J. Eatwell on Sraffa and the surplus value

8/22/2019 J. Eatwell on Sraffa and the surplus value

http://slidepdf.com/reader/full/j-eatwell-on-sraffa-and-the-surplus-value 1/14

Mr. Sraffa's Standard Commodity and the Rate of ExploitationAuthor(s): John EatwellReviewed work(s):Source: The Quarterly Journal of Economics, Vol. 89, No. 4 (Nov., 1975), pp. 543-555Published by: Oxford University PressStable URL: http://www.jstor.org/stable/1884691 .

Accessed: 18/04/2012 04:32

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly

Journal of Economics.

http://www.jstor.org

http://www.jstor.org/action/showPublisher?publisherCode=oup

http://www.jstor.org/stable/1884691?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp

http://www.jstor.org/page/info/about/policies/terms.jsp

http://www.jstor.org/stable/1884691?origin=JSTOR-pdf

http://www.jstor.org/action/showPublisher?publisherCode=oup



MR. SRAFFA'S STANDARD COMMODITY AND

THE RATE OF EXPLOITATION *

JOHN EATWELL

I. Introduction, 543.-III. The use of physical analogues in the classicaltheory of value, 544.- III. The rate of exploitation, 550.- IV. A complemen-tary approach, 555.

Piero Sraffa's work on problems of the theory of value,' whichhas provided the analytical framework for the recent debate on

distribution theory, encompasses two distinct, though interrelated

themes. The first, a critique of the marginalist theory of distri-

bution, culminated in his demonstration of the generality of the

"reswitching" phenomenon. The second amounts to a restatement

of the classical theory of distribution. This involves an analysis of

the relationship between wages, profits, and the rate of profit by

means of a "physical" analogue freed from the complications intro-duced by the interdependence of prices and the distribution of

income.

The purpose of this paper is to examine the role of the standard

commodity in the second theme of Mr. Sraffa's analysis. Since the

standard commodity is not indispensable in the analysis of "re-

switching," on which most attention has been focused, the impor-

tance of this analytical device has been somewhat overlooked. This

is unfortunate, for the standard commodity may be used to penetratethe complexities of wages, profits, and prices to reveal the relations

of production and distribution on which they are based. Further-

more, a direct link may be established between this use of the

standard commodity and the use of the labor theory of value by

*I have been greatly helped while writing this paper by advice fromAntonietta Campus, Carlo Jaeger, Michio Morishima, Mario Nuti, Jerzy Osi-atynski, Luigi Pasinetti, Joan Robinson, Bob Rowthorn, Bertram Schefold, and,in particular, Piero Garegnani. The basic approach to the classical theory ofdistribution derives from Part One of Piero Garegnani, I1 Capitale nelle Teoriedella Distribuzione (Milan: Giuffre, 1960).

1. In particular, P. Sraffa, Production of Commodities by Means of Com-modities (Cambridge, England: Cambridge University Press, 1960), but seealso P. Sraffa, "Sulle Relazioni fra Costo e Quantita Prodotta," Annali di Eco-nomia, I (1925), 276-328); P. Sraffa. "The Laws of Returns Under CompetitiveConditions," Economic Journal, XXXVI (1926), 535-50; and Parts IV and Vof the introduction to D. Ricardo, Works and Correspondence, Sraffa edn., tenvolumes and index (Cambridge University Press, 1951-73), Vol. I.



544 QUARTERLY JOURNAL OF ECONOMICS

Marx to expose the nature of exploitation in the creation of surplus.2

The role of the standard commodity in the clarification of the

classical theory of distribution and price formation, and of the directantagonism between capital and labor, is discussed in the second

section of the paper. The third section contains a critique of con-

ventional definitions of the rate of exploitation, and a juxtaposition

of the distributional relations exposed by the standard commodity

and the social relations implicit in the creation of surplus value in

capitalistic production, as revealed by the labor theory of value.

This argument leads to a reformulation of the concept of the rate of

exploitation and its relationship to the rate of profit.

