Piero Sraffa and Counterfactuals: A View from Sraffa's Unpublished Papers in the Late 1920s Free

Abstract

This article reconstructs Sraffa's position with regard to counterfactual reasoning in the second half of the 1920s as documented by his up until now unpublished papers. While Sraffa did not use the term “counterfactual,” it is precisely this concept he had in mind when examining certain non-purely-observational propositions and discussing responses to “what if?” questions. He did so with respect to different contexts, but his attention focused primarily on the marginal theory of value and distribution. At an early time he showed with regard to the latter that any simple analysis of single causation in terms of counterfactuals is difficult to sustain. Sraffa's method of inquiry can be interpreted as an instance of abductive reasoning. The article confirms Sen's interpretation that Sraffa met counterfactual reasoning with suspicion, since it might easily lead to highly misleading propositions. But Sraffa's manuscripts do not support the extreme view (not entertained by Sen) that any counterfactual reasoning ought to be rejected.

1. Introduction

In a series of contributions, Amartya Sen (1978, 1989, 2003, 2004) discussed the methodological foundations of Piero Sraffa's 1960 book, Production of Commodities by Means of Commodities. Sen's focus was particularly on the role of counterfactual reasoning, which, in his view, is central in neoclassical economics and largely absent in Sraffa's.

In 1928 Sraffa showed a draft of the production equations that were to constitute the analytical core of the first two chapters of Production of Commodities to John Maynard Keynes and Arthur Cecil Pigou. In the preface of his book Sraffa emphasizes that he resisted the temptation of assuming constant returns to scale and recollects that when he showed his equations to Keynes, the latter strongly “recommended that, if constant returns were not to be assumed, an emphatic warning to that effect should be given” (Sraffa 1960: vi). On this occasion Sraffa did not mention Pigou's comments on the same topic.¹ Hence, two towering figures of Marshallian scholarship alerted the young Sraffa to the need of taking the issue of returns to scale seriously in order to minimize the risk of being grossly misunderstood. Thirty years later, he showed the manuscript of Production of Commodities, which was almost ready for publication, to Sen (see Sen 2004, 2016). While Keynes and Pigou raised questions concerning returns to scale, Sen did so with regard to counterfactuals. He did not mention the issue of returns to scale perhaps because in the draft of the preface of Production of Commodities he was given, Sraffa had explicitly addressed it, following Keynes's advice. Sen (2004: 27) argued, however, that the absence of counterfactual concepts is a “clear and prominent” feature of the book; he added that such an absence “seemed like a bit of an overkill despite the legitimate doubts that could be raised about specific counterfactual notions, such as marginal product or marginal utility,” and he concluded that “he was not entirely convinced by [Sraffa's] answers” to his questions on this issue.

To avoid misunderstandings, it must be emphasized that Sen did not maintain that Sraffa denied any role for counterfactual reasoning in economics. According to Sen, Sraffa thought, first, that counterfactual reasoning ought to be employed with utmost care and circumspection and, second, that a significant methodological divide separates theories that systematically employ counterfactual magnitudes (such as the marginalist theory of value and distribution) and theories that do not (such as the one proposed in Production of Commodities). In the main part of this article we discuss when and how according to the young Sraffa counterfactual reasoning is legitimate in economics and what precisely he found fault with in its use in the marginal theory of value and distribution.

Before we continue, two clarifications are appropriate. First, Sraffa's work on his 1960 book can be divided into essentially three periods: from the second half of 1927 until early 1931 (period I); from the early 1940s until around 1946 (period II); and from 1956 until the publication of his book (period III). When we speak of the young Sraffa, the reference is obviously to period I. It is the formative period of his thoughts that led up to Production of Commodities, although these thoughts have their roots especially in his earlier critical work on Alfred Marshall's theory of partial equilibrium (see Sraffa 1925, 1926, 1930) and are characterized by a struggle of escape from the marginalist system of thought. However, as we shall see, Sraffa in period I managed to win that struggle, not in each and every respect but with regard to the foundations and main pillars of his novel theoretical construction. When we compare Sraffa's views and achievements in periods II and III with his foundational work in period I, we see that despite important corrections and improvements concerning certain core aspects and a number of details, the development of his analysis is characterized by a remarkable continuity. Since we intend to deal with the issues under consideration in periods II and III in separate contributions, here we will refer to the later periods only in passing. The focus of attention is the young Sraffa. We hope to be able to show that against all expectations to the contrary, this concern provides a valuable complement to a study of modern economic problems.

The second clarification concerns the circumstance that to the best of our knowledge Sraffa in his published and unpublished writings never used the terms “counterfactual reasoning” or “counterfactual.” This is perhaps not surprising, because these terms became popular outside the inner circle of professional philosophers only after the publication of Lewis 1973a and Lewis 1973b; see Collins, Hall, and Paul 2004. However, different words may be used by different authors to describe essentially the same phenomenon or problem. This applies to the case under consideration. We therefore agree with Sen that what Sraffa discusses in certain passages of his writings may be expressed using the vocabulary of counterfactual theories. It hardly needs to be stressed that, as concerns counterfactuals, the field and its various subfields from philosophy to the natural and social sciences have experienced major developments during the past fifty years. These are reflected, inter alia, in a burgeoning of different approaches, notions, concepts, and technical terms. The bewildering and still swiftly growing variety in the field need not concern us here, except in particular cases in which there is compelling evidence that Sraffa in the late 1920s came up with considerations that may be interpreted as early soundings of ideas that became prominent only much later. We shall see that this is in fact the case. According to Menzies and Beebee (2024: 1), “Intense discussion over forty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of counterfactuals.” We shall see that Sraffa's criticism of typical Marshallian propositions concerning supply curves of individual commodities implies indeed a rejection of a simple analysis of singular causation. However, apart from what we consider to be obvious cases, it is not our intention to assess Sraffa's early work in terms of the most advanced contributions to counterfactual theorizing. We rather look at it through Amartya Sen's lens and his interpretation of Sraffa's views, using counterfactual vocabulary.

We may now specify the purpose of this article in greater detail. As has already been mentioned, we focus on period I of Sraffa's constructive and interpretive work on value and distribution. We aim to show in particular the following:

• (i) As a result of his reconstruction of the development of value theory beginning with the approach adopted by Sir William Petty to the then-contemporary neoclassical economics, Sraffa defined the problem that the theory of value was designed to answer in such a way that no reference to counterfactuals was essential.

• (ii) Sraffa raised no categorical objection to the use of counterfactual reasoning in economics in general other than those mentioned sub (i).

• (iii) Sraffa's critique of Marshallian supply curves of individual commodities did not rely on a criticism of counterfactual reasoning as such, but was rather meant to show that in a partial equilibrium framework Marshall's argument involves a defective economic analysis.

• (iv) Sraffa's critique sub (iii) followed from assessing Marshall's partial or “particular” equilibrium approach against the background of a general approach, looking at the economic system as a whole and taking into account interdependences and compensating effects.

• (v) The kind of counterfactuals marginalist theory invoked with reference to the “quantity of capital” in given supply and its marginal product cannot be rendered meaningful except in the uninteresting case of a one-commodity economy. Already in period I we encounter passages in Sraffa's manuscripts that point this out.

