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.

KEYWORDS:

• Karl Marx
• Piero Sraffa
• labour theory of value
• profit rate
• surplus approach

JEL CODES:

• B12
• B14
• B24
• B51

1. Introduction

The publication of Sraffa’s Production of Commodities by Means of Commodities (1960) has been a landmark in the appraisal of Marx’s contribution to economic theory. Sraffa demonstrated that relative prices and the rate of profits are fully determined in terms of the technical conditions of production and the real wage rate; that is, the objective data underlying the approach of the classical economists and Marx. Labour values are derived magnitudes providing no additional information, and are therefore redundant.

With the opening of Sraffa’s papers in the Wren Library at Trinity College, Cambridge, it has become possible to study in detail the development of his interpretive and constructive work culminating in the Production of Commodities by Means of Commodities. The picture that emerges from Sraffa’s papers with regard to the relationship of his own work to Marx’s contribution to economic theory turns out to be both clear and straightforward and more complicated than might have been expected. Sraffa clearly regarded Marx as: (i) an author who had rediscovered the surplus approach to the theory of value and distribution, had reconstructed its analytical structure and historical development and had sought to elaborate on it; and (ii) an economic theorist firmly rooted in the surplus approach tradition who had made important analytical contributions to its further development, thus carrying it beyond the state in which it had been left by Ricardo.

At the same time, however, the picture is also more complicated, because at the beginning of his interpretive and constructive work, which can be dated to the second half of 1927, Sraffa considered it necessary to put Marx’s and Ricardo’s labour-based approach to the theory of value and distribution to one side, and to work out his systems of equations by elaborating on the physical real cost approach which he had encountered in their precursors, in particular William Petty and the French Physiocrats. During the entire first period of his constructive work, which extended roughly from the second half of 1927 to the end of 1931, Sraffa completely eschewed Marx’s labour-based reasoning and concepts, and for quite some time, in fact well into 1929, he was convinced that ‘labour’ must not enter as a quantity at all into his (Sraffa’s) production equations. It is only at the beginning of the 1940s, and then more intensively during the second period of his constructive work, extending mainly from 1942 to 1946, that one encounters clear expressions of a change in Sraffa’s critical attitude towards the labour theory of value and in his critical assessment of the usefulness of Marx’s labour-based concepts. The reason for this was that he saw that Marx had re-captured the circularity aspect of social production (which had to some extent got lost in Smith and Ricardo), and had been struggling with problems similar to those he himself was addressing, and how Marx had tried to cope with them in terms of his labour-based reasoning.

In our reading, Sraffa’s appreciation of Marx’s achievements developed in close relation to his own constructive work, and was undergoing considerable change over time.¹ Hence, in the following sections of this article we provide a brief reconstruction of the development of Sraffa’s thought, with particular emphasis on its relation to his appraisal of Marx’s contributions.²

2. Physical real cost and simultaneous equations

Sraffa’s work on the reconstruction and modern reformulation of the classical approach to the theory of value and distribution emanated from notes that he composed in the summer of 1927 in preparation for his ‘Lectures on Advanced Theory of Value’, which he was supposed to give at the University of Cambridge beginning in October (but which were then postponed for a year and held from 1928–1931). As early as the end of 1927 Sraffa, in one of his notes, referred to ‘mia teoria [my theory]’ and the ‘libro [book]’ he intended to write (D3/12/11, p. 55). Sraffa’s papers show that the years from 1927 to 1931 were the period in which he laid the foundations of his book. It was then that he saw the distinctive character of ‘the standpoint of the old classical economists’ (Sraffa 1960, p. v) in the theory of value and distribution and it became clear to him that it was not just an early and somewhat crude version of Marshall’s theory.³

Sraffa was impressed by the classical authors’ explanation of all incomes other than wages in strictly objective terms on the basis of the social surplus product that obtains after all means of production and all means of subsistence in support of workers have been deducted from given outputs. According to Sraffa, this method had found a particularly clear expression in a passage in Petty’s Political Arithmetick in which Petty advocated the ‘“physician’s” outlook’, which implied expressing himself exclusively

in Terms of Number, Weight or Measure; to use only arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature; leaving those that depend upon the mutable Minds, Opinions, Appetites, and Passions of particular Men, to the Consideration of others.’ ([1899] 1986, Vol. I, p. 244; quoted by Sraffa in D3/12/4, p. 3, original emphasis)

Petty’s physicalist or natural science point of view, which explicitly eschews subjectivist notions, Sraffa also encountered in other classical authors. Even more physicalist in character is Mill’s (1826, p. 165) dictum: ‘The agents of production are the commodities themselves … They are the food of the labourer, the tools and machines with which he works, and the raw materials which he works upon.’ Sraffa in the early period fully endorsed the objectivist methodology advocated by Petty, which he regarded also to be in accordance with the methodological imperatives of modern science, as can be seen from his annotations in and excerpts from contemporary books on modern physics by Planck, Heisenberg and others.⁴

