Shaikh - Transformation From Marx to Sraffa

8/3/2019 Shaikh - Transformation From Marx to Sraffa

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3The Transformation from Marx to

SraffaAnwar ShaikhI. IntroductionRecent history has seen a tremendous revival of Marxist economicanalysis. But this process has also produced its own specific problems,because as Marxist economics gain in respectibility, the temptationto represent itself in respectable terms grows accordingly. And theseterms, in the end, are 'almost always the wrong ones.There is no question but that Marxism must appropriate allmodem developments. But to appropriate them involves much morethan merely adopting them. It involves tearing them out of thebourgeois framework in which they appear, examining their hiddenpremises, and re-situating them (when and if possible) on a Marxistterrain-a terrain which cannot be derived merely by algebraicvariation or sociological transformation of.the premises of orthodoxeconomics. We must, and indeed we do, have our own ground tostand upon.It is my contention that the Sraffian, neo-Ricardian, tradition is byfar too respectable. Its roots in left Keynesianism are easy toestablish, and its refuge in mathematical economics isquite revealing,Nonetheless, the claims made by this school must be addressed, and'its real contributions must be separated out from what is merely partof its cloak of respectability.In this paper I do not intend to reproduce previous criticisms of theneo-Ricardians, nor even to reproduce my own arguments in favourof Marx's theory of value. Instead, in the discussion that follows Iwould like to show that even within the algebraic framework of whichthe neo-Ricardians are so proud, there are a host of issues which theydo not, and cannot, face. These issues depend crucially on thedifference between Marx's concepts and those of the neo-Ricardians.The very same algebra that they use, when asked different questions,

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44will generate different answers. And these answers, it turns out, favourMarx much more than they do the neo-Ricardians. . .In the discussion which follows, I will therefore examme I~ somedetail the neo-Ricardian arguments concerning the redundancies andinconsistencies in Marx's theory of value. Since t~eir treatment


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46social division oflabour that the necessity of the distribution of sociallabour asserts itself as the domination and regulation of wages, pricesand profits by social labour-time. The sphere of exchange has arelative autonomy, but it is ruled, regulated and dominated by theconditions of production and reproduction. The operation of thisdouble relation is what Marx means by the law afvalue: prices as theimmediate regulators of reproduction, social labour-times as theintrinsic regulators of prices and hence of reproduction.'Every child knowsthat a nation which ceased to work, I willnot say for ayear, but even for a fewweeks, would perish. Every.child knows, too, t~atthe masses of products corresponding to the different needs requiredifferent and quantitatively determined masses of the total labour .ofsociety. That this necessity of the distribution of social labour in definiteproportions cannot possibly be done away with by a particular form ofsocial production but can only change the mode ofits appearance, isseJf-evident. No natural laws can be done away with. What can change inhistorically different circumstances is only the form in which these lawsassert themselves. And the form inwhich this proportional distribution oflabour asserts itself, in a state of society where the interconnections ofsocial labour are manifested in the private exchange of the individualproducts of labour, is precisely the exchange-value of these.products.Scienceconsists precisely in demonstrating how the law ofvalue assertsitsell."

3. Money and PriceThe above understanding ofcapitalist exchange implies several thingsfor a Marxist analysis of price phenomena. First of all, it implies t~atmoney is an absolutely necessary aspect of developed.commod~typroduction. Exchange is a process in which people must equahzedifferent use-values that is abstract from their differences as use-values. Asthe sphere ofexchange grows, so too does the necessity for auniversal equivalent in which this abstraction is expressed, andthrough which the articulation of independent labours is accom-plished. Money is the medium of abstraction, and the means offorcible articulation.Second, because money is a necessary aspect of exchange, theelementary relation of exchange issale and purchase, not barter (C-Mnot C-C). This means that each commodity now has a price, aquantity of money which represents its quantitative worth. Con-versely, it also implies that money itself has no price. Itdoes not haveto be sold, it is money.Third, all price phenomena now appear in a double light. On the

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one hand, as price magnitudes they are distinct from value magni-tudes, and have a more complex determination. For instance, even in~hecase of.exchange in proportion to value, the price of a commodityISa ~uantIty of gold determined by the commodity's relative value,that .IS, value relative to the standard of price, say one ounce of gold,and IStherefore already a form of the commodity's value. As such, themovements of prices need not parallel those of commodity values. Afall in a commodity's value, for example, can be manifested as a risein its price if the value of gold happens to fall even faster. 7M?re generally, as the price-form isdeveloped byMarx, so too isitsrelative comp!exity. In the first volume of Capital, price is generallytreate~ as a SImple money-form of value, but wages, as time-wagesand piece-wages, are already more complex forms of the value oflabour-power. In the second volume, costs of circulation andtU?lover add fresh determinations to the price-form, Lastly, in thethud volume, the development of prices of production and of thesplitting of surplus-value into profits, rents and interest furtherconsolidate the price-form, while the distinction between individualvalue and average value consolidates the determination of valuemagnitudes, and thr?ugh them, those ofprice magnitudes (individual,average and regulating prices of production, differential profitability,and rent, absolute and differential). It must be noted here that theincreasing complexity of the price-value relationship isno defect. Sinceprice magnitudes are the immediate regulators of reproduction, thelaw of value m~st contain within it a theory of the structure of pricephenomena, nght down to their most concrete determinations .Otherwise the law remains abstract, unable to grasp the realmovements of the system.On the other hand, because the price magnitudes are themselvesregulated by the socially necessary distribution of labour the variousforms of price categories must be developed in relation to thequantities of socially necessary labour-time whose magnitude andmovements dominate and regulate these price phenomena. We mustbe a~le to conceive not only of the relative autonomy of pricemagnitudes, as expressed in their variability and complexity relativeto values, but also of limits to these' variations and of thec?nnection of these limits to social labour-time. It is significant that inhISown development of the increasingly complex categories of pricephenomena, Marx never loses sight of the domination of thesephenomena by the law of value. .'In whatever way prices are determined, the following is the result:

(1 ) The law ofvalue governs their movement inso far as the reduction or

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48 ,increase in the labour- time needed for their product ion makes the prices ofproduction rise or fall ...

(2 ) The average profi t, which determines the prices of product ion, mustalways be approximately equal to the amount of surplus-value thataccrues to a given capital as an aliquot part of the total social capital ...Since i t is the total value ofthe commodities that governs the total surplus-value , while th is in tu rn governs the leve l of average profit and hence thegeneral rate ofprofi t-as a general law or as governing the f luctuations- itfollows tha t the law of value regu lates the prices of production."

In a highly' modern vein, Marx goes on to note how meaningless itis-but also how very convenient it is-to treat the difference betweenprice and value, that is the relation between the two, as a meresepara tion.'The price of production includes the average profit. And what we call theprice of product ion is in fact the same thing that Adam Smith cal ls "naturalprice", Ricardo "price of production", or "cost of production" and thePhysiocrats "prix necessaire", though none of these people explained thedifference between price of production and value. We call it price ofproduction because in the long term it is the condition of supply, thecondition for the reproduct ion ofcommodities, ineach par ticular sphere ofproduction. We can also understand why those very economists whooppose the determination of commodity value by labour-time, by thequant ity oflabour contained in the commodity, always speak of the pricesof production as the centres around which market prices fluctuate . Theycan allow themselves this because the price of production is already acompletely externalized and prima facia i rrat ional form of commodityvalue, a form that appears in competition and is therefore present in theconsciousness of the vulgar cap italist and consequently also in that of thevulgar economist."

I remind you that Marx is speaking of the economists who claim toground themselves in classical economics-less the embarrassment ofthe labour theory of value, of course!4. Tendential RegulationItfollows from the above that within the moving contradiction that iscapitalist commodity production, the reproduction of society isnecessarily a process of trial through error, in which discrepancies ofone sort are cons tan tly followed by those of an opposite nature -,It isonly in and through perpetual disorder that the necessary distri-bution of social labour-time asserts itself. 10 This is why Marx aiwaysspeaks of a process of tendential regulation and not of some staticequilibrium situation. Conversely, it is precisely the concept of

Shaikh 49equilibrium which enables orthodox economics to abolish all thecontra.dictions of the forcible articulation, thus abolishing both thenecessi ty of money and the possibility of crises. 11'[The] dete rmination of [market] price by[ the price] of production is notto be understood in the sense of the economists. The economists say tha t~heaverage price ofcommodities isequal to the [price] ofproduct ion; thatIS a law. The anarchical movement, inwhich rise iscompensated by fal landfall by rise, is regarded by them as chance ... But it is sole ly thesefluctuations, which, looked at more closely, bring with them the mostfearful devasta tions and, like earthquakes, cause bourgeois soc iety totremble to its founda tions-it is sole ly in the course of these fluctua tionsthat [market] prices are determined by the [price] ofproduct ion. The totalmovement of this disorder is i ts order .t '?

