A Reflection on the Samuelson-Garegnani Debate

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Sraffa’s book (1960), Production of Commodities by Means of Commodities, is perhaps the most enigmatic theoretical work ever published in economic theory. Of course, all classics are somewhat puzzling and do give rise to a number of interpretations over a period of time. But the book of Sraffa is special in this respect. Upon its publication, many contemporaries of Sraffa hailed it as a definite classic but at the same time acknowledged their inability to completely understand what the book was all about (e.g., see Harrod 1961). And Sraffa’s complete silence on explicating its terse prose was of no help. Its destructive potential for the orthodox economics, however, came to the fore in the famous capital theory debates between ‘the two Cambridges’ in the 1960s (see Harcourt 1969), when one of the leaders of the orthodoxy, Paul Samuelson (see ‘Symposium 1966’), admitted that Sraffa’s proposition about ‘re-switching of techniques’ proves that the orthodox parable regarding ‘quantity of homogeneous capital’ is wrong. Pierangelo Garegnani (see ‘Symposium 1966’) was one of the participants on the winning side of this debate. Soon after, however, the orthodoxy came to the conclusion that the destructive potential of Sraffa’s book could be confined to this simplified ‘parable’ only and that the more sophisticated general equilibrium theory, which does not need the notion of aggregate quantity of capital prior to price determination, remains unscathed. Frank Hahn (1975, 1982) further argued that Sraffa’s book can be interpreted as a special case of inter-temporal general equilibrium, and so the orthodoxy need not worry about it anymore.

Posted for comments on 7 Nov 2014, 10:32 am.

Comments (6)

  • Ajit Sinha’s paper addresses the debate between Paul Samuelson and Pierangelo Garegnani, a debate which focused on Piero Sraffa’s contribution to economic theory. Sinha’s paper argues throughout its various sections that Garegnani was unable to answer satisfactorily to Samuelson’s criticisms of Sraffa. But the paper concludes that this happens because Garegnani did not grasp correctly Sraffa’s contribution. Sinha argues that although Samuelson’s criticisms apply to Garegnani’s interpretation of Sraffa (which, Sinha argues, is inconsistent with Sraffa’s own analysis), Samuelson’s criticisms do not apply to a correct interpretation of Sraffa. The paper ends up being indeed a criticism of Garegnani’s interpretation of Sraffa, where the Samuelson-Garegnani exchange provides an occasion to engage in such a criticism.

    It seems, to this reviewer at least, that Sinha’s interpretation of Garegnani’s position springs from several misunderstandings of what Garegnani meant. Garegnani’s contribution must be assessed as an attempt to apply Sraffa’s analysis to the real world. To understand its aim and scope, it is perhaps useful to go back to understand the problem of internal relations, which is behind Sraffa’s and Marshall’s analysis, and is the key problem to address when applying economic theory to the real world.

    A central problem faced by Marshall, which was a central problem in the philosophical context of his time, not least in Cambridge, was the problem of internal relations (which troubled Bertrand Russell a lot). If everything is related to everything else, how can we focus on a given aspect of reality, if it is related to everything else? In his Industry and Trade, Marshall argues that the differential calculus of Newton and Leibniz provides a solution to this problem. In his unpublished papers, Sraffa refers explicitly to the pages of Industry and Trade where Marshall says this. Marshall notes that by focusing on infinitesimal changes, we can focus on the direct effects of X on Y, while assuming that the indirect effects of X on Y through Z can be ignored. As Sraffa writes in his unpublished manuscripts (while referring to Russell’s interpretation of differential calculus in physics), differential calculus considers a “time in which effects follow causes, but so closely that there is no room either for dispersion or for entering of foreign influences: dt does this by differentiation (making time so short as actually to leave no room for change in circumstances: the cause and effect are perfectly contiguous – nothing happens in between)” (quoted in Martins 2013, p. 44).

    Sraffa believes, however, that Marshall’s method is wrong. In economics we are not dealing with infinitesimal small magnitudes. Thus, we cannot simply focus on the direct effects of X on Y while assuming everything else to remain constant, as Marshall does, in the pound of ceteris paribus. Sraffa writes that “What Newton had proved about physics was of course quite irrelevant to Economics, and Marshall must have been short of good arguments to use such an unfair trick.” (quoted in Martins 2013, p. 43).

    Sraffa provides his own approach to the problem. Rather than focusing on the effects of a given change on another change, we should rather focus on the conditions for the reproduction of objective economic phenomena at a given moment (a given instant) in time. Thus Sraffa writes “our «time» does this by «assuming» away all changes (i.e. «ceteris paribus»? no: by positing the problem in the form of finding the conditions of repetition indefinitely, or even once).” (quoted in Martins 2013, p. 44)

    That is, we abstract from time, and look at an “instantaneous photograph” of the economy. For if we would allow for the passing of time, everything can change in an internally related world, and there is no firm ground for a theory of value. Sraffa’s solution, as the problem that triggered it, is nothing new. It is the solution Plato found to Heraclitus’ problem: to look at the forms that persist through time, rather than at the multiple changes in events. Léon Walras was well aware of this and referred explicitly to his Platonic methodology, even though the theory he developed is radically different from Sraffa’s theory since it relies on supply and demand analysis. When Garegnani writes that “The ‘normal position’ may be taken as a typical instance of Pareto’s ‘ideal phenomena’ in economics”, as Sinha notes, he is pointing towards this same issue, that Walras was well aware of.