The next two sections will, first, present some preliminary material concerning Sraffa's intellectual journey as documented by the Sraffa archive and, second, look at Sraffa's analysis as seen against the background of counterfactual reasoning provided by Sen.²

2. Sraffa's Intellectual Journey and the Sraffa Archive

As is well known, Piero Sraffa (1960: vi) designed Production of Commodities “to serve as the basis for a critique of [the marginal theory of value and distribution].” He added, “If the foundation holds, the critique may be attempted later, either by the writer or by someone younger and better equipped for the task” (vi). The critique was in fact attempted by followers of Sraffa in the so-called Cambridge controversies in the theory of capital (see Harcourt 1972; Kurz and Salvadori 1995: chap. 14). However, as we know from his unpublished papers and correspondence kept at Trinity College, Cambridge, Sraffa himself collected material for another book that was explicitly devoted to the task. Alas, he was prevented from accomplishing it because of other obligations (especially the completion of the edition of The Works and Correspondence of David Ricardo [Ricardo 1951–73]) and deteriorating health. Some scholars (especially Pierangelo Garegnani and Luigi Pasinetti) who participated in the Quarterly Journal of Economics symposium on capital theory published in 1966 had, in the process of preparing their contributions, occasionally long and fertile discussions with Sraffa, which are echoed in their papers and provide evidence of Sraffa's views.³

Right at the beginning of the preface of his 1960 book, Sraffa (1960: v) significantly emphasized that “no changes in output and (at any rate in Parts I and II) no changes in the proportions in which different means of production are used in an industry are considered, so that no question arises as to the variation or constancy of returns. The investigation is concerned exclusively with such properties of an economic system as do not depend on changes in the scale of production or in the proportions of ‘factors.’” This implied, he went on, resuming the “standpoint . . . of the old classical economists from Adam Smith to Ricardo, [which] has been submerged and forgotten since the advent of the ‘marginal’ method” (v). He explained that “the marginal approach requires attention to be focused on change, for without change either in the scale of an industry or in the ‘proportions of the factors of production’ there can be neither marginal product nor marginal cost” (v). These propositions met with a considerable lack of understanding by both friend and foe and gave rise to occasionally weird interpretations and heated debates (see, e.g., the debates reported in Kurz 2000). Even someone as close to Sraffa as Pasinetti (2005) famously spoke of the “Sraffa-enigma.” Sraffa's papers in the Wren Library, his correspondence, and his huge personal library with many annotated books document in great detail his highly complex intellectual journey. They contain the key to a better understanding of what he actually published during his lifetime. Many of his statements that at first sight look mysterious or impenetrable can be rendered clear by going back to their sources in the Sraffa archive. Their study is therefore no exercise in morbid antiquarianism, but to the extent to which his literary heritage is concerned with economic problems for which no fully satisfactory answers have yet been found, it can be expected to widen our perspective and improve our understanding of them. This is indeed what we experienced in great measure when working in the archive. The same will also be shown in the following with regard to a particular but important problem in economics and the social sciences with which Sraffa struggled: Which kind of counterfactuals can legitimately be used?

3. Sen on Sraffa

According to Sen (1978: 180), Sraffa sought to explore “how much can be said about the interrelations between prices, distribution and physical quantitative magnitudes using only directly observed data, without making any use of counter-factuals.” Such an exploration, Sen surmised, was motivated, inter alia, by the fact that counterfactual reasoning is an essential element of any model adopting the “‘marginal’ method” (Sraffa 1960: v), whether of the general or the partial equilibrium variety. Since Production of Commodities was intended as a “prelude” to a critique of marginalist (or neoclassical) theory, Sraffa deliberately avoided any demand and supply relationships and was keen to identify and analyze just those “propositions that could be made without using any counter-factual quantities” (Sen 1978: 181).

In the same vein, Sen (1989) first emphasized the heterogeneity of economic models, which may be built for descriptive, predictive, and normative goals; then he underlined the significance of counterfactual reasoning within models expressly built for predictive and normative goals; and finally he claimed that there are many descriptive problems in which counterfactual reasoning is not required. Sen did not specify which kind of descriptive problems he had in mind; but he mentioned Production of Commodities as the most interesting contribution to an analysis of such problems. For Sen (1989: 305), “Sraffa tried to explore whether the relationship between prices, productions, and distributions of income cannot be substantially explored without considering any changes—factual or counterfactual—and without, thus, involving any ‘marginal’ concepts at all (since such concepts take the form of asking what would have happened if something had been one unit more or less).” However, counterfactuals, Sen claimed, are hardly avoidable if one is interested in answering a “why?” question. Since Sraffa in Production of Commodities focused attention on investigating the properties of given systems of production, that is, given configurations of economic magnitudes, he deliberately avoided analyzing the causal mechanism by means of which a given configuration could have come about and how an exogenous variation in one of the givens would change it. In Sen's view, this explains the rare presence of counterfactuals in Production of Commodities.

More specifically, Sen (1989: 305), on the one hand, noted that Sraffa postulated certain characteristics of the economy under scrutiny (in particular a uniform rate of profits) but “did not go into the question as to why these characteristics . . . could be expected to hold.” On the other hand, Sen remarked that “it is possible to argue that such a justificatory inquiry would take one in the direction of equilibrium economics, involving the use of counterfactual considerations.” This last remark may be read as implicitly questioning Sraffa's claim that his construction could, in principle, serve as the basis for an effective critique of neoclassical equilibrium theory. In this context, according to Sen, Sraffa did not intend to provide “a causal system rival to the neoclassical one.” He is instead said to have wished to change “the nature of the inquiry—toward an important but neglected theme—rather than providing a different answer to a given question already in vogue in contemporary economics,” that is, to “return to an important classical interest underlying a part of the motivation for the search for a ‘theory of value’” (306).

Finally, recollecting his numerous conversations with Sraffa while in Cambridge in the 1950s, Sen (2003: 1251) remarked that Sraffa had a “philosophical suspicion of the invoking of ‘counterfactual’ magnitudes in factual descriptions” and “did find that the use of counterfactuals involved difficulties that purely observational propositions did not.” Sen added that while in ordinary life Sraffa did not abstain from counterfactual thinking—“life would have been unbearable with such abstinence”—the Italian economist believed that “a big methodological divide” is involved in the choice of making use of counterfactuals (1251). Unfortunately, we do not learn more about the kind of reservations Sraffa expressed about counterfactuals in these conversations.

A crucial question concerns the relationship between marginalist economics and counterfactual reasoning. Sen is to be credited with having raised this question, but his report on the conversations he had with Sraffa apparently did not place him in a position to provide a definite answer as regards Sraffa's view on the matter.⁴ While he discerns a close connection between Sraffa's critique of marginalist economics and his philosophical reservations about counterfactual reasoning, he refrains from expressing a final judgment on the issue. Marcuzzo and Rosselli (2011) also commented on the issue under discussion and argued that marginalist and counterfactual reasoning are not one and the same thing. This is obviously correct. However, in order to be able to decide whether Sen rightly questions the suitability of Sraffa's theoretical construction as the basis of a critique of the marginal theory of value and distribution, we need to go further and in a first step specify the relationship between marginalist and counterfactual reasoning, as Sraffa perceived it. It is only then that we will be in a position to formulate an informed assessment of Sraffa's approach especially as regards its alleged ability to serve as a prelude to a critique of marginalist economics. As has already been mentioned, in this article we focus attention on period I of Sraffa's work on what was to become his 1960 book. The terminal point of his respective studies will be mentioned only when it is suitable to do so.

As both Sraffa's papers across all three periods of his constructive and interpretive work and also Production of Commodities document, he engaged repeatedly in counterfactual reasoning. While, as we underlined in section 2, large parts of his book (pts. I and II) take output levels and input proportions as given, this is not so in part III, which is devoted to “Switch in Methods of Production,” that is, the choice of technique problem. But there are other cases in which Sraffa discusses hypothetical changes in output levels on quantities of inputs employed, income distribution, and relative prices. These concern, first, systems of production using renewable resources, such as different qualities of land, but then also exhaustible resources, such as coal or various kinds of metals. He does so as early as period I in order to come to grips with the marginalist theory as opposed to the classical theory of extensive and intensive diminishing returns and extensive and intensive rent especially in David Ricardo's analysis. These considerations span from manuscripts drafted in the late 1920s up to chapter 11 of Production of Commodities. They concern, second, the case of joint production proper. After early indications in period I of Sraffa's awareness of the specific difficulties the case of joint production poses, Sraffa in periods II and III analyzes the case in great depth and stresses the importance of quantities of effectual demand, or “requirements for use,” as he calls them, for the properties of the corresponding systems of production; see the upshot of all this in chapters 7–10 of Production of Commodities. He deals with obsolete machines that are no longer produced but are still worth employing for what they can get, depending on effectual demand, in section 91 of chapter 11.

