View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

THE THEORY OF INTEREST

THE MACMILLAN COMPANY

.

NEW YORE * BOSTON * CHICAGO DALLAS
ATLANTA
S A N BpANClscO

.

MACMILLAN 8t CO.. LIMITED
LONDON * BOMBAY * CALCUTTA
MBLBOMNE

THE MACMILLAN COMPANY
OF CANADA, LIMITPD
TORONTO

i

3

I

i

THE
THEORY OF INTEREST
ds DeterPnCned by

IMPATIENCE
To Bparud I w m e
and

OPPORTUNITY
To Invest I t

BY

IRVING FISHER
PROBE880R O F ECONOMICS, YALEUNIVERBITY

.C1

~

NEW YOEX

THE MACMILLAN .COMPANY
1930

All rights reserved, including
the right of reproduction in
whole or in part in
form.

-

sat up and electmtyped. Publkhcd March, IQ)a

TO
The Memwy
OF

JOHNRAE
AND OF

EUGEN VON BOHM-BAWERK

w

WHOLAIDTHE FOUNDATIONS
UPONWHICH
I HAWENDEAVORED

5rs

TO

BUILD

ERRATA
Page xxvi, chart title 45: for ‘‘P” resd P‘ ”; ohart title 46,
t&(j line: for rcj%*11 4rrp/tg;l
Page 182,line 5: for “etTeot” read “&e&.”
Page 305, line 1: for “i” read “4.”
Page 418, line 5: for ‘ I + ” read ‘‘ Page 423, sixth line from bottom: for “6.7” read “7.3.”
page 424, in chart title : for lCp,PI, p r PK1XNI P , P’, F.,’
Page 426, line 2: for “P’ and P” read “P’ and p ” ; line 4:
for tlprtl read Uptl; he7: for Upt21 md.lLF.lt
Page 442, line 6 : for “leaves” read “leaving”; line 10, for
“leaves” read “leaving.”
.jl

PREFACE

THEtremendous expansion of credit during md since
the World War to finance military operations &s well aa
post-war reparations, reconstruction, and the rebuilding
of industry and trade has brought the problems of capitalism and the nature and origin of interest home afresh
to the minds of business men as well as to economists.
This book is addressed, therefore, to financial and industrial leaders, as well &s toprofessors and students of
economics.
Inflationduringandsince the Warcausedprices to
soar and real interest rates to sag in Germany and other
nations far belowzero: thus impoverishingmillions of
investors. In all countries gilt-edge securities with fixed
return became highly speculative, because of the effect
of monetary fluctuations on real interest rates. After the
War the impatience of whole peoples to anticipate future
income by borrowing to spend, coupled with the opportunity to get largereturnsfrominvestments,
raiised
interest rates andkeptthemhigh.Increasednational
income has made the United States a lender nation. At
home, real incomeshavegrownamazinglybecause
of
the newscient&,industrial,
and agriculturalrevolutions. Interest rates have declined somewhat since 1920,
but are still high because the returns upon investments
remain high. Impatience to spend has been exempli6ed
by the organization of consumers’ credit in the form of
financecompaniesspecially organized to accmamodate
and stimulate installment sellingand to stasand
stabilize consumption.
vii

PREFACE
This book, The Theow of Interest, wasbegun aa

viii

’

8

revision of The Rate of Interest, which was published in
1907, and has long since been out of print. Requests for
another edition of that work have been made from time
to time; but I have postponed it year by year for over
two decades, becauseI wished to revise the presentation,
and to rewrite those portions which,if I may judge from
criticisms, have not been understood.
I have considered the criticisms of the form& book
whichhavecome to my notice,andhave, as a consequence,modified the form. of presentationmaterially.
Though,insubstance, ,my theory of interest has been
altered scarcely at all, ita exposition has been so amplified
and recast that it will,I anticipate, seem, t o those who
misunderstood my first .book, more changed
than it seems
t,o me. The result has been a new book, The Theory of
Interest, a complete rewriting of the former book, with
additions of new material.
I wm encouraged to write this new exposition of the
theory of interestbyvariouseconomistsandleading
business men and especially by Mr. Oswald T. Fa&, one
of the representatives of Great Britain at the Versailles
Peace Conference, who was kind enough
to say that he
had gained more insight into economic theory from The
Rate of Interest than from any ot.her book.
Years after The Rate of Interest waa published, I suggested the morepopula,r term “impatience” in place of
“agio” or “timepreference.” This catchword has been
widely adopted, and, to my surprise, has led to a widespread but falseimpression that I had overlookedor
neglected the productivity or investmentopportunity
side entirely. It a b led many to think that, byusing
the new word impatience, I meant to claim a new idea.
Thus I found myself credited with beiig the author of

PREFACE
ir
“the impatience theory” which I am not, snd not credited
with being the author of those parts laeking any ca.tchword. It waa this misunderstanding which led me, after
muchsearch,toadopt
the catchword“investmentopportunity” aa a substitute for the inadequate term “productivity” which had come into such general u
8
e
l
.
In economics it isdifficult to proveoriginality; for
the germ of every new .idea will surely be found over and
over again in earlier writers.For myself, I would be satisfied to have myconclusionsaccepted aa true even if
their origin should be credited by the critics wholly to
earlier writers. While I hope I may be credited with a
certain degree of originality, every thorough student of
this subject will recognizeinmy tretttment of interest
theory features of his own. My own theory is in some
degree every one’s theory. Every essential part of it wtts
at least foreshadowed by John Rae in 1834.
If this combined “impatience and opportunity” theory
can besaid to be at alldistinctfrom all others, it is
because it explicitlyanalysesopportunity,and
fits togetherimpatienceandopportunityandincome.
The
incomeconceptplays the basicr61e in the theory of
interest. I mntwe to hope that the theory, as here presented, will befound not so much to overthrow aa to
co-ordinate previous theories, and to help in making the
chain of explanation complete and strong.
‘This term, investment opportunity, seem ta be the nearest expres
sion in popular language to suggest or denote the technical magnitude t
employed in this book. Thefullexpression for r is the late of return
over cost, and both cost and return are differences between two optional
mcome etreams. So far aa I know,no other writer on interest has made
w e uf income stretuns and their dzerences, or rate8 of return over cost
per annum. Thenearest approximation tothisussge eeems to be in
thewritingsof
Professor Herbert J. Davenport,particularly his Ecom
i
r
x of Entreprise, (Macmillan, Mew York, 1913) pagea 368, rrS,
381, 39&,X6, 396, 410, 411.

I

PREFACE

Chapter I is added for the purpose of giving the reader
who has not read my Natwe of Capital and Income, a
brief summary of ita contents.
I have, for the first time, in a book on pure economic
theory, introduced mathematics into the text, instead of
relegating it entirely to appendices. This is done in view
of the increasing use of mathematics and the increasing
numbers of students equipped to read mathematical economics and statistics.
Parts of Chapters I1 and XIX, with their appendices,
form inmymonograph,
haveappearedindifferent
“AppreciationandInterest.”Thanksaredue
to the
for permission to use
AmericanEconomicAssociation
parts of thismonographunaltered.Since
it appeared
three decades ago, the view expressed in it (that appreciation or deprecbtion in the value of moneyshould,
and to some extent does, lower or raise the rate of interest)hasgainedconsiderablecurrency,andhas
been
illustrated and verifiedby war-time experience.
Chapter XIX is made up, for the most part, of a new
and intensive studyof the relat.ionships existing between
prices and interest rates. These relat,ionships are tested
by new andrigorousstatisticalmethods
of analysis.
While the conclusions
presented
as
the resuh of these
analyses are onlytentative, yet they are, I think,worthy
of further statistical
studies
into
t,he
relation
of interest
rates on the one hand, and prices, business activity, bank
.he onloans
bank
reserves,
and
In the preparation of the original book I received important aid from many persons. Finance MinisterJ36hmBawerk,
whose
writings
on
i n h e s t and whose hi&ory
of the subject are clmsic, kindly read and criticized
the
chapterdevoted to histheory of interest.Afterward,
in the third edition of his Positive Theorie des KapitaZm

z

4

;

r
f
,

I
1

.

I

*i

xi
and the Exkume thereto, he devoted morethan 100 pages
to discussions and criticism, favorable and unfavorable,
of The Rate of Interest aa it first appeared. I have taken
account of his criticism in Chapter XX.
In preparing this book I have received suggestions and
assistancefrom so manyeconomistsandothersin
the
United States andabroad, that it isimpracticable to
mentionthem all byname.My
aasociatea, Dr.Royal
Meeker, Dr. Max Sasuly,and Mr. Benjamin P. Whitaker,
as well as in gatherhave contributed in helpful criticism,
ing material, preparing the manuscript for the printer,
and reading the proof. I am especially indebted to my
brother, Mr. Herbert W. Fisher, for his suggestionsaa to
style and the manner of presentation, and to Professor
Harry G. Brown for his criticism of my statement of the
opportunity principle. Others who have helped me especiallyare:Prof.Lionel D. Edie, Mr. C. 0. Hardy, Mr.
R. G. Hawtry,Prof. Frank H. Knight,Prof.
J. S.
Lawrence, Prof. Arthur W.Marget., Prof. H. B.Meek,
Prof. Wesley C. Mitchell, Mrs. Clara Eliot Raup, Prof.
HenrySchulta,Prof.HenryR.Seager,
Mr. Henry
Simons, Mr. Carl Snyder, Prof. Jacob Viner.
I have also received valuable suggestions from members
of myclass in the economics of distribution;namely,
Howard Berolzheimer,A. G. Buehler, FrancisW. Hopkins,
Richard A. Lester,Daniel T. Selko,AndrewStevenson, Jr., and Ronald B. Welch.
IRVING
FISHER
PREFACE

Yale University,
January, 1930

SUGGESTIONS TO READERS
1. The general reader will

be chiefly interested in Parts

I, 11, and IV.

2. Readers with a distaste for mathematics will find the
essential theory stated in words in Part 11.
3. Thme interested in stathtical anairyak should read
Chapter XIX.
4. The Appendix to Chapter XIX contains the statistical
tables used in the analysis presented in the text.
5. The analytical table of contents, the index,and the
runningpageheadingshavebeenconstructedwith
especialreferenceto the varyingneeds of different
classes of readers. The bookpresents
a complete
theory of interest, and it is hoped that those who approach it from special viewpoints may, in the end,

read it all.

f

?

;
:.
y

i

CONTENTS
FIRST SUMMARY

.

PART I. INTRODUCTION
.

. . . . .

CXAtFEPLI

1-111

. . . . IV-IX
IN MATHEMATICS
. . X-XIV
PART111. THETHEORY
PART
IV. F’URTHER DISCUSSION . . . XV-XXI
PART
11.

THETHEORY
IN WORDS

CONTENTS

xiv

SECOND SUMMARY
PART I. INTRODUCTION

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

CEAP-

I. INCOME
m CAP~AL
11. MONEYIN-T
AND RFALIN-T
111. SoMs COMMON
%ALW

PART II. THE THEORY IN WORDS
,
IV. Tmn PREFERENCE
(HUMANIMPATTENCB) ,
V. F ~ APPROXIMATION
T
TO THE THEORY
OF IN-T
(Aasuming Each Pereon’sIncome Stream Foreknown and
Unchangeable Except by Loans) .
,
VI. SECONDAPPROXIMATIONTO THE THEORY
OF INTEREBT
(AssumingIncomeModifiable
(1) byLoansand
(2) by
Other Means)
VII. THE INVESTMENT
O P P ~ R ~ ~ N IWINTY
VIII. DISCUSSION
OF THE SECOND
APPROXIMATION
,
IX. TED APPROXIMATION TO THE THE~RY
OF INTEREBT
(Aesuming Income
Uncertain)

.

?A-

3
36
45

. . .

.

61

. . . .

.

99

.
.

125
150

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

. .
. ..
. .
. ..
I

.
.

178

206

PART 111. THE THEORY IN MATHEMATICS
X. FIRST APPROXIMATION IN GWMETIUC
TERMS, .
. , 231
XI. SEGWND
APPROXIMATION
IN GEOMEEUC
TERMS
. , . 263
XII. F ~ S TAPPROXIMATIONIN TWMSOF FORMULAS
. . . . 288
XIII. SECUND
APPROXIMATION
IN TEEMSOF FORMULAS
. . . . 302
XIV. THETHD APPROXIMATION UNADAPTED
TO MATHBMATICAL
FORMULATION .
. . . . , . 316

.

.

.. . .. .

.

PART IV. FURTHER DISCUSSION
IN ECON~MICZ
.
325
XVI. RELATION
OF D m m AND
~ INVENTION
TO I N ~ B
R TA 341
~
XVII. PEZ~SONAL
AND BUSINESS
LOANS
356
XVIII. BOMB ILLUSTBllnVE FACTS
,
372
XIX. THEREIATIONOF INT~BBPBT
TO MONWAND Pmm
399

XV. THEPLACEOF IN-T

. . . . .
. . . . . . . . .
. . . - .
.
...
. . . . . . . . . .
I

xx. OBaEXTIONS CONBIDES3D
SWbfMABY . . . , .

XI.

APPENDI~

BIBKWHY

a

452
...,.. .
493
. . . . . , . ,. . . , , . . . . . . 607
. . . , . . . . , . . . . . . 543
e

,

INDHX......,,............

551

. .

ANALYTICALTABLE OF CONTENTS
CHAPTER I
INCOME AND CAPITAL
D 1. S v a r m . OR ENJOYMENT.
INCOMBI
5 2. OBJECTIVE.
OR REAL.
INCOME
(OUR“LMNo”)
5 3. COSTOF LIVING.
A MEASURE
OF REALINCOME
5 4 . COSTOF AN ARTICLE
vs . COSTOF ITSUSE
8 5 . MEASURING
AT THE DOMESTIC TH~E~HOLD
5 6. MONEYINCOME
. . . . . . . . . .
$ 7. CAPITALVALUE
. . . . . . . . . . .
0 8. THERATEOF INTEREST
5 9. DISCOUNTING
Is FUNDAMENTAL
8 10 COSTS.OR NFYJATIVEINCOME
5 11. THEDISCOUNT
PRINCIPW, APPLIED . . . . .
8 12. DOUBLE
ENTRYBOOKKEEPING
5 13. SIMPLICITYUNDERLYINGCOMPUCATIONS
5 14. CAPITAL GAINNOT INCOME
.
5 15 CAPITALINCOME
RELATIONS
5 16. APF-LICATTON
TO THIS BOOK
5 17. CONFUSIONS
TO BE AVOIDED
8 18. AWORKINQCONCEPT
OF THE RATEOF IN-T

.... ....
.

.

.

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

.
.
.
.
.
.
.
.
.

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

.
.

.
.
.
.

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

?A61

3
5
6

8
9
10
12

13
14
15
16
18

22
25
28
29
31
34

CHAPTER I1

.
B 3.
$1
5 2.

5 4.

MONEY INTEREST AND REAL INTEREST
INTRODUC~ON
ASSUMINO
FOBWIGHT
LIMITATIONS
OF THEORY
REAL AND MONEY
IN-T

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

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

36
37
40
41

CHAPTER I11
SOME COMMON PITFALL8
Pl . INTWDUCTION
% 2. THE ITA AT ION EXPLANATION
OF ~NTEEWT
5 3. INTEFJBT-TAXINQ S w m ALLOPFVXITION
5 4 . N APRODUCITVITY
~
EXPLANA~ONS
0 5 . TWOO T H ~PFPFALIA

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

. .. .. .. .. ..

.........
.............
Ip

ds
48
52
53
57

xvi

ANALYTICAL
TABLE

OF CONTENTS

CHAPTER IV
TIME PREFERENCE (HUMAN IMPATIENCE)
PAQS

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

.
.
.
.

51
FOB PRFSENT OVER FUTURE INCOM0
5 2 REDUCZXON
TO ENJOYMENT
INCOME
0 3 IMPATIF.NCE
DEPENDS
ON INCOME
. . . . . .
8 4 INTEREST
AND PRICE THEORY
. . . . . . . .
5 5. SPECIFEATTONS
OF INCOME
. . . . . . . .
8 6. THEI N ~ U E NOFCMEFS
E SIZE . . . . . . . .
8 7 THEINFLUENCE OF TIMEsHAP0
8 8. THEIN FLU EN^ OF RISK
5 9 T H PERSONAL
~
FACMIR. . . . . . . . .
D 10. THEPWSONAL
FACTOR
SUMMARIZED
. . . . .
0 11 INCOMB
RATHER THAN’CAPITAL
IN THE LEADINQ
Ram
5 12 IMPATIENCE
SCHEDULES
. . . . . . . . .

. . .
. ..
. ..

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

.
.
.
.

61

*

6

3

e6
6 8
7 0

7 2
. 7 3
. 7 6

. . .80

. . .89

. . .
. .

91

.94

CHAPTER V
F I B T APPROXIMATION TO THE THEORY OF INTEREST
kssuming EachPerson’sIncomeStream
Foreknom and
Unchangeable Except by Loans
5 1. HYPO THESE^ OF FIRSTAPPROXIMATION . . . . . . . . 99

. . . .
.
.
.

g 2. INCK“PREWBIBED

0 3.

54.

5 5.
86.
8 7.
8 8.
8 9.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

IMPATIENCE
ALPXUNQINCOME
BY LOANS
ALTERINQINCOMEI
BY S m
I N W T INERADICABLE
. . . . . . . .
“MARQINAL”
PRINCIPLE IS “MAXIMUM” PRINQPLPl
MARKET
EQUEIBRIWM
. . . . . . . . .
FOURP r r r ~ a a ~ s
E~JWALIZATION

OF

.
.
.
.

. . . 102
. . . 104
. . . 106
. . . 112

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

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

116
117
119
121

CHAPTER VI
SECOND APPROXIMATION TO THE THEORY OF INTEREST
Assuming Income Modifiable (1) by Loans and (2) by Other Means

.

. . . . . . . . . . . . 125
. . . . . . . . . . . 129

8 1 THENEW HYPOTHES~
5 2. OFTIONALINWMB
STREAMS
8 3. THETwo KINDEOF CHOICE
4 4 . OPPORTUNITYTO INVESTBY CHANWOF

. . . . . . . . . . .
USE OF C m f i . .

8 6. THE REASONINQ
Nm ‘‘Cmamn”.
06. SUMMAF~Y

. . . . . . . .

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

135
141
144
147

ANALYTICAL
TABLE

xvii

OF CONTENTS

CHAPTER VI1
THE I N W T M E N T OPPORTUNITY PRINCIPLES

. . . . . .
$ 2. THEMETHODOF C O M P A IADVANTAQM
U~
. . . .
8 3. THECONCEPT
OF RATE RETURN
O m C o e ~. .
8 4 . THE PRINCIPLEOF RETURNO m COST . . . ,
8 5. MAFXXNAL
RATEOF Romntv O m COST . . . .
0 6. THEILLUSlRATION W CU’ITINQA F-T
. . . ,
7. OTHEB SIMILAR
ILLUETBATXONS
. . . . . . .
58. THECAEEOF P E W ~ ARL ~ N . S. . . , .
8 9. THEGENU CASE . . . . . . , . . .
8 10. RAN^ OF CHOICE
D E ~ N DON
SI
~ R A .T~.

. . .
...
, . ,
. . .
, . .
. . .
. . .
. . ,
. . .
. . .
8 11. THEINVESTMENT
OPPORTWNITP
~INOIPUS S W A R I ~
. .
$12. INlTlWS”FION
HUMANIMPATKEINCE AND INVT8TMENT OPPORTUNITY
. . . . . . . . . . . . . . .
8 1. ELI-

AND INELIQIBLE OFTIONS
OF

I

i

5

?Am
160

162

155
158
159
161
166
167
168
170
175

OF

176

CHAPTER VI11
DISCUSSION OF THE SECOND APPROXIMATION
8 1. OPpORToNITY RJCDUCEZI TO h W B T TERMS
5 2. INVESTMENT
OPPORTUNITY
ESSENTIAL .
0 3. OPTIONS DIFFERINQ IN TIMES H m ONLY .
. .
$ 4 . THE IMAQINARY “HARD-TACK’’
ILLUSTSATION
.
8 5. TEE IMAQINARY
‘‘fiQ8”EXAMPLE
16. THE IMAQINARY
“SHEEP” EXAMPLE
p 7. OPPORTUNITIES
AE TO R m m , RENGIKALB,
BET~WWTB
8 8. OPPORTUNITYTO CHANQE
THE APPLICATION OF L m
8 9. FLUCl“JATION0 IN 1NTE%E$ST RAW S E L P ”
8 10. WIDEOPPORTUNITIEB
STABIWZEINTPBWT

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

.

..
.
.
.
.

.
*

.
. .

178
181
184
le8
191
192

. .
. .
. . 184
. .200
. .
. . . . . . .m4
, 2 0 2

CHAPTER IX
TFiIRD APPROXIMATION TO THE THEORY OF INTEREST
Assuming Income Uncertain

.
.
.
.
. .
.
. .
.

8 1. Mom THANONE RATIO
OF IN-T
. . . . . . .
12. R~LATIONB
BETW~IN
THEIVARIOUS
R A. ~
.
8 3. LIMITATIONS ON LOANS . . . . .
. .
.
84. RISKAND SMALL h A N 0 . . . . . .
. . . .
05. SALABIUTY AB A S
~
.W . . ~ ,
50. Gwr~u.4~
INOOMEI
RISKS .
. .
8 7. 81ccwrm~1s
C~40srrmooAS TO RISK .
. . .
0 8. E m OF RISK ON THE Suc PIUNCI~BS
.
. .
0 9. SWMMUY
OF mT H B
~ U~O X I M A T I O N B ( N u M ~
1,2,3)
.

..
. ..
..
.

.
.
.
.
.
.

f-w

..

208
208
210

. . 213
215
. .. .. 216
218
.
p2

psae 288

wiii

ANALYTICAL TABLE OF CONTENTS

CHAPTER X
FIFtST APPROXIMATION IN GEOMETRIC TERMS rim
f 1 INTRODUCITON
231
0 2. THEMAPOF THISYEAB’SAND NEXTYEAR’SINCOME
231
0 3. TEEMABWLINE
23.5
1 4. TEEWILLINQNESS L I ~
238
0 5. THETwo LINEE COMPAFZEU
240
1 6. THE WHO^ FAMILY
OF MAR^ LINES . . . . . . . 242
$ 7. MANYFAMILIES
OF WI~NONESE
LINB . . . . . . . 244
$ 8. A TYPICAL
FAMILY
OF WILLINQN~~SS
LINES
246
$ 9. TIMEPREFE~ENCE
MAYBENEQATIVE
. . . . . . . . 248
8 10. THEPEUSONAL AND IMPEWONAL
INFLWENCW
ON IMPATIEN~
. 249
8 11. DECIDINQ
W H E T HTO
~ Bomow OB LEND. . . . . . . 250
8 12. INTEREST
hm AN INDIVIDUAL
252
8 13. HOW AN INDIVIDUAL
b.JUSTa HIS INCoMD PWmON TO TED
MAR^ . . . . . . . . . . . . . . . . 253
814. MARKEP
E~UIUBRITJM
. . . . . . . . . . . . . 255
0 15. THEFOUR
PBINCIPLDS
CHARTED
258
8 IS. THEG E S M ~ MEPHOD
C
. . . . . . . . . . . . 259
$ 17 RELATION
TO SUPPLY
AND DEMAND
. . . . . . . . . 260

.

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

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

.
.
.
.

...

.......

. . . . . . . . .

. . . . . . . . . .

.

CHAPTER XI
SECONDAPPROXIMATION IN GE!.UMETRIC TERMS

I 1. IN!IRODUCRON
. .

. . . . . . . . . .
. . . . . . .
5 3. THEINDIVIDUAL’S
ADJUSTMENTWITHOUT
LOANS . . .
D 4. INDMDUAL
ADJUSTMENT WITH LOANS . . . . . . .
05. THEDOUBMI
ADJUSTMENT DISCUSBW
. . . . .. .
$ 6. MAEW EQUILIBFWM . . . . . . . . . . . .
$ 7. THENAWRE THE OPPORTUNITY LINEI
DI~CUBSED
. .
0 a. INVESTMENT OPPOBTUNITYAND IMPATIENCE . . . . .
$ 9. CAN IN-T
DISAPPW? . . . . . . . . . .
.

5 2. TEDINVEBTMENT
OPPOBTUNITYLINE

OF

I

.

.

.
.
.
.
.
.
.

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

I10. D m INTEZWT
STIMULATE SAVINQ?
Dl1 RELATION
TO SUFTLY AND D ~ M A N
Cwvm
D

.

CHAPTER XI1
FIMT APPROXIMATION IN TERMS OF FORMULAS
0 1. CASEor Two Y w AND THBEE
INDMDIJAW
288
$ 2. IMPATIBNCE
P
B
N
Im A (THBEE
E~~JATIONS)
2w)
13. I~~n’llsprm
~ N C I P I ZB. (THBEE
EQUATIONEX)
280

.

......
.....

.....

xix

ANALYTICAL TABLE OF CONTENTS
!
i

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

.
.
.
.
.

Q 4. MARKET PEINA. (TWO EQUATIONS)
.
8 5. "gcr
PRINmU B. (THBEE EQUATIONS)
SB. COUNTINQ
EQUAITONS AND UNXNOWNS
8 7 . CASEOF m YEUU AND n INDMDUALE
,
0 8. IMPATIENC~D
F'IUNA. (n (m - 1) E~UATIONS)
0 9. IMPATIENCE
PRINCIPU
B. (n (m- 1) EQUATIONS)
8 10. MAR^ PEINCIP~
A. m E!~UATIONS
,
9 11. MARKEX
PRINCIPLE
B. n J ~ J A T I O N ~
.
1 12. COUNTINQ EQUAnONS AND UN'KNOWNS
8 13. DIFFE~ENT
RATES OF IN-T
FOB ~
N YEUS T

.
.
.
.
.

.
.
.
.
.

...

...
. . .
. .

* . .

CHAPTER XI11
SECONDAPPROXIMATION IN TERMS OF FORMULAE
81. INTRODUCTION
, ,
302
303
8 2. IMPATIENCE
PRINCIPL~C
A. (n (m-1) EOUATXONS). .
8 3. IMPATIEX~
PRINCIPLE
B. (n (m 1) E~UATXONS) ,
304
4. PRINCIPL.E A. (m EQUATIONS)
.
304
304
15. M.C+m P W N m U ? B.. EQUATIONS) ,
. .
16. INVESTMENT
OPPORTUNIWPRINCIPLE
A. (n EQUA"ION8)
305
8 7. OPFORFUNITYPRINCIPLE
B. (n (m- 1) FLFJATIONS)
306
8 8. COUNTINQ THE EQUATIONS AND UNKNOWNS
. 307
0 9. RECOXCILINQ
m
m NUMBBXS
OF E~UATIONSAND UNKNOWNS309
D 10. Z m (IS N m m RAT=OF I N ~ S , T .
311
5 11. THBFOBMULA
M ~ T H OHELPFUL
D
.
312

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

.
.
.
.
.
.
.
.
.
.

.

CHAPTER XIV
THE THIRD APPROXIMATION UNADAPTED TO
MATHEMATICAL FORMULATION
0 1. INTRODUCTION
,
D 2. THESur S m OF Foaaanws INCWPLWIW
.
03. CON~USIONS ,

. . . . . . . . . . . . . . 316
. . . . . . 317
. . . . . . . . . . . . . a1
CHAPTER XV

01.

8 2.
0 3.
0 4.
0 6.
06.

THE PLACE OF INTEREBT IN ECONOMIC%
IN-TRATESANDVALUIWOF~
,
,
INTEWBTRAW AND VAL^ OF Smmm
IN-T
RATIBAND WAQES
,
INTP~~EBT
AND FUNCTIONAL DISIWBUTION
INTQIB~T
AND E%BONM, Ihs-ox
.
THBLOANM ~ m mAB A HIUHWAY FOB RBDI~TRIBUTION
,

.

.
.. . . .
.
.

. ...

325

. . . . . .m
. . . . . 328
. . . . . . 331
. . . . . . 333

. a38

xx

ANALYTICAL TABLE OF CONTENTS
CHAPTER XVI
RELATION OF DISCOVERY AND INVENTION TO
INTEREST RATES

5 1. THB F'IRST E m OF EACHIMPOBTANT
D I S C O ~ AND
Y INVBINTION Is TO INCREASE
THE RATEOF IN-T
. . . .
52. INVENTION
CAUSES
DISPERSION OF IN-T
RAW . . .
p 3. INWINTION
CAUSES REVALUATION
OF CAPPTAL
. . . . . .
5 4. THB ULTIMATE
EFFEC~S
OF INVENTION
ON I
N ~ RATE
T .
8 5. THE PRESENT
A N AGE OF JNWTION . . . . . . . .
5 6. MASSPRODUIX'XON OF INVENTIONS .
. . . . .
0 7. EFFIW~
ON INVESTMENT
. . . . . . .
. .
5 8. IMPORTANCE
OF INVENTION
. . . . . .
. .

.

.. . ..
. .

.

341

342
343
345

347

349
352
354

1

:

CHAPTER XVII
PERSONAL AND BUSINESS LOANS

PERSONAL
LOANS . . , . . . . . . . .
BUSINESSLOANS . . .
. . . . . .
SHORT
T ~ W LOANS
M
. . . . . . . . . .
LONQTERM~ A N .S . . . . . . . . . .
5.5. BUSINESSvs. PWONALLOANS. . . . . . .
5 6. PURpfXE! OF BoRROWINQ TO INCREASE PRESENT INCOME
$7. P U B L I C h A N S .
. . .
. . .

8 1.
8 2.
5 3.
5 4.

.

.

.

-

.
.
.
.
.
.

.
.
.
.
.

.
.
.
.

.
.

356
359
330
363
365
369

369

,

t.
3

a

CHAPTER XVIII
SOME ILLUSTRATIVE FACTS

.

. . . . . . . .
. .
.
5 4. &UMpLss OF INFLUENCEI
OF &MPOBITION OF INCOMB
p 5. EXAMPLEB
OF INFLUENCE
OF RISK . . . . , .
8 6. EXAM- OF INFLUENCE
OF TIMESEN0 .
.
5 7. RISINQINCOME
MEANSH ~ Q HINTEREST
RATFA. .
$ 8. E m n OF CATASTROPHES
ON INTW~~ST
. . . .
8 9. E x ~ ~ aOFs sINFLUENCB
OF ha?xoDrQTP OF INooMlP
510. SUMMABY
. . . , . . . . . . . . . .

.

81. INTEODUCITON
, .
.
.
0 2. EXAMP- OF INFLUENCES
OF PEBBONAL C H h a A ~ S T f C d
l 3 . EXAMPLF~
OF INFLUENCZ
OF POVERTY
, .
, ,

.
.
.
.
.
.

,

.
.
.
.

. .
. .
. .
. .

. .
. . .

372
374
377
381
381

383
387
391

398
398

?

ANALYTICAL TABLE OF

CONTENTS

xxi

CHAPTER XIX
THE RELATION OF INTEREST TO MONEY AND PRICES

8 1. P ~ l mCHAN-

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

Pun

IN-T
RATES
399
$ 2 . UNITED
S T ACOIN
~ AND CURBENCY
BONW
401
$ 3 . GOLDAND RUPEIEBONDS
403
p 4. MONEYIN-T
AND REALIN-T
. . . . . . . . 401
g 5. REALIN-T
VARIESM o ~ aTHANMONWY
IN-T
. 411
416
$6. INTEZEST
RATES AND RATESOF PRICECHANQE
5 7. SHW Tmrws IN-T
R A AND~ h
a
m IN TEIP U X I ~
S T A .~ . . . . . . . . . . . . . . . . 425
429
5 8 INIXIRFST RATEXAND PBIm IND8 9. ELIMINATION
OF -DE
. . . . . . . . . . . 431
438
0 10 RELATIONS
OF h
as AND INTEBEST
IN443
0 11. RELATIONS
OF INTERBIBT
TO BUSINESSAND Parcrps
444
0 12 IN^ RATESAND BANKR ~ a m m
451
513. SUMMARY
AND

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

.
.
.

. . . . . . . .

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

CHAPTER XX
OBJECTIONS CONSIDERED
452
8 1. I N T R O D U ~ O N
453
8 2. INCOME
AND CAPITAL
0 3. COSTOF PRODUCTION
AS A DFJIIZRMINANT
OF CAPITAL VAL^ . 460
$ 4. IMPATIENCE
AS A D-INANT
OF THE INTEREST
RATE. . 467
$ 5 . PRODUCTIVITY
AS A D ~ M I N A N
OFTIN-T
RATIEI. . . 470
5 6 . TECENICXLSUPERIORITY
OF P R E S ~Goom
T
. . . . . . 473
$ 7. INTEBEST
AS A CCST
. . . . . . . . . . . . . 485
487
5 8. EMPIRICAL
AND INSTITUTIONAL
I N F LON IN-T
~ ~
&TEE
0 9. CONCLUSION
491

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

. . . . . . . . . . . . . . . .
CHAPTER XXI

SUMMARY
5 1. IKTERFBT
AND PUWHASINQ
Powm OF MONEY
$ 2. THE SIX PRINCIPLES
. . . . . . . . . .
S 3. THE NATUREOF INVESTMENT
OPP~RTUNITY
8 4 . INVESTMENT
OPPOBTUNITY
FOB Socmm AS A WHM
$ 5. TIMEPEZFEEENCB
$ 6. CONCLUSION
0 7. TH~D
FTJTUBM

. . . . .

483

. . . . . .

497

. . .

494

. . . WO
. . . . . . . . . . . . . . 503
. . . . . . . . . . . . . . . . 505

. . . . . . . . . . . . . . . 505

XgiV

APPENDICES

APPENDIX TO CHAPTER XIX. THE RELATION OF
INTEREST TOMONEY AND PRICES
PAQE

8 1 (TOCH. =X, 84). TABLES
GIVING
THE BASICDATAUsm

TO

C o ~ AYE~AGB
m
ANNUAL
Rxms OF Pmm CHANGW
AND AnnR m RATES OF INTERE~T
. . . . . . . . . . . 520
8 2 (w CH. XIX, 8 6). TABLEB
Usm IN COMPVITNO
~~ER~LATIONS
OF I
N ~ Rmm
T AND Prum CHANQRS
530
AGW

. . . . . . . .

APPENDIX TO CHAPTER XX. OBTECTIONS CONSIDERED
8 1 (TU CH. xx, 5 17).WAITINCIAS A CWT? . . . . . . . . 513
BIBLIOQIWHY
543

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

INDEX

. . , . l l , . l . . I . . . . . . . ~ l

LIST OF CHARTS

.. .. .. .. . . .. .. . - . . . . . . . . .

O U T

?BI

29
1. INGOMESTNUMUNIFOBM.
a
a
30
2. INCOME
STREAM
INWUSINO
a0
3. INCOME
b~
DECSEASINCA
4. INTFSEBT
RAW BETWEEN
&FFERENT YplARB COMPABABm WITH
69
EXCHANQE R
A
m BETWEEN
DUTEFUENT~~~CIB.
5. E
OF ~ O W I N OUPON WENT
AND Fmum INWME 107
107
6. EFFECTOF LENDIXO
UPONPEESENT AND FUTURE I N m E
109m
7. E m OF BORROWINO
UPONAN INCREASINO
INCOME
%
%
$
i
109
8. E m OF BORROWINOUPONA U N I F OINCOME
~
STBfOAM
109
9. E m OF BORROWIEQUPONA DECSEMINO
INCOME
&xwd
109
10. E m OF LENDINO
UPONA DFAXWSINOINCOME STR!UM
109
11. E m OF LENDINO
UPONA UNIF~RM
INCOME
STBEAM
109
12. E
m OF LENDING
UPONA N INCMWSXNG
INCOME
STBEAM
13. E
m OF ALTERNATEBORROWINGAND LENDINQUPON A
FLUCTTJATTNQ
INCOME
BTatohma
. . . 111
14. THREETYPEB
OF INWMB
STB~UMS: “FARMINO,”
“FOBES~LY,”
AND “MINING”
,
, . .
132
15. ENLARQINOINCOME
STREAM THROUQH
DOUBLE
C E O I ,~ ,
140
10. SEUKTINQTHE TIMEFOR CUTTTNO
A FOREST
.
163
17. D-NCE
BETWEEN
TEIE BWTAND TEIE NEXTBIBT INVEEPMENT OPPORTUNITY IN THE RAISINQOF
A &OF‘.
. .
169
18. D
m
B m m THE
~ BEBTAND THE NEXTBEETINVEEP

. . . .
.
.
.
. .
.

.

.
.

. .

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

. .

. .

MBINT OPPORTUNITY
IN
SWAMP
LAND . . .

THE

DRUNINOAND

BN
-

THE

,

.

C~LTIVATINO op

. . .
MENT OPW~T~NITY
IN THE CUTTINOOF A FOWST
. .
20. ALTIQRNATINOINWTMDNT
AND Rmmm . . . , . .
21. Zmo RATEOF RETURN,
TOTAL
INCOME
F m m , CUE 1 ,
a.Z m h m w R m m ~TOTAL
,
INOOME
FrxEo, CASE2 . .
19. DIFFERENW

. .

B ~ AND
T

,

THBl

,

.

. .
. ,
. .
, .
. .

23. ANNUALINCOME
REpesamm BY Lmm INSTWAD
OF BARS, ,
24. INCOM~P
POSITION
THIBY m AND NEXTYmrt -ENTIXI
HY
POINT (PI)

A

. . . . . . .

,

169

NEXT B H ~INVESTT

.

,

,

170
170

187
188
232

. . . . 234

25. EFFECTOF B o a a o w r ~ QUPONAN INDIVIDUAL’S
I N CP
OW
~ ~ Oa38
N
26. Su-sm
Cam& M AN INDIVIDUAL’S
1w-s
p-0~
WODUW

w11w-l.
-

.

e

BY s U a 9 s S r W BOBSOWINOS AT TBE bfABK,BT RATE
: ,
,

. . . ... ...
xm

. ..m

LIST OF CHARTS

xxvi
o w *

n. V,mmo
OF IMPATIENCE R g e ~ p g ~BY
~m
THE S w n
OF THE Wl LINE . . . . . . . . . . . . . .
28. I N T H ~ ~ EOFCMl~ ~LINE
O NAND W,LINEAT Pl . . . . . .
29. I N ~ E C T IOFO MN, LINEAND 1VI LINBAT PX , . , . , .

. . . . .

30. M

PAQB

239
241

242

L I N WITH
~
R ~ z m a ~TOmWI AND W SLINES
243
31. A T m c u FAMILY
OF W LINES . . . . . . . . . . 246
32. ADJUSTINU IMPATIENCB TO M A B XR~Am OF I N ~THROUQH
T
BORROWlNO

. . . . . . . . . . . . . . . . 250

IMPATIETICE
TO M
m Rxm OF IN-T THROUGH
LBNDING. . . . . . . . . . . . . . . . . 251
34. THEFINAL INCOME
POSITION(QI)OF INDIVIDUAL
Ibm BY
TANUE~CY
OF TEE WlLINETO THB M1LINEAT QI . , . .
35. THEOPPORTUNITY(0)LINE . . . . . . . . . . .
36. W LINE^ SHOWINODIFFEWNTDE.GREESOF IMPATIENCE
AND
0 LINB SHOWINO
D ~ N RATES
T OF RETURN. . . . 268
37. THBPOINT
OF TANQENCY
( R ) OF A W LINETO THE 0 LINE . 269
38. POINT OF &UlUBFUUM WHERIU THE M LINE WHICH I S TANU ~ N TO
T THE 0 LINE AT P Is ALSO TANQENT
TO A LINEAT Q 271
39. MONTHLYA m m DISCOUNTRATES; N m YORK. . . . 395
40. INDEXES
OF SEASONAL
VARIATIONSIN INT~REST
RATEB. . . . 396
41. MONTHLY
A m w OF DISCOUNT
RATES,BANKOF ENQIAND
. 397
42. Avleuce: RAW OF A P P E E C I A ~ O N - A OF
N DIN-T,
LONDON . 409
43. THEOBETICALRELATIONOF Parm L m (P) AND INTWE~T
33, ADJUBTINO

. . . . . . . . . . . . . . . . 412
OF Pam CHAN- (P') TO IN-T
. . . . . . . . . . . . . . . . 414

RATEB(~)
44,

RUTION

TH-CAL
RAW(^)

COEtWICIENTB B&TWBBN P AND i FOR VARIOUS
YWY DATA,GEEATBRITAIN, 1820-1924; UNITED
STATES,

45. COBRELATION
LAQB.

1890-1927

46. W

l T O N

. . . . . . . .
cO~CIENT8B

m

9

. . . . . . . .

AND

418

i FOR VARIOUS DIE-

'IsfBUTIONS OF LAO.
I8 THB COMBINW E"AT
ANY
POINT
.OF TIME OF THB INFLUENCEI
OF P~ECEDINU
P's WITH

47.

48.

LAOSDISTRIBUTEZL
YE~ABLY
DATA,GREITBRITAIN,1820-1924 421
P AND i FOR VARIOUS D15
'IgIBUTIONS OF LAO. P IB THIP COMBINED EFFElGp AT ANY
POINT OF W E OF THE h F " m OF -IN0
P"S WITH
LAW Dmmnnm. Y-Y DATA,
UN- &A=, 19olnSn . 422
Cwvan,SHOWINO
P, P', P AND i.Y ~ DATA,
Y G ~ BIUTAIN,
T

CbBIlFUTION C M C l E N T 8 &FWEEN

. . . . . . . . . . . . . . . . 424
DATA^ U N ~ S D
1esO-lW . . . . . . . . . oppoaitepage 428

1898-1m

49. Cwvm BHOWKNOP, P,p, AND i:QU-Y

m.

&A=,
-TION

QU-Y

mmIBbIW7EiN

P AND i FOB VAXtOnB ha.

DATA,
U

1~1027

N &A=,~

. . . . . . 426

t

LIST OF CHARTS
GauLT

51.

&REELATION

m
C
8
N
lT
s

AND

i

mii
VABJOWS D
I
6

rmaunom OF LAM.
IS THE coar8Ihw, EppB(;T AT ANY
POINTOF TTME OF THI IN~UEWCB
w PRFAXCDINQP"E WITH

LAM D 1 8 l ' d m . & U A R m Y DATA,UNfiarr & A m , 1890.
1927
421
52. Cmma SHOWINQ
ih
c
x
m ONE^ YIMBb m P. ~
YQABCY
~ DATA
GREAT
BRITAIN,1820-1924
oppositRpgge 429
53. C ~ B ~ ~ I COEFFICIENTS
A~ON
B ~ E E PN AND i e FOB VAEIOWE
LACS. YEABLYDATA,GHEATBRITAIN,1820-1924; UNITBIJ

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

54.

&Am,

19oO-1927

. . . . . . . . . . . . . . 430

Cmms SHOWINQ
P AND i WZTH ~ ~ ~ A I O LINE
H T TBENDs AND
PARABOLIC
TRENDE.
YEABLY
DATA,GFSWTBIUTAIN, 1820-1885
55. C!umm SHOWINQ
P AND i wrm ST~AIOHTLINB TElENne AND
PARABOLIC
TRENDS.
YEARLYDATA,GBIEAT BRITAIN,
1865-1897
5 6 , C m v ~ sSHOWINQ
P AND i WITII STU.UQHT LINE TBENDS AND
PABABOLIC
TRENDS. YEABLY~DATA,
GUWTBEITMN, 1888192p
57. Cmvm SHOWINQ
P AND i WITH S ~ ~ Q LIND
H T TRENDS
AND
PARABOLIC
TREKDS. YEARLY
DATA,GWT BRITAIN,
1900-1927
58. COWSLATION
COEFFICIENT^ BEIWEEN
P AND i WITH QTRAIQET
LINEm D S ELXYINATED.
YEARLY DATA,
GWT B ~ A I N18%
,
1965;1885.1897;1897-10!&: U N f
hm
~s
, 1900-1927

. . .

433
434

435
436

437

LIST OF TABLES IN TEXT
rum

TmLm

1. h

a Pummmrn OF T-

INDJYXDULS
WITH Dmm-

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

.
.
.
.
.

.
.
.
.

.
.
.
.

.. . .
.. .
. .. .

~TINCUMES
96
2. THET ~ ~ gOPTIONAL
ar
INCOME
STBELAMB
, 134
3. MININGAND FARMINO
Usn COMPAILEH)
137
4. MININQAND F o m m Urn C O M P ~
138
5. PBESENT
V A LOF~ THE T H OFTIONS
~
AT THW J ~ B X I W N T
RAW OF INTETBEET
142
6. FARMINQ
AND l b u ~ n r yUSP &MPAUBD BY M m ~ ~ oOF
n GMPARATIVE A D V A N T A ~
153
7. FAEMINQ
AND FORE~TRY
Usn COMPAHSI IN =MS OF R A OF~
~ M J F C N o m &ST
.
,
166
8. OFTIONAL I N m M E s FROM FOFCBT
,
, , 162
9. T H O~R I ~ N AOPFIONAL
L
INCOME
b M a OF FABMINQ,
FOBmmy, AND MININQ
,
,
172
10. THEOFTIONAL
INCOME
QTRMMs OF FABMING,
Fo~nam,AND

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

. .. . . .
. . . .
. . . . . . .
IN-T
. . . .

MININQ,A& A ~ m m mBY THE RATBIOF
173
A OF ~INTERBSTREALIZEDFROM DAW NAMED
TO MA402
12. RATESOF IN-T
R m ~ r z a a FEOM DATIOB
NAMIKJ
TO MA11. R

TvarrPMEIN~E7lWITY.

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

13. S w m m , FAVOWAND UNFAVOWBLE
,
14. STANDABD
DEVIATIONS
OF MONEYIN-T
AND REALIN-T

&
410
415

LIST OF TABLES IN APPENDICES
UBI

1ABbLB

I.

RATESOF IN-T

W E C U S ~ €’ram I-

. . . ... . . . . ..
. . . . . . . . . . . .
. - . . . 522
1861-1912 . . . . . . . .
Iv. PARISR A OF ~IN-T
WH-ALIO P B I IN
~DEX,
18721914 . . . . . . . . . . . . .
. 523
V. CALCUTFA
R A ~IN-T
WHOLZSALII
h a INDHX,
1861-1928 . . . . . . . . . . . . . . . 524
VI. TOKYO
R A OF ~INTERS~T
WHOLIEIALSPara 1
1887-1826 . . .
. . . . . . -525
VII. RAW OF I N ~ TREVATION
ANNUALRATES
CHANGE THB Prum LEVEL,LONDON,
18251921 . . . 527
VIII. R
A
m
IN-T
RELATION ANNUAL R A ~
CHANW THB Pam L m , NEW Y ~ K 1880-1927
,
. . 527
LONDON

AND

. .

1820-1927
,
520
11. NEW YORK RATESOF IN-T
AND W
H €’ram ~
INDEX,1866-1927
,
521
111. BEELIN RATESOF IN-T
AND W ~ a a a u g PIKCXI
l
IN*

*

AND

OF

AND

AND

9

.

.

IN

TO

OF

IN

TO

OF

IN

OF

IN

IX. RATEBOF INTEWST IN REMTION TO ANNUAL RATESOF
CHANQE
IN THE Prum Lmm, BEBUN, 1884-1912. . . . 528
X. R A OF~ INTPPLF~T
IN RELATION
TO ANNUAL RAITWOF
CHANWIN THE PRICE
LEVEL,
Pms, 1872-1914 . .
528
RAW OF IN-T
IN RELATION
TO APPBB~CLATION
OF M o m ,
CALCVITA,
1861-1826, TOKYO,
1887-1928 . .
529
XII. IN-T
Y m ON BRITISH CONSOLS,
1820-1924 . .
530
XIII. IN-T
RAW ON 15 RAILUOMIBONDS, UNW &~m,

. .
.. . .
..

XI.

XIV.

1900-1927.

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

631

INTBEEELT
RATESON 4-6 MONTHS’Co” Pmm,
UNITQ STATES,
BY Q U A R 1890-1927
~,
. . .
532
xv. WHOLZWUl &IC% IN0%’ THB UNrW ST-,
ET
Qu~~t-ms,1890-1927 .
.
633
XVI. INCOME
ACCOUNT oaTmmIF WAITINGIs Coe~.
636

.

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

...

XVn. INCOMB AmWNT W h N U I T Y b WMlTNQIS C
O
W
,

ti37

i

k

PART I. INTRODUCTION
i

3

I

i

I

4

CHAFTBR I. INCOMEJ
AND CAPITAL
CHAPTER 11. MONEY
INTEREST
AND REAL1-T
CHAPTER111. SOME COMMONP I m w

CHAPTER I
INCOME AND CAPITAL1
61. Subjective, or Enjoymmt, Income

INCOME
is a aeries of
According to the modern theory of relativity the dementary reaJity is not matter, electricity, pace, time,
life or mind, but events.

e

The Nature of Capi6al and Income (firstp u b l i h i in 1906) waa
marily intended to erveaa a foundation forThe Rate of Interest whmh
immediately followed it. It waa my expectation that the student would
read the former before reading the latter.
But now, for the convenience of those who do not wish to take the
time to read The Natve of Cagital a d Income, I have written this
firet chapter summarizing it. I have availed myselfof thia opportunity
to redistribute the emphasis and to make those amendments in state.
ment which further study has indicated to be deeirable.
A friendly critic, Professor John B. Cannn
i g, suggeeta that Tlre Nature of Capital and Income ehould have been called “The Nature of
Income andCapital”and that the subjectmatter should have been
presented in reverse order, inasmuch as income is the baaia of the concept of capital value and ie, in fact, the most fundamentel concept m
economic science.
While it might not be pnrcticable to employ the revem order in
such a complete preentation as I aimed to make in The Natwe of
Capiful and Income, I have, in this chapter, where brevity may j d f y
some dogmatism, adopted Pmfeeaor Canning‘s mggeatione. This radical
change in mode of presentation may induce aomewho have already
read that book to review it now in the revem order employed in this
chapter. I hope also that some who have not read it may be moved,
after reading this chapter, to read The Nutwe of Capital and 1ncxnn.e in
full. I have tried, in thia chapter, to confinemyself m e d y to &
om
conclueions most w n t i a l as a preliminary for p r o c d i q to the QOILeideration of the origins, nature and determinants of the rate of inter&.
’The first writer to employ the concept of eventa aa fundamental in
intereet theory appeara to have been John Rae, whoee book, wigiarlly
publiahed in 1834, is commented on efsewbe.

c31

THE THEORY OF INTEREST

For each individual only those events whichcome
within the purview of his experience are of direct concern, It is these e v e n t e t h e psychic experiences of the
individual mind-which constitute ultimate income for
that individual. The outside eventshave sign;nificance
for that individual only in so far as they are the means
to these inner events of the mind. The human nervous
system is, like a radio, a great receiving instrument. Our
brains serve to transform into the stream of our psychic
life those outside events, which happen to us and stimulate our nervous system.
But the human ;body is not ordinarily regarded aa an
owned object, and only those events in consciousness
traceable to owned objects other than the human body
am generally admitted to be psychic income. However,
the human machine still plays a rcile in so far as, through
its purposeful activities, it produces, or helps produce,
other owned objects which are m a t e r a sources of desirable e v e n t e f d , houses, tools, and other goods, which
in their turn set in motion a chain of operations whose
ultimate effect is registered in our stream of consciousness. The important considerationfrom this point of
view is that human beings are ever striving to control
the stream of their psychic life by appropriating andutilizing the materials and forces of Nature.
In Man's early history hehad little command over his
environment. He was largely at the mercy of naturd
forcea-windand lightning, rain and snow, heatand
cold. But today Man protects himselffrom these by
means of those contrivances called houses, clothing, and
furnaces. He diverts the lightning by means of lightning
F&
He increases his food supply by meansof appropriated land, farm buildings, plows, and other implements.

C4l

INCOMX AND CAPITAL
Be then refaahions the food by means d milts, grindins
machinery, cook-stoves and other agencies, and by the
labor of human bodia, including his own.
Neither these intermediate processes of creation and
alteration nor the money transactions following them
are of significance except as they are the necessary OF
helpful preliminaries to psychic income-human enjoyment. We must be careful lest, in fixing our eyea on such
preIiminaries,especially money transactions, we overlook the muchmore important enjoyment which it is
their business to yield.
Directors and managemprovidingincome
for thousands of peoplesometimes think of their corporation
merely as a great money-making machine. In their eyes,
its one purpose is to earn money dividend0 for the stockholders, moneyinterest for the bondholdem, money wagea
andmoney salaries for the employees. Whathappens
after these payments are made seems too private a matter
to concern them.Yet thatis the nubof the whole arraagement. It is only what we carry out of the market place
into our homes and private liveswhich really coats.
Money is of no use to us until it is spent. The ultimate
wages are not paid in terms of money but in the enjoyments it buys. The dividend check becomes incomein the
ultimate senseonlywhen
we eatthe food, wear the
clothes, or ride in the automobile which &re bought with
the check.
$2. Objective, or Real, Income (Ow "Living")

Enjoyment income is a psychological entity and cannot
be measured directly. We can approximate it mdirectly,
however, by going one step back of it to what is c&ed
red income. Real wages, a d indeed real inwm in gen-

VI

THE THEORY OF INTEREST
wd, consist of thoae find physicai events in the

oder

world which give ua our inner enjoyments.
This red income includes the shelter of a house, the
music of a victrola or radio, the use of clothes, the eating
of food, the reading of the newspaper and all those other
innumerable events by which we make the world about
us contribute to our enjoyments. Metaphorically we
sometimes refer to this, our real income, aa our “bread
and butter.”
These finals in the stream of outer eventa are what we
call our “living,” as implied in the phrasm cost of h i n g
and earning a living. The final outer events and the inner
events which they entail run closely parallel, or, rather,
the inner eventa generally follow closely in time on the
outer. The enjoyment of music is felt almost instantaneu the piano or singer produces it. The enjoyment
ously z
of food is experienced with the eating or won after
the eating.
These outer events, sueh as the use of food, or clothes,
etc., are like the resultant inner events in notbeing very
easilymeasured. They occur largely in the privacy of
the home; they we often difficult to express in any standard units. They have no common denominator. Even the
individual who experiences them cannot weigh and measure them directly. All he can do is to measure the money
he paid to get them.

93. Cost of Living, a M m e of Red I n e m
So, just as we went back of an individual’s enjoyment
income to his red income, we now go back of his red income, his living, to his coat of living, the money measure of red income. You cannot meamre-in d o h either
the inner event of your enjoyment while eating your din-

161

INCOME AND CAPITAL
ner or the outer event of eating it, but you can find out
definitely how much money that dinner cost you In the
same way, you cannot measure your enjoyment at moving picture theater, but you do know what you paid for
your ticket; you cannotmemure exactly what your
house shelter is really worth to you, but you can tell
howmuchyou
pay for your rent, or what is a fair
equivalent for your rent if you happen to live in your
own house. You cannot measure what it is worth to wear
an evening suit, but you can find out what it costs to
hire one, or a fair equivalent of its hire if, perchance, the
suit belongs to you.Deducingsuch
equivalents is an
accountant’s job.
The total cost of living, in the sense of money payments, is a negative item, being outgo rather than income; but it is our best practical measure of the positive
items of real income for which those payments are made.
For from this total valuationof positive real income may
be subtracted the total valuation of the person’s labor
pain during the sameperiod; if we wish to compare a
laborer’s income with that of a man who does no labor
but liveson his incomefrom capital (other than himself), a “rentier.”
Enjoyment income, real income, and the cost of living
are merely three Merent stages of income. All three
run closely parallel to each other, although they are not
exactly synchronous in time. These discrepancies, as has
been intimated, are negligible as between real and enjoyment income. So also the time elapsing between the
cost of living and the living is w d l y brief. There is a
little dehy between the spending of money at the tKIx
oflice and the seeing of the entertainment, or w
n
paying board or rent and making use of the food or H-

171

THE THEORY OF INTEREST
ing facilitietx In many cases, the money payment follows
rather than precedes the enjoyment.

94. Cost of an Article us. Cost of Ita Use
The only time discrepancy worth careful noting ia that
which occurs when the money spent is not simply for the
temporary use of some object but for the whole object,
which means merely for all its possible future uses. If a
house is not rented but bought, we do not count the purchaee price all spent for this year's shelter. We expect
from it many more years of use. Hence out of the entire
to compute a fair portion of the
purchase price, we
purchase price to becharged up to this year's use. In
like manner, the statisticians of cost of living should distribute byperiods the cost of using a person'shouse
furrii&ings, clothing, musical instruments, automobiles
and other durable goods, and not charge the entire cost
against the income of the year of purchase. To any given
year should be charged only that year's upkeep and re
placement, which measures, at least roughly, the services
rendered by the goods in question during that particular
year. The true real annualincome from such goodsis the
equivalent approximately of the cost of the'services given
off by those goods each year.
Strictly speaking, then, in making up our income statistics, we should always calculate the value of services,
and never the value of the objects rendering those services It is true that, in the case of short-lived objects like
food, we do not ordinarily need, in practice, to go to the
trouble of distinguishing their total cost from the cost of
their use. A loaf of bread is worth ten cents because its
use is worth ten cents. We csnnot rentfood; we ma only
buy it outright. Yet there is mme diecrepancy in time in

=

t r y '

C83

INCOME AND CAPITAL
foods
the c88e aIf foods that keep,s.u& as flour, -wed
a d canned goods. Them we m y buy in one yeax but not
use until bter ye
‘ .such cams the money given
for
the food might
e said to be invested rather
than spent, like the money given for a house. A man who
buys a basket of fruit and eats it within an hour io certainly spending his money for the enjoyment of eating
the fruit. But, if he buys a barrel of apples in the fall to
be eaten during the winter, is he spending his money or
is he investing it for a deferred enjoyment? Theoretically,
the barrel of apples is an investment compctrable to a
house or any other durable good. Practically it is classed
as expenditure, although it is a border-line case.
Spending and investing differ only in degree, depending
on the length of time elapsing between the expenditure
and the enjoyment. To spend is to pay money for enjoyments which come very soon. To invest is to pay money
for enjoyments which are deferred to a later time. We
spend money for our daily bread and butter or for a seat
at the theater, but we invest money in the purchase of
bonds, farms, dwellings, or automobiles, or even of suits
of clothes.
$5. Measuring at tFR Domestic Threshold
In practice, we can estimate with fair mcurmy in all
ordinary cases how much of what we pay is for this year’s
use. That is to say, we ctan find out .pretty nearly our cost
of living for the year. We need only reckon what is spent
on personal wticles and service-n
everything whit&
enters our dwellings (or enters us), food, drink, clothes,
furniture, household rent,fuel and light, amusements,
and so on, our “bread and butter”~xc1wiveof what L
left over for future y m , such aa what w e pay for

I91

THE THEORY OF INTEREST
securities, machinery, or real estate, or what we put into
the savings bank. The domestic threshold is, in general,
a pretty good line of division. The cost of almost every
object whichcrosses it measures a portion of our real
income, and few other expenditures do.
Thus, at the end of production economics, or business
economics, we find home economicsIt ia the housekeeper,
the woman who spends, who takes the final steps through
the cost of living toward getting the real income of the
family, so that the family’s enjoyment income may fol-

low.
$6. Money Income
We have just been dealing with money payments for
consumptiongoods, or money outgo. Wemay now go
back one further step to money received by the individual spender, or money income. Money incomeincludes all
money received which is not obvioudy, and in the nature
of the case, to be devoted to reinvestmenkr, as the
expression is, “earmarked” for reinvestment. In other
words, all money received and readily avaihble and intended to beused for spending is moneyincome. It
sometimes differsfrom real income considerably. For
instmce, if you more than “earn your living” of $6,000
with a salary of $10,000, you voluntarily put by the $4,OOO remaining as savings. This part of your money income
is saved from being turned immedicbtely into real income,
That is, instead of spending all your s a l a r y for this year’s
living you invest $4,000 of it to help toward the cost of
living of future years. And so, the $4O
, OOis not only
credited as income but debited as outgo. With it you buy
durable objects such aa land or buildings, or part rights
in thae, such sa stocks or bonda. Your money income is
101

INCOMEANDCAPITAL

in this caae your salary (or it may be dividends, rent,
interest, or profits) and it exceeds real income by. the
amount of your savings. On the other hand, you may be
living beyondyour(money)income.
This means, expressed in terms of the concepts here used, that your
real income for the year is greater than yourmoney
income.
That all one spends on his living measuree real income,
evenwhen he “lives beyond his income”(beyond his
money income), may be a hard saying to some who have
never attempted to work out consistent definitions of
economic concepts which willnot only satisfy the requirements of economic theory but which will also bring these
economic concepts into conformity with the theory and
practice of accountancy. But a definition of income which
satides both theory and practice, in both economics and
accountancy, must reckon as income in the most bssic
sense alI those uses, services, or living for which the cost
of living is expended even though such expenditure may
exceed the money income.
Thus we have a picture of three successive stages, or
aspects, of a man’s income:
Enjoyment or psychic income, consisting of agreeable
sensations and experiences;
Real income meamred by the cost of living;
Money income, consisting of the money received by a
man for meeting his costs of living;
The lastmoney income-is mostcommonly called
income;and the firshnjoyment income-is the most
fundamental. But, for accounting p u p , red income,
as measured by the cost of living, is the most practical?
‘Later in this chapter we ahall see that these three aorta of income
are all of a piece, parte of the entire economicfabric of mwim and

c 111

THE THEORY OF INTEREST
To recapitulate, we have seen that the enjoyment income is apsychological matter,and hence cannot be
measured directly. So we look to real income instead; but
even real income is a heterogeneous jumble. It includes
quarts of milk, visits to the moving picture house, etc.,
and in thatform cannot be meagured eaailyor as a whole.
Here is where the cost of living comes in. It is the practical, homogeneous measure of real income. As the cost
of living is expressed in terms of dollars it may, therefore,
be taken as our best measure of income in place of enjoyment income, or real income. Between it and real income
there areno important discrepancies as there arebetween
money incomeand red income. Money incomepractically
never conforms exactly to red incomebecause either
savings raise money income above real income, or deficits
push money income belowreal income.

17. CcGpital Value
Savings bring us to the natureof capital. Capitd, in the
sense of capital value, is simply future income discounted
or, in other words, capitalized. The value of any property,
or rights to wealth, is its value as a source of income and
is found by discounting that expected income, We may,
if we so choose, for logical convenience, include as p r o p
erty the ownership in ourselves, or we may, conformably
to custom, regard human beings as in a separate category.
dkervicea Which of the threeoomea out of our accounting d e w &
merely on which groups of these services aad disservices are included
in our summation.
‘Even this ia not homogeneow MI a measure of subjective enjoyment; for a d o h to the poor and a dollar to the rich are not sub.
jectively equal. See my A Stuoistical Method jor MeoaLving ‘‘Mwghd
Utilitf and Teetiq L
h J r c s t k of a prosreasive Inconre Tm.Economic Eseaye contributed in honor of John &tea Clark, pp, 167-193,

[ 121

INCOME AND CAPITAL
!’

i
4

i

j
;
i

;
f

i
j.

’i

\
I

j
f

‘
i

’
:

:

’

:
i
.

;

I define wealth as consisting of materhd objects o w e d
byhumanbeings (including, if youplease, human beings
themselves). The ownershipmay be divided and pascelled
out among different individuals in the form of partnership
rights, shares of stock, bonds, mortgages, and other forms
of property rights. In whateverways the ownership be
dist.ributedand symbolizedindocuments, the entire group
of property rights are merelymeans to an end-income.
Income is the dpha andomega of economics.
$8. Tke Rate of Interest

The bridgeor link betweenincome and capitd is the
rate of interest. Wemay define the rate of interest as the
per cent of premium paid on money a t one date in terms
of money to be in hand one year later. Theoretically, of
course,wemay substitute for money in this statement
wheat or anyother sort of goods. This will be discussed
in Chapter 11. But practically, it is only moneywhich is
traded as between present and future. Hence, therata
of interest is sometimescalled the price of money; and
the market in which present and future money are traded
for tkat price, or premium, is called the money market.
If $100 today willexchange for $105 to be receivedone
year hence, the premiumon present money in terms of
future money is $5 and this, as a percentage of the $100,
or therate of interest, is five per eent. That is to say,
the price of today’s money in terms of next yeark money
is five per cent above par. .It should alwaysberemembered that interest and the rate of interest are not identical. Interestis computed by multiplying capitalvalue
by the rate of interest.
The & of this book is to show how the rate of jntertst
is crtuaed or determined. Some writers have c
h
m
,for
E 131

.

THE THEORY OF INTEREST
purposes of exposition, to postulate two questions involved in the theory of the rate of interest, viz., (1) why
any rate of interest exists and (2) how the rate of interest is determined. This second question, however,embraces also the first, since to explain how the rate of interest is determined involves the question of whether the
rate can or cannot be zero, i.e., whether a positive rate
of interest must necessarily exist.
$9. Discounting is Fundamental
But although the rate of interest may be used either
way-for computingfrom present to future values,or
from future to present values-the latter process (discounting) is by f a r the more important of the two. Accountants, of course, are
constantly computing in both
directions; for they have to deal with both sets of problems. But the basic problem of time valuation which
Nature sets us is always that of translating the future
into the present, that is, the problem of ascertaining the
capital value of future income. The value of capital
must be computedfrom the value of its estimatedfuture
net income, not vice versa.
This statement may at first seem puzzling, for we usually think of causes and effects as running forward not
backward in time. It would seem then that income must
be derived from capital; and, in a sense, this is true. Income is derived from capital goods. But the vdw of the
income is not derived fromthe value of the capital
goods. On the contrary, the value of the capital is d e
rived from the valueof the income. Valuation is a human
process in which foresight enters. Coming eventscast
their shadows before. Our valuations are always anticipa-

tiom.
[ 141

;$

;f
5

:":
L>

.2*
,#

;.

*

L

1
1
i

INCOME AND CAPITAL
These relations am shown in the following scheme in
which the mows represent the order of sequence-(l)
from capital goods to their future services, that is, income; (2) from these services to theirvalue; and (3)
from their value back to capital value:
Capital goods
+ Flow of services
(income)

-

Income value
Capital value
Not untilwe know how much income an item of capital
will probably bring us can we set any valuation on that
capital at all. It is true that the wheat crop depends on
the land which yields it. But the value of the crop does
not depend on the value of the land. On the contrary,
the value of the land depends on the expected value of
ita crops.
The present worehof any article is what buyers are
willing to give for it and sellers are ready to take for it,
In order that each man may logically decide what he is
willing to give or take, he must have: (1) some idea of
the value of the future benefits which that article will
yield, and (2) some idea of the rate of interest by which
these future values may be translated into present values
by discounting.

$10.Costs, or Negative Income
Cost of production of durable agents or capital g o o h
has its influence included in the preceding formulation,
since any cost is simply a negative item of income. Future
negative items are to be discounted exactly $8 future
positive items. It is to be remembered that at the given
point of time when the value is W i g computed only

THE THEORY OF INTEREST
Past costa haveno direct influenceon value. Only indirectly do they enter to the extent that they have determined the existing supply of goods andhavethus

:

either raised or lowered the value of the services of
these goods.
In this indirect way, past costs can determine present
values temporarily anduntilthe
prices ofgoods available are brought into conformitywith the present costs
of production through $he operation of supplyand demand. For example, the cost of producingwoolen cloth
declined verysharplyafter the close of the WorldWar,
butthe price did not decline for many months because
the new cloth made at lessexpensewas not sufficient to
meet the demand,hence the price remainedabove the
new costs of production for a time. Again, the cost of
makingshoesadvanced
rapidly during the early years
of the twentiethcentury, butthe price of shoes did not
advance pari pmssu with increased costs,
because
the
supply of more cheaply made shoeswas still large and
for a time controlled the marketprice. Inthe same indirect way, manyother influences affect the value of
the services of any good, especially anyalternative to
those services. But none of these considerations affects
the principle thatthe value of the gooditself is the
discounted value of the value (however determined) of
its future services.
$11. The Discount Principle Applied

The principlks which have been explained for obtaining
the present value of a future sum apply very definitely
to many commercial trmsactions, such as tu the valuation
of bank wets, which indeed exirt largely in the form of
discount paper, or short time loans of acme other k i n d s .
I: 161

i.

I

i
!

{

$

.$

ti

f

fb

e

>'

J

f

%

'8

&$

:$

$

:

k'
*L"

3

,'$

-I
.%

I1

t
I

INCOME AND CAPITAL
The value of 8 note is always the discounted vahe Of the
future paymentto which it entitles the holder.
Elaboratemathematical tables have been calculated
and are used by brokers for informing their customers
what price should be paid for a five per cent bond in
order that the purchaser may realize 5 per cent, 4 per
cent, or any other rate of interest on the prices to be paid.
The price of the bond is calculated from two items, the
rate of interest to berealized and the series of sums
or other benefits which the bond is going to return to the
investor. Aside from risk, there can never be any other
factors in the calculat.ion except these two. Of course, an
investor may refuse to buy a bond at the market price
because he has, as an alternative, the opportunity to
buy another bond cheaper so that he can realize a higher
rate on his purchase price. But that fact does not alter
the principle thatmarket prices represent discounted
benefits. The only market effect of this man's refusal
will be a slight tendency to lower the market price of
the first bond and raise that of its rival, that is, to alter
the rate of interest reaiized. Later we shall study more
fully the effects of such alternative opportunities. Here
we are concerned only to note that the price of the bond
is dependent solelyontwo factors: (1) its benefita and
(2) the interest rate by which these are discounted.
The principle is, of course, not confined to bonds. It
applies in any market to all property and wealth-stocks,
land (which has a discounted capital value just as truly
&s any other capital), buildings, machinery, or anything
whatsdever. Risk aside, each hss a market value dependent solely on the same two factors, the benefits: or re'Including, of course, all benefits or ~erviceewhatever f m m the pob
seeaion of the wealth such as the option to aubacribe to stock, now often

c 171

THE,THEORY OF INTEREST
t m , expected by the investor and the market rate of
interest by which those benefits are discounted.
The income which he expects may be a perpetual income(flowing uniformly or in recurring cycles) or it
may be any one of innumerable other types. If we a 5
sume that five per cent is the rate of interest, any one of
the following income streams will have a present value
of $1000: aperpetualannuity of $650 per year; or an
annuity of $50 a year for ten years, together with $loo0
at the end of the period; or $100 a year for fourteen
years, after which nothing at all; or $25 a year for ten
years, followed by $187.50 a year for ten years, after
which nothing at all.
512. Double Entry Bookkeeping

We began this chap& with the enjoyment income received ,by a, person and then travelled back, by way of
real income, cost of living, and money income to capital
value, which simply embodies the capitalizationor anticipation of income. This W B S going upstream, as it were,
from the enjoyer of income to its source. We may now reveme our point of view and look downstream. We then
attached to boride, or the priviiege attaching to certain bonds which
Banks to we the bonds for the security of National
Bank notes. Some of thesebenefite may be very indirwt and related
to whole groups. A man seeking voting control as a benefit who already
poeseasee 49 per cent may pay a specially high price for a few more
aharea of stock for the benefit of raising his holdings to 61 per cent.
Or, a man may include in the benefits of his wealth the f u n of running
the businem, or the socia1 Btasding he thinks it gives him, or political
or other puwer and Muence, or the mere miserly eem of possesaion or
the Batidaction in the mere proce%e of further accumulation. However
indirect, un-1,
or biaarre the benefit, the principle still holda that
the vaIue of any capital good or goods ie derived mlely from the
prospect of future benefits.
permits National

I: 18J

F
F
+

i
I

:

INCOME AND CAPITAL

think of the income strerun not so much

i

M flowing to
enjoyers 85 flowing from its various sources.*
Capital value is income capitalized and nothing else.
Income flows from, or is produced ,by, capital goods and
human beings, so that the capital value is also the value
of capital goods. The income is credited to (and outgo or
cost debited to) these goods and (or including) human
beings.
As every bookkeeper knows, most of the item of income (positive or negative) takethe form of money
payments. (These are not a stock of money, which is always capital but a flow of money.) Some are operations
paid for-events in the productive process, such grinding, spinning, weaving, hoisting, hauling, plowing; others
are events of consumption, such as eating food, wearing
clot.hea, hearing music, or seeing a play at the theatre;
while still others are within the human mind, such as enjoyments or their opposite, labor effort or discomfort.
It might seem that in sorting and combining such B

'Possibly it would help to adjust our mental attitudes to this changed
point of viewifwe
couldchange the name of income to oubome, or
output. Income suggestacoming
tourard us while outcomesugg&
coming from the wce.Thua the outcome from a farm is the netvalue
of its crops; the outcome from a railway company is its dividenh, ek.
Under this new procedure, we crediteach item ofincome as outcome from its murce and debit every negative item. Negative itern of
income are outgo. If we couldchange thia name a h , wewould
it
ingo, or input.
It ia a mereclerical matter of bookkeeping thue to credit to its
source every service rendered as 80 muchoutcome (or income) and
debit it with every d i m i c e rendered, aa so much ingo (or outgo).
Having suggested these new terms, however, 80 that the student may
mentally, or literally by lead pencil, substitute them for the old, I M
hereafter, for simplicity, adhere uniformly to the original terminologyJ
wing the term income even when we are thinking merely of ita coming
from its
sowoe while the recipient ia forgotten.

cu-

c 19 1

.

t

1
B
fI

THE THEORY OF INTEREST
miscellany of income items we could never avoid confusion and double counting and that the sum total would
far exceed the truepsychic or enjoyment income. But the
fact is that almost aa many negative items aa positive
items are included here and that, in fact, except for enjoyment income and labor pain, every positive item is
also negative, according to its relation to the capital
source, Thus when SmithpaysJones $100 (no matter
where it came from),Jones receives an item ofincome
of $100 while Smith suffers an item of outgo of the same
amount; and when a coupon of $100 is cut from a bond
and deposited, the bond is credited with yielding $100
and the bank account is debited with the same sum. The
same principle is applicable to the final big coupon called
the principal of the bond. The same item is thus entered
twice,onceonone
side of somebody’s books andthe
other time on the other side of somebody’s books.
The bookkeeping implications of such couples of item
werediscovered byaccountants long ago andarethe
basis of their double entry bookkeeping,though ita economicsignificance has been largely overlooked.One important significance is that this double entry prevents
double counting; when we take the sum total of all income items forsociety, including psychic aa well rn physicd items, this double entry results in cancelling out
everything except the psychic items of enjoyment and
labor pain.
Every operation of
producDion,
transportation, exchange, or consumption-every process, in fact, except
final enjoyment-is double faced, or two items in one. I
have called such an operation an “interaction” because
it is income to be credit,ed to thecapital which yields it,
while it is outgo to be debited to the capital which receives

C%l

’,

4

w
1

:q
8
.b
,s

fF

1

;
:

1
I

i

INCOME AND CAPITAL
it. Thus, in any completebookkeeping, $100 worth Of
I plowing, on the one hand, is credited jointly to the plow,

$

i
!

the plowman, and the team, or motor, which do the plowing; that is, whichyield or bestow the service. On the
; other hand, it is debited to theland which is plowed,
that is, whichreceives the service.
If the plow is owned by one person and the land by
another, the latter paying $100 to the former, then the
service of plowing,though a self-cancelling interaction
! for the twopersons taken together, evidently cannot be
'ignored by either separately. If $100 is paid for this sewi ice of plowing, the $100 item is an expense to the land2i owner to be subtracted from his grossincome. It is no
concern of his that this self-same service of plowing is
$ counted M income by the plow-owner. So thisitem of
5-! $100 worth of plowingaffects our accounts quite differ3 ently according to the point of view. It may be a plus
i item from the point of view of oneperson and a minus
item from that of another. When, however, the two &ci counts are combinedand the plus and minus i t e m s are
:
added, their algebraic s u m is zero. For society aa 8 whole,
1 therefore, no positive income results fromplowing until
the land has yielded s
t
i crop and thecrop has been finally
i consumed.
Thus, simply by the mechanical, clerical processes of
: makingbookkeepers' entries, wereach again, in the opj
posite order, the various stages originally described in
i the opening pages of this chapter. That is, the s u m tow
j
ofincomeflowing
fromagroup
of capital sources is
naturally differentaccording to which capital s o u r c ~me
1
included. There
are
certain cancellations within my
1
group of capital goodswhich have an uncancelled fringe,
: andthis mayitself in turn disappear by cmc&tion if
21 1
i'

1

,'

c

THE THEORY OF INTEREST
the group is enlarged by including other capital items
with interactions between the new and oldmembers.
Henry Ford’sminesyield a net income, the difference
between certain credits and debita. If we include the
to the factory,
railway which transportstheproduct
certain credits to the mines from turning trheir product
over to the railroad now disappear, being debits to the
railway. If the circle be still further enlarged, say to include the Ford factories, other items likewise disappear
as parts of interactions within the enlarged circle, and 80
on.
We must, of course, include all services $8 income. A
dwelling renders income to the owner who dwells in it
himself just as truly as when he lets it to another. In
the first case, his income is shelter; in the second, his income is rent payments in money. All wealth existing at
any moment is capital and yields income in some form.
As a business man said to me, his pleasure yacht is capital and gives him dividends every Saturday afternoon.
813. Simplicity Underlying Complications
In our present-day complicated economic life we are
likely to be confused by the many industrid operatione
and money transactions. But net income still remains
exactly what it was toprimitive
Robinson Crusoe
on his island-the enjoyment from eating the berries we
pick, so to speak, less the discomfort or the labor of picking them. The only difference is that today the picking
is not so entirely hand-to-mouth, but is done by means of
complicated apparatus and after the frequent
exchange of
money; that is, a long chain of middlemen, capital, and
money transactions intervenes between the labor of pickt
& and the satisfaction of eating at the end.
ing at thes

rn3

i

INCOME AND CAPITAL
TOcontinue the literal example of beny picking, we find
today huckleberries picked by hired laborers on the POcon0 Mountains, sorted, graded, shipped by r d and motor
to New York City wholesalers, resold to retailers who sell
and deliver them to the housewife in whose kitchen they

Y

?

me again sorted and prepared for their ultimate mission
of giving enjoyment. The individual's total income when
elaborately worked out, after cancelling, in pairsor
couples, all such credits and debits, whether of money
payments or the money value of services-in production
or exchange"coincidesnecessarily with his enjoyment
income, less the labor pain suffered in the same period,
from which sort of income we started our discussion in
this chapter. This coincidenceoccursnecessarily
and
automatically, by virtue of these mathematical cancellations.
It is interesting to observe that a corporation as such
cm have no net income. Since acorporation is a fictitious,
not a red, person, each of its items without exception is
doubly entered. I ~ B
stockholders may get income from
it, butthe corporation itself, considered aa a sepmte
person apart from these stockholders, receives none.
The total income of a real person is his enjoyment
income only provided we include the credits and debitsof
his own body. The physical music, or vibrations which
pass from his piano to his ear are, atrictly speaking, only
interactions to be credited to his piano and debited to his
bodily ear. The music in his consciousnem comes at the
other, or brain, end of the auditory nerve. The piano plays
to his ear, his ear to his brain, and his brain to his consciousness. His whole body mechanism is a transmitter
from the outer world to his inner life, through ear, eye,
and its other sense organa.

c w

i

THE THEORY OF INTEREST
Or if the body mechanism, with its debits and credits,
be omitted the total result is not his enjoyment income,
subjectively considered, but the real income &s above
set forth. If we measure this, his real income, in money
units, we find it equal to thetotal valuation of his
cost of living less the total valuation of his own labor
pain.
How to place a money valuation on 8 hbor pain is 8
difEcuIt question. This question is important in accounting theory, especially in its relation to the problems of
measuring human welfare. But, fortunately for us, the
difficultiesof this valuation do not disturb the theory
of the rate of interest, since this theory is actually concerned only with differencesin the income stream at different times, notin a meticulous measurement of the
total. Moreover, practically the only point in interest theory where labor pain enters is the case of a worker who
suffers present labor pain in order to secure future satisfactions for himself or his family. This case is that of a
laborer’s savings; and all we need do here is to take the
laborer’s own valuation. Presumably, if the rate of interest is 5 per cent, the labor he will exert this year for the
sake of $100 next year has a valuation in his mind of
about $95.
But a laborer’s savings are practically a negligible element in determining the rate of interest. To others than
laborers the only important way labor enters is through
the payment of wages and salaries, and these are money
expenses incurred for the sake of future money returns.
A laborer building a railway does not work for the future
dividends from the railway. He is paid for immedi& living by his employer in expectation of those future dividends. Thus wages are a sort of measure of labor pain

c241

INCOME AND CAPITAL
to bhe employer of hbor, whether or not they be 80 regarded by the laborer.'
If we exclude labor pain and further exclude from the
laborer'sbookkeeping the income items, positive and
negative, flowing from his household effects-the use of
furniture, clothing, food, and so on-the total income
then turns outto lbe not his realincome but his money income-assuming that, as is ordinarily true, all his income
flows in through money payments and none in kind.
$14. Capital Gain not Income

i

t
t

,!

The most interesting and valuable result of applying
these bookkeeping principles is that thereby we automatically separate capital fromincome,two
things which
are so often confused and in so manyways. It is not
uncommon for economic students to make the mistake
ofincluding capital gains as income. Capital gains, as
already implied, are merely capitalization of future income. They are never present income. Therefore & true
meticulous accounting, item by item, of the income, or of
the servicesanddisservices, rendered by any specified
group of capital items will infallibly grind out this truth.
It will never confuse capital gain in that capital group
with incomerealizedfrom
that group, This is true
whether our capital group and its income are so extended
BS to include enjoyment income (positive and negative)
aa the final net income, or whether our specific group is so
restricted &s to leave plowing or money payments as
the uncancelled fringe.* We shall always find that only
the income actually detached from,or given offfor en-

THE THEORY OF INTEREST
joyment by, that group, aa in cutting coupons from 8
bond, will result from the summation of the accountant,
who will never record as income the increase or decrease
in the capital itself.
A bond price,for example, will grow with accrued interest between twocoupon cuttings. That growth in its
value is not income but increme of capital. Only when
the coupon is detached does the bond render, or give off,
a service, and so yield income. The income consistsin the
event of suchoff-givipg, the yielding or separation, to
use the language of the United States Supreme Court.
If the coupon thus given off is reinvested in another bond,
that event is outgo, and offsets the simult,aneousincome
realized from the first bond. There is then no net income
from the group but only growth of capital. If the final
large payment of the principal is commonly thought of
not as income (which it is if not reinvested) but aa capital it is because it is usually and normally so reinvested.
Likewise, if my savings bank account gains by compound interest, there is no income but only an accretion
of capital. If we adopt the fiction that the bank teller
hands over that accretion at any moment to me through
his window,we must also adopt the fiction that it is
simultaneously handed back by me through the m e
window. If the first event is income, the second is outgo.
If it passes both ways, or does not pass at d,there can
be no net income resulting. This is good bookkeeping
and sound economics. There is noescape from such
mathematical conclusions. By no hocuspocus can we
have our cake and eat it too. This is as impossible tu
perpetual motion, and fundamentally M absurd. The
absurdity is especially evident when the cause of an inc r e w or decrease in the capital value of IL bond or in261

c

INCOME AND CAPITAL
vestment is not dueto m y change in the expected income
at but comes through a change in the rate of interest.
Consoh and rentes fluctuate in value every daywith
every change in the money market. Yet the income they
WtuaIIy yield flows on at the same rate. Merely the capital value is found sometimes on a 3 per cent basis and
sometimes on a 4 per cent basis. A rise in the market
is a capital gain, but it is not income. Income may be
invested and thus transformed intocapital; or capital
may be spent and so transformed into income. In thefirst
case, as we haveseen, capital accumulates; in the second case, capital is diminished. In the first case the maa
is living inside his moneyincome; in the secondcase
he is living beyond his money income.
If Henry Ford receives $1OO,OOO,OOO in dividends but
reinvest.s all but $50,000, then his real income is only
$50,000,9 even if his money income is $lOO,OOO,OOO. And
if, during the year of rebuilding his factories to make his
new car, he received no dividends and yet spent $40,000
in that year for living expenses and all other satisfactions, then his real income wm this $4QOOO even if his
money income that year was zero.
Thus theincome enjoyed in any year is radically different from the ups anddowns of one's capital valuein that
year-whether this is caused by savings or the opposite,
or by changes in the rate of interest or by so-called
chance.
We may in our bookkeeping add our savings to our
real income and call the sum total gain. For my part, I
'Except, aa already stated in a previoua footnote, he derivee in d&tion to this obvious income other lese tangible and more subtle b m e
from the sxwe of p o d o n , prestige, power, etc., which go with great
wealth.

rn1

THE TREORY OF INTEREST
prefer not to call it income. For the two parts of this
totd-enjoyed income and accumulation of capital or
capitalized future enjoyments-are unlike. The only argument for adding them together is that the recipient
codd use the savings as income and still keep his capital
unchanged. Yes, he codd, but he didn't, otherwise there
would be no savings! One part is income, and the other
is capital gain.
This distinction between the real income, actually enjoyed, and the accretion or m r u a l of capital value, that
is, the capitaiination of future enjoyments, is not only
in general vitd, but vital to the understanding of this
book.1°
We cannot understand the theory of interest so long as
we play fast and loose with the concepts of capital and
income. And enjoyment income, which plays the central
r6le in interest theory, is never savings orincreMe of
capital.
$15. CapitaEIncome Relations

In conclusion we may say thatthe chief relations
between capital and income are:
(1) Capital value is income capitalized or discounted.
(2) If the rate of interest falls, the capital value ( c a p
i t h d value of expected income) rises, and vice versa.
(3) This rise or fall in capital value is relatively great
for durable goods like h d , and relatively small for
transitory goods like clothes.
"For fuller freatment of thia eubject the reader ie referred to: 2%
Nature of Capital and Income; Are Saving8 Income, Journal of
Amen" h n o m i o Aasocistion, Third ser
e
i s,Vol. IX, No. 1, pp. 1-27 ;
The Income Coneept in the Light of Experience, privately printed
88 Engiish trsnalation of article in Vol. III, of the Wieeer Feetachrift,

INCOME AND CAPITAL

i

i
t

(4) Capital value is increased by srtvings, the income
being decreased by the same amount that the capital is
increased.
( 5 ) These savings thus diverted fromincome and
turned back into capital will, except for mischance, be
the basis for real income later.
$16.Application to this Book
The problem of the rateof interest is entirely a problem
of spending and investing, of deciding between various
possible enjoyments constituting income,especially between relatively small but immediate enjoyments and
relatively large but deferred enjoyments. There is an
eternal conflictbetween the impulse to spend and the
impulse to invest. The impulse of a man to spend is
causedby his impatience- to get enjoymenta without
delay, and his impulse to invest is caused by the opportunitiesto obtain bydelay relatively more enjoyment
either for himself or others.
For the study of interest from this point of view we
need a,s our chief subject matter a picture of a persods
income stream, We may get this most clearly by plot
ting day by day, month by month, or year by year, the
closest statistical measure of one’s real income, namely,
one’s cost of living.
If this income flowsat a constant rate of $200 a month
or $2400 a year, the picture of the income stream is as
shown in Chart 1.
If the income stream flows at an i n c r e h g rate; the
picture is as shown in Chart 2.
If it flows at a decreasing rate, the picture is 88 in
Chart 3.”
u I n all three examplee, each month’s income is repremmted by a
rectangular column or
In the I& two awes, the resultant
of

bar.

[291

THE THEORY OF INTEREST

CHART 1
IncomeStream Uniform.

CHART 2
IncomeStreamIncreasing.

CHART 3
Inwme Stream Decreasing.

c 301

INCOME ANDCAPITAL

?

Of course, these particular forms are only special types ;
numerous other types might be given.
In interest theory the income with which we deal are
not statistical records of the past but those of the expected future. What is to be one’s future income stream,
chosen from amongseveral income ~treamsavailable, becomes of supreme importance.

$17. Confusions to be Avoided

1

,

The very first effort of the beginner in this subject
should be to rid his mind of all prepossessions &s to the
nature of income and capital. My grandchild of sir recently asked the cashier of a savings bank, “Show me
the money I amgoing to get when I grow up.” T h e
cashier gravely took him into B back room and held up
a bag of coins. The vision of that bagful will doubtleas
persist into adult life as a picture of a savings bank account, even after he has learned in college that the total
deposits of a bank far exceed the cash on hand, and that
the depositor’s capital is not actual cash but the right,
measured in termsof cash, to the services or benefits flowing from the bank’s assets, real estate, mortgages on real
estate, stocks and bonds, and all the rest of its resources.
Both capital and income seem to be simply money. We
can always show a money sample, aa did the cashier, and
where one’s capital is liquid so that it may readily be
turned from one form to another via money-or rather
bars makes a aeries of flat tope or steps. But by taking days h
d
of months, we come ne&rer to a sloping curve which is a better and
simpler ideal picture. Hereafter we shell UBB such continuow m a .
But they mayalwaysbe thought of as made up approximakb of a
aerie8 of column^ or bars. For fuller diaeuasion of such oharts, ( ~ The
e
Nature of Capitad and Income, p. 21)rlL

I 31 3

TEE THEORY OF INTEREST
credit-it is most simply and l a d y pictured to the mind’s
eye as being itself money.
The student should also try to forget all former notions concerning the so-called supply and demand of
capital as the causes of interest. Since capital is merely
the translation of future expectedincome into present
cash value, whatever supply and demand we have to deal
with are rather the supply and demand of future income.
It will further help the student
if he will, from the outset, divest himself of any preconception he may have
acquired &s to the r8le of the rate of interest in the distribution of income. This subject will be dealt with in
Chapter XV; but it may be well here to point out that
interest is not, as traditionaldoctrine would have it, a
separate branch of income in addition to rent, wages
and profits.
The income stream is the most fundamental fact of
economic life. It is the joint product of many agencies
which may be classifiedunder many heads, such as human
beings, land, and (other) capital. The hire of human b e
ings is wages; the hire of land is land rent. What, then,
is the hire of (other) capital-houses, pianos, typewriters,
and 80 forth? Is it interest? Certainly not. Their hire is
obviously house rent, piano rent, typewriter rent, and so
forth, just as the man in the street calls them. Rent is
the ratio of the payment to the physical object-land,
houses, pianos, typewriters, and so forth-so many d o h
per piano, per acre, perroom. Interest, on the other hand,
is theratio of paymenttothe
money value of these
things-so many dollars per hundred dollars (or per
cent). It is, in each case, the ratio of the net rent to the
capitalized value of that rent. I t applies to all the categorieeto land quite as truly as to houses, pianos, type-

c 32 1

i

1
B

8

-4
.r
I

P

k

INCOME AND CAPITAL
writers. The income from land is thus both rent and interest just as truly as the income from a typewriter or a
bond. We can and do capitdim land rent just $8 truly as
wedo house rent. For example, land worth “20 yeam
purchase” yields 5 per cent interest. All this is true q u h
irrespective of the question of distinctions between land
rent, on the one hand, and house rent, piano rent, typewriter rent, and so forth on the other.12 It is a question
of that sort of price which links one point of time with
another point of time in the markets of the world. And
it is a question concerning every branch of economic theory in which the time element enters. The rate of intemt
is the most pervasive price in the whole price structure.
As to profits, I believe the most fruitful concept is also
that of the man in the street. When risk attaches to any
one of the aforementioned forms of capital-human
beings, land,houses,pianos, typewriters and so forththe man in the street calls the net income profits. And
profits,likewise,maybemeasured
either (asrent) in
relation to the physical units producing them, or (asinterest) in relation to the values of these profits; that is,
either as dollarsperacre, per room,perpiano and 80
forth; or dollars per $100 worth of land (houses, pianos,
and so forth) ; or as dollars per share of ownership in any
of these; or dollarsper $100 worth of suchshares. To
pretend that either interestor profits is the income solely
from capital goods other than land and that these two
concepts m inapplicable to land--to pretend, in &tort,
that wages, rent, interest and profits are four m u t u d y
PCf. Fetter, Frank A., Interest Theories Old and New, American &e
nomic Review, March, 1914, pp. 76 and 77; Fetter, P k & ~ b of
nmics, pp. 122127; Davenport, H.J., Interest
Theory
T h a
American Economic Review, Dec., 1821, pp, 636,63%

33 1

f

a

b;*

THE THEORY OF INTEREST

$*

$

exclusive divisions of the income stream of society is to
treat different c l d c a t i o n s of one thing as if they were
themselves different things. It is as if we should speak of
certain total space as consisting partly of acres of land,
partly of tons of soil, and partly of bushels of ore. Or
again, it is like classifying a pack of cards into aces, clubs
and red suits and pretending that these three c l a m are
mutually exclusive.
The simple fwt is that any or all income may be capitalized, including that credited to human beings, thus
giving theresultant economic value of a man. William
Farr, J. Shield Nicholson, Louis I. Dublin, andothers
have made such computations.la However, we so seldom
capitalize wages that we have no practical need to call
wagesor any portion of them interest. Nor where risk
is a dominant factor, as in profits, is there real need to
c a d the income interest. For instance, hoped-for dividends, according as the hope varies, are daily and automaticdy capitalized in the stock market and need not
themselves be called interest. Much less would it be worth
while to call enterpriser’s profits interest. No one ever
attempted to capitalize them. But in meticulous theory,
all may be capitalized and so become interest.
818. A Workiw Concept of the Rate of Interest

of the “human

capital” of the United Statea to be 1,500 billion dollars, or about five
times the value of dl other capital.

c341

,d3

,.*
1:
-3

”5
;a,

a

. ”

.

1:

’

While any exact and practical definition of c1 pure rate
of interest is impoaibble, we may say roughly thatthe
pure rate is the rate on loans which are practically devoid
of chance. In particular, there are two chances which
should thus be eliminated. One tends to raise the rate,
YFor instance, Dr. Dublin computesthetotalvalue

i

k-

g

1

;
i

9
I'E
c

INCOME AND CAPITAL

f

1

namely, the chance of default. The other tends to lower
; it, namely, the chance to use the security aa a substitute
forreadycash. In short, we thus rule out, on the one
hand, all risky loans, and, on the other, all bank deposits
, subject to withdrawal on demand, even if accorded some
interest. We have left safe securities of fixed terms not
lilrely tobe transferred or transferred often before ma; turity. Such securities give usthe nearest approach to
pure interest both for short and long periods according
f
to thetime to maturity.
In this book, I shall usually confine the concept of the
3 rate of interest to the rate in a (humanly apeding) safe
loan, or other contract implying specific sums payable at
one date or set of dates in consideration of repayment at
another date or set of dates. The essentials in this concept are (1) definite and assured payments, and (2) definite and assured repayments, and (3) definite dates. The
concept includes the concept of the raterealized on a safe
security such as a bond purchased in the market. It is this
that concerns us in this book. We are not primarily conf
I cernedwith total interest, but with the rate of interest.

I

i

1

!i
5
1
I

r 35 1

CHAPTER I1
MONEY
INTEREBT

* j

AND REAL INTEREST

ig
c

‘d
4d
i*

$1. Introduction

.

AT the close of the preceding chapter, the rate of interest was descri,bed as the percentagepremium onpresent goodsover future goods of the same kind. Does the
kind of goods affect the premium? This important question-usually overlooked-may well engage our attention
at the very outset. The number, or figure, expressing the
rate of interest in terms of money does depend upon the
monetary standard employed.
I t is perfectly true, as is often pointed out, that when
a man lends $100 this year in order to obtain $105 next
year, he is really sacrificing not $100 in literal money
but one hundred dollars’ worth of other goodssuch as
food, clothing, shelter, or pleasure trips, in order to obtain, next year, not $105 in literal money, but one hundred and five dollars’ worth of other goods. But this fact
does not remove the money factor from our problem. The
money factor affects the rate of interest in many ways.
The one here considered is that which occurs through
change in the value of the monetary standard.
If the monetary standard
were alwaysstable with reference to goods, the rate of interest, reckoned in terms of
money, would be the same as if reckoned in terms of
goods. When,however, moneyand goods change with
reference to each other-in other words, when the m n e y
C361

,v<

,<$

**

.j

i,

t
t

\

MONEY INTEREST AND REAL INTEREST
standard appreciates or d e p r e c b b in value in terms of
goods-the numbers expressing the two rates of interest,
one reckonedin terms of money and the otherreckoned in
terms of goods, w
l
l
ibe quite difTei.ent. Moreover, the former, or money rate, the only rate quoted in the market,
will be influenced by the appreciation or depreciation.
$2. Assuming Foresight
The influence of such changes in the purchasing power
of money on the money rate of interest will be different
according to whether or not that change is foreseen. If
it is not clearlyforeseen, a changein the purchasing
power of money will not, at first,greatly affect the rate
of interest expressed in t e r m s of money. Instead, if the
change is in the direction of appreciation, it will injure
the debtor, because to repay the principal of his debt
will cost him more goods than either he or his creditor
anticipated when the debt was contracted.
In 80 far as the appreciation is foreseen, any increased
burden to the debtor in the principal may be somewhat
offsetby a reduction in the rate of interest. This is a
fact which has seldom been recognized.' The assumption
has been tacitly made that contracting parties arepowerless to forestall gains or losses caused by an upward or
downward movement of the monetary standard even
when that movement is foreseen.
It is theoretically just as possible to make allowance
for an expected change in the unit of value as it would be
for aa expected change in any other unit. If, by Iegislstion, the unit of length were to bechanged, and its
change were set for a certain future date, contracts run'A brief outline of the hietory and theory of appreciation anal i&q&
is given in the Appendix to chapter V of The Ra& of Zlltet.ost,
[ 37 I

THE THEORY OF INTEREST
ning beyond that date’would surely bemodified accordingly. Or suppose that a yard weredefined (as legend
tells UE it once was) as the length of the king’s girdle.
If the kingwere a child, everybodywould then know that
the “yard” would probably increase with the king’s age,
and a merchant who should agree to deliver one thousand
“yards” ten years hence would make his terms correspond
to his expect,ations.
It would be strange, if, in some sirnilar way, an escape
could not be found from the effects of changesin the
monetary yardstick, provided these changes were known
in advance. To offset a foreseen appreciation, therefore,
it would be necessary only that the rate of interest be
correspondinglylower, and to offset a foreseendepreciation, that it be correspondingly higher?
Near the close of the last century, during the uncertainty as to the adoption or rejection of “free silver,” a
syndicate offered to buy from the United States government some $65,000,000 of bonds either on a 3 per cent
basis in gold,or a 394 per cent basis in coin. Everyone
knew that the additional 3/4 per cent in the latter alternative was due to the mere possibility that coin might
not be maintained at full gold value, but might sink to
the level of the value of silver. If the alternative hadbeen
a posdde
between repayment in goldand-notmerely
but a certai.zcrepayment in silver, theadditional in’Since, becsuee of ignorance and
indilTerence, appreciationsand deprecistione are, a8 a matter of fact, never fully foreknown andtheir
relation to interest andother buainea phenomena only dimly perceived, they are only partially provided against in the rate of interest
itself. Aa I have
tried
to show in StubiEizin~the Dollar, in The
MmyI
~and in other
~
writings,
,
the beet remedy ia to atandardise,
or stabilize, the dollar as we have &n&rdid every other important
unit of measure employed in business.

W I

b

I

y$
f

*‘1
,
&

‘d

4

c

F

T

!
j

2-

!i

’

REAL INTEREST
temt wouldobviously have exceeded 3/4 per cent. It

,:

ing firm, when asked by a German concern for & loan in

4

:

MONEY INTEREST AND

wm stated, .afterthe World War, that an American bank-

marks, offered to lend at 100 per cent per annum. The
offer wasrejected-fortunately
for the American firm
which,
it turned out, would actuallyhave lost, and
i
lost heavily, because the subsequent rapid depreciation
of the mark f a r exceeded the compensatory effect of even
*,
so highan interestrate.
The exact t,heoreticalrelation between the rates of interest memured in any two diverging standards of value
and the rate of foreseen appreciation or depreciation of
4 one of these two standards relatively to the other has
a beendevelopedbyme
with many numericalillu&r&
\ tions in a special monographand also in my first book
a’ on intere~t.~
The two rates of interest in the two diverging standards will, in a perfect adjustment, differ from
each other by an amount equal to the rate of divergence
4 between the two standards.6Thus, in order to Compensate
f for every one per cent of appreciation or depreciation,
one point would be subtracted from, or added to, the rate
; of interest; that is, an interest rate of 5 per cent would
t become 4 per cent, or 6 per cent, respectively.

I

;

1

a AppFeciatb and Interest, Publications of the AmericanEconomio
Association, Third Series, Vol. XI, No. 4, Aug., 1898, pp. 3 3 1 4 .
‘The Rate of Interest, Appendix t o Chspter V.
‘This is strictly true only when the rate of interest in ea& standard
is reckoned momently, or continuously. If, aa in practice, therate is
reckoned quarterly, semi-annually, or annually, this equation h slightly
altered. For themathematicaldemonstration
of this proposition, eee
Appendix to Sec. 3, Chapter V, of The Rate of Interest. For the sipnificance of “continuow reckoning:’ ~ e eThe Nature of Capital cwrd
I m e , Chapter X I ; also Apwdix to
12 of Chapter Xm.

8ec.

c 39 1

I

!EIE THEORY OF INTEREST
$3. Limitations of Theory
We next inquire what limits, if any, are imposedon
the two rates of interest in the respective standards and
the rate of divergence between the two standards. From
what hasbeen said it might seem that, when the appreciation is s&ciently rapid, the rate of interest in the upward-moving standard, in order to equalize the burden,
would have to be zero or even negative. For instance, if
the rateof interest expressed in gold is 4 per cent, and if
wheat appreciates relatively to gold at 4 per cent also,
the rate of interest expressed in wheat, if perfectly adjusted, would theoretically have to sink to zero! But
zero or negative interest is practically almost impossible.
If it were definitely foreknown that wheat was to a p
preciate m fast as 4 per cent when the rate of interest
in moneyis 4 per cent, wheat would be hoarded and so
many peoplewould want itthat its present pricewould
tend instantly to come within 4 per cent of its next year's
price. This would, from that instant,prevent the rate
of interest in terms of wheat from passing below the zero
mark.
For instance, if interest is 4 per cent, it is impossible
that wheat should beworth $1 today and $1.10 next
year foreknown today by everybody, For, if suchprices
werepossible,holding for a risewouldgive a sure return
of 10 per cent (neglecting storage charges and other
costs of carrying). The result of such perfect knowledge
of next year'spricewouldbe
that the lowestpossible
price of present wheat would then be the expected $1.10
discounted at 4 per cent, or about $1.06.
This very limitation on the possible rate of interestthat itcannot theoretically sink below zero-carries with
,

IwI

,id
as

~2

:,;;-

:
:I

!
!

f
,

;
.

9

i.
i

MONEY INTEREST AND REAL
INTEREST
it a theoretical limitation on the possible rate of (foreknown) appreciation of any good.
It is important to emphasize the fact that these limita
imposed on the rates of intRrest and appreciation imply
the possibility of hoarding wheat, or other durable commodities, including money, without loss. If money were
a perishable commodity, like fruit, the limits would evidently be pushed into the region of negative quantities.
Onecanimagine
8 loan expressed in strawberries or
peaches, contracted in summer and payable in winter,
with negative interestB8Analogously we m y regard the
storage and other costs of carrying wheat 88 permitting,
to that extent, a negative rate of interest in terms of
wheat. It follows that even the rate of interest in terms
of money may be negative when money is in sufficient
danger of being lost or stolen, as during a riot or invasion.
But as long as our monetary standard is gold or other
imperishable commodity, so that there is always the opportunity to hoardsome of it, no rate of interest expressed therein is likely to fall to zero, much less to fall
below zero. This principle is a special caseof a more general principle of opportunity whichwillbedeveloped
later.
$4. Red and Money Interest

:
i
t
:

1
:

The theoretical relation existingbetween inkre@and
appreciation implies, then, thattherate
of interest is
always relative to the standard in which it is expressed.
The fact that interest expressed in money is high, say
15 per cent, might conceivably indicate merely that general prices are expected to rise (ie., money depreciate)
aBiihm-Bawerk, T b Posdtive Theory of Calital, pp. 252 and 297;
L a n k , L'lnh" du Capital, p. 49.