Against Marshall’s concept of ‘real cost’, which referred to magnitudes that are not directly observable and not measurable, Sraffa therefore put that of physical real cost (see the evidence collected in folder D3/12/42, pp. 33–56).⁵ Marshall had conceived of the ‘real cost’ of a commodity as ‘the exertions of all the different kinds of labour that are directly and indirectly involved in making it; together with the abstinences or rather the waitings required for saving the capital used in making it’ ([1890] 1977, p. 282). While Petty and the Physiocrats focused on the commodities actually consumed or ‘destroyed’ in the production of some other commodities, that is, on physical amounts of things, the notion of ‘real cost’ introduced by Marshall invoked disutility, pain and abstinence experienced by agents, that is, psychic elements. Sraffa firmly rejected Marshall’s subjectivist notion of ‘real cost’ and stressed: ‘The sort of “costs” which determines values is the collection of material things used up in production’ (D3/12/7, p. 106). As to labour, Sraffa sided with Petty, who had insisted that what matters are the means of subsistence in support of the workers or, for short, ‘bread’ or ‘food’—not labour.⁶

From November 1927 Sraffa began to elaborate his equations of production, first for a system without a surplus (‘first equations’), then for one with a surplus (‘second equations’). For example, in a document composed in the winter of 1927 to 1928, Sraffa stated:

No surplus —

These are homogeneous linear equations. They have infinite sets of solutions, but the solutions of each set are proportional. These proportions are univoche [unique].

These proportions we call ratios of Absolute values. They are purely numerical relations between the things A, B … They are not necessarily the ratios, in which exchange will actually take place in any community in which the quantities of things respectively used in production (i.e. consumed) and produced satisfy those equations: such actual ratios of exchange are also conditioned by such things as legal institutions, etc. which vary in different organisations of society and which are ‘arbitrary’, i.e. irrelevant, from our present point of view. (D3/12/5, p. 2, emphasis added)

Sraffa apparently interpreted these equalities in two ways. First, he saw them as the tabulation of production processes with A, B, and C as gross outputs of three commodities and , , and as the amounts of the three commodities used up in the production of the respective gross outputs . Second, he appears to have interpreted them as equations, although there are no unknowns for which a unique solution (except for a proportionality factor) could be found. Yet, in the following months he wrote down systems of his first equations in which he explicitly used two letters for each quantity, one expressing the amount of units of the commodity and the other its value (or price) (see, for example, the system of equations in D3/12/6, p. 18). As Sraffa stressed, the important result of his inquiry was that relative prices are fully determined by solving a set of simultaneous equations in which only objective data describing the social production process mattered as proximate determinants.

Sraffa swiftly also saw that, in the case of his first equations, it was possible to ‘reduce’ the value of a commodity to the amounts of some other commodity needed directly and indirectly in its production (see D3/12/7, pp. 30–31). Therefore, the exchange ratios of any two commodities may be conceived as reflecting the relative amounts of any one of the commodities in the system used up, directly and indirectly, in the production of one unit of the two commodities under consideration. It thus became obvious to him that, once the problem was approached from a rigorous physical real cost point of view, the notion of a ‘common measure’ loses much of the appeal it had in the earlier authors, including Marx.

From the end of November 1927 Sraffa also wrote down equations with a surplus, in which , and at least one inequality is a strong one. These he called his ‘second equations’, which can be seen as a direct extension of the ‘first equations’:

Here, v_j is the value of commodity j , commodity c serving as standard of value , and r is the interest factor (1 + interest rate).⁷

When Sraffa showed this equation system to Frank Ramsey, his mathematical friend reformulated the system of homogeneous linear equations by first putting it into its canonical form and then by setting the determinant of the coefficients equal to zero in order to obtain a non-trivial solution. This was sufficient for him to see that there are solutions for the v_i’s and r for any number of equations; that is, processes and therefore commodities. Hence relative prices and the (competitive, that is, uniform) rate of interest (or profits) can be determined exclusively in terms of physical data.⁸

3. Sraffa’s critical stance towards the labour theory of value

From scrutinizing the contributions of the earlier classical authors, most notably Petty, Cantillon and Quesnay, Sraffa concluded that the adoption of the labour theory of value by the later writers had involved a ‘corruption’ of the surplus approach. In a note entitled ‘Degeneration of cost and value’, probably written in November 1927, he insisted: ‘A. Smith and Ricardo and Marx indeed began to corrupt the old idea of cost—, from food to labour. But their notion was still near enough to be in many cases equivalent’ (D3/12/4, p. 2(1)). He expounded:

The fatal error of Smith, Ricardo, Marx has been to regard ‘labour’ as a quantity, to be measured in hours or in kilowatts of human energy, and thus commensurate to value. … All trouble seems to have been caused by small initial errors, which have cumulated in deductions (e.g. food of worker = quantity of labour, is nearly true). Petty had foreseen the possibility of being misunderstood (D3/12/11, p. 36; similarly D3/12/4, p. 4)

