On Marx, the Transformation Problem and Opacity Baumol - Samuelson - Morishima

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Editor's Note: Few articles in the historyof the JEL have stirred the controversythat Paul A. Samuel- son's "Understandingthe Marxian Notion ofExploitation: A Summary of the So-called Transformation Problembetween Marxian Valuesand CompetitivePrices, "J. Econ. Lit., June 1971, 9 (2), pp. 399-431, did. We have already had one "terminal"discussion of the reaction-Bronfenbrenner, M. "Samuelson, Marx, and TheirLatest Critics,"and "Samuelson's 'Replyon Marxian Matters' "J. Econ. Lit., March 1973, 11 (1), pp. 59-63. ProfessorBaumol has found a history of thought approach to the topic which deserves the attention of all economists who have an interest in Marx, Marxism, or the evolution of classical economic thought. We print his essay here. Professor Samuelson sought to comment on Baumol's work,and wegive his views,as well. In the course ofSamuelson 's reply, he "tookon "Professor Morishimca,who quite naturally wanted to add a few words offurther explanation. We have finally allowed ProfessorsBaumol and Samuelson to share in what we hope are the "last words." M.P.

The Transformation of Values: What Marx "Really" Meant (An Interpretation)

By WILLIAM J. BAUMOL Princeton and New York Universities

I would like to thank the students in my seminar on doctrinal history at Princeton Universitywhose discussions contributedgreatly to the ideas in this paper. I am also grateful to Elizabeth Bailey, Fritz Machlup, Michio Morishima and Paul Samuelson for their very helpful comments on earlier drafts of this paper. I am particularly indebted to ProfessorSamuelson for an extensive, illuminating and delightful correspondence on the subject.

THIS PAPER will suggestthat the meaningof which is certainly not to be found there unless lne the relationship between values and prices reads into them an interpretation different from described in Capital has been widely misunder- that which Marx repeatedly emphasized. stood. Commentators as eminent as Mrs. Robinson Interpretation of the intentions of the writings of and Professor Samuelson have sought in the trans- the dead is always a questionable undertaking, par- formation discussion issues which Karl Marx never ticularly since defunct authors cannot defend them- meant it to contain. Writers on "the transformation selves. Yet there are some cases in which a careful problem" since L. Bortkiewicz have focussed on an rereading of the pertinent writings indicates that issue that is largely peripheral; and others like E. the author did speak for himself and spoke very B6hm-Bawerk have asserted that there is a contra- clearly-the trouble in such cases seems to be that diction between the analyses of Volumes I and III somethinv aboit the onriinal nresentation nrevents 51

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most readers, even some very careful ones, from tion of Marx' intentions is equally evident, and seeing what the writer intended. second, because I will suggest that the false anal- A notable case in point is D. Ricardo's discussion ogy between Ricardo's and Marx' value theories of the labor theory of value. It is hard to understand may help to explain our misunderstanding of the how a careful reader of any edition of the Principles latter. can overlook Ricardo's recognition of the role of the quantity and the durability of capital in the determi- Marx' Interpretation of the TransformationProb- nation of price. The labor theory is explicitly lem: Summary proposed as a remarkably good approximation to In Ricardo, the labor theory of value was meant the determination of competitive price. But, ulti- as a good approximation to a full explanation of the mately, Ricardo holds to a cost of production the- determination of prices. However Marx probably ory of pricing, not to a pure labor theory. Yet until never intended to produce such an approximation Stigler's fine article on the subject (1958),2 in which and it certainly was not his intention when he wrote this is documented beyond any shadow of a doubt, about the transformation problem; yet that objec- virtually any text was prepared to ascribe to tive, or something close to it, is often attributed to Ricardo the purest of labor theories, and even J. H. Marx. Hollander and E. Cannan (see G. J. Stigler for refer- I will provide evidence that Marx did not intend ences) suggested that Ricardo retreated grudgingly his transformation analysis to show how prices can under fire to the cost of production model of the be deduced from values. Marx was well aware that third edition. Only a few commentators, notably A. market prices do not have to be deduced from val- Marshall, J. Viner, and P. Sraffa, saw Ricardo's ues (nor, for that matter, values from prices). analysis for what it so plainly was from the first Rather, the two sets of magnitudes which are edition on.3 derived more or less4 independently were recog- I emphasize this case for two reasons; first, be- nized by Marx to differ in a substantial and a sys- cause I will try to show that the correct interpreta- tematic manner.5A subsidiarypurpose of the transformation calculation was to determine the nature ' I must emphasize that it is not the purpose of this paper to attack or defend the substance of Marx' transfor- of these deviations. But this objective and, indeed, mation discussion or to argue the significance of the in- any explanation of pricing as an end in itself, was sights it offers. This issue can be discussed profitablyonly of very little consequence to Marx, for the primary after clarification of the content of his analysis-which is transformation was not from values into prices but, the only objective of this article. as Marx and Engels repeatedly emphasize, from 2 Obviously, I disagree emphatically with Samuelson's judgment that "It is a sad reflection on the decadence of surplus values into the non-labor income categories literary economics that so much printer's ink has been that are recognized by "vulgar economists," i.e., wasted on the sterile and ambiguous question of whether profits, interest, and rent. Ricardo had or didn't have a labor theory of value, or a Thus we must surely reexamine the implications 93 percent labor theory, or. . ." [13, 1971, p. 405]. If an author speaks for himself as clearly as Ricardo did, it is of Samuelson's conclusion: surely more appropriate to discuss what he did say than The truth has now been laid bare. Strippedof what some commentator has somehow inferred he ought to have said. logical complication and confusion, anybody's I For references on these matters, see Stigler [15, 1958]. methodof solvingthe famoustransformation prob- Note that Marx himself understood Ricardo correctly on lemis seento involvereturning from the unnecessary this issue. Thus in a letter to Engels dated July 6, 1863, detourtaken in VolumeI's analysisof values.... Marx wrote "You know that according to Adam Smith [S]ucha "transformation"is preciselylike that in the 'natural' or 'necessaryprice' is composed of wages, which an eraseris used to rub out an earlierentry, profit (interest), rent.. .. This nonsense was taken over afterwhich we makea new startto end up with the by Ricardo, although he excludes rent, as merely acciden- properlycalculated entry [13, 1971,p. 421]. tal...." (Marx' italics.) All translations, unless otherwise noted, are taken from [8, 1956]. The preceding quotation appears on p. 174. 4Not entirely, since labor time (Marxian value) is a I have chosen to follow the published translations of the technological datum which enters the determination of correspondence, which seem to be reasonably accurate. In cost and, hence, competitive price. a few cases some of the English phrases that Marx scat- ' R. L. Meek [9, 1956] and M. Morishima [10, 1973, tered through his letters have been edited by the transla- Chapter 7] in my view may be the only current authors tnr who have described the transformationproblem correctly.

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I will argue that this conclusion represents no real a given industry withdraw more than it has con- conflict with Marx' intentions, as Samuelson seems tributed, and when will the reverse be true? to suggest. Marx knew perfectly well that price This is a question which cannot, I believe, be determinationcan be explained in terms of the com- answered with the aid of an eraser. Marx proposed petitive process by itself, just as the classical econo- part of the answer, but his argument for even that mists had done, so that if the objective were an portion was incomplete. Morishima, (especially pp. analysis of pricing, Volume I would indeed repre- 80-84) in his excellent book, is, as far as I know, sent an "unnecessary detour." But Marx' interests the first to have supplied a careful answer [10, were not focused on price theory, and as I will 1973]. show, he was well aware that competitive prices can be deduced without prior recourse to Marxian val- The Value Theory Reconsidered ues. In Volume I, Marx does occasionally speak of My contention is that Marx' interest in the trans- values as if they were meant to approximate prices. formation analysis as a sequel to his value theory For example, he asserts "It is true, commodities was not a matter of pricing. Rather it sought to may be sold at prices deviating from their values, describe how non wage incomes are produced and but those deviations are to be considered as infrac- then how this aggregate is redistributed,the first of tions of the laws of the exchange of commodities these being the substantive issue to Marx and the ....ss6 He goes on to describe these deviations as one he discusses in Volume I, while the latter is the "temporary" ascribing them to "Market disturb- surface manifestation known to all bourgeois ances." However, his comments must be inter- economists and which Marx only deigns to consider preted in context: at this point Marx is merely argu- in Volume III. ing that profits or surplus values cannot be ascribed The substance of Marx' analysis can be summa- to a process of inflation of prices above values since rized in a simple parable, in which the economy is in such a universal inflation no one can gain. His described as an aggregation of industries each of language at such points generally seems to be ex- which contributes to a storehouse containing total plainable primarily in terms of his expository objec- surplus value. The contribution of each industry is tives. Certainly by the time we come to Volume III, its total output minus the consumption of its labor values and prices are clearly dissociated, with "cost force. If we use labor units to measure these quanti- prices" based on equality of rates of return on in- ties, each industry's contribution is proportionate vestment in different industries. to the quantity of labor it uses, for reasons to be There seem to be three plausible ways to account noted in a later footnote. This, then, is how society's for the distinction between the role of value in the surplus value is produced. two volumes. The first is that Marx originally in- The distribution of society's surplus value from tended his values as equilibrium relative prices and the central storehouse now takes place via the com- only retreated from this position when he began to petitive process which assigns to each industry for realize it was untenable, doing his best to explain profit, interest payment, and rent an amount strictly away his retreat as a planned regrouping of his proportionate to its capital investment. This is the forces.' This view has been implied by a number of heart of the transformation process-the conver- writers.8 The second and more common inter- sion of surplus value into profit, interest, and rent. pretation is that Marx intended the value theory as It takes from each according to its work force, and a simplified approximation to the correct analysis returns to each according to its total investment. The object of the discussion of the conversion of 6 Volume I. [6, 1906], Chapter V, pp. 176-77-all refer- surplus value into "average profit" is then straight- ences to Capital are to the Charles Kerr edition. ' R. Hilferding (p. 155) seems to ascribe this view to forward. Given the contribution of some one in- Bohm-Bawerk but I have not been able to find any such dustry to the social surplus (as described by the assertion by the latter. Bohm-Bawerk does assert that value analysis) and the largely independent deter- there is an irreconcilable contradiction between the value mination of that same industry's withdrawals in the theory of Volume I and the price theory of Volume III (p. 29 and Chapter III in general). However, he does not form of profits, interest payments, and the rent, attempt to account for its origin [2, B6hm-Bawerk, 1949]. question is how those two compare. Put another 8 For an illustrative reference see Sweezy [16, 1942, p. way, the question is, under what circumstances will 111].

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of prices (somewhat in the manner of Ricardo) and "Volume III ... was written for the greater part that the transformation calculation of Volume III in 1864 and 1865" (Preface to Volume II, p. 9), that is his way of producing the appropriatecorrection.9 is, two years before the appearance of Volume I." The third explanation, which I suspect is the cor- In fact, in that same place Engels states Marx had rect one, is that the value theory was never intended reached his solution "even in his manuscript for His as a theory of price, which, as a superficialmanifes- 'Critique of Political Economy'" on which Marx tation of the bourgeois economy, Marx considered had worked in the 1850's (p. 28).'2 worth very little attention, but was instead designed But substance rather than tedious arguments to explain something to him far more fundamental: about dating is our real purpose here. Later, I will the process of production, i.e., the extraction of show explicitly that what Marx had revealed in his surplus values in the various sectors of the econ- Volume III analysis of price he considered to be no omy. improvement over his Volume I analysis of value. Turning to the first of the hypotheses, we cannot On the contrary, from his point of view the price hope to prove that Marx never changed his mind analysis of Volume III dealt with the "outward on the relation of his values to prices. But we do different rates of profit, since profit is nothing but know that at least half a decade before the comple- the proportionof the surplusvalue to the total tion of the preface to Volume I his views of the capitaladvanced. This will dependon the organic transformationproblem were quite fully formed. A compositionof the capital,i.e., on how it is divided letter from Marx to written five before into constant and variable capital .... And capi- Engels, years talistsare brothers. of the of Volume a clear state- Competition(transfer capi- publication I, provides tal or withdrawalof capital from one trade to ment of the transformation problem and Marx' another)brings it aboutthat equalsums of capital proposed solution.10Moreover, Engels tells us that in differenttrades, despite their differentorganic compositions,yield the sameaverage rate of profit. 9See M. Bronfenbrenner[3, 1973] where Marx' "ap- In otherwords: the averageprofit which a capital proximation"is explicitlylikened to Ricardo's.P. M. of £100, for instance,yields in a certaintrade it Sweezyalso arguesin a way that temptsthe readerto yieldsnot as the capitalemployed in thisparticular imputethis positionto him: way, nor in the proportion,therefore, in whichit itself but as an It is to a producessurplus value, aliquotpart perfectlylegitimate postulate capitalist of the aggregatecapital of the capitalistclass. It system in which organiccompositions of capital is a shareon in to its divi- are and hence the law of value which, proportion size, everywhereequal dendsare paid from the total sum of surplusvalue does hold.... Whetheror not this procedureis whichthe total variable . be (or unpaidlabour) capital valid .. must tested by dropping the assump- out in of the class 1956, tion. . . . Volume III abandons this (laid wages) produces[8, [I]n [Marx] pp. 158-59, Marx'italics]. assumptionand attemptsto show that, from the point of view of the problemswhich he was at- " On p. 209 of VolumeIII in a footnote,Engels explic- temptingto solve, the modificationswhich result itly dates at least that portionof the transformationdis- are of a relativelyminor character. (Ibid, p. 70.) cussionas 1865. A bit of chronologymay be helpfulin followingthe However,in a veryhelpful letter to me, Sweezyrejects issue. this of dating interpretation his views: Marx'preface to VolumeI is datedJuly 24, 1867.The I neverhad any inclination to acceptwhat you call lettertelling Engels he had finallyfinished reading proof the "secondand more common interpretation ... for the volumeis dated 2 A.M.,August 16, 1867.There thatMarx intended the valuetheory as a simplified are at leastfour letters in whichMarx and Engelsdiscuss approximationto the correctanalysis of prices." the transformationproblem. The firstis datedAugust 2, On certainassumptions, most importantlyequal 1862,five years before the publicationof VolumeI. There organiccompositions of capital,value theory was is an exchangedated June 26 and June27, 1867,written alsoa validprice theory; but of courseMarx never whileMarx and Engelswere reading proof for the volume for a momententertained the notionthat the equal and one dated April 30, 1868, less than one year after organic compositionsassumption was realistic, publicationof VolumeI [8, 1956]. from which it followsthat for him the notionof Quotationsfrom all fourletters are offeredlater in this values"approximating" prices was nonsense. paper.They show clearly that there was no significant changein Marx'position on the subjectover the period. 10For example,Marx writes in this letter: 12 Hilferdingand Sweezyare among those who have . . . with equalexploitation of the workerin dif- previouslypointed out thatMarx had worked through the ferenttrades, different capitals of the samesize will transformationissue before Volume I was published.See yield very differentamounts of surplusvalue in Hilferding[2, 1949, p. 155] and Sweezy [16, 1942, p. differentspheres of productionand thereforevery 11lfn].

