Piero Sraffa: Making a Revolution in Economic Theory

Sraffa and the Marshallian Theory of Competitive Equilibrium

Professor Ajit Sinha has written an excellent book about the evolution of the major theoretical work, PCMC, Cambridge University Press, 1960, authored by Piero Sraffa, one of the most powerful intellectuals of the twentieth century. Sraffa was a close friend of Antonio Gramsci and helped sustain Gramsci’s intellectual labours during his incarceration by the fascist regime of Mussolini by opening an account for supplying him with books and preserving his legacy by helping Tatiana Schucht, Gramsci’s sister-in-law, who conserved Gramsci’s letters. Sraffa, a committed communist in all his life, was however dissatisfied with the labour theory of value and prices put forward by Ricardo and Marx. Sinha traces the evolution of Sraffa’s thought from way back in 1920, when Sraffa, a lad of 22, wrote on Italian inflation during and after World War I. This was a dissertation needed for his law degree in the University of Turin. There, Sraffa argued, going against the conventional view that the cure for the inflation would be to revalue the lira to its pre-war parity with gold: it would cause a serious recession in the economy, as it in fact did. His second work on the bank crisis in Italy, written at Keynes’s invitation was published in the Manchester Guardian Commercial Supplement. By then Mussolini had come to power through his March on Rome with his fascist cadres. He was displeased with Sraffa’s article because it contained a severe criticism of the use of the government’s money for rescue of a large private bank.

Sinha then meticulously traces Sraffa’s evolution as an economic theorist. Although a committed communist in his political beliefs, he was essentially a Marshallian in his economic theory. His next publication in English was in the Economic Journal of 1926, with the title, ‘Laws of Returns Under Competitive Conditions’. Sraffa pointed out that increasing cost follows exclusively from changes in the proportions of inputs rather than changes in the size of the industry or the firm. Sraffa then takes up the use of diminishing returns in deriving Marshall’s supply curve. To quote Sinha:

Marshall then argues that one can consider the whole industry as a single firm that employs the constant factor {responsible for diminishing returns-AKB}. In this case, the marginal revenue product curve of the firm would also represent the supply curve of the industry. This procedure amounts to assuming that the industry supply curve can be derived by horizontally adding the marginal revenue product curves of all the firms in the industry … Sraffa’s objection to this is {that} although it may be true that a factor of production is fixed for the industry as a whole, it is not fixed for any individual firm in the industry, and a firm may be free to an extent, the use of this factor and its output while lowering its private cost of production due to economies of scale, without impacting on the price of the factor … Thus the upward sloping supply curve can be drawn only under the condition that the number of firms is fixed and their share in the constant factor is fixed too. (pp. 36–37)

This is obviously an untenable postulate under competitive conditions in which firms are free to enter and exit an industry.

There may be two different causes for a firm to experience decreasing costs with increasing output: first, with unchanging factor proportions, the firm may be able to utilize a finer division of labour. Second, its overhead costs fall with an expansion of its output. But the existence of firms with decreasing costs is incompatible with competitive conditions: such firms would either drive out or absorb firms with increasing costs and the industry would tend towards a monopoly. One cause that could be applicable to the Marshallian case is given by the instance of economies of scale that is external to the firms but internal to the industry … By plotting industrial output on the horizontal axis and the corresponding minimum average costs of firms (assuming all firms have the same cost conditions) one can draw an industry supply curve, which would be downward sloping. However, this supply curve is not the marginal cost curve but rather the average cost curve of the industry, and its marginal cost curve will be always below it … Most of the external economies are due to general ‘progress of industrial environment’ or improvement of ‘means of communication or transportation’ and … affect other industries in the same manner and thus destroying the assumption of ‘partial equilibrium’ (Sinha, 2006, p. 38). After establishing that only the highly restrictive and rather unstable case of constant returns was the only feasible condition for competition to prevail, Sraffa argued that in general an industry would likely be characterized by imperfect competition. Sraffa proposed that the industry would be characterized by several small firms which would know its customers and enjoy customer loyalty. Thus each firm would face a downward sloping demand curve. This proposal then led to the first revolution caused by Sraffa’s work: the principal fruits were Edward Chamberlin’s Theory of Monopolistic Competition (1933) ¹ and Joan Robinson’s Economics of Imperfect Competition (1932). Sraffa, however, ceased to take any interest in the matter beyond participating in a debate organized by Keynes, the editor of the Economic Journal, among D. H. Robertson, Piero Sraffa and G. F. Shove (Sraffa, 1930, pp. 89–92).