1411

TKE THEORY OF INTEREST
at the rate of 10 per cent,and thattherate of interest
expressed in terms of goods is not high, but only about 5
per cent.
We thus need to distinguish between interest expressed
in terms of money andinterest expressed in terms of
other goods. But notwo forms of goods can be expected
to maintain an absolutely constant price ratio toward
emh other. There are, therefore,themeticallyjust
as
many rates of interest expressed in t e r m of goo& as
there are k i d of goods diverging from one another in

*-

$4

$;

..4
$
5

'

value.
Is there, then, no absolute standard of value in terms
of which real interest should be expressed? Real income,
a composite of consumption goods and services, in other
words, a Gost of living index in accordance with the principles set forth in Chapter I, affords a practical objective
standard. By means of such an index number we may
tramlate the nominal, or money rate of interest, into a
goods rate or rertl rate of interest, just BS we translate
money wages into real wages. The cost of living plays
the same r6le inboth cases although the process of transhting is somewhat different and morecomplicated
in
the cam of intemt from what it is in the cme of wages,
for the reason that interest involves two points of time,
instead of only one; 80 that we musttranslate from
money into goods not only in the present, when the
money is borrowed, but &o in the future, when it is repaid.
in our economic
Income is the most fundamental factor
lives. The derivation of the value of every durable agent
or goodinvolves the discounting or capitalizing of income
as one of the steps. Consequently, a rate of interest in
terms of fundamental income itself would aeem to come as

c421

.

,?G,

,.,.:I.

!-

F

j
;

I

1
1

5

MONEY INTEREST AND REAL INTEREST

near as we ca,n practically come to any bat& s t s n d d in
which to express a real rate of interest.
1
But, in actual practice, it is the rate in t e r n of money
i withwhichbusinessmendeal
and hereafter the rate of
interest, unless otherwise specified, will in this book be
taken to mean this money rate.
i
The money rateandthe real rate are normally identic d ; that is, they will, m has been said, be the same when
the purchasing power of the dollar in terms of the cost of
i living is constant or stable. When the cost of living is not
stable, the rate of interest takes the appreciahion and dei
4 preciation into account to some extent, but only slightly
and, in general, indirectly. That is, when prices are rising,
\ the rate of interest tends to be high but not so high as
7,
it should be to compensate for the rise; and when prices
are falling, the rate of interest tends to be low, but not
so low as it should be to compensate for the fall.’
The principle of interest being relative to thestandard
B used in loan contracts would(bemore in evidence if it
were customary to make loan contracts in tern of other
iI standardsthan money. Therate is actually expressed
1 in loan contracts in terms of money and only translated
i into terms of goods, if at all, after the contract has been
fulfilled, when it k too late to stipulate compensations
a for the rise or fall in monetary value. If the money rate
of interest were perfectly adjusted to changes inthe
i purchasing power of money-which means, in effect, if
those changes were perfectly and universally foremenf

\
$

‘That the appreciation or depreciation of money doee aetuslly influence the rate of intereet, even though feebly, ia now well r e c o p h d
by thw who have given attention to the eubjeet. See hfeasor Map
shall’s testimony, Z n d k n CW-rency Report, p. 169; and Johneon, Meney
and Cturency. Boston, Ginn t Company, 1905.

c431

THE THEORY OF INTEREST
the relation of the rate of interest to those changes would
have no practical importance but only a theoretical importance. As rnat,ters are,however, in view of almost
universal lack of foresight, the relation has greater practical than theoretical importance. The business man supposes he makes his contracts in a certain rate of interest,
only to wake up later and find that, in terms of real goods,
the rate is quite different.
The real rate of interest in the United States from
March to April,1917, fell below minus 70 per cent! In
Germany at the height of inflation, August to September,
1923, the real rate of interest fell to the absurd level of
minus 99.9 per cent, which means that lenders lost all
interest and nearly all their capitalas well; and then suddenlypricesweredeflated
andthe realinterest rate
jumped to plus 100 per cent.B
The need to &ow incomeandcapitalaccounts
in terms of value
instead of money units is now coming to be recognized by progressive
accountants. For .e clear and complete statement of this new principle in
aocounting, the reader is referred to Ernest F. DeBrul. Unintentional
F&&ation
of Accmnts. NationalAssociation of Cost Accountants
Bulletin,Vol. E.Pp. 1035-1058. NewYork,NationalAseociatibn
of
CostAccountants, 1928. The same theory is expoundedbyHenry W.
Sweeney in hie doctor’s dissertation, Stabilized Accounting, accepted
his article,
byColumbiaUniversity
butnotyet published.Seealso
Gennan Z w f i t h Accounting, in the J o d ofAccountancy,February,
1928, pp. 104-116; Dr. Walter Mahlberg. Bilanztechnik und Bewertung
bei Schwankender Wahmng. Leipaig, G.A. Gloeckner, 1923; E.Schmalenhch. Qrundlogen Dylarndschez Bilanzlehre. Leipzig, G.A. Gloeckner,
1925; LucienThomss.
La Tcnue d e s C o m p t d n W s en P.6rbd.e d ’ h
stabilitk Mone‘taire. Park, Bditione d’expertu, 1927; LucienThomas.
.La R k v b h des Bitans ir L’lsw de la Pk&L 8InstabilU Monktaire.
Paris, k&thna Zexpe~ta,1828. Atso compare Dr. F. Schmidt, Die Induatriekm&nlctw-ein Rechenfehler! Zeitachrift fiir BetriebwJirtschatt,
Jahrg. 1927, and Ist Wertiinderung am tuhen&n V d g e n Uewinn Oder
Verlwt?, Zeibhrift fiir Betriebewirtaohaft, Jahrg. 1928.

:, %
<e”.

r

, x

, <>

7..

,

-

CHAPTER I11
SOME COMMON PITFALIA
3

f

51. Introduction

INthelast chapter wesaw thatthe figureexpressing
the rate of interest depends on the standard of value in
t which present and future goods are expressed, and we saw
how therate of interest inone standard (such m the
!k standard of r e d income) is to be derived from the rate of
2
interest in any other standard (such as the actual monetary standard).
This translation of the rate of interest from one standard into another does not determine the rate of interest
.?
in any standard whatever; for it assumes that the rate in
j some one standard is already known, and merely enables
us, on the baais of this known rate, to calculate the rates
fI
in other standards. The case is somewhat similar to the
conversion of temperature from the Fahrenheit system
1 int.0 the Centigrade system. By suchconversionwe can
1 calculate the Centigrade temperature, but only on coni dition that we already know the Fahrenheit temperature.
The formula connecting the two does not enable us, in
the least, to find out how hot or cold the weather is.
i
While the deviations of the money rate of interest from
i the real rate &reof tremendous practical importance, they
'! may be regarded as belonging more to the problem of
:
money than to the problem of interest, and, in the chap.'
ters whichfollow,
these deviations will, unl- otherI:45 1
1
t

z

a

1

t

THE THEORY OF INTEREST
wise specified, be disregarded. The reader may, therefore,
in this theoretical study keep to the hypothesia that the
monetary unit remains unchanged in purchasing power,
with the result that the money rate of interest and the
real rate coincide. That is to say, the rate of interest is
assumed to be at once the premium on this year’s money
in terms of next year’s and the same premium on this
year’s real income in terms of next year’s.
This premium, that is, the terms of exchange of this
year’sincome and next year’s, maybe said to depend, in
brief,on the relative supply and demand of those two
portions of the income stream; and this statement may
be interpreted &s including almost the entire impatience
and investment opportunitytheory of this book. But, like
many brief statements, this supplyand demand statement
is crude and inadequate. Crude and inadequate notions
beset thissubjectand some of themare so common and
treacherous that it seems worthwhile, before proceeding
with further rtnalyais, to examine these notions in order
to avoid falling into their pitfalls.
To say that the rate of interest is fixed by supply and
demand is merely to state, not to solve the prob1em.l
Every competitive price is fixed by supplyand demand.
The real problem is to analyze the particularsupplyand
demand forces operative in determining the rate of interest.
Nor axe we greatly enlightened by saying that in one
sense the rate of interest is the price of money. For it is

‘InChapters XI and XI1 supply and demand m
e
a will be derived
from the principles of impatience and opportunity. It will also be shown
thatimpatience is not to be associated with demand to the exclusion
of mpply, nor opportunity with supplyrather than demand, nor vioe
versa

[&I

q

-i
i

..-

t

’.t
?

y::
‘

1”
w.

/
!

!

G

4

s

SOME OOMMON PITFAUS
i

eqwUy true, in another sense, that the purchasing power
of money is the price of money. Yet the rate of interest
: and thepurchasing power of money are two very diiferent
things.
i Nor is it very illuminating to say thatthe rate of inj terest is the price paid for the use of money, especially as
; the money whose use is purchased is usually not money
at all but credit-nor is either the money or credit liter' ally used continuously during the loan. It disappears a t
fIP the beginning and reappears at the end.
I Enough has already been said to show that an increase
in the quantity of money in circulation tends to raise the
price level and consequently to depreciate the value of
the money unit. This depreciation in turn tends to increase the rate of interest. Yet, there is a very persistent
belief that an increase or decrease in the quantity of
money in circulation causes a decrease or increase in the
rate of interest. This fallacy seems to be baged on a confused interpretation of the general observation that the
rate of interest generally rises or falls with a decrease or
increase in the reserve ratio of banks. While it is true
i that if new money first finds ita way from the mint into
! the banks, it tends to lower the rate of interest, this ef:. fectis temporary. The maladjustment between the money
in banks and in circulation is soon corrected as the demand
for loans overtakes the supply. As far as the total
$
j supply of money is concerned, if this is doubled in amount
i andprices are thereby, in the end, doubled too, t.here is
double the money to lend, but borrowers will require
4 double the amount of mney. At the doubled prices they
will need twice the money to make the s a w purchM.
The demand is doubled along with the supply and &e
interest rate remains as before.
f
47 1
2

4

I
'

i

,

THE THEORY OF INTERIBT
$2. The Ezploitatwn Explancction of Idereat
Another very persistent idea is that to take intereat
is, necessarily and always, to take an unfair advantage of
the debtor. This notion is something more than the obviously true idea that the rate of interest, like any other
price, may ,be exorbitant. The contention is that there
ought to be no interest at all. Throughout history this
thought recurs. It seems naturd that only what was
borrowed should bereturned. Why any addition? Interest
is therefore called unnatural.
The wordusedby the Greeks to signify interest, or
usury, waa T ~ K O S , “offspring”; and Aristotle declaimed
against the taking of interest, on the ground that money,
being inanimate, did nothave offspring. The Mosaic
law forbade interest taking between Jews, and, similarly
in Rome, interest taking between Romans was prohibited.
Many biblical texts show the hostile attitude of the writers, in both the Old and New Testaments, toward the
practice. The Church Fathers, through the Middle Ages
for over a thousand years, waged a ceaselessbut fruitless
war against interest taking, St. Thomas Aquinas stated
that interest waa an attempt to extort a price for the use
of things which had already been used up,as, for instance,
grain and wine. He also declared that interest constituted
a “pawent for time,” and that no such payment could
be justifled since time was a free g i f t of the Creator to
which all have a natural right.
In fact, interest taking is often prohibited in primitive
societies. Loans under primitive conditions are generally
made for consumption rather than for productive purposes. Industry and trade being almost unknown, the
demand for loans in such communities u~u&1Iybetokens

[a3

SOME COMMON PITFALL8
the personal dietress of the borrowers. The loasnegotiations take place (between two personsunder isolated conditions without a regular market. The protection which B
modern loan market sffords against extortionate prices is
absent. Thus, there is, in many cases, a sound ethical basis
for the complaint9 against interest. But experience shows
that complete prohibition of interest cannot be d e effective. Interest, if not explicitly, will implicitly persist,
deapite all legal prohibitions. It lurks in all purchases and
sales and is an inextricable part of all contracts.
Today the chief survival of the exploitation idea is
among Marxian Socialists. These rtasert that the capitalist exploits the laborer by paying him for only part of
what he produces, withholding a portion of the product
of labor as interest on capital. Interest is therefore condemned as robbery. The capitalist is described aa one who
unjustly reaps what the laborer has sown.
Suppose that & tree twenty-five years old is worth $15,
and was planted at a cost of $5 worth of labor. The laborer
wm paid $5 when the tree was planted, The capitalist
who pays him receivesthe $15 twenty-five years later and
thereby enjoys $10 increase of value, which is interest on
his $5 investment, the cost of planting the tree. Why does
not the laborer who planted the tree get this increase of
$10 instead of the capitalist?
The socialist exploitation theory of interest consists
virtudy of two propositions: first, that the value of any
product, whencompleted, usually exceeds the cost of
production incurred during the proceases of its production; and secondly, that the value of any product, when
completed, “ought” to be exactly equal to that cost of
production. The first of these propositions is true, but the
second is false; or, at any mte, it is an ethical judgment

E491

THE THEORY OF INTEREST
masquerading as a scientific economic fact. Economists,
strange to say, in offering answens to the socialists, have
often attacked the first proposition instead of the second.
The aocialkt is quite right in his contention that thevalue
of the product does exceed the cost,2 In fact, this proposition is fundamental in the whole theory of interest.
There is no necessity that the value of a product must
equal the costs of production. On the contrary, it never
can normally be so.
In attempting to prove that the laborer should receive
the whole product, the socialist stands on stronger
ground than hassometimes been admitted byoverzealous defenders of the capitalist system. The socialist
cannot be answered offhand simply ,by
asserting that capital aids labor, and that the capitalist who owns a plow
earns the interest payment for its use quite as truly as
the laborer operating the plow earns his wagesby his
labor. For the socialist carries the argument back a stage
earlier, and contends that the payment for the use of
the plow should belong, not to the capitalist who owns it,
but to the laborers who originally made it, including
those who made the machinery which helped to make it.
He is quite correct in his contention that the value of
the uses of the plow is attributable to those who made it,
and that, nevertheless, the capitalist, whonowowns it,
not the laborers who madeit in the past, enjoys the value
of these uses. The capitalist is, in a sense,always living on
the product of past labor. An investor who gets his income from railroads, ships, or factories, alI of which m
products of Mor, is reaping what past labor has sown.
'While thie wrtion ie made dogmatically at thia point, the proof
of ita soundness is contained in Chapter XX, 7, and in the Appendix
to chapter XIL

l-501

SOME COMMON PITFALLS
But the investor is not, as a necessaryconsequence, a
robber. He has bought and paid for the right, economic
and moral well aa legal, to enjoy the product ascribable
to the capital goods he owns. The workers' wages, under
free competition, constitute payment in full forwhat they
had produced at the time their wages were paid.
Take the case of the tsee which was planted with labor
worth $5, and which, 25 yeam later, wasworth $15.
The socialist v i r t d y asks, Why should not the laborer
receive $15 instead of $5 for his work? The answer is:
He may receive it, provided he will wait for it 25 years.
As Bohm-Bawerk says:
"The perfectly just proposition that the laborer should receive the
entire value of his product may be understood to mean either that
thelaborer should now receive the entire present value of hia
product, or shouldreceive theentirefuture
vdue of his product
in the future. But Rodbertus and the Socialista expound it aa if it
means that the laborer should w w receive the entire future value

of hia product."

Socialists would cease to think of interest as extortion
if they would try the experiment of sending a colony of
laborers into the unreclaimed lands of the West, letting
them develop and irrigate those lands and build railways
on them, unaidedbyborrowed
capital. The colonists
would h d that interesthadnot disappearedbyany
means, but that by waiting they had themselves reaped
the benefit of it. Let US my they waited five yews before
their lands were irrigated and their railway completed.
At the end of that time they would own every cent of
the earnings of both, and no capitalist could be accusedof
robbing them of it. But they would find that, in spite of
themselves, they had now become capitalists, and that

'BGhm-Bawerk, Capital and Interest,

c 51 1

p. 342.

THE THEORY OF INTEREST
they had become so by stinting for those five years, instead of receiving in advance, in the shape.of food, clothing, and other real income, the discounted value of the
railroad.
This example was almost literally redized in the case
of the Mormon settlement in Utah.Those who wentthere
originally possessed little capital, and they did not pay
interest for the use of the capital of others. They created
their own capitaland passed from the category of
laborers to that of capitalists. It will be seen, then, that
capitalists are not, as such, robbersof labor, but are laborbrokers who buy work at one time and sell its products
at another. Their profit or gain on the transaction, if risk
bedisregarded,is interest, a compensation for waiting
during the time elapsing between the payment to labor
and the income received by the capitalkt from the sale
of the product of labor.
$3. Interest Taking Survives all Opposition
Despite the persistence of the idea that interest is
something unnatural and indefensible, despite the opposition to it by socialists and others who rebel against the
existing economic system, despite all attempts to prohibit interest taking, there is not and never has been in
all recorded history any time or place without the existr
ence of interest.
Several centuries ago, 88 business operations increased
in importance, certain exemptions and exceptions from
the ineffectua1 prohibition of interest were secured.Pawnshops, banks, and money-lenders were licensed, and
the
purchase of annuities and the taking of land on mortgage
for money loaned were made legitimate by subterfuge.
One of the subterfuges by which the taking of interest
t 52 1

SOME COMMON PITFALL8
was excused suggeststhe true idea of interest as an index
ofimpatience. It wasconceded that, although a loan
should be professedly without interest, yet when the
debtor delayed payment, he should be fined for his delay
(mora), and the creditorshouldreceivecompensation
in the form of interesse. Through this loophole it became
common to make an understanding in advance by which
the payment of a loan was to be delayed year after yew,
and with every such postponement a fine was to become
payable.
Some of the Protestant reformem, while not denying
that interest taking was wrong, admitted that it was impossible to suppress it, and proposed that it should therefore be tolerated. This toleration was in the same spirit
as that in which many reformers today defendthe licensing of vicious institutions, such aa saloons,gambling
establishments, and houses of prostitution.
Today interest taking is accepted as a matter of course
except among Marxian socialists and a few others. But
the persistent notion that, fundamentally, interest is unjustified has given the subject a peculiar fascination. It
has been, and still is, the great economic riddle.
84. Naive Productivity Explanations
One of the most common superficialities in this field
of thought is the naive idea that interest expresses the
physical productivity of land, or of nature, or of man.
When the rate of interest is 5 per cent, nothing at first
thought seems more plausible than that this rate obtains
because capital goods will yield 5 per cent in kind. It
is alleged that because fruit trees bear apples or peaches,
and because a bushel of wheat sown has the power to
multiply into 50 bushels, and becauae a herd of cattle

1533

THE THEORY OF INTEREST
if unmolested may double in numbers every two years
intemt is therefore inherent in nature. As a matter of
fact, this productivity, as we shall see, is a real element
in the explanation of interest; but it ia not the only one
nor is it as simple aa it seems.
In some degree, the theory elaborated in this book is
a productivity theory, I am, therefore, not attempting to
refute all productivity theories indiscriminately but
merely to show the inadequacy of what BBhm-Bawerk
called the “na‘ive” productivity theory. This theory, or
fallacy,is not espousedbyany careful student of the
interest problem, but it exists in the minds of many before
they begin to analyse the problem. It confuses phy&al
productivity 4 with value return.
Following the principles of Chapter I, we may take, &s
an illustration, an orchard of ten acres yielding 1000
barreb of apples a year. The physicd productivity, 100
barrels per acre per year, does not of itself give any clue
to what rate of return on its v a l u e the orchard yields. To
obtain the value return on the orchard, we must reduce
both physical income and capital goods (the farm) to a
common standard of value. If the net annual crop of
apples is worth $5000 and the orchard is worth $100,000,
the ratio of the former to the latter, or 5 per cent, is a
rate of value return; and if this rate is maintained without, depreciation of the value of the orchard, this rate of
value return is also the rate of interest. But how can we
thus pass from heterogeneous quantities to homogeneous
values? How can we translate the ten acres of orchard
and the 1000 barrels of apples into a common standarddollars? May not this apparently simple step beg the
whole question? The important fact, and the one lost
The Nature oj Capital and Inwme, Chapter XI.

c541

SOME COMMON PITFALLS
sight of in the naiveproductivityfallacy, is that the
value of the orchard is not independent of the value of
its crops; and, in this dependence, lurks implicitly the
rate of interest itself.
The statement that “capitaJ producea income” is true
only in the physical sense ; it is not true in the value
sense. That is to say, capital value does not produce income value. Onthe,contrary, income value produces capital value. It is not because the orchard is worth $100,000
that the annual crop will be worth $5000, but it is because the annual crop is worth $5000 net that theorchard
willbeworth $100,000, if the rate of interest is 5 per
cent. The $100,000 is the discounted valueof the expected
income of$5000 net per annum; and in t’he process of
discounting, a rat,e of interest of 5 per cent is already
implied. In general, it is not because a man has $100,000
worth of property that he will get $5000 a year, but it is
because he will getthat $5000 a year that his property is
worth $lOO,OOe-if the pre-existing rate of interest remains unchanged.
In short, we are forcedback to the confession that
whenwe are dealing with the values of capital and income, their causal connectionis the reverse of that which
holds true when we are dealingwith their quantities.
The orchard is the source of the apples; but the value of
the apples is the source of the value of the orchard. In
the same way, a dwelling i s the source of the shelter it
yields; but the value of that shelter is the source of the
value of the dwelling. In thesame way a machine, a factory, or any otherspecies of capital instrument is the
source of the services it renders but the value of these
services is the source of the value of the instrument which
renders them.
f 551

T m T&EORY OF INTEREST
This principle is complicated, but not impaired, by the
fact that the cost of production of further dwellings,
machines, tools, and other capital plays B part. The
principlewhich reste on future incomes,including, of
course, items of negative future income (costs) applies
to any existing capital at any stage of its existence. The
value of anything (asindicated in Chapter I, and more
fully in The Nature of Capital and Income) is typified by the case of a bond whose value, as every broker
knows, is calculated solely from the future services, or
sum, expected and the rate of interest and the risk. The
cost of producing other competing housesor other instruments so valued, in so,far as that cost lies in the future,
has an important influence. Past costs may also affect the
value of tbe house by influencing through competition
the
value of the future services or disservices of that house,
or the rate of interest, or the risk. Thus, cost plays an
important r6le but not the simple one usually assumed.
Although business men are constantly employing this
discounting processin the valuation of every specific item
of property bought or sold, they often cherish the illusion
that somehow,somewhere,there is capital whichdoes
not get its value by discounting future services but has
already made value which produces interest.They persist
in thinking of interest as moving forward intime instead
of as discount moving backward.
The necessity of presupposing a rate of interest is reinforced by observing the effect of a change of the rate of
productivity. If an orchardcould in somesudden and
wholly unexpected way be made to yield double ita origind crop per me, only its yield in the sense of physical
productivity would be doubled; its yield in the sense of
the rate of interest would not n e c e d y be affected at

P I

SOME COMMON PITFALLS
d l , certainly not do&"
because the value of the
orchardwould automatically advancewith an increme
in its value productivity.
The rate of physical productivity is evidently not the
rate of interest. The rate of physical productivity is not
ordinarily even the same kind of magnitude 88 the rate
of interest. Bushels of wheatproduced per acre is an
entirely different sort of ratio from the rate per cent of
the net value of the yield of land relative to the value of
the land. Interest is a rate per cent, an abstract number.
Physical productivity is a rate of one concrete thing relatively to another concrete thing incommensurable with
the first.
$5. Two Other Pitfalls
In this chapter I have tried at least to mention, if
not completely to remove in advance, the chief pitfab
or impedimenta to the understanding of the interest
problem. Two other pitfalls, discwed elsewhere, may be
here mentioned so that the reader may 'be on his guard
against them also.
One is the idea that interest is a cost. While an interest
payment, like any other payment, is a cost or outgo to
the payer, it is income to the payee. But interest itself,
as it accrues, is capital gain ; and is neither negative income (cost) nor positive income. The fallacious idea that
it is a cost is simply the other side of th0 fallacious idea,
discussed in Chapter 1, that it is income. There are two
'It is true, however, an will become more apparent later, that if the
inrreu.se in productivity is foreseen, the rate of interest will be temporarily raised. But after the transition period ia over and the supposed
doubledproductivity is thereafter going on at asteadyrate, the rate
of inter& will fall back; in fact, other thing8 equal, it will fall below
what it was before productivity waa increaeed.

f 57 3

THE THEORY OF INTEREST
kinds of economic gain, capital gctin and income gain, the
f m e r being the anticipation or discounted value of the
latter. Interest is the former kind. It gradually &ccrues,
dong a discount curve a8 the income which it anticipates
grows nearer. But it is not itself income, nor is it cost.*
The other pitfall is the idea that interest is a certain
psrt of the income stream of society, the part namely
which goes to capital, the other parts being rent, wages,
and profits. I shd,in Chapter XV, discuss the relation
of interest to the whole problem of the distribution of
wealth. But it may help if the reader is again warned
at this point, as he has already been warned in Chapter I,
against the idea that any one part of the income stream
has an exclusive relation to the rate of interest. All income is subject to discount, or capitalization, that from
land as well as that from (other) capital goods. And if the
whole income stream of society, including all wages, all
rents and all profits were capitalized, that whole income
could still be regarded as a rate per cent, i.e., interest on
its own capitalization, just as truly as can the income of
the bondholder or rentier.
'For fuller discussion see The Rate of Interest, pp. 38-51,and below
Chpter XX, $7 and the Appendix to Chapter M of this volume.

PART 11. THE THEORY IN WORDS
CHAPTER IV. TIME

PREFERENCE

(HUMAN
IMPA-

TIENCE)

CHAPTER V. FIRSTAPPROXIMATION
TO THE) THEORY
OF INTEREST
CEAPTER VI. SECOND
APPROXIMATION
TO THE THEORY
OF INTEREST
CHAPTERVII. THE INVESTMENT
OPPORTUNITYPRINCIPLES

CHAPTERVIII. DISCUSSION
OF THE SECOND
APPROXIMATION

CHAPTER IX.THIRDAPPROXIMATION
TO THE THEORY
OF INTEREST

CHAPTER IV
TIME PREFERENCE (HUMAN IMPATIENCE)
$1. Preference for Present over Future

Income

IN the preceding chapter we mentioned some pitfalls
in the explanation of interest. We are now ready to consider moresearchingly thefundamental causeswhich
determine the rate of interest. We shall find a place for
each of the partial truths contained
the inadequate
theories.
Many people think of interest as dependent directly on
capital. As already suggested, it will help the reader to
proceed in the following analysis if he will try to forget
capital and instead think exclusively of income. Capital
wealth is merely the means to the end calledincome,
tk
while capital value (which is the sense in which the e
capital is ordinarily used 'by interest theorists) is merely
the capitalization of expected @come.
The theory of interest bears a close resemblanceto the
theory of prices, of which, in fact, it is a specid aspect.
The rate of interest expresses a price in the exchange between present and future goods. Just as, in the ordinary
theory of prices, the ratio of exchange of any two articles
is baaed, in part, on rt psychological or subjective element
"their comparative maxginal desirability-so, in the
theory of interest, the rateof interest, or the premium on
the exchange between present and future goods, is based,
in part, on; subjective element, a derivative of marginal
, i n

[el 1

THE THEORY OF INTEREST
desirability; namely, the marginal preference for present
over future goods. This preference has been called time
preference, or humun impdienee. The chief other part is
an objective element, investment opportunity. It is the
impatience factor which we shall now discuss, leaving the
investmentopportunity factor for discussion in later
chaptern.
Time preference, or impatience, plays a central r61e
in the theory of interest. It is essentially what Rae
calls the “effectivedesirefor accumulation,” and what
Bijhm-Bawerk c d s the “perspective undervaluation of
the future.” It is the (percentage) excess of the present
marginal want for one more unit of present goods over
the present marginal want for one more unit of futwe
goods. Thus the rate of t,ime preference, or degree of impat,ience, for present over future goods of like kind is
readily derivedfrom the marginal desirabilities of, or
wants for, those present and future goods respectively?
‘Or ophelimity, utility, wantsbility, or the want for one more unit.
The Natwe oj Capital and Income, Chapter III; also my articles,
Is ‘ V W d the Most Suitable Term for the Concept It Is Used to DeSee

note?

AmericanEconomicReview,June,

Stetistical Method jm Measuring

1918, pp. 335-337; and A
and Testing the

“Marginal Utility”

Justice of a Progressive Income T m . Economic Essays Contributed in
Honor of John Bates Clark,pp. 157-193.
‘To bemorespecific, we obtain the rate of time preferencefor a
present dolIar over a dollar one year hence by the following procese:
(a) tske the present want for one morepresent dollar; and
(b) the present want for one more dollar
due one year henee; and
then
(c) subtract (b) from (a); and finally
(d) measure the result (c) as a percentage of (b).
In tern of the usual illustrative figures, if a pment dollar is worth
105 wantabs(want units) and a next year’s dollar is now worth 100
wantab, then the difference, 6, is 5 per cent of the latter.
For a more strictly mathematical formulation, we Appendix to
Chapter XII, 41.

c 621

TIME PREFERENCE (IMPATIENCE)
82. Reduction to Enjoyment Income

What are these goode.whichaxe thus contrasted? A t
first sight it might seem that the goods compared may
be indiscriminately wealth, property, or services. It is
true that present machines are in generalpreferred to
future machines; present houses to future houses; land
possessed today to land available next year; present
food or clothing to future food or clothing; present stocks
or bonds to future stocks or bonds; present music to future music, and so on. But a sllght examination will show
that some of these cases of preference are reducible to
others.
When present capit.al wealth, or capital property, ie
preferred to future, this preference is really a preference
for the incomeexpected to flow from the first capital
wealth, or capital property, as compared with the income
a
from the second. The reasonwhy wewouldchoose
present fruit tree rather than a similar tree available in
ten years is that the fruit yielded by the &st will come
earlier than the fruit yielded by the second. The reason
one prefers immediate tenancy of a house to the right to
occupy it in six months is that the uses of the house
under the first leasehold begin six months earlier than
under the second. In short,capital wealth, or capital
property, available early is preferred to thecapital
wealth, or capital property of like kind, available at a
more remote time simply and solely because the income
from the former is available earlier than the income from
the latter.
Thus all time preference resolves itself in the end inh
the preference for comparatively early income over comparatively remote, or deferred, income. Moreover, the

c631

THE THEORY OF INTEREST
preference for early, or prompt, income over late, or deferred, income resolves itself into the preference for early
m j o y t m t income over deferred enjoyment income. Any
income item which consista merely of an interaction or,
otherwise expressed, of a preparatory service a (that is,
an itemwhich,while it isincome from onespeciesof
capital, is outgo in respect to another species) is wanted
for the sake of the enjoyment income fo which that interaction paves the way. The consumer prefers the service of milling flour in the present to milling flour in the
future because the enjoyment of the resulting bread is
available earlier in the one cme than in the other. The
manufacturer prefers present weaving to future weaving because the earlier the weaving takes place the sooner
will he be able to Bell the cloth and realize his enjoyment
income.
To him, early sales are more sdvmtageous than deferredsales, not because he desires the cloth to reach
ih ultimate destination mner, but because he will the
m n e r be in a position to make use of the purchase price
for his own personal uses-the helter md comforts of
various kinds constituting his income.
The manufacturer is conscious of only one step toward
the ultimate god of clothes-the money he expects to get
for the cloth from the jobber to whom he sells it. But
this money payment in turn discounts a further step.
To the jobber this money he pays is the discounted value
of the money he will receive from the wholesaler, and so
on through the retailer, tailor and wearer. The result is
that each is unconsciously discounting, BS the ultimate
link in the chain, the enjoyment to be derived by the
wearer of the clothes. Of course this is not the whole
'SeeThe Nature of C a w +andI m m e , Chapter X.

[MI

TIME PREFEJXENCE (IMPATIENCE)
story, but it represents the main psrts relevant to the
present problem.
All preference, therefore, for present over future goods
resolves itself, in the last analysis, into a preference for
early enjoyment income over deferred enjoyment income.
This simple proposition would have received definite attention earlier in the history of economics had there been
at hand a clear-cut concept of income. The stream of
future enjoyment income plays the essential r6le.
But, as explained in Chapter I, for practical purposes
we may well stop at the objective services of wealth, as
measuredby its cost-the cost of living-that is, the
money values of nourishment, clothing, shelter, m u s &
ments, the gratifications of vanity, and theother miscellaneous items in our family budget. It is the money value of
this income stream uponwhich attention now centers.
Henceforth, we may think of time preference as the
preference for a dollar’s worth of early real income over a
dollar’s worth of deferred real income. It is assumed, then,
that the income goods are reduced to a common money
denominator, and that the prices of ad items of real
i n c o m e t h e prices of nourishment, shelter, clothing,
amusements, etc.-are predetermined.
In these caaes, aa already noted, no appreciable time
elapses between valuation and realization. We pay for
a basket of fruit and eat it forthwith. But we pay for a
fruit tree and wait years for the fruit. So in the prices
of many other enjoyable services-nourishment, shelter,
etc.-no discount element, or rate of interest, enters or,
at any rate, it does not enter in the direet way is which
it enters in caae of interaction^.^ That is, in the present,
‘It is true, of coum, that, in determining economic equilibriunh, every
variable theoretically affects every other, and the rate of intemt, aa

c 651

THE THEORY OF INTEREST
the price of present real income contains no appreciable
interest to complicate the problem because these goods
am consumed so soon after purchase; snd for the same
reason in the future price of future real income there is
no appreciable interest element. When,however, any
goods other than enjoyable goods are considered, their
valuea already contain a rate of interest. The price of a
house ie the discounted value of its future income. Hence,
when we compare the values of present and futurehouses,
both terms of the comparison already involve a rate of
interest. Although, m will benoted more specificallylater,
such a complication wouId not necessarily beg the question, its elimination simplifies the picture.
$3. Impatience Depends on Income
Time preference, a concept which psychologicalIy underlies interest, lends it'self to express any situation, either
preference for present as against future goods or preference for future as against present goods or for no preference. The term impatience carries with it the presumption that present goods are preferred. But I shall treat the
two terms (impatience and time preference) as synonymous. Henceforth the term impatience will be the one
chieflyused partly because its meaning is moreselfevident, partly because it is shorter, and partly because
it does carry a presumption as to the uswll direction of
the time preference. The degree of impatience varies, of
course, with the individual, but whenwe have selected
our individual, the degree of his impatience depends on
his entire income stream, beginning at the present instant and stretching indefinitely into the future; that is,
one variable, must therefore be assumed to d e c t i n M y the price of
everything else by atrecting ita supply and demand.

[MI

TIME PREFERENCE (IMPATIENCE)
on the amount of his expected real income and the manner in which it is expected to be distributed in time. It
depends in particular on the relative abundance of the
early as compared with the remote income items-or
what we shall call the time shape of the expected income
stream. If income is particularly abundant in the future;
that is, if the person expects an increase in his income
stream, he would willingly promiseto sacrifice out of that
increase,when it comes, a relatively large s u m for the
sake of receiving a relatively small sum at once. Thus
the possessor of a strawberry patch might, in winter, be
of strawberries, due in
willing to exchangetwoboxes
six months, for one available today. On the other hand,
if immediate income is abundant butfuture income
scarce, the opposite relation may exist. In strawberry
season, the same man might willingly give up two boxes
of his then abundant crop for the right to only one box in
the succeeding winter. That is, time preference may not
always be a preference for present over future goods; it
may, under certain conditions, be the opposite. Impatience may be and sometimes is negative!
It is, therefore, not necessary in beginning our study
of interest to distinguish, as many writers do, between
the principles which lead to the edtence of interest and
those which regulate the rate of interest. By the existence
of interest these writers mean that the rate is greater
than zero. It seems preferable to reverse the order of
the two problems and seek first to find the principles
whichfix the terms on which present and future goods
exchange, without restricting ourselves in advance to the
thesis that, always and necessarily, present goods command a premium over future goods. If our principles permit the deviations from par to be in either direction, this
671

r

TEE THEORY OF INTEREST
will mean that themte of interest may under certain circumstances be zero (i.e., non-existent), or even negative,
so that, in such a case, future goods would command a
premium over present. After these general principles have
been eatabliahed a special study will then be in order to
discover why the rate of interest is, in actual experience,
almost never zero or negative.
We noted, in Chapter 11, that when gold, or any other
durable commodity capable of being stored or kept without cost, is the standard of comparison, the rate of interd below zero. Does
est in terms of that standard cannotf
the reamn why interest is, in general experience,positive rather than negative lie entirely in human nature?
Or does it lie partly in the income stream? These special
questions can best be answered after we have found the
general principles by which the rate of interest, be it
positive, negative, or zero, is determined.
4. Interest and Price Theory

The preference of any individual for early over deferred income depends upon his presentas compared with
his prospective income and corresponds to the ordinary
theory of prices, which recognizes that themarginal want
for any article depends upon the quantity of that article
available. Both propositions arefundamental in their
respective spheres.
The relationship of these problems, and others,may be
schematized roughly as shown in Chart 4 which follows.
In this chart A and B reprment present prices of enjoyable goods, and A ’ and B ’ prices of future enjoyable
goods. A and A ’refer to different years in the same place,
say New York; B and B ’ are similar except that they relate to a Merent place, say London.

c 68 1

TIME PREFERENCE (IMPATIENCE)

All prublems of local prices, exchange, and interest, act
and react on each other in many ways. The problem of
“time” foreignexchange, or forward foreign exchange,
is indicated by the diagonals, and involves both interest
and foreign exchange, i.e., both a time to time factor and
a place to place factor combined in the same transaction.
Both exchange and interest rates, aa well as local prices,
would be, theoretically, combined if, say, present New
York wheat were quoted in term of future London cod.
In this book, for simplicity, the problem of price determinations, in oneplace and at onetime, are supposed
to have been s01ved.~We start with the values of the
’For a &dement of the theory of valuation in general, B ~ BWdras,
8l.h.ents &‘BcoMmie P&&
Pwe; Pareto, Coura d%conomie Po&
t+;
dm, Monusl imwtmie PaE*.

c 69 3

,

THE THEORY OF INTEREST
item in the income stream ready made.Likewisewe
neglect the problem of foreign exchange; we are studying only the problem of interest.
$5. Specifications of Income

In the above schematicpicture only twoperiods of time
are represented. In actual life there are manyperiods-m
indefinite number of them. Theoretically there might be
a rate of interest connecting every pair of possible dates.
For instance, there might be a rate of interest between the
present and one year hence, another between one year
hence and two years hence, and soon, all these rates
being quotable in today’smarkets. In practice no rates are
actually quotedexcept
those connecting the present
(which, of course, merely means a future date near the
present) with several moreremotely future dates. A
rate on LI five year contract may be considered aa a sort
of an average of five theoretically existing rates, one for
each of the five years covered.
Except when the contrary is specifically mentioned, it
will henceforth be understood, for the sake of simplicity,
that there is only one rate of interest, the rate of interest,
appIicable to all time intervals. This may be most conveniently pictured to mean the rate connecting today
with one year hence, Even this rate of interest connecting two specific dates separated by one year depends on
(or, in technical terminology, is a function of) conditions
not only at these two dates but at many other dates.
When it is said that the impatience of an individual depends on his future income stream, it is meant that the
degree of his impatience for, say, $100 worth of this
year’s income over $100 worth of next year’s income depend.~upon the entire character of his expected income
c 70 3

TIME PREFERENCE (IMPATIENCE)
stream pictured as beginning today and extending into
the indefinite future, with specific increases or decreases
at different periods of time.
If we wish to be still more meticulous, we may note
that a person’s incomestream is madeup of a large number of different elements,filaments, strands, or fibem,
some of which represent nourishment, others shelter,
others amusement, and 80 on-all the components of red
income. In a complete enumeration of these elements,
we should need to distinguish the use of each Merent
kind of food, and the gratification of every other variety
of human want. Each of these constitutes a particular
thread of the income stream, extending out from the present into the indefinite future, and varying at different
points of time in respect to size and probability of attainment. A person’s t,ime preference, or impatience for income, therefore, depends theoretically on the size, time
shape, and probability (as looked at in the present) of
this entire collection of income elements as we may picture them stretching out into the entire future.
I n summary, we may say then that an individual’s
impatience depends on the foIlowing four characteristics
of his income stream:
1. The size (measured in dollars) of his expected real
income stream.
2. Its expected distribution in time, or its time ahape
-that is, whether it is constant, or inerewing, or decreaaing, ur sometimes one and sometimes the other.
3. Its composition-to what extent it consista of nourishment, of shelter, of amusement, of education, and
ao on.
4. Its pobabitity, or degree of risk or uncertainty.
We shall consider these four in order.
c71 I

THE THEDRY OF INTEREST
$6. The InfEuence of Mere Size

Our first step, then, is to show how a person’s impatience depends on the size of his income, assuming the
other three conditions to remain constant; for, evidently,
it is possible that two incomes may have the same time
shape, composition and risk, and yet differ in size, one
being, say, twice the other in every period of time.
In general, it may be said that, other things being equal,
the smaller the income, the higher the preference for
present over future income; that is, the greater the impatience to acquire income as early aa possible. It is true,
of course, that a permanent.ly small incomeimplies a
keen appreciation of future wan& as well as of immediate
wants. Poverty bears down heavily on all portions of a
man’sexpectedlife. But it increases the want for immediate income even more than it increases the wast
for future income.
This influence of poverty is partly rational, because
of the importance, by supplying present needs, of keeping
up thecontinuity of life and thus maintaining the ability
to cope with the future ; and partly irrational, becauae
the pressure of present needs blinds a person to the needs
iof the future.
As to the rational aspect, present income is absolutely
indispensable, not only for present needs, but even aa a
pre-condition to the attainment of future income. A man
must live. Anyonewho
values his life would, under
ordinary circumstances, prefer to rob the future for the
benefit of the p r e s e n t s o far, at least, as to keep lice
going. If a person has only one loaf of bread he would
not set it aside for next yeax even if the rate of interest
were loo0 per cent; for if he did so, he w o d starve in

c 72 1

TIME PREFERENCE(IMPATIENCE)
the meantime. A single break in the thread of life euffices to cut off all the future. We stress the importance
of the present because the present is the gateway to the
future. Not only is a certain minimum of present income
necessary to prevent stamation, but thenearer this minimum is approached the more precious does present income appear relative to future income.
A0 to the irrational aspect of the matter, the effect of
poverty is often to relax foresight and self-control and to
tempt us to “trust to luck” for the future, if only the allengrossing need of present necessities can be satisfied.
We see, then, that a small income, other things being
equal, tends to produce a high rate of impatience, partly
from the thought that provision for the present is necessary both for the present itself and for the future as well,
and partlyfrom lackof foresight and self-control.
07. The Znflwnce of Time Shape
The concept of time shape of the income stream is
best treated not apartfrom sizebut as combined with size
and thus will constitute a complete specification of the
size at each successive period of time. Types of income
of different time shap- are shown on the charta in Chapter I. Uniform income is represented in Chart 1; increasingincomein Chart 2 ; decreasing income in Chast 3.
Fluctuating income is represented in both Charts 2 and 3.
The fact that a person’s income is increasing tends to
make his preference for present over future income high,
as compared with what it would be if his income were
flowing uniformly or at a slackening rate; for an increasing income means that the present income is relatively
‘Cf. Landry, L’Zdr8t du Cqittal, Chapter X, 0 149, pp. 311316;
0150, pp. 316317.

C 73 1

THE THEORY OF INTEREST
scarce and future income relatively abundant. A man who
is now enjoying an income of only $5000 a year, but who
expects in ten years to be enjoying one of $lO,OOO a year,
will today prize a dollar in hand far mom than the pros-

pect of a dollar due ten years hence. His great expectations make him impatient torealize on them in advance.
He may, in fact, borrow money to eke out this year’s income and promiserepayments out of his supposedly more
abundant income ten years later. On the other hand, a
progressivelydwindlingincome,onesuch
that present
income is relatively abundant and future incomereltlr
tively scarce, tends to appease impatience-i.e., to reduce
the want for present &s compared with that for future income. A man who has a salary of 9610,000 at present but
expects to retire in a few years on half pay will not have
a veryhigh rate of preferencefor present over future
income. He may even want to savefrom his present
abundance in order to provide for coming needs.
These are, of course, only some of the various effects
which various time shapes have on time preference. The
important point is that it does make a difference to B
man’s time preference whether his income has one time
shape or another, just as it makes a difference whether
his income is, as a whole, Iarger orsmaller.
The extent of these effects will, of course, vary greatly
with Werent individuals. If two persons both have exactly the same sort of ascending income, one may have a
rate of time preference,ordegree of impatience, indicated by 10 per cent, while the other may have one of only
4 per cent. Whet we need to emphmize here is merely
that, if for either man a descending income were substituted for an ascendingincome, he wouldexperience a
reduction of impatience; the first individual’s might fall
c 74 1

TIME PREFERENCE (IMPATIENCE)
from 10 to 7 per cent, and the second’s from, say, 4 to 3
per cent.
If, now, we consider the combined effect on time preference of both the size and the time shape of income, we
shall observe that those with s m a l l incomes are much
more sensitive to time shape in their feeling of impatience
than are those with larger incomes. For a poor man, a
very slight stinting of the present suffices to enhance
enormously his impatience for present income; and o p
positely, a very slight increase in his present income will
sufficeenormously to diminish that impatience. A rich
man,on the other hand, presumably requires a relatively
large variation in the comparative amounts of this year’s
and next year’sincome in order to suffer any material
change in his time preference.
It will be clearto readers of Bohm-Bawerk that thedependence of time preference on the time shape of a person’s income stream is practically identical with what he
called the “first circumstance” making for the superiority
of present over future goods:
“The first great cause of d ~ e r e n c ein value between present and
future goods consists in the difierent circumstances of want and pro, If a person is badly in want of
vision in present and future.
certain goods, or of goods in general, while he has reason to hope
that at a future period he will be better off, he will always value
a given quantity of immediately available goods at a higher figure
than the same quantity of future goods.”

. .

The only important difference between this statement
and that here formulated is that in this book the “provision” has the definite meaning contained in the income
concept.
It is only for completeness that I have included in the
&hm-Bawerk, T b Positive Themy of C a M , p. 249.

c 751

THE THEORY OF INTEREST
list of characteristics of income&ecting interest the
composition of the income. It recognizes the fact that,
strictly speaking, a man’s red income is not one simple
homogeneous flow of money, but a mosaic or skein of
threads of many heterogeneous elements of psychic experience. An income of $5000 may comprise for one individual one set of enjoyable services, and for another, an
entirely different set. The inhabitants of one country may
have relatively more house shelter m d less food in their
real incomes than those of another. Those differences will
have, theoretically, an influence in one direction or the
other upon the time preference. Food being a prime necessity, a decrease of the proportion of food, or nourishment, even though total income remain the same, will
have an effect upon the impatience similar to the effect
of the diminution of total income.
For practical purposes,however, we may ordinariIy
neglect the characteristic of income called composition;
for ordinarily any variation in the mere composition of
family budgets will very seldom be suEcient to have any
appreciable effect on the rate of interest.
Hereafter, therefore, all the elements of income will
beconsidered 88 lumped together in a single sum of
money value. Our picture of income henceforth may be
considered aa a flag or pennant without regard to stripes
but seen as 8 whole, stretching out into the future. Each
man’s pennanthas 8 definite width varying with the
distance from the flagstaff.
$8. T& Influence of Rtkk
We comefinally to the element of risk. Future income is
always subject to some uncertainty, and this uncertainty
must naturally have an influence onthe rate of time prefI76 1

TIME PREFERENCE(IMPATIENCE)
erence, or degreeof impatience, of its pwesaor. It is to be
remembered that the degree of impatience is the percentage preference for $1 certain of immediate income, over
$1, also certain, of income of one year hence, even if all
the income except that dollar be uncertain. The influence
of risk on time preference, therefore, means the influence
of uncertainties in the anticipated income of an individual upon hisrelative valuation of present andfuture
incrementa of income, both increments being certah.
The manner in which risk operates upon time preierence will differ,among other things, according to the particular periods in the future to which the risk applies. If,
as is very common, the possessor of income regards his
immediately future income as fairly well mured, but
fears for the safety or certainty of his income in a more
remote period, he may be aroused to a high appreciation
of the needs of that remote future and hence may feel
forced to save out of his present relatively certaia abunto supplement his relatively uncertain
danceinorder
income later on. He is likely to have a low degree of impatience for a certadn dollar of immediate income aa compared with a certain dollar added to a remoter uncertain
income.
Such a type of income is, in fact, not uncommon. The
remote future is usually less known than the immediate
future, a fact which .of itself means risk or uncertainty.
The chance of disease,accident, disability, or death is
always to be reckoned with ; but under ordinary circumstances this risk is greater in the remote future than in
the immediate future. As a result, uncertainty has a
tendency to keep impatience down. This tendency is expremed in the phrase ‘‘tolay up for a rainy day.” The
greater the risk of rainy days in the future,the greater the

c 77 1

TRE THEORY OF INTEREST
impulse to provide for them at the expenae of the present.
But sometimes the relative uncertainty is reversed, and
immediate income is subject to higher risk than remote
income, Such is the case in the midst of a war, in a strike,
or other misfortune, believed to be temporary. Such is
also the case when an individual is assured a permanent
position with a salary after a certain date, but, in the
meantime, must obtain a precarious subsistence. In these
caaes the effect of the risk element is to enhance the estimation inwhich immediate income isheld.
Again, the risk, instead of applying especially to remote periods of time or especially t o immediate periods,
may apply to all periods alike. Such a general risk largely
explains why salaries and wages, being relatively assured,
are generally lower than the average earnings of those
who take the risks incident to being their own employers.
It rtlso explainswhyt.hebondholder
is content with a
lower average return than the stockholder. The bondholderchoosesfixed and certain income rather than a
variable and uncertain one, even if the latter is, on the
average, larger.In short, a risky income, if the risk applies
evenly to all parts of the income stream, is equivalent to
a low income. And, since a low income, as we have seen,
tends to create a high impatience, risk, if distributed in
time, uniformly or fairly so, tends to raise impatience.
It follows, then, that risk tends in some cases to increase
and in others to decrease impatience, according to the
time incidence of the risk. But there k a common pipciple in all these cases. Whether the result is a high or a
low time preference, the primary fact is that the risk
of losing the income in a particular period of time operates, in the eyes of most people, a virtual impoverish-

c 78 1

TIME PREFERENCE(IMPATIENCE)
ment of the income in that period, and hence increasesthe
estimation in which s unit of certain income in that
particular period is held. If that period is a remote one,
the risk to which it is subject makes for a high regard for
remote income; if it is the present (immediate future),
the risk makes fora high regard for immediate income; if
Ohe risk applies to all periods of time alike, it acta aa a
virtual decrease of income all along the line.
There are, however, exceptional individuals of the
gambler type in whom caution is absent or perverted.
Uponthese, risk will havequitethe opposite effects.
Some persons who like to take great speculative chances
are likely to treat the future as though it were especially
well endowed, and are willing to sacrifice a large amount
of their exaggerated expectations for the sake of a relatively small addition to their present income. In other
words, they will have a high degree of impatience. The
same individuals, if receiving an income which is risky
for all periods of time alike, might, contrary to the rule,
have, as a result, a low instead of a high degree of impatience.
The income to which risk applies may be, of course,
either the income from articles of capital externalto man
or the income from man himself, considered as an income
producer. In the latter case, often called earned income,
the risk of losing the income is the risk of death or invalidism. This risk-the uncertainty as to humanlife,
health and income producing power-ia somewhat Merent from the uncertainty of income flowing fromobjective
capital: for the cessation of life not only causes a cessation of the income produced by the dying human machine, but also a cessation of the enjoyment of all income whatmever-or rather a transfer of the enjoyment
C 79 3

THE THEORY OF INTEREST
to posterity of any income continuing after death. This
is because the individual isin the double capacity of
being at once a producer and a consumer.
The effect of risk, therefore, is manifold, according to
the degree and range of application of risk. to various
periods of times. It also depends on whether or not the
risk relates to the continuation of life; and if so, according to whether or not the individud's interest in
the
future extends beyond his own lifetime. The manner in
which these various tendencies operate upon the rate of
interest will be discussed in Chapter IX.
59. The Personal Factor
The proposition that, in thetheory of interest, the impatience of a person for income depends upon the character of his income" to its size, time shape, and probability-does not deny that it may depend on other factors b o , just as, in the theory of prices, the proposition
that the marginal want for an article depends upon the
quantity of that article does not deny that it may depend
on other elements as well.
But the dependence of impatience on income is of chief
importance; for impatience, whatever else it depends on,
is always impatience for incom-xactly
as the dependence of the marginal want for bread on the quantity of
bread is more important than the dependence of this
marginal want for bread on the quantity of some other
commodity, such as butter.8
We have seen, therefore, how a given man's impatience
'For a theoretical dieouasion of marginal want w B funotion of mriow factore, me my Mathmnatid Investigatione in th The- of
Value and A i c e s . For a mathematical formulation of impatience as
a function of mccesaive installments of income, 8ee Appendix to this
chapter, $7. See also Pareto, Manuel #&wnmnie Politiqwr, p. 886 et reg.

I W

TIME PREFERENGE (IMPATIENCE)
depends both upon the charscteristica of his expected income stream, and on his own personal characteristics. The
rate of impatience which corresponds to a specific income
stream will not be the same for everybody. This has already been noted, incidentally, but requires special discussion here. One man may have an annual rate of time
preference of 6 per cent, and another10 per cent, although
both have the same income. Impatience differs with different persons for the same income and with different incomes for the same person. The personal differences are
caused by differences in at least six personal characteristics #: (1) foresight, (2) self-control, (3) habit, (4) expectation of life, ( 5 ) concern for the lives of other persons, (6) fashion,
(1) Generally speaking, the greater the foresight, the
less the impatience, and vice versa.1oIn the case of primitive races, children, andotheruninstructed
groups in
society, the future is seldom considered in its true proportions. This is illustrated by the story of the farmer
'Cf. Rae, s o e i o l o ~Theory of C-,
p. 5 2 ; Xhm-Bawerk, Ths
Positive Theory of Capital, Book V, Chapter III.
To be exact, however, we should observe that lack of foresight may
either incresse or decrease time preference. Although most peraons who
lackforesight err byfailing to give due weight to the importance of
future needs, or, what amounts to the m e thing, by estimating overconfidently the provision existing for such future needs, case8 are to be
found in which the opposite error is committed; that is, the individual
exaggeratea the needs of thefuture or underestimatesthe provision
likely to be available for them.Such people stint themselves needlessly,
even impairing health by insufficientfood in their &orfa to eave for
the dreaded future. Their lack of foresight in this c & ~ ee m in underestimating instead of overestimating future income and so makes them
too patient inatead of too impatient. But in order not to oomplioste
the text, only the former and more common error will be hereafter referred to when lack of foresight is mentioned. The reader may, in e d
such case, readily add the pomibility of the conbry

error.

C81l

THE TE.fEORY OF INTEREST
who would never mend’his Ieaky roof. When it rained he
could not stop the leak, and when it did not rain there
was no leak to be stopped! Amongsuchpersons,
the
preference for present gratification is powerful because
their anticipation of the futureis weak. In regard to foresight, Rae states: l1
“Theactual presence of the immediate object of desire in the
mind, by exciting t.he attention, 8eem8 to rouse all the faculties, as
it were, to 6x their view on it,and lead^ them to a verylively
conception of the enjoyments which it offers to their instant possession. The prospects of a future good, which future years may hold
out to UB, seem at such a momentdull and dubious, and are apt
to be slighted, for objects on which the daylight is falling strongly,
and showing usin all theirfreshness just within our grasp. There
is no man, perhap, to whom a good to be enjoyed to-day, would not
seem of very diEerentimportance,fromoneexactlysimilar
to be
enjoyedtwelveyears hence, even though the arrival of both were
equallycertain.”

The sagacious business man represents the other extreme; he is constantly forecasting. Many great corporations, banks, and investment trusts today maintain
statistical departments largely for the purpose of gauging the future developments of business. The carefully
calculated forecasts made by these and independent
services tend to reduce the element of risk, and to aid
intelligent speculation.
Differences in degrees of foresight and forecasting ability produce corresponding differences in the dependence
of time preference on the character of income. Thus, for
a given income, say $5000 a year indefinitely, the reckless might have a degree of impatience or rate of time
preference of 10 per cent, when the forehanded would
experience a preference of only 5 per cent. In both e m ,
pRae,SocidogiccrtThemyojfCbpitol,p.64.

I: 82 3

TIME PREFERENCE (IMPATIENCE)
the preference depends on the size, time shape, and risk
of the income; but the particular rates corresponding
to a particular income will be entirely different in the
two cases. Therefore, the degree of impatience, in general,
w
l
l
itend to be higher in community consisting of reckless individuals than in one consisting of the opposite
type.
(2) Self-control, though distinct from foresight, is usually associated with it and has very similar effects. Foresight has to do with thinking; self-control, with wdliazg.
Though a weak will usually goes with a weak intellect,
this is not necessarily so, nor always. The effect of a weak
will is similar to the effect of inferior foresight. Like those
workingmen who, before prohibition, ,could not resist the
lure of the saloon on the way home Saturday night, many
persons cannot deny themselves a present indulgence,
evenwhen they know what the consequenceswillbe.
Others, on the contrary, have no difficulty in stinting
themselves in the face of all temptations.
(3) The third characteristic of human nature which
needs to be considered is the tendency to follow grooves
of habit. The influence of habit may be in either direction. Rich men’s sons, accustomed to the enjoyment of B
largeincome, are likely to put a higher valuation on
present compared with future income than would persons
possessing the same income but brought up under different conditions. When those habituated to luxury suffer a
reverse of fortune they often find it harder to live moderately than do those of equal means who have risen
instead of fallen in the economic scale; and this will be
true even if foresight and self-control are inherently the
same in the two cases. The former, brought up in the lap
of luxury, will be more likely to be the prodigal son,

[SI

THE THEORY OF INTEREST
that is, the more impatient for present income. me k l c
of such traditions among the Negroes tends t o w d 8
high rate of impatience, while thetraditions of thrift
among the Scotch curb impatience.
Our thrift campaigns axe designed to reduce impatience
by cultivating certain habits of regular saving out of income, So also is the propaganda for life insurance with
its high-pressure salesmanship. On the other hand, the
corresponding salesmanship for installment buying tends,
in the first instance, in the opposite direction. The individual can indulge himself in the immediate enjoyment of a radio or an auto.Yet, ,itmust notbe overlooked
that, after the sale is made, there ensues a new responsibility to provide for the future payments agreed upon
which may permanently improve the faculties of foresight and self-control.
(4) The fourth personal circumstance which may influence impatience for immediate real income has to do
with the uncertainty of life of the recipient. We have
already seen, in asomewhat different connection, that
the time preference of an individual will be affected by
the prospect of a long or short life, bothbecause the
termination of life brings the termination of the income
from labor, and because it also terminates the person’s
enjoyment of all income.
It is the latterfact in which we are interested here-the
manner in which the expectation of life of a person
affects the dependence of impatience on his income.
There will be differencesamong different classes, different individuals, and different ages of the same individual. The chance of death may be said to be the most
important r u t W factor tending to increase impatience;
anything that would tend to prolong humm life would
I: 84 1

TIME PREFERENCE (IMPATIENCE)
tend, at the same time, to reduce impatience. Rae goes
so fstr &s to say: la
"Werelife to endure forever, were the capacity to enjoy in perfection all its goods, both mentalandcorporeal,
tobe prolonged
with it, and were we guided solely by the dictates of reaaon, there
could be no limit to,the formation of meam for future gratification, till our utmost wishes were supplied. A pleasure to be enjoyed,
or a pain to be endured, fifty or a hundred years hence, would be
considered deserving the sameattention 88 if it were to befall US
sfty or a hundred minutes hence, andthe sacrifice of a smaller
present good, for a greatm future good, would be readily made, to
whatever period that futurity might extend. But life, and the power
to enjoy it,arethe mostuncertain of all things, and we are not
guidedaltogether by reaaon. We know not the period when death
may come upon us, but we know that it may come in a few day,
and must come in afew years. Why then be providing goods that
cannot be enjoyed until times, which, though not very remote, may
never come to ,w, or until timea still moreremote, and which we
are convinced we shall never see? If life, too, is of uncertain duration andthetime that death comea between us and aU our possessionsunknown, the approaches of old age are at least certain,
and are dulling, day by day, the relish of every pleasure."

The shortness of life thus tends powerfully to increase
the degree of impatience, or rate of time preference, beyond what it would otherwise be. This is especially evident when the income streams compared are long. A lover
of music will be impatient for a piano, i.e., will prefer a
pian? at once to a p b o available next year, because,
l
l
iget one more
since either will outlast his own life, he w
year's use out of a piano available at once.
( 5 ) But whereas the shortness and uncertainty of life
tend to increase impatience, their effect is greatly mitigated by thefifth circumstance, solicitude for the welfare
of one's heirs. Probably the most powerful cause tending
"Rae, The-S

Them of Capita?,pp. 53-54,
[ 85 I

THE

THEORY
OF INTEREST

to reduce the rate of interest is the love of one’s children
and the desire to provide for their good. Wherever these
sentiments decay, as they did at the time of the decline
and fall of the Roman Empire, and it becomes the fashion
to exhaust wealth in self-indulgence and leave little or
nothing to offspring, impatience and the rate of interest
will tend to be high. At such times the motto, “After us
the deluge,” indicates the feverish desire to squander in
the present, at whatever cost to the future.ls
On the other hand, in a country like the United States,
where parents regard their lives as continuing after death
in the lives of their children, there exists a high appreciation of the needs of the future. This tends to produce a
lowdegree of impatience. For persons with children,
the prospect of loss of earnings through death only
spurs them all the more to lay up for that rainy day
in the family. For themthe risk of loss of income
the risk of
through deathisnot
verydifferentfrom
cessation of incomefrom any ordinary investment;in
such a cme the risk of cessation of future income
through death tends to lower their impatience for income. This act supplies the motivefor life insurance.
A man with a wife and children is willing to pay a high
insurance premium in order that they may continue
to enjoy an income after his death. This is partly responsiblefor the enormousextension of life insurance.
At present in the United States the insurance on lives
amounts to over $lOO,OoO,OOO,OOO. This represen&, for
the most part, an investment of the p m n t generation
for the next.
An unmarried man, on the other hand, or a man who
cares only for self-indulgence and does not care for pos*See

Rae, The S o d o g i d Them of Capitcrl, p. 97.
[: 86 1

TIME PREFERENCE (IMPATIENCE)
terity, a man, in short, who wishes to “make the day and
the journey alike,” will not try thus to continue the income after his death. In such a case uncertainty of life is
especially calculated to produce a high rate of time preference. Sailors, especially unmarried sailors, offer the classicexample. Theyare natural spendthrifts, and when
they have money use it lavishly. The risk of shipwreck is
always before them, and their motto is, “A short life and
a merry one.” The same is even more true of the unmarried soldier. For such people the risk of cessation of life
increases their impatience, since there is little future to
be patient for.
Not only does regard for one’s offspring lower impatience, but the increase of offspring has in part the same
effect. So far as it adds to future needs rather than to
immediateneeds, it operates, like a descendingincome
stream, to diminkh impatience. Parents with growing
families often feel the importance of providing for future
years f a r more than parents in similar circumstances but
with small families. They try harder to save and to take
out life insurance; in other words, they are less impatient. Consequently, an increase of the average size of
family would, other things being equal, reduce the rate
of interest.
This proposition does not, of course, conflict with the
converse proposition that the same prudent regard for
the future which is created by the responsibilities of parenthood itself tends to diminish the number of offspring.
Hence it is that the thrifty Frenchman and Dutchman
have small families.
(6) The most fitful of the causes at work is probably
fashion. This at the present time acts, on the one hand,
to stimulate men to save and become millionaires, and,
187 1

THE THEORY OF INTEREST
on the other hand, to stimulate millionaires to live in an
ostentatious manner. F d i o n is one of those potent yet
illusory social f o m which follow the laws of imitation
so muchemphasizedby Tarde;** Le Bon,I6 Baldwin,la
and other writers. In whatever direction the leaders of
fashion first chance to move, the crowd will follow in
mad pursuit until almost the whole social body will be
moving in that direction. Sometimes the fashion becomes
rigid, as in China, a fact emphasized rby Bagehot;l‘ and
sometimes the effect of a too universal follawing is to
stimulate the leaders to throw off their pursuers by taking somenoveldirection-which
explains the constant
vagaries of fashion in drw. Economic fashions may
belong to either of these two groups-the fixed or the
erratic. Examples of both are given by John
It is
of vast importance to a community, in its influence both
on the rate of inhest and on the distribution of wealth
itself, what direction fashion happens to take. For instance, should it become an established custom for
millionaires to consider it “disgraceful to die rich,” as
Carnegie expressedit, andbelieve it de rigzlezlr to give the
bulk of their fortunes for endowing universities, libraries,
hospitals, or other public institutions, the effect would be,
through diffusion of benefits, to lessen t!he disparities in
“Tarde, G.Social Laws. English translation. New Yo&, Macmillan
and Co., 1896. Also Les L
o
& & I’lmitotwn. Paris, Germer Bajllihre e t
C., 1895.
The Psychology of Socialism. Englieh translation. London, T. Fisher
Unwin, 1899. Also The Crowd.
‘SO&-! and Ethioal I n t e r p t e t a h in M e d a l DeveIopment. New
York, Macmillan and Co., 1906.
Bagebot, Walter. Physics and Politics. New York, D. Appleton and
Co., 1873, Chapter ID.
“See The Socioloeiwl Theow of Capita2, Appendix, Article 1, pp.

24-276.

E
S
l

TIME PREFERENCE (IMPATIENCE)
the distribution of w d t h , and also to lower the mte of
interest.

810. The Personal FactorSummarized
Impatience for income, therefore, depends for each
individual on his income,on its size, time shape, and
probability; but the particular form of this dependence
differs according to the various characteristics of the individual, The characteristics which will tend to make his
impatience great are: (1) short-sightedness, (2) a weak
will, (3) the habit of spending freely, (4)emphasis upon
the shortness and uncertainty of his life, ( 5 ) selfishness,
or the absence of any desire to provide for his survivors,
(6) slavish following of the whims of fashion. The reverse conditions will tend to lessen his impatience;
namely, (1) a high degree of foresight, which enables
him to give to the future such attention as it deserves;
(2) a high degree of self-control, which enables him to
abstain from present real income in order to increase
future real income; (3) the habit of thrift; (4) emphasis upon the expectation of a long life; ( 5 ) the possession
of a family and a high regard for their welfare after his
death; (6) the independence to maintain a proper balancebetween
outgo and income, regardless of Mrs.
Grundy and the high-powered salesmen of devices that
are useless or harmful, or which commit the pumha8er
beyond his income prospects.
The resultant of these various tendencies in any one
individual will determine the degree of his impatience at
a given time, under given conditions with a partdczrlar
imome stream. The result will differ as between individuals, and at different times for the same individual.
The same individual in the course of his life may

r 891

THE THEORY OF INTEREST
changefromone
extreme of impatience to the other.
Such an alteration may *be causedby change in the person's nature (aswhen a spendthrift is reformed or a man,
originally prudent, becomes, through intemperance, reckless and thriftless),or by variation in hisincome, whether
in respect to size, distribution' in time, or uncertainty.
Everyone at some time in his life doubtless changes his
degree of impatience for income. Inthe come of an
ordinary lifetime the changes in a man's degree of impatience are probably of the following general character:
as a child he will have a high degree of impatience b e
cause of his lack of foresight and self-control; when he
reaches the age of young manhood he may still have a
highdegree of impatience, but for a different reason,
namely, because he then expects a large future income.
He expects to get on in the world, and he willhave a high
degree of impatience because of the relative &bundance
of the imagined future as compared with the realized
present. When he gets a little further along, and has a
family, the result may be a low degree of impatience,
because then the needs of the future rather than its endowment will appeal to him. He will not think that he
is going to be so very rich ; on the contrary, he will wonder how he is going to get along with so many mouths to
feed. He looks forward to the future expenses of his wife
and children with the idea of providing for them-an
idea which makes for a high relative regard for the future
and 8 low relative regard for t.he present. Then when he
gets a little older, if his children are married and have
gone out into the world and are well able to take care
of themselves, he may again havea high degree of impatience for income,because he expects to die, and he
thinks, "Instead of piling up for the remote future, why

C90l

TIME PREFERENCE (IMPATIENCE)
shouldn’t I enjoy myself during the few years that
remain?”
$11. Income Rather Than Capital in the Leading R6k
The essential fact, however, is that for any gwen individual at any given time, his impatience depends in a
definite lnrtnner upon the size, time shape, and probability of his income stream.
This view, that the degree of impatience and, consequently, the rate of interest depend upon income, needs
to be contrasted with the common view, which makesthe
rate of interest depend merely on the scarcity or abundance of capital. It iscommonlybelieved
that where
capital is scarce, interest is high, and where capital is
plentiful, interest is low. In a general way, there is undoubtedly some truth in this belief; and yet it contains
a misinterpretation of borrowing and lending.
In the first place, we must distinguish between capital
wealth and capital value. It is capital value of which
mostpeople think when theysay capital. But capital
value is merely capitalized income. Behind, or rather beyond, a capital of $100,000 is the stream of income which
that capital represents, or rather the choice of any one
k attention- on the
among many possible streams. To f
$loO,0oO capital instead of on the income which is capitalized is to use the capita,l
a cloak to cover upthe
red factor in the caae.
Moreover, capital value is itself dependent on a preexisting rate of interest. As we know, the capital value
of a f a r m will be doubled if the rate of interest is halved.
In such a case there would seem to be more capital in
farm than before; for the farms in a community would
rise, say, from $lOO,OOO,OOO to $2OO,OOO,0o0. But it is not

[913

THE THEORY OF INTEREST
the rise in capital valuewhich produces this fall in interest. On the contrary, it is the fall in the interest rate which
produces the rise in the capital. If we attempt to make
the rate of interest depend on capital value, then, since
capital value depends on two factors-the
prospective
income and the rate of interest-we thereby make the
interest rate depend partly on income and partly on itself.
The dependence on itself is of course nugatory, and we
are brought back to its dependence on income as the only
fact of real significance. It is present and future income
that are traded against each other.
But, even as thus amended and explained, (that capital
stands for income) the proposition that the rate of interest depends on the m o u n t of capital is not satisfactory.
For the mere amount of capital does not tell us enough
about the income for which the capital stands. To know
that one man has a capital worth $lO,OoO,O00 and another
hm a capital worth $20,000,000 shows, to be sure, that
the latter man can have an income of double the value
of the former; but it tells us absolutely nothing as to the
time shapes of the two incomes actually selected; and
the time shape of income has, as we have seen, a most
profound influence on the time preference of its possessor, and time preference is a prime determiner of interest.
To illustrate this important fact, let us suppose that
two communities differ in the amount of capital and the
character of the income which that capital represents but,
as far as possible, are similar in all other respects. One
of these two communities we &all suppose has a capital
of $lOO,OOO,0oO, invested, as in Nevada, in mines and
quarries nearly exhausted, while in the other community
there is $~,OOO,OOO of capital invested in young orchards and forests, as in Florida. According to the theory

192 1

TIME PREFERENCE (IMPATIENCE)
that abundance of capital makes interest low, we should
expect the Nevada community to have a high rate of interest compared with the Florida community. This would
ordinarily be true if the twocommunities had income
streams differing only in size with the same time shapes
and probabilities. But, under our assumptions, it is evident that, unless other circumstances should interfere,
the opposite would be the case ; for Nevada, due to the
progressive exhaustion of her mines, is faced by a decreasing future income, and in order to offset the depreciation
of capital which follows from this condition,le she would
be seeking to lend or invest part of the income of the
present or immediate future, in the hope of offsetting the
decreased product of the'mines in the more remote future.
The Florida planters, on the contrary, would be inclined
to borrow against their future crops. If t,he two communities are supposed to be commerciallyconnected, it would
be Nevada which would lend to Florida notwithstanding
the fact that the lending community was the poorer in
capital of the two. From this illustration it is clear that
the mere amount of capital value is not only a misleading
but a very inadequate criterion of the rate of interest.2O
Apologists for the common idea that abundance or
scarcity of capital lowers or raises interest might be inclined to argue that it is not the total capital, but only
the loanable capital which should be included, and that
the Nevada community had more loanable capital than
the Florida community. But the phrase loanable capital
is merely another cloak to cover the fact that it is not the

XIV.

mSee The Nature of Capital and Income, Chapter
"One of the few defects in Rae's analysis of interest, or at any rate
of his statement of it, is his emphasis on theaccumulation of capitsl.
Since this accumulation is merely in anticiption of future income, the
emphasis belongs on the latter.

1931

THE THEORY OF INTEREST
m o u n t of capital, but the decision to lend or borrow it,
(or the income stream which the capital standsfor) which
is important.
We end, therefore, byemphasizing again the importance of fixing our eyes on income and not on capital. It
is only 89 we look through capital value at the income beyond that we reach the effective causes which operate
upon the rate of interest. It has, perhaps, been the absence of a definite theory and conception of income which
has so long prevented economists from seeing these relations. Borrowing and lending are in form a transfer of
capital, but they are in fact a transfer of income of which
that capital is merely the present value. In our theory
of interest, therefore, we have to consider not primarily
the amosnt of capital of a community, but the future
expected income for whichthat capital stands.
$12. Impatience Scltedules

Unfortunately for purposes of exposition, the relation
between impatience and income cannot be expressed in a
simple schedule or a simple curve, as can the relation
between demand and price, or supply and price, or marginal want and quantity consumed, for the reason that
income means not a single magnitude merely, but a conglomeration of magnitudes. As mathematicians would
express it, to state that income impatience depends on
the character of income, its size, shape, and probability
is to state that this impatience is a function of all the
different magnitudeswhichneed
to be specified in a
complete description of that income. A geometrical representation, therefore, of the dependence of time preference
on the various magnitudeswhich characterize income
would be impossible. For a curve can be in two dimen-

c 94 1

TIME PREFERENCE (IMPATIENCE)
sions only and hence can represent the dependence of a
magnitude on only one independent variable. Even a
surface can only represent dependence on two. But for
our requirement, i.e., in order to represent the &pendence of a man’s impatience on the infinite number of
successive elements constituting his income stream, we
should need not two or three dimensions simply but a
space of n dimensions.
We may represent, however, the relation between time
preference and income by a schedulelike the ordinary
demand schedule and supply schedule, if we make a list
of income streams of alI possible sizes, shapes, and probabilities, specifying for each individual income all its
characteristicoits size, time shape (that is, its relative
magnitude in successive time intervals),andthe
certainty or uncertainty of its various parts, to say nothing
of its heterogeneous and varying composition. Having
thus compiled a list of all possibleincome streams, it
would only be necessary for us to assign to each of them
the rate of impatience pertaining to it.
Such a schedule would be too complicated and cumbersome to be carried out in detail; but the following will
roughly indicate some of the main groups of which it
wouldconsist. In this schedule I have represented, by
the three horizontal lines, three different classes of income
-two extreme types and one mean type-so that the
corresponding rates of time preference range themselves
in a descending series of numbers. The three vertical columns show three different claases of individuals, two being of extreme types, and the third of a mixed or medium
type. Thus, the numbers in the table grow smaller aa we
proceed toward the right and as we proceed downward,
the smalest numbers of all being the lower right-hand

E 95 1

THE THEORY OF INTEREST
corner. This represents a man whose rate of impatience
is only 1 per cent, being low both because his income is
large, decreasing and assured, and because his nature is
farsighted, self-controlled, accustomed to save, and desirous to provide for heirs.
TABLII
1
TIME+P-CKI

OF D I F ~ ~ N IN^T

.m WITH DXFFI~NT
INCOMES

Individuals whoare
shortsighted,
weak willed, of amixed
accuetomed or medium
to spend,
type
without heim

.

Income small, i n c r e k g
precanous
Income of amixed or me.
dium type
Income large, decreasing, a5
m d

farsighted,
wlf-controlled,
accuetomed
to save, desirous to
provide for
heirs

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

20%

10%

5%

10%

5%

2%

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

6%

2%

1%

This schematic representation is, in the effort to be
general, rather vague.We may bemorespecific if, instead of thinking of a man’s income stream as uncertain
and variable at every point, we think of it, for the moment, m certain throughout and as invariable, or frozen,
at all points of time except two-the present time andone
year hence.
Restricted by this highly artificial hypothesis, we can
construct for the man an impatience and demand schedule and demand andsupply schedulesfor loans and
interest analogous to the ordinary utility schedule aad
demand or supply schedule for commodities and prices.

[MI

TIME PREFERENCE (IMPATIENCE)
Thus the demand schedule might be that a certain prospective borrower is willing, for each successive one hundred dollars added to his present income, to give, out of
nezt year's income, as follows:
For the fir& $100, $120, his impatience rate being, therefore, 20%
U
u
11
"
second $100, $115, u
15%
11
u
11
"
"
third
$100,
$110,
l1
10%
u
u
m
"
'I
fourth
$100, $106, "
"
6%
II
11
11
u
$6
fifth $100, $105, "
l1
5%
u
u
61
I'
sixth $100, $104, "
I'
4%

Such a schedule is expressed geometrically in Chapters
X and XI.
Since the time preference of an individual is a derivative of his marginal want for present and his marginal
want for future income, the abovescheduleislikewise
a sort of derivative of the ordinary want schedules (utility schedules) of present and future income. Butthe
more general schedulepreviouslygiven, not restricted
to two years, but recognizing uncertainty and variabilityl
of the person's income stream at all its points, is more
appropriate for our present purpose.
Wesee then that each individual has a rate of impatience dependent on his own personal nature and on
the nature of his income. If all individuals' incomes were
rigid, that is, incapable of being modified, and if there
were no loan or money market by which immediate and
future income couldbe exchanged, there could beno common market rate of interest. There would be a separate
rate of time preference for each individual. One man
would be willing to part with $100 today for the sake of
$101 next year, while another would require $200 or
$1000. But nothing would happen towad equaJizing these
divergent rates.
C971

THE THEORY OF INTEREST
But given a loan market, the individuals toward the
end of the list will tend to borrow; and those toward the
beginning will tend to lend. The effect of such operations
is to reduce the high rates of time preference and to increase the low ones until a middle ground is reached in
the common rate of interest. This process will be discussed in the following chapter.

CHAPTER V
FIRST APPROXIMATIONTO THE THEORY OF
INTEREST

Assuming Each Person’s Income Stream Foreknown and
Unchangeable Except by Loans
81. Hypothmes of First Approximation

IN the last chapter we reached three conclusions:
(1) that the rateof time preference, or impatience for
present over future goods, is, in the last analysis, a preference for present over future enjoyment income, or, let
us say, real income;
(2) that the degree of impatience depends, for any
given individual, upon the character of his real incomestream-in particular, on its size, time shape, and probability;
(3) that the nature of this dependencediffers with
Merent individuals.
The question a t once arises: will not the actualdegrees
of impatience of different individuals necessarily be very
different, and if so, what relation do these different rates
have to the market rate of interest? Is the market rate
of interest a sort of average of these individual degrees
of impatience, or does it equalize them?
It is doubtless true that the
different rates of impatience
of different individuals who are not connected through a
common loan market do vary widely. In a nation of

c 99 1

THE THEORY O F INTEREST
hermita, in which there existed no mutual lending and
borrowing, individuals wouldbe independent of each
other. But, among ourselves who have access to a common loan market, borrowing and lending do, at least, tend
to bring into equality the marginal rates of impatience
in different minds. Absolute equality is not reached even
among those making use of such a market; but this is
because of the limitations of the market and, in particular, because of the risk element. This element will be
considered in the third approximation, but for simplicity
of exposition is omitted in the first two approximations.
Here we shall assume a perfectly competitive market,
one in which each individual is so small a factor as to
have, singly, no perceptible influence on the rate of interest, and in which there is no limitation on the amount
of lending and borrowing other than that caused by the
rate of interest itself. The would-beborrower is thus
supposed to he able to obtain large or small a loan aa
he wishes at the market price-the rate of interest. He is
not cut down to $5,000 when he iswilling to borrow
$blOO,OOO,merely because he cannot furnish enough collateral security or a satisfactory endorser. He can buy a
loan m he can buy sugar, as much or as little as he
pleases, if he will pay the price.
In the actual world, of course, no such perfect market
exists. While many people in New York City can obtain
aa large loam as they wish, there are thousands who axe
unable to obtain any at d.The price of a loan is paid
not in the present, as the price of sugar is paid, but in the
future. What the lender gets when he makes the loan is
not payment but a promise of payment, and the future
being always uncertain he needs some sort of assurance
that this promise will be kept. We &re asauming in the

11001

FIRST APPROXIMATION
firstand Becond approximations that there will never
be a lack of such assurance. This amounts almost to w
suming that there is no risk in the world. The element
of risk is assumed to be entirely lacking, both.with respect
to the certainty of the expected income streams belonging to the different individuals, and with respect to the
certainty of repayment for loans. In other words, we
assume that each individual in themarket is free to
give up any partof his income during one period of time
to some other person in consideration of receiving back
an addition to his ownincome during another period
of time.
We assume further that thus to buy and sell rights to
various parts of his income stream is the only method
open to any individual to alter his income stream. Such
trading between present and future dollars may be in
the form of loans, since a loan is the sale of future money
for present money, or it may be in the guise of buying
and selling bonds or other securities conveying title to
fixed sums of money. In any case the trading reduces
itself to buying and selling titles to future income. Prior
to such exchange, the income stream of each individual
is assumed to befixedinsize
and shape. Each capitd
instrument whichhepoasesses, including himself, is assumed to be capable of only a single definite series of
services contributing to his income stream. Each individual is a stipendiary with a definite income which he
receives and spends according to a foreknown s c h e d u l c
so much next year, so much the year Sfter,and SO forth.
Thus the assumptions of our first approximation are:
(1) that eachman’sincome stream is initially certain
and fisFed; (2) that he is a negligible element in a v&Bt
and perfect competitive loan market; (3) that, he h u

c 101 1

THE THEORY OF INTEREST
free access to this market,whether as borrower or lender,
to any desired extent, at the market rate; (4) that hie
sole method of modifying his future income stream is
through such borrowing or lending (or, more exactly and
generally, throughtrading income).
$2. Income Prescribed

Such assumptionsare, of course, highly theoretical.
They imagine a world in whichincomes are produced
spontaneously, as mineral water gushes from the spring.
Theypicturetheseincomebearingagents
as pouring
forth their income streams at rates which foUow a foreknown, rigid, and unchangeable schedule. There being
no flexjrbilityin the flow from any one article, there is
no flex&ility in the scheme of combined flow from the
whole group possessedby an individual. His total real
income is scheduled in advance withno possibility of
modScation except by borrowing or lending, buying or
selling.
The abstract natureof this hypothesis need not greatly
trouble us for two reasons: the first, and in itself quite
sufficient reason, is that most of the elements of this
hypothesis will be abandoned when we reach the second
approximation. It is adoptedtemporatily merely for
simplicity of exposition. Secondly, the hypothesis might
easily be made more realistic without changing its essential features. We might even alter our hypothesis of a
‘One consequence of this w m p t i o n (towure which the assumption
was really made) is that the capitalied vslue of each penson’s income
at B given rate of interest wiil be unchangeable. He is, 80 to ppesk, on
a definiteallowance,and any trading, a6 by borrowing, or mortgaging
him richer or poorer. It can only shift hie
the future,cannotmake
incomein time (with interest). The theoreticalsignificance of thie
constancy will appear in the aecond approximation.

c 102 1

FIRST APPROXIMATION
rigidly prescribed income st,ream to the hypothesis of
income stream which, while it may be decreased at will,
cannot beincreasedbeyondafixedamount
at each
period of time. While free to decrease his income in any
period, its possessor would not do so unless thereby he
could secure an increase in some other period.
Not only is such an hypothesis quite thinkable, it is
probably actually approximatedin primitive communities. In our own day most men have opportunities (quit,e
apart from lending to others at interest) to secure much
real income in future years by temporarily sacrificing a
little immediate real income as, for instance, by investing labor in building a house or machine. But we can
readily suppose a situation such that this year’s production and next year’s production wouldbe almost independent of each other. This situation is true of most animals and even of man in the hunting and fishing stage,
and before that stage even more markedly when his only
implements were his hands. And even in our own civilization, manyare mere stipendiaries, virtuallywithout
any opportunity to add to future income except by
lending at interest.
The essence of the hypothesis therefore on which the
first approximation rests is that we are not to be bothered by the posaibility of a man’s thus increasing his income in one period through decreasing it in another except through the process of trading some of one year’s
income with another person for some of another year’s
income.
We may in fact for practical purposes picture the income stream of eachperson aa thus k e d for only a
few y e w , and assume that expectation of income beyond
those years 80 indefinite as to have no effect on the

c 103 1

THE TaEORY OF INTEREST
present rate of interest. Such a community has been approximated in former years by the typical American
a m y camp isolated in a westerncommunityin which
each inhabitant) or family, had a prescribed income. A
aeries of such hypotheses will lead us through successive
approximations to an eventual picture of actuality.
$3. Equalization of Impatknce
Under the hypothetical conditionswhich have been
stated for the first approximation, the rates of time preference for different individuals will, by the process of
borrowing and lending,become. perfectly reconciled to
themarketrate of interest and to each other, forif,
for any particular individual, the rate of preference differs from the market rate, he will, if he can, adjust the
timeshape of his income stream so as to bring his
marginal preference rate into harmony with t,he interest
rate. A man who, for a given income st.ream, has a rate
of preference above the market rate will sell some of his
surplus future income in return for an addition to his
meager present income,i.e., he will borrow. This will
have the effect of enhancing his want for one more dollar
of future income and decreasing his want for one more
dollar of present income. The process will continue until
the rate of preference of this individual, at the margin,
is equal to the rate of interest. In other words, under our
hypothesis, 8 personwhosepreference rate exceeds the
current rate of interest will borrow up to the point at
which the two rates will become equal.
On the other hand, the man,whose temperament or
whose income stream or both give him a preference rate
below the marketrate, will buy future income with some
of his abundant present income, ie.,, he will lend. T h e
C1M1

FIRST APPROXIMATION
effect will be to inmeme his preference rate until, at the
margin, it harmonizes with the rate of interest.
To put t.he matter in figures, let us suppose the rate
of interest is 5 per cent, whereas the rate of preference
of a particular individual is, to start with, 10 per cent.
Then, by hypothesis, the individual is willing to sacrifice
$1.10 of next year’sincome in exchangefor $1 of this
year’s. But, in the market, he finds he is abEe to obtain
$1 for this year by foregoing only $1.05 of next year’s.
To him this latter ratio is a cheapprice.He therefore
borrows, say, $100 for a year, agreeing to return $105;
that is, he contracts a loan at 5 per cent, when he is
willing to pay 10 per cent. This operation partly satisfies
his hunger for present income by drawing on his future
income, andthus reduces his time preferencefrom 10
per cent to, say, 8 per cent. Under these circumstances
he will borrow another $100, being willing to pay 8 per
cent, but required to pay only 5. This operation will still
further reduce his time preference, aad so on through
successive stages, until it is h d y brought down to 5
per cent. Then, for the last or marginal $100, his rate of
time preference will agree withthemarketrate
of
int,erest.2
In like manner, if mother individual, enteringthe
loan market from the oppusite side, has a rate of prefer*The above-mentioned 10 per cent and 8 per cent rates of time preferenceare not ratesactuallyexperienced by him; theymerelymean
therates of preferencewhich he would have experienced had his income notbeen transformed to the time shape cornonding to 5 per
cent. AB in the general theory of prices, this marginal rate, 5 per cent,
being once established,applieainditferently
to dl hle ValUatiOnS Of
presentand future income. Every comparative estimate of present
and
future which he actually makeamay be said to be “on the win“of
his income &
a
m a.g actually determined.

c 105 1

THE THEORY OF INTEREST

ence of 2 per cent, he will become a lender instead of a
borrower. He will be willing to lend $100 of this year’s
. income for $102 of next year’s. As he can lend at 5 per
cent when he would do so at 2, he “jumps at the chance,”
and invests, not $100 only, but another and another. But
his present income, being drawn upon by the process, is
nowmore highly esteemed by him than before, and
his future income,being supplemented, i s less highly
esteemed; and under the influence of successive additions to the sums lent, his rate of preference for the
present wiIl keep rising untiI, at themargin, it will equal
the market rate of interest.
In such an ideal loan market, therefore, where every
individual could freely borrow or lend, the rates of preference or impatience for present over future income for
all the different individurtls would become,at the margin,
exactly equal to each other and to the rate of interest.
$4. Altering Income by Loans

To illustrate this reasoning by a chart, let us suppose
the income stream to be represent.ed as in Chart 5, and
that the possessor wishesto obtain, by borrowing, a small
item X of immediately ensuing income in return for a
somewhat larger item X” later on, X” being the amount
of X’ at interest. By such a loan he modifies his income
stream from ABCD to EBD. But this change will evidently produce a change in his time preference. If the
rate of time preference corresponding tothe income
stream represented by the unbroken line is 10 per cent,
the rate of preference corresponding to the broken line
will be somewhat less, say, 8 per cent. If the market rate
of interest is 5 per cent, it is evident that the person will
proceed to still furtherborrowing. By repeating the operaclw

FIRST APPROXIMATION

"'

"_

\
"
"

CHART 5
Effect of Borrowing Upon Present and Future Income.

tion several times he can evidently produce almost any
required conformation of his income stream.
If, instead of borrowing, he wishes to lend (Chart 6)
he surrenders from his present income stream the amount
X' for the sake of the larger amount X" at a later time.
After the operations are completed and the final conformations of the income streamsme determined, the

CHART 6
Effect of Lending Upon Present and Future Income.

c 107 1

THE THEORY OF INTEREST
rates of time preference are 811 brought into conformity
with the market rate of interest.
In practice, of course, the adjustments are never perfect and, in particular, the income stream is never a
smooth curve, such as it is here for convenience represented.
In practice, also, loans are effected under the guise of
money. We do not confessedly borrow and lend real incomes,,but money and credit. Yet money-that universal
medium in practice and universal stumbling-blockin
theory-merely represent'sreal income, or capitalized real
income. A hundred dollars mean the power to secure
income,-any income the present value of which is $100.
When, therefore, a personborrows $100 today and returns $105 next year, in actual fact hesecures the title to
$100 worth of income-immediately future, perhapsand parts with the title to $105 worth of income a year
later. Every loan contract, or any other contract implying interest, involves, at bottom, a modificat.ion of income
streams, the usual and chief modification being as to time
shape.
Onereasonwhy we often forget that a money loan
represents real income is that it represents so many
possible varieties of real income. A fund of money is
usually the capitalization not simply of one particular
future program, or lay-out, of income but of a large number of optional income streams, and is not restricted, as
in the first approximation, here considered, to a simple
income streamand its modification by loans or their
equivalent.
We may distinguish six principal types of individuals
in a loan market-three borrowing types and three lending types. The first type of borrower (Chart 7) is supc lB1

CEART 7
Effect of Borrowing Upon an
IncreasingIncome Stream.

CHART 8
Effect of Borrowing Upon a
Uniform Income Stream.

C U T9
Effect of Borrowing Upon a
Decreasing Income Stream.

CHART 10
Effect of Lending Upon a Decreasing Income Stream.

CHART I1
Effect of Lending Upon a Uniform Income Stream.

CHART 12
Effect of Lending Upon an Increasing Income Streem.

THE THEORY -OF INTEREST
posed to be possessed of an increasing, or ascending, income stream AB, a fact which, in his mind, results in a
rate of preference above ihe market rate. This leads him
to borrow, and relatively to level up hisascending income
stream toward such a position 85 A‘B’. The second type
of individual already possesses a uniform income stream
AB (Chart 8))but having, a strong propensity to spend,
he too experiences a rate of preference above the market
rate, and will therefore modify his income stream toward
the curve A’B’. The third type is shown in Chart 9 and
represents evenmore of a spendthrift. This individual
has also a rate of preference in excess of the market rate,
in spite of his having a declining income stream pictured
by thedescending curve AB.By his borrowing, he obtains
a curve A’B’ of still steeper descent.
In a similar way, the three types of lenders may be
graphically represented. Chart 10 represents a descending income AB, which the owner, by lending present
income in return for future income, converts into a relatively uniform income A’B’; Chart 11 represents a uniformincome converted, by lending, into an ascending
income; andChart 12 an ascendingincome converted
into a still more steeply ascending income.
The borrower changes his income curve by tipping it
down in the future and up in the present. The lender
tips his income curve in the opposite direction. Of the
three types of borrowers and of lenders, the first in each
group of three (see Charts 7 and lo), is the usual and
normalcase. In both these cases the effort is to transform the given income into a more uniform one, the rising curve (Chart 7) being lowered and the falling curve
(Chart 10) being raised toward a common horizontal
position. Chart 9 and Chart 12, on the other hand, repre-

I 110 3

FIRST APPROXIMATION
sent the extreme and unusual cases of the spendthrift
and the miser.
But whatever the personal equation, it remains true
that, for each individual, ot,her things being equal, the
more ascending his inwme curve, the higher his rate of
preference; and the more descending t'he curve, the lower
the rate of preference. If the descent of the income stream

3

CHART 13
Effects of Alternate Bornowing andLending Upon a Fluctuating
IncomeStream.

is sufficiently mpid, the rate of preference could be made
zero or even negative.8
These foregoing types of income streams axe, of course,
not the only ones which could be considered, but they are
some of the more important. To them we may add the
'This ia the cage mentioned by Carver (The Diatribzltion of WeaEth,
pp. B2-238),
when he remarks that a man with $100 in hia pocket would
not think of spending it all on a dinner today, but would save at least
some of it for tomorrow.Whethertheseconformatiom of the income
etream resulting in cero or negative preferencemayeveractually
be
reached 80 that the market rate of interest itdf may be aero or negative ia another question.

1.111I

THE THEORY OF €NTEREST
type of fluctuating income, as represented in Chart 13,
which may result in alternate borrowing and lending so
&s to produce a more nearly uniform income stream, Such
financing over the lean parts of a year is often practiced
when the income is lumped at oneortwo spots, such
as dividend dates.
It must not be imagined that the classes of borrowers
and lenders correspondrespectively to the classes of
poor and rich. The factors, environmental and personal,
discussed in Chapter IV, will determine whether s man’s
rate of preference is high or low, and therefore whether
he will become a spender or a saver.
When we come to the second and third approximations
and have to study so-called productive loans, especially
of risk-takers, or enterprisers as Professor Fetter ca,lls
them, we shall find stillother influences determining
whether a person shall be a borrower or lender or both.
At present we are only at the first approximation where
it is assumed there is no risk and no such series of opportunities to vary the income stream aa lie at the basis of
so-called productive loans.
55. Altering Income by Sale
But borrowing and lending are not the only wap in
which one’s income streaq may be modified. Exactly the
same result may, theoretically, be accomplished simply by
buying and selling property; for, since property rights
axe merely rights to income stream, their exchange replaces one such stream by another of equal present value
but differing in time shape, composition, or uncertainty.
This method of modifying one’sincome stream, which
we shall call the methodof d e , really includes the former,
or method of loans,for a loan contract is, aa Biihmc 112 3

I

FIRST APPROXIMATION
Bawerk has so well said, at bottom a sale. that is. it is
the exchange of the right to
present or immediately’ensuing incomefor the right to future ormore remote income.
A borrower is simply a seller of a note of which the lender
is the buyer. A man who buys a bond, for example, may
be regarded indifferently as a lender or as a buyer of
property.
The concept of a loan may therefore now be dispensed
with by being merged in the concept of a sale. Every sale
transfers property rights; that is, it transfers the title to
income of some kind.By selling some property rights and
buying others it is possible to transform one’sincome
stream a t will into any desired time shape. Thus, if ~b
man buys an orchard, he is providing himself with future
income in the form of apples. If, instead, he buys apples,
he is providing himself with similar but more immediate
income. If he buys securit.ies, he is providing himself with
future money, convertible, whenreceived, into apples
or other real income. Inasmuch ax the productive life
of a mine is shorter generally than that of a railway, if
his security is a share in a mine, his income stream is
less lasting than if the security is stock in a railway,
though at first it should be larger, relatively to the sum
paid for it.
Purchasing the right to remote enjoyable income, as
was explained in Chapter I, is called investing; while
purchasing more immediate enjoyable income is s p e d ing. These,however, are purely relative concepts; for
remote and immediate are relative terms. Buying an automobile is investing as contrasted with spending the money
for food and drink, but may be c d e d spending as contrasted with investing in red estate. And yet the antithesis between spending money and investing is im-

c 1131

THE THEORY OF INTEREST
portant; it istheantithesis
betweenimmediate

and
remote income. The adjustment between the two determines the time shape of one’s income stream. Spending
increasesimmediate real income but robs thefuture,
whereas investing provides for the future to the detriment of the present. There is often misconception in
reasoning about spending and investing. For example,
Henry Ford’s remark has been widely reported: “No successful boy ever saved any money. They spent it as fast
as they got it for things to improve themselves.’) In this
remarkMr.Forddrew
no hard and fast line <between
spending for personal enjoyment and investment for improvement. And there is no hard and fast line. Spending
merely means expending money
primarily for more or less
immediate enjoyment. Saving or investing is expending
money for moreor less deferred enjoyment. Consequently,
much of what is called spending might legitimately be
called investment. Even the money we spend for food,
clothing and shelter is in a sense really partly invested,
since our lives and capachy to
work can be preserved only
by means of these necessaries. Just so with a set of books,
or any other durable good which increases the efficiency
and hence the earning power of the purchaser; it is an
example, not of spending for consumption merely, but of
saving through investment. Mr. Ford cites the example
of Thomas Edison aa spending his early earnings as fast
as he made them. But Edison did this, not for food and
display, but for experimentation that resulted in time
and labor saving inventions which have benefited everybody. His outlays were in a way investments.
Popular usage has devised manyother terms and
phrases in this field, most of which, like spending and
investing, while containing meaatinga of impartanoe, in[: 114 1

FIRST APPROXIMATION
dude also the alloy of misconception. Thus, the phrase
“capital seeking investment” means that capitalists have
property for which they desire, by exchange, to substitute
other property, the income from which is more remote.
It does not mean that there is any hard and fast line
between invested and uninvested capital, much less does
it mean that theinanimate capitalhas of itself any power
to seek investment. Again, the phrase “saving capital out
of income” means not spending-reserving money which
would otherwise be spent for immediate enjoyabIe income in order to exchange it or invest it forremoter
income; it does not mean the creation of new capital,
though it may lead to that. Many needless controversies
have centered about the phenomenon of saving chiefly
because neither saving nor income was clearly defined.‘
From what has been said it is clear that by buying
and selling property an individual may change the conformation of his income stream precisely as though he
were specifically lending or borrowing. Thus, suppose a
man’s original income stream is $loo0 thisyear and $1500
next year, and suppose that he sells the title to this income stream, and, with the proceeds buys the title to
another income stream yielding$1100 this year and
$1395 next year. Although this man has not, nominally,
borrowed$100
and repaid $105, hehas
done what
amounts to the same thing; he has increased his income
stream of this year by $100 and decreased that of next
year by $105. The very same diagrams which were used

‘Thus,by saving, some writeraunderstsnd thatcapitalneceesarib
increases, and hence the income &ream b made to amend; others, like
Carver (h.
&.,p. 232), apply the term broadly enough to include the
caee where a descendingincome is simply rendered lessdescending.
The latter view harmonizes with that here presented. Saving is simply
postponing enjoyable income.
115 1

THE THEORY OF INTEREST
before mayequally well represent these operations. A
man sells the income stream ABCD (Chart 5 ) and with
the proceeds buys the stream EBD. The X’ and X” are,
aa before, $100 and $105, but now appear explicitly EIA
differences in the value of two income streams, instead
of appearing as direct loans and payments.

86. Interest Ineradicable
Thus interest taking cannot be prevented by prohibiting loan contracts. To forbid the particular form of sale
called a loan contract would leave possible other forms
of sale, and, as was shown in Chapter I, the mere act of
valuation of every propertyright involves a.n implicit
rate of interest. If the prohibition left individualsfree to
deal in bonds, it is clear that they would still virtually
be borrowing and lending, but under the names of selling
and purchasing; and if bonds were tabooed, they could
change to preferred stock. Indeed, as long aa buying and
selling of any kind were permitted, the virtual effect of
lending and borrowing would be retained. The possessor
of a forest of young trees, not being able to mortgage
their future return and
being in need of an income stream
of a less deferredtypethan
that receivable from the
forestitself, could simply sell hisforestandwith
the
proceeds buy, say, a farm, with a uniform flow of income,
or a mine with a decreasing one. On the other hand, the
possessor of a capital which is depreciating, that is, which
represents an income stream great now but steadily declining, and who is eager to have an increasing income,
could sell his depreciating wealth and invest theproceeds
in such instruments as the forest already mentioned.
It was in such a way, as for instance by rent purchase,
that the medievd prohibitions of usury were rendered
116 I

c

FIRST APPROXIMATION
nugatory. Practically, the effect of such restrictive laws
is little more thari to hamper and make d a c u l t the finer
adjustments of the income stream, compelling would-be
borrowers to sell wealth yieldingdistant returns instead of
mortgaging them, and would-belenders to buy such
wealth instead of lending to the present owners. It is
conceivable that explicit interest might disappear under
suchrestrictions, but implicit interest would certainly
remain. The young forest sold for $10,000 would bear this
price, as now, because it is the discounted value of the
estimated future income; and the price of. the farm,
$10,000, would be determinedin like manner. The rate of
discount inthe two cases, the $10,000 forest andthe
$lO,OOO farm, musttend to be the same,because, by
buying and selling, the various parties in the community
would adjust their rates of preference to a common level
-an implicit rate of interest thus lurking in every contract, though never specifically mentioned therein. Interest is too omnipresent a phenomenon to be eradicated by
attacking any particular form of it; nor would any one
undertake to eradicate it who perceived its substance as
well aa its form.
$7. “Margind” Principle Is “Mmhurn” Principle
The fact that, through the loan market, the marginal
rate of time preference for each individual is, by ’borrowing or lending, made equal to the rate of interest may be
stated in another way,namely, that the total present
desirabilityof,
or want for, the individual’sincome
stream is made a maximum. For, consider again the individual who modifies his original fixed income stream by
borrowing until his rate of preference is brought into
unison with the market rate of interest. His degree of
[ 117

THE THEORY OF INTEREST
impatience wm a t fimt, my, 10 per cent; that is, he was
willing, in order to secure anaddition of $100 to his
present income, to sacrifice $110 of next year’s income.
But he needed to sacrificeonly$105;
that is, he was
enabled to get his loan for less than he would have been
willing to pay. He was therefore a gainer to the extent of
the present desirabilityof, (YT present want for, $5 of next
year’sincome. The second$100borrowedwasequivalent, in his present estimation,to $108 of next year’s
income, and the same reasoning shows that, as he pays
only $105, he gains to the extent of the present desirability of $3 nextyear; that is, he addsthispresent
desirability to the entire present total desirability of his
income stream. In like manner, each successive increment
of loans adds to the present total desirability of his income, so long as he is willing to pay more than $105 of
next year’s income for $100 of this year’s income. But,
as he proceeds, his gains and his eagerness diminish until
they cease altogether. At, let us say, the iifth instalment
of $100, he finds himself barely willing topay $105;
the present totaldesirability of his income i s thena
maximum, and any furtherloan would decrease it. A sixth
$100, for instance, is worth in his present estimation less
than $105 due next year, say $104, and since in the loan
market hewould have to sacrifice$105 nextyear to
secure it, this would mean a loss of desirability to the
extent of the desirability today of $1 due in one year.
Thus, by borrowing up to the point where the rate of
preference forpresent over future income is equalto
the rate of interest, five per cent, he secures the greatest
total desirability, or, so-called consumer’s rent.5
We do not hereneed to argue to the zero or &art@point from
which we measure net total dehbility. The crest of a hill is the highest

r 118 1

FIRST APPROXIMATION
Sirnilas remning applies to the individual on the
other side of the market, whose rate of preference is
initially less than the market rate of interest. Healso
will bring his present net totaldesirability to a maximum
by lending up to the point where his rate of preference
corresponds to therate of interest. A t the beginning, $100
this year has to him the same present desirability a,
say, $102 due one year hence, whereas iq the market he
may secure not $102 but $105. Ittis then clear that by
lending $100 he gains the present desirability of $3 due
one year hence. By lending each successive $100 he will
addsomething to t-he total present desirability of his
income, until his rate of preference for present over
future income is raised to a level equal to that of the
rate of interest, five per cent. Beyond that pointhe
would lose by further lending.
58. Market Equilibrium
We axe now in a position to give a preliminary answer
to the question, What determines the rate of interest?
Thus far we have regarded the individual only, and have
seen that he canforms his rate of income-impatience to
the rate of interest. For him the rate of interest is a
relatively fixed fact, since his own impatience and resulting action can affect it only infinitesimally. To him it is
his degree of impatience which is the variable. In short,
for him individually, the rate of interest is cause, and his
lending and borrowing is the effect. For society as a whole,
however, the order of cause and effect is reversed. This
change is like the Corresponding inversion of cause and
effectin the theory of prices. Each individual regards the
point whether the height is meamred above e a level or from the center
of the eartb.