Sraffa establishes his results without any recourse to marginalist concepts, such as schedules of demand and supply, marginal productivity, or marginal cost. He succeeds in reviving a view of the system of production, distribution, and market exchange rooted in the classical tradition from Adam Smith to Ricardo. Therefore it appears to us to be legitimate to claim that, contrary to Sen's view, Sraffa actually did provide “a causal system rival to the neoclassical one.” This is confirmed by the fact that he managed to show why central pillars of the neoclassical doctrine are untenable. This applies especially to its attempted determination of the competitive rate of profits in terms of the marginal productivity of capital.⁵

In addition, the following observations are apposite. Whenever Sraffa (1960) makes the assumption that the quantities of commodities are given and unchanging, he does not intend to address such questions as, “What would happen to relative prices and income distribution if these quantities were to change?”⁶ But it is also true that in a subsistence economy, as it is analyzed in chapter 1 of Production of Commodities, the marginal productivity of, say, labor cannot be observed: no experiment of the ceteris paribus type—add or subtract a little labor leaving all the other inputs unchanged and then measure the resulting change in output—can sensibly be performed since there is a single proportion among inputs that allows reproduction. (The absence of a phenomenon is a sufficient but no necessary condition for its nonobservability.)⁷

4. Sraffa's Reconstruction of the Theoretical Domains of Value Theory in Classical Political Economy and in Marshallian Economics

The Sraffa archive in Cambridge covers some fifty years of Sraffa's intellectual endeavors: it is huge and complex, to say the least (see Kurz 1998). Here we restrict our discussion to some of the manuscripts composed in the years between the two major turning points in Sraffa's intellectual journey. The first one occurred in the second half of 1927 when Sraffa's understanding of the classical approach to the theory of value and distribution grew swiftly, culminating in the elaboration of the first sets of production equations (see Garegnani 2005), while the second one occurred in the spring of 1930 subsequent to Sraffa assuming the task of general editor of David Ricardo's works and correspondence on behalf of the Royal Economic Society (see Naldi 2005). In those years Sraffa's research can be said to have been particularly focused on three closely interrelated themes: first, the rediscovery and reconstruction of a distinct classical approach to the theory of value and distribution; second, a deepening of the critique of Marshallian economics above and beyond Sraffa's papers in the mid-1920s, “Sulle relazioni fra costo e quantità prodotta” (1925, [1925] 1998) and “The Laws of Returns under Competitive Conditions” (1926); and, third, an elaboration of systems of simultaneous equations with and without a surplus product and an investigation of their properties. These systems would become the analytical core of the first two chapters of Production of Commodities.

Sraffa's manuscripts in the late 1920s provide ample evidence that the meticulous reconstruction of Classical economics was actually an essential part of his overall theoretical research program.⁸ In the second half of the 1920s, Sraffa convinced himself that the classical economists had a view of the purpose, analytical structure, and contents of the theory of value and distribution that was radically different from the Marshallian one, which was the orthodox view at the time then (and to a considerable extent still is nowadays). The concepts forged by the classical economists, and the relationships between these concepts, were very different from those contemplated in Marshall's theory. In particular, the reasoning of the classical economists revolved around concepts such as production conceived as a circular flow, physical real costs, and social surplus (see Kurz and Salvadori 2004, 2005). These were highly sophisticated notions, but unfortunately the classical authors lacked the indispensable analytical tools and techniques to bring them to full fruition. In particular, systems in which commodities are produced by means of commodities have to be dealt with in terms of simultaneous equations, which presuppose a knowledge of mathematical tools that were not available to the early classical authors.⁹ Their attempts to cope with the impasse as best as they could were, however, less than perfect and invited criticisms by, among others, William Stanley Jevons, Carl Menger, Léon Walras, and Eugen von Böhm-Bawerk. While some of their objections to propositions by Ricardo et al. were correct, the critics typically missed the genuinely different nature and basic soundness of the classical conceptualization (see Kurz and Salvadori 2002 and Signorino 2004).¹⁰

Besides the notions of physical real cost, social surplus, and production as a circular flow, to Sraffa there was a further aspect that distinguished Classical from Marshallian economics. This concerns the theoretical domain of value theory defined in terms of the problem the theory was designed to solve and the elaboration of analytical concepts and tools congenial to mastering this task. According to Sraffa, in the course of time, vastly different theoretical concepts and analytical tools have been forged under the umbrella of value theory. Moreover, many of the controversies that permeate the history of value theory were caused by the tension between sophisticated concepts and primitive tools and by attempts to solve one set of problems with the help of tools that had been designed for the solution of an entirely different set. In particular, classical economists, when they theorized about value, typically adopted a general perspective, looking at the economic system as a whole and therefore at entire systems of production. Value theory was therefore seen to be an integral part of the theory of wealth formation and how wealth is distributed among different social classes, not to mention which use of wealth is being made (consumption or investment). By contrast, Marshallian economists, when they theorized about value, typically adopted a partial equilibrium perspective. To them, value theory was designed to solve problems such as the determination of the equilibrium price of a particular commodity, given the equilibrium prices of all other commodities and factors of production, and of how an exogenous change of one of the givens affects price and quantity traded of the commodity under consideration. In Sraffa's papers of the late 1920s there are several manuscripts and notes that deal with the issues just mentioned.

In folder D3/12/3, “‘Notes: London, Summer 1927 (Physical real costs etc)’ including preparations for lectures,” there is a document that is of particular interest to us and therefore deserves to be sctutinized carefully. Sraffa titles it “General Scheme.” In it Sraffa writes as follows:

After a quotation from Ricardo, according to whom political economy should not be considered an inquiry into the nature and causes of the wealth of nations but rather an inquiry into the distribution of the total product among the various social classes, the document continues:

A few pages later, Sraffa outlines a possible index of his 1928–31 “Lectures on Advanced Theory of Value”; he emphasizes the need to distinguish between the “two meanings of ‘theory of value’” and plans to discuss some examples of the “confusions arising from failure to distinguish them” (D3/12/3: 12r.).

In his 1928–31 “Lectures” (folder D2/4), Sraffa first discusses various arguments in support of his thesis that a full comprehension of the present state of economic theory requires an in-depth knowledge of its history. From page 17 onward he analyzes in detail the distinction between two radically different concepts of costs of production: the classical objectivist concept, which refers to the necessary minimal amounts of material resources that must be advanced and productively consumed in order to enable the production process to start, and the Marshallian subjectivist concept, which refers to the “disutility” of work, “abstinence,” and so on, reflected in the (usually monetary) rewards that must be promised to the owners of the factors of production to induce them to provide their services. In the course of time, the classical objectivist concept of real physical cost was progressively obliterated and eventually replaced by a subjectivist concept. Nonetheless, Marshall defined as “real costs” his subjectivist notion of costs. One reason why Marshall used this term was that, contra Jevons, he wished to convey the impression that there was a basic continuity from classical to marginalist theory rather than a fundamental break with it. See on this, inter alia, Fratini 2018. For the purpose of this article, the following passage is the most relevant:

What emerges from a scrutiny of these documents may be summarized as follows:

1. A single term “cost of production” is used in the economic literature to denote two different theoretical concepts devised for tackling different theoretical problems.

2. The failure to distinguish between them (as Marshall's case shows) results in a defective economic analysis.

3. The failure to acknowledge that two different value theories, based on different notions of cost, have been elaborated to solve different theoretical quaesita leads to the categorial error of judging one of the two different value theories as “right” and the other as “wrong.” The error derives from the fact that the two theories are not in pari materia.¹²

4. From a methodological point of view, no a priori reason compels economists to employ the same theoretical conceptualization or analytical tool for the solution of different sets of problems. Hence, economists may legitimately choose to employ a given theoretical conceptualization or analytical tool for the solution of one set of problems and a thoroughly different one for the solution of another set of problems.

