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THE NATURE OF CAPITAL AND INCOME

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THE NATURE OF CAPITAL
AND INCOME

IRVING FISHER, Ph.D.
PBOFESSOE OF POLITICAL ECONOMY, TALE UNIVERSITT

THE MACMILLAN COMPANY
LONDON: MACMILLAN &
1906
All rights reserved

CO., Ltd.

HB4o
II

1906

OOPYB

COPYEIGHT, 1906,

bt the macmillan company.
Set up and electrotyped.

J. S.

Published September, 1906.

ITortoaotr ^ress
Berwick & Smith Co.
Gushing & Co.
Norwood, Mass., U.S.A.

—

(

WILLIAM GRAHAM SUMNER

WHO

FIRST INSPIRED

WITH

A LOVE FOR
ECONOMIC SCIENCE

PREFACE
This book

an attempt to put on a rational foundation

the concepts and fundamental theorems of capital and

income.

It therefore

forms a sort of philosophy of eco-

nomic accounting, and, it is hoped, may supply a link long
missing between the ideas and usages underlying practical business transactions and the theories of abstract
To some readers it may seem that certain
economics.
elementary topics have been treated at undue length but,
as experience shows that economic structures built on
hasty and inadequate generalizations inevitably collapse,
it seems hardly possible to take too much pains in making
On the other hand, topics which
the foundations secure.
are in their nature technical or which digress from the
and in particular mathematical formulae
main theme
have been relegated to appendices.
Many of the theses maintained will undoubtedly fail
to command assent on a first reading, for in any orderly
;

—

presentation of a subject
serve a
the

way

definite

for those

cessitated

it is

impossible to forestall

all

The aim has been to presequence by which each step prepares

objections as they

occur.

which follow; but

this plan

has ne-

the postponement of some topics beyond the

at which a consciousness of their difficulties
might begin to trouble the reader.
He is therefore
asked to stay judgment until he has finished the work,
and, if necessary, to reread those parts in which his difficulties were first encountered.
This suggestion is especially urged in regard to the treatment of income, the
concept of which forms the central theme of the book.

point

Many

of the friendly critics to

whom

the manuscript has

PREFACE

viii

been shown have at first dissented strongly from the conclusions of Chapter VII, but have invariably withdrawn
their objections after finishing Chapter XIV.
The nature of income is a subject which has not hitherto
received, in economic literature, the attention it deserves.
Income plays an important role in all economic problems
it is income for which capital exists
it is income for which
labor is exerted and it is the distribution of income which
constitutes the disparity between rich and poor.
;

;

Nor
mists.

who

the subject of interest solely to theoretical econo-

It appeals to practical

men

of affairs

and

to those

are interested in problems of social reform, as well as

to the special classes of accountants, actuaries, and mathe-

The book

is so arranged that the general
he so desires, omit the technical portions, such as the appendices and possibly Chapter XVII.
It is suggested that all readers should give special attention to Chapters VI, VII, IX, and XIV.
The problem of nomenclature has proved not a little
puzzling.
In general, each term has been employed in
one, and only one, sense but to follow this plan exclusively has not been found practicable.
Several words are
sometimes used for the same concept,
for instance, "resources" and "assets," or "utility "and "desirability"; and
sometimes the same word has been used in more than one

maticians.

reader may,

;

—

sense, as in the case of " capital," which may mean capitalgoods or capital- value. But special pains have been taken
to avoid any confusion or uncertainty of meaning.
The
definitions have been carefully framed, and will be found

collected in a glossary at the end.

A few fragments of the book have appeared in a somewhat different form in economic periodicals, and the
whole book may be said to be only the elaboration of the
ideas outlined some years ago in the Economic Journal.
I would express my thanks to the publishers of the
Economic Journal for permission to use unaltered some

PREFACE
passages from "

What

Capital," 1898, and "

Capital ? "

The Role

1897,

" Senses

of Capital in

Economic

Theory," 1898, and to the Quarterly Journal of Economics
for similar permission with reference to "Precedents for
Defining Capital," 1904.
I wish also to express my obligations to the many
persons who have aided me in the preparation of this
work, among them especially my wife my brother, Mr.
Herbert W. Fisher my colleagues. Professor Henry C.
Emery, Professor John P. Norton, and Dr. Lester W.
Zartman; and my friends, Mr. Richard M. Hurd and
Mr. Orland S. Isbell of New York City.
;

;

IRVING FISHER.
New

Haven, Conn., June,

1906.

CONTENTS
FIRST

SUMMARY
OHAPTEKS

INTEODUCTION. FUNDAMENTAL CONCEPTS

PART

CAPITAL

PART

II.

INCOME

PART

III.

CAPITAL AND INCOME

PART

IV.

SUMMARIES

I-III

IV-VI
.

....

VII-X

XI-XVI

XVII-XVIII

CONTENTS

SECOND SUMMARY
INTRODUCTION
OHAFTEB
I.

II.

III.

Wealth

..........

V.
VI.

Utility

Capital
Capital Accounts
Capital Summation

PART
VII.
VIII.

IX.

Income
Income Accounts
Income Summation
Psychic Income

XL Four
XIII.

XIV.

XV.
XVI.

101
119
.

PART
XII.

Propbrtt

PART
IV.

FAeS

141
165

III

Income-capital Ratios

Concept of Rate of Interest
Value of Capital
Earnings and Income
Capital and Income Accounts
The Risk Element
.

183
191

202
227

256

265

PART IV

........

Summary of Part III
General Summary
Glossary. Summary of Definitions

303
323

APPENDICES

341

INDEX

413

XVII.

XVIIL

329

ANALYTICAL TABLE OF CONTENTS
CHAPTER

Wealth
§ 1.

Definition of wealth

§ 2.

Classification of wealth

§ 3.

Measurement

§ 4.

Price of wealth

of wealth

3
5
8
9

§ 5.

Market-, asking-, appraised-price

§ 6,

Value of wealth

§ 7.

Quantity, price, and value contrasted

§ 8.

Accuracy in measurement of quantity,

CHAPTER

14
price,

and value

Pkopekty
§ 1.

Definition of property

§ 2.

Definition of services

§ 3.

Definition of rights

§ 4.

Wealth and property

§ 5.

Table illustrating this correlation
guide for finding wealth underlying given property rights
A second guide One property right overlaid by another
A third guide Property rights are always to existing wealth
Total ownership is aggregate of partial rights

§ 6.
§ 7.
§ 8.
§ 9.

correlative

32
34
36

§ 11.

Importance of a clear understanding of wealth and property

CHAPTER

...

Classification of property rights

§ 10.

III

Utility
§ 1.

Desirability vs. satisfaction

§ 2.

Synonyms

§ ;l

Desirability vs. services

for desirability (utility, etc.)

43
xiii

ANALYTICAL TABLE OF CONTENTS

xiv

§ 4.

Total and marginal desirability

§ 5.

Law

44
46

of decreasing marginal desirability

CHAPTER rV
Capital
§ 1.

Pund and

§ 2.

Discordant definitions of capital

§ 3.

Fundamental truths

§ 4.

Confusions resulting from neglect to introduce time element
The weight of economic usage

§ 5.
§ 6.
§ 7.

flow distinguished.

Capital

and income

in these conflicting definitions

Popular and business usage
Correct terminology less important than correct thinking

60
61
65

CHAPTER V
Capital Accounts
§ 1.

Senses of capital

§ 2.

§ 3.

Book capitalization
Book and market values

§ 4.

Summary

of senses of capital

Case of decreasing capital-balance
.
§ 6. Effect of payments between stockholders and company
§7. " Rights to subscribe "
§ 8. Stock watering
§ 9. Insolvency
§ 10. Pseudo-insolvency
§ 11. Creditor nominally takes no risk
§5.

.73
.

75
77

79
81

82
82

§ 14.

But practically creditor is risk-taker
Winding up a bankrupt company
One bankruptcy leads to another

§ 15.

Summary

§ 12.
§ 13.

84
87

CHAPTER VI
Capital Summation
and balances

§ 1.

Methods

§ 2.

Distinction between accounts of real and fictitious persons

§ 3.

Summation by couples brings

of couples

into relief concrete capital

90
.

ANALYTICAL TABLE OF CONTENTS

xv
PAOB

§ 4.
§ 6.

Nature of credit
Importance of distinguishing methods of couples and balances

CHAPTER

96
97

VII

Income
§

§ 2.
§ 3.

Difficulties of defining

income

101

The money-income concept
The real-income concept

103

104

....

§ 7.

Error of including as income both commodities and services
Vain attempts to escape the pitfalls thus laid
Income not restricted to " enjoyable " elements
So-called social and individual income

§ 8.

Conclusion

§ 4.
§ 5.
§ 6.

106

109

.112
113
115

CHAPTER

VIII

Income Accounts
§ 1.

Introduction

119

§ 2,

Specimen income and outgo accounts
Cost of construction is to be included in outgo accounts
Devices for making income regular
Applications of income accounting

121

§ 3.

§ 4.
§ 5.

§ 6.
§

Example of individual accounts
Income and outgo account for negative

124
127

129
131

capital (liabilities)

§ 8.

Limitations of practical bookkeeping

§ 9.

Income accounts for fictitious persons
Relation of income accounts to capital accounts

§ 10.

134
135

138
139

CHAPTER IX
Income Summation
§1. Summation by " method of balances "
§2. "Interactions"
§ 3. Interactions which change the form of wealth (production)
§ 4. Interactions which change the place of wealth (transportation)
§ 5. Interactions which change the ownership of wealth (exchange)
§ 6. Accounts illustrative of the first class (production)
§ 7. Results of combining these accounts
§ 8. Methods of balances and couples contrasted
§ 9. Accounts illustrative of the third class, for fictitious persons
§ 10. Accounts illustrative of the third class, for real persons
.

....
.

§ 11.

Conclusion

141

143

145
148
149
152
156
157

158
162
164

•

ANALYTICAL TABLE OF CONTENTS

XVI

CHAPTER X
Psychic Income
PAGE
§ 1.

Objective income leads up to subjective

§ 2.

Illustrative cases

§ 3.

§ 7.

Concept of subjective income
Objective and subjective incomes differ in time
Objective and subjective incomes differ as to labor
Labor the only ultimate cost of production
Objective and subjective income differ as to pain

§ 8.

Summary

177

§ 9.

Classification of services

178

§ 4.
§ 5.
§ 6.

165

....

165
167

169
170
173
175

CHAPTER XI
Tour Income-capital Ratios
§ 1.

Besume

§ 2.

and value-productivity, physical- and value-return
Errors from confusing them
How costs, past and future, affect values

§ 8.

§ 4.

183

of previous chapters

Physical-

CHAPTER

184

Ib6
188

XII

Concept of Rate of Interest —

191

§ 4.

rate of interest as a case of " value-return "
.
.
Annual, semi-annual, quarterly, and continuous reckoning
Rate of capitalization or reciprocal of the rate of interest
The " premium " and " price " concepts of the rate of interest

§ 5.

The conditions under

vphich they are interchangeable

196

§ 6.

Conditions under vrhich they are not interchangeable

198

§ 7.

The

§ 8.

Summary

§ 1.
§ 2.
§ 3.

The

192

19i
194

.199

rate of discount

199

CHAPTER

XIII

Value of Capital „
The "discount curve

§ 1.

Capital- value of a single future item.

§ 2.

Application to valuing capital, property, and wealth

202
204'

§ 3.

Capital-value of a perpetual annuity

205'

§ 4.

Application to valuing capital, property, and wealth

208

§ 5.

Capital-value of a terminable annuity

§ 6.

Application to valuing capital, property, and wealth

209
210

bond

§ 7.

Capital-value of a

§ 8.

Capital-value of any income stream whatever

211

217

ANALYTICAL TABLE OF CONTENTS

§ 9.

Capital-value

when

alternative

XVll
PAOE
221

income streams are possible

§ 10.

Capital-value of a group of articles

§ 11.

General conclusion

223
223

CHAPTER XIV
Earnings and Income
§

....

Capital-value less than total anticipated income

§2. Effect of a change in the rate of interest
§ 3. Value-return may be greater or less than rate of interest
§ 4. Standard or earned income vs. realized income
.

§ 5.

Increase of capital equals excess of earnings over income

§ 6.

A depreciation fund as a means of standardizing income

§ 7.

Sinking funds

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

Other devices for making income regular
device of keeping a large stock of instruments
§ 10. Savings are not a part of realized income
§11. Imaginary case of three brothers
income tax on the three brothers
§ 12. An
§ 13. A misconceived income tax affects the use of capital
§ 14. To consider " savings " income confuses capital and income
§ 8.
§ 9.

The

227

229
229
231
236
238
243
244
246
247
249
250
253
254

CHAPTER XV
Capital and Income Accounts
§ 1.
§ 2.

§ 3.

and income accounts when items recur regularly.
Case in which repairs occur at long intervals
The same, when there is a repair fund but no repairs as yet
Capital

§ 5.

The same, when repairs actually occur
Extraordinary increases or decreases

§ 6.

Conclusion

§ 4.

....
....

256
257
259
261
263
264

CHAPTER XVI
The Risk Element
§

Subjective nature of chance

....
....

§ 2.

Definition of chance

§ 3.

Risk as applied to the rate of interest
Same, in case future income is dependent on rate of interest
Risk as applied to immediate income
"Riskless," "mathematical," and "commercial" values

§ 4.

§ 5.
§ 6.

bond
and commercial

§ 7.

Capital-value of a risky

§ 8.

Riskless, mathematical,

§ 9.

Inverse case, where instead of risk of loss there is chance of gain

265
269
271
273
275
276
277

rates of interest

279
280

ANALYTICAL TABLE OF CONTENTS

xviii

§ 10.

The general

§ 11.

Difficulties in practice

§ 12.

Enumeration

§ 13.

case,

where both are present

....
.

§ 19.
§ 20.

Forms

§21.

Shifting risks to speculators.

§ 22.

Buying and

§ 15.
§ 16.

§ 17.
§ 18.

281
283

of causes affecting capital-value

on the form of the " discount curve "
Effect of chance on bookkeeping
Five methods of avoiding risk
The method of guaranties
The method of safeguards
The method of increasing knowledge
The method of insurance

§ 14.

PAGE

Effect of chance

284
286
287
288

of insurance

Dangers of imitative speculations

selling futures

288
289
291
291
294
295
298

CHAPTER XVII
Summary of Part
§

Mode

III

bt Means op Diagrams

of representation adopted

303
304.

§ 4.

income
Capital-value as mean between past cost and future income
How to combine capital curves

§ 5.

Resultant in case of interactions

311

§ 6.

Application to summation of capital of individuals

§ 7.
§ 8.

Application to summation of capital of society
An " interaction " as preparatory to enjoyable services

§ 9.

The

§ 2.
§ 3.

Capital- value as discounted

309
314

risk element

305-

316
.

317

320

CHAPTER

XVIII

General Summary
§ 1.

Picture of capital and income

§ 2.

Summation

of capital

and income

....

323
324

§ 3.

Subjective counterparts of objective capital and income

326

§ 4.

Relative changes in values of capital and income

327

§ 5.

Final

summary

328

GLOSSARY
Summary of Definitions

329

APPENDICES
Appendix to Chapter

FAGB
§ 1 (to

Ch.

Dimensions of quantity, value, and price of

§ 7).

341

wealth

Appendix to Chapter
§ 1 (to

Ch. Ill,

III

Mathematical expression for marginal desir-

§ 4).

344

ability

Appendix to Chapter VII
§ 1 (to

Ch. VII,

Specimens of current definitions of income

§ 1).

345

Appendix to Chapter XI
§ 1 (to

Mathematical dimensions of income-capital

Ch. XI, § 2).

357

ratios

Appendix to Chapter XII
Mathematical relations between rates of
reckoned annually, semi-annually, etc., when the rates
are conceived in the " price " sense
2 (to Ch. XII, § 4). The same, when the interest rates are conceived in the " premium " sense.
Diagrammatic representation.

§ 1

(to Ch. XII, § 2).

interest

Economic interpretation
§ 3 (to Ch. XII, § 6).

of e

357

358

A premium rate of 4 per cent in one year and

3 per cent thereafter, means a price rate of 3.03 per cent the

first year and 3 per cent thereafter
4 (to Ch. XII, § 6).
price rate of 4 per cent in one year and
3 per cent thereafter means a premium rate of 37^ per cent the
first year and 3 per cent thereafter
Mathematical relations between the rates of
5 (to Ch. XII, § 6).

362

interest as a
§ 6 (to

Ch. XII,

interest

premium and
§ 7)

as a price

362
363

Mathematical relations between the rates of

and discount

Mathematical relations between rates of discount for different time reckonings
§ 8 (to Ch. XII, § 8). Dimensions of rates of interest, discount,

364

§ 7 (to Ch. XII, § 7).

and

capitalization

366
367

ANALYTICAL TABLE OF CONTENTS

Appendix to Chapter XIII
PAGE

...........

Ch. XIII,
one year
§ 2 (to Ch. XIII,

§ 1 (to

§ 1).

Formula

for capital-value of a

sum due

§ 1).

Formula

for capital-value of a

sum

end of any time

368

F, due

368

Formula

3 (to Ch. XIII, § 3).
annuity

for capital- value of a perpetual

369

4 (to Ch. XIII, § 3). Formulae and diagrams for capital- value of
annuities payable annually, semi-annually, quarterly, and con-

369

tinuously
§ 5 (to

Ch. XIII,

ous income
Ch. XIII,

§ 6 (to

§ 3).

Diagrams

for discontinuous

and continu371

§ 5).

Formula

for capital- value of a terminable

374

annuity

Ch. XIII,

§ 7 (to

annuities
§ 8 (to
§

Discussion of formulae for terminable

§ 5).

by diagrams.

Ch. XIII,

§ 7).

9 (to Ch. XIII, § 7).
of a bond

"Total discount."
" Total interest " 374
.378
Formula} for value of bond
Alternative method for computing value
380
.

10 (to Ch. XIII, § 7). Formula for a bond -when interest
reckoned oftener than yearly

§ 11 (to

Ch. XIII,

§ 8).

Formula

for capital-value of

any

382

series of

382

income installments
§

....

12 (to Ch. XIII, § 8). Diagram and formula for deriving capitalvalue from a given continuous income stream

Diagram showing the accumulated
XIII, § 8).
"amount" of a given income stream
14 (to Ch. XIII, § 10). Effect of reckoning semi-annually, quarterly, and continuously, on the rate of interest realized from
the income of a continuously replenished stock of articles

15 (to Ch. XIII, § 11).

§ 13

(to

interest

390

Appendix to Chapter
Ch. XIV,

§ 5).

rival concepts of

§ 2 (to Ch.

XIV,

§ 12).

XIV,

§ 13).

When

•

393

XIV

the interest rate varies, there are

" standard income "
Effect of

396

foreknown tax on increase of
398

capital
§ 3 (to Ch.

388

Kepresentation of capital and income by

polar coordinates

two

387

Influence of variation in the rate of

§ 16 (to Ch. XIII, § 11).

§ 1 (to

383

Ch.

tax impracticable

Unrestricted application of a true income
••

•

400

ANALYTICAL TABLE OF CONTENTS

xxi

Appendix to Chapter XVI
PAOB

XVi, § 6). Mathematical coefficients of proTjability,
caution, and risk
403
2 (to Ch. XVI, § 7). Formula for mathematical value of a riskybond
403
3 (to Ch. XVI, § 10).
Variability about a mean, as measured
by the " standard deviation "
406
4 (to Ch. XVI, § 20).
Method of computing a pure level life
insurance premium
410

§ 1 (to Ch.

INDEX

413

INTRODUCTION.

Fundamental Concepts

Chapter

II.

Chapter

III.

Wealth
Property
Utility

THE NATUEE OF CAPITAL AND INCOME
CHAPTER

WEALTH
§

The term " wealth"

is used in this book to signify material
owned by human beings. According to this definition, an object, to be wealth, must conform to only two
conditions it must be material, and it must be owned. To
these, some writers add a third condition, namely, that it
must be useful. But while utility is undoubtedly an essential attribute of wealth, it is not a distinctive one, being
implied in the attribute of appropriation hence it is redundant in a definition. Other writers, like Cannan, while
specifying that an object, to be wealth, must be useful,
do not specify that it must be owned. They therefore

objects

;

define wealth as " useful material objects."

This definition,

however, includes too much.
Rain, wind, clouds, the
Gulf Stream, the heavenly bodies
especially the sun,

—

from which we derive most of our light, heat, and energy
are all useful, but are not appropriated, and so are not

—

wealth

commonly imderstood.

Still

other

writers

be wealth, must be "exchangeable."
would exclude parks. Houses of Parhament, the Hague Temple of Peace, and much other
trusteed wealth all wealth, in fact, which happens to fall
into permanent hands. Although it is essential that wealth
insist that

But

article, to

this restriction

;

should be owned,

it is

not essential that
3

should contin-

NATURE OF CAPITAL AND INCOME

[Chap. I

Again, many writers, like McLeod,
"material" altogether, in order to
make room for the inclusion of such "immaterial wealth"
as stocks, bonds, and other property rights, and for human
and other services. Property and services are, it is true,
inseparable from wealth, and wealth from them, but they
ually change owners.

omit

the

quaHfier

are not wealth.

To embrace

these under one term

all

A railway, a railway
not three separate items of

involves a species of triple counting.
share,

and a railway

wealth;

trip are

they are respectively wealth, a

wealth, and a service of that wealth.
mists, like Tuttle,

title

that

Finally, a few econo-

have endeavored to break away from
The term " wealth," they main-

concrete objects entirely.
tain, applies,

not to the concrete objects, but to the value

these objects.

contention.

Much may be

But as the question

said in support of this
is

chiefly verbal, that

is,

not a question of finding a suitable concept, but of finding
a suitable word for a concept, it does not seem advisable
to depart from the prevailing usage among economists.

Wealth, then, includes

all

those parts of the material

universe which have been appropriated to the uses of

mankind. It does not include the sun, moon, or stars,
because no man owns them. It is confined to this little
planet, and only to parts of that namely, the appropriated
;

portions of the earth's surface

upon
it

as in

and the appropriated

objects

The appropriation need not
partial and for a particular purpose,
the case of the Newfoundland Banks, which are approbe

it.

complete;

often only

priated only in the sense that the fishermen of certain

nations have the right to take fish in their vicinity, while
their waters are open to all men for all other purposes.

fact, it is

doubtful

any objects owned
them may use them

there are

unrestrictedly that the owner of

absolute defiance of the wishes of others.

By appropriation

any object is therefore meant that degree
tion to which the object is subjected.
of

of appropria-

WEALTH

Sec. 2]

Any single object of wealth is called an article of wealth,
an item of wealth, or an instrument. The term "instrument" is perhaps the most convenient. It appears to
have been first employed by John Rae in 1834.^
§

Various classes of wealth

may

Wealth
any
fixed structures upon it, land improvements; and the two
together, constituting
immovable wealth, real estate.
All wealth which is movable (except man himself) we
which consists

A third group includes human beings

shall call commodities.

— not

only

be distinguished.

of the earth's surface is called land;

who

slaves

beings, but also freemen

owned by other human
own masters.

are

who

are their

It is true that freemen are not ordinarily counted as

wealth;

and, indeed, they are a very peculiar form of

wealth, for various reasons:

because they are not,

first,

bought and sold; secondly, because
the owner usually estimates his own importance so much
more highly than any one else and finally, because the
owner and the thing owned in this case coincide.
Yet
they are, like other wealth, "material" and "owned."
These attributes, and others which depend on them, justify*
the inclusion of man as wealth. But in order to concede as
like ordinary wealth,

;

much

as possible to popular usage, the following supple-

mentary

definition

restricted sense)

framed:

we mean

external to the owner.

New

wealth

(in its

material objects owned by

man and

This definition obviously includes

but not freemen. But it
cation than the wider definition
slaves,

first

difficult of

given, as

appU-

requires

Principles of Political Economy, recently reprinted under the
Theory of Capital, Macmillan, 1905.
^ Among those writers who have included man in the category of
wealth are Davenant, Petty, Canard, Say, McCuUoch, Roscher, Wittstein, Walras, Engel, Weiss, Dargun, Ofner, Nicholson, and Pareto.
^

title Sociological

NATURE OF CAPITAL AND INCOME

[Chap. I

US to separate into arbitrary classes those persons

who

are

intermediate between freemen and slaves, such as vassals,

indentured servants, long-time apprentices, and negroes held
in peonage.
A man bound out to service for thirty years
almost
indistinguishable
from a slave, and if the term of
is
service be long

enough and the control absolute enough,

the distinction becomes a distinction without a difference.

the other hand, the shorter the term of service, the

As a matter

nearer does his condition approach freedom.

most workers in modern society are "hired," i.e.
bound by contract to some extent and for some period of
time, even though it be for no more than an hour, and to
that extent are not free. In short, there are many degrees
of freedom and many degrees of slavery, with no fixed
of fact,

line of

Two

demarcation.
concepts have been defined which

ignated as "wealth in
in its

may

be des-

more general sense " and " wealth

restricted sense."

between them.
is

its

Ordinarily,

There need be no confusion

when the simple term " wealth

used, the former concept will be understood, and

any

propositions which hold true of this broader concept will

we have occasion at any time to refer to the latter exclusively, we may
always make use of the full phrase, "wealth in its more
necessarily apply also to the narrower one.

restricted sense."

There are many admissible ways of classifying wealth,
one being more or less desirable than another according to the purpose for which it is intended. The
scheme on page 7 is not based on any one logical criterion, but is intended merely to give the principal groups
into which wealth, as it actually exists, naturally falls.
It scarcely needs to be stated that the various classes are
not always absolutely distinct. Like all classes of concrete
things, they merge imperceptibly from one into another.
For this reason the classification is of httle importance

WEALTH

Sec. 2]

a bird's-eye view of economic science.

except to give

In fact, the classification
paramount importance in
tion,

but analysis, solves

of concrete things is
scientific study.

Not

seldom of
classifica-

scientific problems.^

productive land

crop land
grazing land
timber land

mining land
hunting land
fisheries

riand

]

ways

of transit

railways

roadways
waterways

parks

building land
'

land improvements

raw materials

[

buildings

improvements on
highways
minor

overhead
underground
surfacing

bridging

mineral
agricultural

manufactured

by being burned
by being eaten or drunk
[ by being otherwise used
r

consumable

^
o

finished

mechanical devices
animals

products

durable

-I

"hard money"
and jewelry
furniture and works of art
clothing

reading matter
"3

minor

slaves
free

See the writer's

ber, 1896, p. 516;

"What

Capital?" Economic Journal, Decem-

and "Precedents

Journal of Economics, March, 1904.

for Defining Capital," Quarterly

NATUEE OF CAPITAL AND INCOME

[Chap.

In the definition of wealth were included two attributes
is material;
and, it is owned. These attributes,
materiality and appropriation, need to be considered separately.
The remainder of this chapter will be devoted to
wealth

the former.

important and useful result of the materiality of
is that it provides a basis for the physical measurement of wealth. Wealth is of many kinds, and each kind
is measured in its own proper physical unit.
These units
have been handed down to us from various sources and in
great diversity, but all of them are in the last analysis
wealth

arbitrary.

Many
This

kinds of wealth are measured by weight-units.
true of

"commodities."

some

coal,

iron,

Each

beef,

unit

and

consists

particular piece of matter which

in
of
is

fact,

most

the weight

adopted for con-

For instance, the English pound is
simply a lump of platinum kept in London and called arbitrarily the pound.
venience as a standard.

Many

are not so conveniently measured by
by space-units, whether of volume, area, or
length.
Thus we have, for volume, milk measured by the
quart, wheat by the bushel, wood by the cord, and gas by
the cubic foot for areas, we have lumber sold by the square
foot and land by the acre; for length, we have rope, wire,
ribbons, and cloth measured in feet and yards.
All these
units of length, area, and volume are also quite arbitrary
or conventional.
The definition of the English yard, for
instance, is an imaginary line drawn between two small
articles

weight-units as

;

dots on gold plugs in a particular brass rod in London.

Many articles exist in more or less definite units which
need only to be counted, as for instance, eggs or oranges,
which are measured by the dozen. Similarly, writing paper
is reckoned by the quire
pencils and screws by the gross.
;

WEALTH

Sec, 3]

In such cases we say that the article is measured
by number. But "number" is by no means peculiar to the
last-named case. All measurement implies both an abstract number, and a concrete unit, as "ten screws," "six
eggs," or "four pounds-of-granulated-sugar."

The

example suggests that in order to specify fully
it is necessary to enumerate
attributes,
or
enough
of them to distinguish
particular
its
with
which it may become conit from other sorts of wealth
Thus, it is often necessary to specify what "grade"
fused.
or "brand" is meant, as "Grade A," "Eagle Brand,"
"Lackawanna" coal. Sometimes the special sort is denoted
by a trade mark or hallmark. It is in this way that the
last

the unit of any kind of wealth,

attributes of particular kinds of wealth enter into the con-

sideration of economic science,

and

not, as

some have

er-

roneously supposed, separately as an "immaterial" sort of

The

wealth.

"fertility" of land

wealth apart from the land

which

wealth.

The "skill"

in addition to the

man

itself;

of a

himself;

not to be counted as
it is

the "fertile land"

mechanic
it

not wealth

the "skilled

me-

chanic" who should be put in the category of wealth.

Of course, the number expressing the measure of wealth
be unity, as for instance, "one dwelling." Sometimes
there is only one article of the particular kind in existence.
There is but one Battery Park, one Buckingham Palace,
one Koh-i-noor diamond, one Rhynd papyrus. Dealers

may

call

such articles "uniques."

Strictly speaking, every ar-

might be called a unique, even as no two grains of
wheat are precisely alike; but for practical purposes we
overlook minor differences and regard articles sufficiently
similar as homogeneous.
ticle

Thus each individual kind
its

own

special unit,

purposes

it is

4
of wealth

may be measured

— pounds, gallons, yards

more important

;

but for most

measure the value of wealth.

NATURE OF CAPITAL AND INCOME

[Chap. I

may be

done in dollars and cents, pounds and shiland centimes, and so forth. This is also a species of physical measurement, but involves the principle of
exchange. So much mystery has surrounded the term

and

this

lings, francs

''value" that

we cannot be

too careful to obtain correct

In the explanation which
to depend on that
of price; that of price in turn on exchange; and finally,
that of exchange on transfer.
An article of wealth is said to be transferred when it
changes owners. It is to be observed that such a change
does not necessarily imply any change of place. Ordinarily,
the transfer of an article involves change in its position.
The purchase of tea or sugar is accompanied by
the delivery of these articles across the counter from dealer
But in many cases such a change of position
to customer.
does not occur, and in the case of real estate it is even imThis distinction between change of ownership
possible.
and change of position is not always borne in mind. It is
sometimes said, for instance, that exports and imports
must balance in a certain manner. But if by "exports"

and simple ideas on the

subject.

follows, the concept of value is

we mean

made

articles that are sent out of the country,

''imports" those which come into

and by

the proposition will

it,

When, some years ago. Englishmen were
buying American breweries, these articles, of course,
were not exported, though they were transferred to foreign
not hold true.

ownership.

may

be voluntary or involuntary. Examples
of involuntary transfers of wealth are transfers effected
either (1) through force and fraud of individuals, as in robbery, burglary, embezzlement, etc.; or (2) through force
Transfers

of government, as in taxes, court fines, etc.

we have

But

at present

do with voluntary transfers.
Voluntary transfers are of two kinds (1) one-sided transfers, i.e. gifts and bequests and (2) reciprocal transfers or exchanges, which are the most important for economic science.
to

;

WEALTH

Sec. 5]

Exchange

of wealth, then,

means the mutual and volun-

tary transfer of wealth between two owners, each transfer being
If either of the

in consideration of the other.
ties

of wealth

quotient

exchanged

two quanti-

divided by the other, the

Thus, when three

called the price of the latter.

bushels of wheat are traded for two dollars of gold, the
price of the

wheat

two

times, one of the

condition

other wealth,

one

who

wheat per

articles is

not essential, and in

When

even common.

it is

who

the exchange

dollar.

one of money for

called a purchase (with reference to the

parts with the

to the person

and the price
In modern
usually money, but this
primitive times was not

§ of a dollar per bushel,

of the gold is IJ bushels of

money) and a

sale (with reference

receives the money).

In order that there

may

be a price,

it is

not necessary

that the exchange in question should actually take place.
It

may

be only a contemplated exchange.

agent often has an "asking price," that

is,

real estate

a price at which

he tries to sell, usually above the price of an actual sale.
In the same way there is often a "bidding price," which is
usually below the price of actual sale. The price of sale
thus generally Ues between the prices first bid and asked.
But it sometimes happens that the bidder refuses to raise
his bid and the seller refuses to lower his asking price.
In such a case no sale takes place and the only prices are
those bid and asked. Trade journals report, for many
commodities, the price of sale if there is a sale, otherwise
the two prices bid and asked, or if both do not exist, the one

which does.

When

there

price bid or asked,

What

ment"

the price?

sale,

it is

and

especially

when

there

not so easy to answer the question.

Recourse

or appraisal, which

then had to an "appraise-

simply a more or

less skilful

NATUKE OF CAPITAL AND INCOME

[Chap. I

guess as to what price the article would or should fetch.

Appraising or guessing at prices is often very difficult in
It is necessarily employed, however, by the govpractice.

ernment in assessing taxes and customs and condemning
land by insurance companies in settUng claims and adjusting losses by merchants in making up inventories and other
statements; and by statisticians and others. In fact,
some people make a living by simply appraising wealth on
which, for one purpose or another, a price of some sort must
;

;

Evidently, the purpose makes a great difference in

set.

Sometimes we need to know the price for
which an article could be sold at an immediate forced sale;
sometimes, what it might be expected to bring if a reasonable time were allowed sometimes, what the owner would
probably take; sometimes, what a possible purchaser
would probably give. These appraised prices may all be
A family portrait may be worth an untold
different.
amount to the owner, but might bring next to nothing if
The owner would endeavor to appraise it at
actually sold.
a high figure if he wished to insure it against fire; but if
he wished to borrow money on it, the appraisement would
doubtless be small, for the pawnbroker would consider it
the appraisal.

;

almost worthless.

Thus, in practically making an appraisement we encounmany difficulties, owing partly to the unknown char-

ter

acter

and condition

But whatever the

and partly
by the appraisal.

of the parties involved,

to the variety of interests to be served

and ambiguities in asany article, the price or
without ambiguity. The vague-

difficulties

certaining a price or prices for
prices

do actually exist

ness comes wholly from failure to specify sufficiently the

conditions under which the exchange

to take place.

specify in sufficient detail the conditions of the contem-

plated exchange,
or not

its

we can guess

matter.

terms

will

be quite definite but whether
is quite another

at those terms correctly

;

WEALTH

Sec. 6]

Having obtained the price of any kind of wealth, we may
compute the value of any given quantity of that wealth,
without necessarily supposing that particular quantity to
be exchanged. The value of a given quantity of wealth is
found by multiplying the quantity by the price. Thus, if
the price of wheat is § of a dollar per bushel, then a lot
consisting of 3000 bushels would have a value of 3000 x
In other words, the value of a
$1 per bushel or $2000.
certain

amount

of one kind of wealth is the quantity of

some other kind for which it would be exchanged, if the
whole amount were exchanged at the price set upon it.
The exchange which sets the price need not be the exchange of the particular 3000 bushels which we are valuing
some other exchange of, say, 300 bushels for $200 may set
the price. This is one reason why it is preferable to ex-

and value afterward.
which has been given, applying,
an
of wealth instead of the unit,
it
does,
to
aggregate
as
departs somewhat from economic usage; but it follows
closely the usage of business men and practical statisticians.
Economists have not usually thought it necessary
to distinguish between the purchasing power of the unit
and the aggregate, but have employed the term "value"
indiscriminately to both. In other respects also their usage
has been somewhat different from that here employed.
Some of them have confined "price" to a money expression,
i.e. to what is here called money price, and appHed the term
"value" to purchasing power in "goods." Others have
used the term "price" in the sense of what an article actually sells for (market price) and "value" in the sense of
what it ought to sell for (appraised price or reasonable price).
Others, in turn, have used the term "price "in the sense employed in this book, but "value" in the sense of the degree
of esteem in which an article is held ("marginal utility"

plain price

The

first

definition of value

NATURE OF CAPITAL AND INCOME

[Chap. I

It seems preferable to conform
our definitions of value and price as closely as possible to
business usage, which instinctively and consistently apphes

or "subjective value").

the term " price" to the unit and " value " to the aggregate.

§7
The
wealth

between quantity, price, and value of
be seen clearly in any "inventory," such as the

distinction

may

following

—

WEALTH

Sec. 7]

in the

mind

or wheat value.

man, but purely

objective, as

money

value,

It has, of course, subjective causes, but

these do not concern us yet.^

The measurement of wealth in "value" has this great
advantage over its measurement in "quantity," that it
translates the many kinds of wealth into a single kind.
All the items in the third

expressed in a

common

column

of the inventory are thus

unit, the bushel.

We may

conse-

quently add together this column and obtain a single sum,

namely, 14,410 bushels but summation of the first column
impossible, because shoes, pounds of beef, houses, and
bushels of wheat are incommensurable. We see here one
;

money

of the important functions of
of

measurement out

;

brings uniformity

of diversity.

But, although this reduction to a
practically convenient,

common measure

would, of course, be a great mis-

take to suppose that it gives what may be called "the true
measure of wealth." "The value of wealth" is an incomplete phrase; to be definite we should say, "the value of
wealth in terms of gold," or in terms of some other particuWe cannot, therefore, use such values for
lar article.
comparing different groups of wealth except under certain
To compare the
conditions and to a Hmited degree.
wealth-values of America and England, of Ancient Rome and
Modern Italy, of Carnegie and Crcesus, will give different
results according to the standard of value employed.

§8

have seen how to measure the three magnitudes,
quantity, price, and value of wealth. This measurement
The degree of acis, practically, a very inaccurate affair.
curacy attained is exaggerated in the minds of most perIn measurements of
sons, even including business men.
quantities of wealth there are two sources of error, for every
*

Further explanation as to the dimensions of the quantity, price,
of wealth are given in the Appendix to Chap. I, § 1.

and value

NATURE OF CAPITAL AND INCOME

[Chap. I

measurement includes, as we have seen, two elements:
a unit of measure, which may be inaccurate and a number
or ratio between the quantity to be measured and the unit,
which number may also be inaccurate. In modern times
the first source of error is practically ehminated. Our
units of weight and measure are standardized by law, and
a pound weight in CaUfornia is equal to one in Connecticut,
within one part in many thousand. The chief source of
;

error, therefore, Hes not in the unit,

but in the ratio of the
inaccuracy is as
great as five per cent, or greater. Wholesale transactions
are more accurate. A large manufacturing concern of
Syracuse had its measurement of the weight of caustic
soda sold in carload lots compared with the measurement
made by its customers, and the results agreed within one
Probably
fifth of one per cent on two fifty-carload lots.

wealth to that unit.

retail trade the

the greatest degree of accuracy ever obtained in com-

on the Mint scales used by the
United States in Philadelphia and San Francisco. These
scales weigh accurately to within about one part in ten

mercial measurements

million.

When we
we

introduce

proceed from quantities of wealth to values,
still a third source of inaccuracy, namely, in

by which we multiply. This is especially
the price be merely an " appraised " price. The price
of any actual sale is an absolute fact and cannot be said to
have any inaccuracy; but the price at which we estimate
the price factor
true

that a thing would

sell

under certain conditions

always

In the case of staple articles, i.e. articles regularly on the market, a dealer can often appraise correctly
within one per cent. Real estate in certain parts of a city
where sales are active can sometimes be appraised correctly
within five or ten per cent; but in the "dead" or out-ofthe-way parts of some towns, where sales are infrequent, the
appraisement becomes merely a rough guess. Again, in
the country districts, while farms in the settled parts of
uncertain.

WEALTH

Sec. 8]

Iowa and Texas can be appraised within ten or fifteen per
cent, in the backward parts even an expert's valuation is
often proved wrong by more than fifty per cent. In some
cases, in fact, where a sale of the article is scarcely conceivTo
able, an appraisement is almost out of the question.
estimate the value of the Yellowstone Park is impossible,
unless we allow ourselves a range of several hundred per
Similar wide limits must be allowed when we try
cent.

human beings. We can often give a lower
but seldom an upper one. The estimates may vary
enormously with the point of view. It is sometimes said,
"If I could buy Mr. So-and-So at my valuation and sell
to value free
limit,

him

at his, I'd get rich."

some

conclude, as

would be wrong, however, to

writers have, that because

we cannot

value them accurately, public parks or freemen cannot be
called wealth.

When

the slaves in the South became free-

men

they ceased to be appraised as wealth. The result
has been somewhat confusing to our census statistics.

The Manufacturers' Record

of Baltimore recently issued
showing a sharp drop in the assessed valuations of
wealth in the South after the war, and the inference was
drawn that wealth had immensely decreased. But a large
part of this so-called decrease consisted merely in the change
of ownership of slaves from their old masters to themselves,
and the consequent omission of them from the statistics.
Various writers, from Petty down to Engel and Nicholson, have tried to assess the value of human beings.
Professor Nicholson estimates roughly that the English
nation is worth at least five times the value of other existing wealth in England.^
Such calculations are of course
figures

moment. They are also
and involve in each case some par-

theoretical than practical

necessarily inaccurate,

ticular supposition as to the purpose of the
for instance,

whether

it is

appraisement

to indicate the earning

the population, their value to themselves, or to others.
*

Economic Journal, March, 1891,

p. 95.

;

power of

CHAPTER

PROPERTY

The

definition of Wealth in the previous chapter restricts
meaning to concrete material objects. But economics
has also to deal with abstract services, utilities, and propertyrights.
These, like material wealth, are bought and sold,
and are, in fact, often regarded as a sort of "immaterial"
its

or " incorporeal " wealth.

is,

however, needless as well as

confusing to include these elements under the general cate-

They are not wealth, though they are
The definition given shows
that wealth has two attributes: it must be material, and
it must be owned.
Its materiality was the subject of the
gory of wealth.

intimately related to wealth.

previous chapter;

its

ownership

will

be the subject of the

present chapter.

meant by owning wealth? We answer:
to have the right to use it. Such a right is called 'property, or, more explicitly, a property right.
To own a loaf of
bread, or to have property or proprietorship in it, means
nothing more nor less than to have the right to eat it, or sell
it, or otherwise employ it to satisfy one's desires.
To own
a suit of clothes is to have the exclusive right to wear it.
But what

To own a

carriage

have the right to drive in

To own a plot
of land means to have the right to its use forever.
The concept of property
"right
wealth"
is more
the
to use
fully expressed by the phrase, the "right to the uses of
wealth." In this phrase we have to deal with two new
otherwise utilize

as long

—

ideas

lasts.

—

— rights and uses — each

separately.
18

which needs to be treated

PROPERTY

Sec. 2]

§2

We need first to understand what is the nature of the uses
The

or services of wealth.

services of

an instrument

wealth are the desirable changes effected (or the undesirable changes prevented)

by means of that instrument. For
loom consist in changing yarn into

instance, the services of a
cloth, or

what

called weaving.

Similarly, a

plow per-

forms the service of changing the soil in a particular manner
a bricklayer, of changing the position of bricks. A dam
or dike performs the service of preventing the water from

overflowing the land; a fence, of preventing cattle from
roaming; a necklace, of sparkling or reflecting light, and
thereby satisfying the love of beauty or the vanity of the
owner.

When

services are described as desirable events,

meant that they are desired or esteemed by the owner or
owners, not necessarily by every one, or even any one, else.
It may even happen that the events are distinctly distaste-

A factory whistle may be a nuisance to every
one except the factory owner.
In this connection it is important to distinguish between
ful to others.

the uses or desirable events, and the utility or desirability

The desirable service is a thing; it is
The desirability of the service, on the
a quality, and is purely subjective. It is

of those events.

usually objective.

other hand,

a feeling toward the events, not the events themselves.
In the present chapter we do not have to deal with the desirability, and it will form the subject of the next chapter.
Each sort of service is measured in its own appropriate
unit.
Sometimes the measurement is by number, i.e.
obtained by simply counting the acts in which the specified
service consists, as, for instance, in the case of the strokes

sometimes the measurement is by time,
day laborer; while sometimes the
measurement of the services is expressed in terms of the
of a printing press

;

as in the case of the

NATURE OF CAPITAL AND INCOME

[Chap, II

by those services, as in the case of
The services of a miner are measured by reference to the quantity of coal mined the services of a planter, by the number of acres planted
and of a
spinning machine, by the number of yards spun. Services,
units of wealth affected
so-called piecework.

;

like wealth, are subject to

have

prices.

The quantity

When

price gives its value.

standard,

exchange and, in consequence,

any

service multiplied

reduced to value in a

all varieties of services

its

common

become commensurable

with each other and with wealth.

The opposite

of a service

a disservice, which

an un-

desirable change effected (or a desirable change prevented)

by means

For instance, a locomotive renders
coal; a farm, by requiring fertilizers and labor
a factory, by requiring costs of working.
Disservices, like services, are measured in quantity
by special units and made commensurable in value by
disservices

of wealth.

by consuming
;

reduction to a

common

standard.

Having seen what is meant by services of wealth, we next
is meant by the right to those services.
"Right"
is a term of jurisprudence, and brings economics into contact with the whole subject of legal and custom-sanctioned
ask what

relations; but, for our present purpose,

to go far in this direction.

it is

not necessary

The

right of a person to the
be defined as his liberty,
under the sanction of law and society, to enjoy the services

uses of an article of wealth

may

of that article.

Lawyers distinguish between property rights and personal rights; but, to the economist,

The

tary.

rights exists only so long as

wealth to the narrower of
long as

we exclude

free

all

rights are proprie-

between property

distinction

its

two

human

and personal
meaning of

restrict the

definitions, that

beings.

instance in which logical convenience

is,

only so

Here we have an
served by adopting

PEOPERTY

Sec. 3]

the broader definition of wealth, which includes
beings even

when free, and by adopting

broad definition of property so as to include
This being premised,

to jurisprudence.

every right

a property right.

human

also a coextensively

known

all

rights

follows

that

have ever been
suggested which are not rights to obtain and enjoy the
is

rights

uses of wealth, either persons or things.
to

liberty,

fife,

and the pursuit

one's right to certain uses of his
of a

husband over

and the

his wife

and

Even

the "right

of happiness"

own

The

person.

simply
rights

of a wife over her husband,

reciprocal rights between parents

and

children, as

well as all other rights in 'personam, are claims against particular persons;

while the right to reputation, to the free

immunity from boycott, perseupon the community generally.^

exercise of one's calling, to
cution, etc., are claims

These rights are not ordinarily called property

rights, just

as persons are not ordinarily called wealth, and for a similar

—

they do not enter into trade. When wives
were bought and sold they were regarded as wealth, and
marital rights as property. To-day, both are taken out of
commerce and therefore removed from commercial ideas
and terms. The economist need not, perhaps, absolutely
like the business man, he is chiefly
insist on restoring them
But in framing his definiinterested in what is salable.
reason,

;

tions he finds it difficult, if not impossible, to confine the
terms "wealth" and "property" to objects which are ex-

changeable, without thereby sacrificing simplicity and logical convenience, and excluding certain objects, such as public

parks and former Enghsh entails, which, though never sold,
even business men would call wealth and property respectively.

We therefore

choose in this book to frame our

nitions so as to include such elements, even

not further referred
to include too
1

Cf. T.

90, 128.

much

to.

defi-

though they be

definitions, it is usually better

rather than too

little,

and

in this case,

E. Holland, Jurisprudence, Macmillan, 1898, pp. 50, 80, 87,

NATURE OF CAPITAL AND INCOME

at least, the superfluous which

[Chap. II

included will seldom con-

cern and never embarrass us.

Property rights, then, consist of rights to the uses or
services of wealth.

ways and

But the

which we own are alfuture services; the past have per-

necessarily

Moreover, since

ished.

all

services

future events are uncertain,

are always constrained to reckon with the element of chance.

strictly

complete definition of a property right, therefore,

would read as follows A property right is the right to the
chance of obtaining some or all of the future services of one
or more articles of wealth.
:

Property
each in
is

its

measurable, just as are wealth and services,

own

"by number,"

of the

Usually the measurement
by counting the number of rights

particular unit.

that

same kind.

is,

Thus, one hundred shares of preferred

stock in a particular

company

of that particular property.

a statement of the amount

The concepts

transfer, exchange, price, and value apply to property as to wealth and

Indeed, as an exchange of wealth

to services.

but a con-

cealed exchange of services, so an exchange of services

is but
a concealed exchange of the right thereto, namely, property.
Hence the exchange of property is the final form

of exchange,

and includes

in itself all other forms whatso-

ever,

§4
Wealth and property, then, are correlative terms.
Wealth is the concrete thing owned; property is the abstract right of ownership.
The two concepts mutually
imply each other. There can be no wealth without property rights applying to

which

it,

nor property rights without wealth

In fact, the proposition that
and wealth are coextensive follows necessarily from
the definitions of wealth and property
which we have adopted. But it may readily be objected
that in the actual concrete world, for which these definitions were designed, the correspondence between what are
to

property

they

apply.

PROPERTY

Sec. 4]

known

as wealth

and property does not hold

true.

of the case, however, will

ough examination

A thor-

remove

this

objection.

Sometimes wealth and property

rights are so closely

associated as to be confused with each other, so that, unless

one stops to consider the matter, the existence of the

two separate concepts would not be suspected. This is
true in the case of "fee simple," where a piece of
land is spoken of as a "piece of property." For practical

purposes,

little

objection can be raised to such popular

usage, but even in such cases strict accuracy requires that

the two ideas should be distinguished. The distinction is
more easily remembered if we employ the full phrase "property right."

A loaf

of bread

erty right; the right to eat

other hand, in the

concrete wealth, not a prop-

more involved

we encounter the opposite

the property.

it is

The danger here

difficulty.

separating the concepts of wealth and property too
so as to consider

them

the

cases of property rights,
is

far,

as independent instead of interde-

When railway shares are sold in Wall Street, the
prone to think of those shares as entirely detached from any concrete wealth. It is unlikely that he
has ever seen or ever will see the steel rails, cars, and locopendent.

investor

motives upon which those shares are based; and indeed,
the only concrete object of which he is Hkely to be distinctly conscious
is

the paper certificate

clear that this paper certificate

not

itself.

itself

But

the prop-

but merely the written evidence of it and that the
railway shares, to be property, involve a real railway
(v>^ealth) underneath.
That all wealth involves a property right is not likely
to be denied by any one; and that all property rights involve underlying wealth should be equally evident. But
this is not the case.
In fact, some of the most dangerous
fallacies which beset the business world, including many of
the sophisms of credit, are due to the difficulty of recogerty,

NATUEE OF CAPITAL AND INCOME

nizing the wealth lying behind property in

[Chap. II

some

of its sub-

limated forms.

§5
In order not to devote too much space to

this subject

the best procedure will be to give types of the chief forms

and to specify in each case what wealth underThis is done in the table on pages 26 and
lies the right.
27, which also specifies the services involved, and (where they
of property,

exist) the certificate or written evidence of

the property

right.

§6
Probably ninety per cent of the actual property in the
United States would be included under the cases entitled
Fee Simple, Partnership Rights, Stocks, Bonds, Notes, and
In all of these cases, the existence of the
Lease Rights.
real wealth behind them is well known and acknowledged.
For practical purposes, therefore, the proposition that
wealth and property are coextensive is already established.
Of the remaining cases some seem a Uttle obscure at
first, but they may be readily solved if we bear in mind a
few general principles
The first thought which should guide us is that, given
any particular property right, we should first discover the
benefits or "services" secured by that right, then the physThese
ical means by which those services are obtained.
means are not always identical with the "cause" of those
For instance, real estate with a southern exservices.
posure is especially desired because of the sunlight which

The sun may be called the cause of the sunit.
but the land is the practical means of obtaining it.
To own or not to own the land is to obtain or not to
obtain the sunlight which goes with it. It is the land which
falls

upon

light,

puts the sunlight at the disposal of its owner. On the other
hand, when a lamp gives its fight it is not only means, but
also cause.

PROPERTY

Sec. 6]

Following this idea, that wealth is simply the means
and not necessarily the cause, we can better understand some
We see clearly what it is that lies
of the items in the table.

behind a street railway franchise, or the franchise of the
underground system of New York City. It must be the
wealth by means of which the transportation can take place.
The streets which the railway has the right to use form the
necessary means for

its

transportation services.

To own
them

the streets involves the possession of the right to use
for transportation purposes, and,

or sold, as

when a

franchise

when

this right is given

granted, this act constitutes

a partial surrender of the ownership of the streets.
Again, let us consider the case of a promise. The physical
means of fulfilling a promise are. evidently the person who

made

the promise and the wealth which that person can or

will use for that purpose.

by a mortgage
he

may

But

Thus, a debt or bond secured

primarily a claim upon the promisor which

satisfy out of his earnings or his general wealth.

advantage over other forms of
upon a
specific portion of the promisor's wealth, which may be
taken in payment even against his will, if the promisor
otherwise fails to make good his promise. Here the means
of perfecting the right evidenced by the bond include the
it

offers

this great

indebtedness, that

also a contingent claim

person of the promisor, his general wealth, and the specific
part of that wealth covered

by the mortgage.

On the

other

hand, a "labor due" is principally a claim upon the person
of the laborer, for he must be the means of performing the
labor required. In country districts farmers are often
under obUgations to the county to furnish a certain amount
The right to such work
of roadwork of men and horses.
a species of property belonging to the county. A still
is found in cases where the labor or services
to be rendered are of a personal or artistic character, such
for,
as the singing of a Patti or the acting of a Bernhardt

better example

;

while one under contract to lay bricks might reasonably

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NATURE OF CAPITAL AND INCOME

28
fulfil

his contract

bricklayer,

[Chap. II

by furnishing another equally

no audience attracted by either of those

skilful

artists

would accept in return for its entrance money the performThis
ance of any understudy, no matter how capable.
right to the services of a particular person, as distinguished

from the right to services of a particular character, gives
rise to

many

Similarly, a personal

curious cases in law.

note is to a large extent a claim upon the person of the
drawer, though also a claim upon his other wealth; for
both the man himself and his external wealth are the means
of keeping good the promise and finally paying the debt.
Another case is that of a ''factor's agreement" or some
other promise by which a firm or person agrees to refrain
from certain acts, such as selling in competition with the
promisee. Some years ago a paper manufacturer near New
Haven was offered a round sum if he would close his mills.
This he did, to the benefit of both himself and his former
In this case the contract
rivals, though not of the public.

which he made with his

rivals constituted a

kind of prop-

by means of which his promise
was made good was evidently his own person, together with
and the service performed was the inactivity of
his plant
erty for

them

the wealth

;

both.

Good

will is

of property.

less certain

though

still

a valuable form

A few years ago one of the largest newspapers

was sold. The property included,
besides presses, type, Hnotype machines, office building, etc.,
An overthe items of overdue subscriptions and good will.
due subscription is a debt which constitutes a virtual promise of the subscriber, and thousands of these in the aggregate make up a considerable value. By good will is meant

in the United States

something very similar; namely, the quasi-promise of the
subscribers to continue to pay as long as the newspaper is
sent to

them and they

These quasi-promises

are satisfied.

are also property, being almost equivalent to a signed agreement of the subscribers to the effect "We hereby promise
:

PROPERTY

Sec. 6]

PubHshing Compay the annual sum of $8 to the
is received
newspaper
its
long
as
and
so
that
provided
pany,
the right
merely
will
is
Thus
good
and is satisfactory."
and patsupport
of
promise
to a tacit, loose, and contingent
owns a
will
ronage, less cost. The firm possessing good
precarious yet valuable claim upon its patrons, namely,
the chance of their continued patronage. The persons of
these subscribers, and their other wealth, are what underUe the property right, because they are the means to the
Of course
desired services to which those rights apply.
to

the chance of obtaining these services

would be

very

much

less

the services were specifically promised

than it
but chance, either large or small,
if

involved in

all

property

rights.

In the same way, the ''custom" of a tailor or the "pracis simply the right to the chance of

tice" of a physician

future patronage.

A franchise in the sense of a monopoly privilege granted
by a government is quite different from a street railway
The object of the monopoly is to prevent cerfranchise.
The means to that end are,
tain acts of certain persons.
in the last analysis, the persons
refrain,

who

are constrained to

and the wealth withdrawn from competition.

We may

similarly regard a copyright.

case of the paper trust, part of whose property

RecalUng the
was the prom-

a paper manufacturer not to compete, we may regard
a copyright as the right to a similar refraining from or reAt one time, an English pubstraining of competition.

ise of

lisher

would obtain the promise of an American publisher
It would have been property

not to "pirate" his works.

of great value to the publishers of the Encyclopaedia Bri-

they could have prevented the pirating of their
work in this country. Prevention can now be accomphshed
tannica

through the instrumentality of international copyright.
The wealth underlying this property right is the wealth
which, if employed in the specified line, would enter into

NATURE OF CAPITAL AND INCOME

[Chap. II

It mainly consists
and plants of possible competing publishers
their nonand it does not matter whether their inactivity
is purchased by a money payment or encompetition
forced by government intervention.
In like manner we may resolve the problem of irredeemable paper money. Where this exists in its purest
form, with no promise or intention of ultimate redemption
by the government which issues it, it amounts to a forced
It is like a check drawn by the govloan, or rather, a levy.
ernment upon the public, which each individual is obliged
to cash. It is an order to surrender on demand a certain
amount of the community's goods. The government usually employs paper money to obtain ammunition or soldiers' supphes.
The merchants who give these goods are
forced to accept paper money in return, and allowed to
recoup themselves by passing on these orders to others.
In this way people are deluded into believing that no one
The
really loses, but that the loss is perpetually passed on.

competition with the property owner.
of the persons

—

;

—

loss is shifted,

but nevertheless

exists ; for, since a definite

quantity of supplies has been abstracted from the pubUc
by the government, it is clear that this much loss has been
suffered,

however

irredeemable paper

may be
money

distributed
is

rotation.

Thus,

a claim on the general wealth

Of course it seldom occurs that it conand when it becomes redeemable it
changes its character; for when the government assumes
the obligation involved, it becomes a special claim upon
the government gold and other wealth.
A somewhat similar vague property right is the government's taxing power, which is the right to take from the
of a

community.

tinues irredeemable,

individual so
as

may

much

of the services or product of his wealth

be necessary for the pubhc good.

The heavier

the tax, the greater the reduction in the value of the individual

It is well known
Henry George proposed, means

wealth of the community.

that to nationaHze land, as

PROPERTY

Sec. 7]

merely to increase the tax upon it until all its value has
been taxed out of it; that is, to take from the individual
all of the services or profit of his landed wealth for the benefit of the pubhc, leaving him merely the empty shell of

nominal ownership. The case is analogous to that of a person or a community which has mortgaged its wealth so

consumed
payment of interest, and nothing is left with which
redeem the pledge. The same principle applies to all

heavily that the value of

its services is entirely

in the

taxes,

even when not carried to such an extreme.

§7

second helpful guide in resolving the various obscure

forms of property

found in the fact that one property right

by another. For instance, a mill is owned in
shares; a railway company owns some of those shares; a
bank owns some of the railway shares; and John Smith
owns some of the bank shares. It is evident that John
Smith has a claim upon the wealth constituted by the mill,

often overlaid

although his property

only distantly connected with

it,

and through several intermediate layers of property rights.
A common example of such secondary relation between
wealth and property occurs when the property is held in
At common law, the trustee is the legal owner but
trust.
;

the law of equity recognizes the fact that the beneficiary

the true owner.

He has

a claim against the trustee, and the

trustee holds the right to the wealth as against the rest of

the world.

The

beneficiary

must work out

his

rights

through the rights of the trustee.
Another good example is that of a claim upon a government, as, for instance, a government bond. This is really
a claim against the community, for the government is
merely an intermediary between the bondholder and the
pubhc wealth which is taxed to satisfy the bondholder's
claims.
The government owns property only as a sort of
trustee for the pubhc.

The Boston Common

held by the

NATURE OF CAPITAL AND INCOME

city of Boston, but

owned by the citizens, who are
Each individual who has the right

really

the true beneficiaries.
to enjoy

it is

[Chap. II

to that extent a part owner.

uncommon

thus to have, between a property
and the wealth underlying it, several layers of property.
A man who owns an ordinary foreign bank note has
a claim upon the property of the bank. But the bank's
property consists, for the most part, not of tangible wealth,
but of promissory notes and other claims on merchants.
It

not

right

These notes represent a part right in the wealth (including
community; consequently the holder of a
bank note quite unconsciously owns a claim upon the dry
goods, groceries, and other wealth of merchants, which make
good the debts of these merchants to the bank.
In the case of United States bank notes he also owns an
alternative claim on government bonds, and therefore on
the taxable wealth which makes these bonds good. It is
erroneous to think of a bank note as representing simply
persons) of the

money.

This

true of gold certificates; for there are in

many

the United States Treasury as

there are certificates in circulation.

other hand,

made

actual gold dollars as

A bank

note,

on the

good, not solely by the metallic reserve

of the bank, but also by the other property or "assets,"
which the bank is constantly changing or transforming into
cash. The Bank of England, for instance, had £60,000,000
of notes out at a given date, and only £43,000,000 of gold
in its vaults.
But the £17,000,000 deficiency which thus
seemed to exist was represented by securities, that is, other

property held by the bank.

§8

third guide

erty and wealth

That

that the correspondence between propis

a contemporaneous correspondence.

to say, the existing property rights are rights to

the use of existing wealth, so that existing wealth underlies
all existing

property rights.

would seem at

first

sight

PROPERTY

Sec. 8]

that "credit" forms an exception, for credit

payment.

right to a future

But

it is

a present

impossible to have a

any future wealth which is not also a right to some
means of securing that future wealth.

right to

present wealth as a

The

right to next year's fruit

trees.

The

right to next year's

a right to or in present fruit

wheat

a right to or in the

present farm, farmer, and farm implements.
receive a future chair or table yet

unmade is

The

right to

the right to or

and other wealth of the carpenter, which are the means by which that chair or table
To own a note falling due next year is
is to be secured.
a part right in the person and other "assets" of the promisor, and ceases to have value as soon as he ceases to be
"good for it." The courts do not restrict a debtor in the
in the present person, tools,

disposition of his possessions prior to the maturity of a note.

He may

elect to squander these, and even to commit suiBut such destruction of the present means of providing for future payment carries with it the impairment
or destruction of the value of the note. No future commodities or benefits whatever can be owned in the present
except as claims on certain requisites of their production
cide.

now

in existence.

pended in mid

air,

We
as

kite without a cord.

means

own next

not only

year's goods sus-

more than we can fly a
There must always be some present
were, any

of controlling the future.

other property right,

And

cannot

Thus, credit,

every

a part right upon existing wealth.

every right to a future benefit a claim

on present wealth, but conversely, every claim on present
wealth

"futures"

a right to a future benefit.
is

therefore not

an exceptional

Owning

rights to

case, but the gen-

eral one.
As we have seen, all wealth is merely existing
means toward future services, and all property, merely present rights to some of those future services. It is only
through the future services that wealth and property are
bound together at all. The sequence of ideas is, first, pres-

ent wealth second, future services
;

;

third, present rights to

NATURE OF CAPITAL AND INCOME

[Chap. II

these future services and therefore to the present wealth

which yields them.
chance

Property

future

thus always a right to the
It always contemplates

benefit.

both present and future time. We are here emphasizing the fact that property always constitutes an interin

est

nothing

the present
is

means

for acquiring it.
Property in
This principle applies even to the

nothing.

extreme case of good will. We saw that good will is the
ownership of a chance of continued patronage. The future
patronage may in some cases include that of persons yet
unborn; but the road to their patronage must lie through
the present generation.

Existing persons and things must

always constitute the means for the attainment of any
benefits expected in the future.

§9

fourth guide

that, in the case of partial ownership

of wealth, the aggregate of all the partial rights constitutes

the total ownership.

We may

picture to ourselves

all ar-

wealth as having attached to them streams of
services stretching out into the future.
These services
ticles of

up among separate owners in different ways, sometimes transversely, sometimes longitudinally, and sometimes definite parts of them are separated out. The total
are cut

ownership of the wealth is simply the aggregate of the rights
to the entire stream of future services.
It may, of course,
be true that the character and size of this stream of services
will differ according
its

ownership

to the different

parceled out.

methods by which

This fact, however, does

not invalidate the principle that the total ownership
the combination of all the partial rights.

common

speech the minor rights to wealth are not

ordinarily dignified as rights of ownership.
ant's right in the dwelling he occupies

an estate

Thus, a tensharply distin-

Yet the law recogthe land, and when the

guished from the right of the owner.
nizes a leasehold as

PROPERTY

Sec. 9]

owner

of land wishes to sell

fee simple title, he finds

and convey an unencumbered

necessary to extinguish

all

out-

standing leases, or claims for future services, often at considerable

cost.

Recently the

New York Reform

Club

sold its leasehold in a building for $25,000, because the pur-

chaser could not afford to wait for the expiration of the
lease.

The

total ownership

always includes the ownership

of the tenant.

In
is

manner, the total value of any concrete wealth

the total value of the property rights in

it.

The

correspondence between wealth and property gives us a

new method

of appraising wealth, namely,

by appraising

In fact, we are here provided
with another sense of appraisement of wealth, in addition
to the several already given in Chapter I, Such appraisement may mean, not what the whole article of wealth
would sell for en bloc, but the sum of the values of the partial rights to it when these latter are appraised on the basis
the property rights to

it.

of small individual sales.

Thus, the value of a railroad,

found by taking the
Railways are
seldom sold as a whole, but their stocks and bonds are
constantly on the market, and are often the only means of
affording a valuation.
It is true that under these circumstances the market price
of the stock would form no basis for judging what would
be the value of the road if sold as a whole. There would
need to be added the value of "control." But this will
be accounted for by an addition to the value of such of the
shares as will secure this control.
"Control" is the power,
coming from a majority of votes, to obtain from the road
some services which would not be possible without such
majority ownership. The additional benefit thus obtained
may be illegitimate, as when the parties in control vote
themselves large salaries. But whether legitimate or illegitimate, the power to make the road better serve one's
operating under normal conditions,

sum

of the values of its stocks

and bonds.

NATURE OF CAPITAL AND INCOME

[Chap. II

interest often affects profoundly the value of the shares.

The stock of the Chicago, Burlington, and Quincy Railroad
was quoted at $132 when a certain capitalist determined to
buy it. Knowing that it would be almost impossible to
acquire all the stock by ordinary means, he offered instead
to take over as

much

as should be offered to him, provided

and to give $200 in four per-cent
an offer which was accepted by
bonds for each $100 share,
most of the stockholders. The acceptance added at once
fifty per cent to the market value of the stock, and improved
even the value of the bonds so that the value of the system,
sold virtually as a whole, was much more than of the stock
it

was more than

half,

—
;

and bonds before the negotiation was opened.

The valua-

tion of the road will thus be different according to whether

under the control of a particular interest or whether
is widely distributed, as well as according to
But in every
the purpose for which the valuation is made.^
instance the value of the railroad is the sum of the values
of the complete aggregate of rights in it.
If one bears in mind the explanations which have been
given, there can scarcely be any difficulty in tracing out for
each property right some underlying wealth, so that we may
give adherence to the general principle that wealth and property are coextensive. That this is true as a "general fact"
cannot fail to be admitted even were it necessary to reject
But if our definitions of wealth
it as a "necessary truth."
it is

ownership

its

and property are adopted, it becomes

also a necessary truth.

§10
Having seen what property is, we may now classify
property rights. There are two chief classes, complete
A complete, or practically
rights and partial rights.
complete, right, or "fee simple" to an article of wealth,
right to all those uses of that article
^

which are owned; a

The completest account of railway valuation is that contained
"The Commercial Valuation of Railway Operating

in Bulletin 21,

Property," United States Census, 1905.

PROPERTY

Sec. 10]

partial right

a right to a part of

rights are the only ones

The

among

services of

its uses.

which make

The

partial

difficulty.

wealth may be apportioned
owners in many ways. If they are

article of

different part

divided longitudinally in time, the rights of the various

The

coowners are similar to each other.
are the rights of partners

well-defined rights of the individual

commune

family, or

common, and,

to the

finally,

examples

chief

and stockholders, and the

common

members

less

of a club,

property and

all

rights

the rights to the different kinds of

where one person owns the right of
farming a piece of land, another the right of mining its
minerals, and a third the right of fishing in the streams
uses, as, for instance,

which run through

it.

If the services are divided transversely in time,

son has the rights of

and another

all

one per-

up to a particular date,
beyond that. The former

all services

the rights

and the latter the landlord.
Hmited both in time and also in quantity
or value, we have still another group of property rights.
These and other classes are seen in the following scheme

person

called the tenant

If the services are

of classification.
r

Complete (Fee Simple)

rights in

common

rights to different

to services cut longitudinally

-i

usufructs
partnership rights
joint stock shares

(lease
reversion
patent and copyright

to services cut transversely
Ph

(bonds
.

private notes

Partial

banknotes
bank deposits

rights to definite parts
of services

(checks,

drafts,

orders

money
,

..,„.,
mdennite

mmor and

f
<
[

will and custom
taxmg power

good
°
.

and

exchange
irredeemable paper
bills of

NATURE OF CAPITAL AND INCOME

[Chap. II

§11
Since wealth and property are each the opposite aspect
of the other, economics

might be described as the "sci-

ence of property" quite as truly as the "science of wealth."
If we are studying the economic condition of a whole
country,
less

we prefer to fix our attention upon wealth, caring
how its ownership is divided. We are then inter-

about

ested in the acreage of wheat

mines, railways, factories,

owners.

the other hand,

tribution of wealth"
classes

—

The idea

it is

the extent of coal

in their

are studying the "dis-

— the condition of individuals

property on which

we need

community

or of

to fix attention.

of wealth, therefore, is associated

fare of the
is

fields,

and homesteads, and not

with the wel-

in general, while that of property

associated with the welfare of the different individuals

in the

community.

But,

may

be asked,

why

much

stress laid

the principle that wealth and property are coextensive?
It

may

be conceded that most of the principles of political
will be unaffected whether or not this one is ac-

economy

cepted as rigorously true.

Its usefulness consists in help-

At present there seems
mind a confusion of the concepts

ing us to arrange our ideas.

exist in the popular

wealth, property, certificates of property, services, and utihty,

which should be carefully separated from each other.
No one can fully understand monetary problems, for instance,
unless he distinguishes carefully the three elements to which
the term "money" is indiscriminately applied. There is
all

raonej-wealth, such as a gold eagle; money-property, such
as the right of a holder of "greenbacks";

and money-cer-

such as the paper "greenbacks" themselves. If
the fact that wealth and property are coextensive were more
tificates,

generally

known and acknowledged, some very practical and

salutary results would follow.
inflation,

Wild schemes

of currency

which are based on the idea that wealth

may

PROPERTY

Sec. 11]

by multiplying the titles to it, would be
checked, and the usual atrocities of double taxation, for inincreased simply

and mortgage, or
would be avoided/

stance, of farm
shares,
If

we bear

mind the
we shall

and railway

of railways

and

distinctions in this

in the

no advantage,
but much disadvantage, in including any "immaterial"
elements in wealth. "Immaterial wealth" is, in fact, one
of those bugaboos which have done a great deal to obscure
the simplicity of economic relations. Legal advice or
medical attendance are not "immaterial wealth" they are,
as we have seen, simply services of wealth (human wealth
previous chapter,

see that there is

;

The "properties and powers

in this case).

of nature"

are not wealth, but, as explained in the previous chapter,
are attributes of land

and enter economic

science merely

as giving characterization to that particular kind of wealth.

They cannot be counted as wealth
any more properly than can the

in addition to the land

rubber be
counted as wealth in addition to the rubber. Likewise,
swift horses are wealth, but not their swiftness honest, wise,
successful, and healthy men are wealth, but not their honesty, wisdom, skill, or health.
Most of the mystery of
banking to the ordinary mind consists in the mistaken noelasticity of

;

tion that credit
basis.

something "inflated," without a tangible

A mere inspection
make

of a bank's balance sheet should

behind every claim upon
something to make it good. If the anterior
something be itself a claim on some other bank or person,
there lies behind it, in turn, some basis, and so on until a
concrete instrument is finally found.
Another common error is the belief that "wealth consists of utility."
If this were true, the law of diminishing

serve to

the bank

clear the fact that

^ See
Report of Professor Edward W. Bemis and Carl H. Nau, on
Value of Ohio Railroads, 1903; also, Report of the Interstate Commerce Commission on Railways in the United States in 1902, 1903,
Part V.

NATURE OF CAPITAL AND INCOME

40
utility,

[Chap. II

that equal increments of wealth have decreasing

increments of

To plead

utility,

would be a contradiction

in terms.

in extenuation of such confusions the fact that

popular usage

guilty of them,

is like

trying to justify in

the science of physics a jumbling together of the concepts

mass and density, or of velocity and acceleration, or of
and energy, on the ground that the ordinary man does
distinguish
between them. The proper method of
not
avoiding large errors in any science is to avoid small ones
This can be accomplished only by scrupuat the outset.
of

force

lous attention to elementary distinctions.

CHAPTER

III

UTILITY

have seen that

all

wealth and property imply pro-

spective services or "desirable events."

the desir-

which gives meaning
would therefore be im-

ability of these future expected services

to all economic
possible, in

any

phenomena. It
view of the subject, to confine our-

full

selves strictly to the study of objective wealth, property,

In the present chapter we shall consider
element in economics.
Wealth is wealth only because of its services and services are services only because of their desirability in the
mind of man, and of the satisfactions which man expects

and

services.

briefly the subjective or psychical

;

them

to render.

Indeed, the desirability of services

implied in their very definition as "desirable events."

The mind of man supplies the mainspring in the whole economic machinery. It is in his mind that desires originate,
and in his mind that the train of events which he sets
going in nature comes to an end in the experience of subjective satisfactions.
initial desire

services

and the

only in the interim between the

final satisfaction that

have place as intermediaries.

wealth and

its

—

that
are thus led to consider two. new concepts,
Both of
of " desirability " and that of " satisfaction."
these enter into our consideration only as they are applied

—

wealth, property,
economic elements,
services.
To avoid unnecessary repetitions, we may treat
these three elements under the one rubric of "goods."
to

the

three

NATURE OF CAPITAL AND INCOME

[Chap. Ill

§2
The

any particular goods,

desirahility, then, of

particular time, to

any

particular conditions,

particular individual, under

any
any

the strength or intensity of his de-

goods at that time and under those conditions.
What is here called desirability is identical with what has
usually been called in economic writings "utihty." But
utility, though not to be utterly displaced, is not the happiest term for our purpose.
To say nothing of the mere
awkwardness of its only antithetical term
"disutility"
sire for those

—

— as

compared with "undesirability," it has fallen heir
to so many different meanings that its use here is apt to
be confusing. The term "useful," for instance, in ordinary
language is employed in opposition to "ornamental."
In this sense diamonds are said to be ornamental and not
useful, though in economic science they are adjudged
useful.
Again, "utility" usually imphes intrinsic merit,
whereas, when we employ it in economic science, we are
obliged to apply it to any noxious thing considered by its
owner desirable, for instance, opium, alcohol, or degrading literature. Finally, in the last few years, the word
"utility" has come into a new and technical meaning as
employed in the phrase "public utilities," which designates electric lighting plants, street railway systems, gas

works, and

many

other things which are merely collections

of wealth of a peculiar kind.

In order to obviate these objections, Professor Pareto
has proposed an entirely new term, "ophelimity." This
has both the advantages and the disadvantages of any
newly invented technical term, and has thus far shared
the fate which usually befalls the attempt to coin words.

The word "utility"

is still

employed, and

it is

not likely

that "desirability," "ophelimity," or any other term will

soon displace

it.

In the present book we shall use both
but preferably the latter.

"utility" and "desirability,"

UTILITY

Sec. 3]

In proposing that economists substitute so far as possible
the term " desirabihty " for '^utihty/' the author is simply
following the example of Professor Gide ^ and Professor
Marshall.

If the

term "utility"

to be used at

all,

we must

dis-

tinguish the utihty of goods from the use of the goods.

As has been pointed

out, the uses or services of goods are

the desirable events which occur by their means.

on the other hand,

Utihty,
not these desirable events, but their

desirability.

Again, the desirabihty or utility of goods must not be

confused with the pleasure which
tained from those goods.
involved, for pleasure
tion of the desire.

means the

be ultimately obis

not the desire, but the satisfacan experience in time, and requires

It is

duration of time for

may

Here our second concept

its

existence.

Desirability,

which

intensity of desire of an individual under certain

mind

conditions, merely indicates a state of

at a particular

point of time, namely, the point of time at which he mentally
weighs and measures the desirability of any contemplated
service, property, or wealth.
We may speak of the desirability of a fruit orchard to a particular person on Janu-

ary
is

1905; but the pleasure derivable from that orchard

only to be experienced during future years, as

fruit

and the

fruit gives

bears

enjoyment to those who eat

it.

—

Thus we have two concepts utility or desirability,
a
and pleasure or satisfacstate of mind at a point of time
tion,
an experience of mind through a period of time.
These two concepts are closely related for the desirabihty
of goods is simply the present esteem in which the future
:

;

—

;

Gide's Principles of Political Economy, 2d American ed., 1904,
See also the present writer's " Mathematical Investigations in the
Theory of Value and Prices," Transactions of the Connecticut Academy,
1

p. 48.

1892, p. 23.

NATURE OF CAPITAL AND INCOME

44
satisfactions

none the

that

The

[Chap. Ill

from those goods are held. But the two are
It is with utihty or desirability

less distinct.

are concerned in this chapter.

desirability of

any particular goods may

relate to

the whole or to any part of the group of goods. The desirability of the entire group is called the total desirability
the desirability of one unit more or less of the group

In economic science we
with total desirability,
than
marginal
with
more
to
do
have
of marginal desirthe
concept
that
important
and it is
ability should be thoroughly understood.
That marginal desirability is the desirabihty of one unit,
called the marginal desirabihty.

more or

less,

may

be illustrated as follows: If a person

possesses ten chairs, their marginal desirabihty

the differ-

ence, in his mind, between the desirabihty of having ten

having nine chairs; that is,
by having one chair less.
it
thing,
the marginal desirabihty
same
the
almost
Or, what is
desirability of one chair
chairs
is
the
of the group of ten
chairs
is

more,

and

and the desirabihty

the desirability sacrificed

— the difference in desirability between eleven chairs

ten.

Whether the marginal desirabihty is taken
more or to one unit less is usually

referring to one unit

as
of

so httle importance as not to require separate designations

to distinguish them,

and in case the commodity

one which

admits of indefinite subdivision, as flour, wheat, coal, etc.,
the two coalesce as the size of the increment is reduced indefinitely.^

This fact

usually expressed

by saying that

the marginal desirability of the chairs is the desirabihty of

But though

this

mode

of statement is

"the tenth"

chair.

correct,

not intended to convey the idea that any par-

it is

ticular chair is the

The group

"tenth"

under consideration
1

chair.

of goods the marginal desirabihty of

may

which

be any specified group of goods

For a mathematical treatment see Appendix to Chap.

Ill, § 1.

UTILITY

Sec. 4]

whatever. Reference may be had to a specified group of
goods now existing, or to a specified group of goods in the
future, or to a specified flow of goods through a period of
time.
For instance, the marginal desirabiHty of coal to an
individual

may

be taken to refer to the particular stock of
moment. If this stock con-

coal in his bin at the present
sists of fifteen tons, its

marginal desirability

the desir-

him between

ability of the fifteenth ton, or the difference to

the desirability of having fifteen and that of having four-

teen tons.

Or, reference

may

be had to an intended pur-

chase of coal to be delivered in three months.

we con-

sider a possible purchase of future coal to the extent of

marginal desirability then represents the

fifteen tons, its

same
an existing stock.

present desire for the fifteenth ton, in exactly the

way

as though reference were

Again,

a person

had

consuming in

his

household

fifteen tons

any instant is
the
sacrifice
which
ton,
or
fifteenth
desirability
of
the
the
his
yearly
consumpwould be occasioned were he to reduce
tion from fifteen tons to fourteen.
of coal a year, its marginal desirability at

Again, the group of goods considered

may

consist of ar-

which are of the same kind, or of a heterogeneous
collection.
In the preceding examples the goods were of
exactly the same kind. As an example of the marginal
desirability of a group consisting of diverse kinds, we
may cite the desirability of an additional monthly magazine
ticles all of

or newspaper.