[: 119 1

THE THEORY OF INTEREST
market price, say, of sugar, as fixed, and adjusts his margind utility, or desirability, to it; whereas, for the entire
group of persons forming the market, the adjustment is
the other way around, the price of sugar conforming to
its marginal desirability to the consumer.6 I n the same
way, while for the individual the rate of interest determines the degree of impatience, for society the degrees
of impatience of the aggregate of individuals determine,
or help to determine, the rate of interest. The rate of
interest is equal to the degree of impatience upon which
the wholecommunitymay
concur in order that the
market of loam m y be exactly cleared.
To put the matterin figures: Suppose that at the outset
the rate of interest is arbitrarily set very high, say, 20
per cent. There will be relatively few borrowersand many
would-be lenders, so thatthe total extent to which
would-be lenders are willing to reduce their income
streams for the present year for the sake of a much larger
future income will be, say, 100 million dollars; whereas,
the extent to whichwould-beborrowers are willing to
increase their income streams in the present a t the high
price of 20 per cent will be only, say, one million. Under
such conditions the demand for loans is far short of the
supply and the rate of interest will therefore go down.
At an interest rate of 10 per cent the lenders may offer
50 millions, and the borrowers .bid for 20 millions. There
is still anexcess of supply over demand,and interest must
needs fall further. At5 per cent we may suppose the market cleared, borrowers and lenders being willing to take
or give respectively 30 millions. In like manner it can
be shown that the rate would not fall below this, aa in
‘See my
P6738.

Ma.themotiwl Investigath in the Theory of Vdue cmd

c 120 3

FIRST APPROXIMATION
that case it would result in an excess of demand ov&
supply and cause the rate to rise again.
Thus, the rate of interest registers in the market the
common marginal rate of preference for present over future income, as determined by the supply and demand of
to start with,
present and future income.Thosewho,
have a high degree of impatience, strive to acquire more
present income at the cost of future income, and thus
tend to mise the rate of interest. These are the borrowers, the spenders, the sellers of property yielding remote
income,such aa bonds and stocks. On the other hand,
t.hose who, to start with, have a low rate of preference,
strive to acquire more future income at the cost of present income, and so tend to lower the rateof interest. Such
are the lenders, the savers, the investors.
Not only will the mechanism just described result in a
rate of interest which will clear the market for loans
connecting the present with next year, but, applied to
exchanges between the present and the more remote future, it will make similar clearings. While some individuals may wish to exchange this year’s income ‘for next
year’s, others wish to exchange this year’sincomefor
. the year after next, or for a portion of several
that of
future years’incomes, The rates of intereat for these
various periods are so adjusted as to clear the market
for each of the periods of time for which COTt&Wt8 are
made.
89. Four Principle8
If we retain our original assumption that every man
is initially endowed with a rigidly fixed or prescribed income stream which can be freely bought and sold and
thereby redistributed in time, the foregoing d i s c U s s i o n
gives us a complete theoryof the causes which determine
~

c 121 1

THE THEORY OF INTEREST
the rate of interest, or rather, the rates of interest, there
being, theoretically, a separate rate for each time period.
These rates of interest would, under these circumstances,
be fully determined by the following four principles, to
which all the magnitudes in the problem of interest must
conform:

THE TWO IMPATIENCE PRINCIPLES
G Empirical Principle

The rate of time preference or degree of impatience of
each individual depends upon-hisincome stream.

B. Principle of M&uimum Desirability
Throughthealterationsin
the income streams produced by loans or sales, the marginal degrees of impatience for all individuals in the market are brought into
equality with each other and with the market rate of
interest.
This 'condition B is equivalent to another, namely,
that each individual exchanges present against future
income, or vice versa, at the market rate of interest up
to the point of the muximum totd desirability of the
forms of income available to h&.

THE T W O MARKET PRINCIPLES
A. Principle of Clearing the Market
The market rate of interest will .be such BS will just
clear the market, that is, will make the l o w and borrowings or, more generally expressed, purchases and ealee of
income equal for each period of time.

ClBl

FIRST APPROXIMATION
B. Principle of Repayment
All loans are repaid with interest, that is, the present
value of the payments, reckoned at the time of contract,
equah the present value of the repayments. More generally expressed, the pIus and minus alterations or d e
parturea from a pereon’s original income stream effected
by buying and selling at two different points are such
that the algebraic sum of their present values is zero.

Will these four sets of conditions determine the rate
of interest? And why should there be so many conditions?
Ought not one single condition to suffice?
These are really questions in mathematics. It is a
fundamental principle that in order to solve an equation
containing only one unknown quantity only one equation
is necessary; and that to solve one containing two unknowns,twoindependent equations are needed; and so
on, one additional equation for each additional unknown
quantity introduced.
In thepresent problem we are tryingto determine only
one unknown, the rate of interest. But we can do so only
by determining, at the same time, the other unknowns
that are involved. To say that the rateof interest is equal
to Smith’s marginal rate of impatience is saying something, but not enough. It merely,expresses one unknown,
the rateof interest, in terms of another unknown, Smith’s
marginal rate; and two unknowns cannot be determined
by one equation or condition. If we add that the rate of
interest must also equal Jones’ rate of impatience, while
this statement gives us another equation it also adds another unknown and three unknowns cannqt be determined
by two equktions; and so on. If we include Jones and

v231

THE THEORY OF INTEREST
everybody else in the market, we shall still be one q u a tion short. This is equivalent to saying that the second
set of conditions (Impatience Principle B) is not enough.
In a market comprising 1000 persons there will be, as
our unknowns, not only the rate of interest, but 1000 rates
of impatience, and the additions to or deductions from
the income of these 1000 persons in each period of time.
The rate of interestand these thousands of variables
act and react oneach otherand the determination of
each can be accomplished.only with the determination
of all the rest.
In Chapter XI1 this problem .is stated in mathematical
formulas such that the number of equations is exactly
q u a l to the number of unknown quantities.

CHAPTER VI

SECOND APPROXIMATION TO THE THEORY OF
INTEREST
AssumingIncomeModifiable (1) by loans and (2) by
other means

01. The New Hypothesis
HITHERT~
we have assumed:
(1) perfect foresight, and
(2) absence of anyopportunity to alter income
save by trading.
We now abandon the second of these hypotheses. Still
assuming that all available income st.reams can be definitely foreseen, we now introduce the new hypothesis,
much neareractual life, that the income streams are
not rigid, but are flexible, that is, that the owner of any
item of capital-wealth or capital property, including, of
course and especially, his own person, is not restricted
to a sole me to which he may put it, but has open to his
choice several possible or alternative uses, each of which
will produce a separate optional income stream. He has,
therefore, two kinds of choice: first, the choosing one
from many optiond income streams, and secondly, as
under the first approximation, the choosing of the most
desirable time shape of his income stream by exchanging
present income against future.
The two sorts of choice me exercised concurrently in
125 1

c

THE THEORY OF INTEREST
practice and each in consideration of the other. But, for
purposes of exposition, we may take one at a time. Or
rather, we maysuppose the doublechoicemade
and
then, in order to analyze it, we go back and consider each
process separately, assuming the other constant. Let the
varying process be the loan, that k, let us suppose oneindividual to have irrevocably made his choice from among
options mutually available, This done, he is limited, &s
in the first hypothesis, to buying and selling or borrowing and lending as a means of changing the shape of that
particular income stream. In this process he cannot
change the present value, but in making his initial choice
he had the privilege of selecting that option having the
maximum present value.
For example, the owner of a piece of land may use it
in any one of several different ways. He may, let us say,
use it to grow crops, graze animals, plant forests, extract
minerals, or to support buildings. Again, the owner of a
building may use it, say, for office purposes, apartments,
manufacturing, salesrooms, or a warehouse. Most raw materials, too, may be usedfor any one of a number of
purposes. Iron may be wrought into steel rails, or into
machinery, implements, tools, armor for ships, or girders
for buildings.Andso
of tools and otherimplements;
a derrick maybeused for quarrying stone, building a
house, or unloading a boat. A ship may be used to c a n y
any sort of cargo, and sent over any one of numerous
different routes. Hammers,saws, nails, and other tools
may be used in almost numberless ways.
Perhaps the most adaptable of all instruments of
wealth is man himself. He may be simply a passive enjoyer or “transformer” 1 of the services of other wealth
‘See Chapter I, or The Natwe of Capital and Income, Chapter X.
c 126 3

SECOND APPROXIMATION
m d as such derive his satisfactions in any one or more
of several different ways, sensual, esthetic, intellectual,
or spiritual. Or, he may also be an active producer, and,
as such, perform work in any one or more of several different ways, physical or mental. Even the skilled laborer
who is most specialized and restricted has many ways to
turn. And each of these varieties includes numerous subvarieties. If his work is physical, it may consist in anything from wielding a pick and shovel to the deft
manipulation of the instruments employed in the jeweler’s art. If his work is mental, he may be a bookkeeper,
clerk, superintendent, manager, director, lawyer, physician, clergyman, editor, teacher, or scientist. Some of
these options, of course, may be out of the question and,
in eachcase, there will be only one best choice. That
choice is what is now under discussion.
In consequence of such a range of choice, any given
productive instrument, or any given set of productive
instruments, including human beings, may produce any
one of many different income streams. Men may work to
produce cheap frame houses or durable stone ones; to
equip a city with trolleys, elevated, or under-ground
rapid transit; to secure an income stream which shall
consist of the pleasures of the fable, of the amusements
of the theatre, of the gratification of social vanities, or
of endless combinations of these groups, as well as of all
others. Each individual must select one particular income stream out of a thousand possible income streams
differing in size,composition, time shape, and uncertainty; but, in this chapter, the element of uncertainty
is, as already stated, supposed absent, being reserved for
the third approximation (Chapter IX)
Aa in the first approximation, a perfect marketis

.

r 127 1

THE THEORY OF INTEREST
assumed in whicheach individual is so insignificant a
part that he wts aa if the market rate of interest were
fixed and merely has to decide how much at that rate he
is willing to borrow or lend.
Because of the existence of a wide range of choice,
the owner of a given capital has ample opportunity to
modify the income stream he derives from it by changing
the uses to which that capital is put. He is seldom so
committed to a d e h i t e future program but that he can
consider some alternative. It is on this principle that the
cotton belt of the United States, by diversifying ita crops
and industries, has increased its r e d income. The production of these Southern States has recently risen with
expanding industries, diversified agriculture, water power
development, and improved highways. It was largely by
changing the uses to which its income, natural resources,
and technological equipment had been put that theSouth
has entered B new em.
Under the first approximation, our first glimpse of any
flexibility of income was by borrowing and lending. Next
we introduced the process of buying or selling and noted
that this really included as a special case borrowing and
lending. It might be claimedhere that, just &s buying and
selling virtually include borrowing and lending, so the
substitution of one use of a person’s capital for another
use may be said to include buying and selling, and therefore also to include borrowing and lending. It is evidently quite possible to say that one method of utilizing
capital is to sell it. In fact, a merchant regards himself
as making u s of his stock in trade only in the sense of
selling it.
While we could thus extend the meaning of optional
me8 to include buying and selling (which in turn include

[I281

I

SECOND APPROXIMATION
borrowing and lending) it will better serve the purpose
of our analysis not to do so.
There are two principal reasons for this. First, borrowing and lending, the narrower method of modifying income streams, cannot be applied to society aa a whole,
since there is no one outside to trade with; and yet
society
does have opportunitiesradically to change the character
of its income stream by changing the employment of its
capital. Secondly, when borrowing and lending, or ordinary buying and selling, are employed to modify an income stream, the present value of the original income
streamand the present value of the modifiedincome
stream are the same, for each $100 added to this year’s
income has the same present value aa the $100 with interest, returned out of next year’s income, so that every
loan adds and subtracts equal present values. But when
an income stream is modified by a change in the use of
capital yielding it, the present value of the alternative, as
in the cme of the South, may not, and,in general, will not,
be the same as the present value of the original. This fact,
that thepresent value is not changed by buying or selling
(or, in particular, byborrowing or lending) but is changed
by otherwise altering the use of one’s capit,d, marks an
important distinction between the two methods of altering one’s income stream. The distinction and its importance are most clearly seen by a mathematical analysis
such as that shown in Chapter XI and XIII.
$2. Optional Income Streams
The choice amongall available optional income streams
will fall on that one which has the maximum desirability

or wmtability.
We have seen in the preceding chapter that income
I: 1291

THE THEORY OF INTEREST
streams may difTer in size, time shape, composition and
certainty. As among income streams of different sizes but
similar in other respects, the most desirable will, of
course, be the largest.
As among income streams of different composition but
simiiar in other respects, the most desirable will be that
in which, to the given individual, the margin4 desirabilities of the different constituents are proportionalto their
several prices, in accordance with the fundamental principle of marginal desirability in the theory of pricesm2
Finally, and principally, as amongincome streams
differing in t h e shape alone, the most desirable is
found in accordance with the principles whichgovern
the rate of interest, and which are to be expounded in
this book. It is, therefore, with income streams differing
in time shape that we are here chiefly concerned.
In order definitely to illustrate income streams differing in time shape, let us begin by supposing only three.
An individual is, let us say, possessed of a piece of land
almost equally good for farming, lumbering, or mining.
These terms are used merely to fix the reader's thought in
concrete pictures. Logically, it would be better to designate t:he threeoptional supposititious income streams'
simply by the lettersA, €3,and C, for there is nopretense
that the income streams closely resemble in more than
a very general and sketchy way those of actual farming, lumbering, or mining; nor is it essential that the
three products should differ in kind. Thus, the three
streams might represent three different methods of producing the same product, one moreroundabout or capitalistic than another. They axe here given the concrete
'See my Mobhematical Znveet+atioM in the

Plks.

c1301

Theory

of

Vdw and

SECOND APPROXIMATION
nrtmes of f d g , lumbering, mining, merely for convenience in distinguishing and remembering the three types,
not because these types are true to these names,nor
because examplesconcerned with land compriseopportunities any more important than those concerned with
commercial or industrial examples. The only essential
point is that the three series of numbers representing the
income streams A, B, and C are different.
Our imaginary land owner thus hau the option of
securing any one of these three different income streams.
While they will, in the first instance, differ in composition-one income stream consisting in the production of
crops, another in the production of lumber, and the third
in the production of minerals-we may, for our present
purpose, assume that these are all reduced to real income
measured interms of money. That is, we here rtssume that
the prices and values of the crops, lumber, and minerals
are givenanddetermined in accordance with the principles which determine p r i ~ e s . ~
'It is, of c o r n , realized that the principles of price determination
involveinterestjust
as the principleedetermining
interest involve
prices. A complete picture of economic equilibrium includes every p o s
siblevariable,each
actingand reacting on the others.Theoretically
we cannot determinethe price of bread by itselfand then go on to
determine, each separately, other prices, including the rate of interest.
Theoretically any analysis of one part of the economic organim must
include an analysia of the whole, 80 that a complete interesttheory
would have to include also price theory, wage theory and, in fact, all
other economic theory.
element by a m m But it is convenient to isolateaparticular
ing theotherelements to have beendetermined. So thia book is a
monograph, restricted, 80 far as may be, to the theory of interest, and
excludingprice-theory, wage theory and all other economic theory.
Afterward it will be easy to dovetail together this interesttheory, which
asumea prices predetermined, with priw theory which885umes interest
predetermined, thus reaching a syntheaia in which the previously a+
awned constants become varieblea But all the prineiplea remain valid.

I: 131 1

THE THEORY OF INTEREST
Assuming, then, that the land ownerfinds predetermined pricesand quantities of crops, lumber and minerals,
with predetermined costs for obtaining them, hehas
before him simply the choice‘ of three definite income
streams, eachexpressible in terms of money, according
as he uses his labor, land, and capital in one or the other
of the following three ways:
(1) ,for farming purposes, which, let us say, will give
him a regular and perpetual succession of crops and income equally valuable year after year, that is, with an
income stream of the type AA’ in Chart 14;

CHART 14
Three Types of Income Streams; “Farming”, “Forestry”, and“Mining.”

(2) for forestry purposes, with very slight, returns for
the first few decades, and larger returns in the future, as
indicated by the curve BB’;
(3) for mining purposes, in whichcase
we shall
suppose that the income is greatest for the early years
and thereafter gradually decreases until the mine is exhausted; illustrated by Curve CC’.
The important question now beforeus is: What are the
principles upon which the owner of the land chooses the
best one among these three income dreams, A, B, and C?
I 132 1

SECOND APPROXIMATION
This question is fundamental and typical in the second
approximation.
The rate of interest is just as relevant to this initial
choice of uses for maximum present value as to the subsequent choice for shape done, for it is used in finding
the present value; and when the ratechanges, the relative
present values of dserently shaped streams may change
about.
We shall suppose, aa heretofore, that there is a uniform
rate of interest in the communityand that any individual
is free either to borrow or to lend at that rate and up to
any amount desired.Under this hypothesis the choice
among thethree available options will simply fall on
that onewhichyields
the maximum present value,
reckoned at the market rate of interest.
Let us assume a market rate of interest at five per cent.
To reckon the bhree respective present values, suppose
the use of the land for mining purposes will yield an income stream, let us say, = follows: $ZOO0 the fist year,
$1800 the second, $1600 the third, and so on, diminishing
annually by $200 to the point of the mine’s exhaustion.
The present value of these ten sums, discounted at five
per cent, is 19110. If the land is used for farning purposes and yields a net income of $450 a year perpetually,
the present value at five percent will be $9b9ooo. If, finally,
the land is used for forestry purposes,we shall suppose it
yields the following sums: zero €or the fmt two years,
$300 for the third, $400 for the fourth, $500 for the fifth, .
and $so0 thereafter forever-then the value of the land,
reckoning at 5 per cent, will be $8820.
Under these conditions the choice will evidently fall
on the mining use, because, for mining purposes,
the land
is worth $9110, which is greater than $9000, its value

c1331

TEE THEORY OF INTEREST
for farming purposes, and than $8820, itsvalue for
forestry purposes.
The three options may be contrafiltedas to distribution
in time as follows:
T m2
The Three Optional Ingome Stream
A
B
For farming For forestry
let yr.
2nd yr.
3rd yr.
4thyr.
5th yr.
6th yr.
7thyr.
8th yr.
9th yr.
10th yr.
11thyr.

Present
Value

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

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

so00

$ 450

t2OOo

ooo

450

450
450
4x50
460
450
450

1800
1600

300
400

1400

500
500

1200

loOD
800
600
400

m

500
500
500
500

450
450
450

200

ooo

etc.

etc.

............I tw

C

For mining

]

$8820

etc.

1

$9110

The particular income stream selected will tend to
leave its impress on the time shape of the total income
stream of the individual wbo owns it. For, aa was seen
in Chapter I, the total net, or final, incomestream of any
individual during any interval of time is simply the sum
total of the items of income flowing during tha.t interval
from all the articles of property belonging to him. Hence,
if one selects the mining use for his land, whereby the
income stream gradually decreases, its tendency will be
to produce a similarlydecreasing trend in the total income
stream enjoyed by the individual. This tendency may
be counteracted, of course, by some opposing tendency,
but will have full may if the income from all other capital
than the land remains the same in value and time shape.
It ia true that the direct income from the mine ia not

E1341

SECOND APPROXIMATION
itself real income, but consists of serviceswhich,relatively to some other capital source, are disservices, thus
constituting intermediate income or interaetions. But
those items are readily transformed, through a chain of
credits and debits, into real, and then into enjoyment income. Thus the ore of the mine is exchanged for money,
and the money spent for enjoyable services or for commodities which soon yield enjoyable services, so that the
real incomecloselycopies
in time shape the original
intermediate income from the mine.

43. The Two Kinds of Choice
The possessor of the mine, however, is not compelled
thus to copy in his real income the mine’s fluctuations
of physical or natural income. He may counteract any
fluctuations in his whole net income which maybe caused,
in the first instance, by the choice of income C rather
than B, or A. O r , if he prefers, he may further exaggerate
those fluctuations. In fact he maymake the time shape of
his incomefollow any model he likes. He may do this
as described under the first approximation, by either
borrowing or lending in suitable amounts and at suitable
times along his income stream; or, more generally, by
buying and selling income streams or parts of income
streams so as to fashion the time shape of his own final
net enjoyable income to suit himself.
Be may, for instance, so far as time shape is concerned,
achieve m even flow of income such as he could get from
the farm use of his land. But hewill not on that account
choose this farm use in preference to the mining use;
for the mining use has the larger present value, and the
.undeaira,ble time shape of ita income stream, under our
‘8ee The Nature of Capital a d Inconw, Chaptern V m , IX,
[ ,1353

XVII.

THE TEl3ORY OF INTEREST
present hypothesis,canbeveryeasilyremedied.
For
instance, he may lend some of the proceeds of its earlier
output and in later yews be paid baek with interest.
Of course, his loan at five per cent does not alter in the
least the figure $9110, the discounted value at fiveper
cent of all the ten items of income ($2000,$1800, $lsoO,
$1400,$1200,$1000, $soO,$600,$400, $200); it simply
adds to the later of these ten figures and subtracts from
the earlier ones. The present value of the additions is
necessarily equal to the present valueof the subtractions;
for the additions are the repayments, while the subtractions are the loans, and the present value of any loan
equals that of its repayment.
We may totally separate, therefore, in thought the two
choices made by the land owner, namely, (1) the choice
of C (mining) in preference to A and B on the ground
of greater present value, and, (2) the choice of time
shape. If, aa just supposedfor illustration, the second
sort. of choice is that of an even income stream, it will
be at the rate of $455.50 a year perpetually. That is to
say, the mine owner will lendat interest $1544.50 the first
year (all but $455.50 out of his original mining incomeof
$2000); in the second year he will lend $1344.50 (all but
$455.50 out of his original $1800); and so on. When the
ninth year is reached, he ceases to lend further, for the
mine then yields only $400. Instead, he thenekes this out
by $55.50 returned from the previous loans. Likewise, in
the tenth year he ekes out the $200 from mining by
$255.50 returned from loans. Thereafter he will get nothing further from mining; but his loans will have mcumulated a sinking fund (of $9110) to take the place of the
mine and from this fund he caa annually derive a 5 pec

cent revenue of

$455.50.

tu63

SECOND APPROXIMATION
Consequently, the net resultof the double choice (mining use and even time shape) is to increase the perpetual
income of $450 offeredby farming to a perpetual income
of $455.50. This new perpetual annuity has exactly the
same time shape aa that derived from the farming use,
but is larger by $5.50 per annum.
Incidentally it may beobfjerved that this mining
income, thus evened outby financing into a uniform
$455.50 per year, exceeds the uniform farming income of
$450 in exactly the same ratio as the present value
($9110) of the miningincomeexceeds that ($9OOO) of
the farming income.
The following table exhibits the operations in detail:
Mining

1st year
2nd year
3rd year
4thyear
5th year
6thyear
7th year
8thyear
9th year
10th year
11thyear
~~