This content downloaded from 193.49.18.51 on Mon, 25 Aug 2014 11:37:14 UTC All use subject to JSTOR Terms and Conditions Colloquium: On Marx, the TransformationProblem 55 disguise" assumed by the subject of his discussion. argument. It is rather a self-satisfied superior's play- Only the analysis of the relation of profit and sur- ful mystification of those readers (critics) whose lim- plus value permitted "the actual state of things [to ited powers do not enable them to see that his propo- be] revealed for the first time" (Vol. III, Chapter sition is self-evident [17, 1919, pp. 419-20]. IX, p. 199). Thus Marx tells us he had something This failure to attempt any rationalization should more in mind than mere revision of the value theory be evident to anyone who rereads carefully the few in accord with the workings of competitive equili- pages in Volume I that are ostensibly devoted to an brating forces. explanation of the workings of his value theory. One must also reject the assertion that Marx (See especially Chapter I, section 1, pp. 44 46.) thought prices had to be deduced from values via Now, this lacuna seems strange in light of two his transformation calculation. Marx knew very facts: Marx' near-talmudic skill in conducting an well that his "prices of production" were the same argument and his avowed intention to write Capital as the "natural values" of classical economics. He in as prolix a style as possible.'3 If Marx had in mind apparently ascribes to Malthus the basic observa- or felt he needed some substitute for the competitive tion underlying their construction: "The theoretical mechanism in the Ricardian analysis of prices, why conception . . . according to which every part of does he not bring it out? In the discussion of values the capital yields uniformly the same profit...." such a mechanism is never mentioned while, by [6, 1909, Vol. III, Chapter IX, p. 200; see also, contrast, it plays a clear and explicit role in the Chapter I, pp. 48-49]. In his first letter on the trans- determination of prices in Volume III and in the formation problem (1862), Marx is quite explicit on justification of the premise that the rate of surplus the identity of his prices with the classical prices value tends to be equal in all industries.'4 based on cost of production: "Price regulated in this Presumably, the reason Marx attempts no ration- way [i.e., via the transformation process] = the ex- alization of his theory of value is, in Veblen's words, penses of capital + the average profit . . . is what that at least to him it was "self-evident."'5 This Smith calls the natural price, cost price, etc." (p.

160, Marx' italics). Thus, he does not accuse the '3 Letter to Engels, June 18, 1862. "I am stretching out classical authors of having erred in deducing their this volume, since those German dogs estimate the value price relationships without using Marxian values in of books by their cubic contents" [8, 1956, p. 156]. '4 The argument for the equality of rates of surplus the process. Rather, the charge repeatedly reas- values in all industries is straightforward,and applies only serted is that they dealt only with "this form of to a capitalist economy in which labor is free to move. On appearance." Marx' assumption (which is shared by Ricardo as well as Prices and values are, in short, not the same J. von Neumann, R. Solow, H. Uzawa and many other thing. Values are not approximations to prices nor contemporary writers) that labor is homogeneous and re- ceives equal wages and if all work is equally unpleasant, a necessary step in their calculation. Rather, one is the working day in all industries must tend to equality, a surface manifestation, while the latter is intended for otherwise workers would move from industries with to reveal an underlying reality. But what are these long working days to those in which working days are values and what is their rationale? shorter. With working days everywhere equal, total value production per laborer (measured in hours of "socially An Interpretationof Marxian Values necessary labor") must also be equal. Subtract from this in every industry the same subsistence wage (also meas- T. B. Veblen calls to our attention a mystery ured in value units), and we are left with the same surplus which no one since seems to have attempted to clear value per worker everywhere. (See Volume III, p. 206.) up. Veblen writes 1 "Inhis Critiqueofpolitical economy, the fragment published eight years before Volume I of Capital, Marx stated explicitly that he took his value theory to be a tautology: It is scarcely worth while to question what serves as the beginning of wisdom in the current criticisms of Since the exchange value of commodities is, in fact, Marx; namely, that he offers no adequate proof of nothing but a mutual relation of the labours of individuals . . . it is a his labor-value theory. It is even safe to go farther, tautology to say that labour is the only source of exchange value and conse- and say that he offers no proof of it. The feint which quently of wealth, in so far as the latter consists occupies the opening paragraphs of the Kapital and of exchange values. Similarly, it is a tautology to the corresponding passages of Zur Kritik, etc., is not say that matter in its natural state has no exchange to be taken seriously as an attempt to prove his value, because it does not contain any labour.... position on this head by the ordinary recourse to (pp. 31-2, Marx' italics). In other words, "ex-

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value theory was intended to explain the gestation, here is valid, Marx was concerned primarily with i.e., the production of total surplus value, describing the relationship between profits and surplus value the contribution of each activity in the economy to and only incidentally (as a means to get at the that total. The tautology used by Marx in this ex- former) with that between prices and values. As a planation is that each industry contributes to the first piece of evidence, I reproduce in full Engels' total surplus its entire output minus the amount famous challenge in the preface to Volume II, the used up in supporting labor. The part of the asser- first public statement of the transformation prob- tion that is not tautological or self-evident is that lem, in which it will be noted that the word "price" the "freedom" (mobility) of labor, which Marx does not appear even once: stresses so heavily in Volume I as a prerequisite of According to the Ricardian law of value, two capi- the historical stage of capitalist production, guaran- tals employing the same and equally paid labor, all tees a tendency toward equality of surplus value per other conditions being equal, produce the same value laborer in every industry, when value is measured and surplus-value, or profit, in the same time. But in terms of labor. if they employ unequal quantities of actual labor, Moreover, as is now generally recognized, cer- they cannot produce equal surplus-values, or, as the tainly the determination of the magnitudes of the Ricardians say, equal profits. Now in reality, the values is straightforward on the Ricardo-Marx- exact opposite takes place. As a matter of fact, equal Leontief assumption of fixed production coeffi- capitals, regardless of the quantity of actual labor cients. To summarize the standard interpretationof employed by them, produce equal average profits in the matter as described, e.g., by Morishima, a set equal times. Here we have, therefore, a clash with the law of value, which had been noticed by Ricardo of input-output equations can be used to express the himself, but which his school was unable to recon- value of each output as the amount of labor used cile. Rodbertus likewise could not but note this con- directly in its production plus the amount of labor tradiction. But instead of solving it, he made it a used up indirectly in the form of capital ("congealed starting point of his utopia (Zur Erkenntniss, etc.). labor"), where that indirect labor component is de- Marx had solved this contradiction even in his termined by the unit values of the capital inputs.'6 manuscript for his "CRITIQUE OF POLITICAL These values are entirely determined by techno- ECONOMY." logical relationships and, under the simple fixed According to the plan of "CAPITAL," this solution coefficient assumptions shared by both modem and will be made public in Volume III. Several months classical models, are entirely independent of pric- will pass before this can be published. Hence those economists, who claim to have discovered that Rod- ing." That is, the input-output formulation of the bertus is the secret source and the superior predeces- to rest Joan problem puts Robinson's suggestion sor of Marx, have now an opportunity to demon- [11, 1959, p. 362] that ". . . the values which have strate what the economics of Rodbertus can to be 'transformed into prices' are arrived at in the accomplish. If they can show in which way an equal first instance by transforming prices into values." average rate of profit can and must come about, not only without a violation of the law of value, but by Values into Prices or Surplus Values into Profits? means of it, I am willing to discuss the matter further Let us turn now to the textual evidence for the with them (Vol. II, pps. 27-8).'8 preceding discussion. If the interpretationproposed Turning to Marx' own words, we notice that he change value" is, by definition, related to labor entitled the two books in Volume III that are de- content, and consequently not necessarily the same voted to the subject "Part I: The Conversion of as price [5,1904]. Surplus-valueinto Profit and of the Rate of Surplus- 16 For an explicit discussion of this construction, see Morishima, [10, 1973, Chapter 1]. Of course, this interpre- 18 In a letter to me Samuelson writes: tation also appears in various other writings. "1Note also that by treating the training of labor as By the way, Engels"challenge' is absurd;there was investment in human capital it removes any difficulty of no 1830's crisis of the Ricardian system; there was comparing the value contribution of different qualities of no contradiction in it, for as you remind people, labor. When the coefficients of production of different when Ricardo is not assuming the labor theory of types of labor are constant, the Ricardian and Marxian value he is not assuming it and there is no reason treatment of an hour of skilled labor as several hours of why such cases should not disagree with the unskilled labor, with their ratio based on relative training labor-theory-of-value cases.. .. When you revise costs, runs into no logical difficulty. your paper you might point this out.

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value into the Rate of Profit" and "Part II: Conver- * the capitalists in the various spheres of produc- sion of Profit into Average Profit." Pricing is again tion . . . do not secure the surplus-value, and conse- not mentioned. It is true that in Chapter IX of Part quently the profit, created in their own sphere by the II he does get around to dealing with prices and production of these commodities, but only as much surplus-value, and profit, as falls to the share of every says so in the title "Formation of a General Rate aliquot part of the total social capital out of the total of Profit (Average Rate of Profit) and Transforma- social surplus-value, or social profit produced by the tion of the Values of Commodities into Prices of total capital of society in all spheres of production Production." But is should be clear from the order- * . . . The various capitalists, so far as profits are ing which issue has the star billing. concerned, are so many stockholders in a stock com- Finally, we may note how Marx described the pany in which the shares of profit are uniformly di- issue to Engels in his 1868 letter: videdfor every 100 shares of capital, so that profits . . .it is proper that you should know the method differ in the case of the individual capitalists only each by which the rate of profit is developed. I will there- according to the amount of capital invested by one of them in the social enterprise, according to his fore give you the most generalfeatures of the process. . . .In Book III we come to the transformation of investment in social production as a whole, accord- surplus value into its different forms and separate ing to his shares. (Vol. III, Chapter IX, pp. 186-7. component parts. ... My italics.) Profit is for us first of all only another name or an- The Transformed Profits as a Mere Surface Man- other category of surplus value . . . surplus value ifestation gets the form of profit, without any quantitativedif- We economists have always had a somewhat ference between the one and the other. This is only warmer spot in our hearts for Volume III, and have the illusory form in which surplus value appears [8, 1956, pp. 245-6; all italics are Marx']. tended to treat Volume I as an "unnecessary detour" to the issue that really matters-the explana- The Parable: "Capitalist Communism" tion of competitive pricing. But that is merely a I have attempted to explain the transformation reflection of our own prejudices as bourgeois (shall process in terms of a parable in which the econo- I say, "vulgar"?) economists. From the point of my's total surplus value is first aggregated19and view of the objectives of Marx' analysis, what is all then redivided by the competitive process. It is easy that important about an explanation of the determi- to show by a quotation from Capital that this para- nation of competitive prices?2"To Marx, indeed, it ble describes Marx' intentions accurately.20 was worth discussing only to reveal its irrelevance

'9 To Marx this aggregation was of fundamental importance. He lists it as the first of ferent spheres of production-is striving to produce is capitalist communism, namely that the . . . the three fundamentally new elements of the mass of capital belonging to each sphere of produc- book [Capital,Vol. I] . . . that in contrast to all tion should snatch an aliquot part of the total sur- former political the economy, whichfrom veryout- plus value proportionate to the part of the total set treats the particular fragments of surplus value social capital which it forms [8,1956, p. 248, Marx' with their fixed forms of rent, profit, and interest italics]. as already given, I first deal with the general form of surplus value, in which all these fragments are Recall from our first quotation from that letter, that the still undifferentiated-in solution, as it were (Marx parable also appears in the earliest (1862) transformation to Engels, January 8, 1868, p. 238). letter, which uses the phrase "and all capitalists are brothers" for what has here become "capitalist communism." The other two fundamentally new contributions of In the text of Volume III it becomes the metaphor about Volume I, are, in Marx' view, the difference between the proportionate dividends on shares in a joint stock com- use value and the exchange value of labor, and the evalua- pany, a metaphor that had also been used in the 1862 tion of wages as an "irrational form in which a relation letter. hidden behind them appears." Note these are all matters 21 Note that to Marx, Volume I deals with "The Process relating to income distribution, not pricing of commodi- of Capitalist Production" (Marx' italics), that is, not ties in general. (primarily) with price theory (Marx to S. Meyer, April 30, 20 The parable is also described several times in Marx' 1867, p. 224). Similarly, in two letters to Engels, dated correspondence. For example in his later 1868 transfor- August 24, 1867 and January 8, 1868 (the one cited in the mation problem letter he wrote: preceding footnote) Marx gives his lists of the main contri- What competition between the various masses of butions of Volume I, none of which relates to the pricing capital-differently composed and invested in dif-' of commodities [8, 1956].