III. The Aggregate Effects of Price-Value Deviations

In the preceding section I have been concerned to emphasize the, distinctiveness of Marx's conception of the relation between pro-duction and exchange in the process of social reproduction. But thesedifferences between Marx's conceptions and those of orthodoxeconomics, be they classical or marginalist, need not, indeed cannot,be restricted to this level of abstraction. Every real difference inconception inevitably implies a difference in the questions to be asked,in the empirical phenomena to be examined, and ultimately in theconclusions to be drawn. Consequently, in the sections that follow Iwould like to demonstrate exactly how these differences manifestthemselves in a set of problems which, according to some modemMarxists, have a lready been definitively resolved.!" namely, the hostof issues which have their origins in the debates around the so-calledtransformation problem.!" Since the transformation problem is itselfa special case of the general problem of price-value deviations(differential rent and market prices are two other equally importantcases), I will often deal with the general case first and only then, wherenecessary, restrict the analysis to the consideration of prices ofproduction alone .One last point. Throughout what follows I will explicitly accept the

mathematical formulations which are now so widely accepted in the1post-Sraffian literature on these issues. These are exactly the toolsand formulations which are the cornerstone of the most recent attackson Marx's theory of value, and it is my intention to show that even onthis terrain, Marx's answers are superior because Marx's questions


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are superior. Only at a later point will it be possible to show how theexisting formulations are themselves inadequate-precisely becausetheir very structure already embodies many conceptions of orthodoxeconomics.

1. Calculation Versus Conception; The Redundancy ArgumentIthas always been a popular claim among Marx's critics that valuecategories are unnecessary in the analysis of capitalism because theyare somehow less direct than price categories. Steedman, for instance,insists that given the physical flows of inputs and outputs, of thelabour requirements for these outputs, and of the real wage of thislabour, one can determine prices of production and the rate of profitwithout 'any reference to value magnitudes'. Indeed, Steedman goeson, since the 'physical data' which is required to determine values isalso an element in the determination of prices of production, it wouldfollow that values can 'play no essential role in the determination ofthe rate of profit or of prices of production.l'"Steedman's use of words is quite revealing. To begin with, the veryuse of the term 'physical data' is symptomatic of the whole neo-Ricardian approach to social reproduction. In Marx's analysis,'relations between men within the process of creating and repro-ducing their material life' appear as a double relation, in which thepeople-nature relation exists in-and-through the people-peoplerelation.l" These are different aspects of the same set of humanactivities. In the neo-Ricardian conception, however, these double-edged relations are separated and alienated into 'physical data' and'distribution'. The labour process, a fundamental social relationwhich involves the performance of labour and the forcible extractionof surplus labour, disappears from view. It is replaced instead by so-called given conditions of production.' 7Itisworth considering the various senses in which the conditions ofproduction may be said to be 'given'. We begin by noting that theoverall circuit of capital can be represented as M-C ... p ... C-M'.In the first phase, capitalists invest money-capital M in the purchaseof commodity-capital C-means of production and labour-power. Atthis point, therefore, we might say that they possess given conditionsof production, but only as pre-conditions of production: as thenecessary objective and subjective factors of the yet-to-be-performedlabour process. 18The capitalists must still unite these factors in thelabour process itself, in the form of productive capital P, and only if

Shaikh 51this isdone successfully will they be in the possession of the results ofproduction: expanded commodity-capital C.Once the labour process has been completed, and input translatedinto output through the actual performance oflabour, then, and onlythen, can we conceptually appropriate the results of the labourprocess in the form of input-output measurements-the so-calledphysical data to which Steedman constantly refers. But now thisphysical data is itself a conceptual summary of the real expendituresof social labour-time. In the real economy, the results of productionon which the so-called physical data are based are themselves givenonly through the actual materialization of social labour-time, andhence only because value has been actually created. Values are, so tospeak, built into the very fabric of this physical data.As observers of the process, we can now extract from this dataestimates ofthe value flows that were actually involved,just as we canalso extract from it estimates of the prices of production that mightcorrespond to such data (actual prices are of course market prices).We might then fall into the simple error of confusing our estimationprocess with the real determination of values. We might even naivelybelieve that since we can calculate estimates of values and prices ofproduction with almost equal facility from the physical data.l? theyare indeed co-equal in reality-ignoring completely how this so-called physical data comes into being. We might then, in this idealis tfashion, arrive at the neo-Ricardian conception of production, inwhich input proceeds magically to output without the toil and miseryof real labour, and in which values acquire a real existence only if wedeign to consider them. The production of things by means ofthings.2. The Sum of Values and the Sum of Surplus- ValuesWe noted earlier that for Marx price is itself always the monetaryexpression of value, the form necessarily taken by value in the sphereof exchange. The social labour process results in a given mass ofcommodities with given values: in circulation, these commoditiesacquire specific monetary expression in the form of prices. But it isobvious that in exchange these money prices can do no more thanbring about the distribution of the social product among theindividuals involved. They cannot in themselves change the mass ofuse-values so distributed. As such, neither can they change the mass ofvalue and surplus-value represented by these commodities.Itfollows from the above that different possible exchange relationsamong producers of a given mass of commodities involve only


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52Idifferent possible distributions ofthe total mass of value and surplus-value contained in these commodities. This is precisely why Marxargues that price-value deviations cannot in themselves alter the sumsofvalues and surplus-values involved. 'It needs no further elaborationhere that, if a commodity is sold above or below its value, there issimply a different distribution of the surplus-value, and that this

distribution, the altered ratio in which various individuals partake ofthe surplus-value, in no way affects either the magnitude or thecharacter of the surplus-value itself .'20It must be said, however, that just because different patterns ofdistribution cannot alter the total mass of surplus-value to bedistributed, it by no means follows that the monetary expression ofthis total surplus-value (money profit) cannot-within certain strictlimits-vary in magnitude. In what follows we shall show that Marxapproaches the question of how and why a given mass of surplus-value materialized in a given surplus product can nonetheless have avariable monetary expression in circulation. How and why, in otherwords, profits can deviate from surplus-value and still remain

determined by it.3. Profit and Surplus- ValueThe distinction between the sphere of production and the sphere ofcirculation is essential in Marx's analysis of reproduction. Theproduction of social wealth (goods and services) occurs in the former,while in the latter the objects or performances produced aretransferred via exchange from their owners to their consumers.Obviously, both production and circulation are absolutely necessaryfor capitalist reproduction. Nonetheless, their effects are quitedistinct: the former sphere results in the creation ofvalue and surplus-value, and the la tter in their transfers."The essential mechanism for the transfer of value is the deviation ofprices from proportionality to values. We will follow Marx inreferring to these as price-value deviations with the understandingthat, as in Marx, this always means deviations of prices from directprices. For instance, when a commodity is sold at a price below itsdirect price, then the seller receives in money-form a value less thanthe value represented by the commodity sold. Conversely, the buyerreceives in commodity-form a value greater than that which he or shehanded over in the form of money. The surplus-value transferred outof the hands of the seller therefore directly reappears in the hands ofthe buyer. Something quite important follows from this, Suppose that

Shaikh 53some sellers have prices below direct prices, and others have pricesabove direct prices, but that for the economy as a whole the sum ofthese prices is equal to the sum of direct prices. Then what someselle~slos~ in exch~.nge is exactly offset by what other sellers gain, sothat m their capacity as sellers the capitalist c lass as a whole receivesmoney in proportion to the total value materialized in theircommodity-capitaL But note: the capitalist sellers who lose in valuedo ~o to their own buyers, while those who gain in value do so fromtheir own b~yers: The question then arises: who are these buyers andhow do their gams and losses appear in the determination of totalmoney profits?To ans~er. this, we need to look at the process of capitalist~ep:oductlOn 10greater detail. To keep the exposition simple, let usinitially assume a system in simple reproduction in which allprodu.ction takes one year, at the end ofwhich capitalists and workersmeet in t?e market~p~~ce to buy and to sell. Capitalists enter themarket With ~ommodltles. C', and wi~h money M'. Workers, havingconsumed th~Ir wages dunng the previous period ofproduction, enter

the market WIth only their labour-power LP which they hope to sell~fresh so as to be able to consume once again. On the basis of theirmvestment plansfor the coming year, capitalists invest money-capitalM to purchase the elements for next year 's production. Of this money,M e ~epresents co.nstant money-capital advanced for means of pro-duction MOP: It therefore buys back a portion of the overallcommodity-product C. The remaining portion of capitalist invest-ment expenditures consists of variable-capital M v , which is used topurchase labour-power LP for next year's production. The workers inturn spend this money on their means of subsistence MOS thusb~ying back. a s~cond portion of the available commodity-prod~ct C'.Finally, capitalists must also buy a certain amount of goods for theirown personal consumption. They therefore expend an amount ofmoney-revenue m to buy back the remaining portion c of the totalproduct C. Figure 1 below summarizes money flows in the overallprocess. The flows remaining within the circuit ofcapital, which as weshall see shortly are crucia l to the analysis, are contained within therectangle drawn below.It is evident from the above that the circuit of capital M~C (therectangle in Figure 1) encompasses the purchase ofthe vast bulk ofthesocial commodit'y-~roduct C': directly, through the exchangeMe-MOP, and indirectly through the circuit Mv~LP~MOS. Itfollows that any transfer of value arising from price-value deviations

of means of production MOP and workers' means of subsistence


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54Figure 1

c--------------------C'


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56value), :n:=actual 'money profits, b=the fraction of actual profitswhich goes towards capitalist consumption, g=the average growthrate of the economy, and bF=the average percentage price-valuedeviation of articles consumed by capitalists. Then, as derived inappendix A,it can be shown that the percentage deviation of profitsfrom surplus-value (from direct profits) is a fraction b(l/l + g)of theaverage percentage price-value deviation of capitalist consumptiongoods.