II

The interest that classical economists displayed in the problem

of distribution arose from their fundamental conception of the eco-

nomic roles of social classes. Workers worked, and all their earnings

were devoted to the needs of consumption and survival; capitalists

accumulated, and landlords' extravagant consumption was regardedas a deduction from the fund available for accumulation. The dis-

tribution of income between these classes was, therefore, seen as the

causal antecedent to the dynamic behavior of the economy.

Net social product was regarded as a given bundle of com-

modities, the division of which depended on the relative economic

power with which social classes are endowed in a market economy,

which is determined by their ownership of the means of production.3

Abstracting from problems of rent, the distribution of the commodi-ties comprising net product between wages and profits in a simple

model without joint production,4 may be characterized by the

expression,

(1) s = [x-A'x] -ba'ox,

where s, b, and x are vectors of the commodities comprising total

profits, the wage per man and gross output bundles, respectively,

2. The causal significance of the theory of exploitation willnot be dis-cussed in this paper, which is devoted to the derivation of a set of unambiguous

categories in terms of which distributive relations may be analyzed.3. Classical theories of value and distribution concentrate on the deter-

mination of the "natural" prices (rather than market prices) appropriate to aknown real wage and the technology and output structure of the economy asit is. Changes in the scale of production or composition of output thus play norole in the analysis. See Ricardo, op. cit., Vol. I, Chs. IV, XXX.

4. In the most important case of joint production, that of fixed capital,all the propositions developed in this paper hold. Indeed, they hold whenever,for a particular system, a standard commodity exists. See B. Schefold, Theorieder Kuppelproduktion (Basel: 1971).



MR. SRAFFA'S STANDARD COMMODITY 545

A and ao represent the matrix of commodity input coefficients and

the vector of labor input coefficients,A' = transpose A.

If variations (of both size and composition) in the heterogeneouscommodity bundles s and b are to reflect accurately the command

over resources, including labor power, acquired by the capitalists,the components of these bundles must be weighted by the proportionsat which, in reality, they exchange. Normal exchange ratios are

determined by the level of wages and the rate of profit in the familiar

relation,

(2) Ap (1 +X) +aow=p,

where p is the vector of prices, Pi= 1, w (a scalar) = p'b, and X isthe rate of profit.

The rate of profit w is the amount of profits s divided by the

produced means of production used in the production process A'x,the two heterogeneous bundles being reduced to a homogeneousmeasure by valuation at natural prices,

(3) p'[I-A'] x-p'b a'ox

p'A'x

The argument appears to be in danger of circularity since (3) is

merely a rearrangement of (2). But if b is given, and the value of

the produced means of production in terms of the numeraire is aknown function of 7r, (3) is soluble for wr.5

Nonetheless, it is clear from examination of (2) and (3) thatthe dependence of the values of the commodity bundles, p'[I-A']x,p'b a'ox, and p'A'x on a, will obscure the simple "physical" trade-offbetween wages and profits implied in (1). Similarly, no simpleproportional relationship can be found between wages and the rateof profit as would be the case if the ratio of net product less wagesto produced means of production were expressed in "physical" terms.These problems apply a fortiori in the case of joint production.

A measure of value independent of Xr would penetrate the com-plexity of the price relations, a complexity that derives from thefunctional dependence on r of all prices, including that of any

arbitrary numeraire.6 Such a measure would reveal the origin of avalue surplus, analogous to the commodity surplus of (1).

5. Thus, if the matrix A is known, the value of capital is known as afunction of 7r. Piero Garegnani has shown that within the context of theclassical theory of distribution the amount of capital may be expressed as aset of magnitudes (a dated labor stream), the value of which is a function ofthe rate of profit. P. Garegnani, "A Problem in the Theory of Distributionfrom Ricardo to Wicksell," Ph.D. thesis, University of Cambridge, 1959, Part I,Ch. IV; and Garegnani, I1 Capitale nelle Teorie delta Distribuzione, pp. 50-59.

