The theory of prices a re examination of the central problems of monetary theory vol i

REPRINTS OF ECONOMIC CLASSICS

The
THEORY OF PRICES
VOLUME I



The
THEORY OF PRICES
A Re-Examination
of the
Central Problems of Monetary Theory
BY

ARTHUR W. MARGET, Ph. D.
PROFESSOR OF ECONOMICS, UNIVERSITY OF MINNESOTA

VOLUME I

REPRINTS OF ECONOMIC CLASSICS
AUGUSTUS

M.

KELLEY· PUBLISHERS

NEW YORK •

1966

FIRST PUlJLISHED I
REPRINTED I

966

938 - 19+Z

BY ARRANGEMENT

WITH MRS. ARTHUR

W.

MARGET

LIBRARY OF CONGRESS CATALOGUE CARD NUMBER

PRINTED IN THE UNITED STATES OF AMERICA

by

SENTR:Y PRESS, NEW YORK,

N. Y.

10019


TO MY MOTHER AND

FATHER


WHETHE:R a writer or a speaker undertakes to unfold
principles, to set them in a novel and more striking light,
or to recommend their application, he should know what
has been already undertaken, what has been accomplished,
and what remains for discovery and elucidation. The following work gives sundry examples of the inconveniences
resulting from the want of this information, by exhibiting
able men engaged in the investigation of principles and the
development of laws which had been previously established and traced, and putting forward speculations as
original which had been long before the public.
-J. R. McCulloch, The Literature of
Political Economy

ARE we not . . . justified in affirming that Political
Economy represents, and that in a very eminent degree,
one at least of those symptoms which M. Comte has declared to be among the least equivocal evidences of really
scientific conceptions-continuity of doctrine?
. . . I VENTURE to assert that a more remarkable example of continuity of doctrine, of development of seminal
ideas, of original aper,us extended, corrected, occasionally
re-cast, of new discoveries supplementing, sometimes modifying, the old-in short, of all the indications of progressive science-will not easily be found even in the history
of physical speculation. . . .
-J. E. Cairnes, M. Comte and Political Economy

WHAT, then, remains in the attitude of the medieval
masters to offend or embarrass us? Probably nothing save
their docile modesty in instructing themselves in philosophy before setting out to further its progress. . . . They
believed that philosophy could not possibly be the work of

a single man, no matter what his genius might be, but that
it progresses, like science, slowly, as the result of the patient collaboration of generations, each leaning on its predecessors in order to surpass their achievement. ' , We are
like dwarfs," said Bernard of Chartres, "seated on the
shoulders of giants. We see more things than the Ancients
and things more distant, but it is due neither to the sharpness of our sight nor the greatness of our stature; it is
simply because they have lent us their own."
-Etienne Gilson, The Spirit of Medieval Philosophy


Preface
HE fundamental proposition from which this study
. . proceeds is that the Theory of Prices must be conceived
of as an organon, in the sense in which Marshall's Principles
may be said to be an organon. The Theory of Prices, for
those who accept this view, is not a set of maxims of monetary policy, which can claim neither· the general validity nor
the authority that may be said to attach to a set of conceptual tools. N or is it a series of speculations as to matters
of fact, with respect to which the last word must be provided by investigations of the "facts" themselves. The
reader, therefore, who expects a discussion of such matters
as the wisdom of attempting to stabilize the price level, or
a "theory" of the business cycle, in the sense of a surmise
as to the facts of cyclical variation, is warned that he will
be disappointed.
It will be apparent that this book, which has the dimensions and the purpose of a formal treatise, has also, by virtue
of its continued concern with the writings of Mr. J. M.
Keynes, many of the characteristics of a polemical tract.
To the "apology for polemics" which is offered in the Introductory chapter, I have only two comments to add here.
The first is the obvious one that those of us who disagree
most categorically with Mr. Keynes, and insist upon subjecting his contentions to a severely critical examination,
pay him the clearest of compliments as a creator of the
kind of intellectual ferment out of which it is hoped truth

will ultimately arise, even at the moment that we protest
most emphatically against those of his utterances which we
believe have introduced serious confusion into our subject.
The second comment is that by far the greater part of
such criticism of Mr. Keynes as this· work contains is criticism not of Mr. Keynes's positive analysis, but of his own
criticism of received doctrine upon the subject with which
t-his book is concerned. The difference is surely important.
vii

T


viii

Preface

There are, indeed, precedents for extended critiques of the
work of an author of great eminence in his generation. The
spirit of those parts of the present work which can be regarded as a "critique" of Mr. Keynes's writings, however,
is akin to that with which John Stuart Mill insisted that his
two-volume Examination of Sir William Hamilton's Philosophy was imbued. "My subject," said Mill, "is not Sir
W. Hamilton, but the questions which Sir W. Hamilton
discussed." The subject of this work is not Mr. Keynes,
but the questions which Mr. Keynes has discussed. It is
the importance of these questions, and not the importance
of Mr. Keynes or any of his critics, which alone can justify
the length at which this book treats the questions constituting its subject matter.
It follows, from the fact that by far the greater part of
such polemics as are contained in this study are polemics
on behalf of the Principle of Continuity as a maxim of doctrinal development, that the work as a whole is intended