If a subscriber is already taking ten periodi-

a specified journal
additional to the existing assortment may be regarded as
the marginal desirability with reference to the entire group
cals of different kinds, the desirabiHty of

of journals.

In the same way we

may

speak of the marginal desir-

ability of a series of characteristics or features connected with

any

article or articles of wealth.

the building of a house

dows he

will

put

in.

may have

person contemplating
how many win-

to decide

If he contemplates fifty

windows, the

NATURE OF CAPITAL AND INCOME

marginal desirability of the windows

[Chap. Ill

the desirability of

the fiftieth window, or the difference in the desirability
of having fifty

windows rather than

forty-nine.

§5
The
is

first

principle in regard to marginal

desirability

that an increase in the quantity of goods in the group

the marginal desirabihty of which

is under consideration,
a decrease in the marginal desirability of the
group. Each successive increment is less desirable than
the preceding increment. The marginal desirability of
sugar to the householder consuming five pounds weekly is
greater than the marginal desirability if six pounds are consumed, and is successively diminished as each successive
pound is added to his consumption.
It is well to remember that when the term "successively"
The
is here employed, it is not used in a temporal sense.
succession to which it refers is not a succession in time, but
a succession in thought. We consider the consumer of
sugar under a series of different hypotheses which we
examine successively. We begin with the hypothesis of
a weekly consumption of five pounds, and take up successively the hypotheses of six pounds, seven pounds, eight
pounds, etc. The desirabihty of the "last" pound in this
series is the marginal desirability for the group ending at
that point; but the "last" pound refers to the one considered last in our mental review, and not the one acquired last
by the consumer. This fact needs to be emphasized, in

results in

view of frequent confusion on the subject occasioned by too
loose an employment of the words "last" and "successive."
It is presumably because of the time confusions involved
in these words that, under the leadership of Wieser^ and
Marshall,^ economists have substituted the phrase "marginal utihty " for the older phrase of Jevons, "final utility."

With

these provisos and explanations in view,

it is

Ursprung des Werthes,

Principles of Economics, 3d ed., 1895, p. 168.

128.

clear

UTILITY

Sec. 5]

that the total desirability of any group of goods
of the desirabilities of

the

sum

The total
found by add-

the successive units.

desirability of the ten chairs, for instance, is

ing together (1) the desirability of having only one chair,
(2)

the desirability of having a second chair, (3) a third,

a fourth, etc., until ten chairs have been considered.
These successive desirabilities will evidently continually
diminish. Hence their sum, or the total desirability of the
group, is not the same thing as ten times the marginal deIn this is found the explanation of the fact that
sirability.
(4)

them as possessing much
him than the total desirability
the money which they cost, although the loss of any one
the ten chairs may not represent more desirability than

the possessor of the chairs regards

more
of
of

total desirability to

the desirability of the

known

well

money which

that one chair cost.^

to all students of the

modern theory

of value, marginal desirability lies at the root of the deter-

mination of value and price. We are here concerned,
however, not in applying the concept of marginal desirability to the determination of economic magnitudes, but
merely in explaining its nature.
Although the definitions which have been given of dethey do not enable
manner. The exact
a subject of much impor-

sirability serve to explain its nature,

us to employ

measurement

in a quantitative

of desirability is

tance, as well as of great difficulty.

Inasmuch as

present work only an incidental use will be
concepts,

made

in the

of these

does not seem proper here to enter into these

discussions.^
Economics, New York, 1904, pp. 25-26.
See the writer's " Mathematical Investigations in the Theory of
Value and Prices," Transactions of the Connecticut Academy of Arts
and Sciences, 1893, Vol. IX; Pigou, Economic Journal, March, 1903,
Vol. XIII; Pareto, Cours d' Economic Politique, Vol. I; Giornale
d'Economisti, August, 1892; J. B. Clark, "Ultimate Standard of
Value," Yale Review, November, 1892; Seligman, Principles of
Economics, Longmans, Green & Co., 1905, Chap. XIII; Chin tao
Chen's Societary Circulation, a doctor's thesis, Yale Univ., 1906.
^
^

Cf. Fetter's Principles of

PART
Chapter IV.
Chapter V.
Chapter VI.

Capital

Capital
Capital Accounts
Capital Summation

CHAPTER IV
CAPITAL

In the foregoing introduction we have set forth several
fundamental concepts of economic science,
wealth,

—

property, services, satisfactions, utility, price, and value.

We have seen that wealth consists of material appropriated
objects,

and property,

of rights in these objects

human

in its broadest sense includes

beings,

;

that wealth

and property

in its broadest sense includes all rights whatsoever;

that

services are the benefits of wealth, satisfactions the enjoy-

ment

of services,

and

desirability or utility the desire for

wealth, property, services, or satisfactions; that prices are
the ratios of exchange between quantities of wealth, property, or services ; and, finally, that value is the price of

of these multiplied

by the quantity.

any

These concepts are

the chief tools needed in economic study.

Nothing has yet been said as to the relation of these
various magnitudes to that great " independent variable
of

human

experience, time.

quantity of wealth

When we

we may have

speak of a certain

reference either to a quan-

quanconsumed, exchanged, or transported during
a period of time. The first quantity is a stock (or fund)
of wealth; the second quantity is a flow (or stream) of
wealth. The contents of a granary at noon, January 1,
1906, is a stock of wheat the amount of wheat which has
been hoisted into it during a week, or the amount of wheat
which has been exported from the port of New York during
tity existing at a particular instant of time, or to a
tity produced,

;

NATURE OF CAPITAL AND INCOME

[Chap. IV

a flow of wheat. The term "wealth" by itself is
determine which of these two kinds of magnitudes is meant. Similarly, when we speak of property
or of value, we may have in mind either a fund or a flow.
A thousand shares in a certain company owned by a certain man at a certain time constitute a particular fund of
property the number of shares transferred in a week on the
stock exchange constitute a flow of property. Again, the
value of the checks held at noon of any day by one bank
drawn on other banks constitutes a fund of value the value
of the checks which pass through a clearing-house in twentyfour hours constitutes a flow of value. Services and satisfactions, unUke wealth and property, can exist only as
flows a fund of either is impossible.
A fund is fully specified by one magnitude only a flow
1905,

insufficient to

;

— the amount of flow and the duration
— the of flow or the
two a third

requires two,

From

these

of flow.

follows,

quotient of the
of flow

amount divided by the duration. The rate
more importance than the amount of flow.

often of

Thus we care

man

rate

less to

know

the aggregate wages of a work-

during a fifetime than the rate of his wages during

various periods of his

fife.

between a fund and a flow has many
applications in economic science.^ The most important appfication is to differentiate between capital and income.
Capital is a fund and income a flow. This difference between capital and income is, however, not the only one.
There is another important difference, namely, that capital
is wealth, and income is the service of wealth.
We have

The

distinction

therefore the following definitions:
isting at

instant of time

stock of wealth ex-

A flow of serv-

called capital.

through a period of time is called income. Thus, a
dwelling house now existing is capital the shelter it affords
ices

;

the
1

bringing

money-rent

its

income.

For some of these applications, e.g. to monetary circulation, see:
is Capital ? " Economic Journal, 1897.

What

CAPITAL

Sec. 2]

The railways

of the country are capital

transportation or the

their services of

;

dividends from the sale of that

transportation are the income they yield.

The

between capital and income

distinction

somewhat

analogous to the distinction between desirability and satisfactions, which was emphasized in Chapter III for desira;

bility was

shown

to relate to a point of time

and satisfactions

to a period of time.

§2
The foregoing
it

define

and income are

definitions of capital

true, universally accepted.

not

capital,

Many

wealth

not,

authors attempt

particular

as-

pect with reference to time, but as a particular kind or
species of wealth, or as wealth restricted to a particular

purpose; in short, as some specific part of wealth instead
of

any or

all

it.

are obliged, therefore, to pause a

moment to consider these opinions. In this chapter
we are concerned with the concept of capital only.
From the time of Adam Smith it has been asserted
by economists, though not

usually

by business men,

that only particular kinds of wealth could be capital, and

the burning question has been,

What kinds ?

But the

fail-

ure to agree on any dividing hne between wealth which

and wealth which
of

discussion,

such hne
is

suggests

certainly

exists.^

not capital, after a century and a half

What

the suspicion that no

Senior wrote seven decades ago

"Capital has been so variously defined,
be doubtful whether it have any generally
meaning."^ In consequence, "almost every

true to-day:

that

received

may

year there appears some
conception,

but,

new attempt

unfortunately,

to settle the disputed

no authoritative result

has as yet followed these attempts.

the contrary,

^ For
a fuller statement than that which follows of the disagreements and confusions on this subject, see the writer's "What is
Capital?" Economic Journal, December, 1896.
^ "Political Economy," Encyclopcedia MetropoUtana, Vol. VI, p, 153.

NATURE OF CAPITAL AND INCOME

many
field

[Chap.

of them only served to put more combatants in the
and furnish more matter to the dispute."^ Many

own treatment

authors express dissatisfaction with their

and even recast

of capital,

Adam

Smith's

in successive editions.^

concept

He would

3delds "revenue."

capital

Hermann/ on

occupied by the owner.

wealth

which

therefore exclude a dwelling

the other hand,

includes dwelUngs, on the ground that they are durable

But a fruiterer's stock in trade, which is capital
according to Smith, because used for profit, according to
Hermann does not seem to be capital, because it is perish-

goods.

able.

Knies

any wealth, whether durable or
^
reserved for future use. Walras

calls capital

not, so long as

attempts to settle the question of durabihty or futurity
by counting the uses. Any wealth which serves more than
one use is capital. A can of preserved fruit is therefore
capital to Knies if stored away for the future, but is not
capital to

Walras because

To Kleinwachter,^

will perish

duction, such as railways.

single use.

excludes food, for instance,

Jevons,^ on the contrary,

as passive.

by a

capital consists only of "tools" of pro-

makes food the most

and excludes railways, except as representing the food and sustenance of the laborers who built
typical capital of

all,

them.

While most authors make the distinction between capital
and non-capital depend on the kind of wealth, objectively
considered. Mill ^ makes it depend on the intention in the

mind

of the capitalist as to

how he

1 Bohm-Bawerk, Positive Theory
London and New York, 1891, p. 23.
2

of Capital,

of Nations,

Book

Chap.

Wealth

Staaiswirtschaftliche Untersuchungen,

Das

»
*

English translation,

E.g. Roscher, Marshall, Schaffle.

shall use his wealth,

II,

Munich, 1832, p. 59.
Berhn, 1885, pp. 69-70.
Elements d'Economie Politique Pure, 4th ed., Lausanne, p. 177.
Grundlagen des Socialismus, 1885, p. 184.
Theory of Political Economy, 3d ed., 1888, Chap. VII, pp. 222, 242.
Principles of Political Economy, Book I, Chap. IV, § 1.
Geld,

ed.,

CAPITAL

Sec. 2]

Marx makes

depend on the effect of the wealth on the
laborer, and Tuttle,^ upon the amount of wealth possessed.
Again, while most authors confine the concept of capital
^

MacLeod^ extends it to all immaterial
goods which produce profit, including workmen's labor,
credit, and what he styles "incorporeal estates," such as
the Law, the Church, Literature, Art, Education, an author's Mind.
Clark ^ takes what he styles "pure" capital
out of the material realm entirely, making it consist, not
to material goods,

of things, but of their utiHty.

Most authors leave no

place,

in their concept of capital, for the value of goods as distinct

from the concrete goods themselves, whereas Fetter,^ in
definition, leaves place for

nothing

else.

Some

his

definitions

are framed with especial reference to particular problem^s
of capital;

many,

lem of capital and

for instance,

have reference to the prob-

labor, but they fail to agree as to the re-

MacCuUoch ® regards it
means of supporting laborers by a wage fund Marx,^
a means of humiliating and exploiting them Ricardo,^

lation of capital to that problem.

as a
as

;

as a labor saver; MacLeod,^ as including labor itself as
a special form of capital.
Many definitions have reference to the problem of
production, but in no less discordant ways.
Accord-

ing to Senior,^ Mill,® and
itself

a product.

many

must be
and others admit

others, capital

Walras,*" MacLeod,^

London, 1887, Vol. II, p. 792.
Capital Concept," Quarterly Journal of Economics
November, 1903.
^ Dictionary
of Political Economy, article "Capital," p. 331.
* Capital and
its Earnings, Publications of American Economic
Association, 1888, pp. 11-13.
^ "Recent Discussion of the Capital Concept," Quarterly Journal
of
Economics, November, 1900, and Principles of Economics, 1904.
^ Principles
of Political Economy, 4th ed., p. 100.
' Principles
of Political Economy, § 37.
^

Capital, English translation,

"The Real

"Political

Economy,"

Encyclopaedia Metropolitana, Vol. VI, p.

153.
^

^°

Principles of Political Economy, Book I, Chap. IV, § 1.
Elements d'^conomie Politique Pure, Lausanne, 4th ed., p. 177.

NATUKE OF CAPITAL AND INCOME

56
land ^ and

all

must not apply
is

Bohm-Bawerk,^
must be a product, insists that it

natural agents under capital.

while agreeing that
capital

[Chap.

Marx ^

to a finished product.

productive.

Bohm-Bawerk

denies that

admits that

not "independently" productive, but denies the Marxian
Other writers
corollary that it should not receive interest.
make it coordinate with land and labor as a productive
element.

what

disagreement.

it is

that capital produces there

Adam

Smith

further

affirms that capital produces

"revenue," Senior,^ that it produces "wealth." Others
vaguely imply that it produces value, services, or utiUty.

Most

of the definitions involve

some reference

to time,

but in many different ways. Hermann ^ has in mind the
time the wealth will last; Clark,^ the permanency of the
fund capital as contrasted with the transitoriness of its
1 The fancied distinction between land and capital, viz.,
that the
former yields rent and the latter interest, and that rent varies with
different grades of land whereas interest is uniform for all sorts of
capital, is based on a confusion between quantity and value of wealth.
The return from land per acre will, it is true,' vary according to the
quality of the land. But so also the return from machinery of different grades will vary per machine. The return from different kinds of
capital per $100 worth will, it is true, be uniform; but so will the
For a full treatment of this confureturn from land per $100 worth.
sion see Fetter's "The Relations between Rent and Interest," a paper
presented before the American Economic Association, December, 1903.
Cf. Clark, Capital and its Earnings, p. 27, and Distribution of Wealth
(Macmillan, 1899), Chaps. IX and XIII. Cannan developed the same
idea in " What is Capital ? " Economic Journal, June, 1897. Cf the
writer's " R61e of Capital," Economic Journal, December, 1897, pp. 524,
.

526.
2

Positive Theory of Capital,

York, 1891,

Enghsh

translation,

London and New

p. 38.

Enghsh

translation,

London, 1887, Vol.

II, p. 792.

Capital,

«
Capital and Interest, Book VI.
Wealth of Nations, Book II, Chap. I.
"Political Economy," Encyclopcedia Metropolitana, Vol. VI, p.

^
^

153.
'

Staatswirtschaftliche Vntersuchungen,

Capital and

its

Munich, 1832,

p. 59.

Earnings, PubUcations of American Economic

Association, 1888, pp. 11-13.

CAPITAL

Sec. 3]

Knies/ the futurity of satisJevons/ and Landry/ specifically the time between the "investment" of the capital and its return.

elements, "capital goods";
factions;

§3
attempt any reconcihation between concepts
and yet there are elements of
truth in all. Though generally wrongly and narrowly
interpreted, there are certain recurrent ideas which are
entirely correct.
The definitions concur in striving to express the important facts that capital is productive, that it
is antithetical to income, that it is a provision for the future,
or that it is a reserve. But they assume that only a part of
To the authors
all wealth can conform to these conditions.
of the definitions quoted, it would seem absurd to include all
wealth as capital, as there would be nothing left with which
And yet, as
to contrast it and by which to define it.
Professor Marshall says, when one attempts to draw a
It is idle to

of capital so conflicting,

hard-and-fast line between wealth which

wealth which

capital

and

not capital, he finds himself "on an in-

chned plane," constantly tending, by being more Hberal
in his interpretation of terms, to include more and more in
the term capital, until there is little or nothing left outside
of it.
We are told, for instance, that capital is "wealth
for future use."
But "future" is an elastic term. As was
shown in Chapter II, all wealth is, strictly speaking, for
future use. It is impossible to push back its use into the
past; neither

possible to confine

to the present.

The present is but an instant of time, and all use of wealth
A plateful of food, howrequires some duration of time.
though
"future"
the future is but the next few seconds; and if by
we mean to exclude the "immediate future," where is the

ever hurriedly

it is

being eaten,

Das

Theory of Political Economy, 3d

L'Interet

Geld,

ed., 1885, pp.

is still

for future use,

69-70.
ed., 1888,

du Capital, Paris (Giard), 1904,

Chap. VII, pp. 222-242.
p. 16.

NATURE OF CAPITAL AND INCOME

[Chap.

be drawn ? Are we to say, for instance, that capital
that wealth whose use extends beyond seventeen days ?
And as all wealth is for future use it is also, by the same

line to
is

token,

a "reserve."

all

call capital

a reserve does not,

from other wealth. Even
a beggar's crust in his pocket will tide him over a few hours.^
Equally futile is any attempt definitely to mark off
We have
capital as that wealth which is "productive."
therefore, in strictness, delimit

seen that

all

wealth

productive in the sense that

yields

the question was hotly

There was a time when
services.
debated what labor was productive and what unproductive.
The distinction was barren and came to be so recognized.
No one now objects to calHng all labor productive. And

this productivity is common to all labor, it is equally
common to all wealth. If we admit that a private coachman is a productive worker, how can we deny that the
if

horse and carriage are also productive, especially as the
three merely cooperate in rendering the very

— transportation
Finally,

same

service,

we cannot

which bears income.

distinguish capital as that wealth
All wealth bears income, for income

But the idea
some wealth bears income and some not has been persistent from the time of Adam Smith, who, meaning by income only money income, conceived capital as the wealth
consists simply of the services of wealth.

that

which produces income in

this sense, as distinguished from
the wealth, such as dwellings, equipages, clothing, and food,

which dissipates that income. A home, according to him,
is not a source of income, but of expense, and therefore cannot be capital,

§4
In these and other ways have economists introduced, in
place of the fundamental distinctions between fund and flow,

and between wealth and

services, the

merely relative

dis-

See the writer's "Precedents for Defining Capital," Quarterly
Journal of Economics, May, 1904, p. 404.
1

CAPITAL

Sec. 4]

As a

and another.

of wealth

between one kind

tinction

have

consequence, their studies of the problems of capital

Among

the

many

confusions

been full of confusion.
which have come from overlooking the time distinction
between a stock and a flow was the famous wage fund
theory, that the rate of wages varies inversely with the
amount of capital in the supposed "wage fund." MacCulloch wrote
"

—

suppose that the capital of a
country appropriated to the payment of wages would, if reduced to
the standard of wheat, form a mass of 10,000,000 quarters; if the
number of laborers in that country were two millions, it is evident
that the wages of each, reducing them all to the same common
standard, would be five quarters."

illustrate this principle, let us

"The wages would be

loch — but

five

five quarters in

hour, per day, or per year
concept, this definition
:

MacCul-

it is

from any time

meaningless.

Even so acute a writer as John Stuart
states

— thus

Five quarters per

Divorced as

quarters"

what time ?

—

Mill unhesitatingly

"Wages, then, depend mainly upon the demand and supply of
labour; or, as it is often expressed, on the proportion between popuBy population is here meant the number only
lation and capital.
of the labouring class, or rather of those who work for hire and by
capital, only circulating capital, and not even the whole of that, but
the part which is expended in the direct purchase of labour. To this,
however, must be added all funds which, without forming a part of
capital, are paid in exchange for labour, such as the wages of soldiers,
With
domestic servants, and all other unproductive labourers.
these limitations of the terms, wages not only depend upon the relative amount of capital and population, but cannot under the rule of
;

competition be affected by anything
the general rate [sic]). ..."

Wages (meaning,

else.

of course,

A httle attention to business bookkeeping would have
saved economists from such errors for the keeping of records in business involves a practical if unconscious recog;

See

"What

Capital?"

loc. cit.

Principles of Political Economy, 1st ed., pp. 327-328,
377-378. See Cannan, History of Theories of Production
2

bution, p. 264.
^

Political

Economy, Book

II,

Chap. XI,

§ 1.

2d ed., pp.
and Distri-

NATURE OF CAPITAL AND INCOME

[Chap.

The "capi-

nition of the time principle here propounded.

account" of a railway, for instance, gives the condition
of the railway at a particular instant of time, and the "income account" gives its operation through a period of time.

tal

§5
been objected that the proposed definition does
So far as economic precedent is concerned, we have already seen that there is no
established usage.^
Moreover, in the immense Uterature
on the subject there is no lack of precedent for the definition here proposed.
Turgot ^ employed the term capital
It has

not conform to established usage.

in practically the sense of a stock of wealth.

Courcelle-Seneuil,^

among

and Guyot

followed.

B. Say,^

Edwin Cannan,^

present economists, reintroduced

it, and in a very
To-day it is used in five or six
standard works,^ as well as in some minor writings. Many
economists have orally expressed their approval of the pro-

clear

and

explicit

way.

posed definition.
Others virtually or approximately adopt
stance, Knies,« Clark,« Pareto,' Giffen,^

it,

as, for in-

Foville," Flux,^^

1 For a fuller statement of this fact see the writer's "Precedents
for Defining Capital," Quarterly Journal of Economics, May, 1904.
2 Formation and Distribution of Riches, § 58, Ashley's translation

(Macmillan, New York), pp. 50-59.
^ See Tuttle,
"The Real Capital Concept," Quarterly Journal of
Economics, November, 1903, p. 83; but of. Bohm-Bawerk, Positive
Theory, English translation, p. 59, n.
* Traite theorique et pratique d' Economie Politique, 1867, tome I, p. 47.
^ Principles
of Social Economy, English translation, p. 50.
^ Theories
of Production and Distribution, London, 1894, p. 14.
' Among
them are Cannan's History of Theories of Distribution,
Hadley's Economics, Smart's Distribution of Income, Daniels's Finance, Fetter's Principles of Economics, Seligman's Principles of Economics.
8 See

"What is Capital?" loc. cit.
In his Growth of Capital.
^^ In his "Wealth of France and of Other Countries," English
translation, Journal of the Royal Statistical Society, 1894.
** Economic Principles, London (Methuen),
1904, pp. 16-18.
'

CAPITAL

Sec. 6]

Nicholson/ Hicks/ and the "Committee
Association for the

Advancement

[of

of Science]

the British

on a

Common

Professor MarMeasm-e of Value in Direct Taxation," ^
shall says that in earlier years he "invariably thought of
capital as the whole stock of goods, and of interest as the
whole of the usance or benefits derived from the use of that
stock";* that "when one approaches the problem of distribution from the mathematical point of view, there is
practically no choice" ^ but to do so; and that "wealth in
the form of houses or private carriages helped to give emplo3niient to labour as much as when in the form of hotels
or cabs."

expressly concedes what

really the chief

when he says: "I concur
whatever we do with the word

contention of the present writer

[my] conclusion that
we cannot solve problems of capital by classifying
wealth," ^ Yet he concludes, "not without doubt, that it
is best to" ^ base his definition of capital on such a classification, purely out of deference to what he conceives to be
the dominant usage.
in his

capital,

§6
As

and business usage,

to popular

careful study of this usage as reflected

who have sought from time

may

be said that a

by lexicographers,

to time to record

the fact that before the time of

Adam

it,^

reveals

Smith capital was

not regarded as a part of the stock of wealth, but as synony-

mous with

that stock.^^

Sometimes the inclusion of

all

In his Elements, pp. 42, 43.
Lectures on Economics, Cincinnati, 1901, pp. 91, 244.
^ Report of
British Association for Advancement of Science, 1878,
Dubhn, p. 220.
^

"Distribution and Exchange," Economic Journal, 1898, p. 56.

Ihid. p. 55.

Ihid. p. 57.

Ihid. p. 50.

Ibid. p. 56.

See the writer's "Precedents for Defining Capital," loc. cit., where
are presented the results of an examination of seventy-two diction*

aries.

Originally .the term "capital" was not a noun, but an adjective.
debiti " indicated the principal part of a debt, i.e. the
"principal " as distinguished from the interest.
This virtually repre^°

" Capitalis pars

NATURE OF CAPITAL AND INCOME

[Chap, IV

stock as capital was explicit, as, for instance, in the year
1611, Cotgrave defined capital as, "wealth, worth; a stocked

Again,

find

1678, Dufresne

omne quod

du Cange, Glossarium.

possidetur.

More often
business, as
1759,

—

Rider,

capital

—

— Capitale

dicitur

bonum

explained as a term employed in

A New

Universal

English

Dictionary.

London.
Capital.
Among merchants, the sum of money brought
in by each party to make up the common stock.
Likewise the money
which a merchant first brings into trade on his own account.

Here the phrase "among merchants" is perhaps intended
to specify the sphere in which the term is generally found,
rather than as a necessary limitation to that sphere, just
as "hawser"

is explained as a "nautical term" without
implying that a hawser could not be employed on shore.
With the advent of the economists the dictionary
definitions were thrown into confusion, although the great
majority of them continue still to adhere to the original

usage;

e.g.

—

Simmonds, P. L. The Commercial Dictionary.
Capital
.
the net worth of a party.
1894. Palgrave's Dictionary of Political Economy, under "Assets."
The assets remaining after the discharge of liabilities are a person's
actual capital.
1883,

In many cases it is thought necessary to distinguish
between the meaning of capital among economists and its

meaning among business men

;

e.g.

—

A New English Dictionary.
Vol. II,
1893, Murray, J. A. H.
Oxford.
Capital, B. sh. 3. A capital stock or fund. a. Comtnerce.
The stock of a company, corporation, or individual with which they
enter into business and on which profits or dividends are calculated;

—

sented the distinction between a fund and a flow. The term soon
became applied to a merchant's stock in contradistinction to the flow
of profits springing from it, and hence to any fund or stock whatever.
See "Precedents for Defining Capital," Quarterly Journal of
Economics, May, 1904, p. 395.
^ See "Precedents,"
pp. 8, 9.

CAPITAL

Sec. 6]
in a joint stock

company,

tions of the shareholders,

consists of the total

Pol. Econ.

sum

of the contribu-

The accumulated wealth

an individual, company, or community, used as a fund for carrying
on fresh production; wealth in any form used to help in producing
more wealth.

In business manuals and

articles on practical accountemployed in the sense of the
net value of a man's wealth. Thus L. W. Lafrentz, speaking of the difference between assets and habiUties/ states
"The residue will be the net worth of the proprietor

ing

find that capital is

—

the capital of the proprietor."

Inquiry

among

men

business

in business usage all wealth

also reveals the fact that

included in the term "capital."

would astonish a business man to have an economist
from his assets as non-capital his raw materials,
as would Kleinwachter
his perishable goods, as would
Hermann; his fuel, as would Walras; or, above all, his
land, as would most of the classical economists.
That land
It

strike out

;

is capital, business men all emphatically declare.
As the
manufacturer would express it, land is the very first thing
into which the "paid-in" capital of a new concern is converted. Again, business men maintain that the function
of any given wealth has nothing to do with its classification
as capital. It need not be "for production" nor "for sustaining laborers," nor for any particular object whatever.
The only point on which some of them hesitate is whether
The
or not all articles in consumers' hands are capital.
reason for this hesitation may possibly be found in the customs of bookkeeping. As one business man expressed it,
"Capital is simply a bookkeeping term." Consequently
the business man naturally associates the term with his
shop and not his home, for he keeps a balance sheet in the
former and not in the latter but, once given a balance sheet,
;

1" Economic Aspects of Accounting and Auditing," Journal of
Accountancy, April, 1906, p. 482. Cf Victor Branford, Economics and
Accountancy, London (Gee & Co.), 1901, and Charles E. Sprague, The
Accountancy of Investment, New York (Business Publishing Co.), 1904,
.

p. 12.

NATURE OF CAPITAL AND INCOME

does not matter what purpose

club,

an art

gallery, or a hospital

behind

[Chap.

it.

may have

social

a capital.

In one year a joint stock company with capital stock was
proposed for the purpose of building the yacht for defendIf a private family should call iting the America Cup.
self a joint stock company and draw up a balance sheet,
entering

on one

all its

side,

property, house, furniture, provisions,

imagine, would hesitate to

liabilities,

which

call

the balance of assets over

the total wealth-value of the family,

by the name "capital."

As a

the writer, "Capital isn't a

man

business

said

part of wealth, but

has got, including his automobile."

in your

etc.,

with the debts on the other, no business man,

mouth capital?" he was

asked.

all

"Is that cigar
"No," he said,

but this opinion he quickly reversed as inconsistent with his former statement, and admitted that a
box of cigars and each cigar in it, or out of it, for that matter,

hesitatingly;

were a part of his stock or reserve.
The phrases "to capitalize" and "to Uve on capital,"
as used by business men, imply that capital is simply a fund.
When we "capitaUze" an annuity of $5 a year at a
given sum, as $100, we mean that $100 is the fund of
ready-money equivalent of $5 flowing in annually. It does
not matter what kind of goods the $5 of income or the

$100 of capital represents. Again, when we say that a
man is "Uving on capital," we mean that he is using up
The reference
his stock faster than he is replacing it.
A
is not to any particular part or kind of the stock.
wealthy New Yorker who was recently forced to "live
on capital" did so by selling his accumulations of art treasures; it would be the same if he had sold his stocks and
bonds.

far, then, as

popular and business usage

we have ample warrant

concerned,

for the definition of capital here

accepted, and no warrant

whatever

for

ordinarily found in economic text-books.

the

definitions

CAPITAL

Sec. 7]

§7
Should economists continue to reject the simple definition above explained, and insist on restricting the
term capital to some narrower meaning, our only recourse will be to follow the example of John Rae,^ and,
after defining capital as

a part of stock, quietly shelve

the term and proceed to the analysis of "stock" instead.^

shall

then be in the curious position of acknowledging
'

that the "problems of capital 'are not problems of " capital
only, but of stock,

and

shall

have to regard such common

phrases as "the interest on capital," "I'interit du capital,"

and

But

capitalzins" as misnomers.

tired of the present confusion of tongues.

recently complained that he

was

any other

this or

settlement of the difficulty will be welcome to

all

who

are

business friend

chiefly deterred

from read-

ing the books of economists because they seemed to have no
settled terminology.

name we

select

matter what
The important

It does not so greatly

by which

to call a concept.

which are
That the concept
by whatof a stock of wealth at an instant of
ever name we call it
time is thus fruitful will, we believe, appear more plainly
as we proceed to apply it to what have been called, rightly
or wrongly, the "problems of capital."
matter

to select for consideration those concepts

—

fruitful in scientific analysis.

—

Sociological Theory of Capital, edited

Professor Mixter, Mac-

millan, 1905.

denied that " stock " falls into several more or
One classification has already been given in the
chapter on "Wealth," and there are many others. One of the most
striking divisions of the stock of wealth as it exists in modern society
is between that at home and that in business.
This is the basis of
^

It is not, of course,

less distinct

groups.

many

definitions of capital, especially that of Komorzynski (Credit,
Innsbruck, 1903, p. 138). But the distinction applies only to modern
and highly differentiated societies. Like all classifications of concrete
things, it serves a descriptive purpose but does not help analysis.
It is well known that in science the most general conceptions are
the most fruitful.
Professor J. Willard Gibbs, noted for the generality and simplicity of his methods in mathematical physics, used

to say,

"The whole
F

simpler than

its

parts."

CHAPTER V
CAPITAL ACCOUNTS

§1

We have defined capital

as a quantity of wealth existing
an instant of time. A full view of capital would be
afforded by an instantaneous photograph of wealth. This
would reveal, in addition to the durable wealth, a large
amount of goods of rapid consumption. It would disclose,
not the annual procession of such goods, but the members
of that procession that had not yet been transmuted in
form or passed off the stage of existence, however swiftly
It would show trainthey might be moving across it.
loads of meat, eggs, and milk in transit, cargoes of fish,
spices, and sugar, as well as the contents of private pantries,
Even the supplies on the table
ice chests, and wine cellars.
of a man bolting his dinner would find a place.
So the
clothes in one's wardrobe or on one's back, the tobacco in
a smoker's pouch or pipe, the oil in the can or lamp,
would all be elements in this flash-light picture of capital.
Such a collection of wealth is, however, heterogeneous;
We can inventory
it cannot be expressed in a single sum.
the separate items, but we cannot add them together.
They may, however, be reduced to a homogeneous mass by
considering, not their kinds and quantities, but their
And this value of any stock of wealth is also called
values.
"capital." To distinguish these two senses of capital, we
call a stock, store, or accumulation of existing instruments
of wealth, each instrument being measured in its own unit,
capital-instruments, or capital-wealth, and we call the
value of this stock, when all articles are measured in a comat

CAPITAL ACCOUNTS

Sec. 1]

mon

Similarly, a

unit, capital-value.

quantum

of property

any instant is called capital-property,
and its value, capital-valice. As a general term to include
both capital-instruments and capital-property, we may
employ capital-goods, a term first suggested by Professor
rights existing

Clark.

We have, then, a definite antithesis between capitalgoods and capital-value, capital-goods being measured in
various units appropriate to the various goods, as, for instance, in bushels of wheat, gallons of

oil,

acres of land,

and capital-value being measured in a
single uniform manner, as in dollars or other convenient
The simple term "capital" is only emunits of value.
ployed as an abbreviation of either of the compound terms
The business man
"capital-goods" and "capital- value."
"capital"
in
the
sense of capitalordinarily uses the term
value, and hereafter, unless it is otherwise specified, the
shares of stock,

In
term "capital" will be understood in this sense.
adopting this nomenclature we find ourselves in harmony
with Professors Clark, Fetter, Tuttle, and others referred to
in the preceding chapter.

are

now ready

employed in business.
of

these

accounts

to consider the "capital accounts"
It is strange that

generally

any treatment

omitted from economic

There seems to be no systematic study of capital accounts in any work on political economy.
A capital account is a statement of the amount and

text-books.

value of the property of a specific owner at any instant of

—

the assets and the
two colirams,
an owner are the debts and
other obligations owing to others; that is, they are the
property-rights of others for which such owner is responsible.
The assets or resources of the owner are all his propThe assets
erty-rights, irrespective of his liabilities.
liabilities,
the
include both the property which makes good
and the property, if any, in excess of the liabilities. They

time.

It consists of

liabilities.

The

liabilities of

NATUKE OF CAPITAL AND INCOME

68
^^

also include,

[Chap.

exhaustively considered, the person of the

owner himself.
The owner may be

either an individual human being, or
a collection of human beings, such as a family, an association, a joint stock company, a corporation, or a government. With respect to a debt or Hability, the person
who owes it is the debtor and the person owed is the
creditor.

Every item

in a capital account

an element

of the

owner's total capital, the assets being positive elements

and the
braic

liabilities

sum

being negative.

Consequently, the alge-

of the elements of capital, or

the difference in

value between the total assets and the total

liabilities, is

the

net capital, or capital-balance indicated in the account.

§2
The items in a capital account are constantly changing,
and their value also, so that when, after one statement of
assets and liabilities is drawn up, another is constructed at a
point of time six months later, the balancing item, or net
However, bookcapital, may have changed considerably.
keepers are accustomed to keep the item "capital" intact

from the beginning of their account, and to denominate any
There
it as "surplus" or "undivided profits."
are several reasons for this. In the first place, the less

increase of

often the bookkeeper's entries are altered, the simpler the

bookkeeping.
capital

and

Again, by stating separately the original
the books show at a glance

its later increase,

what the history

of the

company has been

as to the

accumucom-

lations of capital.

Finally, in the case of joint stock

panies, the capital

represented by stock certificates, the

engraved "face value" of which cannot conveniently be
altered to keep pace with changes in real value. Consequently it is customary for bookkeepers to maintain the

book value of the "capital" equal
certificates.

to the face value of the

CAPITAL ACCOUNTS

Sec. 2]

The following two balance sheets
mulation of "surplus."
January

will

show the accu-

1900

Assets

Liabilities

Plant

$200,000

Debts
Capital

$200,000

January
$246,324

Plant, etc

$200,000
1,

1901

Debts

$100,000
100,000
46,324

Capital

Surplus

$246,324

But not only

$100,000
100,000

the book item, capital, maintained intact

as long as possible, but often the surplus also

numbers and kept

at the

same

put in round

figure for several succes-

have an

effect

simply on a third item called "undivided profits."

The

sive reports.

distinction

All the smaller fluctuations

between surplus and undivided

—

profits is thus

capital, surplus,
merely one of degree. The three items
together make up the present net
and undivided profits
capital.
Of this, "capital" represents the original amount,
"surplus" the earHer and larger accumulations, and "undivided profits " the later and minor. The undivided profits

—

are

likely to

appear in dividends, that

divided profits, although this

or even in certain cases to the capital

see, then, that

is,

become

may also happen to the surplus,
itself.

the capital of a company, firm, or

person is to be understood in two senses; first, as the
the
item entered by the bookkeeper under that head,
original capital; and, secondly, this sum plus surplus and

—

undivided

profits,

— the

true net capital at

the instant

under consideration.

Inasmuch as the stock certificates were issued at the
formation of the company and cannot be perpetually
changed, they ordinarily correspond to the original instead

NATURE OF CAPITAL AND INCOME

of to the present capital.

Recapitalization

[Chap,

may

ef-

fected, however, by recalling the stock certificates or issuing new ones. In these ways the nominal or book value
may be either decreased or increased. It is sometimes

scaled

down because of shrinking assets, and
new subscriptions or expanding

because of

often increased
assets.

If, for

was $100,000, and the present
capital (that is, including surplus and undivided profits)
is $200,000, it would be possible, in order that the total
certificates outstanding might become $200,000, and the
surplus and undivided profits be enrolled as capital, to
instance, the original capital

issue free to each stockholder stock certificates of a face

already held.

value equal to those

ever, such a proceeding is very rare.

In practice, howOrdinarily the stock

and merely increase in
is as in the above
example, $200,000, whereas the original capital and the
outstanding certificates amount to only $100,000, the
market value of the shares will be double the face value;
certificates

value.

remain as

Thus,

for the stockholders

originally,

the present capital

own

a total of $200,000, represented

certificates of the face value of $100,000.

If,

however, we attempt to verify such a relation by

we shall find some disFor instance, the Second National

reference to the company's books,

crepancies in the results.

Bank

New York

had, at a recent statement, a total

and undivided profits of $1,295,952.59, of
which the original capital was only $300,000. We should
expect, therefore, that the stock certificates, amounting
to $300,000, would be worth $1,295,952.59, or, in other
words, that each $100 of stock certificates would be worth
The actual selling price, however, is found to be
$432.
$700. Again, the Fourth National Bank of New York
City had a total capital, surplus, and undivided profits of
$5,700,000, of which $3,000,000 was capital. From this
capital, surplus,

CAPITAL ACCOUNTS

Sec. 3]

we should expect

at l%,o,m —^^^The
Here
actual selling price, however, is $240.
are discrep-

the shares to

ancies which call for explanation.

sell

a business

man

were

upon to explain them, he would say that book
values and market values are entirely distinct, the latter
depending on estimated "earning power," The stock is
worth its "capitalized earning power," and its value
fluctuates from day to day in response to a thousand
called

causes.

This

tinction between

quite true, but

does not constitute a dis-

book values and market values,

values also represent estimated earning power.

for book
The book

valuations of the company's lands, buildings, machinery, etc.,

were originally determined by their earning power; their
market estimate
of earning power as truly as the market price of stock.
This
cost value was, at the time of purchase, a

The

principle holds true of liabiHties as well as of assets.
liabihties are

simply capitalized charges, interest, rentals,

and other expenses.
The meaning of the discrepancy is, therefore, not that one
valuation depends on earning power and the other not,
but that there are two estimates, one that of the bookkeeper, which is seldom revised and usually conservative,
and the other that of the market, which is revised daily.
Thus the stockholders of the Second National Bank are
credited by their bookkeeper with owning $1,295,952.59,
whereas in reality the total value of their property is more
nearly $2,100,000.
The bookkeeper has systematically
undervalued the assets of the bank, and even omitted some
valuable assets altogether, such as good will. The object
of a conservative business

man

in keeping his books

to give mathematical accuracy, but to

make

tive a valuation as to be well within the market,

times of financial stress.

not

so conserva-

even in

interested in safety

than in precision, and in maintaining his solvency even in
the face of heavy shrinkage of market values than in meeting the requirements of ideal statistics.

NATUKE OF CAPITAL AND INCOME

[Chap.

There are thus two valuations of the capital of a company,

— the bookkeeper's and the market's.

apt to be the truer of the two, although

bered that each of them
see, therefore,

The latter is
must be remem-

merely an appraisement.

that the balance of a company's books which

worked out to the last cent, and which has
an appearance of accuracy, may be in reality
very wide of the mark.
is

so carefully

so imposing

§4
Not only is there a discrepancy between the market estimate of the present capital of a company and the bookkeeper's entries, but the original capital paid in to the

company may itself have been quite different from the
nominal capitalization, for the stock may have been sold
below or above par. We see, then, that the "capital" of a
person or firm has four separate meanings
the nominal

—

"capitalization"; the actual original "paid-in capital";

the present accumulated capital, or "capital, surplus, and

undivided profits" as given by the bookkeeper; and the
market estimate of the same, i.e. the "value of the shares."
These and the other senses of capital are given in the
following scheme, which displays the various uses of the
term "capital."
'

e apital-instruments

Capital-goods

c apital-property

assets

Capital

and

liabilities

in general
f

original

Capital- value

nominal capitalization
paid-up
actual

capital
I

net capital

present
capital

[

capital

recorded

the company's
books, consisting of capital,
surplus, and undivided profits
market value of
the shares

Sec. 5]

CAPITAL ACCOUNTS

We have seen that the effect upon the balance sheet of
an increase in the value of the assets was to swell the surplus or the undivided profits. Reversely, a shrinkage of
value tends to diminish those items. For instance, if the
plant of a company having a capital of $100,000 and a
surplus of $50,000 depreciates to the extent of $40,000, the
on the books will be as follows

effect

—

NATURE OF CAPITAL AND INCOME

Sometimes

the value of the assets.
ically, as in the case of

done systematUnscrupu-

stock-jobbing concerns.

lous promoters often invest the

this is

[Chap,

sums entrusted

them

confiding stockholders, in unwise or fraudulent ways.

For instance, we
California,

may

imagine an Oil Well

of the type

called

Company

"stock-producing wells,"

which borrows $50,000 and collects $50,000 more from the
sale of stock (at par), and with this $100,000 purchases
land of friends at a fancy price, collusively providing that
the proceeds be returned in large part to the promoter.
In such a case the books of the bubble concern will show
the following figures

—

Assets

Liabilities

Land

$100,000

Debts

$50,000
50,000

Capital

$100,000

But

the land

should read

—

$100,000

worth, say, only $60,000, these accounts

Assets

Liabilities

Land

$60,000

Debts

$50,000
10,000

Capital

$60,000

In other words, the investor has only $10,000 worth

property, instead of the $50,000 which he put in, or 20
cents for every

dollar he invested.

The

rest

has been

diverted into the pockets of the promoter and those in
collusion with him,

favorite

company

method

to enter

of concealing the real condition of a

among

at their nominal value.

the assets the bad debts due it,
Sometimes bad debts are bought

company investsome bankrupt concern, which can be
obtained for very little, but may be entered on the books
at face value.
It is clear that any exaggeration on the
assets side of the ledger produces an equal exaggeration of
for that special purpose, the fraudulent

ing in the notes of

CAPITAL ACCOUNTS

Sec. 6]

the capital, surplus, and undivided profits, on the opposite

side.

great responsibility, therefore, rests on those

who

construct commercial accounts.

§6
Thus

we have

far

considered the fluctuations of the

items of a capital account independently of any payments

between the company and the stockholders. When payments are made to the stockholders in the shape of dividends, the effect

to reduce both sides of the account, de-

and the undivided profits
each by the amount of the dividend.
declared larger than the undivided profits,

pleting the cash on the assets side,

on the

liabilities side,

a dividend

the effect will be to reduce the surplus, or even the capital.

For most business concerns

regarded as bad policy,

or even fraudulent, to pay dividends out of capital.

How-

no inherent reason why such dividends
should not be paid, and in some sorts of business it is not
only proper but necessary. In these cases when dividends are paid out of capital there should be a correever,

there

sponding reduction in the amount of outstanding capital
stock, in order that those dealing with the concern may not
be deceived. For instance, land companies in Colorado
and California, such as the Redondo Land Company, are
formed for the express purpose of investing in land and selling

again.

among

fast as it is sold, the proceeds are divided

the stockholders, and stock certificates cancelled,

until the

whole capital of the company

cleared away.

Ordinarily, however, reduction in capital takes other forms

than dividend payments.
of capital

is,

creditors of a

The payment

of dividends out

generally speaking, unlawful, otherwise the

company might suddenly

find themselves

without any adequate security for their loans.
Payments are, of course, also made from the stock-

We will suppose that a company
formed with a capital stock of $100,000, but that when its

holders to the company.
is

NATUKE OF CAPITAL AND INCOME

76
first

statement

subscribed.

made

only $60,000 of this stock has been

would be possible

[Chap.

enter the capital at that

moment

for the

bookkeeper to

as $60,000; but, follow-

ing his rule of keeping the capital item the

same

in all suc-

on the
on the other side

cessive accounts, he will place the whole $100,000

and, to offset

liabilities side,

it,

will insert

assets of $40,000 in the

form of treasury stock, the idea

company

holds, in its treasury, stock cer-

being that the
tificates for

Of course
keeping

$40,000, which are to be regarded as an asset.

mode

this

of entering treasury stock is

for this

fiction,

sum

a book-

what

of $40,000 represents

is neither owned by nor owing to the company, except in the
sense that the company owes itself; yet promoters will

upon the credulous investor the statement that
amount of the stock of the company in its
own treasury increases by that much the property of the
often impose

to keep a certain

stockholders.

After the capital stock has been fully paid

in, it is

often

Let us suppose that before the
increase in capital the account stands as follows
necessary to enlarge

it.

Liabilities

Assets

Miscellaneous

—

$300,000

Debts
Capital
Surplus

$100,000
100,000

and undivided

....

profits

100,000

$300,000

Next let new capital to the extent of $100,000 be issued
and sold to old stockholders at par, in lots proportionate
The new stock certificates of
to their original holdings.
The
face value of $100,000 are thus sold for $100,000.
accounts will then stand as follows

—

Liabilities

Assets

Miscellaneous

$400,000

Debts
Capital
Surplus and undivided
profits

$400,000

....

$100,000
200,000
100.000

$400,000

CAPITAL ACCOUNTS

Sec. 7]

The

additional capital will

first

take the form of cash,

but afterward, by the purchase of plant, equipment, etc.,
wiU be changed into these or other forms of wealth or
property.
We shall suppose, however, for the present, that
in whatever form invested, the value remains exactly equal
to the cost, namely, $100,000, so that the assets are
changed from $300,000 to $400,000.
§

Let us assume that the books accurately represent actual
values and correspond to market prices.

of stock,

After the

new issue

find $200,000 of stock certificates representing

$300,000 of actual value of capital, surplus and undivided
But the new stock was, we
or $150 per share.
assumed, issued to them at $100 a share. Hence the
profits,

original stockholders will be able to

new

stock

by buying

$150

selling at

;

make

a profit on their

at the issue price of $100

or they

may shorten

and then
by sell-

this operation

ing their "right to subscribe" for $50.

first

sight

would seem as though this right to subscribe represented
a mysterious bonus to the stockholders, due to the issue of
the new stock. It must be remembered, however, that
the $100,000 par value of original stock certificates represented, including the surplus, $200,000 worth of property

belonging to the stockholders, consequently the original
That is, the efi'ect
certificates were worth $200 per share.
of issuing

new

stock below the original market price was

from $200 per share to
$150 per share. Consequently the loss of $50 to the stockholders on their old stock will exactly compensate for the
to lower the value of the old stock

$50 of excess value represented in the rights to subscribe.

individual stockholder owning 10 of the original shares

will find

his 10
for

them worth, instead

will lose $500.

new

them.

of $2000, only $1500, that is,
This will equal the profit of $500 on

shares or the value of his rights to subscribe

The outside public would be

willing to

pay

NATURE OF CAPITAL AND INCOME

him $500

for the privilege of

[Chap.

buying $1500 worth

of stock

for $1000.

thus see that the price at which the

issued does not of

And

holders.

itself affect

yet the price

of indifference.

The lower the

new

stock

the balance due the shareof

issue

not a matter

price of issue, the greater

the inducement to the individual stockholder to subscribe,
or to find

some one

"right."

Neglect to subscribe (or to

else to subscribe instead,
sell

and buy

his

the right to sub-

would then cause a loss. The value of the old shares
be lowered in any event, and in such subscription or

scribe)
will

only means of indemnification.

sale lies the

reasons,

it is

usual for

new

For these

stock to be offered to the original

stockholders below the market price.

The exact compensation between the value of the new
and the depreciation of the old stock is seldom realized
in practice, because the company may be in a position to
invest the new sums to advantage, in other words, to buy
In this case there
assets which are worth more than cost.
may be Uttle or no loss in the value of the old shares. But
rights

the point emphasized

still

of issue does not of itself

remains true, that the price
create additional capital value

through the "right to subscribe." Any increase of value
to
be due to unusual opportunities for investment,
economic causes and not to mere bookkeeping changes.
Of course, it may be true that the very fact of issu-

—

will

may of itself create a different opinion
market and influence prices there for better or
worse. A low price of issue may, for instance, make the
stock more available for small investors, and the consequent increase in the volume of the stock on the market

ing

new

in the stock

may make

it,

temporarily at

lation of pools.

do not

Such

least,

facts, while

affect the principle.

a subject for the specuthey modify the results,

CAPITAL ACCOUNTS

Sec. 8]

§8

have considered two ways through which the bookvalue of capital, surplus, and divided profits may exaggerate the true condition of the stockholders' property,
namely, through misfortune or the unforeseen shrink-

age of the assets, and through misappropriation of stock-

even when stock had at the outset been
There remains to be considered a third
way, namely, through the issue of stock below par, or for
services, patents, etc., at unduly high prices.
holders' funds,

issued at par.

way of overvaluing capital, or " stockcompany to be capitahzed at $200,000,
company issues at the beginning 1000 certifi-

illustrate this

watering," suppose a

and that

this

cates of the par value of $100,000, but sells

per share actually paid into the treasury.

them for only $60
Here is $60,000

by $100,000 face value of stock
a margin of $40,000 " water." Suppose, further, that another block of $100,000 of the stock is
given to an inventor for his patent, the real value of which
Finally, suppose that bonds are issued
is only $10,000.
paid-in capital, represented
certificates, leaving

and are floated at par. Then the
company has received in actual cash only $360,000. Of
this sum only $60,000 has been received from the stockholders.
The patent, which has also been contributed in
to the extent of $300,000,

return for $100,000 of stock, and which

worth only one

tenth of that sum, makes the total balance due the stockholders

But,

$70,000.

$200,000.

Consequently

the

company

it will

is capitahzed at
be necessary for the book-

keeper to exaggerate the assets to the extent of $130,000.

He may do

this as follows:

—

Assets

Plant [cost S360,000]
Patent [worth 10,000]

Liabilities
.

$400,000 Bonds
100,000 Capital
$500,000

$300,000
200,000
$500,000

Here $90,000 of the exaggeration is put under patent
and the remainder in an overvaluation of the plant. Many

NATURE OF CAPITAL AND INCOME

other methods of stock-watering are possible.

[Chap.

A common

one is to allow the plant to run down; i.e. to fail to make
proper repairs, while retaining its old book value in the
balance sheet. A railway may be "skinned" in this way,
by diverting to dividends what should be paid to a depreciation account.
This operation, however, is not com-

monly

mismanagement.
sometimes said that stock-watering is not wrong,
as long as all the terms and conditions are known.
This
is much Hke saying that lying is not wrong, provided everycalled stock-watering, but

It is

body knows that

it is lying; for a false balance sheet
only one form of a false statement, and, ordinarily, a
false statement is made with intent to deceive.
The object

may

be, for instance, to mislead intending bondholders

making them

believe that there

loans than actually exists.

honest
if

men

there

see here one reason

often undervalue their assets.

any

a larger security for their

They

why

prefer,

error in their valuations, that the error

be against themselves rather than in their favor;
in other words, that their representations as to financial strength shall be well within the truth.
Yet it
not infrequently happens that undervaluations of assets
shall

may,

like overvaluations, serve the

purposes of dishonesty,

— to "bear" the speculative market,
Many
which

attempts have been

result

or National

made

for instance.

to prevent the frauds

from stock-watering. For instance, the State
governments compel publicity of accounts in

the case of insurance companies, national banks, and inter-

The stock exchanges require similar pubAny company whose
securities are listed on the New York Stock Exchange
must pubUsh its assets and habilities at stated intervals.
But this rule is too general to be very effective. In some
state railways.

Hcity in regard to "listed" securities.

cases the law requires the entire nominal capital to be paid
into the

company,

in cash or securities at their

value, as in the case of national banks.
1

Revised Statutes,

5140 (Act June

1864, § 13).

market

CAPITAL ACCOUNTS

Sec. 9]

The
it

may

original capital of a concern

increased or decreased.

of liabilities.

therefore be either

In the course of

sometimes shrink to

have insolvency,

its

If it sinks

zero.

fluctuations

below zero we

— the condition in which assets

The

capital-balance

fall

short

intended to prevent

very calamity; that is, it is for the express purpose
of guaranteeing the value of the other liabilities.
this

These other

Uabilities represent, for the

blocks of property carved out, as

most

part, fixed

were, of the assets, and

which the merchant or company has agreed to keep intact

The fortunes

at all hazards.

of business will naturally cause

the whole volume of assets to vary in value, but
" slack" ought properly to be taken
capital, surplus, and

undivided

all this

up or given out by the

profits.

Capital thus acts as a

from overtaking the assets. It is
interested in an enterprise, as a guarantee to others who advance their capital to it.
The amount of capital-balance necessary to make a business
buffer to keep the liabilities

the "margin" put up

by those most

reasonably safe will differ with circumstances.

capital-

balance equal to five per cent of the habihties may, in one

kind of business, such as mortgage companies, be perfectly
adequate, whereas fifty per cent may be required in another

Much depends on how likely the assets are to shrink
and how much and much, likewise, on the character of the
kind.

;

If the assets

habihties.
will

be required than

The

may

risk of insolvency

shrink below the

have

stability of value, less capital

they consist of speculative securities.
is,

then, the chance that the assets

liabilities.

more shrinkable the

This risk

the greater,

and the less the margin of
The subject
capital-value between assets and Habihties.
lends itself to mathematical and statistical treatment;
but to work out the quantitative relations would lead us
far afield
it would require much statistical material, and
its analysis by the mathematics of chances.
the

;

assets,

NATURE OF CAPITAL AND INCOME

[Chap.

may exist for a time without being known;
be no legal bankruptcy.
Legal bankruptcy
exists as soon as there is a legal declaration of inability
This may not be true insolvency.
to meet obligations.
Insolvency

there

may

For instance, the assets

may

exceed the

cash assets at the particular time

may

but the
than the cash

liabilities,

less

due at that time. This condition we may call
In such a case, a little forbearance on
the part of creditors may be all that is necessary to prevent

liabilities

pseudo-insolvency.

financial shipwreck.

A wise merchant, however, will not only avoid insolvency,
but also pseudo-insolvency; that is, he will not only keep
his assets in excess of his liabilities

by a

safe margin, but

will also see that his assets are invested in the right

so as to enable
in the

to cancel each claim at the time

form
and

manner agreed upon.

From
assets,

him

this point of

— cash

view there are three chief forms of

quick assets, and slow assets.

assets,

A cash

money, or what is acceptable in
quick asset is one which may be ex-

asset is property in actual

place of money.

changed

for cash in

call loans,

a relatively short time,

as, for instance,

short-time loans, and other marketable securities.

A slow asset is one which can be exchanged for cash only in a
relatively long time, as real estate, office fixtures,
facturers' equipment.

The

skill of

and manu-

a good business

man

consists in properly marshaling these various constituents

of his assets.
§

When we speak of the assets falHng short of the liabilities,
we

which are included in the
company,
private means of stockholders adequate to meet the debts
In fact, in the case of a
of a company, but unavailable.
express
provision for ''limited
joint stock company, there is
refer only to those assets

balance sheet.

There

may

be, outside of the

CAPITAL ACCOUNTS

Sec. 11]

liability," so that the

only assets which can be considered

in determining solvency are those

on the balance sheet

the company.

cases, as in the case of

However,

some

national banks, the stockholders are liable for double the

amount

of the capital.

In the case of a partnership, on

the other hand, the partners are liable for almost
their private property, so that

the individual

all

member

the firm has always to reckon w^th a contingent liabiUty
to the creditors of the firm.

was separated from private
even including his own person,

Originally, before business
life, all

of a debtor's assets,

were regarded as pledged to the payment of a debt. The
attitude of the law and public opinion toward this matter
has changed greatly.
Only a few generations ago an insolvent debtor was imprisoned, the theory being that insolvency was a crime. When intentional, or due to gross
negligence, it is; but when due to the ordinary chances of
business it is not. To put a debtor in prison did not of
course help him to pay his debts. When this practical point
was admitted, special bankruptcy acts were passed to relieve insolvency if very widespread, as after a panic.
Such
acts were at first merely temporary, and regarded as
justified only under extraordinary circumstances.
To-day,
however, laws exist by which a bankrupt may be discharged
free of further liability, and without the necessity of any
special legislation. The Ray Act in the United States, under
which our present system of bankruptcy has been worked
out, was passed as late as 1898.
In some places, as in
France, the older view of limited liabiHty still prevails;
but the EngHsh and American system is not only sounder
in practice, as shown by its results in encouraging legitimate
enterprise, but is also based on sounder theory, for it
recognizes the fact that the creditor is a risk-taker. This
has always been and is necessarily the case, however much
the debtor may try to safeguard his creditors' interests.
The capital of a company exists, as we have seen, for the

NATUEE OF CAPITAL AND INCOME

purpose of mimmizing this

but

risk,

[Chap. "V

cannot eliminate

altogether.

The principle that a creditor of a concern is a risk-taker
has two important corollaries. The first is that, when
bankruptcy occurs, though the nominal liabiUties exceed
the assets, their actual value does not. We may say that
so far as their actual value
liabilities

of a

concerned, the value of the

company can never be

greater than the

they derive their value from these assets. A company which can pay only fifty cents on the dollar must have
its obligations classified as "bad debts," worth only half
assets, for

their

nominal amount.

This fact does not, of course,

Some

justify the intentional repudiation of debts.

of the United States have,

it is

the burden of their debt

own bonds

market

their

true,

offering

price,

states

attempted to reduce

buy up

their

this price

was

when

below par, owing to a lack of confidence in their ultimate
redemption. Such an operation is evidently a species of
repudiation.

the other hand,

we must not

regard

givable sin for the bona fide bankrupt not to

an unfor-

pay

his debts

in
So long as the creditor understands in advance
the nature of the risk he is taking, he must abide by the
full.

result.

Nowadays,

corporations,

this

in the case
is

perfectly

.of

well

investments in large
understood.

Many

have been bonded for almost their entire cost, the
bondholder reaUzing fully that he could obtain nothing
This participation in risk
unless the road was a success.
is particularly evident in the case of income bonds, which
specifically pay interest only so long as the road's income
railroads

adequate.

The principle that the true value of the liabiUties is derived
from the assets and can never exceed them may seem to
have an exception in the case of a person who succeeds
in borrowing money "without capital." It is clear, how-

CAPITAL ACCOUNTS

Sec. 12]

ever, that

we employ
who is

sense, a person

the term "wealth" in

good

its

larger

himHis present value must in the
estimation' of his creditors be at least equal to the discounted value of his debt-paying power; otherwise he
could not borrow. It follows that his liability, being only
self assets

really

for his

debt

to that extent.

part of the discounted value of his debt-paying power,
cannot exceed his assets.

The second corollary, from the
imply

risk, is

principle that all seciu-ities

that the distinction between stockholders

and bondholders is chiefly one of degree, and may be
bridged over by intermediate forms.
Preferred stock
and income bonds amount to very nearly the same thing.
The preferred stockholder is elevated above the common
stockholder, and resembles a bondholder in that he is assigned a certain fixed amount of the earnings before any
accrue to the common stockholder. The income bondholder,
on the other hand, is depressed below the other bondholders,
and resembles a stockholder in that he will not be paid until
the ordinary bondholders have been satisfied. The chief
remaining differences between these two forms of security
are that the stock confers voting power, while the bond
does not and that the bond has a due date for final ex;

tinguishment, while the stock continues until the
is

company

"wound up."
The

between the different classes of creditors
further swept away in some cases where
there is no capital stock, as in that of a mutual insurance
company. Here the policy holders, instead of being
creditors for fixed sums due them from the company, as
distinction

of a concern

is still

are the bondholders of a joint stock concern, themselves

assume the
chance there

and also take whatever
They are, as it were, both

risk of the business

may

be of

profit.

In the accounts of a mutual
In
therefore, bankruptcy would seem to

stockholders and creditors.

company

there will be almost no outside creditors.

such companies,

NATUEE OF CAPITAL AND INCOME

[Chap.

be impossible; but as their debts for death claims are
for specific sums, they may be forced into Hquidation, if
unable to obtain these sums by remitting dividends or by
assessments.

§13

When

bankruptcy occurs, the claims of creditors are
settled in one of three ways: through an agreement of
"composition," by which the creditor agrees to take
what he can get and excuse the debtor for the difference; through an assignment by the debtor of his assets
to his creditors; or through foreclosure by the holder of

some obligation.
The final result of bankruptcy will be either liquidation,
by which the business assets are sold and distributed and
the business wound up or reorganization, by which the
business is continued and the habilities are entirely changed
;

in character.
capital,

as,

In the case of companies with large fixed
for

instance, raihoads, reorganization

the

usual result, and the old bondholders often become the
stockholders, the old stockholders surrendering their rights
altogether.

While

the affairs of the

this reorganization is being

company

are administered

appointed by the bankruptcy court.

effected,

by a

receiver

calls in all

stock and bonds, and issues temporary receiver's

the

certifi-

These in turn are exchanged for the new securities
However, the bondholder seldom wishes to
assume his right of control and become a stockholder, and

cates.

when
is

ready.

usually offered instead the option of cash or

some new

security similar in kind to that which he held before, but
less in

amount.

tives, realizing that

likely to

apt to accept one of these alternaforeclose

and take possession

be more troublesome, and, in the end,

less

advan-

Thus the losses of the old company are "written
and the reorganized company starts afresh with a clean
The change is simply a change in the forms
set of books.
of ownership of wealth and in the individual owners.
tageous.
off,"

—
CAPITAL ACCOUNTS

Sec. 14]

§14
The bankruptcy

may

often causes the bankfirms

be clearly seen in the following table, where the

liabil-

ity of

thus

of one firm

The interdependence between

ruptcy of another.

one person

represented by the asset of another,

Person
Assets

Miscellaneous

NATURE OF CAPITAL AND INCOME

down

a bad asset
that

worth

only $10,000

B's assets shrink $40,000.

[Chap.

instead

A's loss

$50,000

;

enough

to wipe out all of B's capital of $30,000,

is,

V
of

thus

and pare

down the value of his other liabilities by $10,000, so that B
can now pay only $30,000 out of the $40,000 he owes. In
other words, he

Next comes

able to

pay only 75 cents on the

who has $20,000

dollar.

invested in B's note.

gets only 75 cents on the dollar, so that this asset, nominally

found to be worth only $15,000, and his
This loss is not enough to wipe out all
his capital, but only reduces it from $30,000 to $25,000,
Consequently D, who owns C's
so that C remains solvent.

worth $20,000,
loss is

only $5000.

bills for

The force of the catasruined A and B and injured C,

$5000, will lose nothing.

trophe has been spent.

but stopped short of D.

From

this

example we

may

see that the statistics of

bankruptcies are often misleading.
the statistician to
firms.

But

sum up

Thus,

it is

the liabilities of

all

usual for

bankrupt

in case the various firms are connected, as in

the above example, the total

sum

lost is

not as great as

though the same amount of bankruptcy occurred in independent firms. In the preceding example the only loss is
$90,000, all in A's assets. But there would appear to be
a loss of $90,000 in A's account, one of $40,000 in B's
account, and one of $5000 in C's, or $135,000 in all.
This misleading result is evidently due to counting parts
of the loss twice and three times.
Failures are sometimes due to a false fear of calamity,
a shock to business confidence. This will cause a shrinkage
For instance, it will induce
of values in several ways.
creditors to demand payment and refuse renewals of bills.
Forced liquidation and contraction of credit are the result.
No physical capital is destroyed, but the form of ownership
is violently disturbed, and often the management, being
transferred from stockholders to bondholders,

from competent to incompetent hands.

Above

turned
all,

the

CAPITAL ACCOUNTS

Sec. 15]

expectations

the

future

are

changed and confused.

Plans are given up, orders are countermanded, and trade
is stopped.
Assets, representing as they do the value of
future expectations, suffer sudden

and heavy reductions.

§15
summarizing

Briefly

son

who has

this chapter

liabilities is, in

we may say

a sense, a trustee.

that a per-

holds

more than he owns. He holds all his assets; he owns
only the margin between these and his liabilities. His
responsibility for the liabilities requires

that

he should

keep his

own margin

there

always risk of losing his margin and becoming

insolvent.

assumed

This

risk,

of capital comparatively safe.

whether large or small,

his creditors,

and

its

But

necessarily

existence should be

recognized in law as well as in business practice.

The

record of the relations which at any time exist between
assets, liabilities, and the margin of capital separating
them constitutes what we have called the "capital ac-

counts."

CHAPTER VI
CAPITAL SUMMATION

The

interdependence of the balance sheets of different
firms or companies which has been revealed by the communication of bankruptcies exists, of course, irrespecwherever any item
It
exists
tive of bankruptcies.

two accounts, in one as asset and in the other as
In fact, every liability item in a balance sheet
impUes the existence of an equal asset in some other balConseance sheet, for every debtor impUes a creditor.
offset
balance
sheet
is
one
term
in
quently every negative
The
conother.
by a corresponding positive term in some

enters

liability.

verse, however, does not follow, namely, that every asset

implies a liability.

When we attempt to sima up the items in the balance sheets of various persons, the positive and negative
elements may be canceled out by pairs or couples.
This method of cancellation may be called the method of
Each debt or Habihty between any two persons
couples.

whose accounts are included, being a liability to one and
an asset to the other, constitutes a couple or pair of equal
and opposite items. We have already noted another way
in which liabihties may be canceled against assets, namely,
by subtracting the Habilities in any capital account from
the assets in the same account. This method may be
called the method of balances, since for each individual
account liabilities are deducted from assets and the net
Both methods must, of course, lead to
balance is taken.
result.
the same
90

Sec. 1]

CAPITAL SUMMATION

The two methods may be illustrated by the balance
X, Y, and Z

sheets of three persons, say

—

NATURE OF CAPITAL AND INCOME

The

[Chap.

same by both methods, but the method
shows the share of this total capital which is

totals are the

of balances

owned by each individual, while the method of couples shows
the various items of capital-goods of which this total
posed, namely, residence, personal effects, farm
shares

and

com-

railroad

and bonds.

§2
It is well to note here the distinction

between the accounting of real persons and of fictitious persons. For
a real person, the assets may be and usually are in excess
of the Habihties,

and the

of that person.

This capital

difference is the capital-balance

is not to be regarded as a
but as a balance or difference between the Habihties and the assets.
For a fictitious person, on the
other hand, as for instance a corporation or partnership,

liability,

the
for

liabilities

the

obligation
holders,

person,

always

are

balancing item

from the

as
in

any
fact,

of
is

exactly

called

equal to

capital

the assets;
as

truly

person to the real stockother Kabilities.
A fictitious

fictitious

the

a mere bookkeeping

ing certain assets and

dummy,

hold-

them out again to
real persons.
Bookkeepers, it is true, apply the same
methods in both cases, but they do so by regarding the
owing

all

accounts even of a real person as relating to a fictitious
entity for bookkeeping purposes.
one's real self are separated.

One's business

Thus

self

and

X's business shows a
balance in X's favor of $10,000, he enters this as a
habihty item in his business accounts and considers his
"business" as owing him this sum. There is no objection
to such a procedure.
But we must remember that when
we say that "X's business" owes
$10,000, we imply that
if

the real

amount

in his

own accounts

holds a claim of that

In other words, we are
compelled, in order to be consistent, to open a separate
account for
and carry forward the $10,000 balance
against his "business."

to the opposite side, thus

—

CAPITAL SUMMATION

Sec. 3]

X's Business
Assets

Miscellaneous

$50,000

Due
Due

to ott
to

NATURE OF CAPITAL AND INCOME

[Chap. VI

which were obtained by the method of balances before
the railroad was introduced into the discussion. The
totals will stand as follows

—

X's capital balance
Y's capital balance
Z's capital balance
R.R. Co.'s capital balance

$ 70,000
40,000
80,000

000
$190,000

When we

apply the method of couples, however, we
of the railway company's capiThe
tal account will affect the items in the final sum.
stocks and bonds, as assets of X, Y, and Z, will now pair off
find

the inclusion

that

with the corresponding liabilities of the railroad company
and their place will be taken by the concrete railroad itself,
as follows

—

Method op Couples
Residence
Personal Effects

$ 70,000
20,000
50,000
50,000

Farm
Railway

$190,000

The appearance

of the capital inventory

thus changed.

Formerly, the items of property-rights in it included part
rights, as stocks and bonds; now they consist only of
complete property-rights
solely

residence,

the right to

The items

property rights

speaking,

complete right to any

the farm,

article of

in terms of the article of wealth

phrase,

the

"right

consist, strictly

still

— the

wealth

itself,

right

to the

But, since the

etc.
is

best expressed

instead of the long

residence,"

we merely

use

The property no longer veils the wealth
beneath it, and the inventory, which before was called
an inventory of property-capital, is now also an inventory
"residence."

of wealth-capital.

CAPITAL SUMMATION

Sec. 3]

Such a

when we combine
we combine enough of them to

every

liability

which have no

its

counterpart

supply,

and

item, its counterpart asset,

every asset which has one,
assets

capital

result is sure to follow

accounts, provided
for

counterparts are what

for

The

liability.

we have

called complete rights to wealth, or "fee simples"; those

The

which have them are the partial rights to wealth.
reason

that every article of concrete wealth

garded as owned in "fee simple"
have to set up a fictitious person
purpose. Hence every part right
essarily appear as a liability on the

to be re-

by some one, even
as

dummy

for that

very

to that wealth will nec-

opposite side of that per-

and again as an asset on the account of some
other person. Thus, if two brothers own a farm in
equal shares, the farm as a whole is regarded as owned
by the partnership person called "Smith Brothers." The
balance sheet of this fictitious person will show as assets
the farm and as Habihties the "undivided half-interest" of
each brother, and these same items enter the individual
son's account,

accounts of the brothers as assets.

follow out capital

clusion of

many

summations thus requires the

fictitious persons, for it is often

in-

only the

who hold the complete rights to articles
Locomotives and railway stations, for instance,
are owned by corporations, not individuals. In fact, these

fictitious

persons

of wealth.

fictitious

persons

municipalities,

— partnerships,

associations,

corporations,

and the

trusts,

— are

formed

purpose of holding large aggregations of
concrete wealth and parceling out its ownership among a
for the express

larger
If,

number of real persons.
we suppose balance

then,

sheets so constructed as to

include the whole world of real

and

fictitious

persons,

with entries in them for every asset and liability, even
pubhc parks and streets, household furniture, persons
themselves, and other possessions not ordinarily accounted
for in practice, it is evident that

shall obtain,

by the

NATURE OF CAPITAL AND INCOME

method

[Chap.

of balances, a complete account of the distribution

of capital-value

among

of couples, a complete

thus owned.

mortgages,

real persons;
list

and, by the method

of the articles of actual wealth

this hst there will

be no stocks, bonds,

other part rights, but

notes, or

only land,

buildings and other land improvements, commodities and
In other words, we arrive again at the
real persons.

and

proposition of Chapter III, that wealth underhes

cor-

responds to property.

§4

Among

other part-rights in real wealth

There has been

called "credit."

much

find

what

discussion as to the

nature of credit; whether, in particular, credit is to be
regarded as a "part of capital." It has been claimed that,

from the merchant's point of view, credit
cause

enables a business

In this view

MacLeod

revenue

borrowed capital.
includes credit under capital. Pro-

Nicholson

capital,^

capital be-

to enlarge his business.

though

is capital,

specifically

fessor J. Shield

man

but

that

says that credit
"strictly

a sort of

and taking only

material (productive) capital, this would involve counting

the same elements twice over."
of capital accounts,

That part

of a

how

see,

from our study

to avoid such double counting.

man's so-called capital which

should not enter his books as his capital at

borrowed

being but a

all,

manifestation of the fact that the total capital of the com-

munity which he in part owns is also owned in part by
Indeed, the phenomenon of credit means nothing
others.
more nor less than a specific form of divided ownership
of wealth.

to control
is,

Credit merely enables one

more wealth

some part

man

temporarily

or property than he owns, that

of the wealth or property of others.

occurs generally on the theory that he can use

advantage than the real owner.
^

Palgrave's Dictionary of Political Economy, Vol.

This

to better

I, p.

452.

CAPITAL SUMMATION

Sec. 5]

therefore a cardinal error to regard credit as in-

creasing capital

may

by the amount

of that credit.

Indirectly,

in an increase of capital, through
and production and by getting the
management of capital into the right hands and its
ownership into the most effective form; but the amount
of any such increase of capital thus indirectly produced
bears no necessary relation to the amount of the credit

credit

result

stimulating

trade

If capital is increased, the credit does not constitute

itself.

the increase, but merely represents a part ownership in the
final total, after all the

increments have been counted

in.

§5

A great

deal of confusion in legislation

be avoided

the two methods of

and writing could

summing up

capital were

distinguished and their interrelations recognized.
tion, the

two methods are often confused.

In taxa-

chief prob-

lem of efficient taxation is how to tax all property once,
and none of it more than once. There are two solutions

One
list

to tax the

amount owned by each

which expresses the method

real person in a

of balances

;

this

method
The

seeks out the real owners or part owners of wealth.

other

to tax the actual concrete wealth in a Ust which

expresses the
real wealth

method of couples this method seeks out the
At present the two are much confused.
;

owned.

Legislators too often fail to perceive that under the

first,

or owner-method, corporations should not be taxed, for

they are not true owners; and that under the second, or
wealth-method, bonds,

stocks,

and other

part-rights

wealth should not be taxed, for these are sufficiently included

when the

which these

actual railways and other wealth are taxed,

securities represent.

It is not claimed, of course, that a complete

system of

taxation can be worked out merely by choosing one of the
of taxes just indicated.
We are here only concerned in pointing out that the distinction between the

two forms

NATURE OF CAPITAL AND INCOME

two should be observed and that where one

[Chap.

applied the

other cannot also be applied without duplicating the tax.

The failure to distinguish
and couples also manifests

clearly the
itself in

methods

of balances

the form of fallacious

Statistics of railway capital have been
compiled in which the value of all railway property is obtained by adding up the assets of the railways, regardless
statistics of capital.

of the fact that

bonds

many

of these assets consist in stocks

and

of other railways.

We should therefore distinguish carefully the two methone the method of
ods for the summation of capital,

—

owned by different inand the other the method of couples, which

balances, which exhibits capital as
dividuals,

exhibits capital as consisting of different concrete instru-

ments.

The one relates to the owner, the other to the
They do not conflict, but present the same

things owned.

facts in different aspects.

PART

II.

Chapter VII.
Chapter VIII.
Chapter IX.
Chapter
X.

Income

Income
Income Accounts

Income Summation

Lora

Psychic Income

CHAPTER

VII

INCOME

Income has already been defined as a flow through a
and not, like capital, as a fund at an instant
of time, and as consisting of abstract services and not,
like capital, of concrete wealth. The income from any instrument is thus the flow of services rendered by that
instrument. The income of a community is the total flow of
The income of an indiservices from all its instruments.
vidual is the total flow of services yielded to him from his
period of time

property.

Before attempting to elaborate or even to justify

this definition,

we have first to examine the erroneous
now current. The present chapter is

concepts of income

devoted to such an examination.
It is no exaggeration to say that at present the state of
economic opinion on this important subject is deplorably
confused and conflicting. Many writers fail to construct

any
too

definition whatever, either because they find the task
difficult,

or because they

deem

the concept too obvious

And

those

who do

to require definition.

set

themselves

the task of reaching a working concept of income do not
find it

an easy one

tion with their

own

;

and authors often confess

dissatisfac-

results.

The definitions which are given are usually vague.*
Their authors, often able and distinguished, and keenly
alive to the difficulties of the subject, seem to take refuge
^

VII,

F®r a collection of conflicting definitions see Appendix to Chap.
§ 1.

101

NATURE OF CAPITAL AND INCOME

102
in
for

[Chap. VII

an obscure and ambiguous phraseology.^ Were it not
an instinctive feeling that there exists a definite income-

concept, the repeated failure to formulate

it might lead one
not susceptible of any exact and rigorous definition, and that the best course is to abandon its

to conclude that

it is

Kleinwachter, who wrote a book espedevoted to this subject, specifically takes this course.

search as futile
cially

no useful concept of income,^
merchants attempted to keep a
record of their transactions by counting the money which
they received and disbursed, and that, in consequence of
this, arose the "illusory" notion that through some such
record the complete economic standing of an individual or
firm could be expressed.
He observes, that such a complete picture could not be obtained by recording merely
the incomings and outgoings of money, but should
include Hkewise the incomings and outgoings of every other
kind of wealth.^
A complete record, he states, would
that there

states

His idea

that, originally,

alone cover the required ground.

So-called statistics of in-

come are, he maintains, merely a makeshift for such a record.*
But why should the possibility of a concept of income
be rejected because it does not reveal a " complete" picture
of an individual's economic condition ?
On the same plea
we might also reject the possibility of a concept of capital.
Y. Edgeworth, Falgrave's Dictionary of Political Economy,
"Income," Vol. II, p. 374:
" Income may be defined as the wealth, measured in money, which
at the disposal of an individual, or a community, per year or other
^

E.g. F.

—

article,

(The italics are the present writer's.) This formulaadopted by N. G. Pierson, Principles of Economics, London

unit of time."
tion

(Macmillan), 1902, p. 76.
^

Das EinJcommen und

Op.

cit.,

seine Verteilung, Leipzig, 1896, p. 11.

p. 14.

* The present writer
at one time also expressed these doubts
{Economic Journal, December, 1896, pp. 553, 554). By aid of the
criticisms of Cannan and Edgeworth, the conclusions here stated were
reached. These were first outlined in "Senses of Capital," Economic
Journal, June, 1897, and in " The R61e of Capital in Economic
Theory," Economic Journal, December, 1897.

INCOME

Sec. 2]

103

good definition should always conform to two tests:
useful for scientific analysis; and it must
harmonize with popular and instinctive usage. We shall
see that the usual definitions of income fail in one or both
it

must be

Many

of these requisites.

fail

to lend themselves to scien-

by committing the fallacy of double counting,
others by confusing income and capital, while almost all fail
to harmonize with popular usage by making out income
larger or smaller than common sense would dictate.
Like most familiar notions, the notion of income seems
to the uninitiated clear enough without definition.
But
tific

analysis

pitfalls

which are unseen are

more dangerous.

for

that very reason

shall point out

all

the

a few of them by

criticising, not the specific definitions of particular authors,
but the general concepts of income which the reader is
likely, more or less unconsciously, to have acquired.

§2
of income which is the most common is
"money-income." A business man's "moneyincome" means to him the money receipts from his busi-

The concept

that

ness,

less

applied

money expenses of obtaining them. As
commercial affairs, this concept is nearly

the

adequate, and in fact

it coincides, as a special case, with the
income
which we have adopted
concept
for the
services which a man's business capital yields him usually
consist exclusively of bringing him money, and the disservices which it causes him, of taking money from him.
Thus
the net value of its services to him, or difference between
the value of the services and disservices, is simply the
difference between the money brought in and the money
taken away from him by his business.