6. Although the value of the numeraire is always defined equal to one,




Problems of measurement of this type were not encountered in

Physiocratic theory, since the capital, consumed inputs ("wages"

of thepeasants),

and netoutput

ofthe only

sector toyield a surpluscould be regarded as consisting of a single agricultural commodity.7

Similarly, Ricardo, in his Essay on Profits, defined corn as the only

commodity entering the production of all other commodities, yet

requiring no other commodities for its own reproduction. This

procedure elevated the distributional relations of the corn sector to

the position of a physical analogue of the distributional relations of

the system as a whole. But physical surplus may originate in all

branches of production, and all sectors require direct or indirectinputs of many commodities. Thus, any physical analogue used to

describe the distributional relations of a complex system must in-

clude all the appropriate commodities used as means of production

and appearing as outputs.

A satisfactory measure of value, which takes account of the

complexity of the economy and yet possesses the characteristics ofa physical analogue, would be a commodity for which the ratio of

the value of its output to the value of its means of production wasinvariant under distributional changes. Such a commodity would

exhibit a simple one-to-one relationship in the division of the value

added in its production between wages (expressed in terms of unitsof this commodity) and profits.

As Mr. Sraffa has pointed out, this can be the case only whena "commodity" is the sole input to its own production, and thuswhen proportions of labor to means of production are "balanced"

(are the same), at all "layers" of the production process. ButIt is not likely that an individual commodity could be found which

possessed even approximately the necessary requisites. A mixture of commodi-

ties, however, or a "composite commodity" would do equally well .... We

should, however, not get very far with the attempt to concoct such a mixture

before realising that the perfect composite commodity of this type, in which

the requirements are fulfilled to the letter, is one which consists of the same

variation in the price of a commodity may be due as much to the conditions ofproduction of the numeraire as to the conditions of production of the com-modity the price of which has varied. For a full discussion of this problem, seeSraffa, Production of Commodities by Means of Commodities, Ch. III.

7. Quesnay does not in fact assume a single agricultural product, but heclearly believed there to be a broad proportionate uniformity between inputsand outputs of the "productive" sector. See F. Quesnay, Tableau Economique,3rd edition, M. Kuczynski and R. Meek, eds. (London: Macmillan, 1972), pp.i-iv.

8. On the part played by the Essay on Profits in the development ofRicardo's theory of value, see P. Sraffa's introduction to Ricardo, op. cit., Vol.I; and L. L. Pasinetti, "A Mathematical Formulation of the Ricardian System,"Review of Economic Studies, XXVII (Feb. 1960), 78-98.




commodities (combined in the same proportions) as does the aggregate of its

own means of production...

An "average" commodity of this type was sought by Ricardo to actas "an invariable standard of value." 10

A composite commodity with the requisite characteristics may

always be found for any particular technology denoted by A (whereA is nonnegative and indecomposable - in Mr. Sraffa's terms all

nonbasics have been eliminated from the system)."l From (2)

(4) [Iv-q-A p = aow?7,where -q=1/(1+T). If w= 0, the existence of a nontrivial solution

to (4) implies the existence of a single nonnegative eigen value ofA, v with which a nonnegative eigen vector x* may be associated.12

Then R= (1-*) /* is the maximum rate of profit of the system

attained at w=O. Furthermore, the components of A'x* bear the

same proportionate relationship to each other as the components of

[I-A']x*, i.e., in the production system the proportions of inputs

are the same as the proportions of outputs.13 The proportionate

composition of x* is that of Mr. Sraffa's Standard Commodity. The

scale of standard net product [I- A'] x* is defined such that 1= aox*

=a'Ox=L, where x is the vector of actual gross outputs and L the

total number of man hours worked in the actual system.

