Theories of Aggregate Income Distribution [Reprint 2022 ed.] 9781978817043

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THEORIES OF AGGREGATE INCOME DISTRIBUTION

THEORIES OF AGGREGATE INCOME DISTRIBUTION

by Paul Davidson

Rutgers University Press New Brunswick, New Jersey

Copyright © 1959 by Paul Davidson Copyright © 1960 by Rutgers, The State University Library of Congress Catalogue Card Number:

Manufactured in the United States of A m e r i c a by Edwards B r o t h e r s , Inc.

60-11523

To LOUISE

A

cknowledgments

No book is completely the result of the author's efforts. Many persons sacrifice time and energy to bring the work to fruition. This book is no exception. I, therefore, take this opportunity to express my grateful appreciation to Professor Sidney Weintraub, under whose supervision this work was first completed as a doctoral dissertation in 1958. Though he and I occasionally could agree only to disagree, this book would never have been completed without the guidance, advice, and criticism which he so generously rendered. I also wish to express my gratitude to David Horlacher, Eugene Smolensky, Benjamin Stevens, Nathan Rosenberg, and others who allowed me to use them as "sounding-boards" for my ideas. I also thank Professor Kenneth K. Kurihara for his help at a later stage when I was preparing the manuscript for publication. Finally, I am indebted to my wife, Louise, and my children, Robert and Diane, who, during the preparation of this study, must have often thought themselves to be widowed and orphaned.

vii

Table of Contents CHAPTER I II

Page INTRODUCTION

1

THE CLASSICAL THEORIES OF RELATIVE SHARES David Ricardo Karl Marx Ricardo and Marx: A Macroeconomic Evaluation

IH

THE NEOCLASSICAL MARGINAL PRODUCTIVITY DOCTRINE Alfred Marshall John Bates Clark The "Adding-Up" Problem Monopoly and Marginal Productivity . . . . Modern Marginal Productivity Doctrine . . Comments on the Neoclassical Analysis . .

IV

MARGINAL PRODUCTIVITY DOCTRINE AS A THEORY OF CLASS SHARES: THE COBB-DOUGLAS FUNCTION The Cobb-Douglas Production Function . . Marginal Productivity as a Theory of Relative Shares

V

VI

MONOPOLY AS A DETERMINANT OF CLASS SHARES Michael Kalecki Ashok Mitra Monopoly and Relative Shares: A Tentative Conclusion AGGREGATE DEMAND AND MACRODISTRIBUTION: KEYNES AND BOULDING . . . John Maynard Keynes Kenneth E . Boulding

ix

3 3 11 16 19 21 23 29 31 32 33

36 36 42 44 44 54 59 60 60 63

TABLE OF CONTENTS

X

VII

VIII

IX

AGGREGATE DEMAND AND MACRODISTRIBUTION: ROBINSON AND KALDOR Joan Robinson Nicholas Kaldor

71 71 82

AGGREGATE SUPPLY AND RELATIVE SHARES Comments on the Weintraubian System. . .

87 97

SOME CONCLUSIONS AND OBSERVATIONS O F DISTRIBUTION ANALYSIS A Comparison of the Various T h e o r i e s . .

100 100

APPENDIX A Note 1 Note 2 Note 3 Note 4

108 110 Ill 112

APPENDIX B

114

NOTES

120

BIBLIOGRAPHY

144

INDEX

149

"The mystery of the constant relative shares remains a reproach to theoretical economics." —Joan Robinson

Introduction Keynes has written: The stability of the proportion of the national dividend accruing to labour. . . is one of the most surprising, yet best-established facts in the whole range of economic statistics. . . . It is the stability of this ratio for each country which is chiefly remarkable, and this appears to be a long-run, and not merely a short-period phenomenon.1 This amazing constancy of the wage share should, in itself, be sufficient justification for theoretical studies of the determinants of the proportional partition of aggregate income into functional s h a r e s . 2 Besides the challenge of explaining this empirical " l a w , " however, the question of relative shares is of the utmost importance in such diverse public problems as the significance of union power, profit-sharing plans, tax legislation, the farm problem, economic development, and egalitarian movements. It is the purpose of this study to summarize and examine the major theoretical attempts to explain the distribution of the total product of an economy into proportionate shares which a c crue to the various economic classes. All these explanations have at least a twofold division of income between labor on the one hand and capitalists on the other. 3 It has been our intention in the selection of the material to be encompassed by this study to trace the development of the significant concepts in this important but oft-neglected area of analysis. Thus, the emphasis throughout is on the concepts and analytical procedures which, in the different theoretical systems, are germane to a theory of relative shares. In the following chapters, we will call attention to the various likenesses and differences, and comment on the method that has been advanced in each theory. Our r e m a r k s will be centered essentially on (a) the consistency of the a s sumptions and the reasoning involved in the analysis, and (b) the empirical applicability of the system. 1

2

AGGREGATE INCOME DISTRIBUTION

The order is mainly chronological. In Chapter II, the classical theories relating labor value to class shares are considered. Chapters III and IV deal with the neoclassical marginal productivity doctrine and the Cobb-Douglas empirical studies. The relationship between monopoly and relative shares is examined in Chapter V, while Chapters VI and VII deal with recent attempts to relate aggregate demand and shares. In Chapter VIII, the role of aggregate supply in determining the relative distribution of output is studied. Finally, in Chapter IX, a summary and appraisal of the development of the theories of r e l a tive shares is presented.

The Classical Theories of Relative Shares Classical economics holds at least two variants of a macroeconomic theory of distribution, the Ricardian Labor Theory of Value and the Marxian Exploitation Theory. In this chapter, we shall examine how, in the hands of Ricardo, the labor theory of value was shaped into a theory of relative shares. Then we shall investigate how Marx, drawing on Ricardo's analysis, developed his exploitation theory of class shares. David Ricardo Ricardo believed that the solution to the problem of relative shares was the principle desideratum of economics. 1 In a famous letter to Malthus, Ricardo wrote: Political Economy you think is an enquiry into the nature and causes of wealth—I think it should rather be called an enquiry into the laws which determine the division of the produce of industry amongst the classes who concur in its formation. No law can be laid down respecting quantity, but a tolerably correct one can be laid down respecting proportions. Every day I am more satisfied that the former enquiry is vain and delusive and the latter only the true object of the science. 2 Sraffa has indicated that in attempting to solve the problem of the proportionate shares in total output, Ricardo "was troubled by the fact that the size of this product appears to change when the division changes" 3 —that is, Ricardo was bothered by the problem of measuring a heterogeneous basket of goods—the index number problem. In estimating the relative values of commodities by the "labour bestowed on their production; not on their immediate production only, but on all those implements 3

4

AGGREGATE INCOME DISTRIBUTION

or machines required to give effect to the p a r t i c u l a r labour to which they a r e applied," 4 Ricardo believed that he had a measuring unit—which Keynes was to employ in our own g e n e r ation—that was independent of changes in distribution. Hence, unambiguous comparisons of proportionate s h a r e s in the value of output can be made. The Essential

Concepts

The Ricardian theory is based on three simplifying a s s u m p tions : 1. Diminishing r e t u r n s in agriculture because "land i s not unlimited in quantity and uniform in quality," 5 2. The Malthusian law of population, 3. The profit motive as an inducement to-capital accumulation. Ricardo divided the total output of the economy into three s h a r e s : rents, wages, and profits. According to Ricardo, rent "invariably proceeds f r o m the employment of an additional quantity of labour with a proportionally l e s s r e t u r n , " 6 i.e., rent occurs because of diminishing r e t u r n s . The amount of rent paid " i s always the difference between the produce obtained by the employment of two equal quantities of capital and l a b o r . " (I, p. 71) As to labor and wages, Ricardo argued, the natural p r i c e of labor tended towards subsistence; the latter being defined as that wage which would just keep the size of the laboring population constant. The subsistence level was not an objectively set minimum, r a t h e r it depended upon " t h e habits and customs of the p e o p l e . " Nevertheless, it could be assumed constant f o r long periods of time and t h e r e f o r e the natural price of labor depended upon " t h e price of the commodities on which the wages of labour a r e expended." (I, p. 97) The market price for labor, on the other hand, depended on the demand and supply for labor, with the f o r m e r determined by the stock of capital. Capital accumulation was defined as that portion of output which is added to the "fund allotted to productive consumption," 7 i.e., to a fund to be consumed by laborers— a wage fund. 8 The supply of labor r e s t e d upon the rate of population growth, itself a function of the wage r a t e . When the rate of capital accumulation exceeded the r a t e of population growth, the market wage rate would r i s e above the natural r a t e . With the price of

CLASSICAL THEORIES OF RELATIVE SHARES

5

labor above subsistence, the rate of population growth will increase, tending to drive wages back to subsistence. 9 In the Ricardian scheme, profit is a residual—it is whatever the capitalist has left after subtracting rent and wage payments from total revenue. For production to be maintained, however, some minimum profit rate must be met. (I, p. 122) The Antithesis

of Wages and Profits

Every increase in population augments the demand for corn. (Ricardo used corn as the basic wage-good.) This increment in demand leads to the extension of agricultural cultivation, involving more labor and capital (in a fixed proportion) applied to the land. Because of the increasing difficulty of providing more foodstuffs, the value of corn rises. Consequently, the natural price of labor advances. Ricardo argued that with every rise in wages there will be a fall in profits, and there is no other adequate reason for a fall of profit but a rise of wages, and further it may be added, that the only adequate and permanent cause for the rise in wages is the increasing difficulty of providing food and necessaries for the increasing number of workmen. 10 Every extension of cultivation in the face of diminishing r e turns, must raise the rent payments on what we now term the intra-marginal land. Hence, the farmer on this latter land will have a smaller physical product remaining after paying rent, i.e., the corn-price of land will have risen while the productafter-rent per input dose of labor and capital will diminish. If the wage rate in terms of corn is constant, then the workers will receive a relatively larger share of the smaller productafter-rent. Competition will insure the same profit per dose on all land, hence the rate of profit (in physical terms) will have declined. Thus, Ricardo noted that profits depend upon the "proportion of annual labour of the country . . . devoted to the support of labourers." 1 1 Ricardo's class share theory is presented in labor value rather than physical output terms; however, since labor value varies inversely with the physical productivity of labor, the conclusions on relative shares will be identical no matter which unit of measurement is used. Ricardo argued that in early stages of society, both the landlord's and the labourer's share of the value of the produce of the earth,

6

AGGREGATE INCOME DISTRIBUTION would be small; and that it would increase in proportion to the progress of wealth, and the difficulty of procuring food. (I, P- 112)

Every increase in accumulation will lead to an increase in the total value of output since no part of the former capital will be rendered less productive. The produce of the land and labour of the country must increase, and its value will be raised, not only by the value of the addition which is made to the former quantity of productions, but by the new value which is given to the whole produce of the land, by the increasing difficulty of producing the last portion of it. (I, p. 124) The price of corn will rise because " m o r e labour is employed in the production of the last portion," (I, p. 74) and Ricardo declared that the value of r commodity is always regulated by the most unfavorable circumstances in which production has to be carried on. Ricardo argued that this rise in the price of corn would "always be equalled in value by the additional rent, . . . so that the farmer will obtain for that which remains to him, after paying rent, the same value." 1 2 Therefore, the value of the product-after-rent per dose is always the same. From the value of the product-after-rent, wages must be paid. The residual will be profits. Since the natural wage varies with the price of corn, Ricardo concluded that although a greater value is produced, a greater proportion of what remains of that value, after paying rent, is consumed by the producers [labourers], and it is this alone, which regulates profits. . . . (I, pp. 125-126) i.e., the proportion of the product-after-rent going to wages will rise, and therefore the proportion going to profits must fall. Ricardo indicated that when the corn price rises, profits will also fall in the manufacturing sector of the economy. He a s sumed that manufacturing was not subject to diminishing r e turns, and therefore, the value of manufactured goods remained constant. With the increase in the value of corn, however, the manufacturer would have to pay higher wages, thus raising costs; therefore, he would be caught in a profit squeeze. 13 Hence, profits would fall in both manufacturing and agriculture, and competition and mobility of capital assured that profits fell by the same proportion in all industries.

CLASSICAL THEORIES OF RELATIVE SHARES

7

The Relative Rent Share14 So far, we have discussed Ricardo's ideas on the effect of capital accumulation, in a given state of the arts, on the proportionate division of the product-after-rent between wages and profits. Ricardo was much less explicit on the proportional distribution of total output between rent, on one hand, and wages plus profits, on the other. In the first two editions of his Principles, Ricardo had written that the proportion of the "whole produce" going to rent increased with accumulation, because of diminishing returns. 15 In the third edition, however, he observed that all he meant to imply was that the rent proportion "obtained with a given capital on any given farm," 1 6 increased due to diminishing returns. This does not necessarily mean that the rent share as a proportion of total output expanded, since it is possible that the added increment of output from the no-rent marginal land may increase total output by a proportion equal to, or greater than, the percentage increment in rent payments on the intra-marginal land. Nevertheless, in all Ricardo's arithmetic examples, the relative rent share in total output does increase with accumulation. 17 Ricardo apparently vacillated about the consequence of diminishing returns on the proportional size of the rent share. In a paragraph which he finally deleted from his Notes on Malthus, he indicated that he could not make any statement about the proportion of total output accruing to rent. He wrote: Rent is not a proportion of the produce obtained—it is not governed like wages or profits by proportions—depending as it does on the difference between the quantity of produce obtained by two equal capitals. If therefore I have anywhere said that rent rises or falls in the proportion that the produce obtained is increased or diminished I have committed an error. I am not however conscious of having so done. 18 Nevertheless, Ricardo had stated in the Preface to his Principles that his purpose was to show the movement of relative shares in the total product, not the distribution of the productafter-rent. Hence, it becomes necessary to investigate whether, in the Ricardian system, we can make any statements about the rent share, and whether the inverse relationship between the wage and profit shares in the product-after-rent, is also applicable to these class shares as a proportion of total product.

8

AGGREGATE INCOME DISTRIBUTION

A Mathematical

Interpretation

Underlying the Ricardian scheme are the assumptions that, in a given state of the arts, capital and labor are used in fixed proportions in each industry, and that diminishing returns occurs in agriculture. To avoid the index number problem, let us assume the production of a composite commodity; therefore, we can draw the schedules of the marginal physical product (M) and average physical product (A) of labor 19 as shown in Figure 1. If ON equals the total labor force employed, then total output is OERN (or OCDN). Total rent payments are equal to BER (or BCDR); and if Ow is the subsistence wage rate, then OwSN is the total wage bill. The residual, wBRS, is total profits. Using the following symbols, we can derive formulae for the three shares. Q = total product N = total quantity of labor employed

Figure 1

CLASSICAL THEORIES OF RELATIVE SHARES

g

- the wage bill = the real wage rate (subsistence) = total rent payments = total profits = the marginal physical product of a dose of labor and capital A - the average physical product of a dose of labor and capital , Ep = the elasticity of productivity = [ I W w R P M

If all workers receive the same wages, then W = wN. Thus the formula for the wage share at any given level of employment and output may be written as: W _ wN _ w Q AN A

/-v K '

Assuming a constant real wage rate, we may differentiate equation (1) with respect to N and obtain: w

dA TÎÏ7 (2)

dN V Q )

Thus, as employment increases in the face of diminishing returns, dA/dN is negative,20 and therefore the right-hand side of equation (2) is positive, i.e., the relative wage share varies in the same direction as changes in employment. Similarly, the rent share at any level of employment can be designated as: R _ AN - MN _ Q ~ AN

1 1

M " X

, , W

When there is only one variable factor (or in this case, one variable dose), then the ratio of marginal to average product is equal to the elasticity of productivity.21 Therefore equation (3) may be written as: £ = 1 - Ep

(4)

Thus, as we would expect, when diminishing returns occur (Ep < 1), the rent share will be positive. Differentiating equation (4) with respect to N, we obtain: d_ (R\ _ d (Ep) dN \QJ ~ ~ dN

. , w

10

AGGREGATE INCOME DISTRIBUTION

Equation (5) denotes that if the proportion of output going to r e n t i n c r e a s e s , then Ep m u s t decline a s employment r i s e s , implying that M falls at a m o r e rapid r a t e than A. R i c a r d o ' s uncertainty about the effect of accumulation on the relative rent s h a r e in the total product is t h e r e f o r e understandable. Diminishing r e t u r n s simply imply a positive s h a r e , but one must specify the r a t e s of change of the m a r g i n a l product compared to the a v e r a g e product to obtain a generalization about the proportional changes in the r e n t share. 2 2 In the n o r m a l case, the M/A-ratio will either r e m a i n constant or d e c r e a s e 2 3 (and consequently the r e n t s h a r e will either be constant or increase) with r i s i n g levels of employment. The Ep could i n c r e a s e only if, a f t e r a point, either (a) the m a r g i n a l product of labor began to r i s e , or (b) the a v e r a g e product of labor began to fall at a f a s t e r r a t e than the r a t e of decline in the m a r g i n a l product. The f o r m e r possibility would violate the a s sumption of diminishing r e t u r n s , while the latter can be r e j e c t e d on the assumption that the total product curve is of the n o r m a l type. 2 4 At any level of employment, the profit s h a r e may be designated as: P _ MN - W _ M Q AN A

W _ M AN A

W Q

^

or P

-F

W

Q~ P'Q Differentiating A (?) dN \q)

C7\ (7)

E

equation (7) with respect = ^EpI A (E\ dN ' dN \ Q)

to N, we obtain: W K '

Equation (2) d e m o n s t r a t e s that the wage s h a r e r i s e s with an inc r e a s e in employment. Consequently, it follows f r o m equation (8) that the profit share will decline if either: (a) Ep is i n v a r i ant to changes in employment, in which c a s e the rent s h a r e is constant, the wage s h a r e r i s e s , and the profit s h a r e falls; or (b) Ep declines a s employment r i s e s , in which case, the r e l a t i v e rent and wage s h a r e s i n c r e a s e , and the profit s h a r e declines. The profit s h a r e could i n c r e a s e (with r i s i n g employment levels) only if Ep i n c r e a s e d at a m o r e rapid r a t e than the r a t e of inc r e a s e in the wage share. It has a l r e a d y been indicated, however, that the M/A-ratio cannot, under n o r m a l conditions, increase.

CLASSICAL THEORIES OF RELATIVE SHARES

11

Thus we may conclude that in the Ricardian system (given the physical limitations of production in a given state of technology, and assuming a constant real wage rate), the relative wage share in the total product increases with rising levels of employment because of diminishing returns. The profit share declines when the wage share rises. Rent as a proportion of the total product may remain constant or may increase depending on whether the ratio of the marginal to average product remains constant or declines. Assuming a normal production function, the M/A-vz.tio can never increase (and therefore the rent share can never decrease) with rising employment levels in the region of rational factor hire. Karl Marx Karl Marx's theory of class shares was an intimate part of his inquiry into "the economic law of the motion of modern society," 2 5 holding that the economic development of capitalism was tied to the distribution of class shares. Marx realized that the market valuation of output depended on the distribution of income, and therefore "absolutely nothing can be explained by the relation of supply and demand, unless the basis has f i r s t been ascertained on which this relation r e s t s . " 2 6 Thus, Marx, following Ricardo's lead, adopted a labor theory of value as a theory of long-run pricing which is independent of the distribution of income. The Essential

Concepts

In the Marxian scheme, the value of any commodity is determined by the "labour-time necessary for production, and consequently the reproduction, of this special a r t i c l e . " 2 7 In this system, one commodity, "labour-power" has a unique place; it is the source of all value, yet the value of labor power is equal to the value of maintenance (subsistence) of the laborer. Consequently, if a worker produces in a day, more than the value of a day's subsistence, the " s u r p l u s value" can be expropriated by the capitalist, i.e., the worker can be exploited. Marx observed, "when the process of production is finished, we get a commodity whose value = c + v + s" where c, the constant capital, represents the raw material and capital depreciation, v, the variable capital, is the "value of labour-power" (the wage bill), and s is the " s u r p l u s value" (profits). (I, p. 235)

12

AGGREGATE INCOME DISTRIBUTION

By aggregating the value of all the commodities produced in the economy in a period of time (taking care not to double-count), we obtain the value of gross output as C + V + S, and net output as V + S, where C is the total capital depreciation in the period, V = S v, and S = L s , Thus, the value of the total net product is divided into two original shares, V (the wage share) and 5 (the profit share). The subsequent partition of the surplus among the capitalists, landlord, and others, via rents, dividends, interest, and retained profits, is regarded as of trivial importance by Marx. 28 Much of the Marxian analysis runs in terms of three basic ratios: Q

1. The organic composition of capital - , 2. The rate of profit — — , c +v' s 3. The rate of exploitation or the rate of surplus value - . Through much of his work, Marx assumed a constant organic composition of capital which in modern parlance means fixed input coefficients. (I, pp. 671-672) He also assumed constant r e turns to labor, i.e., " a l l other things being equal, the mass and value of the product will rise in direct proportion to the labour expended." (I, p. 661) Marx did recognize the possibility of diminishing returns on the extensive margin in agriculture, but he relegated it to an innocuous position in his scheme. The fertility of the soil would not affect the distribution of income except, given the length of the working day, to set a maximum limit to the absolute size of the surplus. 29 The second ratio, s/(c+'v), measures the rate of profit on the quantity of capital and raw materials actually consumed during the period, whereas the usual capitalist rate of profit is computed on the basis of total investment. 30 To bring Marx's concept into conformity with the conventional one, therefore, we must either assume that all capital turns over once during an accounting period, or we must adjust the denominator of the r a tio for the varying durabilities of the different types of capital. For purposes of simplicity, we may assume a single turnover period for all capital. 31 Anything that induces a change in the magnitude of the third ratio (s/v), will also bring about a change in the relative shares; for, when wages are at subsistence, the proportion of the value of net output going to profits, s/(f+s), divided by the proportion accruing to wages, v/(v+s), is equal to the rate of exploitation.

CLASSICAL THEORIES OF RELATIVE SHARES

13

In the Ricardian system, changes in the rate of population growth in response to changes in the real wage rate was the adjusting mechanism for maintaining a long-run subsistence wage. Marx, however, rejected the Malthusian law (I, pp. 699-700). In its place, he substituted the "industrial reserve a r m y " to maintain the subsistence rate. In the Marxian scheme, given the supply of labor, the demand for labor depends on capital accumulation, itself dependent on s. Assuming fixed proportions, the accumulation of capital leads to proportionate increases in c and v, and therefore "the demand for labour and the subsistence-fund of labourers clearly increase in the same proportion a s the capital." 3 2 If the increased demand for labor exceeds the supply, wages will r i s e above subsistence, reducing the amount of surplus per worker that can be expropriated by the capitalist. When there is no change in technology, the ultimate consequence of the r i s e in the price of labor is to lower the rate of accumulation "because the stimulus of gain is blunted." (I, p. 679) In familiar t e r m s , a r i s e in real wages relative to profits would lower the inducement to invest and this would tend to reduce the demand for labor and therefore check the r i s e in wages. Marx argued, however, that the rise in the real wage rate would induce capitalists to introduce labor-saving innovations, i.e., "methods which lessen the number of labourers employed in proportion to the increase in production." 3 3 The adoption of these more mechanized techniques will make some of the lab o r e r s redundant, and swell the ranks of the industrial r e s e r v e army of the unemployed. This army, by competing for jobs, will tend to depress the wage rate to subsistence. Any increase in mechanization means a r i s e in the organic composition of, capital, which, under the assumption of a constant rate of exploitation, 34 led Marx to formulate his famous law of the falling rate of profit. 3 5 This law follows from the definition of the rate of profits as:

¿=

for if we divide the numerator and denominator by v, we obtain (10)

14

AGGREGATE INCOME DISTRIBUTION

It is obvious, from equation (10) that if s/v is constant when c/v increases, then p must fall. In current terms, this would involve an unchanged income division (s/i>) even while industry becomes more "capital-using"—a rise in c relative to v. Thus, the profit " r a t e " would be reduced. The assumption of a constant rate of exploitation, however, is inconsistent with Marx's own belief that an increase in the organic composition of capital increases the physical productivity of labor, and therefore, changes the rate of surplus value. (I, pp. 346-361, 568-574) We shall discuss Marx's inferences on productivity and relative shares in detail in the next section of this chapter, but at this point we may indicate the nature of this inconsistency. If the wage rate in terms of physical commodities is constant, then the value of v in terms of labor time falls as productivity rises. 3 6 Thus, the rate of exploitation will increase, if the duration of the working day is constant. The assumption of a constant rate of exploitation with an increase in the organic composition of capital implies rising real wages with increases in productivity and hence, labor would obtain a constant proportion of an increasing total product.37 Changes in the Rate of Exploitation and in Relative Shares Assuming real wages are constant at subsistence, the rate of exploitation (and hence the relative shares) depend upon three factors: (1) the length of the working day, or the extensive magnitude of labour; (2) the normal intensity of labour, its intensive magnitude, whereby a given quantity of labour is expended in a given time; (3) the productiveness of labour, whereby the same quantum of labour yields, in a given time, a greater or less quantum of product. (I, p. 569) Increases in either the length of the working day or the intensity of labor input will increase the amount of value produced per laborer in a day. Since v is constant, s must rise; this is called an increase in "absolute surplus value." It implies a rise in the absolute and relative share of value going to profits, and therefore, a decline in the relative wage share. 3 8 On the other hand, a shortening of the workday, leaves "the value of labour-power unaltered. However, it reduces the surplus labour and surplus-value. Along with the absolute magnitude of the latter, its relative magnitude also falls." (I, p. 576) Thus, a shorter workday, reduces the absolute and relative share of the

CLASSICAL THEORIES OF RELATIVE SHARES

15

capitalists, while the absolute share of wages is constant and labor's relative share rises. Changes in the productivity of labor, ceteris paribus, change the quantity of physical output, but not the value of total output produced per laborer in a day of given duration. Any increase in the productivity of labor means it is possible to produce the same quantity of necessaries in less labor time. Since subsistence, in real t e r m s , is unchanged, the value of labor-power (v) declines, and, assuming a constant length of the working day, the surplus-value (s) increases. This increase in the rate of exploitation Marx called an increase in "relative surplus value," and he noted that changes in relative surplus value always vary directly with the productivity of labor. (I, pp. 569-574, 350) With technical progress, the productivity of labor r i s e s , and therefore, the relative profit share r i s e s , while the wage share falls. " T h u s , " Marx inferred, "the abyss between the laboure r ' s position and that of the capitalist would keep widening," 39 so that with the accumulation of capital, the lot of the labourer, be his payment high or low, must grow worse. The law, finally, that always equilibrates the relative surplus population, or industrial r e s e r v e army, to the extent and energy of accumulation, this law rivets the labourer to capital more firmly than the wedges of Vulcan did Prometheus to the rock. It establishes an accumulation of misery, corresponding with accumulation of capital. (I, p. 709) This increasing misery of the working class is not due to a lowering of real wages, but rather to a failure of real wages to r i s e with productivity. Thus, all increments in output due to technical progress will accrue to the capitalist class. Marx concurred with Ricardo in the belief that the relative wage and profit shares always moved in opposite directions, for he wrote: no change can take place in the absolute magnitude, either of the surplus value, or of the value of labour-power, without a simultaneous change in their relative magnitudes, i.e., relatively to each other. It is impossible for them to r i s e or fall simultaneously. (I, p. 570) However, Marx predicted that the profit share will r i s e , while Ricardo forecast that the wage share would increase. Almost as an afterthought, Marx recognized the possibility

16

AGGREGATE INCOME DISTRIBUTION

that diminishing returns in agriculture due to "decreasing f e r tility of the soil" 4 0 may affect class shares. In this case, if the length of the working day is constant, then the relative share of wages in the value of output r i s e s while the absolute and relative profit share falls. To offset this decline in profits, the capitalist can extend the length of the working day. Depending on the amount of lengthening in relation to the fall in productivity, the result will be either (a) total profits remain unchanged but the profit proportion in output falls; (b) total profits r i s e while the relative shares a r e unaltered; or (c) both total profits and the relative profit share rise, "provided the lengthening of the day be sufficient." (I, p. 579) Marx believed that Ricardo had unduly emphasized diminishing returns in agriculture as "the starting-point of important investigations into the relative magnitudes of wages, profits, and r e n t s . " Marx insisted that historical facts showed that the "increased intensity of labour, and . . . the prolongation of the working day" had more than offset diminishing returns so that profits had increased both as an absolute amount and a relative share. (I, pp. 579-580) Hence, in the Marxian system, the distribution of total product in the economy is, for all intents and purposes, independent of diminishing returns. Ricardo and Marx: A Macroeconomic

Evaluation

The classical theories of relative shares, a s exemplified by Ricardo and Marx, provided sweeping generalizations based on sweeping simplifications. Both writers assumed fixed proportions (in a given state of technology) between labor and equipment, and, for somewhat different reasons, a long-run constant real wage rate. Both believed that the total wage bill at any point of time, the market period, was determined by the size of a portion of the total stock of capital—a wage fund. Profits were a residual in both systems. In the Marxian scheme, there are only two shares, wages and profits. (Since diminishing returns are ignored, there is no basis for a distinction between rents and profits.) The income per worker is fixed by the level of subsistence, while the output per worker depends on the state of the a r t s and the length of the working day; if these two magnitudes of output and subsistence are not equal, the difference goes to the capitalist. Hence, the Marxian analysis yields a determinate solution once the real wage rate and the state of technology is given. With progress

CLASSICAL THEORIES OF RELATIVE SHARES

17

the discrepancy between output per head and the wage rate increases; consequently, the wage share falls. The industrial reserve army assures that the real wage rate will not rise for any given time span. If the level of real wages is permitted to increase with time, then the Marxian theory becomes indeterminate, or reduces to the simple tautology—capitalist income consists of that portion of the product that does not go to labor. Hence, the applicability of the Marxian analysis hinges on the assumption of a constant long-run real wage rate. Historically, this is a manifest error as judged by the evolving facts; only a slavish Marxist would dispute this, though, to be sure, we have the advantage of hindsight over Marx. In the Ricardian system, the proportionate division of the total product between the rent share and the wage plus profit shares depends, as we have shown, on the ratio of the marginal to average productivity of labor. The further division between wages and profits was based on the increasing labor effort required to produce the goods for a constant real wage rate in the face of diminishing returns. Consequently, Ricardo predicted a rise in the wage share relative to the profit share. Ricardo realized that technical progress could counterbalance diminishing returns, but he expected any offset to be just a temporary postponement of the inevitable path of the economy. Progress might initially increase the profit share, but this would stimulate an increase in the rate of capital accumulation, which would induce an increase in the rate of population growth. The increase in the number of workers would require an extension of the margin of cultivation and ultimately, Ricardo argued, technical progress would not be able to fend off diminishing returns. (I, pp. 78-84, 120-127) If, however, technical progress actually does counterbalance decreasing returns in agriculture, 41 then there is no basis for the Ricardian prognosis. His analysis is conclusive only under the assumption of a fixed level of real wages and a given state of technology. Both these presuppositions have proved to be inapplicable to the historical development of the western capitalist countries during the past one hundred and forty years. In both the Ricardian and the Marxian theories of relative shares, the importance of aggregate demand was overlooked. Both writers assumed that the workers always spend their entire income as they receive it, and that the capitalists save only to invest these funds immediately. 42 They both emphasized aggregate supply as the important determinant—Ricardo stressed

18

AGGREGATE INCOME DISTRIBUTION

supply under conditions of diminishing returns, while Marx insisted upon supply under short-run constant returns, and longrun increasing return conditions. Nevertheless, despite what we regard as shortcomings, since their analysis was of the total share of profits, rents, and wages to total output or to each other, their theories rightly deserve to be classified as pioneer studies in the macroeconomics of distribution. The contrast of their position and that of the neoclassicists becomes particularly evident when we examine the fascination of the latter group with factor prices rather than aggregate and relative shares.