But while the concept

;

"money-income"

correct so

from exhausting the complete income concept. As soon as we pass outside of commercial
circles, we find cases in which money-receipts are evifar as it goes, it is far

NATURE OF CAPITAL AND INCOME

104

[Chap. VII

all receipts and money-costs only
In primitive communities, and even in
highly organized communities, the income of many persons

dently only a part of

a part of

all costs.

consists; partly

the

acquisition of goods other than

money. /"The clergyman receives, besides his salary, the
use of a parsonage and domestic servants receive, besides
their wages, their food and lodging.
Again, many goods
considered as constituting income are not acquired by
exchange at all, but produced by the individual himself.
It is usually recognized that a farmer's income includes
not only what he gets in money by sale and barter, but
what he obtains "in kind,"
the products of his farm
consumed by his own family.
;

—

the other side of the ledger there are

many

costs

which are not in money form, namely, sacrifices of commodities and labor in the process of acquisition. The

him
money

for

some

farmer's crops cost

may

sacrifice

not pay
for

these

labor as well as wages.
his seed

the

and

products

Again,

fertilizer,

his

but
farm

instead.

While the acknowledged existence of non-monetary reand costs is of itself a sufficient proof of the inadequacy of the money-income idea, there is the further
objection that money-income itself exists, so far as it has
any existence, merely for the purpose of purchasing
other goods. The laborer's wages are not his "real wages,"
but the means to them. He transforms his money-wages
into food, clothing, housing, and other uses.
These, and
not the money which buys them, constitute his real income.
If we acknowledge this, we are led away from moneyincome to another concept common in economic literature, but still inadequate, namely, "real income."
ceipts

§3
"Real income" has been defined in various ways, and,
income in general, is often not defined at all. So

INCOME

Sec. 3]

105

far as it has any recognized meaning, it may perhaps be
expressed in the phrase "enjoyable commodities and services."

This concept

that of money-income;

elements which

certainly

for

we found

more adequate

than

includes the supplementary

lacking under the head of

money-

income, such as the clergyman's use of a parsonage, the
servant's board and lodging, and the farmer's produce for
his

own consumption.

It is also less superficial

concept of money-income; for
is

than the

recognizes that

money

only an intermediary, and seeks to discover the real ele-

ments for which that money-income stands.
But the definition errs in two particulars first, instead of
making income consist simply and consistently of one kind
:

attempts to include with this
totally incongruous element, commodities;

element,

element

services,

the

and, secondly,

unnecessarily restricts

itself to

enjoyable

though enjoyable elements are, in the last
analysis, the final income of society or of an individual,
the fact that they are should constitute the end of our reasonings and not the beginning. We shall now take up these
two errors in order.
That the two elements
"commodities" and "services"
form a heterogeneous combination is evident from the
fact that one is concrete wealth and the other, abstract use
of that wealth.
To bring about homogeneity we could
exclude uses altogether and confine "income" to concrete
commodities or we could exclude commodities altogether
and restrict the term whollj'' to uses. The latter alternative, which is the solution offered in the present book,
seems never to have occurred to those who have written
on the subject. The former alternative is quite untenable
and has been instinctively discarded. Instead of either
alternative, the course which has actually been pursued has
been the eclectic makeshift of including some commodities
and the services or uses of others, and even sometimes both
elements;

for,

—

;

the commodities and the uses of these very commodities.

NATURE OF CAPITAL AND INCOME

106

[Chap. VII

The choice of the commodities to be included has usually
on the less durable varieties, such as food, fuel,
and clothing, while the objects the uses of which have been
more durable instruments,
included have been the
fallen

In the case of intermediate types,
and musical instruments, no
fixed rule seems to have been observed.
Some economists
are inclined to regard a newly acquired piano as a part of
real income, others to regard the music which comes from
it as the real income, while still others apparently regard
both the piano and its music as real income. Evidently
such a patchwork of arbitrarily selected elements is insuch as dwelling-houses.

such as carriages, furniture,

capable of furnishing any consistent, reliable, and logical

theory of income.

§4
The only

true method, in our view,

to regard uniformly

as income the service of a dwelling to
or

money

rental),

the

service of

the service of food (nourishment)

;

its

owner

(shelter

a piano (music), and
and in the same uni-

form manner to exclude alike from the category of income
the dwelling, the piano, and even the food. These are capital, not income; and the instant we include any such concrete wealth under the head of income, that instant we begin
to confuse capital and income.
The newly purchased or
newly constructed house is not an element of income, but
of capital.
The income appears afterward in the services
the house yields its owner,
the shelter it affords through

—

subsequent years or the bringing in of a money rent to its
owner. In like manner the newly acquired piano and loaf
of bread are not income, but capital.

Their income

fol-

lows later in the form of piano music and nourishment.

No reason

has ever been given

why

the short-lived bread

should be treated differently from the long-lived dwelling.

The use

of the bread

the use of the dwelling

from the bread as
from the dwelling. The

just as distinct
is

distinct

INCOME

Sec. 4]

107

between the case of the bread and that of the
purely one of degree. The uses of the bread follow the acquisition of the bread almost instantly, whereas
the uses of the dwelling are not completely ended until
difference

dwelling

many

years after the dwelling

difference in time

The value

of the use of the

bread

From

acquired.

comes a corresponding
is

this

difference in value.

practically identical

with the value of the bread. A man will give ten cents today for a loaf if he expects its use (consumption) to-morrow
to be worth ten cents. The value of the dwelling, however,
will

less

than the value of

its

prospective uses, owing to

the fact that these uses are so remote in the future.
the dwelling

expected to

and its shelter
$50,000 worth of shelter will

last fifty years,

to be worth $1000 a year, this
not by any means be worth $50,000 in advance, but only,
say, $15,000. This "capitalized" value of the expected

uses of the dwelhng will be the value of the dwelling.
short, the bread

and

its

uses are practically contemporane-

ous and equal in value, whereas the dwelling and

its

uses

are widely diverse in both particulars.

Consequently it
has not seemed worth while to economists to distinguish
between the bread and its uses; whereas they could not
help distinguishing between the dwelling and

But in
and their

science,

logical

distinctions

its uses.

are

inexorable,

violation always brings retribution.

be said in truth that

may

economists had been scrupu-

lous enough to distinguish a loaf of bread from

its uses,

they would have escaped most of the confusions which

have so long enveloped the theory of income. Having
once chosen as the income element the food instead of its
use, economists have proceeded to do the same in the case
of clothing and other moderately durable commodities.
Naturally they have not known where to cease calling the
concrete instrument income and begin calling its use income
instead. In their hesitation they have in some cases ended
by including both. By so doing they commit the fallacy

NATURE OF CAPITAL AND INCOME

108

of double counting.

[Chap. VII

This fallacy they escape only in the

case of the very durable instruments, such as the dwelling,

and the very perishable instruments, such as the bread.
The dwelUng is too evidently not income ever to be so
regarded, and, as to bread, one of the two elements
its
But it is felt that interuse
is overlooked altogether.

—

mediate types, like the piano, are as fairly entitled to be
called income, when acquired, as the bread, and that their
services are as fairly entitled to be called income as are the
services of the dwelling.
Consequently both are deemed
income. But a piano valued at $500 is so valued because

sum

this

the capitalized value of the future expected

uses which, let us say, are

$600, distributed over the

lifetime of the instrument.

Consequently

piano

first

purchased,

the extent of $500, and then later
in providing its

if,

when

the

entered as real income to
its

subsequent services
also counted as

owner with music are

income to the extent of $600, it is clear that there has
been double (though successive) counting.
The services
of the piano have been counted as income in anticipation
as well as in realization.

Yet

this error, in

committed.

one form or another,

It is virtually in this

way

not infrequently

that

Cannan ^ and

others regard "savings" as income in the year in which

the savings are accumulated, although the interest upon
those savings will
years.

translate

man
it is

The nature
saves

be counted as income in subsequent
of the fallacy is seen as soon as

from money to other instruments.
If a
up money and purchases an automobile,

clearly double counting to call the automobile thus ob-

tained "real income," and then include
in the real

income

of ensuing years.

its

subsequent uses
matter

It does not

Elementary Political Economy, London, 1888, pp. 58, 59. The
income will be treated at greater
length in Chap. XIV. The reader who believes that savings ought to
be regarded as income is asked to stay judgment until he has finished
Chap. XIV.
^

fallacy of including savings in

INCOME

Sec. 5]

how

durable the instrument;

to include the instrument

it is

and

109

always double counting

its uses.

be invested in land or in confectionery.

income

tionery.

The savings may
The only true

the use of the land or the use of the confec-

To include

also the value of

value of the confectionery

the land or the

to count as income the capi-

taUzation of income.

§5
Economists have been more or less aware of the pitfall
of double counting, but not of the reason for it.
They
have therefore attempted to avoid it, not by excluding all
commodities from the income concept and restricting it to
services, but by specifically excluding from income certain
groups of commodities.
Naturally, they have been at
a loss to formulate a satisfactory and logical principle for
this exclusion.
Some of them have no better suggestion to
offer than that all "large" or "unusual" acquisitions should
be ruled out, and that only those commodities which come
into a man's possession in a "regular" stream shall be entitled to the name income.
This makeshift has received
much currency among German writers. To be sure, it
serves the purpose of excluding from income such obviously inappropriate elements as bequests and gifts of large
fortunes.
It is clear that when a well-known millionaire
recently fell heir to seventy millions, this did not constitute his income for the year in which he received it, but
that it merely constituted the principal or capital from
which he would receive income in subsequent years. But
the reason that it is improper to call this suddenly acquired
fortune income is not that it was large, nor that it was
sudden, but that it consisted of rights to concrete wealth
factories, ships, railways, and dwellings.
These things
are not under any circumstances income, but yield income
through future uses. It is idle to call income "regular";

—

for

all

know

that

it is

irregular.

NATURE OF CAPITAL AND INCOME

110

[Chap. VII

Another but very similar attempt to escape the
of double counting

and

of confusing capital

difficulties

and income

vague way be "regular," but that it must be such as to leave unimpaired the
Such a definition has the merit
capital which yields it/
as its source, but it merely
with
capital
income
connecting
of
of uniformity from the
attribute
shifts the pretended
In actual fact it
income itself to its parent capital.
is seldom true either that income flows uniformly or that
to specify, not that income

must

in a

capital remains at a constant level.

stipulate such uni-

formity as a necessary limitation of income

to define, not

the actual irregular income which exists in fact, but an

which we set up for reference. It cannot
be denied that the term "income" is sometimes used in the
sense of such an ideal instead of in the sense of actual income and we shall follow this usage so far as to call such
an ideal by the name of "standard income." What we
insist on is that such standard income is not, and must not
ideal standard

;

be confused with, the actual income which a man receives
from his capital. It is simply the income which he would
receive if he chose to keep his capital unimpaired and unIf a man has his capital invested in the form of
increased.

a house which yields him rent, this actual rent, less any
actual expenses for repairs, taxes, etc., is his income
from that house, even though the house may be depreciating in value. The ideal or standard income whi h the house
might yield without depreciation will be somewhat lower

than

this actual income, the difference being

what

called

amortization.
^~{

This

not the place to discuss amortization and the relabetween standard and real income. These

tions subsisting

topics will be fully discussed in Chapter

present

concerned with actual, not

XIV.
ideal,

are at

income;

This specification is characteristic of Hermann, SchmoUer, and
See Kleinwachter, Das Ei^kommen und seine Verteilung,
pp. 22-23.
1

many others.

Sec. 5]

INCOME

far as popular usage goes,

gives

111
its

sanction to the use of

the term "income " in the one sense quite as

much

as in the

though usually with very little intelligent discrimination between the two. For instance, a life annuity from
an insurance company, or a pension from a government,
is universally recognized as "income."
Yet this income
trenches on the capital which produces it, eating it up year
by year until, at the end of its allotted period, it is entirely
exhausted. Let us suppose that the annuity is one of $1000
a year for twenty years. Reckoning interest at five per cent,
such an annuity is worth, by the actuaries' tables, $12,462.
That is, the annuitant could sell his annuity, on a five
per cent basis, for $12,462 in ready money. But this
$12,462 invested at five per cent would bring in, without impairing the principal, not $1000 a year, but
If then he actually gets $1000 he is
only $623.10.
trenching on his capital the first year to the extent of
Yet we regard him, and very properly too, as
$376.90.
having a true income of $1000 a year.
If it were true that income could never trench on capital,
we could not reckon a laboring man's wages as income
without first deducting a premium or sinking fund sufficient
to provide for the continuance of this income after the destruction by death of the laborer. If the annuitant or
laborer should actually set aside such an annual sum as to
maintain the capital value of his property unimpaired, we
should be quite justified in considering the net sum, and
not the gross sum, as income. The $1000 annuitant who
pays $376.90 annually into a sinking fund is getting
only $623.10 annually, not $1000, for an income, and the
laboring man who pays an insurance premium reduces his
income by that amount. '^-It surely makes a difference
whether these "sinking funds" or "premiums" are actually
To reckon what one ought
set aside or merely reckoned.
other,

to save in

and a

order to maintain capital

definition of

not to save

income which depends upon an

it,

ideal

NATURE OF CAPITAL AND INCOME

112
reckoning

instead

of a real

payment

[Chap. VII

to that extent

inadequate.

§6

have now seen how the

fatal inclusion of concrete

wealth by the side of abstract services as a part of income
has led economists into two errors,
one the confusion of

—

and the other the

capital with income,

counting.

We now

fallacy of double

proceed to consider the other mistake

in the ordinary concept of real income, namely, that due

by the term "enjoyReal income, we were told, consists of "enjoyable
commodities and services." We have thus far succeeded
in eliminating "commodities" from this formula; we now
proceed to show that we may also eliminate "enjoyable,"
and leave the very simple formula: Income consists of
to the needless restriction introduced

able."

services.

when we put together all the
make up the total income of a com-

quite true that

elements which go to

munity or

an individual, and deduct

all

the negative

shall find that there are then left

solely enjoyable services.

But the various elements which

elements, or outgoes,
are

thus combined

— the

income from

factories, mines,

farms, and other instruments or groups of instruments

do not

all consist of

enjoyable services.

Most

—

them

consist of intermediate services preparatory to enjoyable
services.

How

these intermediate services cancel them-

summation will form the subject
At present we are merely concerned
in pointing out that any adequate concept of income must
leave room for these intermediate services, i.e. for the
income rendered by a factory or a bank as well as that
yielded by a dwelling or a pleasure yacht. We have already
had occasion to note the inadequacy of that concept of
income which restricts it to the yielding of money we now
selves out in the final
of a future chapter.

;

need to observe the inadequacy of that concept which

INCOME

Sec. 7]

113

money income
Having found "money income
insufficient for their purposes, economists have conceived
of "real income."
But by making real income consist of
"enjoyable" elements, they have excluded money income
altogether.
Some of them more or less avowedly retain
both concepts, but they do not show how to coordinate them
nor how to include them both under a more general incomeconcept. In their minds the two seem to stand totally disconnected, except that, in a partial and incomplete way,
real income is thought of as that for which money income
goes to the opposite extreme and leaves

out of account altogether.

spent,

§7
The ordinary concepts

income fail to conform to any
In consequence, among other
are those which have been drawn
of

consistent scheme whatever.

needless distinctions,

between

social

and individual income.

Social income has usually been conceived as the "net

—

not in the sense of the net difference
product" of society,
between services and disservices, but in a sense which
includes commodities.
this net

consistent

product has been furnished.

cannot include

new

capital,

all

products.

Some

method

of reckoning

It is clear that

are only too evidently

such as newly constructed railways, steam-

ships, tunnels, bridges,

and buildings and would not be
Others must

included by most persons in social income.

certainly be omitted to avoid duplication in our reckoning.

we were

wheat crop of the farmer, the
and the bread of the baker, we would
be counting the same thing three times over,
once for
each of three successive processes. Some economists have
sought to avoid this repetition, either by excluding the production and consumption of raw materials, or, if these are
included, by not including the whole value ol the finished
If

to include the

flour of the miller,

—

product, but only the increment of value over that of the

raw

materials.

NATURE OF CAPITAL AND INCOME

114

[Chap. VII

"We must be careful not to count the same thing twice. If we
have counted a carpet at its full value, we have already counted the
values of the yarn and the labour that were used in making it; and
But if the carpet is cleaned by
these must not be counted again.
domestic servants or at steam scouring works, the value of the labour
spent in cleaning it must be counted separately; for otherwise the
results of this labour would be altogether omitted from the inventory
of those newly-produced commodities and conveniences which constitute the real income of the country." ^
These reservations are entirely correct; but they furmeans of avoiding double counting. For
instance, are fuel and labor to be deducted in the same
way as raw materials ? Some writers have gone so far as
to claim that, just as the cost of feeding work animals
must be deducted from the value of the work they do, so
the cost of supporting laborers must be deducted from the
value of their product.^ If this view were correct, it would
seem that the laborer could not share at all in the distribution of the social income, since all that comes to him
is deducted
nish no general

similar question as to deductions arises in the oft-

cited

case where one profession

irksome than another.

more disagreeable

Should any deduction be made

from the income of the hangman, for instance, to equalize
his net income with the net income of a more desirable
calling ?

When

income is called "net product," the same
question arises which was met with in the case of individual
income, viz., whether by "product" is meant concrete
"
wealth, or services, or both. In our own theory, " services
are taken, but the usual concepts adopt wealth, or both
wealth and services. According to them, part of the insocial

new

come

of society consists of

sihps,

and dwellings, while the services of these new creations

wealth, such as factories,

Marshall, Principles of Economics, Vol.

E.g.

"Report

Committee on a

I, p.

Common

150.

Measure of Value in

Direct Taxation," Report of British Association for Advancement of
Science, 1878, p. 220.

INCOME

Sec. 7]

figure as

115

income in future years. We have already observed
new dwelHng or piano as income this year,

that to count a

and

its

use as income in succeeding years,

a species of

double counting as well as a confusion of capital and income.
of these errors are repeated in any concept of social
income which includes at once additions to the world's
wealth, and the income which this very wealth subse-

Both

quently yields.

§8

When

a wrong road

happens that
ther astray.
of

income to

once taken,

leads those

who

almost inevitably

further

and

fur-

Economists, having selected a wrong idea

found it so ill suited to
problem to which they at-

start with, naturally

their purposes that, in each

tempted to apply it, some special interpretation or amendment became necessary, until, instead of one concept,
they became possessed of a miscellaneous assortment^ of
They have been compelled not only to disconcepts
sociate money-income and real-income, but also to dissociate the income of the individual and the income of society.
When it is understood that the entire and only contribution
to the income stream which any given instrument of capital
!

can make consists in the services which that instrument
it will be found that all subsidiary meanings of
income are simply incomes from particular instruments
or groups of instruments. If the instrument in question is a
private carriage, the services which it brings forth, as events
desirable to its owner, are the acts of conveying him from
one place to another. These are primary or natural-incouie.
If the in trument is a public carriage, the services which it
brings forth, as events desirable to its owner, are the payments of fares. These are money-mcoiaej' If the group of

renders,

^ The reader who cares to study them in detail will find a collection of definitions in the Appendix to Chapter VII.

be borne in mind that the income is not the money
which is a concrete commodity, but the bringing in of the
money, which is an abstract service.
^

It should

itself,

NATURE OP CAPITAL AND INCOME

116

[Chap. VII

instruments

is the entire group of instruments constituting
the entire capital of a community, the net total of their

services

and

munity.

disservices

This

the entire income of the com-

social income.

If the group be the entire
property of an individual
the rights which he owns,
complete or partial, in instruments
the net total of the
is

—

services

and

disservices to

tutes his income.

This

—

which he

thus entitled consti-

individual income.

In science, the chief test of a definition is its adaptability
to analysis.
Judged by this test, none of the current concepts of income which we have passed in review can
claim to be adequate for we have found them subject to
;

the confusions of capital and income, and of double count-

A secondary test

ing.

also

fit

that a working definition should

into, or rather, give clear

and consistent

outlines

vague notions of income which we find ready made in
the actual world of business and accounts.
Of our own concept of income, as consisting exclusively
of services, we shall endeavor to show that it includes the
commercial bookkeeper's concept of "money income";
to the

that it is coextensive with the popular notions of income,
including what those notions include and excluding what

they exclude

;

that

affords a place for the usage

by which

sinking funds are reckoned and justifies the phrase "living

beyond income"; that it avoids double counting automatically and without the necessity for the exercise of judgment in each special case that it makes capital and income
;

strictly correlative

but never in danger of being confused;

and last, but not least, that it lends itself readily to economic
analysis and serves as a foundation for the theory of interest.
The concept of income to be elaborated is similar to
several which have been put forward by other writers.
It is almost identical with that of Edwin Cannan ^ it
;

See History of the Theory of Production and Distribution ; ElemenEconomy; and "What is Capital?" Economic Journal,

tary Political

1837.

INCOME

Sec. 8J

117

harmonizes with what Professor Marshall ^ calls
"usance" of wealth, and with the psychological
concepts of income in President Hadley's Economics^ in
Professor Flux's Economic Principles,^ and in Professor
also

the

Fetter's Principles of Economics.*

closely

than at

first

Finally,

harmonizes

glance might be supposed, with

the etymological and popular meaning of income.

In-

come from any source is what comes in from that source.
The income from any capital is what that capital brings in
to its owner, no matter what may be the form of benefit
brought in. If the capital serves to bring in money, the
income is ''money-income." If it serves to bring in crops
or products, as does a self-supporting farm, the income is
of another form.
If it serves to bring in enjoyable comforts, as does a dwelling house, the income is of a still
different form.

the

capital

But

in all cases, the essential fact

performs

service,

— accomplishes

that

something

desired.

usage makes income include

this

cannot be maintained that
usage.

may

— often

many

all

includes too

much;

— of the non-monetary benefits con-

income by economists,
as have studied the
subject with care. A business man who had bought a
yacht remarked: "It's a good investment, and I get my
dividends every Saturday afternoon when I take a sail in
it."
And the writer has never had any difficulty in perferred

money-income, it
with commercial

be objected by the unreflecting that by

including non-monetary elements

but

all

conflicts

capital are recognized as

as well as

by such men

suading other business

of affairs

men

of the propriety of such usage.

without an enjoyable use in prospect, money-income
would have no existence or meaning. A house could

fact,

itself

^ See Principles
of Economics, 3d ed. (Macmillan), Vol. I, p. 156.
part of this passage is quoted in Appendix to Chap. VII. See also
Carver's Distribution of Wealth (New York, Macmillan, 1904), p. 123.

Chap.

p_ i7_

43^ 571^

NATURE OF CAPITAL AND INCOME

118
never

command

money

rent to the landlord

[Chap. VII

did

not also 3deld shelter to the tenant, and even from the

money only
own rent and

standpoint of the landlord the receipt of the
intervenes as a

medium

for

payment

of his

other expenses of living, in other words for securing his
enjoyable income.

Income

is,

then, a very general concept.

services rendered

capital.

are included several special concepts

vidual income,

income.

It consists of

have seen that under
:

Social income, indi-

money income, natural income, and enjoyable

shall

soon see that the net income of society

or of an individual consists wholly of enjoyable income.

This

because the

non-enjoyable elements of income,

such, for example, as money-income, are

by equal items

of outgo.

all

exactly offset

But the non-enjoyable elements

are none the less a part in the grand total, and, in fact,

The money-income of ordinary
bookkeeping forms the bulk of any true inventory of inby

far the greater part.

come; but

its significance

counterpart in outgo

cannot be understood until

its

also taken into account, nor until,

in fact, a complete picture of all elements of

income

brought before the mind's eye. To present this picture
will be the object of the next three chapters.

CHAPTER

VIII

INCOME ACCOUNTS

The income

of our capital, then, is simply that

does for us.

Whether

brings us

money

which

or other return

does not matter;

the flow of its services is its income.
These services of wealth, as was previously explained, consist of any desirable events which occur by means of that
wealth or any undesirable events prevented.
Services exist in infinite variety. All work done by

human

beings, all the operations of industry, all the trans-

actions of commerce, are services,

accounts.

wealth

—

and enter into income

A bird's-eye view of this busy planet would reveal
real estate, commodities,

and human

beings,

—

Land, men, and
ceaselessly at work performing services.
implements are changing land, seed, and live stock into
Manufacturing plants are
grain, beef, lumber, and steel.
converting raw materials into flour, furniture, cloth, and
implements. In domestic establishments we find the servAgriices of cooking, warming, cleaning, and sheltering.
culture, mining, transportation,

names that we give

and commerce are simply
by

to the group of services performed

farm, mine, railroad, and business capital.

A disservice is a negative service. It is an undesirable
event occasioned, or a desirable one prevented, by means of
an article of wealth. A flow of disservices or negative income is called outgo. It does not matter whether the outgo
occasioned by an article consists in depriving the owner
of money or in some other evil.
If the outgo is in mone119

NATURE OF CAPITAL AND INCOME

120
tary form

it is

called expense;

if it is

in the

It includes all of

have called

trouble,

cost, i.e. labor,

form

human

what economists
expense, and sacrifices of

exertion it is called labor.

all

[Chap. VIII

kinds.

instrument very seldom yields services without in-

volving some disservices.

not only gives

dwelling house, for instance,

off services called shelter,

disservices in the

form

but also occasions

of labor (or expense) for renewals,

and taxes. Any
by that house is a disservice;

painting, cleaning, caretaking, insurance,

disagreeable event occasioned
just as

any agreeable event

a service.

Again, while

its owner a
performs disservices in being stabled, fed,
A farmer gets services out of his land when it

a saddle horse performs services in giving
daily ride,

and shod.
yields him crops; but to get these services he has to put
fertilizer, seed, labor, and expense into that land.
A rail-

way performs a

vast service of transportation,

passengers and commodities, but

amount

of coal, suppHes,

hauling

requires a prodigious

and labor to keep

going.

Disservices are not essential to the idea of wealth; an
article of

wealth sometimes offers services without any dis-

When

services.

disservices exist they are usually over-

balanced, in the estimation of the owner, by prospective

As soon

services.

as the disservices of

preponderate, in the est mation of

its

article of

wealth

owner, over the serv-

regarded as "more trouble than

it is worth,"
In
meantime
the
is
constitute
all,
a
such articles, if regarded as owned at
Jevons calls them
sort of wealth of negative utiUty,
"discommodities." They are never of great importance
and need receive no special attention. The chief examples

ices, it

cast aside

and ceases to be wealth.

—

of such articles are garbage, ashes, sewage, carrion, rubbish,

and waste.
It
ices,

has already been observed that services and disservin quantity
hke wealth, are measured in two ways

and value

— and

—

that the quantity of

each

service is

INCOME ACCOUNTS

Sec. 2]

measured

in its

own

special unit.

121

The quantity of the

serv-

measured by the number of
hours he works the services of a windmill, by the number
Quantities of services (or
of gallons of water pumped.
ices

of a gardener is often
;

very hetero-

disservices) are thus, like instruments of wealth,

geneous and are incapable of being combined in a single sum.
To obtain a homogeneous mass of value, we must multiply
the quantity of services (or disservices) by their several
prices.

Income and outgo, then,
senses:

income-services

like capital, are

used in two

(as well as outgo-disservices)

income-value (as well as outgo-value).

Hereafter,

and

when

the terms "income" or "outgo" are used alone, the value
sense will be understood.
of any individual service or disservice conan element of income or outgo. The value of all
the services flowing from an article of wealth through any

The value

stitutes

period, that

is,

the

sum

of all the elements of income,

called its gross income^ '-The excess of the gross

income

over the outgo, in other words, the algebraic or net
of all elements of

income and outgo,

instead of an excess, there

the net income.

a deficiency,

sum
If,

called net

Net income is of far more impoi^tance, both in
and in theory, than gross income;|- Gross income
may often be measured in more than one way, according
as the elements of which it is composed are considered
with or without accompanying olBFsets but the sum called
net income will be the same in either case.
outgo.

practice

;

§2
Income (or outgo) always implies (1) capital as the
and (2) an owner of capital as the beneficiary.
Mr. Smith's income from his farm imphes that the farm
yields the income and that Mr. Smith receives it.
In this
book we shall need to consider income chiefly in its relasource,

tion to the capital yielding

rather than in

its

relation to

NATURE OF CAPITAL AND INCOME

122

the owner receiving

it.^

[Chap. VIII

This twofold aspect of income

expressed in accounts by regarding the farm as "in account
with " its owner. All income from it to him is placed on one
side of the ledger

and

said to be "credited" to the farm,

Hke manner, "debited." A credit
item, then, signifies income which is yielded by a given
capital, and a debit item signifies outgo which it occasions.
The terms refer respectively to positive and negative elements in the income and outgo accounts of that capital.
We are now in a position to apply the foregoing definitions to income accounts.
We begin by imagining a "house
and lot" as an article of wealth or capital, and shall first
consider its income and outgo during the period of the calendar year 1900. The income which this capital brings
in to its owner may be either a money rental or the services of shelter for himself and family.
In either case the
income may be measured in money, although in the case of
occupancy by the owner this measurement requires a special
appraisement. We shall suppose that the house was built
many years ago and in 1900 is nearly worn out. It yields
an income worth $1000 a year. Against this income there
are offsets in the form of repairs, taxes, etc.
for these payments are "undesirable events" occasioned by the house
and lot. We have, then, the following "income account"
while

its

outgo

is,

;

Income for House and Lot during Year 1900
Income

Use

house and

lot

Outgo
.

$1000

Repairs

Taxes
Insurance

$1000

The net income

$200
100
100
$400

therefore $600.

1 The
terms income and outgo are somewhat unfortunate, as,
etymologically, they suggest the relation to the owner Smith rather
than to its source, the farm. Smith's income is the farm's "outcome"or "yield" (in German, ertrag). Similarly, when the farmer

INCOME ACCOUNTS

Sec. 2]

123

Next year we may suppose that the house is found to
have rotted beams, is condemned, and must be abandoned
Its services are ended, but the land is still
or torn down.
good and the owner can build a new house. This operation
consmnes,

let

us say, the

first six

months

of the year 1901,

no income, but only outgo.
During the second half of the year the house is occupied and
In the first six months not only
its use is valued at $600.
did the "house and lot" fail to yield any income, but on the
contrary occasioned an expense. The cost of production of
the house was a disservice; for this was an "undesirable
event" occasioned by the house and lot. It was withstood
only for the sake of future services which it would bring in
When we
It was not itself a desirable event.
its wake.
so that during that period there

say, then, that

straction

any event

future

we make

undesirable,

compensations.

ab-

All disservices are

"necessary evils"; they lead to good, but are themselves
evils.

We have,

then, the following account

—

Income for House and Lot during Year 1901
Income

Use of house and
months)

Outgo

Expense

lot (six

building

house

$600

$10,000
100

Taxes
$600

During

this year, then, the

$10,100

house yields a net outgo of $9500.

This adverse balance will be more than

which

follow.

lowing

—

made up

For the year 1902 we

may

in the years

have the

fol-

puts fertilizers on his land, this, his outgo, is the farm's ingo. But,
although we shall be largely concerned with income and outgo in
relation to capital as their source,
employ the terms outcome and ingo,

and might therefore

logically

seems preferable, for reasons
of usage, to retain the usual terms, income and outgo.
it

NATURE OF CAPITAL AND INCOME

124

[Chap. VIII

Income for House and Lot during Year 1902
Outgo

Income
$1200

Use

$ 50

Repairs

Taxes

150

$200

$1200

Net income

....

$1000

Let US suppose that these figures remain about the same
years, and give $50,000 net income during that time, which cancels the excess in cost for 1901
of $9500 and leaves a large margin besides, the nature
Then a
of which, as interest, need not here be considered.
second time the house is worn out and has to be rebuilt.
for forty-nine

The same cycle is repeated, one year of excess
offset by forty-nine years of excess of income.

of cost being

§3

It will be observed that the cost of reconstructing the
house was entered in the accounts in exactly the same way
There may seem to
as repairs or other "current" costs.
be objection to such a proceeding in the thought that reconstruction appears to be not a part of "running expense"

but a "capital cost," and belongs, not to income accounts,
but to capital accounts. It is true that the value of the
new house must be entered on the capital balance sheet,
but the cost of "producing it belongs properly to income

The former represents wealth; the latter repreThe former relates to an instant of time
(which may be any instant from the time it is begun till

accounts.

sents disservices.

the time

when

ceases to exist)

period of time (which

may

all

;

the latter relates to a

any part

of the time

during which the labor and other sacrifices occasioned by
A house is quite distinct from the
the house occur).
which it was fashioned. The consacrifices
by
series of
fusion between the two

natural in view of the practice

INCOME ACCOUNTS

Sec, 3]

125

bookkeepers in often entering capital at its " cost value."
In fact it is sometimes said that "liabilities represent money
received by a company, and assets, how it has been expended." But this is not strictly true. Since its market
value depends on its suitabihty to the uses to which it is
put, not on the money sunk in its construction, the house on
which was expended $10,000 for construction may be worth
more or less than $10,000. In this case the income
account should contain $10,000 on the outgo side, and
of

tlie

capital account

should contain a larger or smaller

figure.^

And

yet

undoubtedly true that we instinctively
building the house in its

object to entering the cost of

income-and-outgo account; and we express this objection
by calling this cost a "capital cost," rather than a part of
running expenses.

so classing

we mean

that

does

any rate, only at long intervals. 'On this
basis Wagner and others have erroneously claimed that
income and outgo should be confined to "regular" items.
At first glance this seems feasible because, in actual practice, an extraordinary expense in a given year, like the
not recur,

or, at

cost of constructing a house, does not usually reduce the

owner's net income for that year by that amount.

He will

avoid such a result by offsetting
the extraordinary expense of the house by a correspondingly extraordinary income from some other source, such
generally contrive to

as a depreciation fund.

It is evident that the house

owner

^ Even in the normal case the value of the house, as is well known,
not exactly equal to the cost expended in construction, but to that
amount plus interest. A house which costs $10,000, expended through
six months, ought to be worth a few hundred dollars more than this
sum at the time of completion otherwise the man who expended those
$10,000, and at completion has only $10,000 worth of house to show
The relation
for it, has evidently received no interest on his money.
between the value of capital, and its cost, and interest, will form a

;

subject to be taken up in a later chapter, where the common error
that accrued, but unpaid, interest is itself a cost will also be discussed.

126

NATURE OF CAPITAL AND INCOME

who has had

the foresight to set aside annually throughout

[Chap. VIII

the period of existence of the house a small deposit in a

savings bank,

may

derive therefrom,

sum

when

the time for

money, the receipt of
which is just as properly an element of income as its
expenditure for rebuilding is an element of outgo. The
great outgo for rebuilding is then offset by a great income
from the savings bank account, so that the combined net
depreciation fund and
income from the two sources
will be approximately zero and the total net inhouse
rebuilding arrives, a large

—

come of the individual will be affected little or not at all.
The depreciation fund, therefore, does not prevent, but
merely offsets the large negative balance in the income
account from the "house and lot" considered by itself.
The combined income from the two sources taken together
will be negligible, but that from the one source, the "house
and lot," will fluctuate. In figures, from this single source,
the net income is evidently +11000 a year for each of fortynine years, and

—$9500

for the fiftieth year <X It is mislead-

is "gross" income from which must
be deducted the depreciation fund or "amortization" supposed to be laid aside each year against the cost of rebuilding.
Merely to suppose a depreciation fund is not to have
one.
It is quite true that the $1000 income which the house
yields during each of forty-nine years is more than the income
which would have been left after an annual payment into
a depreciation fund had actually been made; but an income
which simply might have been is only an ideal standard.
Confusing the actual and the ideal is one of the commonest
fallacies in this field.
The actual net income of the house
and lot is alone the object of our present study, and this
actual income, in the example we are supposing, is $1000
each year for forty-nine years. While this sum is in excess
of the ideal standard income during each of these fortynine years, this overplus is atoned for by the sudden and
large deficiency every fiftieth year.

ing to say that the $1000

INCOME ACCOUNTS

Sec. 4]

127

§4
Such irregularity of income may be avoided, not only
by a depreciation fund, but by other devices, for instance,
by paying for the house in installments, by borrowing
money to defray cost and mortgaging the house, or by selling other property. Another method of steadying income
and one which ought to set at rest any remaining qualms

—

which the reader

may

feel at

adopted, of entering cost of

the procedure, which has been

new construction under "outgo"

— applies when the same owner possesses so many of the
articles in question that the reconstruction of

them must occur

one or another

Consider, for in-

at short intervals.

and loan association which
and each of
which lasts fifty years, so that the houses have to be
In the accounts of
rebuilt at the rate of one every year.
such an association the expense side should include the

stance, the case of a building

has

houses, each built in a different year

fifty

new

cost of

construction as a regular annual item, thus

—

Building and Loan Association
Fifty houses (with land) 1900

Outgo

Income

Construction of one new

Rents of 49 houses at
$1000 a year
$49,000
Rent of one house for
.

part of

which

house
Repairs on 49 houses

Taxes

the year in
constructed

500

it is

$19,900

$49,500

Net income

....

We have here

$29,600

a net annual income of $29,600, which con-

tinues year after year without interruption.
larity of

ceases

income which we found

when

$10,000
4,900
5,000

the larger

number

The

irregu-

in the case of a single

taken.

But

if it is

house

proper

to regard the cost of reconstructing the houses as outgo
in the case of a large

number

of houses,

must be equally

NATURE OF CAPITAL AND INCOME

128

[Chap. VIII

proper to regard it as outgo in the case of each single house
for the income account of the total mass of the community's capital is simply the combined accounts of the
individual

elements.

wise than regard

all

We
costs,

cannot consistently do otherwhether recurrent or not, as

outgo.

In actual business there are usually many articles of
the same kind, so that it is seldom necessary to reckon the
net income from each individual article. Such articles may
be conveniently lumped together. This we have just seen

As anwe may take the stock-in-trade of a merThis stock yields him income, not, as in the case
house, by rent, but by sale the difference between

in the case of the houses of the loan association.

other example
chant.
of the

;

rent and sale being simply that rent consists of a series of

contributions to income, whereas sale consists only of one.

A stock
which

of stoves, just as a stock of houses, yields

the

constituents.

sum

income

of the net incomes from its individual

But the stove

dealer

would

find the book-

keeping very troublesome were he to reckon in a separate

account the net income from each individual stove which

he buys and sells. He reaches the same final result for
his stock as a whole (or rather, for each specific category
of articles in his stock) by taking from his gross receipts
obtained by selhng stoves the year's cost of replenishing
his stock, the rent of his warehouse, salaries of clerks, and
Were he to arrive at this result by applying
other outgo.
the same process to each individual stove, the individual

vary widely for a stove left over
year (and therefore free from any item of cost
in this year's accounts), if sold this year, would give a
large net income, while another stove, bought this year,
results would, of course,

from

;

last

but not sold until next, would only have debit items in
this

year's

account.

But the sum

these

irregular

incomes from individual parts of the merchant's stock
will give a steady income for the whole.

INCOME ACCOUNTS

Sec. 5]

129

Any merchant's stock that rapidly changes
elements of which

treated as a whole.

constituted

To use

the individual

most conveniently

Professor Clark's admirable

Niagara Falls, which remains a waterfall,
although consisting each day of entirely different drops of
simile, it is like

The stock

of a butcher, grocer, or fruiterer consists
changing elements, but remains as a whole
relatively unchanged.
Though it would be logically sound,

water.

of rapidly

would be foolish and impracticable to keep an income
and outgo account for each individual leg of mutton or
box of figs. The tendency to-day, however, is distinctly
toward a more detailed accounting. Some business firms,
by means of modern card indices, keep a careful record for
each separate variety of commodity dealt with, if not for
each individual article in that variety. The important
it

thing to observe
is

that the net income of the entire group

simply the difference between the sums of the incomes

and outgoes of the elementary units which constitute that
group. The very item which, for the elementary unit,
constitutes "capital" cost, and which, for that unit, occurs
but once, becomes, for the group, the regular cost of

re-

and recurs annually. From the explanations
which have been given, it is clear that
consistency and logic must assign to every cost, whether
large or small, regular or irregular, a place as an element of

plenishing,

and

illustrations

outgo in the income-and-outgo accounts,

§5
Whether

or not

the irregularities of income from indi-

vidual articles of wealth are smoothed

away

in the total,

the combined income, even from a large group of articles,
We usually
is not necessarily an absolutely steady flow.
strive to make it so to some extent
but we do not always
succeed, nor do we even always try. When income does
vary, the method of measuring which has been given will
The
unerringly register that variation automatically.
;

NATURE OF CAPITAL AND INCOME

130

[Chap. VIII

method is not, of course, restricted to a group of articles
of the same kind, hke the fifty houses of the building and
loan association or the stock of stoves of the stove dealer.
It

appUes to any stock of miscellaneous

to the entire stock of wealth of a

articles,

community

The net income from any such group

and even

or the world.

simply the

sum

the net incomes of the various articles of wealth in exist-

ence at

all

that income

the points of time within the period for which
is

reckoned.

In hke manner

may

be obtained the income from any
This application
collection of
of income-and-outgo accounts occurs especially in the case
For we then find that the sources of
of an individual.
income consist largely, not of capital-wealth, but of capipartial rights to wealth, such as bonds,
tal-property,
property rights as capital.

—

and mortgages. But the introduction of the idea
of property as distinct from that of wealth involves no new
difficulties
for we have seen that property is only another
aspect of wealth, and represents simply rights to some of
the services of wealth. Thus in respect to partnership
rights, each partner in the firm of Smith & Jones, farmers,
The same principle
receives half the income of the farm.
stocks,

;

applies in respect to shares, bonds, or other forms of property.

Business

men

are accustomed to say that a railway

bond yields or earns so much income. But this merely
means that the railway behind this bond yields income, a
Thus
specified share of which belongs to the bondholder.
the true source of the services which flow to the property
holder

specifies

income

the concrete wealth; his property-right merely

such portion of those services as are

his.

The

of a stockholder, for instance, consists of all the

benefits he receives
sacrifices.

from being a stockholder,

less all

the

Usually, for him, both benefits and sacrifices

accrue in monetary form.

His income from his stock

usually the receipt of dividends.

The

total net

income of a person

is,

then, the

sum

INCOME ACCOUNTS

Sec. 6]

131

the net incomes from each individual article of property

which he holds within the time interval considered.

§6
To illustrate this, let us consider the case of a lawyer
hving in a rented house, but owning the furniture. We
shall assume, for simplicity, that his property is grouped
under the following nine heads: (1) stocks and bonds,
(2) lease of house (including not only the privilege of occupancy but

also the obligation to

other

house, (4)

(5)

money and bank account,

(6)

ing not only the claim on their
to

pay wages),

pay

rent),

(3)

furniture

household supplies, especially food,

(7) like

claim on servants (includ-

work but also the obligation

claims on, coupled with obligations
own person, (9) " etc." We

from, office clerks, (8) his
shall take, as the

time interval, a period of a month.

During the month, the stocks and bonds bring in checks
aggregating $2,000 and the lawyer buys

new

securities to

His total net income, therefore, during this particular month from this particular group of
property rights is $1500. Under his lease he enjoys a
month's use of a house, this use being regarded by him as
the extent of $500.

worth,

let

us say, exactly what

costs, or

him $100 worth

$100 a rnonth.

and costs
furniincome.
His
no
net
it leaves
ture yields him comfort worth $50, from which cost of
repairs, etc., amounting to $30, has to be deducted, leaving a balance of $20. His stock of food and similar suppUes yields him the board of himself and family for the
month, worth $150 but the cost of replenishing this stock
and the services of cook and waitress in preparing and
serving it absorb, let us say, all of this sum, leaving for
the month no net income from the pantry's stock.
The next source of income (or outgo) is " cash." By
this is meant the stock of property which includes money
on hand and money on deposit in bank. To find how
Since the lease yields

him $100

money,

;

of shelter

NATURE OF CAPITAL AND INCOME

132

much income

[Chap. VIII

comes from " cash " we need only
usage of bookkeepers which
cash as though it were a gold mine

or outgo

follow the well-established

regards a stock of

which, consequently,

to be credited with all the gold or

cash which comes out of
into

it, and debited with all that goes
This usage often puzzles the novice, but its cor-

it.

undoubted and it harmonizes with our definiand disservices.
For the services or
desirable events which come from one's stock of cash
the events, in fact, for the sake of which that stock of
cash exists
are the furnishing of money from time to

rectness

tion

services

—

time

;

the disservices, or the undesirable events occasioned

by that stock

of cash, are the absorption

money

from time to time. In other words, my purse serves me
whenever it pays my bills it costs me whenever I, so to
speak, pay its bills. In this respect it is precisely similar
to any other stock of wealth.
A bin of coal serves its owner
when it renders him fuel; it costs him when it has to be
The cost may be the sacrifice of money, of labor, or
filled.
of coal taken from some other store of coal.
In the case
before us, the income from "cash," or all the payments the
lawyer takes out of his pocket-book or check book, amounts,
let us say, to $3780, whereas the outgo to "cash"
all
amounts to $4000, leaving $220 as a
sums paid to it
;

—

net outgo.

The claim on the

servants, like the lease of the house,

involves an obligation to pay as well as a right to receive.

suppose that the servants render services during
the month worth $100, and also cost $100 in wages, leavshall

ing no net balance.
in

Similarly the office clerks cost $500

wages and yield $500 worth

of assistance to the lawyer

in the preparation of his cases.

The man himself receives from his practice during the
month $2000. But his office and professional expenses
amount to $500 and leave a balance of $1500. The class
called "etc." comprises

all

sources of income not other-

INCOME ACCOUNTS

Sec. 6]

133

wise included, such as clothing, watches, jewelry, and other
articles of

wealth or property not contained in the other

For simplicity we shall suppose that the income and outgo connected with etc." are equal to each
other, and amount to $2500.
The total income of this man is therefore as follows
categories.

Income,

—

NATURE OF CAPITAL AND INCOME

134

[Chap. VIII

A little consideration will show that if we credit the servants
with the services of cooking and waiting, and debit them
with wages as a distinct item, we must debit the food
with their services of cooking and waiting. If we prefer
to drop out these services both from the credit side of the

and the debit

servants' account

side of the food account,

are then at liberty to omit the category of servants

and

only the charge of their wages
There are endless admissible modifications of the accounting here described, many of which
have practical advantages, but the preceding is presented as a complete and detailed record of all income and
outgo arranged by sources.

entirely,

leave

against the food.

In complete accounting we must not omit the negative
items of property,

liabilities.

The same

principles

apply here as for positive items, or assets. Items which
are negative are such because they yield negative income,
or outgo.
If the lawyer whose accounts we have followed
is in debt, the payments on his debt (whether "interest"
or "principal") which he

considered are outgo.

makes during the

the other hand,

time-interval
if

a debt

contracted during the time-interval considered,

its

pro-

ceeds are for that period an addition to gross income.

Thus an income-and-outgo account may always be comformed by recording the values of the services and
disservices occasioned by all the articles of capital under
consideration.
In the case of an individual these articles
of capital are his assets and his liabilities.
No other items
than the services and disservices mentioned can properly
find a place in the accounts.
We have already warned
pletely

the reader against the fallacy of deducting from income

any depletion

capital;

should

also

warned

against the opposite fallacy of adding to income any savings of capital.

This fallacy

common and

so subtle

INCOME ACCOUNTS

Sec. 8]

that

its

where

135

discussion will be postponed to Chapter

may

receive the attention

XIV,

deserves.

con-

tent ourselves at present with a preliminary illustration.

savings bank depositor is sometimes thought to draw
income from his deposit when the interest "accumulates."
This is an error. He draws income when, and only when,
he draws money out of the bank; he suffers outgo when,
and only when, he puts money into it. If he merely lets
his deposit accumulate, he derives no income and suffers
no outgo. There is no effect on income. What does occur
He cannot have his cake and eat it
is increase of capital.

/.'-A

too.

we make

the fiction that the

man who

allows his

savings to accumulate virtually receives the interest,

must, to be consistent, also make the fiction that he redeIf the teller hands over the interest across the
posits it.
counter, the depositor's account certainly yields

up "in-

come" to him, but if he hands it back it must, in consistency, be charged as "outgo," and the net result on his
income is simply a cancellation. This procedure reveals
clearly the fact that the accumulation is not income.
_^

§8
The method

lawyer's account

accounting employed in the preceding
is,

of course, not the only, nor is

the

method, however, which shows
the shares of the total income attributable to each individual source. In practice, the minor sources of income
The income and outgo of one's " cash
are neglected.
almost balance in the long run, and the same is true of
the lease, the servants' contracts, and the household supplies.
One's furniture probably yields a larger net income
than is commonly realized, but even this is usually a small
usual, method.

It is the

total.
It is only in case the lawyer lives in
house that a serious correction would need to be made
on this account. In this case, his shelter is not offset by
any rent payment, and enters the accounts as pure income.

element in the
his own

NATURE OF CAPITAL AND INCOME

136

[Chap. VIII

income is obtained
two principal
the
income
from
items,
investments and the income from
Practically, therefore, the lawyer's

by taking from the above

table only the

Each

his professional work.

these

$1500, so that

according to this approximate accomiting the net income
$3000. Another and more common method of approximating an income account is to record simply money
receipts and disbursements, in other words, to record
only the items of the preceding account under "cash."
The lawyer's cash account book would present an appearis

ance

the following

—

Disbursements

Receipts

Investments,

From
From

stocks and bonds
personal labor
.

2000

stocks

and bonds
Rent

$ 500

....

100
30
50
100
500
2500

Furniture repairs
Cost of food
Servants
Clerk hire
.

"Etc."

$4000

$3780

This leaves a cash balance of $220, which is to be added,
end of the month, to the cash on hand at the begin-

at the
ning.

This balance does not here indicate the net income

of the lawyer, as did the balance in the completer account-

ing which preceded.

The net income

of the lawyer, in the

incomplete and makeshift accounting
eration,
total

is,

so far as

cash receipts

it is

now under

represented at

less certain

all,

consid-

shown

makeshift corrections.

in the

The

such accounting, so far as any exists, is that
income,
from whatever source, passes through the
most
justification of

cash drawer.
It will

account,

be noticed that the receipts side of the above
$4000, greatly exceeds the true net income,

$2800, shown in the previous accounting.
any one using such mere money accounting

Instinctively
feels

the need

INCOME ACCOUNTS

Sec. 8]

making some deductions from the

137

total

money

receipts.

also instinctively feels that not all of the disbursements

should be thus deducted

otherwise little or nothing would
The ordinary makeshift is to deduct the " business
expenses,"
the $500 invested in stocks and bonds and
the $500 for clerk hire. The remainder will then be

remain.

;

—

$3000, which

is,

for practical purposes, a sufficiently close

approximation to the true net income of $2800.
Practically, therefore, either

ness" expenses) or the

sum

money

receipts (less "busi-

incomes from secuand labor, are good makeshifts for true income. But
even from a practical point of view they will not always
of the net

rities

serve, while as a

wrong.

They

matter of

strict

theory they are always

could be right only under the condition that

income, from whatever source, flowed through the cash
drawer. If it were true that the net income from stocks and

all

bonds, the net income from the lawyer's practice, and, in

manner, the net income from every other source flowed
on the other hand, the flow out
of that drawer consisted exclusively of expenditures for
each and every satisfaction as it occurred, then the flow of
money through the cash drawer would serve as a true measure of income, and the cash drawer might be called a sort of
income meter. The flow into it would be money income
and the eventual satisfactions obtained from it would be
real income.
The two would then also have the relation
like

into the cash drawer, while,

usually ascribed to

them by economists.

practically reahzed in the case of a rentier,

ceives

This case

who simply

money from investments and spends

for

re-

imme-

diate satisfactions, renting, let us say, not only a dwelling

but its furniture as well, so that practically no part of his
income can reach him except by passing through the money
stage.
But few people are in exactly this position, so that
not all income passes through the meter. Some passes
around it, as, for instance, the shelter derived from a man's
own house or the comforts from his own furniture, and hence

NATURE OF CAPITAL AND INCOME

138

[Chap. VIII

not be registered by the meter at all. On the other
hand, some passes through it not toward direct satisfactions
will

but toward some "business" expenditure likely later on to
repour cash through the money meter and hence to cause

happens that the money
and sometimes registers
It is therefore only a rough and imperfect instrutwice.
ment for measuring net income.

to register too

much.

meter sometimes

fails

Thus

to register

§9

When we turn from real to fictitious persons, we find, for
income accounts, as for capital accounts, that the two sides
necessarily balance exactly.
A corporation, as an entity
distinct from its stockholders, cannot enjoy income or
suffer outgo.
All the income not devoted to other expenses is absorbed in paying dividends. A railway company, for instance, has an income account as follows
;

—

Income Account op Railroad Corporation for Year
Income

passenger

freight service

Outgo

and
.

$1,246,147

operating

ex-

$800,000

pense's

interest

holders

To dividends
To

bond-

....

holders
surplus applied to

200,000

purchase of
land
(2) cash in treasury

(1)

$1,246,147

100,000

to stock-

....

140,000
6,1^7

$1,246,147

In these accounts we see that the gross income from all
was $1,246,147, of which $800,000 disappeared for
running expenses, $100,000 for paying bondholders, and
$200,000 for paying stockholders, leaving a balancing item
of $146,147.
But this balance is likewise expended, $140,000 of it being outgo for new land, and the small odd sum
sources

INCOME ACCOUNTS

Sec. 10]

139

$6147 being put into the safes of the company or deposited
Even this last operation is a true outgo; for a
cash drawer and a bank account are, as we have seen, always
debited with what is put into them. There remains, therefore, no final balance for the abstraction called the "company." Just as, in the capital accounts, the company's
excess of assets over liabilities to other than stockholders
in bank.

constitutes the true liability to the stockholders themselves,
so, in

income accounts, any excess

income over outgo to

other purposes than dividends paid to stockholders con-

a true outgo for the benefit of those stockholders.

stitutes

§10

We see,

then, that the guiding principle for the construc-

tion of the income account, either of real or fictitious per-

make a complete list of the services and
which flow from each and every item of the assets
and liabilities. This simple relation between capital and
income accounts is commonly obscured by the fact that it
sons, is simply to

disservices

not practically convenient to include in one's capital ac-

counts certain items of assets and Uabilities, although their

and

services

This

disservices are entered in the income account.

true, in particular, of one's

own

person,

and such

claims as are coupled with equal obligations, as leases and
contracts with laborers.

These are not and, from a purely

practical point of view, ought not to be entered in the
capital account but much of the income and outgo from
them, such as wages and rent, are entered in the income
account.
In respect of income accounts the use of one's
;

dwelling

omitted, as well as the unpaid-for services and

human beings. A shopkeeper usually keeps
a punctilious record of the work of his employees, but seldisservices of

dom any

of his

own

personal work.

he owns the build-

ing he occupies, he will not usually include

accounts.

In private

life

its

use in his

he seldom or never includes in

his accounts the use of furniture.

140

NATURE OF CAPITAL AND INCOME

Our present

[Chap. VIII

object, however, is to show, not the

methods

but merely the application of
economic principles to such bookkeeping. The chief obof practical bookkeeping,

ject is to find the philosophical basis of accounting.

Care-

ful examination shows that accounting is at bottom not a
mere makeshift but a complete, consistent, and logical system. When thus conceived and understood it will be seen
to be of importance, not alone to the accountant but also to
the economist. For his purposes, the only method of constructing income and outgo accounts which is philosophically correct, and which can serve as a basis for economic
analysis, is the method by which are recorded, for each

article of capital, the values of all its services

and

disserv-

These services and disservices are of many kinds.
ices.
Sometimes they consist of money payments, sometimes of
productive operations, and sometimes of enjoyable elements. These all enter the accounts on the same footing,
but in the next chapter we shall see that after being thus
entered, the items may be so combined that all except the
enjoyable elements will cancel among themselves.

CHAPTER IX
INCOME SUMMATION

have now seen how to reckon the income of either a
By combining the net incomes
real or a fictitious person.
of all persons, the net income of society may be obtained.
As we have seen, fictitious persons have no net income,
and would therefore not affect such a method of summation.
Another way to obtain the total social income is by adding
together the net incomes from each individual article of
concrete capital, regardless of its ownership. In such a
summation no partial property-rights, such as stocks and
bonds, would appear. Instead we would only find actual
For
railways, mills, refineries, and other concrete capital.
Pacific
Southern
the
instance, the net income earned by
Railroad, considered as an aggregate of roadbed, termi-

and other existing instruments, would
be taken. This would not be the income of the Southern
Pacific Railroad Company, for, as we have seen, the company, as such, has no net income. Nor would it be the
nals, rolling stock,

income of the stockholders of the company, for this conNor
stitutes only a part of the earnings of the road.
would it be exactly the sum of the incomes of the stockholders and bondholders, inasmuch as the company may
earn income from other sources than the railroad itself, as,
for instance, through leases of other roads and shares held
in other companies, none of which income is produced by
the railway. It would be simply the difference between
the total value of the services of transportation rendered
141

NATURE OF CAPITAL AND INCOME

142

[Chap.

by the railroad and the value of the disservices occasioned
by it, whether through cost of operation, repairs, renewals,
or betterments.

The two ways of obtaining the total social income which
have just been outlined
(1) by summing the net incomes

—

of individual persons as owners,

and

(2)

by summing the net

—

incomes from individual articles of wealth as sources
may
be illustrated by supposing two ledgers to be opened containing the income for a given community, one ledger
being devoted to each way. Each page of Ledger No. 1
would be devoted to the income-account of a particular
individual, stating in detail, in two columns, the items of
income and outgo in the minute manner already shown.
In Ledger No. 2 likewise each page would be devoted to

The

the income-account of a particular article of wealth.
first

ledger would represent, therefore, the distribution of

income among

summary

The
the mag-

community.

different persons in the

of such a ledger, arranged according to

nitude of the incomes, would give us the "distribution

curve" of incomes shown by Professor Pareto.^
Let us suppose, for the sake of illustration, that the
lowing is such a summary for the United States
:

Distribution Ledger No.

—

fol-

Net Income for 1900
15,000 millionaire families
100,000 families, incomes ranging from $10,000 to
$50,000
1,000,000 families, incomes $1000 to $10,000
20,000,000 families below $1000
.

$ 2,000,000,000
3,000,000,000
5,000,000,000
10,000,000,000

$20,000,000,000

The second

ledger would

show the same

total income,

but distributed according to the source which produced

We may
follows

—

See his Cours d'Economie Politique, Lausanne, 1897, Vol.
299-345.
^

it.

suppose a summary of Ledger No. 2 to be as

II,

pp.

INCOME SUMMATION

Sec. 2]

143

Distribution Ledger No. 2
Net Income for 1900

From land
"
"
"
"

buildings
railways and

etc

$ 2,000,000,000
2,000,000,000
1,000,000,000
1,000,000,000
13,000,000,000
1,000,000,000

tramways

factories

persons

$20,000,000,000

§2
Both these ledgers would be constructed by combining a
number of separate net incomes, each one of which was the
balance remaining after deducting the outgo from the gross
income of the particular group of capital considered. In
other words, both ledgers would be constructed
to adopt
the phrase which was employed under capital accounts

—

—
by the "method of balances."
But there also a second method of summing incomes, —
is

the

"method

accounts

view, and

of couples."

both asset and

is,

Just as the same item in capital
liability,

according to the point of

therefore, self-canceling, so the

income accounts

same item

both service and disservice, and

is,

there-

The reader may, in fact, have felt
examples cited, what we called disHe may have asked
services seemed to him to be services.
himself. Why should we call rebuilding a house a disservice ?
When a carpenter and his tools repair it, do we not credit
him and them with services? Is not any production a
service? Are not, then, repairs placed on the wrong side
of the ledger ?
In answer it may be said that when a carpenter with his plane, hammer, and saw helps to rebuild a
house, we have to consider two groups of capital. One
group, the carpenter and tools, is acting on the other group,
the house. The carpenter and tools used in the process
certainly perform a service, but the house does not. Con-

fore, also self-canceUng.

that, in

many

of the

by the hoiise, the repairs are disThe house absorbs or soaks up these costs.

sidered as occasioned
services.

NATURE OF CAPITAL AND INCOME

144

[Chap.

promising to compensate for them by better service later
is certainly not what
but is only a necessary evil. On the part
of the hammer, however, these same events are services.
The service called " nailing " is credited to the hammer.

on.

Tiie renailing of loose shingles

the house

is for,

Therefore the repairing of the house

at once a service

and a disservice.
Such double-faced events require a special name. We
may christen them interactions between two instruments
or groups of instruments. Alternative names are interacting services,

coupled

or preparatory services,
simply "couples." They underlie

intermediate,
or

services,

what business men

call

"double entry bookkeeping."

An interaction, then, is a service of the acting instrument,
a disservice of the instrument acted on. There can never
arise the shghtest doubt as to when it is to be regarded as
positive

and when negative.

The

and
by referring it
the owner of the service

definitions of service

disservice settle this question in each case,

to the desire of a

or disservice.

human being, viz.

As he

desires that the house should not occa-

sion repairs, these repairs are disservices of the house;

he desires that the tools should occasion repairs, they are
services of those tools.
its

value from

its

The hammer

exists for

and derives

prospective services in renailing shingles.

The house does not

exist for nor derive its value

renailing of its shingles;

that event detracts from

from the

on the contrary, the prospect
its

value.

The example given is typical of the general relations
between interacting instruments. The mental picture we
should construct is that of two distinct groups of capital.
Group A acts on group B for the benefit of the latter.
Whatever the nature of this interaction, A is credited with it
and B debited. The credit and debit are equal and simultaneous, the only result of the interaction being that, in
consequence of it, B is enabled at some later time to yield
more income.

INCOME SUMMATION

Sec. 3]

145

Interactions are essentially identical with

cussed a generation ago under the

title

what were

dis-

"productive serv-

But inasmuch as the name "productive services"
is not a very happy one, and its use has been so confused and
ices."

has engendered so many verbal quibbles, it seems advisable
not to revive it. The essential fact that these "productive
services" were two-faced

— negative as well as positive —

was always overlooked, and there remained no other characteristic which could give the phrase a definite and scientific
meaning.
Interactions constitute the great majority of the elements

which enter into income and outgo accounts. The only
services which are not merely the positive side of interacdesirable conscious experitions are mental satisfactions
ences
often miscalled "consumption"; and the only
disservices which are not the negative side of interactions

—

But these are only the outer fringes
Between them is a connective network of productive processes and commercial transactions,
every fiber of which has two sides, a positive side of services and a negative side of disservices.
are pains or "labor."
of the

economic

fabric.

§3
The interactions between two articles or groups of articles
may, of course, consist either in causing or preventing
changes or events. The events or changes which are
caused or prevented are of three chief kinds,

— changes of

and changes of ownership or, transformation, transportation, and transfer. We
shall take these up in order.

form of wealth, changes

of position,

;

What

here called transformation of wealth

tically identical

with what

prac-

usually understood by "pro-

duction" or "productive processes." ^ By the transformation of wealth, or the changes produced in its form, is

meant the changes
^

of relative position of its parts.

Cf. Marshall, Principles of

Economics, 3d

Weav-

ed., p. 132.

NATURE OF CAPITAL AND INCOME

146

ing, for instance, is the

by a rearrangement

[Chap. IX

transformation of yarn into cloth

in the relative position of the

warp and

Spinning, likewise, consists of moving, stretching,

woof.

and twisting

fibers into

yarn

;

sewing, of changing the posi-

may

hold cloth together; and so
with carding, wool-sorting, shearing, and all the other
operations which constitute the manufactm-e of fabrics.
tion of thread so that

and agriculture consist simply of a
and each transformation

All manufacture

series of transformations of wealth,
is

two-faced.

the part of the transformed instrument

(or instruments) the transformation is

a disservice

;

part of the transforming instrument (or instruments)

it is

We have seen that when a carpenter and his tools

service.

transform a house,
are credited

when the

When

on the

i.e.

build or repair

and the house

painter decorates

he and his tools
The same is true

it,

debited.

or the janitor cleans

a cobbler transforms leather into shoes, he

it.

per-

forming services; the shoes at each stage are occasioning
disservices, or costs.
When a bootblack transforms dirty
shoes into clean and polished ones, he Hkewise
services,

and the

shoes, disservices.

which produces cloth out

yarn

rendering

manner, a loom
to be credited with this
In

operation as income, while the stock of cloth receiving the

product of the loom

to be debited with the very

same item

as part of its outgo or "cost of production,"

Again, land renders a service in producing wheat.
the part of the wheat, however, this

production

stock

of a granary, the entry of

a disservice.

its

Wheat

a service of land, a disservice *of wheat.

consider a farm as pouring

wheat

crop into the stock of

wheat from farm to wheat
and debited to the

credited to the farm as its service

wheat stock as

its disservice.

Sometimes, as has been

said, the interaction consists not
but in preventing one. A warehouse
renders its service as a means of storing bales of cotton, i.e.
protecting them from the elements. This storage is, how-

in causing a change,

INCOME SUMMATION

Sec, 3]

ever,

on the part

of the stock of cotton,

147

an element

of outgo

or expense.

As has already been intimated, there may be, and usually
more articles than one in either or both of the two

are,

interacting capitals.

Plowing, or the transformation of

is performed by a plow, a horse,
The plowing is a cost debited to the land on
the one hand, and at the same time a service credited to
the group of capital consisting of the plow, horse, and man

land into a furrowed form,

and a man.

on the other.
of

how much

are not here concerned with the problem

should be placed to the credit of each

operating agent, but merely with the fact that the

co-

sum

total of the three is equal to the debit for the land.

The principle is not altered if one or more of the transforming agents perishes and another comes for the first time
into existence in the transformation.

Bread-baking

transformation debited to the bread and credited to the
cook, the range, the flour, and the fuel, of which the last

two perish as soon as they perform their services. Agents
which disappear in the transformation but reappear, in
whole or in part, in the product are called "raw materials."
The production of cloth from yarn is a transformation effected by means, not only of the loom, but also of a number
The cost
of other agents, and among them the yarn itself.

consumption of raw material,
consumption of yarn, on the part of the
yarn itself, is not cost or disservice, but service. It is
the event for which the yarn had existed. When cloth
is turned into clothes this transformation is a service to
be credited to the cloth, and a disservice to be debited to the
clothes.
All raw materials yield services as they are conof weaving includes as cost the

yarn,

and

this

verted into finished products.

Their conversion

is,

however,

always outgo on the part of those products.
In this way, when an article passes through various stages
of production, it is often an arbitrary matter whether we
designate those stages by different names or not. A "sap-

NATURE OF CAPITAL AND INCOME

148

ling" grows into a "tree."

We may, if we choose,

[Chap.

consider

the sapUng as one category and the tree as another.
this case the

"sapUng" performs a

service at the

moment

becomes a "tree," just as the "tree" performs one later
when it, in turn, becomes "lumber"; but no effect on
social income is produced, because, if we credit the sapUng

with the value of the tree, we must debit the tree with the
Likewise we may arbitrarily designate
cost of the sapling.

moment when a
"new" wine becomes
the

"calf" becomes a "cow," or

when

"old," without disturbing the income

accounts of society; for such events are always two-faced
and cancel themselves out in the total. We may, in fact,

by an
and regard the passage across this Hne as a
on the part of the capital on one side of the line

mark any

stage whatever in the course of production

arbitrary Une,
service

and a

disservice

on the part of the capital on the other

side.

§4
The

second class of interactions

transportation, or the

change in place of wealth. It is a very thin Hne which
separates this class from the preceding class. Transforming or producing wealth consists of changing the position
transporting wealth
of its parts relatively to each other
But
is changing the position of that wealth as a whole.
;

"part" and "whole" are themselves loose and relative
Bookbinding is a transformation or production of
wealth; it assembles the paper, leather, thread, and paste
Delivering books to a library is transinto a whole book.
portation.
Yet the library is, in a sense, a whole and to
assemble books into a classified and organized Ubrary is to
make a whole out of parts. The distinction between transformation and transportation is thus merely one of convenMany writers prefer to include them both under
ience.
"production." We prefer to include them under the less
ambiguous and more inclusive rubric "interactions," and
terms.

;

our object here

not to emphasize their difference, but

INCOME SUMMATION

Sec. 5]

their similarity.

The same

149

principle of equal

and opposite

appUes to both. When merchandise is changed
from one warehouse to another, the first warehouse is
The
credited with the change and the second debited.
warehouse which has rendered up the merchandise has
done a service; that which has received it has done a
disservice.
A banker who takes money from his vault and
puts it in his till will, if he keeps separate accounts for the
two, credit the vault and debit the till. When wheat is
imported from Canada, that nation is credited and the
United States is debited with the value of the operation.
services

may, as

cesses, divide
lines,

lines

in the case of continuous productive pro-

up transportation

and consider the passage
as an interaction.

districts

any

by any

arbitrary

articles across those

§5
The

third class of interactions

ship of wealth or property.

the change of owner-

This has been called transfer.

and involve two objects
between two owners.
This double transfer, we have called an exchange. Since
an exchange consists of two transfers, and since a transfer
is a species of interaction and as such is self-canceling,
every exchange is self-canceling and cannot of itself contribute anything to the total income of society.^ When a
Transfers usually occur in pairs,
transferred in opposite

directions

bookseller, for instance, sells a book, he credits his stock
with the fact that it has brought in money, and the customer debits his Hbrary to the same amount.
1 The exchange does not dupHcate income, but merely shuffles it
about. It may and does put services of wealth where they are most
needed, and thus results in a more effective use of income, just as
credit and other forms of the divided ownership of wealth may make
a more effective ownership of capital. In both these cases there is an
increase of "total utility." This needs to be considered in its proper
place, but it must not stand in the way of our canceling the values
These values,
of assets and liabilities or of services and disservices.
as is well known, are connected, not with total utilities, but with mar-

ginal utilities.

NATURE OF CAPITAL AND INCOME

150

[Chap.

These two items constitute the transfer between the
stock of books of the dealer and the stock of books of the

The remaining two items constitute a transfer
between the stocks of cash of the two men; the dealer
debits his " cash " and the customer credits his.
When therefore an article of wealth changes hands,
it occasions an element of income to the seller and an
element of outgo to the purchaser, and therefore no income
customer.

all

to society.

The

effect of canceling these

items

—

the credit item of the seller and the debit item of the pur-

—

is to free the income account of that article from
entanglements with exchange, to wipe out all moneyincome, and to leave exposed to view what we have called
the natural income of the article. Thus, books yield their
natural income, not when the book dealer sells them, but

chaser
all

the reader peruses them. The sale is a mere preparatory service, a credit item to the book dealer and a
debit item to the buyer. The fact of bookselling adds
nothing to the income of society, but the reading of the

when

Again, a forest of trees yields no natural
does.
income, until the trees are felled and pass into then ext
The owner of the forest may, to be sure,
stage of logs.

book

ready to be cut,
the forest has
by simply selling it to another
then yielded income but, as the purchaser has suffered an
equal outgo, the forest has as yet yielded nothing to society.

"reaUze" on the

forest long before it is
;

and

him

;

The principle that an article of capital yields, to society,
no income except its natural income, is not altered when
its

ownership

divided nor

when

the part rights are

bought and sold. Adam Smith regarded a rented house
as bearing income in the form of rent, but a house occuThe truth
pied by the owner as bearing no income at all.
and both
income,
Both houses yield
is nearly the reverse.
incomes are of the same kind, viz. shelter. The rent of the
rented house is, for society, not income at all. It is income
outgo which he
to the landlord but outgo to the tenant,

—

INCOME SUMMATION

Sec. 5]

151

willing to suffer solely because of the shelter

he receives.

This shelter alone remains as the income from the house
after the rent transaction

parties concerned.

canceled out between the two

The shelter-income

abiding item, and without

the essential and

there could be no rent-income

to the landlord.

Again, a railway yields as its income solely the natural
one of transporting goods and passengers. Its owners sell

money and regard the railmoney
way
maker; but to the shippers and
passengers this same money is an expense and exactly offsets the railway's money earnings.
Of the three items
money income of the road, money outgo of its patrons,
this transportation service for

simply as a

—

and transportation

— the

first

two mutually cancel and

leave only the third, transportation, as the real contribution of the railway to the

see, then, that the

sum

total of income.

method

of couples,

applied

buyer and seller, denudes all capital of its so-called
"money-income," and lays bare the only income it can
really produce, the natural income.
We see that capital
is not a money-making machine, but that its income to
society is simply its services of production, transportation, and gratification.
The income from the farm is the
yielding of its crops from the mine, the production of its
ore; from the factory, its transformation of raw into finished products; from commercial capital, its passage of
goods from producer to consumer; from articles in consumers' hands, their enjoyment or so-called " consumption."
Similar principles apply to outgo, no part of which, for
society, exists in money form.
The great bulk of what mer;

chants

call

money

"cost of production," expense, or outgo, consists

which carry with them their own cancellaFor manufacturers, merchants, and other business
men, almost every outgo is an expense, i.e. consists of a
money payment. Such money payments are for wages,
raw materials, rent, and interest charges. Now all these
of

tion.

costs

NATURE OF CAPITAL AND INCOME

152

[Chap.

The wages are the
raw material is rethe rent by the land-

outgoes are incomes for other people.
earnings of labor;
ceived
lord;

the

payment

for

by some other manufacturer
the interest charges by the creditor.
;

§6
Not only do exchange

transactions completely cancel

themselves out in reckoning total income, but the great
majority of the natural services of capital do so also.

Even
most

these

natural

uses

part, of "interactions,"

capital

— they

or transportations of wealth.

consist,

for

the

are transformations

These intermediate stages

are merely preparatory to the final use or so-called "con-

sumption"

of wealth, and, after the interactions

have been

canceled out, do not enter as items either on the income
or outgo side of the social balance sheet.

In order to show the

and

opposite

items

canceUng out the equal
every interaction

effect of

entering

into

throughout the productive processes,

let

us observe the

various stages of production which begin with the forest

above referred
come,

to.

The product

of the forest, its gross in-

the series of events called the turning out of

logs.

a mere preparatory service, a credit
item to the forest and a debit item to the stock of logs of
the saw mill, to which they next pass. As the sawmill
turns its logs into lumber, the lumber yard is debited with
the production of lumber, and the sawmill is credited with
This log-production

its

share in this transformation.

Intermediate categories may, of course, be created, and

we may

manner, the further transformation,
and exchange to the end of the stages of
production, or rather, to the ends for these stages split up
and form several streams flowing in different directions.
To indicate merely one of these streams, let us suppose that
the lumber which goes out from the yard is used in repairing
a certain warehouse. The warehouse is used for storing
follow, in like

transportation,

;

INCOME SUMMATION

Sec. 6]

153

the cloth goes from the warehouse to the tailor;

cloth;

the tailor

converts the cloth into suits for his customers; and

and wear those suits. In

his customers receive

this series, all

the intermediate services cancel out in "couples"

and leave

as the only uncanceled element, or final fringe of services,

the use of clothes in consumers' hands.

Should we stop our accounts, however, at

earlier points

in the series, the uncanceled fringe will be not consumers'

but the positive side of intermediate services or
The negative side will not appear, as it belongs to later stages in the series. This will all be clear, if
we put the matter in figures, stage by stage. The following are the items for the logging camp above mentioned,
in the accounts of its owner
services,

interactions.

—

Income Account for Logging Camp for Year 1900
Income

Outgo

Production of logs

The
itself,

(Omitted)

$50,000

gross income from the logging camp, considered

and without any deductions

for expenses, is here seen

to consist in the production of $50,000 worth of logs.

however,
shall

we combine

have accounts

the logging

camp with

the sawmill,

If,

like the following, in which, to

no account

irrelevant complications,

avoid
taken of any ex-

penses which are not interactions between the groups of
capital considered

—

Income Account for Logging Camp and Sawmill for 1900

Capital Source

Logging camp

Yielding logs to
sawmill
$50,000
Yielding lumber
to lumber yard $60,000
.

Sawmill

Outgo

Income

Receiving logs

from camp

$50,000

NATURE OF CAPITAL AND INCOME

154

[Chap. IX

In this case, canceling the two log items we have left only
the lumber item; i.e. the income from the combined logging
camp and sawmill consists only of the production of lumber,
The transfer of logs from one department
its final product.
This transfer is hke the
to the other no longer appears.
taking of money from one pocket and putting it in another,
as

particularly evident

case the logging

camp and

sawmill are combined under the same management.

Extending the same principles to the entire series, we have
the accounts as given on the opposite page.
It should be noted that these entries relate not to sucthat all the items refer
cessive but to simultaneous events
;

to a fixed period of time; that

to say,

are not following

the fortunes of the original logs through succeeding stages,

but comparing the simultaneous operations of the series of
groups of instruments.
If we successively cancel items pair by pair by offsetting any item on the right side by the item in the line

on the left side, we shall find, if we stop after the
first two cancellations, that the net income from logging
camp, sawmill, and lumber yard, consists only of the proabove

duction of retail lumber, $70,000

;

does not include either

the transfer of logs or the transfer of wholesale lumber.
like

manner,

we proceed one

stage further, that

stop our cancellations, at the end of the
tions, the

production of

first

four interac-

lumber no longer appears as

of income and so on, step by step to the end,
the only surviving item will be the " wear " of the

an element

when

retail

is, if

;

suits.
is, of course, true that in any actual accounts there
be numerous other items than those which have been
exhibited in this simple chainlike fashion. Were it worth

will

we might insert these additional entries of income
and outgo elements. Most of them would consist of the positive or negative side of an interaction, and if we were to
introduce its mate, the opposite aspect of the same transac-

while,

Sec. 6]

o
o
Oi

w
O

INCOME SUMMATION
155

NATURE OF CAPITAL AND INCOME

156

[Chap.

would be necessary to include still other accounts.
follow up all such leads we should soon have an
But the same prinintricate network of related accounts.
ciple of the interaction as a self-effacing element would apply.
The only items of outgo which are not the negative sides of
interactions will be the items of subjective labor and
trouble.
These alone will finally remain as uncanceled
tion, it

we should

elements of outgo.

on the question, Of what
The question is not a thoroughly
definite one.
If we ask instead, Of what does the income
particular
group of capital consist ? we shall make it
a
from
definite.
Whether the production of logs is income or not
depends upon the point of view. It is income from the
it is not
first link of capital (logging camp) in our series

The

table given will throw light

does income consist?

;

income from the
link

first

two

occurs as outgo.

links combined, for in the second

Likewise, the use of the ware-

house is true income with respect to the first four links
or groups of capital, but is no longer income when the fifth
is

included.

see,

income from any group of
any degree of the interactions

therefore, that the

capital does not consist in

taking place within

it,

but only of the

final or outer fringe

As the group is enby being
joined to the next part of the economic fabric, and another
frmge, still more remote, appears. The question naturally
arises. When is the economic fabric complete, and has it any
final outer fringe ?
But this question must be deferred for
of services

larged,

performed by the group.

this particular

outer fringe disappears

the present.

Nor do we yet inquire what relations exist between the
two sides of the same account, say the expense to the sawIn the illusmill for logs and its income from sawn lumber.
trative tables the latter is entered as

greater than the

INCOME SUMMATION

Sec. 8]

former, and this

normally the case,

sawmill remains constant.

157
the capital of the

present, however,

are

not concerned with the effects of income and outgo on
capital, but only with the summation of income.

The method of couples, then, is useful in showing of
what elements income consists in any given case. The
method of balances, on the other hand, exhibits the amount
of income contributed from each article of capital as its
source.
The two methods, as applied to the example just
given, are as follows

—

Method of Balances
Income

Capital

Logging camp
Sawmill
Lumber yard
Stock of cloth in warehouse
Stock of cloth of tailor
Stock of clothes of customers

....
.

Outgo

Income

= + $50,000
$50,000 = + 10,000
60,000 = + 10,000
80,000- 70,000 = + 10,000
90,000 - 80,000 = + 10,000
100,000 - 90,000 = + 10,000
110,000-100,000 = + 10,000

Warehouse

50,000 60,000 70,000 -

$110,000

Method of Couples
Income

Outgo

iio^ooo^i^oorooa

—

The two methods
balances and couples
show the
same result, but from different points of view. By means
of the method of balances we are enabled to see what part
of the final net income is contributed by each of the articles
in the group.
By means of the method of couples, we are
enabled to see of what the net income from the entire group

NATURE OF CAPITAL AND INCOME

158

consists;

of articles

[Chap. IX

canceling by the oblique lines,

but one item, $110,000, representing the *' wear "
The two methods must not be confused.
of the suits.

have

left

When we
income

find

by the method

suits of clothes, this does
is all
it is

of couples that

the net

$110,000 consists exclusively of the

due to the stock

due, recourse

use of
not imply that this net income

of clothes.

must be had

To discover to what
method of balances.

to the

thereby see that only $10,000 of it is due to the stock
of clothes, the remainder being due to the other capital
instruments in the table and most of

Combining the

logging camp.

we may
group

all

($50,000) to the

hoth methods,
income from the specified
"
of $110,000 worth of " wear
results

state that the total net

of instruments consists

and that this is due partly to the stock of clothes
and partly to other capital.
The two methods, that of balances and that of couples,
correspond in a general way to the two methods for
The
canceling liabilities and assets in capital accounts.
method of balances gave, it will be remembered, the
amount of capital belonging to each individual the method
of couples showed of what elements the total capital conof suits

;

sisted.