    When we want to adopt this method in reality, we need the analogue of an “instantaneous photograph” that persists through time. This is the normal position, which depends upon human conventions that persist. The source of many misinterpretations of Garegnani’s perspective in this paper spring from the failure to note that mathematics (or arithmetic, to be more precise) is employed only to provide a general description of the core conditions of reproduction of the economy. Gravitation, in turn, is described drawing upon a social analysis of human conventions that cannot be framed into mathematical terms, since everything is changing at the same time, and we cannot employ mathematics (such as differential calculus) to model changes while assuming everything else to remain constant, as if we were in a closed system. Closed systems exist typically in laboratorial situations, or in some aspects of celestial mechanics. The tendency to believe that all economic analysis must assume a mathematical form that presupposes closed systems is behind this misunderstanding. This is something that Sraffa was well aware of, as we can see in his critique of Marshall’s use of differential calculus – I discuss this issue in more detail in Martins (2013: Ch. 2).

    After this preliminary remark, we can now understand better the specific misunderstandings of Garegnani’s position that appear in Sinha’s paper. In page 3, Sinha writes:

    “Garegnani’s response is that Samuelson confuses Sraffa’s argument about abstract mathematical operations on equations with changes in the real system itself: ‘… That of course is true, but it applies to proportions between actual outputs and not to proportions between equations, as Sraffa is careful to specify in the one word we italicized in this passage’ (p. 58, Garegnani’s emphasis).”

    Sinha continues and writes, criticising Garegnani reply quoted above:

    “This I find highly unsatisfactory. Sraffa clearly states that ‘every system of the type under consideration is capable of being brought to such a state…’. Hence the reference is to the ‘system’, which is capable of being brought to such a state and not simply a mathematical operation on equations.”

    But describing changes in the real system through mathematical operations is something that cannot be done, according to Sraffa and Garegnani, since the economic world is interconnected in a too complex way. So mathematical operations can be applied only to equations that describe the core elements for socio-economic reproduction at a moment in time, rather than changes in the real system as Sinha seems to be assuming. In pages 5 and 6 Sinha criticises Garegnani again while assuming that the process of gravitation must be described mathematically. In page 7, it becomes clear that Sinha really believes that the whole economic process (rather than merely the instantaneous conditions of reproduction) must be described mathematically, for Sinha writes:

    “Garegnani nowhere explains what he means by the ‘techniques’. Are they production functions, which specify all the levels of outputs that would be produced with changes in inputs or are they simply an observed set of inputs utilized to produce the observed set of outputs? The former case implies some assumption regarding returns to scale, e.g., Leontief technique with constant returns implicit in it; whereas the latter case is a one point observation and cannot predict how outputs would behave with changes in inputs. Since Garegnani accepts that most likely the observed input-output data will not be in the classical centre of gravitation, the problem with the ‘given output’ position turns out to be this: even if we know what the output set must be, we still have no way of knowing what the input set must go along with that output set, unless we know the production function.”

    The answer to Sinha is that the techniques are not production functions. Therefore, we cannot predict mathematically how outputs will change with inputs, or how inputs change with outputs, as Sinha rightly complains. But this is no problem at all, unless we want to impose a mathematical function into a reality that often cannot be described satisfactorily by it, as Sinha seems to want. It is more reasonable to take both outputs and inputs as given data, as Sraffa and Garegnani do, rather than assuming a function that explains outputs in terms of inputs, as Samuelson and Sinha seem to want. More generally, it seems more reasonable to explain social processes in terms of human conventions, as Garegnani does, while using mathematics for simple arithmetical operations that do apply to reality. In fact, this was the classical method, which was abandoned subsequently when differential calculus invaded economic analysis, drawing upon the unrealistic ceteris paribus clause, which was Marshall’s surrogate method, based upon the differential calculus of Newton and Leibniz.

    John Maynard Keynes also thought that studying economic processes in terms of human conventions was a more reasonable procedure. Keynes, who was well aware of the problem of internal relations, and of Marshall’s way of dealing with it through differential calculus, writes:

    “It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis … that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep “at the back of our heads” the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials “at the back” of several pages of algebra which assume that they all vanish. Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.” (Keynes 1936: 297-298)

    Garegnani uses ordinary language when explaining gravitation, the real wage, and several given data of the economic system, rather than mathematical functions. Ordinary language, as Keynes notes, enable us to keep at the back of our heads the necessary assumptions when dealing with open systems. The various confusions that emerge throughout the paper spring from Sinha’s attempt to impose a mathematical methodology that presupposes closed systems to the process of adjustment and gravitation, a methodology that Sraffa and Garegnani never used. It is exactly the same thing Samuelson was doing. This is why Sinha ends up agreeing with Samuelson’s criticism of Garegnani, and why both Samuelson and Sinha believe that Garegnani would need linear functions, constant returns to scale, and the like, under his interpretation of Sraffa.