III. The Neoclassical Marginal Productivity Doctrine Evolving from the Ricardian device of measuring value at the margin, the neoclassical marginal productivity doctrine was developed during the second half of the nineteenth century. By a peculiar twist, however, as the importance of studying relations at the margin was stressed, the emphasis shifted from a study of relative shares to a study of factor prices. Hence, most of the writings of the neoclassicists are only indirectly germane to a study of class shares. In this chapter, we shall indicate the essential contributions to the evolution of the neoclassical doctrine. By the turn of the century, with the writings of J. B. Clark and Alfred Marshall, this doctrine was finally accepted as the theory of distribution. Since Clark was one of the few who attempted to give a macrointerpretation to the analysis, we shall set out his scheme in some detail. Modern marginal productivity analysis has maintained basically the same framework as the neoclassical approach. The major refinement has been in relaxing the assumption of a purely competitive market. We shall briefly indicate how this has been added to the theory. Finally, at the end of this chapter, we shall comment on the limitations of the neoclassical approach for a macrotheory of distribution. The origin of the neoclassical marginal productivity doctrine can be traced to the second volume of von Tinmen's Der isolirte Staat published in 1850.1 Von Thunen's work is significant in that it is the first explicit application of the calculus to the theory of distribution. He recognized that each successive increment of a factor, applied with some fixed factor to the production process, would add a smaller increment to the total product. He demonstrated that interest was determined marginally, while wages were a residual, and then he was able to reverse the process and show that wages were determined 19

20

AGGREGATE INCOME DISTRIBUTION

marginally and interest was a residual. (Leigh, p. 495) Finally, he indicated that labor and capital were substitutes and that the entrepreneur will, if he knows and is following his own interests, alter the proportion between the quantity of labor and the quantity of capital he employs until the ratio between the " e f fectiveness" (marginal productivity) of each equals the ratio between their respective unit costs. (Leigh, p. 498) Thus, the major analytical precursors of the neoclassical marginal productivity doctrine can be found in rudimentary form in the writings of von Thunen.2 W. Stanley Jevons was the forerunner of the English neoclassical school, the first to note that "wages are governed by the same formal laws as rents." 3 His main contributions to the development of distribution theory is the introduction of the incremental productivity concepts into the English literature and the first presentation of the graphics of the calculus of productivity. The curve in Figure 1 is Jevons' representation of the relationship between changes in physical output (x) and changes in the quantity of labor {l) employed on a given farm. Jevons pointed out that as "more and more labour is applied to the same piece of land, the produce ultimately does not increase proportionally to the labour. This means the function dx/dl diminishes without limit after x has passed a certain quantity."4 Jevons argued that labor would be employed until the "final degree of utility" of the product equaled the most painful increment of labor, so that if a person is recompensed for the last increment which is applied to the land by the rate of production dx/dl, it follows that all the labour he applies might be recompensed sufficiently at the same rate. The whole labour is I, so that if the recompense were equal over the whole the result will be I • dx/dl. (p. 218) The residual will go to rent. By a similar graphic representation, Jevons demonstrated that capital would receive a payment equal to the rate of production of the final increment of capital multiplied by the quantity of capital, (pp. 258-259) In the last decade of the nineteenth century, Alfred Marshall and John Bates Clark developed these ideas of Thunen and Jevons into what we now call the neoclassical marginal productivity doctrine.

NEOCLASSICAL PRODUCTIVITY DOCTRINE

21

Figure 1 Source: Jevons, op. cit., p. 219.

Alfred Marshall Marshall believed that the problem of distribution was "much more difficult than it was thought to be by the earlier [classical] economists, and that no solution of it which claims to be simple can be t r u e . " 5 Marshall argued that a complete understanding of distribution involved going behind demand and supply schedules to study motivating forces. These forces, he felt, were complex and interrelated.

AGGREGATE INCOME DISTRIBUTION

22

The Marshallian

Analysis

The three essential concepts of the Marshallian analysis of the demand for a factor of production are (a) the principle of derived demand, (b) the principle of substitution, and (c) the principle of net productivity. Assuming a constant demand schedule for a product and assuming no change in the supply of other factors, Marshall noted that the demand schedule for any factor of production of a commodity can be derived from that for the commodity by subtracting from the demand price of each separate amount of the commodity the sum of the supply prices for corresponding amounts of the other factors, (p. 383) In his famous knife blades-knife handles example, Marshall, using the principle of derived demand, showed that, when the factors are used in fixed proportions, the demand for a factor is always less elastic than the demand for the final product. He indicated, however, that the essentiality of the factor, which is implied by this principle, will be modified by the principle of substitution. In the production of most commodities, factors are substitutable,and each entrepreneur, attempting to maximize his profits, would choose that factor mix which, for a given level of output, yielded minimum cost. (p. 341) When contemplating substitution of one factor for another, the entrepreneur estimates and compares the net product for each factor. The net product is defined as "the net addition to the value of his [the entrepreneur's] total product . . . , net that is after deducting for any extra expenses that may be indirectly caused by the change, and adding for any incidental savings." (p. 406) Thus, in the case where there are no complementary factors, the net product of the marginal worker is the increment in the total physical product "taken at the normal selling value of the product." (p. 850) In his celebrated marginal shepherd example, Marshall notes, however, that "theoretically a deduction from this has to be made for the fact, by throwing twenty extra sheep on the market, the farmer will lower the price of sheep generally, and therefore, lose a little on his other sheep." (p. 517n) But in a purely competitive market this deduction is so small that it may be neglected, and the price can be assumed constant; therefore, net productivity is directly related to marginal physical productivity. Hence, if, after comparing the net product and the costs of

NEOCLASSICAL PRODUCTIVITY DOCTRINE

23

the various factors, the entrepreneur thinks he can gain by shifting some expenditures from one factor to another, he will do so, and though he works "by trained instinct rather than formal calculations," he tends to hire each agent up to the "margin at which its net product would no longer exceed the price he would have to pay for it." (p. 406) In summary, Marshall noted that the uses of each agent of production are governed by the general conditions of demand in relation to supply: that is, on the one hand, by the urgency of all the uses to which the agent can be put, taken together with the means at the command of those who need it; and, on the other hand, by the available stocks of it. And equality is maintained between its values for each use by the constant tendency to shift it from uses, in which its services are of less value toothers in which they are of greater value,in accordance with the principle of substitution, (pp. 521-522) Marshall argued, however, that the tenet of net productivity was not a self-contained explanation of the value of a factor. He believed that the neoclassicists were overreacting to Ricardo's emphasis on supply, and in so doing "too much insistence has been laid on the fact that the earnings of every agent of production come from, and are for the time mainly governed by the value of the product which it takes its part in producing." (p. 525) Marshall reasoned that although "we must go to the margin to study the action of those forces which govern the value of the whole," (p. 410), it is the forces behind the demand and supply curves, rather than the schedules themselves, which must be investigated for a complete understanding of factor prices. Hence, although Marshall accepted the validity of the net productivity doctrine, he pursued a study of the interaction of the long-run sociological, historical, and economic forces which are the elements behind the supply and demand of the agents of production. (pp. 525-667) John Bates Clark In his book, The Distribution of Wealth,6 J. B. Clark conceived relative shares to be the cardinal problem of economic analysis. He began his book as follows:

24

AGGREGATE INCOME DISTRIBUTION For practical men, and hence for students, supreme importance attaches to one economic problem—that of the distribution of wealth among different claimants. Is there a natural law according to which the income of society is divided into wages, interest and profit? If so, what is that law? This is a problem which demands solution, (p. 1)

Clark attempted to demonstrate that the answer to this problem was: . . . where natural laws have their way, the share of income that attaches to any productive function is gauged by the actual product of it. In other words, free competition tends to give to labor what labor creates, to capital what capital creates, and to entrepreneurs what the coordinating function creates . . . . To each agent a distinguishable share in production, and to each a corresponding r e ward—such is the natural law of distribution, (p. 3) The Distributive

Stages

Clark indicated that distribution occurred in three distinct stages, (pp. 14-15) First income is divided by industrial group: agriculture, mining, transportation, retailing, etc. Secondly, it is divided by subgroup in each industry: dairy farmers, wheat farmers, etc. Finally, it is divided among the various factors within each subgroup. The divisions by group and subgroup depend upon market prices which are determined b y " . . . the law of market value. Market value, however, depends upon the relative quantities of the different articles that are produced . . . it depends on comparative group production." 7 What each agent of production in each subgroup receives, however, will be determined by its marginal product. Market prices tend, in the long run, to conform with normal or natural prices. " P r i c e s are at their natural level when labor and capital in one industry produce as much and get as much as they do in any other." (p. 16) When prices are normal, there are no profits for the entrepreneur; a laborer cannot increase his income by moving from one industry to another; and the r e turn per unit capital is the same in every industry. It is the mobility of the factors in response to factor price differentials which, in a competitive society, establishes normal prices, (pp. 16-17, 29) Clark distinguishes between a static and a dynamic society. In a static system,

NEOCLASSICAL PRODUCTIVITY DOCTRINE

25

men might conceivably produce to the end of time the same kinds of goods and they might do it by the same processes. Their tools and materials never change; and they might not alter . . . the amount of wealth that industry would yield. Social production can thus be thought of as static, (p. 28) Clark recognized that a static economy is unrealistic and that "all natural societies are dynamic." (p. 29) Nevertheless, he attempted to formulate a static law of distribution, since all the forces operating in an unchanging world would also be present in a dynamic system and " a r e even the dominant forces in it." 8 Thus, Clark argued: Static laws furnish the natural standards to which the incomes of economic groups and those of laborers and capitalists within them tend to conform. Dynamic laws, on the other hand, account, first, for the variations of actual incomes from these natural standards; and secondly, for the slow and steady change that, as time progresses, is taking place in the standards themselves, (p. 36) In Clark's static system there are two factors of production, social capital and social labor. He carefully separates social capital from capital goods. The latter consists of land and the physical tools of production, whereas the former is " a sum of productive wealth, invested in material things which are perpetually shifting—which come and go continually—although the fund abides." (pp. 119-120) This permanent fund earns interest, rather than rents. Rent and interest describe the same income in two different ways, for "rent is the aggregate of the lump sums earned by capital goods; while interest is the fraction of itself that is earned by the permanent fund of capital." (p. 124) In a similar fashion, Clark differentiates laborers from social labor. Social labor is " a permanent fund—a fund of human energy that never ceases to exist and to act. Men [however] are as perishable as capital-goods." (p. 157) It is the productive power of social labor and social capital that determines the wage rate and the rate of interest respectively. (pp. 157, 246, 266) In a static society, the social labor fund and the social capital fund are unchanging, and "the final productivity of labor, as it is employed in connection with the total fund of productive wealth in all . . . industries . . . sets the standard of wages." (p. 168) Similarly it is the product of

26

AGGREGATE INCOME DISTRIBUTION

the final unit of social capital that sets the rate of interest, (p. 187) How does one measure the final unit of social labor? It " i s a composite unit, consisting of some labor from every industrial group that the community contains." (p. 170) Similarly, the final unit of capital "does not, as a rule, consist of instruments of production in their entirety. It consists of elements in such instruments." 9 Distribution in a Static Society Using this "law of final productivity," Clark attempted to demonstrate that the income of a static competitive society is distributed between wages and interest payments without residue. In his now quite familiar diagrams (See Figures 2 and 3), he deduced that the summing of the marginal product of each factor multiplied by the number of units of the factor would exactly equal the total product. If BC (Figure 2) is the marginal productivity curve of social labor with a given fund of capital (A'D' of Figure 3), then the area under the curve BC is the total output of the community. If AD is the fund of social labor, then CD is the marginal product of labor, and AECD is equal to the total wage bill. Hence, by one mode of statement of the law [Figure 2], we get wages as the amount directly determined by this principle; it is the area AECD . . . . The earnings of all labor equal the product of the final unit of labor multiplied by the number of units. In [Figure 2] . . . interest \EBC] is a surplus, (pp. 200-201) If instead, we had first determined the return to capital via the marginal productivity of capital curve (C'B'), then if the social fund of capital equals A'D*, the total return to capital will be A*E'C'D1 and fi'B'C' is the residue which through competition goes to wages. Thus, by another mode of stating the law [Figure 3], we get interest as the amount that is positively fixed by the final productivity law, and wages are now the surplus that is akin to rent. These amounts together make up the whole static income of society.10 The possibility of a residual income (profits) is eliminated by definition. In Figure 2, the entrepreneur pays out AECD as wages and has EBC as a remainder; but in Figure 3 he has to

NEOCLASSICAL PRODUCTIVITY DOCTRINE

27

Output

wages

D

Labor

Figure 2

Output

interest A'

D'

Capital

Figure 3 Source: J. B. Clark, The Distribution of Wealth, p. 201.

pay out A'E'C'D' as interest. If the area EBC was larger than the area A'E'C'D', then pure profits would exist. However, we know that, by our hypothesis of perfect competition and, a complete static adjustment, there is no profit realized

28

AGGREGATE INCOME DISTRIBUTION by the entrepreneur as such . . . . The amount EBC is, therefore, not larger than is [A'E'C'.D'], . . . and all of EBC is the product of capital.11

In a competitive static economy, therefore, the profit share would be zero. 12 Distribution in a Dynamic World Clark indicated that there are five main forces which cause changes and progress in society, and which therefore, give rise to profit opportunities. These forces are: increase in population, capital formation, changes in technical knowledge, changes in the organization of labor and capital, and changes in consumer tastes, (pp. 400-401) Hence "from all these changes two general results must follow: first, values, wages and interest will differ from the static standards; secondly, the static standards themselves will always be changing." (p. 404) If each of these changes occurred individually in time, then the actual distribution would be quite different from the static standard. Clark maintained that they occur concurrently and therefore, he argued, they tend to neutralize each other so that society is kept "near the shape that static law calls for." (p. 420) Clark did not explicitly attempt to predict the effect of progress on the wage share. He did believe, however, that capital accumulation and/or technical progress would increase the marginal productivity of labor, thereby raising the natural rate of wages. He also expected the natural rate of interest to fall as the quantity of capital increased, (pp. 407, 409-410) Profits arise when improvements in industry increase the total income of the economy. (Thus, entrepreneurs can obtain a share of income in a dynamic world.) These profits are temporary, however, and pass via competition from the hands of the entrepreneurs to increments in wages and interest payments, but they "add themselves chiefly to wages." 13 This implies that the major proportion of all increments in the community's real income will ultimately accrue to wages—that aggregate wages will increase by larger amounts than aggregate rents. Therefore, the wage share will, sooner or later, be larger than half the national income. Thus Clark felt he had also established a law for the division of "the gross earnings of [a dynamic] society into three generic shares that are unlike in kind. It causes the whole annual gains of society to distribute themselves into three great sums—

NEOCLASSICAL PRODUCTIVITY DOCTRINE

29

general wages, general interest and aggregate profits." In a static world, however, only wages and interest would remain. The "Adding-Up"

Problem

If the share of the total product that each factor obtains is determined by its marginal productivity multiplied by the quantity of factor employed, and if it is possible to determine each factor payment independently, then it remains to be proven that there will be no residual share. The problem of demonstrating such a relationship is called the "adding-up" problem. Philip Henry Wicksteed, in 1894, was the first to demonstrate a set of conditions that would eliminate any residual share when each factor received payment equal to its marginal productivity. 15 He required that the production function be linear and homogeneous with respect to all its variables. 16 Wicksteed indicated, however, that if all the factors of production are included in a physical production function (where the dependent variable is measured in physical rather than value terms) then the linear and homogeneous requirement is a " t r u i s m [that] has no economic significance, for what we are interested in is not the amount of material product but the amount of industrial vantage that command of the product confers on its p o s s e s s o r . " (p. 33) To obtain a production function that is linear and homogeneous for the firm, with output in value terms, Wicksteed assumed "perfectly free competition." Then, for a small increment in output due to a small proportionate increase in all factors, the market price will be approximately unchanged, and therefore, the increase in value output will be directly related to the increment in physical product. In this case, = P

(1)

where P is the value of output, and A, B, and C are the various factors of production, and therefore "if every factor of production draws a remuneration determined by its marginal efficiency or significance, the whole product will be exactly distributed." 1 7 Thus Wicksteed concluded: Our law may be regarded as perfectly general. In its strict form it merely a s s e r t s that the sum of the actual dP — • Ks cover the actual product. In this form it is not a uK

30

AGGREGATE INCOME DISTRIBUTION law of distribution but an analytical and synthetic law of composition and resolution of industrial factors and products which would hold equally inRobinsonCrusoe's island, in an American commune, in an Indian village ruled by custom, and in the competitive centers of the typical modern industry, (p. 42)

Letting P ' be the "total communal product," Wichsteed states: In its practical form the law asserts that, in a fully competing community, no group of factors will willingly relinquish to any one of their number a larger remuneration than is fixed by the formula dP/dK, nor will any factor willingly accept for itself a smaller share than is fixed by the formula dP'/dK. There is equilibrium, therefore, dP

when we have for any industry ^

dP'

*or

ever

Y K>

an
l. 6 Every decrease in the wage rate must, therefore, lead to an increase in the aggregate wage bill, although the wage share would remain constant. For example, assuming k = .75 and therefore E = 4, if the quantity of labor employed increases by 1 per cent, ceteris paribus, total output will increase by .75 per cent, while the marginal product of labor will decline by .25 per cent, so that labor will receive 75 per cent of the increment in output. Thus, the constancy of shares will be maintained. The Statistical

Analysis

Using index numbers of fixed capital (C) and of labor (L), and Day's index of physical production (P), Cobb and Douglas originally found the values of the parameters for the period 18991922 to be: 7 b = 1.01 k=

.75

Further statistical studies of both time series and c r o s s - s e c tional data for the United States, Australia, South Africa, and New Zealand, using the more generalized form of the function, have shown amazing constancy of the parameters. For example, different time series data for the United States have shown k to

MARGINAL PRODUCTIVITY DOCTRINE

39

vary between .63 and .81, while j varied between .15 and .30 and ft + j varied between .93 and 1.04. Cross-sectional studies for the United States based on industry aggregates show that ft and j average .63 and .34 respectively. 8 Douglas has compared the actual share of wages and salaries in the value of net output with the computed values of ft and k/(k + j) for these countries and has found that the calculated parameters are consistently good estimators. For example, in the United States, ft averages .63 and ft/(ft + j) averages .65, while labor's actual share was .605 for the period of observation. He therefore suggests that the degree of agreement between the value of k and W/P is most striking and that the results conform to what normally would be expected to occur under the competitive productivity theory. Hence this constitutes a still further reinforcement to the productivity function itself. 9 An

Evaluation

Several criticisms of the theoretical assumptions underlying the Cobb-Douglas scheme have appeared in the literature. Durand10 was one of the first to object to the form of the production function used by Cobb and Douglas in their original study. Durand reproached them for not determining the exponents for labor and capital (ft and 1-ft respectively) independently. (Of course, this criticism is not applicable to the latter studies where the more generalized form of the function was used.) Furthermore, Durand noted, land had not been included as an independent variable. This omission could be justified only if the supply of land was constant during the period of observation. But, Durand argued, if this latter supposition was correct, then a proportionate increase in both labor and capital should yield diminishing returns rather than the constant returns suggested by the function. Horst Mendershausen condemned the assumptions of constant factor utilization and the absence of technical progress between 1899 and 1922 (the period covered in the original empirical study). He stated: These assumptions are manifestly in contradiction to all that economists know about the industrial development during this period. Professor Douglas made strong reservations with respect to the realism of his hypothesis of a constant production function. But nevertheless he

40

AGGREGATE INCOME DISTRIBUTION maintained it without advancing decisive arguments in its favor. The reiterated references to the good fit of the function to the data is in fact a petitio principii, since only if this hypothesis is justified can the function claim to be taken as a production function. 11

The empirical data and results of the Douglas studies are also open to severe criticisms. Mendershausen has questioned the validity of the use of a statistical index of fixed capital which is really an estimate of "fixed capital used and idle." 12 If there is any excess capacity during the period of observation, then the interpretation of the capital coefficient is obscure. In Chapter III, we indicated that value rather than physical productivity is important in distribution theory. Douglas, however, uses the Day index of physical production as his dependent variable. 13 Such an index would be applicable only if there was no change in market prices. Furthermore, it is argued below that the interpretation of exactly what this index does measure is obscure, and the construction of the index introduces a bias in the empirical results. The Day index is based on a sample of single commodities which are used to calculate individual "indices of relative production." 14 These indices of relatives are then weighted by the aggregate value added for each product and combined into an index of physical production. 15 It has been pointed out that all such indices suffer from two fundamental limitations, (a) a value weighting system which assumes a constant income distribution, and (&) the assumption of no change in the pattern of production. Thus, A. F. Burns indicates "one can hardly speak (except in the vaguest terms) of trends of general production and any inquiry into secular movements of general production will rest on an insecure logical foundation." 16 The use of an index which assumes a given and constant distribution of income in the analysis of a long-run theory of relative shares introduces an obvious bias for constancy of class shares. Hence the reliability of all the empirical time series evidence is in doubt. Despite the criticisms of the underlying theoretical assumptions and the questionability of the statistical indexes used, Douglas does get a surprisingly excellent statistical fit. How can one ejqplain the apparent paradox? According to Mendershausen, examination of the data used in the original Douglas study showed that each pair of variables was highly correlated, i.e., that the variables formed " a nearly

MARGINAL PRODUCTIVITY DOCTRINE

41

perfect multicollinear set." 1 7 If multicollinearity is present, then the " l e a s t - s q u a r e s " method of fitting a regression line cannot yield a unique solution; there are an infinite number of combinations of regression coefficients which will give a good fit. Therefore, Mendershausen concluded that there is not "one single determinate systematic relation in this set of three variates." 1 8 Furthermore, Mendershausen demonstrated that the multicollinearity was due to the rates of growth of all three variables over time, and therefore the Cobb-Douglas k was merely an expression of the relationship between the differential rates of growth of the variables. 19 In a more recent reconsideration of the "Meaning of the Fitted Cobb-Douglas Function," Phelps Brown comes to the same conclusion as Mendershausen, i.e., that such a fit has not yielded, and can not yield, the statistical realization of a production function. It can describe the relations between the historical rates of growth of labor, capital and product, but the coefficients that do this do not measure the marginal productivity.20 Phelps Brown has also criticized the fitting of the CobbDouglas function to cross-sectional data. He believes that there is a widespread tendency for L, C, and P to change in the same proportion between industries. In his words: we expect that, in the manufacture of any one product, a larger scale of output will generally go with bigger equipment per worker; but when we move from one industry to another in the pages of the census, we change not merely the size, as measured by the labor force, but the product and the technique, and there seems to be no general r e a son why products that occupy a larger number of workers should systematically use more, or less, capital per head than those that occupy a few . . . . If this is so, the way is clear for L, C, and P all to vary in the same proportion between one industry and another, (p. 556) If this is true, then the cross-sectional results are also subject to the criticism of multicollinearity. The consistent relationship between the computed k (of the cross-sectional censuses) and the actual wage share has, according to Phelps Brown, a simple explanation. The output of each industry is in t e r m s of net value product, which is equal to the total earnings of labor plus the total return to "capital" for each industry. Thus for any industry, i, we may write

AGGREGATE INCOME DISTRIBUTION

42 P. = wL, + rC. i i i

(9)

"where w is the average earnings per employee, and r, the average rate of return on capital, over all industries." (p. 556) Hence, given w and r, the difference in net product between any two industries depends upon the proportion of labor and capital used in each. If we compare any two industries that approximately satisfy equation (9)21 and that have equal capital inputs, then the difference between the net products "will always approximate to the compensation at the wage rate w of the difference in labor intake. The Cobb-Douglas k, and the share of earnings in income, will be only two sides of the same penny." (p. 557) Thus, Phelps Brown concludes that to the extent equation (9) holds, the apparent differential productivity of factors is only the projection of their prices, and cannot be measured separately to see whether their prices conform . . . . it seems unlikely that the differential contributions of factors to the physical product have been isolated by any interindustry comparison, (p. 559) The Significance of the Cobb-Douglas Function What then may we conclude about the significance of the Cobb-Douglas analysis? Its theoretical and statistical foundations have been shown to be insecure. Its proponents' main defense is the "surprising degree of agreement between results for the United States, Australia, and South Africa. . . . It is hard to believe that these results can be purely accidental." 22 Yet, the statistical indeterminance of multicollinearity and the inapplicability of the underlying theoretical assumptions should make even the most naive operationalist wonder whether the test of good economic theory is only measurability and an apparently fortuitous (in retrospect) predictability. Marginal Productivity as a Theory of Relative

Shares

The analysis of Chapters III and IV indicate that neoclassical marginal productivity doctrine has not solved the conundrum of relative shares. Some economists, such as Walras 23 and Samuelson,24 believe that marginal productivity cannot resolve this question. Boulding succinctly stated the problem when he wrote that the marginal productivity doctrine is

MARGINAL PRODUCTIVITY DOCTRINE

43

essentially. . .micro-economic. . . its real significance is that it gives us a useful first approximation theory of the demand of firms for inputs . . . . Because demand and supply curves cannot be aggregated for the whole economy . . . we need, therefore, a macroeconomic theory of distribution that is a direct attack upon the distribution of the income of society taken as a whole rather than one dealing with individual items which cannot be added.25 The marginal productivity doctrine will have macroeconomic implications only if the level of total output is given. For then, as Hicks has indicated, the major "consequence of a change in factor prices is the change in the proportion of factors employed relative to output—the effect of output itself cannot be made determinate at all without some reference to demand conditions being brought into the argument at once." 26 The neglect of changes in aggregate demand conditions reduces the usefulness of neoclassical productivity theory as an explanatory or predictive device for a theory of relative shares.