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and to tear away the curtain it formed before our truth that Marx is trying to reveal? In other words, eyes, so that the basic truth about the production what is the value theory really about? Is it just a of surplus value could be revealed. That is why the bit of revolutionary propaganda, or mere playing first volume is indeed the important one for Marx with persuasive definitions, or a bit of Hegelian and his followers. To argue that he and Engels stuck mysticism?22 by Volume I in order to put up a brave show when I believe that the answer is none of the above, but they had realized the weakness of its analysis is to to see why, it is suggestive to look ahead in time. reveal one's own misunderstanding of Marx' pur- Think of the economists at the turn of the century pose. who were seeking evidence of justice in the capital- Once again it is easy to document this conclusion. istic process of distribution with the aid of marginal I quote a rather long but very significant passage productivity theory. It is not totally unfair to char- from Capital: acterize their argument as proceeding from the position that labor, land,23and capital each contrib- . . . the mass of the surplus-value produced in any utes toward the production of society's output. It particularsphere of production. . . has any impor- tancefor the individualcapitalist only to the extent is surely only just, therefore, that each of these that the quantityof surplus-valueproduced in his should share in that output. Since, regrettably, line playsa determiningrole in regulatingthe aver- mother nature is not available to collect her share, age profit.But this is a processwhich takes place it is indeed fortunate that the landlord is willing to behindhis back,which he does not see, nor under- accept it in her stead.24 stand,and whichindeed does not interesthim at all. Such nonsense is precisely what Marx' analysis The actual differenceof magnitudebetween profit anticipates and what it is intended to expose. Again, and surplus-value-notmerely between the rate of let Marx speak for himself. profitand of surplus-value-inthe variousspheres of productionnow concealscompletely the truena- In Capital-Profit, or better Capital-Interest, ture and originof profit,not only for the capitalist, Land-Rent, Labor-Wages of Labor,in this eco- whohas a specialinterest in deceivinghimself on this nomic trinityexpressing professedly the connection score,but alsofor the laborer.By the transformation of valueand of wealthin generalwith theirsources, of values into prices of production, the basis of the we have the completemystification of the capitalist determination of value is itself removedfrom direct . . observation . The fact that the actual state of 22 "Taken on the Hegelian (neo-Hegelian) ground, and thingsis hererevealed for the firsttime; that political seen in the light of the general materialistic conception, economyup to the presenttime . . . [hasclung] to the proposition that value = labor-cost is self-evident, not the obvious phenomenaof these differences-this to say tautological. Seen in any other light, it has no confusion of the theoreticaleconomists demon- particular force." (Veblen, loc. cit.) strates most strikinglythe utter incapacityof the 23 Marx was at pains to emphasize the contribution of capitalist,when blinded by competition,to penetrate land to the productiveprocess: throughthe outwarddisguise into the internales- The use-values, coat, linen, etc., i.e., the bodies of senceand the innerform of the capitalistprocess of commodities, are combinations of two elements- production.(Volume III, ChapterIX, pp. 198-99, matter and labour. If we take away the useful la- my italics.) bour expended upon them, a material substratum is always left, which is furnished by Nature with- The Significance of the Transformationto Marx out the help of man. . . . As William Petty puts it, labour is its father and the earth its mother. If Marx considered pricing an unimportant phe- (Vol. I, Chapter I, section 2, p. 50.) nomenon which only served to obscure the relevant Why Marx denied that "land" contributed value to the relationships, then why did he devote so much ef- product should soon become clear. fort and space to the transformation problem? The 24 Marx' objections to Adam Smith on this score pre- answer has already been suggested in the preceding sumably arise out of passages such as the following: section-it must be explained in order to get it out . . . rent may be considered as the produce of of the way. It is important because it had misled those powers of Nature, the use of which the land- so many people-capitalists, laborers (see the lord lends to the farmer. . . It is the work of Nature which remains after deducting or compen- preceding quote), vulgar economists and even sating every thing which can be regarded as the economists as considerable as Ricardo. work of man [14, 1937, Book II, Chapter V, pp. But-and this is the essential issue-what is this 344-5].

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mode of production. ... It is an enchanted,per- upof thisprofit into entrepreneur's profit and interest. verted,topsy-turvy world, in which MisterCapital Interest-bearingcapital. The creditsystem. and MistressLand carryon their goblin tricksas VI. Transformationof surplusprofit into ground socialcharacters and at the sametime as merethings rent. . . .it is . . . naturalthat the actualagents of pro- VII. At last we havearrived at theforms of appear- ductionfelt completelyat home in these estranged ance which serveas the startingpoint in the vulgar and irrationalforms of Capital-Interest, Land- conception:ground rent coming from the earth, Rent, Labor-Wages of Labor, for these are the profit(interest) from capital, wages from labour. But formsof the illusion,in whichthey moveabout and fromour pointof view the thing is now seen differ- in which they findtheir daily occupation.It is also ently. The apparentmovement is explained.More- quitenatural that vulgareconomy, which is nothing over,Adam Smith's nonsense, which has become the but a didactic,more or less dogmatic,translation of mainpillar of -alleconomics hitherto existing, that the ordinaryconceptions of the agentsof production the price of a commodityconsists of those three and whicharranges them in a certainintelligent or- revenues,i.e., only of variablecapital (wages) and der, shouldsee in this trinity,which is devoidof all surplusvalue (ground rent, profit (interest) ), is over- internalconnection, the naturaland indubitableba- thrown.Then-the wholemovement takes placein sis of its shallow assumptionof importance.This this form of appearance.Finally since these three formulacorresponds at the sametime to the interests (wages,ground rent, profit (interest) ) constitutethe of the ruling classes, by proclaiming the natural respectivesources of incomeof the three classesof necessity and eternal justification of their sources of landowners,capitalists and wage labourers, we have, revenueand raising them to the positionof a dogma. in conclusion,the class struggle,into which the (VolumeIII, Chapter48, pp. 966-67, my italics.) movementand the smash-upof the whole business resolvesitself. ...26 This discussion is clearly pertinent to an understanding of the significance of the value theory to The point of the value theory may then be Marx. But if it is relevant for the transformation summed up as follows: goods are indeed produced analysis it may well be asked why he let some 700 by labor and natural resources together. But the pages intervene between this passage and the trans- relevant social source of production is labor, not an formation discussion in Volume III. We can never inanimate "land." Thus profits, interest, and rent be sure of the answer but it must be remembered must also be attributed to labor, and their total is that Engels tells us (in the preface to Volume II) equal (tautologically) to the total value produced that the manuscript from which he produced by labor minus the amount consumed by labor it- Volumes II and III was made up of many bits and self. The competitive process, that appears to show pieces which he fitted together as best he could. Part that land is the source of rent and capital the source VII of Volume III, from which the preceding quota- of profits and interest, is merely a distributive phe- tion is taken, is one of the most fragmentary, with nomenon and conceals the fact that labor is the only sentences reported to have been illegible, (e.g., Ch. socially relevant source of output. This is the signifi- 48, p. 948) and pieces of manuscript left uncom- cance of the value theory and the transformation pleted, (e.g., p. 950). It might only have been natu- analysis to Marx. ral for Engels to have put it off to the end.25 Conclusion: Sources of Misunderstanding But we are not forced to rely on conjectures on this issue either. Once again, Marx tells us about Having come to so unequivocal a conclusion the matter; for in his later transformation letter to about what Marx hoped to accomplish through his Engels (1868), he juxtaposes the two issues very notion of a transformationprocess one may well ask clearly, completing his discussion of the transfor- how the apparent misunderstanding of so many mation issue thus: commentators might have arisen. But before turning to this it should be noted again that Meek and V. We havenow reduced profit to the formin which Morishima are very clear cut exceptions and that it appears in practice . . . Next comes the splitting my interpretation is very close to theirs. Thus, Morishima reminds us of Samuelson's remark that 25 Engels also reported that the transformation discussion "(relation of Mehrwertsrate to Profit rate)" required "a great deal of work" on his part to prepareit for publica- 26 The (anonymous) Russian translator exhibits some tion (Letter to N. F. Danielson, November 13, 1885.) [8, delicacy in this rendition. The word he translates as "busi- 1956, p. 464]. ness" is "scheisse"in the original [8, 1956, p. 250].

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"the proportionality of market price to labor con- gested one explanatory hypothesis-that many tent applies validly only when surplus value is zero readers may have been misled by the analogy with and not worth talking about!" [12, 1957, p. 888]. Ricardo. Ricardo tells us explicitly when he gets to On this Morishima remarks: the role of capital in price determination that the "labor theory" model gives us answers that are still . . . in the transformation problem Marx did not intendto establisha proportionalitybetween values very nearly correct, so that in his view it remains and pricesbut, on the contrary,to show that in- a good model to use in explaining the determination dividualexploitation and individualprofit are dis- of individual prices. Marx, on the other hand, proportionalunless some restrictiveconditions are points out that the deviations between the two mod- imposed. . .. Thus it is clear that the transforma- els are systematic and significant enough to conceal tionproblem has the aim of showinghow 'theaggre- the underlying relationships from other observers. gate exploitationof labouron the part of the total Moreover, as we have seen, at this point, at least, social capital'is, in a capitalisteconomy, obscured Marx is not even interested to any significant degree by the distortionof pricesfrom values; the otheraim in the theory of price. is to show how livinglabour can be the sole source Yet Marx himself must bear a good share of the of profit"[10, 1973,pp. 85-6.]. blame for the confusion. Since it seems true that Meek begins his discussion with a statement of Volume I and Volume III were written with per- the issue that is just as clear. However, he does go fectly consistent intentions he should surely not on to treat the transformation problem as though have adopted the word "value" for the magnitude it were primarily a matter of explaining price deter- on which he focuses his discussion. He was per- mination. fectly aware that "value theory" was used in the Sweezy [16, 1942, esp. pp. 125-130] also comes economic literature to refer to the theory of price close to the Meek-Morishima position arguing that determination (though he felt that Ricardo had also prices and profits of individual capitalists are micro groped, albeit unsuccessfully, for a deeper phe- issues while Marxian values are intended to deal nomenon when he discussed values). Consequently, with the macro issues of distribution in which Marx if he deliberately used the term to denote a magni- is interested (pp. 125-6). He notes that the "price tude that differs from price in a significant and sys- calculation . . . mystifies the underlying social rela- tematic manner he was certainly asking for the sort tions of capitalist production. Since profit is cal- of misunderstanding to which the work has been culated as a return on total capital, the idea inevita- subject. Moreover, in the bulk of Volume I Marx bly arises that capital as such is in some way does speak as though the "exchange value" which 'productive'" (p. 129). he explains in terms of labor were a normal mar- His book does follow the Bortkiewicz tradition ket price. If he meant otherwise he hardly hinted in treating prices as magnitudes to be determined at it.27 from values. However, Sweezy's letter to me also 27 There seem to be only three points in Volume I where casts additional light on this matter. He writes: the reader is given some warning on the matter; on pp. To the bestof my recollection,I nevertreated 'the 184-5, footnote, p. 244, footnote, and on pp. 335-6. In the in transformation second of these, he writes "We have fact assumed that problemprimarily as a matterof de- prices = values. We shall, however, see, in Volume III, terminingprices from values.' Values are in fact an that even in the case of average prices the assumption abstractionfrom capitalist reality, not an observable cannot be made in this very simple manner." phenomenon,and could not possibly 'determine' pricesof production(which are also an abstraction Similarly on p. 335-6 we have the statement albeit on a lower level). The justificationfor such This law [that the masses of surplus value pro- abstractions,esp. value, is that they revealthe es- duced by differentcapitals vary directly as the vari- sence of capitalistreality as opposedto the appear- able constituents of these capitals] clearly ance-an argumentwhich orthodoxeconomics of contradicts all experience based on appearance. a cotton spinner, who, reck- courseis unableto Everyone knows that totally comprehend. oning the percentage on the whole of his applied In any event, it is clear that with these and per- capital, employs much constant and little variable capital, does not, on account of this, pocket less a few other the I haps exceptions, interpretation profit or surplus-value than a baker, who relatively have offered and sought to document is hardly the sets in motion much variable and little constant view that is held universally. I have already sug- capital. For the solution of this apparent contradic-