and

T m3
F a k w Use Compared

Owner
Of which
Receives He
Lends
from Mine

Leaving
for Red
Income

81544.50
1344.50
1144.50

$455.50

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

944.60

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

"-

400
200

455.50
455.50

144.50
-55.50

455.50
455.60
455.50
455.50
455.60

-256.60
-455.50

ooo
~~~

Would%Iave
Yielded

45550
455.50
455.60

744.50
544.50
344.50

As Againat
Which the
Farmin Uee

~

Or, instead of wanting a perpetualeven flowing income,
the land owner may prefer &s his model the time shape of
the forestry income. He will not, however, on that account, choose this forestry use in preference to the mining
use. He will simply lend at interest from the items of minI137 3

THE THEORY OF INTEREST
ing income all of his $2000 the first year, leaving no income for that year; likewise, all of his $1800 the second;
all but $310 the third; all but 8413 the fourth andall but
$516 the fifth, and every succeeding year until the ninth
year. He will then turn around and use $116 from his
loans just described to eke out his $400 and bring up his
income in that year to $516. Thetenth mining item,
$200, willlikewise be brought up to $516 after which
he will depend entirely on his outside loans at five per
cent, deriving therefrom exactly $516 every year.
The result will then be aseries of income items exactly
similar to the B, or forestry, series but each item magnified in the ratio of $9110 to $8820, the present values
respectively of C and B.
The following table exhibits these operations:
T m4
Mining

and

Forestry Use Compared

Owqer
Of Which
Receives He
Lends
from Mme

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

1styear
2nd year
3rd year
4thyear
5th year
6thyear
7th year
8thyear
9th year
10th year
11th year
eta.

.........

Leaving
for Real
Income

)2ooo

82000
1800

)ooo

1600

1290
987

310
413
516
516
516
516

1800

1400
1200
loo0
800

800

400
200
O00
etc.

884
484

284

84
-118
-316
"516

etc.

AsAgainst
Which the
Forestry Use
Would Have
I Yielded

ooo

616

518
516

etc.

I

eta.

Since, therefore, any time shape may !x transformed
into any other timeshape, nobody need be deterred from
selecting an income because of its time shape, but everyc1381

I

m

SECOND APPROXIMATION
one may choose an incomeexclusivelyon the basis of
maximum present value. It will then happen that his
income, as finally transformed, will be larger than it
would have been if he had chosen some other use which
afforded that same time shape.
All this is true under the assumption used throughout
this chapter, namely, that after themost vdusble option
has been chosen, you can borrowand lend or buy and sell
ad libitum and without risk. If this assumption is not
true, if a person were cut off from a free loan market,
the choice amongoptional income streams mightor might
not f a l l upon that one having the ma,ximum present
value, dependingon the other circumstances involved,
particularly his preferences as regards time shape.
Of course our assumption is a violent one, made in this
second approximation, as in the first, in order to simplify
the theory of interest. But already it must be evident that
the principle involved has important practical applications. To a very considerable extent a modern business
man, with access to loan markets, can choose from among
the various options open to him on the basis of present
value, and trust to loans or other financing to rectify
any inconvenience in time shape.
The lines AB and A'B' in Chart 15 picture alternative
income streams, of which the descending one, AB,has the
larger present value. The choice will fall on AB, and if
the individual prefers the timeshape of A'B', he will then
lend some of the early receipts from the income stream
AB and receive back some of the latter, converting his
income AB of undesirable shape into the income stream
A"B" which has the desired shape. This final income
A"B" combines the virtues of both the original dternative incomes AB and ofA'B'; it possesses the superior
I 139 1

TII[E

THEORY OF INTEREST

shape of A’B’ and the superior present value of AB. As
compared with A’B’ it has the same shape but a greater
size.

CHART 15
Enlarging Income Stream Through DoubleChoice.

In practice, of course, the two steps we usually made
simultaneously, not successively. In fact, usually the borrowing or financing often precedes the choice of option,
thus reversing the order of presentation here adopted for
convenience of exposition. So it would be quite as true
to say that the loan, with the choice of option it makes
possible, is made to secure an increased income aa it is to
say that theloan is made to even up the distortedincome
given by the option chosen.
But were it not for the possibility here assumed of
modifying the time shape of his income stream by borrowing and lending, or buying and selling, the land owner
would not feel free to choose the one from among the
optional income streams whieh possesed the higheet pres-

c1401

SECOND APPROXIMATION
ent value. He might find it advantageous, or even necessary, to take one of the others, being scarcely able to live
if his property offered only distant income. If his capital
were &u in the form of growing young forests, and he
could not mortgage the future in some way, he would
have to starve or give up some of his holdings. In actual
life we find such people-people who are said to be “land
poor,” In fact, we are all somewhathampered in the
choiceof options by di3iculties and risks both in the
choice of options and in the financing it requires.
But we see that, in such a fluid world of options as
we arehere assuming, the capitalist reaches his final
income through the co-operation of two kinds of choice of
incomes which, under our assumptions, may be considered
andtreated as entirely separate. Torepeat, these two
kinds of choice are: first, the choice from among many
possible incomestreams of that particular income stream
which has the highest present value, and, secondly, the
choice among different possiblemodifications of this
income stream by borrowing and lending or buying and
selling. The first is a selection fromamong income streams
of diflering market d u e s , and the second, a selection
from among income streams of the same market value.
$4. Opportunity to Invest b y Change of Use of Capital
Since this double choice results, whenmade, in 8
perfectly definite income stream, it might seem that the
situation does not materially differ from the case of the
rigid income stream discussed in the first approximation.
But the twocwes do differ materially, for under the
present hypothesis (of optional income streams) the particular choice made by the individual &peds upom w k t
th rute of interest is. A change in that rate may shift
141 1

c

TEE THEORY OF INTEREST
the maximum present value to some other option, or
alternative income stream, and that shift reacts on the
rate of interest.
In the example cited, if the rate of interest should be
4% per cent instead of 5 per cent, the order of choice
would be changed. The present value of the land for A
(farming) would be, $10,000, for B (forestry), $9920, and
for C (mining), $9280. The farming use, or A, would
now be the bestchoice.Again,
if the rate of interest
should be 4 per cent instead of 4% per cent, the present
value of the use of the land for A, farming purposes,
would be $11,250; for B, forestry pu(rposes, $11,300; and
for C, mining purposes,$9450. In this case, B, the forestry
use, would be chosen.
Thus, it would pay best to employ the land for mining
if the rate of interest were 5 per cent, for farming if it,
were 4% per cent, and for forestry if it were 4 per cent.
The three options open to the owner of the land a.t
these three different rates of interest may be summwized
88 follows:
T m ti
Present Values of the Three O
p
hat Three Diferent Rates oj
Interest

I

OPtiOM

For fore&ry
For mining
farming

.........I

I

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

Present Value at
6%
$8,820

1
I

4%%
$ 9,920

1;)

I

4%
~11,300

Thus a change in the rate of interest resulta in a change
in the relative attractivenessof different optional income
stream opportunities. A high rate of interest will encourage investment in the quickly returning incomeg,

11421

SECOND APPROXIMATION
whereaa a low rate of interest will encourage investment
in incomes which yield distant returns. As the businw
man puts it, when interest is high, he can less afford to
wait for a remote return. because he will “lose so much
interest.” An investor will, therefore, make very different
choices among the various options open to him, according as interest is at one rate or another.
Consequently, the existence of various options to use
one’s capital introduces a new variable into the problem
of interest determination. For the individual, the rate of
interest will determine the choice among his optional income streams, but, for society as a whole, t.he order of
cause and effect is reversed-the rate of interest will be
influenced by the range of options open to choice. If we
live in a land coveredwithyoung forests or otherwise
affording plenty of opportunities for distant income but
affording fewopportunities for immediate income (aswaa
the case in the pioneer days in this country) the rate of
interest will, other things being equal, be very much
higher than in a land full of nearly worked out mines and
oil fields or otherwise affording many opportunities for
immediate but few opportunities for remote income.
We are thus coming in sight of a principle, applying to
interest determination, new in our study, the principle
of opportunity to invest, not simply by lending but by
changing the use of one’s capital. This newprinciple,
largely physical or technical, is just as important $8 the
psychical principle of h u m n impatience. It is really old in
the sense thst, implicitly, it has been recognizedin almost
aU theories of interest, and explicitly in those of Rae,
Landry, Walras, and Pareto.To trace this new influence
on interest is the special purpose of the second approximation.

THE THEORY OF INTEREST
55. The Reasoning not “CirCiJar’

At first sight it may appear to those not f d a r with
the msthematicsof simultaneous equations andvariables
that the reasoning is circular; the rate of interest depends on individual rates of impatience; these rates of
impatience depend on the time shapes of individual income streams; aad the choice of these time shapes of
income streams depends, as we have just seen, on the
rate of interest itself.
It is perfectly true that, in this statement, the rate of
interest depends in parton a chain of factors which h d y
depend in part on the rate of interest. Yet this chain is
not the vicious circle it seems, for the laat step in the
circle is not the inverse of the first.
To distinguish between tl true and a seeming example
of a circular dependence we may cite simple problems in
algebra or mentd arithmetic. Suppose we wish to find the
height of a father who is known to be three times as
tall as his child. To solve this we need to know something
more about these two heights. rf we are told in addition
that the child’s height M e r s from his father’s by twice
itself, the problem is really circular and insoluble, for the
additional condition is really reducible to the first, being
merely a thinly veiled inversion of it. Theproblem essentially s t a M (1) that the father’s height is three times
the child’s and (2) that the child’s is one-third of the
father’eaa obvious circle.
But if the dependence of the father’s height on the
child’s is essentially dif€erent from-independent ofthe dependence of the child’s on its father’s, there &.no
circle. Thus supposing, as before, that the father is three
times as tall as the child, let u8 stipulate in addition that
C1MI

SECOND APPROXIMATION
the child’s height differs from the father’s by four times
aa much as the child‘s less two feet. This may sound aa
circulas $8 the first statement-the father’s height is expressed in terms of the child’s, and thechild’s is expressed
in terms of the father’s; but the second stipulation is not
now reducible to the first. The heights are entirelydeterminate, tshat of the father being six feet. and that of the
child, two. The mere fact that both of these magnitudes,
the father’s height and the child’s height, are specified
each in terms of the other does not constitute a vicious
circle. The general principle,as Cournot and othermathe
matical economists have often pointed out,, is simply the
well known algebraic principleof simultaneous equations.
In order that the equations may determine the unknown
quantities involved, there must be as many independent
equations &s there are unknown quantities, although any
or all of these equations may contain all the unknowns.
(The equations are independent if no one of them can
be derived from another or the others.) Many an example
of economicconfusion and wrongreasoningcould
be
avoided if thisfundamental principle of mathematics
were more generally applied.
This mathematicalprinciple of determinateness appliea
in our present problem. Real exasnples of circular reasoning in the theory of interest am common enough, but the
dependence, above stated, of interest on the range of options and the dependence of the choice among them on
interest is not a case in point, for this last determinilag
condition is not derivable from ih others.6
For our .present purpose we need only present the
matter to the reader’s imagination by 8 process of trial
‘That this ia the case under our present hrpotheeie ie shown fullg in
Chapter

XIII.

[I451

THE THEORY OF INTEREST

and error. To find the rate of interest on which the market will finally settle, let us try successively a number
of Merent rates. First, let us suppose a rate of 5 per cent.
This rate will determine the choice between options for
each individual. The land owner formerly supposed will,
as we have seen, choose C, the mining use, because the
present value of the income 80 obtained ($9110) exceeds
the present values of the rival uses. Every other individual in the market, in Iike manner, will select that particular use for his capital which will give him the maximum
present worth. With these choices made, the different individuals will then enter the market of loans or d e s ,
desiring to modify the time shapes of their income
streams to suit their particular desires.
As a result of all these choices, the total amount which
. all the would-be lenders are willing to lend a t 5 per cent
out of this year’s instalment of their chosenincome
stream will be perfectly definite, and likewise the total
amount which all the wouldibe borrowers are willing to
take. This wesaw in the preceding chapter. In other
words, the demand and supply of loans for the present
l
l
iboth be
year, at th.e given rate of interest, 5 per cent, w
definite quantities. Should it happen that the supply of
loans exceeds the demand, it would follow that 5 per cent
could not be the correct solution of the rate of interest,
for it would be too high to clear the market.
In that case, let us try again; suppose a rate of 4 per
cent. Following the same reasoning as before, we now find
that the land owner will select the forestry opportunity
for his land because the present value ($11,300) of the
income from forestry-now reckoned at 4 per cent-will
exceed that of the two rival income possibilities. Other
capitalists will likewise select theirbest option from
1.1461.

SECOND APPROXIMATION
among those available to them and on the basis of these
incomestreams-not
the m e w before under 5 per
cent. I n a word, there will now be a different supply and
demand. The land owner, for instance, instead of lending,
may now borrow (or sell securities) to even up hisincome
stream. Should it thenhappen that the demand and
supply of loans, on th,e basis of 4 per cent, are still not
equal, but that, thistime, the demand exceeds the supply,
it would be a proof that not 4 per cent is the true solution, but some higher rate. By again changing our trial
rate-part way back toward 5 per cent, we may evidently
reach some intermediate point, let us say 4+” per cent,
at which rate not only will each indhk-luul choose the
best use of his capital-that having the highest present
worth-but also, at the same time,the demand and
supply of loam engendered by all such choices will exactly clear the market,ie., bids and offers at the given rate
will be equal. Likewise, the same clearing will be worked
out for next year and for all
The introduction, therefore, of flexibility into our
income stream still leaves the rate of interest entirely determinate, even though the income streams are now, in
the second approximation, not fixed or rigid but subject
to choice, and even though that choice will depend on
the rate of interest itself.

86. S u m m y
For the determination of the rate of interest we must
now,therefore, in thesecond approximation, add two new
principles to the four principles already given in the first
approximation described in the previous chapter.
am
e det& of such a multiform equilibrium are given
matical term in Chapter XIII.

E 147 1

in mthe-

THE THEORY OF INTEREST

THE TWO INVESTMENT OPPORTUNITY
PRINCIPLES

A. Empirical Principle
There exists, for each individual, a given specific set or
list of optional income streams to choose from, differing
in size and time shape (but without any uncertainty as to
what will happen if any particular one is chosen).

B. Principle of Maximum Present Worth
Out of this list of options each individual will choose
that particular income stream possessing thegreatest
present worth when calculated by m e m of the rate of
interest as S n d y determined by these six conditions.
THE TWO IMPATIENCE PRINCIPLES
A. Empirical Principle
The degree of impatience, or rate of time preference,
of any given individual depends upon his income stretbm
aa chosen by him and as modified by exchange.

B. Principle of Maximum Desir&ility
Each person, after or whilefirstchoosing the option
of greatest present worth, will then modify it by exchange
so as to convert it into that particular form most wanted
by him.
This implies, aa we have seen, that each person's degree
of impatience, or rate of time preference, will at the
margin, be brought to equality with the market rate of
interest and, therefore, with the marginal preference rates
of all the other persons.

[I481

.

"'

SECOND APPROXIMATION
THE TWO MARKET PRINCIPLES
A. Principle of Clearing the Market
The rate of interest must be such as will clear t.he
market, that is, equalize supply and demand. That is, for
every time interval, the additionsto some individuals' incomes caused by borrowing or selling must balance the
deductions from others caused by lending or buying.

B. Principle of Repayment
The loans must be equivalent in present worth to repayments, or,more generally, the additions to any individual's income, brought about by borrowing or selling, in some time intervals mustbe equivalent in present

worth to the deductions from his income in other time
intervals brought about bylending or buying.
Thus we see that the rate of interest is determined by
two principles of investment opportunity aa well as by
two principles of impatience and by the two self-evident
market principles.
More briefly stated, the rate of interest is determined
so a~ (1) to make the most of opportunities to invest, (2)
to make the best adjustment for impatience and (3) to
clear the market andrepay debts.
In short, the theory is thus one of investment opportunity and human impatience, aa well as exchange.
But while we have reached the two chief theoretical
foundations of our subject, we are still,of course, far from
the r e d world. The red world is vastly more complex
than the imaginary world described in this chapter. In
particular, we still need to take account of riak. This
we shall do in the third approximation.
1.149 1

.

CHAPTER VI1
THE INVESTMENT OPPORTUNITY PRINCIPLES
$1.Eligible and Ineligible Options
THEessential point of the preceding chapter is that the
possibility of more than one use of our resources affords
opportunity to invest by substituting onesuchuse for
another. Whenever there is such a choice of dternatives,
as for instance by changing from the “mining” to the
“farming” use of one’s land, as per Table 3, there is a
differential sacrifice or investment of income during the
earlier years for the sake of a differential return later.
The fact that such alternative uses of labor, land, and
capital exist, introduces on the scene the whole subject
of “productivity”.
Bijhm-Bawerk was profoundly right when he wrote:
“Thestatement of how theproductivity of capital works i n t ~
and together with the other two grounds of the &her valuation of
present goods, I consider one of the most difficult points in the
theory of interest, and, a t the same time, the one which must
decide the fate of that theory.”l

I have generally avoided the term productivity of capital because it may be used ambiguously to mean physical
productivity, or value return, or return over costs; and
because it suggests that capital producesincome value
instead of the reverse; and because it attributesthe
Poai6ive T h e w of Capitol, p. 2
!77,footnote.

r 1501

INVESTMENT OPPORTUNITY PRINCIPLES
value of manufactured things to the cost of production,
instead of to their discounted future services.
I prefer the term investment opportunity. It has aome
of the demerits as well as th_e merits belonging to any new
term. It is unfamiliar and therafure requires precise
definit’ion.The concept of investment opportunity rests
on that of an “option.” An option is any possible income
stream open to an individual by utilizing his resources,
capital, labor, land, money, to produce or secure said income stream. An investment opportunity is the opportunity to shift from one such option, or optional income
stream, to another,
It includes all possible opportunities to i n v e s t
those that can yieldonly negatiye ret,urns upon the investment as well as those which are capable of yielding very
large surpluses over the amount of the investment or
cost.
The first (A) of the two investment opportunity principles specifies a given range of choice of optional income
streams. Some of the optional income streams, however,
would never be chosen, because none of their respective
present values could possibly be the maximum. We have
seen that the land, in our example, would be most profitably employed forfarming, for mining, or for forestry, according to the rate of interest. But it would not be employed, let us say, for a quarry, no matter what might
be the rate of interest.
The optional uses which are thus out of the question,
whatever be the rate of interest, are called ineligible.
The rest are the eligible options. We need to consider the
eligible ones-any one of which might be made to have
the maximum present value, given the right rate of interest to make it 80.
[: 151 1

THE THEORY OF INTEREST
$2, The Method of Comparative Advantage

The second (B) investment opportunity principle, that
of maximum present value, is of great importance and has
many aspects not always recognized 89 related to one
another. Let us restate this maximum value principle in
an alternative form, thus: one option will be chosen over
another if its income p~sessescomparative advantages
outweighing (in present value) its disadvantages.
To illustratethisalternative
method of statingthe
Same principle-whichmethodmight
becalled
the
method of comparative advantage-letus
recur to the
example of the land. We found that, when the rate of
interest w&s 4 per cent, the ownerwould elect the forestry use, since this possessed the greatest present value.
If wenow compare, year by year,. the income from the
land whenused for forestry purposes with the income
which it might have yielded if used in one of the other
ways, 85 for instance farming, we shall see that in some
years there is an excess in favor of t.he forestry use, and
in other years a deficiency, aa shown in the table on the
foliowing page.
Here we see that, in the first four years, there are comparative disadvantages, a differential s d c e , amounting
in the four respective years to $450, $450, $150, $50.
These are the disadvantages from the use of the land for
forestry purposes as compared with its use for farming,
but the disadvantages are offset later by advantages in
return mounting to $50 each year perpetually. If prior to
the first year listed above the owner has been using the
land for farming purposes andwas considering the advisability of changing over to forestry, he would think of the
disadvantages or sacrifices of $450, $450, $150 and $50

c 153 1

INVESTMENTOPPORTUNITYPRINCIPLES
T w6
Farming a d Forestry Use Compared by Method of Canparatdv~
Advantage

Annual Value D u a l Valu Difference in
of Farming
of Forestry
Favor of
URS

1styear .................
2nd year ................
3rd year ................
4thyear .................
6th year .................
0thyear .................

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

7th year
8thyear
9th year
loth year
11th year
Each year thereafter..

$450
450
450

450
450
450
450
450
450
450

450
450

USeS

Forestry Use
"50

-460
-150
"bo

+50
+50
+50
$50
$50
+50
+50
+50

as investments or costs and the advantages of $50 each
year inperpetuity as returns onthese investments or
costs. And he could1 think of the proposal to substitute
the forestry use for the farming use as an opportunity
to invest the $450, $450, $150, and $50 for the sake of
securing the return of $50 each year thereafter. If, now,
we take the total present value, at 4 per cent, of the deficiencies, or dnvestmnts, of $450, $450, $150, and $50, we
shall obtain $1025, whereas the present value of the returns of $50 per annum beginning in five years and continuing in perpetuity will be $1069. Thus the present
value (at 4 per cent) of the gains exceeds the present
value of the sacrifices or costs by the difference between
$1069 and $1025. As reckoned in present estimation, the
gains of income outweigh the costa or sacrifices of income. We may my, therefore, that, the rate of inteneat
being 4 per cent, forestry is preferable to farming because
of a surpluiusof advantages over disadvantages reokcmed
fn piwent value, Thus, the opportunity to invest by

E1531

THE THEORY OF INTEREST
switching over from farming to forestry is, if money can
be borrowed at 4 per cent, more than worth while.
But if the rate of interest were 4% per cent, the comparison would be different.The present value of the sacrifices orcosts would be $1016, and thepresent valueof the
gains or returns $932, showing a preponderanceof the
sacrifices or coats. That is, if the rate of interest is 4%
per cent, the cost from using the land for forestry rather
than farming outweighs the returns. Therefore, when
money is at 4% per cent, the land would not be used for
forestry purposes.
The general principle is, therefore, that among the
various options open to the capitalist he chooses the most
advantageous, ormore fully expressed, the onewhich,
compared withanyother,
offers advantages which in
present value at the given rate of interest outweigh the
disadvantages. But this is evidently merely another formulation of the original principle that the usechosen
will be the one which has themaximum present value at
the given rate of interest.
We may summarize the methodof comparative advantage as follows: We are constantly confronted with the
opportunity to choose one income streamrather than
another. We inquire what diference it makes whether
one or the other alternative is chosen. We find often it
makestwo kinds of differences, advantages and disadvantages. If we start with the option which has the more
immediate advantages and ask whether it is or is not
worth while to give up this option andadopt the other instead, we may call the proposal so to do an opportunity
to invest, i.e., to incur certain disadvantages or, as they
will hereafter be called, costs, for the sake of certain advmtagea or, as they will hereafter be ,called, retwns.

C1MI

INVESTMENT OPPORTUNITY PRINCIPLES
And we decide whether or not this investment opportunity is worth while by weighing the costs against the returns in terms of present worth, as reckoned by the rate
of interest.

53. The Concept of Rate of Return O v e Cost
When we compare two optional income streams, and
either may be preferable to the other according as one
rate of interest or another obtains, the two options would
stand on a par if the right intermediate rate were used
for calculating the present vaIues of the two options. That
is, this equalizing rate is such that the present values of
the two options would be equal, or what amounts to the
same thing, it is such that, if that rate is used for discounting, the present value of the cost of choosing one
option instead of the other would be equal to thepresent
value of the return.
This hypothetical rate of interest which if used in
calculating the present worth of the two options compared would1 equalize them or their differences (cost and
return) may be called the rate of r e t m over cost and
hereafter this name will generally be employed. This new
magnitude (or factor) in our study plays the central r61e
on the investment opportunity side of interest theory.
Let us now apply this rate of return over cost to the
case of the options already used for illustration.
We have seen that, in our land example, if the rate of
interest is 4 per cent, the net advantage is in favor of the
forestry we, and if the rate of interest is 4% per cent,
the netadvantage is in favor of the farming use. It is evident then that at some intermediate rate of interest the
comparative advantages of the two uses wouldbe exactly
equal. This intermediate rate is approximately 4.2 per
I: 1551

THE THEORY OF INTEREST
cent, and this equalizing rate is the rate of return over
cost.
But we may reduce the comparison to its simplest form
if we change the figures in the example to the following:
T.mm 7
Fanning and Forestry Use Compared in T

m of Rate of Return

Over Cost

I

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

1st year
2nd year ..................
3rd year
4th year ..................
Each subsequent year

,

DitTerence
Net Value of N~~Value of Net
in Favor of
Farming Use Forestry
Forestry Use
$100

100
100

100
100

do00

210
100

100
100

"t100
$110

ooo

OOO
OOO

In this caae the equaJizing rate, or the rate of return
over cost, is evidently 10 per cent. At the cost of $100
there is a return of$110, or 10 per cent over the $100.
At 10 per cent thepresent worth of the two will beequal;
for the present worth of the return $110 due next year is,
reckoning at 10 per cent, exactly $100 and the present
value of the cost, $100, due immediately, is also $100.
The example just given, in which the cost($100) is
only one item and the return ($110) is also only one item
received one year later, is the simplest possible example.
But the m e principle holds true however complicated
may be the series of items constituting the costs and
returns.
Perhaps thenext simplest example is that in which one
option shows in the present year a cost (of, say, $100)
compared with the other but shows a return (of, say, $8)
for every future year in perpetuity. Under these circumstances the equalizing rate (or the rate of return over
cost) is 8 per cent.
c1561

INVESTMENTOPPORTUNITYPRINCIPLES
Thus theexpression “rate of return over cost” is applied
to tbe comparative merits of twoalternative income
streams. I repeat that by cost is meantthe comparative loss fromone’sincome stream at fist, causedby
substituting one use of capitd for another, and by retunz
is meantthe comparative gain whichaccruesusually
later, byreason of this same substitution. The cost is
literally the difference it makes today and the return is
the differenceit makes in the future-the first negative,
the second positive.
It will be noted that this description is all inclusive.
It applies to every possible costand every possible return.
The problem of the investor-andeveryoneis
an investor in some degree and manner-is alwag to answer
the question: “What difference does it make to my income stream whether I choose one way rather than another? What do I sacrifice and what do I gain?” If the
cost comes k t and the return comes lata-, he wants to
know if the return exceeds the cost ‘by enough to be
worth while. The excess is his return over cost and the
important magnitudeis the rate per annum of this return
over cost.
Usually this question, “What difference does it make?”,
is asked with reference to a proposedchange from an
old to a new layout of one’s plans. Will a little more
tilling of the soil bring a big or a littlereturn, both
the tilling and return in crops being translated at their
market prices into money? Will a new harvesting machine at market prices make enough difference in the harvest to be worth while? Will a merger of two companies
make a return in future
profits sufficient to make the temporary costs involved inthe merging process worthwhile?
It will be seen, then, that the concept here used of in-

C 157 1

THE THEORY OF INTEREST
vestment opportunity is not contrary to ordinary ideas.
It includes them. Every time a personconsiders what
he calls an opportunity to invest, he weighs in his mind
the differences in his expected income-the expected future additions against the more immediate subtractions.
Even when the investment is not made in installments
out of savings from current income, but is made in one
lump sum, it must not be forgotten that this lump sum
invested merely represents the sacriiice of some alternative income stream.
The rate of return over cost is not, of course, to be
confused with the rate of interest which it helps to determine, any more than the rate of impatience is to be
so confused.
$4.Tlze Principle of Return over Cost
Now let us restate the forestry-farming-mining comparison in the land example of the preceding chapter in
terms of the rate of return over cost.
If the actual market rate of interest is 4 per cent, a
person using the land for farming, or thinking of so doing, wouldfind forestry preferable. The change from
farming to forestry would cost certain sacrifices of income
in the first four years, as specified in Table 6, but would
return certain net additions thereafter. The rate of return
over cost whichwould be realized by choosing the forestry rather than the
farming use is 4.2 per cent. He
would be realizing 4.2 per cent, which is more than the
market rate, 4 per cent.
If, however, the market rate of interest were 4.5 per
cent, it would not pay to change from farming to forestry;
for to do so would return only 4.2 per cent as compared
with 4.5 per cent which he could get in the loan market.

IlS1

INVESTMENT OPPORTUNITY PRINCIPLES
Our farmer would pFefer to investat 4.5 per cent by lending in the first four years $450, $450, $150, $50 rather than
sacrsce these s m e amounts for 4.2 per cent by giving
up farming for forestry. To induce him to make a change,
the rate of retwn over cost rnwt exceed t b rate of interest?
Thus, by employing the concept of a rate of return over
cost, we may restate the investment opportunity
principle
of maximum present value, or the principle of comparative advantage, as the principle of greatest return
over cost. So stated the principle i:
Out of all possible options open to a person that particular one is selected, the comparison of which with any
other option affords a rate of return over cost equrtl to
or greater than the rateof interest.
$5. Marginal Rate of Return Over Cost
Next let us apply this statementof principle to the case
in which the range of choice is not confined to a few
definite options, but extends to an infinite number v q ing by continuous gradations. This case is really more
like the facts of life than the imaginary case of a few
fixed options, such m the farming, mining,or forestry
uses of land. In fact, each of these th~e
u8es is in actual

I
'n case the advantages (returns) precede the dieadvantages (costs),
aa is the c888 when the merits of the mining w e are compared with
tho= of the farming use, the propaition must be reversed, aa follows:
The earlier advantage will be chosen only in case the rate of future
costs overpresent returns is h a thm the rate of interest. In such a
case it would be moreconvenient, in comparing the two optione, to
regard them in the reverse order, that is, to consider the advantages of
the farming uee over the mining we, so t h a t the disadvanma may
come fbt, Le., the investment precede the retums. AB long aa the costa
alwaya precede the returne, we need only to consider whether or not
the rate of return over cost m
e
& the lrrte of interest.
[: 159 1

TffE THEORY OF INTE;REST
life not merely a single use, as was assumed for simplicity, but a whole group of optional uses. Thus, the
farmer maycarry farming to any degree of intensity, and
the same may be said of mining or lumbering. For each
particular degree of intensityhe will have a different
income stream. He may, for instance, fmd it possible at
the beginning of the scale of intensity to invest an extra
$100 worth of his or other labor in the present in order
that one year later he may havean income of $150 more
than he would otherwise have. If the rate of interest is
4 per cent per annum, he would evidently prefer this
course, for while hispresent income is diminished by
$100 he would re&e an increase of $150 in his income
one yeax later, or $50 overcost, making a rate of return over cost of 50 per cent per annum, whereag the interest is only 4 per cent. If he invests another $100 in
present cultivation, thiswill add to his income in a year’s
time something less than the $150, say $130,making a
rate of return of 30 per cent. And so eachsuccessive
choice compared with its predecessor follows the law of
decreasing retwm. A third $100 will add, let us say, $120
or $20 more than the cost. A fourth $100 may secure a
return of an additional $10 a year over and above the
cost; a fifth $100 may secure a return of an additional$8;
a sixth $100 may bring $6; a seventh $100,
Thus far, in the scale of intensity, each option yield8
4 per cent or more, while the rate of interest is 4 per
cent a year. The lure of a rate of return equal to or in
excess of the interest rate will induce the farmer to incur
the additional cost. But the next option, let us say, is to
invest an eighth $100 for an additional $3 a year. Evidently, it will not be to the farmer’s advantage to take
this last step; he will stop at the previous step, at which

$4.

Clf30I

INVESTMENT OPPORTUNITY PRINCIPLES
he barely gets a 4 per cent return. As we saw in the preceding section, each successiveinvestment opportunity is
chosen as long as the rate of return over cost of that option compared with the previous one is greater than the
rate of interest, and that use is rejected at which the rate
of return over cost becomes less than the rate of interest.
The intensiveness of his farming is thus determined by the
rate of interest. In our example, he will stop at the seventh $100 which barely returnsthe equivalent of the
rate of interest. We may say, then, that he chooses that
degree of intensiveness at which the rate of return over
cost is barely more than the rate of interest. This envisages a series of possibleincome streams arranged
successively in order of intensiveness of the cultivation
required for each. By substituting successively one of
these income streams for the preceding we incur more
cost but obtain more return. The rate of the return over
the cost compared with the market rate of interest is our
guide aa to how far to go in the series. We thus reach the
marginal rate of return over cost.
$6. The Illustration of Cutting a Forest

To vary the illustration from intensive agriculture to
forestry, let us apply theoption selection idea to cutting a
forest. Let us consider as the first option the cutting of
the forest at the end of nine years, when the income
stream consists of the single-item, the production of 900
cords of wood (or $900 if wood is $1 a cord).3
The second option-is holding the forest for another

'h a m u & aa we aasume that the incomefrom the forest is all to
a w e et one time-the time of cutting-instead of being distributed
over a long p e r i o d , the income stream becomes a single jet and might
here better be called income item.

c 161 1

THE THEORY OF INTEREST
year of growth and cutting it at the end of ten years, to
receive an income item of loo0 cords (or $1000,aasuming
sn unchanging price of $1 a cord). The two alternatives
may be put inprecisely the same tabular form as the one
for the case of forestry andfarming
previously employed
-~
follows:

as

TABLE
8
Optional Incomes from Forest
10-Year Plan 9-Year Plan

1st year .................
2nd year

................
....................
9th year ................
loth year .................

SO00
OOO

...

DiBerence in
Favor of
10-Year Plan

so00

ooo
...
900

"goo

+IO00

The last column shows that the ten-year plan, compared
with the nine-year plan, involves a. cost of 900 in the
ninth year, but involves a return of lo00 in the tenth
year. The rate of the return (100) over the cost (900)
would thus be a litt,le over 11 per cent. If the rate of interest in the market is 5 per cent, it would evidently pay
to wait, that is, to postpone the cuttingto the tenth year.
The next option would be to cut in the eleventh year,
which, as compared with the previous or ten-year plan,
would, let us say, cost lo00 in the tenth year and return
1050 in the eleventh year-in other words, give a rate
of return over cost of 5 per cent, Evidently, then,it would
be a matter of indifference whether the forest were cut
in the tenth or eleventh year, inasmuch aa the rate of
return over cost would be exactly equal to the rate of
interest.
Similar reasoning might show that the choice of the
next option, that of cutting theforest in the twelfth y m ,

c 162 1

INVESTMENT OPPORTUNITY PRINCIPLES
would yield a returnof say *?40 5 0 or 2 per cent. Inasmuch
as 2 per cent is less than the rate of interest, this alternative would be rejected. Thus, equilibrium is found where
the rateof return on cost equals 5 per cent, the rateof interest.
The catx may be illustrated by Chart 16. Let AB represent the number of cords of wood on an acre of growing

D
CHART 16
Selecting the Time for Cutting a Forest.

Y

trees; let A' B' represent the amount of wood which may
be expected at the end of five years; let AN B" represent
what may be expected in ten years and so on for successive years until the forest reaches its maximum growth,
MN, at the end of AM years. The percentage-slope, or
rate of ascent,' of the curve BN at any point, therefore,

' The Nature

of Ca$d and Inoom~,pp. 221-222.

c1631

THE THEORY OF INTEREST
represents the rate of growth, at any time, of the forest.
The value at present (at the point of time A) of the forest, in terms of cords of wood, will be represented, not by
the height AB, but in a different manner, aa follows: If
from B' the discount curve B' Ct be drawn, the ordinate
of which, at any time, will represent thediscounted values
of A'B' at that time, then AC' will represent the present
value of A' B', i.e., of the amount of the wood if cut in
fiveyears. SiIpilarly, AC" will represent the present
value of A" B", the wood if cut in ten years.We
of discount curves
draw in like manneranumber
until one is found, tT, which is tangent to the curve
BN. At will then be the correct value of the young
forest, and D will represent the time at which it should
be cut. Clearly, At is quite different from AB, the
amount of wood at the present time, and also from DT,
the amountof wood at thetime of cutting. At is the maximum present value out of all possible choices as to the
time of cutting. If the forest is for some reason to be cut
at once, its value will be only AB; if it is to be cut at A'
its present value will be AC'; at A", it will be AC";
if at D,it will be At. At is the maximum, for if the forest
were cut at any other point of time on either side of T
the discount curve passing through that point would
evidently lie below the curve t T .
At the time A, then, the wood in the forest is only AB
but, sssuming proper foresting, the value of the forest in
terms of wood is At; the rate of growth of the forest is the
percentage-slope of BN at B, but therate of interest is the
percentage-slope (the same at all points) of tT.
A t the point of tangency alone, namely T,are the rate
of growth and rate of interest (both in terms of wood)
'if

'The Ncdwe of Ca&d asrd Income, Chapter Xm.

11641

INVESTMENT OPPORTUNITY PRINCIPLES
identical, and to that extent at least there is truth in the
thesis that therate of interest is the rate of growth, This,
however, is not the average rate of growth but the rate of
growth at the time of cutting. This is the element of
truth in the organic productivity theory of Henry George
and Alexander Del Mar. These writers based their theories of interest on theproductivity of those particular
kinds of capital which reproduce themselves, and reached
the conclusion that, in the laat analysis, the rate of interest consists in the “average rate of growth of animals
and plants.” II
Evidentlythe theory would besubstantially correct
if “average” were replaced by “marginal.” The example
of cutting the forest illustrates the simplest theoretical
case of marginal productivity as a true basis of the rate
of interest.
But thatthis element of truth is insufficient of itself to
afford a complete determination of the rate.of interest is
evident when we consider that the point at which the
forest is to be cut itselfdepends, among other causes,
upon the rate of interest! If the interest rate rises, the
discount curves employed become steeper and the point
of tangency T moves toward the left, that is, the forest
will be cut earlier.
In no case, of course, is the time of cutting t,he time of
maximum stumpage. To wait for that time would eat up
too much interest. The theories of Del Mar and Henry
George thus constitute a specid case under the opportunity principles.
‘Del Mar, Alexander. Science of Monev. New York, M a c d a n &
Co., 1898; George, Henry. Progress ond Poverty. New York, Sterling
Publishing CO.,1879. For a general critioism of this theory .we Lowry,
The &reis ofIntereat, American A d e m y of Political and Social Science,
March, 1833, pp. S76.

c1w

TKE THEORY OF INTEREST
$7. Other Similar Illustrations

Both the preceding examples, one of intensive agriculture and the other of forest cutting, involve (1) an immediate cost and (2) 8 return one yew later, thus reducing the marginal rate of return over cost to such simple
calculations as (105 - 100) + 100 = 5 per cent.
We may vary the illustration indefinitely and still preserve this elementary simplicity. A merchant has always
before him an indefinite number- of possibleincomestreams from which to choose. As in the cme of the land
cultivation and the forest cutting we may simplify his
choice by s u p p i n g successivedoses of costs of $100,
each spent on more or better machinery, more or better
workmen, more or better advertising, more or better
supervision, and so forth, each $100 cost being immediate,
and then supposing the returns to these successive doses
of invested cost to come respectively one year later and
to be respectively, say, $140, $130, $115, $106, $105, $104;
so that the excess of return over the cost will be respectively $40, $30, $15, $6, $5, $4. Thus the rate of return
over cost will be respectively 40, 30, 15, 6, 5, and 4 per
cent. The enterpriser will incur the costs BB long as
the rate of return over these costs is greater than the
market rate of interest. In thb case, therefore, he will
stop at 5 per cent if the market rate of interest is 5
per cent. Again we have ($105 - $100) +$100 = 5 per
cent.
In practice, however, we seldom, if ever, have such
simplicity in calculating the rate of return over cost and
there are innumerable other types of contrast between the
successive incomestreams which may be at the same time
under consideration by the investor.
E1663

INVESTMENT OPPORTUNITY PRINCIPLES
88. The Case of Perpetual Returns

Next in simplicity is the typein which $100 of immediate cost is incurred for the sake of a perpetual annuity of
$5 a year. Let us suppose the individual possesses some
swamp land in a primitive condition. He hasa large range
of choice &s to the method of utilizing this land. He wants
to make the most of his opportunities. One option is to
allow the land to remain a swamp. Others occur if, by
clearing and draining it, it is converted into crop-yielding
land, the yield varying with the thoroughness with which
the clearing and draining are accomplished. Let us suppose that, under the first option, he derives a perpetual
net income of $50 a year, and let us suppose that, at an
immediate cost of $100 in his labor or in payment for
the labor of others for clearing and draining, he can secure an addition of $25 a year. That is, &s between retaining these two options, the swamp undrained and_draining
it partially, thelatter involves a $100decrease of immediate income and thereafter an income of $75 8 year, or an
increase of $25 a year, In other words, a t the cost of
$100 he will obtain a return of 25 per cent per annum in
perpetuity.
Evidently, if the rate of interest in the market is 5
per cent, or anything less than 25 per cent, it will pay
him to makesuch an investment, borrowing at 5 per
cent if he wishes the $100 required for the improvement.
Next suppose that another $100 invested in improving
the swamp would yield crop returns of $90,or $15 more
than before, The investment of this second $100 yields
15 per cent, and is therefore also a lucrative one, when
the rate of interest is only 5 per cent. A third $100 may
increase the annual mop still further, say by $10,netting
I: 167 1

THE THEORY OF INTEREST
a return of 10 per cent over the cost. A fourth $100 invested will cause the annual crop to be increased by $5
giving a return of 5 per cent. A fifth $100 will cause the
crop to increase by $3-a ret- of 3 per cent. Evidently
it will pay the farmer to invest in draining and improving his swamp up to the fourth $100, but not to the fifth
$100, Ratherthan investthisfifth
$100 and receive
thereon an annual income of $3 ti year, he would prefer
to invest $100in the savings bank and receive 5 per cent
a year.
In other words, the exact degree of intensity with which
he will improve and cultivate his land is determined by
the current rate of interest. Should the rate of interest
in the market fall from the 5 per cent just assumed to
2 per cent, it would then pay him to invest the Mth $100.
For, evidently, if need be, he could borrow $100at 2 per
cent and receive from his land a return of 3 per cent. As
Raie has 80 clearly pointed out, in communities where
the rateof interest is low, swamps will be morethoroughly
improved, roads better made,dwellingsmore
durably
built, and all instruments developed to a higher degree of
efficiency so aa to yield a lower marginal return over
cost than in a community where the rate of interest is
high.
$9. The Generat Case

In general, the rate of return over cost has to be derived by more complicated methods.As already indicated,
the rateof return over cost % always that rate which, employed in computing the present worth of all the costs and
the present worth of all the returns, will make these two
equal.Or, as a mathematician would prefer to put it,
the ratewhich, employedin cbmputing the present worth
ClMI

INVESTMENT OPPORTUNITY PRINCIPLES
of the whole series of differences between the two income
streams (some differences being positive and others negative) will make the total zero.
If the rate, 80 computed, were taken for every possible
pair of income streams compared as to their advantages
and disadvantages, it would authentically decide in each

.' 4

"
"
"
"
"

CJURT 17
Diflerence Between the

Beat and the Next Best Investment Opportunity

In the Raising of

a Crop,

caae which of the pair is to be preferred. That one which
compared with the other shows a rate of return on sacrifice greater than the rate of interest would be preferred
and the otherrejected. By such preferencesand rejections
the individual would be led to a final margin of choice of
the beatoption. This contrasted with its nearest rival

""--"--"""CHART 18

DSerence Between the Best and the Next Best Investment Opportunity
in the Draining and Cultivating of Swamp Land.

would show a marginal rate of return over cost equal to
the market rate of interest.
The problems of choosing when to cut a forest, of what
length to make a production period, how f a r to push m y
industrial policy, to what degree of intensivenew to cultivate land, are d the same problem of choosing the
beat out of innumerable possibleincome streams, i.e.,
E 169 1

THE THEORY OF INTEREST
problems of making the best out of one’s investment o p
portunities.
In each problem the rivd income streams present differences as to size and shape. They can best be compared

CHART 19
Difierence Between the Best and the Next Best Investment Opportunity
m the Cutting of a Forest.

by means of diagrams. Charta 17 to 20 show typicd
ways in which the income streams may conceivably be
subjected to slight variation. The unbroken line in each
case indicates the income stream chosen, and the dotted

AlternatingInvestmentand

Return.

line the next best opportunity, rejected on behalf of the
unbroken line. Chart 17 may be taken 89 applying to
the planting of a crop; Chart 18 to the draining of a
swamp; Chart 19 to the cutting of a forest; and Chart
20 to tlie case of alternating costs and returns.
$10. Range of

Choice Depends on Interest Rate

Up to this point one complication in the problem of
interest has been kept in the background. Although this
complicationdoes not invalidate any of the principles

c 170 1

INVESTMENT OPPORTUNITY PRINCIPUS
which have been developed, it seemed advimble not to
distract attentionfrom the essential features of the theory
by introducing it prematurely. The complication referred
to is, after all, more intricate than important, It consists in the fact that not only, as we have seen, does the
choicebetween different optional income streams d e
pend upon the rate of interest, ,but also that even the
range of choice depends upon that rate. If the rate of
interest is changed, a change is produced not only in the
present values of the income item but in the income
items themselves.
The net income from any instrument or group of instruments of wealth is the difference between the total
gross income and the outgo. But many of the elements,
both of income and outgo, are materially dependent upon
the rate of interest. This is especially true of those items
of income and outgo which are not final but merely intermediate or interactions.' In the case of interactions, a
change in the rate of interest affects the income stream
directly, because, as has been shown elsewhere,s the valuation of an interaction (ie., intermediate service) involves the discount process and is therefore dependent
upon the rate of interest. Thus, the iron yielded by an
iron mine has its value determined in part by the discounted value of the machinery to be made of it and
therefore its value will be affected by a change in the rate
by which this discount is reckoned.
For present purposes, it is only necessary to emphasize
the bare fact that the range of choice between different
income streams is somewhat dependent upon the rate of
interest. If the modification due to this fact were intro'See Chapter I or The N a v e 01 Capital and I w m e , Chaptern VII,
'Ibid., p. 317.
VIII, IX, and X.

c 171 1

THE THEORY OF INTEREST
duced into the tables previously given for the three different uses of land, we should find thatthe income
streams from using the land for farming, forestry, and
mining would differ according to the rate of interest.
Thus, let us suppose, as before in Chapter VI, $2, that
for a rate of interest of 5 per cent the three optional income streams are:
TAB^ 9
The original O p t b u d Income S+mm of Fanndng, Forestry, and
M t w

................
.................
.................
.................
5th year .................
6th year .................
7th year .................
8th year .................
9th year .................
loth year .................
Thereafter ................
1st year
2nd year
3rd year
4th year

In our previous discussioq, when we changed the rate
of interest from the 5 per cent of the foregoing table to
4 per cent, we supposed the items in the foregoing
table to remain unchanged. The only change we had
then to deal with was the change in their present values.
Now, however, we admit the possibility of a change in
the table items themselves. If the rate of interest falls
to 4 per cent, the product of forest, farm, and mine will
be more nearly equalto the valueof the ultimateservices
to which they lead. The value of lumber will be more
nearly equal to the value of the houses it makes, and
these to the value of the shelter they give ; the value of
wheat from a farm will be nearer the value of the bread
it will d e ; and the value of ore from a mine will be
c 172 1

INVESTMENT OPPORTUNITY PRINCIPLE3
nearer the value of the steel it will become, and this, in
turn, more nearly equal to the values of those innumerable satisfactions which come a b u t through the use of
steel. These shiftings forward of the values of the intermediate income of forest, farmand minetoward the
values of the ultimate satisfactions to which they lead,
combinedwithpossible readjustments in the values of
these satisfactions themselvewthe values of house shelter, bread consumption, etc.-will result in a change, say,
in the items inthe foregoing table, where we were muming a 5 per cent rate of interest, to the following table
wherein the rate is 4 per cent.
T m 10
The Optional Incosne Stream of Farming, Formtry, and Mining, a
Affected bv the Rate of Interest

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

'g

2nd year
4th
3rd
1st year
year.......

.................
year
6th year .................
6th year .................
7th yesr .................
8th year .................
9th year .................
loth year .................
Thereafter ................

'~

1300
1500
1100

500

500
500
500

600
600

850
650
450
225

ooo

If, then, therate is 5 per cent,the land owner w
l
l
imake
the most of his opportunitiesby choosing that use among
the three which, computing from the figures in the first
table, has the greatest present value; while if tKe rate is
4 per cent, he will choose that which, computing from
the figures in the second table, has the greatest present
l
I
ichoose minvalue. If, then, the rate is 5 per cent, he w
ing, since,as we saw in Chapter VI, 84, the present values,
whenwe compute at 5 per cent,are:forestry, $8820;
[: 173 3

THE THEORY OF INTEREST
farming, $99ooo;mining, $9110; but if the rate is 4 per
cent, he will choose the highest from the present values
at 4 per cent, computed from the second table. These
present d u e s now are: forestry, 813,520;farming, $12,500;mining, $10,100.
Whatever the final outcgme of all the readjustments,
it is evident that the introduction of the influence of the
rate of interest on the range of choice does not in any
material way affect the reasoning already given in regard
to the determination of the rate of interest. Since the
rate of interest will itself fix the range of choice, it will
still be true that, once the range of choice is fixed for a
given rate of interest, the individual will choose, as before, that use which has the maximum present value. On
the basis of this choice he is then led to borrow or lend
in order to modify his income stream so that h a degree
of impatience may harmonize with the rate of interest.
If, upon an assumed rate of interest, the borrowing and
lending for different individuals actually cancel one another-in other words, clear the m a r k e t t h e n the rate
of interest assumed is clearly the onewhichsolves the
problem of interest; otherwise the borrowing and lending will not be in equilibrium, and some other rate of interest must be selected. By successively postulating different rates of interest, apd remembering that each rate
carries with it its own range of options and its own set
of present values of those options, we finally obtain that
rate which will clear the market.
The rate which will clear the market, while drawing
into equality withitaelf all marginal impatience rates
and all marginal rates of return on cost, is the one which
solves the problem of interest under the assumed conditions.
c 1741

INVESTMENT OPPORTUNITY PRINCIPLES
$11. The Investment Opportunity Principles

Summarized
The chief results of the chain of reasoning which has
been followed in this chapter axe that the same principle
of investment opportunity may nowbe stated in four
ways as:

The Principle of Maximum Present Value.
Out of all options, that. one is selected which has the
maximum present value reckoned at the market
rate of interest.
T b Principle of Comparative Advantage.
Out of all options, that one is selected the advantages
of whichover any other option outweighs its disadvantages, when both these advantages and disadvantages-returns and costtiare discounted at the
market rate of interest.
The Principle of Return ovw Cost.
Out of all options, that one is selectedwhich, in
comparison with anX other, yields a rate of return
over cost equal to or greater than the market rate of
interest.
The SamePrinciple when the Optbns Differ by Continuous Gradations.
Out of all options, that one is selected the differences
of which from its nearest rival gives a rate of return
over cost equal to themaxket rate of interest. Such a
rate is called the marginal rate of return on cost.
In whichever of these aspects it is regarded, this is the
principle of vestment opportunity, However he reckons
it, every onemeasures his opportunities to invest-t~
[ 175 1

THE THEORY OF INTEREST
modify his income stream-in reference to the rate of interest by applying this principle.
We can scarcely exaggerate the importance of the concept of “rate of ret,urn over cost” and of its special variety
“marginal rate of return over cost” as an eIement in our
analysis of the conditions determining the rate of interest. It supplies, on the physical or technical or productivity side of the analysis, what the marginal rate of time
preference supplies on the psychicalside. The subject
is, as has been seen, one which may be looked upon from
many points of view, which may seem at fist to be inconsistent yet which may be thoroughly c96rdinated
under the foregoing generalizations.

$12. Intmelation of Humn Impatience and Investment
Opportunity
The rate of interest, then, is the resultant of three sets
of principles of which the market principles are selfevident. The other two great sets of principles are theone
comprising two principles of human impatience and the
other comprising two principles of investment opportunity. The principles of impa,tience relate to subjective
facts; those of invest.ment opportunity, to objective facts.
Our inner impatience urges us to hasten the coming of
future incom-to
shift it toward the present. If incomes
could be shifted at will, without shrinking in the process,
they wouldbe shifted muchmore thanthey a,re. But
technical limitations prevent free shifting by penalizing
haste and rewarding waiting. Thus Henry Ford might
have continued making his Model T car. He would have
thereby enjoyed a large immediate income but a gradually decreasing one. Instead, he resolved to place a better
type of car on the market. To do so, he had to suspend
I 176 I

INVESTMENT OPPORTUNITY PRINCIPLES
the productive operations of his plant for a year, to scrap
much of his old machinery and to provide a new installation at the cost of millions. The larger returns which he
expected from the sale of the new car were only obtainable by the sacrifice of immediate income-by waiting.
Our outer opportunities urge us to postponepresent
income-to shift it toward the future, because it will
expand in theprocess. Impatience is impatience to spend,
while opportunity is opportunity to invest. The more we
invest and postpone our gratification, the lower the investment 0pportunit.y rate becomes, but the greater the
impatience rat,e; themore we spend and hasten our gratification, the lower the impatience rate becomes but the
higher t,he opportunity rate.
If the pendulum swings too far toward the investment
extreme and awayfrom the spendingextreme, it is
broughtback by the strengthening of impatience and
the weakening of investment opportunity. Impatience is
strengthened by growing wants, andopportunity
is
weakenedbecause of the diminishing returns. If the
pendulumswingstoo far toward the spen,dingextreme
and away fromthe investment extreme it is brought back
by the weakening of impatience and the strengthening
of opportunity for reasons oppositeto those stated above.
Between these two extremes lies the equilibrium point
which clears the market, and clears it at a rate of int.erest registering (in a perfect market) all impatience rates
and all 0pportunit.y rates.
It is all a question of the time and amount of the
series of items constituting real income. Shall we get income enjoyment now or later and how much? Shall we
spend or invest?

E 177 1

CHAPTER VI11
DISCUSSION OF THE SECONDAPPROXIMATION
$1. Opportunity Reduced to Lowest Terms

SINCEthe second approximation contains theheart
of the theory of interest, a further brief summary and discussion of the steps already taken will be helpful before
proceeding to the third approximation.
Any opportunity to invest simply reducesitself to
this: for a time there is more labor or less satisfaction
than there would be in the absence of such opportunity,
while there is expected later less labor or more satisfaction. The earlier item of labor or abstinence is less than
the expected satisfaction or labor saving. This picture of
temporary labor exerted, or abstinence from satisfactions
which would otherwise be enjoyed, for the sake of later
satisfaction or labor saving is the ultimate picture of cost
and return.
When thus reduced to these lowest terms of labor and
satisfaction, not only is our picture simplified, but, with
the simplification, we have rid it. of a certain suspicion of
begging the question of the interest problem. That is,
as long as interactions, capital, and money were in the
investment opportunity picture, interest was already
implied in each of their valuations and there might r e
main a haunting fear that this new rate of return over
cost as an interest-determining factor was simply involving us in a circle. The question might be asked: Is
c 178 1

DISCUSSION OF SECOND APPROXIMATION
the rate of return a new in%uence? Is there really any
important distinction between therate realizedon a
bond, which is interest pureand simple, and the raterealized on any other investment?Are they not allsimply interest, and is there anything else behind this interest besides human impatience? Is not the suminvested simply
the discounted value of the return expectedwithdue
regard to the risk element, which has not yet been considered?
The answer, as should now be clear, is that the rateof
return over cost really is a new element, not included in
the first approximation, howevermixed that element
may be, in practice, with the elements considered earlier.
When labor and satisfactions are concerned there is something more than exchange. The labor of planting a fruit
tree is not the same thing as the discounted value of the
fruit yielded by the tree, even though the value of the
labor and the value of the fruit may be equal at a given
time. The satisfaction from eating fruit is pleasure and
the labor of planting it is pain, and these can be direct19
compared, despite the fact that iq practice they are
usually compared only indirectly in terms of their exchange equivalents.
Instinctively we feel the presence of this factor of rate
of return over cost whenever we invest in a new enterprise. To invest in the original telephone enterprise, or
in a railway under construction, seems somehow different
from today buying telephone or railway securities. In the
latter transactions we feel we are dealing with mentrading; in the former we feel we are dealing with Nature
or our technical environmentexploiting. Infact, I came
near selecting the term exploitation for a suitable catch
word rather than investment opportunity to exprea the
c 179 1

THE THEORY OF INTEREST
objective factor of a return over cost.Of course, even after
the period of early exploitation is passed there are plenty
of opportunities within the iqdustry for variation in the
rates of return over cost, but they are no longer so conspicuous.
Even when there is no exchange possible, as with Robinson Crusoe alone on hi8 island, there will be dealings
with Nature. Crusoe mayplanttrees or build a boat
and balance his immediate labor against his future satisfactions without the presence of any exchangeprocess. It would have been possible, of course, to have
begun the presentation with Robinson Crusoe instead of
ending with him. In that case, we should have first considered the primitive facts of labor exerted for the sake
of future satisfaction, or their equivalent in berries. We
could then bring in ManFriday,and proceed step by
step to the complications of modern civilization. We
should have seen how the primitive cost and return typified by labor and satisfaction became gradually hidden
in a mass of exchanges until today we think of both in
terms of money. The capitalist of today, instead of laboring for a future satisfaction, may simply abstain temporarily from a part of the satisfactions he could otherwise
enjoy and, with the money which he would have spent
for them, buy the labor to build a railway. The laborer
is no longer the one who has to wait for the satisfactions
to follow the completion of the railway. He is paid in
advance and converts his pay into realwages veryspeedily, while the capitalist waits and receives the rewards for
waiting.
In all these and theother manifold exchange relations
the terms are partly set by the principles of discount in
relation to impatience. Butthe primitive ingredients

c 180 1

DISCUSSION OF SECOND APPROXIMATION
of labor and satisfaction, or their cost of living equivalents, with a time interval between, are never s h d e d
out of existence, however much they may be s h a d out
of sight. They are ever present and exert their influence
just &s truly 88 they did with Robinson Crusoe.
In making the first of these two adjustments, the individual is not trading with other human beings, but k,
aa it were, trading with his environment-Nature and
the Arts. That is why industry today maintains laboratories of research. These aim to improve products and
service by scientifk means, to develop new fields of application in by-products and materials, and to evolve new
products and met'hods and so new investment opportunities, Trading with the environment is making the most
of investment opportunity-ofthefuture
income returnedperunit
of present incomesacrificed.Trading
with mankind is making the most of impatience-of the
preference for a unit of present income over a unit of
future income.
When the individual sets out totrade with the environment he finds that the rate of return over cost varies
with the extent to which he pushes this trading; he adjusts the trading so as to harmonize the marginal rate of
return with the r?te of interest. In his trading with other
human beings, on the contrary, he finds the terms of the
contract interest fixed, so far as any effort by him is concerned, but impatience varies with the extent to which
he pushes this trading.
$2. Investment Opportunity Essential
Someeconomists,however, still seem to cling to the
idea that there can be no objective determinant of the
rate of interest, If subjective impatience, or time prefer-

I 181 1

THE THEORY OF INTEREST
ence, is a true principle, they conclude that because of
that fact aJl productivity principles must be false. But
they overlook twoimportant points. One is that, obviously
and as a matter of practical fact, the technique of production does affect the rate of interest, and therefore cannot
be ignored; the other, that their proposed solutions are
indeterminate-i.e., they have more unknown quantities
than determining conditions.
If, then, I am asked to whichschool I belong-subject,ive or objective, time preference or productivity-I
answer “To both.” So far as I have anything new to offer,
in substance or manner of presentation, it is chiefly onthe
objective side.l
In my oEinion minute differences of opinion as t.0 the
relative importance of human impatience and investment
opportunity are of too little consequence to justify violent quarrels as to which of the two is the more fundamentaI, although I shall here and later,as occasion offers,
note certain differencesbetweenthem.
Theimportant
point is that the two rates, that of marginal time preference and that of marginal return over cost, must be equal,
granted continuity of variation, that is, variation by infinitesimal gradations. If, as Harry G. Brown: in a very
interesting Robinson Crusoe phantasy, assumes as a
theoretical possibility, the rateof return over cost is fixed
immutably at 10 per cent, the rates of impatience must
conform thereto and the rate of interest can only be 10
per cent. L&er inthis chapter an even simpler and
more easily imagined case, while at the same time more
‘A somewhat similar treatment is that of Professor Hany c). Brown,
Economic Science and the Comma Wdjure. Mathematical treatments
substantially in harmonywithmine
are those of Walraa and Pareto
referred to in Appendix to Chapter XIII.
H. G. Brown, Eoonomic Science and the Common Welfare, pp. 137-145.

c 182 1

DISCUSSION OF SECOND APPROXIMATION
startling in its conclusions, is presented in which the
technical limitations impose a fixed rate of interest and
of dumm impatience of zero per cent. There, investment
opportunity dominates.
On the other hand, we could also imagine the converse
case; we could assume, as a theoretica1 possibility, a society of persons having an obstinate constancy in their
rates of impatience, all being 10 per cent. In such a case,
the marginal rate of return over cost would be adjusted
thereto.
A person’s rate of impatience dependson the extent
to which he modifies his income stream by loans or sales.
It isevident that if loans c a n be used to anyextent
desired, impatience will vary cont.inuously with them.
The rateof return over cost, onthe other hand,depends
on the ext,ent to which a personmodifies his income
stream by altering the way in which he utilizes his capital
resources.Such alteration, while partly continuous, is
partly discontinuous, as when new machinery, buildings,
personnel or systems are introduced.
It was to emphasize this distinction between impatience
and opportunity that I chose to begin with the case of a
supposedly rigid income stream, as in the first approximation, with no opportunity to substitute any other; then
to proceed to the case of three optional uses of land (distinguished for convenience as farming, mining, forestry)
affording opportunity to subst,itutefor one of them either
of theothersandthus
discIosing in such substitution
two alternative rates of return over cost; and finally to
reach the supposed case of an infinite variety of income
streams differing from one another byinfinitesimal gradations. Only in the last named c8se is the rate of return
over cost aa variable as the rateof impatience.

[I831

THE THEORY OF INTEREST

It should benoted that in the first approximation,
where the income stream is fixed or rigid and there is
noalternative income stream,there canbe no comparative cost or return and therefore no rate of return
over cost. But we cannot so easily imagine a similar disappearance of impatience. It would be quite impossible to
have any exchange between present and future-any rate
of interestwithout $he existence of time preference, as
it would be quite impossible to have any exchange whatever without human wants. They arean omnipresent and
necessary condition of all exchange and valuation.
$3. Options Differing in Time Shape Only
Options differ in three chief ways corresponding to the
characteristics, already noted, of the income 'stream,
namely, (1) in composition, (2) in risk, and (3) in size
and time shape. Options which differ primarily in composition or the kind of services rendered are illustrated
by theoptions of using a building as a dwelling, as a shop,
or as a factory. Options whichdiffer primarily in the
probability or risk are exemplified by the use of a ship on
a hazardous voyage or in safe river transportation. O p
tions which differ in size and time shape of the income
stream are illustrated by the innumerable uses of land
and artificial capit,al to produce different kinds of goods
(income) of different degrees of immediateness as to the
satisfactions they render.
The thirdgroup of options (which differ in the size and
time shape of the income stream) is the one which especially concerns UB here: First, let ussuppose only one
degree of flexibility, permittingvariation in the time
when the income items arrive but no variation in their
amounts. Let us suppose, then, that the income stream

[I841

DISCUSSION OF SECOND APPROXIMATION
from any capital is fixed in aggregate amount, but that
the times of receiving that income ire controllable at
will. This species of choice occurs approximately in the
case of durable goods for consumption, which neitherimprovenor deteriorate with time. A stuck of graip, for
instance, may be used at almost any time, with little difference in the e5ciency of the use and little cost except
for storage.The same is true of coal, cloth, iron,and other
durable raw materials, aa well as, to some extent, of finished products such as tools and machinery, though usually deterioration from rust, or other injury by the elements, will set in if the use is too long deferred. Another
simple example is a definite sum of money in a strong
box which may be spent at any time, or times, desired.
Thus a strong box containing $100,000 may be so used
as to yield a r$al incomeof $100,000 for one year,or $10,000 a year for ten years, or $4,000 a year for twenty-five
years.
Such options afforded by durable goods (as when to
use them) are perhaps the simplest of all options. Since
extreme CMM are especially instructive, let us imagine a
community in which the income from all capital is of
the character just described. That is, we suppose the
total quantity of income obtainable is absolutelyfixed,
but the times at which it can be obtained are absolutely
optional. This community would then be endowed with
a definite quant,um of income as fked as the quantity of
money in a strong box. That is, every dollar of income
sacrificed from oneyear’sincomewouldeke
out my
other income by that same amount, a dollar, no moreand
no less; conversely, every dollar of income enjoyed
in one
year would reduce indulgence elsewhereby exactly a dollar, The rate of interest would be reduced to zero.
[ 185 1.

THE THEORY OF INTEREST
04. T h Inaag.inary “Hard-Tack” Illustration

To fix our ideas, let us suppose these conditions to be
realized on a desert island onwhichsome
sailors axe
shipwrecked and each left with a specified number of
pounds of hard-tack and with no prospect of ever improving his lot. We shall suppose the use of this hard-tack
. t o be the only real income open to these castaways,
and that theyhave given up all hope of ever adding
to it byaccessions from outside or by cultivating the
island which, for our hypothesis, must be barren. No
change in their human nature need be sssumed. We assume that they would react to the same income just as
before the shipwreck. Merely their circumstances have
changed. I n consequence, the only possible variation of
.their income streams”consisting solely of the use of
hard-tack-is that made possible by varying the time of
its consumption. Suppose one of themhas an initial
stock of 100,OOO pounds. He has the option of consuming
his entire store during the first year, or of spreading its
use over two or more years, but in any case he will eventually aggregate the same total income, measured in
hard-tack, spread over the future,namely 100,000pounds,
A little reflection will show that, in such a community,
the rateof interest in terms of hard-tack would necessarily
be zero! For, by hypothesis, the giving up of one pound
of hard-tack out of present consumption can only result
in an equal increase in future consumption. One pound
next year can be obtained at the cost of exactly one pound
this year. In other words, the rate of return over cost is
zero. Since, as we have seen, this rate must equal the
rates of preference, or impatience, and a3so the rate of
interest, all these rates must be zero also.

C.Wl

DISCUSSION OF SECOND APPROXIMATION
This case is illustrated in Chart 21. One option is to
consume the hard-tack at an even rate OA through the
time OB. The total income will then be represented by
the area OACB. Another option is to spread it over OB’,
double the above-mentioned time, and consume it at the
rate of OA’, half the rate first mentioned,so that the
same total incomewill be representedby
the area
OA’C’B’. The choice of the second use rather than the

A

C

1-

D

0.

B

d
B‘

CHART 21
Zero Rate of Return, Total Income Fixed, Case 1.

first is at the cost of that part, of the earlier income repreturn
resented by the rectangle AD, and givesa
exactly equal in amount represented by the rectangle
DB’. If the hard-tack is not consumed at a uniform rate,
the alternative income streams will not be represented
by rectangles, but by the irregular and equal areas OADB
and OA’DB’, shown in Chart 22. The substitution of the
alternative OA’DB’ for OADB increases immediate income by ADA’ and decreases subsequent income by the
exactly equal amount BDB’.
The ConcIusion, that the rate of interest, under such

C 187 3

THE TREORY OF INTEREST
extreme conditions supposed in the hard-tack case, must
be zero, is at first startling,but it is easy to convince ourselves of its correctness. It would be impossible for m y
would-be lender to obtaininterest above zeroon his
loan for the only way in which a bomower could repay
a loan would be to pay it out of his original stock of hardtack. For assuming he had the impulse to borrow 100

Zero Rste of Return, Total Income Fixed, Case 2.

pounds to consume today and pay back 105 pounds at the
end of a year, he would instantly Ferceive that he could
better consume the 100 pounds of his own hard-tack,
thereby sacrificing next yearnot 105, but only 100 pounds
out of his own stock. It is equally impossible that there
should be a negative rate of interest. No one would lend
100 pounds of hard-tack today for 95 receivabIe a year
later, when he had the option of simply storing away
his 100 pounds today and taking it out, undiminished, a
year later. Hence; exchanges of present for future hctrd-

c 188 1

DISCUSSION OF SECOND APPROXIMATION
tack could not exist, except a t par. There could be no
premium or discount in such exchange.
Nor (to turn to thesubjective side) could there be any
rate of preference for present over future hard-tack. The
sailors would so adjust the time shape of their respective
income streams that any possible rate of preference for
a present over a future allowance of hard-t,ack would disappear, and a pound of this year’s hard-tack and a pound
of next year’s hard-tack wouldbe equally balanced in
present estimation. For, should a man prefer one rather
than the other, he would transfer some of it from the unpreferred time to the preferred time, andthis process
would be continued, pound by,pound, until his want for
a pound of immediate hard-tackandhiswant
for a
pound of future hard-tack were brought into equilibrium.
Thus, if through insufficient self-control, he prefers, however foolishly, to use up much of his store in the present
and so. to cut down his reserve for the future to a minimum, the very scantiness of the provision for the future
will enhance his appreciation of its claims, and the very
abundance of his provision for the present will diminish
the urgency of his desire to indulge so freely in the
present.
Provided each individual is free to apportion his share
of the total stock of hard-tack between present use and
future use as he pleases, and provided there is some hardtack available for both uses, the present desire for a
pound of each will necessarily be the Same.
(Failure of such equilibrium of want could only occur
when, as in starvation, the want for
the present use WM SO
intense as to outweigh the want for even the very last
pound for future use, in which case there would be none
whatever reserved for the future.)

r 189 I

THE THEORY OF INTEREST

All persons, however Werent in nature, would alike
have a zero rate of impatience. They would differ simply
in the way they distributed their income over present and
future. The spendthrift and the miser would still spend
and save respectively but both would valueaunit of
hard-tack today as the exact equivalent of one due a year
hence. It is evident t,hat some of the sailors, with a
naturally keen appreciation of the future, would plan to
consume their stores sparingly. Others would prefer generous rations, even with the full knowledge that st.arvation would thereby be brought nearer, but none of them
would consume all of his stock immediately. They would,
generally speaking, prefer to save out of suchreckless
waste at least something to satisfy the more urgent needs
of the future.
I n other words, a certain amount of saving (if such
an operation can be called saving) would take place,
withoutanyinterest
a t all. This conclusioncoincides
with conclusionsexpressed by Professor Carver in hie
Distribution of Wealth.8 It shows also that the preference for present over future goods of like kind and number is not, as some writers assume, a necessary attribute
of humannature, butthat it depends always on the
relative provisioning of the present and future,
The foregoing imaginary hard-tack case is of great help,
therefore, in emphasizing the essential r6le of the rate of
return over cost. This simple example, of itself, demonstrates that no theory of interest is complete which
ignores the rate of return over cost. In the example we
have both elements, investmentopportunityand
impatience, although both are a t the vanishing point, that
a p. 232. See also carver, T.M. The P&# oj Abstinence in the Theory
oj Interest, Quarterly Journal of Economics, Oct., 1893, pp. 4061.

E1901

DISCUSSION

OF SECOND APPROXIMATION

is, the rateof return and the rate of impatience are both
zero, the former, rate of return, being fixed at zero by the
technical conditions of the particular environment on the
desert island, and the impatiencerate
being forced
thereby to be zero also. In this case opportunity (or the
lack of it.) rules impatience.
It would be possible, of coume, to make this illustration
somewhat more realist’icby adding to our supposed supplies of hard-tack supplies of other foods, as well as of
clothing and sundry other real income. But the value of
the illust,ration is not in any realism which can be made
out of it. Rather does the fact that conditions in real life
do not permit such freedom of shifting real income in
time (because of change in quantity or quality) reveal
some of the reasons why the rate of interest is not zero.
$5. The Imaginary “Figs” Emmple
Not only may the rate of interest conceivably be zero;
it may conceivably be negative. Suppose our sailors were
left not with a stock of hard-tack, but with a stock of figs
which, like t,he hard-tack, can be used a.t any time as desired, but which, unlike the hard-tack, will deteriorate.
The deterioration will be, let us say, at a fixed and forek_nown rate of 50 per cent per annum. In this case (assuming that there is no other option available, such m
preserving the figs) the rate of interest in terms of figs
would be necessarily minus 50 per cent per annum, rts
may be shown by thesame reasoning that established the
zero rate in the hard-tack case.
More generally, this would be true if there were a
world in which the only provisioning of the future consisted in carrying over initial stocks of perishable food,
clothing, and so forth and if every unit so carried over
191 3

c

THE THEORY OF INTEREST
into the futurewere predestined to melt way eachyear by
50 per cent.

One reason why we do not encounter such cases, with
negative rates of return over cost, negative rates of interest, and negative rates of time preference is that we have
other income available for the future besides what can
be cmied over from present stocks. Future figs will come
into being from fig trees and even existing stocks of figs
and other perishables may be carried over for future use
by canning, cold storage, preservation and similar processes. Yet we do, even in our real world,occasionally
have cases such as of spoiling strawberries, where, the
rate of hterest reckoned in terms of the strawberries
is occasionally negative.
Wesee, then, that there is no absolutely necessary
reason inherent in the nature of man or things why the
rat.e of interest in terms of any commodity standard
should be positive rather than negative. The fact that
weseldom see an example of zero or negative interest
is because of the accident that we happen to live in an
environment so entirely different from that of the shipwrecked sailors.

96. The Irnaginarzl “Shep” Exurnple
The next example is more like that in our real world.
I n the real world our options are such that if present
income is sacriiiced for the sake of future income, the
amount of future income secured thereby is greater than
the present income sacrificed. That is, the income which
we can extract from our environment is not, in the
aggregate, a fixed quantum like a storehouse of hardtack; stillless isit like a storehouse of dwindling contents.
On the contrary, Nature is, to a great extent, reproduc-

c 192 3

DISCUSSION OF SECOND APPROXIMATION
tive. Growing crops and animals often make it possible
to endow the future more richly than the present. Man
can obtain from the forest or the farm more by waiting
than by premature cutting of trees or by exhausting the
soil. In other words, Nature's productivity has a strong
tendency to keep up the rate of interest. Nature offers
man many opportunities for future abundance at trifling
present cost. So also human technique and invention tend
to produce big returns over cost.
It is difEcult to imagine a precise and simple case in
which the rate of return over cost is fixed as in the case
of the hard-tack or the figs but, instead of being zero
or negative, is positive, say 10 per cent, neither more
nor less. The ,best example is the ingenious one worked
out by Professor Harry G.Brown in which fruit trees
are planted at the cost of 100 units of fruit and automatically produce 110 units of fruit a year laterand
then die.' A simpler imaginary example, if we can forget certain obvious practical limitations, is that of the
proverbial flock of sheep, which multiply in geometric
progressionaffording alternately 100 units of mutton
and wool today or 110 next year and ten per cent mare
each succeeding year. These examples symbolize a state
of things in which it is always possible a t the cost of
100 units out of this year's income to secure a return of
110 units next year, making a return over cost of 10 per
cent. In such examples, just
in the hrd-tack case
with ita zero per cent, or the fig case with its minus 50
per cent, the investment opportunity principles prescribe
or dictate therate of interestand therate of time
preference, These rates will in the present instance of the
sheep all be 10 per cent.
'Brown, Economic Science and the C m m Wfd@e, pp. 137-147.

[ 193 3

THE THEORY OF INTEREST
We see then that, given the appropriate environment,
the investment opportunity principle may dominate interest and force it to be zero, or minus 50 per cent, or
plus 10 per cent, or any other figure. Under such conditions, the rate of impatience and the rate of interest
will follow suit.
In actual life, however, any shoving ofread income
forward or backward in time can never be done without
causing a variation in the rate of ret.urn over cost. The
result is that therate of impatience influences the rate of
returnquite as truly &s therate of return influences
impatience.

87. Opportunities m to Repairs, Renewals, Betterments
In the foregoing examples the options consisted of
different employments of a particular instrument or set
of instruments of capital which were assumed to retain
their physical identities throughout the period of those
employments. But now let us regard an instrument, or
group of instruments, of capital as retaining only a sort
of fictitious identity,through renewals or repairs, just
as the proverbial jack-knife is said to be the same knife
after its blade and then its handle have been replaced.
This brings us to another large andimportant class
of options; namely, the options of effecting, or not
effecting, renewals and repairs, and the options of effecting them in any one of many different degrees. If the
repairs are just sufficient for the up-keep they may be
called renewals; if more than sufficient, or if involving
improvement in quality, they may be called betterments.
But it will be convenient to include in thought all alterations as to the form, position, or condition of an instrument or group of instruments affecting ita stream of ser-

c 194 1

DISCUSSION OF SECOND APPROXIMATION
vices. This will cover the whole subject of the production
of reproducible goods.
This class of optional emplo.yments, when the employment involves sales from a stock, merges imperceptibly
into the special case which we originally called the method
of modifying an income s t r e w b y buying orselling.
Thus, consider a merchant who buys and sells rugs. His
stock of rugs is conveniently regarded as retaining its
identity, although the particular rugs in
it are continually
changing. This stock yields its owner a net income equal
to the difference between the gross income, consisting of
the proceeds of sales, and the outgo, consisting chiefly
of the cost of purchases, but including also cost of warehousing, insurance, wages of salesmen, and so on.
If the merchant buys and sells equal amounts of rugs
and at a uniform rate, his stock of rugs will remain constant and its net income to be credited to that stock will
theoretically, that is, under our present assumption of a
riskless world, be equal to the interest upon its value.
It will be standard i n c ~ m e This
. ~ income to be credited
to his stock in trade is, of course, to be distinguished from
that, to becredited to his own efforts-his wages of superintending(neither need be called profits in a riskless
world).
But the owner has many other options &
an that of
thusmaintaining a constant stock of goods. He may
choose to enlarge his business aa fast as he makes money
from it, in which case his net realized income will be zero
for a time, because all return is “plowed back” into the
business. His stock will increase and eventually his income will be larger. In this option, t.herefore, his income
stream is not contmt, but ascends from zero to some
‘See The Notwe of C@d and I-,

C 195 I

chapter

m,No. 4.

THE THEORY OF INTEREST
figure above the standard income which constituted the
first option.
A third option is gradually to go out of business by
buying less rugs than are sold, or none at all. In this case
the realized income at first is very large, as it is relieved
of the burden of purchases; but it declines gradually to
zero.
Intermediate among these three options there are, of
course, endless other options. The merchant thus has a
very flexible income stream.
If the expenses and receipts for each rug bought and
sold are the same, whichever option is chosen, and if the
time of turnover is also the same, it will follow that all
of the options possess the same present value and differ
only in desirability. We should then be dealing withwhat
we have calledmodifications of the income stream
through buying and selling. The reason for placing optional employments of capital on a Merent footing from
buying and selling is that the optional employments do
not all possess the same present value. In actual fact,
the rug merchant, and merchants in general, would not
find that all the optional methods of proportioning sales
and purchases of merchandisepossessed equal present
values. For one thing, if the rug merchant attempted to
enlarge his business too fast he would findthat his time of
turnover would be lengthened, and if he reduced it too
fast he would find that his selling expenses per unit of
merchandise would be increased. There is, for each merchant, at any time, one particular line of business policy
which is the best, namely, that which will yield him the
income stream having the maximum present value. Since,
therefore, the various methods of renewing one’s capital
usually yield income streams differing in present value,

c 190 1

DISCUSSION OF SECOND APPROXIMATION

.

they may be properly classed as optional employments
of such capital.
The propriety of such a classiiicationbecomes still
more evident when, instead of mere renewals, we consider repairsandbetterments,
for it is clear that the
income from a farm has a very different present value
according as it is tilled or untilled, or tilled in different
degrees of intensity, that the income from a house so
neglected that a leak in the roof or a broken window pane
results in injuring the interior is less valuable than the
income it would yield if properly kept up, and that real
estate may be underimproved or overimproved as compared with that degree of improvement whichsecures
the best results.
In all cases the “best” results are secured when that
particular series of renewals, repairs, or betterments is
chosen which renders the present value of the prospective
income streamthe maximum. This, as we have seen, is
tant,amount to saying that the renewals, repairs, or betterments are carried up to the point at which the marginal rate of return over cost which they bring is equal to
the rate of interest. The owner of an automobile, for
instance, will replace a broken part and so prolong the
life of his automobile. The-first repair may cost him $10
and may save him $200. But such a twenty-fold return
cannot be expected from every repair, and beyond a few
such really necessary repairs, it soon becomes a question
to what extent it is worth while to keep an automobile in
repair, Repainting the body and regrinding the valves
are both costly, and though, in such instances, the senice
of the automobile is increased in quantity and improved
in quality, the return grows less and less as the owner
strives after increased efficiency.Under our present hypo-

c 197 I

THE THEORY OF INTEREST
thesis in which risk is disregarded, he will spend money
on his automobile for repairs and renewals up to that
point where the last increment of repairs will secure a
return which will just cover the cost with interest.
Beyond this he will not go.
In practice, of course, the choice between the various
possible repairs, renewals, or betterments will involve
some corresponding choice between possible employment
of labor, land, and every agent of production. But I have
tried here to isolate for study the services and disservices
of a physical instrument subject to repairs, renewals, or
betterments.
Another case of optional income streams is found in the
choice betweendifferent methods of production, especially
between different degrees of so-called capitalistic production. It is always open to the prospective house builder
to build of stone, wood, or brick, to the prospective railroad builder to use steel or iron rails, to the maker of
roads to use macadam, asphalt, wood,cobble, brick, or
cement, or to leave the earth unchanged except for a little
rolling and hardening. The choice in all cases will depend
theoretically on the principles which have been already
explained.
To take another example, the mere services of a house
which has a durability of 100 years will be equivalent to
the services of two houses,each of which h a a durability of 50 years, one built today and lasting 50 years,
and the other built at the expiration of that period and
laating 50 years more; yet the one house may well be bett,er than the two. The difference between the one and the
two will not be in the services but in the cost of construction. The cost of constructing the 100-year house occurs
in the present; that of the two successive 50-year houses
I: 198 1

DISCUSSION OF

SECOND APPROXIMATION

occurs half in the present and half at the end of 50 years.
In order that the more durable house may have any advantage as to cost, the excess of its cost over the cost
of the less durable one must be less than the present
value of the cost of replacing it 50 years later.
The choice between different instruments for effecting
the same purpose may, of course, depend on their relative
efficiency, that is, the rate of flowof income, or upon
their relative durability, that is, the time of the flow. It
is true, however, as John Rae has pointed out: that efficiency and durability usually go hand in hand. A house
which will endure longer than another is usually more
comfortable also; a tool which will cut betterwill usually
wear out more slowly; a machine which does the fastest
work will generally be the strongest and most durable.
The alternatives const,antly presented to most business
men are between policies which may be distinguished as
temporary and permanent. The temporary policy involves
the use of easily constructed instruments whichsoon
wear out, and the permanent policy involves the construction at great cost of instruments of great durability.
When one method of production requires a greater cost
at first and yields a greater return afterward, it may be
called, conformably to popular usage, the more capitalistic of the two. The word capitalistic refers to methods
of employing capit.al which tend toward an ascending income stream. Although the term is not a happy one, it
has a plausible justification in the fact that an ascending income stream means the accumulation of capital,
or saving, and still more in the fact that only a capitalist can afford to choose a method of production which
at first yields little or no income, or even costs some
‘Rae, The Sociological Theoty of Capitd, p. 47.

f 199 1

THE THEORY OF INTEREST
outgo. Capital involvescommandoverincome
without which no one could subsist, or at any rate subsist
with comfort. The capitalist, by using his capital, even
to the extent of using up some of his accumulations, can
supply himself with the immediate incomenecessary
while he is waiting for ret.urns on his new ventures. It is
as a possessor of income that he is enabled to subsist
while waiting. He is enabled to invest in an ascending, or
slowly returning, income stream only by first having at
command a quickly returning income stream. We may
say, therefore, that a capitalistic method is a qethod resulting in an ascending income stream, and it is so called
because it is open chiefly to those who have command
of other-often descending-income streams, such persons beingnecessarily capitalists, that is, possessors of
much rather than little capital.
$8. Opportunity to Change the Application of Labor

The best example of the choice between those uses of
capital instrumentsaffording immediate and those affording remote returns is found in the case of human capital,
commonly called labor. Man is the most versatile of all
forms of capital, and a m n g the wide range of choices aa
to the disposition of his energies is the choice between
using them for immediate or for remote returns. This
choice usually carries with it a choice between corresponding uses of other instruments than man, such as land or
machines. But the existence of optional employments of
labor, however inextricably bound up with optional employments of other instruments, deserves separate mention here both because of its importance and because it
u s d l y supplies the basis for the optiond employments
of other forms of capital,
. . .

CWl

DISCUSSION OF SECOND APPROXIMATION
It is almost exclusively through varying the employment of labor that the income stream ofsociety, rn a
whole, is capable of changing its time shape. The individual may modify the time shape of his particular income
stream through exchange, but in this casesome other
person must modify his income stream in the opposite
manner, and the two sorts of modifications,some plus
and others minus, offset each other in the total of the
world’s income. On the other hand, if an income is modified in time shape merely through a change in t.he exertions of laborers, there is no suchoffset, and the total
social income is actually modifled thereby.
The labor of a community is exerted in numerous ways,
some of which bring about enjoyable incomequickly,
others slowly. The labor of domestic servants is of the
former variety. The cook’s and waitress’ efforts result in
the enjoyment of food within a day. Within h o s t as
short a time, the chambermaid and the laundress promote t.he enjoyment of house, furniture, and clothing.
The baker, the grocer, the tailor are but one step behind
the cook andlaundress;their efforts mature inenjoyments within a few days or weeks. And so we may pass
back to labor increasingly more remote from enjoyable
income, until we reach the miner whose work comes to
fruition years later, or the laborer on the Panama Canal
or the vehicular tunnels, whose work was in the service
of coming generations.
The proportions in which these various kinds of labor
may be assorted vary grestly, and it is largely through
varying this assortment that the income stream of the
community changes its time shape. If there are at any
time relatively few persons employed ths cooks, bakers,
and tailors, and relatively many employed as builders,

c 201 3

THE THEORY OF INTEREST
miners, canal and tunnel diggers, there will tend to be
less immediately enjoyable income and correspondingly
moreenjoyableincome in later years. Thus, bywit.hdrawing labor from one employment and transferring it
to another, it is in the power of society to determine the
character of its income stream in time shape, and also in
size, composition, and uncertainty. This power is exerted
through t,he “enterpriser,” to use Professor Fetter’s term,
accordingto the enterpriser’s estimate of what return
willcomefromeach
particular employmenttakenin
connection with the cost involved and the ruling rate of
interest.
$9. Fluctmtwns in Interest Rates Self-Corrective

Since the choice,foranindividual,amongdifferent
options, depends on the rate of intereat in the manner
describedin Chapter VI, it is clear that a low rate
favors the choice of the more ascending income streams,
but also that t,he choice of such income streams reacts to
raise the rate of interest. If, on the contrary, the rate is
high, the opposite of both these propositions holds true;
the high rate favors the choice of the less ascending ‘income streams, but that choice reacts to lower the rate of
interest.
Thus, if we apply these principles to repairs, renewals,
and betterments, it is evident that the lower the rate of
interest, the better can the owner of an automobile afford
to keep it in repair, and the better can the owner of a
railroad keep up its efficiency, and the same applies to
all other instruments. But it is equallyclear that the
very attempt to improve the efficiency of instruments
tends, in turn, to increase the rate of interest, for every
repair means a reduction in present income for the sake

12021

DISCUSSION OF SECONDAPPROXIMATION
of future-a shifting forward in time of the income stream
-and this will cause a rise in the rate of interest. Thus,
it follows that any fall in the rate of interest will tend to
bring its own correction.
Again, it is evident that a choice of the more durable
instruments, as compared with those less durable, will be
favored by a low rate of interest, and a choice of shortlived instruments will be favored by a high rate of interest. If the rate of interest should fall, there would be a
greater tendency to build stone houses &s compared with
wooden ones. The present value of the prospective services and disservices of stone houses as conpared with
wooden houses wouldbeincreased, for although stone
houses are more expensive at thestart, they endure
longer, and their extra, future uses, which constitute their
advantage, will have a higher present value if the rate
of interest is low than if it is high. We find, therefore,
as John Rae has so well pointed out, that where the
rate of interest is low, instruments are substantial and
durable, and where the rate of interest is high they are
unsubstantial and perishable.
We see, then, that the existence of numerous options
has a regulative effect. Beyond the margin of choice there
always lie untouched options ready to be exploited the
instant the rateof interest falls. Among these, as Cassel
has pointed out, are waterworks of various kinds. Not
only works of stupendous size but hundreds of less conspicuous improvements are subjects of possible investment as soon as the rate of interest falls low enough to
make the return upon cost equal to the rate of interest.
The sarpe is true of the improving, dredging, and deepening of harbors and rivers, the use of dikes and jetties,
The Nature and Necessity of Interest, p. 122.

I: 203 1

THETHEORY OF INTEREST
the construction of irrigation works for arid lands, and
Boulder Dam projects.
There is still room for much improvement in our railwaysystemsbyma,kingthemmoreefficient
and more
durable, bymaking the roads straighter, the roadbeds
more secure, the rolling stock heavier, the bridges larger
and stronger, by further electrifications, and similar improvements. In a new country where the rateof interest is
high, the cheapest and most primitive form of railway is
first constructed. Very often it is a narrow-gaugeroad
with many curves,costing lit,tle to construct, though
much to operate. Later, when the rate of interest falls,
or the tr&c so increases that the rate of return on sacrifice is greater, the broad-gauge comes int,o use and the
curves are eliminated. This is the kind of change which
has been proceeding in this country with great rapidity
during recent years. There is a transition from relatively
small first cost and large running expenses to precisely
the opposite type of plant, in which the cost is almost all
initial and the expense of operation relatively insignificast.
$10. Wide OpportunitiesStabilizeInterest

The existence of a wide variety of available income
streams, then, acts as a sort of governor or balance wheel
which tends to check any excessive changes in the rate of
interest. Interest cannot fall or rise unduly;any such
fluctuation correctsitself through the choice of appropriate income streams.
We see here a reason why interest does not suffer very
violentfluctuations. It is not only truethat natural
processes are regularenough to prevent sudden and
great changes in the income stream; it is also true that

c 204 I

DISCUSSION OF SECOND APPROXIMATION
man constantly aims to prevent such changes, Man is not
the slave of Nature; to some extent he is her mwter. He
has many ways to turn. He possesses, within limits, the
power to flex his income stream to suit himself. For SOciet'y as a whole, the flexibility is due to the adaptability
and versatility of capital-especially human capital commonly called labor; for the individual, the flexibility is
greater still, since he possesses a two-fold freedom. He is
not only freeto choose from among innumerable different
employments of capital, but he is free to choosefrom
among different ways of exchanging with other individuals. This power to exchange is the power to trade incomes; for under whatever form an exchange takes place,
at bottom what is exchanged is income and income only.

CHAPTER I X
THIRD APPROXIMATION TO THE THEORY OF
INTEREST

Assuming Income Uncertain
$1.More than One Rate of Interest

THEgreat shortcoming of the first and second approximations, from the standpoint of real life, is the complete
ruling out of uncertainty. This exclusion of the risk element was made in order to make the exposition simpler
and to focus the reader's attention on the factors most
releva,nt to thetheory of interest. But in real life the most
conspicuous characteristic of the future is in its uncertainty. Consequently, the introduction of the element of
chanoe, or risk, will at once endow our hypothetical picture with the aspect of reality. The foundation for our
study of risk in relation to interesthas already been
laid in Chapter IV where the relation of risk to time
preference was noted.
One consequence of changing our assumption as to the
certainty of future events is to compel the abandonment
of the idea of a single rate of interest. Instead of a single
rate of interest, representing the rateof exchange between
this year and next year, wenow find a great variety of
so-called interest rates. These rates vary because of 'risk,
nature of security, services in addition to the loan itself,
lack of free competition among lendersor borrowers,
length of timethe loan has to run, and other causes
c 206 1

THIRD APPROXIMATION
which most economists term economic friction. The very
definition of loan interest as one implying no ,risk must
now be modified so aa to imply some risk that the loan
may not be repaid in full according to bhe contrmt.
Practically all of themare varieties of risk. Even in
loans which theoretically are assumed to be riskless, there
is always some risk. Modern corporate finance makes no
pretence that risk is completely absent, but merely concerns itself with providing a more or less safe margin of
protection varying with each specific case.
Furthermore, for our present purposes, contract or
explicit interest is too narrow a concept. We now include
not only the implicit interest realized,by the investor who
buys a bond, but the implicit interest realized by the investor who buys preferred stock. We mayeveninclude
the rates realized on common stock, real estate, or any-'
t,hingelse. Thus extended, the concept of interest becomes somewhat vague. And yet, if we exclude exceptional
cases, there tend to emerge, at any time, several fairly
definite market rates of interest according to the character of the security.
We find quoted rates on call loans, four months prime
commercial paper, prime bankers' acceptances, first mortgages, second mortgages, 85 well as rates given by savings
banks, rates allowed on active checking accounts, pawn
shop rates,MorrisPlan
bank rates, rates realized on
government bonds, railroad bonds, on other bonds,
whether mortgage, debenture, or incomebonds (all of
which bond ratesvary according to the character and
credit of the issuer m well m in accordance with 0 t h
circumstances), rates reabed on preferred stock, and
somet.imes even the rates realizedoncommon
Stocks.
Wherever there is a suEciently definite rate per cent Per

[a71

THE THEORY OF INTEREST
annum to be quoted aa an expression of the current market, whether the quotation be in print or a verbal quotation in a broker’s or banker’s office, it seems proper to
call it in a broad sense a rate of interest. Even when
confined to such market rates, and excluding exceptional
or individual rates, the rate of interest ceases to be the
ideal, imaginary, single-valued magnitudehitherto assumed and takes on the myriad forms which we find in
actual business transactions.
As indicated, this profuse variety is brought about
chiefly by the introduction of risks of various sorts. The
rate on call money is affected by t,he chance of the loan
being “cded” by the lender, or t.he sudden reduction of
the total of such loam outstanding and the raising of the
rate for those remaining. The rate on a loan-shark’s loan
is high because of the risk of non-payment by t’he borrower; the rate on a debenture and the rate on a second
preferred stock of a moribund corporation are affected by
the risk of inadequate corporate assets in event of liquidation; the rateon a government bond of a nation a t war is
affected by the chance of that nation’s defeat; the rate of
dividends on common stock is afiected by the risks of the
business; and so on in an infkite number of different cases.
82. Relations Between the Various Rates

No very satisfactory theoretical treatment of the
general relations between interest and risk has yet been
worked out. But for practical purposes, a good uswe is to
limit the term “interest” to fairly safe loans and staple
or standard market quotations and to designate by some
other term, such as dividends or profits, the other less
certain and less standaxdized rates. Another usage is to
reckon as net profits or net losses the difference between

c=1

THIRDAPPROXIMATION
these less standardized rates and a normal rate of interest
so far M this can be expressed in figures. Thus a man who
has invested $100,000in common stock and is getting an
income of $15,000 may think of $5,000 of this, or 5 per
cent, as a fair interest on his investment and the remaining $10,000, or 10 per cent, as net profit. But we do not
need here to enter into such discussions, especially in so
far BS they are only verbal. All that is here needed is to
show briefly how risk modilies
the theoretically perfect
determination of the interest rate thus far made.
The rate in every lorn contract is adjusted according
to the degree of security given. Thus, security or guarantee may be furnished by a simple endorsement of reputable persons, in which case the degree of security will
be the greater the larger the number of endorsers and
the higher the credit which they possess, or it may be
by the deposit of collateral securities. Thusthevery
name security has come to mean the properties themselves rather than their safety.
If we pass from explicit interest, or the rate of interest
involved in a loan contract, to implicit interest, or the
rate involved in purchases and sales of property in general, we see again that the greater the risk, the higher the
basis on which a security will sell. A gilt-edge security
may sell on a 3 per cent basis, when a less known or less
salable security may sell only on a 6, or even on a 9 per
cent basis?
The period of time 8 loan or bond runs is aLS0 an
important factor M regards risk? There is a see-saw be'For a more complete treatment of the relation of riak to the interest
yield of securities, aee The Nature of Capital and Income, Chapter XVI.
'Even in
and second approximations the rate of interest for
different perioda would not ne&ly
be the asme.

c2091

THE THEORY OF INTEREST
tween the rates on short term and long term loans. That

is, if the short term rate is greatly above the long term,
it is likely to fall, or if greatly below, to rise. The long
term rates thus set a rough norm forthe short term rates,
which are much more variable. When the future is regarded as safer than usual, loan contracts tend to be
longer in time than otherwise. In a stable country like
the United States, railway and governmentsecurities
are thus often drawn for half a century or more. There is
also a variability according to the degree of liquidity. A
call loan which may be recalled on
a few hours’ notice
has a very differentrelat,ionto risk than does a mortgage,
for instance.The call rate is usuallylower t,han time rates
because money on call is a little like money on deposit,
or ready money.It is ready, or nearly ready, foruse whenThis readiness or convenience
everoccasiondemands.
takes the place of some of the interest. On the other hand,
a sudden shortage of funds in the call loan market may
send the call rates far above time rates and keep them
there until the slow working forces release “time-money”
and transfer it to the call loan market. Thus the call loan
rates are very volatile and mobile in both directions.
The element of risk will affect also the value and basis
of the collateral securities.Their availability for collateral
will increase their salability and enhance their price. On
the other hand, when, as in times of crisis, the collateral
hasto be sold, it often happens that forpurposes of
liquidation it is sold at a sacriilce.

$3. timitations on Loans
The necessity of having to offer collateral will affect
not only the ratewhich man has to pay, but the amount
he can borrow. It will limit therefore the extent to which
c 210 I

THIRD APPROXIMATION
he can modify his income stream by this means. Consequently it will not be possible, as assumed in the first
two approximations, for a man to modify his income
stream at will; its possible modification willbe limited by
the fear of the borrower that hemay not be able to repay
and the greater fear of the lender that he may not be repaid-because the borrower’s credit may not prove good.
In consequence of thislimitation upon his borrowing
power, the borrower may not succeed in modifying his
income stream sufficiently to bring his rate of preference
for present over future income down to agreement with
the rate or rates of int.erest ruling in the market; and
for like reasons he may not succeed in bringing the rate
of return over cost into conformity with any rate of
interest.
One feature of these h i t a t i o n s on borrowing mayhere
be noted. The ability and willingness to borrow depend
not only on the amount of capital which the would-be
borrower possesses, but also on the form in which that
capital happens to exist. Some securities are readily accepted as collateral, and accepted as collateral at a high
percentage of their marketvalue, whereas others will pass
with daculty and only at a low percentage of that value.
The drift, especially during the last generation, toward
the corporate form of business has had a striking effectin
increasing the power and readiness to borrow. Whereas
formerly many businesses wereconducted as partnerships
and on a s m d scale, numerous stocks and bonds have
now been substituted for the old rights of partnership
and other less negotiable forms of security. similarly the
small local companies, the stock of which was held almost
exclusively by one f d l y or group of friends, have been
merged into h g e nationally known companies,the
c 211 1

THE THEORY O F INTEREST
ties of which are widely marketable. This increase in
size of business units, although it tends to decrease their
number, has resulted in a rapid growth of the number of
securities listed on the stock exchanges. The possessors
of these Securities have far wider opportunities to make
use of collateral, and the tendency to borrow haa received
a decided impulse.
Where, on the other hand, the security needed is not
available in the convenient form of engraved certificates,
there isoften considerable dBculty in negotiating a loan.
A poor man may see what he believes to be an investment opportunity to make millions by exploiting an invention of his own, and he may be right, This option
would have a much higher present value than the one
he actually chooses, if only he could borrow the money
needed to exploit it. But, being poor and hence without
adequate collateral or other guarantees, hecannotget
the loan. His choice of income etream, therefore, although the maximum open to him, is quite. different from
what it would be if he had that collateral or guarantee.
If he goes into the enterprise a t all he must choose a
stopping point f a r short of what hewould choose were he
a large capitalist. This means that his marginal rate of
return over cost will be hlgher than the market rate of
interest,just as hisrate of impatience will be higher
than the market rate of interest. The last $100 he ventures to put in may promise a yield of 25 per cent as
compared with a rate of interest of 5 per cent. Yet he
does not go further into debt because he cannot. Supposing a definite limit of possible debt, all he can do
toward further investing mustbeout of his own income, obtained by abstinence. But this possibility is also
limited. He cannot cut his income down to gero, or he

c 212 1

THIRD APPROXIMATION
would starve. He can however cut it “to the quick”,
stopping at the point where his impatience has risen to
meet the rate of return over cost which in turn will tend
to fall with each additional dollar invested.
The story is told of the inventorof rubber making a la&
desperate-and,fortunately, successful-sacrifice in his
experiments in which he resorted to burning up his furniture because he could not get funds with which to buy
fuel.
Many such cases exist-cases of limitation on loamwhich prevent a person’s degree of impatience and his
rate of return over cost from reaching the level of the
rate of interest. But there is anot.her part of the picture.
The poor man who cannot borrow enough to exploit his
invention can often find substitutes for loans and lenders.
He may associate himself with others in a joint stock
company and get the required capital partly from loans,
by selling bonds secured by mortgage, partly by selling
debentures on a higher interest basis, partly by selling
preferred stock on a still higher basis, and partly by selling common stock. That is, the risks are recognized and
pooled. Oneresult may be to
bring both his estimated rate
of return over cost and hisrate of impatience more nearly
into harmony with these various rates of interest when
due account,has been taken of the various risks involved.
$4. Risk and Small Loans

Where the borrowing takes place in pawn shops, the
rate of interest is usually very high, not so much because
of the inadequacy of the security aa because of its inconvenient form. The pawnbroker will need to charge a high
rate of interest, if it is to be called interest, partlybecause
he needs storage room for the security he accepts, p d y
213 1

TIIE THEORY OF INTEREST
because he needs special clerks and experts to appraise
the articles deposited, and partly because, in many cases,
when not redeemed, hehas to make an effort to find markets in which to sell them.He is, moreover, able to secure
these high rates partly becausepawnbroking is inbad
odor, so that those who go into the business find a relative monopoly, and partly because of the fact that the
customers usually have,either from poverty or from personal peculiarity, a relatively high preference for present
over future income. While the effect of their accommodrttion at the pawn shop is to reduce their impatience to
some extent, it will not reduce it to the general level in
the community, because these personsdo not have access
to the loan market in which the ordinary business man
deals. To them, undoubtedly, the fact that they cannot
borrow except at high, or usurious, rates is often a great
hardahip, but it has one beneficent effect,that is, the discouraging of the improvident from getting unwisely into
debt.
One of the very greatest needs has always been to sift
out the relatively safe and sane from the relatively risky
and reckless loans of the poor in order to encourage the
one and discourage the other. When this has been more
fully accomplished, the scandal of the loan shark will be
largely a thing of the past. A loan which, to the shortsighted or weak willed borrower, seems to be a blessing,
but which is really sure to prove a curs, ought certainly
to be discouraged no matter. what may be the rate of
interrest. The Russell Sage Foundation hae studied the
loan shark problem intensively and aa a result has
formulated a model small loans act which has been
adopted by the legislatures in a large number of our
States. This model act recognizes the greater risk and

c 214 3

THIRD APPROXIMATION
trouble involved in small loans forshort,periods,
by
permitting a maximum rate per month of 3% per cent.
Only in t,he present generation has the age-long curse
of the loan shark been met by constructive measures on
a large scale. These are based on the simple principle that
a man’s friendsand neighbors possess the necewary
knowledgewhereby to distinguish between a safe and
unsafe extension of credit to him. The Morris Plan banks
are founded on that principle. More effective are the
Credit Unions founded by Edward Filene and others in
America somewhat. on the models of the Raseisen and
other plans in Europe. Labor banks are rendering a similar service. These are enabling the poor to make effective
use of personal character as a substitute for collateral security and are t,hereby greatly reducing the rate of interest on the loans of the poor. In 1928 one large bank in
Wall Street instituted a similar system for loans without
collateral to salaried employees. These devices and others
are doing much to solve the problem of accommodating
the reliable man of small means with loans at rates comparable with those ruling in the markets for the well-

to-do.
$5. Salability as a Safeguard

When a security, because it is well known, or for any
other reason, has a high degree of salability, that is, c8.n
be sold on short notice without risk of great sacrifice, ita
price will be higher than less favored securities, and the
rate it yields will therefore be low. Salability is a,safeguard against contingencies which may make quick selling advisable. In other words, in a world of chance and
sudden changes, quick salability, or liguidity, is a great
advantage. For this reaon, the rate of intereat on in-

c 215 1

THE THEORY OF INTEREST
dividud mortgages will be higher than the rate of interest on more marketable securities. It is, in general, advantageous to have stock listed on the stock exchange, for,
being thus widelyknown,should the necessity to sell
arise, sucha stock will find a more ready market.
The most salable of all properties is, of course, money;
and as Karl Menger pointed out, it is precisely this salability which makes it money. The convenience of surely
being able, without any previous preparation, to dispose
of it for any exchange, in other words, its liquidity, is itself a sufficient return upon the capital which a man seems
to keep idle in money form.This liquidity of our cash balance takes the place of any rate of interest in the ordinary
sense of the word. A man whokeeps an averagecash
balance of $100, rather than put his money in a savings
bank to yield him $5 a year, does so because of its liquidity. Its readiness for use at a moment’s notice is, to him,
worth at least $5 a year. There is a certain experienced
buyer and seller of forests, in Michigan,whomakes a
practice of keeping a ready cash balance in banks of several million dollars in order better to be able to compete
with other forestpurchasersby having available spot
cash to offersome forestowner who,becomingforestpoor,wishes to sell. Forests are extremelynon-liquid
while cash balances are extremely liquid.
$6. General Income Risks
Even when there is no risk (humanly speaking) in the
loan ikelf, the rate realized on it is affected by risk in

other connections. The uncertainty of life itself casts a
shadowoneverybusiness
transaction into which time
enters. Uncertainty of human life increases the rate of
preference for present over future income for many peo-

c 216 1

THIRD APPROXIMATION
ple? although for those with loved dependents it may
decrease impatience. Consequently the rate of interest,
even on the safest loans, will, in general, be r&ed by the
existence of suchlife risks. The sailor or soldier who looks
forward to a short or precarious existencewillbeless
likely to make permanent investments, or, if he should
make them, is less likely to pay a high price for them,
Only a low price, that is, a high rate of interest, will induce him to invest for long ahead.
When the risk relates, however, not to the individual’s
duration of life, but tohis income stream, the effectupon
the rate of interest wiI1 depend upon which portions of
the income stream are most subject to risk. If the immediately ensuing income is insecure,
whereas
the
remoter income is sure, t.he rate of preference for an
additional sure dollar immediately over an additional
swe dollar in the remoter period will, as was shown in
Chapter IV, tend to be high, and consequently the effect
of such a risk of immediate incomeupon the rate of
interest will be to raise it. A risky immediate income acts
on interest like a small immediate income.
But if, as is ordinarily the case, the risk applies more
especially to the remoter income than to the immediate,
the effect is the exact opposite, namely, to lower the rate
of interest on a safe loan. The risky remote income acts 89
the equivalent of a small remote income. This example
is, perhaps, the most usual case. If a man regards the
income for the next few years aa sure, but is in doubt as to
its continuance into the more remote future, he will be
more keenly alive to the needs of that future, a d will
consequently have a less keen preference for the present.
‘&e Carver, Th.e Diski6ution
W d h , P. 256, a d C-1,
Theow of sodal Econom~,PP 246-247.

c 217 1

A

THE THEORY OF INTEREST

He will then be willing, even at a very low rate of interest,
to invest, out of his present assured income, something
to eke out with certainty the uncertain income of the
future.The effect of risk in this case, therefore, is to
lower the rate of interest on safe loans, though at the
same time, aa already explained, it will raise the rate
of interest on unsafe loans. Consequently, in times of
great social unrest and danger, making the future risky,
we witness the anomalous combination of high rates
where inadequate security is given coexistent with low
rates on investments regarded aa perfectly safe. When
an investor cannot find many investments into which he
may put his money without risk of losing it, he will pay
a high price-i.e., accept a low rate of return-for the few
which are open to him. It has been noted in times of
revolution that some capitalists have preferred to forego
the chance of all interest andmerely to hoard their capital
in money form, even paying for storage charges, a payment which amounts to a negative rate of interest.
During the World War some investors in the warring
countries sought safekeeping for their funds in neutral
countries.
57. Securities Classified as to Risk
When risk thus operates to lower the rate of interest
on safe investments andto raise the rateon unsafe investments, there immediately arises a tendency to differentiate two classes of securities and two classes of investors
"precarious securities and adventurous investors on the
one hand, and safe securities and conservative investors
on the other. Some risk is inevitable in every business,
but is regarded by most people aa a burden; hence the
few who are &le and willing to wsume this burden tend

I:218 3

THIRDAPPROXIMATION
to become a separate class. When enterprises came to
organized in corporate form, this classification of investors was recognized by dividing the securities into stocks
and bonds, the stockholder being t.he person who assumes
the risk and, theoretically a t least, guaranteeing that the
bondholder shad be free of all risk. Which person shall
fall into the class of risk-takers and which not is determined by their relative coefficients of caution,' as well
as by the relative degree of risk which an enterprise would
involve for the various individuals concerned. The same
enterprise maybe perilous for one and comparatively safe
for another because, of superior knowledge on the part of
the latter, and the same degree of risk may repel one
individual more than another, owing to differences in
temperament or, most important of all, to differences in
amount of available capitaL6
This shiftingof risk from those on whom it bears heavily to those who can more easily mume it discloses
mother motive for borrowing and lending besides those
whichwerediscussedin
a previous chapter. Borrowing
or lending in corporate finance usually indicates not
simply a difference in time shape as between two income
streams, but also a difference of risk.The object of lending which was emphasized in earlier chapters, before the
risk element was introduced into the discussion, was to
alter the time shape of the income stream, the borrower
desiring to increase his present income and decrease his
future, and the lender desiring, on the contrary, to decrease his present income and add to his future. But the
ordinary stockholder and bondholder do not differin this
way so much as they do in respect to risk. They are both
'&e

The Nature of Capital and I m m r ~ chapter
,
xm,g6.

'Ibid., Appendix to Chapter XVI, p. 409.

c 219 1

THE THEORY OF INTEREST
investors, and the positions, in which they stand 85 to
the effect of their investment on t,he time shape of their
income, are really very similar. But the stockholder has a
risk attached to his income stream from which the bondholder seeks to be free. It is this difference in risk which
is the primary reason for the distinction between stockholders and bondholders. The bondholder gives up his
chance of a high income for the assurance, or imagined
assurance, of a steady income. The stockholder gives up
assurance for the chance of bigger gains.
The existence of this risk, tending aa we have seen to
raise the rate of interest on unsafe loans and lower that
on safe loans, has, as its effect, the lowering of the price
of stocks and the raising of the price of bonds from what
would have been their respective prices had the risk in
question been absent.
I n the last few years, however, this disparity has been
decreased from both ends. The public have come to believe that they have paid too dearly for the supposed
safety of bonds and that stocks have been too cheap.