    As for the reference to population dynamics and unemployment at the end of Sinha’s paper, it suffices to say that for Garegnani, as for the classical authors, the existence of labour available for further production is simply a basic assumption, one that Walras rejected. Ricardo assumes that labour is available for further production, and so if demand increases supply will increase too leading the price back to the cost of production, except in cases where goods are scarce (such as rare goods). Walras criticised Ricardo, assuming that labour is scarce, and assuming thus full employment (that is, that there is no labour available for further production). There is no need of bringing in Ricardo’s remarks on machinery to see how unemployment exists in the classical analysis, and in Garegnani’s analysis. The possibility that unemployment of labour persists through time is indeed another very realistic feature of Garegnani’s analysis, and the classical analysis.

    Besides misconstruing Garegnani, Sinha also argues that Garegnani’s position is inconsistent with Sraffa’s. However, we must also understand the different motivation behind each author. Sraffa wanted to provide an internal critique of marginalist economics (or “marginism”, as he called it). Therefore, it was sufficient to focus on an instantaneous photograph of the economy, so as to engage in an internal critique of marginalist theory. Internal critique is a very important task, given the importance of established ideology noted by Antonio Gramsci.

    Garegnani, however, also wanted to apply Sraffa’s method to the real world. To do so, he had to identify the core conditions Sraffa was studying in the real world, taking into account the limits of mathematical analysis when studying actual human activity. Sraffa writes:

    “The general confusion in all theories of value (. . .) 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?

    2) what determines the changes in the values of commodities at different times? (e.g. of one commodity). (Sraffa D3/12/7, as cited in Garegnani 2005: 471-472)

    So a theory of value explains differences at a given instant, and a theory of industrial fluctuations explains changes through time. Thus, a theory of value does not explain the process through which a given position is reached. Rather, it explains the conditions for the reproduction of that position at a given moment (or instant) in time.

    But in order to apply the theory of value to the real world, we must provide an explanation of how a given position is reached. This explanation is provided by what Garegnani and the classical authors called “gravitation”. However, by gravitation they mean only a vague reference to the process through which a given position is reached. Given the existence of internal relations, it is not possible to provide a mathematical model of the process of adjustment. Thus, Garegnani restricts the scope of mathematical analysis (by which he means arithmetic such as the one Sraffa used, rather than differential calculus) to the study of the core elements for the reproduction of a given position, which he calls the “normal” position.

    Why “normal”? Because if any position is to become a centre of gravitation, to be reached by a complex socio-economic process, it must be a reference point for human conventions to emerge. Garegnani refers often to the conventional nature of economic phenomena. Clearly, this means that Garegnani is referring to the more persistent forces of the socio-economic system, which become manifest in the long period, as a normal, or conventional, position. As Sinha notes in page 6, Garegnani writes:

    “The ‘normal position’ may be taken as a typical instance of Pareto’s ‘ideal phenomena’ in economics, centred as it is on Adam Smith’s ‘central price’, to which ‘the prices of all commodities are continually gravitating’ (1776, I: 51) and therefore providing what Pareto calls here a ‘general or average fact’.”

    Sinha, however, does not seem to understand the method which is implied in Garegnani’s very intelligent application of Sraffa’s theory for the development of a constructive project. This can be seen in page 9 of Sinha’s paper, when Sinha fails to note the distinction between Garegnani’s use of the notion of an average rate of profits (in line with the classical economists), and the Maximum rate of profits that ensures positive prices in Sraffa’s system. One thing is the mathematical analysis Sraffa undertakes in order to prove that the lowest amongst the Maximum rates of profits (that are mathematically possible rates in his system) is the rate that ensures positive prices (by the way, Sraffa never used the Perron-Frobenius theorem which Sinha refers to since he used a constructive approach to mathematics). Another thing is the average rate that emerges through a social process of gravitation, which will of course be below the Maximum rate of profits, which is the lowest rate only amongst the Maximum rate of profits which are mathematically possible. This average rate of profit is not an average in the sense of being an average amongst the mathematically possible Maximum rates in Sraffa’s system, since by definition an average rate cannot be above the Maximum rate of profits. Rather, it is the average rate that, through habit and custom, becomes a reference point for economic activity, where this social process of adjustment is not described mathematically.

    As David Ricardo noted in chapter IV of his Principles, it is very difficult to trace the steps through which the movement towards an average rate of profit is effected. Much less we can provide a mathematical treatment of it. It seems that Sinha confuses Sraffa’s mathematical analysis of the conditions for the reproduction of the core elements of the economic system with the socio-economic process of gravitation around conventional (or normal) values.

    Of course, one could question the strategy followed by Garegnani when applying Sraffa’s method to the real world. Sinha’s paper does not provide a correct interpretation of Garegnani, much less a proper critique of it. But it would be a legitimate question. Does historical evidence point towards the usefulness of Garegnani’s methodology? Does capital move around looking for an average rate of profit, over the long period? Is the long period a useful notion? Historical evidence from Fernand Braudel to Thomas Piketty appears to suggest so: capital does move around looking for the rate of profits that tends to persist, on average, as a normal position, throughout the long period (or, as Braudel and Piketty would prefer to say, the “longue durée”). But this is an empirical issue to be further discussed.

    The paper, however, is trying to do something different: to show that Garegnani failed to reply to Samuelson. Sinha’s paper is a criticism of Garegnani’s method, trying to find inconsistencies within it, and with Sraffa’s approach. In all this, I think the paper fails. I think Sinha misrepresents Garegnani, for the reasons mentioned above. Samuelson’s critique of Sraffa misses the target, as Sinha rightly argues. But so does Sinha’s critique of Garegnani, which fails to understand Garegnani’s method, and the way in which it tried to use Sraffa’s theory in the analysis of the real world.