Robertson has criticized Sraffa’s position by arguing that in a state of disequilibrium, an individual firm may experience economies of scale, which may continue to prevail even in equilibrium. Sraffa pointed out that such an equilibrium is impossible, unless at the point of equilibrium the economies of scale of the firm concerned are exactly balanced by diseconomies of size. Otherwise, the firm experiencing economies of scale would undercut the prices of other firms not experiencing such economies, and no competitive equilibrium would be reached.

Sraffa Begins His Search for an Objective Theory of Value

Sinha shows that by 1927, when he was preparing his Cambridge lectures, he had lost interest in the Marshallian problem and was zeroing on the problems that occupied the classical economists. Sraffa argues that classical economics was mainly interested in the question of national wealth, that is, ‘how to increase national wealth’ (D3/12/3:13) or the question of the distribution of aggregate income to various factors, that is, ‘how to change its distribution, or how to justify the present distribution’ (Sinha, 2006) (Numbers beginning with D refer to Sraffa’s papers in the Wren Library, Trinity College, Cambridge). According to Sraffa two sets of factors have been responsible for the change from the classical economists’ focus on aggregate wealth or aggregate income to the focus of modern economics on problems of market prices. Two sets of causes have contributed to bring about this change. In the first place the general progress of economics as a science, with its consequent shifting from the consideration of broad philosophical questions to the technical analysis of the mechanism through which economic equilibrium is reached. In the second place, the change in the perception of practical issues which have confronted the economists and the influence of of the latter on theories which are supposed to be abstract is interesting.

As quoted by Sinha (2006):

The labour theory of value was devised by Ricardo as a stick to beat landlords (rent does not enter into cost of production). But later, having been adopted by Marx to beat the capitalists, it was necessary to devise a new theory. The utility theory. (D3/12/3:13-15) (p. 44)

This shows that Sraffa was fully aware of the political reason for the resurgence of the advent of neoclassical theory. Thus began Sraffa’s 33-year long quest for an objective theory of value. He found the labour theory of value unsatisfactory. ‘One way to objectivize’ labour would be to reduce it to available real items of consumption (or subsistence) of the worker. But if there are substitutes available for consumption (or the worker can consume various combinations of the same goods), then again there is no way of reducing ‘labour’ to some ultimate value or standard (Sinha, 2006, p. 46; refer also to Garegnani, 2005). Sraffa then began his search for the classical theory of value by taking only the empirical physical costs into account. He worked out the essentials of his theory between 1927 and 1931, although it took him another 30 years to produce the full-fledged PCMC, mainly because he was busy editing The Works and Correspondence of David Ricardo.

Preoccupation with the measurement of economic magnitudes is a hallmark of Sraffa’s thinking, and we see it recurring throughout his writings. A time span stretching from the writing of his notes in the early 1920s (refer to his endorsement of Sidgwick’s statement on ‘the necessity of unit of measurement, not for measurement, but for conception’ in D1/20/5) to ‘his contribution to a conference in Corfu in 1958 saw Sraffa in quest of a measurement criterion valid in theoretical analysis that should prove univocal, in contrast with the approach in statistical investigation, which requires some arbitrary choices as in the case of electing weights in constructing index numbers’ (Marcuzzo & Rosselli, 2001, pp. 210–211). On 3 November 1955, when he resumed working on his book after completing the editing of Ricardo’s works and correspondence, he wrote:

The most striking feature of the marginal theory of distribution is that it asserts that the method of production and the quantities of the factors of production determine the distribution. And yet, if we suppose that a man from another planet came down to see the system postulated by the marginal theory, he would never, by observation, no matter how searching, succeed in discovering the determinants of distribution. He would himself have to bring them into the open by changing the proportions of the factors, and then observe them. He could discover them ‘by experiment, but never by pure observation. (D3/12/42/86)’. (Marcuzzo & Rosselli, 2001, p. 222)

Having established that marginal magnitudes are not of natural occurrence but, if any, the result of an experiment, Sraffa questions the feasibility of the experiment required. He wrote in October 1929:

These experiments cannot be carried out (and never have been, as a matter of fact) for various reasons: 1) the practical difficulties, 2) the lack of definition of the conditions to be required, which are always summed up in the absurd ‘other things being equal’. (D3/12/13/3) (Marcuzzo & Rosselli, 2001, p. 223)

Thus his objection to marginalism or neoclassical economics, which was the way Veblen had characterized it, had nothing to do with the political use to which it was put, namely, justifying the political status quo, but purely on scientific grounds, because it dealt with entities that were unobservable. It is necessary to remember that as Sinha (pp. 72–85) puts it, Sraffa was intensively reading from 1927 on the popularizing scientific works of Heinrich Hertz, Percy Bridgman, Henri Poincaré, Werner Heisenberg and Arthur Eddington. Following these physicists, Sraffa attempted ‘to distinguish his theory of value as “geometrical” or non-causal in opposition to orthodox “mechanical” or causal theory of value’ (Sinha, p. 76).