In this early phase, which extended well into 1929, Sraffa was strictly opposed to employing the concept of labour as a ‘quantity’ in his equations. In an illuminating document stemming from November 1927, he insisted:

It is the whole process of production that must be called ‘human labour’, and thus causes all product and all value. Marx and Ricardo used ‘labour’ in two different senses: the above, and that of one of the factors of production (‘hours of labour’ or ‘quantity of labour’ has a meaning only in the latter sense). It is by confusing the two senses that they got mixed up and said that value is proportional to quantity of labour (in second sense) whereas they ought to have said that it is due to human labour (in first sense: a non measurable quantity, or rather not a quantity at all).⁹ (D3/12/11, p. 64; emphasis added)

Sraffa’s critical stance at the beginning of his constructive work towards using the concept of labour in the second sense is documented in several notes and manuscripts composed in the late 1920s, and in annotations in his books.

According to Sraffa, Petty and the Physiocrats not only had the right notion of cost; they also advocated a view of production that was congenial to modern industrial societies. They envisaged production as a circular flow rather than, as is the case in the ‘Austrian’ view of production, prominently advocated by Eugen von Böhm-Bawerk, as a one-way avenue leading from the services of original factors of production via a finite number of stages to consumption goods. However, as Sraffa noted, when ‘commodities are produced by commodities … the idea that the process of production has a beginning and an end [must be replaced] with that that it is a circular one—an idea first introduced by the Tableau économique’ (D3/12/7, p. 2). Sraffa paid tribute to François Quesnay’s ingenious analytical expression of the circular flow idea in terms of his Tableau Économique by equating his equations with it (see D3/12/16, p. 7).¹⁰

Why, then, had the classical economists and Marx failed to elaborate a consistent theory of value and distribution on the basis of (i) production viewed as a circular flow and (ii) the twin concepts of physical real costs and social surplus? In Sraffa’s view, the main reason derived from a mismatch between the analytical concepts and the (mathematical) tools at their disposal. More specifically, as Sraffa had demonstrated with his first and second equations, the tool needed to bring to fruition both conceptual elements (i) and (ii) were simultaneous equations and the knowledge of what their properties are and how to solve them. As Sraffa stressed in a document written in all probability in late 1927 or early 1928, the role of physical real costs in determining value is ‘seen only in general equilibrium’ (D3/12/42, p. 46).¹¹ The indispensable tool—simultaneous equations—alas, was not at the disposal of the classical authors and Marx, who therefore tried to solve the problems in a roundabout way, typically by first identifying some ‘ultimate measure of value’ by means of which heterogeneous commodities were meant to be rendered homogeneous. Several authors, including Smith, Ricardo and Marx, had taken ‘labour’ to be the sought standard and therefore arrived at some version of the labour theory of value. However, the route via labour values was not really a way out of the impasse: commodities are produced by means of commodities and therefore the quantities of labour embodied in them cannot be determined, except in special cases, other than from simultaneous equations.¹²

3.1. Tertium comparationis

Sraffa variously contemplated the problem of the ‘common third’—that is, the problem of whether qualitatively different commodities could be said to represent equal or different quantities of the same substance—by discussing the statement in a famous fragment of Heraclitus, quoted by Marx in Volume I of Capital (see Marx 1954, p. 107 n.), whose English translation reads: ‘All things are exchanged for fire, and fire for all things, as goods for gold and gold for goods’. In a note written in the Lent term of 1928, Sraffa suggested that ‘electricity’ might be substituted for ‘fire’ as the ‘common third’ or ‘substance’.¹³ A possible explanation for this suggestion is that, in modern times, electricity is an input in each and every commodity and that, in particular circumstances, there may be exchange ratios of commodities that are proportional to the relative overall amounts of electricity ‘embodied’ in the various commodities. Or perhaps Sraffa’s reference to ‘electricity’ derived from his reading of some contemporary books on modern physics. Max Planck, in The Universe in the Light of Modern Physics, stated:

If we compare the old theory with the new, we find that the process of tracing back all qualitative distinctions to quantitative distinctions has been advanced very considerably … According to the modern view, there are no more than two ultimate substances, namely positive and negative electricity. (1931, p. 16, emphasis added)

Interestingly, in his personal copy of the book Sraffa had annotated these statements.