5. If the question under scrutiny is “what determines at a given instant the price of boots?” and not “what determines the evolution of the price of boots through time?,” Sraffa decides in favor of the overall amounts of material resources actually employed in the production of boots as the most plausible of all competing explanations. (The usual Marshallian explanation in terms of the inner feelings or motivations of the shoemaker Sraffa does not reject as plain wrong, but as less plausible, given the question under scrutiny.) Sraffa's argument is an instance of abductive reasoning: he is here proposing his “best guess” solution to the question under discussion. In this perspective, the production equations Sraffa starts investigating from November 1927 onward may be interpreted as an attempt to give a formal answer to the question “what determines the n prices of the n produced commodities at a given instant?” In this way he intends to adequately support his abductive inference.

In this section we have clarified the reasons why for Sraffa it was so important to define accurately the theoretical domain of value theory. In the following two sections we highlight Sraffa's views concerning this domain and which theoretical conceptualizations and analytical tools he thought to be congenial to addressing the problems under consideration. In this context we investigate the role he assigned to counterfactuals in the theoretical domain of value theory and beyond.

5. Theoretical Problems Related to Price Fixing

As was shown in the previous section, Sraffa was of the opinion that contemporary economists, through the adoption of the notion of equilibrium, had given up the classical quest for “one single ultimate cause of value” underlying the “relation of commodities as a whole to mankind.” Accordingly, they had redefined the theoretical domain of value theory as the explanation of the price-fixing process of individual commodities or factors of production. In this section we reconstruct Sraffa's late-1920s views concerning the theoretical problems related to the price-fixing process.

In folder D3/12/7, “Notes, essentially on industries using hypothetical examples with a note on language,” dated 1928, there are two documents. The first is titled “Why I neglect Incr. & Dim. Ret. in equations” (D3/12/7: 85r.–87r.) and the second, “Difference (simultaneous) v. Change (succession in time)” (D3/12/7: 115r.–119r.).¹³ In these two documents Sraffa shows full awareness of the fact that he cannot sidestep the question of which assumptions, if any, he makes about returns to scale with regard to his production equations. He seeks to clarify for himself whether or not there is a place for variable returns in them and, in so doing, explicitly links the issue of variable returns to the use of counterfactual reasoning.

In what follows we provide an interpretation based on a reconstruction of the analytical core of these two documents. A full quotation of the documents is provided in the  appendix. Two preliminary remarks are appropriate before entering into the analysis. First, apparently, Sraffa had second thoughts on some issues, particularly those concerning the role of time in relation to variable returns in his production equations. Second, as is only natural for someone who is writing for himself, many ideas and logical inferences are just sketched and not fully worked out.

In this section our interpretation focuses mainly on the second document, whereas in the next section it mainly focuses on the first one. Sraffa stresses that, within the price-fixing process of individual commodities, two different theoretical problems ought to be kept distinct:

For Sraffa the importance of this distinction lies in the fact that “the general confusion in all theories of value (except Marx probably) must be explained by the failure to distinguish between two entirely distinct types of questions and the universal attempt of solving them both by one single theory” (D3/12/7: 115r.).¹⁴

To Sraffa, these two problems ought to be analyzed in terms of two different approaches based on different theoretical assumptions. As regards the First Problem, Sraffa invokes without further ado the so-called law of indifference, which assumes a uniform rate of wages for homogeneous labor, a uniform rate of interest, and a single money price for each and every unit of a given commodity. By contrast, as regards the Second Problem, such assumptions are inappropriate. In order to solve the latter, theorists must first study what causes changes in wages and the rate of interest, variables that in the treatment of the First Problem were assumed to be given and constant (see D3/12/7: 115r., 116r.). The upshot of this distinction reads as follows: “It is possible that the two problems have to be solved in different ways: and that of two opposite general theories of value, one may be true in respect of one question and the other in respect of the second” (D3/12/7: 116r.).

Hence, in order to avoid confusion, it is necessary to assign the analysis of each problem to a specific branch of economic theory. Sraffa leaves no doubt that the analysis of the First Problem falls within the theoretical domain of value theory. However, as regards the Second Problem he appears to have not yet fully made up his mind. He considers two options: to elaborate a specific value theory for it, or to assign it to the theory of business cycles (see D3/12/7: 117r.). In the former case, one would still have two types of value theory pertaining to different problems, whereas in the latter case, one would have only one theory dealing with the First Problem.

Another difficulty concerns the role of time in Sraffa's equations in relation to variable returns. In the first document Sraffa emphasizes that his equations deal only with the First Problem. The Second Problem is not considered, because his equations do not explicitly include the element of time:

With regard to an analysis of the Second Problem, he appears to be of the opinion that what really causes the difference is the absence or presence of the element of time and not of variable returns to scale. From this perspective, Sraffa seems to have found a convincing justification for being silent about returns in his equations: no assumption about them is needed, given the kind of problem his production equations are supposed to solve. In his view, in fact, “no system of equations, whether it considers variable returns or not, could tell this if time does not enter as variable. Take a pair of Marshall's D. & S. curves. They tell that, giving the conditions the price will be AB: to this effect it is quite indifferent whether the supply curve is SS₁ or S₂S₃” (D3/12/7: 85r.). See figure 1.

However, in the second document Sraffa then claims that the element of time is also not the distinguishing feature of the analyses of the two kinds of problems. He rather insists that “time is not the fundamentum divisionis. The really fundamental discriminating criterion is that in one case [the determination of the change of commodities’ relative prices] certain general conditions are different (or change) and in the other [the determination of commodities’ relative prices] they are uniform (or constant)” (D3/12/7: 118r.–119r.).

Apparently, Sraffa felt the need to reconsider the issue of the role of time in his equations. One possible explanation is the following. Taking the absence or presence of time as the differentia specifica of the analyses of the two kinds of problems leads to considering the First Problem as a static one and the Second Problem as a dynamic one. Yet since static analysis is but a special case of dynamic analysis, it is possible to argue that a solution of the Second Problem carries with it, as a by-product, a solution of the First Problem.

However, such a conclusion Sraffa does not endorse.¹⁶ This is evident from what he writes about Marshall's symmetric theory of value. This theory, he surmises, can be understood as an attempt to solve the Second Problem:

The fact that Marshallian economists de facto ignore the First Problem may be seen to reflect the implicit assumption that a solution of it is but a special case of a solution of the Second Problem.¹⁷ By contrast, Sraffa sharply rejects the “special case” interpretation of the First Problem. Had Sraffa conceded that the First Problem is but a special case of the Second Problem, he would then implicitly have admitted that the two problems are nested and that his criticism of Marshall's partial equilibrium analysis, while pointing out important deficiencies of it, could not be devastating.

This is the reason why, in our interpretation, the element of time is of no decisive importance. To Sraffa, the two problems are completely different in nature. He claims that while the analysis of the First Problem suggests “a geometrical theory,” the analysis of the Second Problem suggests “a mechanical theory” (see D3/12/7: 117r.). Unfortunately, he leaves it at that. He stresses only one consequence of his distinction: to claim that the theory designed to tackle the First Problem ought to be geometrical implies that it is misleading to call the problem static. He emphasizes that the First Problem “is so much timeless that it cannot even be called static” (D3/12/7: 117r.). A few lines later Sraffa seeks to clarify things in terms of a metaphor: the object [of the First Problem] “is, as it were, the photograph of a marketplace.”