definitely to be constructive; and I hope that it will be so
regarded by all those for whom "construction" is not necessarily construction ex nihilo. I am aware, to be sure, that
some of my readers will regret that the line of ·positive
analysis may appear to be obscured by what will seem to
them an unnecessary degree of concern with the works of
other writers, including lVlr. Keynes. To this, my answer
is twofold. In the first place, it is my intention to follow
this treatise with a publication which will be frankly in the
nature of a textbook, and which should satisfy those who
would insist that it is the proper function of an author to
state only the conclusions which he himself believes· to be
sound, and not the reasons why he prefers these conclusions
to those reached by other writers.
In the second place, I happen myself to be of the opinion
that if it is a vice to be concerned "excessively" with the
views of other writers, it is at least equally a vice to proceed
in complete disregard of what other writers have done or
are .doing. One is reminded of the Cockatoo in Alfred
de MU8set's Histoired'un merle blanc, who attributed the
distaste of the public for his attempts at versifying to the
fact that the public also read the works of poets other than


Preface

ix

himself, and was "distracted" thereby. I confess to the
vice of opening myself to the danger of being "distracted"
by a consideration of the works of others, if it is a vice; and

since I am entirely prepared to forgive the trespasses of
those who follow a procedure different from that which I
have followed, provided only that the results that they reach
are sound, I ask only that my own trespasses, if I have
sinned in the opposite direction, may be forgiven also.
I am aware that it will be objected that familiarity with
the work of other writers can be demonstrated in other ways
than by specific citation of, or discursive comment upon,
the contentions of these other writers, and that it is not
necessary to bring into the exhibition gallery all the shavings
of the workshop. To this I can reply only as follows: First,
in all honesty, not all the shavings of the workshop are here
presented; indeed, I am only too keenly aware that some
of my readers will feel that justice is not done to the specific
contributions which they have made or believe they have
made. Second, there are various kinds of workshops, each
producing its own kind of shavings. A tortuous concern
with problems which the author himself ends by characterizing as side issues that do not strike the heart of the matter
surely results in a mass of "excess" shavings, particularly
when no one but the author himself seems, to have been
bothered by these side issues, so that no citations to the
works of other authors are necessary. It is at least arguable that the fact that other writers can be cited would
indicate that the matters under discussion are of interest to
some one besides the author. Finally, I trust that I may
be permitted to lay at least part of the blame, if blame is
called for, upon what were undoubtedly overgenerous com...
ments on some of my published articles in .which much attention was paid to the existing literature on the subject
with which they were concerned, in that these comments
have encouraged me to believe that there are others who
experience the same pleasure that I do in viewing the results

of an adventure of exploration into the field of the history
of ideas.
Familiarity with existing prejudices on the subject leads
me to fear, also, that most of the obloquy which maybe


x

Preface

directed against the form of exposition adopted in this study
will concern the number and volulne of the footnotes. The
footnotes are chiefly of three kinds: (1) page citations to the
work of authors quoted or discussed in the text; (2) detailed
specification in support of a generalization advanced in the
text; and (3) supplementary comments designed to reinforce
or protect an argument stated in the text. For the first
type of footnote, I have no apology at all. As for the second and third types, I ask the querulous reader to consider
whether it is not better, assuming that the material is to be
included at all-and in this matter I can only refer again
to what was said above concerning the shavings of the workshop-to put it where he need look at it only in case he feels
the need of further supporting argument. The same answer
is offered to those who may object to my adoption of the
practice-very common on the European continent, and becoming increasingly common in English-speaking countries
with the translation of continental works in which the device
was employed-of putting into a smaller type, material of
an essentially supplementary character. There is nothing
to force the reading of either footnotes or material printed
in smaller type by those who dislike such devices; and if I
have erred in putting into footnotes or smaller type, material which a reader thinks should have gone into the main

text, or vice versa, I can only ask humbly to be forgiven for
the mistake in judgment.
I fear, finally, that even such merits as may be discovered
in this work will not reconcile those who have an implacable
hatred for books that run to many pages. Surely, however,
the physical compass of a work is not a criterion for judging
its usefulness; it is something imposed by the nature of the
task which the author sets himself. One of the tasks which
I have set myself in this book is the illustration of theprocesses by which monetary theory has come to be what it is.
In the nature of the case, this has involved a continuing and
detailed concern with the works of earlier writers, over the
whole of the field of the Theory of Money and Prices. Only
those who know the vastness and the richness of that field
will be aware of how much I have left out that I might have
put in; and it is their forgiveness that I beg, rather than


Preface

xi

the forgiveness of those who will not be reconciled to fat
books.
The physical dimensions of the work have recommended
its publication in two volumes rather than in one. The
second volume, to which frequent references are made in
the volume now offered to the public, will contain the material dealing with the theory of the effect of money upon
output; the theory of savings and investment as related to
the Theory of Prices; and a final evaluation, in the light of
the received alternatives, of the Theory of Prices presented