§9

have now followed the cancellations to which

inter-

actions lead, whether they be interactions of exchange or

production.

The

consideration.
fers,

and every

case of exchange, however, needs further

Since every exchange consists of two transtransfer of

two items, a

credit

and a

debit,

two
which are credits and two, debits. These four may be
paired off in two ways, only one of which has thus far
the exchange evidently consists of four items in

all,

been mentioned.

They

stand, as

were, at the four

corners of a square, as in the following scheme, which

shows the credits and debits involved when goods worth $2

Sec. 9]

are sold.

INCOME SUMMATION

goods and debits
buyer does the opposite.

Tlie dealer credits his stock of

his "cash," while the

159

NATURE OF CAPITAL AND INCOME

160

[Chap.

by an equal and opposite item on the outgo side. All
items thus paired are represented by the same letters, the
capitals being used for positive items and the small letters
for negative.

Income and Outgo of Dry Goods Company, for

Year
Capital Source

1906

INCOME SUMMATION

Sec. 9]

income

credited (B).

involving a

payment

all

the transactions

or receipt of cash are entered on one

side with respect to the cash,

and on the opposite

side

with

capital som"ce.
The category of the
source called " rights to and obligations from

respect to
capital

manner

161

some other

employees " yields a certain amount of

work and

clerical

This item credited {H)

other services appraised at $1500.

above-named source is here debited (h) to the stock
goods, to sell which requires the services of these

to the
of

employees.

may

be that

the store which they clean, or to

should be debited to

some other

article of

on which they do work; but in any case it must
be debited imder some head or heads.
It will be seen that among the other items of capital
which are sources of income or outgo are the bonds and
stocks of the company. The bonds absorb $800 of interest, and the capital-stock, which is a residual claim on
the company, absorbs any surplus of cash which it is
capital

decided to distribute in dividends.

The two

sides of the account of such a fictitious person

necessarily balance.

It cannot be otherwise,

company accumulates

its

profit instead of

the shareholders; for, as has been seen, the
received

even if the
paying it to

money thus

debited to the cash account.

In practical accounting, the items would usually be simsomewhat. It would not ordinarily be worth while

plified

make an appraisement

of the value of the use of the

ware-

house for storage as distinct from
the value of the work performed by the employees as distinct
from the wages paid them. In the above accounts we have

the storage charge, nor of

purposely distinguished these magnitudes, estimating the
storage benefit as $1000 though the rent paid for

it is

$1200,

and estimating the work done by employees as worth $1500
though their wages were $1600. If, instead, we estimate
the storage benefit at the rent figure and the employees'
work at the wages figure, our accounts would contain four

NATURE OP CAPITAL AND INCOME

162

items of $1200 and four of $1600.

these,

[Chap.

two

each

might well be, and
These are the pair of items "storage service" ((? and g)
and the pair "clerk work" {H and h). Omitting these,
which are both appraised items, there will be left only
cash transactions. These may be further simplified by
dispensing with the two categories called " store lease
and "rights to and obligations from employees," by placing
the rent (6) and the wages (d) under the head of " stock of
goods." In other words, we charge the expenses for rent
and wages directly against the goods stored and cared for
in practice usually are, dispensed with.

them " storage
There is no difficulty in
service" and "work of selling."
recognizing the resulting accounts as those employed in
ordinary bookkeeping. Occasionally the more elaborate
accounting is necessary, as when a very old lease, hke some
instead

of,

as ui the table, charging against

in force in London, requires only a nominal rent charge
compared with the benefits conferred.

still

§10
In the case

of real persons, however, the

two

sides

do not

balance, for the accounts do not consist solely of double
To show this, let us recur to the accounts of the
entries.

lawyer considered in Chapter VIII. The table on the
opposite page reproduces those accounts, with some of the
items given in greater detail.

In these accounts, as in the previous ones, we have indicated the like items on opposite sides by like letters, the
positive being represented

capitals

and the negative

observe that, as in the corporation
But, unUke the
accounts, many of the items will " pair."
corporation accounts, the present accounts contain a resi-

by small

letters.

due of items which

will not pair.

The letters representing
by being inclosed in

these unpaired items are designated

square brackets.

They show that

[B], [C], [D], [0]

— the

shelter of the house, use of furniture, use of food, use of

Sec. 10]

o
o

O
HH 1^ T3

o
o

INCOME SUMMATION

e a

163

164

NATURE OF CAPITAL AND INCOME

clothes, jewelry, etc.

— constitute

[Chap, IX

a kind of income which

does not appear elsewhere as outgo.

§11

We found, when studying the accounts of instruments, the
chain of productive services of the lumber camp, etc., that
there always remains some outer fringe of uncanceled in-

come produced by the capitalistic machine. We have now
reached this same kind of outer fringe in studying the
accounts of persons, provided they are real persons. This
outer fringe consists of what economists have usually called
" consumption."

All other services are merely preparatory

to such services, and pass themselves on from one category

Thus the income from investments,
being deposited in bank, is outgo with respect to the bank
account; the bank account yields income by paying for
stocks and bonds, food, etc., but in each case the same

of capital to another.

item enters as outgo with respect to these or other categories of capital. In all these cases the individual receives
no income which is not at the same time outgo. It is
only as he consumes the food, wears the clothes, or uses
the furniture that he receives income.

The question
reached

still

remains whether the fringe we have
we must not

the final outer fringe, or whether

proceed one step further and regard the final services just
mentioned as merely interactions between a man's external
wealth and his own body. This question will be discussed
in the following chapter.

We are

content here to leave the

chains of services at the point where they reach the person
of the recipient.

CHAPTER X
PSYCHIC INCOME

§1

The

stage at which, in the previous chapter,

come may be

left in-

called the stage of final objective services.

In other words, it is the stage at which the wealth of the objective world at last acts upon the person of the recipient of
income. This final income is that for which the economist
is usually in search, and is that which the ordinary statistics
It is clear from what
of workingmen's budgets represent.
has been said, that in this fiinal net income all interactions
all the
between articles of external wealth drop out,
transformations of production, such as the operations of

—

mining, agriculture, and industry,
transportation,

For, in

all

and

all

the

operations

business transactions or exchanges.

such cases, the debits and credits inevitably
and opposite items. The only

occur in pairs of equal

items which survive are the final personal uses of wealth,
ordinarily called "consumption."

Let us rather

The main

enjoyable objective services.

objective services are the following
'

call

them

sorts of enjoyable

services of nourish-

ment, services of housing and warming, services of clothing
and personal adornment, services of personal attendance,
services of amusement, instruction, and recreation, services of gratification of vanity.

§2
It is usually recognized

by economists that we must not

stop at the stage of this objective income.^

more step before the process
^

See Fetter's Principles of Economics,
165

complete.

New

There

one

Indeed, no

York, 1904, Chap. VI.

NATUEE OF CAPITAL AND INCOME

166

objective services are of significance to

man

[Chap.

except as they

are preparatory to subjective satisfactions.

The
body.

come through the human

final subjective services

agent outside the body can yield them.

that persons or things outside of
his bodily organism.

ment

man

can do

All

to stimulate

Even what are called services of amuseamuse or instruct the

or instruction cannot directly

mind; they can only

the body.

affect

book, for instance, renders

its

service simply

reflecting light into the eye of the reader.

instructive

and

solely

It is necessary

that these stimuU on the optic nerve should be transmitted

through the nervous system before any mental instruction
So a piano can of itself produce no sensations

takes place.

It merely produces external vibrations, which,
of tone.
through the ear and auditory nerve, ultimately result in
All sound, sight, taste, smell, touch, come
sensation.
about through reactions of the nervous system to external
stimuli.
A man who receives a Turkish bath has received

enjoyable income in the objective sense, but
ices of the water, towels, attendants,

all

the serv-

and other cooperat-

ing agencies, while credited to them, must,

treat

man

They
result simply in cleaning and stimulating his skin.
They
are income from outside agencies absorbed by his body in
himself as capital, be regarded as debited to him.

order that he

may

later experience pleasant sensations or

avoid unpleasant ones, through the enjoyment of health.
Similarly the

use of clothing and shelter prevents the

occurrence of the sensation of cold, but their immediate
objective service

heat from the body.

simply in hindering the dissipation of
They are disservices with reference to

the body, just as similar care and protection of a horse are
disservices with reference to

it.

When medicine is taken, it may, from the objective standpoint, be counted as a part of income, just as food, clothing,

and other ordinary items.
of medicine are (or are

But

it is

clear that the services

supposed to be) the repairing of the

PSYCHIC INCOME

Sec. 3]

167

body, and, although credited to the medicine, should be
debited to the body, just as the services of a carpenter are
credited to

him but debited

which he mends.
from producing any immedithe moment quite an opposite
to the house

the services of a dentist, far

ate satisfactions, have for
effect,

but result later in better service of one's

own

teeth.

They are credited to the dentist, but debited to the body.
The "consumption," or use of food, though it is a service of
the food, is a disservice of the body for food stands in the
same relation to the body as fuel to a furnace or repairs to
a house. The final income consists of the subjective satisfaction of appetite and the other satisfactions which
the intake of food enables the body to yield to the mind.
;

These include not simply the immediate gratification of the
palate, but the promotion of pleasant sensations or the
avoidance of unpleasant ones later on. In other words,
the consumption of food, by preserving health and maintaining

life,

enables the body to yield better and longer-

continued income to the mind in future years, just as the
repairs

on a house enable

to yield shelter a long time after

the repairs are made.

§3
These and other illustrations will show that, if we inbody as a transforming instrument, while we
must credit with their respective services all these outside
agencies, such as food, clothing, dwelHng, furniture, ornaments, and other articles which, as it were, bombard a
man's sensory system, we must also at the same time debit
the body with these same items. In this case the only surclude the

viving credit items after these equal debits and credits are

canceled are the resulting final satisfactions in the

human

mind. In other words, in order that the external world
should become effective to man, the human body must be
considered as the last transforming instrument. Just as
there is a gradual transformation of services through the

NATURE OF CAPITAL AND INCOME

168

[Chap.

farm, flour mill, and bakery, so is there a final transformation within the human body itself.
It is a sort of factory,
the products of which are the only final uncanceled income
of the consumer.
In a complete view of productive processes, the

human machine is no more

sideration than machines

to be left out of con-

which handle the wheat in

its

prior stages.

All

objective

income, therefore,

negatived as soon as
of the recipient.

empty

out, as

The

entirely erased or

to the

body

which that income consists
quota into the human body, but

services of

were, their

the ultimate result

we apply our accounting

not finally received until

emerges

in the stream of consciousness.

define subjective income, then, as the stream of con-

sciousness of

any human

being.

All his conscious

from his birth to his death, constitutes his subjective
come. Sensations, thoughts, feelings, voHtions, and

life,

inall

psychical events, in fact, are a part of this income stream.
All these conscious experiences which are desirable are positive items of income, or services

which are undesirable
have avoided expressly the statement that subjective income consists of
pleasure, or of pleasure minus pain.
These terms have been
too loosely used by economists, and such use has involved
them in unnecessary controversy with psychologists. It is
better to avoid such disputes, and content ourselves with
the simple statement that subjective events which are desirable are services, and those which are undesirable are
disservices.
This statement conforms to the definition of
services and disservices originally given, and does not commit us to any psychological theory of pleasure or pain.
Some psychologists would maintain that pain, to an ascetic,
may be just as much an object of desire as pleasure.^
;

all

are negative items, or disservices.

For instance, of the founder of the Sacred Heart Order, we read

that,

—

"Her

love of pain

and

suffering

was

insatiable.

•

'Nothing

PSYCHIC INCOME

Sec. 4]

Nor

is it

169

necessary to take sides in the controversies re-

garding the relations between mind and body.

are

but with means and
end, and, whatever may be the causation of mental states,
the human body is certainly the means by which the good
not concerned with cause and

from external wealth

is finally

effect,

communicated

to the con-

sciousness of the owner.

§4
The two kinds

of final income, the physical

psychical, or the objective

mate

and

in their proper spheres.

and the

subjective, are both legiti-

Usually the physical and

psychical income are equal to each other in value.

loaf

of bread which yields ten cents'

worth of services presumably
gives ten cents' worth of immediate satisfaction. When one
enjoys a musical concert worth one dollar, it does not matter
whether we say that the services of the musicians in producing vibrations are worth one dollar, or the enjoyment
which these vibrations occasion in the mind is worth this
sum. When rent is paid for a house, this is generally
taken to measure also the subjective comfort obtained
through it.
Nevertheless, there are several points at which the valuations of subjective and objective income are different, and
three of these are sufficiently important to emphasize.
The first case is that in which the transformation within
the body takes a long time. Here the two species of income do not correspond.
For instance, the instruction
received by an apprentice in preparation for his trade is a
service rendered to

him in the

body in manual
manual
income-earning power.
Aptraining of his

dexterity, in order that, a few years later, this

dexterity

may

increase his

but pain,' she continually said in her
able.' "

Bougand,

1894, pp. 171, 265.

James, Varieties

letters,

'makes

my life

support-

Hist, de la bienheureuse Marguerite Marie, Paris,
Cf.

also pp. 386, 387.

Quoted from William

of Religious Experience, 1902, p. 310.

170

NATURE OF CAPITAL AND INCOME

prenticeship

is,

[Chap.

were, an investment in the body, to be

returned at a later time (with interest), just as the plantis an investment in the tree in order that its

ing of a tree

may

At the time of tree
work credited the
tree planter is debited the tree; it is only when in after
years the tree bears fruit or other product that any return
is obtained from the planting.
Similarly, the work of
fruit

be secured in later years.

planting there

no net income,

for the

teaching the apprentice should be credited to the teacher

and debited to the apprentice's body the final satisfactions
will not come until the acquired knowledge becomes
;

All this can be faithfully recorded only in the
complete accounting which includes subjective income.
The same principles apply to any training or education

effective.

for a profession.

When

a young

man

cine, journalism, music, or prepares for

sion,

investing in his

own

studies law, medi-

any other

profes-

person, with the hope that

may ultimately be returned to him
The same is true of physical training.
Many of the most successful men are those who, Uke
President Roosevelt, in early life saw the wisdom of
developing a strong body, and in consequence have increased their productive power in mature years.
the sums thus invested
(with

interest).

§5
The second point
income diverges

at which subjective and objective
found in occupations whose special grati-

fication or irksomeness renders their return in psychical in-

come widely
This

different

from their return

frequent in conditions of labor.

in objective income.

Properly speaking,

objective income takes no account of the toil of the laborer.

The workingman who earns $2 a day earns double the obincome of one who earns SI a day. Yet if the work

jective

of the former is difficult, loathsome, or dangerous,

well be that

many would

may

prefer the nominally smaller in-

come rather than endure these disadvantages.

These facts

PSYCHIC INCOME

Sec. 5]

171

have often puzzled economists, and the question has been
asked whether any allowance should be made for disagreeable trades, such as that of the hangman, and whether it is
fair to

say that a workingman

who

the sweat of his brow really gets as

who

receives

The answer

earns $500 a year

much

as a capitalist

$500 from stocks and bonds.
is now evident.
So far as
concerned, no allowance should be

effortless

to these questions

income is
made. That is, the returns to the laborer are all to be
counted gross and not net, no deduction being made on
account of so-called "mental anguish" or painful feelings.
Objective income stops at the threshold of the laborer's
body. It does not follow beyond this point and include
what the body communicates to the mind.^
objective

But, by passing to subjective income, we avoid some of
the manifest unfairness in the usual statistical comparisons

which contrast a

capitalist's

income with that of a laborer,

or contrast with each other the incomes of various laborers,

some

whose tasks are

obtain one's net income

difficult

we must

and others

easy.

subtract from the sub-

jective satisfactions the subjective efforts of attainment.

laborer

who

receives $2 a

day

may work

so hard for

as to justify a deduction of $1,50 for the effort, whereas

the laborer

who

day may possibly need to
The nominally $2 man would then

receives $1 a

deduct only 25 cents.

be receiving a net income of only 50 cents a day, whereas
the nominally $1 man would be receiving one worth 75
The only way

in which a man's person contributes to such objecincome is, as has been imphed in our illustrative accounts, through
the work he performs upon external objects, in order that these may, in
turn, yield back service to him.
Objective income thus includes all
the results of his own bodily exertions so far as they come to him via
A farmer, for instance, sows wheat, which
these outside agencies.
The farmer's services here start a
is sold and yields him income.
circuitous process which is transmitted through the farm, the crops,
the wheat, the proceeds from selling the wheat, the enjoyable commodities purchased with these proceeds, and finally his own person
again, to which those commodities minister.
^

tive

NATURE OF CAPITAL AND INCOME

172

we ought

laborer's income,

who

receives $500 a year, with

appraised at $250,

income as the
effort

and

of effort

only receiving one half as great an

who

obtains, during

same

the

interest to the extent of $500, with

asked

how an appraisement

of labor is possible.

practical or statistical standpoint the appraisement

is difficult, if

able.

to say that the laborer

an expenditure

whatever.

may be

From a

capitalist

period, dividends

Again, in the comparison between the capitalist's

cents.

and

[Chap.

Yet certain data are obtainwork asks not simply in

not impossible.

servant applying for

regard to the wages, but in regard to the difficulty of the

work, and

will

consent to do extra or disagreeable tasks only

on condition

of a definite increase in wages.

we may say

that the increase in wages which

In
is

this case

necessary

to procure the consent of the laborer represents subjectively,

him

or her, the increased difficulty of the work.

manner, a government employee who has at any time the
option of retiring on half-pay may, at the point when he decides to retire, be said to regard the difficulty of his

work

as equal in his estimation to half of the income he receives
for

it.

In general we

may say that

the proper

method of appraiswork is to de-

ing the disagreeable element involved in one's

sum which the worker would
were it possible for him so to avoid the
That is, he is supposed to imagine
disagreeable element.
an alternative condition, considered as an equivalent in his
mind to the actual conditions under which he works, but
which differs from them in two particulars in being free
from the labor or pain of toil and being deprived of a cerduct from the gross income that

be willing to sacrifice

;

tain

amount

the laborer

of its earnings or rewards.

who

estimates that this would be to

instance,

him the equivalent

without labor, he has virtually
cents a day

If, for

obtains $2 a day for eight hours'

made

work

of $1.50

a deduction of 50

for the irksomeness of his work.

PSYCHIC INCOME

Sec. 6]

173

§6

have reached a convenient place in which to emphaa point of great importance, but one which is seldom
understood. This is, that most of what is called "cost of
size

production"

is,

in the last analysis, not cost at

all.

have found, in using the method of couples, that every
objective item of cost is also an item of income, and that in
the final total, no objective items of outgo survive cancellation.
This principle holds true whether we stop our accounts at
the bodily threshold, confining
jective income, or extend

them

to a record of ob-

to include the body, thus

income.
Those who have
been accustomed to construct their theories of political
economy on the assumption that "cost of production" is
an essential and ultimate item, may do well to reflect carefully on this proposition.
It means that in a comprehenyielding a record of psychic

sive view of production there is
objective sense at all.

All of

what

cost of
is

production in

its

ordinarily called cost

cost only with respect to certain accounts; it is
always also income with respect to other accounts. This

is really

true, for instance, of the cost of

raw

materials.

It costs

produce bread but all that the flour costs to the
baker is income to the miller. The same is true of wages.
The employer counts his pay roll as cost of production,
but the laborer counts it as earnings.
Glimpses of the fact that all objective costs are always also
objective income, and therefore disappear in the final summation, are occasionally found in the books, especially
those on land and interest, although the points of view have
been variable and uncertain. There have been long disflour to

;

cussions as to whether rent enters into cost of production.

The question has by many been negatively answered.^
Bohm-Bawerk has also maintained that interest was not
^

See the interesting remarks of Jevons in the preface to his Theory

of Political

Economy, 3d

ed., 1888, p. xlvii.

NATUEE OF CAPITAL AND INCOME

174

[Chap,

an element in the cost of production. From what has
been said it is evident that every rent and interest payment, while it is a cost to the payer, is income to the payee.
The total objective income of society consists wholly of
positive items, such as the use of food and furniture, the
shelter from houses, and the other direct services of wealth.
There are no negative items in the account of social income
which survive in the form of "costs of production."

When we turn, however, to subjective income, we find the
case

somewhat

as capital acted

different.

Including the

human organism

upon by the outer world and

upon the inner world
the uncanceled

of consciousness,

fringe of

itself

acting

we not only carry

services one step

further

and

obtain as net income the subjective satisfactions from the
use of food, clothing, furniture, dwelling,

etc.,

but we find

necessary to include also the subjective efforts put forth by

human

beings in order that these satisfactions

may accrue.

Thus, to revert to the income account of the lawyer.

found that his net income consisted of the use of house $100,
use of furniture $50, use of food $150, and other uses $2500,

making a

total of $2800.

own person
addition
following
Capital
Source

to
:

—

all

the

if we include
we should have

But

in our accounts,

items

the lawyer's
to enter, in

income,

the

PSYCHIC INCOME

Sec. 7]

of the recipient,

have

all

175

equal and opposite counterparts

accounts as given in Chapter IX, §10. These
same items were there entered as credits and constituted
in the

the "uncanceled fringe" of final objective income.

were designated as

[B],

[D],

[C],

after the introduction of the

new

the debits of like letters,

'd,

h, c,

;

[0].

They
Now, however,

items, they cancel with

but another uncanceled

fringe appears, namely, [P], [Q], [R], [S], which items are
wholly subjective. These we have, for convenience, entered

at the

same

sum

therefore also $2800.

figures as their objective prototypes.

jective labor cost,

and pain

[t],

But there

also appears

Their

a sub-

$500 to express the personal labor

of the lawyer in his work.

The

result is that

income is not equal to the objective income of $2800, but is only $2300.
When we have reached this final stage in our inquiries,
therefore, we find the only ultimate item of cost to be labor
cost, or, if the term "labor" be not itself suflaciently
broad, labor, anxiety, trouble, annoyance, and all the other
subjective experiences of an undesirable nature which are
necessary in order that the experiences of an agreeable nature may be secured.^ In a sense, therefore, the socialists
his net subjective

are quite right

when they say

of production, although

deduce from

some

that labor

the only true cost

of the conclusions

which they

this proposition are not justifiable.

§7
The
income

third discrepancy between subjective

and objective

due to the fact that certain agreeable and disagreeable experiences are due directly to the character of
is

1 It may be well here to emphasize the distinction between work
and labor which has been so well drawn by Professor J. B. Clark.
The work performed consists of the services rendered, and is posi-

tive; the labor consists of the efforts of performing those services

and

is negative.
The work is objective; the labor is subjective.
Properly speaking, an employer does not pay a man for his labor,
but for his work.

NATURE OF CAPITAL AND INCOME

176

[Chap.

income is
with a
conhas
more
agreeable
stream
of
a
good constitution
The
sciousness, or subjective income, than one without.
pains and sufferings of illness here find a place in the comIt is evident that
plete accounts of income and outgo.
the wealthy man who confessed that he would exchange all
his millions for a young and vigorous body may be the
recipient of a large objective income, but not enjoy as
much subjective income as Walt Whitman, who had
the body

itself.

large part of our subjective

due to our condition of health or disease.

A man

scarcely a dollar in the world.

That these subjective items are by no means to be despised

by the economist, who has

far too long busied himself

with a study of the superficial objective phenomena, is evident when we consider that a healthy body is absolutely
essential for receiving and enjoying the income from external
wealth.

The man who

short-sighted enough to lose his

health in the pursuit of what he calls wealth will soon be

and we
all of this sort of wealth to regain health
need only visit the health resorts of Colorado and Cahfornia
to be struck with the number of cases of business men who
have found themselves in this predicament. Economists,
by fixing attention exclusively on physical phenomena,
leave out of account the most essential element of all, the
vigor of human fife. The true "wealth of nations" is the
health of its individuals. A nation consisting of weak,
sickly, and short-hved individuals is poor compared with a
nation whose inhabitants are of the opposite type. Hence
spending

it is

that the devices of

;

modern hygiene,

sanitation,

preventive medicine, which tend to increase

and

human work-

and enjoying power, are of greater economic
import than many of the luxurious and enervating devices
commonly connoted by ''wealth."
We see, then, that subjective income means simply one's
whole conscious fife. Every item of it comes via the body
ing power

of the person.

;

PSYCHIC INCOME

Sec. 8]

177

§8
As

to the

measurement

of the items entering into this

psychic stream, the same principles apply which

already been laid
nitudes.

counting.

First,

have
measurement of other magHke events are measured by simple

down

all

for the

Secondly, so far as

terms of money

To accomplish

it is

possible, a valuation in

placed on them, as on objective services.

this

appraisement

it is

only necessary for the

what money is he willing
any enjoyment brought about by means of exterIf the event
nal wealth, such as a box of sweets or a cigar.
is one which cannot be connected with purchasable commodities, it is necessary to imagine an exchange, even when
individual to answer the question
to

pay

for

actual exchange

impossible.

have now followed the method

of couples

from the

balance sheet for a particular article of capital, or group

goods of an individual or
been
inevitably to lead us to a
of society.
consideration of the psychic stream of events as final income, all the agreeable items being on the credit side and
the disagreeable ones on the debit side. But the methods
which have been given also enable us to stop at any earher
point.
There are two such earlier points which are
convenient and logical. The final objective income is one
the other has its existence only in a highly developed
civilization Uke the one now existing in western Europe
of articles, to the entire capital

The

result has

and America, and consists of the familiar "money income" of an individual, that is, his money receipts from
The
all capital sources, less his money outgo to them.
income of a person reckoned by these three methods will
ordinarily be very similar, though in theory, and sometimes
in practice, it may differ widely.
As long as we understand the various kinds of income, and the relations between them, we are at liberty to consider any one of them
But we can scarcely
as "income" in its proper place.

NATURE OF CAPITAL AND INCOME

178

[Chap.

understand any one without having had at
view of both of the others.

some

least

§9
Having completed our survey
elements of income,

They

items.

fall

we may

of the

summation

of the

properly pause to classify these

naturally into three groups.

The

first

group includes those items of income which are positive

and not negative, that

is,

the agreeable experiences of sub-

jective income, for these, as
final

we have seen, are the only
The second group in-

uncanceled positive items.

cludes items which are negative but not positive, namely,
disagreeable psychical experiences,

and

consists

two

(1) the labor and trouble which are sacrificed for
the sake of procuring income through objective channels,

classes:

in other words, the toil of the producer;

and

(2)

the dis-

by an
abnormal state of the body, as aches, pains, and all sorts
of illness, but which are not, like toil, voluntarily incurred
The third group includes
for the sake of future return.
what we have called interactions, or items which are at
once positive and negative, according to the point of view.
Both of the first two groups are entirely subjective, and
agreeable impressions produced in one's consciousness

the last

entirely objective.

The

third group, interac-

bulk of the items entering
into income accounts, and includes all of those which
enter into practical bookkeeping. It may be subdivided
tions,

constitutes

far the

two groups: (1) interactions outside of the human
body, and (2) interactions between external wealth and
the human body, or what have been called "final objec-

into

tive services."

divisions

—

The following scheme shows

further sub-

179

PSYCHIC INCOME

Sec. 9]

Pure services (subjective)
labor (cost of production)

f
Pure disservices (subjective) | ^^^^ ^^^ ^^^^j. discomforts

nutrition
clothing

between objective wealth
and body of owner

Services

(final

housing

amusements

objective services)

instruction
etc.

Interactions

agricultural

| manufacturing

transportation

between
objective

, .

production

commerce

articles

(advertising
organizing
indemnifying
etc.

PART

III.

Capital and Income

Chapter XI. Foue Income-Capital Ratios
Chapter XII. Concept of Eate of Interest
Chapter XIII. Value op Capital
Chapter XIV. Earnings and Income
Chapter XV. Income and Capital Accounts
Chapter XVI. The Risk Element

;

CHAPTER XI
FOUR INCOME-CAPITAL RATIOS

§1

have now learned what capital and income are and
We have seen that capital is not to
is measured.
be confined to any particular part or kind of wealth, but that
it applies to any or all wealth existing at an instant of time,

how each

or to property-rights in that wealth, or to the values of that

wealth or of those property-rights.

come

not restricted to

of a flow of commodities, nor

and services, nor

must

is it

have seen that

is it

in-

consist

a composite of commodities

necessarily regular in its receipt, nor

necessarily be such as to leave capital unimpaired

but that

consists simply of the services of wealth,

that, analogously to capital,

either

money income, nor does

by the mere quantity

income

may

and

be measured

of the various services rendered,

have seen that in the summation
both of capital-value and of income-value there are two
methods available for canceling positive and negative
items called the "method of balances" and the "method
or

their value.

By the method of balances the negative items
any individual account are deducted from the positive
items in the same account, and the difference, or balance,
shows the net capital (or income, as the case may be) with
which that account deals, whether this be the net capital
of couples."

(or

income) of a particular owner, or of a particular

article

The method of couples, on
the other hand, cancels items in pairs and is founded
on the fact that, as to capital, every liabihty relaor group of articles of capital.

183

NATURE OF CAPITAL AND INCOME

184

and

tion has a credit as well as a debit side,

income, every interaction

[Chap.

that,

at once a service

as to

and a

dis-

service.

We observed that the method of couples, fully carried out,
reveals

mately

respectively

consist.

and income ultihave seen that such a summation,
wherein

capital

applied to capital, gradually obliterates

partial rights,

all

such as stocks and bonds, and leaves as the final result the
concrete capital wealth of a community; and that when
the

method

of couples is applied to

income accounts, the

"interactions" involved disappear, leaving an uncanceled
outer fringe of services and disservices.

If the

method

continued as far as possible in the world of objective services, it

leaves simply the direct or final services of objec-

tive wealth
if

the

as they affect

method

the

human

organism; while,

pushed one step further,

leaves, as the

income stream, simply the pleasant and unpleasant
experiences of human consciousness. We found as one
result of our study that so-called cost of production has no
existence as an element of the objective income stream, and
that, therefore, the only costs of production which are not
also elements of income are the subjective labor and trouble
of those engaged in that production.
We have seen that capital and income are in many refinal

spects analogous,

and are

strictly correlative

;

that

all

capi-

—

income and that all income flows from capital
at
least when the term " capital " is used in its broader sense,
which includes human beings. The old proposition of the
economists, therefore, that capital is that wealth which
tal yields

yields income,

statement

correct, although the idea that such a

is restrictive,

and applicable only to certain kinds

of wealth, is incorrect.

§2
Since capital and income are so intimately related, it
becomes necessary to examine in detail what their relations
are.
The chief relations between capital and income are

FOUR INCOME-CAPITAL RATIOS

Sec. 2]

represented

by four

and income

may

185

ratios.
As we have seen, both capital
be measured either in quantity or value.
It follows that the relation of income to the capital which

bears it takes four different forms, according as the income
and the capital are measured in one or the other of these
two ways. These four forms of the income-to-capital
ratio follow
(1)

The

—

ratio of the quantity of services per unit of time

to the quantity of capital

may

which yields those services

be called the physical productivity of capital.

Thus,

acres of land yield, in a certain year, 60 bushels of wheat, the
ratio of

income to the capital
This

per acre per year.

Uke manner,

may

is its

be expressed as 6 bushels
In

physical productivity.

10 looms will weave 500 yards of cloth in a

day, the ratio of services to the quantity of capital, or the
physical

productivity

the

looms,

yards

per

machine per day.
(2)

The

ratio of the valv^ of the

income from capital to

may

be called the value produc10 acres of land yield a net return worth

the quantity of the capital

Thus, if
$200 a year, the value productivity is $20 per acre per
year.
This is what has ordinarily been called the rent of
land.
The same principles apply to the rent of a dwelling
tivity.

or of

any other

article of capital.

value productivity
(3)

The

ratio of

found in the

the quantity of services rendered

capital to the valu^ of the capital
ical return.

Thus,

Another example of
wages of the laborer.

may

be called

its

phys-

$100 worth of capital applied to land

in the form, say, of agricultural implements adds to the yield
of the land one bushel, the physical return of this capital

of a bushel per year per dollar invested.

cept of physical return

Such a con-

familiar to students of classical

economics under the head of "doses" of capital appHed to
land.
(4)

The

ratio of the valu£ of services to the valv£ of the

capital yielding

them may be

called the value return.

Thus,

NATURE OF CAPITAL AND INCOME

186
if

[Chap.

a house worth $10,000 yields in any given year a net rent

of $1000, the value return is ten per cent per year.

important case of value return
terest.

Thus we have four
1-

ratios

evidently the rate of in-

—

Quantity of services per unit of time,^ physical productivity.
quantity of capital,
Value of services per unit of time,
^ ^^^^^ productivity.
quantity of capital,
Quantity of services per unit of time, ^ physical return.
value of capital,

Value of services per unit of time,

^^^^^ return.

value of capital,

These four magnitudes must be carefully distinguished.
They are, as mathematicians say, of different " dimensions." *
This fact

may

suggested in the four following phrases, which

be taken as typical
1.

2.
3.
4.

—

Bushels per acre per year.
Dollars per acre per year.
Bushels per dollar|per year.
Dollars per dollar per year.

§3
The

failure to

keep these four magnitudes clearly

tinguished has already led to a great

many

dis-

confusions in

economic science. The spurious distinction between rent as
the income from "land" and interest as the income from
"capital" is a case in point.^ From this confusion comes
the notion that land differs from "capital" in that there is
a margin of cultivation for the former and none for the
For a mathematical statement, see Appendix to Chap. XI.
error is fully exposed in Cannan's "What is Capital?" Eco'
nomic Journal, June, 1897, pp. 283-284, and in Fetter's "The Relations between Rent and Interest," a paper presented before the
American Economic Association, December, 1903. See also Hicks's
Lectures on Economics, Cincinnati, 1901, p. 228, and the present
writer's "R61e of Capital in Economic Theory," Economic Journal,
December, 1897, p. 524, and "Precedents for Defining Capital,"
Quarterly Journal of Economics, May, 1904.
^

The

FOUR INCOME-CAPITAL RATIOS

Sec. 3]

and

latter;

that,

187

whereas different qualities of land bear
in advantage

different rents, representing the difference

between a particular grade
parts of capital bear the
errors

of land and no-rent land, all
same rate of interest. These

come from unconsciously regarding the land

terms of quantity and the so-called "capital" in terms of
value; in other words, from considering the income from

land in the sense of value productivity, but that from capital in

the very different sense of value return.

ing our comparisons,
of these ratios, the

interest

If,

mak-

abide consistently by either one

imagined distinction between rent and

and between land and

capital will vanish.

quite true that the value productivity of land differs with
different grades of land;

but

equally true that the

value productivity of machinery, or of any other element of
capital, so varies.

bears exactly the

New, high-grade, and efficient machinery
same relation to machinery which is out

date and inefficient that

land bears to

fertile

sterile.

have different degrees of prohaving
high
ductivity, some
and others low earning power.
It was on this basis, in fact, that Francis Walker applied
Similarly, different persons

the Ricardian theory of rent to the explanation of entrepreneur's profits.

On the other hand, if we fix our attention on value return,
we find it indeed true that the value return called the rate of
on "capital" (however narrowly capital may be
is uniform, but we find it equally true that the
value return on land is also uniform for land which yields
a high rent will have a correspondingly high value, and, in
consequence, the ratio of the rental to the value will be

interest

conceived)

;

exactly the same as for lower grades.

Other examples of confusion might be

some of them in the cruder
"naive" productivity theory,^
^

See Bohm-Bawerk, Capital and

pp. 120-141.

cited.

find

interest.

The

for instance, confuses

phys-

theories of

Interest,

English translation, 1888,

NATUEE OF CAPITAL AND INCOME

188
ical

[Chap.

productivity and value return, and attempts to deduce

the rate of interest from mere physical productivity, which
is

impossible.

§4
In

this

book we are concerned

chiefly with the fourth

relation, value return, or the ratio of the value of

income

to the value of capital.

{^ The fundamental principle which applies here is that the
value of capital at any instant is derived from the value of
the future income which that capital

The expected
services.

services

may,

In our ignorance of the future

valuations on the basis of

The

expected to yield.

of course, not

be the actual
fix

our present

what we expect the future

principle of present

worth

to be.

fundamental impor-

tance in the theory of value and prices.

value of any article of wealth or property

means that the

dependent alone
on the future, not the past. The principle has been imperfectly stated as follows: "The value of any article is not
determined by its cost of production, but by its uses."
But the costs of production are disservices, and these, if they
be future, enter into value on precisely the same terms as
uses or services.

They

are

discounted as are services.

For
the Panama Canal to-day is
dependent upon the future expected services, taken in coninstance, the value of

nection with the expected cost of completion.

these

future elements be given, the value of the canal will be the

same whether past cost was large or small, or nothing at
all.
Of course, the future expected cost for completing the
canal is less than if some of the work had not been done
already, so that the greater the past cost has been, the less

the future cost will be, and hence the greater the value of

the canal at present.

Thus normally the value
past cost of production.

past enables us to

make a

of capital will

vary with the

Moreover, the experience of the
better estimate as to future cost.

/—

FOUR INCOME-CAPITAL RATIOS

Sec. 4]

189

But, however determined, it is the estimated future cost
alone which enters into the calculation of present value.
All of these principles are well illustrated in the case of

After some $300,000,000 had been sunk in the
enterprise, the proprietors were willing to sell out for only
the canal.

To them, therefore, it was worth less than it
The effect of the work already done on the canal

$40,000,000.

had
was

cost.

certainly to lessen the labors of the present possessors,

but it also at the same time opened their eyes to the magnitude of the task still before them; hence the reduction in
value to correspond to the new forecast of the future.
No one will dispute that the buyer of any article of capital
will value it for its expected services to him, and that " at
the margin" of his purchases, the price he will pay is the
equivalent to

words,

him

of those expected services, or, in other

their "present worth," their

"discounted value

speculator as to

But some doubt may be felt reAs to him, he is simply a
the possible demand. He sells for what he

can

whatever price he believes

or "capitalized value."

garding the professional
get, affixing

profit

seller.

him most, sometimes making out

will, in

the end,

of the transaction

sometimes less, usually, or
normally, covering those costs plus interest on them for the
time elapsing between their occurrence and the sale.
The same principle applies all the way back in the production processes. The labor expended is staked (either by

more than his

costs of acquisition,

the laborer or entrepreneur) in anticipation of the prices

which the buyers will be willing to pay. If these anticipated
prices are not expected to cover the value of the labor and
other costs plus the interest upon them, the result will be
that the labor and other costs will not be expended. Hence
by trial and error the labor and other costs will, imder nor-

mal

conditions, gradually be fitted to the prices.

When

prices find this

normal

level at

which costs plus

interest are covered, it is not because the past costs of pro-

duction have determined prices in advance, but because

NATURE OF CAPITAL AND INCOME

190

the sellers have been good speculators as to

would be.
costs and

[Chap,

what

prices

they had foreseen that prices would not cover

interest

costs,

production entirely, while

they would have refrained from

they had foreseen the opposite

condition, that of large profits, competition

would have

tended to reduce these profits to the usual dimensions.
We see, then, that although prices bear a normal relation
to past costs, this relation does not always hold true
that,

whether

;

and

holds true or not, the costs do not prede-

termine the prices except in the sense that the producers

have

skillfully

adapted the stocks available now, and those

to be available at succeeding points of time, to the expected

demand

for them.
not our purpose in the present book, however, to
emphasize these principles, for they belong properly to the

theory of prices.
We merely premise them in order to
proceed to the study of the relation between capital-value

and income-value, that
return."

is,

what we have

called

value-

CHAPTER

XII

CONCEPT OF RATE OF INTEREST

§1
From

we obtained the concept of
be explicitly defined as the ratio
of the value of the income which flows from a specified
capital during a specified interval of time, to the value of
that capital at a specified point of time. Thus, if on January 1, 1900, a capital is worth $10,000, and during the year
1900 this capital jdelds an income worth $500, the valuethe

return

come

is five

return

chapter

last

may

This

value-return.

per cent per

annum

for that year.

If the in-

perpetual and flows at a uniform rate, the valuecalled the rate of interest realized

other words, the rate of interest

is,

on the

capital.

briefly stated, the ratio

As business men say, the rate
capital.
the " price of money," or the " price of capital."

between income and
of interest

This very

common

capital simi

usage

based on the thought that any

the equivalent of

some annuity.

The usage

has been needlessly condemned by economists on the

ground that a different meaning should be assigned to the
expression "price of money," viz. its "purchasing power"
over goods in general. But the objection is not well
founded, for it is evident that "purchasing power" includes
not only purchasing power over a stock of goods but also
purchasing power over a flow of income. If $100 will buy
a perpetual annuity of $6 a year in Japan, while in England
it will buy one of only $3 a year, the purchasing power of
capital over income

much

in England.

able to

six per cent in Japan,

and only

half as

A millionaire in the first country will be

command an income

$60,000 without trenching on

191

NATURE OF CAPITAL AND INCOME

192

[Chap. XII

England he can get but $30,000, and
be just half as wealthy in actual income.

his capital, whereas in
will, therefore,

§2
The

rate of interest has

concept

many

so vital to our study,

in the present chapter,

The meaning implied

meanings, and since the

shall specify carefully,

what these various meanings

are.

in the previous section postulates the
i.e. a uniform and perAlthough such an annuity does
often convenient to employ it as

existence of a perpetual annuity,

petual flow of income.

not actually

exist, it is

a vehicle of thought. Suppose $10,000 to-day will secure
a perpetual annuity of $400 per year payable annually,
the first payment accruing one year from the day of purchase then the rate of interest is said to be four per cent
;

per

annum

payable annually; that

is,

the rate of interest

(when the interest is payable annually) is the ratio between
the rate of flow of a perpetual annuity and its equivalent in
present capital.

In case the income accrues semi-annually the case is
Let $10,000 to-day yield a perpetual annuity of $400 a year in semi-annual payments of $200 each,
the first payment being due six months from date. Then
slightly different.

the rate of interest

said to be four per cent per

annum

payable semi-annually.

That these four-per-cent rates are not equivalent to
is well recognized in practice, and can be made
The holder of the semi-annual
evident in various ways.

each other

annuity has a slight advantage over the holder of the annual
annuity, because he receives half of each year's income
He may, in fact, convert his income
six months earlier.
of $200 twice a year into

an income

for in six months, besides receiving his

$200, he

may

receive $10,000,

$404 once a year
first

installment of

selling his annuity.

then reinvest the entire $10,200 on
4 per cent payable semi-annually, and hence obtain a perthe original terms,

CONCEPT OF RATE OF INTEREST

Sec. 2]

193

petual annuity of $408, in semi-annual installments of $204.
In six months more, or one year from the original investment, he may realize $204 of income and $10,200 of " prinOf this he may reinvest the
cipal," or $10,404 in all.
original $10,000, retaining $404,

may

repeat

From

same annual

the

this point

cycles

onward
and

sales

reinvestments, and, therefore, receive $404 net, payable

He is, consequently, better off by $4 a year,
than the holder of an annuity of $400 a year, payable
annually. In other words, a rate of interest of 4 per cent
once a year.

per annum,

the income is payable semi-annually, is
a rate of interest of 4.04 per cent per
annum, if the income is payable annually.
The same reasoning may be applied when the income

equivalent

accrues at quarterly or any other intervals.^

subdividing the time of payment indefinitely,

we may

pass from an income obtained in installments to a continu-

ous flow of income. The idea of a uniform and perpetual
stream of income is nearly realized in certain cases, as in the
West, where water rights are sometimes bought in the form
a perpetual flow through a square
of a "miner's inch"

—

inch opening under a head of six inches.

Let us suppose
worth $100 a year. If the right to such
a perpetual and uniform flow can be bought for $2000, the
rate of interest is five per cent "reckoned contiauously."

that the water

thus reach the conclusion that there are various

senses of the rate of interest, according to the
of pajmaent, namely,

The
The
The
The
The

—

annum,
annum,
annum,
annum,
per annum,

rate of interest per
rate of interest per
rate of interest per
rate of interest per
rate of interest

income
income
income
income
income

payable
payable
payable
payable
payable

frequency

annually.
semi-annually.
quarterly.
at other intervals.
continuously.

The last named, while it is the least familiar in practice, is in
some respects the most natural, and lends itself the most
^

See Appendix to Chap. XII,

§ 1.

NATURE OF CAPITAL AND INCOME

194

[Chap. XII

The first, on the
used in practical

readily to mathematical transformations.

other hand,

the most

frequently

computations.

§3

have considered the rate

capital in terms of income.

of interest as the price of

consider reciprocally

the price of income in terms of capital,
is

years, namely, the

number

would flow an amount
if

have what
measured in
years during which there

called the "rate of capitalization."

125,000 will
''

shall
is

income equal to the capital. Thus,
buy a perpetual annuity of $1000 a year, the

rate of capitalization

concept of

" twenty-five years' purchase."

years' purchase " is

applied to land rents.

common

The
England as

It is evidently interconvertible with

the rate of interest.
rate of interest of four per cent indi"
cates a
years' purchase " or rate of capitalization of

twenty-five years.

rate

interest

two per cent

indicates a rate of capitalization of fifty years.
capitalization has thus as
interest,

many meanings

according as the income

semi-annually, quarterly,

etc., or

The

rate of

as the rate of

payable

annually,

continuously.

§4
The concepts of interest which have been given depend
upon the concept of a perpetual annuity. But they can be

made

may

to apply also to terminable annuities.

Thus, $10,000

an income of $400 a year for
ten years, at the expiration of which time the $10,000, or
the "original loan," is returned. In such a case the loan
may evidently be regarded as a purchase and resale of a
perpetual annuity. A perpetual annuity of $400 is, for the
price of $10,000, diverted to the lender's benefit, and at the
end of ten years is restored to the borrower for the same
sum.
yield at four per cent

We may regard in this light even short-time loans.

Thus,

CONCEPT OF RATE OF INTEREST

Sec. 4]

195

man

borrows $100 to-day and agrees to pay it back with
4% in one year, we may conceive of him as
having sold a perpetual annuity of $4 a year for $100, and
at the same time as having bound himself to buy it back for
if

interest at

$100 at the end of one year. The combined result of these
operations amounts to an exchange of $100 this year for
$104 next year. It is possible to use such a simple exchange

between this year's and next year's money, as the basis of
an entirely new definition of the rate of interest, and one
which is independent of the idea of an annuity. When
$100 to-day is exchanged for $104 next year, the ratio of
exchange between the two simis is j^^. This ratio is not,
of course, itself the rate of interest;

the rate of interest

the excess, or premium, of \^^, above unity. In other
words, the rate of interest is the premium, or " agio," above

par of this year's dollars in terms of next year's dollars.
of interest may be called the premium conwhereas the concept hitherto employed, or the price of
capital in terms of an annuity, may be called the price con-

Such a concept

cept,

To say that the rate of interest
means that the price of $100
of capital is $4 of income per annum forever.
To say that
the rate of interest in the premium sense is four per cent
means that the price of $100 of one year's goods is $104 of
cept of the rate of interest.

in the price sense is four per cent

the next year's goods.

The premium concept

much

emphasized,

of the rate of interest has been so

notably

seems advisable to repeat

by Bohm-Bawerk, that

briefly,

with respect to

it,

the dis-

tinctions as to annual, semi-annual, quarterly, etc., reckoning.

Let us suppose that $100 to-day

months hence.

The

rate of interest in the

worth $102 six

premium

here 2 per cent for the six months' interval, and

sense

said
"
4 per cent per annimi payable or reckoned semi-anto be

nuallyy

It will be evident, however, that this is a little

higher rate than 4 per cent per

annum

reckoned annually.

Let us suppose that at the end of six months, at which time

NATURE OF CAPITAL AND INCOME

196

$102
the

due, the debt

same

rate.

renewed

[Chap. XII

for another six

It is evident that the

$102

months

by
The

will then,

''compounding," amount to $102 x 1.02, or $104.04.
end of a year, instead of being $4, is
In other words, 4 per cent interest reckoned half$4.04,

interest then, at the

yearly

equivalent to 4.04 per cent reckoned yearly, as was

also the case

under the price concept of the rate of

interest.

In the same way we may consider quarterly or other intervals for compounding. At the limit, the interval for com-

pounding may be reduced to an instant.^
We have then two methods of defining interest. In
both of them the time element is prominent. Before passing on we should here remark that the time element enters
not only as referring to the times of payment but also to
A rate of interest implies not only
the time of contract.
the two points of time between which the goods for
exchange are available, but also the point at which the deIt would be quite poscision to exchange them is made.
sible, for instance, to agree in the year 1900 to exchange
$1000 in the year 1901 for a given sum or series of sums
In this case the rate of
returnable at still later dates.
interest for this exchange appertains to the year 1900,
although execution of the contract does not begin until a
year later and

not concluded until later

conditions have often been overlooked
tics of

still.

These

in treating statis-

the rate of interest.

§5

We have defined the rate of interest both in the
"price" and the "premium" sense. The question now
arises whether these two concepts are interchangeable.
Under certain conditions they are, and under others they
are not. Cases in which the two are interchangeable are
shown
^

in the following propositions.

For the mathematical relations involved, see Appendix

XII,

§ 2.

Chap.

CONCEPT OF RATE OF INTEREST

Sec. 5]

197

a premium on
goods in terms of next year's goods, is the same
year after year forever, then the rate of interest considered
as the price of capital in terms of a perpetual annuity will be
equal to it.
(1)

If the rate of interest, in the sense of

this year's

A numerical example will make this clear. We shall suppose that the rate of interest
sense,

i.e.

that $100 at any

consideration will
are to

show that

four per cent in the

buy $104

premium

during the period under

to be paid one year later.

as a consequence $100 will necessarily

an annuity of $4 a year

premium

moment

forever.

Let us suppose, then, the

rate being 4 per cent, that $100

to be repaid one year

later.

We
buy

this

spent for $104,

$104,

when

received at the end of the year, the investor reinvests $100.

By our hypothesis
bring,

will

which in turn $100

an unchanged

interest rate, this $100

the end of the second year, another $104,

reinvested

;

and so on

indefinitely.

continually reinvesting, he obtains for his original $100,

$4 a year indefinitely and $100 deferred indefinitely. If
the process is perpetual, the $100 is deferred to infinity,
and has no present value. Hence the original $100 obtains
simply a perpetual annuity of $4 a year, and the rate of interest in the price sense is therefore also 4 per cent, which
was to have been proved.^
It is evident that this reasoning may all be put in general
terms, and that it applies equally to interest reckoned
semi-annually, quarterly, etc., and continuously.
(2)

Conversely,

a given rate of interest in the price

sense holds good to-day, next year, two years later, and so

indefinitely,

then the rate of interest in the premium

sense will be equal to

This also
will

may be

buy $4 a year

it.

readily

shown by an example.

forever, the first $4 being

$100
due one year
If

^ An alternative proof consists in obtaining the present value of
each successive item of income and adding the results. This process
is exemplified in the next chapter in obtaining the capital-value of a

perpetual annuity.

NATURE OF CAPITAL AND INCOME

198

[Chap. XII

hence, the buyer of such an annuity at the end
may, immediately upon the receipt of his first
his rights.

one year

$4, sell out

hypothesis they will bring $100.

Conse-

$100 a year ago. He
quently, he receives $104
has thus virtually exchanged $100 one year for $104 the
That is, the premium rate of interest for this
year after.
year is also 4 per cent.
in all for his

see, then,

two senses

that

— price

the rate of interest in either of the

premium

— remains

constant, the

rate in the other sense will also remain constant

and equal

to the former.
It is clear that the

same reasoning

reckoned for any period of

applies to interest

time, — semi-annually,

quar-

terly, continuously.

§6
But if the rate of interest does not remain constant, its
two senses of price and premium are no longer interchangeable.

Thus, suppose that the rate is 4 per cent in the
sense for the first year, but 3 per cent for the

premium

second year and for all succeeding years. This means that
$100 to-day will buy $104 next year, and that $100 next year
Then $100 to-day will eviwill buy $103 the year after.
dently not buy $4 a year forever, nor $3, but an intermediate

amount, approximately $3.03, so that the rate
the price sense

of interest in

3.03 per cent.^

Again, suppose that the rate of interest in the price sense
4 per cent this year, but 3 per cent next year. This

buy $4 a year forever, and
then
buy $3 a year forever.
that $100 next year will
Then $100 to-day will not buy $104 next year, nor $103,

means that $100 to-day

but $137^.
is

37^ per

of interest

will

That is, the rate of interest in the premium sense
Thus a very slight change in the price rate
implies a great change in the premium rate of in-

cent.^

See Appendix to Chap. XII,
See Appendix to Chap. XII,

§ 3.
§ 4.

CONCEPT OF RATE OF INTEREST

Sec. 7]

199

This goes to explain why, in the actual market, the

terest.

rate of interest for short-time loans fluctuates so

more widely than the
ments.

much

rate of interest on long-time invest-

scarcely necessary to exhibit statistics to

show

though they are easily obtained by comparing the
fluctuations in the rate of interest on short-term and longterm loans, in the United States or in England.
We see, then, that the two concepts of interest rate, though
definitely related,^ are not always interchangeable.
this,

§7
There is yet another device for indicating the terms of
time exchanges. Besides the rates of interest and their
reciprocals, the ratios of capitalization, there is the rate of

discount.

have seen that

$104 due one year hence

win buy $100 of present goods, then \^^ is the rate of exchange between the two times and exceeds unity or par by
the rate of interest. The rate of exchange between the
two times, when taken in the opposite direction, is \^^ and
This deficiency,
this is less than unity or par by -^^^.
which amounts to 3.9 per cent, is called the rate of discount.
The nimiber representing the rate of discount is always
slightly less than that representing the corresponding rate
The rate of discount is practically employed
of interest.^
only for short-time loans, usually less than a year, in which
yf-g-,

cases

better serves the purposes of rapid computation.

The present chapter may be
lows

—

briefly

summarized as

First, the rate of interest is a special case of

return," and

may

fol-

"value-

be approached from either of two stand-

points, according as

consider

the price of capital in

See Appendix to Chap. XII, § 5.
For further discussion of the rate of discount, see Appendix to
Chap. XII, §§ 6, 7.
^

NATURE OF CAPITAL AND INCOME

200

[Chap. XII

terms of a perpetual annuity, or the premium on the price
of this year's goods in terms of next year's goods.
These

two

we have found
them is assumed

definitions of the rate of interest

when
but when

to be

interchangeable

either one of

invariable ;

this condition is not fulfilled the

to be

two

are not interchangeable.

Secondly, not only does the rate of interest have the two

meanings which have been given, but each mean-

distinct

ing

subject to various interpretations, according as the

interest is payable or

reckoned annually, semi-annually,

quarterly, etc., or continuously.

Thirdly, as alternatives to the rate of interest

we may em-

ploy the rate of discount and the rate of capitalization.

Both

magnitudes also apply either in the price sense
sense.
Furthermore, like the rate of inthey apply somewhat differently according as the

of these

or the
terest,

premium

reckoning

annual, semi-annual, quarterly,

etc.,

or con-

tinuous.

The following

table illustrates the various magnitudes

which have been considered:^

—

Equivalent Rates of Interest, Discount, and Capitalization

CONCEPT OF RATE OF INTEREST

Sec. 8]

201

constancy enters, the two senses will involve two unequal
magnitudes, we have here represented or implied thirty-

two possible magnitudes. The means for expressing time
exchanges between goods of the same kind thus present
an embarrassing variety. But since it is easy to proceed
from any one of them to all the others, it is evident that we
need not, in general, employ more than one. The one
which is practically the simplest, and which, therefore, we
shall hereafter

per

annum

the goods of

ing.

employ

in this

book

is:

the rate of interest

reckoned annually and considered as a

premium

one year compared with those of the year follow-

CHAPTER

XIII

VALUE OF CAPITAL

Having found what constitutes a rate of interest, we are
now enabled to pursue our study of the relation between
capital and income. We found in Chapter XI that these relations are of four kinds, according to

and the

capital are

measured

whether the income

in quantity or in value.

The

fourth of these, "value-return," brought us to the concept
of a rate of interest.

The rate of interest acts as a link between income-value
and capital-value, and by means of this link it is possible
to derive from any given income-value its capital-value, i.e.
to "capitalize" income.

To do this, we assume that the expected income
known with certainty, and that the rate of interest
sense of an annual premium)
is

fore-

(in the

foreknown, and also that

constant during successive years.

With

these provisos

very simple to derive the capital-value of the income to
be yielded by any article of wealth or item of property in
other words, to derive the value of that wealth or property.
That value is simply the present worth of the future
income from the specified capital. This is true whether
the income accrues continuously or discontinuously
whether it is uniform or fluctuating; whether the installments of income are few or infinite in number.
We begin by considering the simplest case, that, namely,
in which the future income consists of a single item accruIf, for instance, one holds
ing at a definite instant of time.
a property right by virtue of which he will receive, at the end

it is

;

202

VALUE OF CAPITAL

Sec. 1]

of one year, the
right,

sum

of $104, the present value of this

the rate of interest

If the property

203

4 per cent, will be $100.

the right to $1 one year hence,

its

present

is evidently oi or $0,962, and if the sum to which the
property entitles the owner is any other amount than $1,

value

present value

its

or multiplied

due in one year
If the future

interest

is still

simply that amount divided by 1.04
Thus the present value of $432

.962.

sum

x .962, which is $416.^
due in two years, and the rate of

or 432

4 per cent,

evident that $1 to-day

the present value of $1.04 next year, which in turn (by

compounding)

will

then be the present value of $1.04 x 1.04

or $1,082) at the end of the second year.

The
"amount" of $1 at the end of two
years, and $1.04 is the "amount" of $1 in one year.
Similarly, in three years (1.04)^ is the "amount" or sum
worth $1 in present value; and so on for any number of
(i. e.

[1.04]

$1,082

called the

These results show what $1 to-day

is worth at
number
of
years.
And
any
conversely,
the end
from
them it is easy to see what $1 due at the end of any number
of years is worth to-day.
We have already seen that the
present worth of $1 due in one year is j^, or $0,962.
Similarly, the present value of $1 due at the end of two,

years.

three, etc., years is respectively

the present value of $1,

other

sum by

we may

i^„

^j;^, etc.^

Knowing

evidently find that of any

simple proportion.

illustrate these results geometrically, let us represent

time by horizontal

and the value of the capital by
A A' A" A'", as shown in
Figure 1, will exhibit the relative values at any two instants, exchangeable on the basis of a given rate of interest,
lines,

vertical Hues; then the curve

compounded annually.
The point B represents the present
1

B', the in-

For the general mathematical treatment, see Appendix to Chap.

XIII,
^

instant;

§ 1.

For a mathematical formulation, see Appendix to Chap. XIII,

§ 2.

NATURE OF CAPITAL AND INCOME

204

stant a year hence;

years hence; and B^^\

[Chap. XIII

that two years hence; B'" three
represents any
years hence.
,

present value, A'5' the " amount of this sum one year hence,
A"B" the ''amount" two years hence, etc. Consequently,
year
also represents the present value of A'B' due one
'

A"B" due two years hence, or of A'-'^B^'^ due
The curve AA(*) is an " exponential curve,"
t years hence.
in geothis being the name given to a curve which ascends

hence, or of

B"'

Fig.

metrical progression, i.e. ascends so that the successive
vertical lines, AB, A'B', A"B", andA"'5'"(ordinates),

taken at equal intervals, increase in length at a uniform
We shall, however, for economic purposes, christen
ratio.
this curve the "discount curve."

§2
The

principles

which have been explained for obtaining
sum apply to many

the present value of a single future

commercial transactions, especially to the valuation of bank
assets, which exist largely in the form of "discount paper,"
or short-time loans of other kinds. The principles also
apply, though in combination with those of risk and foreign exchange, to that form of property called "bills of

VALUE OF CAPITAL

Sec. 2]

exchange."

another application

Still

and

in course of trade

to the

owner

205
to wealth which

of which, therefore, the only service

consists in its sale.

It is

this principle

that a dealer reckons the value of his stock, by discounting

its selling price for

before

it is

expense of

the time which will probably elapse

sold — deducting,

of course, the prospective

discounted in like manner.

selling,

value of any article of wealth reckoned
is

in course of construction

will bring

when completed,

Similarly, the

when

that wealth

the present value of what

less

the present value of the

For instance, the maker of an autoat any of its stages in course of
construction, as worth the discounted value of its probable
return when subsequently finished and sold, less the discounted value of the costs of construction and selling
which still remain. Of course, the element of risk cannot,
in such cases, be overlooked but its consideration belongs
cost of completion.

mobile will appraise

it,

;

to a later chapter.

Another application of these principles of capitalization
to goods in transit.
A cargo leaving Sydney for Liverpool is worth the discounted value of what it will fetch
is

in Liverpool, less the discounted value of the cost of carry-

examples are wine, the value
what it will be when
"mellow" and ready for consumption; and young forests,
which are worth the discounted value of the lumber they
will ultimately form.
In Germany and some other countries, such appraisement of forests is now worked out with

ing
of

there.

which

Other

classical

the present worth of

considerable precision.

§3
It seldom happens, however, that there is one item only of
income or outgo earned by an article of capital. The items
are unusually numerous.
Perpetual annuities, for instance, form an important class, in which these items recur
in equal amounts and during equal intervals forever.
We

NATURE OF CAPITAL AND INCOME

206

have already seen,

in the last chapter, that

[Chap. XIII

a person owns

the right to $1 a year payable at annual intervals forever,
its

present value, reckoned at four per cent,

If his annuity

$2 per year,

present value

its

~, or $25.
is

evidently

any other sum, its present
value is found by multiplying in the same way. Thus, an
annuity of $17 is worth jj. In other words, the value of a
perpetual annuity is found by dividing the annual income
by the rate of interest,^ or, what amounts to the same thing,
by multiplying the income by the rate of capitalization,
double

this, or

also called the

$50

;

and

number

if it is

of years' purchase.

This proposi-

tion, however, serves to determine only that capital-value

which an annuity possesses at
before the

first

its

inception

{i.e.

one year

installment) or at any other point taken

one year in advance of the

first

of the installments to be

The value

included in the calculation.

the annuity,

taken immediately before any installment of income falls
due, is evidently greater than the above, by the amount
of that installment.

Thus,

the rate of interest

four

per cent, a perpetual annuity of $4 a year, of which the
first payment falls due one year hence, is worth $100 today, and is also worth this same sum at any instant
immediately following the payment of an installment.
But next year, immediately before the first paj^ment
becomes due, it will be worth $104. At any intermediate
point between the present when it is worth $100 and a
year hence when it is worth $104, it will be worth an

intermediate amount, determined by the discount curve;
for its value will always be the discounted value of the
$104, which could be realized on

at the time of the next

payment. As soon as this payment has passed by,
the value will drop to $100 again, after which it will gradually ascend as before, and so on, following a series of curves
In this
like the teeth of a saw, as shown in Figure 2.

interest

diagram, the value of the annuity
*

represented

For a mathematical statement, see Appendix to Chap. XIII,

suc§ 3.

VALUE OF CAPITAL

Sec. 3]

207

cessive vertical lines, four units in height, each representing
$4,

and situated one unit

If the

annuity

future time,

of time apart/

deferred,"

present value

its

will possess

till

some

the discounted value of

JlFig.

that value

does not begin

i.e.

11.

when

does begin.

Thus, in-

$100 is the value of a $4
annuity beginning to-day (by which, as we have seen, is
terest being four per cent, while

meant that

its

falls due one year from
an annuity deferred one year
or $96.15, and the present value of an

first

installment

to-day), the present value of
later will

be only j^,

is ^^„ or $92.46.
The value
any time before its inception at the point
shown by the height at any point of the discount

annuity deferred five years
of the annuity at

curve through A.

In the preceding discussion, the income, which
posed to accrue in installments,
successive vertical lines.

represented

sup-

by separate

But when the income

sup-

posed to flow continuously, it becom.es necessary to represent it by an area.
In the "area" method, time is still
^

For further discussion of the

ferent time-intervals, see

reckoning interest for
Chap. XIII, § 4.

effect of

Appendix

dif-

NATURE OF CAPITAL AND INCOME

208

represented by horizontal
nates are employed

income.

lines,

and

[Chap. XIII

vertical lines or ordi-

— not to represent income, but

Thus, in Figure

ing at the instant A, and

rate of

3, AC is the rate of income flowBD is the rate at the instant B.

Fig.

As a consequence, the income which flows through any
period of time, AB, is represented by the area ABDC. It
is therefore the time AB multiplied by the average rate.
In the case of a uniform flow of income,
horizontal straight line.

The area method

be used wherever continuous income

reduces to a

will hereafter

in question.^

§4
Actual examples of true perpetual annuities cannot be
but for practical purposes, some government
"rentes" are perpetual annuities, also railway leases for
999 years. While the capital value of a perpetual annuity
of $4 a year, capitalized at 4 per cent, is $100, that of an
annuity of $4 a year for 50 years is $85, for 75 years is $94,
It will be seen,
for 100 years $98, and for 200 years $99.96.
therefore, that for any ordinary rate of interest, an annuity

said to exist

;

extending a century or more

practically equal in value to

a perpetual annuity.
Among non-monetary examples

may

be cited as per-

petual annuities the before-mentioned water rights in the

These are often sold by the miner's inch, i.e. a
theoretically perpetual flow of 1^ cubic feet per minute,
West.

^ For a fuller statement of the area method, as related to the
method, see Appendix to Chap. XIII, § 5.

line

VALUE OF CAPITAL

Sec. 5]

209

which is supposed to be the rate at which water will flow
through an aperture of one square inch with a "head"

The

of six inches.

"first" inches are often so sure to con-

Again,

tinue as to

be guaranteed.

element of

risk, the S^ hares

overlook the

stock

joint

companies

often exemplify perpetual annuities.

Turning from capital proper y to capital wealth, we find
in land an approximate example of capital yielding a perpetual annuity. Land is often capitaUzed on the basis of a
perpetual and uniform income, in the form of crops or other
uses.
It is then valued at a certain number of years' purchase.
These so-called " natural and indestructible powers
of the soil," however, which such a calculation assumes, do
not always exist, and when they do exist, do not always
Mines and quarries become
yield a perpetual annuity.
exhausted, while much land yields an irregular, increasing,
or decreasing income stream.

turn

now from

Suppose that a
year.

man

perpetual to terminable annuities.

possesses a ten-year annuity of $100 a

This means that he has the right to receive ten annual

payments

of $100 each, the first falling

the present moment.

due one year from
an annuity differs

clear that such

from a perpetual one by lacking the infinite succession of
payments after the ten years are past. In short, the
terminable annuity

simply a perpetual annuity dated

to-day, less a perpetual annuity deferred ten years.
fore, the present

value of the terminable annuity

Thereis

simply

the difference between the present value of the two perpet-

Of these two perpetual annuities, the present value of the one which begins immediately, interest
being four per cent, is $2500, and that of the one which is
ual annuities.

deferred ten years

^^,

or $1689.

Their difference

$2500 -$1689 or 811. Now such a difference as this, i.e.
the difference between any particular sum (as $2500) and

NATURE OF CAPITAL AND INCOME

210
its

discounted value for any time,

on that sum.

may,

[Chap. XIII

called the total discount

therefore, express our result

saying that the present value of a terminable annuity is the
total discount on a perpetual annuity of the same annual

amount beginning when the terminable one
If the

value

terminable annuity

the discounted value of

ends.^

deferred, its present

is itself

its

value reckoned at

inception.

§6
Terminable annuities are sometimes employed by insurance companies and governments, but are otherwise comparatively rare as specific forms of property rights. Approximate cases, however, of such income exist in the case
Thus, a
of many, if not most, durable articles of wealth.
fairly
uniform
of
value
for
series
of
services
machine yields a
same
may
of
of
and
the
be
true
a
years,
a fairly fixed term
rolling
stock
ship,
the
and
other
house or other building, a
equipment of a railroad, etc. Such terminable income is
also exemplified in many kinds of land, in the case of mines
and quarries, peat beds and other tracts whose yield brings
exhaustion. The state of Nevada presents an example of
a large area of land which once yielded large incomes, but
to-day is quite or nearly unproductive. It is evident,
however, that in all these cases risk is an important factor
in determining capital-value.
This factor is for the present

excluded from consideration.

As the date

for the termination of the

the total discount diminishes;

annuity approaches,

hence, the capital- value of

the terminable annuity diminishes.

The decrease

of capi-

sometimes known as ''wear and tear";
namely, the depreciation of an article due to the fact that the
tal-value

what

it to render gradually diminish.
The approaching cessation of services may or may not be due to

services left for

physical wear, so that the expression

"wear and tear"

For a mathematical presentation of this proposition, see Appendix to Chap. XIII, §§ 6, 7.
^

VALUE OF CAPITAL

Sec. 6]

misnomer.

can imagine an

211

article

which

suffers

material change, and of which the services will nevertheless

only a limited period.

last

the Atlantic coast the fish-

temporary platforms which
ermen sometimes
It
are pretty sure to disappear in the September gales.
construct

evident that the value of such a property will decrease

rapidly as the end of the fishing season approaches, without
this decrease being
tion.

due

in the least to

The ''World's Fair"

any physical

deteriora-

buildings at St. Louis depre-

ciated, during the brief period of the fair, from $15,000,000,
which was first paid for their construction, to $386,000, for
which they were sold after they had served the purpose for
which they were built. In like manner, a small wooden
bridge, which is to be supplanted by a larger and better
structure near by, will decrease in value rapidly as the time
approaches for the other structure to divert its traffic,
without any corresponding physical deterioration. Examples are common enough of productive instruments losing

known

their value, because of its being

that better devices

''Wear and tear," therefore, is
a phrase which we must use only in a metaphorical sense.
Even when the wear and tear take place because of physical deterioration, this deterioration acts upon the value only
in so far as it decreases or terminates the flow of income,
and not because of a physical change in the capital which
are soon to displace them.

bears this income.^
clusively on the

The value

income from

of the capital

it,

depends ex-

upon

its

a terminable annuity,

and not

directly

physical condition.

Having considered the case
turn

the case of a bond, which entitles the holder

not only to a terminable annuity, but also to a single deferred
*

Cf.

sum

called the " principal."

Bohm-Bawerk,

1891, p. 347.

Thus, a so-called " five

Positive Theory of Capital, English translation,

NATURE OF CAPITAL AND INCOME

212

per cent, ten-year, $100

bond" means

[Chap. XIII

the right to receive

an annuity of $5 a year for ten years, and, in addition,
^100 at the end of the ten years.
If the rate of interest is five per cent, and one buys a bond
which entitles him to an annual income of $5 a year for ten
years and $100 returnable at the end of this period, it is
evident that the purchase price of the bond must be $100.
In this case the $5 of annual income is the interest on the
purchase price, and the sum of $100 which is to be received
at maturity is equal to the originally invested capital or
"principal." For these reasons such a bond is called a five
per cent bond, the annual installments of income are called
" interest," and the final payment of $100 is called "principal."

But more
sequently

nomers.
is

not

often than not the

all of

If the

bond is not

sold at par

;

con-

the three terms just mentioned are mis-

bond

five per cent,

but

sold above par the rate of interest
less

than

five per cent, so that it is

only nominally a "five per cent bond";

the $5 annually

received is only nominally "interest"; and the $100
turnable at the end is only nominally "principal."

In order to obtain the capital-value of a so-called

when the market rate
when the bond is sold on a

per cent bond

cent

{i.e.

we need simply

re-

five

of interest is four per

four per cent basis),

add together the present values (reckoned
at four per cent) of the ten payments of $5 and of the final
payment of $100. We may consider these items as consisting of (1) a ten-year annuity of $5 a year, and (2) a sum of
$100 deferred ten years. Both of these we can easily find
from the explanations already given.
to

been explained^ that the present value of a tenyear annuity is the "total discount" on the capitalized
value of a corresponding perpetual annuity beginning when
the terminable annuity ceases. Now a perpetual annuity
It has

of $5

worth,
1

See §

interest is four per cent,
supra.

See §

;^,

supra.

or $125.^

VALUE OF CAPITAL

Sec. 7]

213

perpetual annuity beginning in ten years will thus be

worth $125

To-day, therefore,

in ten years.

by discounting

four

"total discount"

is,

per cent, (^^> or

therefore,

$125

worth,

it is

The

$84.45.

less $84.45, or $40.55.

We need to add to this the other element in the bond,
namely, the present value of the so-called "principal" of
$100 due in ten years. Discounted at four per cent, this
Combining our two figures we
is worth (1^10, or $67.56.
Lave, for the value of the bond, $40.55 + $67.56, or $108.11.
We

find, therefore, that

a so-called five per cent bond

yields the investor four per cent

manner

per cent,

In general a bond

interest)

;

bought at $108^^0.
it will

yield

him

six

bought at $92.50.^
sells

or nominal "interest,"
principal

if it is

could be shown that

it sells

at par

when

the annual income,

equal to the true interest on the

above par

the annual income (nominal

greater than the interest on the principal

;

and

below par if it is less.
In a similar way we may calculate the value of a bond in
cases where the installments of income, or nominal interest,
are semi-annual and the rate of interest is reckoned semiannually, and in the case of

more frequent

intervals, as well

as in the limiting case of continuous payment.^

Elaborate tables have been constructed, called "bond
value books," calculated on the foregoing principles, which
are used by brokers for showing the value of bonds under
The tables are usually employed,
different circumstances.
however, for the converse problem, to find the rate of interest "realized"

when a bond

The following

an abridgment

bought at a given

called) three per cent, four per cent,

The

prices of the

bonds in

all

price.

of these tables, for (so-

and

five per cent

bonds.

cases are the prices taken

^ For
a mathematical statement, see Appendix to Chap. XIII,
8; for an alternative method of calculating the value of a bond
and one which gives the "premium" separately, see Appendix to
<:hap. XIII, § 9.

For mathematical statement, see Appendix to Chap. XIII,

§ 10.

214

NATURE OF CAPITAL AND INCOME

[Chap. XIII

Rates of Interest
(reckoned semi-annually) realized on a bond (with semi-annual coupons) known as a
" Three per cent

bond"

Sec. 7]

VALUE OF CAPITAL

215

Rates of Interest
(reckoned semi-annually) realized on a bond (with semi-annual coupons) known as a
" Five per cent bond "

NATURE OF CAPITAL AND INCOME

216

The

original

investment

the discounted value of expected

the final "returned" principal

receipts;

The only

largest one) of those receipts.
this large receipt
it

employed

[Chap. XIII

simply one (the

difference

and the other smaller ones

when

differently

between

that, usually,

received.

usually

reinvested in other long-time securities, whereas the smaller

items of income, the so-called "interest," are spent for
cles

shorter duration, and,

into true "final income."
therefore, while both are

considered by

itself,

thereby,

arti-

soon converted

The "principal" and "interest,"
income with reference to the bond

are apt to lead to different results

when

followed into the final transformations of purchase and
sale,

by the

pounded.
sold on a

and

debit

credit cancellations previously ex-

we suppose a

five per cent

five per cent basis,

reinvested in the

same kind

bond

to be always

and the principal
of security, it

to be always

evident, in

relation to the whole series of operations, including the reinvestment, that the principal,

canceled

though income, is immediately
In other words,
income from one bond, it

by reinvestment as outgo.

whenever it appears as
immediately disappears again as outgo for another; consequently the owner is virtually in possession of a perpetual annuity of $5 a year. It is with a view to such an
operation that the final payment of $100 on a bond is instinctively regarded on a different footing from the other
payments called "interest." It is called "principal" on
the theory that

it is

the annuity of $5.

to be reinvested in order to continue
It thus in theory represents capital,

whereas the other payments represent only income. But
we see now that both are income received from the bond

may, by reinvestment,
them is usually put back

as a source of income, although either

That one

be put into

capital.

into capital

and the other

a matter of subsequent
the immediate study of the

not,

and does not affect
bond itself.
Even when the "principal" received at the maturity

history

VALUE OF CAPITAL

Sec. 8]

bond

the

reinvested,

may

be that

217
it is

not equal to

the original investment, nor, therefore, to the capital-value
of the bond at any time before maturity.
This equality
would hold true only in case the bond is always kept at
par.
When it is worth more or less than par the capitalvalue is more or less than the "principal," and for this
reason, if for no other, the capital-value should not be
confounded with the " principal."
In order to determine whether or not a nominally five
per cent bond really yields five per cent, we must refer to
the price at which it sells, and while there is no necessity to abandon the terminology by which ''principal"
and "interest" are used with reference to bonds, these
terms are undoubtedly misnomers and their existence is
responsible for considerable confusion. For instance,
insurance companies have recently been offering their
policy holders an option between the receipt at the death

the insured of a definite insurance of $1300, or of a

"five per cent gold

ment
but

bond"

for $1000.

many

it is

—

evident that such a bond, considered as the equiva-

lent of $1300 in cash,

Hitherto

we have

on a lower basis than

income item

;

(2)

five per cent.

considered only four special cases of

capitalizing income, viz. (1)

(3)

The gold bond has

policy holders, a tempting form of investfive per cent
because of the " high rate of interest,"

seemed, to

the capital-value of a single

the capital- value of a perpetual annuity

the capital- value of an annuity terminable in a definite

number

of years

;

and

(4)

the capital- value of a bond.

But

income from any property may
occur in many other forms, may last for any length of time,
and may be distributed through this time in any manner
whatever. Let us, therefore, consider the general case in
which any random series of income items, AB, A'B' A"B"
it is

clear that the items of

A'"B''' are received^ as
,

shown

in Figure 4.

The

capital-

NATUKE OF CAPITAL AND INCOME

218

[Chap. XIII

is found by
adding together the present value of the separate items.
The best way to exhibit this is to begin at the last income
payment, A"'B"'. Just after this last installment, of

value of this series at the point of time

course, the property
zero.

valueless

;

that

is, its

capital-value

Just tefore this installment the capital- value

to the installment

itself,

and is represented by A"'B"'

equal
.

Fig.

^ny time

in the interval

between

this installment of

income

and the next preceding installment, the value will evidently
be found by following the discount curve B"'C" C" being
vertically over A"
The height A"C" is, therefore, the
capital-value of the property just after the payment A"B"
Its capital-value just before this payment is found by adding
the vertical line C"D", equal to the installment of income
A"B". From D" in turn we proceed backward along the
discount curve D"C' to C, at which point A'C represents the
,

A'B\
amount
an

capital- value of the property just after the installment

this is added,

CD'

pass back an instant,

equal to the installment A'B'.

The

result

the capital-value just before said installment.

A'!/,

From D',

VALUE OF CAPITAL

Sec. 8]

219

turn, the capital-value descends along the discount curve

where CD, equal to AB, is added, and from D we
proceed finally by discount curve to P, vertically over 0.
to C,

OP is, therefore, the capital-value of the property at the
" present " instant, and its value at any succeeding instant

shown by following the course of the broken line
This curve must descend to zero

PDCD'C'D"C"B"'A'"}

B
Fig.

finally,

when

income

the

exhausted, and

shows a tendency to decrease before this last
is

usually

payment

reached.
If,

in a series of

income items, a negative one occurs,

it is

only necessary to reverse the capital curve, as shown in
Figure

where the

of income.

first

installment,

AB,

outgo instead

The curve PB" evidently represents the be-

havior of capital- value, rising suddenly as the outgo
is

passed and falling

when

the income A'B'

received,

and so on to the end.
We may, if we choose, trace the history of the value of a
security from the time immediately before its purchase, and
consider the purchase price itself as an outgo. If this price

^ For the mathematical formula for the capital-value of any
income installments, see Appendix to Chap. XIII, § 11.

series

NATURE OF CAPITAL AND INCOME

220
is

[Chap. XIII

exactly equal to the discounted value of the succeeding

it is evident that the value immediately before its
purchase must be exactly zero. Thus in Figure 6 let
be the purchase price, and equal to OA, which is the capital-

income,

The capital-value
immediately after purchase.
immediately before purchase is, therefore, zero, and the
entire capital curve is the line OABCDEFH, which starts
value

Fig.

at zero

and ends

at zero, but

above the zero

line at all

This represents the normal hisany capital instrument if bought at a " fair

intermediate intervals.
tory

price."
If the flow of

income

we may obtain the
by dividing the continuous

continuous,

capital-value approximately

VALUE OF CAPITAL

Sec. 9]

221

income stream into arbitrary installment sand discounting
each installment separately/
The value of the income stream has heretofore been
always reckoned in advance of its occurrence; that is, we
have discounted income to obtain present value. We may,
however, consider an income as paid for at the close of
the period, in which case we have to deal with its "accumulated" value or its "amount." ^

§9
Thus far we have considered the possibility of but one
income stream from any given capital wealth. But it often
happens that, with one capital instrument, there is a choice
between various income streams. Land may be used for
grazing,

agriculture,

building,

recreation

purposes.

may

be employed in a variety of ways, and the same
Tools
is true of innumerable articles of wealth, particularly when
taken in combination. What determines the choice of the
series of uses to

which any given instrument

may

be put ?