We interpret this metaphor in the following way: Sraffa thought that framing the distinction between the First and the Second Problem in terms of the absence or presence of motion is misleading, because such a framing would imply the “special case” interpretation of the First Problem, which Sraffa strictly rejected. This is why, in our view, Sraffa emphasized that, in an analysis of the First Problem, to assume the absence of any kind of movement is unnecessarily restrictive.¹⁸ The metaphor of a photograph may, in fact, be seen to convey the idea that some of the movements that do occur in the marketplace are captured in terms of an analysis of the First Problem.¹⁹

Closely related considerations are to be found in another document from around the same time concerning magnitudes to be taken as data. In D3/12/13: 2–5, Sraffa summarizes his view as to which magnitudes are involved in economic theory and distinguishes between three kinds. First, there are those quantities, “which cannot possibly be measured, because they are not defined in terms of the method of measuring them, e.g. marg. utility and sacrifice. (No definition at all is given for measuring them in the case of several individuals. . . .).” He concludes that “such quantities must be excluded altogether: at the worst, they may be used as a fictitious device for solving problems, but must not appear either in the premises nor in the conclusions” (D3/12/13: 2). About the second kind he writes,

Then there is a third kind, that is, “the class of quantities, which form the basis of Marshall's theory (or, rather, of Pareto's), such as demand & supply curves, marginal productivities, (i.e. rate of growth of total) indifference curves, etc. Here the constant quantities have no names–they are the parameters of curves.” Sraffa continues:

Sraffa goes on to argue that “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.’” Yet this is not all. He adds that

In an adjunct (D3/12/13: 4), he mentions under the heading of “inexistent possibilities” the “Fantastic character of S & D curves. Also of Productivity curves. But not of Different lands.” Interestingly, he admits that “there is some reality in Pr. [productivity] curves. Because, after all, the only explanation (cause) of a thing being what it is, is that, ‘if it were different, absurd consequences would follow.’” He concludes his respective considerations with two remarks, the first one summarizing his concerns regarding marginalist theory and the second one delineating the route he wished to follow in his own analysis: (1) “The mistake is to assume direct knowledge of these (inexistent) consequences.” And (2) “Changes (possible) must only be predicted from (actual) differences.”

The way in which he sought to realize the principle stated in conclusion (2) is first seen in terms of his treatment of extensive diminishing returns and extensive rent, but then (in the 1940s) also with respect to intensive diminishing returns, which caused him a lot of headaches for quite some time. He eventually managed to overcome his difficulties without violating the above principle in terms of the coexistence side by side of two methods of production by means of which land of a given quality is cultivated. It suffices to change the combination in which the two methods are employed to cultivate the land in order to meet the requirements for use (see Salvadori and Signorino 2023).

6. On the Role of Counterfactuals in the Theory of Value

After having discussed the different assumptions, which, according to Sraffa, must be adopted in the analyses of the two problems he distinguished, we now have a closer look at his view of the issue of variable returns and the role of counterfactual reasoning.

Given the hegemonic status of Marshall's economics in Cambridge at the time, it should not come as a surprise that Sraffa repeatedly elaborated his own views on value theory against the background of those of Marshall. According to Sraffa, Marshall's symmetric theory of value was explicitly designed to answer questions of the following kind:

All these “what if?” questions invite economists to elaborate consistent explanations of changes through time of the market price of a given commodity. According to Sraffa's taxonomy, they are all questions belonging to the Second Problem. Marshall had developed a value theory based inter alia on unobservable magnitudes (e.g., marginal utility and disutility) and on assumptions about variable returns to scale, which he illustrated with the help of mechanical metaphors (forces, pillars, scissors). He was compelled to do so, because for the kind of questions he was interested in it was of paramount importance to assume (i) the existence of a market supply and a market demand curve with regard to a given commodity and (ii) to determine the slope of the market supply curve by means of specific assumptions about variable returns.²⁰ In both regards, counterfactual reasoning was indispensable.

From this viewpoint, we claim that Sraffa's critique concerns two features of Marshall's symmetric theory of value.

First, Marshall's analysis of the price-fixing process of individual commodities implicitly plays down the importance of the First Problem by considering it simply as a special case of the Second Problem. In contrast, Sraffa was convinced that the First Problem deserves to be analyzed in its own right and requires neither a recourse to particular forces at work nor to any counterfactual reasoning. Sraffa in fact writes,

And, “I am afraid it will be difficult to make it clear that we are considering what has actually happened in the markets, and not what might have happened had things been different” (D3/12/7: 86r.). By contrast, for Sraffa, counterfactual reasoning is indispensable only with regard to the Second Problem. As he put it,

Second, Sraffa argued that Marshall's answers to the various “what if?” questions are implicitly based on the assumption that it is irrelevant to take into account the cause of the initial change in the given magnitude that activates market forces and triggers price dynamics. Such an assumption, Sraffa insisted, is highly questionable: “The point is—can such questions be answered in a general way, i.e. assuming the ‘initial’ movement to be entirely arbitrary? or is it not necessary to know how it has arisen?” (D3/12/7: 118r.). Not caring about what caused the initial change is bound to lead to defective economic analysis. As we have seen, Sraffa concluded that “simple statements” of the kind implied by supply curves—“if output increases 10%, cost falls 2%”—must not be made, because they cannot be “unconditional.” The result, he emphasized, “depends upon how the demand increases, i.e. whence is the transference of cap. & lab. made. Entirely different results will take place if the increase in the demand for bicycles is due to a smaller demand of guns or of wine” (D3/12/7: 87r.).²¹

The main results arising from our reconstruction of Sraffa's critique of Marshall's value theory may be summarized in the following way:

• (A) Counterfactual reasoning can play no role in analyzing the First Problem, which Sraffa approached in terms of his equations of production.

• (B) Counterfactual reasoning may and typically will be indispensable when analyzing the Second Problem, that is, when answering the various “what if?” questions for which Marshall had elaborated his symmetric theory of value.

• (C) However, the specific counterfactual reasoning underlying Marshallian market supply curves is defective because it assumes a partial equilibrium perspective.

• (D) The simple analysis of singular causation in terms of counterfactuals entertained in the marginal theory of value and distribution is difficult to sustain and bound to lead to misleading results.

To substantiate claim (C) and, as a consequence, claim (D), we show in the following section that Sraffa sketches a model with two aggregate sectors in order to analyze sectoral cost dynamics. Seen through the lens of a general analysis, the results derived within a partial equilibrium framework typically turn out to be untenable.

7. Counterfactual Reasoning and General Competitive Analysis

In the document “Why I neglect Incr. & Dim. Ret. in equations” (D3/12/7: 85r.–87r.) Sraffa argues that knowing the slope of the market supply curve of a given commodity is relevant if and only if one is interested in answering a “what if?” question related to the change through time of the market price triggered by an exogenous change in the respective market demand curve. As we saw in the previous section, this kind of question belongs to the Second Problem, whereas Sraffa's production equations are designed to answer the First Problem. To clarify this, Sraffa in the document under consideration states that

• (i) knowing the slope of the market supply curve is irrelevant;

• (ii) postulating the existence of market forces (allegedly) triggered by an exogenous change in one of the givens is therefore redundant; and

• (iii) no counterfactual reasoning of the kind “what might have happened had things been different” needs to be taken into consideration.

Sraffa leaves no doubt that his production equations entail a radical change in theoretical perspective. He therefore expected it to be received with some irritation by people brought up with Marshallian economics. In order to alienate or even antagonize such readers as little as possible, Sraffa proposes to adopt the assumption of constant costs. Note that Sraffa does not say “in my equations I am assuming constant costs”; he rather remarks that it is “useful to explain that the reader may assume” constant costs (see D3/12/7: 86r.). He supports his suggestion by adding that “on the assumption of free competition, incr. & dim. costs are impossible” (D3/12/7: 86r.).