    Garegnani, P. (2005), ‘On a turning point in Sraffa’s theoretical and interpretative position in the late 1920s’, European Journal of the History of Economic Thought, 12, 453-492.

    Keynes, J.M. (1936), The General Theory of Employment, Interest and Money, London: Macmillan.

    Martins, N.O. (2013), The Cambridge Revival of Political Economy, London and New York, Routledge.

    • Ajit Sinha says:

      I must confess that I have not been able to make much sense of Mr. Martins’s comments even after reading it carefully several times. Martins claims that ‘It seems, to this reviewer at least, that Sinha’s interpretation of Garegnani’s position springs from several misunderstandings of what Garegnani meant’, to which I suppose he must have some special access. I, of course, rely on what Garegnani wrote, to which a larger community of scholars have access and so my interpretation of his writings can be checked and rechecked by others—I do not claim to be a mind reader nor do I think reading minds of authors is a good strategy for interpretation of anyone’s writings. Martins then goes on to add, ‘Garegnani’s contribution must be assessed as an attempt to apply Sraffa’s analysis to the real world’. But Martins does not tell us what Sraffa’s analysis is of, if not of the ‘real world’? After this, he tells us that ‘[t]o understand its aim and scope, it is perhaps useful to go back to understand the problem of internal relations, which is behind Sraffa’s and Marshall’s analysis, and is the key problem to address when applying economic theory to the real world’. Yet again, it is not clear that the ‘aim and scope’ that Martins wants to understand relates to Garegnani’s ‘application’ of Sraffa’s ‘analysis’ to the real world or Sraffa’s analysis itself. The confusion on this score could be deliberate so that the distinction between Garegnani and Sraffa could be blurred or slowly erased from reader’s mind.

      In any case, we are told that it would ‘perhaps’ be ‘useful to go back to understand the problem of internal relations’, which is apparently behind both Sraffa’s and Marshall’s analysis. By ‘internal relations’ Martins means ‘everything is related to everything else’, which apparently gives rise to the problem: ‘If everything is related to everything else, how can we focus on a given aspect of reality, if it is related to everything else?’ Sraffa’s solution of this problem, according to Martins, was to use the notion of an ‘instantaneous photograph’: ‘That is, we abstract from time, and look at an “instantaneous photograph” of the economy. For if we would allow for the passing of time, everything can change in an internally related world, and there is no firm ground for a theory of value.’ Now the question is: what could be the ‘instantaneous photograph of the economy’, if not the real economy (the ‘real world’) itself? Can one take a ‘photograph’ of something that does not empirically exist, say an ‘ideal’ situation such as an economy at its ‘centre of gravitation’? Well, Martins’s answer turns out to be that: ‘Sraffa’s solution, as the problem that triggered it, is nothing new. It is the solution Plato found to Heraclitus’ problem: to look at the forms that persist through time, rather than at the multiple changes in events’. So first we were told that everything relates to everything else and therefore with the passage of time everything must change. Now we are told that there is something that does not fall under the set of ‘everything’ and that is the ‘form’ that persists through time. So what is this ‘form’ that is not part of ‘everything’ and persists through time? It, according to Martins, ‘is the normal position, which depends upon human conventions that persist’. So there is something called ‘normal position’ which does not change when ‘everything changes’ and it ‘depends upon human conventions that persist’.

      Now we have another thing called ‘human conventions’ that is also not a part of the set of ‘everything’. So we have two things that remain constant when ‘everything’ changes: (1) ‘normal position’ and (2) ‘human conventions’ and it is ‘human conventions’ that are primary in the sense that ‘normal position’ depends upon it. Further down Martins elaborates:

      ‘Given the existence of internal relations, it is not possible to provide a mathematical model of the process of adjustment. Thus, Garegnani restricts the scope of mathematical analysis (by which he means arithmetic such as the one Sraffa used, rather than differential calculus) to the study of the core elements for the reproduction of a given position, which he calls the “normal” position. Why “normal”? Because if any position is to become a centre of gravitation, to be reached by a complex socio-economic process, it must be a reference point for human conventions to emerge.’

      Now let me try to put the sequence of the argument in order. According to Martins, in the real world everything is related to everything else; therefore, everything is changing with passage of time. So to understand an aspect of the real, one must stop time. One does that by taking an instantaneous photograph. A photograph of what? Not of what exists at that moment of time, no. One takes a photograph of a ‘normal’ position. What is this normal position? It is a position that does not exist but to which the real or empirical position would adjust to over a period of time. But since everything is internally related to everything the process of adjustment over time cannot be described mathematically. One has to just take it as given that the real adjusts to the ‘normal’ over a period of time, even though ex hypothesis, we cannot focus on a given aspect of reality when everything is changing. But then the ‘normal’ position does not change when everything changes and that is because the ‘normal’ conditions depend on ‘human conventions’, which, of course, also do not change when everything changes. And, where do the ‘human conventions’ come from? Well, of course, those normal positions provide the reference points for those human conventions to emerge.