V Monopoly as a Determinant of Class Shares In this chapter, we ming primarily from of monopoly with the views are presented, a suggested extension

shall discuss the modern attempts, stemthe works of Kalecki, to relate the degree determination of class shares. After his we shall consider several criticisms, and of his ideas. Michael Kalecki

Kalecki, in several writings, 1 has attempted to demonstrate that the relative wage share of manual labor in the gross homeproduced national income is inversely related to both the degree of monopoly and the ratio of raw material costs compared to labor costs. While his emphasis has altered somewhat over a period of fifteen years, Kalecki still ascribes to monopoly one of the main roles in holding constant the relative share of wages in the national income. In his 1939 essay, the degree of monopoly is estimated by the Lerner measure of monopoly power—the ratio of the difference between price and marginal cost compared to price.* By 1943, his index of monopoly power, ¡1, was the "average percentage gross margin" and reflected "not only the changes in the degree of market imperfection and oligopoly and the bottlenecks in available capacities, but also changes in the rates of prime selling costs." 3 By 1954, 1a had been reduced to the ratio of aggregate proceeds to aggregate prime costs. 4 Let us consider the implications of these definitions in more detail. Monopoly and the Wage Share In the earliest formulation of his theory, building from the microtheory of the firm, Kalecki assumes imperfect competition 44

MONOPOLY AS A DETERMINANT

45

and the existence of idle capacity; therefore, the short-run marginal cost curve (MC) is taken to be horizontal and coincident with the short-run average variable cost curve (AVC) up to capacity (OA in Figure l). 5 Marginal cost is assumed to consist solely of wages plus raw material costs. Thus, the total wage and raw material bill is equal to LMNO in Figure 1 when output in ON. The degree of monopoly is defined as: =

p -

MC

(1)

where p is the unit price of the product. Assuming profits are being maximized in the short run, i.e., that the short-run marginal revenue equals the short-run marginal costs at the equilibrium output; then /i is equal to the reciprocal of the elasticity of demand.6 If the degree of monopoly is given, then at all out-

Price

O

N

A

Quantity

Figure 1 Source: Kalecki, Readings in the Theory of Distribution, p. 207.

Income

AGGREGATE INCOME DISTRIBUTION

46

puts below capacity "the relation of price to marginal cost is a 1 »7 1" * " The shaded area of Figure 1 represents profits, interest, depreciation, and salaries, or what Kalecki calls "gross capitalist income and salaries." It is equal to the difference between price and marginal cost multiplied by the output of the firm. The unshaded area representing the wage and raw materials bill is equal to the marginal cost multiplied by the output. Given the degree of monopoly, the ratio of the shaded to unshaded area is a constant at any level of output below capacity. Since the price equals the average entrepreneurial income (e a ) plus average overhead of interest, depreciation and salaries (o a ) plus average wage (wa) and average raw material costs (r a ), and since marginal costs consists of marginal overhead (om) plus marginal wage (wm) and marginal raw material costs ( r m ) , then p - MC = ea + (oa - om) + {wa - wm) + (ra - rm) (2) Since marginal cost is assumed to be constant,then w a - w m =0, and ra - rm = 0. If the marginal overhead cost is assumed negligible, then p-MC

= ea + oa

(3)

Multiplying both sides of equation (3) by the output of the firm (*), Kalecki obtains the gross capitalist income and salaries as * (p - MC) =x {ea+ oa)

(4)

Also, multiplying equation (1) by output yields xpii

= x (p - MC)

(5)

Combining equations (4) and (5), and summating over the economy Z xp iu= Tx (p - MC) = Tx (ea + oa)

(6)

and writing E for aggregate entrepreneurial income and O for aggregate overhead costs, Kalecki obtains: S xp M = E + O

(7)

Defining aggregate turnover as T = S xp, Kalecki finally derives E +O M = rp

, . (8)

MONOPOLY AS A DETERMINANT

47

where 71 is a weighted average of the degree of monopoly in the economy. If A is the gross home-produced national income, then it is also true that A 3 E + 0 +W

where W is the aggregate wage bill. 8 Hence, equation (8) can be written as

Multiplying both sides of equation (9) by T/W yields: - T -A ~ W ^ W

W

Rearranging terms, Kalecki obtains: i — i - r

a»)

From equation (10) Kalecki concludes that the wage share is inversely related to the degree of monopoly and the ratio of raw material costs compared to wage costs. In his words: [an] increase in the degree of monopoly reduces the relative share of manual labour. The expression increases not only because of the rise in /i, but also because T/W is increased by a rise in the degree of monopoly since this raises prices in relation to wages. . . . It is easy to see that a rise in the price of "basic raw materials" in relation to wage-cost must result in an increase of all prices in relation to wage-cost and consequently in an increase of T/W. . . . Thus it is obvious from the formula . . . that with a given degree of monopoly . . . a rise in the price of "basic raw materials" as compared with wagecosts by raising T/W must lower the relative share of manual labour. 9 A

Reformulation

To overcome some of the criticisms 10 of his first formulation of the monopoly-wage share thesis, Kalecki has attempted a new approach involving the elimination of the Lerner measure of the degree of monopoly and the deletion of the assumption "that the

48

AGGREGATE INCOME DISTRIBUTION

firm attempts to maximize its profits in any precise sort of manner." 1 1 In his restatement, the individual f i r m ' s price is based on average prime costs, which are assumed constant over the relevant range of output, and the weighted average price of all firms in the industry, 12 i.e., p = mu + rip

(11)

where p is the unit price set by the firm, u is the unit prime costs, and ~p is the weighted average price in the industry (weighted for each firm by its respective output and inclusive of the firm in question). Both m and n are positive coefficients and n must be less than unity.13 Furthermore, Kalecki notes: "The coefficients m and n characterizing the price-fixing policy of the firm reflect what may be called the degree of monopoly of the firm's position." (p. 13) Kalecki obtains an equation similar to (11) for each firm in the industry. Each equation is weighted by the respective firm's output; all are added together and then divided by the output of the industry to obtain: p = mu + np

(12)

where the bar over a symbol indicates a weighted average. Rearranging terms, Kalecki obtains: (13) Equation (13) indicates that the ratio of the average price in the industry to the average unit cost depends on m / 1 - n which Kalecki chooses to call the average degree of monopoly. Hence if the degree of monopoly rises, price increases relative to unit prime costs. To develop equation (13) as a basis for his theory of distribution, Kalecki remarks: The ratio of average price to average prime costs is equal to the ratio of the aggregate proceeds of industry to aggregate prime costs of industry. It follows that the ratio of proceeds to prime costs is stable, increases or diminishes depending on what happens to the degree of monopoly. (p. 16) Kalecki then proceeds to link the ratio of proceeds to prime costs to the relative wage share in the value added of an industry. His derivation may be clarified by using the following symbols: 14

49

MONOPOLY AS A DETERMINANT W = the aggregate wage bill for the industry M = the aggregate raw material bill for the industry O = the aggregate overhead costs for the industry P = the aggregate profits for the industry

A = the aggregate proceeds or the sales value of the industry's output =W+M+0+P ft = the ratio of aggregate proceeds to aggregate prime costs, i.e., the degree of monopoly If we multiply both sides of the identity A = by W + M/W + M, then we obtain: a

W T W

=

w

+

M

+

0

+ p

W+M+0+P,

(14)

Writing ft = A/W + M, equation (14) can be stated as: k(W+M)-W-M

= 0 + P

(15)

which amounts to: overhead + profits = {k - 1) (W + M)

(16)

If we add the total wage bill to both sides of equation (16) and then divide by W, from the reciprocal of the resulting equation we obtain the wage share (w) in the value added of the industry as: W

=

W W + (ft - 1) {W + M)

(17)

Denoting the ratio of the raw materials bill to the wage bill by j, and dividing both numerator and denominator of (17) by W, Kalecki obtains: W

=

l

+

(k-\)

(j + 1) '

(18)

Hence, Kalecki remarks: It follows that the relative share of wages in the value added is determined by the degree of monopoly and the ratio of the materials bill to the wage bill. (p. 28) That this is so can be seen by considering that ft must be equal to, or greater than unity, if proceeds are to at least cover variable costs. Thus, when ft = 1, total proceeds equals the

50

AGGREGATE INCOME DISTRIBUTION

wage plus raw materials bill, the sum of overhead plus profit equals zero, and the wage bill is the value added by the industry. When k > 1, on the other hand, the wage bill is a positive fraction of the value added, and the higher the ratio of the raw materials bill to the wage bill, the lower the wage share in the value added for any given value of k. Kalecki then obtains an equation similar to (18) for each industry in the economy and aggregates these equations by weighting each industry's formula by the importance of that industry in the total proceeds. Thus he concludes, "broadly speaking, the degree of monopoly, the ratio of the prices of raw materials to unit wage costs and industrial composition are the determinants of the relative share of wages." 1 5 An Alternative

Approach

to

Macrodistribution

Kalecki has also derived a theory for the determination of aggregate profits 16 (non-labor income) which parallels later statements of Mrs. Robinson and Mr. Kaldor, and which has not received as much attention or criticism as his monopoly-wage share thesis. In his theory of profit determination, Kalecki assumes a closed laissez-faire economy where the role of government is negligible. He also assumes that there are only two economic classes, workers and capitalists. Under these suppositions, Kalecki indicates that the value of the gross national product (F) is equal to the value of gross investment plus the value of aggregate consumption, i.e., V = I+Cp

+ Cw

(19)

where I is the value of gross investment, Cp is the consumption expenditures of the capitalists, and Cw is the consumption spending of the workers. Gross national product, however, is also equivalent to aggregate wages (W) plus gross profits (P) where the latter "includes depreciation and undistributed profits, dividends and withdrawals from unincorporated business, rent and interest," 1 7 that is: V = W + P

(20)

Kalecki assumes that workers spend their entire income on consumption goods, i.e., W = Cw. Hence, combining (19) and (20) yields: P = I + Cp

(21)

MONOPOLY AS A DETERMINANT

51

Thus, Kalecki draws the following vital inference: What is the significance of this equation?. . . it is clear that capitalists may decide to consume or to invest more in a given period than in a preceding one, but they cannot decide to earn more. It is, therefore, their investment and consumption decisions which determine profits, and not vice versa, (pp. 45-46) This conclusion led Kaldor, at a later date, to paraphrase Kalecki's theory as indicating that "capitalists earn what they spend and workers spend what they earn." 1 8 If valid, such a proposition would have some major implications on the functioning of our economy.19 Kalecki lists two qualifications to the inference drawn from equation (21). First, if the period of observation is small, then the capitalists' actual investment and consumption expenditures are determined by decisions reached in prior periods. Unexpected inventory changes, however, may cause actual investment in the period to differ from intended investment, although in Kalecki's view "the importance of this factor . . . seems to have been frequently exaggerated." (p. 46) A more important reservation, he argues, comes from the fact that "consumption and investment decisions will usually be made in real terms, and in the meantime prices may change." 20 Thus, the variables in equation (21) should be deflated by appropriate price indices to obtain the " r e a l " concepts. Kalecki attempts to blend his aggregate profits theory with his monopoly-wage share theory as follows: Since profits in a given short period are determined by capitalists' decisions . . . formed in the past, the factors determining the distribution of income will affect not real profits but the real wage and salary bill—and consequently national output. If, for instance, the degree of market imperfection . . . increases, and, as a result, so does the ratio of profits to wages, real profits do not change, but the real wage bill falls, first, because of the fall in real wage rates, and secondly, because of the consequent reduction in the demand for wage goods, and thus output and employment in the wage-good industries . . . . Percentage gross margins increase, but the national output falls so much that, as a result, the real total profits remain the same. 21

52

AGGREGATE INCOME DISTRIBUTION

Criticism

and Appraisal

A great deal of critical comment on Kalecki's degree of monopoly-wage share thesis has appeared in the literature. In this section, we will analyze the major criticisms of the monopolywage share thesis. The criticisms and implications of the aggregate profits theory will be considered in Chapter VII, along with the theories of Robinson and Kaldor. Underlying Kalecki's degree of monopoly theory is the a s sumption that the short-run marginal cost curve of the firm is horizontal and coincident with the average variable cost curve for the relevant range of output (up to practical capacity) for most f i r m s , and therefore, as a f i r s t approximation, for the entire economy. This constancy of costs is due to (a) the presence of idle capacity because of imperfections in the product market, and (b) the absence of monopsony in the labor and raw materials markets. Keynes, in a related context, has criticized Kalecki's a s sumption of constant marginal costs. 2 2 Keynes believed that marginal user costs will increase as output r i s e s (even though we are operating below capacity), and therefore, the short-run marginal cost curve would be upward sloping. (It may also be so inclined because of the use of less efficient labor and equipment as output increases.) Mrs. Robinson, on the other hand, would not include user cost in marginal cost. She has written: The loss of earning power of plant due to the passage of time (including expected obsolescence) is often hard to distinguish from user-cost, and when output is running within normal capacity of plant it is better to throw u s e r cost in with amortization than treat it as an element of prime cost. 2 3 A much more serious criticism of Kalecki's constant m a r ginal cost assumption has been raised by Reder. 2 4 The gist of his comment is that even if all f i r m s in an industry have constant prime costs, the industry's supply curve may be positively inclined. If, for example, the ordinate intercepts of the marginal cost curves of some f i r m s in each industry are higher than the intercepts of others in the industry, then when the output of the industry was at low levels, the low cost f i r m s would be the predominant ones. If demand increased rapidly, however, these latter f i r m s would, in the short run, be unable to expand their output in proportion to the increase in demand. Hence, the output of the high cost f i r m s would expand more than proportionately,

MONOPOLY AS A DETERMINANT

53

causing the marginal cost curve for each industry to rise with an increase in output, even though there was idle capacity. Since Kalecki's thesis is based on a horizontal supply curve, he would have to assume that the marginal costs are constant and equal for each firm, a rather heroic assumption. In the original formulation of the theory, entrepreneurs are conceived to be profit maximizers. The ratio of price to prime costs, therefore, is uniquely determined by the elasticity of demand. Given constant costs, this ratio is assumed constant at all levels of output below capacity. This implies that all changes in total output (below capacity) would be due to isoelastic shifts in the demand curves of the individual firms. There appears to be little justification for this supposition for either the individual firm or the economy as a whole.25 Kalecki claims that his formulation explains the long-run determination of relative shares "even though it was deduced on the basis of, so to speak, pure short-period considerations." 28 He believes that surplus capacity can continue to exist even in long-run equilibrium because economies of scale may prevent the firm from reducing the size of its plant, while the diversity of demand may prevent expansion to capacity. Thus, Kalecki argues that changes in the "basic data" (e.g., technical progress) will not affect relative shares " a s long as the degree of monopoly is unaltered" and idle capacity exists. 27 This statement tends to obscure the fact that innovations will lower marginal costs and hence, if the degree of monopoly is to remain unchanged, it would imply synchronous fortuitous changes in the demand and marginal revenue curves. One cannot evolve conclusions about macrodistribution from microdemand and supply curves—at least not without substantial modification and amendment.28 The individual product demand curve is usually drawn on the assumptions of given tastes, given total income (and the distribution of it), and all other prices constant or moving in some prescribed manner. Hence, these curves cannot be used in analyzing changes in macrodistribution, for the individual curves would have to be redrawn with every change in total income or its distribution.29 Similarly, the supply curve of the firm is based on some assumption as to the output of the industry and it will change if total output changes.30 Kalecki, in his later formulation, dropped both the Lerner monopoly measure and the assumption of profit maximization. The degree of monopoly is simply a ratio of price to unit costs, and is aggregated on an industry basis. But how does one define

54

AGGREGATE INCOME DISTRIBUTION

an industry in monopolistic competition? One may speak of a "group of firms" 3 1 having a high elasticity of substitution among their products, but any boundary line must be an arbitrary one. Hence, the weighted average price for an industry, upon which Kalecki builds his new concept of the degree of monopoly, is a nebulous concept. On the other hand, defining the degree of monopoly as the ratio of aggregate proceeds to aggregate prime costs reduces it to a tautological explanation of class shares. In a closed economy, excluding user costs, the only aggregate prime cost is wages, and therefore the difference between aggregate proceeds and aggregate prime costs must, by definition, accrue to gross profits. Thus, even though the latest formulation uses fewer assumptions to arrive at the same conclusion, it explains less than the previous attempt. Ashok

Mitra

Mitra, unable to empirically verify Kalecki's original thesis, has suggested an extension of Kalecki's ideas into a more complex model of relative share determination. 32 Mitra attempted a crude empirical test of the degree of monopoly thesis, (pp. 34-51) Using 1871-1912 data for the United Kingdom, Mitra endeavored to measure p - MC/p separately for the home and export markets. For p, in the former sector, a cost of living index was used, while an export price index was used in the latter. To obtain a value for MC, the marginal cost function was assumed to have the form, MC = giL + g2r, where L is the average money wage rate, r is the price level of imports, gi is the "labour quota," and g2 is the "import or raw material quota." The labor quota is defined as "the marginal significance of labour performance in the production function" (p. 34)—it is the marginal input of labor for an increment in output. The import quota is similarly defined. By calculating a linear regression equation, P - a + giN, where P is the value of total output and N is the level of labor employment, Mitra determined the magnitude of gi. Similarly, by calculating P = b + g2M, where M is the value of total imports, the raw material quota was obtained.33 Plugging these calculated regression coefficients into the linear MC function described above, Mitra arrived " a t the marginal cost of the economy as a whole." (p. 34) Having calculated MC and armed with the above-mentioned price indices, Mitra obtained meas-

MONOPOLY AS A DETERMINANT

55

ures of the degree of monopoly in the two markets. The empirical results led Mitra to conclude: contrary to all theoretical expectations, the degree of monopoly does not vary much over time . . . . These illustrations should certainly prove sufficient to cast some doubt on the basis of Kalecki's assertion that the secular stability in the share of wages in national income is maintained by simultaneous antipodal movements in the degree of monopoly and the price level of raw materials. For it becomes obvious that whereas historically the price level of raw materials has been subject to violent fluctuations, there is a particular inertia which rigorously checks any runaway movement in the degree of monopoly, (p. 41) This is certainly a remarkable result, for if true, it would mean that despite the growth of industrial concentration during the period, the degree of monopoly has not varied. The crudeness of the statistical technique and the controversial forms assumed for the cost and underlying production functions, 34 however, diminish the creditability of the results. Mitra then establishes a model of his own based onCournot's microanalysis. In Mitra's system, the wage share is a function of the following variables: the labor quota—the quantity of labor 35 per unit of output (gi), the raw material quota—the quantity of imports per unit of output (gz), the ratio of money wages to product prices—the real wage rate (s), the number of sellers in the market (n), the zero demand price—the price where a zero quantity of output would be demanded (/30), and the rate of depreciation (&). The model is derived as follows:36 Mitra assumes that the ¿th entrepreneur in an imperfectly competitive industry can sell x^ output at price p and at a cost c{xj). Profits Zj will then be: z t = pXi - c{xi)

(22)

The necessary condition for profit maximization is

dzj _ p | x dp xi dxi Using an inverse linear demand function, p - fio - P X f , where /3o is the zero demand price and /3 is the flexibility of demand, it follows that

56

AGGREGATE INCOME DISTRIBUTION

Therefore, equation (23) may be rewritten as: p - p xi - c' (*¿) = 0

(25)

Assuming that all entrepreneurs have a similar cost function of the type c(Xj) = co + ci X{ where c\ is the marginal cost, and aggregating for the economy, Mitra obtains: np - p x - nci = 0 or n(p - d) = P x

(26)

where n is the total number of sellers in the market. Thus aggregate proceeds minus aggregate prime costs equal the "flexibility" of demand multiplied by aggregate output, with the "flexibility" defined as the reciprocal of the elasticity of demand. When profits are being maximized, however, Lerner's measure is also equal to the reciprocal of the elasticity of demand; therefore equation (26) is comparable to Kalecki's equation (5) above. Substituting fio - P for px in equation (26), Mitra obtains: p

_ nci + Po ~ « + 1

„\

(0 (27)

Dividing (27) by n and transposing n + 1 yields p (1 + 1/n) = c i + Po/n

(28)

Mitra assumes that depreciation allowances are a component of prime costs, 3 7 and that the same rate of depreciation (k) exists for all entrepreneurs, therefore Ci = gxL +g2r

+k p

(29)

where kp is the rate of depreciation per unit of product. Substituting the real wage rate s = (L/p) into (29), and then (29) into (28), and finally rearranging terms, Mitra obtains p=

^r + Po/n 1 + 1/n - g!S - k Since the total wage bill is (giL)x and the net national product i s [ ( l - k)p - g2 r]x, where x is output, then the relative share of wages can be defined as: 1

y

giL (1 - k)p-g2r

= ~ (1

gisp -k)p-g2r

,

n

57

MONOPOLY AS A DETERMINANT

By multiplying the numerator and denominator of the right-hand side of (31) by the reciprocal of price, and then substituting from equation (30) for p, Mitra obtains: the wage share =

- g2r sgigz r +, (1 - *) ft n

(32)

Mitra argues that equation (32) gives all the instrumental variables in the distribution of national income—the number of sellers and the zero demand price indicate the market relationships, the labor and import quotas reflect the structure of production, and the wage-price ratio connects the labor and product markets, (p. 59) Mitra then partially differentiates equation (32) with respect to each independent variable and arrives at the following ceteris paribus conclusions: (pp. 65-66) First, an increase in the wage-price ratio (s) will increase the wage share. Since s represents the real wage rate, any increase in it, with a given level of output and employment, must increase the wage share. Secondly, an increase in the labor quota will increase the wage share. But this is a tautology, since any increase in employment with a constant level of output and real wage rate, must increase the wage share. Thirdly, any increase in the rate of depreciation or in the raw material quota will increase labor's relative share. Since depreciation and imports are, in Mitra's model, subtractions from the value of gross output, then the greater either of these items, with constant values for gross output and aggregate wages, the smaller the net output will be and the larger the wage bill as a proportion of the net figure. Mitra also presents his model geometrically (Figure 2). In his words: Let OM be the actual output and PM the price, so that gross national income is represented by the rectangle PQOM. OMJE is total depreciation allowances and GEJH is the import volume, w.b. is the wage bill line giving aggregate labour income at different levels of output and is partly shapedby the technical coefficient [gi], and partly by the ratio at which the money wage rate and price level stand to each other, (p. 60) Hence SGHT is the aggregate wage bill and QPHG is the net national income. Once output is determined, the wage share can

AGGREGATE INCOME DISTRIBUTION

58

Price ßo

\ t \

P'

H J

M

Mi

\

Output

Figure 2 Source: Mitra, The Share of Wages in National Income, p. 60.

be obtained from the diagram. According to Mitra, output (OM) is determined via the height of the zero demand price and the number of sellers. Any increase in the number of competitors, he argues, will increase total output. When there is an infinite number of sellers, output will be OMi and the wage share equals unity, (p. 61) Mitra's approach raises more questions than it seems to answer. His diagram cannot be used for output in general, while if it applies to the firm or the industry, then he must present some means of aggregation. Mitra attempts to laterally sum individual demand curves, and although a zero demand price may have a meaning for an individual firm or industry, it is senseless to speak of the zero demand price for national output. Furthermore, it should be noted that Chamberlin has demonstrated that an increase in the number of sellers may raise,

MONOPOLY AS A DETERMINANT

59

rather than lower, prices in a world of monopolistic competition. 38 Mitra's belief that an economy which is predominantly monopolistic will have a smaller total output than if it was competitive is based on a fallacy of composition. As Mrs. Robinson has indicated: When we are considering one industry in isolation, we can find the monopoly output with the existing demand curve, but if output is restricted in all industries all demand curves will alter. The method which applies to one industry separately cannot be applied to all taken together.39 Monopoly and Relative Shares:

A Tenative

Conclusion

It follows from our preceding comments that neither Kalecki nor Mitra has sufficiently defined the relationship between monopoly and relative shares. The difficulty is at least partly due to the fact that a monopoly position is not necessarily a profitable one. It is quite possible that if part of the economy is monopolistic and part competitive, then the income of all those engaged in the former sector may be higher (or lower) than their counterparts in the latter sector. It is fallacious to assume that the cost conditions (unit, marginal or hourly) of the firm r e mains the same when it obtains a greater control over the market. 40 Furthermore, there is no easy way of defining the degree of monopoly in the economy or predicting how it will change when output alters in response to macroeconomic variables. As a result, it has been suggested that we assume that the degree of monopoly is constant at all levels of output.41 This, however, is a temporary dodge and much more work remains to be done on the subject. On the positive side, this chapter has shown that the higher prices are relative to money wage rates, at any given level of output, the lower the relative wage share. Increases in the degree of monopoly, however, will change the level of output by reducing the effective demand of workers.

VI Aggregate

Demand

and

Macro distribution'. and Boulding

Keynes

Despite Keynes' recognition in The General Theory and that the two major economic problems of a capitalist society are full employment and the distribution of income, 1 it is not inaccurate to say that he applied the theory of aggregate demand mainly to the former issue. Distribution aspects appeared only implicitly in his emphasis on diminishing returns or in his statements about money wage changes and their influences. 2 In the Treatise on Money, however, among the "many skins which I have sloughed." 3 Keynes had the germinal ingredients of a theory of aggregate distribution, at least as far as profits were determined. In this chapter, we shall examine Keynes' earlier ideas and then their later development by Boulding. John Maynard

Keynes

In the Treatise, Keynes directs attention to some fundamental relationships between profits, the price level, investment, and consumption. (I, pp. 123-129) Profits are defined as the difference between the sales value of output and its cost of production, where the latter consists of wages, rents, interest, and. the normal remuneration of entrepreneurs. The money income of society is defined as equal to the total costs of production as defined above. The flow of money income is dichotomous in nature and may be separated into an earnings stream, subdivided between: (a) the proportion earned in the production of consumer goods and (b) the proportion earned in the production of investment goods; as against an expenditures stream involving: {•a) the proportion spent on consumption goods and (b) the proportion of income that is saved. 60

AGGREGATE DEMAND AND MACRODISTRIBUTION

61

On this basis, Keynes develops the proposition that if the proportion of total income earned in the production of consumption goods is different from the proportion expended on consumer goods, then the sales value of these goods will differ from their costs of production. The difference is, by definition, the profits of' the consumption sector. As a rule, the earningsoutlay divisions are not likely to be equal, for, as Keynes argues, workers are paid just as much when they are producing for investment as when they are producing for consumption; but having earned their wages, it is they who please themselves yhether they spend or refrain from spending them on consumption. Meanwhile, the entrepreneurs have been deciding quite independently in what proportions they shall produce the two categories of output.4 Profits in the investment sector are equal to the difference between the sales value of investment goods and their costs of production; therefore, given the costs, profits depend on the price level of capital goods. Keynes notes, however, that: the price level of investments as a whole, and hence of new investments, is that price level at which the desire of the public to hold savings-deposits is equal to the amount of savings-deposits which the banking system is willing and able to create. 5 Consequently, the total profits in the community are determined by the behavioral decisions of different groups in the system. These decisions relate to consumption by laborers, investment by entrepreneurs, liquidity desires on the part of the community, and monetary decisions by the monetary authority. It was at this point that Keynes noted a peculiarity of profits which was, at the time, to excite much attention and discussion. If, given the costs of production, entrepreneurs spend some of their profits on consumption goods, then, he showed, profits in the consumption sector will rise by an amount equal to this expenditure. In his words: Thus however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before. Thus profits, as a source of capital increment for entrepreneurs, are a widow's cruse which remains undepleted however much of them may be devoted to riotous living. When, on the other hand, entrepreneurs are making losses, and seek to recoup

62

AGGREGATE INCOME DISTRIBUTION these losses by curtailing their normal expenditure on consumption, i.e., by saving more, the cruse becomes a Danaid jar which can never be filled up; for the effect of this reduced expenditure is to inflict on the producers of consumption-goods a loss of equal amount. Thus the diminution of their wealth is as great, in spite of their savings, as it was before. 6

Keynes insisted that his "widow's cruse" and "Danaid j a r " conclusions would be valid even if the money rate of earnings of the factors of production changed. He argued that alterations in the money rates do not cause profits or losses, for, as long as the monetary authority does not attempt to counteract these changes, "entrepreneurs will always be recouped for their changed outlay by corresponding change in their receipts, which will result from the proportionate change in the price level." (p. 167) Though Keynes associated entrepreneurial income with entrepreneurial expenditures,7 he never developed these elements into a mature theory of macrodistribution. Moreover, in the Treatise, other aspects of distribution were only circuitously examined. The determination of wage rates or the wage share was not discussed at all, although the influence of productivity on real wages was established in his well-known formulas. 8 Similarly, the redistribution of real income from rentiers to other economic groups with changes in output, appeared only indirectly in Keynes' analysis of "unproductive consumption." He noted that any increase in employment in the investment sector (when the new workers are recruited from the unemployed) results mainly in a redistribution of consumption from the rest of the community to the newly employed. Investment, which requires a redistribution of current consumption but no reduction in its aggregate, may be said to substitute productive consumption for unproductive consumption. (II, pp. 124-125) This redistribution can occur in either of two ways, either (a) the "unproductive consumers" (the rentiers) can voluntarily save a part of their money-income, or (b) the purchasing power of the money incomes of rentiers will fall as a result of the bidding up of the consumption-goods price level. Thus, Keynes concluded that an increase in employment required a redistribution rather than a reduction of aggregate consumption.9

