9.6
20.7

W&see that the true value of the money deposited in banks
in 1896 must in all probability lie between 7.8 and 11.4 billions,
and in 1909, between 19.1 and 22.3 billions. If, in each case,
we split the difference, the estimates become for 1896, 9.6,
and for 1909, 20.7. The truth cannot be far from these
figures, for there are only narrow limits on either side. The
probable error, judged roughly from the calculated limits and
from the character of the estimates of these limits, is placed
at about 1 billion in each case. It will be noted, of course,
that this error is larger proportionally in 1896 than in 1909.
We have now estimated the first term (total deposits) of the
formula for the total circulation of money.
The next term (Nc+N0) is the expenditure of the “ Nondepositors” made to other classes. This is practically the
expenditure of wage earners. The Census gives the average
Wages in manufacturing industries as $430. Mr. William C.
Hunt of the Census Bureau, in an unofficial memorandum
which he has kindly allowed me to see, has estimated that the
laborers in the United States number about 18,400,000. Let
us assume, as a reasonable approximation, that their average
wages are the same as the average in manufacturing industries,
namely, $430. We first apply this to the 8.5 millions of people
which Mr. Hunt estimates are engaged in manufacturing and
mechanical pursuits and trade and transportation. These
2n

466

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

persons, therefore, receive about 3.7 billions of dollars in
wages.
The remaining classes of laborers are domestic servants and
agricultural laborers. These, however, receive board and
lodging as part pay. Since food and rent form about 60 per
cent of workingmen’s budgets, we may assume that the actual
money paid to domestic and agricultural workers is only about
40 per cent of that paid to manufacturing laborers, i.e. about
S170. Mr. Hunt estimates the number of domestic and agri
cultural laborers at 9.9 millions. Hence the total money
they handle in a year is probably about 1.7 billions. This,
added to the previous 3.7 billions, gives 5.4 billions as the to
tal money paid in wages in the United States All these
.figures relate to the year 1900, while the figures for our first
term relate to 1896. In the interim both the number of
laborers and their wages doubtless increased somewhat and
we must, therefore, make a correction for each. We shall as
sume that the number of laborers increased in the same ratio
as population, and that population increased between 1896
and 1900 at the same rate per annum as between 1890 and
1900. This would reduce the 5.4 billions to 5.0 billions.
If, instead of population, we use the number of employees in
manufacturing and mechanical pursuits as given by the
Bureau of Labor,1the result is lower, viz. 4.6. The truth prob
ably lies between, since agricultural labor, for which we
have no statistics, has probably not increased as fast as
manufacturing labor, and, therefore, even if labor as a whole
increased in the same ratio as population, the relative in
crease of manufacturing labor, as compared with agricultural
labor, would mean a greater payment of money wages. We
may select 4.8 billions as close to the truth. As to the rate of
wages, the index numbers of the Bureau of Labor2 for 1896
and 1900 are 99.5 and 104.1 respectively. On this account,
therefore, we should still further reduce our estimate of money
1 Bulletin of the Bureau of Labor, N o. 77, July, 1908, p. 7.
* Ibid., p. 7.

Sec. 7]

APPENDIX TO CHAPTER XII

467

wages paid in 1896, — in the ratio of 104.1 to 99.5 or from
4.8 billions to 4.6 billions. Furthermore, a small fraction
of these laborers are prosperous enough to have bank ac
counts, and the expenditures of these should not be included
among the expenditures of “ Nondepositors.” About 4£ bil
lions is probably as close to the truth as we can expect to get.
But we must now add to this an allowance for “ Nondeposi
tors ” other than wage earners. Some of the 2.1 million clerks
and 8.6 million proprietors and professional men in Mr.
Hunt’s estimates, though not laborers, are nevertheless
“ Nondepositors.” As to the clerks, it is said by business
men that most clerks who receive over §100 a month, and
some who receive less, have bank accounts. Probably, the
great bulk of the 2 millions of persons estimated as clerks
are far below $100 a month, and many are doubtless included
who, like office boys, have less than what are ordinarily
called wages. To make a guess sure to be large enough, let us
say that three-fourths of the clerks have no bank account and
average $60 a month. Even then the total cash-paid clerk hire
Would scarcely exceed a billion.
Among the proprietors and professional men, the only
group we need to consider is agricultural proprietors (5.7
millions). The remainder consists of classes among which
bank accounts are practically universal. Of these agricul
tural proprietors, those who have no bank accounts are doubt
less smaller ones, living in districts where little money changes
hands. Their number could certainly not exceed four mil
lions, which would be over two thirds of the whole. The prob
lem is, What cash do these farmers pay to depositors, com
mercial and other? Practically, this means, What do they
Pay to country storekeepers ? Their payments to laborers or
other farmers are payments to other “ Nondepositors ” and do
*>t concern us here. For rent, food, or such farm supplies
as they can raise themselves, they pay little or nothing.
Thus, the hay crop of the nation is said to exceed in value the
wheat crop; ’but so little hay is marketed that it is seldom
quoted or thought of as a market commodity. Even the

468

THE PURCHASING POWER OF MONEY

(A p p e n d .

XIl

trade of these farmers with the storekeeper is conducted
largely by barter or book credit. Their expenditures in actual
money may be conjectured to average less than $250 a year
for each farmer, making less than a billion dollars at most
(even if the number of such farmers be counted at 4
millions).
It seems safe to say, then, after allowing a billion for clerks
and a billion for farmers, that the total expenditures of
“ Nondepositors ” cannot exceed 4i- + 1 + 1 = 6J- billions.
On the other hand, it can scarcely be less than 5 billions.
To reduce it to this figure would require us practically to ig
nore the existence of “ Nondepositors ” other than wage
earners, or to assume a large error in the estimate of wages.
We conclude that for 1896 the second term lies somewhere
between 5 and 6.Vbillions. Placing it midway, we obtain ap
proximately 5.7 billions with a possible error of .7 or. 8. Sim
ilar calculations for 1909 show 13.1 billions for the second
term with a possible error of 1.0. To quote from Professor
Kinley’s article already referred to:1—
“ The second term of the formula is the money payments of
*Nondepositors, 1 made up principally, as Professor Fisher
thinks, of the wages of working people. The following table
shows an estimate of the increase from 1900 to 1909 in certain
pursuits on the basis of the percentage of increase from 1890
to 1900 and on census and railroad returns since 1900. As
far as possible salaried officers are eliminated.
Increase Estimate
Per
1909
Cent
8,565,926 10,381,765 21.2 12,362,605
1890

1900

Agricultural pursuits .
Domestic and personal
service
. . . .
4,220,S12 5,580,657 32.2 7,377,628
T o ta l...............................................................................
19,740,233
Trade and transporta
.....................
1,977,491 2,617,479 35.2 4,275,913
tion
Manufacturing
and
mechanism . . . 4,251,613 5,208,406
6,935,113
T o t a l...............................................................................11,211,026

1 Publications of the American Statistical Association, March, 1910.

Sec. 7]

APPENDIX TO CHAPTER XII

469

“ A rough calculation based on the figures of Census Bui*
letin No. 93 gives us about §550 as the average yearly wages
of people in manufacturing. If we should include mechani
cal pursuits, probably the average should be raised a little.
Very likely $600 would be more nearly correct for this class.
“ Again the Report of the Interstate Commerce Commission
for 1907 gives figures from which it appears that the average
yearly wage is about $640. It is more difficult to get a ground
for making an estimate of the money wages of those engaged
in agricultural and domestic pursuits. Doubtless it is more
than, at first thought, might be believed. The money wages
of domestic servants at present probably will average not less
than $250 a year. Agricultural laborers are certainly receiv
ing a good deal more than formerly, and $300 or $350 probably
will not be too large a sum to assign to these. Accordingly, we
may recapitulate as follows: —
Trade and transportation
4.3 millions at $640
$2,752 millions
Manufacturing and me#
chanical pursuits
.
6.9 millions at $550
$3,790 millions
Agricultural pursuits . .
12.4 millions at $300
$3,720 millions
■Domestic and personal serv i c e ..........................
7.4 millions at $250
$1,850 millions
Clerks, etc., having no
bank a c c o u n t .................................................... $1,000 millions
T o t a l .....................................................................$13,112 millions

“ This gives us the second term of the formula.”
We have now estimated the first two terms (constituting
together what has been called the first approximation) for
both 1896 and 1909.
To this first approximation must be added the remainder,
r) consisting of the many terms already explained, most of
Which are not known with exactness, but all of which are
known to be small. The term “ small” is always relative,
and in this case a term is small for 1896 which is small com
pared to 16 billions. For instance, 160 millions is a mere
trifle, being only 1 per cent of 16 billions, while 16 millions is
only one tenth of 1 per cent. For purposes of comparison
We do not need exact statistics for the various terms of which

470

THE PURCHASING POWER OF MONEY

[A p p e n d .

X Il

r is composed. All we need to know is that r is small and
that it varies approximately as the rest of circulation varies.
Under these circumstances a large mistake in estimating it
will make a small error in comparisons. Only in case r were
at once large and variable relatively to the other terms could
a mistake in its estimation greatly affect the comparisons.
Our attempt to estimate r has been made, not so much for
the purpose of obtaining its absolute value, as to set for it
wide and safe limits.
The magnitude r consists of all the five terms of our for
mula beyond the second. We shall take these up in order.
The third term of the formula is (C0 + Cn—Bc). This
represents the till-paid commercial expenditures, or the excess
of the money paid out by “ Commercial depositors” over the
money withdrawn by them from banks. Personal inquiry
shows that the great bulk of the money withdrawn by “ Com
mercial depositors” from the banks is drawn for the purpose
of paying wages; also that the great bulk of the actual money
expended by “ Commercial depositors” is expended for wages.
In other words, C0 is very small compared with C„, and the
sum of the two is nearly the same as Bc. Hence the difference
(C0+ Cn—Bc), or till-paid expenses, is nearly zero. Tillpaid expenses, being mostly wages and, as all observation
shows, only a small part of total wages (4-J- billions) — cer
tainly not over one tenth — can be set 'down as less than half
a billion in 1896 and less than a billion in 1909.
The fourth term (C0 + N0 —Ob) is O’s money receipts
which are pocketed instead of being deposited. Now O’s
money receipts, C0-\-N0y are small in the first place, for 0,
being depositors, usually receive their dividends, interest,
and salaries by check. The chief exception is found in the
rents and the professional fees paid by workingmen to land
lords, physicians, etc., payments which constitute most of N0•
But these rents and fees paid by workingmen to private indi
viduals are only a part of total rents and fees of workingmen,
and the total rents and fees themselves are known by statistics
of workingmen’s budgets to be only about 20 per cent of

APPENDIX TO CHAPTER XII

471

wages. From this and other clews, we may safely set half a
billion as an upper limit for the fourth term in 1896. Pro
fessor Kinley places .8 billion as the upper limit in 1909.
The fifth term (c + o + n) is the circulation within each
°f the three groups. Obviously only in trifling cases does
money circulate between one “ Commercial depositor” and
another, between two “ Other depositors,” or between two
‘Nondepositors.” Half a billion is put as an extreme upper
limit for the total for 1896 and .8 by Professor Kinley for 1909.
This would mean that about one dollar out of every thirty-five
expended is passed on to other persons who are within the class
to which the expender belongs. In fact, the universal testi
mony of such few representatives of c, o, and n as I have been
able to interrogate personally is that the true ratio is less than
this.
The remaining three terms are even more insignificant. In
the normal state of equilibrium for the “ CN group” it is evi
dent that the sixth and seventh terms would both be sub
stantially zero. The eighth term, withdrawals from banks
by people who have no bank accounts, represents very excep
tional conditions, such as where workmen cash checks at
banks. Workmen seldom have checks to cash and, when
they have, usually cash them in stores or saloons.
We shall summarize the estimates for each of the eight
terms in the following table. Each term is placed midway
between upper and lower limits estimated as safe, and the
Possible variation in either direction is indicated after a “ ± ” .
Thus, §300,000,000 ± §300,000,000 means simply that, though
$300,000,000 is assigned as the estimate, the true value
may be more or less by an amount not exceeding $300,000,000, in other words, that the truth lies between $600,000,000 and zero. Instead of half billions we have used in the
table $600,000,000 as being more easily divisible by two.
The results for both years are given in the following table, in
which generous estimates are given for the “ probable error”
each case. * In fact most of these “ probable” errors are
improbably large.

472

THE PURCHASING POWER OF MONEY

[A p p e n d .

1896

1. M oney deposited (C& + Ob
+ N ) ..................................
2. Expenditure of “ Nonde
positors” (N c + N 0) . .
3. C’s expenditure, till paid .
(Co + Cn - B c) . . . .
4. O’s
receipts,
pocketed
(Co + N 0 - Ob) . . . .
5. Intraclass circulation ( c +
o 4* n ) ..................................
6. N et undiagramed outflow
from CN (a 4- g 4* e)
7. Net increase of money of
CN (i)
..........................
8. M oney
withdrawn from

banks by “ Nondepositors” ( - B n)
. . . .