      So what all this rigmarole is about? It is to defend Garegnani from my criticism that the classical idea of the mechanism that supposedly takes the real economy to the ideal equilibrium or the ‘normal’ position requires constant returns to scale assumption. Martins argues: ‘The source of many misinterpretations of Garegnani’s perspective in this paper [i.e., my paper] spring from the failure to note that mathematics (or arithmetic, to be more precise) is employed only to provide a general description of the core conditions of reproduction of the economy’. Leaving aside the minor matter of ‘normal positions’ now transmuting into ‘core conditions’, I draw the reader’s attention to the phrase ‘general description’. Here ‘description’ of the ‘core conditions’ needed to be qualified by the term ‘general’, as opposed to ‘particular’, I suppose. So the description of the ‘core conditions’ or the ‘normal positions’ does not relate to any particular empirical system. This is because the distinction is between a ‘vague’ description and a ‘precise’ description. Martins argues that it is the strength of Garegnani’s ‘analysis’ that it relies on ‘vague’ description rather than precise description. Therefore, our precise mathematical argument (see Dupertuis and Sinha 2009) that shows that the mathematical probability of any system of three or more basic goods converging to its centre of gravitation is zero is worth nothing; since what matters is a vague description that simply asserts that the system must converge. But not only this. Martins has by now severed Garegnani’s theory so completely from any relation to the real that the so called adjustment process no longer describes a process of adjustment of the real or empirical system to its so-called normal position, but rather it is all vague. Therefore, to my question: when Garegnani adjusts given empirical outputs to ‘given’ effectual demands, how does he adjust the given inputs in his equations? Martins replies: ‘It is more reasonable to take both outputs and inputs as given data.’ That is, just cook it up from your head—all that matters is vagueness. And all this is in the name of ‘applying’ Sraffa’s analysis to the ‘real world’! So now it turns out that the ‘instantaneous photograph’ is not only not a photograph of an empirical reality but it is not even a photograph of an ideal situation corresponding to an empirical reality—it is supposed to be a photograph of a vaguely specified ideal situation with no relation to reality. And this is supposed to be the strength of not only Garegnani’s but also Sraffa’s analysis. Now if this is what Garegnani had ‘meant’ to do to Sraffa’s theory then Mr. Martin is welcome to have his Garegnani but as far as Sraffa is concerned, I may be allowed to quote just a sentence from one of Sraffa’s letters to Wittgenstein of 1934-35 period: ‘Also I cannot be content with hints or allusions (or things that cannot be laid down black or white), I must have it all thrashed out’ (quoted in Sinha 2009).

      • Nuno Martins says:

        The author writes he could not understand my review even after reading it several times. I shall focus, however, only on the misunderstandings of Professor Garegnani’s position.

        The author states that the normal position is something that does not exist. Now, according to Garegnani, whose contribution is being interpreted and criticised in the paper, the normal position must be something that exists, and consists of economic phenomena that tends to persist through time, in the real world. This persistence is explained by Garegnani in terms of human conventions, and not as an ideal stationary state that does not exist (where the process of convergence towards it would be explained mathematically). I am not arguing that the author must accept Garegnani’s position concerning the existence of persistent economic phenomena (that is an empirical issue), or his idea of what a normal position is. It simply seems to me that Garegnani should be interpreted and criticised for what he wrote, rather than for things he did not say, did not believe in, and do not even exist.

        The author writes that the interpretation of Garegnani I provide springs from a privileged access to Professor Garegnani’s mind, or some mind-reading ability. However, all I am saying is quite explicit in Garegnani’s writings (I provide some references below where all this can be found). Professor Garegnani writes in several occasions that quantitative analysis should be limited to the core elements of an economy, while refering often to the conventional nature of much economic phenomena when explaining the persistence of those elements. To reduce the scope of mathematical analysis in this way is not a lack of rigour. Quite the contrary. Many of the problems of contemporary economics spring from the belief that rigorous analysis must assume a mathematical form. What ends up happening is that mathematics is (mis)used in a non-rigorous way, not least because it seems difficult to use mathematics rigorously when it is applied outside the fields where stable and persistent regularities exist. Sraffa and Keynes saw this clearly when criticising Marshall’s use of differential calculus.

        The author writes that this methodological stance (where mathematics is used only to explain persistent phenomena, rather than processes of change characterised by uncertainty) would make other contributions of him “worth nothing” (sic). This is something I am unable to comment on, as I am unfamiliar with work written by the author other than this specific paper which I was asked to comment.


        Garegnani, P. (1978). ‘Notes on Consumption, Investment and Effective Demand: I’, Cambridge Journal of Economics, 2, 335-353.

        Garegnani, P. (1979a), ‘Notes on Consumption, Investment and Effective Demand: II’, Cambridge Journal of Economics, 3, 63-82.

        Garegnani, P., (1979b), ‘Notes on Consumption, Investment and Effective Demand: A Reply to Joan Robinson’, Cambridge Journal of Economics, 3, 181-187.

        Garegnani, P. (1984), ‘Value and Distribution in the Classical Economists and Marx’, Oxford Economic Papers, 36, 291-325.

        Garegnani, P. (1998), ‘Sraffa: The Theoretical World of the ‘Old Classical Economists’’, European Journal of the History of Economic Thought, 5, 415-429.

        Garegnani, P. (2005), ‘On a turning point in Sraffa’s theoretical and interpretative position in the late 1920s’, European Journal of the History of Economic Thought, 12, 453-492.