If the actual system is such that outputs and inputs are in thesame proportions as the components of x*, i.e., the actual system is

the Standard System, the physical ratio of net product to means of

production [I-A']x*: A'x*=Q=R, even though Q is a physical

ratio and R a ratio of values. Q may be defined without reductionof the physical bundle of commodities to a common standard

(value), only because numerator and denominator consist of thesame proportions of heterogeneous commodities. Q remains the

same whatever prices may be. Fractions of Q may be similarly

9. Sraffa, Production of Commodities by Means of Commodities, pp.18-19.

10. See the letter of Ricardo to MeCulloch, June 13, 1820, Ricardo, op.cit., Vol. VIII, pp. 191-97; and Sraffa, Production of Commodtiies by Means ofCommodities, pp. 13-19.

11. As is now well-known, nonbasics may be eliminated from the systembecause they have no effect on profit-wage configuration (Sraffa, Production ofCommodities by Means of Commodities, p. 25).

12. By Frobenius' theorem, see M. Morishima, Equilibrium,Stability andGrowth (Oxford: Oxford University Press, 1964), p. 195.

13. Let the rate of physical surplus of each commodity be Qu. If the pro-portions of inputs equal the proportions of outputs Qs=Q, all i. If the excessof output over input is cL, then Q =ec/(xs-ec). Since A'x+c=x, A'x(l+Q)=x,and [A'-Ix]x=0, where X=1/(l+Q). But the minimum eigen value associatedwith a nonnegative eigen vector, *= ]*. The associated vector is x*.




expressed as physical ratios. Thus if Q=20 percent and three quar-

ters of the net product A'x*Q goes to wages, one quarter goes to

profits, and the rate of profit is 1/4 Q, i.e., 5 percent. "The rate of

profits in the Standard system thus appears as a ratio between quan-

tities of commodities irrespective of their prices." 14 Thus,

(5) X-=Q(l-w*) =R(1-w*),

where w* represents wages expressed as a proportion of standard net

product.

In a more general system, with Pi used as numeraire (pi= 1),

and w the wage in terms of Pi, the linear relation (5) between r and

w does not hold. But if a unit of standard net product is used asnumeraire, p'[I-A'] x* = 1, then w/p'[I-A'] x* = w*, the wage mea-

sured in units of standard net product. In consequence, the relation

(5) holds whatever the proportions of outputs to inputs may be, and

whatever the combination of commodities on which wages are ac-

tually spent.15 This is a central result of Mr. Sraffa's book.

The implications of this result are quite striking. For any

technology A there exists a standard commodity x*, which, when

standard net product is used as numeraire, yields a relationship be-tween wages and profits identical to that found independently of

prices. This is consistent with the classical view that the determi-

nation of the distribution of income between wages and profits is

logically prior to, and independent of, prices.16 Furthermore, it

reveals the origin of surplus, in a manner freed from the ambiguities

engendered by price calculations.

14. Sraffa,Production of Commodities by Means of Commodities, p. 22.

15. This quite general proposition is proved in ibid., pp. 22-23. In termsof our notation it can be shown as follows:(a) Ap(1+?r)+aow*=p(b) A'x*(1+R) =x*(c) a'ox*=a'ox 1(d) PV -A'] *= 1.(e) From (a), (c) and (d) x*'Apir=l-w*(f) From (b) and (d) p'A'x*R=l.

Multiplying the left-hand side of (e) by 1, and the right-hand side by p'A'x*R,we have immediately

7r=R (1-w*).

Slightly different proofs are provided by P. Newman, "Production of Com-modities by Means of Commodities." Schweizerische Zeitschrift fiur Volks-wirtschaft und Statistik, 1962; and Schefold, op. cit., pp. xxvi-xxvii.

16. This is quite contrary to the neoclassical view, which holds that dis-tribution is a function of price formation. "To understand what determineslabor and property'sshare in national product,and to understand forces actingon the degreeof equality of income, distribution theory studies the problem ofhow the different factors of production land, labor, capital, entrepreneurship,and risk taking-are priced in the market place, or how supply and demandinteract to determine all kinds of wages, rents, interest yields, profits and soforth." P. A. Samuelson,Economics (New York: McGraw-Hill, 1964), pp. 525-526.