X II

1909

9.6 ± 1.5

20.7

1.5

5.7 ±

0.3

0.5 ±

0.3

0.4 ±

0.3

0.4 ±

0.0

0.0 ±

0.0

0.0 ±

-0 .0 0 1 ± .0 0 1
16.2 db 2

13.1 ± 1.0

-0 .0 0 1 ±.0 0 1
35.1 ± 2

The first two terms (F') constitute the great bulk of the
total. The remaining six terms (r) make up less than a billion
more for either year. The total reaches about 16 billions as
the estimated circulation of money in the United States in
1896. This estimate is subject to error, but not as much as
the total of the possible errors of individual terms, which is
over 3 billions. Even if each of the possible errors indicated
were as likely as not to occur, the chance that in all eight
cases they should all simultaneously occur in the same direc
tion is (£)8, or one chance in 256. We may, therefore, “ trust
to luck” that the errors will, to some extent, offset each other.
In fact, the chance of the error reaching the sum of those of
the first three terms, or 3 billions, is less than a half. The
“ probable error” can therefore be placed with some confi
dence as less than 2 billions.
Dividing the figures we have obtained for the total circula
tion of money by the figures for the amount of money in cir
culation, we obtain figures for the velocity of circulation.
These are 18.6 in 1896 and 21.5 in 1909, which show remark
ably little change.
Reverting now to the remark with which we began the dis

Sec. 7]'

APPENDIX TO CHAPTER XII

47 3

cussion of money velocity, namely, that it circulates but sel
dom outside of banks, let us picture our statistical results in
the light of this fact.
Evidently, if all money circulated once only, then the bank
record for 1896, showing about 9} billions annually flowing
into and out of the banks, would also exactly indicate the
volume of the intervening work done. This would then be
92- billions. But the true figure is, as we have shown, prob
ably about 16 billions, and consequently we infer that some
of the 9} billions emanating from banks changes hands more
than once before it returns.
Next let us suppose that all of the 9} billions circulate once,
except the part passing through the hands of “ Nondeposi
tors” (6 billions), and that the latter circulates twice. Then
3j billions circulate once only. Under this assumption we
can account for 3} + 2 X 6 = 15} billions of exchange work.
But we have found in fact 16 billions. The difference of about
half a billion is chiefly due to the existence of some money
which circulates more than twice outside of banks.
The entire 16 billions may be roughly accounted for by
dividing the 9} billions flowing from banks into three streams;
billions circulating once and once only; 5} billions, twice
and twice only; and } billion, three times. This makes 3}
+ 2 X 5 } + 3 X i = 16 billions. Of the three parts, the
first (3-i billions) is mainly the spending money drawn by
Other depositors,” the second (5J billions) is money with
drawn from bank for wages and other payments to “ Non
depositors,” and the third (} billion) is the small amount not
otherwise accounted for. This is only a rough scheme of diviS1°n. A very small part circulates oftener than three times.1
1 It may avoid some confusion to remind tlie reader that we are
dealing with sums of money expended for goods, not with individual
c°ms. Many coins remain “ in circulation” a long time without
^turning to bank, because used “ in change.” But money used in
change enters as a subtractive term in monetary expenditures.
When $ io are given for an $8 purchase, and $2 are received back
111 change, $12 have changed hands, but only $8 of monetary cir
culation against goods havo boon effocted.

474

THE PURCHASING POWER OF MONEY

[A p p e n d .

XI}

Similarly, for 1909, of the 21 billions flowing into and out
of the banks, the 13 billions passing through the hands of
“ Nondepositors” must have circulated twice or more and
thus have accounted for 26 billions or more of the total circu
lation (35 billions), leaving 21 — 13, or 8, to have circulated only
once. This would account for 26 + 8 or 34 billions. The
entire 35 billions may be accounted for by supposing the 21
billions flowing from banks to be divided into the following
three streams: —
8 billions circulating once, making 8 billions,
12 billions circulating twice, making 24 billions,
1 billion circulating three times, making 3 billions.
The whole 21 billions, bank outflow, perform 35 billions of
circulation before returning to bank.
The first two terms of the formula for the monetary circu
lation evidently give 151- billions out of our estimated total
of 16 billions for 1896, and 34 out of 35 for 1909; showing
that the remainder, unless it has been greatly underestimated,
is relatively small. The significance of this fact is that the
terms most difficult to estimate statistically are least impor
tant. Of the two terms constituting the “ first approxima
tion,” the first and most important is susceptible of the m o s t
accurate determination of all, while the second is made up
chiefly of wages, which also are susceptible of statistical
determination, or seem destined to become so.
In fact, if we should, as a statistical makeshift for the first
approximation, merely add the amount of money annuallywith
drawn from bank to the annual money wages, we should, as to
the year 1896, account for 9|- + 44- or 14 out of 16 billions, leav
ing only 2 billions to be otherwise accounted for. In other
words, this makeshift — the part most adapted to statistical
measurement — accounts for about 88 per cent of the total
circulation, leaving only 12 per cent for the part which can
only be determined within wide limits. For 1909, deposits
plus wages make up about 32 billions out of 35, or over 90

S e c . 7]

APPENDIX TO CHAPTER XII

475

per cent. A still simpler makeshift is to add the deposits
to the total wages without attempting to ascertain the part
which is paid in money. This makeshift might be justified
on the ground that total wages are more exactly ascertain
able than the part paid in money, and that presumably the
money part will maintain a fairly constant ratio to the
total wages from year to year. The two parts here indi
cated may be distinguished as the measurable part (com
prising the first term of our formula (1)' and most of the
second term), and the conjectural part, comprising the re
mainder of the second term and the other six terms. Even
^ the allowance for the conjectural part should prove to
be but half the truth, the measurable part would still con
stitute the great bulk of the total. The measurable part
Would therefore still be a safe practical index, or barometer
of changes in the volume of circulation. Any excess of varia
tion in the conjectural part, as compared with the measurable
Part, would, when spread over the whole, produce a disturb
ance only one fourth as great. It is reasonable to suppose
that the conjectural and measurable parts will ordinarily vary
together. If the measurable part varies 10 per cent, it is natu
ral to suppose that the conjectural part, and therefore also the
total of both, will vary likewise. But suppose this assump
tion erroneous and that, while the measurable part varies 10
Per cent, the conjectural part really varies 14 per cent or 6 per
cent. The difference between these and 10 per cent, i.e. 4
Per cent, representing a supposed excess or deficiency of vari
ation of the conjectural part, would produce a difference of
only 1 per cent in the total! That is, the total, instead of
varying 10 per cent, would vary 11 per cent or 9 per cent.
Evidently, therefore, any unknown variation in the conjec
tural part can cause only a trifling variation in the result.
In other words, the measurable part will always be a good
mdex of the total — a reliable barometer of circulation. If
We divide this by the quantity of money in circulation, we
obtain a figure indicating the relative velocity of circulation
of money from year to year. We conclude, therefore, that

476

THE PURCHASING POWER OF MONEY

[A p p e n d .

XIl

money deposits plus wages, divided by money in circulation,
will always afford a good barometer of the velocity of
circulation.
It is not always the absolute value of any magnitude we
find most useful, but its relative value under different con
ditions. We may compare the relative length of two ships by
measuring their water lines, although this method omits the
overhang at either end. Such a comparison will apply roughly
to any two vessels, and with great exactness to two ships of
the same build. Similarly, our proposed barometer will af
ford rough comparisons for any two countries using banking
facilities in comparable degrees, and will afford fairly exact
comparisons for two successive years in the same country.
The proper statistical procedure would, therefore, seem to be
to provide for the conjectural part by an estimated percent
age correction, to be applied to the measurable part as a con
stant factor. Different correction factors will presumably
apply in different countries, as, let us say, 10 per cent in the
United States, 20 per cent in England, 30 per cent in France,
etc. The chief value of such conjectural corrections would be
to enable us to compare roughly the circulations and velocities
of different countries. For comparisons in the same country
at different times it would be almost immaterial what per
centage correction were adopted or whether none at all were
employed.
By means of the method which has been explained, it is be
lieved that some interesting and valuable results can in the
future be obtained, if statisticians in various lands will obtain
(1) the total money deposited each year in banks (except by
other banks), or, what is normally the same thing, the total
money withdrawn from banks (except by other banks); (2)
the total wages expended, or, what is practically the same
thing, the total wages received; (3) if desired, a conjectural
percentage addition to allow for the remaining and less known
part of our formula; (4) the total money in circulation. The
sum each year of (1) and (2) corrected by (3) and divided by
(4) will be a very accurate barometer of the velocity rela

Sec. 8]

APPENDIX TO CHAPTER XII

477

tively considered, as well as a fair approximation to its abso
lute value. The omission of (3) will not invalidate the re
sults for purposes of relative comparison.
The importance of such accurate determinations can
scarcely be overestimated, as the remarks on the subject by
Jevons, Landry, and others have shown. When we know sta
tistically the velocity of circulation of money, we are in a
position to study inductively the “ quantity theory” of money,
and to discover the significance of that velocity in reference
to crises, accumulation of wealth, density of population,
rapid transit, and communication, as well as many other con
ditions. In fact a new realm in monetary statistics is laid
open.
§ 8 ( t o C h a p t e r XII, § 4 )
Interpolating Yaluos of V for 1897-1908

To interpolate values for V we split the difference between
two extreme hypotheses: the one of extreme steadiness; the
other of extreme variability.
The first of these hypotheses is that V changes in a steady
progression from its value of 18.G in 1896 to its value of 21.5
1909. This would imply a perfectly steady growth with
time, with no temporary fluctuations. But it seems unlikely
that the velocity of circulation of money should not fluctuate
somewhat from year to year. We have seen that, theoreti
cally, there is a tendency under normal conditions for money
expenditures (MV) to keep pace with check expenditures
(M'V'). If this correspondence were perfect, we should have
the ratio of MV to M'V', if not constant, at least changing in
a perfectly even manner with time. Now this ratio for
1896 is 16.7 per cent and in 1909, 9.6 per cent. If we were to
assume a perfectly steady change in this ratio during the in
tervening 13 years, the resulting value for V would have to
vary considerably. This assumption is our second hypothesis
of extreme variability. The following table shows the re
sults of the- two extreme hypotheses. It will be seen that
general there is no great difference between them.

478

THE PURCHASING POWER OF MONEY

(2)

(i)

H y p o t h e s is o f
E x t r e m e St e a d i

Y ear

XII

(3 )

H y p o th e s is o f
E x tr e m e V a r ia
b ility

ness

1896 .....................
1897 .....................
1898 .....................
1899 .....................
1900 .....................
1 9 0 1 .....................
1902 .....................
1903 .....................
1904 .....................
1905 .....................
1906 .....................
1907 .....................
1908 .....................
1909 .....................

[A p p e n d .

18.6
18.8
19.0
19.3
19.5
19.7
19.9
20.2
20.4
20.6
20.8
21.1
21.3
21.5

e a n of tw o

V a r y in g a s
needed to pre
s e r v e e v e n ly
c h a n g in g R a t io
o f M V t o M'V'

P r e c e d in g

18.6
19.4
20.6
24.4
20.4
23.9
23.6
20.9
20.9
23.0
22.5
21.0
18.6
21.4

18.6
19.1
19.8
21.9
20.0
21.8
21.8
20.6
20.7
21.8
21.7
21.1
20.0
21.5

A supplementary calculation reveals the interesting fact
that the “ hypothesis of extreme variability” would make
money velocity fluctuate approximately with deposit velocity.
Splitting the difference between the two extreme hypotheses,
— that of extreme steadiness and that of extreme variability,
— we have what would seem to be an approximately correct
estimate of actual velocity. It is probably correct in most
cases for the first two digits. We cannot assume even for
1896 and 1909 that the third digit, that beyond the decimal,
is correct, much less can we assume this to be true for the inter
vening years. But it is sometimes advisable to carry out the
calculations to one digit beyond “ the last significant figure.”
§9

(t o

C hapter

XII, § 5)

Method of Calculating T

The table in the text is taken from the final column of the
following more complete table:—

ir e c t

In tern a l
C om m erce

Y ear

and

(3)
E x p o rts
and
Im p orts

C alendar Y

(4)
S a le s o f
S to ck s

u m b e b s

o f

o l u m e

o f

b a d e

I n d ir e c t I n d ic e s a n d F is c a l
Y ears

ears

(5)
W e ig h te d A v e ra g e
o f T lir e e P r e c e d in g
2 0 x (2 ) + 3 x (3 ) 4-1 x (4 }
24

(6)
R. R.
to n s
C a r r ie d

(7)

(8)

P. 0.

W e ig h te d
average
o f tw o
p r e c e d in g
2 x (6 )+ lx (7 )

L e tters
C a r r ie d

89
103
111
111
111
125
119
139
125
149
152
167
148
153

76
87
96
100
101
107
102
101
101
109
114
117
110
125

55
77
113
176
138
266
189
161
187
263
284
196
197
215

86
100
109
112
111
129
120
135
125
149
153
162
145
152

77
79
91
98
107
108
119
130
127
144
161
172
152
—

63
68
72
78
85
92
101
105
111
128
137
142
152

72
74
83
89
97
100
110
120
120
133
150
160
149
160

(11)

73
78
86
93
99
105
115
120
126
141
155
154
154

—

81
93
101
106
107
121
118
130
126
147
154
160
148
155

209
239
260
273
275
311
304
335
324
378
396
412
381
399

XII

.
.
.
.
.
.
.
.
.
.
.
.
.
.