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63

Kenneth E. Boulding Boulding, at a much later date, though manifestly (as he acknowledges) under the influence of the earlier Keynes, attempted a new approach to the problem of class incomes. 10 He endeavored to demonstrate that the distribution of national income between profits and wages, or rather between labor and non-labor income, is not determined directly by the wage bargain or by the productive efficiency of management, but by a combination of other factors, the most important of which are decisions of management to invest i.e., accumulate real assets, and the complex of decisions of the whole society about liquidity preferences, (p. 174) From these premises, Boulding attempts to discover fundamental identities, in terms of stocks and their composition, 11 by utilizing a balance sheet type of classification and analysis. In the Boulding scheme, income (on his own peculiar though interesting definition) consists of the additions to the total assets of the community, and is reflected in the increases in net worth of the various classes of society. The problem of distribution, in his view, is simply one of explaining how these increments in net worth are distributed among the different economic classes. Dividing the income of the community into two shares, labor income (wages) and non-labor income (profits), he writes: The distribution of non-labor income between contractual income (interest and rent) and residual income (profits) at any one time is historically determined by the nature and extent of contractual obligations and does not present many serious theoretical problems. 12 All economic units are classified either as businesses or households, 13 while three types of assets are recognized: money (M), goods ((?), and securities or debts (K). The following symbols are used to facilitate the manipulation of the microidentities: Mfy = the stock of business cash balances Qft = the value of the stock of businesses' real goods Kfr = Kfyi = debts from businesses to businesses Kfrfo = Ktf = debts from businesses to households

64

AGGREGATE INCOME DISTRIBUTION Kfobi = Ufa = debts from households to businesses Gfo = net worth of businesses Mfo = the stock of household cash balances Qh = the value of the stock of households' real goods Gfrft = net worth of businesses owned by households hh

K

hh' ~ debts from households to households

B K

Gfo - net worth of households V = total profits (non-labor income) D = total business distributions (rents, interest, and dividends) W = total wage income Yfa = total household income C^ = total household consumption (asset destruction) Pn = total net product of the economy With this arsenal of symbols, Boulding proceeds to derive macroidentities from the balance sheet definition of net worthtotal assets minus total liabilities. 1 4 He begins with the summation of all of the individual balance sheets of the business firms in the economy, to obtain an aggregate business balance sheet identity: Mb + Qb+Kb

+ Kh = Ktf + Kh< + Gb

(1)

Since the liability item, debts from businesses to other businesses (Ktf) is equivalent to the asset, debt from other businesses to businesses (Kb), the business net worth identity can be stated as: Gb =Mb + Qb +(KhKtf) (2) where {Kfr- Ktf) is the net household indebtedness to businesses. Similarly, we may derive an aggregate balance sheet identity for all households. Thus: Mh+Qh+

Kbh + Khh + Gbh = Khb< + Kbh< + Gh

(3)

Again, the asset Ky^ must, in the aggregate, equal the liability Kfotf, as they are alternative expressions of interhouseholddebt. Analogously, K^tf and Kfo are equivalent terms for the debt of households to businesses; similarly K ^ Since the net

AGGREGATE DEMAND AND MACRODISTRIBUTION

65

worth of all businesses must ultimately accrue to households, then Gfrfo = Gb. Making these reductions, identity (3) may be r e written as: Gh=Mh

+ Qh- (Rh - Kh') + Gb

(4)

Combining identities (4) and (2), G

h*Mh + Qh+Mb+Qb From identity (5), Boulding concludes:

(5)

The total net worth of households is equal to the total quantity of money in the system (Mfr + M^) plus the total value of the stocks of r e a l a s s e t s (goods) in the system 0Qh+Qb)• (P. 248) These identities will still be valid if they a r e differentiated to denote r a t e s of change, provided the symbols a r e interpreted to mean changes in the quantities available or on hand in a given period r a t h e r than stocks. Hence, from identity (2), Boulding obtains the change in business net worths (= business savings) as: dGb = dMb + dQb + dKh - dKtf

(6)

where the d coefficient symbolizes a change in quantity. A r r i v ing at this stage, Boulding argues that identity (6) i s a significant t r u i s m because: on the whole the various items in it are determined with some degree of independence of each other. Hence we get another "macroeconomic paradox": that business savings a r e for the most p a r t not determined by the decisions of businesses to save, but a r e a result of a complex of other decisions which determine the volume of business savings independently of the decisions of individual b u s i n e s s e s to save, i.e., to increase their net worths. If we accept the fact—which will be elaborated later— that the total of business savings is independently d e t e r mined, then business decisions to save, as reflected in dividend policy, determine not business savings but the level of profits itself. 1 5 Business savings can also be defined a s " t h a t p a r t of total profits which has not been distributed" (p. 249), t h e r e f o r e V s dGb

+

D

(7)

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AGGREGATE INCOME DISTRIBUTION

where V represents total profits (non-labor income) and D represents total business distributions (interest, rent, and dividend payments). If interest and rent payments are fixed by contract, then business decisions to save are executed mainly through dividend declarations. Hence dividend payments will determine the magnitude of total business distributions, and Boulding contends, since dGft is determined via the items of identity (6), the level of total profits as well. In language obviously descendent from Keynes, Boulding states: If we can assume that dGj is determined independently of business distributions— . . . which is true enough to serve as a first approximation—then business distributions are a "widow's cruse and Danaid j a r " . . . . Distributions, as it were, run through the system in a rapid reflux back into the pockets of business again . . . . An increase in the distributions of one firm . . . swells the profits of others, an increase in the distributions of all firms swells the profits of all. 16 Boulding's comment that actual business savings are independently determined is to be interpreted as meaning that the items determining dG^ (via identity [6]) are independent of each other and of business savings decisions (the latter affects D rather than dG¿,). This implies that the level of dividends to be distributed, once decided upon remains unaltered even if total profits differ from their expected level. By combining identities (6) and (7), Boulding derives an identity for total profits, V = dQb + dMf) + dKh - dKtf + D

(8)

which indicates that total profits are equal to the increase in the real assets of businesses plus the increase in business cash balances plus the change in the net indebtedness of households plus business distributions. In a similar fashion, an identity for total wages can be derived by differentiating identity (5): dGh = dQfo + dQb + dMh + dMf,

(9)

Thus identity (9) states that household savings equal the total increase in the value of real assets plus the increase in the stock of money. Boulding assumes that the total stock of money is constant, i.e., dM^ + dM^ = dM - 0, therefore identity (9) can be rewritten as:

AGGREGATE DEMAND AND MACRODISTRD3UTION dGh=dQb+dQh

67 (10)

Hence, the conclusion that total household savings, dG%, is equal to the total savings in the economy; all business savings ultimately accrues to households. Household savings are also equal to household income (Yfo) less household consumption (C^), where the former is defined as the gross additions to the net worth of households and consists of wages earned (W) plus business distributions (D) plus business savings (dGb). Therefore: dGksW

+ D+ dGb-

Ch = dQh + dQb

(11)

Substituting for dGb from identity (6) and for dG^ from identity (10), Boulding obtains W = Ch + dQk - (dMb + dKh - dKh* + D)

(12)

Letting the bracketed items be represented by T, the transfer item, Boulding rewrites identities (12) and (8) as: W=Ch+dQh-T

(13a)

V = dQb + T

(13b)

Also: Pn=

W+V = Ch+dQh+dQb

(14)

where Pn is the total net product of the economy. The difference between gross and net product is called business consumption, i.e., asset destruction by businesses during the production period. Identity (14) denotes that the net product of the community is exhausted by the payment of wages and profits, which is but a slightly disguised form of the famous Keynesian identity of income being the sum of consumption plus investment. Using identities (13a) and (13b), Boulding concludes: the distribution of the product between wages and gross profits is determined by two elements: the composition of the product absorption on the one hand as between business investment and household absorption, and a transfer factor which we add to business absorption to get the total of profits, and subtract from the total of household absorption to get the total wages . . . . these identities are mere truisms. Whether they are useful truisms depends on whether the components are useful as "parameters of behavior," i.e., whether the components vary in a fairly regular fashion with certain changes in human behavior. In particular it is important to examine the composition of

68

AGGREGATE INCOME DISTRIBUTION the transfer factor, T, to see whether . . . it is likely to be determined in some degree independently of the business-accumulation and household absorption factors, (p. 252)

In analyzing the items in the transfer factor and their effects on identities (13a) and (13b), Boulding elicits the following macroeconomic paradoxes: 1. An increase in consumer credit (dKk) will increase the magnitude of the transfer factor and therefore "reduce the proportion of the total output which accrues to labor." (p. 255) 2. An increase in the volume of corporate securities held by households (dKtf) will reduce the size of the transfer factor and therefore shift the distribution "towards wages and away from gross profits." (p. 255) A Criticism of the "Independence

Postulate"

In interpreting the importance of identities (6) and (7), and the transfer item, Boulding assumes that the variables on the right-hand side of his macroidentities are independent. This appearance of independence is but a form of what Keynes once criticized as an "optical illusion." 17 Balance sheet accounting procedures indicate that whenever there is an increase in an asset, there must be either an offsetting increase in a liability, or a decrease in another asset, o r a n increase in net worth. In identity (6), for example, if debts from households to businesses increase (dKy¡), then there must be an offsetting transfer of assets from businesses to households (dQfo or dM^). Similarly, a change in the volume of debts of businesses to households (dK^) will usually involve changes in the asset position of businesses as well. Johnston, in a review of the Reconstruction, indicated that Boulding's supposition of independence between business savings decisions and actual business savings would "hold good only under a most extreme and unrealistic set of circumstances." 1 8 Johnston argued that any increase in dividend payments at the close of the accounting period must involve a simultaneous decrease in business cash balances, and therefore a decrease in business savings. Hence, unless businesses declare all their dividends before the conclusion of the accounting period, business decisions on distributions will affect actual business savings. Consequently, Johnston reasons:

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69

Professor Boulding's conclusions about the determination of business savings would hold good if ALL dividend distributions took the form of interim payments, i.e., were made before the end of the accounting year in which they were earned . . . . [then] at the end of the year . . . it would no longer be in the power of businesses to alter dMfr, since they had already distributed the year's dividends. Automatically, therefore, business savings would be a mere residual, determined by the same complex of forces as Total Profits itself. This model is extremely unrealistic, (pp. 190-191) The macroeconomic paradoxes that were wrested from identities (13a) and (13b) are similarly based on the assumption that the items of the transfer factor are independent of each other and of the other variables on the right-hand side of these identities. But this supposition is also suspect. For example, changes in the net indebtedness of households (dK^ dKcan only be transmitted either via changes in business accumulations (dQfr), or changes in business cash balances (dMjj), or changes in household absorption (dQh + C^). Boulding's consumer credit paradox overlooks the fact that households increase their indebtedness to businesses simply to increase their asset holdings or their consumption. Consequently, an increase in consumer credit would be offset by a synchronous increase in household absorption; thus no change in the magnitude of W or V can be demonstrated via identities (13a) or (13b). In a similar manner, Turvey has criticized Boulding's corporate securities paradox.1® Turvey argues that an increase in business borrowings from households can come about only in two ways: (1) via households purchasing the new securities by decreasing their cash balances and therefore raising dM^} or (2) via households curtailing consumption spending so that there is an unintended increase in inventory investment by businesses. In either case, identity (13b) should show offsetting changes in the magnitudes of the "independent" variables, and therefore, "Profits are not directly affected." 20 Accordingly, the variables of the transfer factor need not be independent of each other, or of household absorption or business accumulation. Boulding's tacit assumption of the independence of the variables on the right-hand side of identities (6), (7), (13a), and (13b), is, therefore, invalid. He has also implicitly assumed that the left-hand terms in these identities are passive. Such an interpretation is dangerous and unwarranted.

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AGGREGATE INCOME DISTRIBUTION

Passivity may be inserted in behavioral functions, but never in definitional identities. 21 The prerequisities for a determinate system for analyzing economic changes go beyond mere definitional identities; it requires behavioral functions which are stable and independent. Finally, Boulding's analysis, since it is based on a balance sheet approach, implies that the total output for the period is given. Hence, changes in the variables can only reflect a reshuffling of the product among the various economic groups. The absence of any schedule concept prevents the system from having any predictive or explanatory value, except in the ex post sense, that is, one may state that if, at the end of a period, profits are positive, businesses must have increased their holdings of some assets. What conclusions may we draw from Boulding's analysis? First, the part of national income which is net investment (business accumulations) cannot accrue to wage earners, if we assume that laborers consume, in the Keynesian sense, their entire income. This latter assumption is implicit in Boulding's scheme. The investment decision is, therefore, an important factor in the distribution of income as well as in the determination of the level of output. Secondly, though the variables in the transfer factor are not independent of business investment or household accumulation decisions, the transfer of income from the firms to rentiers may affect distribution. Mrs. Robinson has recently attempted to indicate how this transfer, as well as other factors, may affect relative shares. We therefore turn now to an examination of her analysis.

VII Aggregate Demand and Macro distribution: Robinson and Kaldor Mrs. Robinson's recent study of The Accumulation of Capital contains a systematic examination of forces determining class incomes and class shares. 1 Her thesis is that it is the investment and consumption demands of the various groups in the community which affect the price of labor, and it is the price of labor time, which, in the long run, "expresses the distribution of the total product of the economy between work and property." (p. 28) Many of Mrs. Robinson's ideas are quite novel and the following section will be devoted to a detailed consideration of her views. In the last section of this chapter, we will analyze Nicholas Kaldor's approach to the relative share question. While he reaches substantially the same conclusions as Mrs. Robinson, he uses a somewhat more mechanical route. Joan Robinson In Mrs. Robinson's scheme there are three economic classes; laborers, who live by selling their work and who earn wages and salaries; rentiers, who receive interest, rents and dividends; and entrepreneurs, whose income is "made up of salaries (in the case of hired managers) and of personal allocation of profits, interest, and dividends which they receive in their capacity as rentiers." (p. 14) The excess of profits over rent, interest and dividend payments is retained as the property of the firm. In what is a key to her system—and this is derived largely from Kalecki's aggregate profits theory—Mrs. Robinson assumes that laborers spend their entire income on consumption goods, (p. 73) The labor force is assumed to be homogeneous with respect to efficiency, so that all workers receive the same 71

72

AGGREGATE INCOME DISTRIBUTION

money wage per man-hour. It is also assumed that all productive equipment " i s produced and reproducible," i.e., land is excluded from the system.2 In a closed system, the sales value of aggregate output (7) can be divided into aggregate wages (W) and aggregate quasirents (Q), where the latter consists of amortization, profits and rents. Total output can also be divided into consumption goods and investment goods. The sales value of the consumption commodities (F c ) will exceed the wagebill in that sector (Wc), since workers employed in the investment sector (who earn wages equal to Wj) as well as consumption-goods employees, and rentiers generally, are buying consumption commodities. Since Mrs. Robinson assumes that workers spend their entire wage income on these goods, then Vc = Wi + Wc + Cp = Qc + Wc

(1)

where Cp is the consumption expenditures of rentiers and Qc is the quasi-rents of the consumption sector. Therefore: QC = WI

+

Cp

(2)

The existence of quasi-rents in the investment sector (Qj) depends upon the sales value of investment goods exceeding their wage costs. This will occur in the usual case when in a non-integrated structure, firms purchase productive equipment from other specialists' firms. If a firm produces capital equipment for its own use, then this equipment will be valued at a price exceeding its wage cost by some notional profit margin based on its expected future earnings.3 Quasi-rents in the investment sector thus originate partly in actual transactions and partly in shadowy concepts based on anticipations. Equation (2) indicates that the more entrepreneurs spend on investment projects or rentiers spend on consumption goods, the greater will be the magnitudes of Wj or Cp, and therefore, ceteris paribus, the larger will be Qc* A higher ratio of Qc to Wc entails a lower real wage rate. Mrs. Robinson introduces a limit to which this ratio can rise without inducing an uncontrollable demand by laborers for higher money wage rates. This limit is called the inflation barrier. When workers' demands for higher money wage rates are met, money expenditures will increase in the same proportion as the increment in money wages causing a wage-price spiral. She declares: "There is a head-on conflict between the desires of the entrepreneurs to invest and the refusal of the system to accept the level of real

AGGREGATE DEMAND AND MACRODISTRIBUTION

73

wages which the investment entails." 5 The result, according to Mrs. Robinson, is either hyper-inflation or the curtailing of investment projects. 6 Therefore, the inflation barrier is a restraint upon the system which sets a lower limit on the wage rate and the relative wage share. Investment expenditures by entrepreneurs and the consumption expenditures of workers and rentiers are the components of aggregate demand; hence, it is aggregate demand which will affect the sales value of goods, the wage bill in each sector, and the quasi-rents in the community. It is the pattern of aggregate demand which determines the distribution of total output. In view of its importance, Mrs. Robinson first discusses the factors determining the level of investment spending, and its effect on class shares. Then she comments on how consumption expenditures by rentiers may alter the distribution. Her views on these subjects are set forth in the following sections. Investiment Demand as a Determinant of Class Shares In her initial models, there are only two economic groups: workers who spend their wages as they receive them, and entrepreneurs "whose consumption is negligible and whose sole function and aim is to organize production and accumulate capital." 7 Consequently, the quasi-rents in the consumption sector are equal to the wage bill in the investment sector, i.e., VC = QC + WC=WI+ or

Wc

Qc = Qi

(3)

The value of gross investment (Vj) is equal to the wage bill in this sector plus quasi-rents (Ql): V/ = Q/ + Wj

(4)

From equations (3) and (4), we can conclude that aggregate quasirents are equal to the value of gross investment: Q = Ql + Qc = Ql + Wi = Vj

(5)

Total profits are equal to total quasi-rents less amortization, or to the value of net investment. The larger the proportion of a given labor force that is employed in the investment sector at a given wage rate, the greater the value of net investment (or profit) relative to consumption output (wages). Hence, and all this is essentially tautological, the relative shares will depend upon the proportional allocation of labor between the two sectors.

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AGGREGATE INCOME DISTRIBUTION

For profits to exist, the worker must produce more than his family consumes and entrepreneurs must invest. On the other hand, entrepreneurs must make profits in order to accumulate capital. Thus, the forceful conclusion: This double interaction between investment and profits is the most troublesome feature of the capitalist rules of the game, both from the point of view of entrepreneurs who have to play it and of economists who have to describe it. (p. 198) If only workers purchase consumption goods, then, by definition, the rate of profit is equal to the ratio of the rate of accumulation to the stock of capital. To maintain a constant rate of profit with a given money wage rate, the rate of accumulation must be increasing at the same rate as the increase in the capital stock, and aggregate demand for commodities must increase with output, so that the ratio of prices to money wages (the degree of monopoly) does not alter, (pp. 76-77) With only a single technique of production, accumulation can continue indefinitely so long as the rate of increase in the labor force equals the rate of capital formation. When the labor force increases outstrips accumulation, then the money wage rate would tend to fall and unemployment increase, (p. 79) If, in the face of a decline in money wages, entrepreneurs decide to maintain a constant rate of investment (in physical terms), then the volume of employment in the investment sector is constant. Hence, Wj and Q c fall in the same proportion as the wage rate, and if prices are flexible, real wages hold constant and there is no change in relative shares. Should prices be sticky, however, the demand for consumption goods output will decline, causing a decrease in employment in the consumption sector, and a cutback of investment replacement orders; in this situation it is unlikely that a constant rate of physical investment will be maintained. Employment will continue to fall as we pass through a period of disinvestment until the excess capacity is worked off. During this period, wages may absorb the whole net product of industry. In an interesting alternative hypothesis, Mrs. Robinson considers entrepreneurs' investment decisions made on the basis of the pecuniary value of capital rather than on its physical quantity. In this event a reduction in the money wage rate will induce an increase in the volume of employment in the investment sector. Prices in the consumption sector fall by less than the wage bill in that sector, increasing quasi-rents and raising

AGGREGATE DEMAND AND MACRODISTRIBUTION

75

the rate of accumulation. Employment rises, therefore, until a new equilibrium is reached where the rates of population growth and capital formation are in harmony; while the relative wage share is now smaller, the profit share is larger. Thus, when the money wage rate falls, investment decisions in " r e a l " t e r m s will have a different effect on class shares than similar decisions made in money terms. A constant physical investment decision may be detrimental to the profit share; a constant money value decision is likely to increase the profit share, (pp. 78-82) If the labor force should increase less rapidly than the rate of capital accumulation, then the money wage rate would tend to rise as machines became available and entrepreneurs ejqperienced ever increasing difficulties in finding workers to man the equipment. In this case, investment decisions to maintain the physical rate of capital goods output would preserve the original allocation of labor between the two sectors. Money expenditures would increase proportionately with increases in money wage rates; and prices and money wages would spiral upward until investment plans were curtailed (the inflation barrier). Should capitalists instead decide to maintain money outlays on investment, employment in the capital goods sector would decline, prices of consumption goods would rise less than money wages, and real wages would increase. The rate of accumulation would decrease until equilibrium is reached between it and the rate of population growth, with the relative wage share higher and the profit share lower. In the limiting case where the supply of labor is constant, the long-run equilibrium position (assuming a single technique of production) requires zero net investment and the wage share comprising all of the net output, (pp. 81-82) Mrs. Robinson indicates that these conclusions will be partially modified when allowance is made for rentier consumption and the diversity of the techniques of production. Distribution and the Degree of Mechanization Changes in the techniques of production arise essentially from two fundamental forces, namely (a) changes in the real wage rate relative to the rate of profit in a given state of the arts, yielding what Mrs. Robinson calls changes in the degree of mechanization, and (b) changes in the state of the a r t s or technical progress. Given all money prices and money wages, quasi-rents per man is higher when the rate of output per man is greater. To

76

AGGREGATE INCOME DISTRIBUTION

increase output per man, in a given state of technology, entrepreneurs must increase investment per man, i.e., they must institute a higher degree of mechanization. Entrepreneurs contemplating investment have a choice of techniques. They will choose that process which offers the highest rate of profit on investment at the given real wage rate. Therefore, Mrs. Robinson concludes, "for the economy as a whole the degree of mechanization of the investment plans being carried out, in a given phase of technical knowledge, is governed by the level of real wages." 8 The higher the real wage rate, the more profitable it is to employ a more mechanized method of production. What is the effect of changes in the degree of mechanization on the relative shares in the value of output? Before making any generalization, one must decide how to estimate the value of total output.9 To avoid the index number problem of a changing output composition, Mrs. Robinson assumes that the same physical consumption goods are always produced in the same proportions, in all economies with all techniques. 10 Allowing the physical composition of investment goods to alter when there is a change in the degree of mechanization, the problem is essentially how to measure the output of capital goods. Four possible methods of measuring capital are suggested: (1) in terms of physical quantities of capital goods, (2) in terms of physical productive capacity, (3) in terms of a stock of capital goods reckoned in commodities (or in money of given purchasing power over commodities), and (4) in terms of labour time required to produce the capital goods, (p. 118) The first two measures are inadequate for comparative purposes when either (a) the technique of production differs in two economies, (b) the age composition of the capital stock differs, or (c) the rate of accumulation differs (even with the same technique) since a larger proportion of new equipment is being used for the production of investment goods, (pp. 118-119) The last two measures, despite their own limitations, are more useful. There are three possible ways of evaluating capital in terms of commodities: (i) the selling price of a productive unit, (it) the discounted expected future earnings, or (in) the costs incurred up to the present, accumulated at a notional interest rate, less the profit already yielded. These three views will yield the same value only if the rate of profit has been constant for a long period of time and is expected to continue far into the future.

AGGREGATE DEMAND AND MACRODISTRIBUTION

77

If, however, two economies have different wage rates, even if the techniques of production are identical, valuation of the same piece of equipment will differ no matter which method is adopted. Once capital has been assessed in terms of commodities, then one may evaluate the quantity of capital in terms of labor time required to produce the capital goods by dividing the commodity value of this stock by the wage per man-hour in terms of commodities. Any difference in wage rates will cancel since each machine will be measured in terms of man-hours alone. However, in comparing two economies where the wage rates and therefore the rates of profit differ, even if the same number of man-hours enter into the production of a unit of capital, different notional interest costs would be used in accumulating these labor costs from the previous time periods. Different values for the same machine would therefore be obtained. 11 Thus, Mrs. Robinson has two units for comparing shares in the value of output, either (a) valuing all output in terms of the composite consumption commodity or (b) valuing output in terms of labor time. By judicious use of these measures, she can determine relative shares in different situations. To generalize about the effects of differences in the degree of mechanization on relative shares, Mrs. Robinson uses the technique of comparing two economies which have all but one or two of the pertinent variables equal. In each economy, she assumes the same size labor force, the same technical knowledge, and the same price of consumption goods, so that differences in real wages are reflected in differences in money wages, (p. 124) First, Mrs. Robinson, compares two economies having equal wage rates, but different degrees of mechanization. The annual output of consumption goods must be equal in the two economies. (This follows from the assumption of equal labor forces, equal wage rates, and equal consumption price levels.) In the economy with the higher degree of mechanization, a smaller number of workers is required to produce this output of consumption goods and maintain the stock of capital. Consequently, more workers will be engaged in net investment and therefore the value of net investment is higher. 12 Hence: The essential difference between them [the two economies] now is that the total value of output (commodities plus net investment) is higher in [the more mechanized economy] . . . . and the whole difference in output accrues to profits. (p. 126)

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AGGREGATE INCOME DISTRIBUTION

Simultaneously, the wage share is lower. Secondly, comparing economies with the same degree of mechanization but different wage rates, the rate of profit and the rate of accumulation are, by definition, higher in the low wage economy. Fewer men are employed in the consumption sector, while more are engaged in the investment sector and therefore, the relative wage share is lower, while the profit share is larger than in the high wage economy, (p. 127) Thirdly, when both the degree of mechanization and the wage rates differ in the two economies, it is impossible to generalize about relative shares. 13 Although the output of consumption goods must be greater in the high wage economy, we cannot draw any conclusion about the ratio of labor employed in the consumption-goods industries to employment in investmentgoods industries. The higher real wage rate tends to increase the ratio of consumption workers to investment workers, while the higher degree of mechanization tends to lower it. Similarly, the profit rate is higher in the low wage economy, but we cannot draw any clear inferences about the value of net investment. 14 Though we know that the total wage bill is greater in the high wage economy, we do not know if total output is more than, less than, or just proportionately higher than the output in the low wage system, because of our inability to generalize about the value of net investment. 15 Distribution and Technical

Progress

Technical progress can now be added to the analysis; this is simplified to the case of "improvements in methods of production without any change in the composite commodity." (pp. 6566) Hence, technical progress manifests itself by increasing output per head. Given the real-capital ratio (i.e., the capital-labor ratio), technical knowledge is said to be superior to another phase "if output per man is greater at that real-capital ratio." 1 6 The relationship between two spectra of techniques is said to be neutral when output per head increases in the same proportion in both the consumption and investment sectors no matter which degree of mechanization is compared. If two economies with equal profit rates (hence equal realcapital ratios) are compared, then real wages in the superior economy are then greater than in the inferior one in the same ratio as output per man.