3.2. Doing away with ‘human energy’

Another objection to the labour theory of value may also be related to Sraffa’s reading of books devoted to the natural sciences and methodological issues. For example, he had carefully studied and annotated Poincaré’s La Science et l’Hypothèse (1902), especially the chapter ‘Énergie et Thermodynamique’, and from these and annotations in other books we may infer that he believed economists must not ignore the laws of physics, chemistry and biology.¹⁴ According to Sraffa, this request spoke in favour of the physical real cost approach and against the labour-based approach:

The difference between the ‘physical real costs’ and the Ricardo–Marxian theory of ‘labour costs’ is that the first does, and the latter does not, include in them the natural resources that are used up in the course of production (such as coal, iron, exaustion [sic] of land) [Air, water, etc. are not used up: as there is an unlimited supply, no subtraction can be made from ∞.] This [is] fundamental because it does away with ‘human energy’ and such metaphysical things.¹⁵ (D3/12/42, p. 33, emphasis added)

3.3. A ‘purely mystical conception’

Closely related to the above is Sraffa’s opposition to the view typically held by advocates of the labour theory of value, according to which the wage labour of human beings must be singled out, to the exclusion of other kinds of labour, when dealing with the problem of value. As Sraffa noted, this view was not restricted to such authors as Ricardo and Marx, but was encountered also in Edgeworth or Marshall (see D3/12/42, p. 36). In fact, a ‘key note’ of Marshall’s Principles was ‘that free human beings are not brought up to their work on the same principles as a machine, a horse, or a slave’ ([1890] 1977, p. 504). Sraffa objected in a note composed between May and July 1928:

There appears to be no objective difference between the labour of a wage earner and that of a slave; of a slave and of a horse; of a horse and of a machine; … It is a purely mystical conception that attributes to human labour a special gift of determining value. Does the capitalist entrepreneur, who is the real ‘subject’ of valuation and exchange, make a great difference whether he employs men or animals? Does the slave owner? (D3/12/9, p. 89, emphasis added)

Sraffa’s argument echoes an observation by McCulloch that had been criticized by Marx in the Histoire (1925, Vol. VII, pp. 22, 24). Sraffa did not agree with the criticism. In his own index of the volume, he stressed: ‘Sbagliata critica c.[ontra] McCulloch [Mistaken criticism of McCulloch] 22, 24.’ He also noted: ‘Smith appelle un boef [sic] un ouvrier productif [Smith calls an ox a productive worker] 23’, which Sraffa considered to be the correct view (and a remnant of the earlier physical real cost approach in Smith’s Wealth).

3.4. The ‘historical’ labour theory of value

Sraffa also reconsidered the view, which had been put forward by several authors, including Smith, McCulloch, Torrens and Engels, that the labour theory of value holds in primitive societies. At the end of the 1920s he consulted contemporary contributions to economic history, anthropology and ethnology and annotated inter alia passages dealing with the historical interpretation of the theory. In Bücher (1910), Sraffa read that ‘labour among primitive peoples is something very ill-defined’ (see D3/129, p. 50); in Eldridge (1923, pp. 21, 22, 42) that ‘in India waiting is a rule’; that ‘time is immaterial where price is concerned’; and that ‘not labour-saving but material-saving devices of modern industry have the greatest vogue in China’ (see D3/12/10, p. 18). He also excerpted from Firth (1929) and noted that Hoyt (1926) provides ‘striking examples’ of a ‘failure to accord value to time and labour even when exchange is well-developed’ (D3/12/9, p. 42). All this confirmed Sraffa’s view that what mattered for the determination of commodity values were physical real costs.

4. Sraffa’s ‘third equations’: The concept of wages as a share

On the basis of his first and second equations, Sraffa had shown that if the physical real cost approach of the classical authors is developed coherently there is no such problem as the ‘transformation’ of values into prices of production, with which Marx had struggled in vain. This does not mean that one cannot get, in certain cases, from labour values to production prices in a logically consistent way. It only means that the latter can be determined entirely independently of the former, which are therefore redundant in the analysis (see Steedman 1977). Interestingly, in non-trivial cases in which one can go from labour values to prices of production, the use of Sraffa’s Standard commodity is required. However, before we can discuss this, we must first take note of some further steps in the development of Sraffa’s constructive work.

While in his first and second equations Sraffa assumed wages to be given as an inventory of commodities, he shortly afterwards began to investigate, for a given system of production, how a hypothetical change in wages affected the rate of profits and relative prices. In this regard, he once again followed Ricardo, who had also investigated the implications of the workers’ participation in the sharing out of the surplus product, and had thus arrived at his fundamental proposition on distribution, according to which the rate of profits is inversely related to ‘proportional’ wages, that is, to the share of wages in the social product. Adopting Ricardo’s share concept of wages forced Sraffa not only to dispense with the concept of given real (i.e. commodity) wages, but also to reconsider his earlier view that there is no good reason for attributing a specific role to ‘human labour’, because there was ‘no objective difference’ between the labour of a slave, a horse, a worker or a machine.