:n:';_:n:0 b--- =--D:n: l+gwhere O~b~l, (1/1+r)~(1/1 +g)~l, r=the uniform rate of profitand

in which Pi' pi refer to actual and direct prices ofthe i-th good, F, tothe capitalist expenditures on these goods.and F = = l : r = IF,to the total. consumption expenditure of capitalists. < > F is therefore a weightedaverage of individual negative and positive deviations.It should be noted at this point that this result holds for arbitraryprices, the only restriction being that aggregate money-value of thesocial product be held constant, so that the purchasing power ofmoney isheld constant. The latter condition ofcourse implies that theaverage price-value deviation for the total product is exactly zero.Insofar as capitalist consumption goods encompass a wide variety ofobjects produced in industries having a wide range of productionconditions, then their average price-value deviation will be theweighted average of many positive and negative individualdeviations. In general, therefore, the average price-value deviation

(b F) of capitalist consumption goods is likely to be quite smalLFurther discussion on this issue willhave to be reserved for section IVof this paper, where the determinants of individual price-valuedeviations will be analysed.To get an idea of the magnitudes actually involved, it is useful torecognize that (1 - b)is the fraction ofprofits invested by capitalists. Itfollows therefore that it is also the ratio of total investment to totalprofits, or, what isthe same thing, the ratio ofthe average growth rateg to the average profit rate r. This means that equation (I ) can also bewritten as

(1 )

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( 2 )

For the US economy over the postwar period, the average rate ofprofits (before taxes) was roughly 12%, and the average growth rateroughly 4%.26For these orders of magnitude the resulting profit-surplus deviation would be roughly 64% of bF, the average price-value deviation of capital ist consumption goods. If the latterdeviations were ofthe order of -10% (giventhe definition ofbF, thismeans that capitalist consumption goods sell at prices roughly(0.1/1.10);;-9% lower than values),the direct profits would differfromactual profits by roughly - 6%.

~:n: tc+n"- - -- ,.._,0.064.:n: 7tIt is worth remembering, incidentally, that the above formulaabstracts from fixedcapital and differencesin turnover time. A propertreatment ofthesefactors isbeyond the scope ofthe present paper, buttheir inclusion would imply an even lower profit-surplus-valuedeviation.With only a little more effortwe can extend the preceding results onthe mass ofprofit to the case ofthe rate ofprofit. Let M, W,Pstandforthe money values ofproduction used up, the total wage bill, and theaggregate sum of prices, respectively, all at arbitrarily given relativeprices. Now let MO, W e, P" stand for the corresponding moneyaggregates when relative prices equal relative values (when prices'equal' values). Then

P = = M+W+:n: (3 )(3a)

Since weare abstracting from turnover and fixed capital, the actualaverage rate of profit r is simply the ratio of profit 7t to cost-price(= capital advanced) M +W. Hence .r = ---M+W whence :n: r(M+W)


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58whence

tt n r (4)~--=--p M+W+n I+I '(4a)

where r=the average money rate of profit with actual prices and r"=the average money rate of profit with prices proportional to values =the average value rate of profit.Finally, since the sum ofprices isheld constant, P=P". Dividing (2)by P and applying (4),we can, after a little manipulation (see appendixA), write: _ ( ~ n ) An

A I' [_rO r- +-n n (5 )- =r(~n)+1r r

Intuitively, given that the sum ofprices isheld constant, ifprice-valuedeviations cause n to be below nO , they must also cause (M +W) to beabove (M O +WO) (see equation (3. This means that the average rateof profit will be lower than the value rate because its numerator (z) islower and also because its denominator (M +W) is higher, which inturn implies that profit rate deviations will tend to be a bit larger thanprofit mass deviations An/n. This is exactly what (5) tells us, and if weuse the previously calculated magnitudes of An/rr:;;::;- 0.064 alongwith the previously given value of (';::0.12, we get

rAn- 0.07 > - =- 0.064.n

It is important to understand what this numerical result implies:given that [;::0.12, (5) implies that r" ; ::0.13! Such a difference,incidentally is considerably less than the probable error in anyempirical measurement of r,and we may as well say that for empiricalpurposes I' and r"(as well as rr and nO ) are virtually indistinguishable-providing, of course, that our estimate of price-value deviations is ofthe correct order of magnitude. Before we come to that, however, we

Shaikh 59need to clarify a bit further the inner relation between value rate ofprofit and its monetary expression.4. Prices of Production: Th e Profit RateThe preceding discussion was based on more or less arbitrary prices.In order to derive more precise results, we must now restrict ourselvesspecifically to prices of production. In this regard, since we havealready established in (5) that even in the general case there exists anintrinsic connection between profit mass deviations and profit ratedeviations, it is sufficient to deal with the latter alone.We begin by noting that for given conditions of the labour process,the value rate of profit r? can always be expressed as a steadilyincreasing function of the rate of surplus-value:

o Sr =--C+Vwhere S=surplus-value, V=value of labour-power. Let L;;:;;V +S=value added by living labour (ifN=he number ofworkers employed,and h = the length of the working day in hours, L=Nh). Letk;;:;;C/L =the ratio of dead to living labour. Then

(6)

( 7 )

Since k depends only on the technology and the length of the workingday h, when these conditions of the labour process are given r" willvary directly with the rate of surplus-value. Thus the value rate ofprofit is a monotonic increasing function of the rate of surplus-value.In recent years, several authors have shown that when direct pricesare transformed into prices of production, though the transformedmoney rate of profit r will in general deviate from the value rate (wehave explained how and why in the preceding section of this paper),nonetheless this transformed rate is also a monotonic increasingfunction of the rate of surplus-value.i? But once it is recognized thatthe value rate of profit r" and the transformed rate r both increase asS/V increases, it follows at once that they must move together: whenthe value rate of profit rises (or falls) its reflection in the sphere ofcirculation, the transformed rate of profit, also rises (or falls).


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60We can be even more specific. In general, the average value rate ofprofit r" is a weighted average of individual industry value rates ofprofit, the weights being all positive and summing to 1 (this is knownas a convex combination of the individual industry value rates ofprofit). Let us suppose that the actual system is growing at a rate g,O:::;g:::;r (this includes simple reproduction). The level of this actual

rate of growth g will of course depend on b, the proportion of profitsconsumed by the capitalist class. By way of comparison with theactual economy, let us now consider what would happen to thesystem if capitalists progressively consumed less and less out ofprofits (b--+O). As this happened, the growth rate would rise, and thefraction of the social product destined for capitalist consumptionwould fall. In the limit, capitalists would consume nothing, all profitswould be invested, and the growth rate g would equal the transformedrate of profit r. Moreover, as indicated in section III.3, when g= r theaverage value rate of profit under these hypothetical circumstanceswould itself equal the transformed rate r.The situation pictured above is one of maximum expandedreproduction (MER). Since there is no capitalist consumption underthese circumstances, it follows that of the industries which exist underthe actual rate of growth, a small subset-industries whose productsare consumed only by capitalists (yachts ?)-would not be inoperation in MER. This in tum implies that the average value rate ofprofit in MER is a weighted average of all industry value rates ofprofit except those industries producing pure luxury goods, theweights being strictly positive fractions determined by the outputproportions necessary for MER.But since this average value rate in MER is exactly equal to thetransformed rate of profit r, we can immediately say that thetransformed rate of profit is itself a weighted average of individualvalue rates of profit, the weights and the industry coverage beingdetermined by the MER output proportions. Though we arrived atthese MER weights by considering what would happen as g= r, wecan equally well consider them to be weights which define a sort of'composite industry' in the actual system. This composite industry,which I will call the central industry, is invariant to the trans-formation process since its transformed rate of profit is equal to itsvalue rate. As such, it corresponds to what Marx calls 'spheres ofmean composition, whether these correspond exactly or onlyapproximately to the social average', for it is to the rate in 'thoseaverage spheres of production where the average composition ofcapital prevails' that the rate of profit isadjusted among industries.i"