        Garegnani, P. (2012), ‘On the present state of the capital controversy’, Cambridge Journal of Economics, 36, 1417-1432.

        Garegnani, P., and Palumbo, A. (1997), ‘Accumulation of Capital’, Departmental Working Papers in Economics – University Roma Tre, Working Paper number 2, 1-18.

        • Ajit Sinha says:

          Unfortunately, I have noticed only now Mr. Martins’s response to my response to his comments, though it was apparently posted more than a month ago. Martins makes two points in his response and I would like to respond to them one by one:

          ‘… no economist had previously supposed the economy to ever actually be in equilibrium position, or more generally in a position of rest, except by fluke: gravitation around such positions and not achievement of them being what was always thought relevant for the positions of the economy in the focus of the analysis.’ (Garegnani, P. 2012, 1429-30, emphasis in original).

          Here Garegnani is unequivocally stating that the actual or the empirical economy is never in the position of rest, except by fluke. So my simple question to Martins is: how does one capture ‘a position of rest’ by a photograph, when the actual economy is never at that position? By the way, a photograph can never capture ‘forces’ and Sraffa was quite explicit in stating that his equations don’t assume any forces:

          The real point is that it is believed that Marshall’s curves provide “forces” which, in case the price falls below or above AB {the equilibrium price} by “chance” will restore it to AB.
          Now I am not 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. (D3/12/7: 65).

          Now, it is Garegnani who claims that Sraffa’s equations represent the ‘position of rest’. If that is the case then Sraffa’s use of the metaphor of a ‘photograph of a market place’ must be highly inapt. But as a matter of fact it is not, as Sraffa explains:

          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?
          2) What determines the changes in the values of commodities at different times? (e.g. of one commodity) …
          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 statical. 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 market place: and its problem is to determine why cabbages bear a label “6d. per lb.” and herrings “8d. 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. … (D3/12/7: 115-119).

          This does not leave much for speculation as far as the difference in Sraffa’s own position on the nature of his equations and Garegnani’s interpretation of it is concerned. I should also remind the reader that in his book Sraffa refers to his system of equations as the ‘actual economic system of observation’ (1960, p. 22). [I’m grateful to Professor John Eatwell, the literary executor of Sraffa’s unpublished papers, for his permission to use them.]

          In his comment to my paper, Martins claimed that ‘It seems, to this reviewer at least, that Sinha’s interpretation of Garegnani’s position springs from several misunderstandings of what Garegnani meant’ and went on to expound on it without quoting or citing Garegnani, except a few excerpts of quotations taken from my paper. So what is one supposed to read into it? Mr. Martins says that what he actually ‘meant’ by the word ‘meant’ is what Garegnani ‘wrote’. Yet again no direct quotation from Garegnani is given to substantiate his interpretation but a long list of Garegnani’s publications is given where the reader could find what Garegnani ‘wrote’. Interestingly, the most relevant publication of Garegnani is missing on this list. The issue under discussion is the mathematical formulation of the gravitation mechanism. Ian Steedman (1984), in his highly mathematical paper had raised some pertinent questions on the veracity of classical gravitation mechanism. A lively debate ensued. Several papers were devoted to answering Steedman in the 1990 issue of ‘Studies in Surplus Approach Economics’ including a paper by Garegnani, which is reprinted in Caravale’s readily available editied book, Equilibrium and Economic Theory. Interestingly, in this paper Garegnani himself develops a mathematical argument in support of the classical gravitation mechanism, which is refuted in Dupertuis and Sinha (2009), which I cited in my response to Mr. Martins’s comment. One would have expected Martins to have checked this publication before writing his response, which would have also directed him to the relevant paper by Garegnani. But Mr. Martins however seems to be quite content with his ignorance of the relevant literature.

          Anyway, what is the issue here? The issue is that Garegnani claims that the ‘core’ of classical economics or the ‘surplus approach economics’ takes (i) technique of production, (ii) wages and (iii) total output as given from outside. Given these three variables the theoretical problem of the ‘core’ of the theory is to solve for the rate of profits and the equilibrium prices. This problem, Garegnani contends, is amenable to precise mathematical formulation (and that’s what in his opinion Sraffa does in his book). However the relationship that pertains between the three given variables and the outside forces as well as between the three given variables themselves are of a nature that is not susceptible to a precise mathematical formulations. Mr. Martins misinterprets Garegnani when he thinks that this applies to the gravitation mechanism. In Garegnani’s formulation the gravitation mechanism cannot affect the three givens of the ‘core’ because if it did then his whole theoretical edifice would collapse. This is one of the central contentions between Hicks-Hollander/Samuelson type orthodox interpretation of classical economics and Garegnani, where the orthodoxy claims that gravitation mechanism could change the total demand for labour and hence wages and, in the presence of more than one technique, even the technique of production as well. Therefore, Garegnani cannot allow gravitation mechanism to touch any of the given variables of the ‘core’ and so this mechanism cannot be put in the set of forces pertaining to either outside forces or the relations pertaining to the given variables themselves as they are supposed to affect those variables.