This result does not depend on any assumption concerning the

fixity of the components of A. Even if the components of A are

different as between time periods, due to variable returns to scale

or technical progress, at every moment of time there will exist a

unique x*, which, when used to express the relevant magnitudes,

will define the relationships between w, r, and total profits in the

form of a physical analogue.17

The standard commodity possesses two fundamental charac-

teristics, which are the criteria that a standard of value must meet

if the distributional relationships proposed by the classical econ-

omists are to be revealed:

(a) the "values" of the commodities as measured in terms of the

standard should bear to each other the proportions at which

they exchange;

(b) the standard should be such that the relationship between

variations in the value of the aggregates comprising out-

put, wages, and produced means of production should be

defined prior to the knowledge of variations in 7r.18

In general, no arbitrary numeraire commodity will be adequate

since it will fail to meet criterion (b). Labor values, based on the

labor embodied in a commodity will fulfill criterion (b) but in

general not (a).19 Labor commanded will fulfill (a) but not (b).

17. The conceptual frameworkof the analysis is thus equivalent to thatof the classical natural price. Cf. note 3 above.

18. The conditions were first developed by Piero Garegnani;see "A Prob-lem in the Theory of Distribution from Ricardo to Wicksell," pp. 26-28; andII Capitale nelle Teorie delta Distribuzione, pp. 11-13. Note that although they

constitute a problem of "measurementof capital" they are quite distinct fromthe neoclassical measurement problem, which involves not a relative measureof aggregates, but a measureof the "quantity of capital" available in an econ-omy, so that its "scarcity"relative to other "factors" may be included in thedata of the exercise of price determination. The analogous criteria for theneoclassical theory of distribution are as follows:

(a) The total quantity of a factor available should be known independ-ently of its price.

(b) The manner in which quantities of each factor are expressed must besuch as to permit the definition of a production function relatingvariations in quantities of factors (quantities so expressed) to out-puts, such that the minimum cost of production is, in turn, related

to the minimum quantity of each factor requiredfor production.In the case of capital for which (b) implies a value measure, these conditionsare mutually inconsistent; see Garegnani,"A Problem in the Theory of Dis-tribution from Ricardo to Wicksell," pp. 100-09; and I1 Capitale nelle Teoriedella Distribuzione, pp. 82-88.

19. As is well-known, in some particularcircumstances labor embodied isa suitable measure. These are when 7r=0 and when the organic compositionof capital is the same in all sectors of the economy. See A. Bhaduri, "On theSignificanceof Recent Controversies on Capital Theory," Economic Journal,LXXIX (Sept. 1969), 532-39; and P. Garegnani,"Heterogeneous Capital, theProduction Function and the Theory of Capital,"Review of Economic Studies,XXXVII (July 1970), 407-36.




III

So far the argument has taken place solely in terms of what

Marx called prices of production. We may now relate Sraffa's resultsto Marx's theory of exploitation, the theory that Marx- used to

explain the origin of profits.

Marx defined the rate of exploitation, or rate of surplus value,

as the ratio of surplus labor time to necessary labor time. In the

first stage of his argument, he assumed that all commodities ex-

change at their labor values, including labor power and the com-

modity money. Necessary labor time was then defined in two ways:

(I) as the value of "the sum of money v expended upon the labourpower," 20 in effect as the share of wages in the value of output, and

(II) as "the value of [the] means of subsistence," 21 that is, as the

value of the commodities comprising the real wage. But since "the

values of the variable capital [v] and of the labour power pur-

chased by that capital are equal," 22 no ambiguity is involved in the

dual definition.