Evidently that series of uses or income stream will be seThus,
lected which yields the maximum present value.
land used for grazing purposes will yield a net service of
$1000 a year forever, and interest is taken at four per cent,
its value for grazing purposes is evidently $25,000.
If,
in like manner, the capital-value for some other use, say for
growing wheat, is $20,000, it is clear that the land will be
if

employed for grazing rather than for growing wheat.
Sometimes the two series of uses to which land or other
wealth may be put differ, not only in their amount, but in
their time of beginning or ending.
In a city, for instance,
land

may be

used either for present dwelling or for future

and it often becomes a question which
more valuable. In case the city is growing

business-purposes,

use

the

For a fuller statement, see Appendix to Chap. XIII, § 12.
For discussion, and for formulae for the capital-value of any
come, discontinuous or continuous, see Appendix to Chap. XIII, §
*

in13,

NATURE OF CAPITAL AND INCOME

222
rapidly,

may happen

[Chap. XIII

that in certain quarters, although

the present use for dwelling purposes

more important,

a few years the locality will cease to be a residence quarter

and the land
cases, it
tirely
it

may

will

be needed for business purposes.

In such

''pay" to keep the land out of present use en-

and reserve

until the city has

profitable to erect a business block.

encumbered with a dwelling,

make
now

grown

so as to

If the

land were

either the possibility of its

subsequent use for business purposes would be cut off,
or the profit from its conversion to those purposes would be
impaired by the prior destruction and waste of the dwelling.

Under such circumstances it would usually happen that
buy up and hold the land. The manner
in which the gain presents itself to them is simply as a prospeculators would

spective rise in value from the growth of the city; they

buy the land to sell it later at a higher price.
Such a speculator is commonly regarded as keeping land
therefore

"out of use." He is, however, only deferring the use, and,
he has foresight, is no more to be condemned than the
wise speculator on the wheat exchange, whose work, as is
The
well known, operates to conserve the supply of wheat.
speculator thus tends to bring about the best utihzation of
the land in the sense that, out of several alternative income
streams which the land might be made to yield, that one is
if

which possesses for him the maximum present
value. In general it is probable that the best uses of the land
The latter confor the public also are found in this way.
clusion does not, however, absolutely follow from the former,
since the " best " uses are not necessarily those which
have the greatest market value; but those who would
prevent all land speculation will at least need to adduce
other arguments than that speculation "keeps land out of
use," before they have- proven their case; for wise land
selected

speculation

number

means simply the discriminating

choice, out of a

of uses, of that use or series of uses

to-day the greatest present value.

which affords

VALUE OF CAPITAL

Sec. 10]

be observed that

It should

the relative advantages of

223

the rate of interest

the

two uses

given might be quite different.

In this case

to put

up the dwelling rather than wait

block

for the holder of the land, as

;

not afford to "lose his interest"

it is

raised,

might pay

for the

he expresses

when

the example

business
it,

could

at so high a rate.

§10
Thus

we have

far

considered the capital-value only of

individual articles of wealth.

The same reasoning

to a group of articles of wealth.

applies

important case

In this case we may prefer
that of a merchant's stock.
to capitalize the stock as a whole rather than to take
the

sum

of the capitalizations of its separate elements.

The net income from the stock
from the gross income

all

the

found by subtracting

outgo, including, besides

the cost of replenishing the stock, the other costs of the
business,

work

— clerk

hire, rent, and even an allowance for the
merchant himself, unless he is a mere "silent
If the net income is supposed to remain constant

of the

partner."

forever, the capital value of the stock will, of course, be

found by dividing the net income by the rate of interest.
In this case the rate of interest must be taken for the proper
installment interval. If the goods are supposed to be continuously bought and sold, the rate to be employed is the
^
"rate of interest per annum reckoned continuously."

§11

conclude, therefore, that the value of any capital-

good, either of wealth or of property-rights, assuming that
all future income is foreknown, is the discounted value of
that income, and consequently that, as time goes on, the

value of that capital will oscillate, rising gradually during
intervals between installments along a "discount curve,"
^

For a mathematical statement in this connection, see Appendix

to Chap. XIII, § 14.

NATURE OF CAPITAL AND INCOME

224

[Chap. XIII

as the future income approaches,

installments are successively

contrary manner

and

an outgo.

This os-

begins at zero,

when

the instrument or group

newly acquired or produced.
as

after

capital-value ends finally at zero, when the
or service of the article or group is ended. It also often

cillation
life

before

and falling suddenly as the
passed by and acting in a

were, a sort of

may seem

life

is one that is
These changes constitute,

history of capital- value.

some readers that there

to the rule that the value of capital

an exception

the discounted

value of

its expected income, in the case where the
income which might be received from the capital is indefinitely postponed.
This is the case in which the "principal" accumulates at compound interest so that no " interest" is withdrawn.
If a person has a deposit of $1000
in a savings bank and leaves it there to accumulate at 4
per cent until it amounts to double that sum, which will
happen in about eighteen years, the $1000 does not appear
to him to be the discounted value of any income.
If he
thinks of it as the discounted value of anything at all, it
will be of the $2000 of capital which he expects to own at
the end of eighteen years. It is perfectly true that the
capital-value of $1000 is the discounted value of the future
capital-value of $2000; but the latter capital-value is
itself the discounted value either of some subsequent
income, or, in turn, of a capital still further deferred, and
so on indefinitely. Actual income is hoped for sometime, even if it be not for a million years.
The present
$1000 is the discounted value of that ultimate income, however far distant. A perpetual accumulation is, humanly

out of the question. But if such perpetual
accumulation be regarded for the moment as possible, it
may still be interpreted as a perpetual postponement of
speaking,

possible income;
^

so that even in this case the $1000

may

For mention of the case where the rate of interest changes and

changes are foreknown, see Appendix to Chap. XIII,

§ 15.

its

VALUE OF CAPITAL

Sec. 11]

225

be regarded as the discounted value of an income
Of
is indefinitely postponed, but indefinitely great.

still

which

course, such a limiting case

of purely theoretical interest.

The prodigious sums which result from the reckoning of
compound interest always surprise those who have never
made such computations. One dollar put at compound
interest at 4 per cent would amount, in one century, to
second century to $2500, in a third century
in a fourth century to $6,500,000, in a
century to $325,000,000, and in a sixth century to

$50, in a
to

$125,000,

fifth

$16,000,000,000.

Beyond

this

the

figures

are

ahnost

unthinkable in magnitude.^

Yet we have few instances in which any one has endeavored to set aside even one dollar for the benefit of posterity
There is too much reluctance to
six centuries removed
build for the remote future, even though the attainable
Benjamin Franklin, at his death
results are enormous.
in 1790, left £1000 to the town of Boston and the same sum
!

it should accumulate
hundred years, at the end of which time he calculated
that at 5 per cent it would amount to £131,000. In the
case of the Boston gift, it actually amounted, at the end
of the century, to $400,000, and has since accimiulated to
about $600,000. The sum received by the city of Phila-

to Philadelphia, with the proviso that
for a

delphia has not increased nearly as fast.

Another interesting case of accumulation

that of the

Lowell Institute in Boston, which was founded by a bequest
of $200,000 in 1838, with the condition that 10 per cent of
the income from
principal.

The

should be reinvested and added to the
peculiarity of this provision is that it
it

There is, therefore, theoretically no
limit to the future accumulation thus made possible.
applies in perpetuity.

The fund,

after

sixty-seven years, amounts

already to

$1,100,000.
It
*

must be remembered however that

practically even a

For a geometrical representation, see Appendix to Chap. XIII,
Q

§ 16.

226

NATURE OF CAPITAL AND INCOME

small sum, such as $1000,

[Chai-.

allowed to accumulate,

say, at 4 per cent for 1000

years, could

attain the theoretical magnitude.

the fact that the theoretical

This

XIII

let

never actually
is

evident from

sum would then amount

over $100,000,000,000,000,000, which is so far in excess of
the total value of capital on this planet, as to be out of
the range of possibility.

The reason the sum would

to accumulate as fast as theoretically required, aside

fail

from

fortuitous losses, lies in the reduction of the rate of interest

which the very accumulation would bring about.

The administrators of such a fund, as the centuries passed
by, would jfind it increasingly difficult to obtain fields in
which to invest it, and their effort so to invest would have
the same effect in reducing the rate of interest realized on
the investments as is now felt by the national banks in
their pressure to buy government bonds.

CHAPTER XIV
EAENINGS AND INCOME

§1
In the

last

chapter

was shown

that, perfect foresight

being assumed, the value of any capital good
its

derived from

by discounting the value of that income.
now remains to compare the capital-value thus derived
future income

with the expected income- value on which

depends.

It is evident at the outset that the capital-value is less

than the total expected income; for the discounted value
of

any future sum

This fact

necessarily less than that simi

the following table of capital
five typical articles

—

itself.

and fourth columns
and income in the cases

illustrated in the third

NATURE OF CAPITAL AND INCOME

228

[Chap.

XIV

value of the house when interest is at the same rate is
$18,300, whereas the total income to be expected from it is
about three times as much, or $50,000 that the value of
;

over $500, whereas the total expected

the horse

income

about $100 more, or $600; that the value of the
whereas its total income is $30, of

little

suit of clothes is $28,

which $20 accrues the

first

year and $10, the second; and,

that the capital-value of the loaf of bread

finally,

cents and the income expected from

also 10 cents.

In this limiting case there is practically no diminution on
account of the interval of time to elapse between the time
of valuing the instrument and the time of receiving its
services, for the reason that this time is too brief.

From

the table

see clearly one reason that certain

have been identified with income and others
Bread has practically the same capital- value as
not.
income- value, so that, if a person were not accustomed to
fine distinctions, he might think it unnecessary to discriminate between the 10 cents which is the value of the use of
the bread, and which is, therefore, income^ and the 10 cents
which is the value of the bread itself, and which is, therefore,
There is almost as much danger of such confusion
capital.
articles

in the case of clothing

and

therefore income,

the suit, and

more enduring
between
of the

for there

;

between the $30 which

only a slight difference

the value of the use of the suit,

and the $28 which is the value of
But as we pass to the

therefore capital.
articles, there

emerges so wide a difference
an instrument and the value

the value of the use of

instrument

itself,

that there

tinguishing between them.

Accordingly

difficulty in dis-

usually find in

on economics some distinction between the value
of the use of a house ($50,000 in the foregoing table) and
the value of the house itself ($18,300 in the table). But if
the distinction is valid in one case it is valid in the others.
The consequence of disregarding it we have already seen
in Chapter VII.
treatises

EARNINGS AND INCOME

Sec. 2]

If the rate of interest is

229

not 5 per cent, but 2^ per cent,

there will result great differences

the capital- values.

The consequences are seen in the last column of the
But the effect on capital-values wrought by thus
table.
-cutting the rate of interest in

two

of the five different articles.

The more enduring ones

will

be different for each
will

be affected the most. When the rate of interest is halved
the value of the land will be doubled, rising from $20,000 to
$40,000, but the value of the house will rise by only about

from $18,300 to $28,400 the value of the
i.e. from $508 to $551
the
value of the suit will rise only from $28 to $29 and, finally,
the value of the loaf of bread will not rise at all, but wiU
remain at 10 cents. We see in these five types of articles
that the sensitiveness of capital-value to a change in the
60 per cent,

i.e.

;

horse will rise only 10 per cent,

;

rate of interest

In general,

the greater the more enduring the income.

also, this sensitiveness is the greater the

remote the periods of time at which the income is concenFor instance, if the total income is $100, and is
trated.
concentrated at a point of time

all

capital-value,

when

fifty

the rate of interest

years distant,

5 per cent,

its

$8.72,

becomes $29.09 when the rate of interest is reduced to
2^ per cent. That is, the rate of interest being halved, the
capital-value is more than trebled. If the same income of
$100 were to be due only one year from date, the change
from 5 per cent to 2^ per cent in the rate of interest would
elevate the capital- value only from $95 to $97.50.
but

§3
Thus

far

we have been concerned only with total income,
we now consider the rate of

in relation to capital- value

;

income per year in relation to capital-value.
This ratio
lias already been called the rate of "value-return."
In accordance with previous explanations the sequence

NATURE OF CAPITAL AND INCOME

230

the

calculating

rate

value-return

[Chap.

XIV

follows:

owner to a future series of
income items which is assumed to be definitely foreknown.
These items are all discounted by means of a specified rate
specified property entitles the

The sum

of interest.

of the discounted values constitutes

the capital- value of the property.

any

time, taken as divisor

This capital- value, at

and the income per year taken

a dividend gives the rate of value-return as quotient.
It

must be

mind

steadily borne in

which forms the divisor

capital

value, nor the value as indicated
originally invested,

but

that the value of the

not a

fictitious

sum

the

book

money

simply the discounted value, at

the specified time, of the expected income subsequent to

that time.

should at the outset rid our minds of

the bogey of an unvarying "principal" perpetually existing

somewhere
entity

to deal with

considered, which

income,

When

The only value

in a debt or other property.

we have

and which

capital

for instance,

the value of the property

the discounted value of the expected
therefore

continually

for the present yielding

vacant land,

time to yield income,

and

nevertheless

it is

changing.

no income,

as,

expected some-

the discounted value of this

remote income which alone constitutes the present value
of the land.
It is true that a speculator may prize the
land simply because he thinks he can sell it later to some
one else, and to him it may seem that its value is independent of any future income, and depends only on the
future capital- value at which he expects to

sell.

But

it is

the discounted

clear that this futuref' capital- value
value of the income which the then purchaser will expect.
is itself

he too be a speculator, and his valuation, hke his
depends on a resale, the dependence on
future income is merely again postponed to the time when
some purchaser shall buy the land for the income it will
This ultimate expected uicome gives the basis for
yield.
Or,

predecessor's,

all

prior capital valuations.

Were

there no expectation

EARNINGS AND INCOME

Sec. 4]

—

231

any future income
or, at least, the expectation that
there would be an expectation of it
there could be no

come,

—

Capital-value, independent of expected in-

capital-value.

impossible.

§4

MJThe

first

proposition to be emphasized as to the rate of

value-return
interest,

but

that

it is

not necessarily equal to the rate of
than that rate, and

may be either greater or less

any degree.

Let us take, for example, the case of the house which we
assumed would endure just fifty years, giving throughout
that period a shelter-service worth, after actual expenses
are deducted, $1000 annually.
We saw that its value,
computed by discounting this fifty-year annuity on a 5 per
cent basis, is $18,300. It therefore yields the first year a
rate of value-return on its capital-value of j|^, or 5.4 per
cent.
At the end of ten years its value, found by discounting the income still remaining, will be $17,200. It
will therefore then be yielding a value-return of j^ per
year, or 5.8 per cent.
At the end of thirty years, in like
manner, it will be worth $12,500 and yielding j^„, or 8 per
Again, the suit of clothes which will last two years,
cent.
and gives services worth $20 the first year and $10 the
second, has a value at the start of about $28, and at the end
of the first year of about $9.50.
The value-return the first
year
9^0,

therefore |, or 71.4 per cent,

or over 100 per cent.

of 10 cents.

which

The

It yields 10 cents'

and the second year

loaf of

worth

bread has a value
income in a day,

at the rate of $36.50 per year

value-return

;

consequently

or a rate of 36,500 per cent per

its

annum

reckoned daily or ''continuously").
In these examples the value-return exceeds the rate

(interest

of interest.

Reversely,

on capital to be

it is

possible for the value-return

than the rate of interest.
stance, forest land with small trees is bought,
less

If,

for in-

may

NATURE OF CAPITAL AND INCOME

232

[Chap.

XIV

that no product can be obtained until the end of ten years..
that then the yield is worth $1000 a year

We may suppose

during the ensuing (second) decade, after which

worth $2000 a year

forever.

may

it will be
be shown that the

present value of the forest, reckoned on a five per cent basis,

about $20,000. This would be the discounted value of an
annuity of $1000 a year, whose commencement is deferred
ten years from the date of investment, and which then

runs ten years, plus the discounted value of a perpetual
annuity of $2000 a year beginning twenty years in the

future.

the

five

per

cent

basis,

the

forest

will,

from the present, be worth about $32,000
(this being the discounted value of an immediate ten-year
annuity of $1000 followed by a perpetuity of $2000)..
Twenty years from the present, the forest will be worth
$40,000 (this being the discounted value of $2000 a year
in ten years

The

forever).

forest land therefore rises gradually in value

from $20,000 to $32,000 in the first decade, during which no
income is realized, and continues to rise, though less rapidly,
to $40,000 in the second decade, during which there is
realized the comparatively small

The rate of

out the

The
first

the rate

income realized divided by the

tient of the

or zero.

income

$1000 a year.

return, therefore, at the beginning, being the quo-

decade.

evidently

of the third

capital, is jpoo,

rate of return evidently remains zero through-

decade

At the beginning

~^,
it

of the second decade

or 3.1 per cent; at the beginning
is

or 5 per cent.

see,

therefore, that in this case the rate of value-return gradually

from zero to a height equal to the rate of interest.
There may even be a negative rate of return. A colt, for
instance, may occasion more trouble than it is worth for the ^
first year, and produce a net expense or disservice of $20_J^
Thereafter it may render a net income of $10 during the
second year, $20 during each year from the third to the
tenth inclusive, and $10 a year the next five years, after
which it dies. Supposing, as our preliminary hypothesis
rises

EARNINGS AND INCOME

Sec. 4]

233

obliges us to do, that all these are definitely foreseen at the

would be worth the discounted value (at 5
It will therefore
these, or about $135.
yield during the first year a return of ^, or — 15 per cent.
The value-return for the second year, reckoned on its capitalstart, the colt

per cent) of

all

value taken at the beginning of that year,

^, or 6 per

cent; on the third year ^, or 13 per cent, on the fifteenth
year about jg, or 100 per cent. The entire series may be

seen from the following table

—

Capital-

Income
DTJKING

value AT

Yeab Beginning of
Year

1st year

;20

$134

2d year
3d year

161
159
146
134
121
107
92

4th year
5th year
6th year
7th year
8th year
9th year
10th year
11th year
12th year
13th year
14th year
15th year

20
20
20
20
20
20
20
20
10
10
10
10
10

76
60
43
35
27
19
10

Rate
OF Retubn

-15%
6
13
14
15
17
19

22
26
34
23
28
37
54
100

C^ From the foregoing examples it is evident that a property which yields 5 per cent to the investor may yield in
individual years either more or less than 5 per cent. The
dwelling house jdelded more than 5 per cent for 50 years,
and then ceased to yield income. The forest yielded less
than 5 per cent for 20 years, and thereafter yielded 5 per
cent on its value at that time. The colt yielded rates ris-

NATUKE OF CAPITAL AND INCOME

234
ing from

—

15 per cent in the

the fifteenth year, and

first

[Chap.

XIV

year to 100 per cent in

then zero forever after.

however, the business reader may feel
He will point out that in our tables the
represented as yielding 5.4 per cent the first year

this juncture,

disposed to object.

house

by neglecting depreciation, and
was represented as yielding in
per cent instead of 5 per cent, by

instead of 5 per cent,

that, contrariwise, the forest

the eleventh year 3.1

For it is true that the house,
worth $18,300 at the beginning of the year, must, under the
given conditions, depreciate $85 during the year; and the
objector will maintain that this ought to be deducted from
the $1000 received from the house, in order to obtain the
The deduction leaves $915, which is
true "net earnings."
According to this
just 5 per cent on the capital of $18,300.
calculation, therefore, the house really returns, not 5.4 per
And, applying the same line
cent, but only 5 per cent.
of reasoning to the case of the forest, the objector might
insist that the forest increased in value just enough to
make up the difference between the 3.1 per cent, which was

neglecting appreciation.

given as the rate of value-return at the beginning of the

second decade, and the 5 per cent to which

would seem

to be entitled.

These calculations are correct.

But they do not

mili-

which has been
given. They merely bring into relief a distinction between
income which is realized by the investor and income which
Realized income is the value of
is earned by the capital.
the actual services secured from the capital; earned income is found by adding to realized income the increase
We
of capital-value, or deducting from it the decrease.
may designate them briefly simply as income and earnings.
To illustrate this distinction and to show its importance,
let us consider a four per cent $1000 bond, the interest on
which is payable annually. From what was shown in the
previous chapter it is clear that (if the bond is valued on a
tate against the treatment of value-return

EARNINGS AND INCOME

JSec. 4]

four per cent basis) the value of the

235

bond

will oscillate

from the former
payments and falling back
suddenly as each payment is made. The income is simply
the payment of $40 at the end of each year. Even our
objector will not deny this. During the entire year up to
the very end there is no income at all; yet the bond
"earns" about $10 each quarter, in the form of an increase
between $1000 and S1040,

rising gradually

to the latter between interest

These earnings are simply equal

in the value of the bond.

to the interest on the capital.

assume that income

And

so in general,

definitely foreknown, earnings

the interest on the capital.

will equal

when

is,

therefore,

main
when they attempt to

to earnings that accountants instinctively give their

But they

attention.

away

spirit

income and put earned income in

Realized income plays the more important

place.

realized

err grievously

depend

all

the other elements,

—

its

role, for

capital- value, value-

and even earnings themselves. To
take the case of the house, the first and primary fact is that
it promises to yield $1000 a year for fifty years. This income

return, depreciation,

series

being given,

by the discounting
income by capital
;

it is

possible to obtain its capital- value

process
its

;

by division of
by comparing its capital
and its earnings, by deducting
its

value-return,

depreciation,

values at successive dates;

depreciation from realized income. Unless the realized
income be given at the start, all these calculations are impossible.

Earnings could not serve as our starting point,

for earnings cannot be calculated except

by the

aid of de-

preciation, depreciation cannot be calculated except
capital- value,

and

capital- value

from expected realized income.
Moreover, the fundamental proposition
ter,

that capital-value

"Which

of the last chap-

the discounted value of expected

income, will cease to hold true,
earniags.

from

cannot be calculated except

by income we mean

Thus, the house has a capital-value of $18,300,
the discounted value of its realized income of

NATURE OF CAPITAL AND INCOME

236

[Chap.

XIV

$1000 a year for 20 years, discounted at 5 per cent. But
it is not true that $18,300 is the discounted value of the
earnings of the house, for the earnings are all less than
$1000, beginning at $918 a year and dwindling each year

have expired; and clearly the discomited value of fifty annual items each less than $1000
must be less than the discounted value of fifty annual items
until the fifty years

of $1000 each.

Since, then, earned income cannot be derived without
assuming realized income, and since capital-value has been
shown to be the present value of the latter, and not of the
former, it is clear that realized income is the more fimda-

mental concept of the two.

y\y^
§5

But

so persistent

realized income

the accountant's instinct to put aside

in favor of earnings that

we need

to point

out in detail the confusions which arise, unless income and
earnings are carefully distinguished. We first observe that,

under the given conditions
interest are equal.

Now if

of foreknowledge, earnings

interest

and

at 5 per cent, a capi-

—

land, houses,
$1000 invested in whatever form
though it is said to
horses, securities, or anything else
earn 5 per cent, does not necessarily receive an income each
tal

—

The $1000 means the present value, discounted at 5 per cent, of some expected income stream;
but that income stream may take any one of an indefmite
number of forms; such, for instance, as a perpetual annuor a terminable
ity of $50 a year, as in the case of land
annuity of $100 a year for 14 years or an income of $25 a
year for 10 years followed by an income of $167.50 a year

year of $50.

;

for 10 years.

All of these are inter-equivalent,

and when

discounted at 5 per cent, each of them represents a capital
of $1000.

Of all these possible forms of income it is usual to take the
perpetual annuity as the standard income (earnings) and to

EAKNINGS AND INCOME

Sec. 5]

compare other incomes with

iti

237

Consider, for instance, the

possessor of a property yielding $100 a year for 14 years.

will, if

he discounts

property at $1000.

this

income at 5 per

cent, value that

thinks of himself as possessing

$1000 ''invested in" that property. From it he gets the
income of $l00 a year for 14 years. But he knows that he
might sell this property for $1000 and reinvest in another
property yielding the standard $50 a year forever. Contrasting with the standard income of $50 a year forever
which he might receive, the income of $100 a year for 14
years which he does receive, we observe that at first his in-

come

double the earned or standard income, being $100
The excess of $50, however, is compen-

instead of $50.

sated for

by a reduction

of $50 in the capital-value of his

property, for at the end of the

first

year the value of his

property will be the discounted value of $100 a year for
thirteen (instead of fourteen) years, which,
still

reckoned at 5 per cent,

$950.

And

interest is

it is

in general

that the owner of $1000 invested at 5 per cent can obtain a

higher income than the standard $50 only at the cost of

trenching on capital to the extent of the excess.

Suppose, on the contrary, that the $1000
5 per cent, but in such a form as to yield at

invested at

than
form which yields the above-mentioned income of $25 a year for 10 years, followed by $167.50 a year
In that case, during the first year the owner
for 10 years.
receives only $25 instead of $50, which is the earned or
"standard" income. But the deficiency of $25 in his income is made up by an augmentation of his capital by that
amount.
The principle is perfectly general, and perhaps too
familiar to require a rigorous demonstration, though there
is no difficulty in framing on^^J We may therefore state
(1) When a property yields a specified foreknown income,
and is valued by discounting that income according to a
specified rate of interest, if the income realized is equal to
$50,

e.g.

first less

in a

—

NATURE OF CAPITAL AND INCOME

238

XIV

[Chap.

the income earned (and hence equal to the rate of interest),
the value of the capital will remain at a uniform level.
(2) If realized

income exceeds earned income, the value

of the capital will be

decreased by the amount of the

excess.
(3) If realized

income

less

than earned income, the

value of the capital will be increased by the deficiency..

These principles hold true whether the period for reckon-

compounding interest is a year, half year, quarter, or
any other period, or shrinks to the vanishing point in the
ing or

case

continuous

interest.

slight

modification

quahfication in the statement of these principles

how-

is,

when, instead of there being a rate of inwhich remains the same year after year, there is a

ever, necessary
terest

succession of different rates.^

Expressed in a single sentence, the general principle
connecting realized and earned income is that they differ

by the appreciation

or depreciation of capital.

It is

thus

depreciation of capital,

income as realized income less
or else as realized income plus

appreciation of capital.

We may therefore

possible to describe earned

fallacy of confusing realized

state

anew the

income with earned income:

the fallacy consists in reckoning depreciation of capital
as a part of outgo, or appreciation of capital as a part of

This usage

income.
it

is difficult

has become habitual.

will

to combat, for with

To expose the

many

fallacy completely

be our object during the remainder of this chapter.

We may at the outset

emphasize a fact already mentioned
namely, that this popular and erroneous
not consistently adhered to. A pension is an

in Chapter

usage

VII

;

income the capital-value of which
^

The

case

continually diminish-

discussed in the Appendix to Chap. XIV, §
is a refinement into which

practical purposes, however, this

dom need

to enter.

For
sel-

EARNINGS AND INCOME

Sec. 6]

239

Yet even popular usage seldom or never deducts

ing.

depreciation from the pension to obtain the

this

''true" in-

come; and the reason we instinctively include (as we
ought) the whole of such a pension in income, is that
the depreciation is not actually offset. In ordinary business, on the other hand, we are accustomed to deduct
depreciation, because this

usually offset

by actual pay-

ments into a depreciation fund. Even in this case the
depreciation is not itself an expense; but there is a concomitant expense approximately equal to it, in the form of
payments into the depreciation fund. It thus makes all
the difference in the world whether the depreciation fund is
actually maintained, or merely reckoned.
tion fund

ing

a deprecia-

actually maintained, the expense of maintain-

serves to reduce realized income so as to

make

coincide with earned income. In such a case, therefore, the
ideal earned income becomes realized in actual fact.
Assuming a fixed rate of interest, the depreciation fund

may

be defined as a fund formed by accumulating that

part of income which must be turned back into capital in

order to maintain the value of capital at a fixed level. A
depreciation fund is thus made from annual contributions

equal to the excess of realized income above earned in-

come.

If,

instead of an excess, there

a deficiency, the

become negative,
being conincome
that is, instead of a certain quantity of
verted into capital, a certain quantity of capital must be
converted into income .^^^
contributions to the depreciation fund

Geometrically, a depreciation fund
sented.

In Figure 7

let

very simply repre-

the income consist of the items

The capitalized value of this income stream is AB. The interest on AB is represented by
the height AC, so that the standard income would be
represented by a series of annual hues of the height of the
dotted line CD. The excess of the lines a, a' a", etc.,

a, a', a", a"', d'^, etc.

above the dotted

line

therefore represents the contri-

240

NATURE OF CAPITAL AND INCOME
Where

butions to the depreciation fund.
ciency, as in

the case of a'",

depreciation fund
time, instead of

the

negative; that

some

of the

there

contribution
is,

XIV

[Chap.

defi-

the

for that particular

income being reinvested, some
income from

of the capital is used as income, to prevent
falling

below the uniform

level prescribed for

a "I

Fig.

a'v

it.

a VI

The same

a VII

principles apply in case the income

a continuous flow, as

shown in Figure 8. Here the earned income is represented
by the elevation of the straight line CD, and the reahzed
income by that of the curved hne EF the deprecia;

tion fund is formed from the successive differences between these elevations. Thus, if $1000 of capital is invested on a 4 per cent basis, but so that the returns are
not $40, but $70 a year for twenty- two years, the annual

EAKNINGS AND INCOME

Sec. 6]

contribution to the depreciation fund

For at the end

241
is

evidently

of the first year, before the

income

re-

ceived, the capital-value will, under the supposed conditions,

become not $1070, but only $1040.

of income, $70,

then received.

from $1040 leaves $970, which

Fig.

capital-value.

Consequently

The

first

item

This being deducted

$30 short of the original

it is

to the capital, in order to bring

necessary to restore $30

up to the

original level of

$1000.
It will evidently

make no

difference

whether the income

items are reinvested simply as additions to the original
capital, or invested at the same rate of interest in some other

form of

capital.

The owner

of depreciating

machinery

may

NATURE OF CAPITAL AND INCOME

242
offset

The

by investing annually
by annually buying investment

that depreciation

new machines,
latter

type of investment

the phrase "depreciation fund"
of the

machines follows

this

a few

securities.

when

usually thought of
is

used.

XIV

[Chap.

If the

owner

procedure, then instead of

the original capital being maintained at a fixed level,

it is

continually decreasing, while the depreciation fund

con-

manner that the value of the
machinery and the depreciation fund
two
remains constant.
Consequently, at the end of the
income term, when the value of the original capital, the
tinually increasing in such a

together — the

—

machinery,

entirely exhausted, the value of the depre-

have exactly taken its place.
sometimes employed in the definition of a
depreciation fund. The fund is then described as formed
of a succession of payments out of income, such that if
each be accumulated at compound interest the total will
equal the original capital at the end of the entire income
ciation fund in securities will

This fact

term.

The most common application of a depreciation fund
bond which does not sell at par. For instance,

to a

is
a.

$100 five per cent bond, when interest is 4 per cent, will, if
The interest at 4 per
it has 20 years to run, sell at $115.
cent on this capital is $4.60, which shows that the depreciation fund, being the difference between the income and the
interest, is $5 minus $4.60, or 40 cents.
This item of 40
cents should annually be saved out of the income and reinvested at 4 per cent, in order that at the end there

may

remain a capital of $115. If the last installment of
income from the bond, $105, is treated as an income Hke
the previous items, the depreciation fund is, in the last
year, $105 minus 84.60, or $100.40 that is, besides the 40
cents annually there should be reinvested, at the end of
the term of the bond, the $100 of so-called "principal.'^
Thus we again reach the reason that the $100 of the last
payment is regarded as "principal" or "capital" and not
still

;

EARNINGS AND INCOME

Sec. 7]

"income."

It is

simply that this $100

243
always supposed
is, to be rein-

to enter into the depreciation fund, that

In case the bond is
an income equal to the
there is no depreciation fund ex-

vested and not retained as income.
sold

par

market rate

{i.e.

of interest),

yields

itself at the end, when the last item
income ($105) exceeds the earned income of

cept the "principal"
of realized

$5 by $100.

This excess, being reinvested at the same

rate, 5 per cent, will secure the

continuance of the same

income.

The operation
it is

of the depreciation

fund presupposes that

possible to invest the small differences each year in such

a manner as to accumulate at compound interest at the
rate which the original capital

earning.

Such

not al-

ways the case, especially with articles of wealth, like land,
In case two different rates of inmachinery, and so forth.
terest are involved, one for computing the capital-value of
the given income, and another for compounding the annual
savings put into the depreciation fund, the calculation of

the depreciation fund

will, of course,

be more complex.^

In close relation to a depreciation fund is the "sinking
fund" employed by governments as a means of meeting
large obligations
in particular of meeting the "principal"

—

public debts.

Needless obscurity has enveloped the

"sinking fund," especially since the intricate but fallacious

and Pitt.
The annual contribution

theories of Price

to the depreciation fund was the
between the income actually experienced and
an ideal perpetual annuity of the same present value.
A sinking fund, however, is formed from the difference
between income (or more commonly outgo) actually expedifference

The reader is referred to the Institute of Actuaries' Text-book,
I, London (Layton), 1901, where this and other problems in an-

Part

nuities are fully dealt with.

NATURE OF CAPITAL AND INCOME

244

[Chap.

XIV

rienced and an ideal terminable annuity of the same present

A government has to meet a series of expenses
connected with its bonded debt. These expenses constitute,
let us say, a stream of outgo lasting ten years, and consisting
and one
nominally "interest"
of nine equal payments
amount
the
much larger payment, exceeding the others by
The sinking fund is merely a
of the so-called "principal."
value.

—

all

ten payments.

ments are S5000 a year

for nine years

device for equaUzing

tenth year (as

If the actual

and $105,000

pay-

in the

the case of 10-year "five per cent" bonds),

the ideal 10-year annuity equivalent to this series would,

on a 4 per cent basis, be $13,329. The government, therefore, if it would pay off its debt, or rather provide for it in
ten equal installments, must during each of the
years, besides paying the $5000

the sinking fund $8329.
reversed,

and the

to its creditors,

first

nine

pay into

In the tenth year the process

entire $100,000 then accumulated in the

is taken to pay the $100,000 of "principal."
Hence, as apphed to bonded debts, the sinking fund may be
defined as formed by accumulating an annual sum during
a specified period, such that its amount will just suffice
to extinguish a given sum at the end of that period.

sinking fund

Depreciation and sinking funds are not the only devices
by which uneven income streams may be, as it were,
smoothed out. Many other devices may be employed. For
instance, a person engaging in an unusual expense, such as
that

of building a house, will not allow this expense to

seriously interrupt the even flow of his income, but will

provide for

come.
shares;
offset

by some correspondingly unusual item

He may

sell

of in-

other property, for instance railway

the unusual simi he realizes on the sale will then
the unusual outgo for the dwelling. Or, he may

mortgage his dwelling and the land on which it stands,
sell a claim upon the
and pay the debt off gradually

—

EAENINGS AND INCOME

Sec. 8]

dwelling

itself

instead of selling

245

some property

distinct

from the dwelling.
Or again, he may make an arrangement at the outset to pay for the house in installments.

methods of maintaining more or less reguincome merely shift the burden of an unusual
expense from one person to another. The first method,
by which the purchaser of the house raises the necessary
All of these

larity of

money by

selling other property, shifts to the

buyer of

that property an expense equal to that which he himself
seeks, for the time, to avoid.

mortgage, presupposes a
ply the necessary funds.

The second method, that

money lender who is ready to
The money lender is in this

supcase

The
payment by installment, implies that the
builder (or some other party) advances the cost of the dwelling.
In other words, the person who attempts to smooth
out his own income does so by throwing his irregularities
on some one else, usually a banker or broker.
To society as a whole such purely shifting devices are
inapplicable, for society can find no outside party on whom
to shift the fluctuations.
There is, however, a method by
which society's income may be more or less standardized.
This is by assorting and combining the various instruments of capital wealth so that the various income
the one who, for the time, shoulders the burden.

third method,

may

mutually compensate. For instance, if a
iron mines, it has a form of property
which, for a time, probably yields more than the standard
income. By the nature of the case, every bucketful of ore
reduces the amount which the mine can yield in future.
streams

community owns

The mine
is

is,

in fact, a sort of terminable annuity.

exhausted there

will

be no further returns.

The

After

capital-

value of the mine will therefore continually decrease.

the other hand, forest land which is covered with young
saplings will not begin to yield much income for many
years.
The income from this capital is therefore tempo-

NATURE OF CAPITAL AND INCOME

246

[Chap. XIV"

below the standard. A community which owns both
mine and timber land will consequently find that the increase and decrease will offset each other, so that its income
will be more nearly standard than if it merely possessed
rarily

either one without the other.

The last-named method is applied to the case of capital
of a large number of instruments in different stages of production or consumption. If a weaving
mill is equipped with 20 looms of the same degree of wear,
the value of this plant will evidently depreciate and a deBut if the 20 looms are
preciation fund may be necessary.
which consists

evenly distributed throughout the different stages of wear,
and if, for convenience, we assume that one loom wears-

Fig.

out each year, no depreciation fund will be necessary. The
replacement of one loom annually is equivalent to such a.
depreciation fund, and the capital

a constant

thereby maintained at

level.

Any income

stream whatever, even

parts are very irregular, will,

its

component

these parts are renewed at

frequent and regular intervals, necessarily produce in total

a uniform or standard income. Let ABC (Figure 9) represent an income stream which at first is negative and after-

ward

positive, such, for instance, as is occasioned

first

constructing and then using a machine.

Let an exactly
begin a short time later, as

income stream A'B'C
It is eviat A' and so on indefinitely, at equal intervals.
our
which
the
point
at
dent that after we have reached
C
first income stream ends, we have a fairly uniform income
similar
,

EARNINGS AND INCOME

Sec. 9]

247

and outgo, the income at any point consisting of the sum
of the ordinates above the base Kne AC^, and the outgo
of the

sum

of the ordinates below.

This case brings into juxtaposition two different points
of view from which the interest

Professor

sidered.

on capital

may

Clark conceives

be coninterest

as the net difference between the rate of total income

and

rate of

total

this net return

point.

outgo at

any

point,

with the capital-value as

and compares
exists at that

This concept treats the outgo or cost of production

as simultaneous with the income, that

is, it

takes into con-

any small section of the curves in Figure 9
contained between any tv/o vertical lines a short interval
apart. Professor Bohm-Bawerk, on the other hand, always
sideration

thinks of cost of production as preceding income.

on the elementary income stream ABC,
and contrasts the outgo or cost between A and B with the
later income between B and C.
These two points of view
are evidently quite reconcilable, though their authors do
not seem to have realized the fact. Each carries his own
special point of view throughout his treatment of capital
and interest. Professor Bohm-Bawerk regards interest as
an agio, or premium, found by contrasting the positive income return between B and C with the investment or outgo
between A and B, whereas Professor Clark regards interest
as the ratio between a perpetual, uniform flow of income and
fixes his attention

the capital-value of the entire stock.

Bawerk has

mind what we have
ous chapter the premium concept of
in

In short,

Bohm-

called in the previinterest,

and Clark,

the price concept of interest.

§10

have seen that earned income

often only an ideal

standard, and not to be confused with actually realized in-

come.

Yet the confusion

common.

Even Edwin Can-

248

NATURE OF CAPITAL AND INCOME

[Chap.

XIV

nan,

who is usually a safe guide, makes an error at
He states in his Elementary Political Economy

this

point.

: ^

—

"If a man has a cellar of port wine, or a plantation of trees, the
annual increment of the value of these things is evidently part of his
annual income. If he likes to spend it, he can do so without decreasing
his property.
If he does not choose to spend it, he is engaged in a
form of saving and is thereby adding to his property."

And

again, in

come

''What

"The

Capital?"^ he states,

divided into two parts,

(1)

in-

the increase of the

and (2) the things enjoyed."
That
"saving" or increase of capital is no^ income cof>
ordinately with ordinary income is evident from the fact
that this item is never discounted in making up capitalvalue.
As we have seen, one of the fundamental characteristics of income is that it is the desirable event which
occurs by means of wealth, and for the sake of which, concapital,

sequently, that wealth

valued.

that every item of income
its

This definition implies

discounted in order to obtain

contribution to capital-value.

The mere

increase or de-

crease of capital-value, on the other hand,

is never thus
Suppose, for instance, with interest at 4 per

discounted.

man buys an

annuity of $4 a year, which
is deferred one year.
Since
this annuity will be worth $100 one year hence, its present
value will be about $96, which, during the ensuing year,
cent, that a

does not begin at once but

will

gradually increase to $100.
(about) $4

itself

If this increase of value

to be called income,

treated like every other item of income,

But

counted.

would be

this is absurd.

$3.85, which,

should be

and should be

The discounted value

dis-

$4
added to the $96, would require
of

that the entire value of the property to-day should be
$99.85, or practically the

less

same

actually the case.

as a year later instead of

In other words, the hy-

pothesis which counts an increase of value as income
self-destructive; for
*

p. 59.

the increment

income,

Economic Journal, Vol. VII, 1897,

must

p. 284.

EARNINGS AND INCOME

Sec. 11]

be discounted, but,

discounted,

that

sense,

practically abolished.

not income in the sense
can be discounted in addition to other items of inIf it is income at all, it is income in a very peculiar

Clearly, then, increase of capital

come.

it is

249

and nothing but confusion can result from having
two kinds of income so widely divergent that

to consider

whereas one
is

not.

—

discounted to obtain capital- value, the other

have seen that the increase

pense of income.

of capital is at the ex-

occasioned by and

equal to

the deficiency of reahzed compared with standard income.

With

this in

mind, Edwin Cannan's definition of income

could be stated as realized income plus the deficiency be-

But

tween realized and earned income.

this is

earned

income, not realized, income.
§

To put

the matter in a practical light, let us imagine the

case of three brothers, each

whom

inherits the

same

Let us assume that interest is 5 per
cent.
The first brother invests his $10,000 in an annual
annuity of $500 a year forever. The second puts his in
trust to accumulate at 5 per cent for fourteen years, at
which time, having doubled in value, it is to be invested
in a perpetual annuity of $1000 a year.
The third, being
fortune, say, $10,000.

of the spendthrift type,

buys an annuity of $2000 a year

for

(nearly) six years.

According to the theory here advocated, the first has
a perpetual income of $500 a year; the second has no
income for 14 years, and thereafter an income of $1000;
the third has an income of $2000 a year for 6 years and
thereafter

none at

all.

This

mode

viewing the matter

also squares with ordinary business reckoning.

the other hand, according to the theory which re-

gards increase of capital as income, although the income

from the

first

would be the same as we have reckoned

it,

NATUKE OF CAPITAL AND INCOME

250

[Chap.

XIV

that of the second and third would be quite different the
of the second would be $500 the first year, for during
:

income

that year his capital increases from S10,000 to $10,500;
would be $525 the second year, during which his capi-

again from $10,500 to $11,025, and so on,
he is receiving an income of $1000 a year.
third brother, during the first year, uses $2000; but

tal increases

imtil in 15 years

The

as his interest
capital.

This

only $500 he

is,

forced to take $1500 out of

in our view, true realized income.

cording to the theory which

But

ac-

are criticising, this deprecia-

tion of $1500 would have to be deducted from the $2000
which the spendthrift actually enjoys, in order to compute
his net income.
The net income would thus be only $500,
or the interest on his original capital. At the beginning
of the second year, this spendthrift brother would possess
a capital of $8500, the ''income" of which would, by the
same theory, be 5 per cent on $8500, or only $425. Following similar reasoning to the end we find that the so-called
"income" would progressively diminish until, in the sixth
year, it would be only $90.
The capital then having been
entirely destroyed, no income would remain.
It would appear from all this that the spendthrift had received from

the original $10,000, during the six years of its hfe, a very
small income, steadily diminishing from $500 to zero, the
simi total being only $1695. Was it for such an ''income"

that he invested $10,000

§12
If

we suppose an income tax

laid

on the three brothers, we

shall find that, according to the different interpretations

which we give to the term "income," the results will
be startlingly different. If the income be taken in its true
sense, namely, as those items whose capital-value is the
$10,000 with which the three brothers started, then an income tax of 10 per cent will yield from the first brother
^50 a year; from the second, nothing for 14 years, after

EARNINGS AND INCOME

Sec. 12]

which
a year

will yield

for 6 years

of the three taxes

$100 a year and from the third,
and nothing thereafter.
The burden
;

on these three brothers

conditions be exactly equal,

by means of
''compound"

251

when

under these

Each brother could

present values.

their

for his taxes (that

will

the three are compared

is,

could pay a fixed

sum

advance in lieu of the annual sums) at the same cost,
namely, SIOOO for SIOOO is the sum in present cash which
is equivalent respectively to $50 a year forever
to $100 a
year beginning 14 years hence; and to $200 a year for 6
in

;

years.

But turning now

income as the value
tal,

to the spurious interpretation of

of uses plus the

accumulation of capi-

or the value of uses less the depreciation of capital,

would be very unequally taxed.
The first would, as before, pay $50 a year indefinitely.
But the second who "saves" for 14 years, will be compelled
find that the three brothers

Second Brother
Capital

At beginning
In 1 year
In 2 years
In 3 years
In 4 years
In 5 years
In 6 years
In 7 years
In 8 years
In 9 years
In 10 years
In 11 years
In 12 years
In 13 years
In 14 years
In 14^ years
Thereafter

$10,000
10,500
11,025
11,576
12,155
12,763

13,401
14,071
14,775

15,513
16,289
17,103
17,959
18,856
19,799
20,000
20,000

Tax
So-called
" Income " Thekeon

525
551
579
608
638
670
704
738
776
816
856
897
943
1000

Or, to be exact, $200 a year for 5 years

inasmuch as the capital

will

$50.00
52.50
55.10
57.90
60.80
63.80
67.00
70.40
73.80
77.60
81.60
85.60
89.70
94.30

True

Tax

Income Thereon

nil

100.00

$1000

$100

and $180

in the last year,

be exhausted in a

little less

than 6 years.

NATURE OF CAPITAL AND INCOME

252

[Chap.

XIV

pay an annually increasing tax on this saving for the 14
years of postponement, and then a tax on the income from
these same savings in which his annuity is to consist.
His first year's savings will be $500 and will be taxed $50.
During the second year his capital grows from $10,500 to
$11,025, making an increase of $525, the tax on which is
$52.50, and so on, as shown in the precedmg table.
The third brother, under such a tax, will fare as shown
below
to

—

Third Brother

Capital

At beginning
In 1 year
In 2 years
In 3 years
In 4 years
In 5 years
In 6 years
Thereafter

$10,000
8,500
6,930
5,270
3,530
1,710

So-called

nil

$500
425
340
260
180
90

nil

Tax

"Income" Theeeoit

$50.00
42.50
34.00
26.00
18.00
9.00
nil

True

Tax

Income Theeeon

$2,000
2,000
2,000
2,000
2,000
1,800
nil

200
200
200
200
180

When we compare the burden of the various taxes imposed on so-called "income," we shall find that the first
brother could

"compound" for his taxes, as before, by a
The second brother, however,

cash payment of $1000.

would need

pay $1714.

For he would have to pay $1000

as the present value of the tax of $100 a year beginning in

14 years, and in addition, $714 as the present value of
the series of taxes on his savings, namely, $50, $52.50, etc.
And the third brother, though the least provident of all,

could compound for only $157.73, this being the present
value of the six small tax payments which he would have

make, namely, $50, $42.50, $34, $26, $18, and

$9.^

In the foregoing calculation it was assumed that the tax did not
itself affect the value of the "income" on which the tax is laid.
But
this would be untrue of "income" which includes the increment of
capital.
For the discussion of this point, see Appendix to Chap.
^

XIV,

§ 2.

EARNINGS AND INCOME

Sec. 13]

253

Instead, therefore, of having a burden of taxes on the three

which have an equal present value of $1000,
and $157.73.
Such a system of taxation is clearly unjust and discourbrothers,

all of

find the unequal burdens of $1000, $1714,

ages the saver, while

spendthrift virtually has

encourages the spendthrift.

some

The

of his taxes remitted to him,

whereas the saver is made the victim of that too frequent
double taxaconcomitant of fallacious economic theory,
tion
for he is first taxed 15 years on his accumulation of
capital ($10,000 in all), and thereafter is taxed again on
the income which he derives from that same accumulation.
And yet this procedure is very common in practice. It
amounts to taxing, not the income actually flowing from

—

;

capital,
ital.

but

its

"earnings" or the interest upon the capin the "general property tax" in

It is famihar

the United States. Under it such wealth as temporarily
unproductive land is taxed, though it bears no income except the purely constructive income of its annual rise in
value.

To some

extent also the British income tax

instance of the same fallacy.
§

In the example which has been given we have supposed
each brother to be possessed of a fixed and definite annuity.
We have considered the effect of an income tax on these
properties,

according to the incorrect interpretation of

It often if not usually happens, however, that
"income."
the owner of a property may use it in any one of many ways,
and thus derive from it any one of many income streams.

have seen in the previous chapter that the choice between the different methods of using the property will depend on the question. Which source of income possesses the
greatest present value? An income tax laid according to
the correct idea of income would not disturb the comparative merits of these different income streams; but if
income be interpreted to include savings, the tax would

NATURE OF CAPITAL AND INCOME

254
disturb

them

greatly.

The

example

illustrated in the

effect of

[Chap.

such a tax as was

of the three brothers

would be

discourage the uses of capital which involve waiting.
fact,

XIV

this discouraging effect is well recognized

and ap-

plauded by the single-tax advocates, although they overAccording to them, it is
look the inequities involved.
right to discourage waiting,

and no speculation

in real estate

such as was described in a previous chapter should be permitted. They would tax all increase of value of land in the

manner

just described.

such a system

Perhaps the most harmful case of

of taxation

that of forest land.

Forestry

advocates have long been aware of the baleful effect of the
taxation of growing forests, producing, as it does, wasteful

and premature

cutting,

and have attempted to secure a
But the persistent

reduction or remission of such taxes.
belief that the

annual increment of value of such forests

income and should be taxed has hitherto prevailed in
America, with the natural consequence that the owners of
these forests have cut them when they should have allowed
them to grow. In Europe, a longer experience in forestry
has led, in some cases, to a more rational system. " Baden
exempts newly established forests from tax for twenty
years (law of 1886). In Austria they are exempt for
twenty-five years (law of 1869). In France three-fourths
^
Even a
on forest land which will yield no
years, becomes a very serious drain in the

of the land tax

small tax,

when

timber for

fifty

remitted for thirty years."

laid

long run.^

§14
The

which has been exposed is not only a conand earned income; it is also a
confusion between income and capital. To regard "savfallacy

fusion between realized

How

shall Forests

be Taxed? " by Alfred Gaskill, Forestry and

Irrigation, April, 1906, p. 173.
^ Some limitations on
come tax are mentioned

the applications of a theoretically correct inin the Appendix to Chap. XIV, § 3.

EARNINGS AND INCOME

Sec. 14]

income,

ings" as

255

essentially to regard

an increase

But from what has been said it is clear
that he who increases his income must decrease his capital
Capital and income are thus mutuallyto an equal extent.
exclusive.
One cannot receive the whole standard income,
and at the same time secure also an increase of his capital. -'i^^
The truth of this has been instinctively expressed in the
adage, "You cannot eat your cake and have it too."
capital as income.

O We have
and

learned, then, to distinguish between standard

realized income.

Tiie one

The one

that income which,

ideal, the other actual.

if it

were received, would

leave the level of capital- value unchanged

;

the other

that

income which is actually received and detached from capital, no matter whether that capital, as a result, is increased
or decreased. In short, the one is earned, the other realized.
The two may, of course, coincide, in which case capitalvalue remains constant. When they do not coincide, the
discrepancy measures the increase or decrease of capitalThis discrepancy may be partially or wholly done
value.
away with by means of a depreciation fund or other devices whereby realized income, otherwise irregular, is made
But, merely to reckon depreciation is not to proregular.
vide for it. It merely stigmatizes part of realized income
as "coming out of capital," but it does not make good
the loss of capital nor prevent its becoming a part of
realized income.
No more does the mere calling of "savings" by the name of income make it reaHzed as income J\_
These two procedin-es are both attempts to standardize
income in thought when it is not standardized in fact.
We have seen that they represent a confusion both between capital and income and between income which is
merely earned and income which is actually realized, and
*

that they lead to inequitable taxation
to the saver

and remission

— double

taxation

of taxes to the spendthrift.

CHAPTER XV
CAPITAL AND INCOME ACCOUNTS
§

The
ing.

last

two chapters have

their counterpart in accomit-

Correctly kept accounts will

increase of income

show that an abnormal

always at the expense of capital.

the case of a corporation, the distribution
holders of such excessive income

among

the stock-

called ''paying divi-

dends out of capital." It is not necessarily or always
wrong. A Land Company of California has already been
A case at the opposite excited as a legitimate case.
in
which
the dividends are made
one
treme would be
unusually small in order that the capital may be inThere is in New York City a company which
creased.
has never declared any dividends, but has been rolling up
a large surplus for years, and whose stock

much above

for this reason

par.

have already seen in Chapter VIII, that every item
an income account represents the income or outgo from
some item in the capital account. That is, the income account consists merely in a statement of the income and
outgo connected with each item of asset or liability, including that class of assets and liabilities which are alike claims
and obligations, such as leases and employees' contracts.
If the income for each item remains steady or standard, the
relation between the capital and income accounts is very
in

In such a case (supposing the rate of interest to
be 5 per cent), each item in the capital account will constantly stand at twenty times the amount of the corre-

simple.

256

CAPITAL AND INCOME ACCOUNTS

Sec. 2]

257

spending item in the income account. Let us suppose a
factory company operating a plant worth $300,000, which

bonded

for

The remainder, $200,000, will
company If these
and not simply a fictitious book

$100,000.

represent the capital and surplus of the

valuations represent a true
value,

and

the rate of interest be taken at 5 per cent, the

worth $300,000 signifies simply that
$15,000 a year, of which $5000 goes
in interest to the bondholders and $10,000 in dividends
The capital and income accounts of
to the stockholders.
fact that the plant is

its

earning power

such a firm, doing a steady and uninterrupted business,

would repeat themselves

monotonous regularity year

after year.

now we suppose

that the repairs and replacement of

the plant do not occur in equal amounts each year, but that
it is

necessary, at long intervals, to

extraordinary repairs

;

make

diate years "depreciations" of the plant,

torations in

Thus,

its

value

large, special, or

there will occur during the interme-

when

and sudden

res-

these special repairs are made.

suppose that during the year 1900, the factory
by $10,000. The capital account at the begin-

depreciates

ning and end of this year, and the income account during
the year, will be given in the following table
:

Capital Account at Beginning op
Assets

Factory

Year

—

1900

Liabilities

$300,000

Bonds
Capital and surplus

$100,000
200,000

$300,000

Capital Account at End op Year 1900
Assets

Factory

Liabilities

$290,000

Bonds
Capital and surplus

$290,000

$100,000
190,000

$290,000

—
NATURE OF CAPITAL AND INCOME

258

[Chap.

Income Account during Year 1900
Income

Capital Source

Product

Factory

$40,000

Bonds
Capital

Net

Outgo

Running expenses

Interest

$15,000
5,000

$25,000
5,000

and
Dividends

Surplus

$40,000

From

this table

20,000

000

$40,000

see that the factory 5delds $25,000;

worth only $300,000 (on a 5 per cent basis), by the
principles of Chapter XIV, it cannot yield more than
$15,000 without depreciating to the extent of the difas

it is

ference ($10,000); but, instead of setting aside something
for depreciation,

pany

has

i.e.

declared

pay

larger

for future repairs, the

dividends.

Hence,

comcorre-

sponding to the depreciation of $10,000 in the value of the
plant there is an excess of $10,000 above the "standard"
income received by the stockholders. Instead of $10,000,
which is the normal interest on their capital and surplus of

The extra $10,000 above

$200,000, they receive $20,000.

the standard thus corresponds precisely to the depreciation

which accordingly sinks in the course
from $200,000 to $190,000.

of their property,
of the year

During the next year we
yields again $25,000.

Since

of the year, $290,000,

shall
its

suppose that the factory

value was, at the beginning

cannot, on a 5 per cent basis, yield

more than $14,500 without depreciating to the extent of
the difference (in this case $25,000-$ 14,500, or $10,500).
Its value at the end of the year exclusive of improvements
consequently $290,000 -$10,500, or $279,500.
We shall
suppose that the entire depreciation for the two years,

$20,500,

amount.

made good by

extraordinary repairs to that

Since the factory yields only $25,000 and only

$20,000 after the bondholders are paid,

it will

be necessary,

meet the $20,500 of repairs to assess the stockholders $500. The accounts will then stand as follows
in order to

CAPITAL AND INCOME ACCOUNTS

Sec. 3]

Year

Capital Account at Beginning of

259
1901

Liabilities

Assets

Factory

Bonds

S290,000

Capital and surplus

$100,000
190,000

$290,000

Capital Account at End of

Year

1901

Liabilities

Assets

Bonds

$300,000

Factory

Capital and surplus

$100,000
200,000

$300,000

Income Account during Year 1901
Factory

Product

Running

$40,000

ex-

penses
Special repairs
Interest
.

Bonds

Capital and
surplus Assessment

Dividends

500

the repair

bill

$15,000
20,500
5,000

000

$45,500

Had

Net

Outgo

Income

Capital Source

$4500

-5000

500

000

been distributed over the two years,

the dividends to the stockholders, instead of being S20,000
the first year and less than nothing the second, would have

In order to make their income thus
been $10,000 in each.
and "standard" instead of irregular, it is only necesThis accumulates for
sary to employ a special repair fund.
investment,
and is then conseparate
years
as
a
a few
which
meanwhile will
verted back into the plant itself,
have continued its depreciation. We shall assume that this
plan is adopted, beginning with the year 1902, for which the
capital and income accounts will be as follows
stable

—

Capital Account at Beginning op
Assets

Factory

Year

1902

Liabilities

$300,000

Bonds
Capital

$300,000

and surplus

$100,000
200,000
$300,000

260

NATURE OF CAPITAL AND INCOME
Capital Account at End of Year 1902
Assets

Factory

Ldabilities

$290,000

[Chap.

CAPITAL AND INCOME ACCOUNTS

Sec. 3]

Capital Account at End of

Year

Assets

Factory
Repair fund

261

1903

Liabilities

$279,500
20,500

....

Bonds
Capital and surplus

$300,000

$100,000
200,000
$300,000

Income Account during Year 1903
Income

Capital Source

Factory

Product

Repair fund

Interest

$40,000

expenses
received

New
500

Net

Outgo

Running
$15,000

invest-

ment

10,000

$25,000

NATURE OF CAPITAL AND INCOME

262

Capital Account at Beginning op

A sse is
Factory
Repair fund

Year

[Chap.

1904

Liabilities

$279,500
20,500

Bonds
Capital

and surplus

Assets

Factory (exclusive of
impro vemen ^s"!

$100,000
200,000

$300,000

Capital Account at

End of Year

1904

Liabilities

CAPITAL AND INCOME ACCOUNTS

Sec. 5]

263

year does not yield the S25,000 which has regularly appeared as the net income in the previous accounts, for during

we have to charge to the factory the special repairs
The factory itself, therefore, produces a net
deficit of $6500, offset by the large proceeds received from
the sale of the repair fund of $31,500, which, less the new

tliis

year

of $31,500.

investment of $10,000 during the year, shows a net return
We see, therefore, that the existfor the year of $21,500.
ence of the repair fund to cover depreciation virtually
maintains the capital accounts at a constant level, merely
changing from year to year the form of the items, but not
affecting either

the interest of the bondholders or the

In other words, the repair

dividends of the stockholders.

fund acts as a means of standardizing the stockholders'
income. In ordinary business accounting, such standardizing is regarded as sound poHcy.

§5
Certain exceptions occur, as in the case of mining companies or land companies which necessarily must terminate
their operations in the

or less remote future.

But

even in such instances, the instinct of the accountant
toward standard accounting is so strong, that he usually
treats the excess or deficiency of real income with relation
to standard income in a special manner.

Thus, when a company winds up business, the final disis not treated as an ordinary
dividend; the most of these proceeds are regarded as

tribution of the proceeds

capital returned

the stockholders.

The "company"

therefore goes through the form of paying for the shares
of its stockholders and enters what it thus pays over to the

stockholders as a cost of purchase instead of as a dividend.
The reverse operations may occur if at any time the stockholders forego their dividends.

company

usually enlarges

It is in

its capital.

such a way that a
It nominally dis-

tributes the regular dividends, but allows the stockholders

NATURE OF CAPITAL AND INCOME

264

who choose to do so to
new stock certificates.

reinvest

them and

[Chap.

receive in return

§6
From

the foregoing accounts

it is

clear that the theory

and income which has been explained appUes
practically to the accounting ordinarily employed in busiSuch accounting is, in fact, nothing but a method of
ness.
recording the items of income and their capitalization at
A merchant's balance sheet is a
different points of time.
statement of the prospects of his business. Each item in it
represents the discounted value of items which he may
expect later to enter in his income account. Rightly inof capital

terpreted, the capital account merely represents as a whole-

the capitalization of expected items in the income account ;
the fluctuations of the capital account correspond with the
deviations from the standard income in the items of the income

account; and where there are no such fluctuations, every

item of the income account is equal to the standard income
from the corresponding items of the capital account.
There are, of course, numerous practical modifications of this general statement to

be made when actual

was shown in Chapter VIII that
such modifications are due to a variety of circumstances,
accounts are treated.

such, for instance, as the influence of that important ele-

ment, risk; the desire of accountants to maintain their
capital accounts unchanged from year to year; and the
omission from their capital accounts of such two-sided
items as leases, employee-contracts, and the like. But none
of the exigencies of practice militate in the least against our
theory of capital and income accounts. In all cases the
income account simply records the values of the services

and

disservices of articles of property through

period

;

and the

any given

capital account records the present values

of those articles, as resulting at

any given instant from the

expected values of their services and disservices.

CHAPTER XVI
THE RISK ELEMENT

Throughout
sumed the

the three previous chapters,

we have

existence of artificially simple conditions.

as-

have assumed that the entire future history of the capital
in question is definitely known in advance in other words,
The factory which was taken
we have ignored chance.
for illustration was supposed to yield definite future income which could be counted upon as a bondholder counts
upon his interest. In actual practice, however, every factory
or other enterprise offers chances both of gain and loss.
How these chances affect capital-value will be discussed
;

in the present chapter.

We have
pated

seen that capital-value increases as an antici-

installment

income approaches in time, and
is reached and passed.
These

diminishes as that installment

changes in capital-value take place when the future in-

The introduction of the
and even more important changes in capital-value. If we take the history of
the prices of stocks and bonds, we shall find it chiefly to
come

regarded as certain.

element of chance

will bring other

due
than of a record of the
foreknown approach and detachment of income. Few, if
any, future events are entirely free from uncertainty. In
fact, property, by its very definition, is simply the right to
A mine owner takes his
the chance of future' services.
chances as to what the mine will yield; the owner of an
consist of a record of changing estimates of futurity,

what

called chance, rather

orange plantation in Florida takes risks of winter frosts;
265

NATURE OF CAPITAL AND INCOME

266

[Chap.

XVI

the owner of a farm takes risks as to the effect of sun

and rain and other meteorological conditions, as well as
In
risks of the ravages of fire, insects, and other pests.
risk
its
as to
effecbuying an overcoat a man takes some
tiveness in excluding cold, and as to the length of time it
Even what are called
will continue to be serviceable.
In
"gilt-edged" securities are not entirely free from risk.
a sense, therefore, every owner of property is a risk-taker.
Some persons will estimate more highly than others the
risks taken.
From this fact it might seem that there
is a distinction between the actual risk incurred and the
But a little
estimate which individuals put upon it.
this
distinction
is spurious;
consideration will show that
for, by the nature of the case, chance is always an estimate.
Although one man's estimate may
Chance is subjective.
be better than another's through superior knowledge, intuition, or experience, the best estimate is still only an estimate,

In the actual world of events there is no
human opinion, there is no such

not a certainty.

Aside from

uncertainty.

thing as chance.

To an omniscient

being, all things are

certain.

must be admitted that this view of chance is not
familiar to the ordinary man, nor is it universally accepted
by the professed students of chance. Thus, writers like
Dr. Venn, adhering to an objective theory, regard the chance
of an event as the number of times it would occur in the
long run, out of the total series of possible occurrences. But
no matter how long the "run," the number of times the
It

event actually occurs seldom corresponds exactly with the
chance of its occurring. Even in so simple a case as cointossing, 1000 trials will not often give exactly 500 heads

and 500

tails.

the chances of

and only .400

Yet even the " long-run
heads and tails as even.

600 heads

fall

To this objec4.
by the long-run theorists is
not long enough, that heads and tails are

tails,

the odds are not 6 to

tion the only answer offered

that the run

" theorists regard

THE RISK ELEMENT

Sec. 1]

267

equally probable because the longer the trial
the

will the

argue in a

circle.

longer the run the

event approach

its

It is

continued

But they

two tend toward equality.

not necessarily true that

the

closely will the frequency of the

probability.

For example,

it is

possible

that though heads and tails have an equal chance, a run
of heads may keep up for any given number of times,
however long, a million, for instance; or that at first heads
and tails may occur with equal frequency and as the experiment proceeds they may diverge more and more from
such equality. No student of chance, whatever his theory
of the philosophy of chance, would claim that these cases
are impossible. The most that can be said is that they are
extremely improbable. The statement, therefore, that the
longer the run the more closely will the frequency of the
event approach its probability turns out to be ''the longer
the run the more probably will the frequency correspond
to the probability."
This is true as a proposition and it is

known as "BernoulU's Theorem"; but it cannot
be made the basis of a sound definition of probability, for

in fact

probability would be defined in terms of

that the probability of heads coming

itself.
is

It states

the frequency

which heads will probably approximate in the long run
How else than in terms of probability can we formulate
the conditions under which in the long run the coin
"will"

fall

according to

its

probability?

precisely

at this point that the radical difficulty with the "long-

run " theory is seen. It is said that in an athletic contest,
the chance of winning is one half when two wrestlers are
so nearly mated that in the long run "under precisely the
same conditions," each will win in half the contests. If
the conditions are, Hterally speaking, precisely the same,
then the same result will necessarily follow and the same
man will always win. It is only as the conditions vary
slightly from time to time in their unknown elements that
there is a change of winner and the instant the unknown;

NATURE OF CAPITAL AND INCOME

268

[Chap.

XVI

introduced into the problem, the
observer unconsciously shifts his ground from the " long
run " to the true theory of chance.
ness of these elements

Chance is, then, an affair of human knowledge or ignotheory, chance
the ignorance
According to this
not objective, but subjective. Outside of the mind,

—

rance.
is

—

chance has no place. If a man holds a coin in his hand and,
without letting it be seen, asks his neighbor what the
"real" chance is that heads are up, will not the latter reply
one half ? But as a matter of fact the position of the coin
Either heads are up, or tails
is absolutely determinate.
Without changing the
are up; there is no ambiguity.

heads are
he repeats the question, "What is the chance that heads are
up?" Will not the latter still reply, "One half"? To
Mm, in his ignorance about the coin, the chances are
coin, the holder

up.

opens his hand.

Without disclosing

exactly even; but to the

man who

whose eye has seen

it,

sees that

this fact to his neighbor

there

holds the coin and

no uncertainty.

He knows

For him the element of chance has

that heads are up.
vanished because the element of ignorance has vanished.
Chance exists only so far as ignorance exists varies with
different persons according to their comparative ignorance
;

of the

matter under consideration and
;

in fact a

measure

of ignorance.

Of course the actual statistical record may afford an important and sometimes the only basis for our degree of
knowledge and ignorance. Practically it therefore often
happens that we derive our estimate of chances from the
behavior of events "in the long run." It is thus that the
chances of fire, shipwreck, and death are estimated by the
insurance companies.

But while

statistics

supply data

do
and even when they
enter into the problem the insurance examiner does not
He always examines the special
follow them blindly.

for the forming of subjective estimates of chances, they

not, themselves, constitute chances;

THE RISK ELEMENT

Sec. 2]

269

circumstances of each case; and his final estimate of the
chance that a particular building will burn, a particular
ship founder, or a particular person die, is based on all the
data available, among which the data supplied by statistics are

an important but by no means the sole element.
this idea of chance to an economic example,

To apply

What

consider a gold mine.

the chance that

conceals

The ordinary man makes an estimate,
based on his experience or inexperience. The geologist
has additional knowledge and would make a different estia rich lead of ore ?

In actual

mate.

fact,

however, gold

either actually

totally absent.

there in certain definite quantities, or
It is

a coin held in nature's closed hand.

§2
But, in showing that chance

purely a psychological

and not an objective magnitude, we are

from deIn order to
measure chance, it is necessary to state (1) when two
chances are equal or unequal; and (2) when one chance
bears any given ratio to the other.
The chance of one event is said to be equal to the chance
fining chance as a mathematical

of another in the

mind

still

far

magnitude.

of a particular individual,

when

that

individual has no inclination to beheve that one will occur

rather than the other.

the other

when

One

of the chances is said to exceed

the individual

"inclined to believe"

that one event will occur rather than the other.

The

test

two chances is mere indecision of opinion
opinion exactly and evenly balanced.
Next comes the question of the ratio of two chances.

of the equality of

—

When

said that the odds in favor of one event as

compared with another are two to one, the meaning

that out of three equally probable combinations of conditions,

two imply the

Thus,

known

first

there are three

that only one will

event and only one the second.
cards in a hat, of which

draw a

prize, the

chance against

NATURE OF CAPITAL AND INCOME

270

[Chap.

XVI

who draws a card from the hat receiving the prize
two to one; for of the three equally probable drawings,
two are blanks.
In general terms the odds in favor of one event as coma person

pared with another are said to be

m+n
the

equally probable cases in

two events may happen, and among

there are

m cases such that

the

n when

there are

which one or the other

first

these

cases

event would happen,

and n cases such that the second event would happen.
The chance of the first event is then —^ and the chance of
the second is ~. The m and the n cases are, it should
be noted, assumed to be mutually exclusive.^
Probability is thus not merely an affair of pure mathematics, as

of concrete

so often imagined.

human

estimate.

What

is, first

all,

a matter

are called the mathe-

matics of probability apply only to arrays of equally probable combinations,

and

consist in calculating the

number

these which are favorable or unfavorable to a given event.
of probability never estabhsh a probbut always rest on some human estimate
Like every other
of chances which are equal to start with.
branch of applied mathematics, it must depend on having

The mathematics
abihty of

itself,

raw material supplied from without. By mathematics
we seem to discover that the chance of throwing double
But this calculasixes with two dice is one in thirty-six.
tion rests on the hypothesis that, in some person's estimation, each die is equally liable to fall on any one of
its

its six faces.

show that

Starting with this assumption,

in throwing

two dice there are

it is

easy to

thirty-six equally

^ It often happens that we cannot divide the field of probability
In such a case the mind is
into separate cases all equally probable.
For instance, the probability of an
forced to make an estimate.
event may be said to be one third against the field if the estimator's
state of opinion toward the field is exactly similar to his state of

mind toward another
combinations

If the state of mind is similar but less definite, then the chance
" about " one third but not definite.

tion.
is

which the division into three separate
and one of them favors the event in ques-

field in

is possible

THE RISK ELEMENT

Sec. 3]

271

probable cases and that only one of these will give double
sixes.

Mathematics could not obtain the

result

unaided

by experience. All that mathematics accomphshed with
the dice was to derive a result from the assumed conWhether these
ditions of two sets of six equal chances.
assumed conditions existed was a question, not of mathematics, but of concrete opinion.

If the dice

were known to

be "loaded," the case would be materially altered.

§3
C'Lln order to apply
of capital,

this theory of

we observe

chance to the valuation

that both the future rate of interest

and the future items of income are uncertain. In the problem of capital-valuation, however, the uncertainty in the
rate of interest does not always enter, for only present
and not future rates are employed at the time at which
the valuation of the capital is made.
When we call a rate
a " present " rate we mean, of course, that the contract
or estimate to which it relates is a present contract or
estimate.^; The very fact of valuation implies a known
rate or rates at which the valuer is contrasting present
and future goods. There may be several " present " rates.
if the " present " be the year 1906, we may imagine
a whole series of rates of interest holding true in 1906 for
such a man for instance, 4 per cent for a 1-year contract,

Thus

;

6 per cent for a 5-year contract, and 5 per cent for a 15-

moment. All
and known and hold true in the
year 1906, but they do not determine the rates which
year contract,

all

originating at the present

of these rates are fixed

will

hold true for the contracts or estimates of 1907 or

1914.

In valuing

capital, therefore, it is not necessary to regard

the rate of interest as uncertain except

question

when the

rate in

a future rate.

Let us suppose that in Figure 10 the income AB is
due at the end of the time FA, and that the rate of interest

NATURE OF CAPITAL AND INCOME

272
is

[Chap.

XVI

such as to produce the discount curve BE.

ent value of

may

AB is

FE.

not follow the line

of interest unchanged.

G, the valuation of

Then the presBut the future valuations of AB
EB as they would were the rate
Thus, at a

midway

AB may be only GD,

point of time,

found by means of

a higher rate of interest involving the steeper discount curve
The history of the value of the property, namely,
the right to AB, therefore follows the broken line ECDB^
abruptly changing from GC to GD, if we suppose G to be

DB.

--^^^=^^^^

Fig. 10.

the point at which the rate of interest changes unexpectedly

from one

level to the other.

foreseen at the start that

Had the owner of the property
the point G was reached

when

the rate of interest would be higher, he would have taken

account in valuing the property at the moment
F, and the value would have been FE% found by using the
this fact into

discount curve BDE'. This curve has a slight angle at D,
being composed of the curve BD, constructed according to
the high rate of interest prevailing at the time G, and the

curve DE,' constructed according to the lower rate of interest which applies to the period FG and which was employed in the curve EC. The essential fact, therefore, is
that because of the failure to foresee the future rise in the

THE RISK ELEMENT

Sec. 4]

rate of interest, the value of the property

273
is

FE, instead

FE', and that the value of the capital will fall, as at CD,
or it may be rise, in accordance with successive future adjustments in the rate of interest. Since these readjust-

ments are usually small and gradual, fluctuations in the
capital-value will not ordinarily be as great or as abrupt

as here represented, but the principle involved will

hold

true.

see,

therefore,

new cause

for

still

the

fluctuations in capital-value, namely, unforeseen changes
in

the rate of interest.

§4

There is, however, a more fundamental way in which a
change in the rate of interest enters into our calculations,
for it will affect the magnitude of the future income items
themselves. In the above example it was assumed that
the income items were not dependent on the rate of interest.
But it often happens that the income items are not elements
of what in Chapter VIII we called "final income," but are
"interactions";

or, in

practical language,

often

happens that the income is to be reinvested. In this case
such an item cancels itself out and leaves in its place a
series of income items in the future, and the magnitude of
the income items in this later series will depend on the rate
of interest at which the preliminary "interaction" was reinvested. If the intention in advance is to reinvest, it
becomes important not simply to know the present rate
This enters
of interest, but to forecast the future rate.
into the calculations of an investor who holds a 25-year

bond
ment

at 5 per cent.

will usually

regard the final pay-

when

it becomes due
be reinvested in a similar 25-year bond. He, therefore, is not really buying a 25-year income stream of 15
a year plus $100 at the end of the term, but is buying, let

as "principal," intending that

shall

us say, a SO-year income stream consisting of $5 per year
for the first 25 years and an unknown amount per year dur-

NATURE OF CAPITAL AND INCOME

274

[Chap.

XVI

In order to forecast what income
be received in the second period, he has to forecast
the rate of interest. In other words, although the bond represents nominally a fixed and certain series of income items,
yet, in view of the intention to reinvest, it actually repre-

ing the second 25 years.
will

which is quite uncertain after 25 years, .
because of the uncertainty in the future rate of interestyC.
Such an investor, if he expected the rate of interest at the
sents an income

end of 25 years to be 2 per cent, would, in purchasing the
above-mentioned bond, be getting %5 a year for 25 years
and $2 a year for the next 25 years. Under these conofitions, if he could buy a 50-year bond at 4 per cent, he would
prefer to do so.
But, if he expected the rate of interest to
remain, for each 25-year period, at 5 per cent, he would prefer, rather than invest now in a 50-year bond at 4 per cent,
to invest in the 25-year

bond

at 5 per cent, intending to

reinvest at 5 per cent at the expiration of the term.
forecast of

what the

His

rate of interest will be in 25 years will

thus materially affect the choice of his investments to-day.

Those who expect the rate of interest to

fall will

prefer to

invest in long-time securities at the present market rates,

even when those rates are
time, while those

who

less

than on securities of shorter

expect the rate of interest to rise will

prefer short-time securities.

In the case of insurance com-

panies which are constantly reinvesting, a change in the
rate of interest

becomes a very serious matter.

the actuaries of a large

company has

One

recently pointed out

that such changes in the rate of interest are not

uncommonly

encountered and are more important for the prosperity
of the

company than

tality tables.

the most unusual changes in the mor-

Insurance companies can only roughly take

account of the chances, reckoning that the greater the
Hkelihood of a rise, the better the policy of making temporary investments at high rates; and the greater the
Hkelihood of a

fall,

the

better

the

policy of

permanent investments, even at moderately low

making

rates.

THE RISK ELEMENT

Sec. 5]

275

§5
The main

to capital valuation

application of risk

however, not to the rate of interest, but to the
items

themselves.

is,

income

we now address

this application

Let us begin by considering the case in which
is wholly absent.
The simplest
case is that of ordinary gambling. If one invests in a
lottery ticket where there is one chance in ten of drawing
a fyize of $50, it is evident that the price of the ticket
must be considerably less than $50, which is the income
it may yield.
Mathematicians have called the product
ourselves.

the element of discounting

of the prize multiplied

probability, the

its

''math-

In the present instance
this "mathematical value" will be $50 x -^^^ or $5.
If a professional gambler should always pay the mathematical value of the chances, he would, in the long run,
probably come out about even, as is well known from
"Bernoulh's Theorem." Thus, if he continued to try for
such $50 prizes, paying each time $5, he would probably
win about one time in ten. In a thousand trials, therefore, he might expect to win 100 times, spending $5 each
for his 1000 tickets, or $5000, and receiving $50 each for
ematical value" of the chance.

his 100 prizes, or $5000.

But the actual

price

which one

will

pay

the mathematical value of the chance.
it is

The gambler

usually lower.

not necessarily

may

be higher

usually a person

;

who

pay more than the mathematical value of the chance.
At Monte Carlo, the "bank" makes its profit in this way,

will

although

its

know

victims

full

well that they are paying

more than the mathematical value
consequence, of course,
nately, persons

who

pay even the
is

The

Fortu-

gamble are in most comThe ordinary man is unwilhng

deliberately

munities in the minority.
to

of their chances.

ruin to most of them.

full

mathematical value of the chance.

reluctant to assume

any

risks,

and

is,

on the

NATURE OF CAPITAL AND INCOME

276

contrary, willing to

Where

of them.

make

[Chap.

XVI

sacrifices in order to rid himself

the gambler would be willing to pay

than $5 for his lottery tickets, the cautious investor would
only be induced to buy such tickets for considerably less
than S5. To him, the chance of gain is outweighed by the
prospect of loss. Rather than risk little in order to obtain
large gains, he prefers to sacrifice much in order to avoid
It is this sentiment which gives rise to
large losses.
the

phenomenon

of insurance.

§6
There are three values which apply to an uncertain
(1) the value which that return would have if the
uncertainty could be eliminated, or its riskless value;
(2) the value which would be attached to it if the investor
were willing to pay the product of the income by the chance

return

of obtaining

which he

Thus

the

holder

it,

or the mathematical value

case

the

chance of

the

(3)

the value
the

lottery ticket, entitling

SlOO,

$100; the mathematical value
cial

;

actually willing to pay, or the commercial value.

value

the

riskless

$5;

and the commer-

more than S5 for the reckless, less for the
ordinary caution, and just $5 for those of an

value,

man

intermediate temperament.