(10)

R e la tiv e
A b s o lu te
T ra de
(8 ) R e
T ra d e (T )
W e ig h te d
du ced to
399
average
C a le n d a r
2 x (5 )+ lx (9 )
X 155
Y ears
3

CHAPTER

.
.
.
.
.
.
.
.
.
.
.
.
.
.

(9)

ears

1896
1897
1S98
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909

C alendar Y

APPENDIX

(2)

(1)

I n d ic e s

n d e x

Sec. 9]

480

THE PURCHASING POWER OF MONEY

[A p p e n d .

XII

This table is constructed as follows: —
Column (2) is constructed for 1900-1909 from monthly
figures on Internal Commerce published in the Monthly
Summary of Commerce and Finance of the United States.
By taking the monthly figures it was possible to obtain re
sults for calendar years. This column is an average of sepa
rate indices for the following articles for which records were
available. The original figures give the quantities of each
article brought into the principal cities of the United States.
These quantities were each multiplied by an assumed price
which remained as a constant multiplier for every year. The
products were then added together and the figures thus ob• tained taken to represent the total trade in these commodi
ties, and to be a barometer of the relative internal commerce
in the United States.
The articles referred to, and the dates for which data
were used (as well as the price factors employed as explained
below) are as follows: —
A

r t ic l e s

C o tto n ....................
R i c e .....................
F r u i t .....................
Lumber (Shipments
from South and
Southwest)
Boots and Shoes .
Anthracite Coal .
Bituminous Coal .
Pig iron, coke, and
anthracite
. .
Petroleum
(Ship
ments by water
from Texas) . .
Cattle (Receipts at
five cities)
. .
Cattle (Receipts at
seven cities) . .
Hogs (Receipts at
five cities)
. .

P r ic e

$45.00 bale
5.00 sack
1000.00 car
.02
80.00
4.74
2.74

ft.
case
ton
ton

19.40 gross ton
1.80 bbl.

ates

Jan., 1900-1909
Aug., 1900-1909
Feb., 1900-1909
Feb.,
Mar.,
Jan.,
Jan.,

1900-1909
1900-1909
1900-1909
1900-1909

July, 1902-1909
Nov., 1901-1909

55.00 head

Jan., 1900-Dec., 1903

55.00 head

Jan., 1900-1909

18.00 head

Jan., 1900-Dec., 1903

4 81

APPENDIX TO CHAPTER XII

Sec. 9]

A r t ic l e s

Hogs (Receipts at
seven cities) . .
Sheep (Receipts at
five cities)
. •
Sheep (Receipts at
seven cities) . .
Wheat (Receipts at
eleven cities)
Wheat (Receipts at
twelve cities)
Wheat (Receipts at
fourteen cities) .
Wheat (Receipts at
fourteen cities) .
Wheat (Roceipts at
fifteen cities)
Corn (Receipts at
twelve cities)
Corn (Receipts at
fourteen cities) .
Corn (Receipts at
thirteen cities) .
Corn (Roceipts at
fifteen cities)
Oats (Receipts at
twelve cities)
Oats (Roceipts at
fourteen cities) .
Oats (Receipts at
fifteen cities)
Barley (Receipts at
nine cities) . •
Barley (Receipts at
ten cities)
* •
Barley (Roceipts at
eleven cities)
Barley (Receipts at
^ twelve cities)
Barley (R eceipts atthirteen cities) .
Barley (R eceipts at
^ fourteen cities) .
% e (R eceipts at
olevon cities)
«y © (R oceipts at
twelve cities)
ttyo (R eceipts at
^ thirteen cities) .
ttye (R eceipts a t
fourteen cities) .

P r ic e

$18.00 head

D ATE8

Jan., 1900-1909

4.00 head

Jan., 1900-Dec., 1903

4.00 bead

Jan., 1900-1909

1.00 bu.

June, 1903

1.00 bu.

Apr., 1903-Dec., 1903

1.00 bu.

M ay, 1904-1909

1.00 bu.

M ay, 1904-1909

1.00 bu.

Apr., 1903-1909

.75 bu.

Apr., 1903-Dec., 1903

.75 bu.

Jan., 1904-1909

.75 bu.

Feb., 1906-Fob., 1907

.75 bu.

Apr., 1903-1909

.53 bu.

Apr., 1903-Dec., 1903

.53 bu.

Feb., 1906-Fob., 1907

.53 bu.

Apr., 1903-1909

.70 bu.

Juno, 1903-Aug., 1908

.70 bu.

Apr., 1903-M ay, 1908

.70 bu.

Sept.,1903~Juno, 1908

.70 bu.

Fob., 1906-Sopt., 1908

.70 bu.

Fob., 1904-1909

.70 bu.

Apr., 1903-1909

.80 bu.

A pr., 1903-Juno, 1906

.80 bu.

Jan., 1905-Aug., 1908

.80 bu.

A pr., 1904-1909

.80 bu.

Apr., 1903-1909

482

THE PURCHASING POWER OF MONEY

r t ic l e s

Flaxseed (Receipts
at four cities)
Flaxseed (Receipts
at five cities)
Flaxseed (Receipts
at six cities). .
Flour (Receipts at
ten cities) . . .
Flour (Receipts at
eleven cities)
Flour (Receipts at
twelve cities)
Flour (Receipts at
thirteen cities) .
Petroleum
(Ship
ments by Pipe
lines— Reg. De
liveries.
App.
Field . . . .

P r ic e

[A p p en d .

XII

ates

S1.50 bu.

Feb., 1905-1909

1.50 bu.

Jan., 1904-1909

1.50 bu.

Jan., 1904-1909

4.80 bbl.

Apr., 1903-1909

4.80 bbl.

Jan., 1904—1909

4.80 bbl.

Mar., 1904-1909

4.80 bbl.

Apr., 1903-1909

1.80 bbl.

Jan., 1901-1909

These articles are representative for the trade of the
country and may well serve as a barometer of that trade.
Yet the amount of trade, actually consisting of the sales of
these articles in the few cities concerned, constitutes of
course only a very small part (probably less than one tenth
of 1 per cent) of the total trade of the country.
The actual figures first obtained were all divided by two
before being entered in column (2) in order to bring them
down to a scale more comparable with the figures of column
(3). Since not all of the commodities were quoted in all
the years, the table had to be “ pieced out” for the defective
years by the principles of proportion as already exemplified.
As the statistics of the Monthly Summary go back only to
1900, the table had to be “ pieced” back to 1896. This was
done by using data from the statistical abstract of the United
States and the abstract of the United States Census for 1900.
The only figures obtainable for important articles in internal
trade were those for grain, received during calendar years at
fifteen principal primary markets, and for the estimated
national consumption during fiscal years of the following

Sec. 9]

APPENDIX TO CHAPTER XII

483

articles, chiefly, or largely, of domestic production: cotton,
wool, bituminous coal, pig iron, iron and steel railroad bars,
and “ distilled spirits, wines, and malt liquors.”
The fiscal year figures were taken from 1896 to 1901 inclu
sive and reduced to calendar years on the assumption, for
instance, that the true figure for the calendar year 1896 is the
average of those for the two fiscal years ending June 30,1896,
and June 30, 1897. In this way we get hypothetical calen
dar year figures for 1896 to 1900. These figures and those for
grains, which were already for calendar years, were then
reduced by a factor so that each was made to be 111 for 1900,
the number for that year found by the calculations involv
ing the articles in the series, 1900-1909. The figures thus
found were then averaged with weights selected to correspond
with the estimates of their respective importance as judged
from the estimates of their national consumption values and
from the fact that some of them are indicators of large re
lated businesses. The weights chosen were: for grains
(including wheat, wheat flour, corn, rye, oats, barley, malt,
and pease *), 20 ; for bituminous coal, iron and steel, liquors,
and cotton, 5 each ; and for pig iron and wool, 1 each.
The data for 1896-1899 are far inferior to those for 19001909 taken from the Monthly Summary, and this for three
reasons : (1) because they are so few in number; (2) be
cause all except the grains are for fiscal years and the hypo
thetical correction to calendar years is subject to error;
and (3) because all except the grains are very rough estimates
°f consumption, not based on shipments or receipts, but based
°n estimated, production, corrected for exports and imports,
Which three elements are all subject to error.
We should not be surprised, therefore, to find larger errors
in the resulting figures for 1896-1899 than for 1900-1909.
In fact, we shall see that such is probably the case.
For carrying out the laborious operations involved in
ascertaining the index numbers from 1900 to 1908, I am in1 Seo Statistical Abstract of United States, 1908, p. 523.

484

THE PURCHASING POWER OF MONEY

[A p p en d .

X II

debted to one of my undergraduate students, Mr. Robert N.
Griswold, and for bringing them down to 1909, to one of my
graduate students, Mr. W. Y. Smiley.
Column (3) is also based on laborious calculations which
were performed by Mr. Griswold. The materials were also
taken from the Monthly Summary of Finance and Commerce
and covered 23 staple articles of import and 25 for export.
The quantities of each were multiplied by a uniform price, and
the sum of the resulting figures for imports and exports was
taken. The articles of imports (with the price multipliers
used) were: —
I m p o r t s o p t h e U n it e d S t a t e s

1896-1909

(Bulletin of Bureau of Commerce and Statistics)

Cocoa .
.13 lb.
.16 lb.
Tea . .
Coffee .
.07 lb.
Sugar
.02 lb.
Lemons
.04 lb.
Bananas
1.60 bunch
.17 lb.
Cheese .
Distilled spirits
(imported) .
5.00 gal.
Sparkling wines
(Champagne) 29.00 doz. qts,
Leaf tobacco
1.00 lb.
Cotton . . .
(mfg. cloth)
.09 sq. yd.
Linens (mfg. flax,
hemp, or ramie) .50 sq. yd.
Woolen dress
goods
. .
.21 sq. yd.

Raw silk . . .
.04 lb.
Hides and skins
(other than fur
s k i n s ) ..................... 11 lb.
. . .
.13 lb.
Raw wool
India rubber. . . .78 lb.
Boards and sawed
lumber . . . 18.00 M .
Coal (anthracite &
bituminous)
2.60 per
T i n .....................
.28 lb.
Copper (pigs, bar,
ingots, old, un
manufactured)
.17 lb.
Pig iron . . . 23.00 per
Sodium nitrate
38.00 per

ft.
t.

t.
t.

The articles of exports were: —
E x p o r t s o p t h e U n it e d S t a t e s

1896-1909

(Bulletin of Bureau of Commerce and Statistics)

Cattle . . . 55.00 head
Hams . . .
.11 lb.
Salt pork . .
.09 lb.
Fresh beef
.10 lb.
Canned beef .
.11 lb.
Bacon . . .
.11 lb.
Lard
. . .
.11 lb.
Butter . . .
.21 lb.
Sole leather
.21 lb.
Boots and shoes 2.75 pr.
Raw cotton
.48 bale
Cotton cloth .
.09 yd.
Corn
. . .
.60 bu.

Wheat . . . .
1.00 bu.
Flour . . . .
4.80 bu.
Tobacco leaf
.10 lb.
Sawed lumber . 23.00 M . ft.
W ood pulp . .
.015 lb.
Linseed oil (cake)
.014 lb.
Refined illuminating
oil
. . . .
.07 gal.
Cottonseed oil .
.40 gal.
Coal
. . . .
3.70 ton
Copper . . . .
. 17 lb.
Steel rails
. . 31.60 ton
Sheet steel
. .
.0135 ton

APPENDIX TO CHAPTER XII

485

The statistics of exports and imports are probably fifty
times as full as those of internal commerce and therefore
(on the principle that probable errors vary inversely as the
square root of the fullness of returns) some seven times as accu
rate. But, on the other hand, exports and imports represent
less than 1 per cent as much trade as the internal commerce
of the United States, and, by the principles already explained
mprevious chapters, should count in the equation of exchange
only at half its value, one of the parties in the exchange being
a foreigner. In spite, however, of the diminutive character
of external commerce, it is to some extent an index of internal
commerce; since a vast amount of internal business is a pre
liminary to exports and a sequel to imports, while perhaps a
still larger amount is in other ways indirectly related to such
commerce. By balancing these and other considerations, the
relative weights to be assigned to the external and internal
trade were selected as given in column (5).
Column (4) gives the sales of stocks according to the
ordinary figures as given, for instance, in the Financial Review.
These figures are, of course, not for values, but for amounts.

Column (6) gives the figures for tons of freight carried by
railroads according to Poor’s Railroad Manual for fiscal years.
Column (7) gives the figures for pieces of first-class mail
matter carried in fiscal years. These figures were kindly
supplied by the Post Office Department. They are lacking
for 1896.
We have still to describe the method employed for combin
ing columns (2), (3), (4), (6), (7).
The first three are regarded as constituting a group by
themselves, representing direct indices of trade: and the last
two are regarded as constituting another group of indirect
indices.
The direct indices are combined by weighting the internal
commerce, twenty, the exports and imports, three, and sales
of stocks, one. These weights are, of course, merely matters
of opinion, but, as is well known, wide differences in systems of
Weighting make only slight differences in the final averages.

486

THE PURCHASING POWER OF MONEY

[A p p e n d .

