On the ‘Origins’ of Sraffa’s Production Equations: A Reply to de Vivo

In this rejoinder to de Vivo’s comment on Gehrke and Kurz (2018, ‘Sraffa’s constructive and interpretive work, and Marx.’ Review of Political Economy) we first ask what could possibly be meant by seeking to identify the ‘origins’ of Sraffa’s production equations. We then show that in his comment de Vivo has abandoned his original view, according to which the magnitudes in Sraffa’s ‘first equations’ are to be interpreted in Marxian (labour) value terms, without advising the reader. In addition, we show that his ‘new’ view is not supported by evidence from Sraffa’s papers. De Vivo misconstrues several propositions of Sraffa and misunderstands his ‘reduction method’ by means of which the values of commodities are reduced to some basic product or to labour. The criticisms de Vivo levels at the interpretation advocated by us are without any foundation.     

Reply to Gehrke

This paper responds to Christian Gehrke's comment, and argues that the main conclusion of my earlier paper is sustained—that, contrary to Sraffa, Marx did not ‘adopt’ in any sense of the word the joint product method of treating fixed capital. It agrees with Gehrke that Torrens adopted a form of the joint product method, and that Malthus seems to have followed Torrens in this regard. However, it argues that Ricardo did not adopt the joint product method, not even in the one instance cited by Sraffa. Finally, it argues briefly that Marx's ‘transformation of value’ method of treating fixed capital and depreciation is superior to Sraffa's joint product method.     

Report card on Sraffa at 100

Sraffa is lauded for (a) his magnificent editing of Ricardo's writings and (b) his 1960 classic on Production of Commodities by Means of Commodities. Regretted is the shortfall from his unlimited potential to his sparse bibliography of publications and oral lecturing, and his diffidence as an editor to interpret and criticize his classical heroes. Admired by Keynes and Wittgenstein and friend to the Marxist Antonio Gramsci, Piero was a much loved character. Because of, and not in spite of, the fact that he early lacked sympathy for the general equilibrium methodology and the mixed-economy ideology that dominated twentieth century mainstream economics, Sraffa was able to uniquely add value to the corpus of economic science.     

Political aspects of the capital controversies and capitalist crises

The Cambridge controversies about the theory of capital were ultimately underpinned by a clash between two different visions of capitalism, the neoclassical view, according to which distribution depends on the supply and demand curves of capital and labor, and the post Keynesian view, according to which distribution depends on political and institutional factors instead. I shall argue that the distinction between “meritocratic capitalism” and “patrimonial capitalism,” which underpins the discussions surrounding Thomas Piketty’s Capital in the Twenty-First Century, is also connected to those two different visions of capitalism, which were behind the Cambridge controversies. These two visions of capitalism have important implications for our understanding of political power over workers, and also to our understanding of political power over land and its natural resources. The role of land and natural resources was not discussed in the Cambridge controversies, but is addressed in Piero Sraffa’s Production of Commodities, and is implied in Piketty’s inclusion of land in his definition of capital, which brings in a geographical dimension to our understanding of capitalism and capitalist crises, as I shall argue.     

A Sraffian interpretation of classical monetary controversies

Abstract

The aim of this paper is to explore the contrasting views of inflation, exchange rate misalignments and determinants of gold flows held by different branches of the classical school during the first half of the nineteenth century. The properties of money neutrality and money endogeneity within the classical system are studied by reinterpreting these controversies through the analytical framework of the surplus approach as reconstructed by Sraffa [Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press, 1960] and his followers.     

Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula

In a recent paper Samuelson and Etula claim to have providedthree examples of the presence of a constant returns to scaleassumption in Sraffa's Production of Commodities. The presentpaper is a refutation of their interpretation of Sraffa's propositions.It shows that they mistakenly take Sraffa's logical propositionsfor empirical propositions. This article also provides evidenceto refute Samuelson's hypothesis that Sraffa consistently confusedthe concept of Marshallian "constant cost" with the generalequilibrium concept of "constant returns to scale". The paperalso argues that Sraffa's prices are not necessarily "equilibrium"prices, and that it is not true that Sraffa maintained thatchanges in demand had no impact on prices; his position appearsrather to be that the impact of demand on prices is unpredictable.     