Already in the 1925 Italian paper Sraffa had argued that Marshallian economists usually tend to downplay the constant cost case since they explain constant cost as the outcome of a perfect balancing of the antagonistic tendencies of increasing and decreasing costs—an empirically exceptional case, indeed. In so doing, they ignore the possibility that constant costs may result not from such a balancing but rather from the absence of both kinds of variable costs. To Sraffa, the usual Marshallian explanation of constant costs is contradicted by the fact that the empirically most relevant cases of variable costs do not fall within the theoretical domain of the Marshallian model, once consistently reconstructed (see Signorino 2000, 2001). Hence, following Sraffa's logic, the constant cost assumption resulting from the absence of both kinds of variable costs is empirically less implausible than Marshall's alternative within the latter's perfect competition model and may arguably be adopted as a first approximation.²²

In the document here under scrutiny Sraffa does not reiterate the results of his mid-1920s papers regarding the constant cost case in Marshallian economics. He rather puts forward an entirely new argument to criticize the way Marshallian economists usually analyze increasing and decreasing costs within a partial equilibrium model. In order to show why Marshall's respective argument cannot be sustained, Sraffa provides a sketch of a little model with two aggregate sectors, to which we turn now. The relevant passage is the following:

Sraffa assumes that total expenditures for the purchase of consumer goods are given and constant. The economy-wide endowment of land, labor, and capital is given and constant: “total demand, since it is simply the other name of total supply, is fixed.” (D3/12/7: 87r.). The various lines of production in the economy may be grouped into two aggregate sectors: an agricultural sector and an industrial one. Industrial commodities employ labor and capital as factors of production, while agricultural commodities employ in addition to labor and capital also land. Labor and capital can freely move both within and between the two aggregate sectors, whereas land is freely mobile within the agricultural sector. Since rising marginal costs are due to the decreasing marginal productivity of a variable factor, given the amount employed of a fixed factor, the absence of a fixed factor in the industrial sector implies the absence of rising marginal costs. Sraffa assumes in addition that the main determinant of average cost dynamics in the industrial sector is scale economies connected to the overall size of the industrial sector. Such scale economies are not specific to the production of any individual industrial commodity: following Sraffa's classification of scale economies in the 1925–26 papers, they may be considered as external economies from the point of view of the production of any individual industrial commodity, but as internal economies from the point of view of the industrial sector as a whole. By contrast, the presence of a specific and fixed factor (land) in the agricultural sector involves the presence of rising marginal costs related to the dynamics of the fixed-to-variable factors’ ratio. No scale economies obtain in the agricultural sector.

Sraffa then analyzes the case of a change in consumers’ preferences leading to a change in the proportion of consumer goods produced. According to him, it is of crucial importance to distinguish three cases:

• (i) An increase in the demand for an industrial commodity (say, bicycles) accompanied by a parallel reduction in the demand for another industrial commodity (say, guns).

• (ii) An increase in the demand for an agricultural commodity (say, potatoes) accompanied by a parallel reduction in the demand for another agricultural commodity (say, wine).

• (iii) An increase in the demand for an agricultural commodity (say, wine) accompanied by a parallel reduction in the demand for an industrial commodity (say, bicycles).

The relevance of such a distinction is due to the fact that in cases (i) and (ii), unlike in case (iii), no net flow of capital and labor between the two aggregate sectors takes place. In case (i) the production of guns decreases; the production of bicycles increases; but the overall size of the industrial sector stays constant. Since scale economies depend on the latter, no variation of scale economies and no variation of average costs obtain in the industrial sector. This contradicts Marshall's partial equilibrium conclusion in the case of economies of scale, because in the present circumstances the supply function of bicycles would not be increasing, but constant. In case (ii) the production of wine decreases, while the production of potatoes increases; but the fixed-to-variable factors’ ratio in the agricultural sector as a whole is taken to stay constant. Hence, no variation of marginal costs arises in the agricultural sector. Again, Marshall's partial equilibrium analysis, which revolves around a rising supply curve for potatoes, is misleading, and, ironically, like in the previous case, the supply function is parallel to the abscissa. Hence, identical results obtain in two vastly different cases as regards economies of scale.

The two aggregate sectors’ cost dynamics are entirely different in case (iii). Here a net flow of capital and labor between the two sectors takes place. The overall size of the industrial sector shrinks, and average costs in it tend to increase due to a reduction of scale economies. At the same time, the overall size of the agricultural sector increases and marginal costs in it go up due to a decrease of the fixed-to-variable factors’ ratio. Hence, as stressed by Sraffa, “entirely different results will take place if the increase in the demand for bicycles is due to a smaller demand of guns or of wine” (D3/12/7: 87r.).²³

The main results arising from our reconstruction of Sraffa's two-sector model may be summarized in the following statements, which elucidate the statements (A)–(D) of the previous section and in particular claim (C):²⁴

• (E) The presence of n ≥ 2 aggregate sectors characterized by different aggregate technologies (such as agriculture, industry, or services) and the presence of factors of production (such as capital and labor) that can freely move both within and between the n sectors, and factors of production (such as land) that can freely move within only one sector (or a limited number of sectors), but are immobile between the remaining sectors (or at least some of them), entail sectoral interdependences of various kinds. A rigorous analysis of sectoral cost dynamics cannot ignore such possibly complex interdependences.

• (F) When total demand is given and constant, a change in consumers’ preferences may entail a reallocation of mobile factors among lines of production belonging to the same aggregate sector; but it may also entail a reallocation of mobile factors among lines of production belonging to different aggregate sectors. Since the dynamics of sectoral costs are different in the two cases, the counterfactual reasoning concerning such dynamics—“what if output should increase/decrease?”—must take these differences into account.

• (G) The usual unconditional answer to the “what if output should increase/decrease?” question given by a partial equilibrium model turns out to be defective in all cases in which complex interdependences cannot be ignored.

• (H) Sraffa's model clarifies implicitly which conditions must be met in order for a partial equilibrium reasoning to lead to the correct answer to the “what if output should increase/decrease?” question. These conditions require that there are only reallocations of mobile factors between lines of production belonging to the same aggregate sector.

The following section covers themes that are directly pertinent to our discussion, although they are concerned with partly different subject matters. As will be shown, an analysis of these themes confirms our interpretation above. Indeed, both in a note on language and in the 1928–31 “Lectures” Sraffa assesses the pros and cons of counterfactual reasoning in particular circumstances.

8. Counterfactuals in a Note on Language and in Marginal Analysis

At the end of folder D3/12/7 there is a short document (D3/12/7: 174) dealing with the question whether the rules of language can be constructed simply by listening. The note was probably stimulated by one of the regular conversations Sraffa had with Ludwig Wittgenstein at the time. It should not come as a surprise that despite its different subject matter, it is to be found in the given folder. Sraffa had the habit of occasionally regrouping thematically his notes and manuscripts written at different times. With regard to our concern here, in the document under consideration the following passage is the most relevant one:

Sraffa suggests that whether or not such a conditional proposition is nonsense depends on whether or not the difference between any two situations contemplated is “big” or “small.” To make use of modern Lewisian terminology, we may say that for Sraffa the acceptability of a conditional sentence in the subjunctive mood in which the antecedent is false (a counterfactual sentence for short) depends on the similarity relation between the actual world A (in which Sraffa is neither a king nor a lecturer) and two possible worlds P₁ (in which Sraffa is a king) and P₂ (in which Sraffa is a lecturer). Sraffa's conclusion, reconstructed by means of Lewisian possible world semantics for counterfactuals, is that the possible world P₂ is both very close to the actual world A and certainly much closer than the possible world P₁. Hence, the counterfactual sentence with the false antecedent “if I were a lecturer” is acceptable since Sraffa being a lecturer implies a “tiny miracle” (Lewis 1979: 468) only. By contrast, the counterfactual sentence with the false antecedent “if I were the King” is not acceptable, since we have no knowledge about a world in which Sraffa would be a king.

In our view this passage confirms Sen's interpretation that Sraffa did make use of counterfactual reasonings although he thought that he latter must be used with great care and circumspection.