XIl

In this way, column (5) is found.
As to the relative weights to be given to the railroad and
post office statistics, the former were weighted as two and the
latter as one. Railway tonnage represents almost every con
ceivable commodity in commerce and comes far closer to
actual trade than post office letters.
After railroad and post office indexes are thus combined,
the transition from fiscal to calendar years is made on the
assumption that the figures for a calendar year are the mean
of the figures for the fiscal years ending June 30 of that year
and June 30 of the next year.
In this way column (9) is obtained.
• From columns (5) and (9) column (10) is obtained by
weighting (5) two, and (9) one.
Finally, column (11) is found by magnifying the figure of
column (10) in the ratio fJHr in order to make the figure for
the base year, 1909, equal to 399 billions of dollars, — the total
value of the left side of the equation (MV + M'V').
The probable errors in the values of T which have been
calculated are believed to be some 5 to 10 per cent for the
years 1900-1909 and 10 to 15 per cent for the years 1896-1900.
§ 10 ( to C h a p t e r

XII, §

M ethod of Calculating P

The table in the text for index numbers of prices is taken
from the last column of the table on page 487.
Column (2) gives the index numbers of the United States
Labor Bureau (No. 81, March, 1909, p. 204).
I am under obligations to the Commissioner of Labor, Mr.
Neill, for his courtesy in supplying me with the figure for 1909
in advance of publication.
Column (3) is taken from the Bulletin of the Bureau oj
Labor, July, 1908, p. 7.
Column (4) is from “ The Prices of American Stocks, 18901909,” by Wesley C. Mitchell, Journal of Political EconomVi

Sec. 10]

487

APPENDIX TO CHAPTER XII

May, 1910. These figures are doubtless the best yet avail
able in this difficult subject.
I n d e x N u m b e r s o p P r ic e s

(1)

(2 )
W

Y ear

1896.
1897.
1898.
1899.
1900.
1901 .
1902.
1903.
1904.
1905.
1906.
1907.
1908.
1909.

h o lesale,

258
C o m m o d it ie s

.
.
.
.
.
.
.
.
.
.
.
.
.
.

90
90
93
102
111
109
113
114
113
116
123
130
123
127

(3 )
W
per

ages

H our

100
100
100
102
105
108
112
116
117
119
124
129
—
—

(4 )

(5 )
W e ig h t e d
A verage

(6)

C o l u m n (5 )
F orty
reduced to
St o c k s 3 0 x ( 2 ) + l x ( 3 ) + 3 x ( 4 ) B a s is o f 100
1 90 9
34

77
84
94
128
134
211
250
201
192
250
267
204
201
277

89
90
93
104
113
118
125
122
120
128
136
137
130
141

63.3
63.7
66.2
73.8
80.2
83.7
88.7
86.5
85.1
90.8
96.5
97.2
92.2
100.0

The general index number in column (5) is a weighted aver
age of the figures in the three preceding columns, the weights
being essentially the same as those used by Professor Kemmerer and for the same reasons.1 For ease in computation the
weights are taken in integers, viz. 30 for column (2), 1 for
column (3) and 3 for column (4). This calculation brings the
table down through 1907. As column (3) is defective for
1908-1909, these years and 1907 are worked out as averages
of columns (2) and (4), the weights being the same as already
mentioned. The result is two series of figures, one for all three
columns ending in 1907, and the other for two columns begin
ning in 1907. As in this case it happens that both series have
the same figure (137) for 1907, no corrections need be made in
1908 and 1909. The probable errors in the figures for P may
be placed as about 5 to 10 per cent.
1 See Money and Credit Instruments, New York (H olt), 1909,
P. 139.

488

THE PURCHASING POWER OP MONEY

§ 11

(to C h a p t e r

[A p p e n d .

X II

XII, § 7)

Mutual Adjustments of Calculated Values of M , M ', V , V P , T

There are various methods of calculating the best adjust
ments, involving the theory of least squares. But the prob
lem may be greatly simplified by dividing the process into a
few separate steps. First, we ascertain the best adjustments of
the calculated values of each side of the equation of exchange
considered as a whole. We shall need to exercise judgment in
deciding the relative errancy of the two sides, but the total
adjustments are so small that differences in judgment could
not make much difference in the results.
’ After a careful weighing of all the evidence, it is believed
that the errors in the right side (PT) are liable to be about
double those in the left (MV + M'Vf). Accordingly, the
discrepancy between the two sides is corrected by changing
PT twice as much as MV + M'V'; that is, by applying to
PT a correction equal to two thirds of the total discrepancy,
and by applying the remaining one third to MV + M'V',
the two corrections being, of course, opposite and such as to
bring the two sides into agreement. Thus, for 1899, the total
discrepancy is 5 per cent, of which we assign about a third,
say 2 per cent, to MV + MfVf, and the remaining 3 per
cent to PT. That is, we propose to increase the calculated
figures for MV + M'Vf by 2 per cent and decrease those of PT
by 3 per cent. The result will bring them nearly into agree
ment at 185 billions. Sometimes the results will not exactly
agree, as this method of adding and subtracting percentage
corrections is only approximately correct; but any remaining
slight discrepancies are readily adjusted by slight empirical
changes in the factors. The result is shown in the Figure 20,
which gives MV + M'V' and PT (reduced by dividing by
1.11) as originally calculated, and a mean (dotted) curve
which is the revised estimate of both MV + M'V' and PTThe corrections which are thus made in MV + M'Vf and
PT, by which they are brought into mutual agreement, are

S e c . 11]

A P P E N D IX

CHAPTER

X II

489

small; but the corrections necessary in the individual factors,
M, V, M', V', P, T, are smaller still. We assume, for simplic
ity, that the percentage corrections to be made in M and M '
are equal to each other and also that the corrections to be
made in V and V' are equal to each other. This is a reason
able assumption; but even if some other assumption were
made, the final results would be scarcely changed.

Fia. 20.

A correction of 1 per cent simultaneously in M and Mf
will produce a correction of 1 per cent in MV + M'V'.
Likewise a correction of 1 per cent simultaneously in V and
V' will produce a correction of 1 per cent in MV + M'V'.
We may then regard the correction of MV + M'V' as
practically consisting of two parts: one, the correction of M
and M'\ and the other, the correction of V and V'. As the
AT8are more accurately ascertained than the V’s, theiu correc
tion should be smaller. Thus, for 1 8 9 7 , the total correction
assigned to MV + M'V' is 3 per cent, of which we assign
1 per cent to M and M'f and the remaining 2 per cent to V

490

THE

P U R C H A S IN G

POW ER

MONEY

[A p p e n d .

XII

and F'. That is, we increase the calculated values of M and
Mr by 1 per cent and those of F and F' by 2 per cent,
thus effecting (approximately) the desired increase of 3 per
cent in MV + M'V'. In like manner the total correction
assigned to PT is distributed over P and T, assigning the
major part to T. By thus distributing the corrections over
(1) M and
(2) F and F', (3) P, and (4) T, we find that
only very slight individual corrections are needed, the maxi
mum being only 5 per cent and the vast majority (50 out of
56 cases) not exceeding 2 per cent. In fact, a decided major
ity (35 out of 56 cases) are within 1 per cent. It is really
astonishing to think that a correction of only 2 per cent or
less is usually required in our calculated values of M, il/', V,
F', P, T, in order to make them conform perfectly to the
equation of exchange. In fact, 2 per cent is less than what
might naturally be considered the probable error in most of
the figures as calculated. This fact justifies confidence in the
general correctness of our results.
Having thus corrected, by mutual adjustment, all the
factors in the equation of exchange, we are left with a figure
for P which is not 100 per cent for any one year. As vre
prefer to call 1909 the unit year, the figures for P are
adjusted on that basis and the figures for T accordingly*
This change disturbs the system of corrections as measured
relatively to the original figures. It reduces to zero the cor
rection of P for 1909. In general, it makes smaller the cor
rections for P and T for years near 1909 and makes corre
spondingly larger those for years remote from 1909. But,
even so, the corrections never exceed 10 per cent for T nor 6
per cent for P. As the entire scheme of corrections thus out
lined is a matter of judgment and each figure was frankly “ doc
tored” on its own individual merits in view of all the circum
stances in the case, it seems inadvisable to burden these pages
by any fuller statement of the voluminous details of the pro
cess. The results as shown in Figures 13, 14, 15, and 16,
already given in the text, speak for themselves.

S e c . 12]

A P P E N D IX

§ 12 (to

CHAPTER

C h a p te r

491

X II

XII, § 17)

Credit and Cash Transactions. Comparison with Kinley’s Estimates

These figures agree surprisingly well with what might be
expected from a rougher calculation from Kinley’s investiga
tions. For July 1, 1896, he found that money deposits con
stituted 7.4 per cent of all deposits and, on March 16,1909, 5.9
per cent. Both of these figures are too low to represent the
percentage of money transactions, for the reason that money
often circulates more than once before being deposited,
whereas checks in general circulate but once. The figure for
1896, especially, is too low, because of the excessive amounts
of checks deposited on July 1. In .fact, it was largely be
cause the 1896 figures had been criticized in this respect that
Kinley made the 1909 investigation. He did not, of course,
take the figures of deposits as indicating exactly the ratios of
check and money transactions. He recognized the fact that
these would give too low a ratio for money and too high a ratio
for checks. He expressed the belief that a safe minimum for
check transactions in 1896 was 75 per cent1 and in 1909, 88
per cent, implying that 25 per cent and 12 per cent were safe
maxima for monetary circulation. Professor Kinley’s pur
pose seems to be to establish safe maxima rather than to at
tempt exact estimates. Tabulating Kinley’s figures, we have
for money transactions expressed in percentage of all trans
actions : —

1896
1909

(i)

(2)

(3)

(4)

(5)

Year

Maximum
(Kinley'a
estimate)

Minimum (as
indicated by
deposits)

Mean of two
preceding

Present
estimate

25
12

7.4
5.9

16J
9

14
9

1His original estimate for a safe minimum was 80 per cent. But
in the Journalof Political Economy, Vol. V, p. 172, and in !1M o n e y /’
p. 44, and pp. 108, 14, ho takes 75 per cent as safer.

492

THE

P U R C H A S IN G

POW ER

M ONEY

[A p p e n d .

XII

According to this table, if we take the percentage of money
in bank deposits as a lower limit of the percentage of money
transactions, and if we take Kinley’s estimates as a safe upper
limit, and if we split the difference between these two limits,
we shall reach almost1the same results as already reached by
the more exact calculations in this book, which results are
given, for comparison, in the last column. Thus the results of
this book strikingly confirm those of Professor Kinley. They
also agree remarkably well with the prevailing impression
among business men that about 90 per cent of trade is now
performed by means of checks.
ADDENDUM FOR SECOND EDITION
The figures in this second edition have been brought down
to date by adding data for 1910,1911, and 1912 to the tables
on pages 304 and 317 and inserting a new diagram between
pages 306 and 307. (For full explanations as to these figures
see page xxiii of this book and “ ‘ The Equation of Exchange/
1896-1910,” American Economic Review, June, 1911; “ ‘ The
Equation of Exchange 9for 1911 and Forecast,” ibid., June,
1912; and “ ‘ The Equation of Exchange ’ for 1912 and Fore
cast,” ibid., June, 1913.)
Professor "Wesley Clair Mitchell has kindly shown me the
sheets of his forthcoming book (University of California
Press) on Business Cycles, in which he has reestimated the
deposits subject to check (Mr) by somewhat different methods
and with the aid of some data not available when the present
book was written.
If I were rewriting this book, I should adopt Professor
Mitchell's more perfect methods and results. But to do so
now would involve a disturbance of a large number of plates
for the sake of a very small net change in final results. I
1 If wo tako Kinley’s original “ safe minimum ” for cheeks of 80
per cent, and consequently the “ safe maximum ” for cash as 20 per
cent, wo shall obtain in the above table 14 per cent, instead of the
figure 16J, which would make the last two columns agree absolutely.

ADDENDUM

FOB

SECOND

493

E D IT IO N

content myself, therefore, by here giving a table of Professor
Mitchell's figures, including columns showing how much mine
are larger or smaller.
P r o f e s so r

M it c h e l l ' s

E s t im a t e s

D e p o s it s

C heck and th e

E x t e n t to w h ic h t h e

exceed

s h o r t o f s a id

fall

189G
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911

it c h e l l 's

2.69
2.75
3.20
3.87
4.21
4.96
5.37
5.54
5.85
6.56
6.86
7.11
6.52
6.81
7.71
8.24

W r it e r ’s

E s t im a t e s .