Sraffa’s Constructive and Interpretive Work,and Marx

ABSTRACT

This article provides a summary account of Piero Sraffa’s constructive and interpretive work on the classical approach to the theory of value and distribution and its relationship with Marx’s contributions. It is shown that in the early phase of his constructive work Sraffa developed his equation systems by adopting a ‘physical real cost’ approach and a strictly objectivist point of view, and completely eschewed Marx’s labour-based approach and the related Marxian concepts. Only at a later stage did he explore systematically the relationship between his own modern re-formulation of the surplus approach to the theory of value and distribution and Marx’s contribution. He considered Marx’s most important analytical contribution to the further development of the surplus approach to consist of the re-integration of circular production relations, which allowed him to see the existence of a maximum rate of profits and its role in an analysis of accumulation and technical change.     

Marx,Sraffa, and Surplus: Observations Prompted by Garegnani (2018)

ABSTRACT

In a posthumously published article, Pierangelo Garegnani (2018. ‘On the Labour Theory of Value in Marx and in the Marxist Tradition.’) depicts Marx’s project in Capital as that of ‘developing systematically the theory of Ricardo and [the] implications of social conflict’ implied by Ricardo’s ‘surplus approach to value and distribution’. This paper argues to the contrary that Marx’s theory of surplus value and exploitation differs from (neo-)Ricardian surplus theory in fundamental ways, and modifies Garegnani’s simple Sraffian model to illustrate the distinctive implications of Marx’s theory.     

Use values and exchange values in Marx’s extended reproduction schemes

Abstract

Marx-Engels’ numerical illustrations of the extended reproduction suggest that a two-sector economy reaches a balanced growth path, from the second period onwards. We explain this surprising result and show that for technical reasons, disproportions between sectors can prevent the system from reproducing itself. But, in Marx’s reproduction schemes, such a crisis is not only due to purely technical factors and one must wonder what role is played by the relative price in the reproduction of the system. The answer is given by comparing two models having a similar structure but quite different rules for the determination of the relative price. In Marx’s model, the price is given by the labour values and thus, it is exogenously fixed. We contrast Marx’s analysis with an endogenous price model in which the price depends on the conditions of the accumulation of capital. The Appendices point out the complete accordance of Engels’ corrections with Marx’s model and Marx’s unfruitful quest for a balanced growth path as a tool for the analysis of crises.     

The equations unveiled: Sraffa's price equations in the making

In the first part of Production of Commodities by Means of Commodities,four equation systems are introduced: three are drawn up inorder to solve the problem of relative prices; the last oneis devised to define a suitable standard of prices. The bookwas published in 1960, but—as we are told in the preface—its‘central propositions’ and a first version of theprice equations had been originally conceived and written morethan 30 years before, when the author was still in his twenties.Having access now to the Sraffa Papers, preserved in the WrenLibrary, we can ascertain the intellectual origin of the equations.In this paper the analytical path that led to the final draftof the price equation is followed, step by step, and the linkbetween these equations and Sraffa's quest for an ‘invariablestandard of value’ is clarified.     

Joan Robinson and the three cambridge revolutions

Joan Robinson's association with three Cambridge ‘revolutions’—imperfect competition, effective demand and capital theory—is examined in the context of her personal and intellectual partnership with Richard Kahn, John Maynard Keynes and Piero Sraffa. Initially, imperfect competition appeared to have successfully extended marginal analysis to all market forms. It also allowed Richard Kahn and Joan Robinson to persuade Keynes to present the main argument of The General Theory in terms of aggregate demand and aggregate supply. By the early 1950s, however, Joan Robinson had rejected the Marshallian methodology and had become a strenuous censor of neoclassical theory. In this paper the origin of her critique is traced to her reading of Sraffa's Introduction to Ricardo's Principles.     