Shaikh 61The preceding result isquite powetful, for it tells us that the averagevalue rate of profit r" and the transformed rate of profit r are merely'different kinds of weighted averages of a common set of individualindustry value rates of profit . The former of course corresponds to thevalue rate of profit for capital of what Marx calls the 'social average'composition, while the latter corresponds to the central composition(what Marx simply calls the 'average' composition), a compositionwhich, as we have seen, he correctly perceives to be 'only approxi-mately the same as the social average' . The sole difference between thetwo types of averages arises from the fact that the industry coveragediffers somewhat, and from the fact that though each set of weights iscomposed of positive fractions which add up to one, the individualweights in the two sets will not exactly correspond to each other. As isexpected, therefore, these two types of averages behave in essentiallythe same way, and in a real economy even their respective magnitudesare likely to be virtually the same.Figure 2 below summarizes the results of the preceding discussion.For the sake ofillustration it isassumed that r"is larger than r,though

ofcourse it could equally well bethe other way around. 29Their actualrelation to each other will in general depend on the relation betweenthe social average composition of capital (which determines r") andthe central composition (which determines r).It is interesting to note that although Marx insists that theequalization of the rate of profit and the formation of individual

Figure 2

__ r_ --.,//.;'" /" transformed rate.;'" of profit,/",/":~sV


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62

prices of production' are ofgreat importance for individual capitals orsubsets of capitals, he at the same time also insists that for the systemas a whole the previously derived laws are basically unaltered. In aletter to Engels, after having developed the basic phenomena arisingfrom the transformation process, Marx goes on to summarize theremaining tasks. 'Further: the changed outward form of the law ofvalue and surplus-value-which were previously set forth and whichare still valid-after the transformation of value into price ofproduction.P"At all times and in all places, price is the outward form of value, thereflection of value in the sphere of circulation. What the trans-formation does, Marx argues, is to transform this outward form, tointroduce into it certain fresh determinations and new sources ofvariation, but to do so exactly in such a way as to leave the intrinsicconnections unchanged. Look again at Figure 2: it illustrates thisconception perfectly. In the relatively autonomous mirror ofcirculation the transformed rate ofprofi t appears as a displaced imageof the value rate of profit, essentially the same in determination butsomewhat different in exact magnitude. The autonomy of the sphereof circulation expresses itself in this displacement of magnitude. Onthe other hand, the limited nature of this autonomy manifests itselfprecisely through the fact that it is the structure of value categories(the pattern of organic compositions, and the proportion of surplus-value which is converted into revenue) which provides the limits tothis displacement effect. The variations in the form of value are thusshown to be conditioned and limited by the very structure of valueitself.

IV. Individual Price-Value DeviationsThe notion of the duality of the exchange process is central toMarx's analysis. On the one hand, it is through the movements ofmarket prices that the day to day regulation of capitalism is broughtabout. But, on the other hand, it is the structure and distribution ofsocial labour-time which in the end regulates and dominates theseday-to-day price fluctations, Thus it is the tendential regulation ofprice by value which transforms this daily disorder into some kind oforder-s-not by abolishing the disorder, but rather by imposingtendential movements upon it. As Marx puts it, the law of value is a'law governing fluctuations'.From this point of view, prices of production are important

Shaikh 63'ii, , because the~ ';l1ediate the relation between values and market prices.!he cO';l1petItIo~ of capitals tends to equalize rates of profi ts acrossIn~ustnes, and I? so doing tends to reduce market prices towardspnces of productIOn: Prices of production are therefore the regulatingpr~ces of market pnce, 'the centre around which the daily market-pn~es ~;iolve, and at ~hich they arc balanced out in definite

periods,' Values then In tum regulate these regulating prices ofproduction, and thereby through them dominate the movements of~a:k,et prices. It is for this reason that the relation betweenIndlVld~al values and individual prices of production, the trans-formation process, plays such an important role in Marx's analysis.. Aswe have seen, at the level of the whole the individual price-vahieddferenc~s brought ab?ut by the transformation process do notsubstantIally alter previously derived laws. But once we move to amore concrete analysis, then these differences and the transfers ofvalu,e which th~y give rise to, become importa~t in their own right.When , :"eexamme the relation of one firm to another, of agricultureversus mdustr~, o~North versus South, of developed versus under-developed. capitalist countries, then knowledge of individual price-value deviations IS of great importance. The current debate onunequal exchange isan excellent example ofthis sort ofproblem even~hough I have argued elsewhere against the unequal exchange thesisItself.32.0 nee. we consider these is~ues, the~ two questions immediatelyanse, FIrSt, what are the relative magnitudes of these deviations and~o~ ~o they affect the regulation ofindividual prices ofproduction byl~dlVl?Ual values? And second, what are the determinants of thedirections of these deviations and how do they bring about transfersof value between capitals?The ~irst question can be answered by analysing the determinantsofthe SIzeofthe typical individual price-value deviation, Of course if~h~sum of prices is.~eld constant, the average deviation is zero, sin~cIt IS the sum of POSItIveand negative deviations. But ifwe look at theabsolut.e size of these d,eviations, regardless oftheir signs, then we canget an Idea of the typical deviation and its effects.The seco?d question is much harder, however, because it requiresus ~o. specify both the size and the direction of all individualdevIatJ~ll:s. Marx ~f course does just this, but the difficulty arises ingener~hzmg ~arx s results. In the traditional case of three 'depart-ments, Francl~ Seton has a,tready established that completelyt~ansf?rmed pnces of production deviate from values in the samedirections as do the prices of production derived by Marx-that is,


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6 4

according to the relation of the individual department's organiccomposition to the social average composition. But in the moregeneral case of a given number of industries the problem remainsunsolved. Therefore, in what follows I will focus on the first problemalone: namely, on the regulation of individual prices by individualvalues.1. The Significance of Individual Price-Value DeviationsThe notion that variations in prices are dominated by variations invalues can be expressed formally through the notion that thecorrelation between prices and values is high. And this notion ofcorrelation can in tum be applied to two distinct questions con-cerning the price-value relation. First of all, as we move acrossindustries during any given period of time, how do the inter-industryprice variations compare to the corresponding variations in values?In other words, how close is the cross-sectional correlation betweenprices and values? Second, how do variations in prices over timecompare to the corresponding variations in values? In other words,how strong is the inter-temporal correlation between prices andvalues?It is worth recalling that neither Marx nor Ricardo argue that cross-sectional variations are negligible. Indeed, they both emphasize thatat any moment of time prices of production may significantly differfrom values. Still, it is interesting to note that even in their ownexamples on the importance of this difference, the actual deviationsinvolved are themselves quite moderate: Ricardo's numericalexamples concerning this problem in fact yield relative prices whichdeviate by only 1 0 % from relative values, whereas Marx's famoustransformation -tables yield a typical deviation on the order of only+ 12%. Even the infamous von Bortkiewicz example, around whichW much debate has swirled over the years, yields a typical deviation ofonly about 10%.33Granted that particular price-value deviations can be quite large(in Marx's tables, they range from a low of + 2.2% to a high of + 85%),it is nonetheless important for two reasons to establish whatdetermines the typical deviation. First ofall, we have already seen thatfor the economy as a whole the percentage deviation of thetransformed rate of profit from the value rate is itself a fraction of thenet price-value deviations of the goods consumed by capitalists. Asimilar statement applies to the transformed mass of profits. If, forinstance, the typical deviation is on the order of 20% of values, then

Shaikh 65.~the net deviation of any bundle of commodities (such as thoseconsumed by capitalists) is l ikely to bemuch smaller than this becausepositive and negative deviations will tend to offset each other so thatthe ear~ier assumption that (5 F ~0.10 is fully justified. This \n tumwould Imply that for the economy as a whole the correspondingprofit-rate and profit-mass deviations would be very small indeed.