in Mr. Keynes's General Theory of Employment, Interest, and
Money-including such elements as Liquidity Preference, the
Multiplier, the so-called Method of Expectations, and so on.
The relegation of the material last mentioned to the second
volume will, it is believed, commend itself to most readers
after the second volume will have appeared.
Dr. C. O. Hardy, who has read the first five chapters, has
given me the benefit of his support where he agrees with
me, and the much more valuable benefit of his frank criticism on the points-suspiciously few, so far as these chapters
are concerned-on which he disagrees with me. Professor
E. A. J. Johnson has read the whole manuscript with a degree of care far beyond anything that was imposed upon
him by his formal duties as editor of the series in which the
work appears; and he has helped me greatly in matters of
presentation. I have been helped greatly in this respect
also by the editorial staff of Prentice-Hall, Inc. Mr. Harold
G. Russell and his assistants on the staff of the University
of Minnesota Library have been extraordinarily helpful in
many ways. Mr. John K. Langum of the University of
Minnesota was kind enough to read the galley proof and
caught several errors of content. In other cases in which
specific parts of the book-including parts of the manuscript
of Volume II~have been submitted to friendly critics, I
have indicated, and desire here to express again, my sense
of profound gratitude to the persons involved.
My obligations to the two to whom this book is dedicated,
on the other hand, do not lend themselves to specification,
precisely because they are measureless. The same thing
must be said of my obligations to my wife, who has helped

xu

Preface

in so many ways that any attempt at particularization would
likewise represent an absurd minimization of her share in
the work.
ARTHUR W. MARGET


Table of Contents
PAGE

CHAP'l'EU

I.

1
1

INTRODUCTORy...............................

I.
II.

An Apology for Polemics. . . . . . . . . . . . . . . . . . . . .
The "Theory of Prices" and Mr. Keynes. . . . .. .

2

PART ONE

"QUANTITY.EQUATIONS" AND THEIR MEANING
II.

"QUANTITY EQUATIONS" AND "THE QUANTITY
THEORY". . . . . .. . . . . . . . . . . . . . . .. . . .. . . . . . ..

I.
II.
III.
IV.
V.
VI.
VII.
VIII.

III.

Quantity Equations and the Theory of Prices. . .
Keynes's Treatise and the Quantity Equations. . .
Quantity Equations versus the Quantity Theory
The Residuum of the Quantity Theory Controversy...........
Quantity Equations and the Quantity Theory in
Keynes's Treatise. . . . . . . . . . . . . . . . . . . . . . . . . .
Quantity Equations and Keynes's General Theory
Greek Gifts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Dead Shall Rise Again .... " . . . . . . .. . . . . .

QUANTITY EQUATIONS AS "STATICAL IDENTITIES"

I.
II.
III.
IV.

The Quantity Equations as "Statical" Equations
"Statical" Conditions as Stationary Conditions. .
The "Truth" of the Quantity Equations. .. . . . . .
Methods of Correction: Insertion of Missing
Terms..
V. Methods of Correction: Redefinition of Terms.. .
VI. A Test Case from Keynes's Treatise. .. . . . . .. . . .

IV.

13
19
22
27
29
33

35
39
39

40
46
55

64
68

QUANTITY EQUATIONS AS "STATICAL IDENTITIES"

(Continued) . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .
I. "Statical" Conditions as Equilibrium Conditions
II. Quantity Equations and "Non-Statical" Analysis
III. Quantity Equations and the Element of Change
IV. The Quantity Equations and Monetary Disequilibrium .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . .
V. The Quantity Equations as "Identities" . . . . . . . .

V.

9
9

THE

"DYNAMICAL"

EQUATIONS

OF

Keynes's Treatise and Monetary "Dynamics"...
Nemesis....................................
Hidden Assumptions: The Attack and Keynes's
Defense ..... , . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IV. The Collapse of "Keynes's Libra" .... " ..... , .

V. Epilogue...................................
XIII

85
88

KEYNES'S

Treatise on Money. . . . . . . . . . . . . . . . . . . . . . . . . ..
I.
II.
III.

72
72
78
81

101
101
102

115
124
138


Table of Contents

XIV

PART

Two

BEHIND THE "QUANTITY EQUATIONS"
PAGE

CHAPTER

VI.

GENERAL CONSIDERATIONS; THE QUANTITY
MONEY OF ULTIMATE REDEMPTION

I.
II.
III.

VII.

II.
III.
IV.

VIII.

M' .....

143

143
145
154
158

Bank Reserves and the "Creation" of Deposit
Currency
.
The Role of the Rate of Interest
.
Bank-Rate and the Quantity Equations
.
The "Traditional" Theory of Bank-Rate
.

158
171
178
189

Plan of the Argument
.
A Simple Quantity Equation and its Justification
The Quantity of Money of Ultimate Redemption

THE QUANTITY OF MONEy-SUBSTITUTES,

I.

THE QUANTITY OF MONEy-SUBSTITUTES,

tinued)
I.
II.
Ill.

IX.

tinued)

x.

XI.

XII.

M' (Con.

Bank-Rate, M', and" Proportional" Price Change
The" Order of Events"
.
M' and the Maintenance of a Low Bank Rate .

THE QUANTITY OF MONEy-SUBSTITUTES,

I.
II.
III.

OF

.

M' (Con.

Interest as "Capitalization-" and "Cost-Factor"
Wicksell on Interest as a Cost, and M'
.
The Argument Applied to Interest as "Capitalization Factor"
.

THE QUANTITY OF MONEy-SUBSTITUTES,

tinued)

M' (Con.

I. Bank Rate and Keynes's Fundamental Equations
II. "Capitalization," Interest as a Cost, and the
Fundamental Equations
.
III. I - S as "Profits," and Bank Rate
.
.
IV. I( -8) as "Investment" and Bank Rate
"VELOCITY OF CIRCULATION" (V)
.
I. The Concept of "Velocity" in Monetary Theory
II. Attacks on "Velocity": Appearance and Reality
III. "Velocity" in Keynes's Treatise
.