Studies of various writers, especially Edgar Smith e and
Kenneth Van Strum have shown that in the long run
stocks yield more than bonds. Economists have pointed
out that the safety of bonds is largely illusory8 since
every bondholder runs the risk of a fall in the purchasing
power of money and this risk does not attach to the same
degree to common stock, while the risks that do attach
to them may be reduced, or insured against, by diversifi‘Smith, Edgar L. Common Stocks as Long Term Investments. New
York, The Macmillan Company, 19%.
‘Van Strum, Kenneth, Investing I n Purciursing P a w . Boston, Barrods, 1925.
‘See The Moneu IUusion. Also When Are Gilt-Edged Bonds Sajd
Magasbe of Wail Street, Apr. 25,1926.

c 2% 1

THIRD APPROXIMATION
cation. The principle of insurance of any kind is by
pooling those risks virtually to reduce them. This raises
the value of the aggregate capital subject in detail to
these risks.
It is in this way that investment trusts andinvestment
counsel tend to diminish the risk to the common stock
investor. This new movement has created a new demand
for suchstocks and raised their prices; at the same time it
has tended to decrease the demand for, and to lower the
price of, bonds.
Again, speculation in grain, for example bysetting
aside a certain class of persons to assume the risks of
trade, has the effect of reducing these risks by putting
them in the hands of those who have most knowledge,
for, as we have seen, risk varies inversely with knowledge.
In this way, the whole plane of business is put more
nearly on a uniform basis so f a r as the rate of interest is
concerned.
Risk is especially conspicuous in the financing of new
inventions or discoveries where past experience is a poor
guide. When new inventions are made, uncertainty is
introduced, speculation follows, andthen comes great
wealth or great ruin according to the success or failure
of the ventures. The history of gold and silver discoveries,
of the invention of rubber, of steel, and of electrical appliances is filled with tales of wrecked fortunes, by the
side of which stand the stories of the fortunes of those
few who drewthe lucky cards, and who are among today's
multi-millionaires.
The rates of interest are always based upon expectation, however little this hope may later be justified by
realization. Man makes his guess of the future and stakes
'See The

Natwe of Capitd a d Incoma, aapter

c 221 1

m.

THE THEORY OF INTEREST
his action upon it. In his guess he discounts everything
he can foresee or estimate, even future inventions and
their effects. In an estimate which I saw in print of the
value of a copper mine, allowance was made for future
inventions which might reasonably be expected. In the
same way, too, the buyer of machinery allows not simply
for its depreciat.ion through physical wear, but for its
obsolescence. New investments in steam railroads are today madewith due regard to the poasibdity that theroad
may, within a few years, be run by electricity, or that it
will be injured by competition of bus lines or helped by
terminal connections with them.
It may easily happen that, in a country consisting of
overly sanguine persons, or during a boom period when
business men are overhopeful, the rate of interest will be
out of line with what actual events, as later developed,
would justify. It seems likely that, in ordinary communities, realization justifies the average expectation. But in
an individual case this is not always true; otherwise there
would be no such thing as risk. Risk is synonymous with
uncertainty-lack of knowledge. Our present behavior
can only be affected by the expectedfuture,-not
the
future as it will turn out but the future as it appears to
-8 beforehand through the veil of the unknown.
$8. Eflect of RGk on the Biz' Principles

Wesee, then, thatthe element of risk introduces
disturbances into those determiniqg conditions which
were expressed in previous chapters as explaining the rate
of interest. To summarize these disturbances, we may now
apply the risk factor to each of the six conditions which
were originally stated a3. determining interest. We shd
find that ita effects are aa follows:

12221

I

THIRD APPROXIMATION

THE TWO PRINCIPLES AS TO INVESTMENT
OPPORTUNITY
A. Empirical Principle
The condition that each individual has a given range
of choice still holds true, but these choices are no longer
confined to absolutely certain optional income streams,
but now include options with risk. That is to say, each
individual finds open to his choice a given set of options
(and opportunities to shift options, that is, opportunities
to invest) which options differ in size, time shape, composition and risk.
B. Principle of Maximum Present Value
When risk was left out of account, it wm stated that
from among a number of different options the individual
would select that one which has the maximum present
valu-in
other words, that one which, compared with
its nearest neighbors, possesses a rate of return over cost
equal totherate of time preference, and therefore to
the rate of interest.
When the risk element is introduced, it may still be
said that the maximum present value is selected, but in
translatingfutureuncertain
income into present cash
d u e , use must nowbe made of the probability and
caution factors.
But when we try to express this principle of maximum
present value in its alternative form in terms of the marginal rate of return over cost, we must qualify thisexpression to: the marginal rate of umticipated return over cost.
Three consequencesfollow. First, thatthe rate of
return over cost which will actually be realized may turn
out to be widely different from that originally anticipated.
[2231

THE THEORY OF INTEREST
Second, there is in the market not simply one single anticipation; there are many, each with a different degree
of risk allowed for in it. Third, the need of security may
be such as to limit also the choice of options.
THE TWO PRINCIPLES AS TO IMPATIENCE

A. Empirical Principle
The rateof bime preference depends upon the character
of the income stream, but it must now take into account the fact that both the immediate and the future
(especially the future) portions of that stream are subject to risk. There are many rates of time preference, or
impatience, according to the risks involved. But they all
depend on the character of the expected and possible income stream of each individual-ita size, shape, composition and especially the degree of uncertainty attaching
to various parts of it as well aa the degree of uncertainty
of life of the recipient.

B. The Principle of Maximum Desirability
It is still true, of course, that the individual decides
on the option most wanted. But, in a world of uncertainty there are two features not present in a world of
certainty. One (which however doesnot affect the formulation of the principle) is that what is now desired may
prove disappointing. That is, though it seems,when
chosen, the most desirable course, it may not prove the
most desirable in the sense of deserving, in view of later
developments, to be desired.The othernew feature isthat
the most desired income stream is no longer necessarily
synonymous with that which harmonizes therate of
preference with the rate of interest.
c2241

THIRD APPROXIMATION
Rates of time preference in any one market tend
toward equality by the practice of borrowing and lending, and more generally, that of buying and selling, but
this equality is no longer, in all cmes, attdnable, because
of limitations on the freedom to modify the income
stream at will, limitations growing out of the existence of
the element of risk and consequent limitations on the
borrowing power.

THE TWO MARKETPRINCIPLES
A. Principle of Clearing the Market
In the fist two approximations, where the element of
risk wm considered absent, it waa shown that the aggregate modification of the income streams of all individuals for every period of time was zero. What wm borrowed equaled what was lent, or what was added by sale
was equal to what was subtracted by purchase. The same
principle still applies, for what one person pays, another
person must receive, The onlydifferenceis that, in a
world of chance, the actual payments may be quite different from those originally anticipated and agreed upon,
that is, w
l
l
ioften be defaulted, in whole or in part.

B. Principle of Repayment
In the former approximations, the total present value
of the prospective modifications of one's income stream
was zero, that is, the present value of the loans equaled
the present value of the borrowings, or the present value
of the additions and subtractions caused by buying and
selling balanced each other. In our present discussion, in
which future income is recognized as uncertain, this principle still holds true, but only in the sense that the present

CWI

THE THEORY OF INTEREST
market values balance at the moment when the future
loansor other modifications are plannedanddecided
upon. The fact of riskmeans that later there may be
a wide discrepancy betweenthe actual realization and the
original expectation. In liquidation there may be default
or bankruptcy. When the case is not one of a loan contract, but relates merely to the differenceinincome
st,reams of two kinds of property bought and sold, the
discrepancy between what was expected and what is actually realizedmaybe still wider.Only &wed in the
present is the estimated value of the future return still
the equivalent of the est,imated cost.
We thus see that, instead of the series of simple equalities which we found to hold true in the vacuum case, so
to speak, where riskwas absent, we have only a t d m y
toward equalities, interfered wit.hbyt,he limitations of
the loan market, and which, therefore,result in a series of
inequalities. Rates of interest, rates of preference, and
rates of return over costare only ideally,not really, equal.
in the accompanying
Weconcludebysummarizing
table the interest-determining conditions not simply for
the third approximation but for all three of our three successiveapproximations(distinguishedby
the numerals
1, 2, 3).
In this sulnmary tabulation the “Principles as to
Investment Opportunity” are formally inserted, under
the first approximation, in order to complete the correspondence with the other two approximations, but of
course they merely re-expressthe hypothesis under which
the firstapproximation was made. They are therefore
bracketed, since only the remaining four conditions axe
of real signiiicance for the first approximation.
The first and second approximations were, of come,

12261

#9. SUMMARY OF THETHREEAPPROXIMATIONS(Numbered

1.

TWO INVESTMENT OPPORTUNITYPRINCIPLES
A. EMPIRICAL
PRINCIPLE

[No range of choioe available]

2. &$I p e y n

3.

1,2,3)

9 ,B limjted rafge 0,’ chece

? I (certain)

opti2nal inc;me stre$ms, accof;ding t,r hyy

(uncertain)

le us.s h,$

la@ a2d o t k resources.

B. PRINCIPLE
OF MAXIMUMP R ~ E NWORTH
T
I. CEazh perpn must accept the one inc;me strzam available, to be modified only by loans]

a.
3.

&oo/es

n

I

tly

preynt wo$h B;S re‘ckyed biy m
t l ay$ e t

$f gre$est

!I

r9;e

sf

interest.

(unlessloanrestrictions

prevent).

This Implies (if the Options Vary by Small Gradations) That

1.
realiyd) marg?nal rat,“ 0,’ retfm o;erco$t
2. th,B ant(c(pat8d (and
s.
but not necessarily

p e y n ’ s ra;e %f ti%e preference d e p n d s o,n h> ce$&

1. E!yh

2.

3.

n

”

n

I,

0

1. Ea;h peTon modiies, ;
b l o ahp4,
2*
n
x
I
w
3.
0

1. hi6
2.
&

1.

f:
1.

C

F2r
n

m#te
”

”

a

a

I,

a

a

a

*e
/I

”

(chyen acd certain)
uncertain) anticipated

” (

”

w

/
I

n

It

rr

of interest.

t t n d s toward t h e particular rate of interestpertainingtotheparticular

,I

,t

I,

pertaining
the
toparticular
set

”

I,

,,

n

,,’

of risks
involved.

TWO MARKET PRINCIPLES
A. PRINCIPLE
OF CLE~RING
THE MARKET
some per$yns’ re$ incymes mFst eqtalthe subtr?;tions frzm ot$ers’.
R

0

aEd ne,?t b y t optipsns) must equal therate

This Implies That

N

I,

I

addi$ons, thronugh losns, in sopetiFeinteyals

,,

compying t;e
be;t

“

Ilf intEreet.

thrfugh loffns,

I,

I,

a;d

uncertain

ty

TWO IMPATIENCE PRINCIPLES
A. EMPIRICAL
PRIKCIPLE
prescribed inc;me
rtre;m,
af$yr bef;ng (a) prescribed for hj,m
optifnal
,,
,,
(a) ch:;en
by ,, C y PZr opporpiity
princpe
”
”
(a)
B. PRINCIPLE
OF MAXIMUM
DESIR~BILITY
inc7,me str$Fm, conve,Fing i;to t+ fo,? mzst wa5ted.

(presclibed)

inttrvaltkeadditiom,

x

F y anJ giv,en pecmn

2.
3 . a

I,

tiFe prefepnee becRmea equ,al $0 tpe
rft;e
n
”
tend8 toward the particular
”

a y gilen %e
a

N

,t

(foyd

n

,,

I,

,,

,!

I,

B. PRINCIPLE
OF REP.4YMENT
m%st b; equiy$ent, iff
I,

,,

I,

”

estimated

,,

n

r,

p r e y n tv a l y , t,p t$ subtrytions i? otlyrs.
”

,I

, ,,

I,

I,

I,

and th;n
€3;)

,,

Bet of risks involved.

(!Imodified by
))

I,

I/

,,

I1

l o p
I!

(B;Bp$r
u

I,

impa4fence

*,

THIRD APPROXIMATION
merely preparatory to the third, which alone corresponds
to the actual world of facts. Yet the other two approximations are of even greater importance than the third
from the point of view of theoretical analysis. They tell
us what would happen under their respective hypotheses.
Both these hypotheses are simpler than reality; hence
they lend themselves better to formal analysis and
mathematical expression.
Moreover, to know what would happenunderthese
hypothetical conditions enables us better to understand
what does happen under actual conditions, just as the
knowledge that a projectile wouldfollow a parabola if
it were in a vacuum enables thestudent of practical
gunnery better to understand the actual behavior of his
bullets or shells. In fact,no scient& law is a perfect
statement of what does happen, but only what would
happen if certain conditions existed which never do actually eXi8t.lo Science consists of the formulation of conditional truths, not of historical facts, though by successive approximations, the conditions assumed may be
mede nearly to coincide with reality."
The second approximation gives a clew cut theory
applicable to the clear cut hypotheses on which it is
based. Thethird
approximationcannot
avoid soma
degree of vagueness.
See the writer's Economics aa a Science, Proceedinga of the American
Association for Advancement of Science, Vol. LVI, 1907.
8ee Appendix to Chapter I X , No. 1.

PART 111. THETHEORY IN MATHEMATICS

CHAPTER X. FWT APPROXIMATION
IN GEOMETRIC
TERMS
CHAPTER XI. SECONDAPPROXIMATTON
IN GEOMETRIC
TERMS
CHAPTERXII. FIRSTAPPROXIMATIONIN TERMS OF
FORMULAS
CHAPTERXIII. SECOND
APPROXIMATION IN TERMS
OF
FORMULAS
CHAPTERXIV. THE THIRD
APPROXIMATION
UNADAPTED
TO MATHEMATICAL FOBMULATION

CHAPTER X
FIRST APPROXIMATION IN GEOMETRIC TERMS

0 1. Introduction
WE found in Chapter V that, if the degree of any given
individual’s impatience depended solely on his income
stream, and if that stream could not be modified through
the loan market or otherwise, his impatience could not
be modified either. In such a world of hermits, each person would have his own individual rate of time preference, the various individual rates ranging from several
thousand per cent per annum down to zero, or below. In
such a world, since there would be no loans, there would
be no market rate of interest.
But we also perceived that, &s soon as our hermits are
allowed to swap income streams, oneman exchanging
some of this year’sincome for some future income of
another, then these myriad rates of time preference or
impatience tend to come together toward a common rate,
and, on the assumption that no risk attends these transactions, a uniform market rate of interest would actudy
be reached. In such a perfect loan market the degree of
impatience of each person would becomeequal to that of
every other person and to the rate of interat.
g2.

The Map

of

This Year’s and NextYear% Income

Expressing the problem with- the aid of the graphic
method, the determination of the rate of interest may
c2311

THE THEORY OF INTEREST
bereduced to a simpleproblem of geometry, just as
the problem of price may be shown by supply and d e
mand curves.
To depict adequately the elements of the interest problem, however, a new kind of chart is required. Our first
t&k is to see the relation of this new kind of chart to
those hitherto used in this book. First, then, let us recur
to Charts 1, 2, and 3, in Chapter I, which picture a person’s income stream over a period of years, This sort of

CHART 23
Annual Income Represented by Linea Instead of Bara.

chart consists of a row of vertical bars representing the
real income, as measured by the cost of living in successive periodedays, months, or years, To prevent confusion, let us, for our present graphic purpose, shrink these
vertical bars into mere vertical lines, without breadth.
Then, each yeax’s income may be pictured as if it were all
concentrated at a point of time, say in the middle of the
month or year concerned.Since the rate of interest is
usually expressed in per umum t e r n , it will simplify tbe
discussion if these lines am drawn, aa in Chart 23, disregarding all time units other than years. To make our
c2321

IN GEOMETRIC TERMS
picture still moreconcrete, specific figuresmay be attached to specific years, the person’s income for 1930 being set at $lOOO,that for 1931at $1200, and 80 on.
We are now ready to pass to the new and radically
different method of representing the real income stream.
In the chart just described, horizontal distance measures
time,while vertical distance measures amount or size.
The reader is now asked to shake off these conceptions.
Moreover, throughout Chapters X and XI, he must be
on his guard against their unconscious return. In the new
charts there is no time scale; time is not measured at aIl;
both axes measure amount of income. The horizontal
axis represents the first year’s income, the vertical, the
secondyear’sincome. Thus the point PI in Chart 24,
through its latitude and longitude, stands in a sense for
bothyews’incomescombined. It represents what may
becaIIed a givenindividual’sincomecombination,income stream, incomeposition, or income situation for
the given pair of yem. On Chart 24 may be showna compIete map of dl possible bcome combinations, or income
positions, so far as two yews, or periods of time, are concerned, To represent the third year, so easily shown in
Chart 23 under the old method, we should need in this
new method 8 third dimension. The chart would then
c e m to be a chart and become a three dimensional
rnode1.l
If on the mapfor two years,we were to draw a straight
line from the origin toward the “northeast”, midway between the twoaxes, every point on it would have its
longitude and latitude equal, that is, would represent ditlThe reader who wishes, after f
i
n
& this chapter, to pursue the
geometric analogy into more dimensione thm the two here considered
may do 80 by reading the Appendix to thia Chapter.

c2331

THETHEORY OF INTEREST
ferent income situations in which the incomes of two
A poor man-poor inboth yearsyearswereequal.
would be situated near the origin, and a rich man far
from the origin. A man whohas less incomethis year than
he expects to get next year would be situated above this

CHART 24
Income Position this Year and Nest Year Represented by Point(P1).

midway line, his latitude (meaning next year's income)
being more than his longitude (meaning this year's). If
we move his position suBciently to the left, so as to reduce his longitude (this year's income), he will be like a
man stranded on a polarexpedition-with
rations run
short, though he might be assured by radio of plentiful

12341

IN GEOMETRIC TERMS
supplies next year. On the other hand,a man who is more
abundantly provided with incorn? this year than he expects to be next year would be situated below the midway
line, his longitude being greater than his latitude.
In this way, within the northeast quadrant (the only
one shown in thecharts) we can, by fixing thepoint
P a t all possible positions, represent all possible combinations of this year’s and next year’s income.
g3. The Market Line

Assuming that the individual’s incomes for all other
years remain unchanged, we shall now study the effects,
for this one man, of changing the income amounts of the
two years pictured. These changes are assumed to be
caused wholly by trading some of his income of one year
for some of anngther man’s income for the other year.
Except for such trading, his income situation is supposed
to be fixed. He has, let us suppose, a rigid allowance of
$1000 for this year and $1200 for next year with no opportunityto change these figures except by swapping
Borne of one year’s income for some of another’s.
Suppose, for instance, that at a rate of interest of 10
per cent the individual borrows $100 in 1930 in return
for $110 which he is to pay back in 1931. In Chart 23,
such changes wouldbe represented by lengthening the
1930 vertical line from $lo00 to $1100 and by shrinking the 1931 vertical line from $1200, not to $1100 but to
$1090. InChart 25 these changes are represented by
shifting the income position from PI, the originally fixed
income position, to M I , whose longitude is $100 more
and latitude $110 less.
If, aa shown in Chart 26, the individual borrows a
second $100,promising to repay $110, his income position
~2351

THETHEORY OF INTEREST
shifts again, this time from M,’ to M P , that is, from
this-year-1100-and-next-year-1090 to this-year-1200-andnext-year-980. Borrowing athird $100 would bringhim to
M,’”, (this-year-1300-and-next-year-870). Every additional borrowing of $100 adds $100 to this year’s income
Chart 26
and subtracts $110 fromnextyear’sincome.
as a “staircase” of which
pictures these successive changes

”
”
”
“
“
”

This Year’s hame

CHART 25
Effect of Borrowing Upon an Individual’s Income

Position.

each “tread” is $100 and each ‘%iser” is $110. The stairs
are steep. So long as there exists a rate of interest their
descent is necessarily always faster than 45 degrees-that
is, future income decreasesfaster than present income increases; the riser is more than 100 percent of the treadmore by the rate of interest.‘
‘The steps could be drawn just aa well on the under side of the line
aa shown by dotted lines on the chart. If the &pa were to COW,
not
of succemive $100 loans, but of successive $1 loaw the steps to P,,Y;,

C2361

IN GEOMETRIC TERMS
If the rate of interest were zero, each $100 borrowed
would require only $100 to be returned next year, The
riser would equal the tread; the Market line would make
an angle of 45" with the axis, and its slope would equal

unity, or, in other worde, 100 per cent. Thus in this new
method of charting, a given rate of interest is represented
by the algebraic dBerence between the slope of the given
Market line, and the 100 per cent slope of the 45" zero
interest line.
Ma",MF',

eto., would

be a hundred thee as numerow and corre-

spondingly emaller.

12371

THE THEORY OF INTEREST
Evidently the line P1M 1is a straight line. It may be
called theMarket line, Loan line, or Rate of Interest
line, and, if prolonged, will contain all the positions to
which thisparticular individual (who may becalled
Individual 1) can shift his income position by borrowing
or lending.
If, starting at PI,he shifts down this straight, staircase
(southeast) he is B borrower or a seller of next year’s
income, because he is adding to this year’s income and
subtracting from next year’s. If, instead, he shifts up
the staircase (northwest) he is a lender or buyer of next
year’sincome, subtracting from this year’sincome and
adding to next.

g4. The Willingness Line
So far we have used the new type of chart only to show
how the individual can move-change his income situation. The next question is: in which one of the two directions on the Market line will he actually move? The
answer depends on his degree of impatience compared
with the market rate of interest. We have seen how the
market rate of interest is represented graphically by the
slope, relatively to 45”, of the Market line in Chart 26.
We are now ready to make a similar graphic representation of the individual’s rate of time preference or impatience. This is expressed by a series of curved lines showing on what term, at any income position (such aa Pl),
the individual would be w i l l i n g to lend or borrow, say
$100. What one is willing to do and what he can do are
two quite different things. The Market line of Chart 26
shows what he can do, while the Willingness lines, now to
be described, will show what he would be willing to do.
Individual 1’s impatience is such that he would be

c2381

IN GEOMETRIC TERMS
willing, if necemry, as shown in Chart 27, to borrow his
first $100 at 30 per cent, considerably above the market
rate, 10 per cent. That is, he would be willing to sacrifice
$130 out of next year's income in order to add $100 to
this year's income. To get s second $100 this year, he

Varying Degrees of Impatience Represented by the Slope of the

W lline.

would not be willing to pay quite so much, but only, say,
$120. A third $100 would be worth to him only $110; a
fourth still less, and so on. These willingnew points make
a cwved staircase, the steps being from PI to Wl',from
W,'to W,", and 80 on, in which each tread is taken to be
$100, but the risers are decreasing as the borrower step

down southeasterly, being successively 130,1~,11U.The
~2391

THE THEORY OF INTEREST
Willingness line,PlW:v, is not a straight line like PlMI
in Chart 26, but a curved line. The steepneas of each
step, or ratio of risers to tread, orslope of the curve8
ahows the degree of impatience at that particular step.
The Willingness line through P extends, of course,
in both directions. It shows not only on what terms Individual 1 would be willing to borrow, but also on what
terms he wouldbewillingtolend.
At point P 1, he is
willing to lend the first $100 at 40 per cent, a second, at
50 per cent, and so on. Everyone theoretically is ready
either to borrow or to lend according to the terms. Individual 1 is here represented as ,barelywilling at Pl
either to borrow $100 at 30 per cent, or to lend $100 at 40
per cent. In short, he would be willing to substitute the
combination represented by any given point on his Willingness line for the combinationrepreaented by any
other point on the same line. All poipts on that line are,
Individual I . Each
by hypothesis,equallydesirable
segment of the Willingness line, by the divergence of its
slope from 100 per cent, shows the degree of impatience
at the particular income position there represented.
Consequently, PI W, might becalled an Impatience
line quite 88 well aa a Willingness line for Individual 2.
There would be another Willingness line, or W line, for
any other individual. The W lines thus differ from the
Market, or M,lines which are common to everybody in
the market.
$5. The Two Lines Compared
The M line of Chart 26 and the W line of Chart 27 are
brought together in Chart 28. &om P, we have a pair of
t o ,

'The latter name WBB &own chiefly because the initial "W,"for
willingness, is more convenient to use in the chart than the letter 'II,"
especially 88 "I" ia the initial sleo of intereet and h e .

CM1

IN GEOMETRIC TERMS
lines, one (MI) showing by its divergence from the 45"
slope the rate which Individual I can get, as a borrower,
and the other ( W,) showing by itaslope the rate at which
he is d1in.g to borrow. Evidently if he is willing to pay
30 per cent for a $100 loan when he can get it at 10 per

CHART 28
Intersection of Ml Line and

wx Line et Pi.

cent, he will borrow. Evidently also he will continue to
borrow as long &s hiswilliugness rate, i.e., his rate of
time preference or impatience, is greater than the rate of
interest, in other words BS long aa, at eachstage, the
Willingness line is steeper than the Market line.
All that has been done 80 far is to describe the income
map, and to place on it 8 point PI to represent the 8&

Cat1

THE THEORY OF INTEREST
s u e d fned income situation of Individual 1, and to draw
through this point P, two lines, one a straight line, t,he
Market line, showing the direction in which Individual 1
can move away from P,, and the other a curved line, the
Willingness line, showing the direction in which he is
willing to move. He is willing to borrow a first $100 at
30 per cent, or lend a first $100 at 40 per cent, but can
do either at 10 per cent.
56. The Whole Family of Market Lines

But before we make use of the contrast between the

M and W lines to follow the individual as he moves
his income position from P either northwest as a lender

CHART 29
Intersection of M ILine and W ILine at Ps.

or southeast as a borrower, we must &st complete our
pictures of the two kinds of lines. Thus far only one line
of each of the two kinds has been drawn. These are the

c2421

IN GEOMETRIC TERMS
only lines applicableto the given income position PI. But
for every other income position in which we may place
Individual 1, the Market line would encounter a different
Willingness line.
In the same way, we could picture a series of pairs of
Market and Willingness lines for any other individual,

CHART 30
M Linea With Reference t o W sand W SLines.

such an Individual 2, depicted in Chart 29. In this caae,
Individual W is represented at one position to be willing
to lend at 2 per cent but to be able todo so at 10 per cent,
the market rate; we have then the Market line P2M2and
the Willingness line P2Wa. In the m e way,wecould
draw PsMs and PoMs,for a third individual and so on.
~2431

THE THEORY OF INTEREST
Underourassumption
of a ‘perfectmarket, all the
Market lines PIMl, P2M2,
P a 8 , etc., axe parallel to
each other, their common divergence from a 100 per cent
slope representing the one universal market rate of interest, here supposed to be 10 per cent.4 Since the Market
lines are thus parallel, they are really impersonal or independent of particular individuals, and we may consequently picture the whole map (Chart 30)) as covered
withstraightand
parallel Market lines, like the conventional picture of a rainstorm, each line being slightly
steeper than 4 5 O , and ib divergence therefrom indicating
a rate of interest.

$7. Many Families of Willingness Lines
The Willingness lines, on the other hand, are personal,
or individual. The particular slope in each cme is, of
course, dependent on the particular income position PI.
A given Individual 1 is concerned with only one Willingness line at a time, out of his whole “family” of linesthe one line which passes through hisactual income
position at P,. By comparing his Willingness line at that
part,icular point with the Market line, we have a graphic
picture of the motives which decide whether he will borrow or lend.
There always exists for him, potentially, otherWillingness lines, passing not through his actual income position
P,, but through any other income position at which he
could be imagined to be. These curves represent the various rates at which Individual 1 would be willing to borrow or lend if his income position were varied. Thus
‘SOlarge a rate a~ 10 per cent is used in the chartsbecause a line
with a divergence from the 100 per cent slope of leas than 10 per cent
cannot be clearlyMen.

t2441

IN GEOMETRICTERMS
the number of Willingness lines for any one Individual
is infinite, and every other individual will have his own
family of lines.
Weconceive, then, of a map for Individual I alone,
covered with a family of such Willingness lines infinite in
number, arranged so as to vary gradually from each to
the next, like the lines of elevation on a geographic contour map of a mountainP
While Individual 1 finds all points on any one Willingness line of equal desirability or “wantability,” he would
rather havehis income position on lines more to the
“northea&,” or farther from the origin. Each Willingness
line might be labelled with a number representing specifically the totaldesirability or “wantability” pertaining to
each and all of the income positions on it. It is the locus
or assemblage of these points (combinations of income
for the two years) equalIy desirable in the estimation of
Individual 1. A greater aggregate income in the two years
may be offset in respect to theresulting total desirability
by a less convenient distribution between the two years
and vice versa.6
But we are not yetinterested in such differences of level
or total desirability between the Willingnesslines.We
are here interested only in the direction8 of the Willingness lines at different points, representing the different
‘Those familiar with a contour map will find the analogy 8. good one,
sinceeachWillingaeas
line represents a level of desirability Merent
from the others, the level or heightbeinghereconceived aa measured
in the third dimemion, that is, at right angles to the page of the map.
‘It would, of coum, be possible to present the Willingness lines in
terms of total demrability or wantability
without
sup&,
any
hypothetical borrowing or lending; this waa done in the Rate of Interest (Appendix to Chapter VII). The Willingness linea were there called
iso-desirability lines. They might also be called linea of

indifference.

12451

THE THEORY OF INTEREST
degrees of impatience pertaining to different income situations. These directions, or divergencesfrom the 45"
line, picture to us how the individual wouldbewilling
to borrow or lend under all possible income circumstances.

$8.A Typical Family of Willingness Lines
While we cannot, of course, tell exactly how any human
being would act if far from the income situation in which
he is actually placed, yet we know what in a way would
be characteristic of him. Chart 31 is believed to represent

CHART 31
A Typical Family of E
' Lines.

roughly a family of Willingness lines typical of most
human beings. It is best analyzed by following the dotted
straight line SS' running northeast, midway between the
axes and therefore comprising points which represent, in
each case, equal incomes in both years.

E2461

IN GEOMETRICTERMS
Four characteristic properties may be noted:
(1) A t S, taken to represent a point near the minimum
of subsistence-the income situation, say, of a polar explorer who is marooned and hopelem-theWillingness
line is nearly vertical. In this income positionof extreme
need a person would scarcely be wilIing to lend at all, for
to give up one iota of this year’s income in exchange for
any amount promised for next year would meantoo great
privation in the present. On the contrary, in order to
get an added dollar today to help keep body and soul together this year, he would be willing to give not only 10
per cent or 25 per cent but perhaps as much as 100 per
cent, or 1000 per cent, or every dollar of next year’s income even though next year is no more promising than
this year.
(2) At S’, taken to represent an exceedingly large income-say $l,O00,000for eachof the twoyeam-the
Willingness line is nearly at right angles to the SS’ line ;
that is, nearly at 45” to the two axes, for with suchlarge
a
income the two years would seem almost on even terms.
Presumably one withthis income wouldnot be willing, in
order to get $lo00 moreincome this year, to give up
much over $lo00 out of next year’s income.
(3) As one passea between the two income situations
S to S ‘,his rate of time preference
above mentioned, from
will gradually decreas+from nearly infinity at S down
nearly to zero at S’, that is, the larger the income, other
things remaining the same, the smaller the degree of impatience.
(4) Any one Willingness line grows steeper as it proceeds upward and leftward, changingfrom a nearly horizontal direction at its lower right end to a nearly vertical
direction at the opposite end.

w 7 1

THE THEORY OF INTEREST
$9. Time Preference May be Negative

If these specificationsare correct, some, at least, of this
family of Willingness curves, especially those far distant
from the origin, and low down-that is, representingsmall
future and large present income-will have an inclinctr
tion less steep than 45" tothe horizontalaxis and a
slopeless than 100 per cent. A t suchincomepositions
therate of t,imepreferencewould
be negative. It is
sometimessaid that it is a fundamental attribute of
human nature to prefer a dinner or a dollar this year to
a dinner or a dollar next year, but this statement is evidently too narrow. Unconsciously it confines our view to
regions of the income map where present income is relatively small orfuture income relatively large. For a starving man it is notably true, that is, the Willingness lines
that Lie in the Eeft part of the map are far steeper than
45". Of a man expecting large future income it is also
true; that is, the Willingness lines toward the top of the
map are also very steep.
But if we turn our attention in the opposite directionto the right, or downward, or both-we find regions on
the map in which, if the foregoing description is correct,
the curves flatten out and incline lessthan 45" ; the man's
income situation is such that he might even be willing to
lend for nothing, or even less than nothing, simply b e
cause he would, in such a case, be so surfeited with this
year's income and so Short, prospectively, of next year's
income that he would be thankful to get rid of some of
this year's superfluity, forthe sake of adding even a trifle
to next year's meager real income. His situation would be
like a Robinson Crusoe on a barren island, well supplied,
but with foods that could serve him only this year. Such

12481

IN GEOMETRIC TERMS
situations are rare in practice, but they axe certainly imaginable and sometimes even occur. In such situations a
man would be willing to save for the futurewithout any
incentive in the form of interest. But this takes us b e
yond our present point; for here we are concerned only
with the Willingness lines, not with the Market lines.
810. The Persoaal and Impersonal Influences on

Impatience
By the aid of this map we can see, anew, and more
clearly, that a man’s actual degree of impatience depends
on two circumstances:
(1) It depends on his “personal equation,” the whole
contour of his whole family of Willingness curves, representing what he would be willing to do under all sorts of
income situations. The Willingness lines of a spendthrift
are steeper and those of a miser less steep than thetypical,
or normal, man’s family of curves.
(2) It depends on his particular income situation on
the mapwhich is represented by the letterP. A poor man
is more impatient than a rich man of the same personal
characteristics. A man withgreat expectations for the
future but with little available for the present is more
impatient than the man oppositely situated with respect
to the future.
Both the family of Willingness lines and the position on
the map are, of course, changing every minute. Only at
one particular time does the map, with its set of curves
for Individual 1, and a particular location Pi,picture his
individual circumstances. What we are doing here is to
take a flashJight, as it were, of his income situation and
his Willingness lines, and to analyze his behavior at the
instant.

12491

THE THEORY OF INTEREST
$11.Deciding Whether to Borrow or to Lend
Individual chauxter and income together withthe market rate of interest determine what the individual will
do in any given situation. Chart 32 pictures graphically
one step in the process by which an individual adjusts
his degree of impatience to the market rate of interest,
by borrowing or lending.

CHART 32
Adjusting Impatience to Market Rate of Interest ThroughBorrowing.

To summarize and repeat, with the interest rate at
10per cent, Individual 1 may,or may not, bewilling
to take a $100 loan,dependinguponwhether
or not,
while his position is at P I , his impatience is or is not
greater than this 10 per cent. If, as portrayed by Chart 32,
his impatience is greater-say, 30 per cent-and if he
can obtain the loan at 10 per cent, he will be glad to do
so. Let W ; be the position to which he is d l i n g to shift
E2501

IN GEOMETRIC TERMS
in order to get $100 added to his present income. This
position would require a sacrifice of $130 out of next
year’sincome,which,however,
he need not make for
he can get his accommodation for $110 of next year’s income and find himself at MI’,
Individual 2, on the other hand, whether because of
his temperament, or because of a different time distribu-

CHART 33
Adjusting Impatience to Market Rate of Interest Through Lending.

tion of his income,maybehave quite differently, His
position to start with, let us say, is P2 in Chart 33. If
his impatience, under these circumstances, is only 2 per
cent, when the market rate is 10 per cent, he wiU not
borrow, but will lend. He will continue to lend until his
degree of impatience is as great as the market rate of
interest, that is as long as his Willingness line, at each
stage, is less steep than the Market line.
Thus, the angle at P between the M line and W line
251 1

c

THE THEORY OF INTEREST
of Individual 1, or of any other individual, shows whether
that individual is potentially a borrower or a lender. If
the individual’s W line is steeper than the M line, he
will borrow; if it is less steep, he will lend.
Therefore, if this second individual lends $100, while
the first individual borrows $100, both at 10 per cent, both
will reap advantage. One will shift down a 10 per cent
andtheother will shift up
Marketline from PIto
the 10 per cent Market line from Pzto M i .
If we had only these two persons trading this year’s
income for next year’s income between themselves, the
rate of interest agreed upon for a loan of $100 this year
would not, of course, necessarily be 10 per cent,but would
be determined by the respective bargaining power of Individual 1 and Individual2. The ratemight fall anywhere
between the 2 per cent, the lowest rate at which Individual B is willing to lend $100, and the 30 per cent, the
highest rate, at which Individual 1 is willing to borrow
$100. But we are less interested in such a special trade, or
haggle than in the general market.
$12. Interest Fixed for an Individual
It is a fact long recognized by price theorists,? that the
theoretical determination of any price in a special trade
or haggle between two persons, each of whom is conscious
of his influence on that one price, is more complicated
than in a full-fledged competitive market in which each
individual is so small a factor BS to be unconscious of his
influence on the market price. We here assume such a
‘See Auapitz und Lieben. Untt?rsuchungen iiber die Theorie &a
Preises. Leipzig, Dunker und Humblot, 1889, p. 405; Marshall, Alfred.
Principles of Ecanomics. London, Macmillan and Co., 1907, p. 332; also
my M a t L m a t i d Investigations in the Theory of Vdue and prices,
p. 25.

c 252 1

IN GEOMETRIC TERMS
general market, in which a single buyer, or lender, is so
small a factor that he is not actuated by any consciousness
of influencing the market rate of interest. Each person
finds the ratefixed for him. We assume, forthe purpose of
the present illustration, that the rate so fixed for him
by the market is 10 per cent.
813. How an Individual Adjusts his Income Position
to the Market
Under these assumptions it is clear that Individual 1
will borrow $100 at precisely 10 per cent, and that Individual 2 will lend $100 at precisely 10 per cent, the
market rate. Their individuality will find conscious play
only in determining how far they will make use of the
market. Let us now me hpw far beyond $100 each will
borrow or lend at this fixed 10 per cent rate.
To do this we need merely compare Willingness lines
with the Market line. Will Individual 1, who has shifted
from P , to M’, along the 10 per cent Market line with a
$100 loain, again shift fromM’l for an additional $100loan,
along this same 10 per cent Market line? He will do 80
only if he is still willing to pay morethan themarket rate.
Whether this is true can be tested by preciselythe same
process as before, namely by drawing from this new income position on the Market line a new Willingness line
and ascertaining whether or not it is steeper than the
Market line. And so, step by step, $100 by $100, as he
shifts along the Market line, we can always test whether
he will shift still further. Any individual has but one
Willingness line, cutting through any one income position,
but when he sets outfrom any P, he is going to shift along
the Market line and, at each shift, he encounters 8 new
Willingness line.
~2531

THE THEORY OF INTEREST
On Chart 34 are represented a number of W lines which
are assumed to depict Individual 1’s varying degree of
impatience at different income positions. A study of the

CHART 34
TheFinal Income Position (&J of Individual 1 Fixed by Tangency
of the WI Line to the Ma Line at QI.

chart will show how Individual 1, in income position PI,
will borrow, because his degree of impatience exceeds
10 per cent, the market rate of interest, H
is borrowing
will continue, of come, until his degree of impatience is
r2g1

IN GEOMETRIC TERMS
reduced to 10 per cent, at which point he no longer secures a net gain from borrowing. This point is located at
Q1where the M line is tangent to Individual 1’s W line
through that point. There at last he reaches a position
where the next $100 shift on the Market line is no longer
less steep than his Willingness line but exactly as steep,
The same principles apply to Individual 2. The only
differences are: first, that he shifts upward from P to his
Q instead of downward-that is, he adds to next year’s
income at the expense of this year’s income; and, secondly, that he acts in reference to a different family of
Willingnesslines entirely his own. Such a picture implies the utmost sen8itiveness or fluidity of inducements
and responses. There would be a continual readjustment
of loans and borrowings, bmk and forth ; practically every
person would beeither a borrower or a lender; the extent
of his borrowings or loans would be very finelygraduated,
and constantly changing.
We have not yet pictured geometricallythe whole problem of the rate of interest; but we have pictured the solution of the problem of how any one individual will adjust,
under the ideal conditions assumed, his lending or borrowing to the market rate of interest. This simplified solution consists, we have seen, in finding Q at the point
where the M line at a given rate of interest is tangent
to one of the given family of W lines.
Having solved this individwL1 problem, we now proceed
to the mwket problem.
$14. Market EquiZibrium

It may seem that little progress has yet been made
toward the ultimate end of determining the rateof interest because of our initial assumption that the rate of
[ 255 1

THE THJZORY OF INTEREST
interest is already fixed for the individual by the market
formed by others. How did they fix it? Have we begged
the whole question?
Only a few steps are now required to finish the whole
market picture. It is true that we aasumed a fixed 10 per
cent rate in order to see how an individual would shift
his income position to harmonize his individual degree
of impatience with that, to him, fixed rate. Nevertheless)
each individual, even if unconsciously, helps to make the
market rate by the very act of shifting his income situ&
tion from a P position to a Q position.
This statement will be clear if we ask ourselves what
would happen were we to suppose the “fixed” market rate
to have been fixed too high, or too low. If we imagine the
market rate to be very high, say 25 per cent, then, the
bulk of individuals would try to lend and few wouldwant
to borrow. The aggregate of loans thus offeredwould
exceed the demand and the interest rate would fall. Conversely, if the rate were too low, demand would exceed
supply and the rate would rise. Since the total sums actually lent must equal, in the aggregate, those borrowed,
the horizontal displacements of all the Q’s in one direction
must equal that of all the other Q’sin the other direction.
Some Q’s, those of borrowers, are to theright of the
correspondingP’s. Others are at the left. As a group, they
are neither. The average Q has the same longitude aa the
average P. The same is true 89 to latitude. In short, the
geometric “center of gravity” of all the Q’s must coincide
with that of all the P’s, in order that the loan market may
be cleared.
In other words, whilethe market rate, 88 represented by
the divergence of slope of the Market line, always s e e m
fixed to the individual adjusting his income eituation to
[ 256 1

IN GEOMETRIC TERMS
that rate, nevertheless that rate is not really completely
fixed independently of his ownborrowing or lending.
What the market does is to keep the Market line for different individuals parallel. There cannot be two rates in
the same market at the same time-at least not in the
perfect market here assumed.
But theseparallellines are alwaysswinging a little
back and forth to “clear the market.” Each person’s Market line may turn slightly about his P aa a pivot. AU
Market lines turning together, that is keeping pardel,
tend to reach the right inclination-that which clears the
market and brings the center of gravity of the Q’s into
coincidence with that of the P’s.
Thus, the economic problem of determining the rate of
interest becomes the geometric problemof experimentalIy
oscillating all the M lines until their common inclination
brings the center of grrtvity of the contacts (Qs) into
coincidence with the center of gravity of the P’s.
We now have the complete geometricrepresentation of
the whole problem of the rate of interest under the assumptions of the first approximation-complete except
that, to put the picture on a two-dimensional chart, we
have had to add the restriction that “other things &re
equal” as to all years beyond the first and
Thus the economic problem of determining the rate of
interest is translated into the geometric problemof drawing a series of parallel straight linea through given points,
P’s, at such a slope as will make the center of gravity of
the Q’s coincide with the center of gravity of the Pe.
There is a one-to-one correspondence between the economic and the geometric problem, 80 that if the “ma.p”
‘A more complete expremion, in mathematical terms, applying to any
number of yegw, is given in Chapter

XIX.

E 257J

THE THEORY OF INTEREST
is correct we have reduced the whole problem to one of
geometry.
Incidentally, it may be remarked here that there is evidently nothing inherent in the geometrical construction
aa presented which necessitates a positive rather than a
negative market rate of interest. A negative rate can
theoretically emerge wheneverthe P‘s and their center of
gravity are of sufficiently low latitude or great longitude,
or both, 50 that the common slope of the Market lines
tangent at the Q’S with the Willingness lines, will beless
than 100 per cent. That this is theoretically possible is
evident frominspection,provided the Willingnesslines
do, aa aasumed, have inclinations at certain income positions less than 45”. The reasons why the rate of interest
is seldom or never negative have chiefly to do with the
conditionsintroduced under the secundapproximation
and will be more apparent in the next chapter.
$15. The Four Principles

Charted
In this geometric picture we me that thefour principles
formerly stated in words (in Chapter V) are now interpreted geometrically on the “map” a3. follows:
(1) Impatience principle A (that each man’s impatience or rate of time preference depends on his income
stream) is represented by a family of Willingness lines
for each individual.
(2) Impatience principle B (that each rate of time
preference is assimilated to the market rate of interest)
is represented by the tangency at each individual’s point
Q, thus making the slope of his W line at that point equal
to the slope of the M h e .
(3) Market principle A (that the market will be
cleared) is represented by the fact that the aggregate
12581
a8

IN GEOMETRIC TERMS
horizontal shift from P’s to Q’s to the right (by all borrowerscombined) must equal the aggregatehorizontal
shift from P’s to Q’s to the left (by all lenders combined);
and also that the two aggregatevertical shiftg representingnextyear’s repayments of loans must likewisebe
equal, so that the centers of gravity of the P’s and theQ’S
coincide.
(4) Market principle B (that all loans axe repaid and
at one rate of interest) is represented by the fact that the
Market lines are straight and parallel.
$16. The Geometric Method

These charts do, for the ideas they illustrate, what
supply anddemandcurvesdo
for the ideas illustrated
by them.
Like all graphic methods, the one here applied is intended to segrega’tebasic tendencies from the rough-andtumble of real life, and set these tendencies going as they
cannot go in real life. It condenses a year‘s income into
an infinitesimal time; it confines our variations to two
years only; it disregards the element of risk; it pictures
next year’s incomeas a certainty; it disregards the lack of
security that limits the ease with which an individual can
slide his series of transactions along the M line; it 88sumes that themarket is perfect.
Again, the Willingness lines should not be drawn as
continuous curves. They are actually rough and jagged,
so that, for this r e m n alone, the nicety of adjustment
which would obtain under the assumption of continuity
is lost. We know also that most individualsrequire a considerable stimulus even to start sliding along a Market
line. Besides the height of the rateof interest, there is the
trouble of negotiatjng a loan, establishinga line of credit,

c 259 1

THE THEORY OF INTEREST
and practical considerations without end.One result is
that in order to reverseone’sdirection on the Market
line, a bigger rise or fall of the interest rate would be
It
needed than the ch& m hereusedwouldsuggest.
takes a push to dislodge the individual from P in either
direction, The same sort of considerations cause hisposition Q to be determined without the nicety of precision
suggested by the continuous curves.
But all these and other practical considerations do not
destroy the fact that each of our four determining conditions represents a reality-a real tendency even whenin
actual practice balked or neutralized.
The relationship of the rate of time preference to income is d o g o u s to that of marginal utility or cpst to
consumption or production. In order to showhow the
marginal desirability of sugar in the case of Individual 1
is related to his consumption of sugar, we employ a curve,
which, under certain assumptions, becomes the familiar
demandcurveforsugar.Such
a curve has come into
universal use.
Why has no similar curve been used to indicate the
corresponding relationship between time preference (a
marginal desirability derivative) and income? There are
many reasons, but perhaps chief is the di5culty of finding & suitable graphic method for variablesso diverse and
related to each other in 80 complicated a manner. The
mEtpof the Willingness, or Impatience, lines partly solves
this problem. So far aa two periodsof time are concerned,
it “puts on the map” the whole problem of interest.

117. Relation to Supply and Demnd
Some students familiar with demandand supply curves
88 applied to the loan market may feel that they can get

r2m3

IN GEOMETRIC TERMS
their bearings better if the exact relation is shown between these and the “map” here used. Therefore,it seems
worth while here to bridge the gap between these two
sorts of representations just as, at the outset, the gap
was bridgedbetween the map and pictures of the income stream earlier in this book.We may readily and
completely derivethe curves of demand and supply from
the map and the constructioss which have been d r a m
on it.
The individual demand curve of Individual 1 is found
88 follows: Rotate the straight line PQ about P as a pivot,
that is, draw a series of PQ’s from P at varying slopeft. On
each suchPQ find Q, the point of tangency with a W line.
The horizontal disphement of Q to the right of P is, the
loan which Individual i is willing t~ take at the rate of
interest represented by the slope of PQ.
Thus we have both coijrdinah (namely, interest rate
and amount of loans demanded at that rate) given by the
map. Having these coordinates, we merely need to plot
them on a sepaxate sheet in the usual way.
I n the sameway we may construct every other individual’s demand curve. The aggregate c m e of all individuals (by adding all demands at a given interest
rate) gives the total demand curve in the market.
The supply curves are constructed similarly; the only
differencebeing that for supply we use the horizontd
displacement of Q to theleft of P,instead of to the right.
Of course, at any given slope near the slope of the
market rate, some individuals will have a right, and others
a left, displacement, and at the market rate itself the two
displacements are equd in the aggregate. This is true
where the supply and demand curves intersect.
Evidently the map gives us the same relationahips as
12611

’

THE THEORY OF INTEREST

the ordinary supply and demand curves and much more.
The supply and demand curves, forinstance, give us only
the displacements, or differences in income position,as between P and &, while the map gives the whole income
position of both points. And while we can reconstruct, M
above, the demand and supply curve from our map, we
cannot reconstruct our map from the supply and demand
curves.

It may also be noted here that the supply curve is derived from the map in spite of the absence, in this fist
approximation, of any investment opportunity or productivity element. The significance of this fact will be more
a p p w n t in Chapter XI where under the second approximation this element is introduced.

CHAPTER XI
SECOND APPROXIMATION IN GEOMETRIC TERMS
11. Introduction
Graphic illustrations of the solutions of two economic

problems incident to the attainment of economic equilibrium, assuming incomes k e d , have been given in Chap
ter X. One waa an individual problem,the other a market
problem. We found their solutions respectively to be:
(1) The income situation Q1which Individual 1 will
reach from his original income position PI by borrowing
or lendingwill be found where his borrower-lender motive
is balanced, i.e., where oneof his Willingness linea is tangent to the Market line M ;and
(2) The rate of interest, or divergency slope of the
Market line from 4 5 O willbesuch that the center of
gravity of all Q’s, aa above found,will coincide with that
of all the Ps.
In this chapter the point P,which was assumed to be
arbitrdy imposed upon the individual, is replaced by B
series of optional points among which he may o h m . If
this group of points is shrunk into a single point, the analysis of this chapter becomes identicalwith that of
Chapter X. In other words, Chapter X represents a special cam, while this chapter represents the general prob-

lem.
In Chart 35 are representedvariouspossible points
supposed to indicate the various income situations avail-

[2631

THE THEORY OF INTEREST
able to Individual 1 aside from any furthershifts through
borrowing or lending. Instead of having no choice but a
fixed position aa in Chapter X, he now has the opportunity to choose any one of many income positions,but will
actually coniine his choice to those positions represented
0 , I v . This may be called the
upon the boundary line 01’
Investment Opportunity lim or briefly the 0 line for Individual 1. Every individual, of course, has his own 0
line.
$2. The Investmnt Opportunity Line

The reason why we may exclude all points inside of
this boundary line is evident. The inside points would
never be chosen under any circumstances, since each inside point is excelled by some point’s onthe boundary in
respect to both years’incomes. Thus the point A in
Chart 35 will certainly not be chosen if the individual has
the opportunity to substituteany other point to the
north or east of it, or between north and east.
But in no case can income be increased indefinitely.
There axe limits in whatever direction we try-whether
this year, next year, or both. These limits make up the
boundary line 0,’ O1IV. Chart 35 represents Individual 1
as having the opportunity to shift his income positionon
this map in an eastward direction only up to the psition 0;.In other words, he can increase hisincome in the
present year without changing his income in the next year
only up to that limit 0;. Technical limitations, including
personal limitations, are assumed to forbid his pushing to
the right beyond 0,’.
Inthe m e way, starting again at A, he has the
opportunity to move northward on this mapthat ia
to increme next year’s income without changing this

[MI

IN GEOMETRIC TERMS
year’s-butonly up to a certain limit OIv.Or he can
move in a somewhat northeasterly direction and better
himself for both years at once, but again he can do this
only up to a certain limit, 01”
or 0,”.

CHART 35
The Opportunity (0)Line.

The boundaxy line 01’O:v, made up of these limiting
points may, of course, take various fonns, but, for the
present it will be assumed to be a curve concave toward
the origin. It is simply a geometric picture of the technical limitations of an individual’s incomein the two years
considered, assuming, aa always, all other years’ incomes
to remain the same. It is the locus, or line, of options

c 265 1

THE THEDRY OF INTEREST
and may be c d e d the Option line or the Opportunity
line,’ snd is designated as 0, for Individual 1.
53. The I n d i d d s Adjwtmnt Without Loans

What we have seen so fax is that Individual 1, having
discarded all income positionsi d e the Investment Opportunity line, has left as still elrgible only the points on
that curve.
As before, we mume that each individual is unconscious of having any influenceon the market rate of
interest. To iix our ideas suppose, as before, this rate to
be 10 per cent. The only adjustments the individual can
make are: (1) adjusting his position on the 0 line; (2)
further adjusting on the M line. Problem (2) is analogous
to that of Chapter X, so that Problem (1) is the only
new one. The solution of Problem (1) will be found to
point the way to the solution of the knottiest part of the
interest problem,purposely omitted from the first approximation. This is the problem of investment opportunity, productivity, or technique of production in
relation to the rate of interest.
The principle by which the individual may shift his
position along the Investment Opportunity line is very
similar to the principle already set forth in Chapter X
by which he shifts along the Market line. It wilI be recalled that the individual shifted along the Market or
An 0Pc;an ie repmnted by any one pointin Chart 35 not outr
aide the areabounded by A ~ ’ O P ’ .Only those points on the curve
Or’OIIvare reauy eligible. The qpportwLity to move from one of thee
points to another implies two points on thia line. If these two pointa
me o l e together,the direction of one from the other is the slope of
the tangent to the m e . Thus, the term “option” suggeets a point on
the curve while the term “opportunity” mggesta the direction of the
me.

CWI

IN GEOMETRIC TERMS
M line according to ita slope whenthat slope is compared,
at any point, with the slope of the Willingness orW lines.
We saw that, if we suppose him situated at a point on the
M line at which the Willingness line drawn through that
point is steeper than the Market line, he will move away
from that point downward, along the M line, that is, he
will borTow; while, if situated where his W line is less
steep than his M line he will move upward along the M
line, that is, he will lend.
Similar comparisons apply to our present problem
merely by substituting Opportunity line for Market line.
Suppose Individual 1 to be situated, to start with, at
01’on the Opportunity line, as shown on Chart 36. He
then has the opportunity to shift to any other point on
that line as formerly he could shift along the Market
steps of $100
line. Let us, aa before,proceedbysmall
each. The first step is from 01’ to 01“.The chart indicates that, by sacrificing $100 of this year’s income, he
can add $150 t b next year’s income, while he is willing
to receive only $115 aa indicated by his Willingness line
drawn through O1’.The $50 net return he willreceive
is a 50 per cent rate of return over cost. This is his investment opportunity rate. He is willing to lend$100
for a net return of $15 or 15 per cent over cost. This
measurea his degree of impatience or rate of time preference. Evidently, as just hinted, he will seize the opportunity to invest for a 50 per cent return when he would be
willing to take 15 per cent. This choice is represented on
Chart 36 by following the Opportunity line from 0,’
to 0,N.
If, as a second step, another $100 can bring him $140
while he would be wiZ2in.g to take $120, he will seize that
opportunity, too, and so move on to 0;’’. That is, he wiU
~
7
1

*

THE THEORY OF INTEREST
choose a 40 per cent investment opportunity when his
degree of impatience.is only 20 per cent. Thus, he may
be pict,ured ascendinga staircase on the Opportunity line.
The successive steps, in
this case, grow less
steep as he proceeds. A t each point he decides whether to take the next
step or not by comparing its steepnem withthat of the W

CHART 36

'iJ Lines Showing W e r e n t Degrees of Impatience and 0 Lines Showing
DitTerent Rates of Return.

line at that point. The successive W lines will be more
and more steep as he goes on investing successive $loo's,
while the Opportunity line will become lessand less steep.
When the point is reached where the Opportunity line
is nolongersteeper than the Willingnessline,hewill
stop investing. The Willingness line through that point
will have the same steepness as the Opportunity line,
say 30 per cent. That is, the two curves will there be
tangent. This point of tangency, R, is shown in Chart 37.

c 268 I

IN GEOMETRIC TERMS
The reasoning which has just been used is evidently
exactly like that used in Chapter X, the only impmtant
difference being that then we had a stmight line to deal
with to expreas what the individual can do while here

CHART 37
The Point of Tangency (R)of a W Line to the 0 Line.

we have instead a curved line, or a t any rate, a line which
need not be straight.
And the result of this reasoning so far is also similar.
The stopping point is where the can line (in Chapter X,
the Market line; here, the Opportunity line) is tangent
to the Willingness h e .

with Loans
Up to this point in the second approximation we have
reasoned as though the Individual did not have freedom
$4. Individual Adjustment

c 269 1

THE THEORY OF INTEREST
to borrow or lend in the loan market. We purposely excluded that possibility for the moment and went ahead
as if the man were shut off from the loan market completely, 80 that any investment must be out of his own
income and notbe made with borrowed money. Were
this
the case (as inpractice it often is) Chart 37 would
correctly represent the result of the individual’s shift.
It would be a one-way shift, entirely dong the Opportunity line.
But ifnowwe return to the hypothesis of a perfect
loan market, accessible to all concerned and to any extent desired, then Chart 37 does not fully picture our
problem because it fails to take account of the fact that
the individual not only can shift along the Opportunity
line, but can also shift along a Market line by borrowingandlending. That is, he now has two “can”lines,
both the Market line of Chapter X and the Opportunity
line of t.his chapter.
Chart 38 pictures the double movementof Individual 1.
Starting at O,: he movesalong the Opportunity line
to PI where the Opportunity linebecomes tangent to
the M line, then dong the M line to Q1 where the M
line becomes tangent to a Wl line. That is, the fixed
rate of interest will cause the individual so to shift
that the marginal rate of return over cost (investment
opportunity rate and the marginal rate of time preference(degree of impatience) will, each of them, be
equal to the market rate of interest. Chart 38 depicts
Individual 1’s adjustment of his rate of investment
opportunity and his degree of impatience to the market
rate of interest. The rate of interest is, aa always, represented in the slope of the M line, and the rate of return
over cost is represented in the slope at P1 of the O1line.
[ 270 1

IN GEOMETRIC TERMS
These two slopes are the same, since the two line5 are
there tangent.
The slopes of the M line and the O1 line at Pi are
identical since the two lines are tangent at that point.
The degree of impatience is represented by the identical

CHART 38
Point of Equilibrium Where the M Line PJPich is Tfcngent to the 0
Line at P is also Tangent to a Wllllngneee Lme at Q.

slopes of the M line and of the Wlline at their point of
tangency Q1.Since the M line is a straight line, the slopes
of the 0,line and the M line at P1and the slop of the
M line and the W1line at Q1are all identical and the
identity of the opportunity rate, the impatience rate,
and the market rate is shown.

THE THEORY OF INTEREST
$5. T h e Double Adjustment Discussed
In such a double adjustment, P,, the point of tangency
on the InvestmentOpportunity line, has to be found first
and Q1, the point of tangency on a W , line last, for there
is only one Opportunity line and only one point on it
at which the slope corresponds to the rate of interest;
while there arean infinite number of W lines with a point
on each having that slope or direction?
It is worth noting that thepoint P, thus located on the
Opportunity line will be quite differentfrom the Point R
on that line shown in Chart 37 when the individual wvls
assumed to be cut off from
The two may differ in
either direction.
It is also to be not’ed that the Wllines always say the
last word, that is, fix the final income position at Q,, the
point of tangency of the M line to a W , line. All other
income positions representpoints reviewed in Individual 1’s mind but rejected in favor of Q,. The point P
on any individual’s Opportunity line is merely a point in
transit toward Q, which is the final point of equilibrium.
If we wishto be even more realistic, our individualneed
The point PI may also be described as that income position,or option,
on the Opportunity Iine which ha^ the greatest presentvalue, aa has
been shown in Chapter VII and aa may also be shown geometrically if
desired.
*It would not then be true that he would choose the option of highest present value. That point ia not R but PI.Thus it is not self-evident,
as it might seem, that a man will always choose the income stream of
highest p e n t value in the market. He will only do BO provided he hss,
in addition, perfect freedom to move from that atuation by m e w of
a loan market. Otherwise he might not bewilling to suffer the inconvenience, say, of a very small income this year even if his expected income next year ia very large. The only maximum principle preserved in
all e r e 8 is not that of maximum market value but that of maximum
desirsbility.

c 272 1

IN GEOMETRIC TERMS
not be pictured m traveling along the Opportunity line
at d,even on a non-stop flight to Q1.He may, more properly, be pictured BS making a more direct jump, across
lots, directly from 0; his income position, on the Opportunity line to Q1.
The reader may, starting at O l , trace the individual by
small steps of combined $100 investments and loans.
Thusthe first $100 step would carry him from 01’
to B. Successive investments and borrowings of equal
amounts would increase the individual’s next year’s income while leaving his present year’s income the same
&s before. On the chart his income position would move
first from 0; to B and then step by step in a vertical
line above B . But he will not necessarily confine his borrowings to the mount of his investments. Thechart
represents a man whose impatience leads him to borrow
for this year’s consumption the amount represented by
CF. His borrowings represented by the horizontal difference between 0; and P1 (that is the distance CE)
is what is often called a productive loan, while the horizontal difference between 0: and Q1 (that is the distance
C F ) is what is called a consumption or convenience or
personal loan.‘
Properly speaking, however, no part of the loan is
itself productive. It is the investment which is properly
to be called productive, To shift along the M line adds
nothing to the total present worth of the individual, for
it merely substitutes $110 next year for $100 this year,
or a series of such sums, and each $110 next year has the
‘With mother individual, on the other hand, the most desirable point
might be verydifferent.Hemi&borrow
only
of what he invests,
or even not borrow at all but lend M well as invest. All depends on the
particular &ape and position of his 0 and TV linea

c 273 1

THE THEORY OF INTEREST
same present worth as $100 this year.. A shift along the
Opportunity line, however, does add to a man’s present
worth. Up to the last $100 invested,each $100 yields
more than $110 nextyear and so possesses a greater
present worth, reckoned at 10 per cent, than $100.
The sole advantage of any shift along the M line done
is to gain not more market worth, but to gain in cona greater total desirability. This is
venience-toreach
true in boththe first approximation and the second. Every
loan, merely as such, is a shift on the M line alone, and
is in itself always a convenience loan. Strictly speaking,
no loan, as such, is “productive.”
It is only in so f a r as the loan makes a difference in
the other shift, that along the 0 line, that it can claim to
be called a productive loan, and it is quite true, in the
case pictured, that the loan does make such a difference.
That is, we call the loanproductivebecause, without
it, the investment would not be made, or would not be
so great-because it would be inconvenient (or even impossible) to invest so much out of this year’s income.
The essentialeffect of a so-calledproductiveloan is
to enable the individual (under our hypothesis of perfect
fluidity and no risk) to disregard entirely what has been
called the time shape of the income stream P,that is, the
proportion of this to next year’s income represented byP.
It enables him to push P as far to the left as he wishes
without threatening him with starvation, or causing him
m y inconvenience. He need practice no abstinence. For
whatever P lacks in this year’s income may be made up
by loans,that is, by use of the Market line. In fact, P m y
be pushed even to the left of the vertical axis, a position
of negative this year’sincome,which is physically impossible except as simultaneously offset by a loan 80 as

c 274 1

IN GEOMETRIC TERMS
to bring him back again to a position of red income this
YW.

In short the investment, or 0 shift, affects the size of
income as measured in present worth of the entire income
position while the loan, or M shift, atrects its final shape.
TheChart 38 is evidently only one type among
many and the reader who wishes to pursue the subject
into special cases will find it easy to do 80 by varying the
curves to suit himseK6
$6. Market Equilibrium

Just as in the k t approximation, so in this second
approximation there are two successive problems:
(1) How the individual reacts to a given rate of interest.
(2) How market equilibrium determines that rate.
The k t of these two problems having now been solved,
we are ready for the second, the market problem-to
show how market equilibrium is established. This is
precisely as in Chapter X, except that theM line, instead
of rotating about a k e d point P, now rolls around the
0 line.
The problem, then, is simply to draw a set of straight
M lines, one for each individual, each person's M line
being tangent to his Opportunity line at a point P, all
such M lines being parallel to each other, to find on each
of them the point Q at which it is tangent to a W line of
the personconcerned, then to roll these straight lines
around said Opportunity lines, while still keeping them
'Of course, the ehift along the 0 line depends entirely on where we
suppose the individual to be situated on that line in the first place. If
we wish, we mny suppose him to start on the opposite side of P from
that hitherto pictured, in which case he doea not enter into a c ~ ~ t e m c
plated investment but withdraws from one.

c 275 1

THE THEORY OF INTEREST
all parallel, until they so slant that the center of gravity
of the Q’s shall coincide with the center of gravity of
the P’s. This slope, thus determined,signifies the rate
of interest which will clear the market.
Let us recapitulate. We have given:
(1) The Market lines, just &s in the b t approximation.
(2) The families of Willingness lines, one family for
each individual, just as in t’he first approximation.
(3) The Opportunity lines,oneonly
for eachindividual, t,hat is, a series of points takes the place of the
single point PI in the first approximation.
We also have, correspondingly, three rates:
(1) The market rate of interest represented by the
slope (over and above that of 100 per cent) of each and
every straight Market line.
(2) The degree of impatience, or rate of time preference, one of each person, represented by the slope of the
Willingness lines and depending on his income situation,
~ E Ifinally determined after all adjustments have been
made.
(3) The rate of return overcost, or the investment
opportunity rate, one for each person, represented by the
slope of theOpportunity line and dependingon the
position chosen on it.
Thecharts of this chapter interpretthe second approximation exactly &s the charts of Chapter X interpreted the first approximation, but with two new investment opportunity principles added to the four principles
common to bot,h Chapters X and XI and already geometrically interpreted in Chapter X. That is:
The Investment Opport,unity Principle A is represented by the Opportunity line.
276 1

c

IN GEOMETRICTERMS
The Investment Opportunity Principle B is represented by the tangency of the Opportunity line with the
Market line, so that the marginal rate of return over cost
is equal t.o the rate of interest.
This last principle,combined with Impatience Principle B, means that each individual so adjusts his position
(first along the Opportunity line to P and then along
the Market line to Q ) that the-Market line PQ sha,ll be
tangent to the first at P and to the second at Q. This Q
will be his income sit.uation finally chosen. To clear the
market the Q’s must be so chosen that their center of
gravity coincides with that of the P’s.
$7. The Nature of the Opportunity Line Discussed
This chapter dXers from Chapter X chiefly in the
introduction of the concept of investment opportunity
which is depicted on the charts as the Opportunity line,
or 0 line. Just what does this line represent in the real
world? Is there any distinction between investing in the
opportunities offered by man’s environment and lending
at the market rate of interest? Is not lending, or buying
a bond, just as truly investing as digging an oil well,
building a factory, or making shoes? Reservingthe merely
verbal part of the answer, let us first go to the main question as to the possibility of definitely distinguishing the
two lines.
Under the assumptions explained in Chapters V, VI,
VII, and VIII, there is a clear distinction between an 0
line and an M line. The 0 line, unlike the Market lines,
is not straight, is not common to all individuals, and is not
family of lines but a single line, It may be defined as the
limiting line of a group of points which represent all the
optional income situations available to an individual who
277 I

c

THE THEORY OF INTEREST
neither borrows nor lends. Every one has opportunities
to shift along his 0 line at a rate above or below the market rate of interest, evenif it be merely in the degree
of care he gives his clothes, his house, his fences, or even
his food. A t a certain stage it is literdy true that a “stitch
in time saves nine”. That is, mending one’s clothes yields
900 per cent, But beyond a certain point mending one’s
clothes, or a roof, painting a house,ortilling the soil
will not repay the cost. Each activity has its marginal
point and enters into the construction of every person’s
0 line. An individua,l’sOpportunity line is a composite
of his separate potential activities-what he might do
if he chose.
Of course the 0 line cannot be drawn without the aid
of valuations whichinvolve the market principles and
so involve the rateof interest. The farmer who encounters
the law of diminishing returns in agriculture buys machinery and labor and sells grain. His 0 line is thus somewhat dependent on the prices of machinery and, since the
price of every good is a discounted valuation, it depends
on the rate of interest, Only in a primitive or imaginary
RobinsonCrusoe land can we get a pure case of investing successive amounts of this year’s income for the
sake of getting a diminishing return in future years without thepresence of some buyingor selling &B an ingredient
in the make-up of the 0 line. It is largely h a u s e the
element of the rate of interest is almost omnipresent in
the valuations entering into the 0 line that the other
and essential ingredient of technical limitations has been
overlooked so generally. Even the farmer doessomeof
that omnipresent trading, but besides this trading with
other men,he is dealing with nature-the soil, the wasons,
the weather, insect enemies, and all the rest. Every in278 1

c

IN GEOMETRIC TERMS
vestment in hi8 farm will have a variable decreasing return as contrasted with the (to him) constant return to
be got in the loan market. Yet every investment in his
f a r m will somewhat imply an interest element and will
theoretically change as the interest rate changes. Thus,
strict,ly speaking, his 0 line is not to be pictured as
immovablelike a rock but as subject to someslight
change with every change in the slope of the M line.
Nevertheless this fact evidently does not alter the principles by which the slope of the M line is determined.
The M line still r o b around an 0 line, even if that curve
changes a little as it rolls.
The 0 lines have been exemplified by the law of decreasing returns in agriculture. Such a curve is concave
toward the origin and represents a law of decreasing returns in the sense that each succeeding dose of $100 invested out of this year’s income will return less and less
next year.
But may there not be a law of increasing return? That
is, may not the curvebeconvex in parts instead of
concave?
We may imagine the 0 line, bounding or enclosing the
group of points representing the possible options, to be
convex or to have any conceivable shape. It may be reentrant, jagged,discontinuous, straight in parts. It is
largely for conveniencethat we have hitherto pictured it
as concave, curved and continuous. But if it were otherwise, almost the Same result would follow. The line PQ
would still roll around it. The result would evidently be
that, wherever the curve W&SI reentrant (convex toward
the origin), the straight Market line, in rolling around
the group of points, would jump across this chasm at the
slightest provocation due to change in the interest rate.

1 279 1

i

THE THEORY OF INTEREST
These reentrant parts would be as inoperative as if they
did not exist, and only the points on which the rolling
t,ook place would really count in establishing equilibrium.
Wha.t is left, after dropping out such re-ent.rant parts as
ineligible, is thus the “envelope” of the group of points
representing an individual’s opportunities to invest r&tionally and must therefore be concave toward the origin.
We are justified then in assuming the curved concave
Opportunity line as typical.
As to the applicability of the terminvestment to a
shift on the M line, this is a matter of choice of words.
Undoubtedly it is so applied in ordinaxy usage. In fact,
such investments are more commonly so called than any
other. I have not been able to think of a short phrase in
common use whichwill apply exclusively to an investmentthereturn on which varieswith eachsuccessive
amount invested. Perhaps “investment with diminishing
reburns” or “investment involving exploitation,” az~dist.inct from investment by mere sale and purchase, would
come nearer to conforming both to usage and to the requirements of the case. Yet the full phrase which I have
provisionally adopted,investmentopportunity,
seems
fairly correct in its implications. Weseldom speak of
buying a bond as an investment opportunity, but investing in new industrial, mining or agricultural enterprises,
such as radio production, or in oil wells, or orange groves,
is spoken of as a real opportunity because the return is
not a standardized market figure but subject to technical
conditions aa to productivity.
88. Investment Opportunity and Impatience
We see then how distinct is the 0 line from the M line.
It is still more distinct from the W line. The Willingness
[ 280 1

IN GEOMETRIC TERMS
linea represent subjectiveconditions; the Opportunity
line representsobjectiveconditions. The 0 line of an
individual is simply ow curve, while the W l i e is one
of many. There is some rate of time preference represented by the angle or slopeof a W line on the charts, be
it positive,negative, or zero,corresponding to every
possible income positionof an individual wherever on the
chart it may be. But this is not true of the 0 line. There
is only a limited region of options on the map, bounded
by a single curve.
As already explained, if the opportunity area enclosed
by the 0 line shrinks to a single point, there is no determinate tangent and we automatically revert to the first
approximation in whichthere is no opportunity to choose
from among opt,ions.
Thus the investment opportunity influence may, theoretically at least, vanish entirely and lead us back to the
first approximat,ion, butthe impatienceinfluence c m
never vanish. Practically however, investment opportunity never quite vanishes. There is always at least some
flexibilityineverybody’s i n m e , but in primitive society, the range of opportunity is relatively small. While
the Opportunity line never entirely collapses into a m t h ematical point, yet, for a person in primitive society it
is an almost negligible spot or ring and could exert only
a negligible influence on the rate of interest, even if it
were to double in diameter or were to change in form.
In such a society the only important influences on the
rate of interest must come largely from a change in the
map, that is, in the distribution of impatience relatively
to income.
But when, as in modern society, the range of inveetc
ment opportunity is great, the slopes of the Opportunity

12811

THE THEORY OF INTEREST
lines exert a great and more controlling influence on the
slope of the Market lines.
If the investment opportunity area is large so &s to
cause the Opportunity line to curve slowly, its relative
fixity of slope indicatesa relatively stable rate of interest.
If the slope is absolutely constant and the same for all
individuals, &s in the case of the hard-tack island,8 represented by a 45" straight line, or the example of Professor
Harry G. Brown's imaginary fruit trees, represented by .
a straight linesteeper than 45", this fixed shape may,
within limits, fix the rate of interest absolutely, forcing
it to agree with that fixed slope whatever may be the
Willingnesslines representing impatience. The limits
within which this would be true may readily be charted
by the reader.
The most important result here is that the Opportunit.y line cannot bedispensedwith in the theory of
the rate of interest. It is something distinct from and in
addition to the Impatience lines as well as to the Market
lines. If those theorists who still insist on the subjective
principle as the only principle of interest will try to picture its determination on this map, they will find it impossible to get any determinate direction of the Market
lines without invoking the Opportunity lines. To adapt
a simile of Alfred Marshall's, both blades
of a pair of
scissors are needed to make the scissors work,

$9. Can Interest Disappear?
One use of this graphic method is to help us form a
more complete picture of the problem as to whether the
rate of interest may ever be zero or negative.
Just as there L a prevalent idea among the economi'&e

Chapter VIII, 64, for discussion of these examples.

12821

IN GEOMETRIC TERMS
cally illiterate that all interest. should bez e r d o u l d be
abolished-so among the economically literate there is a
prevalent idea that the rate of interest could under no
imaginable conditions ever be zero orbelow. Let us then
see, under the assumption of the second approximation,
what are the conditions, if any, which will permit of a
zero or negative rate of interest.
A zero rate of interest means, in our chart, that PQ
has an inchatmionof 45") that is, a slope of 100 per cent.
Our question,therefore, is: must PQ necesmrilybe
steeper than 45". The slope of PQ depends entirely on
the conformation of the 0 curve and the W curves of
eachperson in the loan market. The less steep these
curves are, the less steep will be the Market lines. We
have seen that toward the southeast parts of the map the
W curves are flatter than 45") that is, a man with a r e b
tively large income this year and a relatively small one
next year would be willing, if he had to, to trade more
than $100 today to get only $100next year. Probably this
is potentially t.rue of everyone. It is also true that seldom if ever are actual income situations (Q's) located
in this southeast region.
We turn now to the 0 line. For the average man in a
progressive country and age, like America today,this will
be steeper than in a retrograde country or in a decadent
age-a country or an age in which the natural resources
are becoming exhausted. But if we go sufficiently to the
northwest, it will always be flatter than
that is, if
any investment opportunity be exploited f a r enough it
will yield lessfuture return than its immediate cost. This
is not only true of land cultivation and extractive industries generally but of all industries. Everywhere, in the
end, any law of increasing returns will give place to a hw
4.5")

12831

THE THEORY OF INTEREST
of decreasing returns. And if we keeppursuingthese
decreasing returns f a r enough there will always come a
point where additional investment would be worse than
useless or where the rate of return over cost is less than
nothing. Even in such cases of extraordinary returns aa
the example of the BellTelephoneCompany, to have
tried to push the development faster than new construction could be built or than the public, even with every
device of the advertiser, could absorb, would have been
sheer wmte.7
Thus the charts depict regions in which the 0 curve
of each individual is less steep than 45' and regions in
which his W curves are likewise less st.eepthan 45O. But
that fact does not itself prove that. the resultant market
rate of interest may ever actually be zero. For the flatter
parts of the W curves are to the southeast, as shown in
Charts 31 and 34,while the flatter parts of the 0 curve
are to the northwest, as shown in Chart 35. If this relative position of the flatter m7 and 0 lines were peculiar
only to a few individuals, negative interest might well
exist. The P of such m individual might be in the northwestern part of the map and the Q in the southeastern,
the Market line PQ sloping less steeply than 45" and
being tangent at P to the 0 line and at, Q to a W line.
He would thus be a borrower, and there would be plenty
of lenders.
But if, aa is the truth, practically everybody else has
'Explanations of thelaw of diminishing returns sometimes miss this
point by ignoring the time element. Thia element ia alwayseaeential
and especially in interest theory. Enlarging a f s e t o r y may in the fUtUr8
lower costa and 80 in time increasetherate of returnobtained or attainable, but we are here concerned with a hypothetical series of doe8
of costa or investments all relating to the 8(pme period of time such aa
the preeentyear and with thereturnoverthem
c o d , srry next Y W .

[2Ul

IN GEOMETRIC TERMS
the same sort of map, that is, with the partsof the 0 and
W curves which are flatter than 45" located northwest
and southeast respectively; and if we should draw everybody else's PQ at the same slopeas above, we would have
only borrowers and no lenders at interest rates pictured
bysuchslopes.Everyonewould
be glad to borrow at
negative rates of interest. But a rate of interest at which
It could not
there is nolendingwouldneceaarilyrise.
clear the market. It couldremain negative only .if a
sufficient number of people had maps on which the TV
lines were flatter than 45" even in the northwest and 0
lines flatter than 45"even in the southeast. Otherwise
the center of gravity of the P's and Q's could not coincide.
But there is nothing inconceivable in having such a layout overlapping the flatter-tha11-45~regions. In other
words, if enough persons in the market were sufficiently
miserly, or their income opportunities were su&iatlg
unpromising, or both, then the rate of interest could be
zero or below.
To meet these conditions would require
either a change
in average human nature as to impatience under given
income situations, or a change in the future prospects
of production and investment opportunity, due, say, to
impending exhaustion of natural resources or retrogression generally, instead of progrem, in the industrial arts.
Finally, the Opportunity line can never get very much
flatter thanthe 45" inclination, if as flat as that, 90
long as among our opportunities there are even the present possibilities of preserving food and other goods, that
is postponing their uses. We can scarcely expect a time
to come when we cannot do at least as well for the future
aa the shipwrecked sailors with their hrtrd-tack That is,
as long aa such an alternative exists as being able to
~
5
1

THE THEORY OF INTEREST
postpone much of our present income by preserving the
goods which yield it, the real rate of interest can scarcely
get below zero.8
Our conclusion is that negative interest is theoretically
possible,thoughin
practice the necessaryconditions
never occur.

$10.Does Interest Stimulate Saving?
Just as the map helps visualize the theoretical possibility, yet practical improbability, of negative interest,
80 also it helps us to see clearly the answer to the much
debated question whether savingis stimulated by raising
the rate of interest.
If the reader will draw on the map any desired family
of Willingness lines, place the individual at any desired
income situation (or draw an Opportunity line to indicate all possible positions), and then incline a ruler at
45" and rotate it about that point (or roll it around that
line) he will note that thepoints of tangency of the ruler
with the severalWillingnesslineswillthemselvesconstitute a curve. The savings (or lendings) are evidently
represented by the horizontal displacement of Q to the
left of P . Opportunity and Willingness lines may easily
be so constructed that, as the ruler turns clockwise interest rises and the amount saved and lent out of this
year's income will first increaseand then decrease.
411. Relation to Supply and Demand Curves
In $17 of Chapter X it was shown how supply and demand curve8 can be derived from the M line and the W
'It is true that unstable money sometimee drivw the r e d rate below
y rate
zero unintentionally. (See Chapters 11 and XIX.) But the m
cannot get below zero 80 long as the standard is, like gold, orrpeble of
being stored substantially without coat. (Chapter II.)

[a61

IN GEOMETRICTERMS
lines depicted in Chart 34. Supply and demand curvea
caa equally well be derived from the M line, the 0 line
and the W lines shown in Chart 38. A series of positions
of PQ, with different slopes, gives us all the material
needed, each slope giving a rate of interestand each
horizontal spread between P and Q being the demand for
loans (if Q is east of P) or supply of loans (if Q is west
of P),The only difference is that P is not now fixed as in
the first approximation, but shifts as PQ has different
slopes.
It will be noted that the Opportunity line which embodies the technical or production elements in the problem has no more relation tothe supply thantothe
demand, although thisruns
counter tothe common
notions that productivity rules one side of the market and
time preference the other.
It will also be noted that the mapgives us vastly more
light on the analysis of interest than do the mere supply
and demand curves. But even the map fails to give a
complete picture because, in particular, it shows only
two years. The truth seems to be that no complete vimahation of this difficult problem is possible. The only
complete symbolization which seems to be possible is in
terms of mathematical formulas as in the next two
chapters.

CHAPTER XI1
FIRST APPROXIMATION IN TERMS OF FORMULAS

$1. Case of Two Years and Three I n d i v i d d s
IN this chapter, the four principles constituting t.he
&st approximation,previouslyexpressedverbally
and
geometrically,2 will be expressed algebraically. Inasmuch
88 the equations, the solutions of which express the solution of the interest problem, are necessarilynumerous
and complicated, we shall h t consider a simplified special case where there are to be considered only two years
in which there is income and three individuals who
borrow or lend. We shall then pass to the general case
where there are any given number of years and any number of individuals.
In the simplified case, we mume, therefore, that each
individual’s degreeof impatience for this year’s over next
year’sincome can beexpressed as dependent solely on
the amount of this year’s and next year’sincome, the
incomes of all other future years beingdisregarded.
We also assume, for simplicity, that the income of each
of the two years is concentrated at the middle of the
year, making the two points just a year apart, and that
borrowing and lending are so restricted aa to affect only
this year’s and next year’s income.
‘In Chapter V , $9, and

in Chapter IX, 89, firet of the three lines,

in each caw.
‘In Chapter X, 815.

cm1

IN TERMS OF FORMULAS
Let flrepresent the marginal rate of time preference 8
for this year’s over next year’s income for Individual 1
(this is the slope at Q of a Willingness line relatively to
the 45’ line). Let his original endowment ofincome
for the two years be respectively
c; and .’c:
(These are the longitude and latitude of P in Chapter
X.) This original income stream, consisting merely of
the two jets, 60 to speak, c,; c?, is modified by borrowing this year and repaying next year. The sum borrowed
this year is called 2: (this is the horizontal shift from
P to Q). To represent the final income of this year this
sum z< is therefore to be added to the present income
cl’. Next year the debt is to be paid, and consequently
the income finally arrived at for that year is C? reduced
by the sum thus paid. For the sake of uniformity, however, we shall regard both additions to and subtractions
from pre-existingincomes
algebraically aa additions.
Thus, the addition $1’say $100, to the first year’s income
is a positive quantity, and the addition, which we shall
designate by zl”, to the second year’s income, is a negative quantity - $105. The first year’s income is, therefore, changed from
c: to c1‘
x:,
and the second yeax’s from
:c to c?
SF.
(Just aa C; and c/ are the longitude and latitude of P in
Chapter X, so c{
xl’ and cl”
x / are those of Q.)

+

+

+

+’

‘The relation of 1, representingthe mte of timepreference of any
individual to the mmginol &&ability, or“wantability,” of this year‘s,
and of next year’s income, is given in the Appendix to this Chapter, 01.
*The tern “year” is wed for simplicity, but “month”or “day” would
be equally ”e
md would do lees violence to f a t s .

~

9

1

THE THEORY OF INTEREST
By the use of this notation we avoid negative signs and
80 the necessity of distinguishing lbetween the expressions
for loans and repayments or for lenders and borrowers.
$2. Impatience Principle A (Three Equations)

The first condition determining interest, namely, Impatience Principle A, that the rate of preference for each
individual dependsupon his income stream, is represented for Individual I by the following equation:
f~ = FI (GI’
Z,’I
cI”
51’)
which expresses fl as dependent on, or, in mathematical
language, aa a function of the two income items of the
two respectiveyears, F1being not a symbol of a quantity
but an abbreviation for“function.” In case the individual lends instead of borrows, the equation represents
the resulting relation between hismarginal rate of preference and his income stream as modified by lending; the
onlydifference is that, in t.his case, the particular numerical value of x‘ is negative and that of x” positive.
The equation is the algebraic expression for the dependence of the slope of a Willingness line on the income
position of Individual 1.
In like manner, for Individual 2, we have the equation
f2 = F2 (czl+ %,’ cz” +d’>,
and, for the third individud,
h = FS (cg’ zs’, d’ Zi’).
These three equations therefore express Impatience
Principle A.

+

+

+

+

83. Impatience Principle B (Three E q u a t h )
Impatience Principle B requires thatthe marginal
rates of time preference of the three Merent individuals

l-2901

IN TERMS OF FORMULAS
for presentover future income shall eachbe equal to
the rate of interest, and is expressedby the following
three equations: 6
j1 = i
fi = i
ja
i
where i denotes the rate of interest. These three e q u s
tions are best written as the continuous equation:
i = f l = f2 = fa.
(These equations express the fact that at the Q’s the
slope of the Willingness lineis the m e as of the Market
lines.)
$4. Market Principle A (Two Equations)

Market Principle A, which requires that the market
is
becleared, or that loans and borrowingsbeequal,
formulated by the following two equations:

x[
x?

+ + x{ = 0,
+ + xi’ = 0.
52’

XZP‘

That is, thetotal
of this year’sborrowings is zero
(Iendingsbeingregarded &s negativeborrowings), and
the total of next year’s repayments is likewise zero (paymentafrom a person,beingregarded as negative payments to him).
$5. Market Principle B (Three Equations)

Market Principle B requires that the present value of
this year’sloans and the present value of next ~~s
‘Strictly speaking these equalities are true only when the individual
is 80 mall a factor inthemarket aa to have no appreciableinfluence
on the market rate of interest. The equality of f and i imptiea that the
total desirability, or wantabiiity, of the individual ie a maximum. (See
Appendix to thie chapter(Chapter =I), 82.

TKE TmORY OF INTEREST
returns, for each individual, be equal. This condition is
ful6lled in the followingequations,eachcorresponding
to one individual:
SI”+

Xif
l+i
= 0,

$6. Counting Equations and Unknovms
We now proceed to compare the number of the foregoing equations with the number of unknowns, for one
of the most important advantages of an algebraic statement of any economic problem is the facility with which,
by such a count, we may check up on whether the problem is solved and determinate. There are evidently 3
equations in the first set, 3 in the second, 2 in the third,
and 3 in the fourth, making in all 11 equations. The unknown quantities are the marginal rates of time preference, the amounts borrowed, lent and returned, and the
rate of intereet aa follows:
fa, fs, or 3 unknown89
x i , 2:) or 3 unknowns,
G”,xSttJor 3 unknowns,

€1,

and finally,

i, or I

unknown,

making in
IO unknowns.
We have, then, onemore equation than necessary.
But examination of the equations will show that they
are not all independent, since any one equation in the
third and fourth sets may be determined from the others
c2921

IN TERMS OF FORMULAS
of those sets. Thus, if we add together all the equations
of the fourth set, we get the first equation of the third
set. (namely, x[
x:
G' = 0). The addition gives

+ +

In this equation we may substitute zero for the numerator of the fraction (asis evident by consulting the
second equation of the third set). Making this substitution, the above equation becomes
x[
x;
xat = 0,
which was to have been proved. Since we have here derived one of the five equations of the last two sets from
the other four, the equations are not all independent.
Any one of these five may be omitted as it could be obtained from the others. We have left then only ten equations. Since no one of these ten equations can be derived
from the other nine, the ten axe independent and are
just sufficient to determine the ten unknown quantities,
namely, the j's, f ' s , E's and i.

+ +

fj7. Case of m Y a m and n Individuals
We may now proceed to the case in which more than
three individuals (let us say n individuals) and more
than two years (let us say m years) are involved. We
shall Mume, as before, that the x's, representing loans
or borrowings, are to be consideredof positive value when
they represent additions to income, and of negative value
when they represent deductions.

@.Impatience Principle A

(@(m- 1)

Equutiom)
The equations expressing Impatience Principle A will
now be in several groups, of which the first is:
c2931

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

.............................................
j,,' = F,,' (c,,' + z,,', c,," '+X,,", ....,c,Cm)+.32"').
These n, equations express the rates of time preference
of different individuals (fl' of Individual 1, fiof Individual 2, . . . . f,,' of Individual n ) for the first year's income compared with the next.
To express their preference for the second year's income compared with the next there will be another group
of equations, namely:
f? = F," (c;
z,",cI"'
X?,
., ~ 1 ' ~ ) ~ 1 ' ~ )
fir' = Fz" (h"
sf',c'';
G'",
,
X Z (m)),

+
+

+
+

....

+
'+

+

+

.

+

...

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

j,," = F,," ( c,,"
X,,", c,,'"
X,,"',
, . ., c,,("')
z,,(~)).
For the third year there will be still another group,
formed by inserting the superscript "' for ?', and so on
up to the year ( m - l), for t.he year ( m - 1) is the last
onewhich has any exchange relations with the next,
since that next is the last year, or year m. There will
therefore be ( m - 1) groups each of n equations, like the
above group, making in all n ( m- 1) equations in the
entire set.
$9. I m p a t h e Principle 3 ( n ( m - 1) Equations)
To express algebraically Impatience Principle B e we
are compelled to recognize for each year a separate rate

"
'hieprinciple here expressed in "marginal" terms haa been alternatively stated in worda in Chapter V and in geometric t e r n in Chapter

[MI

) ~

IN TERMS OF FORMULAS
of interest. The rate of interest connecting the first year
with the second will becalled ,'i that connecting the
second year with the third, i", and so on to i(*--l).
Under
this principle, the rates of time preference for all the
different individuals inthe community for each yew will
be reduced to a level equd to the rate of interest. This
oondition, algabraically expressed, is contained in several
continuous equations, of which the firat is:
'i - fl' = f2' = . ,. . = fn'.
This expresses the fact that the rate of time preference
of the first year's income compared with next is the same
for all the individuals, and is equal to the rate of interest
between the first year and the next. A similar continuous
equation may be written with reference to the time preferences and the rate of interest as between the second
year's income and the next, namely:

i" = fl" -fT= ....=fi".
Since the element of risk is supposed to be absent, it does
not matter whether we consider these second-year rate
of interest and time preference as the oneswhich are
expected, or those which will a c t d y obtain, for, under
our assumed conditions of no risk, there is no discrepancy between expectations and realizations.
A similar set of continuous equations applies to timeexchangebetweeneachsucceeding
year and the next,
up to that connecting year ( m - 1) with year m. There
will therefore be wa - 1 continuous equations of the
X 88 the principle of maximum desirability. The equivalence of the
principlewhether stated with reference to a maximum or to a marginal equality ia obvious, but the mathematical reader may aue to aee
it put in f o r m a 88 a "maximum" proposition aa in the Appendi. to
thie chapter (Chap@ XII), 82.

~2951

above type. Since each such continuous equation is evidently made up of n constituent equations, there axe in
all n (m- 1) equations in the second set of equations.
$10. Market Principle A ( m Equations)
The next set of equations,expressing Market Principle A, represents the clearing of the market. These
equations axe as follows:

:+. ... +xJ
:+. .. . +x/

XI'+Xi

xp+x/
.

.

.

.

.

.

e

.

=o,

=o,
.

. . . . . .
Xl(rn) +
,+. .. . + 2"(rn)
= 0.
I

.

.

xz(m)

There are here m equations.
$11.Market Principle B (n Eqwctiom)
The equations for Market Principle B express the
equivalence of loans and repayments, or, more generally,
the fact that for each individual the present value of the
total additions (amount borrowed, or lent) to his income
strem, algebraicallyconsidered, will equal zero. Thus,
for Individual 1, the addition the first or present year
is xl', the present value of which is also 8/, the addition
the second year is x / , the present value of which is

.i.X<'

1+2

The addition the third year is x?,
which is

the present value of

21"'

(1

+ i')(l + i")

This is ubtained by two successive steps, namely, discounting x?' one year by dividing it by 1 i", thereby

+

[WI

IN TERMS OF FORMULAS
obtaining its value not in the present or first year but in
the second year, andthen discounting thisvalue so
obtained by dividing it in turn by 1
The next item
dv is converted into present value, through three such
successive steps,and so on. Adding toget,her allthe
present values we obtain as resulting equations for Indi.... n:
viduals I , I,

+ &".

x¶"

~ ' + ~ + ' (1+2)
" + (1+i")

.... ( 1 + i ( m - l ) ) = O *

Similar equations will hold for each of the other individuals, namely :
P'+1a
+'
'+

....+ ( l + i ' )

(l+Cy')

.... (l+i("))=o*

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

. . . . . . . . . . . .
d i n g in all n equations.
512. Counting Equations and Unknowns

We therefore have aa the total number of equations
the following :
n (m
1) equations exprewing Impatience Principle A,
n ( m- 1) equations expressing Impatience Principle B,
m equations expressing Market Principle A, and
n equations expressing Market Principle B.
The s u m of these gives 2 mn m - n.equations in d.
We next proceed to count the unknown quantities
(rates of time preference, loans, and rates of interest);
First as to the f)s:
For Individual I there are ,f: fl",
the
number of which is m - 1, and, as there is an equal
'-

+

.....

12971

THE THEORY OF INTEREST
number for each of the n individuals, there will be in all
n ( m - 1) unknown f’s.
As to the x‘s, there will be one for each of the m years
for each of the n individuals, or mn.
As to the i’s, there will be one for each year up to the
last year, m - 1. In short there will be
n ( m - 1) unknown ps,
man unknown ds,
??a - 1 unknown i’s,
or 2 mn m - n - 1 unknown quantities in all. Comparing this number with the number of equations, we
see that there is one more equation than the number of
unknown quantities.
This is accounted for, as in the simplified case, by the
fact that not all the equations are independent. This
may be shown if we add together all the equations of
the fourth set, and substitute in the numerators of the
fractions thus obtained their value as obtained from the
third set, namely,zero.We shall then evidently obtain
the first equation of the third set. Consequently we may
omit any one of the equations in the last two sets. There
will then remain just rn many equations as unknown
quantities, each independent (that is non-derivable from
the rest), and our solution is determinate.
Inthe precedinganalysis, we have throughout 88sumed a rate of interest between two points of time a
year apart. A more minute analysiswouldinvolve
a
greater subdivision of the income stream, and the employment of a rate of interest between each two successive time elements. This will evidently occasion no cornplication except to increase enormously the number of
equations and unknowns.
C2981

+

IN TERMS OF FORMULAS
813. Different Rates of Interest for Different Years

The system of equations thus involved when n p m n s
instead of three and m yeam instead of two are consideredintroducesveryfew
features of the problem not
already contained in the simpler set of equations for two
years and three persons. The new feature of chief importance is that, instead of only one rate of interest to be
determined, there are now a large number of rates. It is
usually assumed, in theories of interest, that the problem
is to determine “the” rate of interest, as though one rate
would hold true for all time. But in the preceding equations we have m - l sepazate rates of interest, viz., i’,
it’, ... ‘, ih-l),
Under the hypothesis of a rigid allotment of future incomeamongdifferent time intervals, which is the hypothesis of the first approximation, there is nothing to
prevent great differences in the rate of interest from
year to year, even when all factors in the case are foreknown and there is every opportunity for arbitrage. By
a suitable distribution of the values of clr G, . . .., c,,
there may be produced any differencesdesired in the
magnitudes of i’, i”,
i(”I).
Thus if the total enjoyableincome of societyahouldbeforeknown
to be 10
billion dollars in the ensuing year, 1 billion in the following year, and 20 billion in the third year, and if there
were no way of avoiding these enormous disparities in
the social income, it is very evident that the income of
the middle year would have a very high valuation compared with either of its neighbors, and therefore that the
rate of interest connecting that middle year with the first
year would be very low, whereas that connecting it with
the third year would be very high. It might be that a

....,

12991

THE THEORY OF INTEREST
member of such a communitywouldbewilling
to exchange $100 of the plentiful 10 billions for the first year,
for only $101 out of the scarce 1 billion of next year,
but would be glad to give, out of the third year’s still
more plentiful 20 billions, $150 for the sake of $100 in
the middle and lean year.
In actudmarkets we find some influenceof such differences between future years (aslooked at today) in the
differencesbetween short term and long term interest
rates.
The reasonwhy,in
actual fact, no abrupt or large
variations in the rate of interest, such as from 1 per cent
to 50 per cent, is ordinarily encountered is that the s u p
posed sudden and abrupt changes in the income stream
seldom occur. The causes which prevent their occurrence
are:
(1) The fact that history is constantly repeating itself. For instance, there is regularity in the population,
so that, at any point of time, the outlook toward the
next year is similar to what it waa at any other point of
time. The individual may grow old, but the population
does not. As individuals are hurried across the stage of
life, their places are constantly taken by others, so that,
whatever the tendency in the individual life for the rates
of preference to go up or down with age, it will not
be cumulative in society. Relatively speaking,society
stands still.
Again, the processes of nature recur in almost cemeless regulasity. Crops repeat themselves in a yearly cycle.
Even when there are large fluctuations in crops, the variations are seldom world-wide, and a shortage in the Mississippi Vdley may be compensated for by an unusudy
abundant crop in Russia or Asia. The resultant regularity
~3001

IN TERMS OF FORMULAS
of events is thus sufficient to maintain a fair uniformity
in the income stream for society as a whole.
(2) The tendencytoward uniformity is a b favored
in real lifeby the fact that the income stream is not
fixed, but may be modified in other ways than by borrowing and lending as in accordance with investment o p
portunities. The significance of thesemodifications is
algebraically consideredin the next chapter.

CHAPTER XI11

SECOND APPROXIMATION IN TERMS OF FORMULAS

0 1. Introduction
T H I object
~
of this chapter is to express in algebraic
formulas the six principlescomprising the secondapproximation.l In Chapter XI1 we assumed that all income streams were unalterable, except as they could be
modified by borrowing and lending, or buying and selling
rights to specified portions of these income streams. In
the second approximation now to be put into formulas,
we substitute for this hypothesis of fixity of the income
streams the hypothesis of a range of choice between different income streams.
The income stream of Individual 1 no longer consists
of known and fixed eIements, cl', c [ , cl"', etc.,in successiveperiods but of unknown and variable elements
whichwe shall designate by ,y: yl*, y?, etc. (y; and
y," are the co6rdinates of the Opportunity line).
This elastic income stream may now be modifiedin
two ways: by the variations in these y's, aa well as by
the method which we found applicable for rigid income
streams, namely, the method of exchange, borrowing and
lending, or buying and selling. The alterations effected
by the latter means we s h d designate as before by the
algebraic addition of x:, x,': x?, . . . ., xlm,for succesThese have already been expressed in words in Chapters VI and
IX and geometrically in Chapter XI.

c3021

IN TmMS OF FORMULAS
sive yem. These are to be applied to the original income
items (the y's), deductions being included by assigning
negative numerical values. The income stream, aa finally
determined, will therefore be expressed by the successive
items,
y1'

+ x,:

vi'

+ x:t,

vi'

+ x?', . .., yl(m) '+

XI("').

*

82. Impatience Principle A . (n(m - 1) Eqmtion8)
Impatience Principle A states that the individual rates
of preference are functions of the income streams, and
gives the followingequations:
fl' = F; ( ~ 1 ' X,: yy,N X,': ..... ~1'"') ~1("')),
fi= Fi (9; ai', vi' X/, ..... ~ 2 ' ~ ) G'"')),

+
+

+
+

+

;+
.................................................
..............................................
f,,' = F,,' (y,,' + X,', y,," + X,,", ..... y:"') + x ~ " " ) ) .

But these equations express the variousindividuals'
rates of impatience only for the first year's income compared with the next. (They are the slopes of the Willingnesslines.)
To express their impatience for the
second year's income compared with the third, there will
be another set of equations, namely:
fl" = F," ':y(
X:', y
":
X:",
vl("') X*("')),
= Fi' (9;'
X/, y p
q'", ..... -, y2(n) %(m)),

+

+

........

+

fc
+
+
+
..................................................
..................................................
f," = F,," (y," + xif, y,,"' + X,,"', .......yS(-) + X.("')).

For the third year, as compared with its successor,
there wouldbe another similm set, with '" in place of
", and 80 on to the ( m - 1) year as compared with the
last, or m year, Since each of these ( m - 1) group of
c 303 1

THE THEORY OF INTEREST
equations contains n separate equations, there are in
all n ( m 1) equations in the entire set expreasing Impatience Principle A.

-

-

$3. Impatience Principle B (n(m 1) Equations)
Impatience Principle B requires that the rates of time
preference and of interest shall be equal. This relationship isrepresented by the same equations as given in
Chapter XII, namely:
3 = fl’ = fi’
....... = fit
a‘! = fl” - fi“ =i
= f?,

=.

.......

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

.........................................
=
=
= ......... = jJ-1).

i(cn-1)

fl(m-l)

fi(m-l)

Here are n(m - 1) equations expresing Impahience
Principle B.

Market Primziple A . ( mEquations)
The sets of equations which express Market Principle
A, the clearing of the market, are also the same aa before, namely:
:x
X[’+. .............
x; = 0,
XI’’ + x2‘t
............. :x = 0,
$4.

+

+

+

+

..................................
..................................
ZI(*) +
+ ......... + xn(m) = 0.
x2(m)

Here are

M

equations expressing Market Principle A.

$5. Market Principle B. (m Equutiom)
Market Principle B, the equivalence of loans and discounted repayments, is also represented algebraically as
before, namely:

c 304 I

IN TERMS OF FORMULAS
a
'
'
'
~ ' ~ + ( L + i ' ) ( l + ~ ~ ~ ) + . ' . +(l+i")..(l+i(")-J
(l+i)
2,"

+ * . * + ( I + $ ) (l+i") .... (l+ic"-1))=O~
.....................................................................
+r n )

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

..,, (I+i(rn-l)) "O.

Zn(")

Zn"
Z"'+l+f

+ . a * +

( I + $ ) (1+i")

These are n equations expressingMarket Principle B.
$6. Investment Opportunity Principle A. ( n Equations)

The equations in the four seta just revieweddiffer
from the equations of Chapter XI1 only in the first set,
which contain yfs in place of c's. The c's were supposed
t.0 begiven or known, but the y's are newunknown
quantities. Consequently, the number of unknowns is
greater than the number in the first approximation,
whereas the number of equations thus f a r expressed is
thesame.
The additional equations needed are supplied by the
two Investment Opportunity Principles, namely, Investment Opportunity Principle A, that the range of choice
is a specified list of optional income streams, and Investment Opportunity Principle B, that the choice amongthe
optional income streams shall fall upon that one which
possesses the maximum present value.
The range of choice, i.e., the complete list of optional
income streams, will include many which are ineligible
those which wouldnot be selected whatevermight be the
rate of interest-whether that rate be zero or one million
per cent. Excluding all ineligibles the remaining options
constitute the effective range of choice which in Chapter
XI is pictured as the 0pportunit;v line.
[ 305 ,I

THE THEORY OF INTEXtEST
If this list of options be assumed for convenience of
analysis to consist of an infinite number of options varying from one to another, not by sudden jumps, but continuously, the complete list canbeexpressedbythose
possible values of y{, y1”, .yl(m)which will satisfy an
empirical equation. There wiU be one such equation for
each individual, thus:

..

= 0,
4)2 (Yz’, !h”, * * .YYZ‘”’)
= 0,

%(Yl’,

Yl”.

* y1‘”’)

......................
......................
( y i , Y/,

%
I

.*

*

yn(m))= 0.

Here are n equations, expressing the Investment Opportunity Principle A. The form of each of these equations
depends on the particular technical conditions to which
the capital of the Individual concerned is subjected. It
corresponds to the 0 h e of Chapter X I except that only
two years were there representedwhereas here all m
years are represented. Any one equation seta the limitations to which the variation of the income stream of a
particular individual must conform. Each set of values
of gl’,y?, , .gl(”)which will satisfy this equation r e p
resents an optional income stream.

.

-

$7. Oppvrtunity Princiile B. (a(m 1) Equations)
Out of this infkite number of options the individual

has opportunity to choose any one rather than any other.
That particular one will be chosen for which the pment
value is greater than for any other, in other words, is the

maximum.
If the eptions M e r by continuous gradations this
03@31

IN TERMS OF FORMULAS
principle that the maximum present market value is
chosen is the same aa the principle that rl, the marginal
rate of return over cost, shd be equal to i, the market
rate of interest.
This is true for each year-to-year relation, so that we
have,for Individual 1, the followingcontinuous e q u s
tions:
if =r; =r; =...=r,',
3' = rl" = r2ff= , = T, t#,

..

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

p-1)

= r l ( o - ~=
) r 2 ( o - ~=
)

. , . = r*(o-~).

Here are n ( m - 1) equations expressing Investment
Opportunity Principle B.
88. Counting the Equations and Unknowns
Collecting our various counts of the numbers of e q u s
tions, we have:
For Impatience Principle A, n(m - 1) equations
$6
B,n(m - 1)
"
(6
" Market
A, m
it
I'
(I
B, n
For Investment Opportunity Principle A, n equations
((

((

((

I(

((

('

'I

B,n ( m - 1)

- +

((

The sum total of these is 3 4 m 1) 2n 4- m, or
3mn+m-nn.
To compare this number withthe number of unknowns,
we note that all the unknowns in the first approximation
am repeated ;
'For the mathematical8tetement on this equivalence me A p p e n b
to thie chapter (Chapter XIII), 03.

[: 307

1

THE THEORY OF INTEREST
the number of f's being n (m - 1)
(6
tt

"

" 2'8

It

It

"

ips

+

mn

??a-1
m - n - 1 camied forward
I'

making a total of 2mn
from the first approximation.
In addition, the new unknowns, the y's and the r's, are
introduced. There is one y for each individual for each
year, the total array of y's being
,:y y,:' * #lC*),

-

vi,Yz", ' * * ,Y2?

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

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

YJ,vc,.
* ',Yr(").
The number of these y's is evidently mn.
There is one r for each individual for each pair of successive years, i.e., first-and-second,second-and-third,etc.,
and next-to-kt-and-last years, the totalarray of r's being
r:, r p , . .,rl(m-l)
r;, ri', . ., r2(m-l)

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

rJ, rJ?,. ., ri-l).
T h e number of these r's is evidently n(m - 1).
In d,then, the number of new unknowns, additional
to the number of old unknowns carried forward fromthe
first approximation, is mn n(m - l), or 2mn - n.
Hence we have:
number of old unknowns, 2mn m - tt 1,
number of new unknowns, 2mn - n,
= total number of unknowns, 4mn m - 2n - 1,
as compaxed with 3mn m - n equations.
c 3 w
!+

+

+

+

-

+

IN TERMS OF FORMULAS
$9. Reconciling t h Numbers of Equutwna and

Unknowns

The reconciliation of thesetwodiscordant results is
effected by two considerations. One reduces the number
of equations. Just t
u under the first approximation, we
have one less independent equation in the two sets expressing the Market Principles than the apparent number, thus making the hal net number of equations

3rn+rn””-.
The other consideration is quite different. It subtracts
from the number of unknowns. This can be done because eachT, of which there are n ( m - l), is a derivative
from the y’s. By definition T is the excess above unity of
the ratio between a small incrementin the y of next year
to the correspondingdecrementin the y of this year.
The same applies to any pair of successive years. This
derivative is, moreexplicitly expressed, a Merentid
quotient.8
The reader not familiar with the notation of the differential calculus will get a clearer picture of the inherent
derivability of the r’s from the y’s by recurring to the
geometric method in Chapter XI. There v’ and y” are
shown as the coiirdinates (“latitude” and “longitude”)
of the Opportunity line, whiler is shown w the tangential
slope of that line. It is evident that, given the Opportunity line, its tangential slope at any point is derived
from it. It is not a new variable but is included in the
variation of y‘ and f r as the positionon the curve
changes.
If,now, we subtract n(m - l), the number of the t’s,
‘See Appendix

to this chapter (Chapter XIII), 01.

c3091

TRE THEORY OF INTEREST
from 4mn m - 2n - 1, we have, as the findnet number of unknowns,

+

3mn+m-n-l

which is the same as the total net number of independent
equations.' Thus t.he problem is fully determinate under
the assumptions made.
'Instead of thus banishing the t's, an alternative reeonciliation is
to retain them but to add for each m equation of definition of 1 r.
Thus 1 r{ (corresponding to the slope of the Opportunity Curve)
is a derivative from the y"s and y"'a of the twosuccessive years
called this year and the next (in other words, a partial derivative)
malung 1 r,' dependent upon (in other words, a function of) the y's.

+

+

That is,

+

r; = cpl(yl', VI",

...,~ d m ) ) ,

which function is empirical and derivable from the opportunity function
cp already given.
Analogously we may expreea the equations of definition for r;, r,' . .rm'
and likewise for the corresponding r" 's, r'" 's, etc., up to
' 8 making
n(m-1) equations of definition. In this way,retaining the r's we have
4mn m - 2 n - 1 independent equations and the same number of

+

UnknOWnS.

The complicationmentioned in Chapter VII, 810, that the income
stream iteelf depends upon the rate of interest, does not affect the
determinateness of the problem. It leaves the number of equations and
unknowns unchanged, but merely introduwa the rate of interest into the
set of equations e x p r e d g the Opportunity principles. These equations
now become
cpl(yr',

VI",

...,y m ;

9, i",

...,i(m)) = 0

etc., and their derivativee, the $ functions, are likewise altered in form
but not in number.
The mathematical reader will have perceived that I have studiously
avoided the notation of the Calculue, aa, unfortunately, feweconomic
etudents are, aa yet, familiar with that notation, and as it has seemed
fairly well without ita
See,
po~aiblehere to express the same red@
however, the A p p e d x to tbis chapter (Chapter XIII), €14.

use.

c 310 1

IN TERMS OF FORMULAS
$10.Zero or Negative Rates of Interest

We have alreadyseen (Chapter XI, $9), that zero
or negative rat,es of interest are theoretically possible. In
terms of formulm all that is needed to make the rate of
interest zero is that the forms of the F and 9 functions
shall be such as to produce this result. This implies that
these functions shall have solut.ion values equal to zero.
Of course it would be possiblethat interest, impatience,
and return over cost for oneparticular year might be zero
or negative without this being true for other years. If they
were zero for all the years, we should have the interesting
result that thevalue of a finite perpetual annuity (greater
than zero per year) would be infinity. No one could buy
a piece of land for instance, expected
to yield a net income
forever, for lessthan an infinite s u m , A perpetual government bondfromwhich an incomeforever was assured
would have an infinite value. Since this is quite impracticable, we thereby reduce to an absurdity the idea that
it is possible to have at one and the same time:
1. A zero rate of interest for each year forever; and
2. a perpetual annuity greater than zeroperyear.
But the absurdity is lessened or disappears altogether
if either:
1. The zero rate of interest is confined to one year; or
2. no perpetual annuity greater than zero per year is
possible.
Unusual conditions may easily reduce the rate of interest foroneyear to zero. As to an unproductive or
barrenworld, like the hard-tack island,only a finite
totality ofincomewould be possible; 8 perpetual annuity even of one crumb of hard-tack a year would be

impossible.

c 311 1

THE THEORY OF INTEREST
811. The Fornula Method Helpful

While this and the previous chapter are largely restatements in terms of formulas of Chapters X a,nd X I
in t e r m of diagram, which, in turn were largely restatements of Chapters V and VI in terms of words, nevertheless, these formula chapters have a value of their
own, just a8 did the geometric chapters.
In particular, the formula method has value in showing
definitely the equality between the number of equations
and the number of unknowns, without which no problem
of determining variables is ever completely solved.
It is for this reason that these restatements are included in this book. In fact, if I were writing primarily
for mathematically trained readers, I would have reversed
the order, givingthe first place to the formulas, following
these with the charts for visualization purposes, and ending with verbal discussion. Each method contributes its
distinctive help toward a complete understanding of what
is, at best, a d8icult problem to encompassby any
method at all. I have, therefore, includedin these formula
chapters, as in the geometric ones, severalpoints not well
adapted to the more purely verbal presentations of Chapters V and VI.
Twocorollaries follow.One is that any attempt to
solve the prcxblemof the rate of interest exclusively as
one of productivity or exclusively aa one of psychology
is n d y futile. The fact that there are still two
schools, the productivity school andthe psychological
school, constantly crossing swords on this subject is a
scandal in economic science and a reflection on the inadequate methods employed by these would-be destroyers
of each other. Each sees half of the truth and wrongly
312 1

c

IN TEXMS OF FORMULAS
infers that it disproves the existence of the other half.
The illusion of their apparent incompatibility is solely
due to the failure to formulate the problem literally and
to count the formulas thus formulated.
The other corollrtry is that such a formulation reveals the necessity of positing a theoretically separate
rate of interest for each separate period of time, or to put
the same thing in more practical terms, to recognize the
divergencebetween the rate for short t e r m s and long
terms. This divergence is not merely due to an imperfect
market and therefore theoretically subject to annihilation
by arbitrage transactions, as Biihm-Bawerk, for instance,
seemed to think. They are definitely and normally distinct and due to the endless variety in the conformations
of income streams. No amount of mere price arbitrages
could erase these differences.
Thus, there should always be, theoretically, a separate
market rate of interest for eachsuccessiveyear. Since,
in practice, no loan contracts are made in advance 80
that there axe no market quotations for a rate of interest
connecting, for example, one yearin the future with two
years in the future, we never encounter such separate
year to yew rates. We do, however, have such rates implicitly in long term loans. The rate of interest on a long
term loan is virtually an average * of the separate rates
‘It ia true, of come, that the attempt to make an individual’s income
stream more even by trading onetime-portion of it foranother ten&
toevenup
the varioue raka of interest pertaining to various time
periods. But thia ie not price arbitrageand not properly to be c$led
arbitrage at all, being more analogous to the partial geographic equalization of freight charges in the price of wheat by intemtioxd trade b
to the equalization by arbitrege of wheat prim in the same &et
et
the =me time.
‘The nature of this average has been expremd in Appredctior, d
Inter&, pp. 26 to 29, and The Rate 01 I-,
pp. 36@ to
It b

c 313 3

373.

THE THEORY OF INTEREST
for the separate yeam constituting that long term. The
proposition afErming the existence of separate rates for
separate yews amounts tothis: that normally there should
be a difference betweenthe rates for short term and long
term loans, sometimes one beingthe larger and sometimes
the other, according to the whole income situation.
impossible to give a concrete example of an average of a rate of inter-

est for a long term loan as an average of the year to year rates, because
as already noted, the year to year rates have only a hypothetical
existence. The nearest approach to the concrete exietence of separate
year to year rates is to be found in the Allied debt settlementa, by
which the United States agreed that Italy, France, Belgium, and other
'
countries should repay the United States through 62 yeam, with specific rates of interest changing from time to time. These are equivalent
to a uniform rate for the whole periodaccording to theory. For
instance, the proposed French debt settlement provided for annual
payments extending over 62 years, beginning with 1926 at interest rates
varyingfrom 0 per cent for the firat 5 years, 1 per cent for the next
10 years, 2 per cent for another 10 years, 2% per cent for 8 years,
3 per cent for 7 years, and 3% per cent for the laat 22 years. The
problem is to find an average rate of interest for the whole period which
when applied in discounting the various payments provided for in the
debt settlement, will give a present worth, as of 1925, equal to the principal of the debt fixed in that year, namely, $4,025,OOO,OOO. Clearly no
form of arithmetic mean, weighted or unweighted, will give the desired
rate. A rough computation indicatea that the rate probably falls between
1% per cent and 1% per cent. Discounting the annual payments by
compound discount gives a total worth in 1925 a t 1% per cent of
$4,197,990,000; at 1% per cent of $3,893,610,000. These results show that
1% per cent is too low, since the present worth obtained by discounting
at this rate is greater than the principal sum whichwaafixed
at
)4,025,ooO,ooO. The rate 1% per cent is too high because the diecounted
present worth is lem than the principal.
Discounting the annual payments at 1.8 per cent we obtain WP72,630O
, OO. We can now locate three points on a curve showing the interest rates oorreeponding to Werent preeentvalues.By
projecting B
parabolic cupye through the three determining pointe, we find the
ordinate of the point on the curve which haa the a b a c k of S4,0!26,oOO,OOO
is 1.64. Hence the average rate of intercut for the whole period, w
iR very mmw margin of error,
IM per cent.

t 314 1

IN TERMS OF FORMULAS
The contention often met with that the mathemtical
formulation of economic problems givesa picture of theoretical exactitude untrue to actual fife is absolutsly
correct. But, to my mind, this is not an objection but LC
very definite advantage, for it brings out the principles
in such aharp relief that it enables us to put our finger
definitely on the points where the picture is untrue to

life.
The object of any theory is not to reproduce concrete

facta but to show the chief underlying principles aa tendencies. There is, for instance, the very real tendency
for aJl marginal rates of time preference and all marginal rates of return over cost to equd themarket rates of