A second reason for examining cross-sectional correlations is thatthey can provide us with a clue to the inter-temporal correlationbetween pnces and values. The closer that prices are to values at anyone moment, the greater is the likelihood that their variations overtime wilt be highly correlated. The reverse is not true however since itis perfectly possible to have prices differing signfficantly from valuesat any m0f!1ent, and still hav~ the two moving at roughly the samespeeds. ThIS latter outcome IS the one Marx emphasizes when heargues (along with ~ic~rdo) that notwithstanding the possibility oflar~e price-value deviations at any moment, Over time the significantva nations IIIprices of production are brought about 'by changes inthe value of commodities, that is [by] changes in the quantity oflabour employed in their production (Ricardo is far from expressingthis truth in these adequate terms)'.34

All of the preceding discussion has concerned the relation betweenvalues and prices of production. But prices of production, it will ber~alled, are important primarily because they mediate the relation-Shl~ between values and market prices, and it is this latter relationwhich a Marxi,st an~lysis ultimately seeks to grasp. Consequently, thislatter connection WIll also be analysed in the sections which follow.:1 : 2. The Determinants of Individual Price-Value Deviations

By definition, price is simply the sum of wage costs, material costs,and ~ome.a rbitrary amount of profit. Let us suppose that the wagerate IS umform, so that the wage cost is w L,where w=the uniformwage per hour, and L=the number of hours worked (the value addedby living lab?ur). If =materials costs and t:=(arbitrary) profits,then any arbitrary pnce P Can be written as

p =wL+n+M. (8 )In this expression, the term M represents the price of the materialinputs _(incl~di?g depreciation) used up in the process of production.But this pnce 10 tum can be thought of as itself being composed ofwages, profits and material costs of the industries which produced


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66these means of production. Designating these by wLl, n(1) and M(1)(the superscript (1) tells us that they refer to a production cycle whichis one conceptual stage behind the current stage), we can writeM=wU1)+n(lI+M(ll, or

(9)Clearly, the new (residual) material cost Ml) is smaller than theoriginal material cost M.What is more, ifwe repeat the above processwe can reduce M(ll to its wages, profits and material costs, so thatM(1)=wU21+n(2)+M(2), and then in turn reduce this remainingmaterial cost to its components, and so on, until in the limit there is noresidual material cost at all. In this way, no matter how the price isactually determined, we can always express it as an infinite series ofwages and profits in conceptually receding stages of production.

(10)

where

arid

In the above expression, the term nT represents the sum of the directprofits n actually received bythe sellers of this commodity, plus all theindirect profits nP), n(21, n


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68 ,n wL ,.(1) WUI) ,.(2) WU2)= WwLT+W(I ) wL T +W(2) WLT + ...

(14)

We see from the above that the integrated profit-wage ratio (n/W)Tis a weighted average of the direct profit-wage ratio (n/W) and of allthe profit-wage ratios of commodities which enter either directly, viathis commodity's means of production, or indirectly, via the means ofproduction ofits means ofproduction, into its production. Moreover,since LT = = L + UI) + Ll2) + .. " the weights themselves are strictlypositive and sum to one. Thus (n/W)T is a convex combination of thedirect and indirect profit-wage ratios of this commodity.But it turns out that as long as the economy is connected, i.e. is .composed of basic goods in the sense of Sraffa, then all industries willenter either directly or indirectly into the production of any givenindustry.l" which in tum implies that the integrated profit-wage ratioof any commodity is a weighted average of all the direct profit-wageratios in the economy. But if that is so, then it follows from equation(13) that the. deviations of relative prices from relative values dependon the extent to which different weighted averages (convexcombinations) of the same set of direct profi t-wage ratios differ fromeach other. In an actual economy with its extensive network ofindustrial interconnections, it becomes quite clear why even largevariations in direct profit-wage ratios (n/W); can be reduced torelatively moderate variations in integrated profit-wage ratios Z, = =(n/W);' The influence of the variations in z, i s then further reduced bythe fact that for price-value deviations it is the variations in (1 +Z i )which are the relevant ones, these latter variations being alwayssmaller than the former ones. For direct, and hence integrated, profi t-wage ratios which are generally less than one, which is the case in allthe major capital ist economies, this lat ter effect is important in its ownright.All of the above applies to any arbitrary prices. It therefore alsoapplies to prices of production. But here we can specify the argumentsomewhat more by noting that in the case of prices of production themass of profit equals the uniform rate of profit r times the(transformed) money value of the capital advanced K. But thenintegrated profits must be equal to r times the integrated capitaladvanced KT. Thus for prices of production:

Shaikh 69

z, = ( . ! ! _ _ ) T =~ ( K : )w. w L iP u = A ij' zij

( 15 )(16)

where nowr1+- kTw Zjj = = - - - r1 +_kTw J

and

k T = = (0) = the integrated capital-labour ratio.In this case ~e see that the v~ri~tion~ in integrated profit-wage ratiosare. proportJon~1 to the va.natiOns I~ the integrated capital-labourratios. !he previous a~alysIS for profIt-wage ratios then applies alsoto ~apltal-Iabour ,ratIOs: namely, even large variations in directcaP.'ta.l-lab?ur. ratios (K/L)j can be reduced to relatively smallvanations III ul: tegra~e~ ratios k! = = (K/L)!, and these in turn are~urther r~d~ced ~ntheir Influence on price-value deviations because itIS t~e ~artatlOns I? [1 + (rjw)kT] ~hich matter. In the end, the resultingdevIat~ons of pnces of production fr~m ?irect prices can be quitemoder~te even though the vanations 10 direct capital-labour ratiosare quite large.~qu.ation (16) applies to cross-sectional variat ions in price-valuedeviations. If we now ~onsidcr observations at two different periods tand to, then we can wnte an expression for the determinants in inter-temporal variations in relative prices and relative values.

.,

.) I

(17)where

( A . . . ) = ( A u ) .I) 6t - (A . .)

IJ to


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70

and_ (Z ;)1(Zi)6t =--.(Zij)to

E uation (17) tells us that the change over time in relative priceswill ~liffer f rom changes over time in relative values to the extent ~~atthe relative integrated capital-labour r~tios of t~e two ~ommodltIesthemselves change over time. What this means IS t~at If


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72Irelation to labour-times. Clearly, neither extreme can be meaningfullysaid to represent prices of production. The relevant range has to besomewhere in between, and for the sake of il lustrat ion I will uti lize theMarzi- Yarri data for r=0.40, the midpoint between the two extremes(see appendix B for the actual data). In figure 3 below, the vertical axisrepresents the natural logarithm of the ratios of individual prices of

production to the average price of production, at r=0.40. TheFigure 3

2 ... 2 .2 . . 0.80

0.00

C l : - 1.60 r-.. s

-0.80 I-

-2.401-1 1 1 1~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~ - - - - - - ~-2.70 -1.80 -0.90 0.00In I'jj

0.90 1.80

horizontal axis, on the other hand, represents the natural log of theratios of individual values to the average value, which as I explainedabove can be calculated from the prices of production at r =0. Lastly,this particular data refers to 1967. The corresponding data for 1959gives virtually the same picture, though, with only a slightly lowercorrelation (see equation (22) below).Since this sort of data is cross-sectional we can test the correlationbetween relative prices of production and relative values using thelog-linear hypothesis of equation (20). The results of both the 1967and 1959 tests are summarized in equation (22) below (t-ratios aregiven in parentheses below each coefficient).For this data, we find that the typical percentage deviation (theabsolute value of the average deviation as a percentage of the averageprice) is about 17% for 1967 and 19% for 1959. .

ShaikhCross-Sectional (r=0.40)

1967: In Pij = 0.0095 +0.8470 in },_.IJ(0.23) (16.60)

73

(22)

R2 =0.920 (adjusted for degrees of freedom)1959: ln p, = -0.0096+0.8717 In A -IJ( - 0.20) (12.48)

R2 =0.866 (adjusted for degrees of freedom).The:above graph an~ regression results are unambiguous. The cross-SeCh?nal variations 10 the calc~lated prices of production are entirelydommated by the corresponding variations in relative values, withbetween 87% and 92% of the former being explained by the latter.. Because th~ data covers two different time periods, we can also useIt ~o test the mter-t~mpor~I correlation between changes in relativepnces and changes In relative values. Figure 4 below pictures In(p.-)and I n ( A . i j ~ . ' t . [ on the vertical and horizontal axes, respectively, wh~r~both are III terms of 1959 prices relative to 1967 prices.

Figure 40.80

0.00

2 2 2 . .~- -0.80 -1.60 '-

-2.40 .1.~m---~--~~--~~--~--~2.70 1.80 - 0.90 0.00 0.90In A i) 1.80


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74Using the log-linear inter-temporal hypothesis of equation (21)above, we get:

Inter-Temporal (r=0.40)1959/1967: In (Pijhl = - 0.0298 + 1 .0 08 I n (Aij)al

( -1.90) (16.08)(23)

R 2 = 0.915 (adjusted for degrees of freedom)In the light of the closeness of the cross-sectional correlation ineach period, the closeness of the inter-temporal correlation is notsurprising. Nonetheless, the above result tells us that almost 92% ofthe changes in calculated prices of production are explained bychanges in calculated values. This is Ricardo with a vengeance=-thevery Ricardo scorned fOTover a century for having a so-called '93%theory' of prices of production! Of course, this particular aspect ofRicardo's analysis is carefully avoided by the neo-Ricardians.