THE "INCOME ApPROACH" TO THE THEORY OF
PRICES: ITS HISTORY
.

I.
II.
III.
IV.
V.
VI.
VII.

Keynes's Treatise and the Income Approach
.
Substance and Shadow in the Income Approach
Tooke and the Income Approach
.
Tooke and Adolf Wagner
; ..
Tooke and Knut Wicksell
.
The Influence of Wicksell and Wagner
.
The Income Approach after 1909
"
.

206
206
212

222

231
231
247
258
268
268
269
274
279
290
290
294
298
302
302
306

311
315
324
327
336


xv

Table of Contents

PAGE

CHAPTER

XIII.

THE "INCOME ApPROACH" AND "VELOCITY": INCOME VELOCITY
.

I.
II.
III.

Income, "Velocity," and the Quantity of Money
Income versus Outlay from Income
.
Keynes's Treatise on Income and Velocity
.
IV. The Concept of Income Velocity Examined
.
V. "Income Payments" and Income Velocity
.

XIV.

THE ALTERNATIVE TO "INCOME VELOCITY"

I.
II.
III.

IV.

XV.

374

388

Income Velocity as a "Hybrid Conception"
. 388
Robertson versus Keynes on "Income Velocity" 398
Keynes and the Traditional Alternative to Income
Velocity
. 402
Keynes's Alternative and the" Quantity Equa. 409
tions"
, .. ,

THE CASH-BALANCE ApPROACH . . . . . . . . . . . . . . • • .

I.
II.
Ill.

XVI.

.

344
344

354
356
364

Keynes and the Cash-Balance Approach, .. ,
,
The" Marshallian K"
,,
,
,
Relevance and Irrelevance in the Cash-Balance
Approach
" .", .,
.

THE CASH-BALANCE ApPROACH

414
414
415

420
. 459

(Continued)

I.

Money "in Circulation" and the Cash-Balance
Approach

,
.
II. "Savings Deposits," Cash Balances, and "Velocity"
,
, .,
'.'
, ..
III. Investment, Borrowing, and" Cash Facilities" ...
IV. Forces Determining the Relative Size of Cash
Balances
,
, ..

XVII.

THE "VOLUME OF TRANSACTIONS"
"PLURALITY" OF PRICE LEVELS

CPT);
,

THE
.

I. Keynes on the Fisherine T
.
II. "Consumers' Goods" Equations and the Plurality
of Price Levels. . . . . . . . . . . . . . . . . . . . .
.
III. "Consumers' Goods" Equations, Plural Price Lev.

els, and Fisherine Equations
IV. Fisherine Equations and the Price Level of Output
V. The Case for a "Total Transactions" Equation ..

XVIII.

THE "VOLUME OF TRANSACTIONS"

459
466
470
478
484
484
485

509
514
518
525
( Continued) ...

I.

Keynes's Treatise and "Non-Output" Transac,
.
tions
,
, .,
II. Output versus Transactions in Output

.
III. Goods Produced versus Goods Intended for Sale
IV. The Velocity of Circulation of Goods
.
V. Keynes's Treatise and the Velocity of Circulation
of Goods
,
, .

525
538

544
548
564


Table of Contents

xvi

PAGE

CHAPTER

XIX.

THE "VOLUME OF TRANSACTIONS"

(Continued). ..

The Price Level of "Services" and the Fisherine
Equation. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II. The Role of Transactions in Securities... . . . . .. .
III. The "Volume" and the "Value" of Transactions
in Securities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IV,. Keynes's Treatise on Transactions in Securities
and the Price Level of Output. . . . . . . . . . . . . .
V. The Role of Output in the Theory of Prices.....

569

I.

569
576

588
595
599

INDEX....................................... 603


Summary
PAGE

CHAPTER

I.

INTRODUCTORy...............................

1

Mr. J. M. Keynes on the present status of the "Theory of
Prices," 1. An apology for polemics, 1. Reasons for the
selection of Mr. Keynes as a case in point, 3,

PART ONE
"QUANTITY EQUATIONS" AND THEIR MEANING
II. "QUANTITY EQUATIONS" AND "THE QUANTITY
THEORY" . . . . . .. .. . . . . . . .... . . .. . . . .. . . ... .
9
The place of "quantity equations" in monetary theory, according to Keynes's Treatise on Money, 9. Quantityequations versus "The Quantity Theory," 19. The residuum
of the "quantity theory" controversy, 22. The confusion
of "Quantity Equations" with" The Quantity Theory" in
the Treatise, 27. The place of "quantity equations" in
monetary theory, according to Keynes's General Theory of
Employment, Interest, and Money, 29. Reasons, nevertheless, for continued concern with the argument of the Treatise,
30. The confusion of "Quantity Equations" with "The
Quantity Theory" in the General Theory, 33.

III.