Sraffa now pointed out that, while the amount of fodder given to a horse, for instance, is decided by its owner exclusively on grounds of economy, the level of wages paid to workers is the outcome of a bargaining process between capitalists and workers. In a manuscript written in 1942, Sraffa (D3/12/16, p. 18) expounded that in his first and second equations ‘the food and sustenance of the workers [are] treated … on the same footing as that of horses’. Significantly, he added: ‘Men however (and in this they are distinguished from horses) kick.’ This implied that wage labour could no longer be treated on a par with other kinds of labour in terms of the physical real costs it involved, but had to be taken explicitly into account. Since wages were typically paid to workers in relation to the work performed, Sraffa eventually convinced himself that human labour had to be treated as a measurable quantity. While soundings of doubt concerning his earlier view can be traced back to the summer of 1929 (see in particular his notebook D3/12/12), it was only from 1931 onward that he began to assume that wages were paid in relation to the labour performed and we encounter equations in which the labour employed in industry i, L_i, is explicitly given (see D3/12/7, pp. 166, 159(1)).

Sraffa at first does not appear to have been aware that with wages absorbing the entire surplus product relative prices can be shown to be proportional to the relative quantities of labour embodied in the various commodities, provided relative wage rates are taken to reduce different kinds of concrete labour to some kind of simple or social labour. Labour values thus simply reflect a very special constellation of the sharing out of the surplus product among workers and capitalists. To emphasize this fact, Sraffa in the early 1940s coined the term ‘value theory of labour’ (see D3/12/44, p. 3). Labour values, far from being simply observable, require the solution of a system of simultaneous equations, which in addition must be associated with a particular distributional constellation.

With workers participating in the sharing out of the surplus, another classical concept lost much of its former appeal: that of ante factum payment of wages, which implied reckoning wages as belonging to the capital advanced at the beginning of the (uniform) period of production. Ricardo and Marx had retained this assumption, but it sat uncomfortably with the rest of their analyses. While Sraffa at first followed them, towards the end of 1943, after careful deliberation,¹⁶ he decided to take wages to be entirely paid out of the product. This prompted him to reconsider the classical distinction between ‘necessaries’ and ‘luxuries’ and to elaborate the more technical distinction between ‘basic’ and ‘non-basic’ products.

When (re-)reading some of Marx’s works in the early 1940s, Sraffa found that the latter had spotted a serious flaw in Ricardo’s argument (see, in particular, Marx [1861–63] 1989, pp. 226–227, 419). Marx approved of Ricardo’s new concept of proportional wages and had translated it into his own concept of ‘rate of surplus value’, S/V, with S as the labour value of the (net) social surplus (profits) and V as the social variable capital, that is, wages. Ricardo had assumed that his fundamental proposition on distribution applied not only to a given system of production in use but also to technologically changing systems. Against this, Marx had objected that Ricardo had erroneously identified the rate of profits with the rate of surplus value and had thus overlooked a second determinant of the former: the technical conditions of production as they are reflected in the ‘organic composition of capital’ of the system as a whole.

Ricardo’s blunder was due to the simplifying assumption he typically entertained in much of his observations on the wage–profit relationship; namely, that capital consists entirely of, or can be resolved entirely into, wages. (The implication of this assumption is that, when wages vanish, the rate of profits goes to infinity.) Yet in a circular system of production, this is not the case: however far back one carries the reduction of prices to dated quantities of labour and thus wages, there is always a commodity residue left. For this reason, there is a finite maximum rate of profits corresponding to zero wages. Therefore the rate of profits can fall or rise even if proportional wages remain constant (and remain constant even if proportional wages change). This becomes clear when we turn to Marx’s expression for the rate of profits¹⁷:(1) with C as the labour value of constant capital, L as the amount of living labour expended during the year, w as the share of wages (V/L, or the rate of surplus value, ) and R as the inverse of the organic composition of capital (C/L). Obviously, the general rate of profits depends on two magnitudes instead of only one: R and w. In Marx’s conceptualization, gives the maximum rate of profits that corresponds to zero wages and thus an infinite rate of surplus value. If, in the course of economic development, the maximum rate of profits happens to fall, and proportional wages remain constant, the actual rate of profits is bound to fall. Differentiating r partially with respect to R, we get

In a manuscript written in 1943, Sraffa criticized von Bortkiewicz (1906–07), who had objected to Marx’s ‘law of the tendency of the rate of profits to fall’ (LTRPF), pointing out inter alia that von Bortkiewicz had followed Ricardo in assuming unidirectional or linear production processes, and had thereby missed the importance of the maximum rate of profits.¹⁸ This does not mean, however, that Sraffa fully endorsed Marx’s argument or considered the LTRPF to be generally valid. It had not escaped his attention that Marx’s statement of the law was marred by some inconsistencies,¹⁹ and that Marx had himself drawn attention to various counter-acting tendencies that could extenuate or even reverse the fall of the rate of profits. Interestingly, annotations in his working copy of Volume III of Capital indicate that Sraffa appears to have entertained doubts about the exposition of the LTRPF being true to the original, and he even seems to have made attempts to study Marx’s original manuscripts at the International Institute of Social History in Amsterdam in order to compare them with the text published by Engels after Marx’s death. As the MEGA² edition shows,²⁰ Engels’s editorial interventions and additions indeed made the statement of the law appear more firm and definitive than seems justified in view of Marx’s original texts.²¹ Focusing attention on the case of a given system of production in use, Sraffa in his book credited Marx with having seen that, in a circular flow framework, the maximum rate of profits (corresponding to zero wages) is finite, not infinite (Sraffa 1960, p. 94).