AGGREGATE DEMAND AND MACRODISTRIBUTION

79

Capital per man (measured in terms of product) is greater in the same proportion, and the relative s h a r e s of wages and profits in the value of output are equal in the two economies, (p. 133) If, on the other hand, the rates of profit differ in the two economies, (while the spectras a r e neutral), we cannot generalize about relative s h a r e s for both the wage r a t e s and the degree of mechanization will differ. A capital-using bias in technical progress involves raising the output per man by a greater proportion in the consumption than in the investment sector, tending to raise the real-capital ratio and shift labor from the consumption to the investment sphere. Alternatively, a capital- saving bias entails a more than proportionate increase in output per man in the investment sector than in the consumption sector, tending to lower the r e a l capital ratio and reapportion labor towards consumption, (p. 133) If we compare two economies with equal r a t e s of profit, a capital-saving bias favors the wage share and the consumption sector in the superior economy. Conversely, with a capitalusing bias, a greater proportion of the total labor force is in the capital goods sector and the relative wage share is, therefore, lower. On general reasoning, however, Mrs. Robinson concludes that it is unlikely that technical progress will have any permanent bias, since capital-using innovations raise the cost of machines in t e r m s of commodities and give entrepreneurs an extra motive to find ways to cheapen them. Capital-savings innovations tend to produce a scarcity of labour in the consumption sector and give entrepreneurs an extra motive to increase productivity. Each type of bias tends to get itself compensated by the other, (p. 170) Rentier Consumption

and Relative

Shares

Mrs. Robinson then introduces the possibility of rentier expenditures on consumption. Profits, therefore, " a r e equal to net investment plus rentier expenditures (net of any secondhand purchases by one rentier from another)." (p. 255) Consequently, when workers do not save, the relative profit share is functionally related to (rather than equal to) the ratio of the value of

80

AGGREGATE INCOME DISTRIBUTION

net investment to the value of total output; and the wage share is inversely correlated with this investment-output ratio. With neutral technical progress, the investment-output ratio and relative shares will be constant if effective demand increases pari passu with output. For consumption demand to grow with capacity, Mrs. Robinson notes that it is necessary that the proportion of profits devoted to expenditures on consumption goods should remain constant. . . . To maintain a constant proportion of rentier consumption to profits it is necessary, first, that the share of profits distributed to rentiers should be constant, and second, that the proportion of rentier receipts saved should be constant (or that changes in one should be offset by opposite changes in the other). 17 Mrs. Robinson points out that decisions to distribute profits will be affected by the interest rate, dividend policy, and the borrowing policy of firms, while the second condition is likely to be fulfilled, i.e., rentiers will spend a constant proportion of their receipts, when "the standard of consumption rises with wealth." 18 Thus, Mrs. Robinson's analysis of the components of aggregate demand leads to the conclusion that the relative class shares depend essentially on three sets of decisions: (a) investment decisions, which are partly determined by the anxiety of entrepreneurs to accumulate, partly by the physical conditions of production and technical progress, and partly by the real wage rate which may affect the degree of mechanization or stimulate biased innovations; (b) decisions on the distribution of profits via dividends and contractual obligations, which will depend on a complex of liquidity desires; and (c) consumption decisions. Rents, Profits and Marginal

Productivity

Finally, Mrs. Robinson introduces the notion of a scarcity of land and the payment of rent. Rent differs from other rentier income since the latter is more or less related to the growth of the capital stock (and output), but the supply of land being fixed, any "increase in rent income is really a levy upon the rest of the economy which is not related to any increase in production." (p. 327). Nevertheless, Mrs. Robinson reasons that rent payments mainly affect the level of real wages since

AGGREGATE DEMAND AND MACRODISTREBUTION

81

expenditure out of rent income keeps prices, relative to money wages, higher than they would be if rents were lower, so that entrepreneurs as a whole receive back (as receipts for the sale of commodities) a large part of what they pay in rent; the main burden therefore falls upon real wages. 19 Profits, on the other hand, exist because anyone who can "command finance" can hire factors of production to produce a good whose sales value exceeds its rent and wage bill. In order to obtain finance, therefore, the entrepreneur may be willing to give up some of his expected future profits via interest payments to rentiers. This, interest can be considered a transfer payment.20 In a completely riskless competitive society, the interest and profit rates would be equal. Mrs. Robinson asserts that the relation of marginal productivity to the income shares is not a simple one. In a competitive economy, each entrepreneur will select a technique of production which will maximize his rate of profit for a given value of capital. Hence, land will be hired until rent per acre equals the addition to the firm's total receipts, with a given quantity of labor and a given value of capital. Similarly, labor will be hired until the marginal return to labor equals the wage rate. The marginal return on capital to the individual entrepreneur is the rate of profit. However, Mrs. Robinson argues: The level of rents and wages and the rate of profit are not determined by the marginal products of land, labour, and investment. All three are determined together, in a complicated way, by the spectrum of technical possibilities, the supplies of land and labour available to the economy as a whole and the amount of accumulation that has already taken place, and by the level of effective demand for commodities and the rate of investment . . . in a given state of knowledge with given supplies of factors, investment itself alters the relative values of commodities, capital goods, and factors of production, so that the return to an individual in terms of value has no meaning for the economy as a whole, (pp. 311-312) Comments on Mrs. Robinson's Analysis Although Mrs. Robinson's analysis gives important insights into investment decision-making, her relative share scheme as stated at the beginning of this chapter is essentially definitional.

82

AGGREGATE INCOME DISTRIBUTION

There can be little doubt that ex post profits, under the assumptions of the early models, equals net investment. 21 Hence, the assumptions of the analysis should be scrutinized to see if the theory is applicable to the real world. First, Mrs. Robinson, influenced by Kalecki's profit theory, has assumed that workers consume their entire income. This presupposition is a reasonable first approximation of reality for European economies and is probably justifiable for the United States economy, especially if we include in consumption expenditures the purchase of all durable consumer goods. 22 Kaldor, on the other hand, has introduced savings out of wages into the analysis without drastically changing the conclusions. 23 Secondly, Mrs. Robinson has posited that consumer goods are always produced in fixed proportions. This assumption is quite unrealistic (as Mrs. Robinson readily acknowledges), 24 though it does enable her to assign some meaning to the concept of changes in total output. This assumption i s closely related to the use of base year weighting in the empirical measures of real gross national product. Thirdly, in her initial analysis, Mrs. Robinson postulates that all equipment is produced and reproduceable, i.e., in the long run, the only scarce resource is labor. 25 She also assumes fixed input coefficients and no lack of effective demand. Hence employment is limited only by the availability of the scarcest resource, which under these assumptions, is labor. Since, in the early models, factors are not substitutable, the wage share is a residual, determined by the unwitting plan of entrepreneurs to employ " a certain number of workers to produce capital goods and whatever further number of workers is required to provide wage goods for all the workers employed." 2 8 Although Mrs. Robinson acknowledges and even emphasizes the possibilities of insufficient aggregate demand in other sections of the book, her analysis of relative shares with different degrees of mechanization and/or technical p r o g r e s s usually a s sumes a fully employed labor force. Thus, the value of total output (in t e r m s of labor time) is exogenous, and the distribution of the total depends solely upon the composition of aggregate demand a s exerted in the market place by the different economic classes. Nicholas

Kaldor

Kaldor has attempted to use the multiplier principle in the development of a macrotheory of distribution. 2 7 His thesis is

AGGREGATE DEMAND AND MACRODISTRIBUTION

83

an interesting one, namely, given the saving functions of wageearners and capitalists, the profit share is a function of the ratio of investment to output. Kaldor assumes full employment; so that the level of total output (Y) is given. Income is divided into aggregate wages and salaries (W) and aggregate profits, or total property income (P). Aggregate savings (S) is composed of savings from wages and salaries (S w ) and savings from profits (Sp). The following identities are then stated: (p. 95) Y =W +P I=S S ~ Sid + Sp Kaldor assumes that the volume of investment is given and that savings functions are of a simple proportional form: Sw ~ swW Sp = spP where sw and Sp are the average proportion saved out of wages and profits respectively, (p. 95) Substituting in the savings-investment identity, Kaldor obtains: / = spP + swW = SpP + sw{Y - P)={sp-

sw)p + swY

(6)

Dividing both sides of equation (6) by Y, and rearranging terms: P_ 1 I Y sp- sw Y

s

w sp - sw

(7)

Hence, he concludes: . . . given the wage earners' and capitalists' propensities to save, the share of profits in income depends simply on the ratio of investment to output, (p. 95) If

s

w ^ SP> then equation (7) has a determinate solution. Kaldor maintains that for stability in the system Sp must exceed sw. We should expect that sp would be larger than sw since a large portion of profits is likely to be retained by corporations. Also he notes that: The degree of stability of the system depends on . . . 1 /Sp - sw which may be defined as the "coefficient of sensitivity of income distribution," since it indicates the

84

AGGREGATE INCOME DISTRIBUTION change in the share of profits in income which follows upon a change in the share of investment in output, (p. 95)

The essential assumption in Kaldor's analysis is that the ratio of investment to output is independent of changes in the savings propensities. 28 Using a Harrodian system, Kaldor determines the investment-output ratio as a function of the rate of growth (G) and the capital-output ratio (v): y ' G v ,

(8)

where G, in a state of continuous full employment, is equal to the rate of growth of technical progress plus the increase in the labor force, and v, the capital-output ratio, depends entirely on technical conditions. 29 In Kaldor's model, the profit share, P/Y, the rate of profit, P/vY, and the real wage rate, W/L (where L equals the labor force) are all implied functions of the investment-output ratio, while the latter is determined independently of the profit share and the wage rate. Kaldor indicates four reasons why I/Y may not be independent of P/Y or W/L:30 1. The real wage rate cannot fall below subsistence (w1) P ^ Y- w" L Y ^ Y

In principle, this restraint is similar to the inflation barrier in Mrs. Robinson's analysis. 2. The rate of profit must be equal to or more than what is necessary to induce capitalists to invest, i.e., the lower limit to the rate of profit is either the " r i s k premium r a t e " r, — > r vY

3. or the socially acceptable minimum, which Kaldor calls the "degree of monopoly r a t e " m, P w

.

> m

Thus, (2) and (3) are alternative restrictions, so that the higher minimum will apply. The profit share must implicitly involve a rate of profit high enough to induce businessmen to invest, otherwise the full employment assumption will be invalid. 31

AGGREGATE DEMAND AND MACRODISTRIBUTION

85

4. The capital-output ratio should be independent of the rate of profit. If v is not independent, then I/Y will also depend on the rate of profit. Kaldor admits that since the value of capital in terms of final consumption goods is affected by; the rate of profit, then "even with a given technique, v will not be independent of P/Y." He argues, though, that it is safe to ignore the point, (p. 98) Comparison of Kaldor's Analysis with Other Systems If sw - 0, then equation (7) reduces to P Y

1 I spY

(8)

The assumption that workers do not save is explicit in both Kalecki's aggregate profits theory and in Mrs. Robinson's system, and, according to Kaldor, it is implicit in Keynes' widow's cruse. Kaldor states: This model (i.e., the "special case" where sw = 0) in a sense is the precise opposite of the Ricardian (or Marxian) one—here wages (not profits) are a residue, profits being governed by the propensity to invest and the capitalists' propensity to consume, which represents a kind of "prior charge" on the national output . . . . Assuming however that I/Y and Sp remain constant over time, the share of wages will also remain constant—i.e., real wages will increase automatically, year by year, with the increase in output per man. (p. 96) Both Kaldor and Mrs. Robinson emphasize the importance of the investment-output ratio. Mrs. Robinson has, however, given valuable insights into the investment decisions explicit in her analysis. Kaldor, on the other hand, by assuming a given rate of investment and output, has used the equation in an almost mechanical way. He unwittingly discards all the important behavioral factors which affect the decisions to allocate resources between consumption and investment and determine aggregate demand. Mrs. Robinson argued that changes in the real wage rate (and therefore the rate of profit) will affect the real-capital ratio; and that this in turn involves a change in the capital-output ratio, either through inducing entrepreneurs to change the degree of mechanization or by stimulating biased technological advances. Kaldor has recognized the possibility that the profit share

86

AGGREGATE INCOME DISTRIBUTION

and its implicit wage and profit r a t e s " m a y affect v through making more or l e s s 'labour-saving' techniques profitable. . . . To exclude this we have to assume that v is invariant to P/Y." (p. 98) The assumption of the invariance of v implies, first, that in a given state of the a r t s , entrepreneurs cannot substitute between factors, i.e., the production coefficients are fixed. Secondly, it suggests that a change in the wage rate will not affect decisions to invest. 32 Thirdly, it implies that technical innovations are neutral; therefore it suggests that new innovations are independent of factor prices, i.e., that a high wage rate will not stimulate labor-saving innovations. This leads Kaldor to exclaim, " I am not sure where 'marginal productivity' comes in in all this—except that in so f a r as it has any importance it does through an extreme sensitivity of v to changes in P/Y." (p. 100) But this sensitivity has been eliminated by assumption, and therefore there is no place for m a r ginal productivity. Mrs. Robinson's analysis, on the other hand, does not expunge marginal productivity; instead, it is placed in the system a s an adjusting mechanism for the hiring of factors by the individual firm. Kaldor has indicated that his theory is applicable only when the "level of output and employment is taken a s given." (p. 94) Since total output is a datum, distribution will depend entirely upon the expenditures of the various groups in the economy. On the other hand, Weintraub has suggested that this approach tends to overlook the importance of changing income and employment levels and the underlying productivity phenomena of the aggregate supply function. We will, therefore, turn now to an examination of his analysis a s developed in An Approach to the Theory of Income Distribution.

Vili Aggregate Supply and Relative Shares In his recent book, Aw Approach to the Theory of Income Distribution, Professor Sidney Weintraub has attempted " t o bring the theory of distribution abreast of modern knowledge of the theory of the firm and the current macroeconomic theory of income and employment determination." 1 He believes that the theory of income determination and the theory of income distribution are interdependent, and that underlying these macrotheories must be a consistent theory of factor hire at the firm level. The Essential

Concepts

At the outset of his analysis, Weintraub makes the following assumptions: 1. 2. 3. 4. 5. 6. 7.

The labor force is homogeneous, The stock of capital is fixed, Money prices of the factors of production are given, The production functions are given, Each firm is fully integrated, Pure competition exists, Entrepreneurs are profit maximizers.

Most of these assumptions will be relaxed in our development of Weintraub's analysis. Weintraub begins by deriving an aggregate supply function (a Z-function) relating employment (N) to expected money proceeds (Z) " i n the sense that each expected-proceeds level generates a particular amount of employment." (p. 25) Each Z-quantity is obtained from the individual industry supply curves by multiplying the supply price by the associated output and summating over all industries. This sum is then related to the volume of employment required for the particular output quantities. Thus, the Z-function can be described from industry supply curves, if 87

AGGREGATE INCOME DISTRIBUTION

88

the latter are determinate and "if the distribution of proceeds for each expected aggregate volume of proceeds, is determinate"2 It is reasonable to assume that entrepreneurs will hire more workers (with a given stock of capital) only if they expect aggregate proceeds to rise; hence, the Z-function will have a positive slope. Also, if they expect zero proceeds they will hire zero workers; consequently, the Z-function emanates from the origin (Figure 1). At each level of employment, proceeds will be divided as follows: Z = wN+F

+R

(1)

where w is the money wage rate, F is the volume of fixed money payments to rentiers, and R is the residual, profits. Thus, proceeds will be distributed between the wage bill (wN) and gross profits (F + R). In Figure 1, assuming the money wage rate is constant, OW represents the total wage bill (W). The slope of the W-line is equal to w. Hence, if the level of employment (as determined by the intersection of the aggregate supply and

Z, W

/ Z

w F

O N Figure 1 Source: Weintraub, An Approach to the Theory of Income Distribution p. 29.

AGGREGATE SUPPLY AND RELATIVE SHARES

89

aggregate demand functions) is ONi, then the relative wage share is N1A/N1B, while the gross profit share is AB/NiB. Consequently, the magnitude of the relative wage share at any employment level will depend upon the position of the Z-function as compared to the W- line. From equation (1) the slope of Z is found to be: 3

dZ dR dN = W + dN

i „x

(2)

If we assume profit maximization, then dR/dN must be equal to or greater than zero, so that at any N- level, the slope of Z must be equal to or greater than the slope of the W- line. Since both curves emanate from the origin, Z must be either coincident with, or lie above, W. Weintraub introduces the concept of the elasticity of the Zfunction (Ez) as a measure of the change in the relative wage share with a change in the level of employment (at a given money wage rate). The relevant relationship is obtained by differentiating, as follows:

d /ivN\ _w_ w N dZ ( ' dN \Z J ~ Z ~ Z Z dN where Z/N is the average proceeds per worker and dZ/dN is the marginal proceeds. Letting (Z) (dN)/(N) (dZ.) equal Ez, the elasticity of the Z-curve, equation (3) can be rewritten as:

dN \ z J

Z K EzJ

W

It can be shown that the magnitude of Ez, and therefore changes in the wage share, will depend upon the rate of change of the slope of the Z-function.4 Since Z is a continuous function

cl^ Z

emanating from the origin, when Z is a straight line, then ^ ¿ = 0 and therefore — = —r t so that Ez = 1, i.e., the wage share is

N dN

constant. Alternatively, if

d?Z

dZ

Z

> 0, then— r > -rr and Ez

i.e., the wage share falls with an increase in N.

< 1,

d2Z

Finally, if —5

aN

< 0, then Ez > 1, and the wage share is rising. 5 So far we have analyzed only the distribution of income into a wage share and a capitalist share. Weintraub subdivides the capitalist share into the rentier share (fixed contractual payments) and the residual, profits. If the money sums paid to rentiers is fixed at OF (Figure 1), then it is obvious that as

90

AGGREGATE INCOME DISTRIBUTION

employment rises, the relative share going to rentiers must decrease. Thus, even if the Z-function is linear, the residual share will rise with increases in employment. This increase in the residual share at the expense of the rentier share has, according to Weintraub, important economic implications. Thus, he argues that those macrotheories which divide output into only two shares lose sight of the possible heterogeneity of interests among "capitalists." 6 Productivity and Relative

Shares

Under the assumptions of profit maximization and pure competition, Weintraub demonstrates that productivity phenomena alone set the position of the Z- curve relative to the W-line. Each firm, accepting the market money wage rate as a datum, will hire labor until its marginal value product equals the money wage rate, i.e., (5)

P§=u>

where P is the product price and Q is the output quantity for the firm. Hence: dN

(6) w

P

The wage share in the proceeds of the firm is: wN dQ N PQ~ dN Q Letting M designate the marginal physical product of labor and A the average physical product, Weintraub obtains the wage share as: wN M _ „ PQ~~A~ P

(7)

where Ep is the elasticity of productivity. 7 Thus, when diminishing returns are present (Ep < 1), the wage share will be a positive fraction of the total proceeds of the firm. Since Z = PQ for each firm, Weintraub concludes that if each firm maximizes profits, then the aggregate relative wage share in total proceeds is equal to the " a v e r a g e " elasticity of productivity:

i=1

AGGREGATE SUPPLY AND RELATIVE SHARES

91

where Ep is a weighted average of the elasticities of the individual firms (i = 1, 2, . . .n), each weighted by the proportion of total proceeds accruing to the firm. Thus, Weintraub notes that "the absolute money wage fails to appear in these analyses of the relative wage share leading to the conclusion that productivity phenomena alone governs the final r e s u l t . " (pp. 53-54) He adds, however, that changes in money wages may cause changes in the level of output, and therefore, alter the ratio of M to A. Thus, at each level of employment, the relative wage share depends on the elasticity of productivity. The effect of changing N-levels on the relative wage share can be shown to be:

^ ( f ) ^ ( f H (?«--)

w

Since both AM and AA a r e normally negative, only their absolute value need be included in the formula inasmuch as the signs in the parenthesis have already been altered. When the t e r m within the parenthesis is negative, i.e., AM AA M > A

(10)

then the relative wage share declines with increasing N-levels. For inequality (10) to be applicable, it is necessary that both the marginal product of labor and the elasticity of productivity decline with increases in employment. 8 Monopoly and Relative

Shares

When the product price is expected to exceed marginal cost at the maximum profit position, the firm is said to have some degree of monopoly power. (This implies a downward sloping product demand curve.) If the labor market is competitive, then the firm maximizes profits when it hires workers until their marginal revenue product equals the money wage rate, i.e., (MR) (M) =w

(11)

where MR is the marginal revenue. Since MR = P

= P ( 1 - 1/Ed)

where Ed is the price elasticity of demand for the product, 9 then equation (11) may be written as: (P) (1 - 1 /Ed) (M) = w

(12)

AGGREGATE INCOME DISTRIBUTION

92

Thus the wage share in the proceeds of a firm with some monopoly power is: W_ wN _ {P) (1 - 1 /Ed) (M) (N) Z ~ PQ (P) (Qi)

(1 - 1 /Ed)

=f

(13)

When profits are being maximized, however, Lerner's measure of the degree of monopoly, ¡i, is equal to l/Erf. 10 Thus equation (13) indicates the effect of monopoly on the wage share in the proceeds of the firm. Generalizing equation (13) for the economy, Weintraub obtains: f

-

E

f

u

-

^

f

Thus, at any given level of employment, the wage share will be lower with monopoly than with competitive pricing. Weintraub observes, "not only productivity phenomena, therefore, but also the reciprocal of the elasticity of demand—the degree of monopoly power influences the income division under monopoly." (p. 67) He points out, however, that the belief that monopoly lowers the wage share would be correct only if the output of each firm was the same under competition as under monopoly. To the extent that monopoly affects the composition of output and makes possible equilibrium solutions where M > A for individual firms, then the conclusion that monopoly reduces the wage share cannot be drawn. Thus, "although the income division for the same employment volume can be compared, as the output composition will differ, then not too much can be assigned to the comparative results in this typical index-number riddle." (p. 68) Changes

in Money

Wages and Relative

Shares

Most of the analysis so far has assumed that the money wage rate is constant at all levels of employment. If we assume that the money wage rate is a function of the level of employment, then a crosscut technique can be used to obtain the relevant locus for the wage bill curve. Thus, in Figure 2, OWi pertains to the wage bill line at a wage rate of wi, OW2 implies a higher wage rate wz, etc. The actual path of the wage bill locus will be OW. A similar locus can be obtained for the Z-function, where

AGGREGATE SUPPLY AND RELATIVE SHARES

93

Figure 2 Source: Weintraub, An Approach Distribution, p. 78.

to the Theory of Income

the latter lies above the CWpath. Weintraub expresses the difference in the slopes between the two pertinent paths as: 1 1 AZ AN

AW AN

/ \

„Aw

-TT-r - "TT? = I w + N-rr-

AM

AR\ AN J

+ —• ) -

( \

„Aw\ (14) AN J

( W + N -rrrz. )

In this case, the analysis of relative shares will be analogous to the one used earlier with a constant money wage rate; it will depend on the position of the Z locus relative to the W locus. It is apparent from equation (14) that changes in the wage share will depend on the rate of change of the marginal proceeds. If both M and Ep decline with increases in employment, the wage share will fall. Changes

in the Capital

Stock

and Relative

Shares

Weintraub points out that changes in the stock of capital will affect the marginal product of labor, and therefore, the position of the Z-curve with respect to the W-line. He argues that capital-deepening should "shift the Z-curve leftward, shifting

AGGREGATE INCOME DISTRIBUTION

94

income from labor at every level of employment." (p. 81) Capital-widening, on the other hand, should, for any N-level, increase the marginal product of labor, and also may intensify competition if the new equipment involves the formation of new firms, so that it would "redound to labor's favor." (p. 82) No definite conclusions about relative shares can be reached, however, for as Weintraub states: What makes the entire analysis of the swing in Z relative to W so elusive is that its resolution r e s t s on the familiar imponderables, namely, the weighted M/A-ratios and the generalized Ed in the new position compared to the old. . . . Further, if the Z-function is dislodged, the equilibrium employment position is likely to alter through repercussions upon aggregate demand so that the new income allocation will have to be compared to the old—not at the same N- position, but at the new N- level, (p. 82) Technical Progress

and Relative

Shares

Weintraub defines capital-using (labor-saving) technological changes as those which use more equipment and less labor for a given amount of output, and therefore presumably the marginal product of labor will be greater. Manifestly, these changes in techniques will not be undertaken unless the capital share can be widened. The effect of labor-saving inventions, therefore, is to lift Z relative to W, to the relative income detriment of labor at each employment position. 12 Capital-saving innovations, on the other hand, will involve a smaller quantity of capital at each level of output. Weintraub assumes the level of employment is the same for each output level, and thus: "The net effect is to pull the Z-function closer to W at each N- point so that the income shift is to labor and away from profits." 1 3 Finally, "neutral innovations can be defined as those which leave Z stationary relative to W" (p. 84), i.e., techniques which leave the M/A- ratio unchanged at each AT-level. With changes in technology, however, there will be changes in the level of employment. Labor saving devices shift the Zcurve upward; thus, the aggregate demand would have to rise to prevent a fall in employment. Weintraub argues that "considering the shift against real wages and the 'higher capitalist'

AGGREGATE SUPPLY AND RELATIVE SHARES

95

saving propensities, the former N-level is unlikely to be sustained." (p. 96) The result will be technological unemployment. Alternatively, labor-using techniques are likely to increase employment, since the Z-function will fall, while it is unlikely that aggregate demand will be reduced by very much. Aggregate Demand and the Equilibrium Level of Employment Weintraub has demonstrated that at any given level of employment, the relative shares depend primarily on the M/Aratio. The equilibrium level of employment, however, will be where the aggregate supply and aggregate demand functions intersect. Furthermore, the latter function depends on the distribution of income among the various economic classes. Hence, Weintraub attempts to derive an aggregate demand function which will reflect this interdependence with aggregate supply. Since price level changes will affect expenditure patterns, Weintraub begins by developing an aggregate demand function (D) in money terms. The D-function is divided into investment demand (Di) and consumption demand (Be).14 Inasmuch as the Be function is very closely dependent on the relative share distribution, we shall examine Weintraub's analysis of this curve in some detail. Consumption expenditures will depend upon the disposable income of individuals {Yd) and their asset position, i.e., Be = c Yd + \ A

(14)

where c is the average propensity to consume and X represents possible dissavings out of assets (A)„ The total disposable income at each N- level is Yd = wN + F + kR.

(15)

where k is the fraction of profits that is actually distributed to individuals. The aggregate consumption function can be built up out of the consumption behavior of the three major classes in the community: rentiers, wage earners, and profit recipients. As N rises, money prices will rise (due to diminishing returns). Since rentiers receive a fixed money sum, their real income will fall. If they attempt to maintain their real consumption by increasing their money expenditures (D/), then the rentiers' expenditures curve will slope upwards towards a ceiling which represents their fixed money payments. The curve OW in Figure 1 represents the total wage bill at

96

AGGREGATE INCOME DISTRIBUTION

different N- levels. Depending upon the assumptions we make about the consumption behavior of workers, their expenditures curve (Djf) will more or less follow the OW line. In the limiting case, where workers consume their entire income, the OW and D™ curves coincide.15 The consumption function of entrepreneurs (D£) will be related to the amount of profits distributed, i.e., = Cr(kR). Weintraub argues that since profits rise with increases in employment,16 then entrepreneurial expenditures may advance as rapidly as the Z- function despite the fact that not all profits are distributed. Hence the curve will be upward sloping. Slimming these components, the resultant aggregate consumption function will be upward sloping, but at a slower rate than the Z- function. The slower rate will be primarily due to (a) the inability of rentiers to maintain their real consumption level as prices rise, and C & ) the personal savings of entrepreneurs and workers.17 The shape of the investment demand function (Di) will depend upon the investment behavior of entrepreneurs. Weintraub argues, however, that "investment outlay is not subject to an income restriction as is Dc—which is contingent primarily on Yd, itself a function of Z . " (p. 44) The simplest assumption would be that money outlays on investment projects are constant regardless of the price and employment levels—so that Di is a horizontal line. On the other hand, if we assume constant real investment expenditures, then Di will be upward sloping, reflecting the higher money outlays that are necessary as prices rise. Another alternative is that increases in employment induce more real investment (an accelerator affect), producing an even more steeply rising Di curve. Whatever assumption we use, the resulting Di curve will provide an addition to the Dc curve to obtain the aggregate demand function. The equilibrium level of employment will emerge where the aggregate demand and aggregate supply functions intersect. As long as the increment in personal savings plus corporate savings exceed the increment in personal dissavings then the slope of the Dc curve will be less than the slope of the Z-function, and therefore, a stable equilibrium situation is possible. Nevertheless, if we assume that real investment is a function of the level of employment which involves a high accelerator coefficient, then the aggregate demand and aggregate supply curves may not intersect, indicating an explosive situation. Weintraub argues, however, that monetary policy would ultimately "choke

AGGREGATE SUPPLY AND RELATIVE SHARES

97

off investment," and therefore, there will eventually be an equilibrium. Also at full employment, Z will become vertical " s o that any flatness in Di will assure the income-equilibrium outcome." (p. 42) Hence, from the Z-function with its implicit levels of factor hire, Weintraub has been able to trace the flow of payments to the factors. Then he has followed the consumption outlays of the factors (at the given product prices) for each level of employment, thus completing the virtuous cycle of income flows. In conclusion, he notes that by summing Dc and Di, the full D- curve can be constructed, embodying on its path exactly the same prices as are built into the Z-functions at the corresponding employment-output positions. The equilibrium of aggregate demand and aggregate supply prevails at the intersection of the two curves, which entails an employment volume at which the expected sum of sales proceeds is exactly equal to the outlays forthcoming from consuming and investing groups, (p. 44) Comments on the Weintraubian System Professor Weintraub has recognized the problem of interdependence that prevails in a macrotheory of distribution. He has been able to eliminate much of the confusion that has beset this area of study, and has, with the aid of new economic tools, revitalized the classical emphasis on aggregate supply and the neoclassical stress of productivity. He has also introduced into the analysis (a) the degree of monopoly, (b) a "forced savings" notion that is similar to Keynes' "unproductive consumption," and (c) a modified "widow's cruse" effect, i.e., Weintraub observes that since every increase in employment involves an increase the absolute and the relative share going to entrepreneurs, therefore the "entrepreneurial motto could well be 'Consume more and grow r i c h ! ' " (p. 93) In emphasizing the importance of productivity phenomena and the relationship of diminishing returns to relative shares, Weintraub has, on occasion, overstated the case. For example, he argues that with a given money wage rate in a competitive economy, the relative wage share will be constant if the Z-curve is linear; and a linear Z-function denotes " a constant marginal product of labor." 1 8 The requirement of a constant marginal product of labor is

98

AGGREGATE INCOME DISTRIBUTION

not a necessary condition for a constant wage share. If, for instance, the production function is of the Cobb-Douglas type,19 then it can be shown that the Z-curve is linear, 20 despite the fact that the marginal product of labor will decrease with increasing N-levels (assuming a constant stock of capital). This particular type of production function has the notable property that the M/A-ratio is constant at all levels of employment. It can be shown, however, that except for Cobb-Douglas type production functions, diminishing returns normally imply a decreasing relative wage share as employment increases. 21 Of course, with diminishing returns, there will always be a shift of income from the rentiers to the entrepreneurs as prices rise. Although not a necessary condition, it is true that a constant marginal product of labor at all levels of employment will be a sufficient condition for a linear Z-function. If wages are the only variable cost, assuming that labor is hired until its marginal value product equals the money wage rate, then the Z and W lines coincide and the relative wage share is equal to unity. Perhaps the most stringent assumption of the Weintraubian scheme is that the "distribution of proceeds, for each expected aggregate volume of proceeds, is determinate." (p. 26) This implies an "expectation of a unique composition of aggregate demand," 22 and therefore a unique composition of output at each AT-level.23 To justify this supposition, Weintraub argues: Empirically it does appear that there is considerable temporal stability in the economy, in the sense that if gross national product is at $425 billions over years close in time, the composition of output and employment will show strong parallel features . . . . Sectors of variability seem more limited than regions of constancy in the e c o n o m i c u n i v e r s e , though this presupposition time passes.24

weakens

as

If we allow the composition of output to vary at any given Nlevelbecause of changes in the composition of effective demand, then, as Weintraub recognizes, the Z-path is no longer unique; and in obtaining the " a v e r a g e " elasticity of productivity via equation (8), the weights for each industry will change with alterations in the composition of output. To admit this possibility is to sacrifice some of the predictive concreteness of the analysis.25 For short periods of time, therefore, this uniqueness of composition is a useful and probably realistic first approximation.