          This, however, leaves Garegnani highly vulnerable. On the one hand he admits that any given empirical system is not at equilibrium and on the other hand he needs to maintain that the given of the ‘core’ of the theory must be associated with the equilibrium position. So he has to bring the empirical disequilibrium position to the equilibrium position of the ‘core’, which he does by the use of the classical gravitation mechanism. But that requires adjustments of inputs and outputs and this cannot be done without affecting any of the givens of the ‘core’ unless constant returns are assumed. As a matter of fact in his Ph.D. dissertation, which was completed in 1958, Garegnani explicitly admitted that the classical economists assumed constant returns: ‘We can here remember that Smith and Ricardo’s theory of price is founded on the assumption of constant returns to scale for manufactures, while the position of the margin in agriculture is given since it is treated as broadly determined by the level of accumulation and population’ (Garegnani 1959, p. 29, f.n. 2). Obviously, at this stage Garegnani did not know Sraffa (1960). It was only after 1960 that Garegnani needed to expunge CRS from classical economics to bring it in line with Sraffa (1960). But whenever Garegnani felt pushed on this issue he highly reluctantly accepted that the gravitation mechanism assumed constant returns, e.g. in his response to Samuelson’s ‘Sraffa’s hits and Misses’, Garegnani wrote: ‘Unlike what happens in neoclassical theory, Smith and Ricardo could therefore leave physical returns to scale quite naturally aside when dealing with relative prices in a given position of the economy, with the kind of small output changes generally involved in that specific analysis’ (Garegnani 2007, p. 188). Here we have an admittance of CRS for ‘small output changes’ [read gravitation mechanism] cloaked in a negative statement about not having to assume some kind of returns to scale. But the fact remains that Sraffa categorically denies the assumption of constant returns for his theory. This point was so important to him that it was mentioned twice in a short Preface to his book. Therefore, a significant theoretical gap remains between Garegnani’s ‘surplus approach economics’ and Sraffa’s ‘production of commodities by means of commodities’.


          Dupertuis, M.-S and A. Sinha. 2009. ‘A Sraffian Critique of the Classical Notion of Centre of Gravitation’, Cambridge Journal of Economics, 33(6): 1065-87.
          Garegnani, P. 1959. A Problem In The Theory Of Distribution From Ricardo To Wicksell, Ph.D. Disseration, Univerisity of Cambridge.
          Garegnani, P. 1997. ‘On Some Supposed Obstacles to the Tendency of Market Prices towards Natural Prices’, in G.A. Caravale (ed.), Equilibrium and Economic Theory, London and New York: Routledge.
          Garegnani, P. 2007. ‘Professor Samuelson on Sraffa and the Classical Economics’, The European Journal of the History of Economic Thought, 14(2): 181-242.
          Garegnani, P. 2012. ‘On the present state of the capital controversy’, Cambridge Journal of Economics, 36(6): 1417-32.
          Steedman, I. 1984. ‘Natural Prices, Differential profit Rates and the Classical Competitive Process’, The Manchester School, 52(2): 123-40.

  • Andrés Lazzarini says:

    Andrés Lazzarini – Federal University of Rio de Janeiro, Brazil & National University of San Martín, Argentina

    The purpose of Sinha’s paper is to discuss the theoretical debate between Paul Samuelson and Pierangelo Garegnani on a number of issues that arose out of Piero Sraffa’s 1960 book, and which has been recently reprinted and edited in one volume (Kurz, 2013). As is well known, Sraffa’s contribution to economic theory has two main elements. One of them is the negative implication for marginalist theory that can be derived from Sraffa’s analysis of prices, which shows the impossibility to obtain a robust measurement of capital independent of distribution, as is indeed needed by marginalist theory (Sraffa, 1960, p. 38). The second element that can be traced in Sraffa’s book is the constructive part of his contribution. In this part Sraffa overcomes the old problems in the classical theory of value and develops a robust theory of value and distribution under the same theoretical premises of the original classical authors (see Sraffa, 1960, pp. 93-95). The Samuelson – Garegnani debate which Sinha addresses in his paper is about issues related to the positive part of Sraffa’s contribution, whilst the issues raised in the critical part of Sraffa’s book were debated during the Cambridge controversy, in which both Samuelson and Garegnani were directly involved (see Samuelson, 1962; Samuelson, 1966; Garegnani, 1966; Garegnani, 1970). In this regard, Sinha (p. 1) correctly notes in passing that the “destructive potential” of Sraffa’s contribution became apparent only in the controversy, a destruction of the theoretical tenets of orthodox theory that Samuelson himself had to admit. Although the negative part of Sraffa’s results is not the main subject of Sinha’s paper, I think that Sinha’s sketch of the controversy at the beginning of the paper is, at least, incomplete, for two main reasons. First, as was acknowledged in the controversy literature (Harcourt, 1972) the negative implications of ‘reswitching’ not only attains a simplified “parable” of the marginalist theory (which in the paper Sinha seems to identify exclusively as an aggregate quantity of capital in turn associated with an aggregate production function) but actually the very basic tenet of the factor substitution principle on which “all versions of the neoclassical theory” (Harcourt, 1972, p. 8, emphasis in the original) has to rely. Second, Sinha seems to be in agreement with Hahn’s position (Hahn, 1982), that the marginalist theory in its new versions of intertemporal and temporary general equilibrium models would remain “unscathed” by reswitching. However, this stance presupposes ignoring one of the strongest positions of the critical side that argued that the same like ‘paradoxes’ related to the treatment of capital by orthodox theory may reappear in its new formulations, as was the case of Garegnani (Garegnani, 2000; 2003). Moreover this later round in the controversy gave rise to further exchanges between the two camps, thereby indicating, at least in part, that part of the profession seems to be worried about the scientific status of orthodox theory in its new versions (Mandler, 2002; Garegnani, 2002; 2005b; Parrinello; 2005). So, in my opinion, a more balanced assessment of the last phase of the controversy would be desirable in the outset of the paper (see, in this connection, Petri, 2009; Lazzarini, 2015).