The ratio of the mathematical to the riskless value may
be called the " coefficient of probability." In the supposed
case of the lottery ticket this coefficient

is -^^q.

The

—

ratio

a ratio
of the commercial to the mathematical value
of
the inwhich will vary according to the temperament
may be called the "coefficient of caution."
dividual
In the case of a man who values his chance at $4, this coeffiGiven these ratios, we can for a given
cient would be f
individual derive the commercial value from the riskless

—

value by multiplying the riskless value by the coefficient
of probability

and the result by the coefficient of caution,
X I = $4. The product of these two ratios

thus $ 100 X if
:

-g-

THE RISK ELEMENT

Sec. 7]

the

ratio

the

commercial

277
the riskless value

(loo"^
To^o) ^^'^ ™^y t>^ called the coefficient of risk}
The coefficient of caution expresses a feature of individ-

by nature and partly
by environment. In times like the colonial period when
lotteries were common, or in places like Monte Carlo, where
ual character as determined partly

gamblers congregate, the coefficient of caution is such as to
represent an abnormal lack of caution.
The opposite
extreme is found in the timid investor who hoards money
rather than risk its investment in any form. The coefficient
of caution also varies with the same individual under
different

circumstances.

Chief

among

these varying cir-

cumstances, as Professor Norton has pointed out,

amount of capital of which the individual
The more capital a man possesses, the less
of serious loss in

reason a rich

The

any enterprise involving

man

finds

the

possessed.

his chance

and for this
grow still richer.
millions where the poor
risk

;

possible to

rich can well afford to lose

There is less likeliUnited States Steel Corporation from its
projected investment of $75,000,000 to found a new steelproducing city than there would be to a workingman
who makes a " safe " investment of $1000.
could barely afford to lose hundreds.

hood

of ruin to the

§7

are

now

in a position to apply these principles of

probability to the valuation of capital,
tion of uncertain income.

i.e.

to the capitaliza-

The most important

classifica-

tion of investments from a practical point of view

two categories

of safe

and unsafe investments.

into

But even

in so-called safe investments the element of risk enters.

As between bonds and stocks, the latter usually represent
the precarious and the former the safe investments; yet
in the case of bonds, the receipt of interest and principal
is always in some degree a matter of uncertainty.
^

For a mathematical statement, see Appendix to Chap. XVI,

§ 1.

NATURE OF CAPITAL AND INCOME

278

[Chap.

XVI

Take, for example, a "5 per cent" bond running for
10 years. Let us assume that the market rate of mterest
4 per cent, in the sense that $100 at any time will exchange

$104 certain one year

for

the bond ought to
is,

sell for

an investor buying

in 10 years

this

"make" 4

Under these

later.

bond

at a

premium

That

of $8 will

per cent provided he receives

The $108

the sums stipulated.

conditions,

$108 (see Chapter XIII).

all

the ''riskless value"

of the bond.

But, while $108 would be the price of the bond were the
investor absolutely sure of the income items to which
entitles

instance,

pa3Tiient

him, he
that
is

may

that

-^q,

there

any

which event

it is

probability

the

only

feel

risk,

given

— for

interest

evident that he

We can easily calculate, on the
assumed probability, that what has been
called the "mathematical value" of the bond would be
This figure is found by multiplying each income
$97.
item by its coefficient of probability and discountingthe result at the market rate of interest, 4 per cent.
We assume here that the risk attached to each individual interest and principal payment is independent of
that attached to all the others. The probability of receiving each payment is -^q, and the risk of its not being received
is in each case -^q. It is evident that the first payment of $5,
due in one year, has at that time a mathematical value of
5 X -^Q, and the present value, when discounted at 4 per cent,,
would be ^^. If the same expressions be obtained for all
the other items of income, and the sum total of the present
will

not pay $108.

basis of the

valuations be found,

it is

evident that in the result the factor

appear for every individual sum, and that the total
will simply be -^-^ as much as though the element of risk were
In other words, the "mathematical value" of
absent.
the bond will be -^^ of its riskless value of $108, or about
j-^o

will

)7.

But the actual "commercial value"

of the

bond

will

THE RISK ELEMENT

Sec. 8]

279

ordinarily be less than this "mathematical value" of $97.

We may

suppose it to be $92.50, indicating a coefficient of
caution of ^"Here, as in the case of the lottery ticket,

we have regarded the actual value of the bond as obtained
from its riskless value by applying first the probability
factor, and second the caution factor, ^.
If the probabilities of receiving

the individual interest

pajnnents were not regarded as independent, the calcula-

would

tions of the mathematical value

from the preceding.

Thus,

differ

somewhat

suppose that default in

one interest payment carried with

it,

by the terms

of the

contract, the default in all subsequent interest payments,

we should have to apply the theory of probability somewhat differently^ but the principle would be the same.

§8
There

another way, and one which conforms more to

ordinary usage, in which the commercial value of the bond

may be derived from

While the price of
the riskless value.
vary inversely with the risk, the rate of
interest varies directly with the risk so that as the value
the

bond

will

;

bond descends, the corresponding rate of interest
Thus we have riskless, mathematical, and
will ascend.
4 per cent, 5.4 per cent, and
commercial rates of interest

of the

cent — corresponding

—

respectively with the
6 per
mathematical, and commercial values of the bond

riskless,

— $108,

$97, $92.50.

The question sometimes
risk thus raises the basis

the 6 per cent
tion

arises, where the element of
on which the bond is sold, whether

a true "rate of interest."

purely one of definition.

Were

The queswould

possible, it

be simpler to confine the application of the phrase " rate of
interest" to an exchange between present and future riskless income.
But in this case, it is always exceedingly diffi^

For the consideration of

this case, see

Appendix to Chap. XVI,

§ 2.

NATURE OF CAPITAL AND INCOME

280
cult to state

what the

riskless rate of interest

[Chap.

since

is,

shght risk attaches to almost every investment.
ingly

it is

all

when

some

Accord-

usual to regard the commercial rate as a true

The best

"rate of interest."
nize

XVI

three as rates of

necessary,

course, therefore,

interest,

to recog-

distinguishing them,

"mathematical,"

"riskless,"

and

"commercial."

§9

When we
we

intend

speak of the riskless value or the riskless rate,

by the employment

the

word

"riskless,''

from consideration the chance element entirely
risk of receiving less, but also the chance of
For cases are
receiving more than the specified income.
not wanting in which the mathematical and commercial
to exclude

— not only the

values of a security are,

by reason

of the chance that it

prove extra-profitable, more than its riskless value.
Take, for mstance, a $100 share of preferred stock, on
which a minimum income of 5 per cent, or $5, is assured.
will

If the true rate of interest

stock should be $125.

be 4 per cent, the value of such

This

the "riskless" value.

The

mathematical value, however, wUl be greater, say $150,
inasmuch as there is a probabiUty that the holder will
receive more than $5 a year, and practically no probAnd the commercial value
ability that he will receive less.
wUl be still different, falling, by reason of the caution of
the investor, somewhat below the mathematical, say to

Another instance
bonds.

that of United States government

The national banks which

invest in these receive,

besides the interest, a special privilege in the form of per-

mission to issue bank notes.

This additional benefit

may

be regarded as a species of additional income, and materially

For this reason,
of the bonds.
United States government bonds are not used for
investment purposes, except among those in whom the eleenhances the value

THE RISK ELEMENT

Sec. 10]

ment

caution

281

unduly strong, but are held for the

most part by national banks. It is therefore misleading
to cite, as some have done, the rates of interest realized
on government bonds as an indication of the true rate of
interest.
A similar benefit attaches to the bonds of the
These are sold on a very low
Credit Foncier in France.
" basis " because of the chance,

winning

connected with them, of

prizes.
§

In the general case we have to do not simply with the
risk of falling below a specified income, nor with the
chance of rising above a specified income, but with both.
Thus, the dividends from common stock have no fixed
minimum as do those from good preferred stock, nor any
fixed maximum as do the interest payments from bonds.

They may vary, and vary widely, in either direction. The
amount of variation may be measured with reference to any
specified amount selected arbitrarily as a basis of comparison.
yielded,
5,

For instance, in the case of stock which has
in successive years,
5,

5,'

the
4,

following percentages:

we may

for

take 5 per cent to serve for a basis of

ience

conven-

computa-

The stock has yielded 1 per cent or more in excess
it has yielded 2 per cent
of this in two cases out of twelve
in excess in one case out of twelve; it has fallen short by
1 per cent or more in three cases out of twelve, and fallen
short by 2 per cent in one case out of twelve. If these fretion.

;

quencies are our only guide for judging the future, they
represent the probabilities of receiving the respective dividends.

the basis of the foregoing figures

late the "riskless"

stock, and,

calculate the

it is

possible to calcu-

and the ''mathematical" value

we know

the caution factor,

"commercial" value

also.

it is

of the

possible to

Thus, the "risk-

less" value, in this case, signifies that value

which the stock

NATURE OF CAPITAL AND INCOME

282

[Chap.

XVI

would have if it were certain to yield the ( arbitrarilynever more and never less.
assumed) 5 per cent forever
The riskless value is therefore simply the capitalized value

—

of a perpetual annuity of $5 per share of $100 face value.
If the rate of interest is

4 per cent, the result

$5 divided

by 4 per cent, or $125.
To obtain the "mathematical" value we simply add

the riskless value the value of the chance of getting more,
and subtract that of the chance of getting less. The
is found by expetwo in twelve, or ^ each

chance of getting an additional $1 a year
rience, as set forth above, to be

year.

The present value

of the right to this chance

has

therefore a mathematical value ^ as great as though the $1
increment were a certainty. But the certainty of $1 a

year would be worth $25. Hence a chance of 1 in 6 of
getting $1 a year would be worth mathematically ^ of $25,
In like manner the chance of a second addior $4.16f
.

one in twelve and is worth (mathematically)
These two terms, $4.16f and $2.08^,
are the additive terms sought. The subtractive terms are
the mathematical value of the chance of getting $1 less
than the $5, and of getting still another $1 less. These
tional dollar

jL of $25, or $2.08^.

chances, being 3 in 12 and 1 in 12 respectively, are worth
-^^ of $25 and ^V of $25 respectively, or $6.25 and $2.08^.

The whole mathematical value

the factor of caution, which, let us say,

The

commercial value to be $110.63.
thus, approximately:

—

" riskless " value
" mathematical " value
" commercial " value

In this manner we
other case.

$125+

therefore

$2.081)- ($6.25 + $2,081), or $122.91f.

($4.16§

Applying to
is

^^o,

this

find the

three values are

S125
$123
$111

may compute

the three values in any

Usually, however, the chances involved are so

indefinite that the reckoning is

made

only by rule of thumb.

THE RISK ELEMENT

Sec. 11]

Any

283

further attempt to apply the theory of

would therefore outrun the exigencies

probabiUty

of practice/

§11
The

practical investor, in order to estimate the influence

of probability, attempts to forecast as nearly as possible all

the elements which

may

affect his interests.

An example

Mining Journal for Decemmine at Cananea,
the Green Consolidated Copper Company, was

occurs in the Engineering and

ber

1904.

belonging to

there stated that the

worth, according to quotations at that time, $30,000,000.

This valuation the journal shows might be justified

suppose the mine to contain a total of 1,040,000,000 pounds
of copper which can be mined at the rate of 104,000,000
a year for 10 years, and if we suppose that the price of copper will be 14 cents, and the cost of production 8 cents, to

which should be added the expense
mission, etc.,

making

we make allowance

of refining, selling,

2^ cents more, or 10| cents in

we should

all.

may be called
pound. On this

for future economies, this

10 cents, leaving a net profit of 4 cents a
basis

com-

obtain a 10-year annuity of $4,160,000 per

annum, the present value of which, at 5 per cent, would be
$32,000,000. But inasmuch as these forecasts involve
great uncertainty, a fair price would be regarded as $30,000,000, the discrepancy between $30,000,000 and $32,000,000 being due to the element of risk, i.e. the combined inThis price represents
fluence of probability and caution.
a basis of

6|-

per cent.^

Nevertheless it is more than conceivable that the time may come
pi'actical brokers will make use of probability computations in
the same way that they now make use of bond tables. The writer's
For a brief
colleague, Professor Norton, has shown this possibility.
statement, see Appendix to Chap. XVI, § 3.
^ For such properties as mines which rapidly depreciate, brokers
^

when

often reckon the "basis" in a somewhat different manner, computing
the percentage realized to the investor on the supposition that he
employs a depreciation fund and reinvests, not at the 6i per cent just

NATURE OF CAPITAL AND INCOME

284

In forecasting the income from
sary to forecast
it

and

their variability.

also

times exceedingly numerous.

XVI

capital, it is thus neces-

the elements which

all

[Chap.

may

influence

These elements are someA stockholder in a railroad,

in order to obtain a true idea of the value of his property,

must look forward
can be charged
volving the

to the traffic of the road, the price

amount

and

of labor, fuel,

paid for these items,
volves, in turn,

which

for this traffic, the cost of operation, in-

etc.

materials, the prices

forecast

some knowledge

any one

of these in-

of outside conditions, as

the outlook for crops, prices of agricultural products, probabilities of increased trade

through connecting lines, increased

population, possible competition, possible ad-

density of

verse legislation, etc.

§12

We now

see that the value of capital actually changes

through any one of four causes:
of discount ;

that

is,

(1)

while no income

Through the

effect

being received, the

value of the capital will rise along a discount curve. (2)
Through the periodic detachment of income; that is, at

when income or outgo occurs, the capital will be
by the amount of the income and increased by the amount of the outgo reached and passed.

times

directly decreased

(3)

Through unexpected changes

in the rate of interest;

that is, when such changes occur causing revaluations of the
future by discounting it at a new rate, the value of the
capital will change correspondingly
of interest falls,

and decreasing

— increasing
it rises.

(4)

the rate

Through

unforeseen changes in expected income.

The fourth cause

the one of most practical importance.

mentioned, but at the true or safe rate of interest, 5 per cent. On
this calculation the investor would be found to make 10 per cent per
annum in addition to the amount set aside for depreciation at 5 per
For the case just
cent, and the "basis" would be called 10 per cent.
mentioned, this 10 per cent realized, with the depreciation fund reinvested at 5 per cent, is equivalent to 6^ per cent realized, with a
reinvestment at 6A per cent.

285

THE RISK ELEMENT

Sec. 12]

The market quotations for any product are constantlybeing changed and revised, not so much through the opera-

—

tion of the first three principles as through the fourth
the constantly changing outlook into the future. Every

rumor as to crops, every storm or pest which is known to
have destroyed them, changes the expectation of future income. Since the third and fourth causes are both due to
lack of foresight, they may be included, if desired, under
the

common head

of ''risk."

In Figure 11 the operation of these four causes is represented as occurring successively in the order enumerated.

The

capital-value

first rises

along the discount curve

AB,

constructed according to a particular rate of interest.
first income coupon, so to speak, BC, is detached,

When the
the value

falls to

C, after which

travels again along the

suddenly when a certain
expected cost DE has been gotten rid of, then following EF
again, whereupon, in consequence of a sudden and unexpected
rise in the rate of interest, it falls to G, after which it ascends
discount

curve

CD,

rising

according to the steeper discount curve

GH, and

then, in

consequence of a change in the estimate of future income,
falls again to /, after which it proceeds along another disThe changes
count curve to /, and so on indefinitely.
caused by actual income and outgo, we here represent by
the continuous lines BC, DE, etc., and the changes due to

a revised estimate of interest and of income we represent by
the dotted lines FG, HI, etc.

NATURE OF CAPITAL AND INCOME

286

[Chap,

XVI

§13
The discount curves just employed are assumed to be the
same as those employed formerly in the discussion of certain
But, as a matter of fact, chance will
even on discount curves. For the increase of
capital- value along a discount curve is due to the approach
of expected income, and this approach, in the case of uncertain income, is quite different from what it is in the case of

prospective income.

have an

effect

owner has a conviction
nearing the time when income will be received,

certain income.

that he

It is only as the

that the capital- value will increase at
of dividends for the declaration of

nitely appointed times; but

This will be true
which there are defi-

all.

the times for the install-

income are wholly fortuitous, the capital-value
will not increase and instead of a discount curve, we
shall have a horizontal line.
If a piano dealer is asked
to value a particular piano in his stock, he will not add
interest because it had been in his stock a long time.
It is impossible for him to say which individual piano will
be sold next, and the mere fact that a particular piano has
stood for a long time in his store will offer no assurance that
it will be sold earlier than the others.
Therefore the value of
the piano will not advance with time, but will remain nearly
at the wholesale price. In the same way, a stock of money
which a man carries as cash does not advance in value by
lying in his pocket. For although the services which it will
render to its owner are actually approaching, their exact
time of occurrence is not known, but is subject to chance.
It is chiefly in the case of bonds and stocks, where there

ments

are definite times for the occurrence of income, that the

actual value ascends strictly along

the discount curve.

In the case of shares of stock if the stockholder fears that
a dividend will be small, the value of the stock will only
slowly increase as the time for the dividend approaches.
It will follow a discount curve, but one which climbs toward

Sec. 13]

THE RISK ELEMENT

287

—

enough to represent the commercial
only a slight elevation
value of the uncertain dividend. Then when the amount
of the dividend is known, just before it is distributed, the
stock (including

the

right to

the impending dividend)

suddenly jump in value. After the dividend is paid,
will again descend and then increase slowly in value until

will
it

This will explain the
been
observed,
that the value
fact which has sometimes
of a dividend-paying stock often remains fairly constant.
Normally its course will be somewhat as in Figure 12.
The capital- value increases only slowly from A to B, when,
with the declaration of a dividend, it immediately jumps
to C, and with the distribution of the dividend at D
the approach of the next dividend.

Fig. 12.

If we omit the
descends to E, and so on indefinitely.
fluctuations between the declarations of dividends and the
distributions, the course of the stock remains relatively

horizontal, as represented

by AB, EF,

IJ.

§14
The introduction of the element of chance does not greatly
bookkeeping except to impair somewhat the correspondence between capital accounts and income accounts.
This is occasioned by mere changes in the size of the
affect

capital items.

new

When

revision of capital- value

estimate of future income, as after a

or other calamity, the immediate result

fire,

due to a

shipwreck,

merely to reduce

The
(or, it may be, to increase) the value of the assets.
and
assets,
the
accountant must "write down" (or up)

—

;

NATURE OF CAPITAL AND INCOME

288

;

[Chap.

XVI

therefore also reduce the balancing item on the other side,
called undivided profits, or profit

account

and

the future

may

lead

But the income
new outlook toward

loss.

not affected except as the

new expenses

for reconstruction,

new income.

or to

§15
Business men try not only to estimate the risks which
they must encounter and to adjust their accounts accordingly, but they also endeavor to avoid such risks altogether.
This follows from the existence of the factor of caution.
Where the coefficient of caution is abnormal, amounting to
tncaution, risks are not avoided, but are expressly sought,
and the phenomena of gambling and indiscriminate specuBut in the great majority of men there
lation are the result.
exists a healthy fear of risks, and in consequence a tendency
to avoid or reduce them.
There are five principal ways in which risks may be reduced,
1.

tracts
2.
3.

viz.

increasing guaranties for the performance of con-

;

By
By

increasing safeguards against incurring losses

By
By

insurance, that

increasing foresight

and thereby diminishing the

risks
4.
.

is,

by consolidating

risks

throwing risks into the hands of a special class

of speculators.

These

will

be considered in order.

§16
The ownership

capital wealth

the income from

necessarily involves

—

never
can only be estimated,
precisely foreknown.
But it is possible, by a division of
the ownership of capital wealth, for one class of property

risk, since

holders to assume the burden of risks and to guarantee to

another class a fixed income.

This

the primary reason

THE RISK ELEMENT

Sec. 16]

289

two great classes called
and bonds. In any large enterprise the stockholders
take the risks, and by so doing guarantee to the bondholders a fixed income. As was remarked in a previous
chapter, the capital stock acts as a buffer between the liabilities and the assets, which amounts to saying that it guaranPresitees a fixed income to the holders of the liabilities.
dent Hadley has emphasized the fact that a bondholder
"commutes" the precarious income of an enterprise into
a fixed annuity and that the system by which one class receives "interest" and another "profits" has its origin in the
desire of one class to avoid and the willingness of another
to assume risks.
Nevertheless the general relation between creditor and
debtor necessarily carries with it a certain amount of risk to
This risk may be reduced by the deposit of
the creditor.
collateral security or endorsement ^ as in the case of bank
loans and discounts; by mortgage on real estate, or occasionally on chattels; by legal regulations, as in the case
of notes of national banks, and by other methods.
for the separation of securities into

stocks

§17
The method
risks rather

of guaranties'

method of shifting
The second method

really a

than of avoiding them.

aims to reduce risk by special safeguards.

Some

articles

But the "rate of commutation" is not a rate of interest, since
commutation is necessarily a ratio between two incomes,
those respectively of the stockholders and the bondholders, whereas
^

any

ratio of

the rate of interest

a ratio of income to capital.

The influence of endorsement in reducing risk is greater than
would appear on the surface. Thus, if there is one chance in a hundred that the signer of a note will default, and a like chance for his
endorser, both these risks being independent, the chance that the bank
'

is the product of these two, or only one chance in ten thouHence, two-name commercial paper is ordinarily a safe se-

will lose

sand.

curity, provided, of course, the

names are those

of reliable business

men, such as have a high "rating" in Bradstreet's or other standard
commercial agency.

NATURE OF CAPITAL AND INCOME

290
of wealth

exist,

ing sudden

XVI

simply for the sake of meet-

fact,

unforeseen

[Chap.

emergencies.

instance, of fire engines, fire

This

true,

for

extinguishers, safety appliances

on railways, safety valves, and other devices connected
with steam engines and machinery, burglar alarms, safety
deposit vaults, etc.

To a

large extent this risk-meeting

function appUes to almost every stock of wealth.
in

pantry

usually

exists

beyond

certain

order to provide for uncertain wants, and

Food

wants

when

sources

need to be large.
Again, a
both of
will
usually
have
large
reserve
stock,
factory
a
raw materials and finished products, in order to meet unexpected demands. In like manner, jobbers, wholesalers,
and retailers maintain a sufficient stock of goods to meet
not only the foreseen, but some of the unforeseen demands
of supply are distant, such stores of food

Especially

this true in the case of

of their customers.

The function

armies.

of speculators in grain or

other commodities consists largely in conserving the stock
of a community as a safeguard against future scarcity.
Almost all of what is called the reserve of a bank is used as a
safety fund to meet the unforeseen demands of note-holders
and depositors, and, in particular, to meet a special "run."
These reserves often remain as idle as a fire extinguisher for
years or even decades against the hour of need. It is said
that there are bars of precious metals in the Bank of England
which have lain there undisturbed for two centuries. A
large part of the cash carried by an ordinary individual is
quite analogous to a bank reserve, being held to meet special
Some individuals even keep in a separate
emergencies.
pocket a special gold piece, lest some day they should become

"stranded."

may be

said that this risk-meeting function

of pocket cash is the chief

compensation for the so-called

"loss of interest" on the

money thus

carried.

The con-

venience and security obtained by having an adequate

supply is a species of income replacing the income which
might be earned were the sum invested. The same prin-

THE RISK ELEMENT

Sec. 18]

291

from the standpoint of an individual, apply to bank
deposits, and thus to the whole volume of the circulating
medium.
ciples,

§18
The

method

third

knowledge.

of reducing risks is

It has been seen that risk

increasing

nothing but an

expression of ignorance, and decreases with the progress
of science.

being

may

made

be said that the chief progress

industrially consists in lifting the veil

hides the future.

now

which

The countless trade journals now

use have their special

reason for existence in enabling

by supplying
them with data as to past and present conditions, as well
as by instructing them in the relations of cause and effect.
The government reports of crops, the technical schools
and agricultural colleges, all tend in the same direction.
Whereas formerly the mine prospector could only guess
wildly at the ore "in sight" and the time and cost
required to mine it, the graduate of mining schools is
now able, through knowledge of geology and metallurgy, to
bring these forecasts into some degree of scientific accuracy.
And, whereas until recently farming was one of the most
imcertain of occupations, it is to-day
thanks to modern
their readers better to forecast the future,

— almost

—

not quite as amenable
to prediction as industry or commerce.
scientific

agriculture

§19

We
and

come now

that important

shifting risks, called insurance.

means

avoiding

Insurance involves

by another; that is, the consolinumber of chances whereby relative cer-

the offsetting of one risk

dation of a large
tainty

is,

illustrate

were, manufactured out of

this, let

uncertainty.

us suppose that 10,000 houses of

the same kind are too distant from each other to be de-

stroyed by the same

fire,

and

let

us suppose that these

NATURE OF CAPITAL AND INCOME

292

[Chap.

XVI

houses in the average would be worth $10,000 each were it
not for the risk of fire; in other words, that $10,000 is the
capitalized value of the services to be rendered by each
house, assuming that

value of

the

lives

total

number

This

$100,000,000.

out
of

its

natural

The

life.

houses would then be

the " riskless value."

the

which the 10,000 houses
were there no loss by fire. If interest is
the income which is thus capitalized is

capitalized value of the income

would bring

in,

at 5 per cent,

$5,000,000 a year.

now we suppose

that the annual

one chance in 200, there will be about 50
houses annually burned. Reckoning the value thus destroyed at an average of $10,000 for each house, there
risk of fire is

be $500,000 annually lost by fire. We must now dethis from the $5,000,000, which would be the
We have left $4,500,000,
income were it not for fires.
In
only $90,000,000.
which
is
of
the capitalization
houses
is
of
property
10,000
other words, the total
instead
of
worth in "mathematical value" $90,000,000
$100,000,000, the reduction being because of the prospect
If we suppose all of these houses to be owned by
of fires.
one corporation, this mathematical value of $90,000,000
might also be the actual value, for such a corporation
could count on about 50 houses burning annually almost
Each house would then be worth, on an
as a certainty.
will

duct

average, $9000.

But

such an individual house

owned

by an individual person, this mathematical value would
not be its " commercial value," on account of the element
Let us say that the caution coefficient is |, in
of caution.
which case the house would be worth $7000. In other
words, we have $10,000 as the "riskless" value of the
house, $9000 as its "mathematical" value, and $7000 as
its actual "commercial" value, assuming that there is not
as yet insurance. Now if the owner of such a house could
secure insurance on a purely mathematical basis of the
risk, which, as we have seen, is one half of one per cent,

THE RISK ELEMENT

Sec. 19]

293

and, therefore, could pay only S50 per annum, in considif destroyed by

eration of which the value of his house,
fire, is

restored to him,

good investment

it is

evident that he has

made

now

assured of a house even
occur, and he has, instead of the risk of fire,
;

for

should a fire
merely to pay his annual premium of $50 a year, the capitalized value of which is $1000.
Consequently, his house
is worth $10,000 - $1,000, or $9000.^
Such an insurance rate, however, being based on the
mathematical or "pure" premiums, would not pay any
profit to the companies conducting it.
But even a higher
insurance would leave a large margin of capital- value saved
If we suppose a "loading," so that the into the insured.
surance premium is not $50 but $100, similar reasoning
would show that the value of the house when insured would
be to the owner $8000 instead of $7000. As long as the
loading is not sufficient to absorb all the margin between
the $7000 and $9000, it will be advantageous to insure.
Between the case of a man owning an individual house,
when the element of caution would have a large influence,
and that where 10,000 houses are owned by the same corporation, in which case the caution element is almost entirely
absent, there are numberless intervening cases. The larger
the number of houses owned by one individual or corporation,
the

less profitable

becomes insurance.

express

in the

language of the business man, the various risks insure each
other.

Thus, the North

German Lloyd Company

finds

profitable not to insure its vessels against shipwreck, be-

cause they have so large a
•a

fleet

that their losses through

period of time can be counted on fairly well in advance.

One

on the individual is to steady
The owner of the house in
question would receive, if it were not insured, a net annual
income, after providing for depreciation, of 5 per cent on
$10,000, or $500 a year until the house was burned, after
effect of insurance

the income from his property.

For a mathematical statement, see Appendix to Chap. XVI,

§ 3.

NATURE OF CAPITAL AND INCOME

294

[Chap.

XVI

which he would receive nothing whereas, if he insures, he
receives this $500 income less his premium up to the date
of the fire, and afterward the income from the indemnity
paid him by the company.
;

§20
The same

principles apply to other forms of insurance,
marine insurance, which, by consolidating in an insurance company the risk on a large number of vessels,
reduces for the individual even the perils of the sea to
relative certainty and regularity; or as steam boiler insurance, which in a similar manner treats the risks of

explosion; or as plate-glass insurance, burglar insurance,

Uve stock insurance,

hail

and cyclone insurance, fideUty

insurance, accident insurance, employer's liabiUty insurance, and, above

all,

Ufe insurance/

This form of insur-

ance, like the other forms, tends to steady the income of

the beneficiary.

a wife holds insurance on her husis that, although what he

band's Ufe, the consequence
gives her during his

come

will

life is

somewhat diminished, her inThe ten-

not suddenly cease at his death.

dency of insurance here as elsewhere

make

regularity

out of irregularity, relative certainty out of relative uncertainty; and where, under the form of insurance contracts, the opposite result follows, the case is

not one of

become one of gambhng.
Thus, if a person insures the life of some one in whom he
has no financial interest, he is merely gambling on that perSome years ago in Michigan there was an abuse
son's Hfe.
true insurance, but tends to

Speculators
called "graveyard insurance."
went through the form of insuring the lives of certain
old persons, in other words of betting on their deaths,
of this type

a procedure not only vicious as gambling, but calculated
The same considerations apply to
also to lead to crime.
fire

insurance, where a person insures a building in which
^

See Appendix to Chap. XVI,

§ 4.

THE RISK ELEMENT

Sec. 21]

295

is not financially interested, or over-insures one in which
he is/

The range
ited

but

;

which insurance can apply

alv/ays lim-

constantly being extended, as business

it is

learn

how

to bring risks of

basis

and

to apply the theory of probabihty.

any kind on

men

to a statistical

At present

the total assets of Ufe insurance companies alone in the

United States are nearly $3,000,000,000.

§21

Where

risks

cannot be reduced to a

statistical basis,

and therefore cannot be insured against, recourse is often
had to the shifting of the risk into the hands of those
who are willing to take it. Such persons are speculators.

is usually one in whom the caution factor is
pronounced
as in the ordinary individual.
not so
In extreme cases he tends to become a simple gambler. The
distinction between a speculator and a gambler, however,
A gambler seeks and makes
is usually fairly well marked.
risks which it is not necessary to assume, whereas the speculator is one who merely volunteers to assume those risks
of business which must inevitably fall somewhere,
A specu-

speculator

lator

also usually fitted for his

so that the risk to

outset less than

Mm, owing
it

work by

would be to

nate prejudice against

all

special knowledge,

to superior foresight,
others.

The

speculation, which

at the

indiscrimi-

so often

met

were there no speculators, the
same risks would have to be borne by those less fitted to
bear them. The chief evils of speculation flow from the
with,

beside the point

;

for,

participation of the general public,

who

lack the special

knowledge, and enter the market in a purely gambling
spirit.

In addition to suffering the usual

evil

consequences

of gambling, they produce evil consequences for the non-

participating

public

by causing

factitious

fluctuations

* For the moral effects of insurance, see Insurance and Crime,
A. C. Campbell, Putnam's, 1902.

NATURE OF CAPITAL AND INCOME

296

XVI

[Chap.

which they

in the values of the products or property in

speculate.

The
are

acute when^
happens with the investing public, the forecasts

evils of speculation are particularly

as generally

made

not

independently.

made up

individual speculator

Were it true that each
his mind independently

of every other as to the future course of events, the errors
of

some would probably be

offset

by those

usually in the

same

Like sheep, they

direction.

How

a single leader.

of others.

they are led

easily

all

are

shown by

the effect on the stock market in the year 1904,

Thomas Lawson published

But,

common herd

as a matter of fact, the mistakes of the

when

scare-head advertisements in

the newspapers advising the public to

certain securi-

sell

ties.

chief cause of crises, panics, runs

on banks,

etc., is

mere
general and
differs from any

that risks are not independently reckoned, but are a

matter of imitation.
forced liquidation.^

crisis

a time of

In other words,

other period in two particulars, viz. that the liquidations
are

more numerous, and that they are for the most part
upon the debtors by the creditors because of threat-

forced

ened or actual bankruptcy.

Neither of these conditions

could exist unless there had been at a prior time a general

Both creditors and debtors
must have made a wrong forecast when their ill-fated agreements were entered into. Hence a crisis is the penalty
which must be paid when a previous general error in preSuch a general error may be due to
diction is discovered.
the coincidence of a number of independent mistakes of
miscalculation of the future.

individuals

pendence,

;

but

— to

almost always

the principle

due to lack of inde-

imitation.

The

error,

whatever it is, when committed by a person of influence, is
Uke an infection; it is caught by hundreds of others and
' See
Chapter

Juglar, Des Crises Commerdales, Paris,
I.

edition, 1889,

THE RISK ELEMENT

Sec. 21]

transmitted to thousands.

great

mob

297
of easily led in-

vestors, eagerly searching for "straight tips"

bring instant wealth,

when

the mistake

make

their mistake in

which

may

common, and

disastrous they try, en masse, to escape.

sudden rush of all the passengers on a ferry-boat to one
side will produce a " list " in the boat's position, and sometimes cause

ment

to capsize, though the independent

produce disaster.
public

also

the

sudden general

realiza-

unforeseen danger on the part of the investing

tion of

move-

the individual passengers will seldom or never

may submerge

the craft of credit and those

whom

has hitherto borne along in safety.

crisis

In short, a general
bears the relation to individual bankruptcies which

a general conflagration bears to individual fires. The key
to the study of either crises or conflagrations is the existence, in place of independent hazards, of interdependent
ones.
So far as conflagrations are concerned the principle of interdependence is distinctly recognized by stuinsurance, and in consequence, each company
keep its own fire risks independent of each
other, by not having too many in the same locality; but
so far as crises are concerned, the principle has not yet been
sufficiently emphasized by students of economic history.

dents of

fire

strives to

The same

phenomenon of a run
on a bank. The opinions of the bank's solvency are not
formed independently but interdependently. A year or
more ago the newspapers reported that, a policeman and
a crowd of people being collected on the steps of one of
the Wilkes-Barre savings banks to escape the rain, two
Hungarian depositors who were passing jumped to the
conclusion that the bank had been attacked by burglars,
and circulated the disturbing news in the Hungarian
colony, with the result that when the bank opened for business many depositors made a run upon it.
We see, then, that where speculation is imitative, it is
dangerous alike to those who engage in it and to the public.
principle applies to the

NATURE OF CAPITAL AND INCOME

298

Where, on the other hand, speculation
ent knowledge,

its utility is

[Chap.

based on independ-

usually enormous.

means of
and also

ates both to reduce risk by

XVI

It oper-

utilizing the special

knowledge of speculators,
to shift risk from
those who lack this knowledge to those who possess it.
The consequence is that normally speculative property will
gravitate into the hands of those most able to forecast its
true income.

Modern production has been
owing to the

tive production,

"captains of industry,"
forecast

and

who

mould the

called capitahstic-specula-

fact that it is

managed by

are specially fitted at once to

future within the special realms

which they operate. The industries of transportation
and manufacturing particularly are under the lead of an
educated and trained speculative class, whose function it is
to assume for themselves the main risks, and leave the
in

ordinary investor,

who

not so equipped, to cooperate as

a mere "lender" or silent partner. Yet it often happens
that they betray the confidence placed in them, and continue to throw the burden of risk on those whom they
pretend to shield.

§22
In the special

— namely,

field

more usually known

that in which attempts are

prices in the great exchange markets,

who

as "speculative,"

made to forecast
we find a similar

—

These speculators are
either "bulls" or "bears"; that is, they speculate either
for a rise or a fall.
Those who believe that wheat
or any other article is likely to rise in value and hence
yield more than the "rate of interest," will hold it. Or if
they do not own it, will buy it or obtain an option on it.
Such an option is known as a "call," and is put in force at
a later time, at a price fixed in advance and considered
low.
On the other hand, those who believe that prices
class

will

are

fall will

specially trained.

sell

out their present holdings, or

may

seU

"short," agreeing to supply such holdings at a later time

THE KISK ELEMENT

Sec. 22]

at a fixed price

to sell

often

299

which they consider high. Such a contract
made in the form of an option, in which

it is known as a "put."
To show how such contracts

case

ples will suffice.

large contract

will shift risks,

building contractor

was asked

a few exam-

who had taken a

he were not taking large

since he could not foreknow the cost of building.

risks,

re-

"No, I am taking no risks at all except on 'labor';
have made contracts to be supphed with all materials

plied,

Those who made these conat fixed prices."
assumed the risk of fluctuation in price in the
materials in which they dealt, relieving the con-

when needed,
tracts thus
special

tractor of the necessity of informing himself of the special

market conditions
as
lic,

for stone, brick, timber, etc.,

him to make a
there was less need

bling

closer bid for the contract,

of the element of caution.

and enainasmuch
The pub-

course, get the benefit of such a shifting of risk

form of reduced cost of building. Similar results
from
most other "short" sales. Again, a woolen
follow
manufacturer need not carry so large a stock of wool if he
can make a contract by which some one will sell short, or
agree to supply the wool at fixed prices and at certain
He can afford to use up his present stock feardates.
lessly, with the certainty that when it is gone he can
obtain a new supply.^ Without such a contract, he would
be under the necessity of carrying a large and idle stock.
An important method of shifting risks is "hedging,"
whereby a dealer, for instance in transporting wheat, may
be relieved of the risk of a change in price. He buys
wheat in the West intending to ship it to New York and
sell it there at enough to cover cost of transportation
and a small profit. In consequence of a sudden fall in
price he might find all his profit wiped out or he might,
on the other hand, by a rise in price, make much more
than normal profits. But, being of a cautious disposition,
in the

;

Cf.

Hadley, Economics, Putnam's, 1896, p. 106.

NATUKE OF CAPITAL AND INCOME

300

[Chap.

XVI

—

he prefers an intermediate course,
a small profit which
is sure, rather than the chances of both gain and loss.
Consequently he "hedges." He enters into some speculative market, knowing that it will move in sympathy
with the New York market, and there he "speculates"
In case the price in New York
for a fall, or sells "short."
falls, what he loses on the wheat which he has transported
he gains through his speculative short selling. Contrariwise, if the price rises, what he gains on his wheat transported he loses in the speculative market. In other words,
he is, as it were, betting on both sides of the market at
once, and therefore eliminating all risk, so that he only
obtains his normal profit, commission, or percentage on
the actual wheat handled, having imposed the burden of
risk of speculation on the speculative dealers to whom he
sold short.^

The

effect

hedging

those

who engage

it,

such as the wheat dealers, is evidently to enable them to
work on a smaller margin of profit. In consequence the
public receives a benefit in lowered prices. The case is
thus very similar to those respectively of the builder and
Short selling, binding the
woolen manufacturer.

of the

future to the past, enables the specialist to

guarantee

to the general public a definite foreseen series of events.

The
and

beneficial effect to the public, in saving useless stocks

reserves, in producing

terprises,

and

intelligent direction of en-

in encouraging accumulation through greater

its future benefits, is both obvious and great.
one of the direst economic evils, and all of the dewhether increased guarvices which aid in overcoming it

certainty of

Risk

—

anties, safeguards, foresight, insurance, or legitimate specu-

lation

— represent a great boon to humanity.

See " Speculations on Stock and Produce Exchanges of the United
by Henry C. 'Emery, Publications of American Economic Association.
For the development of insurance-speculation in England,
see " The Put and Call," by L. R. Higgins, London, Effingham WU^

States,"

son, 1902.

PART
Chapter

IV.

SUMMAKIES

Chapter XVIII.

Summary of Part III
General Summary

Glossary.

Summary of Definitions

XVII.

—

CHAPTER XVII
SUMMARY OF PART

(CHAPTERS XI-XVl) REPRESENTED
BY DIAGRAMS

III

§1

have finished our study of the relations between
and income-value and may now pause to
summarize them briefly. At the beginning of Part III it
was stated that the income from capital wealth consists
that capital and
of whatever service it performs for man
income may each be measured either in specific quantities
of their respective units, or in value and that consequently
there are four ratios between income and capital; namely,
capital-value

;

(1)

the physical productivity of capital, (2) the value pro-

ductivity,

(3)

Our

return.

the relation

the physical return, and

We saw that the value of
value of

value of

(4)

the value-

theme has been the value-return,
between income-value and capital-value.
special

capital wealth

The

the discounted

between the
the income and the value of the capital was indiits

expected income.

cated by diagrams.
of vertical

relation

Income was represented by a

hues as in Figure 13

(a, a',

series

a", a'"), the hori-

them representing intervals of
was then found possible to represent the capitalvalue of this income in anticipation, on the assumption
that the income could be relied upon with certainty.
zontal distances between
time.

—

a broken or
This representation gave the capital curve,
drop is
vertical
each
curve,
toothed curve AB. In this
equal to the corresponding income item shown below it,
and the intervening points are connected by discount
303

NATUKE OF CAPITAL AND INCOME

304

XVII

[Chap.

curves; so that the total capital- value at the time

represented by the altitude BG.
But this separate representation for capital and for income respectively need not be adhered to, because the
capital curve

alone contains in

teeth all

its vertical

that is necessary to indicate the installments of income and
in the present chapter the main propositions relating to
;

Fig. 13.

capital

and income

will

be restated with the aid of geothis capital curve AB

metrical representations of which
is

the type.

§2
First of

any

come.

all,

such a curve exhibits the fact that the value

capital is the discounted value of the expected inIn Figure 14 the several discount curves used in

previous diagrams are

The
continued to meet OB.
will
&',
V",
h"
divided,
thus
6,

all

parts into which GB is
represent respectively the present values of the income
This may readily be proved from
items a, a', a", a'".
,

the nature of the discount curves.

SUMMARY OF PART

Sec. 2]

305

III

The diagram shows, in the second place (tracing it forward chronologically), that the capital- value alternately
rises and falls, rising in anticipation of approaching income
and falling as the installments of this income are, like coupons, successively detached from capital. The alternate rise
and fall of the capital curve may be equal, each to the other,
indicating that the income

"standard"; or the former

Fig. 14.

may

be the greater, indicating respectively
above or below standard.
If any installment of income is negative
in other
words, is not strictly income, but outgo
we need simply
to reverse the direction of one of the teeth, as in Figure
In this case the capital- value is simply the discounted
15.

or the latter

that the income

—

value of the future income

less

—

that of the outgo.

§3
As we have seen, if we trace the entire history of a capital
curve backward in time from the last installment of income
to the beginning of the investment or enterprise, the curve

NATURE OF CAPITAL AND INCOME

306
will
is

[Chap.

XVII

normally be at the zero point at both ends. This
Such a curve shows the normal
in Figure 16.

shown

cycle of capital-value from the
of capital

first utilized

moment when the article
moment when it is ex-

to the

FiG. 15.

hausted.

It is

"normal"

just sufficient to

income is
no more and

in the sense that the

compensate

for the outlay,

and that usually the principal items of outgo all
the cycle, and the principal
items of income all accrue in the latter part. In such a
less,

occur in the early part of

Fig. 16.

normal curve the capital-value (AB in Fig. 16) at any
moment may be said to represent two things first, it represents the discounted value of the future expected income
:

(less

that of future expected outgo,

any)

;

and, secondly,

SUMMARY OF PART

Sec. 3]

307

III

represents the accumulated value of past outgo (less that

of past income,

any).

From

this

follows that the

on the one hand, less than
the future total income which it represents, and greater
than the past outgo. This capital- value may be regarded
as made up of the elements 6, h' h'" which are respecvalue of the capital

is,

tivel}^

the discounted values of the respective larger

nitudes

and, on the other hand, as

a, a', a";

mag-

made up

A
Fig. 17.

which are the accumulated values of the respecmagnitudes a'", a'^, a^. By puttuig together
the elements of which AB is composed, we see, on the one
hand, that AB is less than the anticipated income and
greater than the past outgo; and consequently, a fortiori,
that the past outgo is less than the future income. For
the sake of simplicity in our illustration, we have chosen a
point of time after all the outgo and before any of the income has accrued but the same principles could be worked
out upon such a diagram, no matter what point of time were
chosen. In other words, in the normal case the value of any
b'",

6'^, If,

tive smaller

;

capital

intermediate between the value of

its

of production or acquisition and the value of

income.

past cost
its

future

NATUKE OF CAPITAL AND INCOME

308

In the special case in which there

and one item

of income, the curve

in Figure 17,

where a

[Chap.

XVII

but one item of cost

reduced to that shown
the expected income, and a' the
is

Fig. 18.

past outgo.

If the capital-value

midway between

the income and

be taken at a point

outgo,

evidently fol-

6"
c"

Fig. 19.

lows,

by the nature

of a' to

the

of the discount curve, that the ratio

same

as the ratio of

to a, or that

Fig. 20.

AB is the "mean proportional," or "geometric mean,"
In other words, the normal relation
between a and a'
capital,
and return is expressed in the statebetween cost,
.

SUMMARY OF PART

Sec. 4]

309

III

ment that the capital is a mean proportional between
past cost and its future return.

its

§4
Another use which
representation

may

made

of the diagrammatic
compact manner the sumand the income of any given
This may be done simply by

to exhibit in a

mation of both the capital
enterprise or community.

Fig. 21.

adding together the corresponding ordinates or vertical
lines in

any number

number

of articles of wealth or property.

capital curves, representing

any

Let Figure 18,

one capital curve, and Figure 19 another.
Figure 20, formed by combining Figures 18 and 19,
then represents the sum of the capital and income of both.
Figure 20 is derived from Figures 18 and 19 in such a

for instance, represent

manner that the ordinate
ordinates 6' and h", and in
G,

and
it

the
c".

the

sum

of the individual

manner any other

sum of the corresponding individual
From the rule by which Figure 20 is

ordinate,

ordinates

constructed,

evident that every tooth in the constituent curves,

be reproduced in the combined diagram. In Figure 20, therefore, the ordinates represent the
combined capital-values at various points, while the two

such as

teeth a"

and

a", will

represent the total income accruing in that

time interval which includes them.

Thus, Figure 20 epito-

mizes the summation both of capital and income.

NATURE OF CAPITAL AND INCOME

310

But

it is

[Chap,

XVII

not necessary to have three separate diagrams.

It is possible to superimpose

upon the
the same

other, as

axis

one of the first two figures
shown in Figure 21. In this figure, on
is drawn first FG, corresponding to Fig-

ure 18 above, and, secondly, at distances above

corre-

sponding to the ordinates in Figure 19, is drawn the line
This line
contains an apparent tooth or break
which does not appear in Figure 19, but this is only for
the purpose of preserving at this point the prescribed dis-

tance from the line FG.

Considered relatively to

there

Fig. 22.

measured relatively to
no break. Thus the line
FG, takes the place of the constituent curve of Figure 19,
it represents
and measured relatively to the base line
the combined curve of Figure 20 for both constituents.
The same method applies where there are any number of
constituent capital curves. Thus (Fig. 22), let us draw for
our first capital curve one which has an income item a,
and superimpose upon it a second capital curve, of which
the income item is a' and so on. The capital curve at
is

the top will represent the total of the individual capital

—

it, and each belt between
namely, the
between any two neighboring capital curves

curves beneath
difference

will replace

a constituent curve.

From

the

—

manner

their construction it is clear that the income item a' will
be carried forward successively to each of the curves above
it, and will be represented by a tooth in the curve at the

SUMMARY OF PART

Sec. 5]

top, as represented

by the

top thus shows in

its

Similarly, a' a",

clotted lines.

separate teeth

contained in the curves of which

The

a'" are transmitted to the top.

final

all

it is

311

III

and

curve at the

the income items

the sum.

§5
In case two teeth in separate curves occur at the same
combined curve will, of course, have a large

instant, the

Logging Camp

Fig. 23.

tooth equal to their sum.

In case one tooth

representing income, and the other

positive,

negative, or outgo,

the coincidence of these will result in a small tooth equal to

and

their difference,

this difference will

be zero

the two

items are equal.

The most important

case of this kind occurs

when

there

are" interactions." It has been explained that an interaction
is an income item for one capital which at the same time

two
income and outgo items
will cancel, and the resulting combined curve will be unbroken at the point representing the time of interaction.
is

an outgo item

for another.

If the curves for these

capitals are superimposed, the equal

This

shown

in Figure 23, giving the typical history of

limiber operations.

Every year a logging camp

yields a

NATUKE OF CAPITAL AND INCOME

312

amount

[Chap,

XVII

which is credited
In the diagram,
the space between the base line and the first curve above
it represents the capital curve of the logging camp, and
the space above this curve represents the capital curve of
certain

of logs, the turning out of

to the camp, but debited to the mill.

At the time

the sawmill.

the transfer of logs from

the one category to the other, there

is a corresponding
diminution in the capital-value of the logging camp, but
an increase in the capital-value of the sawmill.
The characteristic of such an interaction or couple is

that

leaves unbroken the upper curve of final summation.

Tree

SaolinE

C
Fig. 24.

There

no carrying forward of

in the previous diagram,

teeth, as

by the dotted

lines

— or rather, the carrying forward

The interaction is merely a
one capital for the benefit of another, and does

results in a cancellation.
sacrifice of

not disturb the

total.

If the interaction
it

BG is greater than we have represented
G is lower and B higher than in-

in the diagram, so that

dicated, the discount curve AB will be nearer coincidence
with MN, and GD nearer coincidence with XY. We may
suppose a case in which coincidence is reached. This case
Here BG represents such an
is represented in Figure 24.
interaction as occurs when one capital good is completely
transformed into another, as when the " sapling" becomes a

" tree " at a certain definite point of time.

The capital-value

SUMMARY OF PART

Sec. 5]

313

III

BC, but there appears in its
The change from one
to the other is evidently entirely nominal, and it is possible, by drawing any other vertical line than BC, to create
an 'interaction" simply by calling the portion on the two
sides of this line by different names.
When, as in Figure 25, a series of curves is constructed
and superimposed to represent the income from any speciof the sapling disappears at

stead the capital- value of the tree.

fied
is

group of capital instruments, the sum total of the income

evidently represented

by the

entire series of teeth in the

Fig. 25.

These teeth form a physical picture of the
of
services, which was discussed in
previous chapters. If in the diagram we omit the uppermost layer of capital, the curve remaining immediately
top curve.

fringe"

"outer

below

this layer will

series

capital

then be the outer fringe for the entire

instruments below

it.

We may

ceed step by step in either direction, leaving

off

pro-

an item

In every case the outer fringe
of teeth wiU represent the sum total of income for the group
of capital represented below it.
capital or taking one on.

NATUKE OF CAPITAL AND INCOME

314

In Figure 25

all

final

XVII

the teeth below the top layer are rep-

resented to be interactions.

[Chap.

But

any

them should

services, they need only be carried forward by dotted

lines to the top, as in

Figure 26,

the capital repre-

sented by one layer interacts with the capital represented

by a

layer two or

more removes above

it,

the connection

Fig. 26.

will

be represented by carrying forward the tooth by dotted
proper stage.

lines to the

As we

are at present interested in the general aspects

we need not take into account such complicabut may assume, for purposes of exposition, that all
capital can be arranged in a single definite series, each member of which acts upon the one above it, and so on to the
end. In the actual world, it is usually possible to arrange
capital roughly in such an interacting series.

of the subject,
tions,

§6

Two

special applications

may

be made of the foregoing

of capital curves.
The
show the total value of capital property and the
total value of income possessed by a particular individual,
and the second will show the same condition as to an entire

representation for the
first will

society.

summation

SUMMARY OF PART

Sec. 6]

315

III

We may

suppose a man's capital to be divided into
first, money-paying investments; second,
money; third, enjoyable articles purchased by money.
three classes:

We may

juxtapose

these

elements,

Figure

27.

Enjoyable Capital

"U-Money

Investments

Fig. 27.

whenever an investment pays money, a tooth
produced in the first curve and a transaction
takes place between the categories "investments" and
Here,

"money."

each such transaction the investments are

reduced in value by the amount of coupons detached, and
the stock of money is increased by the same amount. In
like

manner, every time money

spent, a transaction takes

place between the belt representing

senting enjoyable capital.

By such

and the value
increased by the same amount.
stock

depleted,

money and

that repre-

transaction the

money

of the enjoyable capital

These operations are

NATURE OF CAPITAL AND INCOME

316

[Chap.

XVII

and are not transmitted to the
outer fringe. The total income, therefore, from the entire
group of capital, is represented simply by the vertical unself-canceling

therefore

dulations in the top curve.

By means
meanings

of this

diagram we

"individual

may

see clearly the various

income."

The business man

usually applies the term to the teeth of the investment

curve

the economist to the teeth next above in the

;

money

curve, or the teeth above that in the curve representing

enjoyable capital.

Practically,

which

of the three

does not greatly matter

select, since usually, for

any conThis

siderable period of time, all will closely correspond.

must needs be

so, unless

the stock of

appreciably increasing

articles is

money

or enjoyable

decreasing.

These

exceptional cases have already been discussed in detail,

and there

difficulty in representing

The other application

of our

them by diagrams.

diagrammatic summation

to present a fairly complete picture of the total value of

and the total value of income of an entire
In the capital of a community it is not usual to

capital-wealth
society.

include human beings, and for that reason it is scarcely
worth our while to discuss the theoretical questions as to
the manner in which they might be included in such a repAs a matter of fact, the method of capitalizresentation.
beings
will vary with the special purpose in
ing human
Our present purpose is chiefly concerned with inview.
teractions between man and other capital, and we need
practically only to capitalize the money-earning power of

the individual.

we may

call

This part of the capital-value of a

"labor power."

man

then have the total capi-

tal of a community consisting of labor power, land, intermediate capital, and enjoyable capital, as in Figure 28.
For convenience, and to avoid needless complications, we
assume that labor power interacts only with land, land

SUMMARY OF PART

Sec. 7]

317

III

with intermediate capital, and intermediate capital with
enjoyable capital. The income from the entire series is

by the teeth of the uppermost line.
diagram we see that the total income of a community comes through enjoyable goods. The other capital
items produce income, but this income is in every case also
represented, as before,

From

this

Intermediate Capital

Land

Labor-power

Fig. 28.

an outgo with reference to the layer of capital next above.
Many of the fallacious methods of summing income consist
virtually in adding together the teeth in the various layers.
It

tions

forgotten that the teeth below the top layer are interac-

and therefore both

positive

and negative

— positive

with reference to the layer below and negative with reference to that above

— and

that therefore they

come

the summation of income only to go out again.
function in each case

into

Their

simply to keep up the capital in the

their activities these layers above
would soon be exhausted, and the income at the top would

layers above.

Without

not continue for long.

§8
From

this point of view,

each interaction

may

be con-

sidered as the discounted value of a certain portion of the

318

NATURE OF CAPITAL AND INCOME

[Chap.

XVII

In Figure
items of income from the layer next above.
value
taken
the
discounted
a
may
be
as
29 the interaction

income taken from the layer next above, between
the points P and Q. Here we have a geometrical repre-

of the

sentation of the fact so often insisted

Bohm-Bawerk^ and

Professor

upon by Professor

Taussig,^

that

the

pro-

next year's (or next
month's) yarn, of this year's yarn for next year's cloth, of
this year's cloth for next year's clothes, etc.
In tracing the connection between the income items in
duction of this year's wool

different layers,

tween the

we may

for

consider either a cross-section be-

different layers,

by drawing two

vertical lines

Fig. 29.

separated by a certain interval and noting the intervening

income taking place simultaneously in the various layers;
or

we may

follow the successive time connections involved

between one layer and the next. In the treatment which
has been given in the previous chapters, the former method
was emploj^ed. The present diagrammatic representation
Thus, in Figure 30,
gives us a bird's-eye view of both.
representing the logging camp, sawmill, lumber yard, etc.,
having selected a period represented between the vertical
line drawn at A and B, we may either address ourselves to
the mutual relations of the various layers there comprised;
or we may address ourselves to the income item a, whose
1

Positive Theory of Capital, English translation, 1890, pp. 179-189.
Wages and Capital, New York (Appleton), 1896, Chapters II, III.

SUMMARY OF PART

Sec. 8]

influence traverses the entire section.

the logging camp; ''ripens" into
mill
this

which

all

319

III

It is

produced by

that income of the saw-

comprised between the points P and Q and
income of the lumber yard
;

in turn ripens into the

comprised between the points P' and Q'
In this way we
are virtually following the log as it is transformed in the
various processes from tree to lumber.
It is in consideration of such a relation or set of relations
that an income item like a was called a "preparatory
service."
Each such preliminary process of production
.

takes place in anticipation of future resulting processes,

and derives

its

value from them.

Combining

with the principle that the value of

all

this principle

capital

the dis-

expected income, we see that the value
of the capital in the lower layers is ultimately dependent
on the value of the income in the topmost layer; for the

counted value of

its

value of that earlier capital

income

the discounted value of the

produces, and this income, consisting of interac-

tions or preparatory services,
of the services to

which

in turn the discounted value

leads,

and

on through succes-

NATURE OF CAPITAL AND INCOME

320

sive layers to the top, as seen in Figure 31.

the capital-value of

the lowest layer,

[Chap.

XVII

Here AB,

the discounted

value of the income from that layer, namely the teeth
a, a', a", but this income in turn is the discounted value

income represented by the teeth intervening beand Q from the layer next above, and this income
in turn is the discounted value of the income between P'
of the

tween

Fig. 31.

and Q' on the layer

still

the curves are shown as

above.
all

this representation

terminating in the base line

but the representation may readily be extended to the case
of an income infinitely continued.

§9
In Chapter XVI it was shown that certain modifications
needed to be introduced into our theory of the determination of capital-value when the element of uncertainty was
introduced. We are fresh from the discussion of these, and
they need no extended mention here. The main point to
be kept in mind is that when the element of chance is
taken into account, sudden breaks occur in the capital curve,
so that instead of following the simple order previously
indicated, beginning at zero

and ending

at zero, with inter-

mediate teeth alternately rising and falling along the discount curve, it suffers additional interruptions at points
where the estimates of future chances are changed.
The most important point in the life history of such a

SUMMARY OF PART

Sec. 9]

curve of capital-value

321

III

When

at the beginning.

the ele-

ment

of chance or luck is taken into account, the capital

curve

is less

likely to begin at the zero line.

some point above

at
for

;

it will

may

begin

not begin at any point below

;

the present value of the chance of gain did not out-

weigh the present value of the chance of loss, the enterprise
would never be undertaken at all. In the great majority
of cases, the capital-value at the outset of an enterprise
is greater than zero
that is, in the estimation of those who
enter into it, the gains will not only pay for the costs with
interest, but something in addition, even when the element
of chance is included in the discounting operation.
At any
;

rate,
is

not infrequent that

started, those

possibilities,

who have

and the

first

when a new

enterprise

knowledge of the
opportunity to exploit them,
the

first

expect returns out of proportion to the ordinary rate of

and compensation for risk. The only reason this
is not more generally true is because of the existence of
competition, by which the special advantage of individuals
through special knowledge, foresight, etc., is offset by the
interest

vigilance of their rivals.

With

these points in mind,

of the value of

any particular

we observe

that the history

article of capital-wealth

may

Starting at A, some point
be represented as in Figure 32.
above the zero fine, the capital-value rises to B, because,
From B it
let us say, of the first expenditure involved.
the
through
proceeds along a discount curve to C. There,
influence of the risk element, it suddenly drops to D, at

which point some new information has reduced the prospect
of future gain or increased the risk of future loss. From D in
turn it proceeds along the discount curve to E. At this point
the cost EF is incurred, but at the same time confidence as

to the future receives a shock, and instead of proceeding
from F, the curve drops at once to G. Thence it rises gradually and normally to H, when the first income item, HI,
This being, let us say, less than was anticipated,
is received.

NATURE OF CAPITAL AND INCOME

322

[Chap.

XVII

shows that the capital-values had been hitherto too high.
Consequently the curve drops to J, and thence proceeds

in the

manner indicated in the diagram, ending at the zero
when the last installment of income OP is received.

point P,

Fig. 32.

we have

this chapter

continuously
suggestions

;

but

made

it is

not

treated income as accruing disdifficult, in

accordance with the

in a previous chapter, to extend the prin-

It would also
worth while, to exhibit, by means
of similar diagrammatic representations, numerous propositions other than those already noted.
Our object, however,
has not been to exploit the diagrams, but merely to use them
for a running epitome of the general relations existing between capital and income.
ciples

apply to the continuous case.

be possible, were

CHAPTER

XVIII

GENERAL SUMMARY

§1

the preceding chapters to
It has been the endeavor
of capital and its services
of
the
mass
picture
give a definite
In such a picture we see man standing in the
to man.

midst of a physical universe, the events of which affect
Over many of these events he can exercise no
his life.
control or selection

;

these constitute his natural environ-

ment. Over others he exercises selection and control by
assuming dominion over part of the physical universe,
and fashioning it in new shapes to suit his needs. The
parts of the material world which he thus appropriates
constitute wealth, whether they remain in their natural
state or are "worked up" by him into products to render
This mass of instruthem more adapted to his needs.
ments will consist, first, of the appropriated parts of the
surface of the earth, of the buildings and structm-es
attached to the soil, and of the movable objects or "com-

modities" which

man

upon the earth;

human

population

possesses

and stores in the buildings

and, secondly, of
itself,

—

for these,

the persons of

the

though they are

also

the abode of the owner of wealth, are themselves objects

owned.
This mass of instruments serves man's purpose in so far

him to modify the stream of historical events.
By means of land and the modifications
which he makes upon it he is enabled to increase and improve the growth of the vegetable and animal kingdoms
as its possession enables

323

NATURE OF CAPITAL AND INCOME

324
in such a
rials

way

as to supply

for constructing other

[Chap. XVIII

him with food and the mateBy means of
instruments.

dwellings and other buildings he

enabled to divert the

elements from contact with his body and with the objects
By means of machinof wealth which he stores in them.
ery, tools,

and other instruments

production, he

enabled to fashion new instruments to add
or to take the place of those destroyed or worn out.

to his stocks

means of the final finished products which minister to his
more immediate enjoyments, such, for instance, as food,
clothing, books, ornaments, he is enabled to consummate
the objects for which the entire mass of wealth is produced
and kept in existence, namely, the satisfaction of his desires,

whether these be

for the necessities, the luxuries, the

life.
In these and other
modify
the
course of natural
ways
events in ways more or less agreeable to the owner. These
changes in the historical stream of events which occur by
means of wealth constitute what have been called the serv-

comforts, or the amusements of
the stock of wealth will

ices of wealth.

In our picture, therefore, we observe (1) a stock of instruments existing at an instant of time, and (2) a stream of
services through time, flowing from this stock of wealth.
The stock of wealth is called capital, and its stream of servThe income is the more important
ices is called income.
concept of the two, for the capital exists merely for the
sake of the income, and the ownership of the capital has no
other significance than the ownership of possible income

from that capital. The division of income between different owners constitutes in reahty a division of ownership
of the capital which bears the income, and the individual
shares constitute what are called property rights.

From

this

go side by

apparent that property rights and wealth
and that neither can exist without the other,

it is

side,

GENERAL SUMMARY

Sec. 2]

325

property signifying merely the sharing of wealth
individuals.

When we

tain the ownership of
of the entire

sum

mass

piece together these shares,

all

among
we ob-

wealth. In like manner, the value

of wealth

must be taken

mean simply

ownerattempt to reach this total by combining
the shares of individuals, we do so by making a careful
record of all "capital accounts." In such a record we find
the

ship.

that

of the values of the individual shares of this

When we

many

items occur in pairs,

— negative

items

property or "liabihties" in one account and positive items
or "assets" in another.
will

left

the

final

this pairing of items, there

sum

property value

the

value of the entire stock of physical instruments.
Of the services which flow from the stock of capital,
it

has been seen that the great majority consist merely

between one category of capital and
is accomplished by most instruments
of capital is to hand over something to other instruments of
capital. The great mass of capital
lands, warehouses, railof "interactions"

another.

All that

roads, machinery, ships, etc.
tation," that

is,

—

exists either for "transpor-

for changing the position of wealth

one place to another; or for "production," that

is,

from

for chang-

ing wealth from one state or form to another; or finally

In
for exchange, the mutual transfer of rights to wealth.
every such operation, the instruments which have wrought
the change are said to have rendered a service and in the
;

income account these instruments are credited with the
value of such services while the instruments which receive
the services, and are thus improved in position or condition, are said to have rendered a disservice and are at
the same time debited with exactly the same item. When
;

thus come to put together the entire total of income,

all

such pairs of items or "interactions" cancel.

These

double-faced events or interactions constitute the over-

whelming mass of items in the actual inventory
which enter into the accounts of business men.

income

Out

NATURE OF CAPITAL AND INCOME

326
this fact,
is

also

combined with the

[Chap. XVIII

"
fact that every " transaction

double-faced, grows, as

we have

seen, the entire

theory of double-entry bookkeeping.
Out of the entire mass of instruments thus acting and
reacting upon each other, there finally emerges an uncan-

mere transfer
from one category to another within the mass, but an actual
contribution issuing from the mass to the benefit of man,
the owner. These final elements are his real income. In
celed or net income which does not represent a

the last analysis they consist purely of subjective or psychic
satisfactions; that is, of conscious desirable experiences.

§3
But these

desirable mental experiences occur at the sacri-

fice of certain undesirable ones, namely, of efforts.

The

subjective efforts put forth for the sake of subjective satisfactions constitute the net or uncanceled elements of outgo.
Thus we see that, side by side with the objective income

and outgo stream, and

as the final result of that stream, there

exists its subjective counterpart, namely, the stream of ef-

and satisfactions. In the same way, there exists, side by
with the objective mass of capital, the subjective esteem
in which this capital is held, namely, what we have called

forts

side

its desirability,

or utility.

If efforts

and

satisfactions are

called subjective income, desirabiUty or utihty should be
called

subjective

capital.

The same

antithesis

time

appHes to the subjective as to the objective; desirabihty
is

a state of

mind

an instant

time

;

efforts

and

factions are experiences through a period of time.
ability stands for anticipated efforts

and

satis-

Desir-

satisfactions, just

as objective capital stands for anticipated services.
thus see in the mind of man a microcosm of the objective

economic world, consisting of

desires, efforts,

and

satis-

factions, corresponding respectively in the objective world
to capital, outgo, and income.

GENERAL SUMMARY

Sec. 4]

327

§4

For convenience we have used the term "goods" to comany one or all of the three categories,
wealth, property, and services.
It has been seen that any two goods
may be compared in respect to desirability, and if the
marginal increments of two groups of goods are equally

—

prise

The interbe measured by ex-

desirable, those groups are equivalent in value.

equivalence of goods in this sense
pressing

all

may

goods in terms of any one good,

as, for instance,

When the various goods are thus converted into
common standard, we have a new sense both for capital

money.
a

and income. Capital, instead of consisting of a miscellaneous mass of wealth or property rights, is now taken in the
sense of capital-value; and income, instead of consisting
of a miscellaneous stream of services, some final and some
intermediate, some objective and some subjective, will
consist of a single homogeneous element, income-value.
It is to the relation between capital and income in the
value sense that our attention throughout this book has
been chiefly devoted. It has been noted that the relation
between capital and income, taken in the value sense, is
profoundly different from the relation between capital and
income when either or both are measured in their various
individual units. When capital and value are measured
as "quantities," capital maybe said to produce income;
but when they are measured in "values," we find that it
necessary to reverse this statement, and to say that in-

The manner in which capitalvalue is produced from income-value is by discounting, and
this is done by means of a rate of interest, due attention

come produces

capital.

being given to the fact that future income

more or
of this

less to

the element of chance.

fundamental discount

always subject

As a consequence

relation, it follows that the

value of capital rises as future income approaches, and

falls

reached and passed.

with

as that income

It rises or falls

NATURE OF CAPITAL AND INCOME

328

[Chap. XVIII

each change in the rate of interest employed in the discount
and with each change in the estimate of the chance

process,

and fall in the value of capital
and even, the capital will recur to a constant level, and the income in this case is said to be the
earnings of capital.
The earnings of capital constitute a
standard with respect to which the actual income in any
case may be compared.
If the actual income exceeds the
element.

If the alternate rise

are rhythmic

standard income, there will be a depreciation of capital,

which

may

made

good, however, by paying back the

excess into another fund of capital called the depreciation
fund.

If,

on the contrary, the earnings exceed the actual

income, the excess will constitute savings, and will accumulate

and be added

to the capital.

§5
To

describe in a few words the nature of capital

income, we

may

and

say that those parts of the material

universe which at any time are under the dominion of

man constitute his
property;

its

capital wealth

;

its

ownership, his capital

value, his capital- value ;

subjective capital.

But

capital in

its

any

desirability, his

these senses

stands for anticipated income, which consists of a stream

When values are considered, the
not from capital to income, but from

of services or its value.

causal relation

income to capital; not from present to future, but from
future to present; in other words, the value of capital

the discounted value of the expected income.

The

fluctu-

ations of this capital-value will, chance aside, be equal and
opposite to the deviations of " income" from " earnings,"

when the influence of chance is included, there
be in addition to these fluctuations still others which
mirror the successive changes in the outlook for future
whereas,
will

income.

GLOSSARY

A Summary

of the Definitions used in this Book

Amortization fund.

Amount.

— The

— (See

amount

Fund, depreciation.)
any given sum at a given time

is its

equivalent at a later time. Ch. XIII, § 1.
Assets of a 'person.
His property-rights, including

—

both those
good his liabilities and those, if any, which
excess of and free from any liability.
(Syn. Resources.)

which make
are in

Ch. V, § 1.
Balance sheet.

—A

statement of a person's assets and liabilities.
Ch. V, § 1.
Basis.
The rate of interest yielded by a security when sold at a
specified price.
Ch. XVI, § 9.
commercial, of a security.
The basis corresponding to the
commercial value of the security. Ch. XVI, § 8.
(Syn. Capital account.)

—

—
— The

mathematical, of a security.
basis corresponding to the
mathematical value of the security. Ch. XVI, § 8.
riskless, of

a security.

— The

basis corresponding to the riskless

Ch.

value of the security.

XVI,

§ 8.

— Abbreviation for Capital goods, and
Ch. V,
Ch. V,
account. — (See Balance
balance. — The difference between the value of

Capital.

Capital

value.

§ 1.

sheet.)

§ 1.

the assets in a
balance sheet and of the liabilities.
(Syn. Net capital.)
The capital balance is measured in three different ways:
as the nominal capital (or capitalization), the

book value, and

the market value of the rights of the shareholders or those

whose

capital account

hook value

of.

—

divided profits,
the assets and
account.

considered.

The sum
i.e.

Ch. V,

the capital,

§ 1.

surplus,

and un-

the difference in value at any time between

liabilities

Ch. V,

according to the entries in the capital

§ 4.

— Capital-wealth or capital-property.
—
instruments. — (See Capital
goods.

Ch. V,

The market value of
as market value of shares.
Ch. V, § 4.
holders' rights in a concern.
wealth.)

329

§ 1.

the share-

NATURE OF CAPITAL AND INCOME

330

— (See Capital balance.)
— The par or face value

Capital, net.

Ch. V,

§ 3.

a joint stock
company, and hence also the original book value of the difference between assets and habilities. Ch. V, § 2.

nominal.

of the shares in

— The capital when the capital account

is first opened.
be measured in two different ways, as nominal capital
and paid-up capital. Ch. IV, § 4,
paid-up.
The amount of original capital of a concern actually
paid in by the shareholders. Ch. IV, § 4.
property.
A stock (or fund) of property existing at an instant
of time.
Ch. V, § 1.
wealth.
A stock (or fund) of wealth existing at an instant of
time,
(Syn. Capital instruments.)
Ch. V, § 1.
value.
The value of a stock of wealth or property at an instant.
It is found by discounting (or " capitaHzing ") the value of the
income expected from the wealth or property. Ch. V, § 1.
Capitalization.
A. The process of discounting by which expected income is translated into present capital- value. Usually
employed only when the income is considered uniform and

original.

may

—
—
—
—

—

perpetual, in which case capitalization consists in dividing the
rate of income per

Ch. XIII,

annum by

the rate of interest.

Ch. IV,

§ 1.

B. The nominal capital of a joint stock company. Ch. V, § 4.
The reciprocal of the rate of interest. (Theoretically
of.
also the reciprocal of the rate of discount.
Practically this

rate

—

meaning

— To

never used.)

capitalize income is to find the capital-value
equivalent to that income. Ch. IV, § 6; Ch. XIII, § 1.
Caution, coefficient of.
The ratio of commercial value to mathemat-

Capitalize.

ical value.

Ch.

—
XVI,
— The ratio of the number of cases in which
§ 6.

Chance, of any event.
that event may occur to the total possible

when

all

the cases are equally probable.

number

Any two

of cases,

cases are

equally probable (to any particular person at any particular
time) if the person has no inclination to believe one rather than

the other to be true. Ch. XVI, § 2.
(Syn. Probability.)
commercial value of.
The value which the chance will actually
command in the market. It is equal to the mathematical
value multiplied by the coefficient of caution, Ch. XVI, § 6.
mathematical value of.
The product of the value of the prize
at stake multiplied by the chance of winning it.
Ch. XVI, § 5.
The ratio of commercial value to matheCoefficient, of caution.
matical value. Ch. XVI, § 6.

—

SUMMARY OF DEFINITIONS
Coefjicient, of 'probability.

Ch.

less value.

of risk.

331

— The ratio of mathematical value to

XVI,

risk-

§ 6.

— The ratio of commercial value to

riskless value

the product of the coefficient of caution multiplied
coefficient of probabiUty.

—
—

Ch. XVI,

;

hence

by the

§ 6.

Commercial basis.
(See Basis, commercial.)
value of a chance.
(See Chance, commercial value of.)
Commodities.
Movable instruments not human beings. Ch. I, § 2.
Consumption.
(See Services, enjoyable objective.)
Couple.
A liability to a debtor and its counterpart asset to the
creditor.
Or the service of one instrument acting on another
and the counterpart disservice of the second acted on by the
first.
Ch. VI, § 1 Ch. IX, § 2.
Coupled services.
(See Couple, Interaction.)
Depreciation fund.
(See Fund, depreciation.)

—
—

—

;

—
—

Desirability of goods (wealth, property, or services)
sity of desire, for those goods, of

— The inten-

a particular individual at a

particular time under particular circumstances.

Ch. Ill,
marginal

§ 2.

(Syn. Utility.)

—

— of

a specified aggregate of goods.
Approximate
desirability of one unit more or less of that
aggregate, or the difference between the desirability of that
aggregate and another aggregate one unit larger or smaller.
Ch. Ill, § 4.
Exact definition The limit of the ratio of the increment
(or decrement) of desirability to the increment (or decrement)
of the aggregate when the last-named increment (or decrement)
approaches zero. (Syn. Marginal utility.)
Appendix to Ch.
definition

The

Ill, § 1.

progressive marginal

— of

desirability of one unit

gressive marginal utility.)
regressive marginal
sirability of

—

The
a specified aggregate of goods.
more of that aggregate. (Syn. ProAppendix

to Ch. Ill, §

— of a specified aggregate

one unit

less of

of goods.

that aggregate.

— The

de-

(Syn. Regressive

utility.)
Appendix to Ch. Ill, § 1.
an aggregate of goods.
The difference between the
desirability of goods which include and of those which exclude

marginal
total

— of

—

that aggregate.

Dimension.

its

to Ch.

— The

(Syn. Total

utility.)

Ch. Ill,

§ 4.

kind or species of any magnitude as indicated
measurement in terms of other magnitudes. Appendix
I.

Discount curve.
represents

— A curve so constructed that,
any given sum, any

one of

its

ordinates

later ordinate will represent the

NATURE OF CAPITAL AND INCOME

332

"amount" of
by the

sented

that

sum

at a time later

by an

interval repre-

horizontal distance between the ordinates

;

and

consequently also such that any earlier ordinate will
represent the "present value "of that sum at a time earlier
by an interval represented by the horizontal distance between
the ordinates. Ch. XIII, § 1.

which

—

The deficiency below unity of the ratio of
of.
exchange between the values of present and future goods, taken
in relation to the time interval between the two sets of goods.
Ch. XII, § 7.
The rate of discount may, like the rate of interest, be reckoned annually, semi-annually, quarterly, or continuously. (It
may also, theoretically, be taken in the price sense as well as
in the sense above, but practically never is.)
total.
The difference between any sum and its discounted or

Discount, rate

—

present value.

—

Discounted value.
(See Value, present.)
A negative service. An instrument renders a disDisservice.

—

service when,

its

means, an undesirable event

or a desirable event prevented.

Ch.

II,

§ 2;

promoted

Ch. VIII,

§ 1.

— Negative
(Syn. Undesir
Ch.
§2.
Earnings. — (See Income,
Exchange. — The mutual and voluntary transfer of goods (wealth,
Disutility.

utility.

Ill,

ability.)

earned.)

property, or services) between two owners, each transfer being
in consideration of the other.

Expense.

Ch.

I, §

4; Ch. II, § 3.

— Outgo in the form of money-spending.

Ch. VIII,

§ 1.

— The quantity of any
thing undergoing any
change during any
period of time. Ch. IV,
— The
duration.
a flow to
Ch. IV,
value.
Ch. IV,
Fund. — A stock of wealth or property or
amortization. — (See Fund,
— A fund formed by accumulating that part

Flow.

specified

speci-

specified

fied

ratio of

rate of.

§ 1.

its

§ 1.

its

§ 1.

depreciation.)

depreciation.

income which must be turned back into capital to maintain the
It may also be defined as formed from
capital-value intact.
the difference between real income and earnings, when that
difference

accumulated.

income is uniform and runs only for a fixed term, the
depreciation fund may also be defined as formed from a succession of equal payments out of income, such that if each be
accumulated at compound interest, the total will be equal to the
(Syn. Amortioriginal capital at the end of the income term.
If the

zation fund.)

Ch. XIV,

§ 6.

SUMMARY OF DEFINITIONS

333

—

A fund formed by accumulating the difference
Fund, sinking.
between actual income and a terminable annuity which has
the same present worth.
As applied to bonded debts it may also be defined as
formed by accumulating an annual sum such that its amount
will just suffice to

end

—

Abbreviation
Income.
Ch. VIII, § 1.

— Statement

account.

for

any

earned,

Income

of specified

capital or to a person.

sum

at the

and Income

value.

equal (or extinguish) a given
Ch. XIV, § 7.

of a given period.

services

income and outgo, whether from

— Income

capital.

the capital (or minus

its

appreciation

plus

realized

depreciation).

I.e.

that income

which a given capital can yield without alteration in its value.
If interest be assumed invariable and all future income foreknown, this definition is equivalent to another, viz. the uniform
and perpetual income which a given capital might yield;
but the equivalence ceases if interest varies (see Appendix to
Ch. XIV, § 1) or if future income is unknown. (Syn. Earnings,
Standard income.)
enjoyable.

VII,

— Income

XIV,

Ch.

§ 4.

which consists of enjoyable

services.

Ch.

§ 6.

— Sum of positive income elements. Ch. VII,
— The income from the entire capital of an individual.
Ch. VII,
money. — Income which consists of the receipt of money.
Ch. VII,
7 Ch. IX,
natural. — Income which consists of services not obtained by
exchange. Ch. VII,
7; Ch. IX,
— The difference between gross income and outgo. Ch. VIII, §1.
(Syn. Subjective
psychic. — Agreeable conscious experiences.
income.)
Ch. X,
— Actual income, the value of
from any
actual
— The flow services from that capital
any
through a period of time. Ch. VIII,
— The income from the entire capital of the
Ch. VII,
standard. — (See Income,
— (See Income,
— The value of income-services.
from any
Ch. VIII,
Ch.
of wealth.
Instrument. — An individual
gross.

§ 1.

all

individual.

§ 7.

§ 5.

;

§ 5.

net.

§ 3.

capital

realized,

its

i.e.

services.

capital.

services, of

§ 1.

society.

social.

§ 7.

earned.)

psychic.)

subjective.

capital.

value,

its

§ 1.

article

§ 1.

NATURE OF CAPITAL AND INCOME

334
Interaction.

— An event which

a service of one capital and at the

same time a

disservice of another.

Intermediate

service,

Ch. IX,

§ 2.

Interacting services.

Preparatory

— (See
— (See

(Syn. Interacting service,
service,

Coupled

service.)