AGGREGATE SUPPLY AND RELATIVE SHARES

99

As Weintraub has intimated in the previous quotation, this assumption would not be applicable to any long-run theory of relative shares, for in the long run, the Z-function may alter its shape and position. Weintraub therefore does not attempt to present a long-run theory of relative shares, for he does not believe that long-run equilibrium is meaningful. Instead, any long-run explanation of relative shares would have to be stated in terms of shifting unique short-run Z- curves relative to short-run wage bill lines. Commenting on the observed longrun stability of the wage share, Weintraub notes: either the M/A- ratios and the E^- magnitudes must have remained constant or they must have operated systematically and fortuitously to neutralize each other's variation when the stock of equipment, the level of employment, and the nature of the product-mix underwent change, (p. 82) Finally, it should be noted that the aggregate supply approach does meet a fundamental requisite established by Solow, an outspoken critic of macrodistribution theory. Solow asserts that a theory of aggregate income shares should say "something about the component sectors." 2 8 Weintraub's aggregate supply function is built up from industry components. Nevertheless, in reviewing Weintraub's book, Solow has argued: I do not think the [aggregate supply] curve is a very useful device for analyzing distribution. The trouble is that all of the important theoretical questions are buried in the shape of the curve, the things that make it shift, and the way it shifts . . . . Thus to use such a curve as a basic tool seems mainly to transform explicit theorizing into implicit theorizing and into casual statements about the shape of the function itself. 27 Would Solow question the usefulness of The General Theory because of Keynes' implicit theorizing via the propensity to consume?

IX Some Conclusions and Observations on Distribution Analysis Outlines of the major theoretical explanations of relative shares have been presented in the previous chapters. Some comments have been advanced in each chapter and no attempt will be made at this point to recapitulate that material in detail. Instead, a few over-all comparisons will be made to indicate the capricious development of ideas in this area of analysis, and some observations on the present status of macrodistribution theory will be presented. A Comparison of the Various Theories The classical theories have been described as the "magnificent dynamics" 1 because of the boldness of their method and the comprehensive scope of their subject matter. These explanations encompassed sociological and biological phenomena, as well as economic occurrences. The neoclassicists, on the other hand, tended to narrow the range of economic analysis to the study of factors directly emerging in the market place. It is only in recent years, and then mainly in the area of economic development, that economists have broadened their scope to include these wider aspects once again. Ricardo and Marx believed that capital accumulation, economic development, and relative shares were intimately related. They believed in the antipodal movements in wages and profits, and offered sweeping prognostications about the inevitable path of an expanding economy from simple assumptions about changes in productivity and the constancy of the real wage rate. Ricardo predicted an increasing relative wage share, while Marx foresaw a declining wage share. For different reasons, however, neither one forecasted the fate of the relative rent share. Marx ignored diminishing returns and therefore could not distinguish between rents and other capitalist income, while 100

SOME CONCLUSIONS AND OBSERVATIONS

101

Ricardo, although he often argued as though he believed that rent would become a larger proportion of the total product, was unable to demonstrate that this result necessarily followed from his analysis. 2 The Ricardian and Marxian wage share prophesies have not been borne out by the empirical studies of the national income of the western capitalist countries. This incompatibility between classical theory and fact is primarily due to the inapplicability of the classical assumptions rather than to any logical inconsistency in their analysis. By stressing productivity phenomena—hence assuming a definite form of the aggregate supply function—while ignoring the possibility of either a lack of effective demand or a change in the real wage rate, the classicists severely restricted the relevancy of their systems. Moreover, the classical omission of a fixed income class tended to slur the importance of price phenomena in determining relative shares. These theories, however, were not developed primarily for the purpose of producing the solution to the general case, but rather to bring forth answers to contemporary problems of vital importance. The classicists employed a macroscopic approach in their analysis of relative shares. Their theories were conceived in terms of macroeconomic concepts, i.e., the fundamental variables were broad aggregates related to society as a whole and represented either averages or totals of the behavior of the individual units. The functioning of the economy was summarized in terms of several simple magnitudes related by a few elementary relationships. The neoclassicists, on the other hand, replaced this macroapproach with a concentration on microscopic detail, and it was not until recently that the macroscopic analysis was restored into the main body of economic thought. The neoclassicists shunted the theory of distribution into another direction. They treated distribution as essentially a static problem, completely divorced from economic growth. The neoclassical economists became interested in the development of tools of analysis and the advancement of a rigorous science. 3 For them, distribution was but one aspect of the general problem of price determination; whereas, for the classicists, the distributive relationships were considered the keystone of economic activity. Thus, by the latter part of the nineteenth century, the emphasis had shifted from investigations of the "immutable" path of an expanding economy, to how, in a static economy, the prices of the agents of production are determined.

102

AGGREGATE INCOME DISTRIBUTION

In concentrating so intently on microscopic particulars and in working out an endless number of individual cases where events are influenced by particular idiosyncracies, the neoclassicists failed to notice the flaw in their implicit assumption of the independence of product demand and factor prices. As we have already noted, the neoclassical macroeconomic analysis of distribution, as exemplified by J. B. Clark's system, implied a given level of aggregate output and a unique composition of effective demand independent of the distribution of income. Once the level of aggregate activity is permitted to vary, the neoclassical approach is clearly inadequate. It is interesting to note, however, that Keynes, who criticized the neoclassicists for their constant aggregate income hypothesis, 4 did not abandon the principles of marginal productivity. The neo-classical marginal productivity doctrine is useful as an explanatory or predictive device once the level of aggregate income is given. The neoclassicists, by introducing the concept of a demand schedule, did contribute a counterbalance to the classical emphasis on supply conditions, and, as we have already noted, Marshall was aware of the possibility of interdependence between aggregate demand and aggregate supply. Neoclassical analysis, however, in its beautiful simplicity, concentrated its attention upon the shapes of the microdemand curves rather than on an examination of the assumptions behind them. It is not surprising, therefore, that the macroanalysis of the neoclassical economists has come to appear as unsound, not in its logic but in its relevance. The Cobb-Douglas studies attempted to apply empirically the marginal principles of the neoclassical system directly to macroeconomic variables. The dubious nature of the theoretical assumptions (e.g., the assumed form of the aggregate production function, the omission of land as a factor of production, the absence of technical progress during the period of observation) and the use of a statistical production index which presupposes a constant income distribution, as well as the presence of multicollinearity in the data, has tended to undermine the significance of these empirical findings. Influenced by the neoclassical approach, the monopoly theories of relative shares were hampered by the same overemphasis on microeconomic detail. Kalecki and Mitra attempted to construct hypotheses based on individual market structures, without paying sufficient attention to changes in the macroeconomic variables. Although it can be demonstrated that higher

SOME CONCLUSIONS AND OBSERVATIONS

103

prices, given the money wage rate and the level of output, imply a lower relative wage share in the proceeds of the firm, neither Kalecki nor Mitra were able to aggregate this microphenomena without involving their systems in the neoclassical fallacy of an assumed independence of product demand and factor prices. Also, one cannot assume, as they did, that cost schedules will be unaltered when the degree of monopoly changes. Moreover, at present, there is no definitive theory explaining how the degree of monopoly will alter in response to changes in the macroeconomic variables. Nevertheless, Weintraub has been able to introduce into the analysis the effect of changes in the degree of monopoly on relative shares. If these changes in monopoly power are related to changes in the level of employment, then the resultant alteration in the composition of output can be built into the shape of the aggregate supply function and the equilibrium solution can be obtained directly from Weintraub's apparatus. 5 If, on the other hand, the degree of monopoly should vary, at the same level of employment, because of an exogenous change in entrepreneurial expectations about consumers' preferences, then the resultant change in the composition of output would induce a shift in the ^-function. This would involve a redistribution of income at each iV-level, and consequently, a shift in the aggregate demand function. The new equilibrium position can be determined once the pattern of change is posited. 6 With the advent of the modern aggregate demand theories, a relationship between capital accumulation and relative shares was re-established. Mrs. Robinson's analysis (which is acknowledged to be "startlingly familiar to learned r e a d e r s " 7 ) is especially rich inRicardian and Marxian overtones. In her system, fixed coefficients of production, the rate of population growth, the real wage rate, and the rate of accumulation play important roles in determining relative shares. Although such an emphasis implies a reincarnation of the classical view, and although some all-encompassing simplifications are employed, predictions about the inevitable path of the economy are not found in her theory. The aggregate demand theories stress the dichotomous nature of the income flow from the dual processes of («:) an expenditure stream and (b) an income stream. In these theories, given the level of output, the determinant of the proportional distribution of the income stream is the proportional division of the expenditure stream, i.e., the composition of effective

104

AGGREGATE INCOME DISTRIBUTION

demand. These theories bear a striking resemblance to their classical predecessors, for there is never a lack of " r e a l " effective demand. By neglecting the importance of changing employment levels, however, the applicability of these modern theories is limited mainly to economies where the level of employment is stable. In economies such as our own, where employment is likely to fluctuate, these theories are incomplete explanations of the real world. The recent aggregate demand theories have, however, revitalized the study of the interrelationships between problems of economic growth and problems of distribution. They have emphasized that, given the propensities of the various economic classes and the state of technology, there may be a unique proportionate distribution of income between wages and gross profits which is consonant with a given rate of growth. This does suggest the possibility of incompatible policy objectives, e.g., attempting to simultaneously increase the growth rate and the relative wage share. Hence, the question of an optimum rate of growth and an optimum income distribution is open for critical review and evaluation. The macroscopic method of the classicists has been revived by the modern aggregate demand theorists. Boulding's scheme, for example, represents an extreme macroscopic approach where the relationships between the aggregate variables have been reduced to definitional identities incapable of analyzing the causes of economic change, for it is devoid of operational or functional concepts. Boulding's macroeconomic paradoxes and his explanation of macrodistribution phenomena depend on assumptions about the independence and passivity of the aggregate variables in his macrobalance sheet identities. As we have indicated, these characteristics cannot be attributed to magnitudes that are only definitionally related. 8 Propositions based solely on definitions are tautologous and have no explanatory value; they do not represent a hypothesis, and therefore, their validity and applicability cannot be judged. Mrs. Robinson and Kaldor do combine functional relationships regarding expenditure behavior with definitional statements on income composition. Nevertheless, the marginal productivity functions of the neoclassical system are conspicuous by their atrophied position in these aggregate demand theories. Kaldor disdains the use of marginal productivity analysis, while Mrs. Robinson subjugates it to a minor role. Weintraub has attempted to balance the aggregate approach

SOME CONCLUSIONS AND OBSERVATIONS

105

of the classicists and modern demand theorists with the microemphasis of the neoclassical economists. He argues: Implicit in each output quantum are precise magnitudes of factor hire, factor prices and factor earnings . . . . To overlook these relations would create an irreparable rift from the modern theory of the firm depriving us of information it can impart, and impede the synthesis and the systemization that a distributive theory must achieve. 9 Hence, he has combined many of the important elements of the earlier explanations into his analysis. For example, we have demonstrated that the elasticity of productivity was implicitly a determining factor in the Ricardian system, while Weintraub has explicitly used this concept in his analysis. Besides restoring the classical stress on aggregate supply to a par with the neoclassical and modern emphasis on demand, Weintraub has brought forth the problem of the interdependence of aggregate demand and aggregate supply. Moreover, he has suggested how this interaction can be advantageously used to elicit conclusions. Although indicating the inadequacies of the aggregate demand theories, Weintraub has made use of some of the important concepts originating in their Keynesian antecedent. For example, his analysis of the effect of changes in the level of employment on rentiers' expenditures is similar to Keynes' Treatise analysis of the effect of increased investment expenditures on "unproductive consumption;" while Weintraub's observation that increasing JV-levels increase the residual income share, and that, therefore, the more entrepreneurs spend, the richer they will become, is a sophisticated form of the "widow's c r u s e " effect. Weintraub has re-emphasized the Keynesian conclusion that, given the level of output, the money wage rate has no effect on the magnitude of the relative wage share. Thus, in all share theories which accept the level of output as a datum (i.e., all but Weintraub's system), macrodistribution phenomena are independent of the money wage rate. It is the real wage rate which is the essential determinant of the wage share in most of these theories. In the Weintraubian system, on the other hand, changes in money wages affect prices, and consequently affect the positions of the aggregate demand and aggregate supply functions, and hence, the ultimate equilibrium outcome. In his attempt to avoid the savings-investment polemics, however, Weintraub has de-emphasized the role of the investment sector, indicating that the latter is no more important than

106

AGGREGATE INCOME DISTRIBUTION

the consumption sector in determining the level of aggregate income and its distribution. 1 0 He even intimates that the consumption component of aggregate demand, because of its i n t e r dependence with aggregate supply, may be m o r e s t r a t e g i c in macrodistribution phenomena. 1 1 M r s . Robinson, on the other hand, has implied an interdependence between investment expenditures and aggregate supply a s an e s s e n t i a l factor d e t e r mining relative s h a r e s . She notes that d i s s i m i l a r i t i e s in the techniques of production (i.e., different aggregate supply functions) will induce d i f f e r e n c e s in the investment component of aggregate demand; hence, relative s h a r e s at the s a m e level of employment will differ. This interaction is entirely consistent with Weintraub's system, for a s we have already noted, his a s sumption of a unique composition of aggregate demand at each N-level implies interdependence between investment demand and aggregate supply a s well as between consumption spending and supply. Weintraub's subordination of the role of capital formation may be attributed to the s h o r t - r u n nature of his analysis a s well a s the assumption of fully integrated f i r m s . We can show, however, that the aggregate demand t h e o r i e s and the Weintraubian system a r e compatible. In the aggregate demand t h e o r i e s of Robinson and K a l d o r , t h e relative s h a r e s a r e determined essentially by the proportional allocation of labor between the consumption and the investment s e c t o r . In the Weintraubian scheme, on the other hand, the s h a r e s depend on a weighted elasticity of productivity. If the e n t r e p r e n e u r s a r e maximizing p r o f i t s in a competitive economy, then they a r e hiring labor until its m a r g i n a l value product equals the money wage r a t e . The r e m a i n d e r of output will, by definition, go to the capitalists. Weintraub a s s u m e s expectations of a unique composition of aggregate demand, hence, the s t r e s s is placed on aggregate supply. Alternatively, underlying the aggregate demand s c h e m e s is the assumption that at any level of employment, the composition of aggregate demand, at l e a s t between investment goods and consumption goods, can vary. Thus, by a s s e r t i n g that the capitalist group does m o s t , if not all, of the actual savings in the community, these s c h e m e s argue that it i s essentially the composition of effective demand that d e t e r m i n e s relative s h a r e s . These two approaches a r e compatible, the main difference being one of e m p h a s i s . The Robinson and Kaldor t h e o r i e s e m phasize changes in the composition of " r e a l " effective demand

SOME CONCLUSIONS AND OBSERVATIONS

107

at a given level of employment, while price level and productivity phenomena are relegated to a subordinate role. 12 In the Weintraubian scheme, it is the price and productivity relations and changes in the level of employment which are placed in a position of predominance. These apparent differences in the determining factors are but a further indication of the interdependence of aggregate demand and aggregate supply. Given the level of employment and the composition of output, the distribution of income will depend on productivity phenomena. If, however, we allow the composition of effective demand to vary, then the output quantities of the individual firms and industries will change, altering the average M/A-ratio 13 at any given employment level and therefore altering the relative shares. In the equilibrium solution, the conclusions of both methods are valid. As Weintraub has written: To argue that (most) savings comes out of profits and that, therefore, investment determines profits is only slightly less tautologous than to argue that investment "determines" savings; one might almost say that by definition I = S = R. Yet investment, with consumption, determines income. To produce the income, however, requires employment which, in itself, entails some principle of factor hire. It is here that marginal productivity ideas enter. . . the wage share "depends" on the ratio of marginal to average product, as well as the level of investment. (p. 107) Hence, Weintraub indicates that the two approaches must be compatible. Thus, for certain economic problems relating to economic growth at full employment, it may be desirable to use the aggregate demand analysis explicitly, while keeping in mind the necessary productivity relationships as indicated by the aggregate supply thesis. In determining short-run effects, however, the Weintraubian analysis may prove to be more valuable.14 The present status of macrodistribution theory may be appraised by indicating that the Weintraubian analysis represents a combination and a culmination of much of the theoretical work in searching for a solution to the riddle of relative shares. Weintraub has correctly entitled his work An Approach to the Theory of Income Distribution, for further investigations will, for the most part, adopt his approach and extend and elaborate his system to treat related questions.

Appendix A Note 1 Proposition:

To prove that for the Cobb-Douglas function dZ

Z

dN = EPN

+

w

Ts

.

'

= COnstant

,

(1)

>

where Z is total proceeds, N is the level of employment, Ep is the elasticity of productivity, w is the money wage rate and Es is the elasticity of supply. For small changes, Z, N, and w are constant, and therefore the magnitude of dZ/dN will depend on the elasticities of productivity and supply. In a purely competitive market, Es is the elasticity of the marginal cost (MC) curve, i.e., E s

_ (MC) dQ " Qd (MC)

W

Since MC = w/M, where M is the marginal product of labor, 1 then d (MC) _ d (w\ dN dN\Mj

_'W

dM dN M*

, . W

By differentiating the Cobb-Douglas Function (Q = bCJNk), we obtain: ££

- * (*-i) b Cj j*

= ft (k-i) £

(4)

Substituting equation (4) into (3), we obtain d (MC) _-w (fe-1) dN fe Q

(5)

Multiplying both sides by dN/dQ: 'We are assuming that labor is the only variable factor.

108

APPENDIX A

109

d (MC) ~dQ~

-w(k-l)N =

*V

(6)

Substituting equation (6) into (2) _ (MC) k? Q Es

~ -w(k-1)

N

(V

Letting MC = w/M, we obtain Es

=

1

k2

' Tplk-T)

(8)

It can be demonstrated (Note 2) that, given k, Ep is a constant for the Cobb-Douglas function, and therefore it follows from equation (8) that Es is also a constant. Substituting these constants into equation (1) demonstrates that, for the Cobb-Douglas formulation, dZ/dN is a constant.

110

AGGREGATE INCOME DISTRIBUTION

Note

Proposition:

2

To demonstrate what form the production function must have to have a constant M/A-ratio at all levels of employment.

Let the M/A- ratio for labor be equal to a constant (k): dQ/dN^ Q/N

(1)

where Q is output and N represents the level of labor employed. Hence: Q ~

N

W

Integrating, we obtain: log Q = k log N + log a

(3)

where a is a constant. Thus the production function will have the following form with respect to N: Q = a A^ This function is one variable is mathematically akin to the two variable Cobb-Douglas function, Q = b W, the latter being the production function usually associated with constant relative shares.

111

APPENDIX A

Note 3

Proposition:

To demonstrate that the M/A-ratio either remains constant or declines with diminishing returns, when the total product function is a normal, continuous, monotonic function within the region of rational factor hire.

Mrs. Robinson has shown1 that at any given abscissa value, the relation between the points on the marginal and average curves can be expressed as

H

-

H)

«

where e is the absolute value of the elasticity of A at that point. It follows from equation (1) that the M/A-ratio varies in the same direction as e. It can be shown that if the average curve is a normal, downward-sloping curve, then either e is a constant (and A has the general form A = (a/Nph , where a and b are constants) or € declines towards unity as employment increases and M approaches zero.2 Since M must always be greater than zero in the region of rational factor hire, e can never be equal to or less than unity in this region.

' j . Robinson, The Economics of Imperfect Competition (London: Macmillan, 1954), p. 36. 2See S. Carlson, A Study on the Pure Theory of Production (New York: Kelley and Millman, 1956), pp. 56-58; R. G. D. Allen, Mathematical Analysis for Economists (New York: Macmillan, 1939), p. 258.

112

AGGREGATE INCOME DISTRIBUTION

Note 4 Proposition:

To demonstrate that when a normal production function is linear and homogeneous, an increase in the labor-capital ratio cannot induce an inc r e a s e in the ratio of the marginal product to the average product of labor.

Assume that in the pretrade position, the labor intensive industry (X) is operating at point R on its isoquant map (Figure 1). After trade, the output of X is contracted to point S. E r e c t a line from S, perpendicular to the ordinate axis, which intersects the vector OR at point T. Since the production function is linear and homogeneous, the M / A - r a t i o will be constant along any given straight line emanating from the origin. Thus, the M/Aratio at R is equal to the M/A- ratio at T. If starting from T, labor inputs are added to reach S (by moving along TS), then the marginal and average products will fall (because of diminishing returns). It can be demonstrated, however, that with diminishing returns, the M/A-ratio will either be constant (if the function is of the Cobb-Douglas type) or it will decline. 1 Hence, the M / A - r a t i o at point S is equal to, or less than, the M/A-ratio at points T or R. Thus, with an increase in the labor-capital ratio, the M/A-ratio either remains constant or declines in industry X. In a similar manner, it can be demonstrated that the M/Aratio in industry Y cannot increase as the labor-capital ratio r i s e s . In Figure 2, point R' is the pretrade output position of industry Y, while the posttrade situation is represented by S'. By erecting lines similar to Figure 1, it can be shown that the M/A-ratio at R' is equal to the M/A-ratio at T \ which in turn, is equal to or greater than the M/A-ratio at S'.

'See Appendix A: Notes 2 and 3.

113

APPENDIX A

Figure 1

Industry Y

Figure 2

Appendix B Relative Shares, The Level of Employment, and International Trade (An Extension

of the Aggregate

Analysis of Relative

Supply

Shares)

One interesting extension of Weintraub's aggregate supply approach is to demonstrate the effect of international trade on the relative wage share in a labor scarce competitive economy. In an article in 1941, Stolper and Samuelson indicated that in such an economy with a constant level of employment, the relative and absolute share of labor will decline, since the marginal physical product of labor will be lower after trade. 1 Since Weintraub has demonstrated that the relative wage share depends not only on the marginal product of labor, but rather on the relation of the marginal product to the average product,2 the Stolper-Samuelson model should be examined to see (a) if the average ratio of marginal to average product (M/A) declines with the introduction of trade, and (b) if the assumption of a constant level of employment can be relaxed. Stolper and Samuelson assumed that in a labor scarce (fully integrated) economy, only two commodities (X and F) are produced both before and after trade. The production functions are linear and homogeneous. They also assumed that there are only two factors of production, labor (N) and capital (C), and that the XW. F. Stolper and P. A. Samuelson, "Protection and Real Wages," Review of Economic Studies, IX (1941); reprinted in the Readings in the Theory of International Trade, ed. American Economic Association (Philadelphia: Blakiston Company, 1949), pp. 333-357. All further references are to the Readings reprint. 2 S. Weintraub, An Approach to the Theory of Income Distribution, pp. 51-52.

114

APPENDIX B

115

level of employment of both factors is constant throughout the analysis. Furthermore, it is assumed that the introduction of trade shifts resources from industry X (which is relatively labor intensive at any given factor price ratio), decreasing its output, to industry Y (which is relatively capital intensive), increasing the output of the latter. 3 The authors were able to demonstrate that the labor to capital ratio increased in each industry after trade, as labor became cheap relative to capital. 4 Since the production functions are linear and homogeneous, the marginal productivity of labor is a function of factor proportions; with a rise in the labor-capital ratio, the marginal physical product of labor will decline in each industry. 5 Since the level of labor employed in the economy is unchanged (by assumption), Stolper and Samuelson argue that the relative wage share must be lower. Nevertheless, another mathematical property of linear and homogeneous production functions is that the average product depends solely on factor proportions, 6 and therefore both the marginal and average product of labor in each industry declines as the labor-capital ratio rises. Hence, the M/A-ratio (and therefore the relative wage share) in each industry may either fall or remain constant—it can be demonstrated that if an industry has a normal production function, then its M/A- ratio cannot rise when the labor to capital ratio increases. 7 The wage share in the total proceeds of the economy is equal to, as Weintraub has demonstrated, the weighted average of the M/A-ratios of the individual industries, 8 i.e., W _

z~

Zx

z

Zy_

z

(1)

Lancaster has suggested that under certain demand conditions, the composition of output might change in the reverse direction. [See K. Lancaster, "Protection and Real Wages: A Restatement," Economic Journal, LXVII (1957), 206-207.1 T h e approach presented in this appendix could, of course, be used in analyzing the results of Lancaster's reverse situation. Since this appendix is essentially illustrative, the analysis is left to the reader. 4 Stolper and Samuelson, op. cit., pp. 347-351. * Ibid.., p. 346. 6 R. G. D. Allen, Mathematical Analysis for Economists (New York: Macmillan, 1939), p. 322. 7 See Appendix A, Note 4. 8 Weintraub, op. cit., p. 53.

AGGREGATE INCOME DISTRIBUTION

116

where W is the total wage bill, Z is total sales proceeds in the economy, Zx is the total proceeds in the X industry, Zy is the total proceeds in the Y industry, M and A with their respective subscripts represent the marginal and average product of labor in the appropriate industry. For any given ratio of factor prices, the wage share will be greater in the labor intensive industry than in the capital intensive one; hence, before trade, Mx/Ax > My/Ay. With the introduction of trade, however, the importance of industry Y increases relative to X, i.e., Zy/Z increases while Zx/Z decreases. Thus, even if the M/A- ratio (and therefore the wage share) in each industry is unchanged, equation (1) indicates that the wage share in the total proceeds of the economy will decline as trade induces a change in the composition of output. The effect of trade on the relative wage share in a labor scarce economy is similar to the introduction of capital-using technological innovations in the Weintraubian system. 9 In the latter case, at the same level of labor employment, the average product (weighted) of labor increased more than the marginal product (weighted), while in the trade situation, the average product (weighted) fell less than the marginal product (weighted) of labor. Although capital-using technological changes and the introduction of trade have the same effect on the relative wage share, at any given employment level, the former induces an increase in real wages, while the latter tends to decrease the real wage bill at the same level of employment. Thus, it can be demonstrated that the Stolper-Samuelson results are confirmed by a Weintraubian approach. It is possible, by employing the concept of an aggregate supply function, to relax the assumption of an unchanging level of labor employment. In a labor scarce economy, trade may induce a change in the composition of output and a possible decline in each industry's M/A-ratio which will lower the relative wage share in the total proceeds at any given employment level. The effect of trade, therefore, is to lift the Z- function relative to the money wage bill line of the Weintraubian system, at each employment level. If a constant money wage rate is assumed, 10 'ibid., p. 83. 10 A

constant money wage rate before and after trade is not inconsistent with labor becoming cheaper relative to capital, since the money price of capital can rise. Since the relative wage share depends only on the position of Z relative to the wage bill line, a f a l l in the money wage rate could also be handled by the analysis. The assumption of a constant money wage rate, however, simplifies the diagrammatic p r e s entation.