QUANTITY EQUATIONS AS "STATICAL IDENTITIES"
Keynes's charge that the older "quantity equations" are
"statical" in character, 39. "Statical" conditions as "stationary" conditions with respect to the variables included
in the Quantity Equations, 40. When the charge is translated to mean that the equations a..-,sume the presence of
stationary conditions with respect to relations not given

specific notation in the equations themselves, it reduces to
the charge that" Quantity Equations" are not under all circumstances true equations, 46. History of the latter
charge: statistical, considerations, 46. Analytical cOllsiderations: the "incompleteness" of the equations as lists of
variables affecting prices, 49. Recognition of the issues involved by Newcomb and others, 51. The first method for
meeting the difficulty: the insertion of the missing factors,
55. Examples from the practise of Newcomb, Fisher, and
others, including Keynes himself, 56. Usefulness of the
method, 59. The second method for meeting the difficulty:
redefinition of the terms, 64. Invalid objections to this
method, 65. Examples of the method as applied by Newcomb and others, 66. A crucial passage in Keynes's T1'eatise
tested in the light of the considerations developed in this
chapter, 68.
XVll

39


Summary

xviii

rAGE

CHAP'fER

IV.

QUANTITY EQUATIONS AS "STATICAL IDENTITIES"

(Continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

"Statical" conditions as "equilibrium" conditions, 72. The
validity of the "Quantity Equations" under non-statical
conditions, in this sense, 73. Their validity in the light of
the criteria for" equilibrium" indicated in the Treatise, 76.
The validity and usefulness of the" Quantity Equations"
for non-statical analysis, 79. The Quantity Equations and
analysis with respect to the causes and the process of change
in prices and in the variables determining prices, 81. The
Quantity Equations and analysis with respect to the nature
and causes of monetary" disequilibrium/' 85. The Quantity Equations as "identities," 88. The charge viewed in
the light of the historical development of the" equation of
exchange," 90; and in the light of the results obtained by
the use of Quantity Equations which are true by definition,
99.

V.

THE

"DYNAMICAL"

EQUATIONS

OF

KEYNES'S

Treatise on Money... . . . . . . . . . . . . . . . . . . . . . . ..
Reasons for dealing with the problem: the claims of the
Treatise itself, and tile subsequent challenge, 101. Unfounded criticisms of the Fundamental Equations as being
supposedly "statical" in character, 102. The case oi "dynamic equilibrium," 103. The theory of output presented
in the Treatise is not inherent in the Fundamental Equations themselves, and therefore does not invalidate those
equations for the case of "dynamic equilibrium," 103. The
same thing is to be said with respect to the argument of the
Treatise concerning the conditions for" equilibrium" other
than an equality between costs and prices, and between
"savings" and "investment," 107. The Fundamental Equations, as such, do not assume an independent relation between the level of earnings and the rate of interest, 110.
Nor do they necessarily lead to an argument for the stability of general prices, and therefore to an assumption that
the level of costs remains unchanged, 113. Sound criticisms of the validity of the Fundamental Equations under
changing conditions: the relation of the costs of production
of capital goods and consumers' goods, respectively, 115.
"Short period" and "long period" analysis as a statement
of the relation between the older quantity equations and
the fundamental equations of the Treatise, 118. Keynes's
reply to the criticism in question, 120. The decisive obstacle to the utilization of the Fundamental Equations under changing conditions, 124. The twofold purpose of the
Equations, 124. The truistic character of the expression
P R = E - S could be defended only at the cost of a series
of tortuous constructions with respect to the meaning of
"savin~" and "investment," 125. But even these constructions did not justify the identification of "cash earnings
available for outlay" with" costs," under changing conditions, 126. Not all "costs" are associated with equivalent
cash payments, 127. The identification of "earnings available for outlay" with "costs of production" is impossible
when account is taken of the time relations involved, 130.
The result is to destroy the claim that the Equations per-

101

Summary

XIX
PAGE

CHAPTER

V.

THE

"DYNAMICAL"

EQUATIONS

OF

KEYNES'S

Treatise on Money (C ont.)
form the twofold purpose assigned to them under changing
conditions, 133. Keynes's comment, in the General Theory,
on the Fundamental Equations of the Treatise, and its interpretation, 138.

Two
BEHIND THE "QUANTITY EQUATIONS"
PART

VI.

GENERAL CONSIDERATIONS; THE QUANTITY OF
MONEY OF ULTIMATE REDEMPTION. . . . . . . . . . ..

143

Relation of the topics treated to the writings of Mr. Keynes,
144. Justification of this procedure, 144. A Quantity
Equation of the general Fisherine form, 145. The criteria
on which it is based, 145. The treatment ofuvelocity," 148.
Meaning of Uthe quantity of money," 148. "Money of
ultimate redemption" and its relation to Umoney in circulation" and the quantity of money-substitutes, 150. A
brief summary of the theory with respect to the forces determining the quantity of money of ultimate redemption,
154.

VII.

THE QUANTITY OF MONEy-SUBSTITUTES,

M'. . . ..

158

The size of bank reserves and their ratio to the quantity of
money-substitutes, 158. The" creation" of bank deposits,
160. The mechanism of changes in general prices consequent upon changes in the quantity of money of ultimate
redemption, 171. The role of the rate of interest, 173.
Bearing upon the relation between monetary theory and
"value theory," 176. The relation of Bank-rate to the
Quantity Equations, 178. Wicksell on Bank-rate and the
quantity of M', 183. The argument of Keynes's Treatise

on this point, 188. The" invariability" of the association
between Bank-rate and changes in M': Tooke's supposed
"refutation" of the classical position, 189. The irrelevance
of this type of empirical argument, 190. The argument of
Keynes's Treatise and the classical position, 191. The contrasting case of Wicksell, 195. The" Gibson Paradox," 196.
Market rate and "natural rate" in Keynes's Treatise, 199.
The meaning of the "natural rate" in Wicksell's Interest and
Prices, 201. The present position of the theory of the
"natural rate," 204.