As Sinha mentioned in his Prologue:

the classical cost based theory was unable to resolve the problem of the contradiction between the notions of cost and surplus. If surplus is accounted for as cost then the surplus must disappear, but as long as it is not accounted for as cost, we have no satisfactory explanation for its existence. (Sinha, p. 82)

The standpoint of the capitalist society itself, is that of the ruling class, & therefore the surplus is composed of rent, interest & profit: Marx is the only economist who takes explicitly & consistently this point of view -& also Ricardo (spec. Notes to Malthus) but not consistently.

Marshall, who tries to take a classless human standpoint, regards all men as responsible subjects, & therefore all human consumption (he includes savings: this question of the inclusion of savings in income is also a question of who is the ‘subject’), i.e. wages, interest & rent as parts of the surplus (which he calls the national dividend).

… Keynes, who takes the standpoint of the company director, regards only the entrepreneur’s (who is responsible for production) ‘profits’ specially defined as surplus, all the factors having to be induced or paid according to contract … (D3/12/7:161(1-3) (Sinha, p. 83)

Sraffa, in the meanwhile, continued his active association with L’Ordine Nuovo and in its April 1924 issue wrote anonymously a letter, signed ‘S’, which critically assessed the strategy of the Italian Communist Party in the light of the growing peril of fascism. It counselled against the strategy which would isolate the working class, insightfully recognising the wider social basis and the pervasive form of control that fascism was rapidly gaining. It initiated a serious debate, Gramsci himself countering Sraffa’s letter in defence of the official party position. Gramsci was to change his stand later. (Bharadwaj, 1984, p. 1236)

It was apparently the ‘failure’ of the labour theory of value to yield a consistent explanation of relative prices and hence of the rate of profits-the so-called problem of transformation-that was offered, at an analytical level, as the ground for abandoning the classical and Marxian approach to distribution. Sraffa now sought to turn the tables: the neo- classicists’ explanation of distribution was fundamentally erroneous. In the initial at- tacks on Marshall, Sraffa was to concentrate on demolishing the marginalist notion of supply schedules resting on the laws of returns within the particular equilibrium context. In his ‘Production of Commodities’ the attack was squarely on the explanation of profit within the general equilibrium framework, as became evident through the capital theoretic controversies that emanated from that work. (Bharadwaj, 1984, p. 1239)

Sinha’s book has many virtues. He recognizes unlike practically all the neoclassical commentators and many of the sympathetic commentators also that PCMC is a snapshot of an economy and not the portrayal of the economy in equilibrium in any sense and does not, therefore, require the assumption of constant returns to scale (refer also, Gilibert, 1989). Second, Sraffa while recognizing that Marx’s solution to the problem of transformation of values into prices had an intractable analytical problem, he was grappling with a problem set out by Marx. As he writes:

The idea of a proportional distribution of the net output between capitalists and workers takes centre stage in Marx’s theory of exploitation. In this case, V+S can be separated out, even though V is treated as part of total capital investment, as the value of total net output, and S/V can be shown to be the relative shares of the two classes in the total value of the net output. This Marx is able to do on the basis of his definition of value as ‘embodied labour’ independently of its expression or appearance as prices in relative terms, unlike Ricardo who recognized value only in relative terms. It is, however, important to note that Marx had presented the transformation of values into prices of production in, what Sraffa describes as, the context of ‘difference’ rather than the context of ‘çhange’. In other words, Marx’s transformation is an answer precisely to the question of C not of the same exchangeable value. Unlike Sraffa’s notes of 1942–43, Marx does not begin (in Capital, vol. III, chapters 8 & 9) with the case when the rate of profits is zero and therefore labour values are identical to price ratios. Instead he begins with positive surplus value and unequal organic compositions of capital, and argues that ‘two commodities produced by the same quantities of capital must be of same exchangeable value stands in contradiction to the requirement of a competitive capitalist system that the returns to capital must be uniform. Marx’s transformation of values to prices of production’ (Sraffa, PCMC, 1960, chapter 9) was designed to resolve this contradiction by showing that what the price mechanism does behind the scenes is to pool the total surplus value produced in the system and redistribute it to all of the individual capitals uniformly by systematically deviating price ratios … from their labour-value ratios. This is the answer to the question of ‘why two commodities produced by the same quantities of labour do not have the same exchangeable value’. (Sinha, p. 169)