117

APPENDIX B

Figure 1

then, in Figure 1, OW represents the money wage bill line, Zfr denotes the pretrade aggregate supply function, and Zt,the posttrade Z-function. If Db is the pretrade aggregate demand function, the Nb is the pretrade level of employment, OR is the total money wage bill, and R'Nb/SNb is the relative wage share. If, after trade, the aggregate demand function for home production is Dt (where Dt includes a component for the demand for the output of industry Y by foreigners, and excludes the domestic demand for the import of commodity X from the foreign nation), then the level

118

AGGREGATE INCOME DISTRIBUTION

of employment will increase to Nt, while the money wage bill r i s e s to OT, and the relative wage share declines to T'Nt/VNt. Although the marginal product of labor in each industry has fallen (i.e., the real wage rate is lower 11 ), the level of employment has risen. One cannot deduce, therefore, the effect on labor's real absolute share. The possibility does exist that trade may be beneficial to labor as a group. Thus, the definiteness of the Stolper-Samuel son conclusion on labor's absolute share is lost once the level of employment is permitted to vary; it may not be necessary to invoke the "compensationprinciple," as Stolper and Samuelson do, to ward off protectionist arguments for tariffs. Thus, it has been suggested how the effect of international trade on macrodistribution could be analyzed. A complete r e s olution of the problem would involve the comparison of the r e sultant M/A-ratio at the new AT-level with the M/A- ratio at the pretrade employment level. This, however, necessitates a thorough analysis of the magnitudes of the propensities to import and to save of each of the economic groups in the domestic and the foreign economy, and, since there are fixed income r e cipients, a comparison of the pretrade and posttrade commodity price ratios (which Stolper and Samuelson consider irrelevant for their argument 12 ). Then the posttrade aggregate demand function could be built up from its components, and it would be possible to indicate whether the introduction of trade increases real effective demand for home production and, therefore, increases the level of labor employment. (We have assumed this to be true in order to simplify our illustrative analysis.) The International

Trade

Multiplier

At the present time, the most definitive and comprehensive theoretical study of the effect of international trade on the level of economic activity has been presented by Machlup. 13 He a s sumes, throughout his lengthy analysis, stable prices with

"Assuming no change in leisure income preferences, a lower real wage rate at the higher posttrade employment level implies some involuntary unemployment at the pretrade equilibrium position. 12 Stolper and Samuelson, op. cit., pp. 340-341. 13 F. Machlup, International Trade and the National Income Multiplier (Philadelphia: Blakiston Co., 1950).

APPENDIX B

119

changing output levels (i.e., infinitely e l a s t i c industry supply curves), while he does not take into account either distributional e f f e c t s or changes in the money wage r a t e . Machlup indicates that he i s " n o t equipped" to deal with the p r o b l e m s of changing p r i c e s and distributional effects. 1 4 He defends his stable p r i c e assumption on the grounds that it r u l e s out a g r e a t many complications and that " t h e r e is little that a general theory can do about this m a s s of ' p o s s i b i l i t i e s ' . " 1 5 Nevertheless, our basic model a s derived f r o m W e i n t r a u b ' s analysis does have p r i c e and distributional phenomena built into it, and t h e r e f o r e we a r e equipped to deal with these p r o b l e m s . Thus, macrodistribution analysis could be extended to the theory of the foreign t r a d e multiplier. Rather than, at this t i m e , a t tempt to r e i n t e r p r e t the multitude of Machlupian models into aggregate demand and supply functions, it may be indicated that the solution to those models where the initial i n c r e a s e in exp o r t s is " a u t o n o m o u s " (implying a change in the composition of output at each employment level) will involve a shift in the aggregate supply function. Induced changes in exports, on the other hand, imply movements along the Z- function. In either case, the equilibrium position can be determined by the i n t e r section of the resultant aggregate demand and supply functions. Finally, Machlup's omission of changes in money wages can also be r e m e d i e d by the Weintraubian approach. Weintraub h a s indicated that t h e r e a r e f a m i l i e s of aggregate demand, a g g r e gate supply, and wage bill lines, where along each curve a given money wage r a t e and given p r i c e phenomena a r e posited. 1 6 Hence it i s possible to extend Weintraub's close s y s t e m analys i s of the e f f e c t s of changes in money wages to include foreign t r a d e effects. In this way, one could use these analytical tools to introduce wage changes into foreign t r a d e multiplier theory.

204n. p. 205. l6 See Chapter VIII, Figure 2. 14Ibidp. l5Ibid.,

Notes Notes to Chapter I M. M. Keynes, "Relative Movements of Real Wages and Output," Economic Journal, XLIX (1939), 48. 2 Recently, there have been several empirical studies tending to derogate the concept of constant income shares. Kravis, analyzing the share of national income going to employee compensation has concluded that the "notion of long-run constancy in relative shares is false." Solow, while questioning the "relative" stability of the employee compensation share, has admitted the possibility of having "an aggregate distribution theory without believing in the historical constancy of relative shares." [See I. Kravis, "Relative Income Shares in Fact and Theory," American Economic Review, XLIX (1959), 917; and R. Solow, "A Skeptical Note on the Constancy of Relative Shares," American Economic Review, XLVIII (1958), 618.] On the other hand, Johnson has shown that the share of wage earners plus the imputed earnings of the self-employed (which is conceptually close to labor's functional share) does not show any significant secular change, while Weintraub has demonstrated that the proportion of business gross product going to employee compensation has been constant. [See, D. G. Johnson, "The Functional Distribution of Income in the United States, 1850-1952," Review of Economics and Statistics, XXXVI (1954); and S. Weintraub, A General Theory of the Price Level, Output, Income Distribution, and Economic Growth (Philadelphia: Chilton Company, 1959).] 3

In some theories, the authors have believed it desirable to further subdivide the capitalist share.

Notes to Chapter II J

In the preface to his Principles, Ricardo wrote: "The produce of the earth—all that i s derived from its surface by the united application of labour, machinery, and capital, is divided among three classes of the community . . . . 120

NOTES

121

"But in different stages of society, the proportions of the whole produce of the earth which will be allotted to each of these classes, under the names of rent, profit, and wages, will be essentially different; depending mainly on the actual fertility of the soil, on the accumulation of capital and population, and the skill, ingenuity, and instruments employed in agriculture. "To determine the laws which regulate this distribution, is the principal problem in Political Economy." D. Ricardo, On the Principles of Political Economy and Taxation, Sraffa Edition (Cambridge, Eng.: Cambridge University Press, 1952), I, 5. All of the following references on Ricardo come from Sraffa's collected volumes of Ricardo's writings. *Works and Correspondence of David Ricardo, edited by Sraffa, VIII, 278-279. Cf. the opening passages in J. M. Keynes, The General Theory of Employment, Interest and Money (New York: Harcourt, Brace and Co., 1936). 3

Ibid., I, xlviii. In the limiting case where the same total physical output is produced, a change in the distribution of income will induce an apparent change in the pecuniary magnitude of the produce. *Ibid., I, 24. 3

Ibid., I, 70.

°Ibid., I, 72. Rent is defined as "that portion of the product of the earth, which is paid to the landlord for the use of the original and indestructable powers of the soil." (I, 67). 7

Ibid., I, 151. Also see I, 78, 96-101, 122-123. Ricardo did qualify this doctrine by indicating that only circulating capital gives rise to a demand for labor, but he believed that every increase in total capital would be accompanied by an increase in circulating capital. (See 396n.) 8

This concept of a wage fund was elaborated by Adam Smith from the initial idea of the Physiocrats. The capitalists decide what portion of total output they will advance to labor; this advance constitutes the wage fund. See A. Smith, The Wealth of Nations (New York: Modern Library Edition, 1937), 69, 316-317. 326. "Ricardo, Principles, I, 78, 94, 406-407. 10

Ibid., I, 296. Cf. also 411.

AGGREGATE INCOME DISTRIBUTION

122 lx

lbid„ I, 49. Cf. also 126.

12

Ibid., I, 114. Thus, Ricardo concluded that the landlord gained twice. First, he obtained a larger physical portion and secondly, the price per unit increased. See also pp. 403-404 including note, 411, 118. 13

Ibid., I, 102, 110-111.

14

Most of the important ideas in the following analysis of the Ricardian system can be found in my articles "A Clarification of the Ricardian Rent Share" (May 1959) and "Increasing Employment, Diminishing Returns, Relative Shares, and Ricardo" (February 1960). Both appeared in the Canadian Journal of Economics and Political Science. Permission to reprint has been granted by the editors of this Journal. ls

Ricardo, op. cit., I, 83n.l, 49n.l, 402n.4.

ia

Ibid., I, 83. Also see I, 49; II, 198n.2.

"Ibid., I, 83-84n., 115-117. E. Cannan in his book, Theories of Production and Distribution 3rd ed. (London: P. S. King and Son, Ltd., 1924), argued that "For the belief that rent becomes a larger proportion he [Ricardo] had no grounds except possibly the fact that it happened to do so in certain arbitrarily chosen arithmetical examples." (p. 353) In his own arbitrarily chosen arithmetic example, Cannon indicates the possibility of a decline in the relative rent share even though the absolute rent bill increases, (p. 353n) 1B

Ibid., II, 196-197n.l. See also II, 198-199n.2.

"Actually these are the marginal and average physical products of a dose of labor and capital, that is, labor and capital are always applied in fixed proportions. ^Diminishing returns imply only that M is decreasing (A may still be rising if at lower levels of employment there were increasing returns to labor). Ricardo, however, assumed constant returns to scale; diminishing returns occurred only when the labor to land ratio increased. In other words, he implied that the production function was homogeneous of the first degree. One of the properties of such functions is that the marginal productivity of the variable factor always diminishes as more of it is added to a fixed factor. Thus, in the Ricardian system, there can never be increasing returns to labor; hence, when M turns down, A must fall.

NOTES

123

S. Weintraub, Price Theory (New York: Pitman Publishing Corp., 1956), p. 83n. 21

For a further discussion of the importance of the elasticity of productivity for relative shares, see Chapter VIII, infra. 22

It is demonstrated (Appendix A: Note 2) that the M/A-ratio will be constant when the proportion of labor to land increases (i.e., with diminishing returns) only if the output function is of the form Q = Otherwise, diminishing returns with a normal, continuous monotonic total product function implies a decrease in the rent share (Appendix A: Note 3) and consequently a rise in the rent share. The assumption of a normal continuous, monotonic total product function underlies the usual textbook drawings of M and A (such as Figure 1). Once kinks and/or bends are introduced into the product curve, it is possible to demonstrate all sorts of unusual distributive results in the r e gions immediately adjacent to these oddities. TheCannan arithmetic demonstration of a decline in the rent share (with rising employment levels) is based on an implicit assumption of a kink in the total product curve. 23

A normal total product curve (the vertical section of the production surface obtained via a plane perpendicular to the land axis) is defined as a continuous monotonic function which reaches, or at least approaches, a maximum as the proportion of variable to fixed factor increases. 24

^ K a r l Marx, Capital (Chicago: Charles H. Kerr and Co., 1921), I, 14. All further references to Capital are from the volumes published by Kerr and Co. unless otherwise stated. *eIbid„ IU, 214. 27Ibid., I, 189. The problem of valuation of non-reproducible goods does not enter into Marx's scheme, since he is interested primarily in the distribution of the present flow of output.

Ibid., I, 574, 583-584, IE, 993-994.

ZB

z0Ibid., I, 565. In discussing agriculture (I, 578-579), he did indicate that decreasing productivity of labor due to decreasing fertility of the soil may affect relative shares. See infra. w Marx's profit rate concept is perhaps more close to the ratio of profits to sales which would be s/(c + v + s).

AGGREGATE INCOME DISTRIBUTION

124

31P. Sweezy states that "Marx makes the assumption that all capital has an identical turnover period." (P. Sweezy, The Theory of Capitalist Development [New York: Oxford University Press, 1942], p. 167.) See also J. Robinson, An Essay on Marxian Economics (London: Macmillan, 1952), p. 7. In a recent article, H. D. Dickinson ("The Falling Rate of Profits in Marxian Economics," Review of Economic Studies, XXIV [1957], 21) indicates how the correction for varying durabilities of capital goods may be inserted into the model. 32Marx, op. cit., I, 672. Marx's stock of variable capital is identical with Ricardo's notion of circulating capital—a wage fund concept. 33Ibid.,

I, 694. See also I, 700.

"ibid.,

Ill, 247, 259, 268.

35Ibid.,

Ill, 247-271.

^Marx does take "passing notice" that the rate of exploitation may rise due to " a lowering of the value of wages through a development of the productive power of labour" (III, 275); but he ignored the importance of this and continued to develop his law of the falling rate of profit under the assumption of a constant rate of exploitation. ^Cf. J. Robinson, op. cit., pp. 20, 36, 39. 38Marx,

op. cit., I, 574-578. Marx indicated that it was possible, when either the duration of the day or the intensity of labor increased, that the quantity of goods making up the subsistence wage basket would be increased to compensate for the "increased wear and tear of labour-power." (I, 578) In this case, both s and v might increase, and therefore it would be impossible to generalize about the effect on relative shares. Marx did believe, however, that v would not rise as much as s; hence the wage share would fall. 39Ibid.,

I, 573.

"ibid.,

I, 577.

4l The

present American "farm-problem" would indicate that progress has more than offset diminishing returns. 42See

Ricardo, Principles, I, 290-292. Also, see Marx, Capital, II, 456, 466. It is true that Marx recognized the fallacy of Say's law (I, 127-128), and he indicated that a crisis was the

125

NOTES

possible outcome of the lack of aggregate demand. However, Marx's theory of the production of surplus value is independent of any references to aggregate demand. For an interesting a r ticle on Marx's position on Say's law, see B. Shoul, " K a r l Marx and Say's Law," Quarterly Journal of Economics, LXXI, (1957).

Notes to Chapter III 1

For an excellent interpretation of von Thunen's theory in terms of modern marginal productivity theory, see A. H. Leigh, "Von Thunen's Theory of Distribution and the Advent of Marginal Analysis," Journal of Political Economy, LIV, 1946. Also see L. H. Haney, History of Economic Thought, 3rd ed. (New York: Macmillan, 1936), pp. 361-373. z

Tributes to von Thunen for the first explicit statements of marginal productivity can be found in the writings of A. Marshall and J. B. Clark. See A. Marshall, Principles of Economics, 8th ed. (New York: Macmillan, 1950), p. 522n; and J. B. Clark, The Distribution of Wealth (London: Macmillan, 1899), p. 321n-324n. >W. S. Jevons, The Theory of Political (London: Macmillan, 1911), xivii.

Economy,

4th ed.

i

Ibid., 217. The dx/dl "represents the ratio of produce, or the productiveness of labour, as regards to the last increment of labour applied," (p. 216) or in modern parlance, it is the m a r ginal physical productivity of labor. 5

A. Marshall, Principles Macmillan, 1950), p. 510.

of Economics,

8th ed. (New York:

6

J. B. Clark, The Distribution of Wealth (London: Macmillan, 1899). 1

Ibid., p. 22. The composition of demand is implicitly assumed constant. B

Ibid., p. 30. Further justification for a study of statics is that " a l l real knowledge of the laws of movement depends upon an adequate knowledge of the laws of r e s t . " (p. 442) B

Ibid., p. 246. In a dynamic society, therefore, changes in the social funds of capital and/or labor can be qualitative as well as quantitative. 10

Ibid., p. 201. Italics mine.

AGGREGATE INCOME DISTRIBUTION

126 u

Ibid., p. 331. Also see pp. 117, 201-203. The mathematics of the situation requires that the production function be linear and homogeneous if the area EBC is to equal the area A'E'C'D'. 12

Since both the total output of the community and the total wage bill are represented in one diagram (Figure 2), it is a simple matter for us to go one step beyond Clark's analysis and indicate that the relative wage share is equal to the ratio of the area of the rectangle AECD to the total area under the curve BC. In a similar manner, the capitalist share could be calculated from Figure 3. i3

Ibid., p. 412. By the time the temporary source,of profits had disappeared, "gains from new sources will be accruing to the captains of industry, so that there will always be profits." "ibid., p. 2. l5

Philip H. Wicksteed, The Co-ordination of the Laws of Distribution (London: Macmillan, 1894, reprinted by the London School of Economics and Political Science, 1932). 19

Ibid.,pp. 10, 15, 24-32, 37. It follows directly from Euler's theorem that if a function is linear and homogeneous, then the sum of its partial derivatives, each multiplied by the magnitude of its respective independent variable, equals the magnitude of the dependent variable at each point on the function. See R. G. D. Allen, Mathematical Analysis for Economists (New York: Macmillan, 1939), pp. 317-322. 17

Ibid., p. 38. Wicksteed was aware that indivisibilities of the factors might introduce an air of indeterminancy into the analysis. He argued however, that there are discontinuities in all economic functions, but "this does not derogate from the extreme value of such expressions, as giving precise expression to the theoretical limits of accuracy in assigning competitive shares in a product which the sundry factors of production would secure in an open market." (p. 39) 1

F r a n c i s Y. Edgeworth, "The Theory of Distribution," Quarterly Journal of Economics, XVIII (1904), 182. 19

Leon Walras, Elements of Pure Economics, trans. W. Jaffee (London: George Allen and Unwin, 1954), pp. 494-495. 20

Knut Wicksell, Lectures on Political Economy, trans. E. Classen (London: Routledge and Sons, 1934), I, 125-131.

NOTES

127

Ibid., p. 130.

2i

J. B. Clark, op. cit., especially pp. 1-9.

22

A. C. Pigou, The Economics of Welfare, 4th ed. (London: Macmillan, 1948), p. 549. 23

*Ibid., Part in, Chapter XIV, and pp. 609-610.

2

See Wicksteed, op. cit., p. 37; Clark, op. cit., p. 3; Marshall, op. cit., pp. 849-850. 25

28 Joan Robinson, The Economics of Imperfect Competition (London: Macmillan, 1933); E. Chamberlin, The Theory of Monopolistic Competition, 6th ed. (Cambridge: Harvard University Press, 1950).

George J . Stigler, The Theory of Price, Revised Edition (New York: Macmillan, 1952), p. 189. This assumes that the product demand curve is normally downward sloping, and that it is constant throughout the analysis. 27

Ibid., p. 190. Cf. Marshall, op. cit., p. 388n.

28

2 9 Fritz Machlup, "On the Meaning of the Marginal Product," in Readings in the Theory of Income Distribution (Philadelphia: Blakiston Company, 1949), p. 168.

^See Clark, op. cit., p. 302; Marshall, op. cit., p. 850; Wicksteed, op. cit., p. 33; Wicksell, op. cit., p. 112. See Marshall, op. cit., p. 382.

M

Ibid., pp. 462-463.

32

Cf. Keynes' criticism of the neoclassical determination of the rate of interest in The General Theory, pp. 179-180. 33

Ibid., Chapter 19.

M

Even this statement must be qualified to indicate that not only must these agents purchase an insignificant portion, but that any further income that is generated (by the spending of these agents) will not be used to purchase an influential amount from the industry. Hence this approach is applicable only to the hiring of factors by a firm in a competitive industry, when the industry is a very small segment of the economy. 35

^For a derivation of a factor demand curve based on changing income levels, see S. Weintraub, An Approach to the Theory

AGGREGATE INCOME DISTRIBUTION

128

of Income Distribution Chapter 2.

(Philadelphia: Chilton Company, 1958),

'"Clark, op. cit., p. 365. Cf. pp. 360-361, "the fact that one person rather than another has this income is not anything that affects value."

Notes to Chapter IV 1

Charles W. Cobb and Paul H. Douglas, "A Theory of Production," American Economic Review Proceedings, XVIII, 1928. Also P. H. Douglas, The Theory of Wages (New York: Macmillan, 1934), and his Presidential Address to the American Economic Association, "Are There Laws of Production?", American Economic Review, XXXVIII (1948). 2

P. Douglas, The Theory of Wages, p. 132.

Douglas, "Are There Laws of Production?", loc. cit., 15n., 36n. 4

Douglas, The Theory of Wages, pp. 150-151n.

Substituting = ft (fe-1) b C3

= k (ft-1) (P/L 2 )

and 6P _ 6L

P L

into equation (6) yields equation (7). of

®Neglecting the negative sign and taking the absolute value EL. 7

Douglas, The Theory of Wages, p. 133.

"Douglas, "Are There Laws of Production?", loc. p. 12.

cit.,

9

Ibid., 38.

10

D. Durand, "Some Thoughts on Marginal Productivity," Journal of Political Economy, XIV (1937), 740-758.

NOTES

129

u

Horst Mendershausen, "On the Significance of Professor Douglas' Function," Econometrica, VI (1938), 145. iz

Ibid., 145. Douglas did recognize this deficiency in his fixed capital index; see Douglas, The Theory of Wages, p. 122. l3

In the cross-sectional studies, Douglas uses, albeit apologetically, the net value product as the dependent variable. See Douglas, "Are There Laws of Production?", loc. cit., 38. 14

E. E. Day and W. M. Persons, "An Index of the Physical Volume of Production, "Review of Economic Statistics, 11(1920), 310. 15

Letting q be the physical quantity of the commodity, and letting the subscript represent the time period, then the index of relative production can be designated as qi/qo. If we weight by the aggregate value added (phqo) where p1 is the price per unit (less an allowance for purchases from other firms), then the physical production index reduces to a modified Laspeyre index: Ziplqi) Lipbqo) 16

Arthur F. Burns, "The Measurement of the Physical Volume of Production," Quarterly Journal of Economics, XLIV (1930), 255. 17

Mendershausen, op. cit., 147. Mendershausen obtained the following correlation coefficients: r p L = .91, rpc = .93, r^c = .91. la

Jbid., 148. For a further discussion of multicollinearity see H. Wold and L. Jureen, Demand Analysis (New York: John Wiley and Sons, 1953), pp. 46-47. l

*Ibid., 153. Mendershausen was able to demonstrate this as follows: He fitted the following equations to the data; log P=f T; log L = g T; log C = h T; where T is time. He obtained the following correlation coefficients, r p y = .91, R¿y = .89, YQy = 1. Since Douglas had originally fitted the equation, (log P - log C) = b + &(log L - log C), Mendershausen could show that k

=

(log P - log C ) _ f T - g T _ f - h (log L - log C) g T - h T g - h

130

AGGREGATE INCOME DISTRIBUTION 20

E. H. Phelps Brown, "The Meaning of the Fitted CobbDouglas Function," Quarterly Journal of Economics, LXXI (1957), 551. Italics mine. 2l

Phelps Brown, analyzing the same data used by Douglas to obtain a fitted function for Australian manufactures (Quarterly Journal of Economics, LVI [1941]), indicates that equation (9) is a good approximation for most industries. See Phelps Brown's footnote, loc. cit., 557-558. 22

Douglas, "Are There Laws of Production?", loc. cit., 40.

23

Walras, commenting on the English neoclassical approach wrote: Thus, the English theory can only determine the price of land services . . . on the two fold assumption that the prices of personal capital, the prices of capital goods proper and the rate of net income are predetermined and constant . . . . the curves or equations representing the product as a function of the capital employed are completely useless either for a comparison of rents over an interval of time during which the successive applications of capital are made, or for enunciating a law of the variation of rent in a progressive society. At best, these curves or equations can only serve to determine rent at a given instant of time . . . . The marginal productivities are taken into account, not in the inept and incorrect way of the English School, for the determination of the prices of land-services, but for the determination of the coefficients of production. L. Walras, Elements of Pure Economics, trans. W. Jaffee (London: George Allen and Unwin, 1954), pp. 415-417. Italics mine. 24

Paul A. Samuelson, Economics, 1st ed. (New York: McGraw-Hill Book Company, 1948), p. 526. He states that marginal productivity " i s not a theory that explains wages, rents, or interest, on the contrary, it simply explains how factors of production are hired by the firm, once their prices are known." 25

Kenneth E. Boulding, "The Background and Structure of a Macro-Economic Theory of Distribution," Economic Theory in Review, ed. C. L. Christenson (Bloomington: Indiana University Publications, Social Science Series No. 8, 1950), pp. 67-68. 28

John R. Hicks, Value and Capital, 2nd ed. (London: Oxford University Press, 1953), p. 95n.

NOTES

131

Notes to Chapter V Michael Kalecki, "The Determinants of the Distribution of Income," Econometrica, VI (1938), 97-112; Kalecki, Essays in the Theory of Economic Fluctuations (London: George Allen and Unwin, 1939), pp. 13-41. These pages are reprinted in Readings in the Theory of Income Distribution, ed. American Economic Association (Philadelphia: Blakiston Co., 1949), pp. 197-217; Kalecki, Studies in Economic Dynamics (London: George Allen and Unwin, 1943); M. Kalecki, Theory of Economic Dynamics (London: George Allen and Unwin, 1954). 2

Kalecki, Readings in the Theory of Income Distribution, p. 201. The concept was originally derived by A. Lerner in "The Concept of Monopoly and the Measurement of Monopoly Power," Review of Economic Studies, I (1934), 169. 3

Kalecki, Studies in Economic Dynamics, p. 16.

4

Kalecki, Theory of Economic Dynamics, p. 16.

s

Kalecki, Readings, pp. 202-203.

s

Ibid., p. 201. Since one definition of the elasticity of demand is Ed = p/p-MR, and in equilibrium MR = MC, then ß = 1 /Ed. •That this is true can be shown as follows: 1 1- ß

1 P _ P _ p-MC p - p + MC MC' P "Ibid., pp. 203, 208. 1

9

Ibid., p. 209. Here Kalecki is implicitly using a Ricardian type model. He states that those industries "producing basic raw materials (agriculture and mining) are normally subject to diminishing returns." (p. 124) Thus if both the wage rate and the degree of monopoly a r e constant, any increase in the price of raw materials must be due to an increase in output in the face of diminishing returns. This leads to an increase in the total rent bill and since Kalecki has assumed no change in gross profit margins or in wage costs, then the rent share must increase relative to the wage share. 10

See infra.

"Kalecki, Theory of Economic Dynamics, p. 12.

132

AGGREGATE INCOME DISTRIBUTION a

Ibid., p. 12.

13

Ibid., p. 13. In the limiting case where the price of the individual firm equals the weighted average price, if n 5> 1 then m would have to be 0, which is improbable. 14

Ibidpp. 28-29. I have attempted to simplify Kalecki's derivation by supplying some of the steps that Kalecki assumes are obvious. He begins his derivation with the equivalent of our equation (16). 13

Ibid., p. 30. By industrial composition, Kalecki means "the composition of the value of the gross income of the private sector. Thus, changes in the composition depend not only on changes in the volume of the industrial components but also on the relative movements of the respective prices." (p. 30n) 16

Ibid., pp. 45-69.

"Ibid., p. 45. 18

Nicholas Kaldor, "Alternative Theories of Distribution," Review of Economic Studies, XXIII (1955-56), 96. 19

For a further discussion of the importance of this aspect see Chapter VII infra. 20

Kalecki, Studies in Economic Dynamics, p. 46. Mrs. Robinson has indicated that investment decisions may be made in either real or pecuniary terms. She has attempted to demonstrate that investment decisions in real terms may have a different effect on class shares than decisions in monetary terms; see Chapter VII infra. Similarly, Weintraub has noted that price level changes may be an important factor in determining consumption outlays of certain capitalists; see Chapter VIII infra. 21

Kalecki, Studies in Economic Dynamics, p. 50. This implies that despite the fall in effective demand for consumption goods and the rise in the price level, capitalists will maintain their investment and consumption expenditures. 22

John M. Keynes, "Relative Movements of Real Wages and Output," Economic Journal, XLIX (1939), 44, 49. 23

Joan Robinson, The Accumulation of Capital (London: Macmillan, 1956), p. 183. 24

Melvin Reder, "Rehabilitation of Partial Equilibrium Theory," American Economic Review Proceedings, XLII (1952), 191-192.

NOTES

133

25

Another possibility is that with a change in output, changes in the elasticity of demand facing one firm just offset changes in the elasticity for another firm, so that on balance there is no change in the degree of monopoly. 28

Kalecki, in Readings in the Theory of Income p. 205.

Distribution,

27

Ibid., p. 208.

28

For a thorough analysis of these modifications see Sidney Weintraub, "The Micro-Foundations of Aggregate Demand and Supply," Economic Journal, LXVII (1957). 2B

This implies the possibility of changes in the elasticity of demand (and hence in the degree of monopoly) with every change in the level of income or its distribution. ^Cf. Keynes, The General Theory, p. 281. 31

Edward H. Chamberlin, The Theory of Monopo* tic Competition, 6th ed. (Cambridge: Harvard University Press, 1950), pp. 196-202. 32

Ashok Mitra, The Share of Wages in the National Income (Centraal Planbureau, The Hague, 1954). 33

Mitra substitutes the concept of imports for raw materials "since for an economy as a whole, whatever goods and services enter into it from outside assume a role similar to that of raw materials." (p. 35) By this substitution, however, Mitra has perverted Kalecki's original concept of raw material costs which arose only in increasing cost industries. We have already shown that Kalecki implied a Ricardian law in the relation of raw material costs to the wage share. The relation between imports and the wage share is not comparable, since the import series used by Mitra was a composite of consumption goods and raw materials from the rest of the world, and therefore does not necessarily imply diminishing returns and an increasing supply function. M

The statistical analysis assumes that the technical structure of production was unaltered during the period of observation. This appears, especially for a period as long as that tested, to be a doubtful hypothesis. ^Mitra assumes that the average and marginal labor quotas are approximately equal, and also that the marginal and average raw material quotas are equal. Op. cit., pp. 42-43, 75-77.