F.’s
M

S ubject

P r esen t

E x ce s s (o r D e fic ie n c y )

e su lts

Unadjusted

Adjusted

-.0 1
+ .05
-.0 1
+ .03
+ .19
+ .17
+ .06
+ .16
-.0 5
-.0 2
-.0 2
+ .0 2
+ .0S
- .0 6
- .4 7
- .4 6

+ .0 2
+.11
+ .02
+ .01
+ .23
+ .17
+ .03
+ .19
- .0 8
- .0 2
- .0 5
+ .02
+ .05
- .1 3
- .4 8
-.4 6

APPENDIX TO THE SECOND EDITION, ON
“ STANDARDIZING THE DOLLAR”
T h e plan for stabilizing the price level (and therefore the
purchasing power of money) sketched in Chapter XIII
(pages 340-346) in relation to the gold exchange standard has
been more fully and more popularly explained since this
book was written. (See, e.g., Report of International Con
gress Chambers of Commerce, September 26, 1912; Inde''pendent, January 2, 1913; New York Times, December 22,
1912; British Economic Journal, December, 1912. The
most complete statement is that in The Quarterly Journal
of Economics, February, 1913.)
The writer also hopes soon to publish a book devoted to
this particular subject.
The following is an extract from an address in Boston
before the American Economic Association, December, 1912,
printed in the American Economic Review Supplement,
March, 1913: —
Briefly stated, the plan is to introduce the multiple stand
ard, in which the unit is a “ composite ton” or “ composite
package” of many staple commodities, not of course by us
ing such a package in any physical way but by employing
instead its gold bullion equivalent. In essence it would
simply vary the weight of gold in the dollar or rather behind
the dollar. The aim is to compensate for losses in the
purchasing power of each grain of gold by adding the neces
sary number of grains of gold to the dollar.
Both on the basis of theory and of facts, we may accept as
sound the principle that the lighter the gold dollar the less
its purchasing power and the more magnified the scale of
prices; and that the heavier the dollar the greater its pur
chasing power and the more contracted the scale of prices.
Evidently if we can find some way to increase the weight of

494

APPENDIX TO THE SECOND EDITION

495

the dollar just fast enough to compensate for the loss in the
purchasing power of each grain of gold, we shall have a fully
“ compensated dollar,” that is, a dollar which has constantly
restored to it any purchasing power it may lose by gold
depreciation.
We now have a dollar of fixed weight (25.8 grains), but
varying purchasing power. Under the plan proposed, we
should have a dollar of fixed purchasing power, but varying
weight.

But how is it possible to have a dollar of varying weight
without the annoyance of a constant recoinage of gold coin ?
Moreover, if this can be done, how can we know at any time
what weight the dollar ought to have without leaving this
to the tender mercies of some political official? Here are
two very vital questions.
As a preparation for answering these two questions, it
will be a little easier to explain the principle of the proposal
if for a moment wre assume that there are no actual gold
coins in circulation, but only gold certificates. This sup
position is, in fact, not very far from the truth in the United
States; for, outside of California, there is very little actual
gold coin in circulation. We have instead nearly a billion
dollars of gold certificates in circulation, representing gold
in the Treasury of the United States. We are supposing
for the moment that gold circulates in no other way. Under
these circumstances it is evident that the ultimate gold
dollar is out of sight in the Treasury of the United States
m bars of gold bullion. Every 25.8 grains of this gold bul
lion is a virtual dollar behind a dollar of gold certificates
outstanding. A gold bar (of standard bullion) weighing
25,800 grains virtually contains 1000 gold dollars.
The gold miner takes such bars of standard gold to the
niint and deposits them without waiting for their coinage,
receiving gold certificates in return, one dollar of gold cer
tificates for each 25.8 grains of standard gold which he de
posits. On the other hand, holders of gold certificates may
at any time receive gold bullion in return, when they desire

496

THE PURCHASING POWER OF MONEY

this for export, or for use in the arts of jewelry, dentistry,
gilding, etc., receiving 25.8 grains of gold for each dollar of
gold certificates. Thus the government on demand gives
or takes money at the rate of 25.8 grains of bullion per
dollar; the virtual, though invisible, dollar being this 25.8
grains of gold bullion, nine-tenths fine.
The proposal here made is to change the weight of the
dollar as an offset to changes in value. If there are no gold
coins, it is very easy to do this. For example, if there should
be a decrease of 1 per cent in the value, that is, purchasing
power of gold, then the weight of gold bullion which consti
tutes the virtual dollar would be declared 1 per cent greater,
becoming 26.058 instead of 25.8. If there should be an
increase in the purchasing power of gold, the weight of the
virtual dollar would be reduced accordingly. Whenever the
gold miner took gold to the mint, he would receive a gold
certificate not necessarily at the rate of one dollar for each
25.8 grains of standard gold, but for a larger or smaller
amount as the case might be, the amount always being that
amount which would possess the same purchasing power.
Similarly the holder of gold certificates who wishes them
redeemed in bullion for export or for the arts, would not
always get exactly 25.8 grains for each dollar of certificates,
but a larger or smaller sum, as the case might be. Thus the
government would be receiving gold from the miner and giv
ing it out to the jeweler just as at present, but in varying
weights per dollar, instead of at the arbitrarily fixed weight
of 25.8 grains. The weight of gold per dollar in which, at
any particular time, gold certificates were redeemable would
constitute the virtual and only gold dollar. Under these
circumstances it is clear that it would be entirely feasible
to change up and down the weight of the gold dollar (that
is, the amount of gold bullion interconvertible with a dollar
of gold certificates), and without any recoinage or other
interference with the outward appearance of the currency in
our pockets.
We should familiarize ourselves with another way of stat

APPENDIX TO THE SECOND EDITION

497

mg all this. Instead of saying that the government receives
gold bullion at the mint and uses this for redeeming gold
certificates, we may, if we prefer, say that the government
buys and sells gold. It buys gold from the miner, paying
for it in gold certificates; it sells gold to the jeweler, who
redeems these certificates. At present, the price at which
gold is bought and sold by the government is $18.60 an
ounce (for standard gold nine-tenths fine). This is easily
figured out from the weight of the gold dollar; for 25.8
grains of gold being our present dollar, each ounce (or 480
grains) of gold bullion contains 480/25.8 or 18.60 virtual
dollars. To say, then, that we now have a fixed weight in
our gold dollar, 25.8 grains, is the same thing as to say that
We have a fixed government price for gold, $18.60 per ounce.
To raise the weight of the gold dollar 1 per cent, or from
25.8 grains to 26.058 grains, is the same thing as to lower
the government price of gold from $18.60 to $18.42 per
ounce.
We come now to the second question: How would it be
possible to know the proper adjustments to be made in the
weight of the virtual dollar — the gold bullion interconver
tible with each dollar of gold certificates — without putting
a dangerous power of discretion in the hands of government
officials? In other words, how can the adjustment in the
Weight of the virtual dollar be made automatic ? The
answer is: By means of statistics called “ index numbers of
prices.” Such statistics are to-day published by the London
Economist, the United States Bureau of Labor, the Canadian
Department of Labour, and several commercial agencies, such
as Bradstreet. The index number of the Bureau of Labor
is based on the wholesale prices of 257 commodities, and
shows from year to year the extent to which prices on the
whole advance or fall, — the average movement of all the
257 prices.
There are various systems of index numbers, but they
practically all agree remarkably well with each other. When
once a system of index numbers is decided upon, their numer

498

THE PURCHASING POWER OF MONEY

ical calculation becomes a purely clerical matter. A sta
tistical bureau (as for instance the present Bureau of Labor
or an international statistical office) would compile and
publish these statistics periodically and the actual prices on
which they were based. If at any time the official index
number showed that the price level had risen 1 per cent above
par, this would be the signal for an increase of 1 per cent in
the virtual dollar.
The plan, then, is: first, to provide for the calculation of
an official index number of prices; second, to adjust corre
spondingly the official weight of the virtual dollar at which
the government shall issue gold certificates to miners or
redeem them for jewelers, in other wrords, to adjust the official
prices of gold at which the government stands ready to buy
or sell at the option of the public.
This, then, is the plan in brief — a plan virtually to mark
up or down the weight of the dollar (that is, to mark down or
up the price of gold bullion) in exact proportion to the devia
tions above or below par of the index number of prices.
A few additional details essential to the working of the
plan may now be briefly mentioned. You are still waiting
to see how actual gold coin could be used in such a system.
To be continually recoining the gold in circulation would,
of course, be quite impracticable. But this would be un
necessary. Existing gold coin would remain unchanged at
25.8 grains per dollar, and new gold coins would be given
the same weight. Gold coins would simply become what
silver dollars now are, token coins. Or, better, they would
be, like the gold certificates, mere warehouse receipts, or, as
it were, “ brass checks” for gold bullion on deposit in the
Treasury. Otherwise expressed, gold coins would be merely
gold certificates printed on gold instead of on paper. They
would be used exactly as gold certificates are used — namely?
issuable to the gold miner in return for his bullion, and
redeemable for those who wished bullion for export or in
the arts.
The excess of bullion over the weight of the coined dollar

APPENDIX TO THE SECOND EDITION

499

itself would be analogous to what has generally been called
“ seigniorage” ; so that in a sense, the plan may be described
as a plan to restore the ancient custom of seigniorage on
gold coin. Thus, if the virtual dollar were at any time
35.8 grains, the excess of ten grains above the weight of the
coin dollar, 25.8 grains, would be “ seigniorage.” The gold
miner, in return for every 35.8 grains of standard gold bul
lion taken to the mint, would receive, at his option, a gold
certificate on paper, or a gold certificate on gold {that is, a
dollar gold coin) — the latter containing, just as at present,
25.8 grains. Any holder of gold coin, old or new, and any
holder of gold certificates could receive from the govern
ment gold bullion at the official rate declared from time to
time. He would thus be receiving a larger quantity of gold
bullion than the amount of bullion in the gold dollar. The
gold coin would then, like all our other coins, be worth more
as coin than as bullion, and its value would be determined
just as the value of a gold certificate or any other paper
money is to-day determined, by the ultimate bullion with
which it would be interconvertible, this bullion being of
greater weight than the weight of the dollar itself.
The only real complication which would be introduced
by allowing gold coin to remain at its present weight and
fineness would be to limit the operation of the system when
prices tended to fall below the par or starting point at winch
the system began. The weight of the virtual gold dollar
could never be reduced below the weight of the coin dollar;
for, if this were done, the seigniorage would become a minus
quantity and all the gold coin would be immediately melted
mto bullion, being worth more melted than coined. One
proviso, therefore, in the system would be that the weight
of the virtual dollar should never be less than 25.8 grains
and that therefore the government price of gold should never
be more than S18.G0 per ounce. Perhaps, in view of the
present dissatisfaction with high prices, many people would
not object to this limitation which permits prices to fall
below the present level, but does not permit them to rise

500

THE PURCHASING POWER OF MONEY

further. Yet it is a poor rule that will not work both ways.
Consequently, while I personally look forward to an upward
tendency of prices in the future, the possibility of a downward
movement should be provided for. For this purpose, gold
coin could, if desired, be recalled at the outset and recoined
in lighter weight, just as the Philippine peso was recalled
and reduced in weight when the recent rise in the price of
silver threatened to lead to melting the silver pesos. But
I do not advocate crossing the bridge until we come to it.
It would be sufficient to provide in advance for crossing it in
case wTe should ever come to it. This could be done in one
of two ways. It could be provided that, if ever the price
level should, in the future, sink more than, say 10 per cent
below the original par or price level from which the system
started, all gold coins should then be withdrawal from cir
culation and gold certificates employed instead. In this way
we should be rid of any complication from the use of gold
coin, and would be at liberty forever after to adjust the
weight of the virtual dollar downward as well as upward.
Or, if preferred, it could be arranged that when prices should
sink more than the suggested limit of 10 per cent below the
original level, we should then recoin and reduce our gold
coins. This would merely mean that the gold on which we
print our gold certificates would be reduced in weight. It
would not, of course, reduce the value of the gold coin any
more than the reduction in the weight of the Philippine peso
which wras made for a similar contingency — or, to take an
example nearer home, the reduction of 10 per cent in the
weight of our subsidiary silver coins half a century ago —■
had any tendency to reduce the value of these coins.
If the latter plan were chosen, the amount of reduction
in the gold coin should be enough to provide a comfortable
margin for any similar emergencies in the future. Any
subsequent recoinages wrould thus be deferred a long time
and similar provision for them could be made. Personally
I should prefer the former method, eliminating gold coins
altogether.

APPENDIX TO THE SECOND EDITION

501

Another essential detail is a proviso to avoid speculation in
gold disastrous to the government. This would be accom
plished by means of a slight government charge, say 1 per
cent, for minting. This charge, which existed in former
days, is called brassage. It would mean that the price at
a^y particular date at which the government bought gold
Would be slightly less than the price at which it sold it.
Without such a margin to protect the government, it is
evident that when the government raised its price, say from
$18 to $18.10 an ounce, speculators might, in anticipation
of this rise, buy all the gold in the government vaults at
§18 in order to sell it back to the government immediately
after the change in price, at $18.10, thus profiting ten cents
per ounce at the expense of the government.
Similarly, a fall in price, say from $18.10 to $18 per ounce,
Would encourage the opposite form of speculation. Holders
°f bullion would then rush it to the government to sell it
at the present rate of $18.10, and immediately after the
change in price, buy it back at $18, thus profiting again
ten cents per ounce at the expense of the government. If,
however, the government were protected by a brassage charge
°f 1 per cent and if it were provided that no single shift in
the government pair of prices, whether they were both moved
UP or both moved down, should exceed the “ brassage” or
Margin between them, it is clear that no such speculation
could occur, for there would be a greater loss from the pay
ments of brassage to the government than any speculative
gain possible from the change in price.
Other details relate to the provisions for establishing and
Maintaining a gold reserve at the outset where no such
reserve existed in the first place. In the United States we
could utilize the 50,000,000 ounces of gold already in the
Treasury for the very purpose of redeeming the $900,000,000
°f gold certificates outstanding.
We have standardized every other unit in commerce
except the most important and universal unit of all, the unit
of purchasing power. What business man would consent

502

THE PURCHASING POWER OF MONEY

for a moment to make a contract in terms of yards of cloth
or tons of coal, and leave the size of the yard or the ton to
chance ? Once the yard was the girth of a man. In order
to make it constant, we have standardized it. We have
standardized even our new units of electricity, the ohm, the
kilowatt, the ampere, and the volt. But the dollar is still
left to the chances of gold mining. At first we could not
standardize units of electricity because wre had no adequate
instruments for measuring those elusive magnitudes. But
as soon as such measuring devices were invented, these units
were standardized. We have hitherto had a similar excuse
for not standardizing the dollar as a unit of purchasing
power, and so a standard for deferred payments; we had
no instrument for measuring it or device for putting the
results in practice. With the development of index numbers,
however, and the device of adjusting the seigniorage accord
ing to those index numbers, we now have at hand all the
materials for scientifically standardizing the dollar and for
realizing the long-coveted ideal of a “ multiple standard7
of value. In this way it is within the power of society, when
it chooses, to create a standard monetary yardstick, a
stable dollar.