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This too constitutes something of a mystery. which provoke them to untimely demonstrations of Since Marx did have his transformation analysis their asininity. (Marx' italics.)28 worked out before Volume I was published, why is there no clear statement of the issue there? But this REFERENCES mysterydoes have a known solution. The definitive answer is provided in an exchange of letters be- 1. BLAUG, M. Economic theory in retrospect.Re- tween Marx and Engels. As they were making the vised edition. Homewood, Ill.: Richard D. Ir- final corrections for Volume I, Engels (gently) win, 1968. rebukedMarx for his failure to deal with the issue 2. B6HM-BAWERK, E. VON Karl Marx and the in Volume I. In a letter dated June 26, 1867 he close of his system and Bdhm-Bawerk'scriticism wrote of Marx by Rudolf Hilferding with an appendix by L. von Bortkiewicz. Edited by P. SWEEZY. . . . As for the origin of surplus value, the follow- New York: Augustus M. Kelley, 1949. ing: The manufacturer, and with him the vulgar 3. BRONFENBRENNER, M. "Samuelson, Marx economist, will at once object: If the capitalist pays and Their Latest Critics," J Econ. Lit., March the worker only the price of 6 hours for his 12 hours 11 58-63. of working time, no surplus value can originate from 1973, (1), pp. this, for then every hour of labor of the factory 4. ENGELS, F. Engels on capital: Synopsis, reviews, worker is only equal to half an hour of labor-equal letters, and supplementarymaterial. Translated to what is paid for it-and enters into the value of and edited by L. MINS. New York: Interna- the product of labor as worth only that much.... tional Publishers, Inc., 1937. No matter how terribly shallow this argument is, no 5. MARX, K. A contribution to the critique of matter how much it identifies exchange-value and political economy. Translated by N. I. STONE. price, value of labor and wages, no matter how ab- Chicago: Charles H. Kerr and Co., 1904. surd its assumption that one hour of labor enters into 6. Capital. A critique ofpolitical economy. value as only half an hour if it is paid for as only half Chicago: Charles H. Kerr and Co., Volume I an hour, I marvel that you have not taken this into consideration already, for it will quite certainly be (1906); Volumes II and III (1909). held up to you at once and it is better to dispose of 7. AND ENGELS, F. Correspondence it in advance. Perhaps you will return to it in the next 1846-95; with explanatory notes. Translated by [printer's proof] sheet . . . (Engels' italics). DONA TORR. New York: International Pub- lishers, [1934, 1936] 1942. To this Marx replied on the next day . . . 8. AND Selected corrrespondence. Moscow: Foreign Languages Publishing . . . As for the inevitable objections you mention House, 1956. of the philistine and the vulgar economist . . . [The 9. MEEK,R. L. "Some Notes on the Transforma- answer to this problem] presupposes [among other matters] . . . that the conversionof surplus value into tion Problem," Econ J., March 1956, 66, pp. profit, of profit into average profit, etc., is set forth. 94-107. This presupposes a previous account of the process 10. MORISHIMA,M. Marx's economics:A dual the- of the circulation of capital, since the turnover of ory of value and growth. New York: Cambridge capital, etc. plays a part here. Hence this matter can University Press, 1973. be set forth only in the third book. . .. 11. ROBINSON, J. "Review of SWEEZY, P., Karl If I were to silence all such objections in advance, Marx and the close of his system . . . I should ruin the whole dialectical method of devel- Econ. J., June 1950, 60, pp. 358-63. [see ref. opment. On the contrary, this method has the advan- 2.] tage of continually setting traps for these fellows 28 I came across this exchange of letters quite acciden- tally (thanks to a fortunate find by my secretary in a 6th tion, many intermediate terms are as yet wanted. Avenue trash canl) after an earlier draft of this paper had . . .It will be seen later how the school of Ricardo been completed. Note how remarkably it confirms Ve- has come to grief over this stumbling-block. Vulgar blen's conjecture about Marx' attitude toward some of his economy which, indeed, "has really learnt noth- expected readers, as well as several of the hypotheses of ing" here as everywhere sticks to appearances in this article. The translation here is taken from Mins, in opposition to the law which regulates and explains whose little volume (presented to me by my secretary) I them [6, 1906]. first came across the exchange [4, 1937].

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12. SAMUELSON,P. "Wages and Interest: A Mod- 14. SMITH, A. An inquiryinto the nature and causes em Dissection of Marxian Economic Models," of the wealth of nations. Edited by EDWIN CAN- Amer. Econ. Rev., Dec. 1957, 47, pp. 884-912; NAN. New York: Modem Library, [1776] 1937. reprinted in SAMUELSON, P., Collected scien- 15. STIGLER, G. J. "Ricardo and the 93% Labor tificpapers, edited by J. STIGLITZ.2 vols. Cam- Theory of Value," Amer. Econ. Rev., June bridge, Mass.: M.I.T. Press, 1965, Ch. 29, pp. 1958, 48 (3), pp. 357-67. 341-69. 16. SWEEZY, P. M. The theoryof capitalist develop- 13. "Understanding the Marxian Notion of ment. New York: Oxford University Press, Exploitation: A Summary of the So-called 1942. Transformation Problem Between Marxian 17. VEBLEN, T. B. The place of science in modern Values and Competitive Prices," J. Econ. Lit., civilization,and other essays. New York: Viking June 1971, 9 (2), pp. 399-431. Press, 1919.

Insight and Detour in the Theory of Exploitation: A Reply to Baumol

By PAUL A. SAMUELSON Massachusetts Institute of Technology

I am grateful for editorial assistance of Norma Wasser,and financial aid from the National Science Foundation. Despite our friendly differences, I've benefittedfrom correspondencewith ProfessorsBaumol and Morishima.

Thesis in my Collected scientific papers, [10, 1972], as Ch. 154, pp. 309-311; my May 1967 AER centennial paper [13, THE THESIS ProfessorBaumol advances about 1967], reproduced there as Ch. 152, pp. 268-275; my June the proper interpretation of Marx deserves 1971 paper with C. C. von Weizsacker in the PNAS, [20, careful analysis because it duplicates a point that 1971], reproduced as Ch. 155, pp. 312-316. Also two replies by me in the JEL 10 and 11 [15, 1972; 14, 1973]. many think important [1, Baumol, 1974]. Essen- My paper in the July 1973 PNAS, "The Optimality of tially, it can be put in 38 words, 38 of Marx's actual Profit-Inducing Prices Under Ideal Planning," [16, 1973] words: carries further the Weizs-acker-Samuelsondemonstration that, even in a planned socialist society, uniform R* = "Weshall see, in Book III, that the rateof profit Sjl(Cj + V,), rather than r* = sl/v, would be needed for is no mystery,so soon as we know the laws of sur- efficient dynamic asymptotes. In the George Halm Fest- plus-value.If we reversethe process,we cannotcom- schrift [4, 1973] and Alice Bourneuf Festschrift [2, forth- prehendthe one or the other" [5, 1906, p. 239, coming], I present analysis relevant to A. Emmanuel's n. 2]. neo-Marxian analysis in Unequal exchange:A study of the imperialism of trade [3, 1972]. My earlier 1957 AER and The valuable Meek paper that I cited in my 1971 1959 QJE articles on Marx and on Ricardo are also rele- survey of the transformation problem' put the es- vant [19, 1957; 9, 1959]; they are reproduced in the 1965 Collected scientificpapers, [10, 1965] Chapters 29-32, pp. sential point this way: 339-408. The ninth edition of my Economics (McGraw- ' See also my September 1970 Proceedings of the Na- Hill, New York, 1973), Ch. 42 Appendix gives the ele- tionalAcademy ofSciences(PNAS), [17, 1970] reproduced ments of Marxian analysis [11, 1973].

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". . according to him [Marx], the profit which the Antithesis capitalistsreceive in each industrymust be con- ceivedof as accruingto them by virtueof a sort of I deny that "surplus value is the source of profit" redivisionof the aggregatesurplus value produced in any useful sense. I deny that Marx (or Morishima by the economyas a whole"[6, 1956,p. 95]. or Baumol) have anywhere cogently given us reason to believe that one can to we Baumol's own words are these: get profits only after know the laws of surplus value. And I accept Bau- ". . the primarytransformation was not fromval- mol's challenge to show that my "erase and re- ues into as Marxand pricesbut, Engelsrepeatedly place" demonstration of the transformation prob- emphasize,from values into the non-labor surplus lem applies, not merely to the transition from incomecategories that are recognizedby 'vulgar industry microeconomic "values" to industry economists,'i.e., profits, interest, and rent." 1974, [1, but to the p. 52]. "prices," equally (unnecessary-detour) transition from "surplusvalues into profits." It will Baumol believes in remedies. To homeopathic be seen to be logically untenable to agree with my offset mathematical-economic my misconceptions, "erase and replace" analysis of the values-prices he invokes the of Mori- high authority Professor transformation, and withhold agreement from my shima's mathematical of Marx in his new analysis "erase and replace" analysis of the surplus-value- book Baumol's citations are from [8, 1973]. Chapter profit transformation. For these are identical. 7, pp. 72-86, and most particularly to pp. 80-84. I shall show that a useful Morishima theorem,3 The following Morishima passages seem germane. Marx thoughthe had successfullyremoved the Actually,Ricardo never had reason to expectindustries maskof capitalism. .. [writingin VolumeIII] 'the with differentdirect-labor intensities to have equalrates rate of profitis from the very outset distinctfrom of surplusvalue (i.e., to have equal ratios of profitsto the rate of surplus value . . . this serves . . . to direct-wageoutlays). So thereis nothingto be reconciled. obscureand mystify the actual origin of surplus And of coursewhen Volume III camein 1894,and after value . .. The individual capitalist. . . rightly be- its proposalswere audited by Veblen, Bohm-Bawerk, lieves that his is not derived from the Bortkiewicz,Sweezy, Dobb, Meek, Winternitz,Seton, profit solely Morishima his 1973 it was nevershown labour him . . . This is true as (including book), employed by quite (and was never to that one can reconcile faras his is concerned.To whatextent possible show) averageprofit equalpositive Sl/ V = S,/ V,with unequalVi/C, VI/C1 this is due to of labour profit aggregateexploitation and equal Sj/( V + C,) = Si/(V, + C,) - in either the on the partof the totalsocial capital. . . thisinterre- "prices"(accounting) regime or in the 1867-1885"val- lationis a completemystery to the individualcapital- ues" (accounting)regime so long as we stay in any one ist; all the moreso, sinceno bourgeoistheorists, the regime.Only by going, with or without the use of an politicaleconomists, have so far revealedit.' eraser,from one to the otherof the mutually-incompatible "Thusit is clearthat the transformationproblem regimes,can one go fromone of the equalitysets to the has the aim of how 'the other.(By mutually-incompatibleaccounting regimes, one showing aggregateexploita- the fact that can tion of labouron the of the total social signifies competitivecapitalism empiri- part capital' conformin its exact to at mostone of in a obscured the distortion cally configuration is, capitalisteconomy, by the two alternativeregimes.) of pricesfrom values; the otheraim is to show how Baumol's quotationsfrom the Engels-Marxcorre- living labourcan be the sole sourceof profit. . . spondenceof the 1860'sshows that Engelswas awareof Marx . . . was very successful in [his conclusion difficultiesin the case which,after Marx's 1883 death, he about]the necessityof aggregateexploitation of la- was forcedto arguefor. Engels'challenge was not one of bourby capitalistsfor the existenceof positiveprofit. his happierperformances as my later quotationfrom (Morishima,pp. 85-6.) Veblensuggests. 3As in my 1971paper [18, 1971],I writeao for the direct On p. 52, Morishima examines "Marx's proposition laborrequirements row vector,a for the squarematrix of that surplus value is the source of profit. . . This input-outputraw materialcoefficients, m for the column result be claimed as the Fundamental Marxian vectorof each worker'ssubsistence requirements. But to may all variablesdistinct from "values"varia- Theorem." keep "prices" bles, I use capitalletters for prices-variablesand lower- One could list another score of similar quota- case lettersfor values-variables,writing the profitrate as tions.2 R and the rate of surplusvalue as r. Likewiseci + v±+ = + + rvtis the valuescounterpart of the prices 2 si ci vl The readermust judge whether Baumol's citing of the relationCj + Vj+ Sj = C + Vj+ R(Cj+ Vp).Morishima "famouschallenge in the Engels 1885preface to Volume writesmy ao as (/), my a as [A,A ],mmy c + vi+ Sfas II" has relevance[1, 1974,p. 56]. L 0 0J