These two definitions correspond, in turn, to two approaches to

the problem of the relationship between labor values and prices ofproduction. The second definition is the basis of what may be called

the "simultaneous equation" solution developed by Bortkiewicz, on

the foundations laid by Dmitriev.23 The first definition is implicit

in the aggregative approach pursued by Marx in the form of the

"average industry." 24 This latter approach is more akin to the

problem as stated by Ricardo, and, indeed, the difficultiesunderlying

Ricardo's search for a suitable standard of value were inherited by

Marx as the problem of the link between labor values and prices ofproduction.25

20. K. Marx, Capital, Vol. I, 1889 edition (London: Allen and Unwin,1957), p. 194.

21. Ibid., p. 198.22. Ibid., p. 200.23. See V. K. Dmitriev, Economic Essays on Value, Competition and

Utility (Cambridge: Cambridge, University Press, 1974), Ch. 1; and L. vonBortkeiwicz, "Wertrechnung und Preisrechnung im Marxschen System." Archivfur Sozialwissenschaft und Sozialpolitik, 1907, part of which is published in

English in International Economic Papers, 1952.24. The distinction between "simultaneous" and "aggregative" approachesto the transformation problem was introduced by Piero Garegnani in a paperpresented to a symposium on the transformation problem held at the Univer-sity of Siena in April, 1972; at which an early version of this paper (which didnot then incorporate the distinction) was also read. Garegnani also demon-strated that an aggregative approach may be developed with the wage givenas a bundle of commodities, on the basis of the wage-goods sector; and empha-sized the clarity of the "image" of exploitation in an aggregative approachvis-a-vis a simultaneous-equation approach.

25. Garegnani, "A Problem in the Theory of Distribution from Ricardoto Wicksell," p. 2.




Post-Marxian discussions have customarily focused on Marx'ssecond definition, (II), of necessary labor time. This requires the

characterization of the wage as a given bundle of commodities, of

"necessaries," the size and composition of the bundle being deter-

mined by social and historical forces. If b is the vector of "the

actual necessaries [the laborer] consumes," (the components of

which are bi), hi the amount of labor time directly and indirectly

embodied in commodity i, and T is the length of the working day,

(in effect the production period), then the rate of exploitation is 26

(6) T-h' b

h'bFurthermore, it has generally been assumed that the wage bun-

dle is advanced at the beginning of the production period, in the

manner of the wage-fund of the classical economists and thus con-

stitutes part of the "capital" of the system. In this case the matrix

of input coefficients may be modified in the form,

jaijj+zij4IA+,where zij= biaoj,27 and the price relations become

(7) A+p(1+7r) =p,

p1=1. The rate of profit 7rr=R+, where R+= (1-y)/y, y being the

appropriate eigen value of A+.

In the market place exchange ratios of all commodities, in-

cluding labor power, are expressed not at labor values, but at prices,

which depend on the relationship between wages and the rate of

26. Morishima develops three alternative definitions of the rate of ex-ploitation, all of which are based on the labor value of a known consumptionbundle and are exactly equivalent to (6). He does not consider the other sideof the coin, the proportion of total value produced paid to workers, presentedin definition (I). See M. Morishima, Marx's Economics (Cambridge: Cam-bridge University Press, 1973), pp. 47-51.

27. (Ap+aow)(1+r) = p,and

b'p = w,thus

pi= (Xajp,+Xbaoap,). (1+7r),

and

A+-=J ai,+z1jwhere

zoj = baos.The wage may contain some components that do not appear in A, in whichcase the methods of production of these new components must be added to Ain the construction of A+. A+ is, therefore, composed of all those commodities"entering directly or indirectly the wage" (Garegnani, "Heterogeneous Capital,the Production Function and the Theory of Capital," p. 418). The "basics" ofthis system therefore include all Mr. Sraffa's basics, plus any extra componentsthat appear in b but not in A. For a full discussion of the characteristics ofthis wage-good system, see the Garegnani article already cited in this note, pp.417-21.




profit. But "profit is the form in which surplus-value presents itself

to the view, and must initially be stripped by analysis to disclose

the latter." 28 Such an analysis is quite unambiguous when relative

labor values are equivalent to prices and b is given. Labor values

then fulfill conditions (a) and (b), outlined above, for a satisfactory

measure of value; and the rate of profit, like the rate of exploitation,

may be expressed as a ratio of labor values, immune from the com-

plications of price variation.