4.1. From the ‘hypothesis’ to the Standard commodity

When in the late 1920s Sraffa began to study the dependence of the rate of profit on wages, he had to face the problem that, with a change in wages, relative prices also change. The existence of these price changes made it difficult to ascertain how a given change in wages affected the rate of profits, which relates to the part of the surplus product going to capital owners. In a document composed in the first half of 1931 Sraffa contemplated the special case in which a change in distribution has no impact on the value of the social capital (or aggregate of the means of production employed) relative to that of the social product (or the totality of the goods produced):

It may be said that the value of total capital in terms of total goods produced cannot vary [as a consequence of a variation of wages and a contrary variation of profits], since the goods are composed in exactly the same proportions as the capitals which have produced them. (D3/12/7, p. 157(3))

Sraffa was clear that the proposition was ‘false’, but surmised that it ‘may contain an element of truth’ (ibid.). When he came back to the issue in November 1943, he clarified that his proposition was based on the ‘statistical compensation of large numbers’ (D3/12/35, p. 28) and henceforth called it ‘My Hypothesis’ or simply ‘Hypothesis’. As Sraffa saw at the beginning of the 1940s, it was precisely this hypothesis that was underlying also Marx’s labour-based concept of a given organic composition of capital for the system as a whole that can be ascertained independently of the distribution of the product. However, at that time he had already convinced himself that the ‘element of truth’ referred to resided neither in the statistical compensation of large numbers nor in the labour-based evaluation of social product and social capital. It was clear to him also that no actual economic system could ever be expected to strictly satisfy the ‘hypothesis’. Sraffa therefore explored the possibility of constructing an artificial system that did so. This artificial system had to possess all the properties of that part of the actual system out of which it was constructed (that is, the set of ‘basic equations’) and at the same time offer a straightforward expression of one of these properties: the inverse relation between the actual rate of profits and the share of wages.

This Sraffa accomplished in January 1944 in terms of the Standard system and Standard commodity in a set of notes he interestingly titled ‘Hypothesis’ (see D3/12/36, pp. 61–85). The upshot of the argument developed with the help of these concepts was the establishment of a simple linear relationship between the rate of profits, r, and proportional wages, w,(2)

where now R is the standard ratio or maximum rate of profits and w is the share of wages in the net income of the Standard system. Equation 2 may be said to incorporate what is sound in Equation 1 and at the same time overcome its deficiencies.

While Sraffa had started to develop his production equations in the late 1920s, assuming wages to be paid post factum, by eschewing Marx’s labour-based constructions, he later realized that the latter had not only re-captured the circular flow conception of social production of Petty and the Physiocrats, but had also operated with a variant of the ‘Hypothesis’, and had come close to working out a correct solution. This is, we believe, the main reason for Sraffa’s appreciation of Marx’s achievements. In fact, Sraffa went so far as to maintain that ‘M. [Marx] knew all this’ (D3/12/36, p. 67 (verso)). This interpretation is confirmed by numerous documents written in the mid-1940s and late 1950s and others following the publication of Sraffa’s 1960 book. Thus in some notes that he drafted in 1961 for a reply to Stephen Bodington, who had reviewed his book under the nom de plume ‘John Eaton’,²² Sraffa stated:

If we want to follow in Marx’s footsteps and pass from values to prices of production and from rate of surplus value to rate of profits, the Standard system is a necessary adjunct: for that passage implies going through certain averages and if these are calculated without weights (or with the weights of the real system), a result which is only approximately numerically correct is obtained. If an exact result is wanted the proportions of the St.[andard] Syst.[em] of eq[uation]’s q’s must be applied as weights.  …  This is not stated explicitly in the book, but is implied. (D3/12/111, p. 118)

Sraffa then composed a set of notes entitled ‘Risposta a Eaton [Reply to Eaton]’ (D3/12/111, pp. 127–130), in which he showed how the general rate of profits can be an exact weighted average of the different industries’ rates of profit, calculated for the different industries on the basis of the labour values of the products, by using the Standard system’s proportions as weights.²³ In connection with his reply to Eaton, Sraffa also composed a note in which he spelt out his reading of Marx’s ‘value hypothesis’, which renders his above exclamation that ‘M. [Marx] knew all this’ intelligible. He insisted:

The propositions of M. [Marx] are based on the assumption that the comp.[osition] of any large aggr.[egate] of commodities, e.g. wages, profits, const.[ant] cap.[ital], consists of a random selection, so that the ratio between the aggr.[egate] values (rate of s.[urplus] v.[alue], rate of p.[rofit]) is approx.[imately] the same whether measured at ‘values’ or at the p.[rices] of prod.[uction] corresp.[onding] to any rate of s.[urplus] v.[alue]