interest. Yet this is only a tendency, an ideal never attai~~ed.~
‘For brief comparison of Chapters XI1 and XI11 with other mathematical formulatione see Appendix to this chapter (Chapter MII).

C 315 1

CHAPTER XIV

THE THIRD APPROXIMATION UNADAPTED TO
MATHEMATICALFORMULATION
$1. Introduction

THEsecond approximation fails to conform to conditions of actual life chiefly with respect to risk. While it
is possible to calculate mathematicdy risks of a certain
type like those in games of chance or in property and
life insurance where the chances are capable of accurate
measurement, most economic risks arenot 80 readily
meamred.l
To attempt to formulate mathematically in any meful, complete manner the lam determining the rate of
interest under the sway of chance would be like attempting to express completely the laws which determine the
path of a projectile when affected by random gusts of
wind. Such formulas would need to be either too general
or too empirical to be of much value.
In science, the most useful formulas are those which
apply to the simplest cases. For instance, in the study
of projectiles, the formula of most fundamental importance is that which appliea to the path of a projectile in
vacuum. Next come8 the formula which applies to the
path of a projectile in stdZ air. Even the mathematician
declines to go beyond this and to take into account the
effect of wind cuments, still l e m to write the equations

S
' ee The Natwe of Capita! and Income, Appendix to Chapter XVI.
[ 316 1

THIRD APPROXIMATION
for the path of a boomerang or a feather. If he should
do so, he would still fall short of actual conditions by
assuming the wind to be constant in direction and velocity.
Scientific determination can never be perfectly exact.
A t best, science can only determine what would happen
under assumed conditions. It cannever state exactly
what does or will happen under actual conditions?
We have thus far stated verbally, geometrically, and
algebraically the laws determining interest under the
simpler conditions first, when it was assumed that the
income streams of individuals were both certain and
fixed in amount, but variable in time shape, and, 6econdly,when it WCIS assumed that the income streams
were certain, but variable in amount as well as in time
shape. Wehave also considered verballythe interest problem under conditions of risk found in the real world.

$2. The Six Sets of Formulas Incomplete
All that I &all attempt here is to point out the shortcomings of the six seta of formulas in the second approximation. Impatience Principle A in the second approximation is expressed by formulas of the type:

+

+

f = F (1/ f,f ' + ' f '.,. .,y(n) dm))
indicating that a person's impatience is a function of his
income stream aa specificallyscheduled,indefinitely in
the future.
Of course, in the uncertainties of actual l i e no such
specific scheduling is possible. The equation is true but
incomplete, as f is properly not only a function of one ex'See my artiole, E&
ab a Seienae, in ptoceedings of the American Aerrociation for the Advancement of &ience, Vol. LvI, 1901.

I:317 3

THE THEORY OF INTEREST
pected income program but of many possible such programs each with its own series of probabilities, and those
probabilities are too vagueeven to bespecificallyexpressed or even pictured by the person concerned. That
is, the average person is merely aware that he is willing,
my, to pay fiveper cent for a $loo0 loanbecause he
thinks his future prospects will justify it. He vaguely
expects that his present $lO,OOO income will probably rise
to $20,000 within a few years, possibly to $30,000-and
possibly not rise at all. He could think of innumerable
possibilities and these would imply many other variables
than those above cited. Much might depend on the income of others besides himself and on the future size of
his family, the stateof their health, and other conditions
without end. His own future income is the important
matter, but that itself is dependent on all sorts of variables onwhich he will reckon summarily in a rule of
thumb fashion.
We could, formally,rewrite for the third approximation
the above equation so aa to read:
merelyrefusing to attempt any enumeration of the
innumerable variables inside the parentheses-among
them being, perhaps, all the variables included in all the
equations in the second approximation, including rates
of interest as well as numberless other variables such as
probabilities not there included. In so f a r as the latter,
or new, variables enter, each of them requirea a new
equation in order to make the problem determinate.
Such new equations would be merely empirical. Among
the equations which would be needed,would be those
expressing the y’s and 5’s in term of red income-that

c 318 3

THIRD APPROXIMATION
is, aa the s u m of the enjoyable services, each multiplied
by ite price. This would lead us into the theory of prices
and the general economic equilibrium.
Impatience Principle B wasexpressed in the second
approximation by formulas of the type:
i = f.
But now we must face not only one i but a series of 28,
according as the market is the call loan market, the 60
to 90 day commercial paper market, the gilt-edge bond
market, the farm mortgage market, and innumerable
others, for eachof which there is its own separate f m d i.
These many magnitudes, including the i’s, require still
other empirical equations impossible to formulate satisfactorily, albeit we know in a general way that the rate
on gilt-edge bonds is lower than on risky bonds, the rate
on first mortgages lower than that on second mortgages,
and that the long term and short term markets do influence each other. But these relations are too indefinite to
be put into any equat,ions of real usefulness, theoretical
or practical
Investment Opportunity Principle A was expressed by
formulas of the type
qJ (g’, y”, . . . ., y‘”’) = 0
Thia becomes
pO=O

where the blank parenthesis st.mds for a multitude of
unknowns (and unknowables) which could be d i s c u d
ad infinitum and each of which, in 80 f a r as it was not
already included among the variables entering into our
system of equations, would require a new empirical equa~
tion of some sort in order that the problem shall be determinate. Moreover, the Q, equation representing a

I: 319 1

THE THEORY OF INTEREST
man’s ensemble of income opportunities is a composite
of separate opportunities, the full and detailed expreasiori
of which would take us again into the theory of prices
and general economic equilibrium.
Investment Opportunity Principle B, expressed in the
second approximation by equations of the type
d = r,
would have to be replaced by BS profuse a variety 88
replaced the i = f above.
A full statement of the margins of investment opportunity wouldinclude the margins of numberlessindividual enterprises and adjustments in the use of every
item of capital. It would again lead us into the theory
of prices and general economic equilibrium. W&BS and
Pareto have formulated systems of equations whichdo
this and in which the theory of interest is merely a part
of a larger whole.
Market Principle A, expressed in the second approximation by equations of the type
x1+x2+ ....+ xm =o,
will remain true only if or in so far as performance of
contracts corresponds to promises and expectations. In
so f a r as, because of defaults, the equations fail of being
precisely true, no useful mathematical relation expressing that failure seems possible.
The same is true of Market Principle B, expressed
under the second approximation by formulas of the type
X”
z(n)
~ f + ~ + ~ ~ ’ ~ + ( l + ~ ’ ) ( l + ~ ~ ~ . , . .

to say nothing of the fact that this type of equation w
l
l
i
take many different form in view of the variety of i’s
and in view of the probability factors.
c
3
~

THIRD APPROXIMATION
The onlyexplicit practical inclusion of suchprobability factors, mathematically, is to be found in the formulas of life insurance actuaries. But these are of little
more than suggestive value in our present effort to express the determination of the rate of interest.

$3. Conclusions
We must, therefore, give up aa a bad job any attempt
to formulate completely the influences whichreally determine the rate of interest. We can say that the system
of equations which has been employed would fully determine the rate of interest were it not for disturbing
factors; that it does do so in combination with those disturbing factors; and that this amounts to saying that it
expresses the fundamental tendenciesunderlying those
disturbing factors.
In short, the theory of interest in this book merely
covers the simple rational part of the cause8 actually in
operation. The other or disturbing causes are those incapable of being so simply and rationally formulated.
Some of them may be empirically studied and will be
treated in Chapter XIX. They pertain to statistics rather
than to pure economics. Rational and empirical laws in
economics are thus analogous to rational and empirical
laws of physics or astronomy. Just &s we may consider
the actual behavior of the tides as a composite result of
the rational Newtonian law of attraction of the moon
and the empirical disturbances of continenb, islands, inlets, and so forth, so we may consider the actual behavior
of the rates of interest in New York City as a composite
of the rational laws of our second approximation and the
empirical disturbances of Federal Reserve policy together
with numberless other institutional, historical, legal, and

c 321 1

THE THEORY OF INTEREST
practical factors. All of these are worthy of careful study
but are not within the scope of the mainproblem of
this book.
In some cases, as in the theory of the moon’s motions,
the pertunbations may beworked out with a high approximation to reality by combining rationally a number of elementary influences. Such resolutionof empirical
problems represents the highest ideal of applied science.
But until that stage is reached there remains a wide gap
between rational and empirical science,and the two have
to be pursued by somewhat Merent methods. That is
the case with economic science in most of its prablems
today.s
In respect to our present problem,while there is a
great field for research, the only perturbing influence of
t.ranscendent importance is that of an unstable monetary
standard, and, as w&s seen in Chapter 11, even that would
make nothing more than a nominaldifference in the
results if it were not for the “money illusion.”
But with respect to this disturbance, theory and practice are miles apart. The disturbances of unstable money
often reverse the normal operation of those supposedly
fundamental forces which determine the rate of interest
and are the chief subject of our study in thisbook.
8See

Mitchell, Wesley C., Qwmtitative Analysis in Economic Them.
March 1925, pp. 1-12.

American Eu-Jnomic Review, Vol. X V , No. 1,

PART IV. FURTHER DISCUSSION
CHAPTER XV. THEPLACE OF INTEREST
IN ECONOMICS
CHAPTER
XVI. RELATION
OF DISCOVERY
AND INVENTIONTO INTEREST RATES
CHAPTERXVII. PERSONAL AND BUSINESSLOANS
CHAPTERXVIII.
SOMEI L L U S ~ T I FA^
VE
CHAPTER XIX. THERELATION
OF PRICESAND INTEREST
RATES
CHAPTER XX. OBJECTIONS
CONSIDERED
CHAPTER

=I.

SUMMABY

CHAPTER XV
THE PLACE OF INTEREST IN ECONOMICS
$1. Interest Rates and Values of G o o h

HAVING
completed the exposition of the theory of the
causation and determination of the rate of interest which
is most acceptable to me, it now remains to &owhow
this theory fits into a complete systemof economic theory
and what results must flow from its acceptance.
Interest plays a central r6Ie in the theory of value
andprices and in the theory of distribution. The rate
of interest is fundamental and indispensable in the determination of the value (or prices) of wealth, property,
and services.
As w&s shown in Chapter I, the price of any good
is equal to the discounted value of ib expected future
service,includingdisservices
aa negative services. If
the value of these services remains the same, a rise or
fall in the rate of interest will coneequently cause a fall
or rise respectivelyin the vdueof all the wealth or prop
erty. The extentof this fall or rise will be the greater the
furtherinto the futurethe services of wealthextend.
Thus, land valuesfromwhich services &re expected to
accrueuniformly and indefinitely will be practically
doubled if the rate of intereat is halved, or halved if the
rate of interest is doubled. The value of dwellings aad
other goods of definitely limited durability will fall less
than half if interest rates double, and will riae to less than

c 325 1

THE THEORY OF INTEREST
double if interest is halved. Fluctuations in the value of
furniture will be even less extensive, clothing still less,
and very perishablecommodities like fruit will not be
sensibly dected in price by a variation in the rate of
interest. In all the foregoing CBSB it is, of course, assumed that the expected services remain unchanged.

$2. Interest Rates and Values of Services

As to the influence of the rate of interest on the price
of services, we first observe that services may be either
find or intermediate.’ The value of a dinner about to be
eaten involves no time of waiting and so no discount or
interest. Nor does the irksomeness of labor about to be
undertaken invohe discount to the laborer. Both the dinner or its enjoyment and the labor are final items of income, the one positive and the other negative. The value
of intermediate services (“interactions”) is derived from
the succeeding future services to which they lead. For
instance, the value to a farmer of the services of his
land in afTording pasture for ,sheep will depend upon the
discounted value of the services of the flock in producing
wool. If he rente the land, he will calculate what he can
afTord to pay for it on the basis of the value of the wool
which he would expect to obtain from his flock. In like
manner, the value of the wool output to the woolen
manufacturer is in turn influenced bythe discounted
value of the output of woolen cloth to which it contributes. In the next stage the value of the production of
woolen cloth will depend upon the discounted value of
the woolen clothing to which that cloth contributes.
Finally,the value of the last named will depend upon
the expected real income which the clothing will bring
‘See Chapter I;

also Ths Natve of CapikJ a d Income, Chapter JX.

[ 326 1

THE PLACE OF INTEREST IN ECONOMICS
to those who wear it, in other words,upon the use or
“wear” of the clothes.
Thus the find services,consisting of the use of the
clothes,will have an influence on the value of all the
anterior services of tailoring, manufacturing cloth, producingwool, and pasturing sheep,whileeach of these
mterior services,whendiscounted,willgive
the value
of the respective capitals which yield them, namely, the
clothes, cloth, wool, sheep, and pasture land. The values,
not only of all articles of wealth, but also of all intermediate services which they render, are dependent upon
the values of final enjoyable uses. Capital valuea and
values of final wes are linked by the rate of interest. A
rise or fall in the rate of interest will be felt most by
the links most distant from these final services.A change
in the rate of interest will tend to affect but slightly the
price of making clothing, but it will tend to &ect considerably the price of pasturing sheep.
The theory of prices, so far as it can be separated into
parts, includes: (1) explanation of the prices of final
services on which the prices of anterior interactions
depend; (2) explaaation of the prices of intermediate
interactions, aa dependent, through the rate of interest,
on the W services; (3) explanation of the prices of
capital instruments aa dependent, through the rate of
interest, upon the prices of their final services. The first
study, which seeks merely to determine the laws regulating the price of final services, is independent of the rate
of interest?
The second and third problems, which seek to show
the dependence on final aervices of the intermediate ser‘8ee my M a t h m a t i d InveebigcltioM in tire T h e w of Vdue crnd
A i c e s . New Haven, Yale University Press, IQB.
I327 I

THE THEORY OF INTEREST
vices and of the capital which bears them, involve the
rate of interest. Under this second study will fall, as a

'

special case, the study of the determination of economic
rent, the rent ,both of land and of other instruments of
wealth. The rent of a pasture consists of the value of
the services of pasturing. This value, in accordance with
the principlesexpounded in Chapter I, is dependent
through the rate of interest upon the discounted value
of the future final services to which the pasturing contributes. It is clear, then, that the rent of the land is
partly dependent upon therate of interest, and that
the samedependence applies to the rent of any other
instrument.
$3. Interest Rates and Wages
Similar considerations apply to the determination of
the rate of wages. From the standpoint of the employer,
the payment of wages to a workman supposedly represents the value of his services. These services are interactions, or intermediate services,leading ultimately to
some future enjoyable service. Thus the shepherd, hired
by the farmer to tend the sheep in the pasture, renders
services the value of which to the farmer is estimated
in precisely the same way as the value of the services of
the land which the farmer hires.
Consequently, if interest varies, wages will vary. Thus,
if the h d is used for farming, the wages paid for plating crops will be gauged in the estimate by the farmer
l
l
i
by discounting the value of the expected crops and w
vary somewhat according to whether the discounting is
at 5 per cent or at 4 per cent. In Iike mmner the workers engaged in bridge building are presumed to be paid
the discounted value of the ultimate benefits which .will
13281

\

THE PLACE OF INTEREST IN ECONOMICS
be yielded by the bridge. The wages of those engaged in
makinglocomotivesnormally represent the discounted
value of the completedlocomotives, and hence, aa the
value of a completed locomotiveis in turn the discounted
value of its expected service, their wages represent t.he
discounted value of the ultimate benefits in the series.a
In all thesecases, the rate of wages is the discounted
value of some future product, and therefore tends to decreme as interest increases. But the effects in the different lines w
l
l
ibe very unequal.
Wages of domestic servants and those engaged in putting the finishing touches on enjoyable goods will have
their wages affected comparatively little by the rate of
interest. On the other hand, for laborerswho are engaged
in work requiring much time the element of discount a p
plied to their wages is a considerably more important
factor. If a tree planter is paid $1 because this is the
discounted value at 5 per cent of the $2 which the tree
will be worth when rmttured in fifteen years, it is clear
that a change in the rate of interest to 4 per cent will
tend materially to increase the value of such work. Supposing the value of the matured tree still to remain at
$2, the value of the services of planting it would be not
one dollar but $1.15. On the other hand, for laborers engaged in a bakery or other industry in which the find
satisfactions mature early, the wages are more nearly
equal to the vdue of these products. If they produce
final services worth $1, due, let us say, in one year, their
wages would be 95 cents when the interest rate is 5 per
cent and 96 cents if interest falls to 4 per cent.
It is clear, nevertheless,that such unequal effectscorn'Thh ie,of cbw,highly theoretical; it 888umea a competitive market
free from legal and other rerrtrictions.

~3291

THE THEORY OF INTEWST
ing from a reduction in therate of interest, as an increase
from $1 to $1.15 in one industry and from 95 cents to
96 centa in another, could not remain permanently. Labor
will tend to shift from the lower paid to the higher paid
occupations until equrtlity of wages for workers of the
same skill is reestablished. In the end,therefore, the
change in $he rate of interest from 5 per cent to 4 per cent
would effecta redistribution in the vslues of intermediate
items of income and in final items of income.
Evidently then, the effect of a change in the rate of
interest on the value of interactions will naturally be the
more pronounced in a country where lengthy processes
are usually employed than in one where the shorter ones
are common. If, for instance, laborers in a given country
are engaged Iargely in building elaborate works, such aa
the Panama Canal, orin digging tunnels and constructing
other great engineering works, or in planting forests and
otherwise investing for the sake of remote returns, a f
d
in the rate of interest will produce a considerable rise
in wages, whereas, in a country where suchlengthy procewes are unknown and workmen are chiefly employed in
tilling the ground and performingpersonalservices, a
change in the rate of interest will hardly &ectwages
or the values of other preparatory services at all.
What has been said, however, applies only to wages
from the standpoint of the employer. The rate of wages
is dependent upon supply as well as upon demmd, that
is, upon the willvlgness of the workman to offer his services, as well as upon the desire of the employer to secure
them. From the standpoint of the laborer, wages constitute an incentive to exertion or labor. This exertion is a
find disservice, or negative item of income, and its valuation by the laborer is not directly affected by the rute of

E3301

THE PLACE OF INTEREST IN ECONOMICS

anterest, as are other services which are not final but intermediute. It is a great mistake to treat the subject of
wages, as many authors do,exclusivelyfrom the employer’s standpoint. The purpose here is not to undertake
to outline a complete theory of wages, but merely to
show why a complete wage theory must take cognizance
of interest and must explain how the interest rate affects some wage rates and not others.
$4. Interest and Functional Distribution

In the theory of distribution interest must be aasigned
a quite different and muchmore important r61e than
economists thus far have given to it. In classical economics the nature of interest and its place in distribution
were not clearly understood. Distribution has been erroneously defined as the division of the income of society
into “interest, rent, wages, and profits.” Rent and interest
are merely two ways of measuring the same income ;
rent, aa the yield per acre or other physical unit, and interest aa the same yield expressedaa a per cent of capital
value. The value of the capital is derived from the income which it yields by capitalizing it at the prevailing
rate of interest. To reverse this process by multiplying
the capitd vdueby the rate of interest gives the original
income, aa long aa the capital value remains stationary.
I t is not really a complex product of two factors, but, on
the contrary, is the single originalfactor, namely, income,
from whichwe started. As explained in previous chapters,
it is this income which affords the basis for the determination of the &e of interest, and through the rate of
interest, of capital value.
The hal enjoyable income of society is the ultimate
andbasic fact fromwhich all values are derived and
c3311

THE THEORY OF INTEREST
toward which all economic action is bent. All of this
income is derived from capital wealth, if land and man
are included in that term, or if not, from capital and man,
or capital, land, and man, according to the terminology
adopted. This income may all be capitalized, and hence
all income(excluding capital gain) may be viewed as
interest upon the capital value thus found.
Viewed as above outlined interest is not a part, but the
whole, of income (except for capital gain). I t includes
what is called rent and profits and even wages, for the
income of the workman may be capitalized quite as truly
as the income of land or machinery. Thus, instead of
having interest, rent, wages, and profits as mutually exclusive portions of socialincome, interest may be regarded as including all four. If we prefer to exclude
profits, the reason is because of the element of risk and
not because profits are not discountable just as truly as
rent and wages. The error of the classicaleconomists
and of their modern followers in regarding interest, rent,
wages and profits as separate but coijrdinate incomes is
partly due to the failure to perceivethzlt,whereas all
income is produced from capital wealth, capital vdue
can emerge only from man’s psychic evaluation and capitalization of that income in advance of its occurrence.
Another oversightcloselyltssociatedwith
thelast
stated fallacy is that in which rent and wages are conceived aa determined independently of the rate of interest, whereas we have just seen that the rate of interest
enters aa a vital element into the determination of both.
The great defect in the theories propounded by the classical economistslay in their inability to conceive of a general equilibrium and the mutual dependence of sacrifice
and enjoyment.

C 332 3

THE PLACE OF INTEREST IN ECONOMICS
In discueeing the theory of distribution, we shall, there
fore, abandon the classical point of view entirely. The
claasical concepts of distribution are quite inappropriate
to explain the every day facts of life and the economic
structure. The phrase distribution of wealth, as understood by the ordinary man, implies the problem of the
relative wealth of individuals, the problem of the rich
and the poor. But the separation of the aggregateincome into four abstract magnitudes,even if correctly
done, has littIe to do with the question ofhow much
income the different individuals in society receive.
Only on condition that society WM composed of four
independent and mutually exclusivegroups,laborers,
landlords, enterprisers, and capitalists, would the fourfold
division of the classical economistsbe even partially d e quate to explain the actual distribution of income. In
fact, the four classes all overlap. The enterpriser is almost invariably a genuine capitalist and usually also
performs labor; the capitalist is frequently a landlord
and laborer, and even the typical laborer is today often
a amall capitalist and sometimes a landlord. It is true
that a century ago in England the lines of social classification corresponded roughlyto the abstract divisions proposed at that time by the classical economists. But this
fact is of little significance except as explaining historically the origin of the classical theory of distrib~tion.~
$5. Interest and Personal Distribution
The main problem of distribution, as I see it, is concerned with the determination and explanation of the
amounts and values of capitala and incomespossemed
'&e Cannan, Edwin, Thoties of production and Dt&ibuticm. hdon, P. 8. King dc Son, 1903.

CWI

THE THEORY OF INTEREST
by Merent individuah in society. It is astonishing how
little economistg have contributed to resolving the probl e m of distribution EO conceived. A statistid beginning
w&s made by Professor Pareto in his present&ionof
interesting “curves of distribution ofincome.” For the
United States, Professor W. I. King and the National
Bureau of Economic Research ?, and for England, Sir
Josiah Stamp have made and analyzed important statistical compilations on the amount and distribution of
income and capital wealth by income groups and social
classes. On the theory of distribution, especially the rcile
of interest in distribution, John Rae seems to have contributed more than any other writer O. He showed in a
vivid way that persons who had naturally what we have
called in this book a low rate of impatience or preference
for present over future income tended to accumulate
savings, whereas those who had t,he opposite trait tended
to spend their incomes and even their capitals.
In previous chapters it is shown that the rates of preference among different individurtls are equalized by borrowing and lending or, what amounts to the same thing,
‘Pareto, C a m 82-k
Politipue, Vol. 11, Book III.
‘King, W. I., The Wealth and Income of the People of the United
State, New York, The Macmillan Co., 1915.
‘Mitchell, W. C., King, W. I., Mseaulay, F. R.,Knauth, 0. W.,
Income in the United States. New York, National Bureau of Economic
Reeearch, Inc., 1922.
Knauth, 0.W.,Dietribution of I ~ ~ c o mbye i3tat-a in 1919. New York,
Harcourt, Brace & Co., 1822.
Leven, Maurice, and King, w.I., Income in the Vuriou8 &utes; Its
sovceS and DietribzLtion, 1910, f9#, and 19tl. New York, National
Bureau of Economic Resesrch, Inc., 1925.
‘Stamp, Sir Josiah, WeaUh and T d l e Capacily. London, P. 9.
King & h n , La., 1922. Also, Btitieh Incomes and Prqperty. London,
P. 8. King & Son, 1916.
’Rae, The Socidogid T h e w o? Capitd, Chapter XIII.

1WI.

THEPLACE OF INTEREST IN ECONOMICS
by buying and selling. An individual whose rate of preferencefor present enjoyment is unduly high w
l
l
icontrive to modify his income stream byincreasing it in
the pment at the expense of the future. The effects upon
incomes may be traced to capital by applying the principles explained in The Nature of Caplltal and Income,
Chapter XIV.
If a modification of the income stream is such as to
make the rateof realized incomerelative to capitd value
exceed the standard rate of income returns, capital will
be depleted to the extent of the excess, and the individual,
ligrow poorer. This
group, orclass, under considerationw
condition may be brought about either by borrowing immediate income and paying future income, or by selling
instruments whose returns extend f a r into the future
and buying those which yield more immediate returns.
Individuals of the type of Rip Van Winkle, if in possession of land and other durable instruments, will either
sell or mortgage them in order to secure the means for
obtaining enjoyable services more rapidly. The effect will
be upon society as a whole that those individuals who
have an abnormally low estimate of the future and its
needs will gradually part with the more durable instruments, and that these will tend to gravitate into the
hand5 of those who have the opposite trait.
By this transfer an inequality in the distribution of
capital is gradually eflected, and this inequality once
achieved tends to perpetuate itself. The poorer a man
grows the more keen is his appreciation of present goods
likely to become. When once the spendthrift is OD. the
downward road, he is likely to continue in the same direction. When he has succeeded in losing all his capital
except his own person, the process usually comee to an

c3351

THE THEORY OF INTEREST
end, becausecivilizedsocieties in self-protectionfrown
upon chattel slavery and involuntary servitude. Many
examples, however, of forced labor and even slavery still
survive. The negro farmers of the Southern States, the
Mexican peons, the peasants of Russia until recently, the
forced labor and slavery in many tropical colonies, such
tts Java,l0 the Congo, and other African countries, are
examples in point.
Reversely, whenan individual has saved a considerable
capital, his rate of preference for the present diminishes
still further,and accumulationbecomes still easier. Hence,
in many countries the rich and poor come to be widely
and permanently separated, the former to constitute an
hereditary aristocracy of wealth and the latter, a helpless proletariat.
This progressive sifting, by which the spenders grow
poorer and the savers richer, would go on even if, as assumed.in our first and second approximations, there were
no risk element. But it goes on far faater when as in
actual life there is risk. While savings unaided by luck
will ultimately enrich the saver, the process is slow as
compared with the rapid enrichment which comes from
the good fortune of those fewwho m u m e risks and
then happen to guess right. Likewise, while millions of
people lose their small properties by thriftlessness, the
more rapid impoverishment comes from guessing wrong.
This will often turn a rich man into a poor man within
a few years and sometimes within a few days.
It should also be noted, especially when the element
of uncertainty is taken into account, that borrowing may
be the m e w of gaining great wealth quite as well as of
See Day, Clive. The Dutch in Juva. New York, The Mscmillan CO.,
19M, Chapter X.
C3361

THE PLACE OF INTEREST IN ECONOMICS
losing it. The business borrower who borrows in order to
invest always hopesto gain and often succeedsbeyond his
expectations.
The rates of return over costin various investment o p
portunities play an important rcile in both. Henry Ford
and others grew rich not so much because of thrift as
because they took advantage of unusual investment opportunities, in which the rates of return over cost proved
to be many times the market rate of interest.
Besides thrift and luck, with their opposites, there is
another factor closely associated with the process of accumulation or dissipation. This is habit. It has been noted
that a person’s rate of preference for present over future
income, given a certain income stream, will be high or
low according to the past habits of the individual. If he
has been accustomed to simple and inexpensive ways, he
finds it fairly easy to save and ultimately to accumulate a
little property. The habita of thrift being transmitted to
the next generation, by imitation or by heredity or both,
result in still further accumulation. The foundations of
some of the world’s great& fortunes have been based
upon thrift.
Reversely, if a man has been brought up in the lap
of luxury, he will have a keener desire for present enjoyment than if he had been accustomed to the simple living
of the poor. The children of the rich, who have been
accustomed to luxurious living and who have inherited
only a fraction of their parents’ means, may spend beyond their means and thus start the process of the dissipation of their family fortune. In the next generation
this retrograde movement is likely to gather headway
and to continue until, with the gradual subdivlision of
the fortune and the reluchce of the successive genera^

c3371

THE THEORY OF INTEREST
tions to curtail their expenses, the third or fourth genetion may come to actual poverty.
The accumulation and dissipation of wed& do sometimes occur in cycles. Thrift, ability, industry and good
fortune enable a few individuals to rise to wealth from
the ranks of the poor. A few thousand d o h s accumulated under favorable circumstances may grow to several
millions in the next generation or two. Then the unfavorable effects of luxury begin, and the cycle of poverty
and wealth beginsanew. The oldadage, “Ram shirt
sleeves to shirt sleeves in four generations,’’ has some
basis in fact. This cyclical movement is more likely to
occur in countries like the United States, where, owing
to the rapidly changing conditions, there is more chance
either to rise or fall in the economic scale. Wherever,aa in
the older countries of Europe, conditions have become
fixed and less subject to changes of any kind, incomes and
wealth are likely to remain relatively unchanged in the
same families, generation after generation. This tendency
is strengthened in England, where the customs of inheritance have helped to keep large fortunes intact in the
hands of the eldest son.
W e are not concerned here with creating a complete
theory of pemnal distribution and its changes. This
would include the effects of many factors other than
thrift, But here we are interested simply in the r6le of
interest and thrift in distribution.

86. The Loan Market Is a Highway for Re-Distrhtion
We s
ee, then, that the exisfence of a market rate of
interest to which the individual adjusts his rate of impatience ~ ~ p panl ieasy
~ highway for the movement
of his fortune in one direction or the other. If rn in&-

c=6

TRE PLACE OF INTEREST IN ECONOMICS
vidual hasspendthrift tendencies, their indulgence is
facilitated by access to a loan market; and reversely, if
he desires to save, he may do so the more easily if there
is market for savings. In like manner, the business
man may, by recourse to loans, either lose or gain. The
inequality of the distribution of capital is thus fundamentally caused in large part by exchanging present for
future income. A rate of interest is simply a market price
for suchexchange. If all individuals were hermits, it
would be muchmoredifEcult either to accumulate or
to dissipate fortunes, and the distribution of wealth
would therefore be much more even.
It is true, as the socialist maintains, that inequality is
due to social arrangements, but these arrangements are
not, as he assumes, primarily such as take away the
chance to rise in the economicscale; they are, on the
contrary, arrangements which facilitate both rising and
falling, according to the choices made by the individual.
The improvident sink like lead to the bottom. Once there,
they or their children find diiliculty in rising. Accumulation is usually a slow process, and especially slow because the great numbers of the poor competing against
each other reduce the values of their services to so low
a point that theinitial saving becomes almost impossible.
While it is truethat
w t e begets
poverty,
it is
equally true that poverty begets waste. Whole communities and peoples, for example, the Chinese and Indians,
are steeped in misery not because of any inherent extravagance, but because they are so poor they must use
up aJl they produce, leaving no marginof savings for bettering their methods of production. Occasiondy a Rockefeller, a Carnegie, or a Ford rises from near the bottom
and ascends to the top. But the great m888e8, once they

13391

THE THEORY OF INTEREST
get near the bottom, are likely to remain there. Their
high rates of impatience manifested through generations
have brought many if not most of them to poverty. A
labor leader once said to me that few labor men have
m y acquisitive instinct. They are a self-selected group
of those impatient by nature or habit or both. They tend
to spend rather than to save. The great need and opportunity for education in thrift is manifest.
This is not the place to answer the many questions
which arise in such an inquiry, such a,what is the effect
of change in the rate of interest in stimulating or discouraging the accumulation or dissipation of capital?
What is the effect on the poor of the luxurious habits of
the rich? Nor am we concerned with the other factors
which influence the distribution of wealth but which do
not involve the rate of interest. We are at present content
merely to prepare the way for their answer by indicating
the nature of the problem and the relation of the theory
of interest to it.
8ee Gonner, interest and Sauinge.

CHAPTER XVI
RELATION OF DISCOVERY AND INVENTION TO
INTEREST RATES
$1. The First Effect of Each Important Discovery and
Inventdon Is to Increase the Rate of Interest

THI interplay of impatience and opportunity on the
rate of interest is profoundlyinfluenced by invention
and discovery. The range of mads investment opportunity widens as his knowledge extends and his utilization
of the forces and materials of Nature grows. With each
advance in knowledge come new opportunities to invest.
The rate of return over cost rises. With the investments
come distortions of the investors’ income stream. These
distortions me softened through l o w , 80 far as the individual is concerned, the distortion being thus transmitted
from borrower to lender and so spread over society generally. This distortion means relative abstinence from
consumption during the period of producing and exploiting the newdevices,followed by greater consumption
later. In the meantime human impatience is increased.
In the field of transportation, for example, man originally had to depend upon his legs and arms to carry himself and his burdens, Later he invested in domesticated
animals, and secured large returns on his investment,
by increasing the range, speed, and efficiency of locomotion. Still later the invention of the wheel introduced
the UBB of vehicles drawn by h o r n The invention of the

c3411

THE THEORY OF INTEREST
steam locomotive forhauling vehicles on rails enormously
increased movements of goods and men, while at the saxne
time the range and diversity of opportunities to invest
wereextended. Today advance in technical knowledge
has multiplied investment opportunities a thousandfold
in the transportation field alone. There is the possibility
of street transit by surface, elevated, or subway lines. On
land, men and goods are moved by steam and electric
locomotives, trolleys, busses, automobiles or motorcycles.
On the sea, sailing ships have been superseded by st.eam
ships, and the old fashioned marine engine is now giving
way to the steam turbine, Diesel engine and the electric
motor. Man’sancient dream of flying through the air
has at last been reaJized.
A t the early stage of these spaceabridging inventions
society temporarily sacrifices some of its income for the
sake of the greater returns to be expected later. For two
generations railway conshction drained off labor and
caused investors to skimp. In these, aa in all pioneering
days, interest was high. In such periods people live on
great expectations.
$2. ~nventioltCauses Dispersion of Interest Rates

Besidea tending to raise the rate of interest, invention
and discovery tend to widen the gap between the interest
rates on the safest securities and the rates of return over
cost to those who first take advantage of the investment
opportunities offered by the new devices.
Early investors makesacrifices and tske great risks
in the expectation of ample rewards in the shape of
enhanced income. When the rewards for their sacrifices
are realizedthese investors often reinvest their larger
incomes for the sake of yet greater and more remote rec3421

RELATION OF DISCOVERYANDINVENTION
turns. For example, in the United States, throughout
the period of national expansion from 1820 to 1880, while
the growth of farming,mining and manufacture went
hand in hand with canal and railroad building, social
income increasedsharply through investment, return, and
partial reinvestment. Rising national income marks aJl
periods of advmcement in industria3 arb and practices.
The statistics of income recently made available by the
National Bureau of Economic Research show just such
rapid rise, concurrently with a period of great inventions
inelectricity, chemistry, automotive engineering, radio
and aviation. Thus in the United States capital investment per workerrosefrom $560 in 1849 to $5,000 in
1919, with a greater yearly increase in capital employed
than the increase in working population. Horsepowerper
industrial worker increased from 1914 to 1925 from 3.3
to 4.3.’ The increased prosperity of the United States,
due largely to increased utilizat.ionof inventions and scientific management, is shownby an increase of about
three-eighths in national income from 1921 to 1927, with
an appreciable increase in real annual wages, while salaries showed a constant rise, as expressed in purchasing
power, after 1919. The total realized national income of
the nation rose from $35,700,000,000 in 1913, to an estimated total of $89,000,OOO,OOO in 192€2i

$3, Invention Causes Revaluation of Capital
Those enterprisers and risk trtkers who are first to enter
t,henew investment field,opened up by an invention,
or, in the slang of business, “get in on the ground floor”
Report on Recent Eamomic C h m p , Nationsl Bureau of Eoonomic
Research, p. 87.
*Zbid.,Chapter XII.

r3431

/

THE THEORY OF INTEREST
often obtain as a consequence a return on their original
investment f a r greater than the rate of interest. Comand Henry Ford
modoreVanderbilt,AndrewCarnegie
are examples in point.
The rate of interest on loan contracts will rise m a resdt of those operations but only slightly. The cause of
the increase which will occur is the increase in the marginal rate of return over cost.
In consequence of the higher interest rates, there occurs a revaluation of investment securities, and, in fact,
of all capital. The value of capital, assuming that the
value of the income from the capital remains the same
as is true of bonds, sinks as the rate of interest rises.
Bonds tend to fall while common stocks tend to rise,
unless counteracting influences prove to be dominant.
This revaluation applies also to the very capital in
which the new invention or discovery is embodied. If it
is found that $O
l OO
, OO invested in a newlydiscovered
gold mine will result in a yield of Sl,OOO,OOOa year, that
mine will no longer sell for its original cost, but for a
s u m f a r above it. It is the relation of the $l,OOO,OOO a
year to the new value of the mine, and not its relation
to the original invest,ment value or cost which will reflect the true rate of interest. Original investors in The
Bell Telephone -Companyrealized returns far beyond
the normal interest on their investment, but the present
investor pays a price for Bell Telephone stock commensurate with its dividends.
New devices will also cause a revaluation of the older
ones which they have displaced, but in this cme the new
values are lower than before. The adoption of the circular
saw rendered nearly valueless the mill plants equipped
with the old up-and-down saw, and the band taw low-

CW1

RELATION OF DISCOVERY

AND INVENTION

ered the value of mills equipped with the circular saws.
Hand loolns and hand printing presses were superseded,
and
except for special types of work,bypowerlooms
presses. The early forms of power machines have in turn
been superseded by improved machiners. The automobile
ruined first the carriage industry and later hurt the bicycle industry and even the perambulator industry. It is
supplanting, in short haulsof freight and passengers, the
railway industry, and both of these, in turn, are bound
to be supplanted, in a measure, by the aviation industry,
through its possibilities for producingthe meam of more
speedy transportaton.
The reasons for these reductions in value are simple.
Each new process produces a larger supply of the particular kind of service rendered. The price of this service
-e.g., sawing or printing-is reduced,
and consequently
the capitalized value of the given amount of such service
which can be expected from the older devices is reduced,
and often so f a r reduced as to make the reproduction or
even the repair of these older instruments wholly unprofitable. Thus progress constantly requires the writing
offof capital value because of obsolescence?
$4.

The Ultimate Eflecta of Invention on Interat Rate

It is important to emphasize the temporary nature of
the effects of invention and discovery in raising the rate
of interest. The effect in raising interest lasts only so
long aa the rate of return over cost continuee to be high
and so tempts society to distort greatly ita income stream
in time shape. This period is the period of development
*The economic effecta of invention, end partidarly ita eff& upon
the rate of ink&, were well treated by John Rae, The sodoloqiad
T h e w of Capital, Chapter IX, pp. 13!h160; chapter X, pp. 161-203.

C3451

THE THEORY OF INTEREST
and exploitation, during whichsociety is sacrificingor
investing present income, or, aa it is inaccurately called,
investing capitd. Society, instead of confining its productive energies to the old channels and obtaining a relatively immediate return in enjoyable income, as by producing food products, clothing, etc., directs its labors to
great engineering enterprises, such as constructing tunneb, railroads, highways, subways, waterworks,irrigation
systems, mining and manufacturing plants. These instruments cannot begin to contribute a return in enjoyable
income for many years. In contemplation, future income
during this period is relatively plentiful, and in consequence of these great expectations, the rate of interest
will be high.
hter, however, there will come a time when, 80 jar at
least as th effect of thatparticular invention is concerned, the income stream ceases to ascend, when most
of the necessary investment has been completed, when
little further exploitation is possible or advisable, and
when it is only necessary to keep up the newlyconstructed capital at a constant level. When this period is
reached, the after effect of the invention will be felt. The
net effect on society will then have been to put the income stream on to a higher plateau, not to boost it up
hill any more. But such a mere increase in the &e of the
income stream, while its shape remains constant, tends,
as we have seen, not to increase, but somewhat to dec r e w the rate of time preference. Therefore, the after
effect of all inventions and discoveries is not t o w d
increasing but toward decrea&ng the rate of intereat.
Thus, though the railway inventions led to a half century of investment in railways, during which the income
stream of society rapidly increased, todslyl the limit of

w31

RELATION OF DISCOVERY AND INVENTION
railway investment haabeen nearly reached in
someplaces, andin others the rapidity of investment
has perceptibly slackened. Railroads have been an outlet
for the investment of savings, and have tended to supply
for them a good return. As the necessity for new railroads
becomesless, thisoutlet diminishes, and the rates of
return as well the rates of interest in general tend to
fall so far as this one influence is effective.
But while the after effect of an old invention is to reduce the rate of interest, it may, of course, be true that
new inventions, often the result of the old, will be made
rapidly enough to neutralize this tendency. It is chiefly
when there is cessation in the world’s output of new
inventions that the rate of interest is thus likely to fall
back, but whenever invention is active the interest rate
may rise continuously. I t thus rises and falls according
aa the introduction or the exploitation of inventions is
active or inactive.
The same principles apply not only to invention in
the narrower mechanical sense, but also to scientific and
geographical discoveries. The opening up of new mines
in West Virginia,Canada, Alaska, South Africa, Australia
and California caused a considerabledepression in the
immediate income streams of those who engaged in the
exploitation of the new territory. Consequently, the rate
of interest in such instances tends at first to be very
high.
steam

$5. The Present an Age of Invention

The present is an age of rapid invention, especially
since the World War. President Hoover’s Committee on
Recent Economic Changes finds the “tempo” of improvement in industrial arts the most striking character~3471

THE

THEORY
OF INTEREST
istic of our times. This increased tempo tends toward a
high interest rate because of the flood of new inventions,
despite the opposing influence of the old and matured
inventions which have made us so much richer.
Some outstanding examples of recent inventions which
greatly increase production and consumption are: the
automobile; the radio; the airplane; motion pictures in
all their many uses; the numerous applications of electric power in factories and on the farm; long distance
telephone, which has finally solved the problem of sending messages across the Atlantic Ocean; the utilization
of cellulose,formerly a waste and a nuisance, in the
manufacture of building materials, paper, and rayon
textiles; the use of cotton seed for oil and fertilizer; the
pulverization of coal by which its fuel value is greatly
increased; the liquefaction of coal whichgives added
supplies of muchneededgasoline;
the innumerable
chemical and dye products made from coal.
Newdiscoveries and inventions, by utilizing wastes
from forests, fields and mines, and increasing the output
of labor have greatly advanced the scale of living in
America
Furthermore, the use of a new invention spreads with
lightning rapidity in this high speed and intercommunicating age, affecting the income streams with a much
greater influence than formerly and, as it spreads, it leads
to further inventions. This is a chief reason why today is
increasingly an age of invention. Nations like Great B r i t
ain, the United States,Germany and France lead in civilization by taking the greatest advantage of this selfpropagating principle of invention, andnations like
China and India, so long aa they give it little attention,
will lag behind,

'C3481

RELATION OF DISCOVERY AND INVENTION
Improvements in transportation developed the world
granaries of Argentina, Canada, and the Mississippi
Valley. The acreage of cotton was increased to feed the
New England and British mills from the Southern and
Gulf States, from Egypt and India The investments in
mining stretched over continents. Chilean nitrates were
brought to American farms, and fresh investments were
made in works that extracted nitrogen from the air. The
coaldeposits of the worldweremade to releasesolar
energy stored up for millions of years, and the oil wells
of Oklahoma and Baku becamesource8 of new wealth and
investment to supply a motor-driven age. Investments
in machines,factories,railways,highways,warehouses,
sewers, and in the ramifications of urban and subwban
development enlargedthe opportunities for surplus funds
to an almost limitless extent. Reconstruction of devastated countries after the World War gave opportunity for
the investment of billions of American dollars abroad,
with flotations of foreign loans in the United States, in
1927 and 1928, averaging a billion and a half each year.
$6. Mass Production of Inventiom
Moreover today we are organhiig invention and discovery aa we organize everything else. Experimental laboratories have spread from universities to government
bureaus and commercial concerns. Millionsare now spent
on researchwhere thousands or hundreds were spent
a generation ago. And inventors are thus led not only
to more intensive effort but to cooperate and pool their
ideas, Mr. Hoover, before he was President, took steps
toward a greater organization of scientific work looking
toward invention.
During 1929, the Engineering Foundetion launched a

[3491

THE THEORY OF INTEREST
drive for fivemilliondollars to aid scientificresearch.
Major General George0. Squier reported in the Nation’s
Business for January, 1929, that in the laboratory of
the American Telephone and Telegraph Company alone,
$15,000,000yearly were being devoted to the work of researchwhichemployed four thousand specialists. With
respect to research General Squier added:
“We hear of expenditures by the m i l l i 0 ~ 2 0 0 , 0 0 0 , 0 0 0a year
by some estimates, $70,000,000through the Government, and $130,OOO0,00 through commercial firms. Any comprehensive inventory of
our researchresourceswouldinclude the bulky items of plant and
equipment, and the incalculableintangiblesreposed in the 300,000
physicists,chemists,engineers,
mathematicians, and trained technicians. As for suggesting the substance of this tremendous adventure, we may turn to the structures erected by the General Electric
Company, the United States Steel Corporation, GeneralMotors,
and the United States Rubber Company.”

A survey by the National Bureau of EconomicResearchrevealed, in ib announcement of May 4, 1929,
theextent to which industrial researchprevailed as a
new trend in manufacturing progress in the United
States. Of 599 manufacturing concerns supplying information, the report stated that 52 per cent recorded the
carrying on of research aa a company activity. Testing
laboratories wereconducted by 7 per cent, leaving a
minority in which no research work was being done. Some
29 per cent reported that they were supporting cdperative research conducted through trade associations, engineering societies, universities or endowedfellowships.
Especially in cement manufacture, leather tanning, and
gas and electric utilities, coiiperative research was highly
developed.
Statistical research has added ita quota to investment
c3501

RELATION OF DISCOVERYAND INVENTION
in
opportunities. There had beenbusinessdepression
1920-1921.Herbert Hoover’sengineering committee on
Elimination of Waste in Industry reported some of the
causesof that depression. The committee had found
throughout industry a faulty control of material and
design, &s well as of production and costs. For example,
the loss from idleness in shoemaking occasionedby waitingfor work and material amounted to about 35 per
cent of the time. It was found that standardization of
the thickness of certain w& might mean a saving of
some six hundred dollars in the cost of the average house.
There were six thousand brands of paper, of which half
were more or less inactive, and the duplication of brands
tied up money in unnecessary stock. A shoe factory with
capacity of twenty-four hundred pairs a day had shortage
of needed racks, reducing output to nineteen hundred
pairs daily. Most p h t s were foundwith no cost systems,
or with incomplete knowledge of general costs, and for
this reason most of them lost money. A multitude of
shops lacked modern personnel relations with their employees; the workers had no unbiased means of approach
to employers, while employers lacked the means of treating with their own men. Few plants had effective employment records; the turnover of labor was high and
expensive. Sales policies were defective. There were cancellations of purchases on long-term contracts ranging
up to 14 per cent., and returns of goods up to 11 per cent
in so-called normal years. h k of scientific management
and of scientific forms of organization found production
restricted by both employers and men. Maintenance of
high prices,collusion in bidding, and unfair practices
contributed to limit output, aa well &s did the practice of
“ca’ canny” by workers and the restrictive rules of the

13511

THE THEORY OF INTEREST
unions. It was found that eighteen hundred million dollars a year might be saved in preventing illness and
deaths among American workers, and eight hundred and
fifty million dollars more in preventing industrial midenh.
With the publication of this report, and of the succeedingHoover report on unemployment and business
cycles,American industrial management awoke to the
possibilities of economic savings and higher organization,
and American investment management found its opportunities correspondingly enhanced. Loans were supplied
by the banks in measured volume, accordingto the needs
of industry. The vast American market, blessed with
free trade between forty-eight state jurisdictions, waa
thoroughly surveyed, and the wonders of technique and
researchwere systematically evoked in the large scale
&s well aa in the smaller but rapidly merging industria

$7. Effects on Investment
Because of these inventions, introducing eccnomies
whichrevolutionized industry, common stocks on the
Americanexchanges have advanced in 1928 and 1929,
so that the dividendyields of dividend paying stocks
were lower than the interest yields of hi@ grade bonds.
As an example of the eagerness of the investing public
to finance newly-evolving industries, the Daniel Guggenheim Fund for the Promotion of Aeronautics announced that it was no longer necessary to grant equipment loans to air-transport companies, bec~we,it stated,
the “investment public is now ready to supply the capital
for enterprises of this kind.” By the close of the third
decade of the twentieth century America had already
shot ahead of Europe in commercial aviation, and waa
I352 3

RELATION OF DISCOVERY AND INVENTION
operating more than eighteen thousand miles of airways,
of which eight thousand miles werelighted for night
travel. The New York Trust Company in its reports took
note that airplane production for 1928 was about five
times that of 1927, and that demand for almostevery
type of aviation market ww rapidly expanding.
Among investors there was knowledge that many of
the inventions and discoveries made by the agencies of
research would quickly find practical u8e. With the certainty that epoch-making inventions and methods of
higher organization werebeing
applied in the arts,
opportunities to invest were multiplied, and thousands
of new investors incremed the transactions of the stock
exchanges.
, This varied and exciting chapter in modern industrial
expansion is s u m m e d up by the Hoover Committee on
Recent Economic Chmges in ib review (p. 844):
“By no meam all the increase in aciency took the form of a
net gain in current livelihood. To we the techniquefounded on
science, men had to build machines, factories, railways, roads, ware
houses and sewers. In developing newresources, they had to dig
mines; to break the prairiea and fence the farms; to make homes
in strange habitats. And this work of re-equippingthemselves for
making consumed goods wasneverdone. Every discovery put to
use on a commercial scalemeant a new equipment job, often of great
extent. But after all this work on the means of production waa done,
there remained an even larger flow of the thugs men eat and WW,
house and amuse themselves with.
“The net gain in ability to provide for their desires brought men
the possibility of rabing their standard of consumption, of d u c i n g
their h o w of work, of giving their children more education, of increasing their numbere. They took a slice of eachof them goode,
rather than all of one. They worked somewhatless hard aa the
decades went by; they raised their W d a r d a of consumption &pp*
ciably; they established compulsoryeducation and reduced illiteracy;
they added to the population.
.“

..

13531

TRE THEORY OF INTEREST
$8. Importame of Invention

It has not been the purpose of this chapter to investigate the general effect of inventions, but merely their
effect on the rate of interest and rates of return.
Before leaving the subject, however, it should at least
be stated that invention is a chief basis for progress in
civilization and for increase in the income of mankind.
The inventions of fire, the alphabet, and the means of
utilizing power-first of animals, then of wind and water,
then of steam and electricity-and their manifold applications, especially to transportation and communication,
have made it possible for the earth to support ita increasing population, and deferred the Malthusian pressure
upon the means of subsistence; t.hey have made possible
the stable existence of great political units such as the
United States; and they have given opportunity for the
presentation, diffusion, and increase of knowledge in all
its forms of art, literature, and science. And thus it happens that invention is self-perpetuating. For not only has
science sprung from inventions such as the printing
press, the telegraph, and specific scientific instruments
for observation, like microscopes and telescopes, or for
measurements, like chronographs, balances, and micrometers, but modern science is now in turn yielding new
inventions. Helmholtz’sresearches in sound led to the
telephone; Maxwell’8 and Hertz’s researches on ethereal
waves led to wirelesa telegraphy and the radio.
T h e conditions for the most rapid multiplication of
inventions are: (1) mental efficiency, dependent on
heredity, hygienic habits, and the education (both general and technical) of human faculties, and for this the
Greek motto “a sane mind in a w e body” ia in point;

c3541

RELATION OF DISCOVERY AND INVENTION
(2) the ease of diffusion of knowledge; (3) the size of
the population within which the dif€usionoccurs-the
larger the population the greater being the number of
inventive geniuses, the greater their incentive, and the
wider their sphere of iduence; (4) the encouragement
of invention especially through the early discovery and
approval of genius, and, to some extent through patent
protection. Inventors are at once therarest m d most
precious flower of the industrial world. Too often they
are crushedby the obstacles of poverty, prejudice, or
ridicule. While this is leas 80 today than in the days of
Roger Bacon or Galileo, it still requires f a r too much
time for t.he Bells, Edisons, Fords, or De Forests to get
their start. The decadesinwhich these rare brains are
doing their wonderful work are at most few, and it is
worth many billions of dollars for their countrymen to
set them to work early. As Huxleysays, it should be
the business of any educational system to seek out the
genius and train him for the service of his fellows, for
whether he will or not,the inventor cannot keep the
benefits of his invent.ion to himself, In fact, it is seldom
that he can get even a small share of the benefits. The
citizens of the world at laxge are the beneficiaries, and
beingt.hemselves not su6ciently clever to invent, they
should at, least be sufliciently alive to their own interests
to subsidize or employ the one mss in a million who can.

CHAPTER XVII
PERSONAL AND BUSINESS LOANS
$1. Personal Loans

IN this chapter, I shall try to show t.hat the theory of
interest elaborated in this book applies to every species
of loan contracts.
From thestandpoint of the borrower, loan contracts
may be classified as follows:
Consumption or
Personal Loam

To offset misfortune or improvidence
To offset fluctuatiom in income and
outgo

To anticipateimprovement in hcial condition

Short or periodic loans

Private
Loans
Productive or
Businem Loane

Crop lieu
Commercial paper
Accommodabon paper
Call loam
Mortgagee on farme
Mortgagee on city real

estate

Long or p
e
r
m
s Mortgage boncia of cornent loans

porntiom
Debentures of corporatione

Public

Loam

Consumption
Loam
Productive
Loans

ions in revenue and
For public improvements

Personal loans are loans of individualsfor persond
purposes rather than those arising out of business relations. Of these, the first class comprises loans contracted
because of misfortune or improvidence. These constitute
today a very small fraction of total indebtedness. It
~3581

PERSONAL AND BUSINESS LOANS
was against interest on such loansthat thebiblical, classical, and medieval prohibitions and regulations were
directed, and it is chiefly against interest on such loans
that today, in enlightened communities, regulations
decting the rate of interest still survive. It is such loans
that supply a large part of the business of pawn shops
and of “loan sharks,” the patrons of which are too often
victims of misfortune or of improvidence.
The theory of interest which has been propounded in
this book applies to this species of loan. Sickness or
death in one’s family, or I m from h,theft, flood,
shipwreck, or other unexpected caums, make temporary
inroads upon one’s income. It is to tide over such stringencies in income that a personal loan is contracted. It
ekes out the inadequate income of the present by sacrificing something from the more adequate incomeexpected in the future. Similar principles apply to the
spendthrift, who, though not a victim of midental misfortune, brings misfortune upon himself. He borrows in
order to supplement an income inadequate to meet his
present requirements, while he trusts to future resources
for repayment. It is evident, therefore, that the loans
just described are made by the borrower for the sake of
correcting an income stream the time shape of which is
unsatisfmtory.
The second class of personal loans comprises those
growing out of such fluctuations in income 88 are not due
to misfortune or improvidence.Some persons receive
theirmoneyincome in very irregular and unequal installments, while their money outgo may likewise have
an irregular time schedule. Unless the two s e r k happen
to synchronize, the individual will be alternately “ahort”
and
Thus, if he receives his large& dividends
357 3

“flush.”

c

THE THEORY OF INTEREST
in January, but has to meet his largest expenses, let us
say taxes, in September, he is likely to borrow at tax
time for the ensuing four months, in anticipation of the
January dividends. That is, he borrows at a time when
be low, and repays
his real incomewouldotherwise
at a time when it would otherwise be high. The effect is
to level up the fluctuations of his income. He could, of
c o w , proceed in the opposite way, lending in January
when “flush” and being repaid in the fall in time to help
him when “short” because of tax payments.
In brief, either he borrows,when short, because his
degree of impatience, in view of the flush time coming,
is higher than the rate of interest, or he lends when flush
because his degree of impatience, in viewof the lean
time coming, is lower than the rate of interest.
The third class of personal loans comprises those which
grow out of large expected additions to income or income
earning power. Heirs to a fortune sometimes borrow in
anticipation of bequests coming to them, the prospect of
which excites their impatience. A considerable volume of
such loans are made perhaps most often in Great Britain.
The borrower under these circumstances borrows 80 that
he can enjoy in the present some of the income which
otherwise he would have to wait for. The same motives
wtuate young men preparing for the earning period of
life and explain the loans which are often contracted
by them for defraying the expenses of education. I t
was for suchpersons that Benjamin Franklin left his
peculiar bequests to the cities of Philadelphia and Boston in 1790. To each he bequeathed €loo0 to be lent out
in small sums at 5 per cent to young married “arti6cers”.
The s u m repaid, including interest, were to be added to
the fund and again lent. Modern building and loan 8880c 3581

PERSONALANDBUSINESS

LOANS

ciations are organized to accommodate young couples and
others wishing to enjoy goodhomes in anticipation of
their power to pay for them in fuU Installment buying,
now so widely used to finance the buying of dwellings,
furniture, automobiles, radios and other long-lasting instrumenta, cater to the same desires. They all appeal to
youngpeople with small immediate incomes but great
expectations for the future.
It is evident that aJl the foregoing c w , comprising
personal loans, are taken care of from the viewpoint of
the borrower in the theory of interest; they are all expressions of impatience for greater incomeexpected in
the future.
$2. Business Loans
Business loans are commonly called productive loans,
in contrast with personal or consumptionloans.Business loans constitute by f a r the most important class of
presentindebtedness. Mr. George K. Holmes,formerly
of the U. S. Census, at one time estimated that at least
nine tenths of the indebtedness in the United States then
existing was incurred for t,he acquirement of the more
durablekinds of property, leaving not more than one
tenth, and probably muchless, as a consumption debt.
The overwhelming preponderance of business loans has
led some economists to account for interest on persond
loans as a reflection of the rate of return lenders can
secure by lending for production.
From another point of view it might seem thatthe
theory which has been given in this book, based 88 it is
on the enjoyable income stream of an individual, can
apply only to consumption loans.
It is slso said, with some appearance of truth, that
c 359 1

THE THEORY OF INTEREST
consumption loans are explained on principles quite other
thanare production loans. In personal loans the two
principles of impatience are dominant, while in business
loans the two principles of investment opportunity are
dominant. But in either case both sets of principles play
their parts. And, since the degree of impatience and the
rate of return over cost both tend toward equality with
the mmket rate of interest, each influencing the other
in that direction, we reach the same result to whichever
one of the two-impatience or investment opportunitywe give our main attention. Lest the r6le of impatience
in business loans be overlooked, let us first fix our eyes on
that.
While business loans differ from consumption loans in
respect to investment opportunity principles, they do
not really differ in respect to the impatience principles.
Both are used to tide over lean times in anticipation of
prosperity, and they are said to be contracted in order
to rectify the distortion of the income stream which
would otherwise result from business operations.
The truth is-and it shouId never be lost sight ofthat the business man conducts his business with an eye
always to ultimately enjoyable income whether for himself, his family or for others. In a sense it is his home that
runs his business rather than his business that runs his

home.
$3. Short Term Loans

!hvo classes of business loans may be distinguished,
namely, short l o w growing out of periodic income variations, and long loans for relatively permanent investment. The short or periodic loans are those which grow
out of the change in the seaaons and the ebb and flow of
c 3 w

PERSONAL AND BUSINESS LOANS
business. These loans are obtained usually but once a
year at a specified time. The ultimate cause is the cyclical change in the position of the earth in reference to the
sun. This gives rise to the cycle of the seasons, the effects
of which are felt not only in agriculture, but in manufacturing, transportation, trade, and banking. The alternate congestion and thinning of the freight business, the
alternate stocking and depletion of raw material in factories, the seseonal ffuctuations of trade activity, both
wholesale and rem, the transfer of bank deposits betweenNewYork
andthe West for moving crops, or
for other uses, all testify to the seasonal rhythm which
is constantly felt in the great network of business operations. Without somecompensating apparatus, such as
that for borrowing and lending, these seasonal fluctuations in production, trade, and finance would transmit
themselves to the final enjoyable income streams of individuals, and those incomes instead of constituting an
even flow would accrue by fits and starts, a summer of
lavish enjoyment, for instance, being followed by a winter on short rations.
To show how borrowing and lending compensate for
these fluctuations, we may consider first what is perhaps
the most primitive type of the short term loan, namely,
that contracted by poor farmers in anticipation of crops.
In the South among the negroes this takes the form of
what is called a crop lien, the cultivator borrowing
money enough to enable him to live until crop time and
pledging repayment from the crop. Here, evidently, the
purpose of the loan is to eke out the meager income of
actual enjoyments. The loan, in other words, is for subsistenm. This case, therefore, clearlyinvolvea the impatience principles.
c 361 1

THE THEORY OF INTEREST
These same principles apply also to loans contracted
in the commercial worlda t large. A short time commercial
loan is contracted for the purpose of buying goods, with
the expectation of repayment after their sale, A common
form is what is called commercial paper. A ready-made
clothing house may buy overcoats in summer in order
to sell them in the fall. If these operations wereconducted on a strictly cash basis, the tendency wouldbe
for the income of the clothier to suffer great fluctuations.
He could realizebut littleduring the summer, on account
of the enormousexpense of stocking in for fall trade,
whereas in the fall he could obtain large returns and live
on a more elaborate scale. This would mean the alternation of famine and feast in his family. One way to avoid
such a result would be to keep on hand a large supply
of cash as a buffer between the money income and personal expenditure. In this case the fluctuat,ions in his
incomewould not attect his personal enjoyment, but
would cause an ebb and flow in his volume of cash. But
a more effective and less wasteful method for the merchant to take the kinks out of his stream of red income
is by negotiahg commercial paper. The clothier, instead
of sdering the large cash expense of stocking up in
summer, willmake out, a note to the manufacturer of
overcoats. After the fall trade, this note is paid, having
fulfilled its function of leveling the income stream of
the clothier.
Sometimes business mencontract short tenn loam, not
for some specific transaction such as the purchase of
stock in trade, but for general business purposes, as, for
instance, improvement or enlargement. In this case, the
extraordinary expense involved may be met by a species
of loan called accommodation paper. Evidently its func[3621

PERSONAL AND BUSINESS LOANS
tion is precisely the same, namely, to rectify the time
shape of the income stream.
In WaII Street and other speculrstivecenters 8 type
of loan known ae the call loan is common, subject to redemption at the pleasure of the lender or the borrower,
and used by the speculator for the purchase of securities.
The speculator borrows when he wishes to buy and repays when he has sold, and by adroitly arranging and
placing his loans he prevents the sudden draining or
flushing of his income stream which these purchases and
sales would otherwise involve, if they were to be made
at all.
In all the casea which have been described, the loan
grows out of a purchase or group of purchrtses, and since
the tendency of every purchase is to decrease one’s income, and of every sale to increase it, it is clear that
loans contracted for a purchase and extinguished by a
sale may be said to have as their function the obliteration of these decreases and increases of the income
stream. We see then that these commercial loans fit into
the impatience part of the theory of interest which has
been propounded
$4. Long Term Loam

The second class of business loans is that of long term
loans or permanent investments. In this class are placed
mortgages, whether on f m s or on urban real estab.
As shown by the I890 Census, almost two-thirds of farm
mortgages are contracted to buy land, and the remainder
principally for improving it, or for the purchase of farm
machinery and animals, or for the purchase of other
durable wealth and property. The Department of Agriculture found that 87 per cent of the mortgages of 94
13631

THE THEORY OF INTEREST
North Carolina farms in 1922 was contracted to buy land,
and almost 10 per cent more to make real estate improvements. These purchases or improvements, involving
as they do large expenditures, would be difEcult or impossible without loans. If theattempt were made to
enter into them without recourse to a loan market, they
would cause large, though temporary, depressions in the
income streams of the farmers. The farmer who attempted to buy his farm without a loan might not be
able to do so at aJJ or at best might have to cut down his
current living expenses to a minimum.
Mortgages on city lots are usually for the purpose of
improving such properties by erecting buildings upon
them. The expense involved would, if taken out of income, reduce the income of the owner temporarily. He
naturally prefers to compensate for such extraordinary
inroads by a mortgageloanwhich
defers this expense
to the future when he expects that his receipts will be
larger.
Wecome next to the loans of business corporations
and firms, such, for instance, as rsilroad bonds and
debentures, the securities of street railroads, telegraph,
and telephone companies, steel mills, textile factories,
and other “industrials.” These loans are usually issued
for new construction, replacement., and for improvement
of p h t and equipment. The borrowers in this case are,
in the last analysis, the stockholders. They may be said
to contract the loan in order not to have the expenses of
the improvement taken out of their dividends.Sometimes, of course,where the earnings are large enough
they are actually applied, in part or wholly, to the
making of improvements. Ordinarily, however, such t~
reduction in the stoc&older’s income stream is avoided
c3&41

PERSONAL AND BUSINESS LOANS
by the device of inviting bondholders to bear the outgoes
connected with t'he improvement, in consideration a i receiving a part of the increased income which it is hoped
will later follow from these improvements.
$5. Business us. Personal Loans
Business loans therefore serve to reshape the income
streams to conform to the time preferences of their
owners just aa truly aa do personal loans. All financing
may be considered as contrived to keep income flowing
smoothly to serve human impatience.
The important difference between business loans and
personal loans is not aa to impatience but as to investment opportunity. In personal loans the opportunity
principle plays a minor r61e or none at all. The personal
borrower borrows not to invest but to remedy or prevent
a present dearth of incomebecause of illness or the
desire to anticipate future income, the amount of which
has little or nothing to do with the loan. The business
borrower, on the other hand, borrows to remedy or prevent a dearth of present incomebecause he wishes to
invest and increase his future incomes. Each is impelled
by impatience to fill a hole in his present income, but
the one hole waa cut by involuntary illness or voluntary
spending, the other by voluntary investment.
Let w examine this difference more in detail. Let us
suppose two borrowers, one a personal borrower, because
of some misfortune such as an illness, and the other a
business borrower, because of an investment. Let US s u p
pose that, otherwise, they are alike in all respects affecting our present problem. Each has a prospective income
of $lO,OOo this year and $12,500 next year, after dowing
for the effects of the misfortune in one case and for that
C361

THE THEORY OF INTEREST
of the investment in the other, but before any loan ia
made.
Each will, let us say, borrow $l,OOOthis year and repay
this with 5 ,per cent interest next year, making a total
repayment of $1,050. Each, therefore, will have a finally
adjusted income this year of $10,OOO $1,000 or $11,000
and next year of $12,500 - $1,050 or $11,450. The effect
of the loan is thus identical on the income s t r e w in the
two cases. The difference is that the unfortunate, if deprived of his loan, could not escape from his lower
income stream this year of $lO,OOO despite his higher income next yew, whereas the business man,if deprived of
his loan, could, if he chose, give up easily the investment
altogether. That is, the merchant has another option
which the unfortunate lacks. He has two options and
therefore the opportunity to r e p h e one by the other.
If the merchant did not have this extra option, the
two cases would be so similar that not even a stickler for
the distinction between a consumption loan and a production loan would assert any essential difference. For,
suppose the merchant had already been committed sometime previously to the investment, not, perhaps, realizing
that he would be unable to pay for it without borrowing or skimping. When the time arrives when he must
of necessity pay in his money, he finds that a loan is
badly needed to avoid pinching himself in income. He
will now think of the loan not as enabling him to invest,
for that has to be done anyway, but as enabling him to
buy his bread and butter. In short, his loan, like the
unfortunate’s, is now consumption loan! It is bemuse
ordinarily the merchant is not thus constrained to make
the investment that the loan is connected in his mind
with the investment rather than with his private neceasi-

+

13683

PERSONAL AND BUSINESS LOANS
ties. Yet, in either case, it 8erves to relieve his needs.In a
sense ail loans are impatience loans,but in the production
caae he has another method of relief-not to invest at all.
The essential contrast, then, between him and the unfortunate is simply that he has a possible course open to
him which the latter does not have.
This is not to deny that the loan (and the investment
which it makes possible) is also to be considered for the
purpose of increasing his income. It is both. Aa stated
already, had he wished, he rmght have refrained, ordinarily, altogether from making the investment. He
would, then, let us suppose, have had an income of
$ll,O00 a year both this year and next. He was attracted
by the opportunity to invest $l,OOO because while this
would reduce this year’sincomeby
that a m o u n t t o
$lO,OOO-it
wouldincrease next year’sby$1,5Oo-to
$12,500. The whole set of operations go together. If we
separate them in thought, the true sequence is: of the
two optional income streams ($ll,OOO,$11,0oO, on the
one hand, and $lO,OOO, $12,500on the other) the merchant selects the latter because it had the greater present
value (or, what amounts to the same thing, because the
rate, 50 per cent, of the return of $1,500 on the sacrifice
of $l,OOO is greater than the rate of interest, 5 per cent).
That being done he then borrows because, although he
will have the same present value, he will get a more
desirable time shape. This description takes account of
the wholeseries of operations, and corresponds to the
principlespropounded in Chapter VI. It is the extra
option which gives rise to the contention that the loas
produces a profit not possible or easy without it, and
that it is, therefore, productive. And this is true in the
sense that the loan carries with it the extra option. The

~3671

THE THEORY OF INTEREST
loan is productive in so f a r as without it thisextra option
which is productive would not be chosen.
We have just seen that the loan phenomena can be
resolved into two separate steps. Yet since it may often
happen, as shown in Chapter VI, that the first step
(choice of options) would not be taken unless the second
step (loan) were already in contemplation, or even fully
contracted, it is true that in a sense the choice of the
loan includes the choicebetween the options. In this
sense, and in this sense alone, is the loan productive. It
is productive in that it gives to the merchant productive
investment opportunity. But it is better, or at any rate
admissible, to say that it is this investment opportunity
which is productive rather than the loan whichmakes
it possible.
In practical life, however, the investment and the loan
are not usually thought of as separate operations.
Rather are they thought of as parts of the stme operations. The investment, especially if a large one,would
not, and often could not, be made unless the resultant
distortion of the income stream is at once and by prearrangement, remedied by a loan. The loan is in fact
often contracted for before any committsl to the investr
ment, and were it not employed, or eomething like it,
the distortion of the income stream needed to make the
investment poseiblewould often reduce it to zero or
below.
The point here is that if we do try to sepwte the
r6les of the loan and the investment we cannot my that
the loan by itself, without the investment, yields a business profit, but we can srty that the invmtment by itself
does. Adopting the latter mode of thought, w0 are free
to think of 8 business h 88 having, by itaelf, just the

[=I

PERSONAL AND BUSINESS LOANS
same function aa any other loan-to even up the income
stream in accordance with the principles of impatience.
$6. Purpose of Borrowing to Increase Present Income

We have now seen &at the theory of interest which

has been propounded is adequate to explain the motives
which lead to borrowing in the actual business world.
The personal loan comes near to exemplifying our first
approximation where there is a supposedly fixed income
stream, while the business loan exemplifiesthe second or
the full fledged third approximation where there are
alternatives. Of course, even the unfortunate who needs
a loan may have alternative ways to turn. No income
stream in actual life is absolutely rigid. But the variow
opportunities open to the typical personal borrower are
not very important or striking as compared with those
open to a business man seeking a loan to finance some
great enterprise.
The foregoing classification of loans is made from the
standpoint of the borrower. From the standpoint of the
lender, loans do not need to be so minutely classified.

87. Public Loans
Public Loans need not be treated in detail since they
have all the characteristics which belong to private loans
for consumption and production. The public loan for
consumption is exemplified in the war loans and the
loans to anticipate future revenues. A government receives its income chiefly in taxes, and in some casea only
once a year, whereas its outgo occurs day by day and
month by month. It thus happens that a government is
alternately Sccumuhting a large surplus and suffering
8 largedeficit. The inconvenient effects of this have

I: 369 I

THE THEORY OF INTEREST
often been commented upon, especially in this country,
where the Treasury forhalf a century waa relatively
independent of such institutions of credit between the
governments and certain centrd banks as have long
existed in England, and exist now in this country. The
government may correct the irregularities in its income
stream #by borrowingfor current expenses in anticipation
of taxes. The United States Government often sells short
term Treasury certificates when government receipts are
low, and redeems these certificates when funds come in
from taxes or other sources. The opposite processmay
be employed. The Government may lend at interest by
depositing surplus funds in banks to draw interest until
needed for disbursements, or, what amounta to receiving
interest, it may, by buying its own bonds or redeeming
them for a sinking fund, save interest which would otherwise have to be paid. But this last operation is normally
employed only when the funds are not needed later for
disbursements.
The public productive, or business loan, is exemplified
in loans for the purpose of constructing railroads,or other
improvements whioh are intended to be business undertakings, such as the erection of government buildings,
the improvement of roads, bridges, and harbors, the construction of municipal waterworks or schoolhouses. In
all such cases it is usual to finance the enterprise by
issuingbonds. The reawn is that these improvements
constitute aa extraordinary cost, similrtr to the expense
of a war, which if undertaken without the issue of bonds
would caw a temporary and inconvenient depression
in the income streams of the taxpayers. They, as a whole,
could not atford any such k t heavy drain, even with
the prospect of substantial benefits to follow. They thereI370 I

PERSONAL AND BUSINESS LOANS
fore prefer to avoidsuch a fluctuating income stream,
and to secure instead a moreuniformone,
This uniformity is secured by the loan, which so far as they
are concerned, spreads the expenditures over part or all
of the period during which the public improvementis
expected to last. Wesee, therefore, that this class of
~ o a n salso exemplities the theory of the relation of borrowing and lending to the time shape of an income
stream. The motives which have been described as operating in the case of private Ioans operate in the same
way with public loans. Borrowing by a public corporation shifts to the purchasers of bonds in first instance the
burden of war expenditure or the cost of improvements.
The taxpayers repay the bondholderswhen the bonds
are finally paid. The effect is the same in public borrowing aa in private borrowing, the shape of the income
stream of the public borrower is changedin the same
manner. There is present also a rate of return over cost,
to put in fqures because public
thoughonedifEcult
benefits are not usually reduced to money values.

CHAPTER XVIII
SOME ILLUSTRATIVE FACTS

$1. Introduction
THIS chapter consists of a brief study of the chief influences affecting t,he rate of interest. It is impossible to
present a veriiication of any theory of interest. The facts
are too meager, too conflicting, and too intermixed to
admit of clear analysis and precise interpretation. In all
places and at aH times the economic causes tending to
make interest high are combined with others tending to
make it low. The fact, therefore, that interest is high or
low, rising or falling, in conformity with the postulates
of a particular theory, does not prove that the theory
is the only true explanation. The best that we cm expect is to show that the facts as we find them are not
inconsistent with the theory maintained.
The causes making for high or low interest rates tend
to counteract themselves. For instance, the economic
c a w , which before the World War tended to make interest high in the United States, ala0 tended to bring in
loans from other countries, especially from Great Britain,
where the rate of interest was then low. The introduction
of the loans prevented interest from being aa high as it
otherwisewould have been. High interest in one community tends to increase the borrowings of that community, provided there exists another community in
which the rate of interest is lower. If borrowing from

K 372 1

SOME ILLUSTRATIVE FACTS
abroad is not practicable, other methods of adding to
present at the expense of future income may be found.
If such processes go far enough they will result in a
dissipation of capital, or in a sloweraccumulation of
capital.
Contrariwiee, the causeswhich work towardlending
may result, if lending is impracticable, in some other
ways of postponing consumption, and may show themselves in a more rapid accumuhtion or in a less rapid
dissipation of capital.
The same economicc a w s which tend to make interest
high will tend also to encourage the production of the less
substantial and durable instruments, whereas those
causes which tend to make interest low will favor the
production of instruments of the more durable and substantial types.
In general, high interest, borrowing, dissipation of
capital, and perishability of instruments go together.
Any cause which produces any one of the four will, in
generd, tend a b to produce the other three. Likewise
low interest, lending, accumulation, and dwability of
instruments, generally go together.
The theory enunciated is that the rate of interest depends on impatience and investment opportunity. As
any cause increases or decreases our impatience for immediate income, it tends to increase or decrease the rate
of interest, Any cause which increases our opportunity
to secure returns on investments in excess of the existing rate of return tends to increase the rate of interest;
and conversely when, for any cause, opportunities to invest proonly returns lea than the existing return on
investment the interest rate tends to decline.
In Chapter TV were enumerated the
which in
373 I

c

THE THEORY OF INTEREST
the nature of man tend to make interest high or low. It
waa there stated that foresight, self-control, and regard
for posterity tend to reduce impatience for income and so
tend to make interest low. We may expect to find therefore in a community possessing these qualities some or
all of the four interrelated phenomena already mentioned
"low interest, lending to other communities, accumul&
tion of capital and construction of substantial capital
instruments. In a community lacking these qualities we
may expect to find some or all of the four opposite conditions.
82. Examples of Influence of Personal Characteristics
The nations and peoples which have been most noted
in thepast for foresight, self-control, and regard for
posterity are probably the Dutch, Scotch, English,
French, Germans and Jews, and the interestrate has been
relatively lower in general in the communities dominated
by these peoples than in communities dominated by
less thrifty peoples. They have been money lenders; they
have had the habit of thrift and accumulation, and their
instruments of wealth have been in general substantial.
The durability of their instruments of wealth is especially
seen in their buildings, both public and private, and
in their ways of transportation-roads, tramways, and
railroads.
John Rae observed of Holland:
"Hitherto the Dutch, of all European nations, seem to have been
inclined to carry instruments to the most slowly returningorders.
Thedurabilitygiven to all the instrumenteconstructed by them,
the care with which they are finished, and the attention paid t o
preserving and repairing thm, have been often noticed by travelers.
In the days when their industry and frugality were most remarksble,

I: 374 3

SOME ILLUSTRATIVE FACTS
w88 very low, government borrowing rtt 2 per cent, and
private people at 3."'

On the other hand, amongcommunities and peopIe
noted for lack of foresight and for negligencewith respect
to the future are India, Java;' the negrocommunities
both North and South,(l the peasant communities of
Russia,l and the North and South American Indians, both
before and after they had been subjugated by the white
ma.n. In all of these communities we find that interest is
high, that there is a tendency to run into debt and to
dissipate rather than accumulate capital, and that their
dwellings and other instruments are of very llimsy and
perishable character.
I t may well be that there are other causes at work
The M l o p i w l Theory of Capital,pp. 12&129.
'My colleague, Professor Clive Day, finds that interest
in Java
have advanced rather than declined since the early years of the twentieth century. He cites as the best s o m e for recent conditions the
Great Investigation (Onderzoek m r der mindere Welvaurt deinlandsch
Beudkinq op Jouu en Modoera. Batavia, 1912, IX bl Dl LI. 1, page 66).
The report &
t
e
e that on small loens under 5 florins unsecured, the
annual rate runa to several hundred per cent. On secured loans, say of
25 florins more or less, the rate varies from 3
6
% to 60%. These rates are
notably higher than his eetimate of 4
0% quoted in The Rate of Interest,
p. 292.
'Professor J. S. Lawrence, of Princeton University, informs me that
needy negroes often pay at the end of the week, 87.00 for $5.00 bop
rowed at the beginning of the week, or more than 40% per week.
'See Bloch, Ivan, The Futute of W w . T n d a t e d by R. C. Long. New
York, Doubleday and McClure Co., 1899, p. 205. It appesre that
thepeasantwould sell a promise to labor a short time in the future
at one third the current wages! See alsoLanin
(mud.), Russian
Finonce, Fortnightly Review,Vol.LV,
February, 1891, pp. 188,1%
198, for typical and extreme cases. Inostranieta, L ' U w e en
Journal des Economietes, Vol. X V I , Ser. 6, 1893, pp. 2
33-243,atates that
the ratespaidbypoor
peasants to well-to-do peasants are frglUentlY
6 per cent per week.

=tea

E 375 1

TEE THEORY OF INTEREST
to produce these results. We are here merely noting the
fact that lack of foresight is one factor present. John
Rae’scharacterization of the Indians both of North and
South America 89 highly improvident and lacking in
foresighted thrift is based on personal observation and
the testimony of missionaries and travelem6 Thenegroes
of Africa are perhaps even lessprovident than the American Indians.
In many if not all of the awes which have been cited
there are, of course, other elements whichwould tend
to explain the facts besides mere mental characteristics.
Thus, the high rate of interest among the negroes and
the Russian peasants is undoubtedly due in part to their
poverty, though their poverty is in turn due in varying
degree to their mental characteristics. Where there is too
little appreciation of the needs of the future, capital tends
to disappear; and the pressure of poverty tends to enhance still further the demands of the present and to
press down its victims from bad to worm.
Not only do we find examples of high rates of preference for present over future goods amongthe prodigally
rich, but often we find low rates of preference for present
over future goods among the thrifty poor. Examples are
especially frequent among the Scotch, the French peasants, and the Jews, whose propensity to accumulate and
to lend money even in the face of misfortune and social
ostracism is well known.
The factor which has been designated 88 ‘‘regard for
posterity” deserves special attention. Perhaps the most
conspicuous example of extreme disregard for posterity
is found in Rome during the time of its decline and fd.
Rae stresses the decay of family affection, the growth of

’Tb SO&&@Z

T k w of Copiid, pp. 11-72.

c 376 1

SOMEILLUSTRATIVEFACTS
extravtqpnt expenditure, and the high interest r a k v
High interest rates in Rome were evidently the result of
reckleas disregard of the future. Before Rome had seriously depleted her capital wealth, at about the end of
the republic, the intereat rate was as low as 4 to 6 per
cent.8
$3. Ezamples of InjEuence of Poumty
The characteristics of foresight, self-control, and regard
for posterity are partly inherent and partly induced by
conditions of the environment. Among the ca-seswhich
havebeengiven are conspicuous examples of both, although it is difficult here, as always, to disentangle the
influence of heredity from that of environment. We are
accustomed, for instance, to ascribe to the Jews a natural
racial tendency to accumulate, though this characteristic
is certainly re-enforced by, if not largely due to, the extraordinary influence of Jewish tradition. Of the Scotch
it would be B c u l t to say how much of their thrift is
due to nature and how much to training handed down
from father to son. The American negro is regarded as
by nature a happy-go-lucky creature, but studies of
negro life in Africa indicate that under favorable conditions the negro is self-denying, while recent experience
with industrial schools has demonstrated the fact that
forethought and saving can be readily fostered by training. Reckless wastefulness has been created in large psrt
among the negroes by tyranny and slavery.
The influence of conditionsuponaccumulation may
be seen everywhere, evenin the most advanced industrial
The Soddogicat T h e w of C q * t d ,pp. 64,9649,129.h'sButhority
for Roman i n t e e mees is Boucher, H&b*re de PUaue, p. 26.
'Mi-,
Eklwin R.A.,
Green and C
o
, 1807, p. 404.

01 Economics. w m , Longmsns,

c 377 1

THE THEORY OF INTEREST
countries. When postal savings banks were first introduced in England, it was objected that the English poor
for whom they were intended were so spendthrift that
they would never make use of them. But Gladstone insisted that habits were an arbitrary matter, and that the
fashion of spending would be displaced by the fashion of
saving as soon aa opportunity and incentive were dorded
and the principle of imitation had had time to operate.
The experience with English postal savings banks justified his predicti~n.~
Rae remarks upon the iiimsiness of the Chinese buildings and implements and explains this by saying that
the people “think not so much of future years as of the
present time.” lo But the high interest rates of China are
probably not due, as Rae seemed to think, to any native
lack of industry, frugality, or parsimony on the part of
the Chinese people, as is evidenced by the large accumulations of capital made by Chinese living abroad where
they are freed from the exactions of arbitrary governors
and from the tyranny of the clan-family system. Presumably the wastefulness and high interest so evident in
China are most largely due to the action of poverty rtnd
uncertainty.
For, 88 has been emphasized in previous chapters, the
rate of preference for present over future goods is not B
question of mere personal characteristics, but depends
also upon the character of one’s income stream; on its
size, shape, composition, and certainty, In respect to size,
our theory maintains that the larger the income, other
things such a8 habits, foresight and self-control being
e q d , the lower the rate of preference for present over
‘Brown, The Development of Thtifi.
“TAe &&lugid Them of Capital, pp. 88ee rrod Ba

13781

SOME ILLUSTRATIVE FACTS
future goods. If +his is true, we shouldexpect to find
poverty and riches associated respectivelywith a high
and a low rate of interest, or with borrowing and lending,
or with spending and saving, or withperishable and
durable instruments. That this characterization is in general correct is not likely to be denied.
It is true of course that the amount loaned to the poor
is small because each individual loan is necessarily smal,
but the number of these loans is very great, and the desire of the poor to borrow, when such desire exists,is very
intense. The many conspicuous exceptions to these rules
axe explainable on other grounds. It not infrequently
happens that the poor, instead of beingborrowers, axe
lenders, but in this case either they have unusual foresight,self-control,regardfor
their children, and other
qualities tending in the same direction, or else their
income stream has such a time shape as to encourage
lending rather than borrowing. Reverse conditions apply
likewise to the case of many wealthy men who are borrowers not lenders. In general, a rich man borrows not
from lack of self-control and foresight, but because of
exceptional opportunities to invest advantageously, including opportunities to protect and extend investments
already made.
As a rule, however, the poor are more eager borrowers
than the rich, and are often obliged to patronize pawn
shops and other agencies in which the rate of interest is
inordinately high. The dwellings and other instruments
of the poor are generally of a very unsubstantial charmter. Their clothes are selected of necessity morefor oheap
nem than durability. Suchuneconomical expenditures
are often even unavoidable, and reflect a very high eatimate on present 88 compared with future goods. The

c 379 1

THE THEORY OF INTEREST
deeper the poverty, the higher the rate which the borrowers are compelled to accept. Even pawnbroking is
not ava&bIe for the extremely poor, but is patronized
rather by the moderately poor. Those who are extremely
poor cannot give the kind of security which the pawnbroker requires. On this account they become the victims
of even higher rates of interest, pledging their stoves,
tables, beds, and other household furniture for the loans
they contract. These loans are repayable in instsllments
such that the rate of interest is seldom lower than 100
per cent per annum.ll
Turning fromsocialclasses to count,ries, it is noteworthy that in the countries in which there axe large
incomes we h d low interest, a tendency to lend as well
as to borrow, to accumulate as well as to spend, and to
form durable ratherthan perishable instruments. In
countries where incomes are low the opposite conditions
prevail. Thus, incomes are large and interest rates are
reIativeIy low in the United States, Holland, France,
Germany, and England, whereas the reverse conditions
hold in Ireland, China, India, Java, the Philippines and
other less developed countries. In Ireland, for instance,
especiaIly in the early part of the nineteenth century,
the rate of interest was high. The cotter waa always in
debt, and hishut and other instrumentswere of the most
unsubstantial variety.I2 Again in the Philippines the rate
x For detaile as to thirteen typical loma of tbk character, Bee U. 6.
Bureau of Labor Bulletin, No. 64, May, 1906, pp. 6!2%633. Thua ‘‘loan 1,”
143 per cent, “loan 3,” 224 per cent, “loan 7,” 166 per cent. For later
facta Bee Ryan, Umry and Uavy Lam; ala0 the publications of the
Ruasell Sage Foundation on Small Lam, espeeidy Raby, The Re&t i a of P&&w.
PLOngfieId, Momtifort. The Tenwe of Land in Z r e W in Probm’s
Bystems of Laad Tenure in Various C
o
u
n
t
r
a
i London, CaSeen,
Fetter, Galpin & Co., 1881, p. 16.

c3801

SOME ILLUSTRATIVE FACTS
of interest ongood security is often 2, 4, and even 10
per cent a month. The Chinese money lender frequently
takes advantage of the Filipino's poverty.1a Many of
these cases may be wholly or partly explained by other
causes such as have been ment.ioned in the Iast section.
$4. Examples of Influence of Compositiun of Income

As to the influence of the composition of income, it is
even more di%icult to obtain any statistical confirmation
of importance. Variations in the amount of that real income which takes the form of food has an effect on the
rate of interest similar to the effect of variations in the
total incomeitself.Scarcity of food tends therefore to
cause high interest, and abundance of food, low interest.
During the siege of Paris the rate of interest was high,
although other causes than the scarcity of breadwere
doubtless largely accountable for the fact. While no
statistics of interest rates appear to be in existence for
such periods, the testimony of eyewitnesses agree that in
Belgiumwhen starvat.ion threatened during the World
War the ,rates of interest were extremely high. Likewise
during the blockade of Germany when the food shortage
was acute, abnormally high interest rates are reported.
55. Examples of Influence of Risk

As to the influence of uncertainty or risk, we encounter
similar dif€iculties in getting positive inductive evidence.
But evidence that in general risk tends to raise the com-

mercial rate of interest but to lower pure interest is
abundant, The first part of this proposition is a matter
"From

a letter to the author from Profemr E. W. Kemmerer; see
T& &&ness Monthly, Pitteburgh, Apd, lsCn, p. 2.

also his article in

c 381 1

THE THEORY OF INTEREST
of such common observation that no special collectionof
facts is necessary. Every lender or borrower knows that
the rate of interest varies directly with risk. A bird in the
hand is worth two in the bush.
The principle applies not only to the explicit interest
in loan contracts, but to the implicit interest which goes
with the possession of all capital. Where there is uncertainty whether income saved for the future will ever be
of service, but the certainty that it can be of service if
used immediately, the possessor needs the possibility of
a very high future return in order to induce him to save.
I t is noteworthy that in time of war there is a ruthless
destruction of crops and a tendency among the possessors
of consumable wealth to enjoy it while they may. The
same conditions are characteristic of communities which
. ~ ~ rate
are in a perpetual state of political i n s e c ~ r i t y “The
of interest is everywhere proportional to the safety of
investment. For this reason we find in Korea that a loan
ordinarily brings from 2 to 5 per cent per month. Good
security is generally forthcoming, and one may well ask
why it is so precarious to lend. The answer is not creditable to Korean justice. . . In a land where bribery is
almost second nature, and privaterights are of small
account unless backed up by some sort of influence, the
best apparent security may prove a broken reed when the
creditor comes to lean upon it.” I8
There remains the second part of the proposition in
regard to risk, namely, that, while risk tends to increase
the rate of interest on risky l o w , it tends at the same

.

11

On the uncertainties of Indian life, see Rae, The SocioZ&d Theory

of Capital, pp. 69 and 70.

‘H~rlbert, H.B. The P&g
and Co., lW,p. 283.

of Korea New York, Doubleday, Page

c 382 1

SOME ILLUSTRATIVE FACTS
time to decrease that on safe loans. This proposition is
not familiar to most persons. It has usually caused surprise that during a time of political stress and danger therates of interest on perfectly safe loans were
found to be so small. Many such instances may be cited.
At certain periods during the Civil War when the greatest
uncertainty prevailed loans with good security were contracted a t nomind rates, and bank deposita tended to
rtccumulate for lack of sufEcient outlet in secure investments. The sameconditionsexisted in Europe during
the World. War. Times in whichpublicconfidence
is
shaken are characterized not only by high rates on unsafe loans, but by efforts on the part of timid investors
to find a safe place for their savings, even if they have
to 8&crifice some or all of the interest upon them. They
will even hoard savings in stockings and safe deposit
vaults. We may even occasionally find cases in which the
desire to obtain a safe method of keeping capital is so
keen and so dif3cult to satisfy that the rateof interest is
negative. The investor is then thankful enough to receive
the BBsurance that his capital, by being intrusted to
another, will not be diminished, to say nothing of being
increased.
$6. Examples of Influence of Time Shape
We still need to exemplify the most essential part of
the theory, namely, that the rate of interest depends
through the rate of impatience upon the time shape of
the income stream. The time shape may be due either
to natural or artificial causes, or to choice because of a
high or low rate of return on investment. If the theory
is correct, we should find, other things being equal, that
when in any community the income streams of ita in-

[3831

THE THEORY OF INTEREST
habitants are increasing, therate of interest willbe
high, that when they are decreasing, the rate of interest
will be low, and that when they alternate from one condition to the other, the rate of interest will alternate
dso in accordance with the period of the loan.
The most striking examples of increasingincome
streams are found in new countries. It may be said that
before the World War the United States almost always
belonged to this category.Were it possible to express
by exact statistics or diagrams the size of American incomes, they would undoubtedly show a steady increase
since colonial days. Statistics almost equivalent to these
desiderata are available (though not very accurate) in
the form of the United States Censusfigures of per
capita weakh, as wen as in statistics of production and
consumption of staple commodities and of exports and
imports. These, combined with common observation and
the statements of historians, lead to the conclusion that
Americanincomes have beenon the increasefor two
hundred years. It is also true that during this period
of rising incomes the rate of interest has been high. The
simplest interpretation of these facts is that Americans,
being constantly under the influence of great expectations from the exploitation of great natural resources,
have been always ready to promise a relatively large part
of their abundant prospective future income for a relatively small addition to their present, just as he who
expects won to come into a fortune wishes to anticipate
its realization by contracting a loan.
Not only has the rate of interest been high in America
aa compared with other countries during this period of
ascendingincomes, but some of the other conditions
having the m e significance at3 a high rate of interest

cm3

SOME ILLUSTRATIVE FACTS
have also been in evidence. Thus, the country has been
conspicuously a borrowing country, in debt to other countries. The proceeds of such loans from Europe have shown
themselves in increased imports into the United States
and diminished exports, creating a so-called unfavorable
baltLnce of trade. These phenomena have usually been expressed as a demand forcapital, but, while it is quite true
that .the exploitation of our natural resourcesrequired
the construction of railways and other forms of capital,
this fact is better and more fully expressed interms of income. We wanted, not the railways and machinery themselves, but the future enjoyable products to which this
apparatus led. The labor of constructing these instruments necessarily tended to diminish the immediate enjoyable income of the country, but added to that of the
expected future. I t was to even up this disparity of immediate and remote income that loans were contracted.
I t does not matter whether the loans from the foreigner
were received in the form of machinery and other instruments of production, or in the form of the comforts
of life to support us while we ourselves constructed the
instruments. In either case the essential fact is the tmsformation of the income stream rather than the need of
capital, whioh is merely one of the means thereto.
Not only have we witnessed the phenomena of high
rates of interest and of borrowing during this period of
American development, but it is also true that the character of the instruments created was for the most part
of the unsubstantial and quickly returning kinds. Our
highways, tu John Rae pointed out, were little more than
the natural surface of the earth after the removal of
trees and rocb; our railways were lightly ballast&
sometimes even narrow gauge, and crooked to avoid the

I3861

THE THEORY OF INTEREST
necessity of excavations and tunnels; our earliest buildings were rude and unsubstantial. Everything was done,
not in a permanent manner with reference to the remote
future, but in order to save a large first cost.
During the last generation these conditions have been
changed. The rates of interest in America are, in general,
lower than formerly, and lower than in other countries,
in many of which interest rates have risen.le We have
ceased to be a borrowing nation. We bought back many
of our securities from abroad, and after the World War
began to buy foreign securities. This was accomplished
through the excess of exports of our abundant products
over imports. We are now lendingbillions to Europe.
Europe has become a borrower, the chiefreasonbeing
that in her recovery from the War her income stream is
rising. During that recovery from the impairedincome
wrought by the War,Europe in some places offers bigger
returns over costs than America. That fact, combined
with Europe's poverty, makes for high interest.
The interest rate has fallen in the United States since
1920. This agrees with, or at le& is consistent with, the
theory that raising the level of nationd income tends,
other things equal, to lower the rate of interest.
Again, the character of the instruments which have
beennowforsome
time in process of construction in
the United States is of the most substantial kind. Steel
rails have long since taken the place of iron rails; railways have been straightened byexpensive tunnels, by
bridges, and by excavations ; dwellings and other buildings have been made more substantial; first macadamized
and Zater cement roads have rapidly supplanted the old
dirt roads; and in every direction there has been an evi"See Appendix to Chapter XIX, 8 l.

c3861

SOME ILLUSTRATIVE FACTS
dent tendency to invest a large first cost in order to
reduce future running expenses.

07. Rising Income Means High Interest Rates
Thus, in America and in Europe, we see exemplified
on a very large scale the truth of the theory that a rising
income stream raises and a falling income stream depresses the rate of interest, or that these conformations
of the income stream work out their effects in other
equivalent forms.
A similar causation may be seenin particular localities
in the United States, especially where changeshave been
rapid, as in miningcommunities. In Californiain the
twodecadesbetween 1850 and 1870 following the discovery of gold, the income stream of that state was increasing at a prodigious rate, while the statewas isolated
from the world, railroad connectionwith the East not
having been completed until 1869. During this period of
isolation and ascendingincome,
. opportunities for
investment were innumerable. Hence the ratesof interest
were abnormally high. T h e current rates in the ‘early
days’were quoted at 1% to 2 per cent a month.
The thrifty Michael Reese is said to have half repented
of a generous gift to the University of California with
the exclamation, ‘Ah, but I lose the interest,’ a very
natural regret when interest was 24 per cent per
annum.” l7 After railway connection in 1869, Eastern
loans began to flow in, The decade, 1870-1880, was one of
transition during which the rates stimulated borrowing
from the outside,which brought about lower interest

“. .

. ..

“Plehn, Carl C. Notea Concemhg ths Rut+% of Znteteat in Colifornio.
Quarterly Publications of the American Stati8ticrrl Association, September, 1899, pp. 361-362.

13871

THE THEORY OF INTEREST
rates even though income streams continue to increase.
The rate of interest consequently dropped from 11 per
cent to 6 per cent.18
The same phenomena of enormous interest rates were
also exemplified in Colorado andthe Klondike. There
were many instances in both these places during the
transition period from poverty to duence, when loans
were contracted at over 50 per cent per annum, and the
borrowers regarded themselves as lucky to get rates so
low. It was also conspicuously true t,hat the first buildings and apparatus constructed in these regions werevery
unsubstantial. Rude board cabins were put up in a day.
Thus, hi& interest, borrowing, and unsubstantial capital
were the phenomena which attended these communities
when undergoing their rapid expansion.
In Nevada in the seventies, when the mines were increasing their product and the income of the inhabitants
wag tending upwards, the rate of interest was high and
the people in debt. The bonded state debt itself amounted
to $
5
O
O
O
,O
Oand drew 15 per cent interest.le In the next
decade alI these conditions were reversed.The mines were
on the decline,2O the rate of interest fell, and the state
and territorial debts werelargely paid
The fall of
the rate of interest in this case could not have been due
to the introduction of loans from outside, except so far
aa old debts were refunded at lower rates; fresh loans
were seldom made, aa the state had ceased to be a good
place for new investments. At about the beginning of
this century, new Nevada mines in the gold-field region
"Plehu, p. 353.
*See Me-smge of the Goyenun of tk W e of Nevaah, 1879.
"Mines and Qd,
1802. Special Report U.8.Ceneus, p. 256.
later Messoqes of the Governor of the 8tote of NevoGa

l-3881

SOME ILLUSTRATIVE FACTS
were opened. Loans were again
entering the state, and
the samecycle of history, as above described,wasrepeated.
Lumbering communities often go through a somewhat
similar cycle. The virgin forests when h t attacked tend
to increase rapidly the income streams of thosewho
exploit them; then comes a period of decrease. Thus in
Michigan two or three decades agothe lumber companies
found a profitable investment, and borrowed in order
to exploit the Michiganforests. After the exploitation
was complete and the forests had been (often unwisely)
exhausted, those regions ceased to be a desirable place
for investment, and their owners came into the position,
not of receiving, but of seeking investments.
After the trunk lines of railway were completed, connecting the Mississippi Valley with the East,there arose
B great demand for loans to exploit the rich farming
lands in that section of the country. The rate of interest
frequently was 10 and 12 per cent and even higher. Duringmuch of this time the Northwestern Mutual Life
Insurance Company up to 1880 made an average rate on
all its mortgage loans, $lO,OOO,OOO in amount, of nearly
10 per cent. Another striking proofof the demand for
loans in the Middle West is shown in the experience of
the New York and Connecticut life insurance companies.
New York up to 1880 had B law prohibiting the life insurancecompaniesin that state fromloaning on real
estate outside of New York. Connecticut had no restriction in this regard, and her companies loaned extensively
in the West. The result is seen in the rates of interest
realized on mortgageloans of companies in the two s t a b .
Taking the period 1860-1880 a~ a whole, the Connecticut
companies realized 1.2 per cent more than did the New

I389 1.

THE THEORY OF INTEREST
Yorkcompanies.Since 1880 the MiddleWest has developed less feverishly, and loans on farming lands have
been made at lower rata.
Australia furnishes another example of a country
which, through improvement inthe means of transportation and consequent great investment opportunities,
created a great demand for loans. The rate during the
fifties on safe securities was rather low. This rate increased until during the seventies, 7, 8, and 9 per cent
were usual. After 1880 the rates
England may perhaps be cited as exemplifying the
same phenomenawhich we have seen in the case of
Nevada, though in a lessdegree. Thus as Nevada has
exhausted its mines of precious metals, so England is
on the road toward exhaustion of ita coal and iron supplies. As cod and iron lie at the base of England’s commercialpower their exhaustion must carry with it the
reduction of the income stream from English domestic
industries. This fact has been noted with considerable
ala,rmby some English economists, especially Jevons.
But
it does not necessarily indicate that the economic power
of Englishmen will be greatly or even at all lessened.
Its significance shows i h l f in the tendency of England
to become an investing country. It is the part of those
who have property in mines or other investments yielding terminable income not to use all of the product as
income, but to reinvest some of the earlier income in
order to maintain the capital. This the Englihmen have
done and are doing, and, being unable to make enough
satisfactory investments at home, they have placed their
loans all over the world.
Zartman, L&er W.The Znve&mentu of Life Inswcmcs C M .
New York, Henry Holt and Co., ISM, p. 103.

13901

SOME ILLUSTRATIVE FACTS
The income stream produced for them by their native
island is destined,perhaps, to decline, certainly not
greatly to increase except during the next few years or
decades of recovery fromthe World War. By saving from
this decliningincome and investing in Canada, the
United States, South America,Australia,SouthAfrica,
and other regions where the natural resources are being
exploited and incomes axe on the increase instead of
on the wane, Englishmen maystill maintain their capital
intact or even increase it. The figures given by Giffen
show thatthe national incomeincreased for several
decades, but that the rate of increase slackened for the
decade 1875-1885 compared with 1865-1875. Whereas
in the earlier decades there waa a generalincrease in
all directions, inthelater
decade there were many
items of decreaee,2a the most notable being of mines
and ironw~rks.~'Among the greatest increases was that
of foreign investments.25

$8. Effect of Catastrophe8 on Znterest
The time shape of an income stream is determined,
however, in part by other causes than natural resources.
Among these causes, misfortune holds a highplace in
causing temporary depressions inthe income stream, that
is, in giving to it a time shape which is at first descending
and afterwards ascending. The effect of such temporary
depression is to produce a high valuation of immediate
income during the depression period, as compared with
the valuation of the income expected after the depression is over. It is a matter of commonobservation in
private life that loans often find their source in personal

" Giffen, &moth of C
¶a IM.,
p. as.

M , p. 44.

= IM.,
pp. 40.42.

c 391 1

THE THEORY OF INTEREST
misfortune. Investigations of pawnbrokers and small loan
conditions among the poor 26 show that the chief causes
for borrowing are a death or birth in the family, or a
protracted illness, the expense of
which
evenwhen
amounting to only $10 or $20 would, without the loan,
make serious inroads on the daily necessities.
We may see the operation of the same principle on a
larger scale in the examples of the San Francisco earthquake, the earthquake whichwreckedYokohama
and
Tokyo, the plague which destroyed whole communities in
Russia, and the famines of China. Had it not been for
the succor rendered by more fortunate communities and
countries, the income stream of same of the stricken
communities and provinces in Russia and China would
have sunk so low that scarcely any would have been able
to survive. In addition to the aid of tens of millions of
dollars in gifts, large loans were made which enabled the
afflicted communities to build themselves anew. Whether
these loans were used to produce sustenance, which is
direct income, or to offset the cost of rebuilding and replacing destroyed capital goods, which is outgo, the effect
was the same; they were for the purpose of tiding over
a temporary decline, or loss, in the income stream. The
permanent effect of these catmtrophes on the rate of
interest was slight because of the opportunity to borrow
heavily fromoutside. Had these opportunities not existed, the depression in the income stream could not have
been mitigated, and the rate of interest would inevitabIy
have risen to 8 level comparable with that which prevailed in primitive times or during a gold rush.
In much the same way the income stream of a nation
is affected by war. The effecte in this caae, however, ase
"See U.6. Bureau of M o r Bulletin, No.64, May, 1906, pp. 82aff.
c3921

SOME ILLUSTRATIVE FACTS
more complex, owing,first, to the element of uncertainty
whichwar introduces until peace is declared, and secondly, to the fact that wars axe likely to be more
protracted than most other misfortunes. The effect, according to previous explanations, should be that at the
beginning of the war the rates of interest on risky loans
would be high. This would be especiallytrue of the short
term loans which do not outlast wax. On the other hand,
the rate of interest on safe loans should be lowered for
short term loans, and raised for long term loans. Under
the conditions of a war in its early stages, a short term
loan relates to a descent in the income curve. It is repayable at a time when @come is expected to be less than
when the loan is contracted. The descent in the income
curve, or the element of uncertainty, tends, as has been
seen, to lower the rate of interest on safe loans. On the
other hand, for long term loans intended to outlast the
war, the rate of interest is likely to be high, for the income
stream at the time of repayment may be expected to
exceed the income stream at the time of contract.
A t the close of war, after peace is declared and the
element of uncertainty introduced by it has disappeared,
the rate of interest even on short term loans will, contrary to the common view, be high, for then the country
is, as it were,beginninganew,
and the Same causes
operate to make interest high as apply in the case of all
new countries.
When the effects of war include the issue of depreciated paper money, the rate of interest is affected in a
somewhat more complex manner, being then subject to
the influence of depreciation, according to the principles
explained in Chapter I1 and s t a t i s t i d y treated in
Chapter XIX.
13931

TEE THEORY OF INTEREST
$9. Emmples of Influence of Periodicity of Income

We have considered supposed examplesof the effect on
the rate of preference exerted by those changes in the
income stream due to the growth or waning of natural
resources and t.0 the temporary influence of misfortunes
and inventions. There remain to be considered examples
of more regular changes in the income stream of a
rhythmic or se&sonaJ character. Though mostpersons
arenot aware of the f a t , it can scarcely be doubted
that the annual succession of eeasons produces an annual
cycle in the income stream of the community. This is
especdly true of agriculture. Graips, fruits, vegetables,
cotton, wool, and almost all the organic products flow
from the earth at an uneven rate, and require for their
production also an uneven expenditure of labor from
man during different seasons of the year. Statistics of
consumption show that the income enjoyed conforms in
general to a seasonal rhythm. Food produota are usually
made available in the warm months when crops ripen;
logs are hauled out of the woods in the winter, floated to
mills in the spring, and made into lumber in the summer.
But the tendency to a seasonal rhythm is modsed by
the existence of stocks of commodities to tide over the
periods of scaxcity. The ice of winter is stored for summer,
and the fruits of summer are canned and precserved for
winter. Only so far &s such storage and preservation &pe
difficult and expensive, or impair the quality of the goods
thus held over, or &re impracticable, because of the perishable nature of the goods, does there remain any seam n d change in enjoyed income. The rhythm is dserent
for Werent industries and for different claase~of the
population. The farmer is perhaps the moat typid for

c3941

SOME ILLUSTRATIVE FACTS
the country 88 a whole. For him the lowest ebb is in the
fall, when gathering and marketing his crops cause him a
sudden expenditure of labor, or of money for the labor
of others. To tide him over this period he may need to
borrow. A whole group of other industries, particularly

.

a P

"

d

z

p'

z

3

d

s'

I

ct'

CHART 39
Monthly Avemge Discount Rates; New Yo&.

those connected with transportation, experience a aympsthetic fluctuation in the income stream. In the parlance
of Wall Street, money is needed to move the crops. The
rate of interest tends upward.
Chart 39 &OWE, for the period 1869 to 1905, the

C 395 1

THE THEORY OF INTERrEST
monthly average of interest rates on prime, two-name,
60 to 90 day
The theory that interest rates vary with the seasons,
rising during the late summer and autumn months and
sinking during the winter and early summer months is
borne out by Professor W. L. Crum's article, Cycles of

Rates on Commercial Paper,28 which treats of monthly
fluctuations in commercial paper rates over the period
1874 to 1913.
Chart 40 is a reproduction of Professor Crum's chart
showing monthly deviations of interest rata from the
annual average of monthly rates over the period 1874 to
"The average rate8 for each month plotted on the chazt were Cornpiled from the daily rates publidmi in The Fjnatu5d Review.
='The Review of Economic Btsthtics, JMW, 1023, pp. 17-27.

13961

SOME ILLUSTRATIVE FACTS
1913. It will be noted that the fluctuations shown on
Chart 40 me almost identical with those shown on Chart
39. No comparison of rates is possible because Chart 40
shows only monthly devbtions above and below the average annual rate, while Chart 39 shows the average of
u t u d rates. Both charta show a low for February, a re-

!

b

i

~

j

&

a

&

i

*

$

$

j

CHART 41
Monthly Averages of Discount Rates, Bank of England.

bound in March and April, a deeper depression in June,
then 8 buoyant advance to the peak in September and
October, followed by 8 slump when the autumn demand
for money cmd credit to handle the crops is p a t .
In a community dominated by some industry other
than farming the cycle would be different. The rates are
of course a composite in which the cycles of the mmu-

$

g

~

THE THEORY OF INTEREST
facturer and of other elements are superimposedupon
the cycIe of the farmer. The manufacturer’scycle is a
little later than the farmer’s and shifts the high rates
from fall toward winter. Accordingly in England, which
is more dominated by the manufacturer, the cycle,
though similar tothatjust
observedfor the United
States, is Bhifted slightly forward, 85 is shown in Chart
41

$10. S u m q
Although the fact,s presented in this chapter do not
prove the theory presented in previous chapters they
are not in conflictwith it. According to the theory, if
there is a high degree of foresight, self-control, and regard for posterity and income streams are large and
plentiful in food-element, or have a descendingtime
shape, then, other things being equal, the tendency will
be for the rate of interest to be low, capital will be accumulated, the community will lend to other communities,
and the instruments it creates will bemore durable.
We find these results present in actual fact where the
antecedent conditions enumerated are also present. Reversing the conditions, we find reversedresults. Of course
these statistical evidences axe very general,since we
never can assert that “other things are equal,” and thus
isolate and measure any one particular factor, as in the
more exact inductions of physical science.

S
‘e
ePalgrave, Bank Rate and the Money Market, 9.97.

C 398 3

CHAPTER XIX
THE RELATION OF INTEREST TO MONEY AND
PRICES
$1. Price Changes and Interest Rates

No problem in economics has been more hotly debated
than that of the various relations of price levels to interest rates. These problems are of such vital importance
that I have gone to much trouble and expense to have
such data as could be foundcompiled,compared, and
analyzed. The principal result of these comparisons are
given in this chapter.
The general theory of the relationship between the
rate of interest and thebuying power of money was summarized in Chapter 11. The main object of this chapter
is to ascertain to what extent, if at all, a change in the
general price level actually d e c t s the market rates of

interest.
Since the theory of Chapter I1 presupposes foresight,
the question rtrises at the outset: How is it possible for
a borrower or lender to foresee va.riat,ions in the general
price level with the resultant increase or decrease in the
buying power of his money? A change in the value of
money is hard to determine. Few business menhave any
clear ideas about it. If we ask a merchant whether or not
he takes account of appreciation or depreciation of money
values, he will say he never heard of it, that“a dollar is a
dollar!” In his mind, other things may change in terms
of money, but money itself does not change. Most people
~3991

THE THEORY OF INTEREST
are subject to what may be called “the money illusion,”
and think instinctively of money as constant and incapable of appreciation or depreciation. Yet it may be
true that they do take account, to some extent at leaat,
even if unconsciously, of a change in the buying power of
money, under guise of a change in the level of prices in
general. If the price level falls in such a way that they
may expect for themselves a shrinking margin of profit,
they willbe cautious about borrowingunless interest
falls, and this veryunwillingness to borrow,lessening
the demand in the money market, will tend to bring
interest down. On the other hand, if inflation is going on,
they will scent rising prices ahead and so rising money
profits, and will be stimulated to borrow unless the rate
of interest rises enough to discourage them, and their
willingness to borrow will itself tend to raise int,erest.
And today especially, foresight is clearer and more
prevalent than ever before. The business man makes a
definite effort to look ahead not only as to his own particular business but as to general businessconditions,
including the trend of prices.
Evidence that an expected change in the price level