VIII.

THE QUANTITY OF MONEy-SUBSTITUTES,

tinued)

M' (Con: . . ..

Bank-rate, M', and" proportional" changes in general prices,
206. The "Quantity Theory" versus the Quantity Equations, again, 206. The" six points" of the Treatise with respect to "The Relation of Bank-rate to the Quantity of
Money," 208. The "order of events" in the modus operandi
of Bank-rate, 212. Relation of the argument to the "Quantity Equation," 214; to the "second strand" in the "traditional doctrine," 216; and to the "priority" of changes in
Bank-rate with respect to changes in quantity of M', 217.
The interpretation of the argument of Keynes's Treatise on

206


xx

Summary

CHAPTER

VIII.

PAGE

THE QUANTITY OF MONEy-SUBSTITUTES,

M' (Cont.)

this point, 220. The" effectiveness" of Bank-rate in the
absence of a change in M', 222. The case of the" rationing"
of credit, 223. The "fringe of unsatisfied borrowers," 224.
Keynes on the" traditional doctrine," Wicksell and Cassel
with respect to the relation between the quantity of M' and
the maintenance of a low Bank-rate, 228.

IX.

M' (Con'.' . . . . . . . . . . . . . . . . . ..

THE QUANTITY OF MONEy-SUBSTITUTES,

tinued)

231

The argument of Keynes's Treatise with respect to interest

as a "capitalization factor," 231. The traditional doctrine
on the subject, 233. Limits to the application of interest
as a "capitalization factor" in tracing the modus operandi
of Bank-rate, 233. Bearing of the argument on the exposition in the Treatise, 234. The market rate of interest
versus the rate of "capitalization," 237. Wicksell and
Keynes on the point in question, 237. Relation of the
argument to the question as to the relation between the
short-term and the long-term loan market, 239. Interest
as a "Capitalization Factor" in relation to interest as a
"Cost Factor," 240. The importance of interest as a
H cost," 244.
The interpretation of the Treatise on this
head, 244. Wicksell's argument with respect to the" direct"
influence of changes in the rate of interest upon prices, 247.
General versus "relative" prices, 248. The argument of
Tooke with respect to interest as a "cost," and Wicksell's
rebuttal, 249. The case of rising interest costs, 249. Bearing of the discussion on the question of the "priority" of
changes in P and in M ' , 252. The case of falling interest
costs, 253. The relation of Wicksell's argument to that of
Ricardo, 256. Application of the Wicksellian argument to
the treatment of interest as a "capitalization" factor, 258.
The relation of this part of Keynes's Treatise to the traditional doctrine, 259.

X.

M' (Continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

THE QUANTITY OF MONEy-SUBSTITUTES,

Reasons for examining the problem, 268. The Fundamental Eql.lations and interest as a" capitalization factor," 269.

The Equations and interest as a "cost factor," 270. The
treatment of interest costs in the Fundamental Equations,
270. "Profits" in the Fundamental Equations and the
modus operandi of Bank-rate, 274. The relation of I B( = Q) to the "natural rate," 275. The "price premium,"
276. Aggregate versus marginal costs, 277. The factor
of "anticipations," 278. The decisive objection to the use
of the "profits" (Q) of the Fundamental Equations for a
tracing of the modus operandi of Bank-rate, 279. (l - S)
as a summary of the forces leading to a change in the dimensions of the stream of money expenditure, 280. The
meaning of "Investment," 280. Wicksell and the place of
"investment" in the modus operandi of Bank-rate, 283.
Keynes on "speculation" versus "investment," 283. The
forces determining the amount of entrepreneurial spending,
285. Keynes on the relation of the "third strand" in the

268


.

Summary

XXI

PAGE

CHAPTER

X.

THE QUANTITY OF MONEy-SUBSTITUTES,

M' (Cont.)

"traditional doctrine" to the" first strand," 285. His replies to Robertson and Hayek, 286. The subsequent steps
in the modus operandi of Bank-rate, 287. The re-emergence
of the Quantity Equations, 288.

XI.

"VELOCITY OF CIRCULATION"

(V).. . . . . . . . . . . . ..

290

State of the subject, 290. That the confusion is less than
it appears to be becomes evident when account is taken of
the varying qualifications of the disputants, 295; of the true
nature of the relation between the" cash-balance approach"
and the concept of velocity, 296; and of the initial uncertainty to be expected in the exploration of uncharted fields,
297. The treatment of "velocity" in Keynes's Treatise on
Money, 298.
XII.

THE

"INCOME ApPROACH" TO THE THEORY OF

PRICES: ITS HISTORY. . . . . . . . . . . . . . . . . . . . . . ..