But a number of problems are presented by the fact that, in

general, the organic composition of capital is not the same in all

sectors of the economy, and consequently exchange ratios are notequivalent to relative labor values, (except when =0). Direct

determination of the rate of profit as a ratio of quantities of labor

time is no longer possible, and an investigation of the relation be-

tween the profit rate and different wage rates (or different rates of

exploitation) now requires knowledge of differences in the magni-tudes of the components of the wage bundle at every level of the

wage. Even if different levels of the wage are represented by scalar

multiples of b, (changing the components of A+), the consequent

relationship between the rate of exploitation and the rate of profitmay be found in this approach only by solution of a set of simul-taneous equations encompassing the production of all commoditiesrequired directly and indirectly in the production of wage goods.Furthermore, in general, different wage levels cannot be charac-

terized simply as scalar multiples of the wage bundle b bought inone particular situation. Suppose that the composition of b is dif-

ferent at a higher (labor) value of the wage, hi,A bi > 0. By (6)

e falls. If Abo-Q, all i, then since the eigen value y is a strictlypositive and continuous function of all elements of A+, y must rise,and R+ - (1-y)/y fall.29 But if Abi<O some i, y may increase or

diminish, and R+ may fall or rise. Thus r may rise when e falls andvice versa.

Although the simultaneous-equation approach identifies a rela-

tionship between exploitation and profits, the clarity of the concept

of surplus is somewhat lost in the simultaneity of the solution.Moreover, the possibility of variation in the commodity compositionof the wage presents major difficulties for a definition of the rate ofexploitation in terms of (6). While undoubtedly at different wagelevels part of the wage consists of "necessaries," it is not possibleto define unambiguously which part, since an increase in the con-

28. K. Marx, Capital, Vol. III (New York, International Publishers, 1967),p. 48.

29. See Morishima,Equilibrium, Stability and Growth,pp. 195-215.




sumption of one commodity may substitute for diminution of an-other. Mr. Sraffa considered splitting the wage into necessaries and"surplus" wage.30 His decision to treat the wage solely as a share

of net product (and of standard net product), although apparentlybased only on conceptual convenience, may also be supported ongrounds of logical coherence.

This problem may be avoided by adopting Marx's definition

(I) of necessary labor time and the "aggregative" approach. Butwhen prices are not equivalent to labor values, the two definitionsof necessary labor time no longer coincide. The rate of exploitationcalculated on the basis of the definition of necessary labor time as

a share of net product paid out as wage (I), is no longer equivalentto the rate of exploitation derived from the definition of necessarylabor time as the labor value acquired by the worker in the neces-saries purchased. The image of "exploitation" is just as vivid using(I) or (II), but (I) is far more flexible, encompassing as it does thepossibility that between one situation and another (and one workerand another) the composition of the bundle of commodities pur-chased may vary, and yet the rate of exploitation remain the same.

Furthermore, using (I), it is no longer necessary to know ex antethe commodity composition of the wage at all wage levels.

Before proceeding to a discussion of exactly how the rate ofexploitation should be specified using definition (I) of necessarylabor time, it should be noted that use of this definition must elimi-

nate the possibility of augmenting the input matrix in the manner

of A+. The wage could still be considered as an advance (measured

in terms of an arbitrary numeraire), but this would create an

awkward hybrid denominator for the ratio defining the rate of profit

(3), it then consisting of the value of the commodities used in the

production process plus an amount of value defined solely in terms

of the numeraire. Since it has little bearing on the problem at hand,

wages are assumed to be paid at the end of the production period.

The simplest way by which to generalize a definition of the rateof exploitation in the spirit of (I) is to by-pass the measurement of

necessary labor time as distinct from total labor time and take theratio of total profits to wages. This ratio is not influenced by choice

of numeraire. Net product over a given time period may be regarded

as a number of hours worked, or as a sum of value (in terms of anynumeraire). Proportionate division of the former is exactly equiv-alent to proportionate division of the latter.