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to any non-antiquarian, can dispense completely biguities discerned in an early writer like David with all the sj/Vj = si/vi innovations of Volume I Ricardo or Karl Marx? There is Wittgenstein hu- (innovationswhich I claim to be uninsightful diver- mor in a sentence like this gem of Baumol's: "Only sions and detours). And, for those who like me have a very few [!] commentators, notably R. Marshall an antiquarian'sinterest in relating Marx's detour and J. Viner and P. Sraffa, saw Ricardo's analysis to the geodesic turnpikes of competitive analysis, for what it so plainly [!] was .. ." Years ago the I shall show that there is complete reversible sym- world's greatest living authority laughed at the nai- metry between the two alternative accounting vete of my question: "Did Ricardo 'believe' in a regimes: "profit is the source of surplus value" is labour theory of value?" And, as a student of Viner as formally valid as vice versa; "only if the profit and a reader of Marshall, I can testify that both rate R* can be positive [in the matrix sense, R* > those teachers recognized that Ricardo's mode of 0 in a0(1 + R*) [I-a (1+R*)]-' m = 1], can the rate exposition laid him intrinsically open to misunder- of surplus value r* be positive [in the sense, r* > standings. (When one highway corer claims 50 0 in a0 [I-a]-' (l+r*)m = 1]"-this is as valid as times the number of lives of another, we are obtuse vice versa; and preferable to either is the strength- to explain its accidents by the propensity of its driv- ened Hawkins-Simon condition a0 [I-a]-'m < 1 if ers to drink or to nap. Why don't people argue and only if R* > 0]. about the "meanings" of Wicksell the way they do Since I have recently covered some of this ground about those of Ricardo and Marx?) elgewhere, I shall here be brief [12, 1974]. Third, the diligent readercan judge whether I am right in thinking that the present Baumol thesis was not overlooked in my earlier writings on the transformation problem-which is not to suggest that Let me clear the decks of some extraneous details the present reincarnation of the issue is a waste of to concentrate on Marx's thesis, which if valid, time. would be of considerable interest. How does one go about "proving" assertions like First, although Baumol apparently believes that these above? I see no way other than to isolate the a writer is allowed only one thesis-or one primary final insights agreed to by all parties, and examine thesis-one may deem it safer to assume that there how one arrives at them. How, via the analysis of may be more than one. And certainly Marx and the rates of surplus value, do we arrive at the goal of school of Marxism have been concerned with many explained distribution of actual incomes? What different facets other than that which Baumol con- other paths can lead to that distribution? Which centrates on. Therefore, the many writers-non- paths cannot? What are the arguments advanced by Marxist or Marxist-whom Baumol chides for not the various protagonists, and what is their cogency? seeing his simple truth I think need not plead guilty to any mortal sins. Second, and related, may we put down to the account of conscious or unconscious humor any Baumol's testimony.Most of Baumol's paper is con- writer's belief that there is plainly to be read by any cerned with what Marx's purpose was. On the ques- intelligent reader some simple resolution of the am- tion of whether that purpose was successful in some sense or another, I can find only a few relevant Cj+ V + S, my C + j +S as Cf+ VP+ Sf, my R as 7r,my r as e, my P[1 + 0] = aO[I-a]-'as (X,, ...,), my paragraphs in Baumol's text. n as n + m, my P[1 + R] = ao(1+ R)[I - a(1 + R)]-' First, there is his simple parable, describing how as (p ). In the "values" tableaux, (Cj+ Vj+ rv/), I use "non wage incomes are produced and then how this p[l + r] = - + = + to a[I a]- (1 r) p[l](1 r), signify is redistributed." italics.] Upon p[l + r]aX + aoX+ raoX= + r]X;what I aggregate [Baumol's p[1 express is no as p[l + r] or p[1 + e] would for Morishimabecome exegesis, the jury will conclude that there (Xj(1 + e)). My (mi,.. mi, .. ) Morishima writes cogency in this contention. There exists in actuality as (0 .. 0, b+ ... b). Some of the discrepancies no prior determination of the total non-wage sur- betweenus vanishwhen one realizesthe differencesin after which its can be redistributed. notations.For I shall assumethe of plus, aggregate brevityonly, length I do not this as a economist the workingday, Tin Morishima'snotation, to be fixed say bourgeois writing at unity;to assumeit variable,as Marxoften did, would within a non-Marxian paradigm. I say this within only strengthenmy argument. the Volume I-II-III paradigm, and as a matter of

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logic.4 It involves the fallacy of petitio principii to if we want to understand real-world competitive assert, as Baumol does, to explain Marx's intention, exploitation, and to predict how distribution will "each [industry] . . . contributes to a storehouse change when invention, consumption-demand, or containing total surplus value . . . [which] contri- subsistence-requirements change, we preserve in- bution is proportionate to the quantity of labor it sight by concentrating on the reality of avaricious uses . . . the transformation process . . . takes competitive arbitrage rather than on irrelevant Pla- from each according to its work force, and returns tonic abstractions or dual accounting systems. to each according to its total investment" [1, 1974, None of this soft pedals for a moment the basic p. 53]. Let's see what is actually involved in com- fact that, if you take away all living labor, you take petitive income distribution. away all product. Nor does it distract attention (i) If there were zero profit or surplus, the from Marx's basic reality: The worker does not own value-addedin each industry would be wages only: the raw materials and machinery that is needed if this is the pre-Marx classical labor theory of value. his labor is to produce product (use values). That The simultaneous determination by long-run com- is why the worker must sell or rent out his labor petitive supply and demand would determine power rather than be sole producer and appropria- goods' prices at their embodied labor contents, di- tor of all the product he sets his hand and brain to. rect-plus-indirectlabor. All the Net National Prod- Living labor, yes. But it is a bad pun to confuse ucts would go to wages, and the consumption ex- this with "live labor" in the sense of direct labor, penditure of such incomes would go for the flow of to the neglect of labor "previously" performed and final NNP product. No quarrels here. embodied in raw materials and in equipment-i.e., (ii) Suppose the profit rate is positive for what- "dead" or indirect labor. ever reason (e.g., because labor can be reproduced That there is no cogent sense in which at each at the cost of its subsistence bundle, m, which is less stage surplus or profit springs out of the direct labor than what the labor can produce in the steady state alone and not out of the needed raw materials can net after reproducing its used up cooperating raw be shown by any simple example.' Let 1 coal now materials). Then the NNP flow of final product is be producible by 1 mine-labor a short period ago. composed of labor's consumption plus that of the And let 1 coal now with 1 farm-labor now produce capitalist property owners; within each industry, 1 corn a period from now. Suppose corn is the the prosaic accounting of value-added (a concept "end-all" of economic activity. Then, eschewing already glimpsed in Adam Smith) records its wage any neoclassical variability of production methods, payments and its profit payments; summed, these we have in terms of production causation: industry value-addeds define the NNP, which has = no logical existence other than as the macroeco- Cornt Min[mine-labort2, farm-labort_] nomic sum of the microeconomic items, all simulta- neously defined. To digress, in a corrected Baumol I parable, each industry "puts into" the pot in value- A morecomplicated example can do betterjustice to Marx's non-Austriancircular-flow models. Let 2 coal added what it takes out. and 2 minelabor now produce1 coal a briefperiod from Only simpletons think that accounting labels now. And let 2-coal and 2 farmlabor produce 1 corn a cause the world to move. The apple falls the same periodfrom now. Then whether Newton watches or enunciates its constant Cornt = Min [ farm-labort_, 4 coal-labort2, acceleration. Profit or surplus is no less ugly or 8 coal-labort-3,.. *+ 2k coal-labort-k, * reprehensibleor correctable when it is proportional to each industry's total investment outlay on raw an infinite-sequencethat convergesfor steady-statecorn materials and on direct-labor wage payments; and, productionproducible out of steady-statetotal laborL, = L to

'This does not assert that a "macroeconomic" theory Cor-n= L= (2 +4 + 8+. . 1+2 k + .* L of profits, like Kalecki's widow's cruse model, is self-con- tradictory or illogical. It does point out that there is no with half society'ssteady state labor on the farmand half semblance of such a theory in any of the three Volumes in the mines.This NNP of produciblecorn will go to wage of Marx. Incidentally, a Kalecki-Kaldor-Pasinetti macro earnersin a shareof a anywherefrom 1 to 0 depending theory finds the uniform rate of profit more useful than uponwhere the profitrate per period, R, fallsin the range a detour through a uniform rate of surplus value. 0 < R < 1, where a = 2(1 + R)' - 1.

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and in the steady state with a given labor supply time that demonstrates why such a conclusion is of Lt L, we have wrong.

Corn = Min 2, 2 L Morishima's testimony.This book is of great interest In terms of physical causation, and any ethical for its own sake [8, 1973]. What light does it throw consequences inferrable from that, no more can be on the contention that analysis of said. Nothing in these technocratic facts or in the brute Cj + vj + sj = cj + + rvj facts of competitive arbitrage is illuminated by the where r is the uniform rate of surplus value, is an 1867-85 innovations that postulate dual accounting uninteresting and redundant detour for the econo- identities = s2/v. As Veblen not sl/v, said, unsym- mist interested in the statics and of the Marx never even to his dynamics pathetically, deigns prove distribution of income? contention. As I say, neither Baumol nor Mori- After careful reading of the book, I find no cogent shima nor anyone else has provided a shred of the argumentation that compels, predisposes, or even lacking proof needed to show why si/vi = is Sj/Vj tempts one to withdraw the view that the pre- a useful concept to anyone who understands the = Volume III model with Sj/Vj = si/vi r (= e in self-standing + + + conventional Cj Vj R(Cj Vj) Morishima's is essentially only a diver- tableau. notation) sionary detour. To appraise this thesis of mine, I Beyond Baumol's parable and aside from his evi- divided the book's many interesting theorems into dence on Marx's there is one bearing intention, only three classes: other of his that addresses itself to part paper A. Those theorems that are stated, or can be whether or not Marx's intention misfired. In the restated, to apply to the model of mainstream eco- first paragraphof his section on transformedprofits nomics in which + = + Vi) = R as a mere surface Baumol criticizes Sj/(Cj Vj) Si/(Ci manifestation, in Morishima's the case himself and other economists like me for [7r notation] including bourgeois where R = 0 = 7r, the "classical labor of Volume I as an detour." He theory "treating unnecessary value." does so from the issue of relative shares by turning B. Those theorems that relate the = both sides deem to the issue of Sj/vj si/v (which non-trivial) dual to the relative He "What is all accounting system pre-Marxian primal industry prices only. says, of + = + that . . from the of view of the accounting system Sj/(Cj Vj) Si/(C, V,) important, point much in the that a relates, of Marx's . . about an way bi-lingual dictionary objectives analysis. explana- children's to tion of the determination of say, my private nursery language competitive prices." standard But Baumol has not reckoned with conten- English.6 my 6 tion all microeconomic details "Duality"is an O.K. wordthese days, becauseof its that, price aside, into linear and direct- when we transform from insights programming gametheory, properly rate-of-surplus- and-indirectutility analysisof demand, price-quantity value accounting regime to actual rate-of-competi- symmetriesin planningand growth models, Legendre tive-profit regime, we take an eraser and replace the transformationsin Hamilton-Pontryagincontrol theory, in of ao[I-a]-1(1+r*)m = 1 relation that defines "the rate classicalthermodynamics, and analysis rationing, of and convex of point-linesymmetries projectivegeometry surplus value, r*" by the alternative relation set "and-or-not" of Schr6der-Peirce = theory, symmetries ao(l+R*) [I-a(l+R*)]-'m 1 that defines the symboliclogic; node-branch symmetries of networkthe- "competitive rate of profit, R*;" and literally noth- ory, etc. It representsat best a poor pun in English,at ing in the way of understandingof the latter's actual worst a source of confusion,to employ the Morishima of "dual to denote distribution relation is "revealed," is "uncovered" usage accountingregimes" competitive and MarxianVolume I In this sense, or is "laid bare" the All pricing regimes. by pre-eraser detouring. obsolete phlogiston-caloricand living Cornot-Clausius- that Baumol need do to end disagreement between Gibbs energy-entropythermodynamics are "dual ac- us is to admit that what he calls Marx's intention counting regimes," related by eraser transformation actually misfires-in that, from Marx's own stand- algorithms!If only Marxiansurplus values added the in- to that Maxwell-Boltzmann- actual sights competitiveprofits point of explaining wage-profitsdistribution, Gibbs kinetictheories of statisticalmechanics added to the Volume I analysis is indeed a detour. Or Bau- phenomenologicalthermodynamics-but, alas, not even mol should provide cogent argument for the first the greatskills of a Morishimacan accomplishthis.

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C. Those theorems that apply exclusively to antiquarian interest only. The rate of surplus value, the dual system of values, and which yet do have e or r*, will be numerically greater than the rate an independent interest to an economist who has of profit, R* or 7r,in any system where some subsist- no penchant for antiquarian study in the history of ence-wage good requires directly or indirectly some doctrines and ideas. non-labor input. It can be specified for such a sys- My finding:Class C was a null set. The few inter- tem that I* [I- a]' >0, aI- a]-' > 0, and esting theorems in the book framed exclusively for a4I-a] a'm < 1, for m the non-negative, non-zero the dual "values" regime could, upon straightfor- column vector of subsistence for worker. Then we ward reformulation,be expressed solely in terms of see from the algebra that f(R1, R2) = a, (1 + R1) empirically-observable regimes of competitive- [I - a(l + R2)]m is positive for admissible positive arbitragepricing, and hence could be put into Class R's and is strongly monotone in each and both of A. Class C's emptiness recognized, Class B dwin- its arguments. Consequently Morishima neatly dles in its interest. demonstrates that the respective roots, R* and r*, Let me give some illustrations: of 1. There is a beautiful modem theorem about f(R, R) = 1 and f(r, 0) = 1 non-negative matrices, a, a,, (I-a)-', a,(I-a) ', and the same matrices when all (a0,a) coefficients are must satisfy 0 f(r*, 0). But if my contention is correct that the make detI - a(1 + R)] change its positive sign. In f(r, 0) = 1 dual regime of Volume I is an uninsight- Hicks, Value and capital, the theorem states that ful detour, who but an antiquarianwill be interested the percentage change in an own good's price is, in this simple algebraic result? under certain assumptions about gross substitutes As C. C. von Weizsicker discussed in "Mori- and defined changes in tastes, greater than for any shima on Marx," [21, 1973], the harmless algebra cross-good's price change. In Leontief input-output theorem that ao(l + R*)[I - a(l + R*)-' m = I analysis, the theorem states that a unit increase in has a positive root iff ao[I - a]' (1 + e*) m = 1 hats will cause a greater percentage change in gross has a positive e* root, should not be construed to hat production than in gross shoe or belt produc- mean that a positive interest rate is solely possible tion. In Keynes-Metzler n-country multiplier anal- under "exploitation" of poor laborers by rich capi- ysis, the theorem says that an increase in United talists. We can have a positive profit rate when all States net investment will raise American income people are alike. Algebra should never obscuresoci- more than it will raise the United Kingdom's in- ology and power relations! All that is valuable is come. Connoisseurs know how neatly Morishima conveyed by the Volume III non-Marxian theorem: has enunciated and generalized this nice result in If and only if ajI - a]m < 1 will there be possible his non-Marxian writings. a positiveprofit rate andfeasible positive non-subsist- Now, in his book on Marx, Morishima points out ence consumption. No sj/vj = e > 0 relations are a version of the same theorem: an increase in an involved. input requirement in industry j, say an increase in 3. Under Class C is a Marx-Sraffa theorem aj or a,j (i. e., of raw material or labor requirements), such as (a) the ratio of values in the dual accounting will increase the pure-labor cost of good j by a regime are never affected by the increase in the rate greater percentage than it will increase the pure- of surplus value, even though (b) the ratio of prices labor cost of another good k. It is a nice result. But will be generally affected by changes in the rate of what power, in the Neyman-Pearson sense, does profit, in any system where the ratios of direct-wage such a result have for interesting any economist in to other costs are not uniform between industries. rate-of-surplusversus rate-of-profitanalysis? None! What is interesting about this theorem is the part The theorem holds as well for "prices" as for "val- which already belongs in Class A-namely the ues"; as well for the primal bourgeois accounting alegebra of how any pricej/pricek is affected by a regime as for the dual Volume I regime; it holds at change in R from zero to larger values. Morishima's every admissible positive profit rate. beautiful generalization of this Marx-Sraffa theo- I could give many other examples of Class A rem, which can be stated as giving sufficient condi- theorems. tions for a subset of the goods to keep invariant 2. Let's look at a typical Class B theorem of relative prices [!] as the profit rate changes, belongs