134

AGGREGATE INCOME DISTRIBUTION 3

*Ibid„ pp. 57-59.

37

Ibid., p. 58. This is inconsistent with the f i r m of the m a r ginal cost function that Mitra used in his statistical analysis of Kalecki's hypothesis. Since Mitra's model involves constant marginal costs, it is open to many of the same criticisms that Kalecki's theory received. 38

Chamberlin, op. cit., pp. 105-106, 185.

39 Joan Robinson, The Economics of Imperfect p. 310. Italics mine.

Competition,

*°Ibid., pp. 155-158. I have added hourly costs to Mrs. Robinson's comments on marginal and unit costs without doing violence, I think, to the spirit of her ideas. 4l

John R. Hicks, Value and Capital, 2nd ed. (London: Oxford University P r e s s , 1953), p. 84.

Notes to Chapter VI \John M. Keynes, The General Theory of Employment, Interest and Money (New York: Harcourt, Brace and Co., 1936), p. 372. »Ibid., pp. 42-43n., 81, 83, 262-263, 302. 3

J. M. Keynes, A Treatise on Money (London: Macmillan, 1930), I, vi. *Ibid., I, 136. It might be observed that the "multiplier" idea of The General Theory was to emerge from this analytical separation of consumer and investment industries. s

Ibid., I, 143. This emphasis on savings-deposits rather than liquidity may seem curious to the modern reader. The difference, however, is terminological rather than conceptual. (Seel, pp. 140-142.) *Ibid., I, 139. Since, in the Treatise, profits a r e a windfall, those who s t r e s s the dependence of consumption on "permanentincome" might maintain that the widow's cruse relation is not a realistic outcome, for windfalls are usually saved. Other writers—Boulding, Kalecki, and Kaldor—have, however, applied this idea to all non-labor incomes, under the assumption that worke r s spend their entire income.

NOTES

135

'Kalecki independently arrived at a similar conclusion in his aggregate profits theory. See Chapter V supra. *Ibid., I, 135-137. Keynes'coefficient of efficiency, in his formulas, is the average product of labor so that, given the money earnings of labor, the price level of consumption goods varied inversely with the productivity of labor. *Ibid., II, 125-126. Keynes notes that it is the flow of consumption goods "which constitute the true Wages Fund; and it is the distribution of this Fund between relatively productive and relatively unproductive consumption which determines the volume of employment and output." (II, p. 129) Recently, Weintraub has developed the implications of this fall in the purchasing power of rentiers, with increasing employment, on relative shares. (See Chapter VIII infra.) 10

Kenneth E. Boulding, A Reconstruction of Economics (New York: John Wiley and Sons, 1950), pp. 243-269. See also his "The Background and Structure of a Macro-Economic Theory of Distribution" and "The Models for a Macro-Economic Theory of Distribution," in Economic Theory in Review, ed. C. L. Christenson (Indiana University Publications, Social Science Series No. 8, Bloomington, Ind., 1950), 66-95. All references are to the Reconstruction unless otherwise noted. "Boulding maintains that, at least in the short run, it is the composition of output which determines the real distribution of income, especially if prices are flexible. If money wages were to rise, for example, without any change in the output of wage goods, then the prices of these goods would rise proportionately and real wages would be constant, (p. 203) This implies, however, a short-run vertical demand curve for labor and that capitalists do not buy any "wage-goods." 12 lbid., 246. Boulding ignores the problem of price changes affecting the distribution of income between rentiers and entrepreneurs which some writers regard as important. See sections on Mrs. Robinson (Chapter VII) and Weintraub (Chapter VIII) infra. 13

While Boulding indicates that government may be introduced as another type of economic organism, he remarks that this is not essential to the theory. (See pp. 293-302) 14

For the derivation, see the Reconstruction,

pp. 246-251.

136

AGGREGATE INCOME DISTRIBUTION 15

Ibid., p. 249. Italics mine. Savings ex post, is " d e t e r mined" by the level of new investment. Cf. Keynes, Treatise, I, 176-178 or The General Theory, pp. 111-112. 19

Ibid., pp. 249-250. Boulding is implicitly assuming that all business distributions will be spent by their recipients, thus, creating a widow's cruse. 17

J. M. Keynes, The General Theory, p. 81.

18

J. Johnston, "A Note on Professor Boulding's Macro-Economic Theory of Distribution," Economic Journal LXII (1952), 186. 19

R. Turvey, in a book review of the Reconstruction, Economica, XVIII, 1951, 203-207. 20

Ibid.,p. 207. One might argue, however, that the new issue was used to fund a new investment made during the period, and therefore profits will be larger rather than, as Boulding claims, smaller. 21

Cf. Keynes, The General Theory, p. 305.

Notes to Chapter VII x

Joan Robinson, The Accumulation of Capital (London: Macmillan, 1956). 2

Ibid., p. 67. Later in the analysis, the fixity of land will be introduced into the scheme. s

Ibid., pp. 44-45, 75.

4

Note the similarity to Kalecki's profits theory and Keynes' widow's cruse. *Ibid., p. 48. Cf. A. J. Brown, The Great Inflation (London: Macmillan, 1955), or H. Aujac, "Inflation as the Money Consequence of the Behavior of Social Groups," International Economic Papers, No. 4, (London: Macmillan, 1954). 'Robinson, Accumulation of Capital, p. 48. Another possibility which Mrs. Robinson overlooks is the curtailing of real consumption by fixed income recipients. Weintraub, on the other hand, indicates that "forced savings" of rentiers may make possible higher real wages with an increase in real investment and a contraction of aggregate real consumption. See

NOTES

137

S. Weintraub, "A Macroeconomic Theory of Wages: A Reply," American Economic Review, XLVII (1957), 682-683; also S. Weintraub, An Approach to the Theory of Income Distribution, p. 124. r

Ibid., 73. Hence, employment is limited only by the scarcest resource. *Ibid., p. 108. In the presence of uncertainty, a technique may be adopted which yields a lower rate of profit because it allows more flexibility in the production process. B

This decision was unnecessary when there was only a single technique of production, since, in that case, the composition of output would never change. 10

Ibid., pp. 64, 115.

lx

Ibid., pp. 121-122. The ratio of capital, in terms of past labor time (compounded at interest) to the amount of labor currently employed when working the capital equipment at "normal capacity" is called the real-capital ratio. This ratio is conceptually akin to the capital-labor ratio. The real-capital ratio also bears a direct relationship toHarrod's capital-output ratio. When the former changes, the latter changes in the same direction. (Cf. Ibid., p. 319) 12

The rate of profit (which is equal to the ratio of net investment to the value of the capital stock) is equal in both economies, and the value of capital per man is proportionately higher in the more mechanized economy. 13

On p. 406, Mrs. Robinson indicates that a higher degree of mechanization "may (though it need not) mean a larger share of profits in the value of output (more capital per head outweighing a lower rate of profit per unit of capital)." 14

In the more mechanized (high wage) economy, a unit of productive capacity requires more labor time, and each unit of labor time costs more in terms of commodities; therefore, the value of annual investment may be greater in the highly mechanized economy even though the rate of profit is lower. ^Ibid., pp. 127-129. Only if net investment equals zero, can comparisons be made; but in this case, wages would comprise all of the total net output in both economies. 18

Ibid., p. 132. Comparisons of the superiority of phases can only be made at positions of the same degree of mechanization

138

AGGREGATE INCOME DISTRIBUTION

in the two spectra. It is possible for an economy to be superior at certain real-capital ratios and inferior at others. Ibid., pp. 258-259. The " s h a r e of profits distributed to r e n t i e r s " is a concept closely allied to Boulding's transfer f a c tor (see Chapter VI) which depends on a complex of liquidity decisions. ia

Jbid., p. 259; also see pp. 250-251.

ia

Ibid., p. 328. Also see p. 331, "Annual Profits, in terms of commodities at any given rate of investment, have been r e duced only to the extent of savings out of r e n t . " Italics mine. ^Cf. Ibid., p. 243. The level of interest rates will affect investment plans "for the expected profit from the investment must exceed the yield of placements or the cost of borrowing to make it worth while." 21

Some have heralded Mrs. Robinson's book mainly because it deals in concepts that are ex post in nature and therefore, it is claimed, these notions can be empirically verified. See T. Barna's review in The Economic Journal, LXVII, 1957, pp. 490-493. Z2

See a summary of empirical studies in M. Friedman, A Theory of the Consumption Function (Princeton, N. J.: Princeton University P r e s s , 1957), especially pp. 41, 77, 227. Also I. Friend and I. B. Kravis, "Entrepreneurial Income, Savings and Investment," American Economic Review, XLVII, 1957, 273. zs

See infra.

^Robinson, Accumulation of Capital, pp. 22, 65-66, 314, 358. Mrs. Robinson indicates that changes in total output will induce changes in the proportions of consumer goods demanded, which will have a bias similar in effect to a bias in technical progress. For example, as the level of income rises there is usually a fall in the proportion of food consumed which would correspond to a land-saving bias. 25

This assumption appears, at f i r s t blush, to be quite unrealistic. Yet a similar assumption underlies the most operational of all economic theories, the input-output analysis. Mrs. Robinson's descriptions of a single technique of production and of changes in the degree of mechanization, and her assumption of constant returns to scale, all have counterparts in the input-

NOTES

139

output schemes which have described the production function in matrix form, with each process (each degree of mechanization?) represented by a unique vector. Furthermore, the wage rate plays essentially the same role as the numeraire in Leontief's open system, as in Mrs. Robinson's scheme, and in Keynes' General Theory. See W. Leontief, The Structure of the American Economy, 1919-39 (Cambridge, Mass.: Harvard University Press, 1941); also R. G. D. Allen, Mathematical Economics (London: Macmillan, 1956), pp. 333-351; and J. M. Keynes, The General Theory, pp. 41-42. 26

Robinson, The Accumulation sentially a wage-fund concept.

of Capital, p. 75. This is es-

27

N. Kaldor, "Alternative Theories of Distribution," Review of Economic Studies, XXIII (1955-56), pp. 94-100. ZB

Ibid., p. 96. Weintraub has argued that since corporations retain a large portion of profits, then sp and I/Y are not "wholly independent." See S. Weintraub, An Approach to the Theory of Income Distribution, p. 107. 20

Ibid. pp. 96-98.

30

Ibid., pp. 97-100. There is a misprint in the original text which formulates the rate of profit in reason (3) as P/Y instead of P/vY. 31 Due to the assumed form of the savings functions, if investment is zero then income will be zero. Hence, some capital formation is essential to the model, i.e., it cannot be used for a static society. 32

This situation is comparable to Mrs. Robinson's analysis of a single technique with constant real investment decisions when the money wage rate changes and prices are flexible.

Notes to Chapter VIII 1

Sidney Weintraub, An Approach to the Theory of Income Distribution (Philadelphia: Chilton Company, 1958), vi. z

Ibid., p. 26. Italics mine. The importance of this assumption will be commented on below. s

Ibid., p. 28. Weintraub demonstrates that productivity phenomena determine the magnitude of dZ/dN. In a mathematical

140

AGGREGATE INCOME DISTRIBUTION

appendix (p. 45), he shows that for the economy, n Zi+Jv_ = 2 i=l

(2a)

where Ep is the elasticity of productivity and Es is the elasticity of supply, summed over each industry, i. 4

Weintraub states that " s o long as the Z-function advances more steeply than W, the income shift is away from wage incomes and towards profits; relative shares would be maintained only if there were an equivalent rise in both curves. With a constant money wage, this can occur only if the Z curve is linear, denoting a constant marginal product of labor under pure competition and Ez = 1." (p. 46) The wording here is somewhat ambiguous; "advancing more steeply" must be taken to mean an increasing rate of change in the slope of the Z-curve. It can be demonstrated that a constant marginal product may be a sufficient but is not a necessary condition for a linear 2-function. See the comments at the end of this chapter. 5

Equation (4) indicates that the wage share will not fluctuate greatly even if Ez « 1, if the ratio of w/Z is very small. Weintraub illustrates this short-run constancy of the wage share by assuming the absurdly low value of 1/10,000 for Ez when w equals $5,000 per annum and Z is $350 billion. Substituting these values into equation (4) indicates that the wage share will fall by less than 0.015%. e

Cf. Keynes, The General Theory of Employment, and Money, pp. 290, 376-377.

Interest

7

Prior to the publication of Weintraub's book, I had independently arrived at, via a different route, a similar conclusion in analyzing the Ricardian system, where the wage plus profit share equaled the elasticity of productivity of the homogeneous doses of labor plus capital. See Chapter II. ®It is possible to have diminishing returns to a factor and a constant elasticity of productivity. 8 J. Robinson, Economics of Imperfect Competition, p. 36. Since Ed is normally negative, the signs have been altered so that only the absolute value of Erf need be inserted into the f o r mula. 10

See Chapter V.

141

NOTES " W e i n t r a u b , Theory of Income Distribution,

p. 78n.

lzIbid.,

p. 83. This implies that labor-saving innovations raise the average product of labor more than they raise the marginal product at each N- level. 13Ibid.,

p. 83. This implies that capital-saving techniques will be those which raise the marginal product of labor relative to the average product at each level of employment. 14

Weintraub also introduces a government demand function (Dg) but this is not essential to the theory. Thus, for exposition purposes, we may assume no government spending, no taxes and no transfer payments. For Weintraub's complete derivation, see Ibid., pp. 30-39.

^Weintraub introduces some novel ideas about the effects of changing N- and price-levels on the behavior of the previously employed laborers. (See Ibid., pp. 35-36.) Essentially, however, Dff will be upward sloping. 18

This profit rise will be partly due to the shifting of real income from rentiers to profits. If the relative wage share is also decreasing with rising N-levels, there will be a tendency to to accentuate the upward slope of the curve. l7

Weintraub indicates that pensioners, workers, and profit recipients are likely to dissave out of assets at low N-levels. As employment rises, however, the dissaving of the latter two groups will decline, tending to moderate the upward slope of the aggregate Dc curve, (pp. 36-37) In a similar fashion, Weintraub demonstrates that the introduction of government relief payments will moderate the ascent of the Dc curve, (pp. 34-35) 18Ibid.,

p. 46. Cf. pp. 56, 103.

"This is not to argue that the real world is one of CobbDouglas functions but only to indicate the theoretical possibility of diminishing marginal productivity with a constant elasticity of productivity. ^See Appendix A, Note 1. 21

See Appendix A, Notes 2 and 3.

Weintraub, op. cit., p. 132. It should be noted that Weintraub believes that the investment demand function is independent of the aggregate supply function. Yet, the assumption of a unique composition of aggregate demand and output indicates 22

142

AGGREGATE INCOME DISTRIBUTION

that the volume of investment at any JV-level is implicit in the Z-function. Any changes in the quality or quantity of investment projects (at any N-level) will alter the magnitude of the " a v e r a g e " elasticity of productivity at that N- level and therefore alter the shape and position of the Z-function. 23

Although Weintraub has not assumed a fixed proportionate composition of output with changing N-levels, implicit in a smooth upward sloping non-linear Z-function is the notion that the "average elasticity of productivity declines as employment rises, and that, therefore, as N- increases, the composition of output does not radically shift from industries with low M/Aratios to industries with high M/A-ratios. Otherwise, it would be possible, because of the changing importance of different industries, for the " a v e r a g e " elasticity of productivity to increase with increasing employment, even though the elasticity of productivity of each industry was declining. Thus, the shape of Weintraub's Z-function (Figure 1) i s a restraint similar to, but not nearly as restrictive or unrealistic as, Mrs. Robinson's assumption that consumption goods are always produced in fixed proportions. 24

Ibid., p. 132. Italics mine. This implies that the highly publicized "rolling readjustments" of recent years were really of small magnitude. 2S

Cf. Keynes, The General Theory, p. 286.

M

R. Solow, "A Skeptical Note on the Constancy of Relative Shares," American Economic Review, XLVIII 1958, p. 628. Z7

R. Solow, review of An Approach to the Theory of Income Distribution, in the Journal of Political Economy, LXVII 1959, p. 420.

Notes to Chapter IX William J . Baumol, Economic Dynamics (New York: Macmillan, 1952), p. 6. z

As we have shown, the destiny of the relative rent share cannot be elicited from the Ricardian system, since diminishing returns is a necessary, but not a sufficient, condition for an increasing rent share. See Chapter n .

NOTES

143

3 Jevons, in his Preface to the second edition of The Theory of Political Economy, argued that "that able but wrong-headed man, David Ricardo, shunted the car of Economic science on a wrong line . . . . It will be a labour to pick up the fragments of a shattered science and start anew, but it is a work from which they must not shrink who wish to see any advance of Economic Science." (3rd ed., London: Macmillan, 1889, p. 1) 4

Keynes, The General Theory, pp. 258-259.

5

The form of the relationship between changes in employment and changes in the degree of monopoly would have to be given. 'Alterations in the composition of output at the same Nlevel can be handled in a manner similar to the method used in Appendix B in analyzing the effect of international trade on macrodistribution. ^Robinson, The Accumulation 8

of Capital, p. vi.

See Chapter VI.

®Weintraub, An Approach to the Theory of Income tion, pp. 18-19.

Distribu-

10

Weintraub, op. cit., p. 44n. In other sections of his book, Weintraub indicates that changes in the investment sector may have different distributional effects than changes in the consumption sector. See pp. 86-101, 140-144. n

Ibid.,

pp. 105-106.

12

Mrs. Robinson does emphasize money relationships in her analysis of investment spending and rentier consumption. "Except in the case where all firms have identical CobbDouglas functions. 14

For illustrative purposes, the aggregate supply approach is used in Appendix B to analyze the relationship between r e l a tive shares, the level of employment, and international trade.

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148

AGGREGATE INCOME DISTRIBUTION

Mendershausen, Horst. "On the Significance of Professor Douglas' Function," Econometrica, VI, 1938. Phelps Brown, E. H. "The Meaning of the Fitted Cobb-Douglas Function," Quarterly Journal of Economics, LXXI, 1957. Phelps Brown, E. H., and Hart, P. E. "The Share of Wages in National Income," Economic Journal, LXII, 1952. Reder,Melvin. "Rehabilitation of Partial Equilibrium Theory," American Economic Review, Proceedings, XLII, 1952. Shoul, Bernice. " K a r l Marx and Say's Law," Quarterly Journal of Economics, LXXI, 1957. Solow, R. "A Skeptical Note on the Constancy of Relative Shares," American Economic Review, XLVm, 1958. Review of An Approach to the Theory of Income Distribution, in the Journal of Political Economy, LXVII. 1959. Stolper, W. F., and Samuelson, P. A. "Protection and Real Wages," Review of Economic Studies, IX, 1941; reprinted in Readings in the Theory of International Trade, edited by the American Economic Association, Philadelphia: Blakiston Co., 1949. Tinbergen, Jan. "On the Theory of Income Distribution," Central Planning Bureau Reprint Series No. 49, 1956. Turvey, Ralph. A book review in Economica, XVIII, 1951. Weintraub, Sidney. "The Micro-Foundations of Aggregate Demand and Supply," Economic Journal, LXVII, 1957. "A Macroeconomic Theory of Wages," Economic Review, XLVI, 1956. "A Macroeconomic Theory of Wages: American Economic Review, XLVII, 1957.

American A Reply,"

Index user, 52, 54

Adding-up problem, 29-31 Allen, R. G. D., l l l n . , 115 n., 139 Aujac, H., 136 Barna, T., 138 Baumol, W. J . , 142 Boulding, K. E., 42, 60, 63-70, 104, 130, 134, 135, 136, 138 Brown, A. J . , 136 Burns, A. F., 40, 129 Business savings, 67-68 Cannan, E., 122, 123 Capital, accumulation of, 4, 6, 7, 10, 13, 15, 17, 71, 73, 74, 75, 100, 103 marginal productivity of, 20, 26, 36 measurement of, 76-77 Capital-labor ratio, 18, 112, 115, 137 Capital-output ratio, 84, 85, 137 Capital-using inventions, 14, 79, 94, 116 Capital-saving inventions, 79, 94 Capitalists, 1, 12, 13, 15, 50, 51, 83, 84, 85, 90,94, 106, 132, 135 Chamberlin, E., 31, 32, 58, 127, 133, 134 Clark, J . B., 19, 20, 23-29, 31, 34, 35, 102, 125, 127, 128 Cobb-Douglas function, 2, 36-42, 130 Competition, imperfect, 31-32, 44, 54, 59, pure, 19, 22, 31, 87, 90, 108, 140 Consumption, 50, 51, 60, 61, 62, 67, 79-80, 85, 95-97, 106, 136, 143 Costs, average, 30 average variable, 45, 48, 49, 51, marginal, 45, 46,52, 53, 56, 59, 108, 134 149

Day, E. E., 129 Demand, aggregate, 2, 17, 35, 60-86, 89, 94, 95-97, 102, 103, 105, 106, 107, 118, 119, 125 composition of, 35, 82, 98, 102, 103, 104, 106, 125, 141 derived, 22 elasticity of, 22, 38, 45, 53, 56, 91, 92, 94, 99, 131, 133, 140 Diminishing returns, 4, 5, 6, 7-12, 16-18, 33, 39, 60, 90, 95, 97, 98, 100, 111, 122, 123, 124, 131, 133, 142 Dividends, 12, 50, 64-66, 69, 71, 80 Douglas, P. H., 36-42, 128, 129, 130 Durand, D., 39, 128 Dynamics, 24-25, 28, 100, 125 Edgeworth, F. Y., 30, 126 Elasticity of demand, 22, 38, 45, 53, 56, 91, 92, 94, 99, 131, 133, 140 of productivity, 9-11, 90, 91, 93, 98, 106, 108, 140, 141, 142 of Z-function, 89 Entrepreneurs, 20, 22, 23, 24, 26, 27, 28, 30, 31, 55, 56, 60, 61, 71, 72, 73, 74, 76, 79, 81, 82, 86, 87, 88, 89, 95, 97, 98, 106 Euler's theorem, 126 Exploitation, 11, 31, 32 rate of, 12, 13-16, 124 Finance, 81 Forced savings, 97, 136 Friedman, M., 138 Friend, 1., 138 Gross national product, 50, 57, 82, 98

150

INDEX

Haney, L. H., 125 Harrod, E., 137 Hicks, J . R., 43, 130, 134 Inflation b a r r i e r , 72, 73, 75 Input-output, 138-139 Interest, 12, 19, 20, 24, 25, 26, 28, 29, 46, 50, 60, 63, 64, 66, 71, 76, 77, 130 Investment demand, 50, 51, 60, 61, 71, 73-75, 95-97, 105, 106, 132, 136, 138, 139, 141 Jevons, W. S„ 20, 21, 33, 125, 143 Johnson, D. G., 120 Johnston, J., 68, 136 Jureen, L., 129 Kaldor, N., 50, 71, 82-86, 104, 106, 132, 134, 139 Kalecki, M., 44-54, 55, 56, 59, 71, 82, 102, 103, 131-133, 134,135, 136 Keynes, J. M., 1, 4, 35, 60-62, 63, 68, 99, 102, 105, 120, 127, 132, 133, 134, 135, 136, 139, 140, 142, 143 Kravis, I., 120, 138 Labor, 2, 8, 13, 16, 20, 24, 25, 39, 63, 73, 82, 87 average product of, 8, 10, 90, 91, 114-116, 141 marginal product of, 8, 10, 26, 36, 81, 90, 91, 93, 94, 98, 114-116, 118, 140, 141 natural price of, 4, 6 quota, 54, 55, 57 Leigh, A. H., 20, 135 Leontief, W., 139 Lerner, A., 44, 47, 53, 56, 92, Liquidity, 61, 63, 80, 134, 137

36, 36, 20, 97,

131

Machlup, F., 118, 119, 127 Malthus, T. R., 3 law of population, 4, 13 Notes on, 7 Marginal productivity, 2, 19-43, 102, 104, 107

Marshall, A., 19, 20-23, 31, 34, 102, 125, 127 Marx, K., 3, 11-18, 100, 101, 123 Mechanization, degree of, 75-78, 79, 80, 85, 137, 138, 139 Mendershausen, H., 39, 40, 41,129 Mitra, A., 54-59,102, 103, 133-134 Monopoly, 2, 31-32, 44-59, 91-92, 102 degree of, 44-56, 59, 74, 84, 91-92, 97, 103, 133 profitless, 32 Multicollinearity, 41-42, 102 Multiplier, 82, 118-119, 134 Permanent income, 134 Persons, W. M., 129 Phelps Brown, E. H., 41-42, 130 Physiocrats, 121 Pigou, A. C., 31, 127 Production function, 11, 29, 39, 40, 41, 54, 55, 87, 98, 102, 108-113, 122, 126, 139 Cobb-Douglas, 2, 36-42, 98, 102, 108, 109, 110, 113, 141, 143 linear and homogeneous, 29, 30, 36, 37, 114, 115, 122, 126 Productivity, elasticity of, 9-11, 90, 91, 93, 98, 106, 108, 140, 141, 142 net, 22 Profits, 4, 11, 13, 14, 16, 17, 22, 24, 26, 28, 29, 30, 45, 46, 49, 50, 51, 59, 60, 62-69, 71, 73, 74, 76, 77, 79, 80, 82-85, 89, 95, 100, 104, 137, 140 rate of, 5, 12, 13, 74, 75, 76, 78, 79, 81, 84, 86, 123, 137, 139 retained, 12, 71, 139 relative share of, 10-12,15, 16, 28, 75, 79, 83-85, 89 Progress, technical, 15-17, 28, 36, 39, 53, 55, 75, 78-80, 84, 94-95, 102 Quasi-rents, 72, 73, 74 Raw material quota, 54, 55 Real-capital ratio, 78, 79, 85, 137

INDEX Reder, M., 52, 132 Rentiers, 62, 70, 73, 75, 79-80, 81, 89, 95, 98, 105, 135, 136, 137, 141, 143 Rents, 4, 5, 12, 20, 25, 26, 28, 50, 60, 63, 64, 66, 71, 80, 81, 100, 101, 121, 130, 137 relative share, 7-11, 17, 79, 100, 122, 123, 142 Ricardo, D., 3-11, 15, 16, 17, 23, 100, 101, 120, 123, 124, 143 Robinson, J., 31, 50, 52, 59, 70, 71-82, 85, 86, 103, 104, 106, 111, 124, 127, 132, 134, 135, 136-139, 140, 143 Samuelson, P. A., 42, 114, 115, 116, 118, 130 Say's law, 34, 124-125 Savings function, 83, 94, 139 Shoul, B., 125 Smith, A., 121 Solow, R., 99, 120, 142 Sraffa, P., 3, 121 Static society, 24-28,101, 125, 139 Stigler, G. J., 32-33, 127 Stolper, W. F., 114-116, 118 Subsistence, 4, 8,11,12, 13, 16, 84 Supply, aggregate, 2,17, 86, 87-99, 101, 102, 103, 105, 106, 107, 116, 117, 119, 143 industry, 87, 88, 119 Surplus value, 11, 14, 15 rate of, 12-16 Sweezy, P., 69, 136

151 Unproductive consumption, 62, 97, 105 Value, Labor Theory of, 2, 3, 11 Von Thunen, 19, 20, 125 Wage bill, 11, 38, 46, 47, 49, 50, 51, 56, 57, 72, 73, 74, 75, 78, 81, 88, 95, 116, 117 Wage fund, 4, 16, 121, 124, 135, 139 Wage share, 1, 7, 9, 11, 12, 14, 15, 16,17, 28, 37, 38, 41, 44, 48, 49, 50, 51, 56, 57, 58, 59, 63, 73, 78, 79,80, 82, 85, 89, 90,91,92, 97, 98,100, 103,105, 107, 124, 126, 140 Wages, 4, 5, 13, 19, 20, 24, 26, 28, 45, 50, 51, 60, 63, 66, 67, 72, 73, 74, 77, 81, 83, 85, 100, 104, 130, 140 Walras, L., 30, 42, 126, 130 Weintraub, S., 86, 87-99, 103, 104-107, 114, 119, 120, 123, 127-128, 132, 133, 135, 136, 137, 139, 140, 141, 143 Wicksell, K., 30, 126, 127 Wicksteed, P. H., 29-31, 34, 126, 127 Widow's cruse, 61, 66, 97, 105, 134, 136 Wold, H., 129 Zero demand price, 55, 57, 58