B. Th e Leontief DataThe Marzi- Varri data pertains to prices of production and valuescalculated from a 25-order input-output table. But for the relation ofmarket prices to values, even more detailed data is available in someearlier work by Leontief. In his now famous 1953 article on theempirical relevance of the Heckscher-Ohlin Theorem, Leontief listsvarious calculations made on the 1947 input-output table for theUnited States at 190-order. Among these he includes what he callseach sector's direct and total (direct plus indirect) labour and capitalrequirements, per million dollars ofthat sector's output (seeappendixC).Let us suppose some sector's total value is 200 worker-years oflabour-time, which sells for a price of 10 million dollars. Then itsvalue/market price ratio (its integrated labour/market price ratio)would be 20 worker-years per million dollars worth of output. Thistel ls us that Leontief's total labour requirements per million dollars ofoutput really represent the value/lmarket) price ratios of the variousindustries. Similarly, his total capital requirements measureintegrated capital/unarket) price ratios in various industries, and hisdirect labour and capital requirements measure directlabour/tmarket) price and direct capital/(market] price ratios.' 7In my discussion of the determinants of price-value deviations, I

Shaikh 75had argued on theoretical grounds that the integration process bywhich one moves from direct capital-labour (and profit-wage) ratiosto the corresponding integrated ratios will greatly reduce thev~l.fiationsinvolved. Leontief's data enables us to test this proposition.since has direct and total labour and capital requirements data enableus to compute direct and integrated capital-labour ratios. We thenfind that although the coefficient of variation (the ratio of thestandard deviation to the mean) of the direct ratios (K/L); is 1.14, thatofthe integrated ratios (K/L)Tis only 0.60. The integration process, inother words, cuts the degree of variation by almost 50%.Leont~efs data does not provide us with data on integrated profit-wage ratios. Nonetheless, we can approximate these by assuming thatthe integration process more or lessaverages out whatever variationsexist in market profit rates and wage rates so the ratio of theintegrated pr~fit J:te t


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. . . . . . ~ ,J./'..,r . .....~ . . . . . ~A,.j.. :

....... _l.I2fi:~ 2~2. ~~2.. "~2...t~ 2,).2J~~l: 2 ..

2 := 'Z 2 X 'Z;2:./.,,)./ ..././-2.100 f- ~ 45 line/'-2.475t;.:~ II I I 1

- 2.400 - 1.600 - 0.800 0.000- 2.000 - 1.200 - 0.400

76

0.9000.5250.150

-0.225tf -0.600-0.975-1.350- 1.725

Figure 5Input-Output Table. 1947(192-0 rder)[Real Estate and Rental Excluded]

0.8000.400

(standard errors are In parentheses below the coefficients. Aparametric test indicates no significant heteroskedasticity in thedata) :40Cross-Sectional: 1947

I n ( P ij ) = - 0.00095 + 0 .9 68 09 I n ( Ai)(0.0106) (0.01498)R2 =0.95814

On the basis of data made available by Edward Wolff of New YorkUniversity, I was able to repeat the preceding experiment for the 1967input-output table, on 83-order data. The results are virtuallyidentical to those for Leontief's data:Cross-Sectional.' 1963

I n ( Pij ) = 0.01380 + 0.99078 In ( A ' i j )(0.01457) (0.02602)R 2 =0.94894

(24)

(25)

1.200I

Shaikh 77Both the preceding results attempt to test the relation betweenmarket prices and values directly. But we also have on hand indirectevidence on this very same issue, in the form of a very clever statisticaltest performed on business-cycle data by the US mathematicianJacob Schwartz. To understand the rationale of this test, let us lookagain at equation (13):

where1 +z,

Zij = = I+Zj'This quite general relation tells us that relative prices equal relativevalues times a disturbance term Zij' a term whose elements aredependent on the integrated profit-wage ratios of the twocommodities involved.In the course of a business cycle, the movement from peak to troughcan be very rapid, usually taking less than a year. Both because of thephase of the cycle and the short length of time involved, there is littlechange in the structure of production under these circumstances butthere are large fluctuations in outputs and profits. Since Aij reflects the(input-output) structure of production and zij the conditions ofprofitability, the relative prices in this phase of a business cycle arebound to primarily reflect the variations in the disturbance term Zjj:variations which are themselves likely to be abnormally high becauseof the very turbulent conditions under which they are examined.Reasoning in a similar way, Schwartz proceeds to examine relativeprice movements for the average of four business cycles from1919-1938 (one of these 'business cycles' is the Great Depression 1 ). Hisresults, summarized below, once again reveal that even under theseextreme circumstances the average relative price variation is about7 % .Itis interesting that a brilliant mathematician like Jacob Schwartzshould so strikingly parallel Ricardo's famous argument while themany grey eminences who populate mathematical economics shouldso confidently dismiss it as being unrigorous. But then, no doubt thisis in good part because much of the so-called mathematics inmathematical economics is merely bourgeois economics in thin

disguise.


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78

Figure 6Peak to Trough Average Prices, Relative to theWholesale Price Level, For 4 Cycles 1919-1938

% VariationWholesale Prices ofSemi-Manufactured GoodsRaw MaterialsWholesale FoodsRetail FoodsPig IronFarm Prices

0.070.090.020.040.120.10

(Simple) Average 0.07

4. Summary of the Empirical EvidenceThe results of the previous section can now be briefly summarized. Ingeneral , for both prices of production and for market prices, the typicalpercentage deviation (the sum of the absolute values of deviationsdivided by the sum of prices) is moderate: for the price of productiondata it is of the order of 17-19%; and for the market price data ofthe order of 20-25%. The fact that for an individual commodity atypical deviation is on the order of 20% means that when weconsider a bundle of commodities such as those consumed bycapitalists, then the net deviation JF of this bundle is likely to be muchsmaller than 20% because negative and positive deviations willtend to offset each other. This jus tifies the assumption that JF ~ 10%,which I used earlier (see p. 65) to estimate aggregate profit and profit-ra te deviations from their corresponding value categories.A typical deviation of 20% of course implies that the typical non-deviation is onthe order of 80%. In other words, it implies that thevariations in prices are likely to be highly correlated with corre-sponding variations in values. And we find that this is just the case.For price of production data , the cross-sectional regression yields anR2=0.92 for 1967 and R2 =0.87 for 1959, while the inter-temporalregression yields an R2=0.92. For market price data, we get a cross-sectional R2=0.96 for 1947 and R2=0.95 for 1963. Finally, on thebasis of the data utilized by Jacob Schwartz, we find that even under

Shaikh 79the turbulent conditions of business cycle downturns, relative pricevariations are small enough (about 7% ) for us to conclude that by farthe major source of variations in relative prices over a period ofseveral years will be the variations in the corresponding relativevalues. Ricardo, it seems, had a vastly superior grasp of these issuesthan the neo-Ricardians,

V, summaryand\ondusionsThroughout this paper, I have tried to emphasize "that Marx'sconception ofcapitalist production and reproduction isquite distinctfrom that underlying the work of many modern Marxists (such asSteedman). I have particularly stressed Marx's concept of the relativeautonomy of the sphere of circulation, because it is only thus that itbecomes possible to understand why and how prices can differsystematically from values and yet at the same time be regulated bythem. Moreover, the preceding conceptions enable us to examine thestatus of arguments concerning so-called redundancies and incon-sistencies between values and prices. Even accepting the conventionalmathematical formulations on these subjects, it becomes possible toshow that these formulations exhibit a set of properties which remainhidden to the neo-Ricardians because they lack (or refuse) theconceptions necessary to uncover them. These properties are,moreover, by and large exactly those anticipated by Marx.To take an example, it is a well-known mathematical result that thetransformation from direct prices (prices proportional to values) to

prices of production will in general cause the transformed rate ofprofit to deviate from the overall value rate of profit. To the critics ofMarx, this difference implies a break, a complete divorce ofany innerconnection. But the notion of relative autonomy requires us to shownot only how and why such a difference can exist, but also how andwhy its effects are strictly limited. This approach then enables us toshow that the value rate of profit and its transformed rate necessarilymove together: in the mirror of circulation, the value rate of profitappears as a displaced image, somewhat different in magnitude butessential ly the same in determination. Further consideration enablesus to argue that even the displacement effect is likely to be quite small,with typical differences in magnitude of the order of 8-10%.These results for the economy as a whole are then extended toindividual price-value deviations , which are important in their ownright because they mediate the transfer of value between capitals,


20/24

80between regions 'and even between nations. Here too, it becomespossible to argue on both theoretical and empirical grounds thatthese deviations are strictly limited in magnitude (20% for theabsolute value of the typical deviation) and even more limited inscope since deviations of this magnitude necessarily imply a high co-variation of prices and values. This latter concept of co-variation isvery important because Marx's argument (and Ricardo's also) thatthe variations in prices are dominated by variations in values can beexpressed in terms of the correlation between the two. Theoreticalconsiderations developed in this paper provide strong support forMarx' s argument, and what is more, a variety of empirical tests of therelations involved fully bear out the theoretical expectations. As atypical result, for both prices of production and market prices,roughly 93% of both cross-sectional and inter-temporal variations inthese prices can be explained by the corresponding variations invalues.As I noted earlier, these are results which can be derived from thevery same framework that the neo-Ricardians themselves use tocriticize Marx. It is a great irony that this so-called Ricardo-Marxtradition is so adamant in its opposition to these fundamental thesesof Ricardo and Marx, while at the same time its own ties to orthodoxeconomics are seldom explicitly acknowledged.VIn ending, I rriight note that the issues I have analysed here are onlya small part of those that could be treated in a similar manner. I havenot treated fixed capital or joint production, for example, nor indeedthe striking absence of money in an algebraic framework whichclaims to represent the formation of prices. Each of these issues canand must be addressed, and when they are, even the algebra behindwhich the neo-Ricardians hide will become increasingly transparent.