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to my Class A rather than to Class B or Class C. at all, and no proof of a false proposition is ever 4. Again, for antiquarians (I include myself in possible. Indeed, once the system has a choice of this harmless avocation), Morishima provides as a technique-pre- and post-invention--concentrat- Class B theorem his useful generalization of my ing on zero-profit embodied-labor magnitudes equal-internal-compositionsufficiency condition to becomes highly dangerous (and irrelevant!) for ag- a wider "linear dependence" sufficiency condition. gregation or any other purpose. Volume I's dual I applaud this. Morishima's e coefficient is comput- regime gives outsights, not insights. able from technocratic data alone, without our ever 7. Morishima's claim, even if it were true, as detouring to a dual accounting regime of sj/vj = it is not-that zero-profit embodied-labor contents silvi = e, and without ever going beyond the pre- give better weights for aggregation purposes than Marx classical labor theory of value. But, of do prices calculated at positive interest rates that course, the ratio "surplus labour"/"necessary la- are in a nearer neighborhood of actual observed bor" = e does not equal the observable Profit systems-is better formulated and criticized by Share/Wage Share; nor will e equal observable ag- avoiding any detour to SjlVj=silvi = e > 0 analysis. gregate competitive 2Sj/l Vj, or any one industry No need to belabor these points further.' competitive Sj/ Vj,even though it is bounded by the I conclude that Baumol's writing a check on maximum and minimum of observable [Sj/ Vj]. A Morishima to reinforce his thesis leaves him over- change in capitalists' tastes toward goods of greater drawn at the bank. wage intensity will, even at unchanged profit and real wage, result in a lowering of observable a even Synthesis though e has the defect of being invariant under Let me state for dogmatic clarity what I believe such taste changes. to be the position to which, at some future date, 5. One could go on listing how Morishima's Marxian and non-Marxian economists will both findings could be, from the present viewpoint, more agree. (My pen also has a sense of humor.) usefully reformulated. Even his rare mistakes can 1. No new analytical insight is given, statically or be made to be independent of any detours. Thus, dynamically, by Marx's own novelties of theoretical on p. 142, he says "the following treatment based analysis that involve-macroeconomically or mi- on the [Morishima] true formula (12) may be croeconomically-the concept of the "rate of sur- claimed as the first rigorous proof of the law [of the plus-value," either in the form of sj/vj or of Sj/ Vj, Marxian falling rate of profit]" [8, 1973]. What Isjll vj or 2Sjl/ Vj, Morishima purports to show is this: Consider a (a) into the explanation of the distribution of "neutral" invention that enables us to replace an income between labor wages and property capital industry's labor and raw material requirements return, or [ao,and a#, for fixedj] by a new set of requirements (b) into the determination of society's general in which total labor costs [Aojin a0(I- a)-' remains profit rate (or total of profit return), or the same but which the direct labor requirements [a,] are reduced at the expense of an increase in raw I A reader who has mastered the present considerations material requirements [one or more ay]. Such an will be in a position to judge whether, in his occasional alleged increase in the organic composition of capi- stricture against my writings on Marx, Morishima has scored valid points that should cause me to recast my tal will, at the same real wage and r* level, neces- wordings. There is no point in discussing Morishima's p. sarily depress the rate of profit. So goes the asser- 6 mention that his "discussion of the transformationprob- tion. lem . . . is very different from his [Samuelson's] in its Heaven defend Marx from his defenders! The conclusions, in spite of the surprising similarity in the trap I warned against in my 1972 JEL ecumenical mathematics used . . . I [Morishima] am very much more sympathetic than he [Samuelson] is" [8, 1973]. If you reply to Lerner [15, 1972, p. 56] has sprung here. overhear two persons, saying respectively, "2 + 2 = 4 and The invention Morishima prescribes, which he calls Marx was a genius" and "2 + 2 = 4 and Marx fathered by the harmless word "neutral," is a "disimprove- an illegitimate son," you must not think that they are ment" at every positive profit rate, not an "improve- necessarily disagreeing or that you can cogently infer which one is mforesympathetic to Karl Marx! In the cited ment." It will be avoided in ruthless competition Metzler Festschrift,I have replied more specifically, albeit like the plague. It will never come into effect under briefly, to points raised by Morishima about my Marxian the new equilibrium. His rigorous proof is no proof writings [7, 1974].

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(c) into the microeconomic empirical configu- Walras for not using in 1874 the topological meth- ration of goods and prices in a system of perfect or ods von Neumann was to use in 1931 to prove imperfectcompetition (or of imperfect knowledge, existence of a general equilibrium system, I do not or of stochastic exogenous disturbance) or fault Marx-but rather praise him-for coming so (d) into the realities of the class struggle or the close in the 1860's to a correct tableau of steady- understanding of power relations between groups state and exponential-growth-equilibrium. But no and governments, internationally or nationally, or one would dream today of maintaining that Walras' (e) into the ethical nature of "exploitation" 1874 counting of equations and unknowns is as and inequality of income. good or is better than use of fixed-point theorems; 2. More concretely, I assert: likewise, I argue it is absurd, after praising Marx There is no cogent argument, in Baumol, or, for for his early efforts, to extoll his surplus-value that matter in Morishima's 200 pages of mathemat- model over the model that dominates it in every ics, or in the vast literature already surveyed on the virtue. transformation problem, that would 2. To the degree that differences in direct- (a) make one want to qualify the verdict that labor intensities are deemed minor or that their the Volumes I and II excursion into the realms of effects are macroeconomically ignorable, the "val- Sj/Vj = si/vi was anything but a detour, anything but ues" or surplus-value regime may be a useful first- at best a wasteful redundancy and at worst a digres- approximation to the "prices" or profit regime. sion that fails to "penetrate" and "lay bare," and 3. In the history of thought, we realize that "reveal"the "deceptive character" of "capitalist ac- detours may serve useful purposes. An error of counting." Newton is rightly dismissed as such by a modern All this is claimed within the paradigm of Marx- student of live physics. But to the antiquarian of ian rejection of the legitimacy of positive property dead physics, to the historian interested in the psy- income at the expense of labor wages gettng 100 per chology of discovery and innovation, errors are cent of the Net National Product. often as interesting as truths. Many seminal contri- 3. What I am arguing is this. If Baumol wishes to butions have grown out of misunderstandings. I regard the transformation problem as, not a transi- doubt that many important contributions of Marx, tion from "values" to "prices," but as a transition such as circular-flow balanced growth models, "from surplus values into. . . profits," then to un- would have been developed by him if he had not, derstand competitive distribution of income I claim for extraneous reasons, been preoccupied with his it to be equally true that what is involved is use of detour paradigms. But just as we do not burn down the eraser to rub out the irrelevant detour's unin- our houses to broil our daily chops, there is no sightful accounting system, and then the replacing reason why the admirer of Marx should go through of that system by the empirically-relevantequalized- his historic circuitous detours and redundancies. rate-of-profitbehavior equations that the economists Summary. Karl Marx did pioneering work that use who preceded Marx, who were contemporary foreshadowed a number of modern analytical mod- with him, and who have succeeded him. Marx's els of economics. He also has an important position own investigation into the trends of distribution, the in the history of ideas and in non-analytical aspects cycles of activity, and the modes of steady repro- of political economy, the social sciences, and duction and exponential growth, I am arguing here, philosophy. were hampered, not helped, by his novel rate-of- Nonetheless, a careful rereading of his claims and surplus-value analysis. those made on his behalf does not disclose cogent arguments that should impel a Marxian or non- Marxian to agree that his novel analytical innovations concerning positive equalized rates of surplus Qualifications: Are there no qualifications to this value are other than a detour to one who would rather sweeping indictment? Yes, the following: understand 19th-century or earlier-century distri- 1. The algebra of the surplus-value regime is bution of income and to one who would understand easier to handle. So, for purposes of elementary the laws of motion of any economic system. exposition and layman persuasion, there is merit in If I am wrong in my answer to this question- the Volume I models. Just as one does not criticize which has been the number one question among

This content downloaded from 193.49.18.51 on Mon, 25 Aug 2014 11:37:22 UTC All use subject to JSTOR Terms and Conditions 70 Journal of Economic Literature pro- and anti-Marx analysts from 1867 to the pres- 10. , Collected scientificpapers. Edited by J. ent day-presentation of some new and cogent ar- Stiglitz. 3 vols. Cambridge, Mass.: M.I.T. gumentation controverting my contention can dis- Press, [1965] 1972. pose of it. 11. , Economics. 9th edition. New York: McGraw-Hill, 1973. REFERENCES 12. , "Karl Marx as a Mathematical Econo- 1. BAUMOL,W. "The Transformation of Values: mist," In G. HORWICHand P. A. SAMUELSON, What Marx 'Really' Meant (An Interpreta- eds. [METZLER, LLOYD] Festschrift. Trade,sta- tion)" J. Econ. Lit., March 1974, 12(1), pp. bility and macroeconomics. New York: Aca- 5 1-62. demic Press, 1974. 2. [BOURNEUF, A.] Pathways to macroeconomics. 13. , "Marxian Economics as Economics," Festschrift. Edited by D. A. BELSLEY; E. J. Amer. Econ. Rev., May 1967, 57(2), pp. 616- KANE; P. A. SAMUELSONAND R. M. SOLOW. 623. Columbus: Ohio State University Press, forth- 14. ,"Samuelson's Reply on Marxian Mat- coming. ters'," J. Econ. Lit., March 1973, 11(1), pp. 3. EMMANUEL, A. Unequal exchange: A study of 64-68. the imperialism of trade. With additional com- 15. , "The Economics of Marx: An ments by Charles Bettelheim. Translated from Ecumenical Reply," J. Econ. Lit., March 1972, the French by BRIAN PEARCE. New York and 10(1), pp. 51-57. London: Montly Review Press, [1969] 1972. 16. , "The Optimality of Profit-Inducing 4. [HALM, GEORGE N.] Festschrift. Leading is- Prices Under Ideal Planning," Proceedings of sues in international economic policy. Essays in the National Academy of Sciences, July 1973, honor of GeorgeN. Halm. Edited by C. FRED 70(7), pp. 2109-2111. BERGSTEN and WILLIAM G. TYLER. Lexing- 17. , "The 'Transformation' from Marxian ton, Mass., Toronto and London: D. C. Heath, 'Values' to Competitive 'Prices': A Process of 1973. Rejection and Replacement," Proceedings of 5. MARX, K. Capital. A critique of political econ- the National Academy of Sciences, Sept. 1970, omy. Chicago: Charles H. Kerr and Co., 67(1), pp. 423-425. Volume I (1906); Volumes II and III (1909). 18. , "Understanding the Marxian Notion 6. MEEK,R. L. "Some Notes on the Transforma- of Exploitation: A Summary of the So-called tion Problem," Econ J., March 1956, 66, pp. Transformation Problem Between Marxian 94-107; reprinted in R. L. MEEK. Economics Values and Competitive Prices," J. Econ. Lit., and ideology and other essays; Studies in the June 1971, 9(2), pp. 399-431. development of economic thought. London: 19. , "Wages and Interest: A Modem Dis- Chapman and Hall, 1967, pp. 143-157. section of Marxian Economic Models," Amer. 7. [METZLER, LLOYD] Festschrift. Trade,stability Econ. Rev., Dec. 1957, 47, pp. 884-912; re- and macroeconomics.Edited by G. HORWICH printed in Collected scientific papers [See no. and P. A. SAMUELSON.New York: Academic 10]. Press, 1974. 20. ,AND VON WEIZSACKER,C. C. "A New 8. MORISHIMA,M. Marx's economics:a dual the- Labor Theory of Value for Rational Planning ory of value and growth. New York: Cambridge Through Use of the Bourgeois Profit Rate," University Press, 1973. Proceedings of the National Academy of 9. SAMUELSON, P. "A Modem Treatment of the Sciences, June 1971, 68, pp. 1192-1194. Ricardian Economy," in two articles, Quart.J. 21. VON WEIZSACKER, C. C. "Morishima on Econ., Feb. 1959, 73(1), pp. 1-35; May 1959, Marx." Econ. J., Dec. 1973, 83, pp. 1245- 73(2), pp. 217-231; reprinted in Collectedscien- 1254. tific papers [See no. 10].