INDEX
A

Aldrich Report on Wholesale Prices,
cited, 259, 260, 399.
Aldrich-Vreeland bill of 1908, 146 n.
American colonies, paper money in

the, 256-258.
Arrays, use of, in calculating
quantities, prices, and averages,
355-362, 367-368.
Arts, influence on quantity of money
of consumption of gold in the, 103.
Assets of bank, must be adequate to
meet liabilities, 38-39; form must
be such as to meet liabilities
promptly, 42-47.

Assignats, experience of French Rev
olutionists with, 252-253.
Atkinson, F. J., on “ Silver Prices in
India,” 243.
Aupetit, Albert, cited, 157, 234, 237,
240.
Australia, rise of prices due to gold
discoveries in (1851-1852), 241-

242.
Austria, adoption of gold standard
by (1892), 243; experience of,
with paper money, 255-256;
monetary system of, referred to,

341-342, 344.
Averages, discussion and explanation
of, 23-24, 198-203, 349-352.

B
Bank checks'. Sec Checks.
Bank deposit circulation, before and
during crises, 267-270. See De
posit currency.
Bank deposits. Sec Deposits.
“ Bank gold,” 115 n.1.
Banking laws, relative increase in de
posits partly due to recent, 315.
Bank- notes, 38-39; circulation of,
before, during, and after crises,

267-270.

Barter, the exchange of goods against
goods, 13.
Base, selection of a, in constructing
index numbers, 203.
Benefits of wealth, meaning of, 6;
future benefits are those referred
to, 6.
Bills of exchange, comparative ad
justability of prices of, 186.
Bimetallism, mechanical operation
of, 115 ff.; two requisites of com
plete : free and unlimited coinage
of both metals at a fixed ratio,
and the unlimited legal tender of
each metal at that ratio, 117;
illustrations of workings of, by
the case of France and the Latin
Monetary Union, 132-135; the
claim that prices would bo
steadied by, 324-325; shown to
bQ an indifferent remedy for vari
ations in price level, 325-326;
possibility of the system breaking
down, 326; possible disruption of
prices by overvaluation of one
metal a risk to be feared, 327;
limits for ratios within wliich bi
metallism is possible, 378.
Bland-Allison Act of 1878, 142.
Bolles, Albert S., cited, 257.
Bonds, prices of, among least ad
justable, 186-187; effect of non
adjustability of, shown in supersensitiveness of stocks, 190-192.
Book credit, velocity of circulation
increased by, 81-83; effect of, on
equation of exchange, 370-371,
491-492.
Boom periods leading to crises, 5867.
Bortldewicz, L. von, cited, 32.
Brace, Harrison H., Gold Production
and Future Prices by, cited, 80,
241, 249.
Brown, Harry G., cited, 37 n., 65,
212 n.2, 269, 426.

503

504

INDEX

Bullion, influence on quantity of
money of melting coin into, 96-99.
Business barometers, 322, 478.
jtti tio*
s~ ^
^
^ ir
C
•
California, rise of prices due to gold
discoveries in, 241-242.
Capital, defined as a stock of goods
existing at an instant of time, 7;
influence of accumulation of, on
volume of trade, 76.
“ Charging,’' velocity of circulation
increased by, 81-83; influence of
habit of, on volume of deposits,
88-89.
Checks, bank, function of, 33-35.
Checks, effect of use of, on velocity
of circulation, 83 ,* increase in,
caused by increase in trade, 105;
statistics of payments by (1909),
305-306; statistics of total ex
change work performed by (1896,
1909), 317-318; constitute nine
tenths of the country’s transac
tions, 318; method of calculating
deposits subject to, 434-441.
Checking accounts, statistics of
amounts of, from 1896-1909, 281282, 491-492.
Check transactions and money trans
actions, statistical statement of
relative importance of, 317-318.
Chili, adoption of gold standard by
(1895), 243.
China, rise of prices in (1874-1893),
243-244.
Circulating credit, or bank deposit
currency, 33 ff. See Deposits.
Circulating media, classification of,
in United States, 12-13. See
Currency.
Circulation, statistics of money in
circulation from 1896-1909, 280281. See Velocity of circulation.
Circulation of bank notes and bank
deposits before and at times of
crises, 267-270.
Circulation of money, signifies the
aggregate amount of its transfers
against goods, 13; general practi
cal formula for calculating, 448460; application of formula to
calculation of circulation during
1896-1909, 460 ff.

Clark, J. B., cited, 221.
Coefficient of correlation, application
of, 294-296.
Coin-transfer concept of velocity, 353.
Commerce, foreign compared with
internal, 305-306, 484-486.
Committee of British Association for
Advancement of Science, report
of on index numbers, 228-229.
Commodities, defined, 2;
com
parative adjustability of prices of,
186-187; changes in quantities
of, corresponding to changes in
prices, 194-195; types of, con
trasted, 382-384.
Conant, Charles A., cited, 132, 140,
223.
Confederate States, value of gold and
index numbers of prices in the,
263-265.
Continental paper money, 257-258.
Contracts, restriction of free move
ment of prices because of, 185,
189; nonadjustability of prices
varies with length of, 189; meas
urement of appreciation or depre
ciation of loan contracts, by use
of index numbers, 208-225.
Costa Rica, adoption of gold stand
ard by (1896), 243.
Cost of living, rise in, concluded to
be merely a part of general move
ment of prices, 316.
Credit, circulating, or bank d e p o s i t
currency, 33 ff.
Credit cycle, history of a, 58-72;
table of statistics illustrating cul
mination of a, 271-273; lessening
of fluctuations by tabular stand
ard of value plan of regulating
price level, 335.
“ Crime of ’73,” the, 141.
Crises, the culmination of an up
ward price movement, 65; be
lated adjustment of rate of
interest as a factor in, 66; corre
spondence between circulation,
private deposits, and, 265-270;
conditions preceding, 266; a
crisis defined as an arrest of the
rise of prices, 266; international
character of, 266-270.
Currency, or circulating media, de
fined as any type of property right
*vhich serves as a means of ex

505

INDEX

change, 10; two chief classes:
money and bank deposits subject
to check, 10; bank deposits, 33 if.
See Deposits.
D
Darwin, Leonard, Bimetallism by,

cited, 127.
D ’Avenel, Vicomtc, estimates by,
cited, 234, 237.

Deferred payments, use of index
numbers for measuring apprecia
tion or depreciation of, 208-225.
De Launay, The World's Gold by,

cited, 98.
Del Mar, History of the Prccious
Metals by, cited, 237, 239.
Demand, difference between effects
of an increased, for an individual
commodity and of an increased
general demand for goods, 180.
Demonetization of silver, lowering
of prices in gold-standard countries
by, 242-245.
Density of population, effects of in
creased, on velocity of circulation
and on volume of trade, 1G4-1GG,
315.
Deposits, bank (deposit currency),
influence of, on equation of ex
change and lienee on purchasing
power, 33 ff.; quantitative rela
tion of, to money in a given com
munity, 51-52, 151; expansion
of, during periods of rising priccs,
58-GO, 273; contraction of, in
period of falling prices, 67-70;
velocity of circulation of, increases
with density of population, 87;
dependence of, on quantity of
money, 1G2; effects of change in
ratio between quantity of money
and, 1G2-1G3; increase in, will
have no appreciable effect on
velocities of circulation and
volume of trade, but will raise
prices slightly, 163-1G4; effects
on prices of changes in (with
special attention to crises and
depressions), 2G5 ff.; statistics of
amounts of, from 1896-1909, 281285; proved to have tripled, and
velocity of circulation of, to have
increased 50 per cent in fourteen

years, 304-305; statistics of
amount per capita and velocity
of circulation (1909), 305; growth
of, shown to be a large factor in
raising prices, 307-311; chief
causes of increase in, 315; velocity
of circulation of, chiefly due to
concentration of population, 315;
description of method of calculat
ing, 434-441.
Depression, causes of period of, 5867, 71-72. See Crises.
Dewey, Davis Rich, cited, 258; use
of the median for wages by, 428.
Dispersion of prices, 184 ff.; caused
by previous contract, legal re
strictions, and custom, 185-189;
by nonvariation of articles related
to the money metal, 189-190;
by variation of individual prices
under influence of law of supply
and demand, 190-194.
Drobisch, M. W., citcd, 396.
Dunbar, Theory and History of Bank
ing by, cited, 35.
E
Economics, defined as the science of
wealth, 1.
Ecuador, adoption of gold standard
by (1899), 243.
Edgeworth, F. Y., cited, 25 n.2, 167,
199, 218, 220, 325, 328, 334, 392,
396, 397, 423, 426, 427.
Egypt, adoption of gold standard by
(1885), 243.
England, statistics of price move
ments in, 238-240; account of
experience of, with paper money,
238-239, 253-255; dates of fi
nancial crises in, 267.
England, Minnie Throop, statistics
by, cited, 174, 273.
Equation of exchange, defined as
the equation between a stream
of transferred rights in goods and
an equivalent stream of trans
ferred money or money substi
tutes, 7; is a statement in mathe
matical form of the total trans
actions effected in a certain period
in a given community, 15-16; tho
money side and the goods side,
16-17; the magnitude called

506

INDEX

velocity of circulation or rapid
ity of turnover, 17; arithmetical
illustration of, 17-21; mechani
cal illustration of, 21-24; alge
braic statement of, 24-28, 3G4,
368; influence of bank deposit
currency on, 33 ff.; application
of, to bank deposits or circulating
credit, 48-49; disturbance of,
during periods of transition, 55
If.; implies no causal sequence,
149-150; statistical verification
of, 276-318; construction of
index numbers required by, 198
ff. (see Index numbers) ; benefits
to business men of a fuller knowl
edge of, 322-323; effect of time
credit on, 370-371; modification
of, required by international
trade, 372-375.
Essars, Pierre des, cited, 63, 87, 269,
270.
Evelyn, Sir G. S., early attempt to
construct series of index numbers
by, 20S n.
Exchange, defined as consisting of
two mutual and voluntary trans
fers of wealth, 3. See Equation
of exchange,
Exchangeability, quality of, which
makes a commodity money, 9;
differing degrees of, found in real
estate, mortgages on real estate,
corporation securities, govern
ment bonds, bills of exchange,
sight drafts, and checks, 9-10.
Exchanges, classification of, into ex
change of goods against goods
(barter), of money against money
(changing money), and of money
against goods (purchase and sale),
13.
Expectation, results of, on prices,
262-263.
F
Failures, causes leading to commer
cial, 64-67.
Fairchild, F. R., article by, cited, 193.
Falkner, Roland P., index numbers
of, 229.
Farm lands, value of, affected by
changes in rate of interest, 193.
Fetter, Frank, cited, 221.
Fiars prices, Scotch, 334,

Fiduciary money, definition of, 11*
Fisher, Irving, The Nature of Capi
tal and Income by, cited, 1, 44,
214; The Rate of Interest by,
cited, 56, 57, 58, 65, 70, 210, 214,
216, 224, 266; papers and a r t ic le s
by, 25 n.2, 115,174, 190, 210, 211,
244, 384.
Fleetwood, Bishop William, work by,
cited, 208 n.
Flow or stream of goods, distinction
between stock or fund of goods
and, 7; three classes of economic
flows, besides income, 7.
Flux, A. W., cited, 423.
Food, rise of wholesale prices of,
compared with general change in
prices, 316.
Forecasts, economic, 321-322.
Foreign trade, influence of, on quan
tity of money, 90-96; volume of,
contrasted with internal, 305306, 484-186.
Forest land, sensitiveness of value of,
to changes in rate of interest, 193.
Foxwell, H. S., cited, 218.
France, experience with bimetallism
in, 132-135; experiences of, with
paper-money schemes, 252-253;
dates of financial crises in, 267.
Freedom of trade, effect of, on
volume of trade and price level,
77-78. Sec Tariff.
G
Geographical influence on volume of
trade, 75.
“ George Smith’s money,” 47.
Germany, adoption of gold standard
by (1871-1873), 242-243.
Giffen, Robert, cited, 206, 392.
Gold, the best example of a money
commodity, 2; comparative non
adjustability of prices of articles
made of, 187, 189-190; statistics
of increase in annual production
of, 235-236; continued increase
in prices predicted, due to in
crease in production of, 248-249;
increasing output of, 249; statis
tical comparison of greenbacks
and, 259; difficulties of finding
substitute for, as a medium, 323324; various proposed substi-

INDEX

507

tu tes: bimetallism, polymetal Index number, use of an, to stand
for prices taken collectively (P )f
lism, convertible paper currency,
184; to stand for volume of trade
tabular standard of value, com
(T), 195-196.
bination of gold-exchange stand
ard and tabular standard, etc., Index numbers, a necessity owing
to dispersion of prices, 184-196;
324-348; variabilities of pro
comparison of, as to form, 198 ff.;
duction of silver and, 326 n.
simple or unweighted averages,
Gold bullion and gold coin, equal
198-199; weighted averages, 199values of, 97-99.