This is obviously true, and one could leave it at that, if it were not for the tiresome objector, who relies on hypothetical deviations … It is clear that M[arx]’s proportions are not intended to deal with such deviations. They are based on the assumption (justified in general) that the aggregates are of some average composition. (D3/12/111, p. 141)

In order to be exactly true, the proportions would have to be those of the Standard commodity. In Sraffa’s reading, this is indeed what Marx had in mind. To the above he added: ‘i.e. Marx assumes that wages and profits consist approximately of quantities of st.[andard] com[modity]’ (D3/12/111, p. 141, original emphasis), and put two straight lines in the margin. Sraffa interprets Marx here as assuming that the properties of the actual economic system come close to those of the Standard system and that therefore profits and wages reflect, approximately, quantities of the Standard commodity.

5. Concluding remarks

When, in 1927 at the latest, Sraffa first realized the existence of a distinctive classical approach to the theory of value and distribution, he composed a note in which he praised Marx for having previously got hold of this approach again, for having reconstructed its development from Petty and Boisguilbert through to Torrens and Ricardo, and for exploring further its potential by divesting it of the ‘vulgar’ reformulations associated with authors like J.-B. Say, N. Senior and J. S. Mill:

Still more terrific. In the middle of the 19th century a man succeeds, either by accident or by superhuman effort, in getting again hold of the classical theory: he improves it, and draws its practical consequences from it. (D3/12/4, p. 17)

However, Sraffa was convinced that the right notion of cost, that of physical real cost, from which Petty and the Physiocrats had correctly started, had been ‘corrupted’ by the adoption of the labour theory of value. In Sraffa’s view, it was therefore necessary to jettison Marx’s labour-based approach and the concepts associated with it, and to make a fresh start by combining the modern tool of systems of simultaneous equations with the classical concepts of physical real cost and the circular flow view of production. Sraffa showed in terms of his ‘second equations’ that the general rate of profits and relative prices are fully determined by the objective data from which he started. Labour value magnitudes, being themselves merely derivatives of the given physical conditions, have no role to play in this determination and are at best superfluous.

The evidence laid out especially from the first period of Sraffa’s reconstructive and interpretive work documents his critical attitude towards the labour theory of value and his advocacy of the concept of physical real cost. However, when towards the end of the first period Sraffa began to discuss systems with a surplus and workers’ participation in the sharing out of the surplus, he convinced himself that quantities of labour had to be included in the objective data from which the rate of profits and relative prices were to be determined.

In the second period of his constructive work, which extended mainly from 1942 to 1946, Sraffa then explored systematically the relationship of his own concepts and findings with those of Marx. He found that Marx had spotted a serious flaw in Ricardo’s fundamental proposition concerning income distribution: in some parts of his analysis Ricardo had for simplicity taken social capital to consist only of wages, or to be reducible to wages in a finite number of steps, and so he had overlooked that, with a circular flow concept of production, the rate of profits depends not only on proportional wages (that is, the share of wages) but also on the technical conditions of production. Sraffa credited Marx with having recaptured the circular flow aspect of social production; with having discovered that in these conditions the maximum rate of profits is finite; and with having specified its magnitude as the inverse of the organic composition of capital as a whole. The latter was seen to be independent of income distribution. The idea of the ratio of the value of the social product to the social capital to be invariant to changes in income distribution had been invoked by Sraffa as early as 1931. This invariance condition, Sraffa soon realized, was not satisfied by any actual system, but could be generated by using a special construction. This was the device of the Standard system elaborated by Sraffa in January 1943.

Acknowledgments

We are grateful to three anonymous referees of this journal for their most helpful comments and suggestions, and to Neri Salvadori for allowing us to draw on some previous work that was carried out jointly with him by one or both of us. The usual caveats apply.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 This implies also that we do not share the interpretations of Marx’s role in the development of Sraffa’s thought suggested by De Vivo (2003) and Gilibert (2003), according to whom Marx’s schemes of simple reproduction in Volume II of Capital ‘were the source of Sraffa’s equations’ (De Vivo 2003, p. 57). These interpretations have been shown to be lacking in textual evidence, and to be contradicted by what Sraffa actually wrote, in Kurz (2015) and Kurz and Salvadori (2015). The following summary account of the development of Sraffa’s thought draws heavily on some of our earlier work, alone or together or in collaboration with Neri Salvadori; in particular on Kurz (2006), Gehrke and Kurz (2006) and Kurz and Salvadori (2009), as well as on Kurz and Salvadori (2001, 2005).

2 With the publication in the MEGA² edition of the manuscripts that Marx composed for Volumes II and III of Capital it has become possible to study in detail the textual differences between Marx’s original manuscripts and Engels’ edition. While this will not be a main object in this article’s discussion, we shall take the opportunity to point out some instances in which Engels presented Marx’s argument in a modified if not distorted way.