302

The argument of Keynes's Treatise as an example of the
"income approach," 302. Shortcomings of existing histories of that approach, 304. The various components of
the" income-approach" are to be found far back in economic
literature, 306. Irrelevancies introduced by historians of
the "income approach": the "nature" of money, 308; the
"marginal utility of money-income," 309; the "passiveness"
of prices, 309. The relation of Tooke to the" income approach," 311. Tooke's influence on Adolf Wagner, 315;
and on Rnut Wicksell, 323. The influence of Wicksell, 327;
and of Wagner (and N. Johannsen), 329. F. von Wieser,
336, and his influence on Schumpeter, 338; and on Aftalion,
339. R. G. Hawtrey and the "income approach," 340.
The concept of "income-velocity": Foster and Catchings,
and "circuit velocity," 341; Robertson and Pigou, and "income velocity," 342. The "income approach" contains so
many heterogeneous elements that it is best handled as part
of the discussion of the analysis "lying behind" each of the
variables of our" Quantity Equation," 342. The Genealogy
of the "Income Approach," 343.
XIII.

THE "INCOME ApPROACH" AND "VELOCITY": INCOME VELOCITY. . . . . . . . . . . . . . . . . . . . . . . . . . . ..

"Velocity" as an element of "superfetation," according to
certain "income-theorists," 344. The supposed antithesis
between emphasis upon a "stream" of money and emphasis
upon the stock of money is an ancient one, 345. The resolution of this antithesis, however, instead of making it possible to dispense with the concept of "velocity," demands
the inclusion of "velocity" among price-making forces, 345.
The income approach "versus" the "quantity theory," 346.

The introduction of the "quantity of money" into the "income theory" becomes necessary as soon as we ask why
the level of money incomes is higher at one time than at
another, 348. History of doctrine on this point, 349. Relation to the question as to the place of "velocity" in an
"income" equation such as that of Aftalion,352. "Income"
versus" outlay from income," 354. Bearing of the distinc-

344


XXll

Summuy
PAGE

CHAPTER

XIII.

THE "INCOME ApPROACH" AND "VELOCITY": INCOME VELOCITY (C ont.)

tion upon the place of "velocity" in an "income-equation,"
356. The position of Keynes's Treatise on the issues thus
far discussed, 356. The concept of "income-velocity" and
its history, 357. Motivation underlying the concept of
"income-velocity," 364. A judgment as to the usefulness
of the concept of "income velocity" is best undertaken by
comparing it with the concept of "virtual velocity," 366.
Objections to the latter concept, 367. The same type of
objection applies to the concept of "income velocity,' 368.
The problem of "velocity" versus the problem of the magnitude and composition of total monetary transactions, 369.

An algebraic demonstration, 369. Importance of the distinction for a study of the mechanism of price change, 371.
Its importance for the study of movements in "velocity,"
properly so called, 372. The methodological implications
of the "cash-balance approach," 373. Further illustrations:
"income measured in money>' versus "income payments,"
375; payments" into" income, and payments" out of" income, 379. The distinction has been concealed by certain
definitions of "income," 379; but is of the greatest importance for an evaluation of the concept of "income velocity,"
381. The problem of payments out of income, when related
to money income received, is properly a problem of "velocity," 382; but the problem of payments into income is
a much broader problem, 382. An algebraic formulation
of the point at issue, 383. The argument against the concept of "income velocity" is not that it necessarily leads to
.analysis that is erroneous, but that it is not of sufficient
precision for use in the central problems involved in the
Theory of Prices, 385.
XIV.

THE ALTERNATIVE TO "INCOME VELOCITY". . . . ..

Keynes's attack on the concept of "income velocity," in the
Treatise, 388. The reply of D. H. Robertson, 388. The
test as to whether the concept of "income velocity" is
"hybrid" in character, 389. Pigou's argument with respect
to "income velocity" as a "genuine physical magnitude,"
judged in the light of the methodological implications of the
cash-balance approach, 390; and of the difficulties raised by
the notion of "physical" movement, 391. Other unsatisfactory defences of the concept of "income velocity" against
the attack of Keynes, 393. Keynes on the notion of "true"
velocities, 394. In what sense "income velocity" is not a
"true" velocity, 395. Results of a failure to recognize its
"hybrid" character, 396. D. H. Robertson on "income

velocity" again, 398. The case of integration of industry,
399. Bearing of the argument on "income velocity," 399.
Robertson's main criticism of Keynes's position with respect to "income velocity" rested upon a misunderstanding
of that position, 401. KeYnes's attack on "income-velocity"
reviewed, 402. The concept of "income-velocity" does not
date from "the earliest literature on our subject," 403. Its
present standing, 403. The antecedents of Keynes's alternative to "income velocity," 404. The analysis of R. G.
Hawtrey, 407. Relation of Keynes's alternative to the
"Quantity EquatioDS," 409.

388


Summary

x.xiii
PAGE

CHAPTER

xv.

THE CASH-BALANCE ApPROACH. . . . . . . . . . . . . . . ..

414

Keynes and the cash-balance approach, 414. The" Marshallian K" and its relation to "velocity," 415. The implications of the expression K = 1/V, 417. The shortcomings
of the concept of "income-velocity" are not to be attributed to the cash-balance approach, 420. The use of the
latter should not be confined to the case of cash balances
held against payments out of income, 422. The H pricelevel" involved in "cash-balance" equations need differ in

no wise from the "price-level" involved in equations of the
Fisherine type, 424. An algebraic demonstration, 427.
The argument of D. H. Robertson with respect to the concept of "latent money" and its bearing upon the relation
between "cash-balance" equations and equations of the
Fisherine type, 431. The cash-balance approach finds its
unequivocal justification only in its use in the explanation
of changes in the velocity of circulation of money, 433. It
is therefore not fair to criticize the approach in question
because it is not well-adapted for the solution of other problems, 434. Misunderstandings of the claims which are
properly to be advanced on behalf of the cash-balance approach are probably to be attributed to certain" real balance" variants of this approach, 436. Keynes on the relation between "cash-balances" and "real balances," 437.
The nature of the connection between the "cash-balance
approach" and "general value theory," 440. The cashbalance approach and" utility analysis," 442. The" absolute" and the "relative" demand for cash balances, 444. It
is a mistake to insist upon the adoption of the" real balance"
variant on the ground that variants of this type are demanded by the postulates of "general value theory," 450.
XVI.