Do the above considerations have any bearing on Sraffa's assessment of marginalist theory? By construction, marginalist economists invoke counterfactuals that prima facie look small and suggest a close proximity between the actual and the contemplated alternative state of affairs and therefore invoke only a “tiny miracle” (to use again Lewis's expression), which might be considered as admissible. However, Sraffa was decidedly not of this view. The reason for this was that upon close scrutiny, the kind of counterfactuals contemplated by marginalist authors may actually turn out to be big or rather to be possessed of a magnitude and dimensions that are totally unclear at first sight and compel the theorist to cover them up by means of piling up illegitimate assumptions. In particular, Sraffa was keen to understand under which conditions the concept of the “marginal product of capital” and that of a “given quantity of capital” are well defined and whether changes in their magnitudes can unambiguously be ascertained. The result of his scrutiny was that only in the case of a one-commodity world—with “corn” as the only capital and the only consumption good—do the two concepts have a clear and unambiguous meaning. In folder D/3/12/13, “Notes on rent and ‘normal profits,’” dated summer–October 1929, there is a document titled “Normal profits, marginal distribution, self-identity” where Sraffa insists that “in order to have a marginal theory of distribution (or, in fact, any such theory) we must have a physical measure of the quantity of each factor, independent (i.e. that can be carried out without knowing . . .) of its share in distribution. . . . This physical measure implies that each factor is perfectly homogeneous with itself, i.e. all its composing particles are identical to one another” (D3/12/13: 17.f.5.r.).²⁶

However, in a world with heterogeneous capital goods, what does it mean to increase the “quantity of capital” in the system as a whole? The main difficulty of the theory, as seen by Sraffa, consists in that it attempts to measure something that is not well defined. If the same methods of production are being used and if the proportions of outputs do not change and if there are constant returns to scale, then an increase in the amount of capital will be associated with a parallel increase in the amount of labor. But this does not lead to the concept of marginal productivity of capital. If, on the other hand, the amount of capital is supposed to be increased for a given employment of labor, what can one possibly mean by this? In the same folder there is a document titled “Puzzles on the Theory of Rent,” in which Sraffa stresses that “great difficulties arise . . . when there is, not only ‘corn,’ but a number of different products. Most economists carefully keep clear of this problem, they simply ignore it” (D3/12/13: 23.f.1.r.). Marshall, Sraffa goes on, while aware of the fact that he would have to measure both product and capital input in physical terms, decided to measure them in value terms. Yet what is the meaning of a sum of value and of an infinitesimal change of such a sum? While unknowns of the problem under consideration, values in this context are impermissibly taken as knowns.

Sraffa stresses the lack of self-identity of “capital” in the same document:²⁷

So what do the 101 as opposed to the 100 doses stand for physically? Sraffa's attempts to make sense of marginalist theory invariably leads to the result that its concept of capital cannot be sustained: it involves a variant of the counterfactual “if I were the King,” which to Sraffa makes no sense since it implies a “radical change” in the identity of the object and the situation under consideration.

9. Final Remarks

In a number of contributions concerned with the epistemological foundations, analytical structure, and contents of Production of Commodities, Amartya Sen maintained that Sraffa was reluctant to engage in counterfactual reasoning. He wondered, therefore, whether Sraffa's contribution could possibly form the basis of a criticism of the marginalist (neoclassical) theory of value and distribution, which was erected upon and actually stood or fell with the acceptability of the particular kind of counterfactual reasoning it entertained.

In the present article we scrutinize the beginnings of Sraffa's constructive and interpretive work in the late 1920s and early 1930s as it is reflected in his hitherto unpublished papers. Interestingly, already in the period under consideration the question of counterfactual reasoning played a central role in his considerations: Which kind of counterfactual reasoning was admissible and which not? In particular, were the kind of counterfactuals invoked as an integral part of marginalist theory—marginal utility and especially marginal productivity of capital—admissible, or were there reasons to presume that they misled economists and made them develop defective theories?

We report in some detail what Sraffa had to say at such an early time on the issues at hand. While he did not use the term “counterfactual,” a term that at the time was not yet en vogue even in philosophy and became so only in the 1970s, it can safely be assumed with Sen that it captures well what he had in mind, when examining certain propositions that were not purely observational and discussing “what if?” questions. His deliberations in the late 1920s show a scholar at work who, using a famous formulation Keynes had coined, was keen to escape from habitual modes of thought and expression. On the one hand he saw that further and even more compelling objections against the dominant Marshallian version of the marginalist theory of value and distribution could be put forward than those he had formulated in his papers in the mid-1920s. At the same time he understood ever more clearly that the approach to the theory of value and distribution of the classical economists was not an early and rude version of the marginalist demand and supply approach, as Marshall and others had contended. It was not a special case of the latter but was fundamentally different from it and had a genuine significance. Sraffa at the time distinguished between two problems the theory of value had been designed to solve, one concerned with the explanation of relative prices at a given time and place, the other with an explanation of the change of prices over time. To Sraffa, the two problems were completely different in nature. Only the former, he insisted, ought to be the subject of the theory of value, while the latter may more appropriately belong to an analysis of the business cycle. He argued that while the analysis of the First Problem suggests a “geometrical theory,” that of the Second Problem suggests a “mechanical theory.” It was as early as November 1927 that Sraffa began to elaborate his systems of production equations without and with a surplus product, by means of which he sought to tackle the problem of value. He arrived at his respective results without any recourse to marginalist concepts, such as marginal productivity or marginal utility: his investigation, he wrote more than thirty years later, “is concerned exclusively with such properties of an economic system as do not depend on changes in the scale of production or in the proportions of ‘factors’” (Sraffa 1960: v).

Particularly the following results of Sraffa's deliberations in the late 1920s deserve to be stressed. Sraffa scrutinized Marshall's partial equilibrium analysis against the background of a general analysis that takes into account an entire system of production. Marshall constructed supply curves precisely in order to answer versions of the “what if?” question: How would the price obtained and the quantity produced be affected, if the demand for the commodity under consideration changed? Sraffa shows that in the three cases contemplated by him, Marshall's analysis came up with wrong results. The reason for this is the ceteris paribus assumption, which postulates that the results derived are unconditional, that is, they do not depend on how the initial change is brought about. However, this assumption cannot be sustained: entirely different results will take place depending on how the demand increases and on the compensating effects that necessarily come with it.

Sraffa's results can be said to anticipate an insight that became prominent in counterfactual theory only much later, that is, in the 1970s: any simple analysis of singular causation in terms of counterfactuals is generally not to be trusted. The Marshallian partial equilibrium theory is a case in point, and Sraffa's argument shows convincingly why doubts as to its sustainability are well taken.

The new criticisms Sraffa leveled at partial equilibrium theory derived from a confrontation of Marshall's results with those obtained within the framework of a general analysis of the economic system as a whole. Sraffa objected, first, that it is illusory to think that a small (infinitesimal) increase in the quantity of capital (or labor), other things being equal, implies a close proximity between the actual situation and the situation caused by the change in the amount of capital (or labor) employed. This is so, second, because there is no presumption that all other things can remain the same: the change might rather necessitate numerous other changes in the system of production in order to accommodate the original change. As Sraffa stressed in a note written in October 1929, “It is with capital that difficulties arise: for, while for labour we have defined a measure by assuming all workmen to be equal, we have no such measure for capital: it is composed of heterogeneous objects, which cannot be measured, ‘qua’ capital, by numer or weight, etc.” (D3/12/13: 2).

Sraffa concluded that right at the beginning of its counterfactual reasoning, marginal theory gets entangled in insurmountable logical difficulties. By postulating a direct knowledge of the consequences of a change in the amount of capital, other things being equal, the theorist leaves the territory of pure observation and enters that of experimentation or rather speculation: as Sraffa put it, the theorist “produces facts.”

Our investigation confirms Sen's interpretation that Sraffa in the late 1920s met counterfactual reasoning with suspicion, because he felt that if used negligently it was the source of misleading propositions and theories. According to him, marginalist theory suffered badly from such a negligent use. This can be seen with regard to its highly problematic employment of the ceteris paribus clause and its use of concepts that are not well defined, such as marginal utility, marginal productivity, and “quantity of capital.” However, Sraffa's papers and notes do not lend any support to the extreme interpretation (not entertained by Sen) that any counterfactual reasoning ought to be rejected. This was definitely not his view. He was clear that economic analysis could not do without counterfactual reasoning, but he insisted that it should do so with the utmost care and circumspection.