30. Sraffa, Production of Commodities by Means of Commodities, pp.




Two objections may be made to this procedure. First, the samerate of profit and the same technology could be associated with

different ratios of profits to wages, simply because activity levels ofeach sector were different. In general, the technology will changewith the composition of output, but while it is reasonable to say that

the rate of exploitation has changed because the technology haschanged, it is not reasonable to claim that the rate of exploitationhas changed simply because, with technology unchanged, the com-position of output has varied. Second, defining the rate of exploita-tion as the ratio of profits to wages involves defining the nature of

the labor process in terms of its outcome.These problems may be overcome by returning to Marx's defi-nition (I), making units of standard net product our "money" and

measuring necessary labor time in terms of this "money." The total

amount of labor performed in one production period and the amountof labor embodied in one unit of standard net product are equal.

Suppose that the economy is operating in standard proportions,i.e.,

(8) A'x* (1+Q) = x*.Net output may be regarded as a collection of bundles of commodi-ties, each bundle produced by one man, and each containing all thecomponents of x* in the proportions of x*. The wage is set as threequarters of one man's net product, the remaining one quarter of thebundle accruing to the capitalists. Put another way, three quartersof the total labor force in employment produces bundles paid to wage

earners, and one quarter of the labor force produces bundles that

the capitalists appropriate. In this case it is easy to see that whetherthe wage is defined as a proportion of standard net product (I) or

as a bundle of commodities (II), the rate of exploitation is1

over3 14 or 3. Measured in physical units of standard net product

w=1, e= (1-w*)/w*, and w=Q(1-w*) =Q

But as we have seen in Section II, the relationship between wagesand the rate of profit is the same in the actual system as in standardsystem, as long as wages are expressed in terms of standard netproduct. Furthermore, the scale of the standard system is such thatthe same amount of labor is expended as in the actual system. If,then, the wage in terms of an arbitrary numeraire, (say pi = 1), is

w, and w/p' [I-A']x*-3= w*, the rate of profit in the actual4




system is equal to R (1- w*). The relation of wages to the rate of

profit is the same as if in the standard system three quarters of the

labor force was producing the share of net product going to theworkers. In other words, if the rate of exploitation is defined as 1

minus the proportion of total labor embodied in the "money" wage,

this is equivalent to the rate of exploitation in the production of an

"average" commodity, the standard commodity, and may thereby

be directly related to the rate of profit in the system as a whole.31

1So the rate of exploitation e- (1-w*)/w* - for technology A,

is unambiguously related to the rate of profit r=R (e

The ratio of total profits to wages in the actual economy will in

general deviate from the profit-wage ratio in the standard system

to the extent that the commodity composition -of net output differs

from the "average," or standard, proportions.

IVThe combination of Marx's definition (I) of necessary labor

time with Mr. Sraffa's device of the standard commodity (playing

the role that Marx intended for the product of his "average indus-

try") provides the advantages both of a physical analogue and of

the aggregative approach. The relationship between exploitation

and profits is clearly revealed, and a direct link established between

exploitation so defined and the distribution of income in the actual

system. The analysis does not depend on prior knowledge of thecommodity composition of the wage and hence refutes the arguments

of those who claim that the foundations of Marx's analysis are

undermined if a "real-wage bundle" may not be identified. The

result is, therefore, complementary to analyses of the transformation

problem, which are based on the traditional definition of the rate of

exploitation. But the same simplicity and generality are not attain-

able by means of the traditional definition.

TRINITY COLLEGE,CAMBRIDGE

31. Marx analyzed the relationship between the rate of exploitation andthe profit rate in terms of a commodity producedby means of capital with "amean, or average composition, that is, it has the same, or almost the samecomposition as average social capital" (Capital, Vol. III, p. 173). But Marxmade the mistake of deriving his "average" n such a way that it was a func-tion of the actual composition of net output (given the technology) and in-cluded nonbasics.

Date post:	08-Aug-2018
Category:	Documents
Upload:	locantore
View:	216 times
Download:	0 times

J. Eatwell on Sraffa and the surplus value

Documents