Appendix AIn the case of a circulating capital model, prices reflecting arbitrary posit iveprofits can be written as:

p = p(A+bl)+n (1 )where p = row vector of unit pricesA =input-output coefficients matrixb =column vector of wage-goods per workerI=row vector of labour coeffic ients

1 = row vector of profi ts per unit output.

Shaikh 81By definition, direct prices are prices proportional to value. These can beexpressed as:

(2)> "


21/24

82

o 1;' 00-0 = - L. (Pi-pj)fj1 +gj=1Let pf = F=he money value of the goods consumed by the capitalist class,and pli = F, =heir expenditure on the i-th good. Then:

0-0 = _1_~ IPP-Pi) F?n 1+g n i= I Pi FThe term in the summation sign is a weighted average of the individualprice/direct price percentage deviations, the weights being determined by thepattern of ~apitalist expenditures on various commodities. Since Fj= 0for allgoods which are not consumed by the capitalist class, the tenn in thesummation sign clearly represents the average price-value deviation ofcapita list consumption goods. This deviation, i t should be noted, is l ikely tobe J?~ch sm.all~r than a typical individual deviation because negative andpositrve deviations will tend to offset each other.

Appendix B(Graziella Marzi and Paolo Varri, Variazioni de Produttiuita Nelt EconomiaItaliana: 1959-1967, Bologna 1977)In Mar~i- Varri's .notation, iWt represents the reciprocal of the i-th price ofproduction relative to the money wage (the wage-price), for the year t(t= 1959,1967). These are listed for rates of profit from r=O to r=0.85. Theactual maximum rate of profi t is [=0.80, however. For reasons explained inthe text I select the midpoint, r=0.40.Cross-s~ctional relative prices of production are formed for year t, r=0.4O,by expressing the i-th wage-price relative to the average wage-price, the latter

calculated as a simple average of the individual wage-prices. Cross-sect ional relat ive values are formed in the same way, by using the r=O data.Inter-temporal data is formed by dividing 1959 relative prices of pro-duction by the corresponding 1967 data, and bydividing 1959 relative valuesby the 1967 ones.Techniques oj Calculation

1. In theory, an input-output mat rix A and the corresponding row vectorof direct labour-cocfficien tsL are:A =: [aij] = = [Xij/Xj].L = = [ I D = = [I/xa

Shaikh 83where x, =amount of commodity j, produced in a given yeari . . . . = amount of commodity iused in the production of

lJ commodity j, in a given year1. = worker-years of di rect labour employed in theJ . production of commodity j in a given year.

From this we may derive the vector of total labour coefficients:1 = L . [1-A] - 1

2. In practice, however, input-output coefficients are measured in terms ofthe dollar cost of the i-th input per dollar ofthe j-th output. If we let A* be thematrix whose coefficients are costs per dollar of output, and L*, the vector ofdirect labour requirements per dollar of output in each sector, then:A* = = [a~]=: [(PiXiN(p.;X)]L* = = [L.iJ = = [I/(Ph)]

where pj=the money price of the commodi ty. From this, we may define thevector 1 '" as:

),* = = L*[I-A*]-l.The question is, what does ),* represent and what is its relation to 1?3. We begin by noting that we can relate (A, L )to (A*, L *) through a

diagonal matrix (Pi) whose elements are the unit prices Pi:A* = (Pi)A(Pi)-1L* = I(Pi)-1

It follows, therefore, that:1* = U[I-A*]-l = L(P)-I(1_(Pi)-l_(Pi)A(P;)-I]-l),* = L(Pi)-l[(Pi)(I-A)(Pi)-l]-l

The term in square brackets is the product of three matrices; its inverse istherefore the product of their inverses, in reverse order: (ABC)-I=C-1B-1A-1:


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84').* = L(pi)-l(p;)(I-A)-l(pi)-l..t'" = {L(I-A)-l}(pi)-l).* = ).(Pi)-I

Thus, the j-th element At=). /P j ' That is, each element of the row vector P isin fact the ratio of total labour requirements per unit output. Clearly, thisratio is independent of any choice of the unit of output (lbs., tons, etc.)4. The preceding results point to a simple way of deriving the datanecessary for our calculatioris . Beginning with the empirical input-output

matrix A * and the corresponding vector L * direct labour requirements perdollar of output, we can immediately calculate ) .*, total labour requirementsper dollar of each sector' s output. These correspond to the data we used fromLeontief. The element.s of..t*~re Ajp] " ~ence ifwe know the gross sales p/xJforeach sector , we can immediately derive the total labour requirements A X -which correspond to these sales (even though we do not at any time actuai' lydefine any units of output x).XA jX j= ~ Pf j = Aj(Pf j}

The last operation gives us total labour requirements X x - in worker-years andtotal prices (gross sales) Pfj in dollars. J J5. Two data sets were used, in which A=A.x- and P- = px, are derived in. di d i J rJ J J Jmanner III icate III4 above. Defining the average value of the dollar as (l=< L A}/(L P), we can then use this to define total direct prices pO=(l/rL)A..Finally, both Pf and Pj ' are expressed as prices relative to theii respect iv~

- 0 ~ 0 - ~~~era_gepnces P =(L.,Pj!N) and P=(L,P/N). Note that by construction,P =P. .The first data set is based on Leontief's 1947 data, from W. Leontief,

Input-Output Economics, Oxford, New York, 1966, appendix III, pp.129-133. Total Sales Pj were taken from US 1947 input-output table, 192-order.The second set was provided by Edward Wolff of New York University. Inthis data, the direct labour requirements vector was computed in two ways:f irst , in worker-years of undifferentiated labour requirements; and second, ina skill-weighted index of worker-years where relative wages were used asweights (for lack of better indexes). The latter data are the ones actuallyshown, but the regression results are substantial ly the same with either set .Lastly, both the graphs and regressions leave out the real estate and rentalsector, since on theoret ical grounds within both the Ricardian and Marxisttheories of rent, though the magnitude of rent can be derived from valuerelations it is not related to any labour-time expended in the collection ofrent (in the real estate and rental sector). Once again, however, this makeslittle difference to the log-regression results.

4/Marx, Sraffa and the Neo-Classicalsin Context

Hector Guillen RomeroI. IntroductionAlthough the terms 'neo-Ricardian school' or 'Cambridge school' aresometimes applied to the contribution on growth theory of JoanRobinson, Nicholas Kaldor, Luigi Pasinetti and others, in this work Ideal almost exclusivelywith the theory of prices elaborated by PieroStaffa.' The school's methodological foundations can be found inthe works ofDmitriev and von Bortkiewicz,who wrote at the tum ofthecentury.! These authors' importance has grown recently followingthe publication of Sraffa's work.The neo-Ricardian school can be assessed either in relation toMarxist value theory or in relation to neo-classical theory, whether inits vulgar form (Jevons, Menger, Marshall) or its general equilibriumform (Arrow, Hahn, Malinvaud, Walras).1. N eo-classicais and N eo-RicardiansThe neo-Ricardian school rejects subjective individualism and therole of supply and demand in the determination of income distri-bution. A recognition of the class division of society is central to itsanalysis.' It makes an internal critique of vulgar economics, showingthat many of its propositions are inconsistent with its own assump-tions. In particular Sraffa shows that neo-classical capital theory isincoherent and indeterminate in its vulgar version. This critical wing,fully developed since Sraffa's book appeared, seemed to haveculminated in the works ofthe Cambridge school onmacro economicproduction functions and problems related to the choice oftechniques.4While these attacks are fundamentally internal, the neo-Ricardiansmake a basically external critique of general equilibrium theory.

85


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26612. Ibid., pp. 163, 198. '13 . Ibid. , p. 187.14. Ibid. , pp. 163, 185.15. Ibid. , p. 163.16. Ibid. , p. 198.17. Ibid. , p. 127.18. Steedman, p. 152.