Further work ought to investigate the evolution of Sraffa's thought on the role of counterfactuals in the 1940s and 1950s and cases of counterfactual reasoning in Production of Commodities. We are working on these issues. Interestingly, in his later work Sraffa largely confirmed the views he held in the late 1920s.

We wish to thank without implicating Amartya Sen for most useful discussions two of us had with him when he was Master of Trinity College, Cambridge, and also with Brian McGuiness and Sergio Parrinello on themes related to the topic of this article. We are grateful to John Davis for his comments on an early version of this article, Alexander Linsbichler for his detailed observations especially on the philosophical aspects of the theme under consideration, and the editor of HOPE, Kevin D. Hoover, and two anonymous referees of the journal for most valuable comments and suggestions. An earlier version of the article was given at the Twenty-Seventh Annual Conference of the European Society for the History of Economic Thought in Graz, Austria, May 10, 2024. We are grateful to the participants in the session for useful interventions. Finally we owe our sincere thanks to Jonathan Smith, former archivist of Trinity College Library in Cambridge, UK, for his assistance while working on the Sraffa papers. Heinz D. Kurz is emeritus professor of economics at the University of Graz, Austria, and Fellow of the Graz Schumpeter Centre. Neri Salvadori is emeritus professor of economics at the University of Pisa and Fellow of Accademia Nazionale dei Lincei, Rome. Rodolfo Signorino is an associate professor of economics at the Law Faculty of the University of Palermo.

Appendix

Sraffa began developing his production equations in winter 1927–28; see Kurz 2012: 1542–51 and the literature cited there. In the folder D3/12/7, “Notes, essentially on industries using hypothetical examples with a note on language,” dated 1928, there are two documents, the first titled “Why I neglect Incr. & Dim. Ret. in equations” (D3/12/7: 85r.–87r.), and the second “Difference (simultaneous) v. Change (succession in time)” (D3/12/7: 115r.–119r.). In these two documents Sraffa shows full awareness of the fact that he cannot sidestep the question of which, if any, assumptions about returns to scale he entertains with regard to his production equations. He seeks to clarify for himself the reasons whether or not there is a place for variable returns in them and, in so doing, explicitly links the issue of variable returns to the use of counterfactual reasoning.

To see Sraffa's argument in full, we provide the transcription of long passages from these two documents. The diagram to which Sraffa refers below in order to explain his point of view is to be found as figure 1 in section 5 above. The reader is kindly asked to turn to it when scrutinizing Sraffa's following explanation.

Why I neglect Incr. & Dim. Ret. in equations

The question is sure to be asked: what about variable returns? The reply is that these equations cannot possibly answer as to how or why prices change. They only explain why, at a given moment (?) prices of different things bear to one another the proportions which they do.²⁸ They explain variation (difference) between individual commodities at one time, not variations of one commodity at different times. No system of equations, whether it considers variable returns or not, could tell this if time does not enter as variable. Take a pair of Marshall's D. & S. curves. They tell that, giving the conditions the price will be AB: to this effect it is quite indifferent whether the supply curve is SS₁ or S₂S₃. It may be thought that this is relevant to a case in which “there is a change of demand.”²⁹

The real point is that it is believed that Marshall's curves provide “forces” which in case the price falls below or above AB by “chance,” will restore it to AB.

Now I am not a assuming any forces: I simply say that, if the values will in reality be as given by the equations certain conditions will be satisfied: if not they will not be satisfied. . . .

I am afraid it will be difficult to make it clear that we are considering what has actually happened in the markets, and not what might have happened had things been different. It will therefore be useful to explain that the reader may assume that constant returns prevail. Because, on the assumption of free competition, incr. & dim. costs are impossible. Exclude internal economies & overhead costs. Then, through external economies, size of industry affects costs: but size of industry as a whole, not size of one given industry. Therefore, transferring capital from one branch of industry to the other does not affect external economies, and therefore not cost. Dim. ret. in agriculture: land common to all agricultural products: if I transfer land and capital from wheat to potatoes there are no dim. ret. Finally if I transfer cap. from industry to agriculture, costs increase in industry because of less ext. econ., they increase in agriculture because of dim. ret.

Therefore I cannot make a simple statement of the sort that is implied in a supply curve: “if output increases 10%, cost falls 2%.” It cannot be unconditional: the result depends upon how the demand increases, i.e. whence is the transference of cap. & lab. made. Entirely different results will take place if the increase in the demand for bicycles is due to a smaller demand of guns or of wine. And total demand, since it is simply the other name of total supply, is fixed. (D3/12/7: 85r.–87r.)

We now turn to the second document.

Difference (simultaneous) v. Change (succession in time)

The general confusion in all theories of value (except Marx probably) must be explained by the failure to distinguish between two entirely distinct types of questions and the universal attempt of solving them both by one single theory. The two questions are:

• 1) What determines the [difference in the?] values at which various commodities are exchanged in a given market on a given instant?³⁰

• 2) What determines the changes in the values of commodities at different times? (e.g. of one commodity)

From this formulation it would appear that the distinction turns upon time entering or not in the account. But this is not the fundamental difference: e.g. the inquiry into the causes of differences of values in different countries at the same time . . . come under the second class, although no lapse of time is involved.

The fundamental difference is that different conditions are assumed in the two cases; the conditions assumed in the first case are:

• a) all the units of one commodity sell at the same value on the market

• b) all workers of the same grade receive the same wage

• c) all capitals receive the same rate of interest. . . . 

In the second question the conditions are entirely different: so much different that the object of the inquiry are the changes in those very magnitudes which in the first case were supposed to be uniform all over the place (we cannot even say that they were assumed be uniform in time: since they referred to simultaneous situations, time changes could not be taken into consideration, not even in order to exclude them) i.e. the value of one commodity.

Therefore it is possible that the two problems have to be solved in different ways: and that of two opposite general theories of value, one may be true in respect of one question and the other in respect of the second. . . .

The first problem gives rise to a geometrical theory, the second to a mechanical one.

The first is so much timeless that it cannot even be called static. It does not represent an ideal stationary state in which it is assumed that no change takes place: but it represents a situation at one instant of time, that is to say something indistinguishable from the real state of things in such a short period of time that no visible movement takes place. Its object is, as it were, the photograph of a marketplace: and its problem is to determine why cabbages bear a label “6 d. per lb.” and herrings “8 d. a pair.”

The first problem must be solved by the theory of value. The second, I think, can only be solved by the theory of industrial fluctuations.

All the confusion between cause and measure of value is connected with the mixing up of the two questions. Marshall's theory of value, with its increasing and diminishing costs and marg. utility, scissors, pillars and forces, can only be understood as an attempt to solve the first question in terms of the second. All his machinery of supply and demand does not help us at all in the first question: but it seems to be directed to answer questions such as “what will happen to price if a tariff be imposed?” “or a bounty or tax? or change in tastes? or invention?” The point is—can such questions be answered in a general way, i.e. assuming the “initial” movement to be entirely arbitrary? or is it not necessary to know how it has arisen? . . .

 . . . Also time is not the fundamentum divisionis. The really fundamental discriminating criterion is that in one case certain general conditions are different (or change) and in the other they are uniform (or constant). These conditions have now to be exactly defined.

They seem to be the conditions usually associated with the definition of “a market,” i.e. the “law of indifference.” . . . The law of indifference applies to the following things: 1) the rate of interest. 2) the rate of wages in each grade or profession. 3) price of different units of the same commodity.

Essentially, in solving the first problem “changes in the productiveness of labour in any one industry” cannot be used to explain differences in values of different commodities: incr. + dim. returns have nothing to do with this problem, since in the given conditions labour has produced what it has produced and it is irrelevant to speculate what it would have produced had conditions been different: This may only be used as between different periods (i.e. comparing the values under different conditions). Comparing two different times we may say “boots have risen in value because they have risen in cost, and they have risen in cost because less are produced”: but at one and the same time one and the same quantity of boots is produced (or brought to market)—how can it be relevant to inquiry what would have happened if the given conditions had been different? (D3/12/7: 115r.–119r.; emphasis added)

Notes

References