THE CASH-BALANCE ApPROACH

(Continued). . . . ..

459

Corollaries of the cash-balance approach: money" in circulation" and money "out of circulation," 459; money as a
"store of value" and "bearer of options," 463. "Savings
deposits," and their relation to "velocity," 466. Investment and borrowing opportunities in relation to the size of
cash balances held relative to outlay, 470. Keynes's" cashfacilities," 472. The forces determining the size of cash
balances. held relative to outlay, according to Keynes's
Monetary Reform, 478. "Habits" as an explanation, 479.
A summary statement of the forces determining the size of
cash balances held relative to outlay, 482.

XVII.

THE "VOLUME OF TRANSACTIONS" (PT); THE
"PLURALITY" OF PRICE LEVELS. . . . . . . . . . . . . ..

Keynes on the T of the "Fisher equation," 484. Alleged
uselessness of the latter as a guide to the" purchasing power
of money," 485. History of the suggestion that pur major
concern must be with the prices of consumers' goods, 486.
The suggestion has not always been accompanied by an
adequate supporting argument: Tooke's treatment, 487;
Wicksell's treatment, 489. Relation of the suggestion to
('utility analysis," 490. The argument for a "consumers'
goods" equation is in reality an argument for a "plurality
of price-levels," 495. History of the latter argument, 496.
Keynes's "plurality of price-levels," 506. Relation of a

484


XXIV

Sununary

CHAPTER

XVII.

PA.GE

THE "VOLUME OF TRANSACTIONS" (PT);
"PLURALITY" OF PRICE LEVELS (Cont.)

THE

"consumers' goods" equation to equations of the general
Fisherine form, 510. Examples, 511. Relation of equations of the general Fisherine form to the use of a "plurality
of price-levels," 512. Relation of these equations to an
equation for the price level of "output," 514. Equations
of the "total transactions" type are capable of telling us as
much as equations dealing solely with the price level of
output, but they also tell us more, 518. The role of "intermediate transactions," 519. Mises versus Wieser, 520.
The conclusion stated in terms of a composite demand for
cash balances, 521.
XVIII.

THE "VOLUME OF TRANSACTIONS"

(Continued). ..

525

The argument developed thus far applied to the debate between Robertson and Keynes on the relation of the latter's
separate price levels to each other, and to the price level for
"output as a whole," 525. The key to the dispute lies in
the treatment of "non-output" transactions, 527. Corollaries: the alleged "independence" of the separate price
levels, and its relation to the question as to the functions
of "partial" and "general" equilibrium analysis, respectively, 531. The Keynes-Robertson debate in the light of
the concept of "real balances," 534; and of the concept of
"income-velocity," 537. The "volume of output" versus

the "volume of transactions in output," 538. "Output"
versus" goods produced for sale," 540. Relation of the distinction to certain distinctions made in the Treatise, 542;
and to the question as to the formal validity of the Fundamental Equations under all conditions, 544. "Goods produced for sale" versus "goods intended for sale," 544.
"Old" goods, 545; and their relation to the argument of the
Treatise with respect to the sources of a discrepancy between
"Savings" and "Investment," 547. "Goods intended for
sale" versus" goods sold," 548. The" velocity of circulation of goods," 548; and its components: the number of
middlemen's sales," 554; and the rate" of sale" of goods, 563.
The treatment of these elements in Keynes's Treatise, 564.
XIX.

THE "VOLUME OF TRANSACTIONS"

(Continued). ..

The case for the segregation of a price level of "services,"
569. The difficulty of "non-specifiable prices," 572. Relation of the argument to equations of the" total transactions"
type, 574. History of discussion of the rOle of "security
transactions" in the Theory of Prices: Sismondi, 576; Tooke,
577; and Hawtrey, 579. The strength of the latter's argument, 581; its weaknesses, 581. The" composite demand
for cash-balances," again, 584. Application to the problem
of the "absorption" of "purchasing power" by the stockmarket, 585. Hawtrey's argument with respect to the role
of "security transactions" further considered: the "volume"
versus the "value" of "security transactions," 587. Hawtrey's real argument has to do with the merging of the price
indexes of dissimilar things, 591; and not with the justification for the inclusion of "security transactions" in the equation of exchange, 593. The conclusions of these chapters

569


xxv

Summary
CHAPTER

XIX.

THE "VOLUME OF TRANSACTIONS"

(Cont.)

applied to the argument of Keynes's Treatise, 595. pI as
the" price-level of new investment goods" versus pi as the
"price-level of securities," 596. The "Financial Circulation," 598; and its relation to an equation of the "total

transactions" type, 598. The place of "output" in such an
equation, again, 599.