Sraffa's path to Production of Commodities by Means of Commodities. An interpretation

The present article provides a reconstruction of the path followedby Sraffa in the long journey (begun in the late 1920s) whichbrought him to his 1960 book. The starting point of Sraffa'sresearch was the formulation of his cost-price equations, whichsurprisingly enough appear to have been derived neither fromRicardo's theory of value, nor from Marx's ‘transformationof values into prices of production’, but rather fromMarx's reproduction schemes, published in volume II of Capital,to which Sraffa was almost certainly brought by his study ofMarx's interpretation of Physiocratic theory in volume I ofTheories of Surplus Value. The main device that Sraffa usedin his attempts to bring to light the existence of solutionsto his system and their properties, which basically meant buildinga consistent wage–profit–price relationship, wasthat of somehow cutting out the prices from this relationship.The paper shows that different routes were attempted by Sraffato achieve this end, and that the main influences on these attemptswere Ricardo and Marx, in particular Ricardo's corn-ratio theoryof profits, and the related conception of a maximum rate ofprofits. In the course of his research, Sraffa was helped bysome distinguished mathematicians, in particular Frank P. Ramseyand Abram S. Besicovitch. Of Ramsey's contribution there areimportant traces, but no more than traces, while ample recordsremain of the relationship between Sraffa and Besicovitch, andthey will play an important part in the story told in this paper.     

Sraffa,Okun, and the theory of the imperfectly competitive firm

Piero Sraffa's Production of Commodities by Means of Commodities is wedded to Arthur Okun's Prices and Quantities to bring out important implications for the theory of the imperfectly competitive firm. The implications relate to firm objectives and to firm behavior in both the ‘vertical’ environment (relations with suppliers) and the ‘horizontal’ environment (relations with customers and competitors).     

Explaining the aggregate price level with Keynes's principle of effective demand

The mainstream view of Keynes's principle of effective demand is that it states something about quantities—and about quantities only. The principle is held to determine the levels of output and employment in a world not governed by Say's law. This paper argues that the principle of effective demand goes beyond this to explain not only ‘real’ activity levels but also the aggregate price level. A variant of the post-Keynesian D/Z-model is brought together with Marxian reproduction schemes to derive this result.     

The Monetization of Profits in a Monetary Circuit Framework

Abstract

This paper offers an explanation of the realization of profits in money. Following Edward Nell's lead, we place Marx's spheres of production and circulation at the centre of the analysis. Production is represented à la Sraffa–von Neumann while circulation is analysed following the basic insights of the Franco-Italian theory of the monetary circuit. Once production has taken place, money is created by banks ex nihilo and then circulates through certain channels allowing the reproduction of the system and monetizing profits plus the payment of interest on long-term debts within one single circuit. The novelty of our approach lies in the treatment of the financing of investment in fixed capacity.     

Marx and Ricardo on machinery: a critical note

This article critically discusses the important and relevant—not to mention controversial— views of Ricardo and Marx on the impact of machinery on labor productivity, the organization of production and the wages and employment prospects of the working class during the capitalism of their day. First, the article turns to Ricardo’s assessment of the introduction of machinery and its likely effects on the laborer and the rate of profit and accumulation—one which went through a substantial revision (and reversal) between the first and third editions of his Principles of Political Economy and Taxation. Then, we discuss Marx’s own critical analysis of the historical development of machinery and its impact on the labor process, the so-called “compensation principle,” and how the rising organic composition of capital ostensibly generates a “redundant or surplus-population” during the course of capitalist development. We highlight Marx’s intellectual debt to Ricardo, John Barton (and George Ramsay) insofar as his theory of technological unemployment is concerned. Lastly, the article summarizes the views of Ricardo and Marx and offers some concluding remarks.     

The so-called “transformation problem” revisited: A comment

This comment shows that Lipietz's Marxist transformation theorem represents but a simple, though useful reinterpretation of obvious mathematical consequences of a standard Sraffa model—by making appropriate use of its known degree of freedom. Labor values are not involved in this new interpretation of conventional prices of production. A proposal is therefore made how their role in Marx's transformation may be investigated further on the basis of Lipietz's theorem and its interpretation of the “value of labor power”.