Ch ap te r Th re e1. For a survey of previous cnticisms, see Ben Fine and Laurence Harris,'Controversial Issues in Marxist Economic Theory', Socialist Register, 1977. For myearlier arguments on Marx's theory of value, see 'Marx's Theory of Value and theTransformation Problem', in Jesse Schwartz, (ed.), The Subtle Anatomy a/Capitalism,Santa Monica, California 1977, pp. 106-137. Finally, for 'The Poverty of Algebra', see

The Value Controversy, London 1981, pp.266-300.2. L. Colletti, From Rousseau to Lenin, New York 1972, p.83 .3 . Karl Marx, A Contribution to the Critique 0/ Political Economy, London, 1972,p.86.4 . Karl Marx , Capital, Volume 3, Harmondsworth 1981, p.1020.5 . Karl Marx , Grundrisse, Harmondsworth 1973, pp. 196-197.6 . Karl Marx , lett er to Kugelmann, II July 1868.7. Capital, Volume I , Harmondsworth, 1976, p . 193.8. Capital, Volume 3, pp. 280-281.9. Ibid., p.300.10 . Marx notes that this necessary distribution of social labour-time has two distinctaspects , which in tum give r ise to two different concepts of social ly necessary labour-time. There is in the Fi rst p lace the (abstract) labour-t ime which under given socialconditions is necessary for the production of a given amount of a commodity. Thisquanti ty of social ly necessary labour-time defines the total value of the commodity-product. It arises from the nature ofa commodity as a value, as a bearer ofexchange-value.Second, from the nature of a commodity as use-value , as an object of soc ial need,there is the question of the correspondence between the total quantity of thecommodity-product and the soc ial need for this product. This correspondence isexpressed as a quantity of labour-time which is socially necessary to produce theappropriate amount of the product, that is an amount of product which at theregulating price fulfi ls the effective demand for it. In the f irst two volumes of Capital,Marx assumes that this regulating price is a direct expression of value; in the thirdvolume he develops it into a transformed expression - the price of production.The first type of socially necessary labour-time thus determines the uni t value of acommodity, and through it the regulating price. The second type ofsocially necessarylabour-time then determines the discrepancy between ac tual supply and effectivedemand: it therefore determines the discrepancy between market price and regulatingprice. (Capital, Volume 3, p.774).I I. Karl Marx , Theories of Surplus Value,Moscow 1968, Part 11,Ch. XVII, section 8(pp.499-507).12. Karl Marx, 'Wage Labour and Capital', in Robert C. Tucker, ed., The Marx-Engels Reader, New York, 1972, pp, 174-175.13. Steedman, pp. 13-14.

Notes 26714, In my' earlier paper (see note 1), I treat the derivation and structure of thisproblem in great detai l. ( 'Marx's Theory of Value and the Transformation Problem' ,pp. 106-137).15 . Ste~dman,p~. 14-15. Steedman's position is not new ofcourse, since ithas alwaysbeen a highly fashionable argument. Both Paul Samuelson and Joan Robinson forittance, have long held this position. '16. Capital, Volume 1, p. 173.

" 1~' .For a related crit ic ism .of~he neo-Ricardian concept ion of production , see myPolitical Economy and Capitalism: Notes on Dobb' s Theory of Crisis' Cambridge!ourn~1 0/ Econo~jcs, no. 2, 1978. pp. 233-251, and the subsequent deb~le on theseIssues in the same Journal, no. 4 , 1980. For a detailed cri tique ofS teedman and otherssee 'The Poverty of Algebra', pp. 266-300. '

18 . Capital Volume I, p. 291.19. Even the facil ity of calculat ion is not at all equal. Es timation of values requiresknowledge of labour flows and flows of means of production used up. Prices ofproduct ion require inaddition knowledge ofthe real wage bundle and ofthe s tocks ofcapital advanced. These latter two pieces ofinformation imply a much more detai ledknowledge-of the structure of the economy.20. Capital Volume 3, p . 134.2!. Capital Volume 2, pp.222-223.22. M: I?obb, '~r Sraffa and the Rehabi li ta tion of Class ical Economics ', p. 1.23 . It IS in teresting to note that Marx addresses th is problem in connection wi th the

theor~ of differential ren t, not that of prices of production. It i s often forgot ten byMarxists that the former theory also implies pr ice-value devia tions since it is themarginal condit ions which rule pr ice but the average condit ions which determinevalue. As such, all the general phenomena involving price-value deviat ions appearhere too.24 . Theories of Surplus Value, Part III, pp. 345.25. ~nwar Shaikh, 'The.ories .of V~luc and Theories of Distribution', unpublishedPhD dissertation, Columbia University 1973,ch, IV, section4: and Michio Morishima,Marx's Economics, Cambridge 1973, p. 142.~hen the ec~n~my is a long the von Neumann ray, the rate of profit (in a circulatingcapital model) IS i ndependent of relative prices. But the rate of profit is the ratio of

profits to cost-prices. If the sum of prices is constant, and the ra tio of profits to cost-price is the same for direct prices and prices of production, then i t fo llows that d irectprofits equal transformed profits and direct cost-price equals transformed cost-price.

26 . Theaver~ge rate ofprofit isfrom T. E.Weisskopf, 'Marxian Crisis Theory and theRate of Profit m the P~st- War us Economy', Cambridge Journal of Economics, no. 3,1979, table 2 (Full Period), p. 351. The average ratio of growth is from 'Long TermEconomic G:owth, 1860-1970', us Department of Commerce, 1973, chart A,fig.3,p. 8.27. 'Theories of Value and Theories of Distr ibut ion ', ch. IV, sect ion 4; and Marx'sEconomics, p. 64.28 . Capital VoI.ume 3,p . 273.Al fredo Medio also argues in favour ofviewing what Icalled the central m?~stry as the industry which satisfies Marx's definit ion ofthe sphereof avera~e c.ompo~ltJ~n. Sec Alfredo Medio, 'Profits and Surplus Value: Appearanceand Reahty 10Capital is t Production ', in E.K.Hunt and J. G. Schwartz, eds., A Critique0/ Economic Theory, Harmondsworth, 1972.

. 29.The re lation ofr to SI V can bederived graphically from Marx's Economics, p, 64,fig. 2.30. Kar l Marx to Friedrich Engels. 30 Apr il 1868.31. Capital Volume 3, p. 280. Marx emphasizes that th is process takes place over


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26 8periods of time defined by the conditions of pr~uction in different industries. The

J ' ti n rocess is therefore not a 'short-run phenomenon. .eq~~.I~n~a/Shaikh, 'Foreign Trade and the Law of Value', Science and Society,Autumn 1979 (part 1) and Spring 1980 (part 2).. 'd33 The Works and Correspondence of David Ricardo, Piero Sraffa , ed. , Camb, !! ~e1962~vol. I,p. 34; Capital Volume 3,p. 356; and Paul Sweezy, The TheoryofCapttal!stDevelopment Oxford 1942, ch. 7. 3 26634. Theori~s of Surplus Value,Part II,pp. 193-194. See also CapitalVolume. , pp.and 280. d . L d and New York 1977,35, L. Pasinetti, Lectures on th.eTh.eory of ~ro, uctlon, on onPasinetti calls this process 'vertical mtegratlon . . . . C b id e36. Piero Sraffa, Production of Commodities by Means of Commodities, am r g1960, p. 8. .37 See appendix B for a formal proof of this, . ed. B d fi 'to T nd KT are the integrated profits and capital advanc ,38 y e ini Ion 1[ a T T . (10)"res~ctively. Define the integrated profit rate as rT==1[ /K .Then from equat Ion 10the text; .

1[T==1[+1[(1) +1[(2) + .. ,

and

K K(1) K(21- [_ + rll)-- + r(l)----y-+ .. ,- KT KT KThus each integrated profit rate i sa convex combination ofindiv idual. i ?dustry p~of:trates at various stages in the integration process. Insofar as t~e ~oT?~etJtlon ofcapl~a sd to e ualize indus try rates ofprofi t, i twil l t end to result In tndl~ldual rates rjfairly~~~s:o ea~h other at anyone moment. This in tum means that the mtegrate? rates ar elikely to be very close indeed. A simi lar argument can be constructed for Integratedwage ~a~esi m 'Marxian Crisis Theory and the Rate of Profit in the Post-War usEc39. r IS,;O 1 p 349 and w from National Income and Product Accounts, /929-1974,us ' ;~p~~~~~t ~fCo~merce, supplement to Survey ojCurrenr Business, January 1976,p. i~hould be noted that Leontiefs total capital requirement is in units of $IO{X)(),Converted to these units, w=0.2612. ki h40 The Goldfie ld-Quardt test for hete roskedasticity was performed by ran mg. t eobse~ations by the size of the independent variable, runni~g separate log-regress~on~on the first 69and the last 69observations, and then performing an ~-test on, th~firaUotold id I ( ,s) to see If the ratio was sigm ican ythe respective sums of the square resl. ua s Sl 2 219) The testdifferent from 1. (J. Johnston, EconomIc Methods, _N.ew,York 1:6_9, p. .indicates that there is no significant heteroskedastlctty In the data.

Sl =0.84671,52 = 0.83568, ~= 0.98698

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Shaikh - Transformation From Marx to Sraffa

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