3 See Garegnani (2005).

4 For more details, see Kurz and Salvadori (2005).

5 To distance himself from Marshall, Sraffa coined the term ‘physical real cost’, but later switched to ‘physical cost’.

6 While Sraffa associated the physical real cost approach with Petty and his notion of ‘the days food of an adult Man, at a Medium’, he also pointed out that it was the latter notion which led to the adoption of labour as a common measure of value by the classical economists and Marx. In an undated document he noted, under the heading ‘Physical real cost’,

This theory coincides with the labour theory of cost. In effect, we cannot measure, for lack of common unit, goods which are in the cost: but ultimately, if we go back enough, all goods come to labour, and if we want to go behind labour, we find the goods commanded by labourers: if we want to measure them, the only unit is ‘quantity of goods necessary to support a labourer for one day’. This is roughly constant, and therefore we can take ‘an hour of ordinary labour’ as unit. (D3/12/42, p. 56)

7 It deserves to be noted that, in his early work on ‘mia teoria [my theory]’, Sraffa used marginalist concepts such as ‘factor of production’ (see D3/12/11, p. 64) or ‘interest rate’ and not Marxian ones. It was only in the early 1940s, after he had resumed his constructive work and thus long after he had laid the groundwork for his own analytical construction, that he began to use Marxian concepts such as ‘reproduction’ or ‘organic composition of capital’. This provides further evidence in support of the view that he developed his ideas not by starting from Marx, but from Marshall and the marginalists, whose theory he wished to refute.

8 For a discussion of the collaboration between Ramsey and Sraffa, see Kurz and Salvadori (2001).

9 In this context, it should be noted that in his copy of the French edition of Marx’s Theorien über den Mehrwert—the eight volumes of the Histoire des doctrines économiques (Marx 1924–25)—which he read in the summer of 1927, Sraffa noted carefully all passages in which Marx distanced himself explicitly from an approach that proceeds exclusively in terms of commodities or ‘use values’. Right at the beginning of the Histoire Marx took issue with Petty, who had singled out food, not labour, as the measure of value. In the margin, Sraffa placed a wrinkled line along the passage in which Marx contended that any such physical input ‘n’est pas la mesure immanente des valeurs’ (1924–25, Vol. I, p. 3 fn). On the flyleaf at the end of Volume VI we find in Sraffa’s own index the entry, ‘Marx against physical costs 122’ (Marx 1924–25, Vol. VI).

10 At this time Sraffa did not relate his equations to Marx’s schemes of reproduction in Volume II of Capital. Only in the early 1940s did he note the family resemblance between Marx’s schemes of simple reproduction and his ‘first equations’; see Kurz (2015).

11 On 11 January 1928 there is in Sraffa’s Cambridge Pocket Diary a reference to page 288 of Volume II of Vilfredo Pareto’s Les systèmes socialistes (1902), where he stresses the necessity of determining (relative) prices in terms of simultaneous equations and criticizes the older economists, who did not have this tool at their disposal, for trying to simplify matters by taking a sufficiently large number of the variables under consideration as known magnitudes.

12 As Sraffa noticed in the second period of his constructive work, in special circumstances the quantity of labour embodied can be seen at a glance. This is the case in Marx’s scheme of simple reproduction, for example, where the quantity of labour employed in both departments—department I producing means of production and department II means of consumption—is equal to the labour value of the net product consisting only of consumption goods. Marx’s scheme can be said to foreshadow the concept of ‘subsystem’ or ‘vertically integrated sector’; see Sraffa (1960, Appendix A) and Pasinetti (1973).

13 See document (D3/12/10, p. 24).

14 For more details, see Kurz and Salvadori (2005).

15 Sraffa, in fact, thought to be able to cover not only renewable natural resources, such as lands of unchanging qualities, but also exhaustible resources, such as mineral ores and oil deposits. For a long time he intended to treat both kinds of resource in his 1960 book, although at the proof stage he dropped the corresponding passage.

16 For a detailed discussion of Sraffa’s vacillation with regard to the adoption of a gross wage concept, see Gehrke (2015).

17 As Marx explicitly pointed out, the definition of ‘profit’ and ‘rate of profit’ he used in this context refers to the total surplus value and thus includes all three components into which surplus value is being transformed: ‘industrial profit’, interest and ground-rent. For a more detailed discussion of this point and its relevance for Marx’s critique of Ricardo’s explanation of the falling rate of profit, see Gehrke (2012, pp. 58–63) and Kurz (2015, pp. 93–95).

18 For a more detailed account, see Gehrke and Kurz (2006).

19 Sraffa noted, for instance, the problem of the incompatibility of a constant real wage rate with a constant rate of surplus value when the productivity of labour is changing.

20 See, in particular, Marx ([1863–67] 2012).

21 For a more detailed account, see Kurz (2013).

22 See Eaton (1960).

23 The point was then established, with some slight differences, also in the secondary literature; see Meek (1961).