Interaction.)

Intermediate services.

Interaction.)

— The product of the rate of interest multiplied by the
Ch. XIV,
capital-value.
nominal. — The stipulated annual payments on a bond or note

Interest.

§ 4.

nominally (but not always in fact) equal to the interest on the
"principal." Ch. XIII, § 7.
Many meanings are given below. The standard meanrate of.
ing used in this book is that called "rate of interest in the premium sense reckoned annually."
In the price sense : The ratio between the annual rate
rate of.
of a perpetual annuity and the equivalent capital- value.

—

Ch. XII,

§ 2.

is said to be reckoned annually if the
annuity is payable in annual installments; it is said to be
reckoned semi-annually, if the annuity is payable in semiannual installments; quarterly, if in quarterly installments;
continuously, if payable continuously.
In the premium sense: The excess above unity of the
rate of.
rate of exchange between the values of future and present goods
taken in relation to the time interval between the two sets of
Ch. XII, § 4.
(Syn. rate of interest in the agio sense.)
goods.
The rate of interest is said to be reckoned annually if the two
This is the standard meaning
sets of goods are one year apart.
It is said to be
of the "rate of interest" as used in this book.

The

rate of interest

—

reckoned semi-annually,
terly,

three

they are a half-year apart; quar-

months apart;

continuously,

infinitesimally

apart.
rate of.
rate

of.

— In agio sense (See in premium
— Reckoned annually, semi-annually,

sense.)

quarterly,

contin-

uously: (See under rate of interest in price sense and rate of
interest in

premium

sense.)

— The difference between any sum and "amount."
Appendix to Ch. XIII,
the form of human exertion. Ch. X,
Labor. — Outgo
Ch.
part of the earth's
Land. — Wealth which
improvements. — Wealth constructed upon and attached to land,
Ch.
§2.
Ch. V,
obligations due
a person. — Amount
its

total.

§ 7.

§ 6.

surface.

§ 2.

Liabilities of

others.

§ 1.

SUMMARY OF DEFINITIONS

335

—
—
—

Mathematical basis.
(See Basis, mathematical.)
(See Chance.)
value of a chance.
The method of summing capital- or inMethod, of balances.
come-accounts which consists in first deducting the sura of
the negative items in each from the sum of the positive items,
and then adding the "balances" thus obtained. Ch. IX, § 2.
The method of summing capital accounts and income
of coufles.
accounts which consists in canceling out the "couples.'
Ch. IX, § 2,
Outgo.
Negative income. Ch. VIII, § 1.
net.
Net income, when negative. Ch. VIII, § 1.
Person.
Any owner of property, whether real or fictitious. Ch.

—

—
—
—

II, § 3.
fictitious.

— An imaginary entity

(such as a firm or corporation)

regarded, for bookkeeping purposes, as holding property for

a number of other persons (real or fictitious.) Ch. II, § 2.
An owner of property who is a living human being.
Price.
A ratio of exchange. Ch. I, § 4.
The quotient found by dividing the money exchanged
money.
for goods by the quantity of the goods themselves.
Ch. I,
real.

—
—

—

§4.
Principal.

— The

final

payment on a bond

or note, supposed to be
sum " lent."

(but not always in fact) equal to the original

Ch. XIII,

§ 7.

— (See Interaction.)
— See Chance.
— The ratio mathematical value to
value.
Ch. XVI,
Production. — (See Transformation.)
— (See Transformation.)
Productive
services of capProductivity, physical. — The
the quantity
Ch. XI,
per unit
time to the quantity of the
— The ratio the value of services of capital per unit
the
Ch. XI,
time to the quantity
— Rights to the chance of future
Property
property
services
wealth.
Ch.
complete. — The exclusive right to
the services of an
instrument. Ch.
— The right to part of the services an instrument, other parts belonging to other owners. Ch.
Purchase. — An exchange of money for goods. Ch.
— Land and land improvements. Ch.
Real
Resources. — (See

Preparatory services.
Probability.

coefficient of.

riskless

§ 6.

process.

ratio of

capital.

ital

§ 2.

value.

rights)

(or

§ 2.

capital,

II, § 3.

right,

all

II, § 10.

right, partial.

II, § 10.

§ 4.

I, § 2.

estate.

Assets.)

NATURE OF CAPITAL AND INCOME

336

Return, physical.

— The

ratio of the quantity of services of capital

to the value of the capital.
value.

— The

Ch. XI,

§ 2.

ratio of the value of services of capital to the value

Ch. XI,

of the capital.

Risk, coefficient

— The

§ 2.

commercial value to riskless value.
product of the coefficient of probability multiplied by the coefficient of caution.
Ch. XVI, § 6.
of.

ratio of

It is equal to the

— (See Basis,
— The value which a thing would have
nated. Ch. XVI,
value
a chance. — (See Chance.)
— An exchange goods money. Ch.
— An instrument renders a service when, by

Riskless basis.

riskless.)

value.

risk

were elimi-

§ 6.

Sale.

for

§ 4.

Service.

desirable event

(Syn. Use.)

Ch.

Services, coupled.

its

means, a

promoted or an undesirable event prevented.
II,

§ 2.

— (See
— Services received directly by human beings,
Interaction.)

enjoyable objective.

and not (hke

by other

interactions) merely received for

objective capital.

Ch. X,

sumption.)

(Syn. (not well

human

beings

chosen) Con-

§ 1.

— (See Interaction.)
preparatory. — (See Interaction.)
Sinking fund. — (See Fund, sinking.)
Standard income. — (See Income, earned.)
Standardize. — To standardize a given income
to convert
into
equivalent income earned.
Stock. — The quantity of any specified thing at any instant.
(Syn.
Fund.) Ch. IV,
Transaction. — That
an exchange which
to one of
intermediate.

its

§ 1.

side

the exchangers

Ch. IX,

;

relates

credit

and a

debit.

§ 9.

— An interaction which
Transformation. — An interaction
Transfer.

Ch. IX,

two items, a

consists of

a change of ownership of wealth.

§ 3.

condition of wealth.

Ch. IX, §§
Transportation.

a change of form or
Productive process.)

2, 3.

— An interaction
Ch. IX,
— Negative

position of wealth.

Undesir ability.

which

(Syn. Production,

which

a change of place or

§§ 2, 3.

desirability.

(Syn.

Ch.

Disutility.)

Ill, § 2.

Utility of goods.

(See Desirability.)

— The value

of goods (wealth, property, or services)
product of their quantity multiplied by their price. Ch.

Value.

the

I, § 6.

SUMMARY OF DEFINITIONS

337

—

Value, commercial, of a chance.
(See Chance.)
discounted.
(See Value, present.)

—

— (See Chance.)
— The quantity of goods multiplied by
money
— The present value of any given future goods

mathematical, of a chance.

money.
Ch. I,

their

price.

§ 6.

is the
quantity of present goods which will exchange for those future
goods.
(Syn. Present worth. Discounted value.) Ch. XIII, § 1.
riskless, of a chance.
(See Chance.)
Wealth (in its broader sense).
Material objects owned by

present.

—

human
(in its

beings.

Ch.

I, § 1.

narrower sense).

— Material

article of.

—A

Instrument.)
of.

Ch.

single object of wealth.

Ch.

article of.)

Ch.

present.)

§ 2.

(Syn. Item of Wealth,

I, § 1.

— (See Wealth,
Worth, present. — (See Value,
item

owned by human

objects

beings and external to their owners.

I, § 1.

APPENDICES
Appendix to Chapter

Appendix to Chapter III
Appendix to Chapter VII

Appendix to Chapter XI
Appendix to Chapter XII
Appendix to Chapter XIII
Appendix to Chapter XIV
Appendix to Chapter XVI

APPENDIX TO CHAPTER
§

1 (to Ch.

§ 7)

Dimensions of Wealth, Price, and Value

What

matliematicians call the "dimension" of a magnitude

simply

its species or

kind, as indicated by

its

measurement in

terms of other magnitudes of the same or different kinds. It
Consider
is expressed mathematically by a letter or letters.
amount
of beef,
any
given
If
represents
for
example.
h
beef,
say three hundred pounds, this letter may be taken to indicate

The

"dimension."

its

where

amount

price of beef in terms of

wheat

—

stands for the amount of wheat exchangeable for an

The expression —

h of beef.

(or, as it

may

be written,

thus expresses the "dimension" of price. It matters
not what particular price of beef in terms of wheat is referred
Every price is of the same form wb~^. Finally, the dito.
wb~'^)

" value " of the beef in terms of

mension of the

for this value is the product of the
price,

w
—

I.e.

its

is,

its price

wheat

beef,

x~w = w.

That

amount of

the dimension of beef

represented by

jp=— =100

bp =

value by

b— = w.

We thus have a different

dimension for each of the three differThis fact is expressed in common language,
We measure cloth in yards, the price of cloth in bushels
also.
per yard, the value of cloth simply in bushels. Price and value
ent magnitudes.

differ as

fundamentally as velocity and distance, which are
feet per second and plain feet; or as

measured respectively in

341

NATURE OF CAPITAL AND INCOME

342

density and weight, which are expressed in pounds per cubic

and simply pounds.
may seem at first that these distinctions between the
dimension of price, quantity, and vahie are somewhat strained.

foot

may

be claimed that price is simply the value of a unit, and
In the
is simply the price of the whole quantity.

that value

same way it
moving body

is
is

sometimes loosely said that the velocity of a
simply the distance traversed in a unit of time.

It is quite true, of course,

the value of a unit of wealth

that the
is

expresses the price per unit.

number which expresses

the same number as that which
It is

likewise true that the

number which expresses velocity is the same as that which expresses the distance which will be traversed in a unit of time.
Yet velocity is not distance, and no more is price, value; although
practically where the wealth under consideration is or may
be regarded as a single unit, it is less necessary to insist on
If the price of a.
the distinction between value and price.
" unique " is $25 per unit, then its value is also $25. If a farm
of 100 acres has a value of $5000, the price of the farm as a.

and not as measured in acres, is $5000 per farm.
But as soon as we have to deal separately with a single unit
and a number of units, we must make a distinction between
price and value.
That they are not of the same dimension is
clear from the fact that the number expressing the price of
beef in terms of wheat varies with both the unit of beef and of
wheat, while the number expressing the value of beef varies
only with the unit of wheat. Thus, if the quantities of beef and
wheat which exchange for each other are 300 pounds and 60'
bushels respectively, the price and value of the beef in terms,
of the wheat will be
single thing,

price of the beef, | bu. per

lb.

value of the beef, 60 bu.

change in the unit of measurement for beef will evidently
two numbers. Thus, if the beef is
measured in ounces (4800 oz.) instead of in pounds, the numaffect only the first of these

bers

become
price of the beef, -^ bu. per oz.

value of the beef, 60 bu.

APPENDIX TO CHAPTER

343

the other hand, a change in the unit for measuring the

wheat

will affect both numbers.
Thus, if wheat is measured in pecks instead of in bushels (while beef is still measured in pounds), the numbers representing price and value will
change from ^ and 60 to |- and 240 respectively, each being
magnified fourfold.
We see then that the value and price of beef are similar

in that they are similarly affected by a change in the unit of

wheat but are different
a change in the unit of
It

may

in that they are differently affected

beef.

aid the reader

who

unfamiliar with the subject of

the dimensionality of magnitudes to indicate a few of
cations to physical science.

its appli-

taken to represent the

di-

mension of length, area will be represented by Z^ and volume
by l^. Consequently, length, area, and volume are said to be
respectively of one, two, and three "dimensions," because
Z, l^, and l^, which represent their dimensionalities, have for exponents 1, 2, and 3 respectively. The term "dimension" was
originally applied simply to these cases of length, area, and
volume. But it soon came to be extended to apply to every
sort of mathematical magnitude. The following examples are
noted without comment (I stands for length, m for mass, and
t

for time)

—

Velocity, of dimension

Acceleration,

lt~'^,

or feet per sec.

or feet per sec. per sec.

pounds feet per sec.
pounds feet per sec. per sec.
or pounds feet feet per sec. per
or pounds feet feet per sec. per

per

sec.
sec.

sec.

To illustrate the meaning of this table, we observe that the
number which represents work (or energy) would be affected
by a change in the units of mass, length, and time, as follows
Halving the unit of mass (so that the number representing any
mass would be doubled) would double the number representing
the work halving the unit of length (so that the number representing any given length would be doubled) would quadruple the number representing work halving the unit of time
:

;

NATURE OF CAPITAL AND INCOME

344

(so that the number representing any given time would be
doubled) would quarter the number representing the unit of
work.
The idea of " dimension " and its mode of representation are

important subjects, for a fuller treatment of which the reader
is referred to the article on the subject in Palgrave's Dictionary
its more general applicaSystem of Units, 1891.

of Political Econoiny, as well as for
tions to J. D. Everett's C.G.S.

APPENDIX TO CHAPTER
§

1 (to Ch. Ill,

III

Definition of Marginal Desirability

express mathematically the marginal utility or desirabil-

ity of

any group of goods,

For instance,
coal containing 15 tons, and if
of that increment.

of 3 tons.

that

—

will

any increment of

let Aa; represent

goods measured in any specified unit, and

mean the

reference

the desirability

Aa? represents

had to a bin of
an increment

desirability of those 3 tons, so

will represent the average desirability per ton of 3 ad-

Aic

ditional tons.

we suppose

the increment Aa; to be succes-

sively decreased to 2 tons, 1 ton,

approaching zero as a

limit,

ton,

and

the expression —

indefinitely,

will

mean

suc-

cessively the average desirability per ton of 2 additional tons,

the desirability of 1 additional ton, the desirability per ton of
i an additional ton {i.e. twice the desirability of that additional half ton), the desirability per ton of \ an additional ton
{i.e. four times the desirability of an additional ^ of a ton),
etc.

The

limit of this series will be the desirability per ton of

an infinitesimal increment of
the fraction

—
dx

This,

which

coal,
is,

and may be expressed by

as mathematicians say, the

assuming continuity,
have the same value if, in place of the increment, a decrement
were considered that is, if instead of supposing the owner of
the 15 tons to add 3 tons, we suppose him to subtract 3 tons.
differential quotient of desirability, will,

;

APPENDIX TO CHAPTER
Then

—
would
Ax

represent the average desirability per ton of

this 3 tons subtracted,

which would evidently be somewhat
ton of 3 additional tons.

greater than the desirability per

But when we

345

VII

substitute for 3 tons, the smaller magnitudes

2 tons, 1 ton, i ton, i ton,

etc.,

the resulting value of

—

or the

desirability peo' ton of this constantly lessening decrement, will

become equal,

at the limit, to the desirability per ton of the

The

constantly lessening increment.

—
dx

The expression

—
indicates
dx

limit of

the

and when the

article

may

expressed

more exactly than could be

indicated in the text the true meaning
ability,

—

marginal desir-

be indefinitely subdivided,

marginal desirability is the same whether reckoned
Practically, however, such
increments or decrements.

mathematical subdivision does not always apply, and it may
even happen that the desirability of one unit more may be
materially different from the desirability of one unit less. For
instance, the owner of one piano may esteem it very highly,
but a second piano would have almost no desirability. Here
the desirability of one unit less is far greater than the desirability of one unit more, owing to the fact that the piano is an
indivisible unit, and we can consider no increments or decrements except of whole pianos. In this case instead of one
marginal desirability we have two, which may be distinguished
as " regressive "

and " progressive."

APPENDIX TO CHAPTER
§

VII

1 (to Ch. 7, § 1)

Specimen Definitions of Income

Murray, English Dictionary on Historical Principles, 1901.

Income

spec{ijically'].

That which comes in as the

periodical produce of one's work, business, lands, or invest-

ments (considered in reference to its amount, and commonly
expressed in terms of money); annual or periodical receipts

NATURE OF CAPITAL AND INCOME

346

accruing to a person or corporation revenue. Formerly also
receipts, emoluments, profits
but the plural is now
in pi.
;

;

used only in reference to more than one person. (The prevailing sense.) 1601, E. Johnson, Kingd. & Commun. (1603) 196.
Paying the expense of one yere with the income of another.
1633, Herbert, Temple,

XXVII. Never exceed thy
Oomm. Angells. 152. Hee hath
paines and cost; now what are his

Cli.

Porch.

1646, H. Laurence,

income.

"beene at a great deale of

in-comes ?

1652, C. B. Stapylton, Herodian, 16.

scraped

and never was content. But studied more his Incomes to
augment. 1697, Dryden, Virg. Georg. II, 285. No Fields afford
So large an Income to the Village Lord. 1789, Loiterer, No.
Having lived, what is called up to his income, that is,
43, 10.
a good deal above it. 1802, Med. Jrnl. VIII, 229. Income, in
its usual acceptation, is a loose and vague term
it applies
equally to gross receipts and to net produce: But when the
Legislature had limited it to be synonimous with profits and
gains, it became as clear and precise as any other word.
1866,
George Eliot, F. Holt, ii, 1, 76. No, I shan't attack the Church
only the incomes of the bishops, perhaps, to make them eke
still

;

out the incomes of the poor clergy.
These definitions afford no means of deciding on net income. If income is simply what comes in and outgo simply what goes out, and if in
any year as much passes out of one's hands as comes in, is the net income
izero?

Dr. N. G. Pierson, Principles of Economics Trans, by A. A.
London (Macmillan & Co.), 1902.
Wotzel, Vol. I, p. 76.

By social income we mean the sum-total of economic goods
which a nation has at its disposal in a given period of time;
the net result of the productive labour of the nation during that
time.
Is not its capital

" at

its

disposal " in

Economy (2d

Is it

then income

Eng. trans.,
speaking of national wealth, says that gross income con-

Eoscher, Principles of Political
p. 5),

any period

sists of,

" (a)

" (6)

vol.,

—

Of the raw material newly obtained in the country.
Of imports from foreign countries, including that which
is secured by piracy, war booty, contributions, etc.

APPENDIX TO CHAPTER
"

(c)

The

increase of values

add

to the first

final

" (d)

two

347

VII

which industry and commerce
up to the time of their

classes

consumption.

Services in the narrower sense and the produce of
capital in use.

find the national net

ing items

—

income we must deduct the follow-

"(a)

All the material employed in production which yields

" (6)
" (c)

The exports which pay for the imports.
The wear and tear of productive capital and

no immediate satisfaction

any personal want.
capital in

use."
illustrated is the method which takes its
from the goods. There is another method which
takes its starting point from the persons who receive them.
By this method the national income is to be calculated as

The method thus

starting point

follows

"(a)

—

From

the net income of all independent private busi-

nesses, etc,

" (b)

From

the net income of the state, of municipalities,

corporations and institutions,
" (c)

derived from their

own resources.
Under the former heads must be taken

into the account
such parts of property as have been immediately

consumed and enjoyed.
"(d) Interest on debt must be added only on the side of
the creditor and deducted from the income of the
debtor."

How

double counting to be avoided if " raw materials produced"
and also "the produce of capital in use" (d)? "Increase

(a) are income
of values" (c)

not income but capital.

Alfred Marshall, Principles of Economics, Vol.
London (Macmillan), 1898.

"Another convenient term

pp. 149, 150.

the usance of wealth.

means

income of benefits of every kind which a person
derives from the ownership of wealth, whether he uses it as
the whole

capital or not.

Thus

includes the benefits which he gets

NATURE OF CAPITAL AND INCOME

348

from the use of his own piano, equally with those which a
piano dealer would win by letting out a piano on hire.
" This income is most easily measured when it takes the form

payment made by a borrower

for the use of a loan for,
then expressed as the ratio which that payment bears to the loan, and is called interest. But this term
is also used more broadly to represent the money equivalent to
the whole income which is derived from capital.
#
*
*
*
*
*
*

of a

say, a year

it is

;

"Social income may be estimated by adding together the
incomes of the individuals in the society in question, whether
it be a nation or any larger or smaller group of persons.
Everything that is produced in the course of a year, every service rendered, every fresh utility brought about is a part of the
national income.

"We

same thing twice.
we have already
counted the values of the yarn and the labour that were used
But if
in making it and these must not be counted again.
the carpet is cleaned by domestic servants or at steam scouring
works, the value of the labour spent in cleaning it must be
If

must be

careful not to count the

we have counted a

carpet at

its full value,

;

counted in separately

;

for otherwise the results of this labour

would be altogether omitted from the inventory of those newlyproduced commodities and conveniences which constitute the
real income of the country."
"Usance

wealth"

is apparently identical with income as explained
"Social income," however, seems at variance with the
concept of " usance " for it includes concrete wealth.

in this book.

;

William Smart, The Distribution of Income, London (Macmillan), 1899, p. 18.

"In any

case, the

attempt at classification seems to bring

out clearly that there are, conceivably, two ways of computing
the one which takes it as the sum
any additions to capital, the other
which takes it as the sum of the services which contribute
to the making of them and that these two are alternatives.
Either alternative, however, may be used when different purposes are in view and the thesis which I put forward is that.

the real National Income

of consumption goods plus

;

APPENDIX TO CHAPTER

349

VII

while the National Income must be conceived of as the total
sum of consumption goods, as these and these alone are the

means of satisfying the end of economic action, the life of man,
must be calculated as the sum of the contributory services."

Includes concrete goods and abstract services.

Taussig, Wages and Capital
York), 1906, p. 36.

would seem

best, therefore, to let the

simply for inchoate wealth
yet serve
houses,

(Appleton

New

Co.,

term capital stand

for all the possessions that do not

human wants. Tools and machines, factories and ware-

raw materials and

— these

half-finished

and nearly finished

go together as being not directly conducive
to enjoyment; while all forms of finished commodities
food,
goods,

houses,

all

clothes,

ornaments

—

— belong

together

enjoyable

wealth and as income."
Are houses income

Henry Rogers

New

Seager, Introduction

Economics (Holt

Co.,

York), 1904, pp. 163-164.

"The money income

merely the convenient medium by
income of the community is divided
among those entitled to share it. This real income consists of
consumable goods for those who spend their entire money
incomes, and partly of consumable goods and partly of capital

means

which the

goods for those

As to
and the

who

real

save."

the inclusion of "savings" under Income, see text of this chapter
fuller

treatment in Chapter XIV.

Charles Jesse Bullock, Introduction

to the

Boston

rev. ed.

"In

this

way

(Silver,

Burdett

the social income for any

be divided into four constituent parts
"1.

Study of Economics,

Co.), 1900, p. 376.

—

month

or year

may

The satisfactions derived from durable consumable goods,

the product of past industry, that

still

remain in the possession

community and add to its material enjoyments.
"2. The personal services at the disposal of the society during the period for which the income is computed.
"3. The material goods of a consumable character that are
of the

the product of the current industry for the period considered.

NATURE OF CAPITAL AND INCOME

350

"4. The producers' goods, or capital, created by the current
industry of the period, and available for the production of
economic goods during the following periods."
double counting avoided

;

Frank A.

Are material goods
from them ?

e.g.

then, in addition, the satisfactions

Fetter, Tlie Principles of Economics,

Century Co.

be counted, and

New York

(The

1904, pp. 40, 41.

3. " Objective income consists of the additional sums of goods
acquired by individuals or by society during the income period.
TV
tF
^
:^
^
^
^

" Income in the logical sense must be a net addition, but the

term gross income

is not loithout popular and practical meaning.
sometimes spoken of in the sense of total
receipts, as the total of goods secured; net income is the remainder after deducting expenditures and after replacing the
goods employed to secure the income. In order to produce
some goods technically, men make use of other goods. While
they are storing up a supply of wood or coal it may be looked
upon as the income, but they may burn it to help grow hotWhile they gather flowers with one hand, they
house plants.
destroy fuel with the other. Only the net increase in value
can be accounted income in the second period. The goods
that come into a man's possession in any period are of many

Gross income

sorts

to get

some he has destroyed many previously existing

goods; while to get others he has not needed to use up the
accumulations of the past or to mortgage the future. The one

kind

is gross,

the other net income.

income of consumption goods is a part of wealth, but
The consumption goods, the 'present
not the whole of it.
5.

goods' at the moment available, are the essential part of
wealth for the moment's enjoyment. The only essential and
immediate conditions of a series of gratifications is a regular
series of consumption goods.
But many things existing which
could be used to secure a gratification are not in fact treated
as

consumption goods.

a time of famine
last year,

A crop

of corn is not all income.

could be used, but seed-corn was saved from

and some must be kept for next year.

This

APPENDIX TO CHAPTER

351

VII

part of wealth, but not of 'present goods'

we understand

the term."
" Goods " are not income.

Increase of value

not income.

See text.

Kleinwachter, Das Einkommen und seine Verteilung, Leipzig,
1896, pp. 11, 12.

So bestimmt beispielweise das Einkommensteuergesetz
26. Marz, 1886, im Sec. 4:

—

Hamburg vom

flir

von dem reinen Einkommen oder
in Geld oder Geldeswert
(etwaige selbstverwohnte Miete, den Wert etwaige freier

"Die Einkommensteuer
Erwerb zu entrichten, d.

ist

h. alien

Wohnung, Naturallieferungen

hinzugerechnet)

beste-

henden Einnalimen des Steuerpflichtigen, ohne Ausnahme,
gleichgiltig aus welcher Quelle sie gefiossen.

."^

Ahnlich sagt das sachsische Einkommensteuergesetz vom
Juli, 1878,

15:

"Als Einkommen

—

gilt die

Summe aller
Einnahmenmit
Wohnung im eigenen Hause,
.

Einschluss des Mietwertes der
sowie des Wertes der

zum Haushalt verbrauchten Erzeugnisse

der eigenen Wirtschaft.

Und

fast mit denselben

Worten, nur etwas minutioser und

sagt der osterreichische

genauer,

betreffend die

§195:

—

Entwurf

direkten Personalsteuren

"Als Einkommen

gilt die

Summe

eines

vom Jahre

aller in

Gesetzes,

1892,

Geld oder Geldes-

wert bestehenden Einnahmen der einzelnen Steuerpflichtigen
mit Einschluss des Mietwertes der Wohnung im eigenen Hause
oder sonstiger freier Wohnung, sowie des Wertes der zum
Haushalte verbrauchten Erzeugnisse der eigenen Wirtschaft
und des eigenen Gewerbebetriebes, sowie sonstiger dem
Steuerpflichtigen

Bemerkenswert

allenfalls
ist,

dass

zukommender

ISTaturaleingange."

keine dieser Gesetzesstellen die

einzelnen Arten oder Zweige oder Bestandteile des Einkom-

mens, die der Steuer unterworfen sein sollen, taxativ aufzahlt,
sondern dass die in Eede stehenden Gesetze das "Einkommen"
ganz allgemein zu definieren bestrebt sind. Und der Tenor ist
jedesmal

Unter Einkommen versteht man

alle in

Geld oder

NATURE OF CAPITAL AND INCOME

352

Geldeswert bestehenden Einndhmen, gleichgiltig aus welcher Quelle
sie gejiossen.''

Da nun

in unserer heutigen auf der Grundlage

des Privateigentums und der Individualwirtschaft aufgebauten

Volkswirtschaft
alle

erdenklichen Sachgtiter,

erdenklichen Nutzungen dieser Sachgiiter und
erdenklichen personlichen Dienstleistungen um Geld
verkauft und gekauft werden konnen und demgemass " Geldes2.

alle

wert haben," so ergiebt sieh, dassder Gesetzgeber alle materiellen und immateriellen Gliter, die in die Wirtschaft des
Einzelnen treten, unter den Begriff des Einkommens subDas heisst also mit anderenWorten:
sumiert wissen will.
.

der Gesetzgeber definiert den Einkommensbegriff in der nam-

und zwar so, dass
werden sollen,
welcbe entweder in die eigene Wirtschaft von aussen hereinkommen, oder welche innerhalb der eigenen Wirtschaft neu
entstehen, und zwar gleichgiltig ob diese Giiter materielle (oder
Sach-) Giiter, oder ob sie immaterielle Giiter (d. i. Nutzungen
von Sachgiitern oder personliche Dienstleistungen) sind.

lichen Weise, wie es oben definiert wurde,

"Einkommen"

unter

Giiter verstanden

include in income all newly acquired or newly produced goods

clearly to include too

shown

alle

much.

To restrict income

in the text, to err both in inclusion

the income shall be

required to

make

Kleinwachter,

"rein" or "net" without

op.

money receipts is, as
and exclusion. To require that
to

defining the deduction

to leave the definition incomplete.

cit.,

pp. 22-23.

An dieser Stelle gentigt die Bemerkung, dass die HekMANN-ScHMOLLEBSCHE Definition oder Auffassung des
(Einzel-) Einkommens bis auf den heutigen Tag so ziemlich
(die abweichenden Meinungen sollen welter unten erwahnt
werden) die herrschende geblieben
wirtschaftliche Untersuchungen."
S.

582

ist.

583) definiert das (Einzel-)

Hermann
Aufl.,

(" Staats-

Miinchen, 1870,

Einkommen wie
so wenig

"So wenig jede Ausgabe Verbrauch ist,
Einnahme Einkommen. Dieses ist vielmehr

die

folgt:
ist

Summe

jede

der

wirtschaftlichen oder Tauschgiiter, welche in einer gewissen
Zeit zu dem ungeschmalert fortbestehenden Stammgut einer
Person neu hinzutreten, die sie daher beliebig verwenden kann.

APPENDIX TO CHAPTER
Dass es ebensowohl korperlicher
konne,

ist

353

VII

als unkdrperlicher

Natur sein

klar."

Und im Anschlusse an diese Hermannschb Definition des
Einkommens sagt Schmolleb ("Die Lehre vom Einkommen
u.

w." in der "Zeitschr.

Bd. 19,

ff.

speciell S. 19):

" Einkommen ist

d. ges,

—

also die

Staatsw. "

Summe von

Jalirg. 1863,

wirtschaftliclien

Giitern, die ein Subjekt in einer gewissen Zeit zur Befriedigung

Schmalerung seines Vermogens verwenden kann. Filr Jeden sind die Frilclite seiner Arbeit und
seines Vermogens sein ursprtingliches Einkommen; ein abseiner Bedlirfnisse ohne

geleitetes hat nur der, welcher solcbe Ertichte nicht hat d. h.
Zum Einkommen
nur er lebt vom Einkommen anderer.
gehoren stets aiich samtliche unmittelbar, d. h. ohne Tausch,
verbrauchten oder genossenen Ertichte der Arbeit und des
Vermogens."
;

The foregoing definitions express in a general way wiiat we have called
" earnings " as distinct from " income." They err however by fixing on
concrete commodities in place of their services and in some other respects.
See text.

In erschopfender Weise hat Adolf

Wagner

bisher geschilderten Auffassung entspringenden

"Grundlegung" (1. Aufl., S. 96
Einzelneinkommen defin-

definitionen in seiner bekannten

97 ) zusammengefasst,
iert wie folgt:

—

"Im Einkommen

wenn

sie

empfangt, daher mit

Das Einkommen
"1.

Diejenige

er das

(einzeln in den Einktlnften)

Einnahmen oder Ertrage

die aus der

Einkommens-

werden die

in Beziehung mit der Person, welche

dem

Wirtschaftssubjekte gebraeht.

einer Person umfasst zweierlei:

—

Summe

welcher der-

wirtschaftlicher

selben in gewissen Perioden

Giiter,

regelmassig und daher mit

der Fahigkeit der regelmassigen Wiederholung als Eeinertrage
einer festen Erwerbsquelle neu als

Dieser Teil des

Einkommens

Vermogen hinzuwachsen.

einer Person rilhrt daher aus der

Wirtschaftsfilrung ilberhaupt und aus einzelnen
lichen Thatigkeiten (Arbeit,

wirtschaft-

Unternehmung) oder aus Eigen-

tums- oder Eorderungsrechten inbesondere (Sklaveneigentum,
Grundeigentum, Kapitaleigentura, Eorderungen aus Kreditge-

NATURE OF CAPITAL AND INCOME

354

endlich

schaften),

aus

regelmassigeu

nahmen (Almosen, Geschenk)

unentgeltlichen Ein-

her.

Die Gentisse (JSTutzungen) oder selbst nur die Genuss-

"2.

moglichkeiten, welche das ISTutzvermogen einer Person nach.

Abrechnung der dabei stattfindenden Abnutzung und Verkehrswertverminderung periodisch. fortdauernd gestattet.
" Das Einkommen einer Person bildet zunacbst den Giiterf end
zur Befriedigung ihrer Bedtirfnisse.

Seine Erwerbung

Es kann

Mittel zu letzterem Zwecke.

ist

das

in derselben Periode,

in der es erlangt wurde, vollstandig verzehrt werden, ohne dass

dadurch das frtihere Vermogen geschmalert wird. Die Tauschwerthohe des Einkommens einer Person entsclieidet liber das
Mass der letzterer moglichen dauernden Bedilrfnisbefriedigungen, ist daher volkswirtscliaftlich von grosster Bedeutung."
The errors in Wagner's definition are the restriction that income must
be "regular" and the inclusion of concrete commodities and abstract
services, side

side.

Kleinwachter,
.

steht

man

—

alle

op. cit., p. 24.

heute unter

dem Einkommen

einer Person ver-

Guter, welclie in die Wirtschaft oder in das

einer Person treten,

und zwar

—

Vermogen

1. gleichgiltig, ob diese Gilter von aussen in die eigene
Wirtschaft hereinkommen, oder ob sie innerhalb der eigenen
Wirtscliaft neu entstanden sind, und

ler

gleicbgiltig,

Natur

ob diese Gtiter materieller oder unmateriel-

sind.

Allerdings mtissen in diese Definition zwei weitere

aufgenommen werden, wenn

Momenta

communis
zwei Momente, die

dieselbe die heutige

opinio der Wissenschaft widerspiegeln

soil,

der "Einleitung"

mit Vorbedacht unberticksichtigt
gelassen babe, well sie ftir den mir dort vorscbwebenden Zweck
bedeutungslos waren, namlich
ich

—

1. dass die in Rede stehenden Gtiter mit einer gewissen
Eegelmassigkeit in die Wirtschaft oder in das Vermogen der
betreffenden Person treten milssen, wenn sie als " Einkommen "

gelten sollen,
2.

und

dass diese Gtiter nur dann als

"Einkommen"

aufgefasst

APPENDIX TO CHAPTER

355

VII

werden konnen, -vvenn sie neu in die Wirtschaft oder in das
Vermogen der betreffenden Person treten, d. h. also wenn sie
zu dem bislierigen Vermogen der betreffenden Person hinzutreten, oder mit anderen Worten: es liegt umgekehrt kein
vor, wenn Guter in die eigene Wirtschaft herwelche Teile des Stammvermogens dieser Wirtschaft
sind, also beispielweise, wenn ausstehende Forderungen zuriickgezalilt oder ausgeliehene Vermogenobjekte zurtickgestellt

"Einkommen"

einfliessen,

werden.
According to Kleinwachter the effort to reach a self-consistent concept
income had led to the inclusion of every element flowing into one's
possession whether by exchange from without or by production from
within his own establishment, and whether these elements are material or
immaterial, so long as we exclude such elements as " irregular " receipts
of

and the return

of old debts.

The

uselessness of such a concept Klein-

wachter himself points out.

Eobert Meyer, Handioorterhucli der Staats- Wissenschaften, Bd.
Ill, Art.

Einkommen

"Begriff," p. 348.

Die englische liberale ISTationalokonomie war von dieser
Grundlage aus zu einseitigen Eesultaten gelangt, indem sie das
Einkommen ganz in der Art verstand, wie die Buchhaltung
einer kaufmannischen oder industriellen Unternekmung den
Eeingewinn ermittelt.
M,
TT

M,
VT

-TS"

•R"

TV"

M,
TV'

Die deutscke Litteratur hat diese Einseitigkeit vermieden,
und die bis auf die Gegenwart herrsckend gebliebene Hermannsche, von Schmoller erganzte und vielleickt tlber Gebiihr
viel bewunderte Lehre versteht unter Einkommen alle TauschStammvergiiter, die nach vollstandiger Herstellung alles
mogens innerhalb des Jahres neu erzeugt und dargeboten
werden und zur Befriedigung der Bedtirfnisse der Nation
dienen raogen (Hermann), oder die Summe der wirtschaftlicken
Guter, die ein Subjekt in einer gewissen Zeit zur Befriedigung
seiner Bediirfnisse

ohne Schmalerung seines Vermogens wer-

wenden kann (Schmoller)
^

-TT

In neuerer Zeit
ausgesetztes

ist

ein frtiher als selbstverstandlich vor-

Merkmal auch

begriflich

den Vordergrund

NATURE OF CAPITAL AND INCOME

356

die Wiederkehr, die regelmassige Wiederkehr oder die Fahigkeit der Wiederkehr der das Einkommen
bildenden Einnahmen.

gestellt -worden:

Formliclie Definitionen des Einkommens werden
vermieden, doch sagt die sachsische Einkommen steuer

haufig

vom

Als Einkommen gilt die Summe aller in
Geld und Geldeswert bestehenden Einnahmen abztlglich der
auf Erlangung, Sicherung und Erhaltung dieser Einnahmen
verwandten Ausgaben sowie etwaiger Schuldzinsen, auch inJuli, 1878, §

25:

sofern diese nicht zu den eben bezeichneten Ausgaben gehoren,

Ausserordentliche Einnahmen durch Erbschaft und ahnliche
Erwerbungen gelten jedoch nicht als steuerpflichtiges EinkomGanz
men, sondern als Yermehrung des Stammvermogens.

ahnlich das osterreichische G. v. 25. Oktober, 1896, welches
jedoch den zweiten Absatz anders gefasst hat:

—

"Ausserordentliche Einnahmen aus Erbschaften, Lebensliapitalsversicherungen,

Zuwendungen
kommen. "

lichen

Schenkungen und ahnlichen unentgelt-

gelten nicht als steuerpflichtiges Ein-

These formulations virtually repeat the definitions given above.

Eranz Guth, Die Lehre vom Einkommen

in dessen

Qesammt-

zweigen, Leipzig, 1878, p. 62.

Einkommen ist jede aus einer Quelle, also mit einer gewissen
^egelmassigkeit widerkehrende Vermehrung des Verm o gens.
Der Bezieher Kann es geniessen, verzehren, oder auf irgend
Lot•einer Art vernichten, ohne seinen Eonds zu schwachen.
teriegewinne, precare Almosen und Geschenke sind daher kein
Einkommen, wohl aber sind

sich auf gewisse Titel griinden.
This view

discussed iu the text.

Almosen und Geschenke,

die

APPENDIX TO CHAPTER

357

XII

APPENDIX TO CHAPTER XI
1 (to Ch. XI,

§ 2)

Dimensions of Income-capital Ratios
If

indicate time

and distinguish the quantity and

value of services by the letters q and v, and the quantity and
value of capital by Q and V, the four ratios mentioned assume

the form

—

Physical productivity, -^,

e.g.

bushels per acre per year.

Yalue productivity,

—

e.g.

dollars per acre per year.

Physical return,

-^,

e.g.

bushels

per dollar's worth of

capital per year.

—

Talue return,

e.g.

dollars per dollar

( i.e.

per cent)

per year.

APPENDIX TO CHAPTER
§

XII

1 (to Ch. XII, § 2)

-Mathematical Relations between Rates, Annually, Semi-annually,
when conceived in the Sense of the Price of Capital

income

annum when the

represents the rate of interest per
is

payable semi-annually (such as 4

in the text) and
the income

the rate which would be

its

payable annually (such as 4.04

the relation between V and

i is,

—

etc.,

<fo

in the example

equivalent

when

in the example),

4
this we observe that under our hypothesis as to i
a capital of f 1 will buy a perpetual income of either i
V
each year, or - each six months. Let us suppose, as in the

To show

and

i',

preceding example, in six months the holder of the latter
i'

annuity, after receiving his

first

installment of income,

„? sells

NATURE OF CAPITAL AND INCOME

358

out for $1, which he

may

remains unchanged.

With

new annuity
1

same

of the

evidently do

the rate of interest

his total receipts, 1

+ -,

he buys a

This will evidently yield him

type.

per annum, payable in semi-annual installments of

amount, or

half that

—

jr-^

the end of another six

months, then, he receives this last-named sum, and, selling his

newly bought annuity

sum

for its original value of 1

hand

a total

vests

$ 1 and retains

of l

+ --f ^

+ 5)'-'

—

+ -,

he has in

sum he

this

income the remainder, or -

-f
'

rein-

may

evidently be obtained year after year simply
by repeating the above process. It constitutes a perpetual
annuity, payable annually, and its value simplified from the

This sum

above formula
Since this

evidently %'-{-—.

the annual income, payable annually, which

of capital will hwj,

that

is, i

We may

-f

definition, the

magnitude we called i;

in like

which case we
i"

it is

manner proceed to quarterly payments, in
by analogous reasoning, denoting by

shall find,

the rate of interest per

annum payable
8

^16

2 (to Ch. XII,

quarterly, that

256
§ 4)

Mathematical Relations between Rates reckoned Annually, Semi-annually,
Diagrammatic Repetc., when Rates are conceived as " Premiums."
resentation.

In general

Economic Interpretation

let

semi-annually.

be the rate of interest per

Then the

amount "

annum reckoned
in six

months

;

APPENDIX TO CHAPTER
i'

and

compound
the "
est,

or,

this

sum

months

in another six

interest to

XII

359

will "

amount " by

which must be equal to 1

amount "

of $1 in one year at the equivalent rate of interreckoned annually; i.e.

expanding and reducing,

—
= 1'+-,

which

was regarded

interest

prove 1

-\- i

the rate of

as the price of capital.

Similarly, for the interest rate

may

when

the same result obtained before

= (1

reckoned n times a year, 1

reckoned quarterly,

and for the

-\-

i",

—11

rate

interest

we
i^"',

)•

^ J

In other words,

= 1^+4

^(.n)\n

o (n)\

J!L

(n)

As n

increases indefinitely, the last expression approaches a
limit. The limit of i'-"^ is the " rate of interest per annum com-

puted continuously," called S. The limit of the square bracket
the base of the Napierian system of logarithms called e for

;

by the

definition of e usually given,

when k
-;

—

any number increasing

such a number, for

indefinitely,

and

i^"-''

it is

the limit of

indefinitely.

by hypothesis,

evidently decreases.

(

Evidently

to be increased

Hence

at the limit

the last formula becomes,
1

Or, substituting for

e its

+ = e«
i

numerical value,

+ =
I

(2.7182818)«.

Another proof of this formula could be given for the case
where the rate of interest is conceived as the price of capital,

NATURE OF CAPITAL AND INCOME

360

by following

to the limit the

method

of this Appendix, §

above.

The number

or 2.7182818, plays almost as important a role

the number 3.141592,

in mathematics as

called

which

ir,

expresses the ratio of the circumference of a circle to its diameter, but the meaning of e is less familiar to most students.

Various definitions and interpretations
economist, the most interesting

"amount"

fl put

compound

may

To the

be given.

the following:

the

interest during the "pur-

chase period," the latter being derived on the assumption that
the rate of interest

is payable continuously.
This proposition is implicitly contained in the demonstration of the equation 1 -\-i= e^, as given above.
The following
is a more explicit statement, with actual illustrative figures
:

consider the rate of interest

annually,

amount

the purchase period

f 1 put

4%,

—

25 years, or

payable

and the

interest for these 25 years will be
(1

If next

amount

take

4% payable

of 25

years will be

at interest at

the interest

/-.

times a year, the amount

amount of $1 put

payable quarterly

And

+ .04)25.

semi-annually, the

$1 during the purchase period

Similarly, the

—

reckoned as payable w
is

/-.

.04V50

2 J
.04V100

4 y
.04\-^

n J

we have the amount of $1 at interest at 4^
for 25 years when the rate of interest is payable continuously.
The limit of the above expression, when n is made indefithe limit,

nitely great, is the definition of

The distinction between the different rates of interest may
be shown by a diagram.
In Figure 33, let the curve B'AB represent a "discount curve," any two ordinates of which represent

exchangeable goods situated at two corresponding points of
time, as a and

the

that

is,

the

sum aA of

" present " goods will

buy

sum bB

beyond

of goods which lie in the future a time interval ab,
the " present." If we take these two points, a and b, a

year apart, the rate of interest as reckoned annually

the

APPENDIX TO CHAPTER
"slope" of the secant

—=^

-5-

aAy

361

XII

in relation to the

ordinate

Similarly, the- slope of the secant

drawn

through points corresponding to times a half year apart, taken
in relation to aA, is the rate of interest reckoned semi-annually.

Fig. 33.

and so

At the limit, the slope
aA) represents the rate of

on.

lation to

of the tangent

(in re-

interest reckoned continu-

ously.

Similarly, the regressive secant, AB', represents the rate of
discount, reckoned annually

(if ab'

represents a year interval),

NATURE OF CAPITAL AND INCOME

362

AC,

the rate reckoned semi-annually, and so on until the tan-

gent AT',OT
interest

AT,

again reached,

and discount disappears.

when the

distinction between

It is easy to

prove (by simi-

lar triangles) that the reciprocal of the rate of interest continu-

ously reckoned, in other words the

represented by

"year's

3 (to Ch. XII,

§ 6)

A Fremium Rate of 4% one Year and 3% Each Year
Rate

purchase,"

the subtangent.

after

means a Price

3.03% the First Year.

4% as the rate of interest (as premium) in
and 3 % as the rate for each year thereafter.
Let us suppose that f 100 to-day is invested for $ 104 next
year, and that at the end of the year, of this $ 104, f 100 is re-

the

have given

first year,

Since thereafter the rate of interest

invested.

premium

always

by proof in the text, also 3%
Consequently, the $100 reinvested next
in the price sense.
year may be used to buy $ 3 a year forever. The result is that
for the $ 100 to-day the return is f 4 next year and $ 3 each
year thereafter. This series of payments is the same as $3 a

in the

sense, it

must

be,

year forever, together with one extra dollar at the end of the
first year.
This extra dollar has a present worth (since the
interest
-i-,

premium between this year and next year is 4%) of
If we deduct this present value of the extra

or .96j\.

dollar

from the $100 (which

series of $4,

$3, f 3, $3,

etc.,

the present value of the entire

inf.),

we have

value of the series without the extra dollar,

i.e.

the present

a year

Since, then, this
The remainder is $99.03^.
$99,031^ will buy f 3 a year forever, the rate of interest in the

forever.

pnce sense
is

$3-j-$99.03i|, or 3.03% approximately. This
After the first year it will evidently

the rate at the outset.

always be 3%.
§

4 (to Ch. XII,

§ 6)

A Price Rate of 4 % this Year and 3 % Each Year after means a Premium
Rate of 371% the Eirst Year.

We have given 4 %
first

year,

after.

and

as the rate (in the price sense) for the

as the rate (in the

same sense) for each year

——
APPENDIX TO CHAPTER

$ 100

buy the right

will to-day

year hence this right to
It will therefore

basis.

consequently receive in

14+ f 1331

may

end of

forever,

and a

be sold on a

The

$ 133.33.

at the

all,

$ 4 a year

annually

fetch

363

XII

investor will

this first year, a total

f 1371. Hence the rate of interest in the
sense of a premium will be for that year 37-^%. In succeeding years the rate of interest, considered either as a premium or
a price, will evidently be 3%.
of

5 (to Ch. XII,

§ 6)

Mathematical Kelations between the Rates of Interest as a Premium and
as a Price

In general,
year,

and so

rates

premium sense

let

represent the rate of interest in the

for this year,

whereas

on,

for next year,

and

ji,J2,

for the third

represent

etc.,

jg,

the

same successive
between the i's and /s may be

interest in the price sense for the

years, the following relations

proved:

+
^

1+J2
^
1

-+7

+
^-+
1

..,

-v^

•

inf.

+ h) (1 + *2)(1 +
ad inf. =
.., +
(1

—

^"^—^

+ ii)(l + Q

...
(i+j^y
..

r-T-+

+7:;

h ... ad inf.

^'3)

(l+i^/

A + Q^

+ 73(1 + i,)(l

+^.
(1

....
+ i,)(l
+ gw.(1 +

rT-+ ... ad

inf.

ii)

etc.

These equations

may

be said to determine

j^,

as a peculiar

mean of the magnitudes ii, i^, h,
ad inf., and J2 as a
similar mean of {2, 4, U, ... ad inf., etc.
Their proof,
which is simple, is left to those readers who are interested in
sort of

•

mathematics.

The preceding equations express the values

of the

NATUKE OF CAPITAL AND INCOME

364
terms of
the /s

The following equations

i's.

—

give the

i's

in terms of

h
h
''5—jz T

etc.

Thus

if,

as in our example,
.04

The proof

= .04 and j^ — .03,
= .371

.04
.03
-^^ 7^-^^
.03

of these formulae

to the mathematical

is also left

may be
proved independently or either set may be proved and the
other set derived from it. To show that either set may be derived from the other, it will be found useful to substitute for
reader.

He will

the left-hand

observe that the two sets of equations

members

of the first set their simpler values as

These

derived by algebra.

111

are, -, r^-, etc.
Jl J'2 Jz

easy proof of

found by actually dividing 1 by Ji, etc.
the formulae it is clear that if ii= t2= ^'3=, etc., then
j.^=J2=J3=, etc., and that then all the t's = the /s. The

this is

From

converse

also evident.

6 (to Ch. XII,

§ 7)

Mathematical Kelations between the Eates of Interest and Discount

Let V, due one year hence, be the equivalent of
in the present.

Then the

rates of interest

expressed respectively by the formulae
l

—

V available

and discount are

+ = ^;
i

l-d = Z.

Whence, by multiplying the two equations together we
derive (1+0 (1 — d) = l, which reduces to d = i — id. That
is, the number representing the rate of discount equals the
number representing the equivalent rate of interest less a

APPENDIX TO CHAPTER

365

XII

small correction, equal to the product of the rates of interest

and discount.

The relation between the rates of discount and interest
when semi-annually reckoned is analogous to the relation which
we found between those annually reckoned. We then have

—
=1——
Z
V

the equations,

Y = ^-2'

and

^Hence

(^1_|:)

+ |') = l.

multiplication and reduction,

We may
interest

reasoning to quarterly-reckoned

apply similar

and discount

It follows that

rates.

+ J)

x) = 1'

d" = i"-''-^.

The same reasoning may obviously be applied
n times a year.

to reckonings

We then find,
n
of parts into

which the

divided, be sufficiently increased, the term

be-

It is evident that if n, the

year

number

comes infinitely small, so that, at the limit, the rate of interest
and the rate of discount become equal. This rate for continuous reckoning, being the same as the rate of interest for continuous reckoning,

Unlike the rate of

also called

interest, the rate of discount is

always

considered as associated with the exchange of present against
future goods, and not with the exchange between capital and
income, i.e. is taken, not in the "price" sense, but in the "pre-

mium"

sense (the

premium

being, in this case, negative).

may, however, to complete our scheme of concepts, construct
for ourselves a "rate of discount" in the sense of the price of
capital in income.

recur to the fact that the rate of

NATUKE OF CAPITAL AND INCOME

366

in the price sense, was defined as the ratio of
income to capital, when the first installment of income is
due at the end of the first time-interval. But if the first
installment is due at the beginning, the ratio of income to
capital is no longer the rate of interest, but may be called a

interest,

sort of rate of discount.

Thus,
first

$ 100

will

buy a perpetual annuity

installment being due one year hence, then

$ 4 a year, the
$ 104 will buy

such a perpetual annuity, the first installment being due at
In the first case, the ratio of income to capital, j^^, is
once.
called the "rate of interest in the price sense." In the second
case, the ratio of income to capital, y|-^, may be called "the rate

The

of discount in the price sense."

rate of discoimt in the

price sense and the rate of discount in the

related in a

manner

premium

sense are

strictly analogous to the relation

between

the rates of interest in the two respective senses.

well known, bonds, just before

an installment of
two ways they may be

interest is due, are sold in either of

payment ("ex-interest"), or with the
interest payment ("flat").
These two methods are associated
respectively with the rate of interest and rate of discount, as
sold without the interest

just described.

7 (to Ch. XII,

Mathematical Eelations between the Eates of Discount for Different
Time Keckonings

The

rates

related in a

of discount for

different

manner quite analogous

time reckonings are

to that in

which the

corre-

sponding rates of interest are related, as shown in this Appendix, § 2.

and

Thus

V to-day will

buy

W~
will then

W in half a year,

buy F' in another half year on the same

terms,

V~
whence, multiplying,

—=

2'
1

-—

APPENDIX TO CHAPTER XII
But

367

yr=l-^'
l

therefore

— d={f 1 — d'
-^
d=

and

/d'\

27'

from which we see that the discount rate reckoned annually
less than its equivalent reckoned semi-annually.
reasoning applies to quarterly and other rates.

Similar

8 (to Ch. XII,

Dimensions of the Rates of Interest, Discount, and Capitalization

The

rate of interest in the price sense

of the

—
Vt

form

where v represents the part of the perpetual income stream
which flows in the time t, and V represents its capital value.
Since, in this fraction, v and V are of the same dimension,
both being measured in dollars, or else in bushels, or in some
other units of same denomination, the dimensionality of the
fraction

—V

reduces to - or f~\*

In like manner, the ratio

of capitalization, being the reciprocal of this fraction, or

—

has the dimensionality t.
These results are recognized in

the rate of interest

capitalization is so

many

common usage, inasmuch
much per annum, and the ratio

years' purchase.

The same dimensionality
interest considered as a

premium

V are

given

obtainable from the rate of

premium.

The

rate of interest as a

V
by the equation — = (1 +

ii)

where F' and

two exchangeable sums separated by the interval

usually a fraction of a year, for which the rate of interest

to be reckoned.

Since
* It

Thus,

the reckoning

V and Fare of the same dimension, —
is

capital"

quarterly,
is

is \.

a pure number.

interesting to observe that the dimensionality of this "price of
is

entirely different

from the dimensionality

of the price of one

kind of goods in terms of another, as shown in the Appendix to Chap.

NATURE OF CAPITAL AND INCOME

368

Hence

its equal,

the term 1

Hence

number.

—

ti,

a pure number.

Since of this sum,

a pure number, the other term,
i

must be

ti,

also a pure

of a dimension reciprocal to

i.e.

or t-\

The

same dimensionality

rate of discount evidently has the

as the rate of interest.

APPENDIX TO CHAPTER
§

Formula

1 (TO Ch. XIII,

for Present Value of

due next year

One Year

it is

evident that 1

worth

hence f 1 due next year

and any sum

§ 1)

Sum due

If the rate of interest be denoted

XIII

$1
is

worth

V due next year is worth

Formula

for Present

to-day,

2 (to Ch. XIII,
Value of

to-day,

which is the general formula for the present value of a
sum due at the end of one year.

to-day,

Sum V due

single

End

Any Time

In general, it is obvious that (1+i)^ is the amount which,
two years hence, has a present value of $ 1, hence that

—

worth to-day

—

V due at the end of 2 ^years is worth to-day^

Similarly,

V due at the end of 3 years is worth to-day

—

and

V due at the end of

$ 1 due at the end
and that

The

of 2 years is

years
^

worth to-day
^

+ if

—

V
+ 0'

formula is perfectly general.
It is not even necThe reader who is mathet should be an integer.
matically inclined will have no difficulty in proving that the
formula applies if the period of time is 3^ years or any other
time whatever.
last

essary that

—
APPENDIX TO CHAPTER
§

3 (to Ch. XIII,

Formula for the Present Value

The
-

annum;

on annui-

Consider a perpetual annuity of $1
required to find the capital value. It is

due

being

has

preceded that the

—
(l

+ if

first

the end of a year, has

value at the present time of

worth of

alternative proof,

usually given in treatises

evident from what

$1,

Annuity

follows:

in the preceding chapter.

and the one which
per

of a Perpetual

proposition that the present value of a perpetuity is

was proved

ties,

369

XIII

the third,

the second has a present

;

•

payment,

a discounted

;

+ if

and so on

indefinitely.
^

Therefore, the present value of the entire series will be,
rr—-If,

for brevity,

/-,

.s2

+ /I

we substitute v
v

for

this

+ v^-{-v^ + ad.

V (l-\-v^-\-a.d.

+ etc.,

-NO

inf.

may

be written,

inf.,

inf.).

Since the series evidently converges, the parenthesis
to

—V

equal

which may be seen by simply dividing 1 by 1 — v.

Hence the value

of the annuity

which reduces

— if we

is,

1-v

substitute for v its original
value.
°

This sum, - dollars,

is,

therefore,

the

capital-value

annuity of f 1.
annuity a

proportion, the capital-value of any other

is -.

4 (to Ch. XIII,

§ 3)

Formulae and Diagrams for Capital-value of Annuities payable Annually,
Semi-annually, Quarterly, Continuously

In case the annuity accrues semi-annually, the teeth will be
but twice as frequent. In Figure 34 we see the behavior
2b

finer,

NATURE OF CAPITAL AND INCOME

370

of the capitalized annuity

the annuity

teeth drop
if

payable annually,

$4 a

year, the

payable annually, $2, if semi-annually, and f 1,
If the frequency of the installments of income be

quarterly.

If the annuity be

semi-annually, or quarterly.

,..-^12,^^^ 13--^'^
2

Semi-annual

Payments

Quarterly Payments

Fig. 34.

we reach the limiting case of a continuous
the teeth disappear entirely and the value of the

indefinitely increased,

income,

when

annuity remains at a constant
of

come
is

received,

4%, provided

will

the rate

be
is

of the annuity

any installment of

after

in-

the rate of interest
respectively " reckoned annually,"

$100,

semi-annually, and quarterly in the
case of continuous income,

The value

level.

in all these cases, just

various cases.

In the

the value of the annuity of

$100 if the rate of interest be 4% "reckoned
continuously."
The same remarks apply, of course, to an
annuity of any number of dollars. Its value after each installment is equal to the annual income divided by the rate of interest, or the annual income multiplied by the purchase period.
will always be

In order to obtain the formulae for the value of a perpetuity
payable semi-annually, quarterly, or continuously, in terms of i,
the rate of interest reckoned annually, we need only to transform
T,)

—,i -,

by means of the equations in the previous chapter.

Thus

APPENDIX TO CHAPTEE

annum payable

the value of an animity of a dollars per

annually

- which, by substituting for

from the relation between
i'

(

-\-

— T)

and

viz.

i',

371

XIII

its

value as derived

+ =
i

becomes

semi-

[

,
)

Similarly, the

2(Vl + ^-l)

quarterly annuity becomes

and the continuous

4(^iq:^i)
annuity,
^' since

l+i=e^

or 8=loge(l+i),

becomes ^=;

log, (1

In every case the value just before an installment is found by
adding that installment to the results just derived; and the
value at intervening points by applying the discount curve,
value (just before the next ini.e. dividing the impending
stallment)

and

(1 4- iy,

where

the time between the present

the time of the next installment.
§

Diagrams

5 (to Ch. XIII,

for Discontinuous

and Continuous Income

If the income installments recur annually, and are

these installments are represented in the line

method by

each,

a, a, a,

Fig. 35.

in Fig. 35.

If they occur semi-annually, in installments of

each, they are represented by

6, b, b.

If they occur quarterly, in

NATURE OF CAPITAL AND INCOME

372

f 1 each, they are represented by c, c, c, and so
on indefinitely, in each case the lines becoming shorter but more
numerous. If this process is continued indefinitely, it is clear
that continuous income would simply be represented by an ininstallments of

—

number of infinitesimally small lines, a representation
which would be unintelligible. It is for this reason that the area
method becomes necessary. To show how it may be used, even
finite

for discontinuous income, let a series of annual payments, a, be

represented in Figure 36 by the rectangles whose bases are equal

and whose altitudes, therefore, are equal to a. The point
which each rectangle is referred is taken, for convenience, as the end of each year in which it occurs. Thus the recto Q.
If the
tangle OF refers to the point of time P, and
payments are semi-annual, we represent them by the areas of
to unity

of time to

Fig. 36.

the rectangles OT,

TV,

etc.,

in the

same manner.

But as the

rectangles are each equal to one half, the altitudes will no
longer represent the individual payments, but double those semi-

annual payments, i.e. the per annum rate. Thus, if the annu$4 per annum payable semi-annually, the rectangle OT
means $2, its base is one half, and its altitude, YT, will not be
2, but 4, the rate per annum.

ity is

payments are represented by rectangles
OS, XT, TU, etc., whose altitudes will again represent the rate
per annum of each quarterly payment.
Finally, for continuous payments, we shall have an infinite
Similarly, quarterly

of infinitesimal rectangles, forming in the aggregate
the whole figure represented, the altitude of which at any point
will be the rate per annum at which income is flowing at that

number

point.

APPENDIX TO CHAPTER

XIII

373

we may pass from income which flows at a uniform
any income stream. Evidently, therefore, any continuous income-stream may be represented by a curve (Fig. 37)
of which the ordinate represents the per annum rate offlow at any
limits

rate to

point of time, and the area

and

CF represents

EC between any two ordinates BE

the total income which flows within the time

intercepted between those ordinates.

For the case of uniform
is

flow, the continuous

represented in Figure 38 by the area OB.

income stream

OA represents the

Fig. 38.

rate of income, and OC represents the capital-value of this inThis capital-value remains constant, as shown by the
come.

NATURE OP CAPITAL AND INCOME

374

horizontal line
ously)

—

CD, and the

Formula

rate of interest (reckoned continu-

6 (to Ch. XIII,

for Capital-value of a Terminable Annuity-

Let a represent the annual payment of the annuity, t its
duration or term, and
its present value.
We are required

t, and i, the
rate of interest.
We
have observed that a man who owns such a terminable
annuity owns the difference between a perpetual annuity beginning at present and another perpetual annuity deferred t

to find

in terms

of a,

Consequently, the value of his property is the difference between the values of these two that is, it is equal to the
value of a perpetual annuity beginning now, less the present
value of a perpetual annuity beginning t years hence.
The
years.

;

deferred annuity which begins at the end of

know, be worth then the sum of

and

will be

years will,

worth now what-

ever

the present value of this -.

This present value

course found simply by discounting the ^ just obtained, and

(1 -L

^^^^ expression should therefore be subtracted from

^-y

the value of the other perpetual annuity which begins now, of

which the present value
formula,

This subtraction gives the

Hi + 0'
§

7 (to Ch. XIII,

§ 5)

Discussion of Formulae for Terminable Annuity by Diagrams.
Discount." "Total Interest." Depreciation.

In Figure 39

let

AB represent the term

"Total

of the annuity,

the value of a perpetual annuity beginning at the point of time

A, and

the equal value, taken at the end of the term, of a

deferred perpetual annuity beginning at that time.

Now

the

APPENDIX TO CHAPTER

XIII

375

Fig. 39.

A of the value BE, at time B, is eviAC, found by drawing the discount curve CE. Therethe value of the terminable annuity is equal to AD — AC,

present value at time
dently
fore

NATURE OF CAPITAL AND INCOME

376
or

DC,

wliicli is

which

it is,

the

total discount

Bohm-Bawerk

BE;

i.e.

the amount by

says, " diminished in time per-

spective."

Similarly, the capital- value of the annuity, taken at
later

A! (just after an installment of income),

smaller

sum GH.

Thus the

capital-value gradually decreases

in accordance with the distance of the curve
line

any time

equal to the

from the

DE.

In this representation the discount curve was drawn through
If another is drawn through D it may be shown that

the

time

"amount"

terminates, if

at interest

EF,

of the terminable annuity, or its value at the

from

its

we suppose that each individual item

date to the point of time B.

is put
This "amount,"

is called the " total interest " on that capital in that interval.
In the same way, at any intermediate time just after an installment, GI will represent the value of the annuity concentrated
at that point, and this value will consist of two parts, HG,
which is the (discounted) value of the part subsequent to K,
and HI, the (accumulated) value of the part preceding K.

APPENDIX TO CHAPTER XIH
The

decrease in capital-value of the annuity, which has been

represented by the approach of

above

377

it,

the position

CE to

the horizontal line

better represented, however,

KB,

by inverting

in order that the capital-value

sented, as in our previous examples,

may be

repre-

by the distance from the

Fig. 41.

horizontal line

in Figure 40.

The value

below

installment of income
of the curve
is

KB, and

it.

This change is accomplished
taken after each

of the annuity

represented by the ordinate, as

mA\

the value just before an installment

represented by the ordinate, as nA^', of a point above this

curve a distance equal to that installment.

The value

at inter-

mediate points evidently follows a discount curve, as mn, between these two points. The result is that the capital-value
will rise

and

fall

according to the steps, or teeth, shown in the

diagram.

As the income items become more numerous the teeth become more frequent and smaller, and disappear when the flow
of income is continuous, as represented in Figure 41, where the

NATURE OF CAPITAL AND INCOME

378
curve

the capital-value at

itself represents

all

points of

time.

The formula

for the present value

income

after each installment of

(F)

of the annuity just

the same, whatever the

time intervals between installments. This is strictly true, however, only on the proviso that the rate of interest i is to be
understood as reckoned in accordance with the frequency of
the installments of income in each case,
terly, etc.,

— instead

— semi-annually, quar-

of annually, as has been hitherto under-

stood.

The formula for the capital-value, V, just before an installment is evidently found by taking the preceding formula for

Fand

adding

This gives,

a
3*

/-#

{1+iy

At intermediate points the capital-value is equal to the
amount just named discounted for the interval elapsed between the point of time considered and the next installment
of income.
§

8 (to Ch. XIII,

Formulge for Value of a Bond
general, let us suppose a bond, the income from which
a dollars per year, payable annually for t years, at the end of
which time, in addition to the final payment a, another larger

To be

payment P,

called " principal, " is paid.

are required to

find the present value, V, of these future expected

for a given rate of interest,

The discounted value

payments

of the terminable annuity has already

been expressed, namely,

The discounted value
explained and

+ iy

deferred

evidently,

P
(1

+ 0'*

years has also been

—
APPENDIX TO CHAPTER
The sum

379

XIII

of these expressions is the value V, "which

are

In other words,

seeking.

L— +

F=^i
or

t;-_

special cases

income a
[

+ 0'

(1 +
be considered.

Some

+ 0*

may

First, if the

the interest on the " principal " P,

orP = ^|, — the

second term vanishes, as

evidently zero, and since the

pothesis P, the equation then becomes

Secondly, if a

greater than iP,

V will

its

term, -,

first

—

i.e.

annual
a = Pi

numerator

by present hy-

V=P.

may be readily shown that

and if a is less than iP, that
be greater than
is
than P.
The formula given is of practical importance, as it enables
us to compute the price at which a bond must sell in order to
;

less

yield a certain rate of interest.

To apply the formula numerically we need only
particular values for the magnitudes involved.

to assign

Let us take the

numerical case already considered, where P=$100, a = $5,
In this case the formula becomes,
i = .04, and t = 10.

—

.04"*"

which reduces
Similarly,

to 108, as

may

(1.04)i«

we found

be shown that

basis, the price of the

before.

bonds are sold on a 6 %
bond in question would be $ 921
if

have derived the value of a bond, V, just after a
In this case the bond is said by
of "interest."
brokers to be sold " ex-interest." If, on the contrary, it is
sold " flat," that is, with interest, its value will evidently be
increased by the " interest " a, and will be 7"+ a. The price

payment

any
^ time between installments

will evidently be
^

(1+0

NATUKE OF CAPITAL AND INCOME

380
where

V represents the value the bond will

"interest" payment, and
Or,
last

it is

F(l + t)'

have after the next

the time elapsing to that payment.

F represents

where

the value after the

"interest" payment, and t" the time since said payment.

F+

Vit", which in turn
a and Vi are practically
equal, each being nearly the true interest for one installment
This is the formula usually employed by brokers, at"
period.

Practically this last formula reduces to
is practically

the same as

V+ at"

;

for

being called the " interest earned " since the last coupon.

9 (to Ch. XIII,

Alternative Method, whereby the
is

§ 7)

"Premium"

in the Price of the

Bond

compounded separately

The so-called 5 % bond running for 10 years, which is sold
on a basis of 4 %, may be considered as consisting of the following two property rights (1) the right to four dollars a year
for 10 years and f 100 at maturity, and (2) the right to one
It is evident that the present
dollar a year for 10 years.
value of the first property is $ 100, to which, therefore, we need
only to add the value of the second property, namely, the annuity of f 1 a year for 10 years. It is therefore the present
:

value of this small annuity, consisting,

we may

say, of the

and nominal interest on $100,
which constitutes the "premium" on the price of the bond.
This present value is f 8, and is found in the manner already
explained for terminable annuities, being the total discount on
$ 25 at the end of 10 years, f 25 being the capital-value of a
difference

between the

perpetual annuity of

4%.
is

real

f1 a

year,

Consequently, the bond

when

interest is reckoned at

worth in

all

f 108. This value

represented diagrammatically in Figure 42.

Let A A' represent the 10-year period, with the f 5 interest
payments shown by the ten vertical lines at unit intervals.
A'B' represents the $100 "principal" due in 10 years, and
AB represents what the bond would be worth ($100) if the
To this must
interest payments were $4 instead of $5.
for 10 years.
year
of
a
present
value
1
the
$
therefore be added
equal
to $25), the
(drawn
discount
on
B'C
the
total
This is
The total
capitalization of a perpetual annuity of $ 1 a year.

APPENDIX TO CHAPTER

381

XIII

$25 is shown by the line BD, which is therepremium in the selling price of the bond. The total
The price at later dates (taken
price is AB-\-BD = AD.
each just before an installment) is represented by points on
discount on this
fore the

Fig. 42.

the

discount curve

D5' drawn

with reference to

as a

horizontal axis.

Adding

at each of these installment points a

line equal to $5,

we have

the value just before interest pay-

ments, and connecting the tops of these lines with the preceding

by discount curves reckoned at 4%, we have
a series of teeth representing the normal course of the price of

interest intervals

the bond from the present to maturity.

In case a bond

sold at a

basis,

we have the curve B'D',

instead of B' D, with the teeth superimposed as before, the
tooth curves, however, being in this case on a

slope.

NATUEE OF CAPITAL AND INCOME

382

Formula

for a Bond,

The formula

10 (to Ch. XIII,

when Interest

§ 7)

reckoned oftener than yearly

in the case of semi-annual income

when

in-

terest is reckoned semi-annually is evidently,

which applies
is

evidently

just after an interest

F+-; and

payment

just before,

;

at intervening intervals it is this value

discounted, or for practical purposes, the

simple formula,

where V is the value taken after the last "interest"
payment, and t the time elapsing since that date. For the case
y-\-at\

of continuous interest,

as in the previous chapter,

let,

continuous interest,

8 represent

have,

p_a
F=?+which formula remains unchanged during the

entire period of

the bond.

These various formulae may, of course, be somewhat transformed and simplified for practical purposes. Moreover, they

may

all

interest.

be transformed in terms of the various rates of

Some

actuaries apparently prefer to use, as the in-

terest rate, only the "effective" rate,

which

the "rate of interest reckoned annually."
formulae,

what we call
The preceding

which employ the semi-annual, quarterly, and other

forms of interest rates, may be transformed by substituting
their values in terms of i, in accordance with the relations
shown in Appendix to Chap. XII, § 2.
§

11 (to Ch. XIII,

Formula for Capital-value

We may

Any

Series of

8)
Income Installments

formulae, the capital-value of

express, in general

any income stream, as follows
Let %, a^, Og, represent the
successive installments of income accruing at various times dis:

—
APPENDIX TO CHAPTER

383

XIII

tant from the present instant by the intervals ^i, U, t^, etc., which
may be equal or unequal, whole or fractional, or even positive
or negative according as the income

Let i represent the rate of
of such an income stream will be,

past.

—+^
(1

t)'i

(

in the future or in the

The present value

interest.

^
+ iy^

^
+ iy

etc.

Or, in briefer notation,

^
V=V
^(1 +

where %

taken in

series of terms of the
§

Diagram and Formula

its

i)''

usual sense of the summation of the

type of that following

12 (to Ch. XIII,

it.

§ 8)

for deriving Capital-value

from a given Continuous

Income Stream

For any income stream flowing continuously, and represented
in Figure 43 by the area below JO/, the capital-value will

be represented by the curve

NO.

The

ordinate of the income

stream at any point, as US, represents the rate of
point,

and any area, as IiSS"Ii", represents

the period

RR".

The

ordinates of the curve

sent the capital-value of this income stream.

its

its total

flow at that

flow through

NO will repreNO is con-

structed from
backward as follows the curve begins at
on the income stream and is generated by a point moving in
such a manner that at any position
its direction of motion
is the resultant
of two tendencies.
To represent these
two tendencies we draw through
the discount curve OP.
Tangent to this curve we draw OH so as to meet the line
drawn vertically and distant to the left one unit from OK.
represents one of the two tendencies mentioned, that due
to discounting the future.
drawn vertically up from
and equal to MS, the rate of income at that time, represents
the other tendency.
The resultant, OQ, drawn according to
the principle of the parallelogram of forces, will represent the
:

which the curve will be moving at the
In other words, a point moving under the influ-

actual direction in

point 0.

ence of two forces,

curve

NO.

and OH,

will generate the required

NATURE OF CAPITAL AND INCOME

384
In order

show that

this is a correct representation let us

first

take the case of semi-annual income.

year

;

Rr represents half

a year.

RR" represents

Draw the ordinate rh.

one

From

h draw vertically upward hq to represent a half-year's installment of income, that is, half of Rs. To avoid complicating the
figure, hq is omitted; were it drawn, q would lie on the line OQ'.
Then, according to our previous representation, the capitalvalue will follow the curve Ohq, which forms a "tooth." The
line

therefore a line

neighboring teeth.

drawn through the top points

Its direction is a first

two

approximation to

Fig. 43.

the direction

of the curve for the continuous case.

This

Oq is the diagonal of a parallelogram formed by
producing Oh to meet the ordinate from
in H', producing
Oq to Q' and completing the parallelogram.
direction

Since H'Q' is twice as far from
as hq {i.e. RR" =2 {rR)
by hypothesis), it follows, by similar triangles (i.e. Ohq and
OH'Q'), that it is also twice as long.
But hq represents a
half year's installment of income.
Hence H'Q' represents two

APPENDIX TO CHAPTER

385

XIII

Therefore
such installments, or the annual rate of income.
OK, being of the same length, also represents this annual rate
of income.
to g lies along a paralIn other words, the direction from
represents the annual rate
lelogram of which the side

of income and the side

OH'

a chord of the discount curve

OP.

Now it is evident that if, instead of a semi-annual installment,
we assume

greater frequency, the

same statement

except that the point h will be nearer 0.

will apply

proceeding in this

Fig. 44.

manner the chord OliIF approaches the tangent
limit,

and the parallelogram OH'Q'K becomes

the parallelogram
sides are

OK,

OHQK as originally

described.

the annual rate of income, and

to the discount curve

drawn from

its

at the limit

OH,

That

is, its

the tangent

to a vertical line

one year

to the left.

That this construction and its demonstration bear a striking
analogy to the construction and demonstration which apply to
2c

NATURE OF CAPITAL AND INCOME

386

the composition of forces or motions
ourselves of this analogy,

we may say

very evident.

Availing

that in the case of dis-

traces the capital curve (back-

continuous income, the point

—

ward) by obeying alternately two tendencies,
one, to follow
the discount curve at times when no income occurs, and the
other, to rise vertically whenever income occurs.
In the case
of continuous income these motions occur simultaneously
instead of alternately, and the resultant is a smooth curve
instead of a series of teeth.
The same principles apply when part of the income curve
is below the horizontal axis, representing negative income.
If

Fig. 45.

at the beginning the prospective cost just counterbalances the

prospective income, the capital-value will at that instant be
zero,

and

will

from that point

rise

and

fall

again to zero at the

end, as indicated in Figure 44.

The formula for capital-value in the case of a continuous
income stream will be,
1^_ r da

^~J

+ 0"

which da may be said to represent the infinitesimal income
which flows in the infinitesimal increment of time dt. In other
words, da represents an infinitesimal element of the area ABC
(Fig. 45), of which element the base or breadth represents the infinitesimal time dt. For the purpose of integration we may substitute for da the expression /(i)d«, where /(i) represents CB, or
the ordinate of the income stream taken as a function of time t.
If the special form of the function / (t) is known, it is evidently
possible to integrate the expression and obtain its value for any

given limits.

APPENDIX TO CHAPTER
§

13 (to Ch. XIII,

XIII

387

§ 8)

Diagram sho-wingthe Accumulated "Amount"

of a Given

Income Stream

in Figure 46 the diagram with which we began
general case of capitalizing income. We now
the
of
study
the
wish to obtain the accumulated value A"'Q, at the close of the
period OA'", of the income items AB, A'B', A"B", and A"'B"'.

We reproduce

This consists of
of

CD"

discount curve

amount
amount

(1)

A"'B"'

(or its equal,

CD"

CD'

itself

;

EF, which in like manner is the
and (4) FQ, which is the
equal AB). Thus, while OP represents

(3)

(or its equal A'B')

(or its

which is the amount
found by continuing the

(2) B"'£!,

A"B"), and

;

NATURE OF CAPITAL AND INCOME

388

the price of the stream

paid for in advance, A"'Q repre-

sents the price if paid for at the end.

similar reasoning

may

be shown that the price at any intermediate point of
the entire series is the height of any point on the one smooth
it

curve

PQ.

This result must not be confused with that which represents
the capital-value of future income. Thus, at the point of time
the line

0',

O'P

represents the value of

past as well as future,

AB,

A'B',

O'P" represents the value
and A"'B"'.

line

all

the income items,

A"B", A"'B"', whereas the

of only the future items

14 (to Ch. XIII,

Effect of reckoning Semi-annually, Quarterly,

10)

and Continuously, on the

Eate of Interest realized on a Stock or Store

usual, the passage

A"B"

of Articles

from the rate of interest reckoned

annually to the rate of interest reckoned continuously, if accurately considered, is not so simple as appears on the surface

and may

afford to

some readers no

little

perplexity.

assume, for convenience, that each article in the merchant's
stock remains there for a definite period, called the time of
"turn-over," and the cost of purchase and all the other costs
connected with the article occur at the time it enters the
stock, while all the receipts or gross

occur at the time that

income from that

leaves the stock,

we may

article

pass from

the case of the rate of interest "reckoned annually" to that
of the rate of interest " reckoned continuously " as follows
:

—

As a first step we assume that all of the stock is bought at
the beginning of a calendar year and sold at the end, so that
the time of turn-over is one year. If the cost of the stock is
represented by

including not only the purchase price but

all

other elements of cost, this must represent the discounted

value of the receipts at the end of the year, which are thereThe net income for the year is, therefore,
fore c(l + i).
c(l

+ i)--c,

ci.

This bears a ratio to the total cost value

reckoned at the beginning of the year, namely
to the rate of interest,

—

equal

For the second step we consider the stock as half purchased

—
APPENDIX TO CHAPTER
on January 1 and half on July

1, six

389

XIII

mouths

later,

and

that,

as before, each element of the stock remains one year before

The

sale.

cost on

January 1

we take inventory on July

is -,

and on July 1

to be disposed of in six

as having a

somewhat greater

also -.

the stock just purchased rep-

resents a value -, while that purchased six

which

months

before,

months more, may be taken

value, namely,

latter being the cost value plus interest, or,

^VT+T

worth on July
2 + 2Vl

The

sales or receipts

months -

the

what amounts

the same thing, the expected selling value less interest.
total stock is therefore

and

—

The

from the stock will evidently be every

six

(l-f-*)> ^^^^ being the accumulated value for one

year of the amount purchased, ^.

For the entire year the

receipts will thus be just double, or c (1

we deduct

the per

net income, ci

The

annum

cost,

ratio of this net

value taken on January 1 or July

-|-

1).

from

this

obtain, as before, the

income to the capitalany year, will therefore

be,
ci

2+2^1+*
This expression, which

evidently the same as

1+ VI +

seems no longer to be equal to the rate of interest but the discrepancy is due to the fact that the merchant's income accrues
semi-annually, whereas i is reckoned annually.
If we substitute for i its value in terms of i the rate of interest reckoned
;

semi-annually (namely,

Chap. XII,

§ 2),

shown

in the

Appendix

shall find, on simplifying, that the above

expression reduces to

i'.

In other words, in the artificially
is supposed to accomplish

simple case in which the merchant

NATURE OF CAPITAL AND INCOME

390

buying and selling in two equal amounts and at semiannual intervals, the ratio of his annual income to his capital,
In the same manner it may be
reckoned at these times, is i
shown that if his buying and selling take place at quarterly
intervals, the ratio of his income to his capital reckoned at these
all his

case,

V, i.e. the rate of interest per annum reckoned
and so on indefinitely until we reach the limiting
approximately true in practice, in which the merchant buys

and

sells

times will be

quarterly

;

daily,

when we

find that

the annual net income,

divided by the value of the capital at any instant,
to the rate of interest reckoned continuously.

that to

make

this

hold good

proposition

equal

be observed
is necessary

It will
it

that the valuation of the merchant's capital
its

wholesale price nor

retail price,

its

shall be, not
but something inter-

mediate, which shall take account of the fact that the stock

cannot

all

be sold immediately, and that, on the other hand, it
it is all sold. Similar

will not be necessary to wait a year before

reasoning

may

evidently be applied in case the time of turn-

over of the stock

more or

less

than a year.