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The FundamentalMarxian Theorem: A Reply to Samuelson

By MICHIO MORISHIMA London School of Economics

JAM happyto findthat Samuelson has no ob- I. jection to my FundamentalMarxian Theo- However,what does the criticalvalue T* stand remif it is put in the followingneutral form: [3, for?This questionis important,especially to Marx 1974,].' because his contemporariescannot swallow down Theorem:The competitiverate ofprofit R* de- the Leontiefinverse, [I - a]'. Probablythe only terminedby way to make themunderstand T* is to appeal to the labor theoryof value, as Marx does. In fact, a, (I + R*) [I -a(1 +R-)] -I m= I (1) a. [I - a]' is nothingelse but the solutionto the is positiveif and onlyif value-determinationequation, < 1. (2) a,[I -a]-'m A = A a + a,, (4) The notationis Samuelson's.2The theoremassumes and, therefore,T* equals the value of the subsist- interalia that wages are fixedat the subsistence ence commodity-bundle,AB, thatis thelabor-time level;evidently the subsistence-consumption vector socially necessaryfor producingB by the tech- per man-hourm equals the subsistence-consump- niques (a, actuallyprevailing in the economy. tion vectorper day (B in my notation)divided by a.) It is importantto emphasizethat there is no element theworking hours per day, my T Then (1) and (2) of competitivearbitrage in (4). It is no morethan can be rewritten,respectively, as the equationfor calculation of the quantitiesof la- a, (1 + R4) [I- a(1 + R)]1 BIT = 1, (1') bor sociallynecessary for producing goods. T* < T, (2') II. where In Marx, competitivearbitrage is exclusively T* = aO[I-a]-lB. (3) made in termsof prices,the wage rates and the profitsrates, not in termsof valuesand therates of Marx regardsa. and a as technologicallygiven surplusvalue at all.3If theeconomy is competitive and B as biologicallygiven; hence, T* can be cal- I culated easily. The theoremthen states that R* In Marx's economics,value calculationplays a role thatis entirelydifferent from the one whichprice calcula- which satisfies(1') is positiveif and only if T is tiondoes. Decision of individualsand firmsare all made largerthan T*. No "mysterious"concepts such as in termsof pricecalculation, while value calculationgives "value" or "exploitation"or anythingelse appear a technocraticassessment of labor requirementfor pro- in thisform of the theorem. It givesan economically duction.Marx's theoryof value shouldnot be considered as a primitiveor obsoleteprice theory. There is no point meaningfulrelationship between T and R*. in comparingtranslation of the price accountingin the value accountingor viceversa with translation of a chil- I For the FundamentalMarxian Theorem see Mori- dren's privatenursery language into ordinaryEnglish. shima [2, 1973, pp. 53-71]. Samuelson'sfootnote [3, 1974, p. 66, f. 6] is not under- 2 a. is the vectorof labor-inputcoefficients that is my standableif thisfact is clearlyrecognized. L = (LI, LI,), a the matrixof physical-inputcoefficients Also, in contrastwith Samuelson's grouping my theo- (myA = [As A]), R* theequilibrium rate of profit(my rems into classes A, B, and C, Marx would probably proposeto groupthem into the followingA', B', and C'. 7T) and m the subsistence-consumptionvector per man- Class A' includes the theoremsconcerning competitive hour (my B/1). arbitragein thecapitalist economy; B' thosethat relate the

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andthe subsistence wages prevail, the following two III. equationsmust be fulfilledin the state of equilib- Let us now assume that all T;s are equalized. rium: Then (9) is writtenas p = (1 + R*)(pa + wa0) (5) s, T-AB wT= pB. (6) v T --AB (10) Equation (5) impliesthat the rate of profitshould In viewof T* = AB, we can say thatT> T* ifand be equalized throughoutthe economyby competi- only if r* > 0. Hence by the theoremabove, the tive arbitrageamong capitalists,while (6) implies equilibriumrate of profitR * is positiveif and only thatthe hourlywage-rate, w, or the lengthof the if the uniformrate of surplusvalue r* is positive. workingday, T,should be equalizedthroughout the Thus r* is a mirror-imageof T, and the latteris economy,by competitive arbitrage among workers, consideredby Marx to be determinedby the relative becausethe wages per day are set at thesubsistence powerfulnessof capitalists and workers.Marx finds level. that the rate of profitis increasedby lengthening Once the lengthof the workingday is equalized the workingday-a view that is very consistent among jobs, thena uniformrate of surplusvalue withhis experiencein the Victorianera. is establishedthroughout the industries. This is seen in thefollowing way. Let 1ibe thelabor-input coeffi- IV. cientof industryi, i.e., the i-th elementof a., and One ofthe purposes of Marx's Capitalis to show Ti the workinghours per day in industryi. Then the productivenessof the capitalistsystem or the by definition positivenessof the von Neumannbalanced-growth Vi = 1i A B/Ti, (7) rate.To showthis we haveto findthe necessary and sufficientcondition for the augmentedinput-coeffi- Si= i-Vi, (8) cientmatrix a + aOm to satisfythe Hawkins-Simon foreach i. Hence, condition.We must,however, remember that when Marx was tacklingthis problem, Frobenius, Perron S, - 1-AB/Ti foreach i. (9) and Markov had eithernot been born or were VI A BIT, merelybabies so thathe could not use theirtheo- rems;Marx had to findhis own way. For thispur- Thereforethe ratesof surplusvalue are equalized pose he assumesthat A, (the submatrixof a con- if and only if Tis are equalized.4 cerningthe capital-goodssectors) is "productive" (thisis Marx's basic and harmlessassumption con- price-profitaccounting system to the value-surplus-value cerningtechnology); and he findsthat a + aOm is accountingsystem; and C' thoseconcerning technocratic "productive"if and onlyif (2') is satisfied.There- calculationof values of commodities.Class A' does not includethe theorems of the classical labor theory of value fore,the von Neumannequilibrium rate of growth (as a primitivecompetitive price theory) because they are is positiveif and onlyif (2') holds;in fact,it is seen valid only in the societyof "simplecommodity produc- thatthe growth rate is equal to thepositive equilib- tion" but not in the capitalistsociety; on the otherhand, riumrate of profit. class C' is not a null set. Marx writes:"This [equalizationof the rate of surplus I takethis as a first-ratecontribution. To examine value] would assume competitionamong labourersand whetherthe cruciallyimportant condition (2') is equalizationthrough their continual migration from one fulfilledor not, we calculate labor values (or sphereof production to another"[1, 1966, p. 175]. aO [I -a]-' if one does not like to call it the value In his footnote2, Samuelsonasks whetherone can rec- vector)and evaluate the commodity-bundlem in oncileequal SJ/Vj = S,/ Viwith VI/C.* VI/C,and equal Sj/(Vj + Cj) = Si/(Vi + Ci) or not (3, 1974,p. 63]. But termsof values. But thisdoes not mean at all that it is obviousthat the two inequalitiesare incompatibleif Marx accepts the theoryof value as a theoryof both are in eitherthe price accountingor in the value prices.In Marx,prices which are determinedin the accounting.Although Marx is confusedsometimes, his competitiveway are distinctfrom values which are problemis not such a trivialone. It is to show thatequal technocraticallycalculated on the basis of the pre- positives1/vj = s,/vi with vjlcj * vi/*cin thevalue regime is compatiblewith equal S/( Vj + C>) = Si/( Vi+ C1) in vailingproduction coefficients; on the contraryhe the priceregime. insiststhat the value equationsmay be takenas the

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equationsfor determining prices only in thesimple- intrinsicallyconnected with the problemsof joint commodity-productionsociety but not in the capi- productionand choice of techniques.I finallyde- talisteconomy. I am against Samuelson's view: cide to discardthe value theory,but I find,at the "The algebraof the surplus-valueregime is easier end of thebook, that the concept of "exploitation" to handle.So forpurposes of elementaryexposition may survive. and layman persuasion,there is merit in the This conclusionhas strongereffects than Sam- VolumeI models." It is truethat Marx oftencon- uelson's "erase and replace" conclusion;it should fusesvalue and price. But in reinterpretingMarx be a seriousattack on Marx. I did not know,when so thatno confusionremains (as we, non-antiquari- I finishedthe book, whetherthe Fundamental ans, do forWalras) we mustdistinguish, again as Marxian Theorem is valid or not in the general non-antiquarians,value of commodityi (ie., the modelwith durable capital goods. But I now know quantityof labor congealedin one unitof i) from thatit does holdtrue: The long-runequilibrium rate itsexchange value (or price).The formerregulates of profitR* is positiveif and only if the rate of the latter;but theydiffer from each otherin the "exploitation"is positive.This propositionis com- long-runas wellas in theshort-run, except in some pletelyindependent of the concept of value, and the specialcases. According to myinterpretation, Marx rate of exploitationis definedas I defineit at the is concernedwith the exceptionalcases in Volume end ofthe book. I have notproven this new general I first,because he may beginwith macroeconomic theoremhere because it was discussedin myWalras analysisof a one-departmentmodel by doing so, Lectureat the 1973North American meeting of the and thenhe generalizesit intotwo-or-three-depart- EconometricSociety in New York. Anyway,we mentalanalysis in Volumes II and III. That is to mayconceive of Marx withoutthe theory of value, say, I understandthat throughoutVolume I it is as long as we agreethat the FundamentalMarxian implicitlyassumed as thecondition for aggregating Theoremis the core of his economictheory. sectorsinto one departmentthat all industrieshave the same value compositionof capital,so thatval- VI. ues are strictlyproportional to prices and hence Thereremain a fewmore points on whichI want surplusvalues to profits.Then it is verynatural for to replyto Samuelson.First, I accept his criticism Marx to attackthese proportionalities in thetrans- aboutmy interpretation of Marx's law ofthe falling formationproblem as soon as he deniesthe aggrega- rateof profit.I have made a similarmistake which tioncondition and startsthe work of disaggregation has been pointedout by Okishio,one of the very in VolumesII and III. best theoristsof Marxianeconomics. It is interest- ingto see thata mistakewhich is favorableto Marx V. has been pointedout by Samuelsonand missedby So farso good. However,in theabove discussion, Okishio and a mistake which is unfavorableto as well as in thefirst thirteen chapters of mybook, Marx has been pointedout by Okishioand missed a numberof assumptions (all abouttechnology) are by Samuelson.However, I do not accept Samuel- madeso as to enableus to calculatevalues unambig- son's criticismconcerning my treatmentof the ag- uously and to assure theirpositiveness. But some gregationproblem. He saysthat I claim "thatzero- of theseassumptions turn out to be inappropriate profitembodied-labor contents give betterweights ifdurable capital goods are allowedfor. Therefore, foraggregation purposes than do pricescalculated in Chapter 14 of my book I reexaminethe theory at positiveinterest rates." But I nevermade such of value (i.e., theprogram for technocratic calcula- a propositionin my book.5Finally, in relationto tion of quantitiesof labor congealedin commodi- Samuelson'sfootnote 7 [3, 1974,p. 68], I pointout ties) and findthat unambiguousand meaningful that the theoremthat prices of commoditiesare calculationof values is notnecessarily possible once proportionalto theirvalues in thesimple-commod- joint productionand choice of techniquesare ad- ity-productioneconomy is a propositionconcerning mitted.As capitalgood i of age t + 1 appearsas the long-runequilibrium. Like the Fundamental a joint outputat theend of the processwhich uses I C. C. von Weizsackerhas made the same misunder- capital good i of age t and capitalistscan choose standing.A fulldetail of my replyon this pointis given amongprocesses which uses capitalgoods of age 0, in my "Marx's Economics: A Commenton C. C. von 1, 2, . . ., the existence of durable capital goods is Weizsacker,"Econ. J.,forthcoming.

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MarxianTheorem, it shouldnot be appliedto prof- REFERENCES its (or monopolyprofits) "which a buyeror seller acquiresthrough an accidentalstate of supplyand 1. MARX,K. Capital,Vol. III. Moscow: Progress demand,"[1, Marx, 1966, pp. 175-178,especially Publishers,1966. p. 178],so thatvon Weizsiicker's corn-wine parable 2. MORISHIMA, M. Marx's economics.London: forshowing a possibilityof existenceof a positive CambridgeUniversity Press, 1973. profitrate in theclassless society is a swingmissing 3. SAMUELSON, P. A. "Insight and Detour in the theball. Its existenceis transitorywhen all people Theoryof Exploitation:A Replyto Baumol," J. are alike.6 Econ. Lit., March 1974, 12 (1), pp. 62-70.