There are two aspects of Marx’s transformation of values to prices that were crucial to Sraffa: (1) the average rate of profits of the system can be determined independently of prices, that is, profit is a non-price phenomenon’; and (2) a commodity produced by the average organic composition of capital’ will show no deviation from value. (Sinha, p. 170)

Although the basic ideas of PCMC were conceptualized already between 1926 and 1931, we find Sraffa struggling with the task of the standard commodity in 1955. As Sinha (p. 173) writes:

Ít appears from [the comments written in 1955] that when Sraffa had written thé Íntroduction’ to Ricardo’s Principles he had not yet come to the conclusion that the Standard commodity does not ensure the constancy of the size of the net output of the actual system with regard to changes in wages or the rate of profits. However, once he realized that, he begins to distance himself from Ricardo’s problem with the requirement of the constancy of the size of the net output and relate it directly to the property of the Standard commodity, which ensures that the price movements measured against this standard would always measure the that have come about in the price of the commodity measured and not in the standard, due to changes in wages’. It took another four years or so (the second note on Ricardo’s problem quoted by Sinha (p. 172) is dated 6 September, 1955, to work out the full set of equations on which he had been working since the late 1920s to develop into the full-fledged PCMC, the basic content of which has been summarized in different parts of this review.

It is interesting that Sraffa, like Marx also thought of his task as the working out of ‘difference’ with different maximum rates of profit rather than working out the consequences of ‘change’ exactly as Marx had thought of in regard to the transformation problem. Sinha has found few notes relating to Sraffa’s Introduction to Ricardo’s Works and Correspondence. The reason maybe because as Pollitt (1990) has noted that for that Introduction the thinking was Sraffa’s but the pen was that of Maurice Dobb, his collaborator in Ricardo’s Works and Correspondence.

Before Sraffa’s book appeared, those who were not dogmatic neoclassical economists had already come across Joan Robinson’s 1953–1954 article where she demonstrated that the marginal productivity theory of income distribution was based on circular reasoning, since the value of capital whose marginal productivity was supposed to determine the rate of interest required that rate of interest to be already known before the value of capital could be measured. Then there were the aggregative theories of income distribution. In the simplest version of the Marxian theory, the distribution was determined by the surplus received by capitalists over what they paid to the workers, the latter being determined by what was needed to get the workers to work. A more sophisticated version of the Marxian theory was produced by the Polish economist Michal Kalecki, which took account of the fact that modern capitalism had always a degree of monopoly built into it. There are several versions of essentially the same theory (Kalecki, 1938, 1939, Chapter 1). Measuring the degree of monopoly as the excess of price over cost and after deducting from total revenues of a firm the depreciation cost of capital and cost of raw materials and the cost of manual labour, what remains is the profit of the capitalist. Aggregating over all firms and all industries, we get the volume of profits and thus the income distribution, since wages of manual workers are given. In a capitalist economy, a macroeconomic condition of saving equalling investment is needed. Kalecki assumes that workers consume what they earn, and capitalists save what they earn. Thus capitalists earn what they invest, and workers spend what they earn. Finally, Nicholas Kaldor (1955–1956) produced a Keynesian theory, in which assuming that capitalists save a higher proportion of income than workers and that in equilibrium aggregate savings must equal aggregate investment, ‘given the wage-earners’ and the capitalists’ propensities to save, the share of profits in income depends simply on the ratio of investment to output’. So several plausible alternatives to the neoclassical theory of distribution were also available. Both Kalecki and Kaldor tested their theories against existing data, but assuming a long-term full employment.

Sraffa’s Detractors and Misunderstandings

Almost from the beginning, Sraffa’s PCMC faced criticisms from both his admirers and his detractors. His admirers, for example Newman (1962), said that it is a work of art. But the proofs of the propositions were incomplete, and then they proceeded to provide what they considered to be kosher proofs primarily depending on linear algebra and the Perron–Frobenius theorem. The detractors said how the propositions can be true, when reliable proofs have not been provided. They range from Quandt (1961) to Burmeister and Kuga (1970) to Hahn (1982).

The admirers include Newman (1962), who uses Perron–Frobenius theorem, and Afriat (2006) who uses the theory of Markov processes to prove the existence and uniqueness of the standard system in an irreducible, self-reproducing economy. But Velupillai (1989) shows that Sraffa provided an adequate constructive proof for the existence and uniqueness of the standard system (in this connection, refer Harcourt & Massaro, 1964).

In Sraffa’s PCMC, ‘the following two assumptions are explicit in the definition of the mathematical object:

The economic system is viable.

The basic industries are those the outputs of which enter into all industries as inputs.