15 (to Ch. XIII,

11)

Influence of Variability of Eate of Interest

Thus

far

we have

treated the rate of interest in successive

years as invariable.
is

As a matter

constantly fluctuating.

fluctuations are foreknown,

of fact, the rate of interest

shall suppose at first that these

and for convenience we

shall confine

Let us
assume that the rate of interest for the first year is ^l, for the
second year, i^, for the third year, 4, and so on indefinitely, all
of these being supposed to be known in advance. By means of
ourselves to a year as the standard interval of time.

these rates of interest

we can

calculate the present value of

any item or series of items of income. Thus, if ^ 1000
in two years and the rate of interest for the first year

5%,

while the rate for the second year

obtain the present value of the f 1000
for one year, thus obtaining

-zr-ir^,

(is)

due
is

3%, we can

by discounting

or $970.87, as

(ij)

its

at 3

value

%
a

APPENDIX TO CHAPTER

391

XIII

year previous to the due date, or one year from the present,
and rediscounting this 970.87 at 5% for one year, giving
'

or $924.30, as the present value.

1.05

In general,
its

V represents the item of income to be received,

value in one year will be
1

and

its

present value,

V
(1

w^hich formula

number
If

-AB,

we
its

is,

i,)

4)'

of course, easily extensible to three or

any

of years.

V in Figure 47 by the line
CF, found by the 3% discount

represent the future value

value in one year

Fig. 47.

curve BC, and

its

present value

ED, found by

the

dis-

count curve DC. In other words, instead of having a uniform
discount curve from B to D, we have a broken discount curve
BCD, with a different percentage rate of rise for the two
years considered.

In this way we may obtain the present value of any series of
income items precisely as before, with the exception that the discount curves are

now somewhat

irregular.

Thus,

of income items at different points of time are of the

the series

magnitude

NATURE OF CAPITAL AND INCOME

392

represented in Figure 48 by AB, CD, EF, and
(read in tlie
order of futurity), the remotest item, AB, is discounted by
means of the discount curve BC, and the next to the last item
is added to the capital-value at C, bringing the capital-value to
the point D, from which the next discount curve
is drawn,

and so on

until

we reach

the point

Z7is thus the

capital-

value of the given series of income items.
In this way it is possible to review

all the special cases
of capitalizing income which were considered in Chapter XIII,

Fig. 48.

and correct them for the general case of a rate of interest
which is variable but foreknown.
Such a calculation, however, is of very little practical consequence, inasmuch as the
variations in the rate of interest are seldom

Were

worth while

pursue

the

ever foreknown.

subject,

would

be convenient to simplify the calculations by substituting,

where

possible,

for

the

series

rates of interest

i-^,

ij,

an average, ,/, such that if the given series of in?3,
come items were discounted uniformly according to the rate
etc.,

we should obtain exactly the same present
when the several separate rates ij, i^, h, etc., are
employed. The formula for the average rate of interest j of

interest j,

value as

APPENDIX TO CHAPTER
any particular number of individual

393

XIII

rates, as

i^,

used for discounting individual items of income,

i^,

is,

ai,

etc.,

ttg,

ag,

would evidently be,
"^

1+i

^^
+ ^^ +...=
+ (i+jy
(i+jY

+ .....:!... +

...

..."^...

Various applications of such formulae might be made, though
they have

little

practical utility.

nable annuity of a given term

Thus, the value of a termi-

found, as before, by taking the

difference in value between a perpetual annuity beginning today and a perpetual annuity deferred to the end of the given

The value

term.

of the perpetual annuity beginning to-day

would be found, as has just been shown, by dividing the annual
income a by ji, the average rate of interest of the individual
The value
rates from the present into the indefinite future.
of the deferred annuity taken at the end of the term would be,
in like manner,

—

where

jt is

the average of the individual

from that point indefinitely forward. The present value
would be found by discounting the
latter value for the term of the annuity according to the rate
ji^t where j^^t is the average of the individual rates of interest
% for the term of the annuity.
h) hf hi
The value of a bond would be found in a similar manner.
We have just shown how to find the present value of the
"interest" of the bond, and the present value of the "princirates

of this deferred annuity

•

pal," P,

•

due at maturity, would be evidently

16 (to Ch. XIII,

— p

—

11)

Representation of Capital and Income by Polar Coordinates

The mathematical
method

reader

may

representing income

be interested in an alternative
and capital, by which polar

Let the

coordinates are employed instead of rectangular.

radius vector in Figure 49 represent the parent capital.

The time

required for a complete revolution of the radius vector

may

394

NATURE OF CAPITAL AND INCOME

taken to represent the " purchase period. " Thus, if the rate of
%, the purchase period is twenty-five years. During
one year the radius vector will move through an angle
of a
interest is 4

Fig. 49.

complete revolution, and the length of the radius vector will
increase from OA to OB by an amount, BC, -^-^ of the original
OA, interest being 4 % reckoned annually. In case the interest BC is not reinvested, but detached from the principal, next

APPENDIX TO CHAPTER

395

XIII

year will bring the radius vector to the position OD, at which
time the same interest, DE, may be detached, and so on indefinitely, the result being a toothed wheel.
Each tooth being
^ig-

OA, the sum

of the radius

of the twenty-five teeth will be

In case the interest is reckoned
semi-annually, the teeth will be fifty in number instead
of twenty-five, but each will be half as large; and so on
until, for "continuous" reckoning, we have an infinite number
of teeth each of infinitesimal size; but the sum of the whole
number in the complete revolution will still be exactly equal
exactly equal to the radius.

OA.
In case no income

received, the accumulation of capital is

represented by increasing the length of the radius vector, the

end of which thus traces a spiral. The radius vector rearound the spiral once every twenty-five years,
and the ratio between the "amount," OA', after a complete revolution, and the original "principal" OA, will be
provided the rate of interest is reckoned
e, that is, 2.718,
volves

continuously.

The same
whatever

spiral

may be the

represents the accumulation of capital,
rate of interest.

For a complete revolution

does not represent a definite length of time, but the purchase

period

;

and it

clear that a

more rapid rate

of interest

sented by a more rapid turning of the radius vector.

repre-

Thus,

4%, but 8%, the radius vector swings around
through the same spiral once in twelve and a half years instead
of once in twenty-five years. Again, if the rate is 2%, the
revolution is fifty years. The spiral is what is known as the
"equiangular spiral," and has the property that the tangent at
any point is inclined at a constant angle to the radius vector.
The angle is in this case such that its tangent is 27r. This
the rate

angle

not

80° 57'.

The equation

of this spiral

—=

e"'^,

which p represents the radius vector, 6 the angle of revolution,
and po the initial radius vector; e and tt are, of course, the
magnitudes ordinarily represented by these letters, namely, the
base of the Napierian system of logarithms and the ratio of
the circumference of a circle to

its

diameter.

NATURE OF CAPITAL AND INCOME

396

APPENDIX TO CHAPTER XIV
§

When

1 (to Ch.

XIV,

the Interest Eate varies, there are

Two

Rival Concepts of Standard

Income.

When

the rate of interest varies during successive years, the

standard of the comparison of income and capital requires
statement.

re-

found, vrhen the rate of interest was assumed

income corresponding to a given
was a perpetual and uniform flow, of which flow that
capital was at any time the present value.
It did not matter
whether standard income was conceived as income which
was constant and perpetual, or as income which would mainconstant, that the standard

capital

tain its capital-value at a constant level

;

for under the con-

dition of a constant rate of interest, a constant income will

necessarily maintain a constant capital-value.

But when we

introduce the possibility of a change in the rate of interest,
these two concepts of standard income are no longer equivalent; under such conditions only

an inconstant income will

maintain a constant capital-value. Thus, if the rate of interest
for the first year is 10%, for the second, 5%, and for the third,
6%, etc., the income stream which will maintain the capital
unimpaired will be, in successive years, proportional to the

numbers

10, 5, 6, etc.

A person

possessed of $100 of capital

can evidently earn with it $10 the first year and still have his
$100 unimpaired, with which, in turn, he can earn $5 the
second year and maintain the principal of $100 and again
;

in the third year,

and

so on, receiving each year

proportional to the rate of interest.

an income

Relatively to this income

stream considered as a standard of reference, the propositions
stated in Chapter XIII will remain true, namely, that if the

income in any year exceeds the standard for that year, the
by the excess and if the income falls
short of the standard in any year, the capital will accumulate
by the amount of the deficiency.
But this concept of standard income is not the only legitimate one. We may, if we choose, employ the other definition
In this
of standard income, as a perpetual and uniform flow.
real

capital will be impaired

;

APPENDIX TO CHAPTER XIV
case, it is the capital-value of

will vary

from

time to time.

397

such an income stream which

As has been

seen, the capital-

value of such an income stream is found by dividing the rate of
income a by the average of the individual rates of interest, such
the above example, 10%, 5%, 6%, etc., ad inf., the average being obtained by the formula given in Appendix to Chap.
XII, § 5. If such average rate of interest be called ji, the
as, in

capital -value will be -.

Suppose, for instance, that the person

has a uniform perpetual income of $5 per annum. If the rate
of interest to-day, ji, is 5%, the capital-value to-day will be f 100.
If next year, Jg (the average of the future rates in individual
years, beginning at that time) is 4.9%, the capital- value will
If, two years from date, js be 5.1%, the capital-value
be f 102.
Adopting such an income stream as a standwill sink to $98.
ard, the propositions as to impairment or increase will still be
true, provided such impairment or increase is measured with

reference to the variable capital-value just shown.

Thus,

if at

year more income than $5 is received, the
capital-value will be impaired by the difference, this impairment to be reckoned with respect, not to f 100, but to $102,
the end of the

first

which would be the value had the income remained standard.
Thus, the effect of a difference between real and standard income may be stated in the same terms, whichever of the
two definitions of standard income is adopted. In the one case
the standard is with reference to constant capital and variable
income in the other, to variable capital and constant income.
In practical life, the former standard is usually employed,
although for certain purposes the latter would be more suitable.
We all know of cases of investors who, twenty years ago, invested at a high rate of interest, and who have taken pains
;

merely to maintain the value of their capital unimpaired,
although they were well aware that the rate of interest was
In consequence, these persons are now
constantly sinking.
forced,

when

reinvesting, to suffer a large decrease in income,

which could have been avoided had they kept

tenance, not of their capital, but of their income,

view the mainand laid aside

sum in order to offset the fall in the rate
The reason such a procedure is not common

each year a certain

interest.

NATURE OF CAPITAL AND INCOME

398

that the fall or other change in the rate of interest can never
be foreseen with precision, and thus a perfectly uniform flow of

income secured, whereas

always possible, in the case of
what is necessary to maintain
the value of the capital at a uniform level.
it

safe investments, to calculate

2 (to Ch. XIV,

Effect of

12)

Foreknown Tax on Increase

of Capital

Let us suppose that the three brothers invest in their respective annuities without realizing that a tax is to be imposed.
The first brother has bought with his $10,000 a perpetual annu-

$500 a year; the second, a perpetual annuity of $1000
and the third, an annuity of $2000 for six
years only. After these investments have been made, let us
suppose that the tax of 10% on income is announced.
If "inity of

deferred 15 years

;

come" is interpreted properly, i.e. as simply the annuities,
the value of each of the three properties will immediately
shrink by $1000, so that any of the three brothers could sell
his annuity, subject to the tax, for $9000.

tax"

interpreted as a tax on "earnings,"

But
i.e.

if the "income
on income and

announcement of such a tax will not only
reduce the values of the three properties very unequally, as has
been shown, but will have the further effect of altering the very
increase of capital, the

annual increase in the value of the capital which
taxation.

To show

is subject to
the effect of this " repercussion," let c rep-

resent the value of the capital of the second brother (who saves)

end of any year during which no (true) income is received.
$18,000 at the end of the fifteenth year when the annuity of $1000 a year is purchased for the capitalization of
the perpetuity of $1000 which begins at that time is $20,000,
from which $2000 is deducted as the capitalized tax. Let i
represent the rate of interest (as 5%) and t the tax rate (as
10%). We wish first to find x, the capital-value one year
earlier than c.
It is clear that x is the discounted value
at the

Thus

c is

;

of c

we
is

[i.e.

——

]

less

the discounted value of the tax, which

The tax
end of the year.
on the increase of capital-value in the year, i.e. on

will suppose is due at the
laid

APPENDIX TO CHAPTER XIV
c

— x.

As the rate

of this tax

vahie,

c
^

1
value, X

+i
;

the tax

is (c

— x)t.

This deducted

The discounted value
from the discounted

of next year's capital-value

i.e.,

Solving for

— x)t
1 + i'

—

1+i

have,

399

this year's capital-

— x)t
+
i

1 — +i
— x), which, if we
t

The tax

itself is t(c

just found, reduces to
1

If we substitute
we have

for

— +
t

and

substitiite for

its

value

their

assumed values,

.05

and

.10,

x = c x .947
tax = c x .0053.

Substituting for c its value at the end of the fifteenth year,
namely, $18,000, we find that x, the value one year earlier,
will be 18,000 x .957, or f 17,046, and that the value one year
previous will be the latter sum multiplied likewise by .947, or
$16,142.56, and so on until the present is reached, when the

value will be $7,952.15.
fore, the total effect of

The

table below will show, there-

10%

tax on the increase of value,

NATURE OF CAPITAL AND INCOME

400
including

" repercussion "

of the tax

on the capital-values

in the table evidently differ

somewhat from the

ttie

themselves.

The taxes

taxes given in the text, which do not include the effect of

The present

"repercussion."

value, therefore, of this tax

the increase of capital should be altered from $714 to $661.81.

similar correction should be

Our main

made

for the case of the spend-

however, is not to study the effects
of different methods of levying taxes, but merely to show how
untenable is the theory which includes savings under income,
and excludes that part of true income or services which brings

thrift.

object,

about a depreciation of capital.

3 (to Ch. XIV,

13)

Unrestricted Application of a True Income

Tax Impracticable

Theoretically, an income tax should tax every element of

income, large or small, positive or negative. That is, all positive items should have a tax and all negative items a bounty.

This system would be ideal in theory but

difficult to

carry out

in practice.

made

book to contrive a practical
all the difficulties which
have been pointed out as belonging to systems now in use. It
is undoubtedly true that it would be impracticable to assess
taxes on each article on the basis of the actual items of income it yields for most of such items are simply the positive
sides of " interactions" and are offset as outgoes in the accounts
of some other article of capital. To carry out such a system in
detail would require that we levy taxes on the proceeds of every
sale and remit them on every investment. It would be difficult
to avoid injustice, evasion, and fraud if the attempt were made
to assess taxes on such income and remit, as would be required
logically, taxes on the corresponding outgo. The taxpayer would
contrive to exaggerate his outgo and understate his income.
Consequently, the sj^stem is not wholly unjust which exempts from taxation that part of income which stands
for impairment of capital, and assesses taxes on that part
The system would be
which swells capital, or savings.
attempt

in this

system of taxation which would avoid

;

APPENDIX TO CHAPTER XIV
entirely just
offset

401

the impairment of one capital were always

by the equal increase of some other

capital,

i.e.

the taxpayer's total capital-value were kept at the same level.

In general, large receipts are usually reinvested and should
therefore not be subject to the income tax at

all.

we could

assume such reinvestment to be the invariable rule, we could
approve of the system by which, in England, a terminable annuity is not taxed as income at its full value, but is taxed only
on that part of it which constitutes "interest." The other part,
which constitutes impairment of principal, is not taxed.
The
system, of course, fails of justice in cases where this impairment
of principal is never restored in some other form of investment
but ultimately represents, like the other part of the annuity,
through personal expenditure, final enjoyable income.
To illustrate the English exemption of impairment of capital,
if $1000 is paid for a five-year annuity on a basis of 4 % interest (reckoned semi-annually), it will purchase an annuity of
$111.33 at the end of each six months, and the following will
be the schedule showing the capital-value at each interval, the
interest accruing

upon

it,

the payment to the beneficiary, and

the impairment of capital resulting.^

NATURE OF CAPITAL AND INCOME

402
first

is left f 908. 67, which has impaired
by f 91.33. This being reinvested and yielding inwould make a total combined fund of $1000 as before.

half

year, there

his capital
terest,

the end of the second half year, in like manner, the original

security

worth $815.52, but

capital invested last year, $91.33,

year, $93.15,

making a

must be added the

to this

and

also the investment this

total again of

$1000; and so on for

each year.
If,

then, as

in England, the tax

annually (second column), no injustice

paid on the interest
is

done, providing the

items in the fourth column are actually reinvested each year,

and

that the interest on such reinvestment in some other form

used as income. In other words, each reinvestment is not accumulated at compound interest, but made a separate fund
yielding perpetual interest which

converted into enjoyable

income as fast as it is received. In this case the man will be receiving, from the given security and the others created out of
his reinvestments, a uniform net income of $20 a year, and
will maintain his capital at $1000.
Consequently the exemption of "impairment of capital" works no ultimate injustice,
since ultimately there is no such impairment.
But as, practically, we can never know to what extent the
" impairments " are actually reinvested, the justification of taxing the sums in the first column instead of those in the third
is entirely on grounds of expediency.
Theoretically, the actual
income from this particular form of capital as represented in
the third column should be taxed, and afterward whatever is
reinvested in some other form should earn remission of taxes.
This method, while impracticable in such detailed application,
might with advantage be applied to the taxation of an individual's income as a whole. After all the individual components
are combined
all the income elements, large or small, and all

—

the outgo elements, including reinvestments

— there will be a

resultant net income for the individual which, and which alone,

system which would accomplish this
any net impairment of his capital,
for such impairment would mean large income; but, on the
other hand, if he were not depleting but laying up capital, it
would exempt the increase, for such increase would not be part
should be taxed.

would

tax, to this individual,

;

APPENDIX TO CHAPTER XVI

income.

tion of income.

403

Such a system would secure justice in the taxaIt is practically what has usually been called

the system of taxing " consumption."

APPENDIX TO CHAPTER XVI
§

Mathematical

Let us

call

1 (to Ch.

XVI,

§ 6)

and Risk

Coeflficients of Probability, Caution,

the riskless value V, the mathematical value V,

the commercial value V", the coefficient of probability P, the

and the entire

coefficient of caution C,

have,

—

P-^
^-r
Whence

B-^'

-C-^'

^—v'

^-v'

follows that

coefficient of risk

B = PC.

That is, the total effect of risk on value is twofold: first,
through mere probability, which gives mathematical value and
secondly, through caution, which gives commercial value.
;

Practically,

it is

usually impossible to separate
is

factor explicitly, as to

make

and P, and
rities is

much

not so

object of this analysis

P and

The

to introduce the caution

the general distinction between

to point out that the actual

market value of secu-

not their actuarial or simple " mathematical " value

that, in other words,

B is
§

Tormula

not the same thing as P.

XYI,

2 (to Ch.

for Mathematical

§ 7)

Value of Risky Bond

Let us denote by p^ the probability of receiving the first
a-^, of income due in one year, and hjp2 the prob-

installment,

ability of receiving the second installment of income,

vided the first year's

is received,

ag,

pro-

and again by pg the probability

of receiving a^ in three years, provided the previous tivo have

been received, and so on for

years to the last payment.

j>4

p„,

where n

The chance

the

number

of receiving the first

payment

is p^, hence the "mathematical value" of the first
payment, when due, is aiPi, the present value of which is

-i-^.
1
i

But the chance

of receiving the second

payment

NATURE OF CAPITAL AND INCOME

404

evidently not pa? but piP2 for one of the first principles of the
theory of probabilities is that the chance of two successive events
is the product of their successive probabilities.
Thus, if the
;

chance of heads appearing in coin tossing is ^, the chance of two
or \, and the chance of three successuccessive heads is -^ x
sive heads is, in like manner, ^ X ^ X |-, or
etc.
Hence the
" mathematical value" of the second installment, a^, when due is
-|-,

-|-,

which the present value

a2PiP2, of

.A -

manner,

the mathematical present value of the third installment
(^zPxP^Pz
(1

gQ QQ_

g^^(j

+ if

value thus obtained
the property.

'^"'

+ i "^

we suppose

denote

all

the

expressions for present

this mathematical value

(1+

by F^,

+ if
we may

that all the probabilities are equal,

simply by p, and simplify by substituting p^

jj's

and p^ for PiPsPs?

for P1P2,

ijJ^q

the total present mathematical value of

+ if

g^jj^

we denote

—

have,

rpjjg

e^c.

Since the p's represent the probability of receiving the installments, it is clear that the chance or risk of not receiving

them

default

and

also p^

shall denote

= 1 — q^,

note them by

by the

letter q.

Thus,

gi = 1 —pi,

If all the g's are equal,

etc.

and the present value

evidently be written,
TT

This risk of

the difference between this and unity.

—

of the property

etc.,

shall de-

may then

_ ai(l-g) "^ a2(l-qy' "^ asjl-qf ^•••^ a„(l-9)"
0"*
(i + if
1+i
(1 +
(1 + if
,

In case the risk of default q
^

the fraction
1

very small,

approximately equal to

•"

it is

evident that

—
+ +q

This

may

be seen by dividing the numerator and denominator of the first
fraction by 1 — g, which will give for the new numerator unity,

and
the

for the denominator 1

fractional

because

the

term

+ + q -|-l-+-!£.
1-g

becomes

denominator,

while the numerator,

+ iq,

made up

when

small,

approximately

unity,

negligible

— g,

In this expression

two terms, each of

—

APPENDIX TO CHAPTER XVI
whicli
is

405

the product of two very small quantities.

and

j^,

i is

Thus,

the value of the fractional term becomes

approximately .0005, which is a negligible quantity (compared
with 1 + ^ + g = l + .04 + .01). Hence when q is small, the
formula for mathematical value becomes approximately,

—

^
+ i + qy

d/
I

+i+q

^
+ + qf

. .

•

+ i^-g)"

^™

_1_

In other words, when the risk of default is small, its effect is
substantially the same as that which follows from a rise in the
If the rate of interest

rate of interest.

when

risk is absent is

on
1%
Thus, if we
which the loan can be contracted to about 5 %
recur to the so-called 5% ten-year bond, and suppose that
the probability of each successive payment is -^^, and the

4%,

will therefore merely increase the "basis"

a risk of

risk of default,

of the bond,

q, is

when

Y =
=

y^, then

interest is
^1

approximately,

—+—

1.05

the mathematical present value

4^,

(1.05)2

—

etc

— + ,etc.
-h—
(1.05)3
'

In other words, the present value is approximately the same
as the present value of a 5% bond on a 5% basis, which is of
course par, or 100.

But if the risk
no longer apply.

the approximate formula given will
Thus, if the chance of default is y^^-, or, in
other words, if the chance of payment is only jL, the formula
for the mathematical value of the property becomes,
is great,

—

_ ^IVT?)

^2(to')

this case it is

ligible
ag, etc.,

l-h^

(1
evident that

compared with the

^sCtW
(1

all

first

_t_

terms after the

first

are neg-

(unless the successive items

a^,

increase with sufficient rapidity to offset the decreasing

fractions

mate value of the bond, obtained by omitting
the

first,

all

terms after

would be _AllZ, or approximately 50 cents

" mathematical value " might be
ef6.cient of caution.

still

This

further reduced by a co-

In other words, the bond

worthless.

NATURE OF CAPITAL AND INCOME

406

case of such high risk

cannot, therefore, apply the simple

rule of adding to the rate of interest the rate of risk to obtain

"mathematical value"; and the "commercial value"
would, of course, be even less than the mathematical value.
In other words, it is practically impossible to compensate for a
the

risky investment by increasing the rate of interest as though
it were an insurance premium.
In actual practice such a

"bond" would be absolutely worthless;

for,

while the above

calculations are correct on the basis of a chance of

payment

one in ten, practically this chance of payment would be zero.
The high risk not only makes the terms of the loan onerous,
but these onerous terms make the uncertainty of repayment
greater,

can

and

on in a vicious circle. A lender who fancies he
high as -^-^ by lending only 50 cents instead of

offset a risk as

f 100

for a returnable principal of

f 100^

not offset that risk, but merely increased

will find that he has

it.

In the previous calculations, we assumed that a default in
one payment carried with it a default in all subsequent payments. We may, however, easily extend our formula to the
general case by designating the chances of payment in successive years, whether interdependent or not, by pi for the first
year, p, for the second (instead of
third, etc.,

and changing the

first

by p^ p^ as before), p^ for the
equation on page 404 accord-

ingly.

3 (to Ch. XVI,

Variability about a Mean, as measured

10)

by the "Standard Deviation"

Eor a more minute analysis of the bearing of chance

it is

preferable to measure the variability with reference to the

mean.

Thus, in the case mentioned, where the dividends are

successively

4%, 5%,

reference to

mean

5%, 5%, 6%, 5%, 5%, 4%, 5%, 7%, 5%, 3%,

instead of measuring the variability of dividends with

rate,

5%, we should measure it with reference to the
is 4.9%.
The deviations from this mean

which

during the twelve successive years were therefore:

+0,1,
+1.1, +0.1, +0.1, -0.9, +0.1, +2.1, +0.1, -1.9,
-0.9, +0.1.

+ 0.1,

APPENDIX TO CHAPTER XVI

407

A simple measure of the extent of variability displayed by
such a series of deviations from the mean is what is called the
" standard deviation. " This is a sort of average of the deviations
not the ordinary arithmetical mean, but the mean
found by taking the arithmetical mean of the squares of the

—

deviations

and extracting the square

root.

The standard

deviation which represents the above twelve individual deviations is thus,

—

+ (-1.9)2+
(.1)2+ (.1)2+ (1.1)2+ (.1)2

(-.9)-'2+ (.1)2

(.1)2+ (_.9)2+ (.1)2^ (2.1)2

(.1)2

which

is .95.

This "standard deviation"
for several reasons.

about the

mean

used instead of other averages

The arithmetical mean
quite unavailable,

of the deviations

because, unless

reckoned by disregarding all minus signs (in which case the
result is an illogical makeshift), it is zero; the standard
deviation is very readily calculated, not by performing the
operations indicated above, but by recourse to a theorem
that the

mean

equal to the

of the

squares of the deviations about the

mean

of the squares of the deviations
about any other magnitude less the square of the difference
between the mean and this other magnitude.
The proof
is

of this theorem

on probability.

Applying

simple,

and may be found in the books
it

to the illustrated case,

first

take the deviations, not about the mean, but about some other

These deviations are

magnitude, say 5%.
2, 0,

- 2, - 1,

The squares

of these are

0, 0, 1, 0, 0,

— 1,

0, 0, 1, 0, 0, 1, 0, 4,

of which the arithmetical mean is \^, or .902.
This
mean of the squares of the deviations about the magnitude 5.
From this we are to deduct the square of the
difference between the mean 4.9 and the other magnitude 5,
about which the deviations were measured. The difference is
Deducting this from .902 we have .892 as
.1, its square is .01.
the mean of the squares of the deviations about the mean. The
0, 4, 1, 0,
is

the

square root of this
deviation sought.

deviation

may

.95,

which

therefore the

Calculated by this

standard

method the standard

usually be obtained in less than one tenth the

time required by the direct method.

NATURE OF CAPITAL AND INCOME

408

The "standard deviation" plays an important
treatment of

all statistics

role in the

involving variation about a mean.

of its simplest uses is to change any given deviation into
a deviation relative to the standard deviation (or to a fixed
This is usually done by dividing the absolute
portion of it).

One

deviation by the standard deviation. Thus, in the above example, where the standard deviation is .95 %, an absolute deviation of, say, 2 % mean is a relative deviation of 2 -=- .95 or

about

2.1.

Such a reduction from absolute to relative deviation brings
the different probability distributions or curves into a common
comparison, so that probability tables may be constructed
applicable to

all.

In one case the deviations may mean inches
pounds of barometric pressure, in an-

of rainfall, in another,

other, the annual percentage of dividends, as in the case above.

These are incommeasurable. But if each be compared with
the standard deviation which applies to that particular case,
and which would therefore be measured in inches, pounds, or
annual percentages, respectively, we obtain three ratios which

numbers indicating the extent
compared with the standard deviation.
are simply pure

we now

consult a probability table

of the deviation

we may

find at once

the probability of any given relative deviation. For
the chance that dividends will, in the case supposed, deviate

what

any given future year by 2 % from the mean rate of 4.9 %
is, from the tables, 1 in 20; for the deviation, measured
relatively, is, we saw, the number 2.1 and the probability corin

responding to this in the tables^ is If. This expresses the
chance that the deviation will keep inside the limits of 2 %
will be between 2.9% and 6.9%.
i.e. that the dividends
The wider the range of deviation considered, the less the
;

chance that the actual dividends in any year will fall outMoreover, the chance decreases far faster
side that range.
than the range increases. This relation, which follows from
the theory of probability, has very important consequences in
1 Thus on p. 55 of Davenport's " Statistical Methods," New York,
Wiley, 1899, we find for a relative deviation 2.1, the number .4822 as the
chance of the deviation in one direction. Hence the chance of the deviation in either direction is double this or .9644, about |f

APPENDIX TO CHAPTER XVI
the theory of distribution.

From

409

follows as a corollary that

the richer an individual, the less risk in taking risks.

Being

possessed of capital, he has a wider range within which he can
safely afford to operate, and therefore he has a far greater
probability of keeping within these limits of safety than his
less fortunate competitors.

Professor Norton has also empha-

sized the fact that the advantage of the capitalist is further
enhanced by the tendency toward monopoly. " The result is a

most interesting
order to force

monopoly

circle,

constant combination at the top in

the commercial price of the risk, and

down

which pays tremendous

of the upper field,

resulting in

still

profits,

greater increase in the financial power of the

risk takers.
To this there is no end, save in the divorce,
through heredity, of ability and financial power." ^
An important application of these methods is to the calculation
of the chance that earnings should fall below the amount required to pay interest on bonds. This chance is found from the
probability table.
It is the probability corresponding to that
relative deviation obtained by dividing the difference between
the mean expected earnings and the interest by two thirds of
the standard deviation. In this and other ways business men
could, as Professor Norton has shown, make better use of their
Merely to glance over past
past experience than they do.
earnings and receive an impression is not a very scientific mode

of utilizing the facts

age them

know

not of

the mean,

which those earnings display. To averWhile it is important to
value.

much more
is

also important to

know

the dispersion

shown by the standard
deviation.
The best procedure would therefore seem to be to
calculate first the mean of past experience as to earnings;
secondly, the standard deviation from that mean; thirdly, the
about the mean.

This dispersion

chances of fluctuations thus displayed

{e.g.

earnings falling below the interest-paying line)
to correct the results thus obtained

degree in which

it is

From

Loan
p. 54.

;

and, fourthly,

by taking into account the

believed that the future will not follow

in the footsteps of the past.
1

the chance of

a letter to the author.

Credit," Publications of the

Only the

last of these four

"Theory of
American Economic Association, 1904,
Cf. also Professor Norton's

NATURE OF CAPITAL AND INCOME

410

operations need be done by rule of thumb.
all

but the

first

and often even that are

left to

But

at present

the merest im-

pression.

There was a time when business men did not use bond
when they did not calculate cost sheets, and even when
life insurance was contracted for in scornful disregard of any
mortality tables. Just as these slipshod methods have been
displaced by the work of expert accountants and actuaries, so
should the mere guessing about future income conditions be
tables,

replaced by making use of the modern statistical applications
of probability.^

Method

The

4 (to Ch. XVI,

20)

of computing a Pure Level Life Insurance

Premium

chief peculiarity of life insurance is that each year's

premiums, in properly organized insurance companies, are
calculated not on the basis of the chance of death in that
year, as in the case of fire insurance, but are computed as " level
premiums," which exceed this chance in the early years of
the policy, and fall short of

in later years.

The wisdom

such an arrangement is justified by the incentive which
is produced for all "risks" to remain insured, whereas when
the "natural" premium only is charged, increasing with
age, there is a tendency for the better risks to withdraw,
making thereby a "selection" adverse to the companies.
A consequence of a "level" premium being charged is that
the policy acquires an increasing mathematical value with
time, so that the policy holder, after a few years, sometimes
possesses a very valuable property, which he can,

he chooses,

use as collateral security for loans, etc. The value of
such a policy, computed on the mathematical basis, is of
sell or

1 Cf. " The Put and Call," byL. E. Higgins, London, 1902, pp. 65, 66.
For some suggestions along this line, see Edgeworth, " Mathematical
Theory of Banking," Jour. Boy. Statis. Soc, March, 1888; for a statement of the modern statistical method, see Karl Pearson, Grammar
of Science, and his journal "Biometrica" for an application of this
method to financial and industrial problems, see J. P. Norton, Statistical Studies in the New York Money Market, New Haven (Tuttle, More;

house

Taylor), 1903.

APPENDIX TO CHAPTER XVI

411

course the present value of the chance of receiving the insur-

present value of the chance of paying the
Thus, for a man aged 30, who was insured 10 years
before, the chance of his death at the age of 35 will be about
g-lffo, or .86%, since of 84,720 living at age 30, about 732 die
less the

ance,

premiums.

Hence the present value of the chance of
f 1000 in that particular year is
assuming the rate of interest to be 4%. In

in their 36th year.

receiving his insurance of

^Ti"

°^ $7.07,

manner we may determine the present value of the similar
chance for every other year of possible life, and the sum total
like

of these present values will be the total present value of the

chance of receiving the insurance, $287.66. From this must be
deducted the present value of the chance that he will pay'
premiums. Thus, the chance of his paying the premium in the
above-named year, when he is 35 years of age, will be the
chance that he will be living at that time, which is .958. This
multiplied by his premium and discounted gives the present
value of this possible

sums

premium payment

;

this

added to the

for every other year will give the total present value of

his obligation to

pay premiums, $222.86

tracted from the present value

;

this, in turn, sub-

of the prospective insurance

namely $287.66, will give the present mathematical value of his property, $64.80, called the value of his

just obtained,

insurance, or the "reserve" on his policy.

The

true "commercial value," or the value

ing to pay, will be somewhat higher.
coeflB-cient

which he

is will-

For, in this case, the

of caution operates to increase, not to diminish, the

value of the property, as insurance tends, not to

but to reduce

make

a risk,

it.

The calculation of mathematical values of life insurance has
been very perfectly worked out. The reader who is interested
will find the most complete explanations in the Institute of
Actuaries' Text-book, 2 vols., London (Layton), 1901.

INDEX
Appraisal of wealth, methods used
in,
11-12, 34-36;
based on
future worth, 204-205.
Accounting, philosophical basis of,
See Capital accounts Appraised price, 13
129, 140.
a source of
and Income accounts.
inaccuracy in measurement of
Accumulation of interest not inwealth,
16-17;
discrepancies
come, but increase of capital,
between, and actual selling price
224134-135, 224; results of,
(of shares in stock company),
70-72.
226.
Apprenticeship considered as an
Adornment, services of, 165.
investment, 169-170.
Agio sense of rate of interest, 195,
Premium
See
con- Area method of representing income,
247, 334.
207-208, 371-374.
cept.
Agriculture amenable to prediction, Assets, definition of, 67-68, 329;
291.
discrepancies in valuation of,
Amortization, definition of, 110, 332.
71-72
effect of increase or
decrease in value of, 73-74;
See Depreciation fund.
fraudulent methods of swelling,
Amount of a sum, definition of, 203,
;

;

relation of stability of, to
capital-balance
necessary for
safety of a business, 81 ; cash,
quick, and slow, 82
true value
of liabilities derived from, 8485, 139 items of, to be included
in capital and income accounts,

329.

Amusement,

services of, 165.
Annuity, regarded as income, 111;
concept of interest based on
perpetual, 191-194, on terminable, 194-195 capital-value of
perpetual, 205-208 "deferred,"
examples of perpetual,
207
208-209
capital-value of terminable, 209-210; examples of
terminable, 210-211
the perpetual, taken as the standard

;

139-140

;

of,

;

come

and

ideal

terminable,

243-244
depreciation
fund
based on difference between
actual income and ideal perpetual, 243-244
mathematical
formula for present value of
perpetual, 369
formulas and
diagrams of capital-value of,
payable annually, semi-annually,
369-371;
formulas
for
etc.,
capital-value of terminable, 374taxation of terminable,
378
in England, 401.
;

;

methods employed

for

obtaining valuation of bank
(discount
paper,
short-time
loans), 194-195, 198-199, 204;
effect of chance element on value

;

income, 236-237
sinking fund
based on difference between in-

;

287-288

;

figures of,

life

insurance companies, 295.
Assignment, settlement of bankruptcy by, 86.
Austria, taxation of forest lands in,
254.

;

method of: in summing
capital or income accounts, 9091, 142-143, 183, 335; taxation
97-98
by,
contrasted with
method of couples in income

Balances,

;

Appraisal of labor, 172.

summation, 157-158.
Balance sheet, definition of, 329.

418

INDEX

414

Balance sheets, to show accumulation of surplus, 69
effect on, of

;

lying, 27.

Bank

notes, wealth underlying, 27;
nature of property right in, 32,
280 ; legal regulations governing, to avoid risk, 289.
Bank reserves, risk-meeting function
of, 290.

communication

income

earned

231-236;

of,

application of depreciation fund
to, 242-243
as investments,
277-281
formulse for computing value of, 378-382 ; formula

;

increase or decrease in value
of assets, 73-75 ; interdependence of, of different firms or
companies, 87-92
show
to
methods of balances and couples,
91 to show distinction between
accounting of real and of fictitious persons, 93-94 prospects
of businesses shown by, 264.
Bank deposit rights, wealth under-

;

mathematical value of risky,
403-406.
Bond value books, 213-215.
Bougand, quoted, 168 n.
Branford, Victor, cited, 63 n.
Building and loan association, income accounts of, 127-128.
for

Bullock, C. J., definition of income
by, 349-350.

C
option known as a, 298.
Campbell, A. C, cited on moral

Call,

effects of insurance, 295 n.
Canard, human beings counted as
wealth by, 5 n.^.
Bankruptcy, state of, 82 laws relating to, 83
bondholders' and Cannan, Edwin, definition of wealth

Bankruptcies,
87-88.

of,

;

stockholders' position in case

83-86; settlement

of,

86; rela-

tion of general crisis to individual, 297.
Banks, national liability of stockholders in, 83
investments of,
in government bonds, 280-281.
Basis of a security, definition of, 329.
:

;

Bemis, Edward W., cited, 39.
Bequests not counted as income, 109.
BernoulU's Theorem, 267, 275.
Bills of exchange, 204-205.
Bohm-Bawerk, quoted on attempts
to define "capital," 53-54; concited,
cept of capital of, 56
60 n.^; statement that interest
is not an element in cost of
cited in
production, 173-174
connection with productivity
theory, 187 concept of interest
on interactions as
of, 195, 247
preparatory to enjoyable serv;

;

ices,

318.

Bondholders, nature of rights of,
31-32, 85
distinction between
stockholders and, 85, 288-289;
;

position

of,

reorganization

after bankruptcy, 85-86; relation of, to risks of enterprises, 289.

Bonds, wealth underlying property
in, 25, 26; nature of rights of
holder, 31-32, 85; capital-value
realized vs.
of, 211-217, 382;

by,

;

cited

capital, 56, n.^

tion with

;

wage

definition of
cited in connecfund theory, 59

use of term "capital" by, 60
and n.^ ; on concept of income,
102 n.^; savings regarded as
income by, 108; concept of
income of, 116; on distinction
between rent and interest, 186
n.^; confusion of earned with
realized income by, 247-248.
Capital, concept of, as stock of wealth
at an instant of time, 51-52,
varying views of, 53-57
324
viewed
relation of labor to, 55
fancied disas productive, 56
tinction between land and, 56 n.^
;

;

errors resulting from narrow
relainterpretations of, 57-58
tion of author's definition to
dicestablished usage, 60-61
tionary definitions of, 61-62
business men's view of, 63-65
two senses of, called capitalgoods and capital-value, 66-67
relation of surplus or undivided
;

;

68-70; original and
330; bookkeeper's vs.
market's estimate of, 70-72
four separate meanings of term
applied to person or firm, 72
nominal
classification of, 72
and paid-up, 72, 330; payment
profits to,

net,

69,

;

;;;

;; ;

INDEX

of perpetual annuity,
est, 202
of terminable
205-208, 369
annuity, 209-210, 374-378 risk
element in determining, 210;
of
of a bond, 211-217, 382;
any income stream, 217-221,
387-388; of alternative income
streams, 221-222
of group of
articles, 223
is the discounted
value of expected income, 223-

of dividends out of, 75, 256
of "real" person and of "fictitious" person, 92-93; relation
fallacious staof credit to, 96
confusion of intistics of, 98

;

come and,

ill

114-115,
351 fallacy of adding to income
savings of, 108, 134-135, 247income need not
255, 349, 353
110-111
unimpaired,
leave
outgo is not, 124; analogous to
and correlative with income,
184; physical productivity and
value productivity of, 185, 186
physical return and value return
mistake of disof, 185, 186;
tinguishing between land and,
186-187 fundamental principle
of value of (value of future
income), 188 increase of, equals
excess of earnings over income,
between
relation
237-238

105-112,

;

304-305; less than total
expected income, 227-228 effect
of change of interest rate on,
229, 271-273, 390-393 enmner-

224,

;

ation of causes affecting, 284285 as mean between past cost
and future income, 305-309
;

for, of sum due in one
and of sum due at any time,

formula

;

year,
368.

;

Capital-wealth. See Capital goods.
Carver, cited, 117 n.^.
amount of, and risk involved, Cash, income and outgo accounts of,
131-132, 135-136 account book
277, 408-409; reserves of, held
of lawyer, 136-137
representaas an into avoid risk, 290
come meter, 137-138.
tion of income and, by polar
effect of Caution, coefficient of 276-277, 330
coordinates, 393-395
applied to insurance, 292 matheforeknown tax on increase of,
matical presentation of, 403.
398-400; taxation of impairCensus (U. S., 1905), cited concernment of, 400-403.
ing railway valuation, 36 n.
Capital accounts, definition of, 67,
ne89 ; methods of balances and Certificates, of property, 23
cessity of separating from wealth,
couples in summing up, 90-92;
property, services, and utility,
relation between income ac38; stock, 68-70; receiver's,
counts and, 139, 256-264.
86.
Capital balance, 81, 329.
Chance, element of, in property
Capital cost, 124-125.
rights, 22, 330; involving risk
Capital curves, 303-322, 369-378.
of insolvency, 81 ; nature of,
Capital-goods, meaning of term, 67,
always an estimate,
265-269
classification of, 72.
329
266 an affair of ignorance,
Capital instruments, 66-67, 72, 329
regulation of income by com268; measurement of, 269-271;
mathematical value of a, 275;
bining, 127-129, 245-246.
in valuing stock, 280-283 effect
Capitalization, definition of, 64, 330
of, on discount curve, 286-287
rate of, 194; employment of
effect of, on bookkeeping, 287rate of, as alternative to rate
288 effect of, on capital curves,
table showing
of interest, 199
320-322.
equivalent rates of interest,
discount, and, 200; of income Chen, Chin tao, cited on utility, 47.
by means of rate of interest, 202 Clark, J. B., cited on utility, 47;
concept of capital of, 55, 56,
dimensions of rates of discount,
interest, and, 367-368.
60; term "capital-goods" suguse of economic
gested by, 67
Capitalize, use of term, 64, 330.
terms by, 67; "Niagara Falls"
Capital property, 67, 72, 330.
simile of, applied to income, 129
Capital-value, 67, 72, 327, 330 deterdistinction between work and
mination of, from rate of inter;

;

INDEX

416
labor drawn by, 175 n.
cept of interest of, 247.

;

con-

Clothing, services of, 165.
Coefficients of caution, probability,

Currency

inflation,

the basis

Custom

(tailor's),

;

Consumption, 145, 152, 164, 165, 336,
350.

Contingent liability, 83.
Control, value of, as applied to
railway ownership, 35-36.
Copyright, wealth underlying, 27,
29.
Cost, included in term "outgo," 120;
influence of past, on present
value, 188-190.
Cost of production, 151, 173-174,
184.
Cotgrave, definition of capital by,
62.
Couple, definition of, 331.
Couples, method of ; in capital sum-

mation, 90-91, 183-184, 335;
applied to accounting of railway company, 94 taxation by,
97-98; income summation by,
143-152, 183-184, 335; natural
income discovered by, 150-151
contrasted with method of balances in income summation, 157;

158.
Courcelle-Seneuil, use of term "capital" by, 60.
Credit, nature of property right
represented by, 32-33
mistaken view of, 39 ; relation of,
to capital, 96-97 in the sense
of an item of a transaction, 158159, 336.
"Credited," income said to be, 122,
132, 325.
Creditors, regarded as risk-takers,
;

;

83-84 bondholders contrasted
with stockholders as, 85.
;

Crises, causes of,

296-297.

mistaken

idea

38-39.

wealth represented

by, 29.

and risk. See Caution, etc.
Combination of capital instruments
to standardize income, 127-129,
245-246.
Commodities, definition of, 5, 323,
331 ; classification of, 7 error of
reckoning as income, 105-106.
Complete rights to property, 36-37,
95-96, 324-325, 335.
Composition, settlement of bankruptcy by, 86.
Computation tables, 243 n., 283284, 408-411.

of,

D
Daniels, use of term "capital" by,

60 n.''.
Dargun, human beings counted as
wealth by, 5 n.^.
Davenant, on human beings as wealth,
5

n.2.

Davenport, "Statistical Methods"
by, 408 n.
Debit, an item of a transaction, 122,
132, 158-159, 336.
Debt, imprisonment for, 83
repudiation of, 84; payments on
(interest or principal) are outgo,
;

134.
Definition, tests of a, 116.
De Foville, use of term "capital"
by, 60.
Depletion of capital, not to be deducted from income, 110, 134;

taxation and, 400-403.
Depreciation not outgo, 234.
Depreciation fund, regulation of income by, 125-126, 239-243;
geometrical figures representing,
240, 241.
Depreciations, item of, in income
capital accounts, 257-263.

concept

Desirability,

of,

41,

and
326;

discussion of term, and term
"utility," 42-43.
See Utility.
Dimension, definition of, 331.
Dimensions wealth, price, and value,
income3-15,
341-344;
of
capital ratios, 186, 357 of rates
and
capiof interest, discount,
:

;

talization, 367-368.
Discommodities, class of articles
termed, 120.
Discount, rate of, 199, 200, 327, 332
table showing equivalent rates
of interest, capitalization, and,
200; total, on a sum, 209-210,
mathematical relations
331
between rates of interest and,
between rates of,
364-366;
for different time reckonings,
366-367
dimensions of rates
of interest, capitalization, and,
367-368.
;

;

;;;

;

INDEX
Discount curve (Exponential curve),
203-204, 223-224, 331-332; applications of, 206-208, 272, 284287, 303-309, 317-322, 360-361,
378, 380-381, 391-394.
Discount paper, banks', 204.
Disservices, definition of, 20, 119120, 325, 332; eniuneration of,
120; measurement of, 120-121;
examples of, 123; "necessary
evils," 123; one phase of, and
services termed "interactions,"
144; transformations of wealth
from one point of view are, 146.
Distribution curve of incomes, 142.
142, 143.
Disutility, criticism of term, 42.
Dividends, effect of payment of,

Distribution ledgers,

on capital account, 75 payment
;

out

of capital, 75,
variability of, 281-282,
of,

256
406-

407.

"Doses"

of capital, 185.

Double counting, fallacy

of, in concept of income, 107-108, 113economists'
115, 116, 347, 350;
attempts to avoid, 109-112.
Double entry bookkeeping, 144, 159,
325-326.
Double taxation, 39, 97-98, 250-253,

255.

Cange,

Dufresne,

definition

capital by, 62.

417

Enjoyable objective services ("Consumption"), enumeration of,
165.

Exchange

of wealth, 10, 11, 22, 149,

332 analysis of an, 158-159.
Expense, definition of, 119-120, 332.
Exponential curve. See Discount
;

curve.

F
Factor's agreement, property right
represented by, 28.
wealth
Fee simple, rights in, 23
definition of,
underlying, 26;
no
counter37 ; an asset having
part liability constitutes a, 95.
Fetter, F. A., cited on utility, 47;
definition of capital by, 55 ; cited
on confusion between quantity
and value of wealth, 56 n.^;
use of term "capital" by, 60
n.^; use of economic terms by,
67; concept of income of, 117,
on distinction
165, 350-351 ;
between rent and capital, 186 n.*^.
Fictitious person, definition of, 335;
accounting of, distinguished from
that of real person, 92, 138-139,
;

153, 160-161.
Finished products, classification of, 7.
Flow, definition of a, 332.
Flow of wealth, income conceived
duration of,
as a, 51-52, 101
52; rate of, 52, 332.
Flux, use of term "capital" by, 60;
concept of income of, 117.
;

of income from capital,
283-284;
by trade journals,
speculators experts in,
distinction
tion of, 234, 333
291
between realized income and,
295 crises caused by a general
error in, 296-297.
234-236, 247-253, 327-328, 353
excess of, over income, equals in- Foreclosure, settlement of bankruptcy by, 86.
crease of capital, 237-238, 328.
Edgeworth, F. Y., definition of in- Forests, appraisal of present value
of, based on future worth, 205
come by, 102 n.' cited, 410 n.
taxation of, 254.
Elements of income or outgo, 121.
Emery, H. C, cited on speculations, France, limited liability in, 83
taxation of forest lands in, 254;
300.
government bonds in, 281.
Endorsement, influence of, in reFranchise rights, wealth underlying,
ducing risk, 289.
Engel, human beings counted as
26, 29.
accumulation of
Franklin fund,
wealth by, 5 n.^, 17.
interest shown by, 225.
England, bankruptcy laws in, 83
Fund, definition of a, 332.
income taxation in, 253, 401.
Enjoyable income, 105, 112-113, Fund of wealth, capital conceived

"Earning power" of stock,
Earnings (Earned income),

71.

Forecasts,

defini-

;

118, 325-326.

51-52.

INDEX

418

Future, value of any capital-good
dependent on the, 188-199, 204223-224;
estimates of,
205,
based on the past, 283-284, 291,
295, 296-297.
Futures, trading in, 298-300.

G
Gambling, uneven value of the
chances in, 275 distinction between speculation and, 295.
Gaskill, Alfred, quoted on taxation
;

Housing and warming, services

of,

165.
Human beings, considered as a form
of wealth, 5, 17 ; classification of,
in scheme of wealth, 7.
Human body, transformation of
services through, 167—168; effect
of condition of, on subjective

and objective income, 175-176.

of forest lands, 254.

General property tax, 253.
George, Henry, proposition
nationalize land, 30-31.

Germany,

Hicks, use of term "capital" by, 61.
Higgins, L. R., cited, 410.
Hire, rights of, wealth underlying, 26.
Holland, T. E., cited concerning
definition of "rights," 21.

of,

in,

Ignorance, element of, in chance, 268
reduction of risk by decrease of,

254.
Gibbs, J. W., quoted, 65 n.^.
Gide, use of economic terms by, 43.
Giffen, use of term "capital" by, 60.

Immaterial wealth, items included
under, 4
disadvantage of theory of, 39.

205

;

appraisal of forests
taxation of forest lands

in,

certificates, nature of property
right in, 32.
Goods wealth, property, and services treated under term, 41, 327 ;
not income, 351.
Good will, wealth underlying rights

Gold

of,

27, 28-29.

Government bonds, 31-32, 280-281.
Government property, wealth underlying, 27.

Government

reports,

reduction

risk by, 291.

Government's taxing power, nature
of, 30.

"Graveyard insurance," 294.
Gross income, definition of, 121, 333.
Guaranties, method of, to avoid
risk, 288-289.
Guth, Franz, on income, 356.
Guyot, use of term "capital" by, 60.

H
;

on commutation

of risks,

289, 299.
Health as wealth, 176.
Hedging, shifting risks by, 299-300.
Hermann, F. B. W. v., concept of
perishable
capital of, 54, 56
goods regarded as non-capital
;

by, 63

;

Impairment

capital,

328; taxation

Imprisonment

110,

134,

400-403.

of,

for debt, 83.

Income, concept of, as flow of services during period of time, 51—
52, 101, 116-118, 324; savings
not to be included in, 108, 134—
135, 247-255, 349, 353; varying concepts of, 101-115, 345356; conceived as money-income, 103-104, 115, 117-118,
333; obtained in kind, 104;
real, 104-106, 112-113; enjoyable, 105, 112-113, 333; services only to be regarded as,
106-107, 112, 116-118; fallacy
of double counting in concept of,
113-115,
107-108,
116,
347,
350; not "regular," 109; standard, 110, 234, 236-237, 328,
396-398 (see Standard
333,
need not leave capital
income)
unimpaired, 110, 328; needless
;

Hadley, A. T., " capital " according
concept of income of,
to, 60 n.^
117;

291.

on income, 352-353.

distinctions between social and
individual, 113-115; confusion
of capital and, 114-115, 351;
primary or natural, 115, 150,
333; social, 116, 141, 333, 348;
130-131, 333
121,
net,
118,
use of term,
(see Net income)
in two senses (services and value),
;

121

;

gross,
element of, 121
viewed from one point

121, 333

;

;;;

419

INDEX
122 n.
fund on,
125-126, 238-243; other methods of steadying, 127-129, 243247, 259-263, 293-294 methods

outcome or

yield,

effect of depreciation

;

of reckoning real person's (law-

and fictitious person's
(railway corporation's), 130-139
Income accounts) ; total
(.see
of,
distribution
social,
141
142-143; objective, 165; objective and subjective final stage
of,
165-169; psychic (subjeccapital
tive), 167-169, 177, 333
analogous to and correlative
value of capital
with, 184;
derived from future, 188; purpaychasing power over, 191
able annually and semi-annually,
192; line method of represent206-207, 371-372; area
ing,
method of representing, 207208, 371-374 determining capicase of
tal-value of, 217-221
capital-value less than total exrealized vs.
pected, 227-228;
earned, 231-236, 238, 247-255,
327-328, 353 ; perpetual annuity
taken as the standard, 236-237
regulation of, by repair fund,
259-263 risk as applied to immediate, 275-276; forecasts of,
j^er's)

;

entrance of interactions
143-145, 325; of logging
camp and sawmill, to illustrate
application of method of couples,

143

;

into,

152-154 of dry goods company,
to illustrate double entry bookof factory
keeping, 159-162;
company, to show relation between capital accounts and,
258-262 ; siunmarized definition
of, 333.
;

Income and outgo accounts, 122140.
*See Income accounts.
Income bonds, 85.
Income meter, "cash" in income
accounts termed an, 137-138.
Income-services, 121.

Income summation, by method
balances, 90-91,

335

;

142-143,

by method

183,
couples,

143-152, 183-184, 335; method
with
contrasted
couples
of
method of balances in, 157—
158.
tax, 250-253, 398-400 effect
misconceived,
capital
of
unrestricted applica253-254
tion of, impracticable, 400-403.
Income-value, 121, 327, 333 ; rate of
interest a link between capital-

Income
on

;

value and, 202, 327-328.
Individual income, distinctions between social and, 113—115.
283-284 effect of changes in, on
true and pseudo, 82.
capital- value, 284-285 insurance Insolvency, 81
a means of steadying, 293-294; Installment, payment by, as a means
of regulating income, 127, 244—
increase of value is not, 351
245.
diagrams for continuous and
discontinuous, 371-374; repre- Instrument of wealth, 5, 19, 333.
sentation of capital and, by Insurance, origins of, 275-276 avoidance and shifting of risks by,
polar coordinates, 393—395 two
291-294;
a means of
288,
rival concepts of standard, when
293-294
income,
steadying
interest rate varies, 396-398.
various forms of, 294.
Income accounts, services and disservices which enter into, 119- Insurance companies, identity of
creditors and stockholders in
121 for house and lot, 122-126
mutual, 85 terminable annuities
of building and loan association,
used by, 210 bonds offered by,
127-128; of lawyer (real per131-134, 135-136, 163,
217; forecast of interest rate
son),
by, 274.
174-175
of railway corporation (fictitious person), 138- Interactions between two instruments or groups of instruments,
139; relation between capital
144, 325, 334; formerly styled
accounts and, 139, 256-264, 325
services,"
"productive
145;
items of assets and liabilities
three classes of (transformation,
139-140,
to be included in,
transportation, and transfer),
325; of society as a total, 141145-152; natural services of
142; of United States, 142;

;

INDEX

420
capital

consist

between amount of capital and

152-156

of,

shown by diagrams to be preparatory to enjoyable services, 317320.
Interest, is capital and not income,
134-135, 224 not an item in cost
of production, 173-174 spurious
distinction between rent and,

risk of, 277, 408-409.
Irredeemable paper money, wealth
underlying, 27; nature of, 30.

Item of wealth,

337.

;

186-187 crude theories of, 187- James, William, quoted, 168 n.
nominal principal and, Jevons, W. S., use of phrase "final
188;
utility" by, 46;
concept of
in case of bond, 211-212, 215,
capital of, 54, 57; use of term
217 accimaulation of, 224-226
discommodities
1 20
by,
definition of nominal and total,
;

;

334.
rate

Interest,

of:

defined,

191,

334; various meanings of, according to frequency of payment, 192-194, 334; payable
annually and semi-annually, 192
premium and price concepts
of, 194-196, 246; interchangeof

premium and

price
concepts of, 196-199;
table
showing equivalent rates of discount, capitalization, and, 200;
a link between capital- value and
income- value, 202, 327 ; table
of, realized per annum on three,
four, and five per c ent bonds, 2 1 4215; effect on capital-value of
change in, 229, 271-273, 390393 value-return may be greater
or less than, 229-234; risk as
applied to, 271-274 forecast of,
ability

;

cited on rent entering into cost
of production, 173.
Joint stock companies, capital accounts of, 68-70; limited Uability in, 82-83
shares in, as
example of perpetual annuities,
209.
;

Joint stock rights, wealth underlying,
26.
Juglar, cited

crises, 296.

K
Kind, income obtained in, 104.
Kleinwachter, concept of capital of,
54; raw materials regarded as
non-capital by, 63 on income,
102, 351-355.
;

Knies, on capital, 54, 57, 60.
Knowledge, reduction of risk by
method of increasing, 288, 291
utility of speculation based on,

by insurance companies, 274;
298.
riskless, mathematical, and comKomorzynski, on
mercial, 279-280; on government bonds, 280-281 mathemat-

capital,

n.^.

;

relations between annual,
semi-annual, and quarteriy rates
conceived in price sense, 357-

ical

premium

sense, 358362 mathematical relation between, and rate of discount,

358,

;

dimensions of, and
rates of discount and capitalization,
367-368
variation of,
produces two rival concepts of
standard income, 396-398.
Interstate Commerce Commission,

364-366

;

Report

of, cited, 39.

Inventory, distinction between quantity, price, and value of wealth

shown

in an, 14.

Investments,
safe

classification

and unsafe, 277;

of,
as
relation

Labor, economists' views of relation
between capital and, 55
defined as outgo in form of htunan
exertion, 120, 334; as form of
appraisal of,
disservice, 145
in a sense the only true
172
discost of production, 175
;

;

drawn between work

tinction

and, 175 n.

Labor power, 316-317.
Lafrentz, L. W., use of term "capital" by, 63.
Land, regarded as one class of wealth,
classification of,
334
5,
7
nationalization of, 30—31, 254;
fancied distinction between capiview of, as nontal and, 56 n^
;

;

INDEX
by

capital

421
Alfred, use of economic
terms by, 43, 46, 61 treatment
of capital by, 54 on distinction

Marshall,

classical economists,

mistake of distinguishing
between capital and, 186-187;

63;

;

between capital and non-capital,
57 on concept of income, 1 14,
117, 347-348; on avoidance of
double counting in concept of
income, 114; on transformation

an example of capital yielding
perpetual
approximately
an

;

annuity, 209 determination of
uses of, 221 benefits of speculation in, 222 taxation of, 254.
Land improvements, 5, 7, 334.
;

;

of wealth, 145.
distinction

between capital
and non-capital according to,
55 on relation between capital
and labor, 55
denies that

Landry, time element in concept of Marx,
capital of, 57.

Lawyer, income and outgo accounts

;

131-137, 162-164, 174-175.
Lease, wealth underlying rights of,
26, 34-35.
of,

Liabilities, definition of, 67, 325,

;

productive, 56.
Measurement of psychic income,
capital

334

177.
of services and disservices, 19-20, 120-121.
Measurement of wealth, by quantity, 8-9; by price, 9-11;
by

Measurement

of capital-balance to,
looking to safety of a business,

relation

;

true value

of,

derived from

assets, 84-85, 139; consideration

income and outgo accounts,
134-135, 139-140, 162-164.
Liability, limited and contingent,
82-83.
Life insurance, steadying of income
by, 294, 295; method of computing pure level premiima,
410-411.
Limited liability, in case of joint
stock company, 82-83.
Line method of representing income,
206-207, 371-372.
Liquidation, resulting from bankruptcy, 86 a crisis defined as a
time of general and forced, 296.
Loans, short-time interest in case
of, 194-195, 198-199;
rate of
discount employed for, 199, 204.
Logging camp accounts, 152—157, 318.
Lowell Institute, possibilities of
accumulation shown by, 225.
of, in

;

13-14; inaccuracies in,
expressed mathematic15-17
ally, 341-344.
Methods of avoiding risk.
See
value,

;

Risk.
of balances and couples.
See Balances and Couples.
Methods of standardizing income,
259-263,
125-129,
243-247,
293-294.
Meyer, R., on income, 355-356.

Methods

between capi-

Mill, J. S., distinction

tal

and

capital

non-capital

by,
54
regarded as a
on
quoted
55

itself

product by,
wage fund theorj^, 59.
Miner's inch, 193, 208-209.
Mines, terminable income exemplified
;

by, 209, 210.
Mixter, editor of Rae's Sociological

Theory

of Capital,

n.i.

Money, uniformity of measurement
by means of, 15 irredeemable

;

distinction bepaper, 27, 30
tween three elements (wealth,
property, certificates) to which
term is applied, 38.
Money-income, concept of, 103-104,
115, 117-118.
Money price, 335.
Money value, 337.
Money-wages not real wages, 104.
;

human beings as
wealth, 5 n.2; concept of capital

MacCulloch, on
of,

;

quoted on wage fund

theory, 59.

Machines, offsetting of depreciation
in, 241-242.
MacLeod, H. D., definition of wealth
by, 4 concept of capital of, 55
;

;

includes credit under capital,. 96.

Marginal utility (desirability), definition of, 46, 331 mathematical
expression for, 344-345.
;

Monopoly, effect of tendency toward,
on risk element, 409.
Monopoly franchise, wealth underlying rights of, 25, 27, 29.

INDEX

422
Mortgage, use

to maintain regu-

of,

larity of income, 127, 244-245 ;
reduction of risk by, 289.
Murray, J. A. H., dictionary definition

of income, 62-63, 345-346.

Mutual insurance companies, creditors and stockholders identical

;

124; offsetting of, by
depreciation
fund,
125-126
method of couples applied to,
151-152; depreciation is not,
234.
Overvaluation of capital, 79-80.
Owner-method of taxation, 97-98.
partial
Ownership, meaning of, 18
and total, 34-36, 95-96, 324capital,

in, 85.

N
National banks, liability of stockgovernment
holders in,
83
bonds bought by, 280-281.
Natural income, 118, 150; ascertaining, by method of couples, 150;

;

change in forms of, in
reorganization after bankruptcy,
credit a form of divided,
86
proper determination
96-97
of, in taxation of property, 97—
98; change of, 149-152, and see
325, 335

151.

Nau, Carl H.,

cited, 39.

Net capital, 69, 330.
Net income, 118, 121, 130-131, 333;
example of, in case of lawyer,
136-137, 163, 174-175; lacking
in case of fictitious persons,
138-139; of society, 141-143;
determining by method of balances and method of couples,
157-158; of merchant's stock,
223.
outgo, definition

Net
Net product,

of,

121, 335.

income conceived

social

as society's, 113-115.
human beings
S.,
Nicholson, J.
counted as wealth by, 5 n.^
use of term "capital" by, 61
on credit as "revenue capital,
96.

Norton, J. P., on relation between
am.ount of capital and risk involved, 277, 409; on use of
probability computations, 283
n.i,

Out-come, income viewed from one
point becomes, 112 n.
Outgo, definition of, 119, 326, 335;
element of, 121; net, 121, 335;
use of, in two senses (disservices
viewed from
and value), 121
one point is ingo, 123 n. not

410

;

Exchange and Transfer.

Palgrave, definition of capital by, 62.
Panama Canal, example of dependency of capital-value on future
services, 188-189.
Panics, causes of, 296-297.
Pareto, human beings counted as
wealth by, 5 n.^; introduction
of term "ophelimity" by, 42;
use of
cited on utility, 47;
term "capital" by, 60; distribution curve of incomes of, 142.
Partial rights to property, 34-37, 9596, 335.
Partnership, wealth underlying rights

in,

Notes, wealth underlying, 26, 28.

Nourishment, services

of,

165.

;

liability of

members

income considered in

of a,
re-

spect to, 130.

wealth underlying, 27.
installment a means of
regulating income, 127, 244-245.
Pearson, Karl, cited, 410 n.
Pension, the diminishing capitalvalue of a, 238-239.
Person, fictitious and real, defined,
335. See Fictitious and Real
persons.
Petty, on human beings as wealth,

Patent

rights,

Payment by

O
Objective cost of production nonexistent, 173.

;

Objective income, 165-169; points of
divergence of, from subjective
income, 169-176.
Ofner, human beings counted as
wealth by, 5 n.^.
Ophelimity, 42.
Options, stock exchange (puts and
calls), 298-299.

5 n.2, 17.
Physical productivity of capital, 185,
186.

;;;

;

INDEX
Physical return of capital, 185, 186.
Piecework, terms used in measurement of, 19-20.
Pierson, N. G., definition of income
adopted by, 102 n.\ 346.
rigou, cited on utility, 47.
Pitt, on sinking fund, 243.
Pocket cash, risk-meeting function
of,

290.

Polar coordinates, representation of
capital and income by, 393395.
Practice (physician's), wealth represented by, 29.
Prediction. See Forecast.
Preferred stock, 85
share of, to
illustrate riskless value, 280.
Premii.un concept of interest, 194interchange196,
247, 334;
ability of, with price concept,
;

196-199, 362-366; represented
mathematically and by diagram,
358-361.
Price, Richard, financial theories of,
243.
Price, definition of, 11, 335; various
usages of term (money, market,
and appraised or reasonable),
13-14
distinction
between
quantity, value, and, 14-15
relation of, to past costs and
future expectations, 189-190;
rate of interest called, of money
or capital, 191 ; money, defined,
dimensions of wealth,
335
value, and, 341-344.
Price concept of interest, 191-194,
interchange196,
247,
334;
;

;

ability of, with premium concept,
196-199,362-366; mathematical
relations between rates reckoned

annually, semi-annually,
according to, 357-358.

Principal, nominal, in case of bonds,
211-212, 215, 217, 335.
Probability, a matter of human
estimate, not merely mathe-

matics, 270-271
coefficient of,
276-277, 331, 335, 403; application of principles of, to valuation of capital, 277-279, 403406 ; theory of, applied to insurance, 295.
Probability computations, 283-284,

408-410.

Production, problem of, in concept of capital, 55-56, 145—
173-174,
148
cost of, 151,
;

184.

Productive processes, 145-148, 335.
Productive services, 145.
Productivity, physical and value,
185-188, 335.
Productivity theory, 187-188.
Profits, undivided, 68.

Promises of refraining, wealth underlying, 27, 28.

Property, definition

325, 335
wealth and,
and coextensive, 22-23, 95-96;
types of
chief forms of, 26-27
partial
and total rights to, 34-37, 9596, 335 necessity of separating
of, 18,

rights in, 20-22
correlative terms

;

from

wealth,
certificates
of
property, services, and utility,
confusion of ideas regard38
regulation of ining, 38-40 ;
;

come by

sale

127,

of,

244-

245.

Property

rights, definition of, 18, 22,
; table illustrating exist-

324, 335

ence of wealth behind, 26-27;
overlying of, by one another, 31—

classification

;

of,

36-37

method
from

of determining income
collection of, 130. See

Ownership.
Pseudo-insolvency, 82.
Psychic
income,
167-169,

measurement

of,

333;

177.

Purchase, definition of, 11, 335.
Purchasing power, use of phrase,
191.

Put, option

etc.,

Primary (natural) income, 115.

;

423

known

as a, 299.

Q
Quantity, measurement of wealth in
units of, 8-9
distinction between price, value, and, 14-15
conceived as a fund (capital)
or a flow (income), 51-52;
measurement of services by, 120ratio of, of services to
121
quantity of capital yielding those
services (physical productivity),
185 dimensions of price, value,
and, 341-344.
Quarries, terminable income exempli;

;

fied by, 209, 210.

INDEX

424

R
Rae, John, use of economic terms
by, 5, 65.

Railway

iDonds,

source

income

from, 130.

Railway

capital,

fallacious

statis-

tics of, 98.

control, value of, 35-36.
Railways, disservices vs. services of,
120; income accounts of, 138real sum total of income
139
leases of, as examples
of, 151
of perpetual annuities, 208 forecasting the value of property in,

Railway

;

284.
of

Rate

capitalization, 194, 330.
Capitalization.
Rate of discount, 199, 200, 327-328,
332. See Discount.
Rate of flow, 52, 332. See Flow.
Rate of interest. See Interest, rate
iSee

of.

Repairs, item of, in income and capital accounts, 257-263.
Report on Direct Taxation cited, 114.
Repudiation of debts, 84.
Reserves of capital held to avoid
risk, 290.
Resources. See Assets.
Return. See Value return.
Ricardo, on relation between capital
and labor, 55 theory of rent of,
;

187.

Rider, W., definition of capital by,
62.

Right, definition of

lying, 27.

Risk, element of, in determining
capital-value,
210;
as
205,
applied to rate of interest, 271274; as applied to immediate

income, 275-276 coefficient of,
relation
between
336;
277,
;

Rate of value-return, 229-238.

amount

Ratios, income-capital, 185-186, 357.
Raw materials, classification of, 7.
Ray Act relating to bankruptcy, 83.
Real estate, regarded as one class of
classification of, 7
wealth, 5
inaccuracy in appraisement of,
16-17; speculation in, 221-222,
254. See Land and Land im-

408-409
ing,
288

;

provements.
Real income, concept
112-113.
Realized income

of,

104-106,

a, 20.

Right to subscribe, 78.
Rights in common, wealth tmder-

;

of capital and, 277,
five methods of avoid;

avoidance

of,

method

of guaranties, 288-289,
safety
of safeguards, 289-291
redevices for meeting, 290
duction of, by increasing knowlavoidance and shiftedge, 291
ing of, by insurance, 291-294;
shifting of, to speculators, 295298; shifting by hedging, 299effect of element of, on
300
capital curves, 320-322 mathematical coefficient of, 403. See
;

;

earned,

vs.

231—

247-255, 327-328,
238,
236,
353.
Real persons, accounting of, distinguished from that of fictitious
persons, 92-93,
164, 174-175.

138-139,

162-

Real wages, money-wages not, 104.
Recapitalization of stock companies,
70.
of, in reorganization
after bankruptcy, 86.
Rent, as example of transfer of
and cost of
wealth, 150-151

;

Chance.
Risk of insolvency, 81.
Roosevelt, Theodore, 170.
Roscher, W., human beings counted
as wealth by, 5 n.^; treatment
definition of
of capital by, 54
income by, 346—347.
Runs on banks, 296, 297.
;

Receiver, office

;

173-174;

spurious
distinction between interest and,
186-187.

production,

Reorganization resulting from bankruptcy, 86.

Repair fund, regulation of income
by, 259-263.

S
Safeguards,

method

of,

avoid

288, 289-291.
Safety devices, risk-meeting function of, 290.
Sale, definition of, 11, 336.
Satisfaction, concept of, 41, 324; distinction between utility and,
43-44, 53.
risk,

INDEX
Savings, to be counted as capital, not
income, 108, 134-135, 247-253,
254-255, 328, 349, 353.
Sawmill, income account for, 152155, 157, 318-320.
Say, J. B., human beings counted
as wealth by, 5 n.^ use of term
"capital" by, 60.
Schafhe, A. E. F., treatment of
capital by, 54.
Schmoller, Gustav, on income, 352353.
Seager, H. R., definition of income
by, 349.
use
Seligman, cited on utility, 47
of term "capital" by, 60 n.'.
"Selling short," 298-300.
;

;

Senior, N. W., quoted on definition
of capital, 53
capital itself
regarded as a product by, 55
on capital as a producer of
wealth, 56.
Services, definition of, 19, 324, 336
;

425

Social income, the concept of, as "net
product" of society, 113-115;
author's concept of, 114, 118,
141, ^333; distinction between
individual income and, 115-116.
for measuring wealth,
8-9.
Speculation, in real estate, 222, 230;
benefits and evils of, 295-298.
Speculators, use of land deferred
by, 222 position of, considered,
risk-meeting function of,
230
288, 290, 295; in futures, 298300.
Sprague, C. E., cited on meaning of
term "capital," 63 n.
Standard deviation, measurement of
extent of variability by, 406—
410.
Standard income, 110, 234, 333;

Space-units

;

realized, 234-236, 247-253,
327-328, 353.
Stock, economic use of term, 51,
measurement of, 19-20, 120336 chance element in valuing
complete
and partial
(in commercial sense), 280-283.
121
rights to, 36-37 to be separated Stock companies, capital accounts
from wealth, property, certifiof, 68-70
two valuations in,
70-72.
cates of property, and utility,
income conceived as flow Stockholders, liability of, in joint
38
of, 51-52, 101, 116-118, 324;
stock companies and in national
commodities wrongly combined
banks, 82-83; preferred, 85;
with, in concept of income, 105bondholders and, contrasted,
position of, in
106 necessity of avoiding con85, 288-289;
fusion of anything else with, in
bankruptcy, 85-86;
case
of
income-concept,
106-107; inrisk-taking function of, 288-289.
finite variety of, 119
one phase Stock jobbing, 74-77.
of, and disservices termed "in- Stock of wealth, concept of capital
teractions," 144;
transformaas a, 51-52, 323-324.
tions of wealth as, 146
method Stocks, contrasted with bonds, 85,
of couples applied to, 152-156
288-289; effect of chance on,
enjoyable objective ("consump276-277.
tion"), 164, 165, 336; stage of Stock-watering, 79-80.
final objective, 165; subjective, Stream of wealth, concept of income
166; classification of, 178-179.
as a, 51-52, 323-324.
Short-time loans, 194-195, 198-199, Subjective income, definition of,
204.
168, 326 points of divergence of,
Simmonds, P. L., definition of
from objective income, 169—
capital by, 62.
176.
See Psychic income.
Single taxation, 253-254.
Surplus, 68, 256-257.
Sinking fund, 243-244, 333.
Smart, William, use of term "capital" by, 60 n.'; definition of
income by, 348-349.
Taussig, F. W., 318; definition of
Smith, Adam, on capital, 53, 54,
income by, 349.
on rent and income, Taxation: double, 39, 253, 255;
56, 58, 61
150.
methods of avoiding double.
vs.

;

INDEX

426

and
owner-method
97-98
wealth-method of, 97-98; of
income, 250-254, 398-403 theory of advocates of single, 254
;

;

nature
27;
30-31.

marginal,

;

total

;

and mar-

consideration of

44-46

;

total,

definition of marginal, expressed

mathematically, 344-345.

of land, 254.

Taxing power,

and, 43-44, 53
ginal, 44, 331

wealth underlying,
of government's,

Valuation of railways, 35-36, 151,
Tenant, rights of, 34-35.
in concept of
284.
Time, element of
in
companies
in con- Valuations
stock
capital, 51-52, 56-57
:

;

sidering

196.

interest,

Todhunter, Ralph, cited, 401.
Total discount on a sum, 209-210,
374-378.
Total social wealth, diagrammatic
summation of, 316-317.
Total

utility

(Total

desirability),

44, 47, 331.
Trade journals, risk element diminished by, 291.
Transaction, definition of, 159, 336.
Transfer of wealth, 10-11, 149-152,
158-159, 325, 336.
Transformation of services through

the

human

body, 167-168.

Transformations

of wealth, definition of, 145, 325, 336 services or
disservices according to point
of view, 146 ; examples of, 147148.
Transportation of wealth, 148-149,
325, 336.
Trust, property held in, 31.
Turgot, use of term "capital "by, 60.
Tuttle, definition of wealth by, 4;
distinction between capital and
;

non-capital according to, 55
use of economic terms by, 60, 67.

(bookkeeper's and market's),
70-72.
Value, definition of, 13, 336-337;
varioiis uses of term, and of
term "price," 13-14; distinction between quantity, price,
and, 14
of control in case of
;

measurement
railways, 35-36
derivaof services by, 120-121
tion of, from future and not from
riskless, mathepast, 188-189
matical, and commercial, 276dimensions of
277, 280-283;
wealth, price, and, 341-344
increase of, not income, 351
formula for, of bond, 378-380.
See Capital-value.
Value productivity of capital, 185,
186, 335.
Value return of capital, 185-186,
188-191, 202, 336; rate of, 229238 ; may be greater or less than
rate of interest, 229-231.
Variation, of income, and its rem;

;

edies,

125-129, 243-247,

;

281-282, 406-407.
Verm, theory of chance

U
Undesirability, definition
Undesirable event, 123.

of, 42,

259-

263, 293-294; of rate of inter284-285,
271-273,
est,
229,
390-393, 396-398 of dividends,
of,

266.

336.

Wage fund theory, 59.
Undivided profits, 68, 256-257.
Wages, money, are not real, 104.
Usance of wealth, 117, 348.
Use of desirable events, "utility" Wagner, Adolf, on income, 125,
353-354.
to be distinguished from, 19, 43.
Walker, Francis, 187.
Walras, human beings counted as
wealth by, 5 n.^; on capital,
41, 42-43;

Usufructs, wealth underlying rights
in, 26.

Utility,

concept

of,

19,

to be separated from wealth,
property, certificate of property,
and services, 38 error of belief
that wealth constitutes, 39-40;
distinction between satisfaction
;

54,

55-56, 63.

Waste, an example of overbalancing
of services

disservices, 120.

Water-rights, an example of perpetual annuity, 193, 208-209.

;

INDEX
Wealth,

definition of, in general
sense, 3-5, 337; "immaterial,"
classes of, distinguished,
4, 39
definition of, in restricted
5
sense, 5-6, 337 scheme showing
measureclassification of, 7
;

;

ment
ment

8-17

of,

(see

Measure-

transfer of,
of wealth)
10-11, 149-152 (see Exchange)
appraisement of, 11-12, 34-36;
distinction between quantity,
price,
and value of, 14-15
sources of error in measure;

ment

of,

15-17

meaning

;

of
of

ownership of, 18
services
instriiments
of,
defined,
19;
rights to services of, 20-22;
and property correlative terms
and coextensive, 22-23, 95, 96
cases in illustration of the correlation of, and property, 24-36;
table illustrating existence of,
;

behind property
partial

and

total

26-27
ownership of,

rights,

34-36
necessity of separating
from property, certificates of
;

427
149
of,

205

health as, 176
appraisal
based on future worth, 204;

;

risk-meeting

;

function of

diagrammatic
summation of total social, 316317 dimensions of price, value,
stocks

of,

290

;

and, 341-344.

Wealth-method of taxation, 97-98.
Wear and tear, depreciation due to,
210-211.
Weight-units for measuring wealth,
8-9.
Weiss, human beings counted
wealth by, 5 n.^.

Whitman, Walt,

176.

Wieser,

phrase

use

"marginal

utility" by, 46.

Wine,

determination
of
present
value of, based on future worth,

205.
Wittstein,
on human beings as
wealth, 5 n.^.
Work, distinction between labor and,

175

Work

n.2.

dues, wealth underlying, 25,

26.

property, services, and utility,
division of, into fund and
38
;

capital and income, Years' purchase, concept of, 194,
transformation of, 145209, 362.
transportation of, 148- Yield, income viewed as, 122 n.

flow,

i.e.

51-53

;

148;

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