6 Also see my commenton von Weizsacker.

Comment

I am enormouslypuzzled by ProfessorSamuel- ing what he actuallysaid, not what we suspecthe son's reply.It is, of course, the brilliantsort of mighthave said, or should have said, or someone commentone expectsof him-but it seemsto be a else says he mighthave said. replyto an articlewhich I neverwrote. Perhaps it 3. Hence, whetheror not I have graspedany does help to explainthe source of the one faultI particularMatrix equation is totally beside the have found with Samuelson's earlierarticle-my point.Indeed, my position is immuneto anyalgebra beliefthat there he deals witha model that Marx thatmay be hurledat it. It can onlybe undermined neverused or intendedto use. by suitablequotations from Marx showingthat he Let me add severalspecific points to tryto make says the thingsI have deniedhe said. the purposeof my paper quite clear: 4. ProfessorSamuelson proposes his peace 1. I have neveraccused ProfessorSamuelson terms,which require me to admitthat for an expla- of "mathematical-economicmisconceptions" or nation of "actual wage-profitsdistribution," pre- any othererror in logic,as the readercan readily sumablyas foran explanationof actual pricingof judge forhimself. I may add parentheticallythat commodities,"the Volume I analysisis indeed a mypiece was noteven particularly directed at Sam- detour." So much I admit readily and without uelson's discussion. reservations,and I contendMarx would readily 2. I am surprisedthat "On the questionof have admittedit too, forin facthe did so repeat- whether[Marx's] purposewas successfulin some edly.2Actual pricesand actual wages,profits, rents sense or another[Samuelson] can findonly a few and interestpayments clearly were to himexplaina- relevantparagraphs in Baumol's text." I am sur- ble by the classical mechanism,3which is what he prisedbecause, so faras I know,there is no such admittedlytook over in Volume III. Marx never paragraph.'The onlyobjective of mypaper was to claimed,in facthe specificallydenied, that one gets determinewhat Marx had set out to accomplish betternumbers for any of these magnitudesfrom and how Marx believedhe had accomplishedhis a Volume I than froma Volume III analysis. objectives,because I don't thinkit is appropriate Thus, forhis part,all thatProfessor Samuelson to criticizeanyone until we are surewe are criticiz- 2 For example,he wrote". . . as forDuhring's modest objectionsto thedefinition of value,he willbe astonished I The one citationSamuelson seems to have foundto whenhe sees in Volume[III] how littlethe determination supporthis beliefthat my purpose is to judge the virtues of value 'directly'counts for in bourgeoissociety." (letter of the Marxianargument is my commentthat he and I fromMarx to Engels,January 8, 1868,quoted in Sowell are interestedmore in Volume III than in Volume I be- [3, 1967, p. 68]. cause we are bothbourgeois economists. How thisobser- 3 Of course,with one exception-theMalthusian mech- vation imputesvirtue or vice to the Marxian analysis anism for the impositionof subsistencewages, which escapes me. Marx rejectedvehemently.

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has to do to end the disagreement between us is to on history of thought. But there are some cases, admit that Marx himself was not particularly inter- albeit rare, where an author has said clearly and ested in the determination of these magnitudes, repeatedly, "I do mean A, I do not mean B," yet which he considered a surface manifestation and many people have refused to listen. Ricardo did were important to him only because he believed repeatedly say that his was a cost of production them to conceal the underlying social production model. He did say, at length, in everyedition of the relationships. Principles that quantity and durability of capital 5. I must take the occasion to apologize for a make a difference to value. I suggest to any inter- major omission from my article, my failure to give ested reader that he treat himself to a reexamination credit to Professor Thomas Sowell for two excellent of pages 3043 (from the third edition) and 52-66 discussions on Marxian economics which I have (from the first edition) of Volume I of Piero Sraffa only recently come across. While he does not deal [5, 1951] to see whether he can come away disagree- explicitly with the transformation problem, his dis- ing with Jacob Viner's (humorous?) conclusion that cussion of Marxian value theory, which is docu- "Ricardo's actual words show that from the first he mented with exquisite care, comes to conclusions held that the relative values of commodities are very similar to my own on the tautological nature always partly dependent on the relative amounts of of the value theory and on the nature of Marx' fixed capital employed in their production" (Viner's interests in the subject. Though he does sometimes italics) [6, 1930]. speak of value theory as a first approximation [3, WILLIAM J. BAUMOL 1967, p. 66] he makes it clear that Marx always considered the deviations between prices and values to be systematic [3, 1967, pp. 65-6]. I recommend REFERENCES these pieces unhesitatingly as models of Marxian 1. MARX, K. Grundrisse:Introduction to the cri- scholarship.4 tique of political economy. Translated with a One final comment. Obviously, Ricardo is not foreword by MARTIN NICKLAUS. London: Peli- easy reading,5and our predecessors did often hold can Books, 1973. a multiplicity of views among which they them- 2. SAMUELSON, P. A. "Insight and Detour in the selves were not always able to distinguish, and such Theory of Exploitation: A Reply to Baumol," J. problems are brushed aside far too often in writings Econ. Lit., March 1974, 12 (1), pp. 62-70. 3. SOWELL, T. "Marx's 'Capital'After One Hun- I Since the completion of my paper, the English transla- dred Years," Can. I Econ., Feb. 1967, 33, pp. tion of Marx' Grundrissehas become available and readers 50-74. can confirm for themselves (p. 435 ff.) Engel's report that 4. , Say's Law. Princeton: Princeton Univer- Marx had arrived at his transformation solution nearly a decade before the publication of Volume I of Capital. The sity Press, 1972, Chapter 6. manuscript that includes the pages in question is dated 5. SRAFFA, P. The worksand correspondenceof Da- mid-December 1857-22 January 1858 [1, 1973]. vid Ricardo. London: Cambridge University 5 But then, Malthus is surely even more obscure, yet we Press, 1951. do not have protracted arguments about Malthus's value theory. Clarity is not the only explanation of the absence 6. VINER, J. "Review of EDWIN CANNAN, A Re- of disputes over what (to use Samuelson's example) Wick- view of Economic Theory," Economica, N.S., sell really meant. March 1930, 28, pp. 74-84.

Rejoinder: Merlin Unclothed, A Final Word

Happily our dialectic registers didactic progress. from two formidable scholars a cogent defense of Like the truth-seeking child in Hans Christian An- Marx as having succeeded in his avowed purpose dersen's tale of the Emperor's Clothes, I ventured of revealing the secrets of profit and income deter- a riskily strong statement in the hope of provoking mination from his Volume I paradigm, in which the

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rate of surplus value is equalized industry by in- * * * dustry. The issue is a momentous one. For, proper as it Political biases of the economist can contaminate is to cast Karl Marx in the role of Prometheus, so the search for truth in this imperfect world. Hence, too did he aspire to the role of a Merlin, who reveals as a check on the degree to which my biases may the mysteries below the surface of things that can- have infected and contaminated my analysis's ob- not yield to conventional political economy. jectivity, I think it will be of interest that, just as There is a school in the history of science whose Baumol by serendipity found fascinating letters of practitionersare concerned primarily with how ear- Marx and Engels in a lower-Manhattan ashcan, by lier scientists perceived their own problems. In similar happy chance I came upon the following caricature,we can say it is all one to them whether answer to what I have called the Number One Prob- Newton wrote on gravitation, alchemy, or the Se- lem by America's leading Leftist, Thorstein Veblen. cret of the Number of the Beast in Deuteronomy. Joseph Dorfman recently unearthed this 1895 They would never dream of grading earlier writers item,2written, it is interesting to note, before Bbhm- for error or fruitfulness. To look back so on earlier Bawerk's critique and while Thorstein Veblen was writers is, I believe, to look down on them as hope- serving as the underpaid sub-editor of the Journal lessly handicapped Neanderthals who lacked our of Political Economy: advantages. I begrudge no one his pastime. But, in the realm of cumulative knowledge, I believe there is a place laborin a collectiveor socialdivision for what be called History of Science. involvingproductive might Whig of labor. A would In it we scholars the of Sraffian,Clarkian, neo-Walrasian, pay past compliment judg- merelybe reposingthe problemof how inventions,thrift, ing how their works contributed (algebraic) value- compositionof demand,and relativefactor supplies alter added to the collective house of knowledge. Eco- (1) the R* profitrate, by askinghow these factorsalter nomics, I know, is not a hard natural science. Still (2) the now-trivially-relatedrate of surplusvalue r*. I have it valuable to treat Marx not as an Cf. also the excellentE. Wolfstetter"Surplus Labour, thought LabourCosts and Marx'sLabour historic Synchronized Theory deity or oddity, but rather to appraise his of Value"[3, 1973].This affirms the truththat, for norma- arguments on the transformation problem in the tive purposesunder socialist planning or Pareto-optimal way a journal referee would treat any serious con- marketexchanges, it is pricestableaux not valuestableaux tributor. If it had been the case that Professors Bau- that are relevantwhen they differ.On p. 799 this also makes the of Morishima's in his mol and Morishima had been able to the point (10) Replythat, supply withinthe valuestableau there is a commonSj/Vj that can demonstration I puzzled over-that the prices tab- be interpretedas the fractionof labornot workedfor the leau of the observed world can be understood only subsistencewage itself. But one is left with no interestin (or, even better) after the novel values tableau of this once he has graspedthe "neutral"technocratic theo- Marx has been mastered-I would have rem: ao [I - a]-'m < 1 implies and is implied by R* regarded in a0 + a + = 1. that as an for positive (1 R*) [I- (1 R*)]-'m Similarly, important finding modern-day politi- withvon Weizsicker,let laborgrow like Lo (1 + g)',work- cal economy. But, alas, apparently the challenge ers' consumptionslike Lom(1 + g)'. Then this will be must still stand.' feasibleonly if the following"neutral" theorem applies: ao (1 + - a + < if and if R* > ' g) [I (1 g)]-'m 1, only g Readingrecent works by two otherauthors worthy of providesa root for ao(1 + R*) [I - a (1 + R*)]-'m = 1. respectand just evaluation,I must recordno reasonto I acceptMorishima's correction that in his bookhe did modify my thesis. Cf. M. Dobb, Theories of value and say that actualprice weights might serve for aggregation distribution since Adam Smith, Ch. 6 on Marx [1, 1973]. as well as valueweights. I reproachmyself for not having To illustratefor Dobb'sreaders the crucialanalytic point, made this clear. But of course this only reinforcesmy suppose(as is possible)that equalorganic composition of pointabout the dispensabilityof ci + vl+ r*v,tableaux in capitaldoes happento obtainin the realworld. Then the comparisonwith C, + Vj+ R* (Cy+ V) tableaux. transformationproblem is agreedby all to be trivially 2 Thatthis was not a momentaryaberration from Veb- simple,and indeed hardly necessary. In thatcase my need len's view will appearfrom a close readingof his famous to objectto a valuestableau as a digressionfrom under- 1906essays in the Quart.J. Econ.,"The Socialist Econom- standingof the actualprices plateau evaporates. But one ics of Karl Marx,I, II." Cf. relevantVeblen passages of is still left, even in this case, with no new insights,stati- 1893, 1895, 1897, and 1922 in Dorfman's Thorstein cally or dynamically,in the distributionof incomeor the Veblen: Essays, reviews and reports-Previously uncol- shareof wagesby Marx'sinnovations concerning rates of lectedwritings at pp. 419, 2634 and 444-5, 462, 241 [2, surplusvalue, commodity fetishism, modes of production 1973].

This content downloaded from 193.49.18.51 on Mon, 25 Aug 2014 11:37:45 UTC All use subject to JSTOR Terms and Conditions Colloquium: On Marx, the TransformationProblem 77

Among the surprises of economic literature is the The full extent of the relation between "surplus- fate that has overtaken Karl Marx's theory of sur- value" and "profits" is this (and even this suffers plus-value in the third volume of his Kapital, lately material qualification in the course of the discus- published. Advocates, expositors and critics of the sion), that the aggregate profits in any industrial Marxianeconomics have exercised their ingenuity in community at any given time may also be styled futile attempts to reconcile that theory with obvious "aggregate surplus-value." The rate of surplus-value facts, while its author has put them off with the bears no tangible relation to the rate of profits. The assurance that the whole mystery would be ex- two vary quite independently of one another. Nor plained and made right in the Third Book of his does the aggregate profits in any concrete case, in work. In the mean time the Marxian dogma of sur- any given industry or enterprise, depend on or coin- plus-value has served the present generation of cide in magnitude with the aggregate surplus-value "scientific" socialists as their fundamental "scien- produced in that industry or enterprise. For all use- tific" principle and the keynote of their criticism of ful purposes the entire surplus-value theory is virtu- existing industrial relations, and its acceptance (on ally avowed to be meaningless lumber [2, Dorfman, faith) by the body of socialists, avowed and una- 1973, pp. 263-264]. vowed, has contributed not a little to the viciousness PAUL A. SAMUELSON of their attack on the existing order of things. And with now, after the theory, accepted literally and full REFERENCES naivete, has done service for a generation as the most redoubtedengine of socialist propaganda,the "Third 1. DOBB, M. Theories of value and distribution Book" comes along and explains with great elabora- since Adam Smith: Ideology and economic the- tion, in the course of some 200 pages, that the whole ory. New York and London: Cambridge Univer- of that jaunty structure is to be understood in a sity Press, 1973. Pickwickian sense. It appears now that the need 2. DORFMAN, J., ed. Thorstein Veblen:Essays, re- which has been felt for some reconciliation of this views and reports-Previously uncollected writ- of the rate of with theory surplus-value the everyday ings. Clifton, N.J.: Augustus M. Kelley, 1973. facts of the rate of profits is due simply to a crude 3. WOLFSTETTER, E. "Surplus Labour, Synchro- and gratuitous misapplication of the Marxian doc- trine of surplus-valueto a question with which it has nised Labour Costs and Marx's Labour Theory nothing to do. That theory has none but the most of Value," Econ. J., Sept. 1973, 83 (331), pp. remote and intangible relation to any concrete facts. 787-809.

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