Sraffa’s algorithm for the construction of the ‘standard system’ is the recursive application of the following two-step programme:

Step 1: ‘…start by adjusting the proportions of the industries in such a way that of each basic commodity a larger quantity is produced than is strictly necessary for replacement’ (Sraffa, PCMC, 1960, p. 26).

Repeat Step 1.

Stopping rule: ‘Terminate the programme when … the products have been reduced to such an extent that all round replacement is just possible without leaving any surplus product’ (Sraffa, PCMC, 1960, p. 27).

Result: ‘The proportions attained by the industries are the proportions of the standard system’ (Sraffa, PCMC, 1960, p. 27). This sequence has been reconstructed by Velupillai (2007).

Two kinds of misunderstanding have continued to bedevil the reception of PCMC. One is typified by Garegnani (2007) who claimed that PCMC prices are the ‘natural prices’ to which market prices would gravitate. As Sinha has again shown, there is no justification for this in the case of the PCMC economy which gives the photographic image of an economy with no movement in it. The other kind of misunderstanding is to portray Sraffa’s relation, r = R (1 − w), where R is the maximum rate of profit, w is the wage rate and r the actual rate of profit as nothing but the rediscovery of the neoclassical wage-price frontier of Samuelson (1957), further formalized by Burmeister and Kuga (1970). Unlike Sraffa, they assume equilibrium in a competitive market, and they are snagged by their inability to get rid of the circularity of the measure of aggregate capital. And of course, they have nothing to say about the rate of exploitation. Schefold (1980) has discussed the mathematical similarities and conceptual differences between von Neumann’s model of economic growth and PCMC in the case of joint products. To quote him (p. 141):

The extension from single product to generalised joint production Sraffa systems meets with some problems: the standard commodity may not exist (Schefold, 1971); the monotonicity of the wage curve is in doubt (Sraffa, 1960, sections 7I-2) and it is not obvious which of the previously used methods of production is replaced if a new method of production is introduced in a joint production system (Sraffa, 1960, p. 96), etc. It can be shown, however, that these and other issues can be faced satisfactorily if some assumptions are added to Sraffa’s approach to joint production, so as to make it comparable with von Neumann- type models. The essential assumption to be introduced … is: balanced growth with constant returns to scale at a pre- assigned growth rate g (usually taken to be equal to the rate of profit) producing a given composition of the bundle of consumption goods (to be denoted by a vector d ). The theories of growth, distribution and composition of output remain, nevertheless, separate matters and thus the assumption does not lead us far away from Sraffa’s way of thinking’. Schefold shows that treatment of technical change by taking depreciated machines as different machines is the same in both the Sraffa and Von Neumann systems. Also, in both systems an innovation has to pass the test of viability. But there the similarity ends. Von Neumann’s model assumes balanced growth, whereas Sraffa’s model does not. There has been some allegation that Sraffa had borrowed many of his ideas from Von Neumann without acknowledging his debt. Kurz and Salvadori (2001) have shown om the basis of the Sraffa Archive that this allegation is false: This paper discusses the relationship between Piero Sraffa’s 1960 book and John von Neumann’s 1937 paper on economic growth in the light of some of the material contained in Sraffa’s unpublished papers and correspondence. It is argued that the two contributions share a similar outlook and exhibit conceptual parallels; in fact, they can both be said to belong to the ‘classical’ approach to the theory of value and distribution.

The latter is characterized, among other things, by an asymmetric treatment of the distributive variables, the rate of return on capital and the real wage rate. Sraffa’s papers show that when he came across the von Neumann model in the mid-1940s his own analysis was already quite advanced, including his analysis of joint production. The paper also contains an exchange of letters between John Richard Hicks and Sraffa on some of the issues dealt with in the latter’s book.