does have an effect on the money rate of interest may be
obt,ained from several sources. Quring the free-silver
agitation of 1895 and 1896, municipalities could sell gold
bonds on better terms than currency bonds. There was a
strong desire onthe partof lenders to insert a gold clause
in their contracts, and to secure it they were willing to
yield something in the interest rate.
The same tendency WBS strikingly shown in California
during the inflation period of the Civil Wu.l For a time,
Mom, Bernard, L
e
& Tender Notes in Cdifomia, Quarterly J0-d

RELATION TO MONEY AND PRICES
gold contracts could not be enforced, and in consequence
interest rates were exceptionally high.
82. United States Coin and Cwrencg Bonds
A more definitetest may be made where twostandards
are simultaneously used. An excellent case of this kind
is suppliedbycomparingtwokinds
of United States
bonds,one payable incoin and the other in currency.
From the prices for which these bonds sold in the market
it is possible to calculate the interest realizedby the
as currency
investor. The currencybondswereknown
sixes and matured in 1898 and 1899. The coin bonds selected for comparison were the fours of 1907. The table
on page 402 gives the rates of interest realized in the two
standards, together with the premium on gold.
Several points in this table deservenotice. In 1870
the investor realized 6.4 per cent in terms of gold but
was willing to accept a return of only 5.4 per cent Cirrrency. Whyshould a goldbondbe
thus inferior to a
paper bond? This has become intelligible in the light of
the theory which was explained in Chapter 11. It meant
the hope of resumption. Just because paper was depreciated below gold and there was a chance of bringing it
up to par, there was in prospect a great rise in its value,
as compared with gold. It was not until 1878, just before
resumption, when the prospect of any further rise disappeared, that the relative position of the two rates of
interestwasreversed. After resumption in 1879, when
paper money did reach par with gold, the two bond rates
remained very nearly equal for several years, until fears
of inflation from Greenbackism and F'ree-Silverh again
produced a divergence. The quotations for 1894, 1895,
and 1896 &owed a considerably higher rate of interest

L4011

THE THEORY OF INTEREST
Rates

of Interest

.Er

..
1871....
1871....

Jan. 1870..
July

Jan.
Julv

1870..5.1
5.3
5.O

”

1872....I
July 1872...
Jan. 1873..
J ~ Y1873..
Jan. 1874...
July 1%’4.. .
Jan. 1875....
July 18/5.. . .
Jan. 1876....
July 1876....
Jan. 1877.. . ,
July 1877
Jan. 1878..
July 1878....
Jan“.

TABLE
11
Realized from Dates Named to Matw:

.
..
..
..

....
..

5.3
5.6
5.7

5.4
5.0
5.1
5.0
4.45.2
4.54.4
4.4
5.0

3.49.4

I 4.9

5.0
5.1
5.0
5.O
4.9
4.7

43
4.6

I*

Cur-

....

119.9
112.2
110.8
1136
109.5
113.9
111.9
115.3
110.3
110.7
112.6
117.0
112.9
112.3
107.0
105.4
102.8

Jan. 1879

3.7

May
July
Jan.
Mar.
Nov.
Aug.
Aug.

2.1
2.4
2.6
2.8
2.7
2.8
33

Ilk: :m:::l”

100.7

1890...;

....
.

1891
1892... .
1893.. .

1894.. . .

1895... .
1896..

..

rency
46
4.O
3.4
3.5
3.3
2.9
2.7
2.6
2.6
2.8
2.6
2.6
3.O
3.1
3.1
3.5
3.6
4.3

price
?

in ’ the currency standard than in the coin standard, as
we11 as a higher rate in both standmds than in previous
years. The contrast is that between 2.7 per cent and 3.5
per cent in 1894, and between 3.2 per cent and 4.3 per
cent in 1896. The divergence of the two rates is explain‘This table has been obtained by the aid of the usual brokers’ bond
tables. In the c88e of currency bonds, it WBS only necessary to deduct
accrued interest (if any) from the quoted price and look in the table
for the interest which corregponds to the price 80 found and the number
of yeara to maturity. Thia gives the rate in terms of “currency.” In
the ~ 8 8 eof coinbonds,since
the quotations are given in currency,
it ie newto divide the quoted price by the price of gold in order
to obtain their price in gold(i.e., “coin”), and then proceed as above
indicated. We thus get the rate in terms of “coin.” The quotations of
prices of bonds and gold are the “opening”prices for the months
named, and are taken from the Financial Review and ita annual Bummaw, The Commercial and Financial Chronicle, 1895, the (New York)
Bankers’Magseine and theBanked
After 1884, JanuarV
quotations were not always available.

Almanac.

c4021

RELATION TO MONEY AND PRICES
able aa the effect of the fear of Bryan’s free-silver proposal, incorporated (July, 1896) in the platform of the
Democratic party.Hadfree coinage of silverbeenrestored at the ratio of 16 to 1, since the bondholders had
the option of demanding either gold or silver in payment, coin bonds presumably would stillhavemeant
gold bonds. Hence investors were ready to accept lower
interest on these bonds than on currency bonds.

$3. Gold and Rupee Bonds
Having compared the rates of interest of paper and
coinbonds, we maynext compare those of gold and
silver securities. The comparison, to be of value, must
be between gold and silver contracts in the same market
and with the same security. Fortunately such contracts
have been available in the London market of government
securities. The loans of India have been made partly in
gold and partly in silver, and both forms of securities
have been quoted in London.a The interest on the silver
bonds, or rather rupee bonds, was paid by draft on India.
The sums actually received in English money depended
on the state of the exchanges. The rate of interest in the
silver standard was calculated * in the same way as was
‘The silver bonda or “rupee paper” were h u e d to raise loam in India,
but they were also edaeed for payment in England, and in 1893.
1894 some Rx. 25,000,W were on the London books. Burdett’s Offici& InteUiqetlcer ( l a ) ,p. 75.
‘Thus, in 1880 the average price paid in London for “rupee paper” of
face value Rx. loo0 yielding 4 per cent, or Rx. 40 per annum, waa f79.
In order to find the rate of interest realized by the investor, we must
translate €79 inb silver. The average rate of exchange in 1880 was zod.
per rupee. Hence 279 were equivalent to 948 rupees. That is, epeaking
in t e r n of silver (or, more exactly, in terms of exchange on India),
the price of a 4 per cent bond waa M.8, which, if the bond be treated
w a perpetual annuity, yielda the investor 4.3 per cent. In the m e
Year, an India gold bond yielded 3.6 per cent.

c4033

THE THEORY OF INTEREST
shown for coin bonds in $2. The results follow:
TAB^ 12
Rates of Interest Realized from Date: N a m d to Maturity or in

Perpetuity

Rupee *

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

1865
1868
1870
1871 ...............
1872
w 3
1874
1875
1876
1877
1878

...............
...............
...............
...............
...............
...............
...............
...............
...............
...............
1881 ...............
1882 ...............
1883 ...............
...............
1885 ...............
18% ...............
...............
...............

1889 ...............
1890 (1st half)
1890 (2nd half)
1891
1892
1893 ...............

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

...............
1894 ...............
1895 ...............
1896 ...............
1897 ...............
18% ...............
1899 ...............
le00 ...............
1901 ...............
...............
1903 ...............
1904 ...............
1905 ...............
1906

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

4.3
4.3
4.3
4.1
3.9
3.9
3.9
4.0

4.1
4.1
42
4.4
4.3
4.0
3.9
4.1
4.1

4.0
3.9
3.8
3.9
3.9
3.9
3.4
3.3
35
3.7
3.6
3.7
3.7
3.6

35
3.6
3.8

Gold

Difference EXC:n&:f:

.2
4.1
3
4.0
3
4.0
3.8
3
a
3.7
2
3.7
.1
38
.4
3.6
.4
3.7
4
3.7
3
3.9
1879 3.7
f
1880 3.6
7
3.4
8
.4
35
.7
3.4
4.1
3.3 4.1 1884 8
.8
35
.6
35
3.4 4.1 188f 7
3.1 4.1 1888 1 0
3.0
4.1 1.1
1.o
3.0
3.1
s
3.1
1533.1
3.0
9
3.0
9
28
6
3.1
2
4
3.1
.5
32
32
4
3
3.4
36
2
1
1902 35
35
0
-.l 3.7
3.6
.0
32
A

.

.
.
.

..

i

..
.
.

.
.

F~otnotesto this table are given on page 406 .

C&l

On

Pence per
Rupee
23.2
P.0
23.6
23.2
22.6
22.4
222
21.9
205
20.9
20.2
19.7
20.0
19.9
195
195
19.5
185
17.5
17.2
165
165
17.6
193
17.1

15.0
13.5
13.4
143
15.1
16.O
16.1
16.0
16.0
16.0
10.0
316.1
.6
16.1
16.0

RELATION TO MONEY AND PRICES

From this table it will be seen that the rates rea&&
to investors in bonds of the two standards differed but
slightly until 1875, when thefall of Indian exchange
began. The average d8wence from 1875 to 1892 inclusive was 0.7 per cent. Within this period, from 1884, exchange fell muchmore rapidly than before, and the
difference in the two rates of interest rose accordingly,
amounting in one year to 1.1 per cent. Inasmuch as the
two bonds were issued by
the same government,possessed
thesamedegree of security, were quoted side by side
in the same market, and were similar in all important
respectsexcept in the standard inwhich they are expressed, the resulta afford evidence that the fall of exchange (after it once began) was, to some extent, discounted in advance and affected the rates of interest in
those standards. Of course investors did not form perfectly definite estimates of the future fall, but the fear
‘The quotation from which the intereat waa computed for 18% and
succeeding years is for 3% per cent rupee paper. All previous quotations
are for 4 per cent’s. The 4 per cent’s were repayable on three months
notice; this notice waa given in 1894, and the bonds redeemed or converted into 3% per cent’s before the close of the year. To obtain the
rate of interest realked, the London quotations in pounds Bterling are
first converted into rupees at the current rates of exchange, snd then
the bonds are treated aa perpetusl annuities. The results differ from
thosegiven in the Investor’s Monthly Manual, because the rupee is
there converted a t a conventional value, not the market value.
bFrom 1865 to 1880 inclusive the figures refer to 4 per cent’s, repcryable October, 1888, or later; those of 1881are for 3% per cent’s maturing
in 1931, and those for 1885 to lsog are for 3 per cent’s maturing in 1948.
‘This table is made from averages of (usually ten) qUOtatiOnS distributed through e
a
& year,
from the Economist, the Investor’s
Monthly Manu& a d the (London) Bankera’Magmine. The fourth
~
h is founded
n
on the table in the Report of the Indh CWenCY
Committee ( l a ) ,p. 21, but is w m k d to apply to calendar b
c
I of
official years.

sen

CW3

THE THEORY OF INTEREST
of a fall predominated in varying degrees over the hope
of a rise.
The year 1890 wasone of great disturbance in exchanges, the average for the first six months being 17.6
and for the last six months, 19.3. The gold price of the
silver bonds rose froman average for the first six months
of 73.8 to 83.5 for the last six mont<hs,but the rise in
their silver price was only from 100.6 to 103.7, showing
that the increase of confidence in the future of silver
was not great, and, in fact, only reduced the disparity in
the interest from 1.0 to .8per cent.
This great rise in exchange and the slight revival in
silver securities occurred simultaneously with the psssage
of the Sherman Act of July, 1890, by which the United
States was to purchase four and a half million ounces of
silver per month. The disturbance was doubtless due in
some measure to the operation, or expected operation, of
that law.
This is not the only case in which the relative prices
of rupee paper and gold bondswere probably affected
by political action. One of the smallest differences in the
two rates occurs in 1878, which waa the year of the Bland
Act and of the first International Monetary Conference.
After the closure of the Indianmints to siIver on
June 26, 1893, exchange rose from 14.7 to 15.9, the gold
price of rupee paper from 62 to 70, and consequently its
rupee price from 101.2 to 105.7.
From this point the exchange again dropped, much to
the mystification of those who had predicted an established parity between gold and silver at the new l e d
rate of 16d per rupee. There was much discussion as to
the reasons for the failure of the legal rate to become
operative. The chief reason seems to have been that the

E4061

RELATION TO MONEY AND PRICES
closure of the mints to silver attracted into thecirculation
silver from other channels, especially old native hoards.
Within a few yeaxs, however, this source of supply was
dried up so that the legal par was reached in 1898 and
waa maintained thereafter, subjectonly to theslight variations of exchange due to the cost of shipping specie.
But until the par was proved actually stable by two
or three years’experience, the public refused to have
confidence that gold and the rupee wereoncemore to
run parallel. Their lack of confidence was shown in the
difference in the rates of interest in gold and rupee securities during the transition period, 1893-1898, and the
two or three succeeding years. From 1893 to 1900 inclusive the two rates averaged .5 per centapart. From
1901 to 1906 inclusive, the average difference was only
.1 per cent,6 showing that confidence in the gold value
of the rupee had been established.
54. Money Interest and Red Interest

The foregoing comparisons relate to simultaneous rates
of interest in two contrasted monetary standards each
actually used for loan cont,racts. We now turn to a comparison between money rates and real rates of interest,
mentioned in Chapter 11. Unfortunately no contracts in
terms of real or commodity standards are available for
quotation. All we can do is to note the changes in the
‘The preceding comparisons erve only to eetsMishtheinfluence of
the expecteddivergencebetweenthetwo
standards on the rate8 of
interest, but &ord no exact measure of thatinfluence. In order to
measure the extent to whichthe fall of silver WBB allowedfor by inbe neto examine the rates realisedduring
specific perioda. Somewhat unpatisfactory attempts to do thia (both for
the case above of American gold and “currency” bonds and for the e ~ e e
below of Indian gold and “rupee bonds”) were made in my Appreciation
and here&, but are not reproduced here.

vestors, it would

r4071

THE THEORY OF INTEREST
price level, translate the actual rates in terms of money
into real rates, and compare successive periods.Such
comparisons arenot very satisfactory, since no two
periods, not even successive periods, are so alike industrially that we can say that they differ only as to the
state of the monetary standard as reflected in the index numbers of prices. Of course, influences other than
changes in money affect interest rates.
Detailed tables showing the average annual rate of
change in the commodity price level,7the rates of money
interest, and the rates of red interest for London, New
York,Berlin, Paris,'Calcutta, and Tokyo are givenin
basic t'ables in the Appendix to this chapter. Wholesale
commoditypriceswereused
in computing these rates
although cost of living indexes would have been preferable for this purpose and morein harmony with my
theory of income. But cost of living indexes do not exist
for the period covered.
Chart 42 shows the annual rate of change in the commodity pricelevel
(upperpart)
compared with the
market rates of interest (lower part) in the London market over the period 1825 to 1927. The ch& also gives
the red rate by a dotted line, but this may, for the
present, be overlooked.
It will be observed that the entire period is broken up
into sub-periods,whichconform to rather d&nite and
subsuccessively contrasted pricemovements.These
periodswereallowed to choose themselves, so to say.
That is, they were so chosen that each period shouldshow
a rather distinct change in the rate of price change &9
compared with the preceding and succeedingperiods.
'The basic tsblea for computing the mte of price changes and the
method of computation are given in the Appendix to this chapter 81.

L-4083

RELATION TO MONEY AND PRICES

L

L

I

THE THEORY OF INTEREST
The periods were not chosen with any reference to, or
indeed withany knowledgeof,how
the choice would
affect the comparisons to be made. For example, the
period 1825-1834 was a period during which commodities
a t wholesale fell at the average (annual) rate of 3.0 per
cent per annum; this is plottedon the chart, in the usual
way, by a horizontal line 3.0 points below the zero line.
In the period 1834-1839 prices rose at the rate of 3.3 per
cent per annum; this is plotted on the chart
by a horizontal line 3.3 points above the zero line.
A brief glance at Chart 42 reveals that when t.he rate
of price change falls from one period to the next, the
money rate of interest usually falls, and when the rate of
price change rises, the interest rateusually rises also. The
comparison of each period with the one following may
be designated &s a sequence. In London eight such
sequences out of ten for bank rates, and nine out of ten
for market rates support the theory that money interest
rates move in the same direction as the price level.
Comparisons of price change rates and interest rates
have also been made for New York, Berlin, Paris, Calcutta, and Tokyo. The results, favorable andunfavorable,
of all these comparisons are summarized in Table 13.
TARLEI
13
Sequences, Favorabk and Unjavurcable

...

Favorable
Unfavorable

.

17

3

3

15

Of the sequences compared, 38 support and 15 oppose
thetheory propounded. Thus, the favorable sequences
are two and a half times as numerous as the unfavorable
c 4 w

RELATION TO MONEY AND PRICES
sequences. This is a large preponderance, especially when
we consider that there are 80 many inexactnesses in the
statistical data and so many other causesaffecting the
rate of interest besides changes in the price level,
The same result may be expressed in terms ofcomelation coefficients. When we correlate interest rates with
pricechanges for theimportant
industrial countries
(England, Germany, United States), fairly high coefficients (about
0.7) are obtained. Correlating the first
differences, that is, changes in interest rates and rates of
price changes, likewise, shows a fairly high relationship
in accord with the theory. However, the correlation for
the data of all count.ries combinedk insignificant. For all
the countries studied we find +.036; for the corresponding first differences, -.165. It is seen that the well defined movements of prices and interest in the principal
countries are largely offset by the movements in the
countries of lesser economic importance. To obtain more
decisiveevidenceupont,he
relationship studied, it is
necessary to resort to the more rigorous analysis given in
subsequent sections.
The evidence obtained from the comparisonsin this
section indicate that there is a very apparent, though
feeble, tendency for the interest rate to be highwhen
prices are rising, and the reverse. The adjustment is imperfect and rather irregular, but in the great majority
of cwes the tendency is evident.

+

55. Real Interest Varies More Than Money Interest
If perfect foresight existed, continuously rising prices
wouldbe associated not with a continuously rising rate
of interest but with a continuing high rate of interest,
and falling prices would be associatednot with a continu411 1

c

THE THEORY O F INTEREST
ously falling rate of interest but with a continuing low
rate of interest, and a constant price level wouldbe aasociated with a constant rate of interestassuming, in
eachcase, that other influences than pricechangeremained the same.
This perfect theoretical relationship of interest rates
to pricelevels, assuming perfectforesight, is shownin

w
lo
5
0

6

lD

CHART 43
Theoretical Relation of Price Level (P)and Interest &tee (i).

Chart 43, showing high (not rising) interest rates while
prices are rising, and low (not falling) interest rates
whileprices are falling. The real rate wouldremain
constant at, say, 5 per cent under the ideal conditions
here assumed.
In this chart, i stands for interest rate and P for price
change, but the upper line indicates &e price level.When

c 412 1

RELATION TO MONEY AND PRICES
in the first period the price level rises, the price change
(P)is assumed to be at the rate of 5 per cent per annum.
In the next period, the price level remains constant so
that price change is zero, and so on as indicated. The
lower curve shows the theoretical effects on the rate of
interest. In the first period, it would be 5 per cent above
normal; in the second period, normal; and 80 on.
One obvious result of such an ideally prompt and perfect adjustment would undoubtedly be that money interest would be far more variable than it really is and that
when it was translated into real interest this real interest
would be comparatively steady. What we actually h d ,
however, is the reverse-a great unsteadiness in real interest when compared with money interest.
Real interest, however, as shown by the dotted lines
on Chart 42, changed in the opposite way to money interest, due to t.he lack of foresight and adjustment.
Attention is called to the period 1852-1857 in London,
during which prices rose very fast (that is, money depreciated) simultaneously with, and mainly because of,
the great gold production. The market rate of interest
averaged 4.7 percent, which was higher than in any
subsequent or in any previous period. Yet during this
period of apparently highest interest rates, lenders were
receiving,in realihterest, less thannothingfortheir
savings.Also in the inflation period 1914-1920, bank
rates reached their highest peak, 5.2 per cent, while average market rates, at 4.4 per cent, were but little lower
than in 1852-1857. Yet in terms of real commodities those
who saved and deposited or invested at thebank rates or
market rates of interest were mulcted 9 to 10 per cent for
their abstinence and sacrifices. In the following period,
1920-1927, however, the savers and lenders gotback more

c 413 1

THE THEORY O F INTEREST
t h k all they, or their predecessors, lost in the previous
period. The tremendous f
d in prices in 1920 and 1921
boosted the real interest rate above 15 per cent. Thus
the computed real rate isexceedingly erratic during a
serious inflation or deflation.
Chart 44 represents in a different way the same theoretical relationship between price change and the rate of
10
5
0
6

10

15
16
u)

6
0
e6

Interest B.te

40

CHART 44
Theoretical Relation of Price Changes (P)
and Interest Rates ( i ) .

interest as that depicted on Chart 43. In Chart 44, price
is represented not by the slope of a line, but
change (P)
by distance measured above or below the zero line. Thus
when the price level is rising at the rate of 5 per cent per
annum, P’ is represented by a horizontal line 5 per cent
above zero. When prices are stationary, P drops to zero,
and so on. If men had perfect foresight, they would adjust
the money interest rate 80 aa exactly to counterbalance

c 414 1

RELATION TO MONEY AND PRICES

cr offset the effect of changes in the pricelevel, thus
causing the realinterest rate to remain unchanged at
t,he normal rate.
The following table shows that the standard deviation
from the mean is far greater for the computed real rate
of interest than for the actual rate of interest.
TABU14
Stantiurd Deviations of M o n e y Interest and Real Interest

1
..............
............
................
..............
...............

London
New York
Berlin
Calcutta
Tokyo

Number of

11

8
7

11
5

I

Standard Deviations

62

6.1

.73

8.5
5.0
75

1.@7

57

.69

71)

TEE THEORY OF INTEREST
justment is the fact that the adjustment is very slow.
When prices begin to rise, money interest is scmely affected. I t requires the cumulative effect of a longrise,
or of a marked rise in prices, to produce a definite advance in the interest rate. If there were no “money illusion” and if adjustments of interest wereperfect, unhindered by any failure to foresee future changes in the
purchasing power of money or by custom or law or any
other impediment, we should have found a very different
set of facts.

$6. Interest Rates and Rates of Price Change
The roughness of the comparisonsbetween interest
rates and pricelevels thus f a r madeimpels to further
study of this important problem. For these more rigorouscomparisons, the statistics of prices and of bond
yields in Great Britain and the United States have been
taken, being the only reliable statistics ready at hand
which permit of long trend comparisons.
Since the theory being investigated is that interest
rates movein the opposite direction to changes in the
value of money, that is, in the same diredon aa price
changes, the first analysis made isthe same aa that
already made by roughermethods, the comparison of
price changes with interest rates.
For the rate of change of prices, the customary link
relative expression waa at first used in a preliminary study
of quarterly United Statesdata for the period 18901904. But to ensure full comparability with my related
studies of several years ago on price changes and trade
variations, the symmetrical expression F (rate of price
change per annum) is used throughout. The precise derivation of P is given in my paper, Ow Urntable Dollar

c 416 1

RELATION TO MONEY AND PRICES
andthe So-Called Business Cycle.8 The upper part of
Chart 45 gives the correlation coefficient ( r ) obtained
by correlating the long term interest rates as reflected
in the yield of British consols with percentage changes
in prices computed from the British wholesale index nume
part of
bers of Sauerbeck and T h e S t a t i ~ t . ~ T hlower
this chart gives the r's for bond yields and percentage
price changes in the United States.l0
In Great Britain, the price changes from 1820 to 1924
fall into three clearly defined periods, namely, 1820 to
1864, a period of fluctuating prices with no marked upward or downward trend in prices; 1865 to 1897, a period
of declining prices; 1898 to 1924, a period chiefly of rising
prices, including a big boom from 1915 to 1920, followed
by a crash and more stable prices since 1922.
A very brief examination of the charta below indicates
that there is little or no apparent relationship between
price changes and interest rates in any of the periods
studied in either country except for 1898-1924 in Great
Britain. For the period 1820-1864 in GreatBritain we
obtain a maximum inverse correlation of -0.459, without
lagging. For the period 1898-1924, we get as a maximum
0.623 when i is lagged 4 years and
0.678 when i is
lagged 6 years. Lag means the time interval between a

+

+

'See Journal of the American StatisticalAssociation.June,

192.5,

p. 81, footnote 3.
e The British bond yieldahere
used were takenfrom an article by
A. H. Gibeon, The Future Course 0) High C h Investment Values,
TheBankers',
Insurance Managers' and Agents' Magazine, January,
1923, p. 15. Reprinted in revised form in TheSpectator, March 7,

1925.

"The United Btates bond yields here wed were taken from the statistical Bulletin, 18281929, of the Standard Statistics Company. Percentageprice changes were computed from the WholesaleCommodity
price Indexes of the United States Bureau of Labor statistics.

c 417 3

TEE THEORY OF INTEREST
price change and the associated change in the interest
rate. Chart 45 shows the results of lagging interest rates
behind price changes on the one hand and lagging price
changes behindinterest rates on the other. For the United
States, without lagging, r = 0.289, while the highest

+

1.0

-"--

0.8

0.6

------

1820-1864
1w-18sr

0.4

---a-

1898-1924

0.8

0.d
4.8
9.4

9.6

a

-6

-4

Lag, in Year.,

-2

0

2

4

.of Interert Rater in respeet t o Prior C h q r a

6

CHART 46
Correlation Coefficients Between P and i for Varioue Lags. Yearly
Data, Great Britain, 1820-19"; United States, 1890-1921.

+

correlation is 0.406 when i is lagged 4 years. These results suggest that no direct and consistent connection of
any real significance exists between P' and i.
The variations in r for d8erent lags may be due to the
zigzag cycles in the data correlated. T h e maximum vdue
418 1

c

0.4

8

RELATION TO MONEY AND PRICES
of r establishes definitely that, characteristically, movements in i lag behind corresponding movements in P.
The small numerical value of T suggests that the rehtion
can be revealed only faintly by P and i directly. But a
little consideration suggests that the influence of P or i
may be assumed to be distributed irt time-aa, in fact,
must evidently be true of any influence. This hypothesis
proved quite fruitful in my studies severalyearsago,
in the course of which the theory of distributed influence
or, if we wish to avoid the implication of cause and effect,
of distributed l a g was developed in considerable detail.ll
The reader may consult the references citedfor details.
It must suffice here to point out only the essence of the
transformation of P into the derived quantity P,measuring the distributed influence of sundry P. Arithmetically, PI is merely a certain weighted average of sundry
successive P’s. (See ( a ) and ( b ) referred to in the footnote.) In any specificproblem the number of succeasive P”s that enter into the average P’s depends on the
length of the time interval during which the influence of
any F is assumed to be perceptible. The weights used
vary in a certain functional form,generally that of a
skew probability curve. Thus,in applying the theory at
least two parameters are involved: (1) the length of the
influence interval (which determines the number of P’s
YThe theory of distributed iduence and lag was developed incidentally in the txurse of my studies of price-trade relations reported in
severalpapera &e (a) The &usiness Cycle Lragely a “Dance of the
Dolhr,” Journal of the American Statistical Association, December,
1923, p. 5, top paragraph; (b) Flwtvations in Phe-Leuek in The
Problem of Bueiness Forecasting by Warren M. Persons, william
T.Foster, Albert Hettinger. Boston, Houghton Mifain Company, 1%
PP. 50-52; and particularly, (c) Ow Unstable DoUar ond the B P C d k d
Bvsines~cycle, J O W of~ the American Statistical Bapociation, June,
I@%,pp. 179-ao2.

C 419 1

THE THEORY OF INTEREST
that enter into the composit,e p ) ,and (2) the form of
variation of the weights. As indicated in reference ( b ) in
the above footnote, the form of variation of the weights
is exactly-but in reverse order-the
form in which the
distri'buted influence of any Pt tapers off during successive periods of time.12
"A price change P', pertaining to the month tmexerts an influence,
F(t, + X ) , whose intensity is proportional to 8 during f + r , t o 7 during
tm+,,
,tolduringtm+lo,toOduringt,+n.

......

(a) Distribution of Iniluenoe of P
' during t h e Time
Subsequent t o the Youth Cinteriw at

Conversely the aggregate influence on the affected variable during
the month t, consists of the varioua PX,
which enter with the following weights tapering off in aritbmeticsl progression;,'P
with weight
8, F
"
with
,
weight 7,
P'with weight 1, Pm- with weight 0.
The numerical measure of this composite influence ia:

....,

P
I
,=+8

1

P'm-*

+ 7 P"* + ....'+ 1 P," + OrY,-nl,

the divieor 38 being the sum of the weights,

38=8+7+

....+l+O.

14201

RELATION TO MONEY AND PRICES
In the present study we must limit our investigation
to only one type of distribution of influence and variation of weights. The form chosen is the simple straight,
line function or arithmetical progressionwhichproved
mosteffective and easily calculated in my 1925 study.

Distributed lag in Team, d l' In
respe& t0'P'

CHART 46
Correlation CoefficientsBetween P and i for Various Distributiona of
Lag. P is the Combined Effect at Any Point of Time of the Influence
of Preceding P 'e with Laga Distributed. Yearly Data, Great Britain,
1820-1924.

Several periods of influence range, however, were tried.
The results for the British and American yearly data are
shown in Charts 46 and 47.
The figures at the bottom of Charta 46 and 47 refer to
the number of years over whichthe effect of price changes
is taken into account in the correlations between and i.
For example, in Chart 46, the figures 1-16 mean that the
[ 421 I

THE THEORY OF INTEREST
effect of a price change is assumed to begin the first year
after the change and to cease at the end of 16 years. The
weighted average of the distributed lag is 5.3 years. The
longest distribution shown at the right is from 1 to 32
years, or a weighted average of 10.7 years.

1
P.
-1

Dlstribllted Lag in Years,
in r a s p d t t o P*

0)

1

CHART 47
Correlation Coefticienta Between 7 and i for Various Distributions
of Lag. P is the CombinedEffect at Any Point of Time of the Influence of Preceding F" ' 8 with Lags Distributed. Yearly Data, United
States, lwx)-ISzI.

The charts picture only the effects of the distributed
lag when interest rates follow behind price changes.
Experiment proved that whenpricechangeswere
lagged behind the distributed influence of changing interest rates, the correlation coefficients were too small to
have any significance.
The high and consistent correlations shown in the
c 422 1

RELATION TO MONEY AND PRICES
above charts are in striking contrast to the results previously obtained from correlating P directly with i. The
assumption that a change in prices occurring during one
year exhausts its influence uponinterest rates in the Same
year or in another single year is shown to be quite wrong,
as might be expected. Our first correlations seemed to indicate that the relationship between P' and i is either
very slight or obscured by other factors. But whenwe
make the much more reasonable supposition that price
changes do not exhaust their effects in a single year but
manifest t,heir influence with diminishing intensity, over
long periods which vary in length with the conditions,
we find a very significant relationship, especially in the
period which includes the World War, when prices were
subject to violent fluctuations.
The British figures for 1820-1864 give the lowest correlations of any included in this study. These low figures
are possibly due in part to the less accurate price indexes
in those early years. It is noteworthy that the correlat,ion coefficientsare distinctly lower for the United States
in the period 1900-1927 than they are for Great Britain in
the period 1898-1924. It is also interesting that for Great
Brit,ain in 1898-1924, the highest value of t (+ 0.980) is
reached when effects of price changes are assumed to be
spreadover 28 years or for a weighted average of 9.3
years, whilefor the United S t a h the highest T (+ 0.857)
is for a distribution of the influence due to price changes
over 20 years or a weighted averageof 6.7 years.
Chart 48 shows graphically the smoothing effectof distributing the influence of P over various periods.
By assuming a distribution of effect of price changes
over several years according to the form described above,
the relationship between price changes and interest rates

14233

RELATION TO MONEY AND PRICES
which wm only faintly revealed by the first direct comparisons is clearly revealed. The high correlation coefficienta obtained by means of the method of distributing
the influence of P' and d show that the theory tested in
this chapter conforms closely to reality, especially during
periods of rather marked price movements.
Furthermore the results and other evidence,indicate
that, over long periodsat least, interest rates follow price
movements. The reverse,whichsome writers have asserted, seems to h d little support. Experiments, made
with United Statea short term interest rates, to test the
alternative hypothesis of distributed influence of interest
rate changes instead of pricechanges,gave
results of
negligiblesignificance. Our investigations thus cormbe
rate convincingly the theory that a direct relation exists
between F and i, the price changes usually preceding and
determining like changes in interest rates.
$7. Short Tern Interest Rates and Prices in the

United States
A study of short term commercial paper rates in relation to short term pricemovementscorroborates the
evidence obtained from correlatinglong term interest
rates and pricechanges. The New York interest rates
on short term commercial paper have been correlated
with changes in the quarterly wholesalepriceindexes
computedfrom monthly indexes of the United States
Bureau of Lrtbor Statistics for the periods 1890-1914 and
19151927.18
"Intereat rata were taken from T h e Statistical Bulletin, 19281929,
of The Standard Statistics Co. The price indexes are computed from the
United Stata Bureau of Labor Statistics. See Appendix to thie chapter,
02, for these quartmly data.

~4251

THE THEORY OF INTEREST
On Chart 49 are plotted the curves showing the quarterly price indexes and the F a.tA r' derived from them,
with the interest rates for the entire period 1890-1927.
F is shown for 120 quarters or 30 years.

CHART 50
Correlation Coefficienta Between P and i : for Variow Lag8, Quarterly
Data, UIUted states, 1890-1927.

These curves of quarterly data tell much the same
story as is told by the curves representing yearly data,
shown in Chart 48, for Great Britain. P obviously corresponds much more closely to i than does P'.
Chart 50 shows the rather erratic variation of the ~ ' 8
computed from i and P directly without distributing the
effects of price changes.

c4261

I

1

r

t

CHART 49
Curves Showing P, P,P,and i. Quarterly Data, United States, 1890-1927,

RELATION TO MONEY AND PRICES
Chart 51, on the contraxy,shows, in sharp contrast,
the steady increasein r computed from i and price
changes with influence distributed over periods from 20
to 120 quarters. This chart shows that, in the period
1915-1927, T reaches its maximum (f 0.738) only when

CHART 51
Correlation'CoefficientsBetween P and i for Various Distributions of
Lags. i" ia the CombmedEffect at Any. Pomt of Tune of the Influence of Preceding P 's wlth Lags Dlstributed. Quarterly Data,
United States, 1890-1927.

a total of 120 quarters, or 30 years, is included in the
period subject to the influence of price changes upon i.
The studies of both the long term and short term
movements of prices and interest rates give very similar
results. In both studies the T'S are insignificant when
F and i are correlated directly, either with or without
lagging, BO long as we ignore the fact that the eBwte
[ 427 1

THE THEORY OF INTEREST
of price changes are distributed over many years. But
when the effects of price changes are distributed, the 8 s
take on an entirely different aspect with an entirely new
meaning, especially during the War period when prices
fluctuated widely and quickly. It would seem then that
price and interest fluctuations are governed by one law,
not, as has been suggested, by two different opposing
laws, for short and for long periods of time.
It seem fantastic, at first glance, to ascribe to events
whichoccurred last century any influence affecting the
rate of interest today. And yet that is what the correlations with distributed effects of P show. A little
thought should convince the reader that the effects of
bumper wheat crops, revolutionary discoveries and inventions, Japanese earthquakes, Mississippi floods, and
similar events project their influence upon prices and
interestrates over manyfuture years even afterthe
original casual event has been f0rgotten.l' The skeptical
reader need only be reminded that the economic effects
" In the form of distribution of influence used in this study, the remote
price changes have comparatively little weight in the composite P'.
For example, in the case of a 20 term influence-range straight line
distribution,

1

X
'w(20)=lS+18...... +2+1
[1o(p'=) 18(P")
. . 2(P'S,) 1 ( p W ) O.(P'ro)].
It is evident, and I have tested it thoroughly, that the composite HI
would be only slightly changed if the tail half of the diskribtation were
omitted. The distribution in the above example would then be,
1
X
phCc(m"(10)1=
19 + 18 + . , + +

+

+ .+

+

+

+ .... +

[lQ(P',) 18(P'~)
1 1 ( P ' d +I?',)].
For the United States yearly data 1890.1027, the correlation of i and
with an influence range of 20 years waa r = 0.857. For this distribution truncated by chopping off the end quarter, r = + O M ; the end
half, r = i-O.7W; and the end three quarters r = +0.439.

+

c 4 w

i
-r

CHART 52
Curves Showing i Lagged One Year Behind P. Yearly Data, Great Britain, 1820-1924.

RELATION TO MONEY AND PRICES

on the farmer of the deflation of 1920 axe now, in 1929,
sdliciently acute to make farm relief a pressing political
problem and that these economic effects may be expected
to persist for many years to come. A further probable
explanation of the surprising length of time bywhich
the rate of interest lags behind price change is that bet,ween price changes andinterestrates
a third factor
intervenes. This is business, &s exemplified or measured
by the volume of trade. It is influenced by price change
and influences in turn the rateof interest.
$8. Interest Rates and Price Indexes
Thus far we have considered the relation of changes
in the price level and interest rates. It remains to study
the relations of the price levels themselves to interest
rates. The same basic data are used as in the preceding
sections, but we now correlate the price indexes directly
with the interest rates in Great Britain and the United
States.
Chart 52 shows the British long terminterestrates
(bond yields) plotted with the wholesale price index for
the years 1820-1924.
It is apparent that the P curve and the i curve, as
plotted, conform very closely. Furthermore, lagging interest rates one year gives the highest obtainable degree
of correspondence. The corresponding data for the United
States,plotted on Chart 57 below without lagging i,
shows the same close relationship between P and i.
On Chart 53 are plotted the curves of the correlation
coefficients computed for P and i for Great Britain and
the United States.
The r’s for the whole period 1820-1924 for Great Britain are not shown on Chart 53 since they reveal nothing
[ 429 1

THE THEORY OF INTEREST
not shown by the r‘s for the shorter periods. These highly
significant correlations seem to establish definitely that
over long periodsof time high or low interest rates folbw
high or low prices by about one year.

k(

P-r

of Intdrst B.ter h Brrpot t o him

CHART 53
Correlation Coefficients Between P and for Various Lags. Yearly
Data, Great Bntam, 1820-1924; Umted Statetr, 1900-1927.

Comparison of short term interest rates with quarterly
index numbers gives resulta of no significance for the
period 1890-1914. On the contrary, the r‘s obtained from
430 1

c

RELATION TO MONEY AND PRICES
comparing these series over the period 1915-1927 are
high; without lagging r = 0.709; lagging one quarter, r = 0.829; two quarters, r = 0.891; four quarters, r = 0.838. In both periods the coefficients of
correlation grow smaller rn the P’s are lagged behind i,
while they grow larger when i is lagged behind P. The
results from the analysis of the short term data, while
differing in some respects, may be aaid to coniirm the results obtained from comparing the long term data.

+
+

+’

+

$9. Elimination of Trends

These high correlations do not necessarily mean that
theinterestrate will always be high when prices are
high and low when prices are low, butthe tendency
toward this is definitely established.
The correlations obtained for all periods andsubperiods considered are unusually high. It is necessary to
guardagainst the possibility that these Coefficients are
of the familiar nonsense type, and are spuriously high
because of the presence of secular trend forces that affect
both P and i. Due consideration was given to the control
devices that have wide acceptance in the literature of
statistics, such as “elimination of trend” and “seasonal”
fluct’uations.The general methodology of analysis of time
series is still in the process of formulation. The specific
problem of t,rend analysis is still largely unsolved.16 In
the present case, i t is rather doubtful that trend forces are
involved which should be eliminated. What is desired in
”See Pearson and Elderton, The Variate DiferenceMethod, Biometrica, Vol. XTV, 1923, pp. 281309; W. M. Persons, Statistics and
Economic Theory, Review of Economic Statistics, Vol. VII, NO.13,
July, 1925, pp. 179-197; Anderson, TheDecomposition of Btatiatical
Series into Components, Journal of the Royal Statistical Sooiety,
Vol. XC,pt. 3, 1927, pp. 548570.

c 431 1

THE THEORY OF INTEREST
all the preceding comparisons of price levels and interest
rates is to discover what precise relation obtains between
interest rates and prices in the long run. It is like giving
theplay of Hamlet withoutHamlet to eliminate the
secular trends of i and P from a study of long term relasecular trends me most
tionships in whichthesevery
important and often dominant influences.
However, to anticipate possible criticisms and errors,
the results of eliminating secular trends of prices and
interest rates have been studied. These additional studies
are also made for another and more important purpose,
namely, to discover whether or not the short,er so-called
cyclical movements of prices influence long-term interest
rates in thesame way as thelong secularprice movements
have beenshown to do. For simplicity, least square
straight line and parabola trends were used. These will
answer sufhiently the present purpose. In addition, a
cubic trend was applied to theyearly data for the United
States for the period 1900 to 1927 and to the British data
for the corresponding period,
Charts 54, 55, and 56 show the curves of price levels
and interest rates in Great Britain for the period 18201924 with straight line trends and parabolic trends
plotted, while Chart 57 shows the corresponding curvea
for the United States for theperiod 1900-1927.
The results, after eliminating these secular trends, are
interesting and amazing. The correlation coefticients with
straight line trends eliminated are naturally smaller than
when these trends are included, but they are still significantly high except for the period 1865-1897 in Great
Britain. In the majority of cases, the characteristic lag
of about a year of interest rates behind prioes gives the
highest correlation.

I4321

RELATION TO MONEYANDPRICES

C 433 1

THE THEORY OF INTEREST
As a further test of t,he validity of the comparisons,
the parabola trend deviations for the recent period, ending with the high point for both P and i in 1920, have
been computedandplotted,though
t,he charts are not
here shown. It might. be supposed that the elimination of
a parabolic trend from these violently fluctuating series
would leave only erratic wiggles in the P and i curves
with little or no correspondence with each other. That

CHART 55
Curves Showing P and i with Straight ,Line Trends Parabolic Trends.
Yearly Data, Great Bntam, 1865-1897.

price levels and interest rates are
very closely related,
even when great secular and cyclical forces are eliminated, is clearly demonstrated by the results of these
investigations. The correlation coefficients obtained from
the data for the period ending in 1920 with the parabolic
trends eliminated are about 0.70, which certainly indicates that yearly fluctuations, as we11 as cyclical and
secular trends, of prices and interest are generally in t'he
same direction. The coefficients obtained from correlating
P and i with straight line trends eliminated are plotkd
on Chart 58.

+

14341

RELATION TO MONEY AND PRICES

CHARTS 66

.. . ..i

THE THEORY OF INTEREST
The reader will see that the 8 s for the latest period
are much higher than for the other periods. For Great
Britain in the period 1898-1924, r = 0.851 with i
+!

~ a ~ s s p s sa s s ~ i ~ a ~ a
r(

rl

rl

4

4

CHART 67
Curves Sowing P and i with Straight Line Trende and Parabolic
Trends. Yearly Data, United States, ISOO-1927.

lagged one year. For the United States for the conesponding period 1900-1927, and with the same lag of ij
we get r = 0.806. It is not worth while to plot the r’s

+

C4361

RELATION TO MONEYAND PRICES
with P lagged behind i, since it is apparent at a glance
that r decreases with the lagging of P.
When the parabolic trend is eliminated, the comelation coefficients for the cycles becomeinsignificant ex-

CHART 68
cOr+ation CoefficientsBetween P .md i with Straight Line Trends
1865-1&27 ; 1897Elimmted. Yearly Data, Great B n h , 182&1885;
1934: United S t a h , 1DW-1027.

cept for the period including the World Wax. The highest
r for the British data for 1820-1864 is 0.319 when i
is lagged one year; for 18651897, the highest t is 0.045
with i lagged two years; for 1898-1924, r is 0.829 with
no lagging, and 0.817 when i is lagged one yew. The

+

+

+

l-4371

+

THE THEORY OF INTEREST

+

United States dats give r's of
0.695 without lag, and
0.876 with i lagged one year, Even when a cubic trend
is eliminated for 1898-1924 the r's still remain significantly high, namely, without lagging, r = 0.794 and
with i lagged one year T = 0.790. For the United States
without lagging, r = 0.525 and with i lagged one year
T =
0.769.
The elimination of the secular trends from the comparisons makes the relationship of i and P depend solely
or
upon the similarity of fluctuations intheshorter
cyclical periods. Even without Hamlet the play proves to
be astonishingly informing and interesting. It is quke
definitely demonstrated that, in times of marked price
changes, as in the World War period, the effects of price
movements are felt ratherquickly upon the ratesof interest, even in the case of long term bond yields.

+

+

+

+

$10. Relations of Prices and Znterest Interpreted

The studies of P, P and P in relation to i have brought
out four relationships:
(1) The rate of interesttends generally to be high
during a rising price level and low during a falling price
level ;
(2) The rate of interest lags behind P' so that often
the relationship is ubscuredwhen direct comparison is
made;
(3) The rate of interest correlates very markedly with
P , representing the d&tributed effect of lag. For recent
years in Grertt Britain, the close relationship is indicated
by r = 0.98 when i is lagged and the effects of Iw are
distributed over 28 years;
(4) The rate of interest tends definitely to be high
with a high price level and low with a low price level.
~4381

+

RELATION TO MONEY AND PRICES
We have also seen that the b t three sets of fa& fit
in with the analysis presented, the f i a t corresponding,
although only roughly, with the ideal assumption of perfect foresight and adjustment, the second and third corresponding to the more realistic assumption of imperfect
foresight and delayed, but accumulated, adjustment.
Two facts have, I think, now beenwellestablished.
The first, that price changes influence the volume of
trade, has been shown in earlier studies made by me.18
The second, that the volume of trade influences the rate
of interest, has lbeen shown by Carl Snyder,l' Col. Leonard A y r e ~ Prof.
, ~ ~ Waldo F. Mitchell,l9 and ot,hers.
The evidence for both relationships is not only empirical but rational. Rising prices increase profits both actual
and prospective, and so the profit taker expands his business. His expanding or risingincome stream requires
financing and increases the demand for loans.
In my study of the so-calledbusinesscycle, the lag
of volume of trade, T, behind price changes when the
influence of P was distributed over a range of 25 months,
WM found to have a modal value of 9y2 months. The
=See especially Our Unstable Dollor and the&Called
Busines
Journal of the American Statistical hociation, June, 1925, pp.
181-202; A Statistical ReIatimr Between Unemployment and Price
Changes, International Labour Review, Vol. XIII, No. 6, June, 1926,
Cycle,

pp.

785-792.

"Snyder, Carl, Tk Influence of the Interest Rate on the B2Lsi7aeJs
Cycle, American Economic Review, Vol. XV, No. 4, Dec., 1925, pp.
684-699; Interest Rates a d the B w i w Cycle, AmericanEconomic
R$view, Vol. XVI, No. 3, Sept., lsZS, pp.
Ayres, Cleveland Trust Co., m
h
e
Bulleh, June 15, 1928, and
Aug. 15, 1928.
Mitchell, Interest Cost and the Bm'ness Cyde, American Economic Review, Vol. XVI, No. 2, June, 1920, pp. 20%221; Sup.demnt5v Note on Intereat costs, American Economic Review, Vol. XVI,
No. 3, Sept., 1928, pp. 651-452

v.

c4391

THE THEORY OF INTEREST
lag of i behind T using a simple lag was found by Carl
Snyder to be 10 to 15 months, by Leonard Apes to be
about 14 months and (by Waldo F. Mitchell about 6%
months.
If we add the lag of T behind F which I found to be
over all about 25 months, and the lag of i behind T of
14 months, found by Snyder and Ayres, we obtain a combined lag of i behind P of 39 months. This combined
lag obtained by simple addition is far shorter than the
lags discovered inthe
calculations presented above,
whether for yearly or for quarterly price changes in relation to i. Apparently the double distribution of the lag
of T behind P and again of i behind T may result in a
greater lag than would be obtained by simple addition.
The fourth relationship stated above must be, I think,
regarded as an accidental consequence of the other three.
At any rate, it seems impossible to interpret it as representing an independent relationship with anyrational
theoretical basis. It certainly stands to reason that in the
long run a high level of prices due to previous monetary
and credit inflation ought not to be associated with any
higher rate of interest than the low level before the inflation took place. It is inconceivable that, for instance, the
rate of interest in France and Italy should tend to be
permanently higher because of the depreciation of the
franc and the lira, or that a billion-fold inflation as in
Germany or Russia would, after stabilization, permanentlyelevateinterest
accordingly. This wouldbe as
absurd as it would be to suppose that the rate of interest
in the United States would be put on a higher level if
we were to call a cent a dollar and thereby raise the price
level a hundredfold. The price level m such can evidently
have no permanent influence on the rate of interest ex-

E4401

RELATION TO MONEY AND PRICES
cept aa a matter of transition from one level or plateau
to another.
The transition from one price level to another may
and does work havoc as we have seen, and the havoc follows with a lag which is widely distributed. The result
is that during a period of inflation the interest rate is
raised cumulatively,so that at the end of this period when
the price level is high, the interest rate is also high. It
would doubtless in time revert to normal if the new high
level were maintained, but this seldom happens. Usually
pricesreach a peak and then fall. During this fall the
interest rate is subject to a cumulative downward pressure 80 that it becomes subnormal at or near the end of
the fall of prices. Thus, at the peak of prices, interest is
high, not because the price level is high, but because it
has beenrising and, at the valley of prices, interest is
low, not because the price level is low, but because it has
beenfalling.
Another consideration seems to complete the explanation of the close association between high and low price
levels with high and low interest respectively. This is the
necessity for banks to cope with mabdjustments following inflation and deflation. M r . R. G. Hawtrey has
emphasized this point in a letter to me, and I have summarized his views almost in his own words:
Whencredit is expanding, the rising pricelevelandhighprofits
bring about a high rate of interest. When the expaneion has r e a c h 4
the limit permitted by the stock of gold, the rate of interest is put
still higher inorder to bringabout a j
d inthepricelevel. when
the fall in prices takes effect, a low rate of interest becomes appw
priate, and whencreditcontraction
has proceeded 80 far that a
redundantsupply of goldhas scoumulated, the mte of interest is
depressed still lowerinorder to bring about s renewed rise in the
price level. Thus a high rate of interest corHsponds first with rising,

14411

THETHEORY OF INTEREST
then with falling, prices, and so synchronizea with high prices. A
low rate of interest corresponds fimt with falling, and then with
rising,prices, and 80 synchronizes with low prices.

.

The process of inflation boosts both prices and interest,
until a still further boost of interest is made by the banks
in order to stop the over extension, leaves a peak of prices
with high interest before, at, and after that p e a k , while,
contrariwise, the process of deflation reduces both prices
and interest until a still further reduction of interest is
made by the banks in order to stop the depression, leaves
a valley of prices with low interest before, at, and after
the valley.
Such considerations seem to be sufficient to explain the
otherwise puzzling and apparently irrational coincidence
which we have so often found to exist between high and
low prices and high and low interest rates.
The only alternativeinterpretation of which I can
think is that a high or Iow price level is not a monetary
and nominal affair but a matter of real commodities.
Sometimes, as in F'rance and Italy just cited, the high
prices may be closelyassociatedwith impoverkhment.
If it were true that a high price level usually signified
a real scarcity ofgoods-a
low income stream-while a
low price level usually signified relative abundance, we
could explain our puzzle by the relation of time preference to the size of the income stream. But the facts in
general do not seem to justify such an interpretation,20
least of all in the United States in the War years when
the correlations are the highest. During that period, incornea increased at a tremendous rate, and interest rates
advanced pan' paem
"See the author!. The M m v IUusion, New York, Adelphi Company,
1928, pp. 4142.

[MI

RELATION TO MONEY AND PRICES
$11. Relations of Interest to Business and Prices

As implied by what hrts just been said regarding banking policy, the relationships of P and i are mutual. A
change in i undoubtedly haa an effect upon P' as well
as the reverse.Ouranalyses have demonstrated that, in
a decisive majority of instances, pricechangesprecede
changes in i. This does not mean that changes in the
interest rate canneverbeused
to forecast changes in
prices and in business activity.21 In fact, an arbitrary
increase in i at any time does tend to pull down the level
of general commodity prices, while a decrease in i tends
to increaae P. This is a fact which has been quite well
established and is made use of by central banka in formulating their banking and credit policies.
The influence of changes in interest rates upon prices
and business activity is made use of also by forecasting
agencies in making their prognostications of business and
price movements for the near future.12 The fact that i
follows P', in most instances over secular and cyclical
periods, is not inconsistent with the other fact that every
increase or decrease in i exerta an influence upon P in the
PProf. &ut Wicksell WBB one of the b t to e
r
c
o
d the iduence
of interest rata upon prices. See his book, GeWm wul GWrpreise;
Prof. Alfred Marshall, Prof. Gustev Cessel, Rt. Hon. Reginald Me
Kenna, Chairman of the MidIand Bank of London, Mr. R. G.Hadtrey,
of the Treasury of Great Britain, and many other well known economists, bankers,and businem men have emphized that businem activity
is influenced and may be largely controlled by manipulation of the discount rate.
"Mr. and Mrs. K. C. I(arSte0,for example, in their forecaatS, make

uee of commercid paper rata in computing their forecasts of wholesale

prim and bueiness activity. They find an I of "0.98 between (1) the
logarithms of Fy and (2) the logarithms of the deviations of ~ m m e r C i a l
interest mtee from bond yielda.

r w

,

THE THEORY OF INTEREST
opposite direction. Within limits, a fall in the rate of
interest may and often does produce a rise in prices and
in business activity almost immediately. This effect may
be continued for many monthsuntil increasedprices
again become dominant andpullthe interesf, rate up

again.

In so far aa the rate of interest is cause and the price
movements are effect, the correspondence is j w t the
opposite of that which occurs inso far 89 the price movements are cause and the interestmovements effect,
It is outside the scope of this treatise, which has to
do only with things which affect the theory of the rate
of interest, to attempt to explain fully all the very complicated relations connecting interest and business. The
studies completed or in progress in my office show some
interesting results which I hope to publish later.
It is unfortunate that many studentsin this field seem
to take it for granted that there is one and only one
definite cycle, or that the cycle is controlled by one and
only one definite influence. I have beenaccused of inconsistency forpresenting several seemingly incompatible
theories concerning the businesscycle. As a matter of
fact, I have never as yet studied the so-called business
cycle as a whole. I have only studied a few of its elements
or aspecte.as
$12. Interest Rates and Bank Reserves
That there is a relationship between bank reserves and
the rate of bank discount is perhaps self-evident. Every
banker and business man is familiar with it. J. P. Nor'For instance, Ow UnstabL D o b and the &-C&d
ByaineS8
Cycle, J o d of the American Ststistical Aeeociation, June, 1925,
pp. 179-202.

tu1

RELATION TO MONEY AND PRICES

ton l4 found such a correlation and the relationship finds
expression in practically every treatment of commercial
banking.
This relationship furthermore carriesover into the
rates fixed on commercial paper. Mr. W. Randolph Burhas made a study of this relationship which he
expresses briefly as follows:
“Banks are the custodiam of money in this country. When the
bankere have muchmoney to lend, money rates tend t o be easy;
when they have little to lend,money rates tend to be firm. The
amount a banker can lend depends upon his reserve position. Therefore, the reserve position of the b a r b of the country determines
short term money rates, and the causes of changes in money rata
are to be found in the cause8 of changes in the reserve position of

banks.”

Mr. Burgess presents &n impressive inductive verification of this theory for the period 1904 to 1909 by comparing the changes in the short term money rate with
the changes in the average surplus or deficit in the re
serves of New York City ClearingHouseAssociation
Banks.
The Same relationship, Mr. Burgess finds, obtains under the Federal Reserve Systembetween the excess or
deficit in reserves of twenty-three New York City Banks
and the closing call money rate for intra-week periods
between the balancing of the reserves by the Federal R e
serve Banks. Over longer periods
of time, the relationship
is shown by the similarity in the movement of the open
“Statistical Studies in the New York Money Market, Chapters M
and VIII.
Factors Afeding Changes in Short Term Interest Rates, Journal
of the American Statisticsl h c i a t i o n , Vol. XXII, New Series, NO.1.58,
June, 1927, pp. 195#)1.

14451

THE THEORY OF INTEREST
market interest rate for prime 4-6 months cornmercid
paper and the average daily bills discounted for member
banks by all Federal Reserve Banks.
The Federal Reserve Act requires the pooling of member banks’ reserves with the Federal ReserveBanks.
These reserves must average the minimum legal requirements and balancing periods are maintained once a week
in large cities and twice a month elsewhere. Surplus and
deficit reservesme, therefore, impossibIe for periods of
more than two weeks at the very maximum under this
system. But the influence of the banks on the money
market rates are now effected through borrowings at the
Federal Reserve Banks. Thus a period of member banks
borrowing correspondsin its relation to the money market
to a period of deficit reservea under the National Banking
Act, and a period whenmember banks axe paying 0%
their loans at the Reserve Bank corresponds to 8 period
of exces reserves.
A similar correspondence between commercial paper
rates and gold reserves is shown by a recent study by
Colonel Leonard Ayres, of the Cleveland Trust Company.20
Curiously enough, this wellknown and sound relationship between baak reserves and interest rates is often
confused with the entirely different, generally incorrect,
but commonly believedproposition that the rateof interest is highwhen money in general is scarce, snd low
when money in general is abundant. The thought seem
to be if the rate of interest is called the price of money
it is natural to conclude that abundance of money, like
abundance of wheat or anything else, makes its price
low, while scarcity of money makes its price high.
Cleveland Trust Company, Bwinea Bulletin, June 16,1928,

C U I

RELATION TO MONEY AND PRICES
But the price of money in the aense of the rate of interest is B very peculiar kind of price. It is, as we know,
the deviation from par of the price of present money in
t e r m of future money. It is not very analogous to the
price of wheat. The real analogy with the price of wheat
is not the rate of interest but the pwchasing power of
money. In that sense it is perfectly true that the price of
money is high or low with its scarcity or abundance. But
in the other sense it is not true. Moreover, aa we have
seen, when the price of money, in the sense of the purchasing power of money, is low, that is, when the price
level is high, and when, therefore, presumably the quantity of money is large, we do not then find the rate of
interest low, as the theory outlined above requires. On the
contrary, we find a high price level associated with a high
interest rate.
That short term interest rates vary inversely with bank
reserves, however, fits in with our theory of interest aa
related to real income. A low bank reserve is, among other
things, B symptom of a prospective general increase in
the income of the community. When business is optimistic, which means when future income looms large, there
is an impatient desire to discount that big future and
to make it even bigger by investing present income, provided the investment can be financed. Evidently the immediate effect is to increase bank loans and consequently
to increase deposits. These results tend to lessen the ratio
of bank reserves to liabilities. Thus the banker is led to
raise his rate. It seems that the rise merely reflects his
reserve situation. But back of this situation is the demand for loans, and back of that something more fundamental-the rising income stream, a period of increasing
prosperity, of invention and progress, or of great h s n c -

~

7

1

THE THEORY OF INTEREST
ing. From these changes, rather than from a merely technicd banking situation, come high rates of interest.
Thus the banker registers t'he effect of the increasing
income stream. The reverse situation of descending income stream, lessened opportunity to invest, lessened
loans and deposits, tend toward idle reserves and low
interest.
Normally the banking function should do little more
in relation to the rate of interest than to transmit the
effects of the income stream. This would be substantially
the cme if we had a scientific adjustment of the ultimate
source of bankers' reserves, the world's supply of monetary gold. If this were so adjusted &s to maintain a constant purchasing power of that gold and so of money
units, the banker could be trusted to adjust properly,
even if unconsciously, the rates of interest to the income
situation of the country.
Unfortunately, wedo not yet have such a scientific
currency system, but are still exposed to every wind that
blows in the gold bullion market. The consequence is that
superimposed on the normal credit operations are abnormal ones by which the rate of interest is perverted
through the very banking machinery which should make
it normal.
Banking thus becomes, in practice, not simply a register of fundamental economicinfluences, not merely
their facilitator, but a most powerful independent influence. Practically, then, the banking machinery often interferes with, rather than transmits, thenormal influence
of society's income situation. If the gold mines become
depleted, gold reserves becomeinadequate to support the
growing inverted pyramid of credit baaed upon it and
required by the expanding income of society. The banker

14431

RELATION TO MONEY AND PRICES
then has no choice, under the law, but to raise his rates
in self-defense. The result is a shrinkage of credit when
an expansion is needed, a fall of prices and high bank
rates at the very time that low money rates of interest
are needed. The real rates are then doubly high-high
because the money rates are high and stillhigher because
of the appreciation of money.
These maladjustments are largely responsible for the
so-called businesa cycle. When they are serious, not only
are the consequences disastrous but there is little then
left in the market figures of interest to register the influence of fundamental incomeconditions.”’ The interest
rate then registem, rather, a choking or stalling of the
banking machinery. I n an acute panic, scarcity of money
itself has made interest high. Money of any kind brought
into the market at such times will relieve the stringency
and lower the rateof interest. To relieve the money stringency, the United States has, in times past, poured
money into the channels of trade by prepaying interest
on bonds, and clearing houses have accomplished it by
issuing clearing house certificates.
T h e establishment of the Federal Reserve System has
stabilized prices rtnd interest rates in the United States,
although the cataclysm of war in 1914-1921 upset the
price level and the normal correspondence between real
and money rates of interest as they had never been upset
before.
At. present, the Federal Reserve System exerts a normalizing influence and seems to be groping to apply the
Conditiow of this type emphaeise the importance of thorough study
of the institutional factors influencing market ink& rata such aa
that made by Mr. A. W. Marget in his doctor$ dkeerttion The Loon
Fund presented to the faculty of Harvard University in 19281!327.

~4491

THE THEORY OF INTEREST
stabilizing principles which for many years have been
suggested by Wicksell, Caasel, and other economists.
Even these efforts, while in the end they save us from
price convulsions and real-interest convulsions, nevertheless themselves involve a slight interference with the
natural effects of the income situation. The rediscount
rate, when raised, restricts credit and stops price inflation; and when lowered, liberates credit and stops price
deflation. As the effect, in either case, tends to be cumulative M long BS the slight artificial raising or lowering
is in force, the interference with the normal course of
events need only be slight, almost negligible. It would
not be surprising if a difference of one half of 1 per cent
from an ideally normal rate &odd prove usually sufficient. Maintained su5ciently long, this deviation from a
normal interest rate may prevent a very abnormal deviation in our monetary standard.
Some slight interferences areinherent in any such
banking system, not only as an incident to the supremely
important function of preventing infiation and deffation,
but also as a necessary price to pay for the very existence
of a banking system.I n order to maintain a liquid condition and to avoid risk of bankruptcy, each bank must
occaaionally put its loan policy out of line with the ideal
requirements of the income situation.
But, as we gradually perfect our banking technique
and policies, we shall get closer and closer to a condition
in which the rate of interest aa a whole will reflect the
income influences discussedin this book. The money rate
and the real rate willbecome substantially the same,
and any action of the banker which can be c&ed an
interference with, ratherthan a registering of, fundamental economic conditions will become almost negligible.
450 1

c

RELATION TOMONEY AND PRICES
813. Suimmary
We have found evidence general and specific, from
correlating F with both bond yields and short term interest rates, t'hat price changes do, generally and perceptibly,
affect the interest rate in the direction indicated by a
p r i o r i theory. But since forethought is imperfect, the effects are smaller than the theory requires and lag behind
price movements,in some periods,very greatly. When the
effects of price changes upon interest rates arecEistn'buted
over several years, we have found remarkably high coefficients of correlation, thus indicating that interest rates
follow price changes closely in degree, though rather distantly in time.
The final result, partly due to foresight and partly to
the lack of it, is that price changes do after several years
and with the intermediation of changes in profits and
business activity affect interest very profoundly. In fact,
while the main object of this book is to showhow the
rate of interest would behave if the purchasing power of
money were stable, there has never been any long period
of time during which this condition has been even approximately fulfilled. When it is not fulfilled, the money
rate of interest, and still more the red rate of interest, is
more affected by the instability of money than by those
more fundamentaland more normal causes connected
with income impatience, and opportunity, to which this
book is chiefly devoted.

CHAPTER XX
OBJECTIONS CONSIDERED
$1. Introduction
SINCE1907, when The Rate of Interest waa published,
other students of the problem of interest have published
their comments, objections, and criticisms. I have taken
t,he opportunity to answer directly in various publications2 most of the criticisms. It would serve no useful
purpose tu reprint these individual replies in this place.
Rather, in this chapter, I shall state my understanding
of the criticisms of my theory and shall offer replies
where reply seems called for. This procedure will serve
two purposes. First, it will present to the reader points of
view and approaches to the problem of interest other
than my own. Secondly, it w
l
l
iprovide occasion for the
statement of my position on the principal controversiad
problems in the theory of interest still remaining unsettled among

'For historical development and detailed criticisms of interest theories
the reader is referred to Bohm-Bawerk, Capital and Interest. A brief
The Notwe and Necessitv oj iw
historical r6sud is given in (2-1,
terest, Chap. I, pp. 147.
'These articles are included in the general bibliography at the end
of the book.
'References to the authors of the view which I am stating impersonally in the text will be made, where possible, in footnotes. It ia
hoped that thie procedure will preventthe i m p d o n that I am attempting any exhaustive critique of the interest theory of others.

c 452 I

OBJECTIONS CONSIDERED
$2. Incorm and CapitaJ
Income,which, as I have stated before, is the most
important factor in all economic theory and in interest
theory in paxticular, resolvesitself in final a d y s i s into's
flow of psychic enjoyments or satisfactions during a
period of time. While this concept is the ideal, we can,
for purposes of objectivity, approximate this ideal and at
the same
impute to the income concept varying
degrees of measurability by using in place of psychic income any of the following: real income, cost of living as
a meaaure of real income, or money income.
One objection to the psychic concept of income as a
basis for a theory of interest is that it is too narrow and
restricted. It is held that theanalysis of interest based on
this concept “finds the cause of the changes in rates solely
in the changed ratio between the stocks of present and of
future consumption goods,” while the “interest rats rnarket is a funds market, not 8 machine or raw material or
present consumables market.”
(‘Nor is it entirely clear,” continues this criticism, “why,
in Fisher’s view, the consumption perspective should read
t.he law in point of interest rates to all equipment loan
contracts, rather than, as Bob-Bawerk sometimes appears to assert, the other way about. Why should not
both sorts of demands be regarded as of equal title in
causaleffectiveness in the interest adjustment on final
loans?” 6
J reply that I do not exclude “equipment loan contracts” from due consideration, but I do maintain that
such intermediate Ioans are made for the purpose of 8e‘Davenport, H.J., Interest T L o w and Theories. American Economic
Review,Vol. XVII, No.4, December, 1927, PP. 63H56.

‘Ibid., p. 850.

c4531

THE THEORY OF INTEREST
curing larger incomes in the future, and larger incomes
mean larger consumption. Production loans then are
made only in contemplation of future consumption.
Hence, though loans for the acquisition of intermediate
goods do great,ly preponderate in the loan markets, these
loans have power to affect the interest rate only by
changing the relative amount of future incomes compared
to present incomes.
To the criticism that the consumption concept of income when used &s the foundation of interest theory presents but a partial analysis of the supply and demand
factors which are operative in determining interest rates,
I make this reply: Interest rates are not a resultant of
the supply of, and demand for, either capital goods or of
of as a loanable
capital values-sometimesconceived
fund or funds, except as these signify the supply of and
demand for income. An investment of capital, so called,
is nothing more nor less than the sacrifice of income in
anticipation of other, larger, and later income. It is a
case of flexing the income stream, reducing it in the present or early future andincreasing it in the remoter future.
The income stream, so fundamental in the interest problem, includes incomes from all sources. It includes the
value of the services of land, machines, buildings, and a11
other income-producing agenta. Upon the value of these
services, discounted at the prevailing rate of interest, the
valuation of said land, machinery, buildings, and so on
depends. What is properly called funds is this valuation
of the income stream or portions of it. It should be evident that theapproach to the problem of interest through
the income stream and the supply of and demand for
income gives to the problem the broadest possible basis.
The second indictment of narrowness of my concept
c4541

OBJECTIONSCONSIDERED
of income denies my contention that savings are not income, One writer states this criticism aa follows: “As a
financial fact, there can be no saving and addition to
capital value until there is first a property right to an
income calculable in monetary terms (a financial present
worth) to be saved. Hence to deny that monetary savings
are monetary income is in simple common sense to deny
a fait accompli; it is to aasume the existence of the effect
before its cause.” 6
In so far as our disagreement here is a matter of words,
it may be that my terminology is at fault. I used the
term earnings to include capital gain and the term income
in the sense of the va.lue of services rendered by capital.
There is little objection to changing this terminology,
if we are willing to give up saying that capital value 6
the capitalized value of expected income. We could then
maintain that capital gain is income. But if income
includes only those elements on the anticipation of which
the value of capital depends, then the increase in the
value of capital is most emphatically not income.’
In my reply to one critic,8 I pointed out that this criticism seems to overlook, or omit, the mutual relations of
‘Fetter, Frank A., C h k ’ s Reformulotion of the Cq.ktol Concept.
Economic Esssys Contributed in Honor of John Bates Clark, pp. 151152, footnote on p. 153; cf. sleo Flux, Irving Fisher on Capital ond Interest, Quarterly Journal of Economics, Vol. X x m , Feb., lW, pp.

307-323.
‘&e my articles: Ate Sad7478 Z n c o m e ? Journal of the American EconomicAssociation, Vol. I X , No. 1, April, 1908, pp. 1-27; Professor
Fetter on CopitaE and Income, Journal of Political Economy, Vol. XV,
No. 7, July, 1907, pp. 421-434; Comment on Prufes8ot Pkhn’8 Ab
dress, AmericanEconomic Review, Vol. XN, No. 1, Mar., 19‘24, pp.
64-07; and The Concept of Znccnne in the Light of Ezperience, figliah reprint from WiaserFeetechrift, Vol. III.
‘ A Reply t o Critics, Qusrterly Journal of Economice, VOL
May, IW,pp.

.

536641.

m,

c 455 1

THE THEORY OF INTEREST
discount and interest which constitute the radson d'ttre
for the concepts which I have called capital and income.
It is chiefly because. savings do not enter into these discount relations on equal terms with other itemsof income
that savings do not form a part of what I have called the
income concept. I do not think there are reasons of terminology alone sufficient to justify the inclusion of savings in income. But, if savings are to be so included, some
other term must be applied to take the place of what I
have called income. The justification of these statements
must rest on my books themselves and on later papers
devoted to this subject.
But it is held that even aside from the relation of
savings and income, a concept of income m services is
quite useless. Services are both heterogeneous and incommens~rable.~
They cannot be summated to constitute a
stock of services. They cannot be thrown together aa if
all were alike.
An examination of my T h Nature Oj Capital and Income (for example p. 121), will show that I do not treat
all services as alike and capable of being added together.
I have emphasized that miscellaneous services cannot be
added together until each is multiplied by its price and
all are thus reduced to a common denominator.
This criticism of my theory of income seems to overlook the fact that, while enjoyable services (psychic
income) and objective services are themselves incommensurable, their values arenot. Moreover, when the
summahion is completely carried out, the values of the
physical elements cancel among thmmelves and leave aa
the netresult only the values of the psychical elementa.
'Fetter, Interest The&,
Old and New, American Eoonomic
view, Vol. IV, No. 1, March, 1914, pp.

68-92.
I: 456 3

Re-

OBJECTIONSCONSIDERED
It may be objected that, at one stage in this process,
income appears to be more closelyrelated to theexpenditure of money than to its receipt and, aa such, seems out
of keeping with the ordinary idea of income. This seeming contradiction between money income and enjoyable
income is readily resolved if we consider debits and
credits. When money is spent, the expenditure itself is,
it is true, outgo to be debited to the commodities bought
with it. But these commodities afterward render a return
in satisfactions. These satisfactions are certainly not expenditures, but receipts. Whether money spending is
associated with outgo or income is entirely dependent on
whether we fix attent,ion on the loss of the money or the
gain of the goods and services for which the money is
spent.
These services, which constitute income, are related to
capit'al in several ways. As incomeservices, they flow
from, or are produced by human beings and the physical
environment. When I first came to the study of income
and capital, I developed the concept of capital as a stock
of wealth existing at an instant of time, and of income as
a flow of wealth during a period of time, which concept I
advanced in 1896.gsI found it necessary in 1897 to modify
my concept of income, and so stated.1° Since then I have
found no reaaon for further modification either of the
concept of capital 8s a stock of wealth exist.ing at an
instant of time, or of the concept of income as a flow of
services through a period of time, while the values of
these are respectively capital value, and income due,
often abbreviated into capital and income.
L.

W h t is CqdaZ? The Economic Journal, Vol. VI, Dec., 1898, pp.

509-534.

The RbEe of Cqitd in Economic Themy, The Economic Journal,
Vol. VII, Dec., 1897, pp. 611-537.

c 457 1

TRE THEORY OF INTEREST

“It is not possible,” it is objected, “to conceive of 8
literal stock of services at aninstant of time; it is possible
to conceive of their present worth &s a financial fund at
an instant of time. Services (taken in the sense of uses
either of wealth or of human beings) may conceivably be
delayed or hastened, but they are in their very nature a
flow; they cannot be heaped up and constitute a stock of
services. They can, at most, as they occur be ‘incorporated’ in durable forme of wealth. If this is so, then why
this elaborate contrast between a flow of services, and a
fund of something quite different? It is t,he vestigial remains of the older conception that Fisher haabeen
obliged to discard,” 11
While, however, I agree that these concepts of capital
(asa fund of wealth) and income (asa flow of services)
arenot commensurate with the theory of interest, it
would be a mistake to conclude from the emphasis placed
on capital value, not capital goods, in the The Nature of
Capital and Income, which was written as an introduction to the t h e o q of interest, that the concept of capital
goods emphasized by me in 1896 has been shelved as
useless.
In the first place, the goods concept is itself a step in
the formulation of the v a l u e concept, and secondly, The
Nature of Capital and Income does not attempt to cover
all of the four diEerent relations between capitaland
income but only that one relation, income value to capital
value, which is of importance to the theory of interest.
This valuation concept of capital, which in my view is
necessary to the solution of the interest problem,does
not distinguish between land and “produced means to
“Fetter, Ckrrkls Refornulation of the Capital Concept. Economic
Essays Contributed in Honor of John Batear Clark, p. 152.

c 458 1

OBJECTIONS CONSIDERED
further production.” Some writers,12 whohold this latter
concept of capital, have contended that my treatment of
land aa typical of capital in general has led me to
erroneous conclusions.
In particular, my criticism of the na;ive productivity
theories is said to fall down because of this consideration. But, as I have before written,la “my strictures on
the ordinary productivity theories are not dependent on
the putting forward of ‘land’ as typical of all forms of
capital” or the particular definition of capital which I
have used, but are, for the most part, merely a r&um6 of
the strictures of Ghm-Bawerk, whose definition of capital excludes land. In other words, these criticisms hold
true quite regardless of whether land is included in the
capital concept or not.
However,while I recognize certain differenceswhich
exist between land and so-called artificial capital, these
differences are of degree only, and do not carry the importance in most phases of economic theory which adherents of this concept of capitalattribute to them.
Professor J. B. Clark has presented the similarities and
dissimilarities of Iand and other durable agents so comprehensively and adequately that I shall not attempt to
go over again this question at this point. However, one
phase of this comparison is of importance. It is claimed
by those l5 who hold land to be non-reproducible and,
therefore, to lack a cost of production, that its value is
Useager, The Impatience Theory oj I&rest, American Economic
Review, Vol. 11, No. 4, December, 1912, pp. 834-851; Brown, Economic
Scisnca and The Comnum Welfare.
The Impatience T h e q of Interest, American Economic Review,
Vol. 111, No. 3, September,1912, pp. 610815.
Clark, Distribution of Wealth, pp. 338344.
=For example, Sewer and Brown, cited above.

c 459 1

TEE THEORY OF INTEREST
governed by factors quite different from those determining the value of reproducible agents whose production
does involve costs of production.
In brief, the contention is that the discount or capitalization principle of valuation upon which my theory rests
is applicable only to land, since land value is not affected
bycost of production. “If land, the limited gift of
nature,” one critic writes, “were truly representative of
capital, then Fisher’s reasoning wouldbe unassailable.” l6
But since land, it is implied, is not representative of
capitd in that itdoes not involve a cost of production, the
valuation process which applies to land does not apply to
those “produced means to further production” which do
incur costs in their production. To a consideration of the
relation of cost of production to capital value, therefore,
we now turn.
$3. Cost of Production as a Determinant of Captal Value

The criticism that my views as to the relation of cost
of production and capital value areinvalid because of the
use of land as typical of capital has been advanced by
several writers.17 In its most concrete form, it applies to
the example which I presented of the casewhere an
orchard was held to be worth $lOO,OOO because this sum
represented the discounted value of the expected income
from the orchard of $5,000 per annum. But even if we
change the orchard to machines, houses, tools, ships (that
is, “produced means to further production”) the principle
that the value of anything is the discounted value of its

$44.

Sager, cited above, p.
=Seager, Brown, and Flux cited above; also Loris, Irving Fiaher‘s
Rate of Interert, Journal of Political Economy, Vol. XVI, Od.,1908,
pp. 331-332.

[ 460 1

OBJECTIONS CONSIDERED
expected income stands unrefuted. This is not to say cost
of production does not have an influence. But past costs
have no influence on the present value of a capital good,
except ts those costs affect the value of the future services it renders and the future costs. Future costs influence this value more directly by beingthemselvesdiscounted at the current rate of discount. It is certainly
true that if the reproduction cost of the capital goods is
lowered, their production will be stimulated, the supply
of services they render will be increased, the valuation
of these services, i.e.,the income from these capital goods
per unit will be lowered, and, therefore, quite aside from
any effect on the discount rate, the capitalization of this
reduced income willtend to be lowered. Furthermore, this
fall in the value of the capital goods willbe brought down
to a point, through the operation of the opportunity principle, where it is brought into conformity with the new
cost of production of the capital good plus a margin to
represent the amount of interest.
But, although it is true, it is objected, that under the
supply and demand analysis, an increase in the supply of
a single commodity will lower its value, the same does not
follow when applied to all goods. “Exchange values m d
prices are relations among goods. Increase the supply of
one good and the ratio at which it exchanges for others
or for money will change to its disadvantage. If, however,
you increase at the m e time the supplies of all goods,
including gold, the standard money material, you affect
simultaneously both sides of all ratios of exchange and
consequently the ratios should remain substantially as
before. It is just such an increase of goods of all sorts and
descriptions that is denoted by Bohm-Bawerk’s phrase,
‘the technical superiority of present over future goods’,

C 4 w

THE THEORY OF INTEREST
or by the more familiar phrase ‘the productivity of capital’, Admitting the physical-productivity of capit,al (and
Fisher does not question it), the value-productivity of
capital or, more accurately, an increase in the total value
product as a consequence of the assistance which capital
renders to production seems to me to follow &s a logically
necessary consequence. . . . Since there is nothing in the
assumption that the productivity of allinstruments is
doubled that involves any serious change in the expense
of producing the instrumenh, the product,ivity theorist
certainly wodd claim that under these condit.ions there
must be, if not EL doubling, certainly a very substantial
increase in the rate of interest.” l 8
I can perhaps do no better than to repeat in part the
reply which I made to this criticism in 1914.l9 “But the
increased pr0ductivit.y of capitd will entail a decreased
price, or value per unit, of the products of that capital.
And in addition there may be an increase in the expense
of producing the capital,if, for instance, it is reproducible
only under the laws of diminishing returns or increasing
costs. Evidently it does not follow that the net returnon
capital-value will be permanently increased, I n short, the
expenses of production, on the one hand, and the price of
the product of thecapital multiplied by the increased
product itself, on the otherhand, will tend to adjust
themselves to each other and to the rate of interest. But
this rake of interest, according to my philosophy, instead
of being permanently raised, will be ultimatdy lowered,
for to double the productivity of capital will mean ultimately B much larger income to society than before, and
useager, cited above, pp. 8423, 847.
* T h e Impatience T h e m of Interest, American Economic Review,
Vol. 111, No. 3, Geptember, 1913, pp. 814415.

c 462 1

OBJECTIONS CONSIDERED
this larger income tends to lower the rates of impatience
of those who own it. So long as the rate of interest does
not fall to correspond with the lower rates of impatience,
there will continue to be profit in reproducing the productive capital until adjustmentis attained-whether by decrease in the price of the products or by increase in the
cost of the capital, or both, does not matter. In any case
this adjustment must be by lowering and not by raising
the rate of interest, for the rate of interest cannot be
raised if the rates of impatience are not raised, and the
rates of impatience cannot be raised if, as is assumed, the
income stream is increased in size without being altered
in other respects.”
Very possibly, Professor Seager and I may have been
arguing at cross purposes, for, of course, in the transition
period while productivity is being doubled, bhe rate of
interest may be raised. This is amply provided for in my
theory. But even during the transition period something
more is required than increased productivity in order
that the rateof interest shallrise; the cost of making the
change must be reckoned with and deducted from the
income stream. Mere physical productivity will not
suEce.
Having stated myviews, it will serve to present clearly
the difference of opinion to quote an illustration which
Professor Harry G. Brown has furnished me of his views
on the matter.
“Smith is a fisherman. His boat (capital necessary to his business)
is wearing out and will last little longer. He catches, in general, 40
halibut a week, which he sells for $1 each, or $40 a week. He is a h
a goodcarpenter and canmakehimselfaboat
in s week’s time.
But to do BO, he must give up the $40 worth of fish he could catch,
or the &io for which he coulcJ sell them. For him the cost of building s boat ia
That is ib cost in the sense of the sacrtflce smith

$40.

~4631

THE THEORY OF INTEREST
must make in other products (fish) of his labor, if he builds the
boat.
“Jones offers to sell him an exactly similar boat already built for
$150. Smith refuses to pay over $40. Since other fishermen do the
same, the demand for boats is such that Jones can’t get $150. The
fact is thatthe income Smith could get from his fish,whichhe
expects to catch this week ($40) affects the price Jones can charge
(value) for a boat (capital good) already built. This $40 worth of
fish is not income f r m n the boat we are about to value. It certainly
is not the value of that income or its discounted value. And it is
not a future cost of the to-bevalued boat.
“The costyou are thinking of as ‘included’ in your formulation
(discount principle of capital value) is, for example, the expected
cost (say 5 years hence) of replacing a worn-out or broken seat,
broken oarlocks, etc., and the annual cost of painting. But the $40
which measurw the cost to Smith of duplicating Jones’ boat will
make Smith unwilling to pay $150 even though your formulation,
taken by itself, would let him-for he must have some boat. And
Smith would have a curious mind if the $40 cost affected him only
through first making him think of more plentiful and therefore less
valuable future services. It has a direct effect on his price offer, not
an effectconsequentsolely
on B revaluation of expected future
services.
“You can’t d e the psychology of the fisherman, Smith, fit into
your formula. It’s better to make B formula that fits what Smiths
mind really does.”

I accept all of Professor Brown’s reasoning and conclusions except his application to me. His contention that
the cost of duplicating existing capital will influence the
value of that capital is perfectly correct, but so is the
discount formula..
The two are not inconsistent. If they were, by thesame
logic, the generally accepted formula by which the value
of a bond is calculated in every broker’s office is contradicted every day whenever & cheaper bond is available.
The h t axiom in economicsis, naturally, to get anything

14641

OBJECTIONS CONSIDERED
the cheapest way whether that way is to make it oneself, buy a substitute or otherwise,for in Professor
Brown% reasoningit is solely the existence of an alternative cheaper way which makes the supposed disturbance.
The reasoning proves too much. Suppose Jones offers
Smith a bond at one price and Smith refuses because he
can get another just like it for less. He would choose the
cheaper and he would have a “curious mind” if the
cheaper cost affeckl him only through first making him
t.hink elaborately of the discount process. All he needs to
know is that if Jones’ bond is worth the price offered the
cheaper one is even more clearly worth while. And Jones
will sit up and take notice, possibly reducing his price.
The cheaper bargain thushas inProfessorBrown’s
sense a “direct” effect on the price of Jones’ bond, not an
effect solely ona revaluation of expected services. But we
cannot here conclude that the usual mathematical formula for the price of a bond was incorrect.
There is no more definite and universally accepted
formula in the whole .realm of economics and business
than that referred to. It isused every day in brokers’
offices. It gives the price of a bond in terms of the interest
basis, the nominal interest and the time of maturity. It
is the type, par excellence, of the capitalization principle
both in theory and practice. It is not impaired by any
undercutting of the market.
The boat is, economically, a sublimated bond. If Jones
offers it to Smith for $150, while Smith can get it cheaper
the discount principle is not invalidated. There is simply
a readjustment in the boat as in the bond market. Moreo v e ~in an individual transaction where there is no marginal point reached by repeating the transaction-only
one boat, not a series-there are wide limits within which

l-4653

THE THEORY OF INTEREST
the buyer gets his consumer’s surplus and the seller his
producer’s surplus. Onlywhen there is a series ofsuccessive boats or bonds do we have a full fledged example
of the margin where consumer’s rent disappears and an
equality replaces inequalities.
In the isolated case we should be content to say that
Smith will not pay more than the capitalized value, In
the case of the conventional series of boats, the marginal
boat will be such that thecapitalization principle and the
cost principle will both apply. The seventh boat, let us
say, will cost Smith $100 whether to make or t~ buy.
Jones and other boat owners willhave reduced their price
from $150 and Smith will have found that to make so
many boats will have cost $100 instead of $40, to say
nothing of theimportantfactthathe
would have to
wait much more than a week.
All these points are covered in my presentation, for
Professor Brown’s example is only one of the myriad examples of alternative opportunities. Smith, like everybody else,willuse
the cheapest way in the sense of
choosing the income stream of labor and satisfaction
having the maximum present worth at the market rate
of interest.
Professor Brown has his eyes on the opportunity part
of the picture and no one has stressed that part more
than I. But interwoven with it and consistent with it, in
the analysis of a perfect market in which the individual
is a negligible factor, is the principle that every article of
capital is vdued at the discounted value of its expected
services and costa.
I do not intend to underestimate the importance of
the cost concept. The importance it holds in my mind
not to be measured by the number of pages devoted to it

[ a 3

OBJECTIONS CONSIDERED
in my books, the main purpose of which was to study
capitalizations of income. I believe that the position on
cost which was taken by Professor Davenport 2o is in general the correct one. What I attempted to point out was
that those double-faced events, which I have called interactions, and which always have a double entry, a positive
and negative entry, in social bookkeeping, are not ultimately cost any more than they are ultimately income.
I also tried to emphasize that cost enters into capitalization on equd terms with income, when the cost is future.
Past cost does not affect present valuations except indirectly, as it affects future expected income and cost.
No one would maintain that obsolete machinery, even
in good condition, could be appraised on the basis of its
cost. The only cases in which cost (with interest) is equal
to value is where this value is also equal to the estimate
of worthon the basis of future expectations; when, in
other words, cost is superfluous as a determinant of value.
That cost does influencevalue by limiting supply, thereby
affecting the quantity and value of future services, cannot be questioned. It is natural that business men should
not follow this roundabout relation, but connect directly
cost with value. This, however, is no reason for economists
to fail to analyze the relation in all its complications.

of the Interest Rate
Certain characteristics of The 3ate of Interest led to
the unfortunate deduction on the part of many readers
$4. Impatience

a8 Determinant

Davenport, Vdue and Dist&tion.
Cf.M e r and Flux, citedabove, andparticularly Fetter, Interest
Theories O M ond New, AmericanEconomicReview, Vol. IV, No. 1,
March, 1914, pp. 69-72.

~

7

1

THE THEORY OF INTEREST
of that volume that I regarded impatience as the sole and
complete determinant of the rate of interest. While 1have
tried in this book to forestall similar misinterpretations
of my theory, and while it does not seem possible to me
that any reader could now charge me with being pure
impatience theorist, it will serve a useful purpose to consider the various factors involved in this question.
We may draw upon Professor Fetter’s writings for a
clear statement of the issuebetween the productivity
theory and the time preference theory of interest. He
states positively that time preference is the sole cause of
interest, although he assumes that physical productivity
is essential to the emergence of value productivity.22 He
declares that his theory wasnew in assigning priority
to capitalization over contract interest and in giving a
“unified psychological explanation of all the phenomena
of the s u r p l u s that emerges w h a undervalue& expected
incomes approach maturity, the surplus all being derived
from the value of enjoyable (direct) goods, not by two
separate theories, for consumption and production goods
respectively.” 23 [Italics mine.]
I have no criticism to make of this statement of the
operation and effect of time preference 80 far as it goes.
It seems to me to coincide sufficientlywith the treatment
which I have presented under the first approximation.
There incomes were assumed to exist and to be rigidly
our bothering to
fixed in amount and in time without
ask how they were produced. Nature offered no options
to substitute one income stream for another. One could
modify his income stream only by borrowing or lending.
PFetter, Interest Theories Old and New, American Economic Review, March, 1914, pp. 74, 76, 77.
= Ibid., p. 7 7 .

14681

OBJECTIONS CONSIDERED
Under the hypothetical conditions so assumed, time preference would causeinterest without helpfrom any rateof
return over cost. But such sssumed conditions never do
or can exist in the real world.
Of course a constant rigid physical productivity, yielding unchanging physical income streams, ia contrary to
the observed facts of life, just LIS unchanging time preference for each individual at all times and under all conditions k an absurdity. In real life men have the opportunity of choosing among many optional income streams.
Whensuch opportunities exist, time preference alone
does not and cannotexplain the emergence of interest. As
a mathematical problem, the rateof interest would under
the conditions of the second or third approximations be
indeterminate without introducing the influence of the
opportunity or productivity factor?'
Productivity, that is, the possibility of increasing the
present value of the income stream, introduces new
variables which have to be determined as a part of the
interest problem and every new variable requires a new
equation or condition.
It happens that, for lack of applying this mathematical
principle, writera have often thought themselves in
greater disagreement on the explanation of interest than
they really were. Wordy warfare has been waged among
the various productivity theorists and the capitalization
Aa is always pomible in solving simultaneous equations we can, if we
wish, express certain of the variables, such aa those relating to productivity, or opportunity, namely the rates of return over cost, in terms of
the other variables and thus seem to eliminate them. In my first book
I tried, for the most part, thus to present the rate of return over cost,
or aa I then called it,the rate of return on sacrifice asdetermined
through the rate of preference. But we can just as well in like m e r
eliminate time preference and present it in t e r n of rate of return.

c 469 1

THE THEORY OF INTEREST
or time preference theorists. Each combatant seems to
think that he and he alone has hit upon the correct and
complete explanat.ion and that, therefore, any other explanation is necessarily false. As a matter of fact, both
productivists and time valuists are substantially right in
their affirmations and wrong in their denials. Thus,
theories which have been presented aa antagonistic and
mutuallyannihilatoryare
in reality harmonious and
complementary.
$5. Productivity as a Determinant of Interest Rates

When the true natureof the income concept is grasped,
it will be found that it includes within itself many special
cases which have been advanced by various writers in
explanation of the rate of interest. The relation of both
impatience and opportunity to the rate of interest, in my
opinion, can be comprehended accurately only by analyzing rigorously these concepts and determining the effect
of each upon the income stream. By this procedure, we
arrive at a fundamental explanation of the nature of impatience and of return on income invested and see how,
by changes in the income stream, these rates are brought
into conformity with the rate of interest.
I have always felt that John Rae came closer than any
of the earlier writers to grasping all the elements of the
interest problem. According to Rae,all instruments may
be arranged in an order depending,on the rate of return
over cost. This amounts to saying that the formation of
any instrument both adds to and subtrackfrom the preexisting income stream of the producer, its cost being the
subtracteditemand
the return, the added one. The
statement of Rae that for a certain cost of production
an instrument will yielda certain return, is merely a form

c 470 1

OBJECTIONS CONSIDERED
of my statementthat a certain decrease of present income
will be accompanied by a certain increase in future income. The relation between the immediate decrease and
future increase will vary within a wide range, wherein
the choicewill fall at the point corresponding to the
ruling rate of interest.
The same relationship wasconceived
by Adolphe
Landry in his Inte‘rJt du Cadtal. He states that one of
the conditions determining therate of interest is the
“productivity of capital”, in the peculiar sense which he
gives to this phra~e,2~
which is, in effect, therate of
return overcost.
It has seemed to me that much of the criticism, both
favorable and unfavorable, of my book, The Rate of Interest, has been based on the erroneous assumption that
the so-called productivity element found no place in my
theory. Much of the misunderstanding of my theory may
have been fostered by the lack, in my first book, of a good
term with which to express this productivity factor in
interest.
As a consequence, one critic, Professor Seager, writes
that I refuse to admit that what Bohm-Bawerk calls the
“technical superiority of present over future goods”, and
what other writers have characterized more briefly as
“the productivity of capital” has any influence on the
comparisonbetween present gratifications andfuture
gratifications in which, as he believes, the complete and
final explanation of interest is to be sought.
“The most striking fact about this method of presenting his factors”, this criticism continues, “is that he dissociates his discussion completely from any account of
the production of wealth. From a perusrtl of his Rate of
SJ

Landry, L’IntMt du Copilol, pp. 6695.

r 471 I

Interest

THE THEORY OF INTEREST
and all but the very la& chapters of his EEe-

mentary Principles (chapters which come after his discussion of the interest problem), the reader might easily
get the impression that becoming rich is a purely psychologicalprocess. It seems to be assumed that income
streams, like mountain brooks, gush spontaneously from
nature’s hillsides and that the determination of the rate
of interest depends entirely upon the mental reactions of
those who are so fortunate as to receive them. . . . The
whole productive process, without which men would have
no income streams to manipulate, is ignored, or, as the
author would probably say, taken for granted.” 26
My views are quite contrary to those here set forth.
As I wrote in 1913:

*’

“What Professor Seagercalls the ‘productivity’ or ‘technique’
element, so far from being lacking in my theory, is one of its cardinal
features and the one the treatment of which I flattered myself was
most original! The fact is that my chief reason in writing the Rate of
Interest at all arose from the belief that Bohm-Bawerk and others
had failed to discover the true way in which the ‘technique of production’ enters into the determination of the rate of interest. Bei
d in previous explanations unsound, and
lieving the ‘technical’ l
realizing as keenly as Professor Seager does the absolute necessity of
such a link, I set myself the task of finding it. In the desirability
of this I emphatically agree with Bohm-Bawerk.”

I do not assume, except temporarily in the first approximation, that “income st’reams,like mountain brooks,
gush spont.aneously from nature’s hillsides”, and this is
temporarily assumed, precisely as physicista temporarily
assume a vacuum in studying falling bodies, or, to take a
“Seager, The Impatience Theory of Interest, AmericanEconomic
Review, Vol. 11, No. 4, December, 1912, pp. 835-837.
The Impcotiem Theory of Interest. AmericanEconomicReview,
Vol. 111, No. 3, September, 1013, p. 010.

r 472 1

OBJECTIONS ,CONSIDERED
better but still imperfect analogy, precisely as, in treating supply and demand, we first assume a k e d supply
before introducing the supply schedule or supply curve,
ThL assumption gives place in the second approximation
and the third approximation to the more complicated
conditions of the actual world. My method of exposition
is here, as usual, to take one step at a time, which means
to introduce one set of variables at atime. All other
things, for the time being, are assumed to remain equal.
I realize that this is not theonly method and that it may
not be the best one, but it is at least a legitimate method.
On the other hand, it does not seem to me that the
theory of interest is called upon to launch itself upon a
lengthy discussion of the productive process, division of
labor, utilization of land, capital, and scientific management. The problem is confined to discover how production is related to the rateof interest.
It should not, however, be assumed from what has been
said that I regaxd all productivity theories as sound.
Mention was made in Chapter 111of the “naive” productivity theories which hold that interest exists simply b e
cause nature, land and capital are productive.
$6. Technical S u ~ & g of Present Good8

Bohm-Bawerk is among those who sensed the inadequacy of time preference or impatience aa the sole determinant of the rate of interest. Yet he calla his theory the
agio theory of interest, since he h
d
s the essence of the
rate of interest in the agio,or premium, on present goods
when exchanged for future goods.
Bohm-Bawerk presented the agio theory, or what is
here called the impatience or time preference theory,
elearly and forcibly, and disentangled it from the crude
C 473 1

THE THEORY OF

INTEREST

and incorrect notions with which it had previously been
associated. It wm only whenhe attempted to explain the
emergence of this agio by means of his special feature of
“technical superiority of present over future goods” that,
in my opinion, he erred greatly.
Bohm-Bawerk distinguishes two questions: (1) Why
does interest exist? and (2) What determines any particular rate of interest?
In answer to the h t question, he states virtually that
this world is so constituted that most of us prefer present
goods to future goods of like kind and number. This preference is due, according to Bohm-Bawerk, to three circumstances: (1) the ‘(perspectiveunderestimate” of the
future, by which is meant the fact that future goods are
less clearly perceived,and therefore less resolutely striven
for, than those more immediately at hand; (2) the relative inadequacy (as a rule) of the provision for present
wants as compared with the provision for future wants,
or, in other words, the relative scarcity of present goods
compared with future goods; (3) the “technical superiority” of present over future goods, or the fact, aa BohmBawerk conceives it, that the roundabout or capitalistic
processes of production are more remunerative than those
which yield immediate returns.
The first two of these three circumstances are undoubtedly pertinent, and are incorporated, under a somewhat different form, in this (book. It is the tihird circumstance-the so-cded technicd superiority of present over
future goods-which, as I shall try to show, contains
funciamental errors.
My criticism of this third thesis, however, does not, as
some have implied, consist in denying the existence or
importance of the “technical” element in intereat but in
474 1

r

OBJECTIONS CONSIDERED
denying thesoundnm of the way in whichBiihmBawerk applies it. It was for the purpose of presenting
what in my view constitutes the true character of this
element that I have placed 80 much emphasis on the opportunity principles givenin Chapters VII, VIII,XI and
XI11 of this book.
According to Bohm-Bawerk, labor investedinlong
processes of production willyield larger returns than
labor invested in short processes. In other words, labor
invested in roundabout processes confers a technical advantage upon those who have command of that labor.
In the reasoning by whichBiihm-Bawerk attempts to
prove this technical superiority, there axe three principal
steps. The first consists of postulating an “average
production period,” representing the length of the
productive processes of the community; the second consists of the proposition that the longer this average production period, the greater will be the product; and the
third consists in the conclusion that, in consequence of
this greater productiveness of lengthy processes, present
goods possess a technical superiority over future goods.
Although the h t two of these three steps are of secondary importance, the following remarks concerning
them are in point. The concept of an average production
period is, I believe, far too arbitrary and indefinite to
form a basis for the reasoning that Bohm-Bawerk attempts to base upon it. At best, it is B special, and very
hypothetical, case not general enough to include the
whole technical situation.
Bohm-Bawerk himself,in his reply to my original criticism,asserts his agreement with my contention concernlong
proceases
in
ing the second stepthat, while
general more productive than short processes, this is not
C 475 1

THE

THEORY
OF INTEREST
a universal truth. Of the infinite number of possible
longerprocessesonly

those which are more productive

than shorter ones are chosen.28This is what was noted in
Chapter XI when it was Shown that the 0 curve is concave simply because the reEntrant parts are skipped!
It is the third step which is crucial to the theory of the
technical superiority of present goods, namely, that the
productiveness of long processes gives a special technical
advantage to the possessor of present goods or present
labor. This advantage produces, so Bohm-Bawerk asserted, a preference for present over future goods which
is entirely apart from, and in addition to, the preference
due to theunderendowment of the present. Granting, for
the moment, the validity of the concept of a production
period, and that the longer the period, thegreater its
product, it may still be shown that no such technical
superiority follows. Bohm-Bawerk regards this part of his
theory as the most essential of all, and repeatedly states
that the theory must stand or fall by the truth or falsity
of that part.
Bohm-Bawerk supports his assertion of the existence
of a technical superiority2@by elaborate illustrative
tables.*O Each table is intended to show the investment
aPoaitive T h o & &8 Kapitalea “Meine These schriinkt vielmehr
diem Wirkungausdriicklich auf ‘kluggewiihlte’Verliingerungenein
und liisst iiberdies, indem me ihr Zutreffen n u ‘in aller Regel’ oder, wie
ich in der ensten Auflage sagte, ‘im gmasen und ganzen’ behauptet, das
Vorkommen von Auanahmenoffen.” E z h n I, p. 3.
“Wenn Fisher hiemit nicht mehr in.Abrede stellen wollte, ale wm ich
oben auf 6.3 des E z h r s e I s e l b s t in Abrede gestellt habe, dase namlieh
nicht aIle lii-ngeren Produktionsumwegenurdeshalb,
weil sie ranger
sind, such produktiver sein m h n , BO wiiren wir in vollem Einklang.”
h’zkurs Iv, p. 105.
T L Positive Theory of Cupitd, p. #Is.
“In The Rate of Intere8t there is p m t e d an exhaustive dpid Of

r 476 1

OBJECTIONS CONSIDERED
possibilities of a month’s Mor available in any particular
year. That longerprocesses are more productive than
shorter ones,Bohm-Bawerk indicated by an increasing
number of units of produet for each successive year. The
marginal utility of eachyear’s yield when obtained is
illustrated by a decreasingseries, since the marginal
utility of a stock of goods decreases as the number of
units in the stock increases. Since the year 1888 was considered as the time of reference, or the first year in which
the investment of labor was to be made, the numerical
series representing the marginal utilities of the optional
products as of the respective years of their production was
reduced, by discounting, to a series of numbers representing the marginal utility of each year‘s yield &s of the
year 1888. The subjective value of each year’s yield as
of the year 1888, Bohm-Bawerk obtained by multiplying
the number of units of each year’s yield by its reduced
marginal utility.
Of course, that investment of the month’s labor availwould be made which
able as of anyparticularyear
showed the maximum present value. When, however, the
table of any one year is compared with that of any succeeding year, the maximum present subjective value
selected is the greater the earlier the month’s labor is
available.
For example, a month’s labor availsble in 1888 was
shown to be most advantageously invested in the process
which yielded the maximum present subjective value of
840 in 1890. But a month’s labor available in 1889 yielded
the validity of the proof presented by these tables of the theory of technieal superiority advanced by Bijhm-Bawerk. While it does not seem
advantageous to repeat here thie analysis, since it is available in my previoua book to any reader who may be interested, it ie pertinent to present the concIuaions drawn therefrom.

c 477 3

THE THEORY OF INTEREST
its maximum present value when invested so as to mature
in 1893. In this latter case, however, the maximum was
only 720 a~ compared with the maximum of 840 for a
month’s labor available in 1888.
Bohm-Bawerk therefore concludes that a month’s labor
available in 1888 is more product,ivethan one available ir.
1889, 1890 or any succeeding year. In other words,entirely independent, according to him, of the perspective
underestimate, and the under-endowment of the present,
there inheres a technical superiority in present over
future goods.
“This result”, he writes,31 “is not an accidental one,
such as might have made its appearance in consequence
of the particular figures used in our hypothesis. On the
single assumption that longer methods of production lead
generally to a greater output, it is a necessary result; a
result which must have occurred, in an exactly similar
way, whatever might have been the figures of quantity
of product and value of unit in the different years.”
But Bohm-Bawerk is mistaken in ascribing any part of
this result to the fact that the longer processes are the
more productive. In his tables he aasumes the existence of
one or both of the other two factors-the relative underprovision for the present aa compared with the future,
and the perspective undervaluation of the future, due to
lsck of intellectual imagination or emotional self-control.
It is these elements, and these alone, which produce the
advantage of prersent over future goods which the tables
display.
That the result does not at all follow from “the single
assumption that longer methods of production lead generally to a greater output” and has nothing whatever to
The Positive Theory of Capitd, p. 208.

c 478 1

OBJECTIONS CONSIDERED
do with that assumption, we can see clearly if we make
the opposite assumption from that of Bohm-Bawerk,
namely, that the longer the productive process the
smaller will be the return. The very same result would
still follow. The labor would still be invested at the
earliest possible moment. In other words, let the figures
representing units of product decrease instead of increase.
The onlydifferencewould
be that the month’s labor
available in 1888 would now be so invested as to bring
returns in that year instead of being invested in a two
years’ process as before. If calculations are performed for
each year and the results are compared, it will appear
that the investment in 1888 yieIds the highest return,
just 8s it did on the previous hypothesis.
Again, the same result would follow if the productivity
increased and then decreased in all the tables, or if the
productivity should first decrease and then increase. As
long as the figure representing reduced marginal utility
decreases, the “units of product” m y be of any description whatever, without in the least affecting the essential
result that the earlier the month’s labor is available, the
higher is ita value.
On the other hand, if the conditions are reversed and
the reduced marginal utility does not decrease,the earlier
available labor will not have a higher value, whatever
may be the character of the “units of product.”
Bohm-Bawerk, however, speci6cally denies this: 8s
(‘The superiority in value of p m n t means of production, which
is based on their technicalsuperiority, ie not one b 0 ~ 0 w e dfrom
these circumstances [ie., the perspective underestimateof the future
and the relative underendowment of the present] ; it would emerge
of its own strength even if these were not active st all. I have i
n
h

‘The Poeitive Themy of C q d d , p. #KI,

C 479 1

THE THEORY OF INTEREST
duced the two circumstances into the hypothesis only to make it a
little more true to life, or, rather, to keep it from being quite a h r d .
Take, for instance, the influence of the reduction due to perspective
entirely out of the illustration.”

In his table it is true that the month’s labor available
in the present is more highly valued thanthe same
month’s labor available at a later date.But Bohm-Bawerk
carefully retained in hisillustration one of the “two
circumstances” which he told us could be discarded,
namely, the relative overprovision for the future. To leave
one of these two circumstances effective instead of both
is merely to change slightly the series of “reduced marginal utility”. The change in the particular numbers is
quit,e immaterialso long as the series is still descending,
and it does not matter whether the descent is due to
perspective or to the relative underprovision for the present, or to both.
The only fair test of the independence of BiihmBawerk’s third factor-the alleged technical superiority
of present over future goods-would be to strike out both
the other elements (underestimate and overprovision of
the future) 80 that there should be no progressivedecrease in marginal utilities; in other words, to make the
numbers representing “reduced marginal utilities” all
equal. Bohm-Bawerk, for somereason, hesitates to do
this.He says: 88
“But if we were also to abstract the difference in the circumstances
of provision in d8erent periods of time, the situation would receive
the stamp of extreme improbability, even of self-contradiction.’’

Even if this be true, and in my view it is not, it is no
reason for refusing to push the inquiry to its limit. When
“Podtive Th.eorg of CtpiM p . aS9.

c4807

OBJECTIONSCONSIDERED
this is done, however, the figures of present value of the
various yearly products become absolutely alike; hence
the maximum of the former, if there be a maximum, must
be identical with the maximum of the latter.
Though Bohm-Bawerk dtid not consider this case in his
tables, he speaks of it briefly in his text, but seems to be.
somewhat puzzled by it. He says:
“If the value of the unit of product were to be the same in all
periods of time, however remote, the most abundant product would,
naturally, at the same time be the most. valuable. But. since the most
abundant product is obtained by the most lengthy and roundabout
methods of production-perhaps extending over decades of yearsthe economic center of gravity, for all present m e w of productioq,
would, on this assumption, be found at extremely remote periods of
timewhich is entirely contrary to all experience.”

Bohm-Bawerk’s
confusion
here is probably to be
ascribed to his insistence on the indefinite increase of
product with a lengthening of the production period.
Practically we ought to assume that somewhere in the
series the product decreases. We would then have a more
practical illustration of the fact that the labor available
this year and that available next year stand on a perfect
equality.
The conclusion is that, if we eliminate the ‘(other two
circumstances” (relative underestimate of, and overprovision for, the future), we eliminate entirely the superiority of present over future goods. The supposed third
circumstance of technical superiority, in the sense that
Bohm-Bawerk givesit, turns out tobe non-existent.
The fact is that theonly reasonany one does prefer the
product of a month’s labor invested today to the product
of a month’s labor invested next year is that tod%y’e

TK% THEORY OF INTEREST
investment will mature earlier than next year’s investment.86 If a fruit tree is planted today which will bear
fruit in four years, the labor available today for planting it is preferred to the same amount of labor available
next year for the reason that if the planting is deferred
a year, the fruit will likewise be deferred a year, maturing in five instead of four years from the present.
It does not alter this essential fact to speak of the possibility of a nurnber of different investments. A month’s
labor today may, it is true, be spent in planting slowgrowing or fast-growing trees, but so may a month’s
labor invested next year. It is from the preference for the
early over the latefruition of any productive process that
the so-called technical superiority of present over future
goods, as conceived by Bohm-Bawerk, derives all its force.
Bohm-Bawerk,however, attempts to prove that his
third circumstance-the alleged
technical superiority of
present goods-is really independent of the first two, by
the following reasoning: se
“. . if every employment of goods for future periods is, not

.

only technically, but economically, mbre remunerative than the em-

ployment of themfor the present or nearfuture, of course men
would withdraw their stocks of goods, to a great extent, from the
service of the present, and direct them to the more remunerative
service of the future. But this would immediately cawe an ebb-tide
in the provision for the present, and a flood in the provision for tbe
future, for thefuture would then have the double advantage of
having a greater amount of productive instruments directed to its
service, and those instruments employed in more fruitful method
of production. Thus the Merence in the circumstances of provision,
’
T
h
bis true under the aseumption, implied in Biihm-Bawerk’s table,
that the product is the same except BB to the time of ite availability,
namely, that the series of figures called “unite of product” are identical
a8 shown in his tablee.
=Positive Theory of Capitol, pp. 289 and 270.

ca21

OBJECTIONS CONSIDERED
which might have disappeared for the moment, would recur of its
o w n accord.
“But it is just at this point that we get the best proof that the
superiority in question is independent of differences in the circumstances of provision: 80 far from being obliged to borrow ita strength
and activity from any suchdifference, it is, on the contrary, able,
if need be, to call forth this very difference. , , We have to deal
with B third cause of the surplus value, and one which is independept
of any of the two already mentioned.”

.

The argument here is that if “the other two circumstances” whichproduce interest, namely, underestimate
of the future and underendowment of the present, are
temporarily absent, they will be forced back into existence by the choice of roundabout processes. In other
words, the technical superiority of present goods produces
interest by restoring the other twocircumstances. But
this is tantamount to the admission that technical superiority actually depends for its force on the presence of
these other two circumstances and is not independent.
The essential fact is thatthe presence of technical
superiority does not produce interest when the other two
are ab~ent.8~
Although BGhm-Bawerk devoted many pages in the
third edition of his book and the Supplements (Exkurse)
to answering my criticisms,8* I can find nothing in his
answers which a$ects the main argument BS set forth
“See von Bortkiewicc, Der Ka&ndjehler der Bahm-Bawerkschen
Zinstheorie. Jahrbuch fiir Gesetsgebung, Verwdtung und VoWrteehaft,
1906, pp. 61-90.

See also von Schaposchnicoff,Die BohmBaredc.?che K q i t a l s i n e t b
Nationdokonomie und Statist&. Verlag von GUStav Fischer, Jena, Dritte Folge, Bd. XXXIII ( L x X m ) , pp. 43341.
”Positive Theorie des Kopitdes. Dritte A M , and Ezzkwae mu
Positive Theorie des Kapitdea. See especially Exhuse N and Ekkuree
XII.

orie. Jahrbiicher fiir

14831

THE THEORY OF’ INTEREST
above.8e I have omitted certain of the less important of
my original criticisms to which Bohm-Bawerk has
replied.
Perhaps the most interesting pointabout
BohmBawerk’s failure correctly to formulate the “technical”
feature which he thus vainly sought is that it i~ really
much simpler than he imagined. It does not require his
elaborate tables and comparisons among their many columns. Merely the first column of his tables contains
implicitly the true “technical” feature in one of its many
forms of choosing from among optional income streams.
This shows the successive amounts of product obtainable
for a series of production periods of different lengths.
This series is exactly analogous tothe successive ordinates in Chart 16 showing the lumber to be obtained
from a forest at different dates. There comes a point in
such a series or such a curve, where a further lengthening
of the time by one year will add to the product over the
preceding year (i.e,, will yield a rate of return over cost
mE%hm-Bawerkclaims that merely to find out the factors operative
in a given problem is not the same thing as to ezpkin those factors.
He thinks that my theory of interest would be adequate only if the
mathematical solution of the problem by meane of simultaneous equations, and what he calk the “caup~l”solution were the same, or at
least gomewhat
Of course, thw two types of solution are not the =me. The causal
solution cannot be BO simply conceived aa to make onefactor solely
a w e and mother solely effect. The advance of all science has required
the abandonment of such mmplified conceptiona of causal relationship
for the more realistic conception of equilibrium.
Here, all factors are considered BB variables. Any disturbance in one
factor reacts on all the others, and the variatione in these other factom
react upon the factor of original disturbance. The mathematical solution
of the problem of interest by means of simultaneoue equationa recogn k e 8 the mutud interdependence of all the factors in the interest problem and, at the mne time, yields a determinate solution for the problem.

mmilar.

E4841

OBJECTIONSCONSIDERED
both reckoned in kind) at a rate harmonizing with the
rate of interest. OddlyenoughBohm-Bawerk does not
mention this derivative from his table. Another form,
more nearly what Bohm-Bawerk apparently was groping
for, could have been presented had his table beenextended to include not merely one dose of 100 days labor
but many such doses and if “labor” and “product” were
reduced to a common denominator. Then the product of
the marginal labor would be the return while the labor
itself would bethe cost from whichreturn over cost could
be derived. But the comparisonswhichBohm-Bawerk
actually employed are beside the point,

$7. Interest as a Cost
From the foregoing criticisms and discussion it will, I
hope, be seen that I have given full recognition, in this
book, to the elements of productivity, technique of production, and cost, and that my chief objections to their
treatment by many otherwriters is either that their treatment is inadequate and leaves the problem of interest
indeterminate, or simply that they do not reduce the
problem to its simplest terms.
In particular, it has been noted thatthe ultimate
economic cost is labor and that all money payments and
industrial operations intervening between labor and satisfactions may, in the large view, be dropped out. I have
endeavored, in this and in other ways, to articulate the
theory of interest with sound accounting principles, even
when no great damage would be done to interest theory,
aa such, if unsound accounting were allowedto enter.
The most flagrant case of unsound accounting injected
into this discussion is, in my opinion,when waiting is
regarded aa a cost.

14861

THE’THEORY OF INTEREST

This grows out of the common tendency to account for
all economic values in terms of cost. When we cannot find

the cost, we invent it. We feel sure interest mustbe fully
accounted for in termsof cost. When we find inadequate
the cost of producing capital or the cost of managing it
or of organizing it or of investing it, we fall backon
waiting, abstinence, or hbor of saving.
It is true that these words are used by some writers to
mean nothing more than what I have included in the
phrase impatience or time preference. In these cases the
question is merely one of terminology. In a large number
of instances, however, the abstinence or waiting theory
seems to me to differ from the impatience theory not only
in words but in essence. In this the assumption is made
that sbstinence or waiting exists ~ 1 san independent item
in the cost of production, to be added to the other costs
and to be treated inall ways likz them.
If abstinence or waiting or labor of saving is in any
sense a cost, it is certainly a cost in a very different sense
from all other items which have previously been considered aa costa. An illustration will make clear the difference
between true costs and the purely fictitious or invented
cost of waiting. According to the theory that waiting is
a cost, if planting a sapling costs $1 worth of labor, and
in 25 years, without further expenditure of labor, or any
other cost whatever (ezcept waiting) this sapling becomes
worth $3,this $3 i~ a mere equivalent for the entire cost
of producing the tree. The items in this cost are, it is
claimed, $1 worth of labor and $2 worth of waiting.
According to the theory of the present book, however,
the cost of producing the tree is the $1 worth of labor,
and nothing more. The vdueof the tree, $3,exceeds that
cost by a surphs of $2, the existence of which aa interest

CN1

OBJECTIONS

CONSIDERED

it is our business to explain. Labor cost and waiting are
too radically different to be grouped together as though
each were a cost in the same sense as the other,
The cost of waiting can neither be located in time, independently of the item waited for, nor can it, like any
other item, be discounted, for it is itself the discounting.
If we discount the discounting, we wouldhave to discount
the discounting of the discounting and repeat the process
indehitely.
If we insist on calling waiting or abstinence a cost we
reduce to absurdity all our economic accounting. Among
other things, the simplest, purest type of income, a perpetual annuity, will be found, by such accounting, to be
no income at all.
An able critic and correspondent, after admitting this
fact, says simply, "What of it?"
Well, perhaps nothing vital as to the theory of intereat