203; methods of constructing,
200-202; selection of the base,
203; the successive base or chain
system, 203-204; selection of
prices, 204 ff.; use of, to measure
capital and to measure income,
205; to measure six subclassifi
cations, 205-206; use of, to serve
Gold mining, chief cause of increase
as basis of loan contracts, or
of money, 315.
standard of deferred payments,
Gold standard, general adoption of,
208 ff.; report of committee of
and resultant fall of prices (1873—
British Association for Advance
1896), 242-243.
ment of Science, 228-229; ad
Goodbody, Robert, article by, cited,
vantages of the median over
188.
other forms of, 230-231; index
Goods, definition of the term, 6.
numbers of prices from 1896Greenbacks, issuance of, in United
1909, 290-293, 486-487; of vol
States, 141; a useless anomaly,
ume of trade from 1896-1909,
145; depreciation of, 258-260;
290, 478 ff.; use of, in tabular
comparison of prices in gold and
standard of value plan for con
in (1861-1879), 259; explanation
trolling price level, 332-337; each
of value of, found in expectation
form of index number for prices
of redemption, 261.
demonstrated to imply a correl
Gresham’s Law, that cheap money
will drive out dear money, 112 ff.
ative form of index number for
Griswold, Robert N., calculations by,
quantities, 385-391; eight tests for
a good index number, 400-417.
484.
India, experience of, with the limp
H
ing standard, 138-140; adoption
Hadley, A. T., Economics by, cited,
of gold standard by (1893), 243;
resultant rise of prices in, 243-244.
25 n.2.
Hardy, S. M., paper by, mentioned, Inflation, rate of interest raised by,
57-58.
277 n.2.
Hazard, Thomas, Account Book of, Insolvency in banking, 43.
Insufficiency of cash, condition of,
quoted, 256-257.
at banks, 43-45.
Hertzka, joint-metallism scheme of,
Interest. See Rate of interest.
328.
Hickernell, W. F., table by, 146, 147. International trade, modification of
equation of exchange required by,
Hildebrand, work by, cited, 161.
90-96, 372-375.
Holt, Byron W., cited, 186.
Hunt, William C., estimates by, Invention, as a disturbing force to the
financial equilibrium, 70; in
465-467.
fluence of, on volume of trade and
price level, 77.
Income, definition of, as flow of Irredeemable paper money, effects of,
on prices, 238-239, 250 ff. Set
benefits from stock of goods
Paper money.
(capital), 7.
I
Gold coin, the only primary money
in the United States, 13.
Gold-exchange standard, system of
partial redeemability known as,
131-132, 337 ff.; in British India,
138-140; in the Philippines,
Mexico, and Panama, 140.

2 k

508

INDEX

Italy, the case of an overissue of paper Legal tender, what constitutes, 8.
money in, 114.
Leslie, Cliffe, cited, 236.
“ Limit of tolerance” of mints, 114J
115.
“ Limping” standard, monetary sys
Jacob, William, cited, 237.
tem called, 127; the gold-ex
Japan, adoption of gold standard by
change standard a kind of, 131(1897), 243; resultant rise of
132; experience of British India
prices in, 243-244.
with, 138-140; in the United
Jevons, W. S., cited, 8, 9, 12, 80, 88,
States, 140-148; Walras’s gold
186, 195, 237 n., 241, 249, 254,
standard with a “ silver regulator’
332, 335, 397; quoted on diffi
a variant of, 328-329.
culties of determining velocity of Loan contracts, measurement of ap'
circulation of money, 286; claim
preciation or depreciation of, by
of, that a bimetallic standard
index numbers, 208 ff. See Con
would tend to steady prices, 325.
tracts.
Johnson, J. F., Money and Currency Logan, Walter S., article by, cited,
by, cited, 136, 251, 333.
188.
Joint-metallisms, schemes of, 328. Loss, influence on quantity of money
Juglar, Clement, cited, 65 n.3, 266,
of consumption of gold by, 103.
267, 269, 270.
Lowe, Joseph, suggestion of use of
index number or tabular stand
K
ard of value by, 208 n., 332.
Kemmerer, E. W., works by, cited,
M
14 n., 25 n.2, 45, 139, 140, 213,
226, 279, 282, 331, 487; pioneer
work of, in testing statistically Macleod, H. D., History of Economics
by, cited, 112.
the quantity theory, 276-278,
Magee, J. D., figures of, on world's
430-432.
production of gold and silver,
Kinley, Money by, cited, 60, 87, 212 ;
235 n., 241.
Credit Instruments, 226, 444, 462;
original statistical work of, 282- Mandats, French paper money, suc
cessors to the assignats, 253.
283, 461-462, 491-492.
Marginal cost of production, ex
Knapp, G. F., cited, 32.
planation of, 99-101.
Knowledge of technique of produc
tion, influence on volume of trade, Marshall, Alfred, Principles of Eco
nomics by, quoted, 71-72; system
76.
called symmetallism suggested by,
L
328; cited, 423.
Labor, influence of division of, on Massachusetts, paper money in
colonial, 256.
volume of trade, 75.
Labor standard of purchasing power Median, advantages of, over other
forms of index numbers, 230-231,
of money, proposed, 222.
425-428.
Labor unions, inability of, to affect
Menger, work by, cited, 5.
general price level, 179-180.
Lake, A. C., pamphlet by, cited, Merriam, Lucius S., cited, 221.
Mexico, adoption of gold standard
347 n.
by (1905), *243.
Landry, Adolphe, cited, 84, 85.
Latin Monetary Union, the, 134-135. Mill, J. S., cited, 25 n.*, 31, 102,
200.
Lauck, cited, 269.
Laughlin, work by, cited, 14 n., 50 n., Mining land, value of, as affected
by changes in rate of interest,
140,242 n.2; quoted, 104 n., 165 n.
193.
Launay, L. de, cited, 248.
Law, John, paper-money scheme of, Minting and melting, influence of,
on quantity of money, 96-99.
252.

509

INDEX

Mitchell, W. C., works by, cited, 141, Mulhall, Dictionary of Statistics, cited,

200, 258, 259, 2G0, 2G5, 426, 48G;
use of the median for price in
dexes, 428.

Money, definition of, as any com
modity generally acceptable in
exchange, 2, 8; three meanings of:
in the sense of wealth, in the sense
of property, and in the sense of
written evidence of property
right (bank-notes, checks, stock
certificates, etc.), 5; “ circula
tion” of, consists of a stream of
transferred money or money sub
stitutes, 7; use of gold dust and
gold nuggets, tobacco, wampum,
shells, etc., for, 8-9; quality of
exchangeability which makes, 910; distinction between bank de
posits subject to check and bank
notes, 11; money rights are what
a payee accepts without question,
by legal-tender laws or wellestablished custom, 11; primary
and fiduciary money, 11-12;
circulation of, siginfies the ag
gregate amount of its transfers
against goods, 13; the purchas
ing power of, is indicated by the
quantities of other goods which
a given quantity of money will
buy, 13-14; bank notes, 38-39,
47; Gresham’s Law, that cheap
money will drive out dear money,
112 ff.; comparison of stocks of,
in Europe, and price levels, 237238; statistics of money in cir
culation from 1896-1909, 280281, 430-434; shown to have
nearly doubled in fourteen years,
304-305; statistics of actual cir
culation of, 305-306; statistical
statement of check and cash trans
actions, 317-318, 491-192; sub
stitutes for, unlike other sub
stitutes, 376-377. See also Quan
tity of money.

240.
N
National Bank notes, United States,
145-146.
Netherlands, adoption of gold stand
ard by (1875-1876), 243.
Newcomb, Simon, Principles of
Political Economy by, 25 n.2.
Nicholson, J. S., cited, 206, 392.
Nitti, cited, 199.
Nogaro, Bertrand, cited, 32, 127.
Norton, J. Pease, cited, 59; index
numbers of, 230.

O
Oresme, Nicolas, 112.
Orient, regarded as the “ sink of
silver,” 236, 247.
P

Pair of prices device, 343-344.
Palgrave, Dictionary of Political
Economy by, cited, 8.
Panics and their causes, 64-66.
Paper money, slight influence on
prices of the English irredeem
able (1801-1820), 238-240; usual
effects of redeemable and of irre
deemable, on prices, 250 ff.; pre
carious value of, 251-252; ex
periences of various countries with,
252 ff.; John Law’s scheme, 252;
account of England’s experience
with, 253-255; in Austria, 25525G; American Continental, 257—
258; experience of United States
with, 258-263 ; Confederate, 263265; redeemable, suggested as a
price-steadying plan, 331-332.
Pareto, work by, cited, 70.
Pars, readjustment of gold, undei
author’s proposed plan for reg
ulating price level, 341-342,
344-345.
Money changing, the exchange of Pearson, Karl, the “ correlation co
efficient” of, 294.
money against money, 13.
Persons, Professor, cited, 278-279,
Money famines, causes of, 67-69.
294.
Morawetz, Victor, cited, 45.
Mortgage notes, prices of, among Person-turnover concept of velocity,
353, 362-363.
least adjustable, 186-187.
Muhleman, Maurice L., calculations Peru, adoption of gold standard by
(1897), 243.
of, 245, 433-434.

510

INDEX

Philippines, buying and selling ex
change in the, 337, 338.
Polymetallism, proposed scheme for
steadying monetary standard,
327-328.
Population, increased density of,
quickens flow of money and
checks, 164-165; changes in
volume of trade and velocity of
circulation caused by changes in
density of, 165-166; concentra
tion of, the chief cause of increase
of velocity of circulation, 315.
Porter, Morgan, calculations by, 326
n.
Price, L. L., Money and its Relation
to Priccs by, cited, 235, 237, 241.
Price level, dependent on three sets
of causes: quantity of money in
circulation, “ efficiency” or ve
locity of circulation, and volume
of trade, 14; the quantity theory,
that prices vary in direct propor
tion to quantity of money, 14,
157-159, 296-297; varies directly
as the quantity of money in cir
culation, directly as the velocity
of circulation, inversely as the
volume of trade done by it, 29;
effect on, of doubling the denomi
nations of all money, 29-30; of
debasing the currency, 30; of
doubling the coinage, 30-31;
effects of rising and of falling, on
rate of interest, 56 ff.; history
of a period of rising, leading to a
crisis, 58-67; the corresponding
downward course of, 67-70; out
side influences which tend to
lower: geographical differences
in natural resources, division of
labor, improved productive tech
nique, and accumulation of capi
tal, 74-76; lowering of, by
changes in human wants, 76-77;
lowering of, by increased trans
portation facilities, relative free
dom of trade, development 6f
efficient monetary and banking
systems, and business confidence,
77-79; increase of, by book
credit, 81-83 ; raising of, by den
sity of population and increased
transportation facilities, 88; regu
lation of, by international and

interlocal trade, 90-96 ; workings
of a protective tariff in regard to,
93-95, 312-314; restatement of
truth that the normal effect of
an increase in the quantity of
money is an exactly proportional
increase in the, 157-159; slight
effect of changes in volume of
trade on, 166-169; held not to
be an independent cause of
changes in any of the other mag
nitudes in equation of exchange,
169 ff.; normally the one abso
lutely passive element in the
equation of exchange, 172; em
phasis laid on distinction between
individual prices relative to each
other and the price level, 175; not
determined by individual prices,
175-180; inability of trusts or
labor combinations to affect, 179180; increased general demand
for goods results in a lower, 180;
effect of dispersion of prices, 184197; general trend upward of,
234; influence on, of discovery
of America and increase in pro
duction of gold and silver, 235236; comparison of metallic
stocks in Europe at various dates
and, 237-238; summary of move
ments of, during nineteenth cen
tury, 240-242; rapid rise of, from
1789-1S09, 240-241; fall of, to
two fifths, between 1S09-1S49,
241; rise of by one third to one
half, in 1849-1873, 241-242;
lowering of, from 1873 to 1896,
242; effect on, of general adop
tion of gold standard, 242-243;
effect on silver countries of adop
tion of gold standard in other
countries, 243-245; rise in, from
1896 to present, 245-246; con
tinued rise in, predicted, due to
increase in gold production, 248249; effects on, of changes in
deposit currency, 265 ff.; con
clusion that expansion of deposit
currency raises, rather than that
rise of prices creates deposit cur
rency, 273 ; statistics of, as shown
by index numbers of general
prices from 1896-1909, 291-292;
importance of appreciating exist-

51 1

INDEX

ence of a law of direct proportion
between quantity of money and,
296-297; shown to have risen by
two thirds, in fourteen years
(1896-1909), 304-305; summingup concerning rise of and causes,
from 1896-1909, 307; discussion
and analysis of the separate fac
tors concerned in rise of, 307-311;
conclusion as to importance of
increase of money as a factor in
price-raising, 311; full effect of
quantity of money on, not felt
on account of overflow to foreign
countries, 311-312; question as
to whether price level is control
lable, 319 ff.; proposed methods
of maintaining a stable level: by
bimetallism, 324-327; by poly
metallism, 327-328; by sym
metallism, joint inetallism, and
other purely academic schemcs,
328-329; by inconvertible paper
money, 329; by a varying seign
iorage charge, 330-331; by
convertible paper currency, re
deemable on demand, 331-332;
by a tabular standard of value
plan, 332-337; by gold-exchange
standard combined with tabular
standard, 337-346; changes in
individual prices demonstrated
not to affect, necessarily, 382384.
Prices, individual: method of ob
taining a price, 3 ; dispersion of,
184 ff.; index numbers of, 184,
486-487; nonadjustment of some,
causes greater ratio of change in
others, 185 ff.; of contracts, cus
tom, and legal restrictions, 185,
187-189; classification of goods
according to adjustability of
prices, 186-187; narrow range
of variation in, of articles made
of money metal, 189-190; factors
working through law of supply
and demand which affect, 192194; effect on, of changes in rate
of interest, 193 ; impossibility of
a uniform change in, 194-195;
changes in quantities of commodi
ties with changes in, 194-195.
Primary money vs. fiduciary money,
11- 12.