Sraffa as a Communist

In the usual literature on Sraffa’s work, his communist side is portrayed as his membership in L’Ordine Nuovo, when Gramsci was its editor, as a supplier of books to Gramsci after he had been arrested and helping Tatiana Schucht, Gramsci’s sister-in-law, to preserve Gramsci’s Quaderni del carcere (Prison Notebooks in English). But his role in the Italian Communist Party (PCI) is even more important than that. Some light on Sraffa’s position in these circumstances is cast by a letter and some observations by Camilla Ravera (Ravera, 1973, p. 267), who was then in charge of the underground office (based in Genoa and known as the albergo dei poveri or almshouse) of the PCI. From a letter by Camilla Ravera to Ruggero Grieco and Palmiro Togliatti (two prominent figures in the PCI; Togliatti virtually became its leader from the moment of Gramsci’s arrest) dated 29 January 1927 and from the memoirs of Ravera herself, we learn that just prior to that date, therefore only a few days after Gramsci’s telegram about his transfer, Sraffa, who was not acquainted with her, went to see her accompanied by Felice Platone, another leader of the PCI. Thus it seems to have been Sraffa himself who informed the PCI underground office of Gramsci’s transfer. So it was that at a time when the PCI found itself going underground and suffering a great many arrests, Sraffa assumed the role of liaison between Gramsci and the PCI, doing so on the strength of certain pre-established contacts and by making further contacts with members of the by now clandestine party. In the meantime, the party and its members or supporters were being subjected to new legislative measures involving, among other things, capital punishment for assassination attempts against the highest representatives of the state, attempted organization of insurrection and crimes of espionage. It was against this background that Camilla Ravera wrote that Sraffa ‘was sharing in our troubles and worries, and wanted to know if it was possible to do anything that might help Gramsci to endure the hardships of imprisonment’ (Naldi, 2012, p. 1403). Gramsci apparently advised Sraffa not to become a member of the PCI (Naldi, 2012, p. 1407). [The Italian sources of Ravera and Sraffa have not been mentioned- AKB] Sraffa advised Gramsci to collaborate with all anti-fascist parties in order to fight their common enemy (Bharadwaj, 1984; Sen, 2003), but under the influence of the Communist International (Comintern) his advice was ignored not only by the PCI but alsoby the whole communist and democratic movement in Europe. Sraffa was also involved in the ‘commerce of dates’, which was undertaken by Gramsci’s brother Gennaro to raise funds for the party (Naldi, 2012, pp. 1411–1414). Sraffa remained a communist to the end of his life. During the Cold War period, in any conflict between the Soviet Union and the USA and its allies, he always backed the former.

Sraffa and Gramsci

Sraffa was in communication with three other great thinkers, namely, Antonio Gramsci, Maynard Keynes and Ludwig Wittgenstein, the one who revolutionized Marxist political thinking and the other who emerged as the greatest philosopher of the twentieth century. There is now a very large literature on their connections, much of it based on inferences, especially as concerns on Sraffa and Wittgenstein, because apart from a few cryptic remarks by Wittgenstein, there is very little on Sraffa’s side to indicate the content of their conversations, which took place over many years. They ceased because Sraffa no longer found it useful to continue the conversations.

But first let me speak about Gramsci and Sraffa. We know that both were committed communists, so they must have many intellectual concerns in common. We also know that they first met in the office of L’Ordine Nuovo sometime between May and September 1919 (Naldi, 2000, p. 81) and it quickly ripened into a close friendship. Sraffa also began working for L’Ordine Nuovo. Despite Sraffa’s frequent visits to England from 1921, the friendship between him and Gramsci remained unbroken. In around 1923, Gramsci suggested that a research unit could be set up with Sraffa at its head to analyse Italian economic problems. When Gramsci moved to Vienna to avoid arrest by the fascist government and began publishing a new series of L’Ordine Nuovo and wanted to involve Sraffa in that venture, Sraffa refused. ‘Sraffa’s view was that Italy needed a bourgeois revolution against the fascist’ regime capable of restoring order and bourgeois freedom and that this situation placed the communist party in a position of secondary importance in comparison with the bourgeois democratic oppositions. Such an attitude, according to Gramsci, would have meant ‘to liquidate a revolutionary organization such as is and must be our Party’. But Gramsci took Sraffa’s analysis very seriously and believed that his views could not but mirror a widespread perception among Italian intellectuals and working class and (we may take this to be implicitly stressed by Gramsci at the end of his comment) a real weakness of the position of the Italian Communist Party, which was lacking a clear consciousness of the problems that the working class had to face under the fascist regime and a clear policy consistent with that state of things. In fact Gramsci, in the second and very important part of his comment, considered how the Italian working class and Communist Party could regain a central position within the Italian situation (Naldi, 2000, p. 85). Although as I have indicated above PCI did not accept Sraffa’s advice, Gramsci took it very seriously. When Gramsci was in prison, in 1931, Sraffa sent him the Macmillan Committee’s report, mainly written by Keynes, and kept him informed about the new thinking on the economic policy. Between 1924 and 1926, Sraffa described his conversations with Gramsci in the following words: ‘The intensity and vividness were such that we could begin to discuss at dinner, and continue throughout the night and the next day, without ever being tired’ (Ginzburg, 2015, p. 33). What was the intellectual content of their discussions? Both were Marxists, but there are many Marxes:

I will try to show the existence, in Sraffa’s unpublished works and his overall theoretical framework that emerges in his 1960 book, Production of Commodities by Means of Commodities, of a correspondence (which does not exclude differences) with important terms of the vocabulary of Gramsci, such as ‘translation and translatability’, ‘structure and superstructure’, ‘historical materialism’, ‘determinism and mechanicism’, ‘dialectics’, ‘strength relations’, ‘metaphor and myth’. In other words, I propose an exercise in ‘translation’:15 according to the meaning attributed by Gramsci, … ‘translate’ is close to the concept of ‘transpose, find matches or differences between the ‘idioms.’ (Ginzburg, 2015, p. 34)

Further:

Working along different paths, our authors [Gramsci and Sraffa] agree on the need for a closer study of Marx’s texts, purged of subsequent encrustations and conceptual ambiguities that have formed around them; they also share a commitment to an anti-idealist and anti-metaphysical stance … In addition, the extant writings of Sraffa provide a strictly analytical (not merely philosophical and moral) interpretation of the labour theory of value, understood as a theory of exchange relationships; nor does any philosophical or moral dimension of the labour theory of value appear to be present in the writings of Gramsci. (Ginzburg, 2015, p. 40)

In Gramsci’s view, in a third meaning, translation is the instrument of the reconstruction of the conception of the world, dictated by the unit of theory and practice. In a note entitled, ‘Philosophy–Politics–Economy’, Gramsci writes:

If we are dealing with the constituent elements of the same conception of the world, there must necessarily be, in the theoretical principles, convertibility from one to another, mutual translation of each constituent part in its own specific language: one element is implicit in the other and ‘all of them together form a homogeneous circle’.46 This meaning of the word ‘translation’ is the most radical since, as Frosini writes, from there follows ‘the relativisation of different languages … and the translation of philosophy into politics.’(Ginzburg, 2015, pp. 41–42)

The issue of translation/translatability appears in Sraffa’s unpublished papers at a crucial moment in his theoretical reflection. As can be seen from some earlier observations, 48 in the fall of 1927, Sraffa, on the basis of insights gained as from the previous August, was planning a book that would show ‘the differences and the superiority of the old classical theories’ with respect to contemporary theory. His aim—he wrote—was twofold: ‘I. Exposition of the history, which is truly the essential. II. Make myself understood: which requires me to proceed from the known to the unknown, from Marshall to Marx, from disutility to material cost’ (Ginzburg, 2015, p. 42).

In a note, dated 22 August 1931, Sraffa writes: ‘The study of the “surplus product” is the true object of economics; the great difficulty of the matter is that this object either vanishes or remains unexplained. It is a typical problem to be handled dialectically.’ Sraffa goes on a little further with these words:

Thus it would appear that the true economic science can only study the conservative side (aspect) of things: and the revolutionary side is the object of the inadequate and contradictory economics. The revolutionary economics can only be completed by practice, which solves the contradictions and changes the facts making them adequate to their reasons. (Ginzburg, 2015, pp. 63–64)

The political implications of the surplus-based approach have already been pointed out in the opening part of this review.

Sraffa and Wittgenstein

The scrutiny of mutual interaction of Gramsci and Sraffa is difficult because of the relative sparseness of materials after Gramsci had been arrested. In a study of the interaction of Sraffa and Wittgenstein from 1929, when Wittgenstein arrived back at Cambridge down to 1946, when Sraffa used to carry on those conversations, we have very little to go by, except certain anecdotes and two fulsome acknowledgements by Wittgenstein of his debt to Sraffa. According to Wittgenstein’s Tractatus Logico-Philosophicus, a proposition and what it describes must have the same logical form. Sraffa found this philosophical position to be altogether erroneous and argued with Wittgenstein on the need for him to rethink his position. According to a famous anecdote, Sraffa responded to Wittgenstein’s claim by brushing his chin with his fingertips, which is apparently readily understood as a Neapolitan gesture of scepticism, and then asked, ‘What is the logical form of this?’ (Sen, 2003, p. 1240). Sraffa was not, in fact, the only critic with whom Wittgenstein had to reckon. Frank Ramsey, the youthful mathematical prodigy in Cambridge, was another. Wittgenstein (1953, p. x) thanked Ramsey but recorded that he was ‘even more’ indebted to the criticism that ‘a teacher of this university, Mr P. Sraffa, for many years unceasingly practiced on my thoughts,’ adding that he was ‘indebted to this stimulus for the most consequential ideas of this book’. Wittgenstein told a friend (Rush Rhees, another Cambridge philosopher) that the most important thing that Sraffa taught him was an ‘anthropological way’ of seeing philosophical problems. In his insightful analysis of the influence of Sraffa and Freud, Kenny and McGuinness (1982) discusses the impact on Wittgenstein of ‘the ethnological or anthropological way of looking at things that came to him from the economist Sraffa’ (Kenny & McGuiness, 1982, pp. 36–39). There is also an earlier, well-known passage, dating from 1932, where Wittgenstein recognized his debt to Sraffa, as the last of an impressive list:

I don’t believe I have ever invented a line of thinking, I have always taken one over from someone else. I have simply straightaway seized on it with enthusiasm for my work of clarification. That is how Boltzmann, Hertz, Schopenhauer, Frege, Russell, Kraus, Loos, Weininger, Spengler, Sraffa have influenced me. (Marion, 2005, p. 383; Wittgenstein, 1980, p. 19)

Before we take up the issue of Sraffa’s influence on Wittgenstein’s general philosophy, the exact nature of the conduit from Gramsci to Wittgenstein via Sraffa on which Sinha differs with practically all the commentators such as Sen (2003), Davis (2002a, 2002b), Marion (2005) and Sinha (2006, pp. 101–109), let me have a brief look at Wittgenstein’s philosophy of mathematics, where he seems to have followed a constructivist approach from the Tractatus. He might have been already influenced by this by the likes of Brouwer and Kronecker. In a relatively early paper on Wittgenstein’s philosophy of mathematics, Michael Dummett (1959, p. 327) wrote:

Wittgenstein adopts a version (as we shall see, an extreme version) of constructivism; for him it is of the essence of a mathematical statement that it is asserted as the conclusion of a proof, whereas I suppose that for a Platonist a being who had direct apprehension of mathematical truth, not mediated by inferences, would not be a complete absurdity. There are many different lines of thought converging upon Wittgenstein’s constructivism.

Wittgenstein’s notes on his philosophy of mathematics were, of course, left incomplete. In the Tractatus we find that a demarcation between truth propositions and mathematical statements is to say that mathematical propositions are decidable by purely formal means (e.g., calculations), while contingent propositions, being about the ‘external’ world, can only be decided, if at all, by determining whether or not a particular fact obtains (i.e., something external to the proposition and the language in which it resides) (2.223; 4.05) (Radych, 2018). When he began his departure from the Tractatus, according to him, Wittgenstein specifically referred to L. E. J. Brouwer’s intuitionist views, which denied the law of the excluded middle and believed that only constructive proofs were valid in mathematics (Brouwer, 1981, in English translation). Thus there is some continuity in Wittgenstein’s conviction about constructivism in mathematics between the Tractatus and his notes constituting philosophical grammar, but his acknowledgement of his debt to Sraffa in his note of 1932, along with that of Boltzmann, Hertz, Frege and so on, shows that this attitude was strengthened by Sraffa’s influence.

Sinha (2006, pp. 101–109) disputes that anything Wittgenstein owes to Gramsci’s ‘anthropological approach’ to language is transmitted through Sraffa. He thinks that what Wittgenstein owed to Sraffa was the distinction between sense and nonsense. But Philosophical Investigations begin with an evocation of the words of Augustine in Confessions. This opening scene has been the object of varying interpretations. The passage reads as follows:

When they (my elders) named some object, and accordingly moved towards something, I saw this and grasped that the thing they called was the sound they uttered when they meant to point it out. Their intention was shewn by their bodily movements, as it were the natural language of all peoples: the expression of the face, the play of the eyes, the movement of other parts of the body, and the tone of voice which expresses our state of mind in seeking, having, or avoiding something. Thus as I heard words repeatedly used in their proper places in various sentences, I gradually learnt to understand what objects they signified; and after I had trained my mouth to form these signs, I used them to express my own desires. (Wittgenstein, 1953, para. 1)

Cavell (1982, 1990), who has given the most sustained reading of this passage, senses here the presence of the child who moves invisible among his or her elders and who must divine speech for himself or herself, training the mouth to form signs so that he or she may use these signs to express his or her own desires. Now contrast this scene of instruction with the famous builders’ scene, which follows soon after, in Wittgenstein (1953, para 2):

Let us imagine a language for which the description given by Augustine is right. The language is meant to serve for communication between a builder A and an assistant B. A is building with building stones: there are blocks, pillars, slabs, and beams. B has to pass the stones, and that in order in which A needs them. For this purpose they use a language consisting of the words ‘block’, ‘pillar’, ‘slab’, ‘beam’. A calls them out; B brings the stone which he has learnt to bring at such-and-such a call.—Conceive this as a complete primitive language’ (Das, 1998). Is this not an anthropological us of language as Sen, Davis and others have claimed, and might have been transmitted to Wittgenstein by Gramsci via Sraffa?

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