itself. And since that is, after all, the sole subject of this
book I shall relegate to the Appendix the discussion of
What of it? aa to accounting."O

$8. Empirical and Institutional InfEuences om Interest
Rates
The probIem of fully determining any specific market
rate of interest is an intricate and b a i n g problem to
solve just as is the problem of fully explaining any historical fact whatsoever. This volume makes no clsim to
being the monumental work necessary to analyze every
possible influence that acts upon sucha rate. The purpose
of the book is rather to isolate the fundamental or basic
forces which are operative in the interest problem
The approach is theoretical, rational, or philosophic, if
OSee

Appendix to thia Chapter, 01.

ca71

THE THEORY OF INTEREST
you Like, 85 contrasted with the statistical, empirical, or
quantitative approach. While it is true that in the discussion of the theoretical portions of the book, empirical
evidence has beenemployed, this analysis is supplemental to rather than independent of the principles to be
illustrated or tested.
The aim in view has therefore dictated the suppression
of the innumerable secondary factors in order to focus
the analysis upon the primary factors involved. It is these
latter factors with which pure economic theory is conconcerned and this book is intended to be a study in pure
theory.
As such, its ultimate objective is to explain how the
rate of interest would be determined in vacuo or under
the ideal operation of the assumptions. Outside this domain, there are literally thousands of forces which would
have to be analyzed and allowed for before an adequate
explanation of an actual market rate of interest could be
made.
Thus,after presenting in Chapter I1 the theoretical
relations of changes in the value of money to the rate of
interest, we assume thereafter (until we reach Chapter
XIX) a constant value of money and therefore the absence of m y influence of a changing value of money.
Yet we know that such an assumption is seldom realised
in this actual world of incessant inflation and deflation.
Although this methodology of pure theory is at one
with that employed in the whole range of scientific investigation, it may seem to some open to the criticism of
being unreal and therefore presumably defective, if not
useless, 80 far as practical affairs go." While it ism
ip
"Veblen, Fid~er'uRote of Intercut, PoliticalScience Quarterly, Yo].

m,June, lsoS, pp. 296.303.Marget, The Loan Fad,a doctors1
EM1

OBJECTIONS CONSIDERED
mble, *becauseof the divergent approaches, to express
succinctly the criticisms which revolve about this point,
certain examples may be given to set forth their general
content and character.
Professor Thontein Veblen, for example,asserted that
interest did not come into existence until a high state of
development had been reached in business and in money
economy and credit economy. He argued that credit
economy giving rise to interest economy has existed for
“only a relatively brief phase of civilization that has been
preceded by thousands of years of cultural growth during
which the existence of such a thing as interest was never
suspected’’ (p. 299).
“In short”, Professor Veblen continued, “interest is a
business proposit,ion and is to be explained only in terms
of business, not in terms of livelihood as Mr. Fisher aims
to do” (p. 299). He adrnitt.ed that business may be the
chief or sole method of getting a livelihood, but asserted
that business gains are not convertible with the sensations of consumption, as he thought my theory requires
(pp. 299 and 300). Any argument for convertibility, or
equivalence, is fallacious because “habitual modes of
activity and relations have grown up and have by convention settled into a fabric of institutions” (p. 300).
If, at the start, we grant the postulate thatthe market
rate of interest as set on money loans under a money
economy or credit economy is the only interest rate existent, we are confronted with the problem of explaining
why such a rate of interest exists. Institutions of them-

I

eertation at W a r d University, 1926; Schumpeter, Theorie der Wirtechaft&h Entroicklcmg, p. 363. Ckiticisma of a similar character have
been received in private correspondence from several of those who read
thia book in manuscript,particularly Profeeom L. D. W e , B. H.
Beckhart, and C. 0.Hamly.

~4891

THE THEORY OF INTEREST
seives donot explain it. Institutions andconventions, like
business, have been created by men, not from some inexplicable purpose unconnected with their living and feeling, but in order to add to the gratitications they obtain
from living, Institutions cannot make men act or think
other than as men. These man-made, man-operated institutions are merely tools devised by man to create for him
gratifications more readily and more abundantly.
In my analysis, I find man’s impatience to enjoy today
and his desire to grasp the opportunities to invest so as
to provide future enjoyments the fundamental causes
which account-for the emergence of incomes and of
interest. To start with business institutions and attempt
to explain the existence of interest as a phenomenon
created by banks is like trying to explain vahe aa something created by produce markets and stock exchanges.
Impatienceandopportunityare
workingthemselves
out in theactivities of businegs institutions, andmen cannot avoid the dominance of these impulses and situations
when engaged in any activity that demands a choice between present andfuture income. Interest, therefore,
cannot be restricted to an explicit or contractual phenomenon but must be inherent in all buying and selling,
and in all transactions andhuman
activities which
involve the present and the future.
While I cannot accept the view which would cast overboard theory because it is theory, I am keenly aware of
the fact that theory aa such does not tell the .whole story
about an actual rate of interest. Pure theory is not called
upon 80 to do.
But after pure theory has said its last word, there is a
broad field for empirical study of omitted factors, While
we assumed that the unstable dollar remained stable t ~ d

14901

OBJECTIONSCONSIDERED
worked no interference with the fundamental forces determining the rate of interest, weknow that in actual
fact, the interference of a changing money value with
these forces is tremendous-because of the “money
illusion.”
Laws,goldmovements,
stock exchange speculation,
banking customs and policies, governmental finance, corporation practice, investment trusts and many other factors work their influences on the so-called money market
where interestratesare
determined. Practically, these
matters are of equal importance with fundamental theory.
While theory, in other words,assumes a waveless sea,
actual, practicd life represents a choppy one.

Q9. c0nc1usiMl
In the study of such a complex and many-sided problem as that of the rate of interest, it is natural (and in
fact, very desirable) that there should be many different
approaches, views, and methods. Unfortunately, however,
this latitude for individual interpretationand analysis
has many times invited misunderstanding, confusion, and
magnification of non-essential differences.
I have attempted to set forth and analyze in this chapter those matters contained in the criticisms of The Rate
of Interest which, to my mind, are of major importance,
and concerning which there still exists considerable disagreement among students of the interest problem.
Many of these questions seem to me to be based on
misunderstandings of my theory of interest. I have been
greatly helped by criticisms of this kind to see the shortcomings ofmy first attempt toexpound that theory. I am
hopeful that my present efforts to set forth i4 sharper
relief and with greater clarity one solution of the problem

r 491 1

THE THEORY OF INTEREST
of interest will succeed in subordinating these secondary
matters to the more important issuea of fundamental
theory.
This done, I am confident that economic theorists will
find that they are not so far apart on matters of fundamental theory as their writings would seem to indicate.
When mutual understanding is achieved, they will undoubtedly find that their differences are often more apparentthan real, consisting chiefly in the methods of
approach and of analysis.

c 492 I

CHAPTER XXI
SUMMARY

$1. Interest and Purchasing Power of Money
We have seen that, theoretically, the rate of interest
should be subject to both a nominal and a real variation,
the nominal variation being that connected with changes
in the standardof value, and the real variation being that
connected with the other and deeper economic causes.
As to the nominal variation in the rate of interest, we
found that, theoretically, an appreciation of 1 per cent of
thestandard of value in which the rate of interest is
expressed, compared wit.hsome other standard, will reduce the rateof interest in the former standard, compared
with the latter, by about 1 per cent, and that, contrariwise, a depreciation of 1 per cent will raise the rate by
that amount. Such a change in the rate of interest would
merely be a change in the number expressing it, and not
fundamentally a real change. Yet, in actual practice, for
the very lack of this perfect theoretical adjustment, the
appreciation or depreciation of the monet.ary standard
does produce a real effect on the rate of interest, and that
a most vicious one. This effect, in times of great changes
in the purchasing power of money, is by far the greatest
of aII effects on the real rate of interest. This effect is
due to the fact that the money rate of interest, while it
does change somewhat according to the theory tw described in Chap&s I1 and XIX, does not usually change
enough to fully compensate for the appreciation or de493 1

r

THE THEORY OF INTEREST
preciation. The inadequacy in the adjustment of the rate
of interest results in an unforeseen loss to the debtor, and
an unforeseen gain to the creditor, or vice versa as the
case may be. When the price level falls, the interest rate
laominally falls slightly, but r e d y rises greatly and when
the price level rises, the rate of interest nominally rises
slightly, but really falls greatly. It is consequently of the
utmost importance, in interpreting the rate of interest
statistically, to ascertain in each case in which direction
the monetary standard is moving and to remember that
the direction in which the interest rate apparently moves
is generally precisely the opposite of that in which it
really moves.
It should also ' b e noted that in so fax aa there exists ar~y
adjustment of the money rate of interest to the changes
in the purchaaing power of money, it is for the most part
(1) lagged and (2) indirect. The lag, distributed, has
been shown to extend over several years. The indirectness
of the effect of changed purchasing power of money
comes largely through the intermediate stepswhich affect
business profits and volume of trade, which in turn affect
the demand for loans and the rate of interest. There is
very little direct and conscious adjustment through foresight. Where such foresight is conspicuous, as in the final
period of German inflation, there is less lag in the effects.
$2. The Six Princ%pks

But the more fundamental theory of interest presupposes a stable purchasing power of money so that the

real and nominal rates coincide. In that case the rate is
theoretically determined by six sets of equations or conditions: the two Opportunity Principles; the two Impatience Principles; and the two Market Principles. The
~4943

SUMMARY
Isst pair may be said to cover prima faeie supply and
demand.
(A) The market must be cleared-andcleared
with
respect to every interval of time, (B) The debts must be
paid.
The other two pairs represent the two sets of forces,
one objective and the other subjective, behind supply
and demand. The subjective pair expresses the influence
of human impatience or time preference.
(A) The rateof time preference depends on the character of the various individuals concerned and on each individual’s prospective income,its size, time-shape and, risk.
(B) Each individual‘s rate of time preference tends, at
the margin of choice, to harmonize with the market rate
of interest. Human impatience to spend and enjoy income
is crystallized into the market rate.
The objective pair expresses the influence of investment opportunities.
(A) Each individual is encompassed about by opportunities to change the character of his prospective income
stream. (B) At the margin of choice, any additions to an
individual’s future income at the cost of more immediate
income constitutes a return over that cost, the rate of
which return over said cost is also crystallized into the
market rate of interest.
So the rate of interest is the mouthpiece at once of
impatience to spend income without delay and of opportunity to increase income by delay.
Thus both from the subjective and the objective field
appear prototypes, one of each for every individud, of the
market rate of interest.
That rate, i, is equal to every individual’s degree of
impatience or rate of time preference, f, and ale0 to his
I495 1

THE THEORY OF INTEREST
investmentopportunity
rate or rate of return Over
cost, r.
Yet these equations are not enough to make the problem determinate without those of the other four sets of
determining conditions (clearing the market, repaying
debts and empirical dependence of impatience and investment opportunity).
Much less is it possible to determine the rate of interest from the subjective side alone, through time preference, or from the objective side alone, through investmentopportunity, or “productivity”, or “technique of
produetion”.
The full explanation requires both (as well aa the
market principles) in order that there may be as many
independent equations as unknown variables in the
problem. Moreover there is not merely one rate of interest; there are many,one for each interval of time. And
even so the explanation is full only under the theoretical
conditions presupposed. If we pass beyond the presuppositions in order to approximate closer to the actual
world, we find that, to be determinate, the problem requires more and more equations of a more and more
empirical nature. This is especially true as (1) we introduce risk with its innumerable and omnipresent
ramifications, involving in particular a multiplicity of
rates of interest even for the same period of time; and
as (2) we extend our view to admitvariations in d
other prices besides the rrttes of interest, involving
thereby the whole economic equilibrium, not only of
the loan market but of all markets, each interacting on
every other; and aa (3) we extend our view from one
theoretical market to the s c t u d markets of the whole
world, involving thereby all the relations of intemtiond
c49u

SUMMARY
trade; and as (4) we take axxount of any other factors
which may not be included in the foregoing specifications
so aa to take account, in particular, of all “institutional”
influences, laws, politics, banking practices, government
finance and so on to theend.
In the economic universe, aa in astronomy, every star
reacts on every other. From a practical point of view
we cannot ignore the many perturbations. But from the
theoretical point of view we gain clearness, simplicity
and beauty, if we allow ourselves to w u m e certain other
things equal, and confine our laws to 4 little part of the
whole, such aa the solar system.
From such a point of view, the second approximation
is the most instructive, rather than the first which rules
out the important element of investment opportunity, or
than the third which becomes too complicated and vague
for any complete theoretical treatment.
$3. The Nature of Investment Opportunity

In the second approximation-which, aa we have just
noted, contains all that is most typical in the theory
of the rate of interest-the distinctive factor is the rate
of return over cost or the investment opportunity rate.
This is also the most dil3icult factor to picture, isolate,
and disentangle from the rate of interest which it helps
determine. Therefore, it is a matter of great importance
pedagogically to make that distinction clear. The investment opportunity rate is &tinct from the m k e t or
loan rate of interest becauuse aa investment opportunity
is distinct from a loan. Investment opportunity, as here
used, does not include a mere loan at the market mte
of interest nor any other purchaseand-sale txsnsaction
made merely on the basis of the market rate. The de&
497 1

c

THE THEORY OF INTEREST
nition of investment opportunity is specially framed to
exclude mere loans. It is any opportunityof an individual
to modify his prospective income other than by merely
lending or borrowing (or the equivalent, buying or selling) at the market rate of interest.
Under this definition and the assumptions employed
in the theory therecan never be any doubt as to whether
a given proposed transaction is an investment opportunity or a market loan or purchase. In the case of a
market loan or purchase the individual cannot vary the
rate of interest by any act of his, such as varying the
size of his transactions. Under our assumptions of a perfect market his influence on the market rate is not only
unconscious but infinitesimal and therefore entirely
negligible in our analysis in which his motivity is of the
essence. In the cese of an investmentopportunity, on
the other hand, he can vary tke rate of return by varying
the size of his operations.
This contrast between the theoretical constancy of the
one and the variability of the other, in relation to individual action, is due to the fact that in the public market
the individual is a neghgible element, while an investment opportunity is more private and personal to him or
his group. The former is typified by the purchase, say, of
a Liberty bond, or other standard securities. The latter is
typified by building a factory, improving a, sales organization, deepening the shaft of a mine-cases where the
marginal rate of return is under the control of the individual since he sets the margin.
Of courae it is true that, in &oat every such operation, there &re elementa of purchase and sale in which
the market rate of interest is an implicit ingredient, but
aa long as the operation ia not exclusively a mere market
498 3

c

SUMMARY
interest affair and contains other hgredienb, the rate is
subject to variation with the extent of the operation and
so is to be called a rate of return over cost. We are here
interested in those other ingredients which produce the
variability and thus differentiate such a rate from the
market rate of interest. They are the non-commercial or
non-trading ingredients; they concernproduction and
technique rather tha.n trade. They deal not with the
market place, but with nature, environment, and the refractory conditions whichsmound and hamper us in our
efforts to secure income. They exist even when nomarket
exists, when a Robinson Crusoe, a hermit, or an isolated
ranchman battles with soil andthe elements for his
daily bread.
The rate of return over cost, under the law of diminishing returns, is thus f a r more elementary and primeval
than the rateof interest, and however incrusted that rate
of return may become with other elements which grow
out of modernmaxket conditions it is still the basic
objective condition underlying our problem.
Thus the rateof return over coat is distinguished from
the rate of interest (1) by varying with the extent of
the individual’s investment; (2) by beingconsciously
recognized, as thus variable 1 and controllable, by the
individud; (3) by being, therefore, a personal and in&vidual matter and not
altogether & public market matter;
(4) by being directly related to producing as contrasted
with trading.
*It is true that in the hard-tack cue and Bone otherextremeand
hypothetical cases considered, it waa assumed that for a certain interval
the 0 w e waa aeuumed to be straight. To include such a theoretical
-, the etatementa in the text need a slight modification. But such
extreme caaw are not typical even in the theory and are probabb’
never exemplified in practice.

~4991

TIIE THEORY OF INTEREST
$4. Investment Opportwity for Society as Q Whole

In modern society hermits and self-supporting ranches
are 80 rare that we cannot find any importantcases where
investment opportunities exist inpure primitive form
and apart from the alloy of trading. In fact, the most
typical investment opportunitiesare not only full of such
alloys but are tied up with market financing operations.
Almost every big investment opportunity is married to a
productive loan.
.The best picture on a big scale of investment opportunity, divested 50 far as may be of all ancillary market
features, is to be found by considering society as a whole
instead of the individual.
Society aa a whole cannot borrow or lend as an individual can. This world can, for instance, add nothing
to this year’s income by a loan from elsewhere and subtract this amount with interest from future income. Yet
it can and does vary and control the total income stream
according to investment opportunity.
This picture, in the large, of society arranging, modifying, adjusting its total income stream as between this
year and later years is the most important picturewe cm
draw of investment opportunitynot only because it automatically leaves out borrowing and lending, or buying
and selling, but a h because it automatically reduces the
picture of income to its fundamental terms of real or,
&s I prefer t
o c d it, enjoyment income and its obverse,
labor pain. We do not have to think so vividly, as we do
in the caae of an individud, of money items and intermediate processes. We can without d s c u l t y fix our attention on the find consumption. Society is like Robinson
Crusoe picking and eating hie berries, however compfi-

CWI

SUMMARY
cated maybe the apparatus which intervenes between
the labor of picking m d the enjoyment of eating,
Society may add to or subtrmt from ita income stream
at will at any period, present or future. Butbeyond a certain point every addition at one period must be at the
cost of a subtraction at some other period. If future income is added, the increment so added is a return on and
at the cost of a decrement in lesa remote income. The rate
of return over cost is thus a social phenomenon of great
significance. There are two and only two ways in which
society may effect the present cost and the futureretFn.
It may effect the present cost by exerting more present
labor or by abstaining more from present consumption;
and it may realize the future return over that cost either
in the form of more future consumption or of less future
toil.
Both the present and the future adjustments are
effected by changing the u s made of capital instruments
including land and human beings. That is, the labor, land,
and other capital of society may be used in many optional ways and in particular may be invested for the
early or remote future.
.
If the capital instruments of the community are of
such a nature as to offer a wide range of choice, we have
seen that the rate of interest will tend to be steacfy. If
the range of choice is narrow, the rate of interest will
tend to be mmXde. If the range of choice is relatively
rich in future income as compared with the more immediate income, the rate of interest will tend to be high.
If the range of choice tends to favor immedkte i3Ecome
as compared with more remote future income, the rate of
interest will tend to be low.
Thus, for the United S t a h during the last Century,
501 1

c

THE THEORY OF INTEREST
its resources were of such a character as to favor future
income. This is true, for a time at least, in every unde
veloped country, and, as we have seen, gives the chief
explanation of the fact that the rate of interest in such
localities is usually high. The same is true of countries
recoveringfromwar.
Today, for instance, Germany
resembles a pioneer country. Her present income is necessarily low, but her prospect of a higher and increasing
income in a few years is very great. The range of choice
is dominated by “low today and high tomorrow.”
The range of choice in any community is subject to
many changes as time goes on, due chiefly to one or more
of three causes: first, a progressive increase or decrease
in resources; second, the discovery of newresourcesor
means of developingold ones; andthird, change in
political conditions.
Under the first head maybe noted the impending
exhaustion of the cod supp1y in England, as noted by
Jevons and other writers. This will tendto make the
income stream from that island decrease, at least in the
remote future, and this in turn will tend to keep the rate
of interest there Iow. Under the second head, the constant stream of new inventions, by making the available
income streams rich in thefuture, at the sacrifice of
immediate income, tends to make the rate of interest
high. This effect,however, is confined to the period of
exploitation of the new invention, and is succeeded later
by an opposite tendency. During the last half century
the exploitation of Stephenson’s invention of the locomotive, by presenting the possibility of a relatively large
future income at the cost of comparatively little sacrifice
in the preeent, tended to keep the rate of interest high.
As the period of extensive railroad building is drawing to

c 5021

I

SUMMARY
a close, this effect is becoming exhausted, and the tend-

ency of therate of interest, 80 far as this particular
influence is concerned, is to fall.
On the other hand, the invention of the automobile,
and the inventions and discoveries in electricity and
chemistry have succeeded the railroads as a fieldfor
investment and have required new sacrifices of immediate income for the sake of future income. Thus, as fast as
the first effect of any one invention, tending to raise interest, weam off and is succeeded by its secondary effect
in lowering interest, this secondary effect i4 likely to be
offset by the oncoming of new inventions.
As to the third head, political conditions which affect
the insecurity of property
therate of interest, such
rights which occurs during political upheaval, BS in
Russia recently, tend to make the pure or riskless rate of
interest low. At the same time it adds an element of risk
to most loans, thereby diminishing the number of safe
and increasing the number of unsafe loans. Hence the
commercial rate of interest in ordinary loans during
periods of lawlessness is likely to be high. Reversely,during times of peace and security, the riskless rate of interest is comparatively high, while the commercial rate
tends to be low.

55. Time Preference

We turn now to the remaining factor, namely, the
dependence of time preference of each individual on his
selected income stream. We have seen that the rate of
preference for immediate as compared with remote income will depend upon the character of the income
stream selected, but the manner of this dependence is
subject to great variation and change. The manner in

[a33

THE THEORY OF INTEREST
which a spendthrift will react to an income stream is
very different from the manner in which the shrewd
accumulator of capital will react tothe same income
stream. We have seen that the time preference of an
individual will vary with six different factors: (1) his
foresight; (2) his self-cont,rol; (3) habit; (4) the prospective length and certainty of his life; ( 5 ) his love of
offspring and regardfor posterity; (6) fashion. It is
evident that each of these circumstances may change.
The causes most likely to effectsuch changes are: ( 1 )
training to foster a realization of the need to provide
against the proverbial “rainy day”; (2) education in selfcontrol; (3) formation of habits of frugality, avoiding
parsimony on the one hand and extravagance on the
other; (4) better hygiene and care of personal health,
leading to longer and more healthful life; ( 5 ) incentives
to provide moregenerouslyforoffspring
and for the
future generations; (6) modification of fashion toward
less wasteful and harmful expenditures for the purpose
of ostentatious display.
These various factors may actand react upon each
other, and may affect profoundly the rate of preference
for present over future income, and thereby influence
greatly the rate of interest. Where, as in Scotland, there
are educational tendencies which instill the habitof thrift
from childhood, therate of interesttends to be low.
Where, as in ancient Rome, at the time of its decline,
there is a tendency toward reckless luxury, competition
in ostentation, and a degeneration in the bonds of family
life, there is a consequent absence of any desire to prolongincome beyond one’s own term of lie, and the
rate of interest tends to be high. Where, as in Russia!
under the Czars, wealth tended to be conoentrated and

cw3

SUMMARY
social strstification to be rigid, the great majority of the
community, on the one hand, through poverty and the
recklessness which poverty begets, tends to have a high
rate of preference for present over future income,
whereas, at the opposite end of the ladder, the inherited
habit of luxurious living tends, though in a different way,
in the m e direction. In such a community, the rate of
interest is likely to be unduly high.
$6. Conclusirm

From the foregoing enumeration, it is clear that the
rate of interest is dependent upon very unstable influences many of which have their origin deep down in the
social fabric and involveconsiderations
not strictly
economic. Any causes tending to affect intelligence, foresight, self-cont.rol, habits, the 'longevity of man, family
affection, and fashion will have their influence upon the
rate of interest.
07. The Future
From what has been said it is clear that, in order to
estimate the possible variation in the rate of interest,
we may, broadly speaking, take account of the following
three groups of causes: (1) thethrift, foresight, selfcontrol, and love of offspring which exist in a community;
(2) the progressof inventions; (3) the changes in the
purchasing power of money.The &st cause tends to lower
the rate of interest; the second, t,o raise it at first and
later to lower it; and the third to affect the nomind rate
of interest, in one direction and the real rate of interest
in the opposite direction.
Were it possible to estimate the strength of the various
forces thus summarized, we might base upon them a

x,m?J

THE THEORY OF INTEREST
prediction &B to the rate of interest in the future. Such a
prediction, however, to be of value, would require more
painstaking studythanhas
ever beengiven to this
subject.
Without such a careful investigation, m y prediction
is hawdous. We can say, however, that the immediate
prospects for a change in the monetary standard seem
to IE toward its stabilization; that this will tend toward
a general prosperity, the main effecta of which should be
in the direction of lowering therate of interest; that
changes in thrift, foresight, self-control, and benevolence
are for the most part likely to intensify these factors
andthus to lower the rate of interest;and that the
progress of discovery and invention shows now a tendency to increase in speed, the immediate reault of which
should be to raise the rate of interest but finally to
lower it.

APPENDIX TO CHAPTER I
B 1 (toCh. I, 8 1)
&uolat;onS jrom Professor Canning’s book
TEE importance to the accountant of a clear and consi&ent
concept of income and of capital ia emphaaized by Professor
John B. Canning in hks book, T h Eumomics of A m & w ;
A Critical Analysis of Accounling Theory.
It may not be amiss at this point to put forward a comparative
’

appraisal of the accountant’s views and those of Fisher. And it may
be convenient to make that appraisal upon the basis adopted for
comparison, vis., scope of subject matter contemplated, modeof
analysis pursued, and point of view taken.
With respect to the first there can be no possible doubt that
Fbher’s work is immensely superior. How much of his views will
ultimately prevail among economists and among accountanta no
one needconsider. Only a guesscould be made. What the event
will ultimately prove, too, might as readily be a fact about the two
profeteions aa a fact about Fisher’s theory. But as a general, comprehensive treatment of the theory of income, there is nothing to
compare favorably with it in either literature. (p. 172.)

..*+

In a late article Fisher ssp:“I believe that the concept of income
is, without exception, the most vital central concept in economic
science and that on fully grasping ita nature and interrelations with
other concepts largely depends the full fruition both of economic
theory and of its applications to taxation and ststistics.”l If he
had written instead that income i8, with& tzccptiun, the simplest
and most fundamental Eoncept of
science, that only aY
of this cone4pf om d b s c o ~ m i cm p k ever &fa?/h
O
e
lp
G
d and
und61.sloOdl and tlrd upon beginning with this concept depen&s *fd
‘AmeriomEconomic Review, Vol. XIV, P. 64.

~5071

APPENDIX
fruition of GeollMnic themy in emwq~icstatistics, it would pave been
an equally true end a more significant statement. (p. 175.)

* * * *

The present writer believes that had Fisher ~ t t e Income
n
and
Capitd, beginning with a chapter on the topic of psychic income and
ending with a chapter on wealth consideredaa a kind of embodiment
of services directly or indirectly to become income, his work would
not only have been more useful to the thoughtful reading public at
large, but rrlso and most particularly, to accountants and economists.
There is very real occasion for regret that theprofessional accountanta have found 80 little occasion to work in the subject of final
objective income. It can hardly be doubted that, in their enterprise
(income accounts) they, at times, lose sight of the fact that such
statistics are wanted primarily for the ordering of the mode of living
of the persona interested. For example, it is usually pressure upon
shareholders for the wherewithal to meet living expenses that excites
the clamor for larger dividends. Full statement of the earning
prospects that condition the upbuilding of surplus would, at least,
prevent their urging dividend payments contrary to their own best
intemts. Full statement, too, even though no dividends are forthcoming, may put the shareholdersin a favorable position through
selling part of their holdings or borrowing upon them - to maintain
their customary scale of living. By keepingmore constantly in
mind the gap between the enterprise earnings and the mode of life
of the persons interested, the usefulness of their income statistics
could be greatly enhanced.
From the economist’s point of view, and for the good of the pubIic,
it is of very great importance that the accountants should make
their income statistics aa full and aa complete aa the conditions of
their profeeaiod practice wil permit. (pp. 170 and 177.)

-

APPENDIX TO CHAPTER X
9 1 (toCh. X, 9 2)

[Gem&+ repramtattion of incomesfor three years

IF we proceed from the consideration of two yeera to that of
three, we m y still represent our problem geometrically by
using a model in three dimemiom. Let u8 imaginethree

15081

APPENDIX
mutually perpendicular axes from an origin 0 called reqectively

OX', OX", OX"', and represent the income combinstion or
income stream for the particular individual by the point P ,
whose coijrdinates c', e", and c"' are the three years' inmme installments with which the individual is initially endowed. Then
through the point P draw, instead of the etraight line in the previous representation, a plane ABC cutting the three mea in
A , B, and C. This plane has a slope with reference to the two
OB
axes OX' and OX" of -equal to 1 'i (unity or 100 per cent
OA
plus the rate of interest connecting the first and second years),
to the axe8 OX" and OX"'
and has aslopewithreference

+

oc

+

represented by - equal to 1 i" (unity plus the rate of interOB
est connecting the second and third years). Now suppose the
spacebetween the axes to be filled with willingness . w f u c e s
laminated like the coats of an onion, such that for d points on
the same surface, the total desirability or wantabfity of the
triple incomecombination or income position represented by
li be the same. These surfacea will be
each of those points w
such as to approach the three axes and the planes betweenthem,
and also such that the attached numbers representing their
respective total wantabditiea shall increase as they recede from
the origin. The plane ABC drawn through P at the slope fixed
by the rates of interest just indicated will now be tangent to
some one of the willingness surfacea at a point &, which i s the
point at which the individual will, under these conditiom, fix
his income situation, for every point on the plane ABC will
have the same present value, and every point on this plane is
available to him by borrowing and lending (or buying and
selling) a t the
'i and i f fbut
, not all of them will have the
same desirability, or wantability. He will select that one which
has the maximum wantability, and this will evidently be the
point Q,at which the plane is tangent to one of the f a d y of
w d l i q p e a ~surface^. This point will be such that the rates of
time preference will be equal to the rate of interest.

l-5091

APPENDIX
So much for the individual. The market problem determining
the rate of interest is here solved by finding such an orientation
for the various planas through the given points called P’s aa
will bring the center of gravity of the tangential points, the
Qs, into coincidence with the fixed center of gravity of the P’s.
To proceed beyond three years would take us into the fourth
dimension and beyond. Such a representation cannot be fully
visualized, and therefore has little meaning except to mathematicians.
APPENDIX TO CHAPTER XI1

i 1 (to Ch. XII, 8 1)
Algebraic expression o j rate o j time preferewe

IF W signifies wantability, or utility, or desirability and this
year’s income is signified by X’ and next year’s by X“, then
A T ’ may be taken to sigmfy the present wantability of, or want
AW’
will be
A X‘
the want-for-one-more unit of money this year. Also A W ” is
the present want for a small increment, AX”, of money availAW”

for, a small increment,AX’ of money this year and

able nezt year, and A~

will be the present want-foranemore

unit of money available next year.
Exact mathematical theory requires that the marginal wants
per unit of money are the limits of those ratios when the inAB’’ and lim A~
AT’’
crementa approach m o aa their limite, or lim

A X‘

ordinarily written in the ditrerential calculus:

dW‘ and
dx‘

dW’!

which, for short, may be called w’ and w”.
The rate of preference, I, for a unit of present money over a

unit of next year’s may be defined 88 f =

-. -

d

W“

10“

APPENDIX

8 2 (toCh. XII,! 3)
Equality of marginal rate of time prefermand rate of interest
i m p h that d”rabt7itty of incanae stream is made a 1IMzLmum
AMU?~Eat first that only two yeam are considered. The fsct
thattotal desirability or wantability of the individual, aa
reckoned at the beginning, depends on the amount of income
this year and next year may be represented by the equation

W” = F(c‘

+

d l

c”

+ d‘),

where W” represents his total wantability, and the equation
represents this W” as a function of his incomestream consisting
of c’ x’ this year and c“ x” next year. This W” is represented in Chapters X and XI by the numbers attached to the
severd Willingness or Wantability lines, each representing a
certain level of wantability of Individual 1. But as we shall
here consider only one individual, we omit the subscript nunbers, 1, 2,. . . . . ., n. The individual under consideration will
attempt to adjust x’ and x” so aa to maximize W. We are to
prove algebraically that the condition that W shall be a maximum implies alsothat the rate of intermt e’ shall be equal to the
individual’s rate of preferencej . The condition’ that W shall
be a mardmum is that the total differential of W or of its equal
F(c’ X I , c”
dl),
called below F( ) shall be zero; thus

+

+

+

+

where the a’s represent the partial Werentials with respect to
x‘ and x”.
From this equation it follows that

+

The &&hand number of this equation is 1 i, as may be Been
by differentiating the equation of the loan &B originally stated,
vis. :
See any taxt book on the calculus, e.g. Wilson, E.B. Adumcd Coblw. Boston, Oinn & &., 1912, pp. 118-126.
511 1

r

APPENDIX
x‘

+ -1.X“+ 2

= 0. This differentiation yields

ax” = 1 + i.
-7
&

The righthand member, being the ratio of this year’s marginal
wetability to next year’s marginal wantability, is by definition
equal to 1 f. Substituting the new value for the right- and
left-hand members, we have
l+i=l+f,
whence it follows that i = jl whichwaa to have been proved.
The m e reasoning may now be applied to three or more
years. The total wantability for any individual is a function
of the total future income stream. In other words,
W = F(c’ x‘, C” X”, . . . , d m ) d m ) ) .
The individual tries to make this magnitude a maximum. In
terms of the calculus, this is equivalent to making the first total
Merentid equal to zero namely,

+

+

+

...

+

This total differential equation is equivalent, according to wellknown principles of the calculus to a number of subsidiary
equations obtained by making particular suppositions aa to the
differentvariations. Let UE, forinstance,suppose that only
x’ and zrfvary in relation to each other and that z“’, I,, . . . . . ,
z(d do not vary. Then in the above equation all terms after
the second disappear and the equation reduces, aa before, to

+

So that, agan
i , 1 i’ = 1 +f’,
and therefore i’ = f’.
This expreeses the relation betweenthe &st and second years.
If we wish, in like manner, to e x p m the corresponding connection between the second and third yearn, let ua mume that
zf aa well aa 6,
. . . . . ., d m ) are constant but that 2‘’ and z”’
vary. Then the h
tterm of the equation and all after the third
dissppear, and the equation redurn to
c 512 1

+

+

In other words, 1 i" = 1 f", or i" = f". Similarly, i= f
for every other pair of successive years.
We have here, in mathematical language, the reason that the
point of maximum total wantability is also the point at which
the marginal rate of time preference for a unit of each year's
income over that of next year's income is equal to the rate of
interest connecting these two years.2
APPENDIX TO CHAPTER XI11
$ 1 (to Ch. XIII, $ 9)

R& of

TdUTn over cost

expressed in th.e notation of the cd.cdw,

INthe notation of the calculus, the rate of return over cost,
called in the text rl', is defined in terms of the partii differential
quotient with the opposite sign of next year's income with
respect to this year'sincome of Individual 1. That is, by
dehition 1

+

- w a n d 1+ ~l)'
= -

Analogous
aYll
ay? *
formulaa expreas the remaining r's for Individuals l , d . . R.
T{

=

. .. .

$ 2 (to Ch. XIII, Q 9)

Rate of T

over wst &rived by di3mential epualions

& U ~

The magnitudes of 1
or

ay!;

- ay,

ayl"'

--

aylll ?

.

+ TI', 1 +

TI",

......, 1 irtd,

"

''*

'1

@,l(m-U*

.

may be expressed in

terms of yl), y i l , . . , . ., yl(d by differentiating the equation
for the effective range of choice, 41 (VI', ,';y .
vi")) = 0.
* The mathematicalreader will nota that the funation F beR repraeentine
total want&iity W is vitally related to the functions F in chsptera XI1
and XIII,repreeenting:the marghd rate of time p d m m f, &T 1 i-f
is the ratioof the diBerential quotientof W &tidy to this w e moome
to the oorreepondingdifferential quotient fm next p d 8 i n m ~ ~ .

.. ...,

[ 513 1

APPENDIX
Q 3 (to Ch. XIII, Q 7, also Q 9)
Mathematical proof that the principle of maximum prment valw
i s identica2 with the principle that the marginal rate of return
over cost is equul to the rate of inter&.
THE mathematical proof that the principle of maximum
present value of optional income streams is identical with the
Investment Opportunity Principle B or that the rate of marginal
return over cost is equal to the rate of interest is as follows:
The present value VI of any income stream yl’, yl”, . . . .. .,
yl(m), of Individual 1 or their combined discounted value is
V 1 = y;+&+

..I...

.

+ (l+it) (l+i”).
Yl‘” .. .(l+i“”

>’

The condition that this expression shall be a maximum is that
the first differential quotient shall be zero. That is,

This last equation expreasea the relations which must exist
between LEY(, dy:‘,. . . . . ., dyl(m), in order that the income
stream, y,: yl”, . , . . ., y1(d, may have the maximum present
value.
This condition containa within itself a number of subsidiary
conditions. To derive these, let us consider a slight v,ariation
in the income stream, d a t i n g only the income i t e m pertaining
to the first two y m , ~ 2and
, yl” (the remaining items, yl”’,
. . . . . .,yll(d,being regarded for the time being aa constsnt) and
let us denote the magnitudes of dyr’ and dy{’, under this assumption of restricted variations, by &{ and ay1”. Then, under
the condition essumed of constancy of yr’“, yl*, . , . . . ., yid,
dyi”, dyP, , , d g P , are equal to zero, and the equation

.

.. ..,

becornea

APPENDIX
From this,it follows directly that
But the left-hand member of this equation is by definition one
we have
plus the marginal rate of return overcost.Since
.designated the rate of return over cost by r~’we may substitute

+

-

1 r,’ for the expression - ay:’ and write the above equation
ayi
thus :
1 r1) = 1 i’,
or thus:
ryl = i‘.
In other words, the condition that the marginal rate of return
over cost is equal to therate of interest follows aa a consequence
of the general condition that the present value of the income
stream must be a maximum. This proposition and its proof
are analogous to those in regard to desirability or wantability,
which have already been discused in the Appendix to Chapter
XII, that the condition of maximum wantability is equivalent
in the condition that the marginal rate of preference is equal to
the rate of interest.
The same reasoning may be applied to any pair of successive
y e m . Thus, if we mume variations in y” and y”’, without
any variations in the other elements of the income stream,
v ’ ~g“, , , . yp, the original Merentid equation becomea

+

. ..

+

APPENDIX
$ 4 (to Ch. XIII, § 9)

Gkamet7ical explundion of the proposition expounded in
this Append&

89

of

BUTthe foregoing proof by algebra may not appeal to many
studenta as much aa the proof by geometry.
We know (see Chapter X, § 3 and Chapter XI, $ $ 4 and 5 )
that the present value of any income position on the Market
line isthe eame as that of any other income positionon that line.
It follows that the present value of any point on a given
Market line is measured by the intercept of that line on the
horizontal axis, for that intercept evidently measures the
present market value of one particular point on the Market
line (namely its lower end) and, aa just stated, this must have
the same present value aa every other point on the Market line.
It follows that aa the Market line is moved further away from
the origin (keeping its direction unchanged) the intercept becomes greater, and thus the present value of every one of the
points on the Market line becomes greater correspondingly.
When, therefore, the line is thus moved as far aa possible, so
that it thereby 888umea the position of tangent to the Opportunity
line, the present value of every point on it and, therefore, of
that point of tangency must be greater than that of any other
point on the Opportunity line, since any other such point will
n d y lie on a Market line nearer the origin.
The m e proof applies in three dimensions, substituting
Opportunity surface for Opportunity line and Market plane for
Market line. By analogy the proof may be extended to n
dimensions.

APPENDIX

Q 5 (toC h , XIII, Q 9)
Maximum total desirability is f m d tchm rate of tim p r e j e r m
is equal to the rate of interest

IN the last section wm outlined a geometric p m f that the
income stream possessing the maximum present value is such
that the rate of interest (connecting each pair of sumwive
years) is equal to the rateof return over cosf (for the m e pair
of successive years).
The geometric method also supplies a simple proof that the
maximum total desirability, or wantability, is to be found in
the w e of that income stream which satisfies the above mentionedcondition and, at the m e time, has a rate of time
preference equal to the rateof intereat. In geometric terms for
twodimensions this means that this most desirableincome
position or point is where the Market line, which is tangent to
the Opportunity line, is tangent to a WUngness line.
Consider twoparallel Market lines,one tangent to the
Opportunity line and the other somewhat nearer the origin; and
consider the two points Q and S where these two are reapedively
tangent to a Willingness line. We are to prove that the total
desirability or wantability of is greater than that of S. Draw
a straight line from the origin through 8 and produce it until
it cuts the first Market line at, say, T.
It is evident, of course, that of d the points on any given
Market line the point of tangency with a Wih@eas line is the
most desirable income position. Therefore, Q is more deairable
than T. We wume thatthe Willingness linea are such that the
farther we recede alongB straight line from the o r i a the more
desirable the income situation. Therefore, T is more desirsble
than S.
Therefore, Q being more desirable than T,and T than 8,6l is
more d&ble than S, which was to have been proved.

APPENDIX
$ 6 (toCh. XIII,

8 9)

Wdma and Parelo
W u and Pareto probably deserve more attention in
interest theory, as in general economic theory, than they have
received.
W h J interest theory forms an integral part of his theory of
general economic
eqUilibrium.l
His solution consists of a
demonstration thatthe problemcomprises a number of independent equations exactly equal to the number of unknowns,
and that the mathematical solution of these simultaneous
equations is a counterpart of the economic process by which
the unknowns are determined in the market. There is thus no
reasoning in a circlein the Walras system. The number of
equations is exactly equal to the number of unknowns.
W h ’treatment of the problem of the determination of
the rate of interest is very detailed and highly mathematical.
For readers who are not familiar with his treatment I venture
to attempt a brief summary. W h assumes a market for
capital goods as well as for services. He wumes that the
prices of capital goods depend on the prices of their services.
Sincesome capital goods last longer than others and all are
subject to risk, he makesallowance for depreciation, amort h t i o n , and insurance.
His treatment combines the subjective and objective elements
in a simple and direct manner. His cost of production equations
correspond, in a general way, to my opportunity principles.
His equation for the demand for savings corrmponds, likewise,
to my impatience principlea.
Pareto’s analysis of the problem of the rate of interest*
along the lines laid down by Walras, although he waa evidently
not fully mtisiied with Walraa’ treatment. Neither he nor
W h has developed a systematic theory of income but he
1 W h ,h,
dId-2
Pdiliqvs Pura
1

Pareto, Vilfredo, Cow8 d’Emwnti.6 Pditiqyc.

c 518 I

APPENDIX
shows, in effect, that the substitution of one income stream for
another or, as he says, the “transformation in time” is only a
particular case of a more general tmfonnation which is dealt

with in the theory of production. His indifferenceequations
for consumers correspond in a general way to my impatience
principles and the analogous equations for the obstacles in
his treatment of production correspond likewise to my opportunity principles.
The fundamental Werencea between the approach of Walras
and Pareto on the one hand and mine on the other seem to be
four:
(1) W h and Pareto determine the rate of interest simultaneously with all the other unknowns of the problem - the
quantities of the commodities exchanged and the senices used
in their production and the prices of the commodities and the
servicee, while I try to isolate the interest problem by assuming
that most of such unknowns have already been determined and
confine my discusion to the special factors directly af€ecting
the rate of interest.
(2) They both treat what I call interactions or intermediate
services along with the ultimate factors - our desires or tsstes
(lea g8uts) and the obstacles which must be overcome to satisfy
them while I try atthe outset to get the interactions canceled
out, l e a v i n g only the income stream and (labor) 88cri6ce.
(3) Neither Wslrss nor Pareto has elaborated the concept
and principlesof an income stream.
(4) Neither has elaborated the conceptorprinciples
of
opportunity as a choice from among a series of income streams,
although it is, in part, implied in Pareto’streatment.:
* C W ~d ’ k m d P d m VOi. I, p. 311

-

APPENDIX
APPENDIX TO CHAPTER XIX

8 1 (to Ch.XIX,$ 4 )
Tables giving basic data
TABLE
I
London I3uf.t~of InterGsf ana' Whksale Price Index, 1820-192Y

I

IBOLBMLE

YEA

-

-YV 0.r
kel

-

-

1822
1823
1824
1825

3.5
3.9
1828 4.5
1827 3.3
1828 a.1
1829 3.4

1837

1.938

1889
1840
1841
1842
1W
1844
1845
1846

1847
1848
1849
1BW
1Sb1
1
m
1653
1964
1955
1868
1857
1858
1859

-100)

4.(
4.(
5s
4*l

4.c

4s

2.8 4 .c

3.7
3.1
2.7
a.4
3.7
43
4.5
3.0
6.1

4.c
4.c
4.c
4.0
4.0
4.4

5.0

5.1
5.0
4.3
4.O
2.5
2.7
3.3
52
3.7
2.9

5.0

4.1
5.1

L.9
3.3

z.a

2.1
3.0

3.8
5.9
3.2

2.a

2.2
3.1
I.9
3.7
1.9

1.7

i.9
.l

1.1

!.5

,

2.5
3 .O
2.2
2.7
2.1
2.9
3.1
3.7

32

I

VEOLESAL
PRICE
INDEX

-

Ma

3M

'1867-187
=loo)

Hru
kef

ke
-4.:

99
98
101
103

92
102
94
69
103

1870
1871
1872
1873
1874
1875
1878
1877
1878
1879

3.1 3.1
2.7 2.9
3.1 4.1
4.:
4.8
3.: 3.7
3.c 3.2
2.1 2.6
2.3 2.9
3.3 3.8
1.E 2.5

103

1880 2.2

1M

117

100
97
97
93

91
92
89
91

!w

78
74

1888
1887
1888
1889

2.9
3.4
3.0
2.8
2.0
2.1
2.4
2.4
2.7

77
75
78
95

1E90
1m1
1892
1893

3.7
2.5
1.5
2.1

100

91
83
84

87
89
85

loa

101
101
105
91

94

1881
1882
1883
1884

1885

1894
1895

1.o
.8

1897
1888

2.6

1886

RATES

-

4.1
5.4 5.3
2.4 2.5
4.: 4.4
7.6 7.4
4 s 4.8
6.i 6.9
2.: 2.6
1.1 2.1
3s 3.2

101
103

rNTERE0

-

1880
1861
1862
1883
1864
1865
1866
1867
1868
1869

LOB

I821

18a8

1867-187

112

182C

lBa0
1831
1882
1833
1634
1835

PRICE

INDEX

105
101

102
100
99
98

1.1
3.6
3 .O
2.9
3 .O

3.3
3.3
3.6

4 .(
3.1
3.:
3.1
3.:
3.(

LO

1.6
1.8

I

83
62
61
62
64
88

4

.:

4.1
3s
3.1

75
70
59
69
70
72
77

80
73
74
78

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

3.2 3.5
2.9 3.:
3.6 3.1
4.4 1.1
2.9 4.c
3.7 5 s
5.2 5.5
4.8 5.2
3.6 5.C
3.9 5.2

85
85
108
136
175
192
206

1920
1921
1922
1923
1924
1925
1926
1927

6.4 6.E

251

2.7
2.7
3.5
6.1

131
128
139
136
126
122

5.2 6.2

3.7
3.5
4.0
4.6
1.5 5.0
L.3 4.7

68

2.1

1.8

-

72
72
68

4.5
3.3
2.5
3.1

3.3

83

85
84
82
76
72
69
68
70
72

3.5

t.5

109
111
102
96
95
94
87

a8

2.8

1.4
1.8

96
100

19oc 3.;
1901 3.1
1902 3 s
1903 3.4
1904 2.7
1905 2.6
1908 4.c
1907 4.5
190E 2.3
1909 2.3

I

80
85

165

APPENDIX
TABLE11
New York Rates of Intereat and Wholesale Price I&z. 1866-1917

-

YlAB

4-6

month

-

WEOLEBPBICP

INDEX

7 .O
6.8
8.9
10.1
6 .O
5.5
5.2
5.2
4.8
5.1

125
119
122
121
117
112
104
97
89

1881
1882
1883
1884
1885
1886
1887
1888
1889

5.2
5.2
5.7
5.6
5.2
4.1
4.8
5.8
4.9
4.9

94
93
95
93

18m
1891
1892
1893
1894
1895
I 896
1897
1898
1899

5.7
5.4
4.1
6.6
3 .O
3.7
5.8
3.5
3.8
4.2

-

85

87

82
81
81

a3
83

--

PBICl
INDEX

4-6

month

( 1913 =

100)

”

151
142
135

6.9
6.5
5.4
7.6
5.2
5.8
7.0
4.7
5.3
5.5

LU2-90
day

- WEO~E~AL~:

Paper
paper
--

168

1880

i

:I813 = 100)

paw
-

6.8
8.2
7.7
9.6

1866
1867
1868
1869

YBAB

81

80
75
77
69
70
67
67
70
75

1900
1901
1902
1903
1904
1906
1906
1907
1908
1909

4.4
4.3
4.9
5.5
4.2
4.4
5.7
6.4
4.3
4.0

5.7
5.4
5.8
6.2
5.1
5.2
6.3
6.7
5.0
4.7

86
86
86
89
94

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

5.0
4.0
4.7
5.6
4.8
3.5
3.4
4.7
5.9
5.4

5.7
4.8
5.4
6.2
5.5
4.0
3.8
5.1
6.0
6.6

101
93
99
100
98
101
127
177
194
206

1920
1921
1922
1923
1924
1925
1926
1927

7.4
6.5
4.4

7.5
6.8
4.7
5 .O
3.9
4.0
4.2
4.0

226
147
149
154
160
159
151
147

81
79

84

90

97

- -Pricedona
p. 167.

APPENDIX
TABLEI11
Berlin Rates of I n h e s t and Wholesole Price Zndez, 1861-1918

YSAR

INTQRQST
RATES

Marke

Bsnk

1869

3 .O
3 .O
3.5
5.1
4.6
6.2
2.9
2.5
3.2

4.0
4.0
4.1
6.3
5.0
6.2
4.0
4 .O
4.1

1870
1871
1872
1873
1874
1875
1876
1877
1878
1879

4.5
3.8
4.0
4.5
3.3
3.7
3.1
3.3
3.4
2.7

4.8
4.2
4.3
5 .O
4.4
4.7
4.1
4.4
4.3
3.7

1880
1881
1882
1883

3.1
3.4
3.9
3.1
2.9
2.9
2.1
2.3
2.1
2.7

4.2
4.4
4.5
4.1
4.0
4.1
3.3
3.4
3.3
3.7

1861
1862
1863
1864
1865

;1868
%

1884
1885
1886
1887
1888
1889

WHO-ALI

--

INTQREST

PRICE

-

INDEX
(1913

96
92
90
90
92
97
105
103
98
92

99
110
119
113
104

101
103
93
83

94
90
86
85

YEAR

1M.

RATES
-

WEOLQSALQ
PRICE

INDEX

Market

Bsnk

1890
1891
1892
1893
1894
1895
1896
1897
1898
1899

3.7
3.0
1.8
3.2
1.7
2.0
3.0
3.1
3.6
4.5

4.5
3.9
3.2
4.1
3.1
3.1
3.7
3.8
4.3
5.0

1900
1901
1902
1903
1904
1905
1906
1907
1908
1909

4.4
3.1
2.2
3.0
3.1
2.9
4.0
5.1
3.6
2.8

6.3
4.1
3 3
3.8
4.2
3.8
5.1
6.0
4.9

3.8

88
98
93
93

1910
1911
1912

3.6
3.5
4.1

4.6
4.4
4.9

91
97
108

(1913 = 100)

89
95

84
77
72
71
71
77
82
82
87
82
81

80
83

88

78
74
69
70
76
84

--

Bonncps:
The market rstes of interest:
Rcport of (hs Rwal Cmm-

on Dcp+ld+ of Tr& 1888. p. 37a: wmputed from
The Emnormat Commerd HUq/ and Rcnao, Supphnent, pubhsbed snnually.

me b~nlrrstes of iAtaterest:

R
a
p
& of the Rovd Commirsionon DaprusMl of Tmdc 1888 p. 3?3. computed from
The Economist Commcrcid Hirtorv and &view. Suppieme& publihed snnuslly.
Wholesale F’rioe Index (1913 100):
The index number used is thst of the Btrtiatiwhm R e i b m t , pubWed in Wirtwbsft und Ststistik and wnverted from tho h u e (1861-1870 100) t o the bsse
(1913 = 100).

-

-

APPENDIX

-

-

1

Mprket

1872
1873
1874
1875
1878
1877
1878
1879

4.2
5.0
4.0
3.2
2.3
1.8
2.0
2.2

5.1
5.2
4.3
4.0
3.4
2.3
2.2
2.6

125
125
114
112
112
113
104
101

1880

2.6
3.7
3.4
2.6
2.4
2.5
2.2
2.4
2.8
2.6

2.8
3.9
3.8
3.1
3.0
3.0
3.0
3.0
3.3
3.1

104
101
99
87
87

2.6
2.6
1.8
2.2
1.8

3 .O
3.0
2.7
2.5
2.5
2.1
2.0
2.0
2.2
3.1

86
85

1881
1882
1883
1884

1885
1886
1887
1888
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899

-

1.6
1.8
1.8
2.1
3.0

86

82

80
83

86
82
81
75
74
71
72
74

80

--

Market

11 9 0 0
IL901
11902
11 9 0 3
11 9 0 4
1L905

3.2
2.5
2.4
2.8
2.2
2.1
2.7
3.4
2.1
1.7

IL 9 0 6
I1907
11 9 0 8
1L 9 0 9

11910
11911
11912
11913
11914

I

Bnnk

”

3.0
2.4
3.1
3.9
3.0

3.3
3.0
3.0
3.0
3.0
3.0
3.0
3.5
3.1
3.0

86
82
81

3.0
3.1
3.3
4.0
4.1

93
98
102
100
102

83
81

85
90
94
87
87

APPENDIX

WEOLESAI
PRICE

YEAR

-

Bar&

1861
1862
1863
1864
1865
1866
1867
1868
1889

4.2
5.1
5.5
8.7
6.9
9.1
5.1
5.8
6.0

1870
1871
1872
1873
1874
1875
1876
1877
1878
1879

5.7
4.7
5.0
3.9
6.2
5.7
6.8
8.4
5.3
6.3

1880

4.7
5.3
6.6
6.8
6.4
5.4
6.0
5.6
5.5
7.0

1881
1882
1883
1884
1885
1886
1887
1888
1889

-

-

!NTm
EST

NTEB

-

bTEI

50
52
56
59
67
63
57
63

58

1900 5.3

w

53
54
58
52
54
69
74

68
59
53

53
53
57
57
55
56

60
63

Bank
-

Bad

1890
1891
1892
1893
1894
1895
1896
1897
1898
1899

50

B8T

RAm

INDEX
(July 191!
= loo)
I

-

5.8
3.1
3.5
4.9 1923
5.4
4.3
5.7 1926
7.9
8.1
5.9

1901
1902
1903
1904
1805
1906
1907
1908
1909

5.5
4.9
4.9
4.9
5.1
6.4
6.1
5.8
5.2

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

5.3
5.5
5.4
6.0
5.5
5.7
6.9
6.0
5.6
6.6

-

63

64
71
69

66
64

70
82
67
65

1920 6 . 1
1921 5 . 6
1922 5.8
6.0
1924 6.7
1925 5.6
5.2

VEOIXSAL~:
PRICE

-

INDEX
[July 1914

loo)

201
178
176
172
173
159
148

77
75
89

66
65
72

85
90

96
80
81
83
93

98
100
112
128
145
178
196

-

8Omcm3:
The bank rate of intereat:
The annuel s v e q e bank rate at the Bank of Bengal and the Im el B a d of India.
1861-1889. Furmnhed by Messrs Pleae Biddonaand Go
E k e m . of Celoutta.
R W n g to Bank8 171
1870-1920; India, Department & Stathea, S
h ?a
‘%
India, 7thIssue, 1920, p. 9.
1921-1926: W ,13thissue, 1928, p. 9. Thme data am for the Imperial Bank of

India.

-

Wholesale price Index (End of July 1914
100)’
issl-lp. From 1m+1818oompiled
1861-19l%Atkilleon’nWhol,+priee I+,
by the Department of Btatletm of Indm on
hne of conatmotton M employed
by Atkinson.Converted to the base of end of July 1914 100Publiehedin
the
Journal of the Royal Btatiaticsl W e t y . March. 1897.June, 1698, March. 1803,
September 1908.
1914-1926; Wholesale Prim Index o f t h e Indian Commsmisl IntelligenceDepartment
(Statiatice!Brunch). Published in pricu and FIWU
in India,July, 1914-Deaemberv
1918, and m the Indian Trade J o d , 1921-1925.
I

APPENDIX
Tor

9

TABLE
VI
Rates of Zntereet a d Wlw&aale Price I&,
INTE~~ST

YEAR

-.

RATES

hlarket

'BICEINDEX

INTEBEST

5.4
6.3
6.6

49

1890
I891
I 892
1893
1894
1895
1896
1897
1898
1899

6.8
7.0
6.2
5.5
7.1
7.7
7.5
8.4
9.1
7.5

60
78
71
78

1900
1901
1902
1903
1904
1905
1906
1907
1W8

8.9
9.9
8.4
6.6
6.9
8.0
6.4
7.3
7.7
6.9

74
72
72
76
80
86
84
90
90
a7

50

52
56
55
56
58
59
65

WHOLE8ALE

h
T
E
0

EWcr INDEX

Market

!1913 = 100)

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

5.7
5.3
6.8
7.3
7.7
8.1
6.6
5.5
5.8
7.3

89
93
99

1920
1921
1922
1923
1924
1925
1926

8.0
8.0
8.0
8.0
8.0
7.7
6.9

YEAB

'1913= lWd/

1887
1888
1889

1909

I

WEOLEEALB

f887-1926

100

95
97
117
147
193
236
259
200
196

199
206
202
180

SOURCES:

The market ratas of intar&'
The rate of d~scountof, h e Bank of Japan for Commercial Loans. taken from Ths
Finon& and &cmmnu Annud of Japan. lasued by The Department of Frnance.
The figurea eken in the table are computed where neDea8ary by tpki the arithmetio mean of the Amhest and L o w e @asoount,'gte,?n Commerclafiills at the
Bank of Japan. Where the quotatron IS gwen In Ben, whch repreeents the dslly
intemt on a loan of 100 en the muroe quotetion has been converted to an annual
basis by multiplying by g.6d.
Wholeeale Rice Index (1913 = 100):
The index number is faken from Franklin L.Ho. Pricsa and
Inds2ps in C%inn.
F i n w e h n o m i o J o u r d , June, 19n. P. 53, and was computed by hun fmm the
Index numbers d the fotloannp,com rlera:
1873-1902: Jspane8e Commmnlon f% the Inmtimtion of MoneW
1902-1913: Department of Agriculture and
1913-1926: Bank of Japan.

cornmeroe.

APPENDIX
In Chapter XIV of The Rate of Interest “virtual, ” or “real,

J

J

rates of interest were computed from“nominal, ” or “money, ”
rates of interest by making adjustments for appreciation in the
value of money calculated from index numbers of prices. In
this book, the money rates of interest me adjusted directly to
the rates of change in the genersl pricelevel.Thesetwo
methods, of course, yield identical results, since the one is the
obverse of the other.
The average annual percentage chsnges in the general price
level,given in the Tables VI1 to XI inclusive, are computed
from the wholesale price indexes of the several countries. The
index numbers for two dates, aa 1825 and 1834, giveus a
measure of the price level at those two dates, and from these
it is easy to calculate the average annual percentage change.
The method is the same as that employed for finding the rateof
interest by which $1, by compounding, will amount to a given
s u m in a giventime.Theoretically,since
the loans here included run usually perhaps thirty to ninety days, the quotations
of rates of interest averaged shouldbegin at the h t of the two
dates, and cease, say, sixty days before the second. But the
index numbers are not always for definite points of time, nor
can the interest quotations be subjected to such minute corrections without an immense expenditure of labor. Hence,the
method adopted has been to average the rates for all the years
of a period, e.g., for theten years, 1824-1834. The annual
percentage change in the price level is reckoned between those
dates. If the index numbers present the pricelevels at the
middle of 1825 and 1834, then the average interest rates ought
in theory to include only the last six months of 1825 and the
first four months of 1834. But it seems better to include too
much at both ends than to omit the averagea for 1825 and 1834
altogether, for the reason that an average is the more valuable
the greater the number of tern included.
The real interest ratm are obtained by subtracting from the
money rate for any period the rate of annual change in the
price level forthe same period.

~52431

APPENDIX

BANX

Ram

1825-1834
1834-1839
1834-1852
1852-1857
1868-1864
1864-1870
1870-1873
1873-1896
1898-1913
1914-1920
1920-1927

-

4.2 3.4
4.4 4.0
3.7 3.4
3.8 4.7
4.4
4.2
4.3
4.1
3.7
3.5
3.2
2.6
3.6+1.9 3.1
4.4
5.2 +14.5
4.2
4.8

-

-3 .O
+3.3

-2.7
+5.8
+2.4
-1.6
+4.8
-2.6
-10.9

+7.2
+1.1
+6.4
-2.0
+2 .o
+5.9
-1.1
+6.8

+1.7.
-9.3
+16.7

$6.4

$0.7
+6.1

-1.1
+1.8
$5.7
-1.3
+5.1
+1.2
-10.1
+15.1

TABLE
VI11
Rata of Interest in R
e
l
d
h to Annual Rdes of Change in the P& Level,
New Ymk, 1860-1987

1860-1865.
1865-1871
1871-1879
1879-1889 ,
1889-1896
1896-1916
19154930

..

...
1920-1827.

.. ..
. .

.. ..
0

.

.. ..

6.9
7.8
6.4
6.1
4.9
4.7
5.1
6.0

-14.3
$8.1
-4.3
-0.2
-3.1
$2.1
+14.9
-6.3

-7.4
+15.9
+lo. 7
$5.3
$8.0

$2.6
-9.8
+11.3

APPENDIX

1 1 10

ANNUALUTES
BANK M A R ~ T OF CHANOE IN
WIOEUrn/

REAL

"

1864-1867
4.7

1

INT~BEST
R E A L INTEXERT
IN COMMODITIES

IN COMMODITIES
(BANS)

(MAIIIWI-)

+5 .O

+o. 1

-0.3

-4.3

+8.6

+7.6

1870-1873

TABLEX
Rales of Interest in Relotion b Ann& Ratss of Chunge in uls Priee Level,
Paris, 1&7~-1314

APPENDIX

T a m XI
Rotcs of Intere& in Rdatia, to A n n d Ratss of Chcmge in the Price h d ,
Cdcuua, 1861-1988, Tokyo, 1887-1986

-

Ru h
T
E
F INTXBEBT IN

BANX

Calcutta. 1861-1866
'

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

1856-1871 .
,
1871-1875
1878-1881
, ,
1883-1897
,
1897-1898 . . . . .

iSsS-iiiii 1 i i i i

. .
.. ..
1920-1926 . .
1887-1899 . .
1899-1902 . .
1902-1913 . .
1913-lezo . .
lQ!W1926. .
1901-1804
1904-1913
1913-1920

Tokyo,

&YYODrrrnS

6.6
6.1

(BANK)

$5.7

+0.9

-6.0
+5.4

f12.1

"11.2
$3.1
-11.2
+6.9

+16.6
+2.5
+18.5
-1.3

5.6

-4.8
+4.4

$1.2

5.9

$11.1

5.8
5.4

5.5
7.3
5.6

+0.4

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

6.9

+11.2
-5.2

7.0
8.7

+3.8
-2.6

$3.2
"11.3

. .
. .

6.9

+2 .9

+4.0

7.0

$12.7

.

"

,
*

. .

"

5.1

7.8

-

-6.4

$9.9
-5.3

-5.7
"14.2

APPENDIX
$ 2 (to Ch. XIX, $ 6 )
Tables of interest rates
TABLE
XI1
Intereat Yield m British Consols, 1820-1924
(Given in pence per IOO-pound investment)

=
ImamST

YEAB

1820.
1821
1822
1823.
1824
1825
1826
1827
1828
1829.

.
.
.
.
.
.
.

1830.
1831.
1832.
1833.
1834.
1835.
1836.
1837.
1838.
1839.
1840.
1841.
1842.
1843.
1844.

1845.
1846.
1847.
1848.

1849.

1850.
1851.
1852,
1853.
1854.

.
.
..
.
.

796
773
784
743
757

...

766
787
774
777
799
805
818
774
767
775

.
.
.
.
.
.
...

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

..
.
.
.

I

778
776
778
778
778
768
758
755
757
739
732
720
716
712
713

725

714
707
724
689

I!

1890.
1891 ,
1892 .
1893 .
1894.
1895
1896.
1897
1898 .
1899.

.
.
.
. .
.
. .

1900.
1901.
1902.
1903.
1904.
1905.
1906.
1907.
1908.
1909.
1910 .
1911
1912
1913
1914 .
1915
1916 .
1917 .
1918 .
1918

I

.

.

.
.
.
.
.
.
.
.
.

.
.

.. ..
. .
.

. .
.
.
.
. .

1920.
1921 .
1922

685

*

,

*

.
. .

689
683
070
653
022
596
587
695
618
862
700
099
078
680

668
I

679
713
697
713
740
750
788
815
801
916

1034
1097
1055

1110
1277
1258
1081
1034
1061

APPENDIX

TABLP~
XI11
ZnteteSl Raiea on 16 Railroad Bonds, United States, 1900-1987
AVEMQE

YEAR

.
.
.
.
.
.
.
.
.
.

1930
1901

1902
1903
1904
1905
1906
1907
1908

1909

&WCE:

%e

e 58.

st.*

.
.

PER

CEKT

.
.

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

4.05
3.90
3.86
4.07
4.03
3.89
3.89
4.27
4.22
4.06

AVERAGE

YEAR

1910
1911
1912
1913
1914
1915
1916
1917
1918
1919

PER
CENT

. .
. .

.
,

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

.
.
.
.

. .
. .
. .
. .

4.16
4.17
4.21
4.42
4.46
4.64
4.49
4.79
5.20
5.29

AwBaae
Fml
CENT

YE-

1920 . .
1921 . .
1922 . .
1923 . .
1924 . .
1925 . .
1926 . .
1927 . .

.

5.79
5.57
4.85
4.98
4.78
. 4.67
. 4.51
. 4.31

.
.
.
.

1

Tirs SWWd.Bul&fin of The Standard StatistiesCompany, Inc.. 1929-1930,

Wholde Prim Indexas used in W
n
g correlations are the indexes of the United
Bureau of Labor &atistias given in Table 11.

APPENDIX

-

jl

YEAR

-

NTEREBT

YEm

’ea CENT

”

1890

4.70
3.89
4.22
4.73

1910

4.56
4.77
6.45
5.24

1920

6.38

7.23
7.95
7.94

1891

5.36
5.30
5.72
5.18

1901

3.M
3.95
4.56
4.75

1911

3.98
3.66
4.17
4.30

1921

7.74
7.02
0.08
5.30

I892

3.94
3.19
4.06
5.24

1802

4.31
4 .49
5.01
5.87

1912

3.95
4.11
6.03
5.88

1922

4.85
4.30
4.03
4.55

1893

5.01
7.05
9.26
4.70

1803

5.22
5,03
5.79
5.84

1913

5.20
5.59
5.95
5.84

1923

4.77
5.05
5.04
5.07

4.78
3.88
3.89
4.27

1914

4.08

1924

4.75
4.26
3.30
3.32

1925

3.74
3.90
4 .OB
4.40

1894

a m

5.81
5.43
3.66
3.68
3.34
3.11

1895

3.51
3.11
3.50
4.48

1905

3.91
3.91
4.35
5.41

1915

1898

5.62
4.09
7.10
5.85

1906

5.13
5.34
0.01
0.27

1918

1897

3.a
3.41
3.76
3.70

1907

6.08
5.61
0.26
7.50

1917

1698

3.72
4.63
3.80
3.25

IWK)

5.72
5.80
5.94
6.94

1899

3.20
3.53
4 s
5.44

1908

6.25
5.43
6.88
5.M

-

4.26
4.02
4.22
4,44
3.92
4.70
4.89
5.45

19.27

4.oo
4.12

3.90

am

.__

APPENDIX

D

NVMBE

YmaB

-

_c

lsso

-

INDEX

YMX

.

78.7
79.4

INDEX

lsoo

..

822

82.2

.

1881

*

*

81.5
82 .O
79.2
77.7

1901

*

1882

.

*

74.9
72.7
75 $0

leoa

..

81.3
78.3
73.7
73.8

1Kla

..

69 .6
67.6
69.5
68.7

1904

..

67.5
71.7
71 .O
70.1

1806

.

88.1

1808

.

60.5
05.2
67.4
68.8

1901

..

69.5

lwyl

.

1893

..

189(

..

1885

..

leBB

..

1887

..

1898

..

1899

..

06.1
64.8
68.0

71.2
68.7
68.8

-=

.

78.6
77 .7
79.3
81 .4

1911

..

81.2
83.4

1912

..

Z:!
79.3

84.0

n.4

71 .O
72.8
76.2
80.2

1

1910

82.0

*

I

.

1 m

.

88.4
85.1
84.5
83.8

1913

.

88.4
84.2
84.8
88.8

1914

.

88.8
85.5
85.6
88.4

1915

.

67.1
87.8
67.3
91.2

1916

.

92.4
83.8
96 .o
93.1

1917

..

88.7

1918

.

88.4

101.7

I

INDZX

?UMBER

233.3
244.9
232.8
195.4

93.3
90.5
93.5
94.2

161.8
144.8
141.3
140.7

95.6
89.7

140.6
148.6
154.4
155.3

100.1
99.3
100.6

89.9

168.9
156.1
151.5
162.1

88.5
97.1
99.8
97 .O

150.9
146.6
148.4
153.9

98.9
99.4
09.9
104.8

160.5
156.3
160 .o
157.2

115.5
122.0
128.4
143.3

154.2
151.5
150.1
148.3

167.4
180.3
188.0
182.7

146.2
144.0
146.8
149.6

188.9
190.5
189.9
202.3

I/ 1919

I

103 .o
103.4
101.2
98.0

89.9
100 .e

88.6

90.5
91.9

NVMBEI
-

-

198.0
201.2
212.7
217.3

-

APPENDIX
APPENDIX TOCHAPTER

XX

$ 1 (to Ch. XX, 5 17)
Waiting QB a Cost
IFwaiting were a cost like other costs, it would be subject to
the law of discount, according to which the capital-value of any
article of wealth is equal to the discounted value of ita expected
incomeless the discounted value of its expectedoutgo. The
value of the tree which has been mentioned, taken, say, at the
end of 14 years, w
liactually be about $2, and this is the discounted value of the $3 of income which the tree will yield at
the end of eleven more years. According to what I believe to
be the correct theory, this $3 is the only future item involved
in this example. But according to the theory here criticised,
this is not the case.Besides this positive item of income, $3
due in eleven years, we have to deal with a series of eleven
negative items called “waiting” distributed through these
eleven years, and amounting to the interest -about 10 cents
for the first year and gradually increating to 15 cents for the
last year. If the waiting-items were b m $de annual costs
like, for instance, actual labor-costs of pruning the trees -the
process of discount would properly be applied to them. That
is, if these waiting costsreally exist, they ought to be discounted
and their discounted value ought to be deducted from the
discounted value of the $3 of expected income. But we should
then have to mign aa the value of the treenot the correct figure
of $2 but an incorrect figure of much less. The fact that we
cannot thus discount so-called “waiting” costs as we discount
all true cosb is a proof that the “cost of waiting” even if we
inskt on calling it such diilers radically from true costs.’
If we are to have any logical, usable self-consistent theory of
income and capital, all items of income, positive or negative
- the negative ones being “costs” -must be discountable.

-

18ee

BBhm-Bswerk, Recat Literature on Interest (1884-1899), p. 35.

~5341

APPENDIX
But, aa an amwer to this objection, it might be argued by
the abstinence theorists (if I may ascribe to them the best
argument I can think of) that while waiting-cost is certainly
not a discountable Cost, nevertheless its inclusion in the list of
costs obviates the necessity of discounting the other items of
cost or of income. If all income and all cost items, including
waiting, are counted at full value - not discounted at allthe capital may be valued simply by taking their net sum.
Thus, to count rrwaiting”m a cost appears as an alternative
and plausible method of keeping accounts. By this system we
could apparently get rid of discounting and merely add and
subtract item regardless of their situation in time. While this
procedure obviates the objection to the abstinence theory of
cost, 80 far aa its application to capital value is concerned, it
leaves objections equally great to its application to income. If
waiting is a genuine economic cost,it must certainly be included
on the outgo side of the income account. To showhow this
would apply to the coat of the tree, the following table is p r e
sented.
Znurme Accovnt of Tree if Wading is Cost
A-QED

OUTW

25th year

3 .oo

.15

$3.00

$3.00

3.00

00.0

According to this method of accounting, we see that, during
the year in which the sapling is planted, its cost COnSistS of labor
to the extent of $1, expended, let us say, at the beginning of the
year, snd 5 cenfa’ worth of waiting suffered during the oourae
~5351

APPENDIX
of that firat year.During the second year a waitingcost of
about the same amount is incurred, and 80 on for each succeeding year, the cost of waiting gradually increasing, ea the tables
of compound interest would indicate, until in the fourteenth
year it amounts to 10 cents, and in the twenty-fifth year to 15
cents. The total cost for the 25 years w
li then be $3,and the
return to the planter at the end, from the eale of the tree, w
li
also be
Consequently, if we take the whole period from the
first application of labor to the final d e of the tree, the net
income will be zero. This result is, to say the least, somewhat
surprising,but not so much so 89 some other results of the same
species of bookkeeping, ea the following additional examples
will show.
Suppose a person owns an annuity amounting to $100 a year
for 10 years. According to the ordinary method of keeping
accounts, his income consists of this $100 a year each yew.
But if we count the waiting as a cost, we shall find that the
income for each year is lesa than $100. The owner of such an
annuity wil, during the first year, have to s d e r “waiting ” to
the extent of $39, supposing interest is at 5 per cent; for this is
the increase in value of his annuity during that year, due to
his waiting for the future installments of income of which his
annuity consists.’ His net income during that year, therefore,
according to such accounting, is not $100, but $100 $39, or
@l. During the second year his income in this second year is
somewhat greater, for the cost of “waiting” is only $35. His
net income is, therefore, $100 $35, or W. Similar computations carried out for succeeding years are ahown in the table
on the following page.
Is it good bookkeeping to introduce a new and anomalous
element of cost which results in making the net income of the
annuitant not the $100 which he actually receivea and which
common sense m
g
n
k
m as the income from the m u i t y but

$3.

-

-

9 This is evident, since the vdue of his annuity, clrpitslised at 6 per WntJ
reckoned at the beginning, ia $772,whereas, e
r
o
k
o
n
e
d at the a d of the h t
year, before hie $100 is paid, it is $811.

15361

APPENDIX

. .
.

let year
2dyear
.
tdyear . .
4th year . .
6th year . .
6th year
.
7th year . .
8th year . .
Qthyear . .
loth year . .

Waf!ing
$100
100

%32

29
25
22
18
14

.

-

$61
65
68
71
75
78
82

I

I

5

dlooo

$228

354

86

9

”

$772
71I
646
678
507
432

91
.~

1

95

$772

I

272
186
95

the queer sums given in the table, namely, $61, $65, $68, and
so forth?
To push this criticism to the limit, let u9 finally consider a
perpetual annuity of $100 a year. In this w e we shaU find that
the “cost of waiting” each year is the full $100, for the value
of such an annuity, reckoned at 5 per cent, is $2000 reckoned
at the beginning of each year, and $2100 reckoned at the end.
It msy be of interest to note that this error is the inverse of, or comple
m e n w to, the more common one by whichthe net income ia the $100 less
the “depreciation.” In the 6rat year this would be $772 lees $711, or $61,
BO that the “income” is $39. T
his sort of accounting, when, inseesd of
depreaiation, there is appreciation or savings, would make savings appesr
as income instead of capital. Thie savings, or depreciation,fallacy is
especially discussed in Are Sauings Inconte? American Economic Aesociation Journal, April, 1908,and The Income Concept in the Light of E-.
It hsa been the subject of much controversy. Same economists who fall
inh thia eavinga91.8-income, depreciation-ie-outgo
fallacy in some parts of
their eyetern fail into the waiting-host fsllscy in other parte. Both
annot be right. Eech exhibib the evil coneequenoeswhichensue from
playing f& and loose with the concepts of cspitd and income. If we
wi&
indulge. in such a metaphor 88 “I got it at the ‘coat’ of waiting,”
we
& 80 but only at the “cost” of ~IUCCWY.
Neither of t h 80.~
d
e
d c c a w t a ” ia more than a metaphor.
J

~5371

APPENDIX

If this annual $100 cost of waiting is to be regarded as a negative
item of income and, like other coets, is to be subtracted from the
positive income,we are forced to conclude that the owner of such
a perpetual annuity receives each year no income whatever!
For, if we deduct from the $100 of positive incomethe $100 cost
of waiting, the remainder each year is zero! Yet a perpetual
annuity is the simplest, purest case of income.
It should now be obvious that the theory which cab “waiting” a cost h&s worked out its own absurdity. If taken seriously
and introduced into an accounting system it either interferes
witli the discount or capitalization principleor else distorts and
even obliterates the income reckoning in ita simplest, or most
typical form, that of a perpetual annuity. It falaely simplifies
the formula for valuing capital.
The idea that the value or price of an article should equal its
cost seem to possess a certain fascination for many students of
economics. That it is falsehaabeensufficiently
shown by
BShm-Bawerk through reasoning somewhatsimilar to the fore
going. That it is absurd when carried to ita logical conclusion
will be evident if we consider what happens if the same method
of bookkeeping is d e d out with respect to the future as well
as the past. It is a poor rule which will not work both ways.
This rule, applied to future expected income and outgo, yields
the strange result that the capital value of any article instead
of being less than ita expected income is equal to it. Thus, to
revert to the case of the tree, let us take ita value at the end of
14 years. It is then worth 82, which, in the parlance of the
abstinence theorists, is equal to ita previous costaof production,
consisting of $1worth of labor plus $1 worth of waiting during
the 14 year13. It is a h , in like manner, equal to the future
income to be derived from it, whichconsiate of $3 worth of
&ual receipta from the sale of the tree, due at the end of eleven
more yesrs, less the cost of waiting for those $3,which amounts
to $1.
In the m e way, the ten-year annuitant just considered has,
at the
property worth $772. This, a m &
to

begn
i nn
i g,

APPENDIX
Proper bookkeeping,is the discounted valueof the futureincome
of $100 Year for 10 years, the total amount of which income is
11oOO. But, according to the abstinence theory, logically
d e d out, the incomewhich the annuitant receives for the
whole period is, as has been shown, not this $1000, but $772,
which is just equal to the value of the property.‘ Pursuing the
method of limits, we b d that, for the ownerof a perpetual
annuity, the same proposition would hold good. According
to
the true and ordinary method of reckoning, the total income
from such an annuity is infinity, although its present capital
value is only $2000. But according to the abstinence theorists
the income itself is not infinite,but only $2000.
Those who are enamored of the alluring simplicity and neatness of the formula of the abstinence theorists, by which the
capital value is not greater than past cost of production, but
exactly equal to it, can scarcelybe attracted by the exaggerated
simplicity of the inverse theoremwhich is also involved, namely,
that the capital value of any future expected income is not Iess
than that income, but exactly equal to it also.
The fallacy of the abstinence theorists lies in the simple fact
that waiting has no independent existenceas a “cost.” We can
never locate it in time, nor estimate ita amount, without first
knowing some other more real and tangible costs. Waiting
m w notlung unIm there is something to be waited for, and
the cost of waiting can only be estimated in proportion to the
magnitude of that which is 80 waited for. What is waited for
is some payment or other event constituting income or outgo.
But waiting for income or outgo is not itself income or outgo.
the non-methemtical reader should be puasled by this d t ,
which ~eemto aontredictthefactbroushtout,
t b t , UJKI~
the
peeu&mkoning of the abstinencetheoriste,thenet income is
eVW
y m , it m w be
t b t thie ~ e r oincome ie ~
p
e
s
t
e
d infinita
of times, a d that when wedealwith infinity weBet
rehbh
find
by the method of limits. Themathematical reader
no diffmdty in &owing, by the method of b i b , that there a “remainder
d,
in the supposed m m t i n g , make the total income distributed through dl etamity eimpb
k~
the =Pitel

15391

APPENDIX
The mere accrual of value aa we draw nearer the i t e m constituting true income is neither income nor outgo but capital
gain. The typical picture we should carry in our mind is of a
saw-tooth curve consistingalternately of a gradual ascent dong
a discount curve, and a sudden drop aa an incomecouponis
detached. The only income inthis picture is the series of sudden
drops, on which all the rest hangs. The gradual ascent in each
saw tooth is not income; otherwise it would (largely) duplicate
the true income. Nor is it outgo; otherwise it would (largely)
negative the true income.
In the case of a bond selling at par these alternate ascents and
drops are equal, and we carelessly speak of both as interest or
aa income. But the instant the bond sells above or below par
we recognize the difference. If we follow this out we can scarcely
go astray.
Even to those who do not formally accept any cost theory
of interest, the interest itself will seem in 8ome8ense to be a
cost, and in most books on economics, interest, howeverexplained, is regarded aa one of the costa of production. It is
true that for a debtor who pays interest, the interest is, to
him, a realcost, and is debited on his books. But we need
only to be reminded of the debit and credit bookkeeping of
the first chapter to see that this item is counterbalanced on
the books of the creditor, to whom this interest is by no means
a cost, but, on the contrary, an item of income. For society
88 a whole, therefore, even in the case of interest which is explicitlypaid, it m o t besaid that it constitutes a cost of
production. In the caae of a personwhoworkswith his own
capital, the truth of this statement is even moreevident. Economists who state that the independent capitalist must charge
off intemt BB one of his costa of production seem to forget
that such self-paid interest must be charged back again BB
income also. Labor sacrifice is quite Werent. It is a real cost
and in no time bookkeeping can it be cancelled out. The fallacy
of assuming that inter& L a cost is doubtless due to the habit
of repding production from the point of view of the “enter-

l-5401

APPENDIX
primr.” Since he usually pays interest, he cornea to think of
it purely aa a cost.
I have devoted considerable space to the refutation of the
abstinence theory so far &s it is more than verbal, and collides
with m y workable theory of income, because ifs errom are so
subtle and insidious as to beguile many of the beat and most
wary of economists.

1

BIBLIOGRAPHY
I. W O R K S ON T-1
THEORY.
1. Books:
B~~KM-BAWBRK,
EUGENVON. Capitd and Intemt. London, Macmillan and Co., 1890.xlv, 431 pp.
B~RM-BAWER~,
EUGEN
VON. The Positive Theory of Capital. Translated by William Smart, London, M a c d a n and Co., 1891. XI,
428 PP.
B~HM-BAWEX~K,
EUGEIN
VON. Recent Litemture on Interest (18841889). New York, The Mumillan Co., 1903.xlii, 151 pp.
B~~HM-BA.WERK,
EUGEN
VON. Positive Thwrk des Kapitdes. Dritte
Adage, Innsbriick, Wagner’schen Universitats-Buchhandlung,
1912. d i , 652 pp. Also Exkurse, 477 pp.
EUQENVON. Kleinere Abhandlungm Cber K a m
B~HM-BAWERK,
u d Zim. Wienund LeipBig, Holder-Pichler-Tempsky A. G.,1926.
viii, 585 pp.
BROWN,HARRY GUNNISON. Economic Science and the Cmmm
Welfare. Columbia, Missouri. Lucas Brothers,1926. xiii, 273 pp.
E8peciaJly Part 11, Chapters I11 and IV,pp. 76170.
C m m , THOMAS
NIXON.The E.stri&hof WeuZth. New York,
The Macmillan Co., 1904. xvi, 290 pp.
CABSEL,GUBTAV,The Nature arld Necessity of IntereSt. London,
Macmillan and &., 1903. xii, 188 pp.
CAS- GUSTAV.The Theory of social E m m y . New York, €Iarcourt, Brace and Co., 1924. xiv, 654 PP.
CLUUC,JOHN BAW. E . s t d m t h of V&k. New York, The Macmillan &., 1899. XKVii, 445 pp.
DAVENPORT,
H. J. Vdue wd Lktribhn university of Chicago
Press, 1908. xi, 582 pp.
l?mm+ FRANK A. Economic principles. New York, The Century
Company, 1915. x, 523 pp.
FIBEBR,JRVINQ. The Raoe of Interest. New York, The hhcmillan
co., 1907.xxi, 442 pp.

L5431

BIBLIOGRAPHY

G
o
-

E. C. I(. Intereat
CO., 1906. m,172 pp.

and Savings. London, M m d a n and

H B n ~ z qG E R H ~Stdische
.
oder &w&he Zinsthemk? Leipzig,
Dr. Werner Scholl, 1928. viii, 165 pp.
Horn, CLbREINm GILBERT.A T h m y of Zntercst. New York, The
Macmillan Co., 1914. x, 228 pp.
JKIVONB,
W. STANLEIY. Themy of Pditical Econonty. 3rd edition,
London, M m d a n and Co., 1888. Ivi, 296 pp.
LNDRY,
ADOLPHEI. L'Znte'r8t du Capital, Paris, V. Biard and E.
Bri&re,1904. 367 pp,
P m , VI-.
Cows d'kmnnk Politiqw. Lawanne, F. Rouge,
1896 and 1897. Tome Premier, viii, 430 pp. Tome Second, 426
PP.
Parrerro, VILFREDO. Manuel d ' 8 d Pditique. Paris, V. Gmrd
and E.Briire, 1909. 695 pp.
Rm, JOHN. The Socidogrcol Theosy oj Capitd. New Yo&, The
Macmillaa Co., 1905. lii, 485 pp.
SAX,
EMm. Der Kapitalzins. Berlin, Julius Springer,1916. viii, 249
PP.
UON.
Z h e n t e CpEccOnomie Pditiquce Pure. Laumne, F.
WALRAS,
Rouge, 1900. XX,491 pp.
2. Articles:

ANsuux, M.Le PhhtnnJne de L'IntSre't et 8on EzpEieation. Revue
de L'Institut de Sociologie. Deuxihme Ann&,Tome I, Bmelles,
1921-1922, pp. 47-57.
BIIQMX,H. Analysis of the Nature of Capital and Interart. Journal
of Politid Economy. Vol. XVI, March, 1908, pp. 129-151.
M ~ - B A W P PEUQEN
L H , VON. Capital and Inter&. Quartariy Journal
of Economics. Vol. xxi, November, 1906, pp. 1-21 ; Februwy,
1907, pp. 247-282.

Bomxmv~cz,L. VON. Der K a r d i d f e h h der BoehmBawrkseb

zinstheorie.

JHhrbuch fuer g&Zgebung, Band 30, 1906, pp. 61-90,
Leipig, Ducker und Humblot, 1906.
C m m , T. N. The Fsoec of Abstinence in tice Thmg of Zpl.tereSt.
Quarterly Journal of Economics, October, 1893, pp. 4061.
C
,8. J. Muat InventioM Reduce the Rate oj Interest?
Economic J o d , Val. X X , September, 1910, pp. 465-469.

15441

BIBLIOGRAPHY
DAVBNFJORT,
H.J. Interest T k q and Theories. American Economic
Review, Vol. XVII, No. 4, December, 1927, pp. 636-656.
DAVIIB,G. R. Factors DetemLining the Inter& Rate. Quarterly
Journal of Economics, Vol. XXXIV, May, 1920, pp. 445461.
E”,
A. Zntmest T M w Old and New. American
Economic Review, Vol. IV, No. 1, March, 1914, pp. 68-92.
lbmq FRANK
A. Clark’s Reformulation of the Capital Concept,
in Economics Essays Contributed in Honor of John Bates Clark,
pp, 136-156, New York, The Maomillan GJ.,1927.
FISHER,IRVING.Professcr Fetter on Capital and Income. J o u d of
Pditicol Economy, Vol. XV, July, 1907, pp. 42144.
FISHER,
IRVING.
Are Savings Income? Journal of the American Economic Association, Vol.IX, No, 1, April, 1908, pp. 1-27.
FISHER,
IRVING.
A Reply to Ciitics. Quarterly Journal of Economies,
Vol. XXIII, May, 1909,pp.536-541.
FISHW, IRVING. Capital and Interest. Politid ScienceQuarterly,
Vol. XXIV, No. 3, 1909, pp. 504-516.
FISEW,IRVING.
c a w and hierest: Reply to PTO~~&WVeblen.
Political Science Quarterly, Vol. XXIV, September,1909, pp.
504-516.

IRVING.
The Impatience Themy of Intereat. Scientia, Vol.
IX, April 1,1911, pp. 3 8 0 4 1 .
F r s ~ m IRVING.
,
The Impatience Theoly oj Iaterapt. American Emnomic Review, Vol. 111, No. 3, September, 1913, pp. 610-615.
FLUX,A. W. Irving Fisher on Capztal and Inter&. Quarterly Journal
of Economics, Vol. XXIII, February, 1909, pp. 307323.
GONNW, E.C.K.Considerath about Interest. Economic J o u d ,
Vol. XVIII, March, 1908, pp. 42-51.
GRAZUNI,AWGU~TQ.
Capitale e Interesse. h i e d Real di N w l i ,
FISHER,

1925, pp. 33-92.

Irving Fisher: The Rate of Interapt. Rewe
dzwnomie Politique, 23 Annb, 1909, Bulletin Bibliogwhbe,
pp. 156-159. Paris, L. Larose and L. T e h , 1909.
k,
A. Irving F&/t.&s Rate of Intere8t. J O U d of pofitid b
nomy, vel. XVI, October, 1908, pp. 331-332. WVby Irving
Fisher, same issue, pp. 532-534.
Low~y,Dwroar M. The Basis of Interest. America A-Y
of
p a w
Science, March, 1892, pp. 53-16. ‘
I,ANDRY, AWLPHB.

c5451

BIBLIOGRAPHY
S
C
H
-

J O S ~ EE&
I . “Dymmische” Theorie des Kapi-.
Zeitschrift fiir Volkswirtschaft, Sodpolit& und Verwdtung, 1913,
pp. 599-639. Vienna, Manzche, K. U. K.Haf-Verlags und Univeratiitsbuchhandlung, 1913.
SHmscHNIcom, N. von. Die Biihm-Bawerksche Kapita&tk&.
Jahrbiichern fiir Nationalokonomie und Statist&, Dritte Folge,
Bd. XXXIII (LXXXVIII), Jena, Guetav Fiacher, pp. 433-451.
TAUS~IG,
F. W. Capital, Interest and Diminishing Returns. Quarterly
Journal of Economics, Vol. XXII, May, 1908, pp. 333363.
VEBW, T.Fisher‘s Rate of Interest. Political Science Quarterly,
Vol. XXIV, June, 1909, pp. 296-303.

11. OPHm W m s DEALINGmm I

~

T

.

1. Books:
AD^, KARL.KapitalzisLs und P r k b e z a e w . Leipzig, Duncker und
Humblot, 1913. 48 pp.
BECKHART,
B E ~ J A MH.
I NThe LXmunt Pdiey of the Federal Re8me
New York, Henry Holt and &., 1924. xii, 604 pp.
B ~ U C H E R ,Pmw B. Histoire de L’Usure. Paris, Chaiieau, 1806.
215 pp.
BROWN,
MARY W.The Devebpment of Thrift. New Yo&, The Macmillan Co., 1900. x, m pp.
CANNING,
JOEN B. The Economics of Accountancy. New Yo&, The
Ronald €’ma Company, 1929. viii, 367 pp.
DICK,ERNST. The Relation Between the Rate of Interest and the
Level of Prices. Distributed by H.R. Scott, Kodaiksnsl, 5. India,
March, 1928. 83 pp.
EDIEI, Lrom D. E c m n n h : Principles and PtoMems. New York,
Thomas Y. Cmwell Co., 1926. xx, 799 pp.
E h , LIONELD. Momg, Bank Credit, mi Prices. New York, Harper
& Brothem, 1928. xiv, 500 pp.
Fmm, FRANK A. Modern Ecollomic Problem& New York, The
Century Company, 1917. xi, 498 pp.
F I B H ~ , N G The
. Income Concept in tL Light of Experience.
English tramlation of article in Die Wirtschjtethsoni der G-egm
d,
VoL I11 of the Wkser Festschsift, Vienna, 19‘27. 29 pp., in
translation.
R s ~ IRYINQ.
q
The Nature of Capital and Income. New York, The
Macmillen Co., 1927. ai, 427 pp.

i3gstem.

15481

BIBLIOGRAPHY
G m ~ m R,o-.
The Growth of Capital. I.ondon,’ceOrge Bel and
%ns, 1889.169 pp.
G~lanm,JOHN ALDEN md Chu~m,W
~ Hoturn.
M Principles
of VaZuation. New York, Prentice Hall Inc., 1928. xvii, 274 pp.
m,KARIN.A study of In.terest Rates. Zandon, P. S.King, 1929.
264 PP.
MONTAGNB,
JUN. Le Capital. Park, Albm Michel, 1919. 253 pp.
NOFCIVN,
JOHN P. Statistical Studies in the New York MoneyMarket. New York, The Mwmillan &., 1902. vi, 180 pp.
Pmuhm, R. H. INGLIB.
Bank Rate and the Money Market. New
York, E. P.Dutton and Co.,1903. xxiii, 237 pp.
b y , R. C. The Regdatiun of Pawnbroking. New York, Ruesell
Sage Foundation, 1924. 63 pp.
RYAN, F’RANKLIN W. Usury and Usurg Lam. Boston, Houghton
Mifflin Company, 1924. xxix, 249 pp.
W~cxsmz,K m . Ober We&, Hapltal uuul Rente. Jena, Gustav
Fischer, 1893..xvi, 143 pp.
WICKBELL,KNUT.Gduki3ts und Giiterprek. Jena, Guatav Fmher,
1898. xi, 189 pp.
2. Adiclea:
BIRCK,L. V. Moderne Seholostik. Eine Rdische DarsteUung der
B6hm-Bawkschen Thewie. Wdt+hftlichw
Archiv., 24 Bd.,
October, 1928, Heft 2, pp. 198-227.
B o r n , H.Geld und Kapitalmrkte im /ahre 1994,Wirtschaftdiemt,
Vol. X,Feb. 6, 1925, pp. 247-248.
B m m , W. RANDOWH.Factors Aflwtinq Chunges in Short Term
Interest Rates. Journal of the American Statistical Amciation,
Vol. XXII, New series, No. 158, June, 1927, pp. 195-201.
CASB~L,
GUBTAV.The Future of the Rete of Interest. Skandinaviska
Kreditauiebolaget, Januery, 19%. Stockholm, P. A. Norstedt &
siiner, 1926, pp. 1-4.
CASBE~,
GUBTAV.The Rate of Inter&, the Bank Rate, and the StabilLotbn of Pricap. Quarterly Journal of Economics, Vol. XLII,
August, 1928, pp. 511-529.
CMBan, GUBTAV.Disemni Pdicy a d stock Ezchange W i M .
Bkandinavieks Kreditaktiebolaget, October, 1928. S W o b P. A.
Norstedt & Saner, 19’28, pp. 57-60,

~5471

BIBLIOGRAPHY
Business Bulletin, June 15, 1928,and
August 15, 1928.
CONRAD,Orro.Der Kapitalzins. Jena, Jahrbiicher fiir Nationalijkonomie und Statist&, 3 Folge, Band 35, 1908,
pp. 325-359.
CRUM, W.L. Cy& of Rata on Crnnmrcb! Paper. Review of Economic Statistics. Prel. Vol.V,No. 1, January, 1923, pp. 17-29.
h m ~FRANK
,
A. Recent Discussion of the Capital Concept. Quarterly Journal of Economics, Vol. XV, November, 1900, pp. 1-45.
FISHER,
IRVING. Appreciation and Interest. Publications of the American Economic Association, Vol, IX, No. 4, August, 1896, pp. 331442.
FISHHE,
IRVINO.E
’
&l a CapitaE? Economic Journ&l, Vol. VI,
December, 1896, pp. 509-534.
FrsHm, IRVING. The R6Ee of Capital in Ecmmic Theory. Economic Journal, Vol. VII, December, 1897, pp. 511-537.
FISHER,
IRVING.
The Rate of Interest after the War. Annab of the
AmericanAcademy of Political and SocialScience, Vol. LXMII,
November, 1916, pp. 244-251.
FISHER,IRVINQ. Cornmat on President Pkhn’s Address. American
Economic Review, Vol. XIV, No. 1, March, 1924, pp. 64-67.
FRIDAY,
DAVID.Factors which D e w t b Future of the Rate
of Interest: Ecanomic Prim*ples of Supply and Demand. T m t
Companies, Vol. XXIII, July, 1921,pp. 9-12.
GIBSON,A. H. The Future Course of High-Chs Investment Vdw,
Banked, Insurance Managers’, and Agents’Magazine, January,
1923, pp. 15-34.
G m , SIRROBW. Accumulations of Capital in the United Kingdom in 1876-86. The J o u d of the Royal Statistical h i a t i o n ,
Vol. LIII, 1890, pp. 135.
HARGER,C. M. Problem of IpLtere-st Ratea. Fintmcd World, Vd.
XXXII, June 23, 1919,p. 19.
INOSTRANXPZ,
M. L’Usure a Russie. Journal des Bconomistes, 1893,
Ser. 5, Vol. XVI, pp. 233-243.Paris, Administration et Redaction,
Librairie Guillaumin et C.,1893.
JAY,
P m . CaU Money Market in New Y w k City and the Interest
Rates Charged Therein. EconomicWorld, Vol. XUE, April 10,
1920, pp. 511413.
KBMMWRIR, E.W.War and the Interest Rate. Economic World, Vol.
XVI, November 2, 1918, pp. 616-619.
C ~ V E M N D TRUST COMPANY.

CWl

BIBLIOGRAPHY
Rediswuntijlg ond tha Federal Reserve Discorcnt
Rate. American Bankers' AssociationJournal, Vol. XII, April, 1920,
pp. 582-584.
L E W , R. G. Lh T a m Actuel de L'lnthAt et de ses Rapports ava la
Productim des Mitam Pre'oieua: et h Autres Phhomdnes ~ c o m miqws. Journal des Economistes, March, 1899, p. April,
334; 1899,
p. 28.
MAG^, JAMESD.Call Rates and the Federal Reserve Board. American Economic Review, Vol. X,March, 1920, pp.
59-65.
MITCHELL,W. F. Interest Cost and the Bm"W Cycle.American
Economic Review, Vol. XVI, No. 2, June, 1926, pp.
209-221.
MIWHHLL,W. F. Supphnmtary Note on Interest Cost. American
Economic Review, Vol. XVI, No. 4, December, 1926, pp.
660-663.
MITCHELL,W. F. Interest Rates as Factors in the Business CgcL;
with a R q d y by J . E. McDonough. American Economic Review,
Vol. XVIII, March, 1928, pp. 217-233.
M o m , BARON.
Les C a w des Variatha du T a u de L'Int6r;t.
Revue d'Economie Politique, 1924, pp.45-64. Paris, Librairie de
la Soci6t6duRecueilSirey, L b n Tenin, Directem, 1924.
PWONB,
WARRENM., and FFXCKEY,
EDWIN. Money Rates and Security Prices. Review of Economic Statistics, Vol. VIII, No. 1,
January, 1926, pp.
29-46.
%ONB,
WARRENM. Money Rates, Bond YieMs and Security Prices.
Review of Economic Statistics, Vol. X,No. 2, April, 1927, pp. 93102.
RNBCHOF,
C.L. The World'sReturn to Gold: the Ultimate Eflect
on Rates of Interest. Acceptance Bulletin of the American Acceptance Council, November 30, 1925, pp.
4-5.
PLDHN,CARLC. Notes Concerning the Rates of Inter& in Cdifornirr. Quarterly Publication of the American Statistical h o c i a tion, September, 1899, pp.
351352.
PRICE,T. H.Do High Interest Rates Presage DefEation? Commerce
and Fiance, Vol. VIII, November 12, 1919, pp. 1511-1512.
R m , S. A. Inter& and Dividends; Other Features of Interest;
Irrevocability of interest. Modern Economic Tendencies, 1921, pp.
204-231,254-342.
RIBT, ~H~RLQB.
La Hawse du T a u de L'Inte'r8t et ta Hawse des
Prk. Revue Ihwwmique ZntenatioMte, h k ,vel. I, pp. 482493.Bmellee, Goemaere, 1913.
KLWMBIZIJR, E.W.

x

r"1

BIBLIOGRAPHY
S ~ ~ ~ M MF.
P Die
,

Abhaengigkeit der Wechseucurse m Ziwgeschaef-

ten und die Marktzinsdiflwm. Schmollera Jahrbuch, 1919, pp. 339385. Miinchen, Leipzig, Duncker und Humblot, 1919.
S m m , H ~ R R.Y Th-5 Impatisnce T b r y of Inter&. American
Economic Review, Vol. 11, No. 4, December, 1912, pp. 834-851.
SMITH,J. G. M w e m e n t of Time Vduation. AmericanEconomic
Review, Vol. XVIII, June, 1928, pp. 227-247.
S m m , C m . The Influence of the Interest Rate on the Bueiness
Cycle. AmericanEconomic Review, Vol. XV, No. 4, December,
1925, pp. 684-699.
S m m , CARL.Interest R a t @ and the Business Cycle. American Economic Review, Vol. XVI, No. 3, September, 1926, pp. 45142.
Tables Showing: Rates on United States Treasury Certificate Issued
During " 8 1 ; Rates of Discozont Charged by th Bank of England and by the Open Market in London; Bank Rates of Discount
Charged in W t e d Money Markets; Changes in Central Bank
Rates in Won2 Monetary Centers. Review of Economic Statisties,
March, 1921, pp. 70, 73.
Wmmmw, R ~ B.
Y Effect of F d h g Prices and Interest on Foreign
Loons and on War Debts. The Annalist, Jmuary 4,1929, pp. 5 7 .
WICKSLILL,
K m . Influence of the Rate of Interat on Pricee. Economic Journal, Vol. XVII, June, 1907, pp. 213-220.
Yomo, ALLYN A. As AnalyBi8 of Bank Statktb for the United
Statea; 111 RegionaZ Differences: 1901-1914. &view of Economic
Statistics, Vol. VII, No. 2,1905, pp. 86104.

INDEX
A

B

Abetinence, E cost, 178-179,486 Bank renerves and interest rates,
487; interest taking justified
by, 180; not diacountable, 634- Betterments, repairs and renew5 3 9 ; (waiting), by capitalist,
als, options of making, 194-200.
180; (waiting) not a cost, 634. Bloch, Ivan, cited, 375.
511; (waiting) theory of inter- Bohm-Bawerk, E. von, x; agio
est, 180, 178-179,
486$87, 534theory, 473ff.;cited, 313, 45273;
541.
discussed, 47346; excludes
Adjustment, individual, of impaland from capital, 459; explatience (Willingness), interest
nation of technical superiority,
475-476;quoted, 47&, 478,479rate (Market), and investment
480,481,482-483;
shows fallacy
(Opportunity), 272275; by investment without loans, 2868.; in socialists’ condemnation of
by loam and investment, 269f.
intereat, 51 ; technical superiority of present goods, 471-485.
Agio theory, of interest, 473.
Bonds, coin and currency, interAllied debt aettlemente, 314n.
& rates on, 4 0 1 4 3 ; gold and
Alternative uses of wealth (cap
rupee, interest on, 433-407;
ital), 125-149, 1.50-177, 178-306.
value of, determined by (1)
Agriculture, seasonal changm in,
expected benefits, (2) interest
atrect interest rates,
Annuities and the waiting theory
rate, 17.
Bond yields and pricechanges
of interest, 538539.
(Great Britain) correlated, 416Appreciation and depreciation,
442; (United States) correlated,
effect of, on interest rates, x,
417.442.
364,493-497; foreaight offsets,
3739; measurea tq offset, 38- Borrower, a seller, 113.
Borrowere, not represented by
39.
poor, 112; types of, 108-111.
humptione of finst approximaBorrowing and lending, changes
tion ateted, 101-102.
ahape .of incame s
rteam, 113;
Auepita und Lieben, cited, W .
determined by personal &
Australia, interest rata in, 390.
ties, income &ream and interAverage, yearly, rata of interest,
est rate, %Of.; equivalent to
d l b g and buying, 112; inAyres, L. P.,cited, 489; rehtion
come (not capital) trsnsfefied
between gold reeer~eea d inby, 94; limita of, for i
n
t
e
d &ea, 448.

446160.

394-398.

lxm426.

c5

1

determined, 2
5
5
2
.5
6
; relati01
of interest rate to, 116-117.
Borrowing and lending (sellinl
andbuying), equalizes differ
ent rates of impatience, 104
106; modifies income streams
128.

Bortkiewicz, L. von, cited, 483
Brown, H. G., argument of, an.
swered, 464-487; cited, 182
193; cost fixes value, hence in.
terest rate, 463-464; criticim
by, on land as capital, 4
6
0
; fixing rate of return, fix- intered
rate, 182.
Brown, Mary W.,cited, 378.
Burgess, W. Randolph, relation
of interest rates and bank rebrves, 445.
Business loans,classified, 3 6 0 - 3 6 6 ,
Business loans m d personal
loans, contrasted, 365-369.
Buying power of money. See
Price level.
Buying and selling. See Borrowing and lending.
C
California, incomes andinterest
rates in, 387, 388, 389.
Cannan, Edwin, cited. 333.
Capital, discounted future income, 12; andhuman beings,
12; includes Iand and produced goods, 458-459; separated from income by bookkeeping principles, 25; loanable, depends on expected
income, not on amount of capital value, 93-94; nature of, 12;
produced by income, not the
reverse, 61; relatione of, to income, 3-35; as a stock of
wealth, 457.
Capital concept, epitamised, 1%
15.

Capital depletions or gains, determined by impatience rates,
335-338.

Capital gains not income, 25-26,

455.

Capital supply and demand, not
the cawe of interest, 32; relation of, to interest, 454.
Capital value, dected by inventions, 343-345; capitalized income, 455; contrasted with
capital wealth, 91-92; derived
from future income, 14-15, 331332; determined by income,
12,457; interest rates not determined by, 93-94; psychic,
332.

Capital wealth, distinguished
from capital value, 91-92; material source of all income, 332;
interest rates not determined
by, 93-94.
Capitalist, abstinence (waiting)
of, 180.
Care for dependents, effect on
impatience, 85-89,
Carver, T. N., cited, I l l , 115,
217; savings withoutinterest
possible, 190.
Cassel, Gustav, cited, 203, 460.
Catastrophes, effect of, on interest rates, 391-393.
China, interest rates in, 378, 380.
381.

Zhoice, among optional uses of
capital, 125-149,
150-177,
17%
205.

l a r k , J. B., on land and other
durable egents, 459
Xothing, price of, aftected by interest rate, 328-328.
2oin bonds, 401-402.
>olorado, interest rates in, 388.
2ommercial paper, interest r a w

on, 445446.

2ommittee on Recent Economio
Changes, quoted, 363.

Commodity intereat, 164-165,179- Cost theory of interest, 57.
182, lso-lsa.
Cost of the w e of a good, 8-9.
Comparative advantage principle, Cost of waiting. See Waiting,
176.
&o Abstinence.
Camparative advantages, method Cnun, W. L., on seamnd variaof, gives maximum present
tions in inter& rates, 8%.
Cmency, depreciation of. See
worth, 152177.
Computation of real rate from
Appreciation and depreciation,
money rate of interest, 526.
dso Price level.
Conditions determining intereet Ccrrency bonds, 401-402.
rate,summary of, 226f.; tabular acheme, 228.
D
Consumption, the end of producDay, Clive, cited, 336; on intertion, 454.
e& rates in Java, 375.
Consumption goods, relation of,
Davenport, H.J., cited, 34, 467;
to interest rate, 453-454.
criticim by,considered, 453Consumption loan. See Personal
454.
loan.
Continuous reckoning of interest, Del Mar, Alexander, theory of
intereat of, 165.
25-20.
Contractual interest.See Explicit Depeciation, appreciation and
Eterest rates, 493-497; (and
interest.
appreciation) of money, effect
Correlation coe5cients, bond
on intereat rates, 36-44, 47;
yields and price changea, 417420; interest ratesand price
foreaight offsets, 3739; meerrurea to &@et,33-39.
changes, 411; obtained by lagDiscoveries, effeds of, similar
ging pricechangea, 418; with
to inventions, 347. See also
price lag distributed, 419-429.
Invention.
Cost, delined, 157; future, alone
enters into valuation, 16; cap M r i b u t e d lag, definition of,
41940, 42on; applied to initalised, 467; a negative income
terest rates and price changes,
e
c
t
s value
item, 15; paet, d
416-429.
through supply, 18; through
income, 467; relation of to in- Distribution, effect on, of thrift,
333338; functional, misconterest, 4 8 5 - 4 8 7 ; return over,
ceived by classicaleoonomiats,
150-188.&e dso Return over
3 3 3 3 3 3 ; functional, relation to
C&.
intereet, 331-333;pemnal, of
costn, 88 dissdvantagw, 154f.
drat importance, 333-338; perCost of living, 6; ever present in
eonal, relation of, to intern&,
interest, 180-181; the money
333338; personal, treatment
measure of real income, 6-7; a
of, by Pareto, King, Stamp,
negative item, 7.
Mitchell, Rae and others, 334;
Cost of production, leea than
theory of, in relation to intervalue of produat, 49-52; pwt
est theory, 336340; of wealth,
and
future,
contrasted, 461dect of, on intemteq
462 ; relation of, to value and
378-381, 384381.
160-487.

intelwt.

INDEX
Discounting, fundamental, 14.
Dividends, enjoyment, 5.
Dividend yields, affected by in.
ventiom, 352353.
Durable goods, income from, a p
proximates cost of servicecI
they render, 8.
Durability of instruments, relation of, to interest rates, 374,
Dwellings,prices of, affected by
interest rates, 325-326.
Dublin, Louis I., cited, 34.
DuBrul, E. F., money fluctuations in accounting, 44.
Dutch, characteristics of, i d u ence interest rates, 374~7.

type of income stream from,

130-139.
Farr, Wm., cited, 34.
Fashion, effect of, on impatience,
87-89; on saving and spending,
378.
Federal Reserve System, influence of, on interest rates, 449450.
Fetter, F. A,, capitalization theory of interest, 468; cited, 33,
467; criticisms by, 454455, 456458.
Filene, Edward A., cited, 215.
First approximation, stated, 99,
101-104.

Flux, A. W.,cited, 460, 467.
Food, scarcity of, effect of, on
E
interest, 381; value of and inEmnomica, businw,and home
terest rates, 5-9,76.
Forced labor and slavery, result
economics, 10.
Edie, L. D.,489.
from poverty, 335337.
England, interestrates in, 374, Ford, Henly, views of, on spending and saving, 114.
389-391, 520, 527;
interestand
Foresight,effect on impatience,
prices in, 520, 527.
81-82; lack of, causa maladEnglish, characteristics of, influence interest rates, 374J7., 378. justment of interest rate to
prices, 493-497; nations noted
Enjoymentandouter events, 6.
for, 374; offsets appreciation
Enjoyment income. See Income,
of money, 38-39.
enjoyment.
Europe a borrower since the Forestry, type of income stream
from, 130-139.
World War, 386; comparison
of, with U. S. as tu wealth disFormula method, inexact, 315;
shortcomings indicated, 317tribution, 384-391 ; interest
321; stating first approximarates in, contrasted with U. S.,
tion, 288-301; second approxi386.
mation, 302315.
Explicit (contract) interest, 8,
209,382.See &o Interest, mar- France, interest rates and prices,
374, 523,
628.
ket rate of.
Exploitationtheory of interest, bench, characteristica of, i d u enoe interest rates, 3748.
49-52.
b c t i o n a l distribution. See DisF
tribution, functional.
Farmers, fluctuations in income ?un&, loanable, 451.
market, 453.164.
streams of, 1308.
Farming, WWMI
changes in, ?urnitwe, &ect of rate of interest on prim of, 8.
and intereat rates, 3944%;

run&

I

INDEX
Q

I

Geometric method, shortcomings Impatience, d8em with Merent
of, 260-262, 287; &owing first
individuals, 96; of first imapproximation, 231-262; 8ecportance, 8 0 ; in interest theond approximation, 263-287.
ory, 61-98; made uniform by
trading incomes, 231; maniGeorge,Henry, theory of interfested in tmding with manest of, 186.
kind, 181; endopportunities
Germans,characteristics of, into invest, codict, 29; relation
fluence interest rates, 374.
of, to investment opportunity,
Germany, interest rates and
176-177; rijle of, inpersonal
prices in, 374,415, 522, 538.
365-367;
and business
loans,
Gibson, A. H.,bondyields in
socisl, determines interest rate,
GreatBritain, 417n.
120.121; substitution of, for
GitTen, R.,cited, 391.
Gloeckner, G. A,, money fluctuaagioand time preference, viii.
tionsandaccounting, 44.
Impatience principles, 77, 495497; in businem loans, 360;
Gold. See Pricelevel, also, A p
dominant in personal loans,
preciation andDepreciation.
360; expressedbyequations,
Gold
bonds,
interest rate on,
290-296; generalized form of,
comparedwith
rupee bonde,
in equations, 293-298.
403-407.
Impatience schedules, morecornGonner, E. C. K., cited, 340.
plex than priceschedulea, 94Graphio method. &e Geometric
95; achematized for Merent
method.
typea of income, 95-97.
Great Britain, intemt rates and
Impatience, degree (rate)of, deprices
in.
See England
and
pends on, the individual and.
English.
his income s t r e a m , 8667, 81Greenbacks. See Money,paper.
89 ; foresight, 81-83; self-control, 8 3 ; habit, 83-84; life expectancy, 84-85; care of deH
pendentsr, E-87; fashion, 878 9 ; adjurrted to interest rate
Habit, efiect of, on impatience,
through borrowing, 250-251
83-84; relation of, to saving
(charted); adjusted to interandspending, 337-338.
eat rate through lending, 250Habit of luxury, 81, 83-84, 337251 (charted); affectedbyin338.
vention, 341342; affected by
Holland, interest rates in, 374loans, 183, 231; cause of pov276.
erty andriches, 336-338; d e
Hurlbert, H.B.,on Korea, 382.
pen& on four characteristics
Hypotheses of Firat Approximaof income streamsize, 72-73;
tion, QB, 101-102.
time shape, 73-75, 144; comHypothesea of Second Approxipoation, 7676; risk, 76-80;
mation, 1&128.
depends on income stream,
Hypotheses of Third Approxima123, 148; determined by intertion. mm.

(5551

INDEX
est rate, 120; determine
spending or saving, 335-338
Were for eaoh individual a n 1
each income, 96-97; preferencl
for present over future income
99; individual, adjueted to in
&rest rate and opportunity
2D-275; individual, depend
on income stream, 249f.;indi
vidual, depends on persona
qualities, Z49f.; measured, 62;
relative to income stream
equatiom for, 290; relative t c
interest rate, equations for
291; represented by a Will.
ingnem line, 238-240, ahom or
chart, 239.
Impatience, rates of, equalized
through borrowing and lending, 104-106,117-119; high d e
gree (rate)of, accompanied by
high intereat, borrowing, spendh g , and flimsy instruments,
373; identical with interest
rate, 104-1013; low rate of,80companied by interest, lending,
saving, durable inetrumenta,
373.
Impatience and Investment opportunity, 2 8 0 - 2 8 2 ,
Impatience and opportunity,
combined in my theory, i x ;
contrasted, 183; determines institutions and intereet rate,
4m-491.

Implicit intereat, 8, 61, 117, 209,

382.
Improvidence, loans to ofiset,
357.
Incrementa in value are not income, 26-28.
Iwo, a eubstitute for &go,
1L.
Interactions, described, 20-21.
Income, annuity, assuming wait
ing a c&, 6 3 6 5 3 8 ; from tree,
aesuming waiting a cost, 6%-

636; all, produced from capital
wealth, 332; all, ie (1) rent,
(2) interest, 32-34;all, subject
to capitalization, 68; assumed
to flow spontaneously, 102;
basis of capital concept, 3; and
capital separated by bookkeeping principles, 25; derived
from capital goods, capital
value derived from income, 1 4
16; early enjoyment, preferred
to deferred enjoyment, 03-85;
excludes capital gain, 332; not
8 flow of wealth, 457; from
land is (1) rent, (2) interest,
33; human enjoyment, 5 ; in
economics, 13; identical with
intereat, 332; and capital gain,
332; increeeed by invention,
354-355; individual, adjusted
to interest rate, 253ff.; the
most fundamental economic
concept, 3, 42; net, equals enjoyment lees labor pain, 22-23;
net, of a corporation ie zero,
2 3 ; the important factor, 9194; objective or real, 5; opportunity to i n c r e a future, 103;
and &m,1%~; produced
by capital goods and men, 19;
psychic, measured, 4 5 3 , 456457; real, condsta of outer
events, which give inner enjoyments, 6 8 ; real, measured
by cost of goods consumed, 4
10; aa 8 rate per cent on its
capitdiced value, 5 8 ; relations
of, to capital, 3-35; a aeries of
events, 3; subjective or psychic, 3, 4, 5; supply and demand of, explaina interest rate,
464; total, equals enjoyment
income, 23-24; variations in,
cam loan olaeeifioation, 380-

366.
noome concept, basic, ix; epitomized, 8-12;reateted, 468.

INDEX
Inwme, enjoyment, cannot be
messured directly, 6; determines our choice of present,
or of future goods and incume,
6 3 ; determines price paid to
manufacturer, to jobber, wholesaler, and retailer, 64-65; the
end of production loana, 453454; involvee no interest,
326jf.; one of three stages of
income, 7; ultimate fact, 331332; and labor pain, the only
uncancelled items of income
and outgo, 20-21.
Income, money, and enjoyment,
contrasted, 457-458; and mal,
differentiated, 10-11; includea
all money intended for spending, 10; the measure of enjoyment income, 453.
Income stream, afTecta borrowing and lending, 2508.;d e c k
impatience, 67, 92-94, 2946.;
altered by loans, 106-112; a s
mmed to Bow spontaneously,
102; changed to any desired
shape byborrowing and lending (eelling and buying), 113;
depicted, 2931; deet of, on
impatience, and interest, 378381 ; &
e& of changing, upon
impatience, 73-75;f i x e d , yields
zero interest, 184-191; 6xity of,
illustrated, 185-191; choice of,
148; includea all services, 454;
changea &own on charts, 107111 ; modified by bornwing
and lending (selling and buying), 102"8; modified by investment opportunity, la7f.;
modified through vsrying we
of labor,
options
among, 1ZSf.; optional, choice
of by individual, determined
by interest rate, 1436.; o p
t i o d , choice
of
by society,
determinea intareat rate, 143f.;

X&=;

plus and minua items of, must
balance, 122,123,149;and productivity, 489; relation of, to
capital and intereat, 454; &lation of, to internet, expremed
by equatione, 2 9 0 ; seesonal
changea in, vary intemt rates,
384; shape of, variable at will,
135f.; &e of, determines
ohoice of urn, 1338.;time
shape of, shown by charts, 2930; variations in, came inter& rates to vary, 299-301,
302-315; variations in, offers
investment opportunities, 1%149,

Income streams, distortion of, by
invention, 341-347; increasing,
examplea of, in United States,
3 8 4 3 8 8 ; optional, compared,
1306.; rising, mean high interest rates, 384-391; time shape
of, most important, 13Ofl.
Income value, 457.
Index Numbem. See Price index,
wholesale.
India, interest rates in, 375,524;
and prices in,
interestrates
wholesale, 524, 529.
indians, characteristics of, make
high interest rates, 375376.
Ingo, a substitute for outgo, 1%.
Institutions, d e & of, on interest,, 487-491; existence of, 80.
cords with impatience and
opportunity, 489-491.
h r a n c e company inveatmenta,

389390.

Interactions (intermediate sewicee),
Instruments, durability of, and
interest r a t a , 374.
Intereat, accrued, not i n m e
u n t i l realired and spent, 2 6 ; a
cornpeneation for waiting, 5 2 ;
as a cost, fallacy of, S7-58;
depends upon value

3!%3!28.

INDEX
tivity,
not
physical produb
steady, variable, high, and low
tivity, “57; determined bJ
rates of, 501; theoretical rate
marginal rather than averagc
of, fixed by six principles,
growth, 165; early lawaanc
494ff.;viem of,by socialists,
practices concerning, 48; ex.
49-52; cero or negative rates
ploitetion theory of, 43-52;a
of, discussed, 40-41, 67, 183,
a fine, 52-53; futility of pro.
185-192,282-286, 311, 415-416.
hibitione of, 52-53, 116-117; Interest, rate of, 3; adjusted to
high rates of, in China, due tc
clear the market, 121; affected
poverty, 378; implicit in sale
by productivity, 182; affected
contmct, 117; includes all inby regard for posterity, 376;
Btrected by rid, 381383; afcome, 331-332; ineradicable!
116-117; loan, involves risk
fected by scarcity of food,381 ;
207-208; many difTerentratee
atrected by time shape of income stream, 383-387; affected
of, 206-210, 2 9 9 ; market rate
of, adjusts impatience rate,
by uncertainty of life, 216-217;
through borrowing, 250-261
affects repairs and investments,
(charted); market rate of, ad2 0 2 - 2 0 4 ; affects wages, 328-330;
on Allied debts, method of
justs impatience rate, through
computing, 314n; as an averlending, 251 (charted); market
rate of, atlects borrowing and
age of individual degrees of
lending, 250; market rate of,
time preference, 9 9 ; on busibrought to equilibrium, 256new loans based on enjoyment
258; market rate of, influenced
income, 359360; cannot be determined by impatience (time
by each individual, 256fl.;
preference) rates alone, 124;
market rate of, represented by
a c h g e in,shifts maximum
a line, 23ft238; shown on
chart, 2 3 7 ; money and real,
preaent value of option, 1418.;
changes choice of income
36-44, 407-416, 416-442;
money
and real, divergence due to
atream
(options),
1428.;
lack of foresight, 43-44; naive
changes in, change capital
value, 91-93; compared with
productivity theories of, 53-57;
changes in price level, 408-451;
not a part but the wbole of
contrasted with return over
income, 5 8 ; as a price, i l l w
coat, 499; defined, 13; depends
trated, 89; in primitive codes,
on individual impatience rates,
48-49; productivity an element
144ff.;depends in part on inbutnot the o d y one, 53-54;
terest rate, 144; depends on
pure mte of, on loam devoid
supply snd demand of tbis
of rislr, 34-36; the ratio of rent
year’s real income relative to
to value of the rent bearer,
next year’s income, 48; deter82 ; real, computed from money
mination of, 119-124;by four
rate, 520; real, more variable,
principl~, 122-124; by imp&because of “money illusion,”
tience and opportunity, 372;
411416; real, negative, 416by investment opportunity,
416; relation of, to rent, 331impatience, and exchange, 149;
332; rent, profita and wagea,
in loan market, 98 : by society’s
not mutually exclusive, 32-34;

INDEX
choice of income etream~
143ff.; determinw choice of in.
come atream, 143fJ.; degree oi
impatience, 120; range of
choice of options, 170-174; duc
to “average late of growth oi
animals and plants,” 185; during decline of Rome, 378377;
examples ofwide fluctustione,
44; exprewed in basic stsndard, 43; fixed for the individual, 119; high on small l o w ,
213-215; individual, adjto impatience and opportmty,
272-275; influence on prices of
services, 32B3tt8; link between
income and capital, 13; masimum present value, maginal
return over cost, in formulas,
514615; maximum present
value, marginal return over
cost, by geometric method,
518; may be gem or negative,
40.11, 67,183,185-192, 282286,
311,
415-416;
measured in
goods and money, 36-44,45-46;
measured in two diverging
standards, 39; the most pervasive price, 33; must clear the
market, 122,149; not explained
a8 price of money, 46-47; not
involved in enjoyment income
or labor pain, 3X3-328; not
reasoning in circle, 144147;
paradox of, 144-149; on personal loam, accounted for, 356);
premium on m n t over future goods, 36; the price between present and future
goode, 81; and price level, 39%
41, 493497; the price of
money, 13; problem of, in
geometric tern, 231-287; problem merely stated not solved
by supply and demand, 46; in
relation to impatience rate,
ec~wtiomfar, A
!H
; relation of,

I

to prices, 398451, 493-497;relation of, to eupply and demand depieted, aaOff.; relative
to standard of measurement,
41; and saving, 286.287; on
short loam, 360383; steadied
by stable income stzeam, 300;
k
r
m
S Of goods, 4;V f U k
with income, 299-301, 302315;
varies with eeaeonal chsngee in
income, 394398.
Interest, lata of, &ected by
invention, 342-347; afected by
risk, 207-227; correlated with
price Chsngerr, 4
2
9
4
3
8
; dispersed by invention, 342-347;
fluctuatiom in, self-corrective,
202-205; France, 523, 528; Germany, 5.24528; on gold (coin)
and paper and silver bonds,
401-407; Great Britain, 520,
527; India, 524,529; influenced
by Federal Reserve System,
449-450; Japan, 525, 530;
money and real, normally
identical, 43; and price
changes, 399-851, 520-533; and
price indexes correlated, 429438; and price level, theoretical relation of, 412414; raised
by catastrophes, 391; relation

of, to bank reservee, 4
4
4
8
5
0
;

relation of, to busineaa and
prices, 4
4
3
4
4
4
;relation of, to
income, 451; to invention, 342347; short term, correlated
with price changes, 4
2
3
4
2
9
;
United States, 521, 527; yearly
average, 520525.
nterest problem, ststed in
mathematical formulas, 288301, 302-315.

nterest theory, complete, indudes price theory and all
other ecobomic theories, 131n;
mu& include wage theory, 331;
of W h a d Psrebo, WXL-

INDEX
trasted with the author’s, 619
Interest, theory of, appliee to all
loans, 358371; fundamental it
distribution, 326-340; funda.
mental in price theory, %?ti#.;
a part of price theory, 61, 6 8 ;
in personal loam, 356359.
Intermediate eervicea See. Interactions.
Invention, Bect of, on impatience, 341342; on income
etreams, 341-343; on intereat
rates,342347; on capital value,
343-345; on dividends, 352363;
on interest rate, 5 0 2 6 0 3 ; 6nal
efiect of, lowens intererst rate,
345347; first deet of, raiaes
interest rate, 343-346; importance of, to progress,
Investing, buying future incomes,
118116; compared with spending, 118116; a form of spending, 114; spendmg deferred, 9;
nnd spending, the problem of

364365.

interest, 29-30,
Investment opportunity, concept
of, agreeswithcurrentusage,
168; c o n t d with loan, 498;
definition of, 161, 164, 498; effects of, on interest, shown by
equations, 302-315;eligible and
ineligible options, 151; for all
society, 5 0 0 - 5 0 3 ; and impatience, 280-282; individual, adjusted to impatience and inter&, 272-275; ally fix internat
rate, 185.194; meaning of,
178ff.
; meam substituting one
income stream for another,
158; nature of, 4974B; objective element in intereat, 62,
181-183; (option) ahown by a
line, mff.
; the productivity
element, 182; relation of, to
impatience, 176.177; to 89 op
tion, 161; tu productivity of
capital, 1608.;mbtituted for

productivity, ix; trading with
environment, 181.
Inveetmentopportunities,introduce a new variable in interest
problem, 143-149.
Investment opportunity principles, 288; income &mame differing in siseand time ehape,
136-149; maximum present
worth, 148; d s e d , 176.
Ireland, intereat rates in, 380.

J
Java, interest rates in, 376.
Japan, interest ratm andprices
in, 526, 630.
Jews, characteristics of, affect interest rata, 374, m-377.

K
Karaten, Mr. and Mra IC. G.,
cited, 443%.
Kemmerer, E.W.,cited, 381.
King, W. I., on W b u t i o n , 334.
Korea, interest r
a
b in, 383.

L
Labor, not eame as discounted
value of its product, 179; op-

tiom to we, 200.202.

hborer todaydoes no waiting,
180.
iborers, by waiting become
capitslista,
; wagea of,
and interest latea, 328880.
kbor cost, 16-16, 178-179. See
ob0

Labor pain.

hbor pain, 16-16,M25,178-179,
191-192; difticut to measure,

8nd enjoyment income
only uncanalled item, 2081;
24;

uw481.

i n v o l v ~no intemt, 8288.
a h a* M e*

INDEX
Land and artificial capital contraated, 4594%; as capital,
458-459.

Marginal time preference must
equal marginal return
over
cost, 182.
Marginal utility, 62,
62%.
See
Marginal desirability.
Market eqdibrium, 255262,275287.
Market line, adjusted to opportunity line, 260fj.; compared to
willingnessline, 240-246.
Market principles,cover supply
and demand of incomes, 495;
generalized form of, in equations, 296-297; shown by e q w
tions, 291-292.
Marshall, Alfred, cited, 252.
Mathematics, use of, in text, ix,

Landry, Adolphe, cited, 73,471.
Lawrence, J. S., cited, 375.
Laws, relating to interest, 214.
Lender, a buyer, 113.
Lenders, not represented by rich,
112; types of, 108-111.
Lending. See Borrowing and
lending.
Life expectancy, effect on impatience,
Loans, change shape of income
stresm, 106-112; long, reasons
for, 363-369; a means of equalking impatience rates, 104-106;
money, represent income trans231-322.
fers, 108; present worth of, Mathematical method, application of, to interest problem,
equal repayments, 123,
149;
productive, present opportu231-262,263-287,288-301,
302315, 318322; value of ineconities to vary income, 112;
public, both conmmption and
nomics, ix. See d o Formula
productive, 369371; remm
m e t h oadnGde o m e t r i c
for and effects of, 371; relation
method.
of, to impatience rate, 231.
Maximum desirability, principle
Loanable capital. See Capital,
of, 148; influence on interest
rate, 118,122; shown by geoloanable.
Loan contract, a sale, 112-113.
metric method, 517.
Loan interest. See Interest, loan. Maximum present value, margiLoan market, evolves a common
nal return over cost, interest
rate, in formulae, 514-515; by
interest rate, 98, 99, 104-112.
geometric method, 516; prinLuxury, habit of. See Habit.
ciple, 175.
Maximum present worth princiM
ple, restatement of, 152-155,
159.
Marginal deairability, determines
choice of income atream, 13Ofl.; Menger, Karl, cited, 216.
relation of, t o interest, 01-62. Michigan, interest rata in, 389.
Marginal return over cost, maxi- Mining, type of income stream
from, 130-139; communities,
mum present value, and interinterest rates in, 387-388.
est rates in formulas, 514-515;
shown by geometric method, Misfortune, loans to offset, 356.
618; must equal marginal time Mitchell,Wesley c., cited, 322,
preference, 182.
Marginal rate of return over cost Mohlberg, Dr. W., money fluctuations and accounting, 44.
Wual to interest rate, 169.

84-85.

439.

INDEX
Money, buying powerof,
and
interest rates, 493-4997; paper
interest rates in terms of, 44
401-402, 415.
Money income. See Income,
money.
Money instability often afectf
inkre& rates more than any
other idhence, 451.
Money interest. See Interest,
money.
Money loans. See Loans, money.
Money rate of interest. See Interest, money rate of.
Monetsnr 8tandard. See Price
level.
Mora (delay),interest justified
by, 53.
Moses, Bernard, cited, 400.

N
National Bureau of Economic
Research, studies of, on income, 334, 343, 350.
N e t d interest. See Productivity theory of interest.
Nature, slowness of, explains interest, 165.
Negative interest (and zero), 4041, 07, 183, 185-192, 2”%,
311, 416-416.
Negroes, oharacteriatica of, make
for high interest ratea, 374,375,
376.
Net income. See Income, net.
Nevada, interegt rates in, 288,

339.

Nicholson, J. Shield, cited,
Norton, J. P.,cited,

446.

34.

0
Objective inuome. &e Income,
objective.
Ophelimity, a n . Bse Marginal

utility.

Opportunity, due to different
urn of goods and services,
125-127; investment. See Investment opportunity; combined with impatience in my
theory, i x ; contrasted with
impatience, 183; and impatience, determine institutiona
andinterest rates, 489-491; to
increase future income by sacrificing present income, 103.
Opportunities, to make repairs,
renewals, bettermenb, 194200;
to

use, 200-202.

Opportunity line, meaning of,
277ff.; and market line, 2868.;
and willingness line, 2688.
Opportunity lines, 264ff.
Opportunity principles, 495-497;
dominant in bueineas loam,
360; operation of, on values
and costa, 461.
Option, definition of, 151; (Investment opportunity) Shown
by a line, Wfl.
Options, among various usea of
income, 1288.; choice of, sftecta income stream, 150;
choice of, depends upon interest rate, 132ff.;Merent types
of, 184-186; eligible and ineligible, 161 ; introduce a new
variable in interest problem,
143-149.
3ptional income streams. See Income streams, optional.
kchard, an example of capital
value, 6467, 460-462.
3utoome, a substitute for income, ISn.
?&go, negative item of income,
1978.

P
?algrave, R.H.I., aited, 398.

?aniea, effeot of, on interest rate,

449.

INDEX
Paper money. See Money, paper.
Pareto, V., cited, 8 9 , 8 0 ; eontribution of, to interest theory,
518-519; on distribution, 334;
tribute to, 518.
Pawnshops (brokers), business
of, 357; interest rates charged
by, 213-215, 379-380, 391-392.
Pearson, Karl, cited, 431.
Personal chamterietics, affect
borrowing and lending, 26011.;
affect impatience, 249f.; deet
impatienceand interest, 374$31; effect of, on impatience,
81-89; summarized, 89-91.
Personal distribution. See Dktribution, personal.
Personal loam, c l d e d , 357359; defined, 366.
Persons, Warren M.,cited, 431.
Plehn, Carl C., on California,

307.

Poor as lenders, 379.gee Poverty.
Posterity, regard for, and interest
rates, 85-87,374377,3!?8.
Poverty, effect of, on impatience,
72-73; makesforhighdegree
of impatience, 73; relation of,
to impatience rate, 335336; to
interest rates, 375381 ; t o
waste,
Premium, interest as. See Agio.
Prices, relation of, to inter&
rates, &Sf.,209, 399-451, 520.

339-340.

533.

Price changes, &e&of, on interest, x, 399-451,680-533; France,
8%; Germmy, 528; GWt
Britain, 527; India, 529; Japan,
5 3 0 ; and short term interest
mtas correlated, 425-429;
United States, 527.
Price index, wholeeale, in France,
523; in Germany, 522; in
Great Britain, 530; m India,
624; in Japan, S26; in United

states, 621.

Price indexesand interest rates
correlated, 429438.
Pricelevel,changesin,and
interest rates, 399.451, 4 9 3 - 4 9 7 3
theoretical relation of, 412414;
rate of change in, compared
with interest rates, 40&451,520533

Price of services, sfIected by interest rate, 326-328.
Production loans, made for consumption, 4.54. See also Busineea loans.
Productivity, physical and value,
54-50; increase in, effect of, on
interest rate, 4
6
2
4
6
3
; increase
infinallylowers interest rate,
462; first raisee interest rate,
463; incnmes present value of
income, 469; one caw of interest, 470-473; physical, cannot determine intemt, 463;
relation of increase in, upon
value return and inkrest rates,
56-57; relation of, to roundabout (longer) processes, 4754 8 5 ; and time preference both
essential to determine interest,
470.
Productivity of capital, criticisms
of term, 15of.; expmsed in
rate of return over cost, 176.
Productivity theory of interest,
53-57, 125-149,1W177,178-205.
Profits, conaidered as, (1) rent,
(2) interest, 33.
Property-right, valuation of, involves interat. See Implicit
intereat.
Feudo-mte of
See Interest, money late of.
Psychic
income.
See Income,

intererrt.

Pmyp.

PubllcImprovements,loana

370.
khaaing power of

Price level.

1

for,

money. &e

INDEX
159165; notthe eame &a interest rate, 158; principle of,
Rae, John, ix; cited, 3, 81, 199
158-159;relation to investment
203,385; inventions treated by
opportunity, 155-158.
345; on American Indians, 376
Return over cost, rate of, applion Indian life, 382; on i n t e w
cation of, 155ff.;
hlances presrate in Holland, 374-375; 01
ent worth of costs and returns,
lack of foresight of Chinese
168-189;contrasted with inter378; on interest in Rome, 376.
est rate, 499; defined, 155; de377; on theory of distribution
pends on use of capital, 183;
334; uncertainty of life anc
described, 155; expresses prodemand for present goods, 8 5 ;
ductivity side of interest thevagaries of fashion, 88.
ory, 176; interest determining,
Railways, improvement of, and
155-179;shorn in charts, 187interest rates, 204.
188.
Range of choice, dependent on Returns (yields), aa advantagep,
interest rate, 170-174.
154ff.
Rate of growth, average, aa re- Rich as borrowers, 379.
lated to interest rate, 165.
Risk, absence of a m e d , 99Rate of interest. See Interest,
148, 148-205; of death, affects
rate of.
interest rate,215218; eiTect of,
Rate of return over cost. See Reon accumulation of wealth,
turn over cost, rate of.
336-337; on impatience, 76-80,
Real income. See Income, real.
224-225;on interest rates, 207Real rate of interest. See Inter227, 381-383; on investment
est, real rate of.
opportunity, 222-224; on market principles, 225-226; on inReal wages. See Wages, real.
come stream, 217-218; interest
Regard for posterity and imparates on d e loam lowered by,
tience. See Posterity.
Renewals, repaim and better382383; present in all loans,
207-227; of m a l l loans, 213Dents, option for making, 194215; vitiates accuracy of form200.
ula method for interest, 316Rent, interest, profits, wages, not
mutually exclusive, 32-34; r e
321.
tobinson Crusoe invested labor,
lation of, to interest, 331-332.
received return over coet (inRepairs, renewals, bettermente,
terest), 180-181.
options of making, 194-200.
Return, defiued, 157.
lomans, intereet-takinp among
early, 48.
Return over cost, lsOf.; concept
Lome, interest forbidden in
of, 155-158;determinee investearly, 48; interest rate in, 375
ment, 157-161; followslaw of
decreasing returns, 1sOff.; in
377.
Roundabout process,” Biihnformulas, 513; by geometric
Bawerk’s, 471-485.
method, 514; marginal rate of,
hpee bonde, intereat rete on,
159-177; more fundamental
than interest rate, 499; must
compared with gold bond, 403equal or exceed intereat rate,
407.

R

INDEX
Ruasell Sage Foundation, studies
of small loans by, 214.
Russia, rate of interest in, 375.
Russians, characteristics of, make
for high interest rates, 376.

s
Savings, not income, 455; relation of, t o inkrest, 286-287.
Schmalenbach, E.,moneyfluctuations and accounting, 44.
Schmidt, Dr. F., money fluctuations and accounting, 44.
Schumpeter, Joseph, cited, 489.
Scotch, characteristics of, lower
interest rates, 374, 377.
Scotland, interest rates in, 374.
Sewer, H.R.,cited, 467; criticisms by, 459, 471-472; viewa
of, on increased productivity
and interest rate, 462; on land
aa capital, 4
60; on physical and
value productivity, 461-462.
Semns, changes in, change income streams and interest
rates, 394-398.
Second approximation, stated,
125-129.
Secular trends, elimination of,
from correlations, 431-438.
Self-control, effect of, on impatience, 83.
Seligman, E. R. A., on interest in
early Rome, 377.
Selling. See Buying and selling;
Borrowing and lending.
Services, criticism of, as income,
458; enjoyable, measurability
of, 956-457; as tree income, 8.
Short loam, ewnce of, 363.
Slavery and forced tabor W l t
from poverty, 335-337.
Smith, Edgar L., cited, 220.
Snyder, Carl,cited, 439.
&cialists, viem of, on ink&,
49-62.

15

Speculation reduces riaka, 22lff.
Spending, buying present income,
113-115; compared with investing, 113-115; depletes future
income, 114; a form of invest
ment, 114.
Spendins and investing, m e r
only in degree, 9; the problem
of interest, 29-30.
Stamp, Sir Josiah, on distribution, 334.
Standard deviations, of money
interest and real interest, 415.
Statistical study of prices and
interest, x, 399-451, 520-533.
Stocks, yield more than bonds,
220.
Stockholders, function of, as risk
takers, 218ff.
Stock prices,affected by inventions, 352-353.
Subjective income. See Income,
subjective; and Income, psychic.
Supply and demand of capital,
notthe Cause of interest, 32;
and income, relation of, to interest, 454; to interest rates,
depicted, 2Wj.;discussed, 260262, 286-287.
Sweeney, H.W.,money fluctuations and accounting, 44.

T
Technical superiority of present
goo&, Bob-Bawerk’s theory
of, 471-485.
Third approximation, stated, 206-

208.
Thrift, relation of, to interest
rate, M;to saving, 333338.
Thomas, L.,money fluctuationa
and accounting, 44.
Time preference, marginal ratea
of, equalized by loans, 117-119;

il

INDEX
one

o ~ u 8 eof

intereat, 467-470;

(Human impatience), defined
65; in interest theory, 61-98;
rate of, measured, 62; sometimes for future over present:
67. See &o Impatience.
Time shape of income stream, effecta of, on interest, 383-387 ;
importance of, 1301J.; influ92-94;
ences impatience, 67,
shown by charts,
Time valuation, 14.
Training, influenceof, on habits
of foresight, self-control, etc.,

29-30.

8384,338338.

U
Uncertainty. See Risk.
United States, comparison of,
with Europe aa to wealth distribution, 384391 ; increasing
incomes in, increase interest
rates, 384-386; interest
rates
in, 384, 386; since the War,
386387; interest rates and
prices, 521, 527.
Uses, alternative, of wealth (cap
ital), 125149, 150-177,178-205.

aa (1) rent, (2) income, 34;
real, wmiste of outer events,
Sf.; ultimate, paid in enjoyment, 5; workers’ estimate of,
not affected by inkre& rate,
330331.
Waiting (abstinence) not a cost,
634-541; of capitslist, 180; as
cost, 485-487; hkre&hking
justified by, 180; not discountable, 634-539; rewards of, 180;
theory of interest, 178179, 180,
488.187, 534-541.
Walraa, Leon, cited, 6 9 ; contribution of, to interest theory,
518419; interest
theory
of,
contrasted with the author’s,
519; tribute to, 518.
Wantability, 62n. See Mawinal
desirability and Mminal
utility.
War, effecte of, on interest rates,
392393; lowers rata on safe
loans, 382-383.
Waste, relation of, to poverty,

339340.

Wealth, definition of, 13; relation of, to impatience rate,

336-338.
Wicksell, &ut, 450; stated effect of interest rates on prices,

V
Value not equal to cost, 538-540;
of a product, belongs to the
producers, 5 0 ; exceeds cost of
production, 49-52; present different from future, 4942; of
all wealth determined by (1)
expected benefits, (2) interest
rate, 17-18.
Van Strum, Kenneth, cited, 220.
Veblen, T., cited,

488.

W
Wages, sffected by interest rates,
M 8 1 1 3 0 ; and profta, reekoned

443n.

Willingness line, represenb impatience, 238-240.
Willingness
lines,
compared to
market lines, 240-246.