Production, influence of knowledge
of technique of, on volume of
trade, 76.
Property, or property right, defined
as the right to enjoy the services
or benefits of wealth, 4; distinc
tion between wealth and, 4;
units for the measurement of,
4-5; distinction between property
rights and the certificates of those
rights, 5.
Purchase and sale, the exchange of
money against goods, 13.
Purchasing power of money, as re
lated to the equation of exchange,
8 ff.; is indicated by the quan
tities of other goods which a given
quantity of money will buy, 1314; influence of deposit currency
on, 33 ff.; disturbance of, during
transition periods, 55-73; vari
ous indirect influences on, —
conditions of production and
consumption, individual habits,
foreign trade, melting and mining,
etc., 74 ff.; influence of monetary
systems, 112-148; influence of
quantity of money, 149 ff.; index
numbers of, 184-233; problem
of making more stable, 319-348.
See Price level.
Q
Quantities of commodities, changes
in, corresponding to changes in
prices, 194-195, 382-384.
Quantity of money, relation of prices
to, 14, 157-159, 296-297 (see
Quantity theory); deposit cur
rency normally proportioned to,
49-53; increase in, a cause of
disturbance to financial equilib
rium, 70; causes outside the
equation of exchange that affect,
90 ff.; influence of foreign trade,
90-96; influence of melting and
minting, 96-99; influences operat
ing through the production and
consumption of money metals,
99-104; influence of monetary
systems, 112 ff.; doubling of,
will double deposits, will not
affect velocity of circulation, but
will increase prices in proportion

512

INDEX

193; small part taken by, in total
to its own increase, 151—159; the
business transactions of United
law of direct proportion betweon
quantity of money and price
States, 226.
level, 157-159, 296-297; ratio Receipts and disbursements, effect
between deposits and, 162; effect
on velocity of circulation of in
on, of changes in velocities of cir
creased frequency of, 83-85;
culation, 164-165; effects on, of
effect of regularity of, 85-86.
changes in volume of trade, 165; Reserves, banking, 45 ff.; legal regu
lation
of, 46; effect of rising
proof of importance of, as a priceraising factor, 307-311; full effect
prices on, 64-65; ratio wThich
of increase in, not felt in United
exists between quantity of money,
States because of overflow abroad,
amount of deposits, and, 162.
311-312; causes working toward Retail prices, data concerning com
increase of, 315.
parative importance and adjust
Quantity theory of money, that prices
ability of, 226-227.
vary proportionately to money, Rhode Island, paper money in
14,
157-159, 296-297; causes colonial, 256-257.
leading to contesting of this Ricardo, theory of equation of ex
theory, 14-15; the equation of
change launched by, 25 n.2;
* exchange, 15-31 (see Equation of
cited, 31 n., 44, 188, 250, 343.
exchange) ; three illustrations of, Robertson, J. Barr, articles by, cited,
29-31; dependent on the fact
244 n.2, 245.
that money has no power to Ross, Edward A., cited, 221.
satisfy human wants except a “ Runs on banks,” caused by period
power to purchase things which
of rising prices, 65.
do have such power, 32 ; in causal Russia, adoption of gold standard by
(1897), 243.
sense, 151 ff.; does not hold
strictly true during transition
S
periods, 159-162.
Quarries, effect on value of, of Sakata, translation by, 243 n.2.
changes in rate of interest, 193. Salaries, relative adjustability of,
regarded as one of class of prices,
187.
R
Sauerbeck, statistics by, cited, 238Railways, influence of, on velocity of
240, 242.
Scandinavian monetary union, adop
circulation, 88.
tion of gold standard by, 243.
Rate of interest, determination of,
in banking, 45; effects of rising Schwab, J. C., Confederate States of
and falling prices on, 56-58, 266
America by, quoted, 263-265.
n.1; the outstripping of, by prices Scott, M oney and Banking by, quoted,
15 n.
in period of rising prices, 59-60,
271-273; commercial crises due Scrope, G. P., use of index number
to belated adjustment of, 66, 71to indicate standard of value sug
72; tardiness of lowering of, in
gested by, 208 n., 332.
period of falling prices, 68; effect Seager, Introduction to Economics by,
of changes in, on individual prices,
cited, 144 n.
193 ; adjustment of, not sufficient Seasonal changes, effects of, on ve
to compensate for fluctuations in
locity of circulation, quantity of
value of money, 223, 232-233.
money and deposits, 72, 161.
Real estate, scope of, as a class of Sea-water gold, 249.
wealth, 1-2; comparative ad Sedgwick, H., cited, 200.
justability of price of rented, 186 ; Seigniorage, charge for changing bul
lion into coin, 98; regulation of
prices of leased, among the least
adjustable, 186 ; value of, affected
supply of metallic money by a
by changes in rate of interest,
varying, proposed, 330-331.

INDE*

513

change standard, suggested, 338Bhaler, N. S., quoted, 324.
346.
Bhaw, W. A., History of the Currency
Tariff, effects of, on purchasing
by, cited, 133, 134, 136.
power of money, 93-95; tem
Sherman Act of 1890, 142-143.
porary effect of a protective, to
Short crops, as a disturbing force to
raise price level of protected
the financial equilibrium, 70.
country, 312; afterward ceases
Siberia, effect of introduction of gold
from, 241.
to affect price level, except for its
Silver, statistics of increase in annual
interfering effect, 312-313; con
sideration of tariffs of 1897 and
production of, 235-236; variabili
1909, 313-314.
ties of production of gold and,
326 n .; danger from overvalua Technical knowledge, influence of, on
tion of, in case bimetallism were
volume of trade and price level, 76.
Telegraph, velocity of circulation in
a standard, 327.
creased by the, 88.
Silver certificates in United States,
143-145.
Tests for index numbers, 400-417.
Silver countries, effect on, of adop Thom, De Courcy W., cited, 266,
267, 268.
tion of gold standard by other
Thrift, influence of, on velocity of cir
countries, 243-245.
culation, 79-81.
Simple averages, 198-199.
Timber land, effect on value of, of
Smiley, W. Y., mentioned, 484.
changes in rate of interest, 193.
Smith, J. Allen, cited, 335.
Soetbcer, Adolf, figures of, on world’s Time, the element' of, and relation
of wealth, property, and benefits
production of gold and silver,
to, 6-7.
235 n., 237.
Sprague, O. M. W., editor Dunbar’s Time of turnover, concept of, 354,
363.
Theory and History of Banking,
Tithe averages in England, 333.
35; cited, 269 n.1.
Stock of goods, distinction between Tokens, forms of fiduciary money
called, 12.
flow of goods and, 7.
Stocks, adjustability of prices of, 187; Trade, defined as a flow of transfers,
7; influence of foreign, on quan
supersensitiveness of, to monetary
tity of money, 90-96; volumes of
190-192;
fluctuations,
trans
foreign and domestic compared,
actions in listed securities con
305-306, 484-486. See Volume
stitute eight per cent of country’s
of trade.
business, 226.
Stokes, joint-metallism schcme of, Transfer of wealth, defined as a
change of its ownership, 3.
328.
Substitutes, prices of, move in sym Transition periods, temporary effects
pathy with prices of articles
of, on equation of exchange, 55
themselves, 189-190; substitutes
ff.; characterized by rising or by
for money unlike other substi
falling prices, 56; effect of, on
equation of exchange, 159-162.
tutes, 376-377.
Sumner, W. G., cited, 8, 9, 255, 256.
See Crises.
Supply and demand, factors working Transportation facilities, effect of,
on volume of trade, 77; relation
through principle of, which affect
between velocity of circulation
individual prices, 192-194.
and, 88, 166.
Symmetalism, system called, 328.
Trusts, inability of, to affect the
general price level, 179-180.
T
Turnover, rapidity of, 17; rates of
individual, dependent on volume
Tabular standard of value plan for
of expenditure, 167; statistics of,
controlling price level, 332-337;
at Yale University, 379-382.
main objections to, 335-337; com
Velocity of circulation.
bination of plan with the gold-ex

514

INDEX

currency shown to be fifty-three
U
times a year (1909), 305; of
United States, sketch of monetary
money shown to be a negligible
system of, 140 ff.; issuance of
factor in raising prices, 307-311;
greenbacks, 141; complicated
of deposits a large factor in raising
and objectionable features of
prices, 307-311; discussion of
monetary system, 143 ff.; ex
concept of, 352-354; coin-transperience of, with paper money,
fer and person-turnover concepts
258-203; dates of financial crises
of, 353, 362-363; time of turn
in, 267.
over concept, 354, 363; method,
Unweighted averages, 198-199, 349of calculating velocity of circula
352.
tion of deposits, 441-446.
Uses of wealth, to be distinguished Venezuela, adoption of gold standard
from utility of wealth, 6.
by (1896), 243.
Utility standard of purchasing power Volume of trade, dependence of price
of money, 220-222.
level on, 14, 18-21, 24 ff.; causes
outside the equation of exchange
which affect: geographical dif
V
ferences, division of labor, extent
Value, the magnitude called, and
and variety of human wants, etc.,
74-79; proved to be independent
its determination, 3; is the price
of quantity of money (except in
of any item of wealth multiplied
by its quantity, 3-4.
transition periods), 155-156; in
Velocity of circulation, dependence
crease in, increases money in
of price level on, 14 ff.; definition
circulation, 165; effects of, on
velocity of circulation, 165-168;
of, 17, 352 ff.; causes outside the
equation of exchange which affect,
statistics of, from 1896-1909, 290291, 304-306; method of calcu
79-89; increase of, by habit of
“ charging,” or book credit, 81lating (1896-1909), 478 ff.; in
dex numbers of, 479.
83; increase of, by use of checks
rather than money, 83; increase
of, by increased frequency of re
W
ceipts and disbursements, 83-85;
effect of regularity of receipts and Wages, effect of frequency of pay
ment of, on velocity of circula
disbursements, 85-86; increased
tion, 83-85; relative adjustability
by density of population, 87, 315;
of, considered as prices, 186-187;
affected by extent and speed of
obtaining a true index number
transportation, 88 ^/tfroved to be
•for, 207-20S; amount to three
unaffected by quantity of moneyper cent of total business transac
or of deposits, 151-154; changes
tions in United States, 226.
in velocities affect prices but not
quantity of money or volume of Walker, Francis A., works by, cited,
8, 11, 251, 265, 333.
trade, 164-165; effects on, of
increase in volume of trade, 165- Walras, scheme of a gold standard
with a silver regulator suggested
168; / before, during, and after
by, 328-329.
crises, 270;/statistics relative to
that of banlc deposits from 1896- Walsh, C. M., cited, 199, 208 n.,
223, 225, 393, 394, 396, 397,
1909, 282-285; statistics of circu
398.
lation of money from 1896-1909,
285-290; velocity of circulation Wealth, defined as material objects
owned by human beings, .1; two
of money proved to have in
essential attributes of, materiality
creased only 10 per cent in thirteen
and appropriation, 1; classifica
years, 304-305 ^ of money shown
tion of, under three heads, real
to be twenty-one times a year,
estate, commodities, and human
(1909), 305-306; of deposit

INDEX

beings, 1-2; possibility of measur
ing, in physical units, 2-3; trans
fer, exchange, price and value of,
defined, 3-4; ownership of, or
property, 4; meaning of “ bene
fits of wealth,” G.
Weighted averages, 199-203, 349352.
Wells, David A., referred to, 176.
White, Andrew D., Paper M oney
Inflation in France by, cited,
252.
White, Horace, M oney and Banking
by, cited, 47.

Wicksell, Knut, article by, cited, 59,
60.
Workmen, relative adjustability of
price of services of, 186-187.
Y
Yale University, statistics of rapidity
of individual turnover at, 167,
379-382.
Z
Zizek, Franz, work by, cited, 349.
Zuckerkandl, cited, 14 n.

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515

Full text of The Purchasing Power of Money : Its Determination and Relation to Credit, Interest and Crises

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