    Turning to the subjects pertaining to the constructive elements in Sraffa’s book, Sinha identifies three main issues in the debate between Samuelson and Garegnani. For that purpose, the author of the paper takes as a starting point Samuelson’s three criticisms of Sraffa´s 1960 contribution: i) that Sraffa’s claim that he does not make any assumption concerning returns to scale is not true; ii) that the Standard commodity is a useless device; iii) that in Sraffa’s book the limitation of land and capital are underplayed and hence the role of demand on prices would be underplayed too. Then Sinha discusses Garegnani’s responses to Samuelson, and assesses whether Garegnani’s replies are persuasive or not. In most cases, Sinha seems to be in disagreement with Garegnani’s arguments to prove Sraffa’s theory right, one of the most important arguments being that Garegnani reinterpreted Sraffa’s price system as being a system in “equilibrium” but which, according to Sinha, is not a faithful representation of Sraffa’s position. Sinha concludes in the end (p.16) that Garegnani, “although having a better intuitive understanding of Sraffa’s project than Samuelson”, assumed “classical equilibrium” and hence, according to Sinha, constant returns, so Samuelson’s critique would appear to hold. Sinha’s main point is, therefore, that Samuelson defeated not Sraffa’s theory but Garegnani’s reconstruction of it, precisely because Sraffa, according to Sinha, would not have assumed equilibrium.

    The purpose of the following comments is twofold: first, to find actually the reasons why Sinha seems to disagree with Garegnani’s reconstruction on some key theoretical points; but second, to argue that there is some commonality on some points between Sinha and Garegnani but which, in Sinha’s own opinion, seem to be at odds.

    Sinha faithfully reconstructs Samuelson critique on the alleged missing hypothesis of constant returns to scale in Sraffa’s system. Samuelson’s position can be succinctly summarized as follows: since in Sraffa’s system, according to Samuelson, demands have no role in determining prices (point iii) of his critique), then the system has to assume that constant returns to scale have to prevail in the production conditions (point i) of his critique). For that purpose Samuelson picks the subsistence economy to argue his point. So, according to Samuelson, Sraffa’s snapshot of an economy in self-replacing state must have arrived at by a Darwinian competitive process that entails adjustment of the quantities produced, and therefore constant returns to scale must prevail. To argue his point Samuelson cites part of the sole footnote of chapter 1 of Sraffa (1960, p.5), in which Sraffa points out that “every system of the type under consideration is capable of being brought to such a state merely by changing the proportions in which the individual equations enter it”. Against this statement, Samuelson argues that “Only in constant returns to scale technologies do proportions matter and alone matter! Otherwise scale and proportions interact to deny the quoted claim” (pp. 18-19, in Kurz, 2013). Sinha (p.3), moreover, argues that Garegnani’s response to Samuelson (“that Samuelson confuses Sraffa’s argument about abstract mathematical operations on equations with changes in the real system itself: ‘… That of course is true, but it applies to proportions between actual outputs and not to proportions between equations, as Sraffa is careful to specify in the one word we italicized in this passage’ (p. 58, in Kurz, 2013, Garegnani’s emphasis))” is “highly unsatisfactory” (p. 3). The argument Sinha uses seems to be originated from a different reading, in Sraffa’s footnote, of the sentence ‘every system of the type under consideration’ which ‘is capable of being brought to such a state’. But Sinha, who actually quotes in full the mentioned footnote on p. 2, makes use of it only partially and he regards “every system” as representing an actual production system. But careful reading of the footnote makes it clear that, ‘every system of the type under consideration’ refers to Sraffa’s system of equations, precisely because, as the full footnote makes sense, every system can be brought to a state of self-replacing merely by changing the individual equations that enter it, i.e., that enter the system of equations. So, Sinha has to argue differently in order to rebut Samuelson critique. According to Sinha, Samuelson’s choice of the subsistence economy to criticize the alleged absent of the constant returns to scale hypothesis missed the target. This is so because, in Sinha’s words (p. 3, Sinha’s emphasis), “it is a mathematical property of a subsistence system, i.e. ‘the system of the type under consideration’ that it must be characterized by constant returns to scale, otherwise slight vibration in the system would convert it into either a surplus or a deficit system. This, however, does not mean that the system producing surplus must also display constant returns”. Sinha reaches this conclusion after having shown how a Sraffa’s subsistence system in disequilibrium (i.e., the sum of total commodities produced is either higher or lower than the requirements of commodities as means of production; see below) can be put back in equilibrium. This is done by having recourse to a property of self-replacing systems that Sinha, correctly in my view, uses to argue that, even in disequilibrium, “if it is a subsistence system then the price ratio between the two industries are still well established”. However, to my surprise, Sinha seems to be defending the hypothesis that constant returns have to be assumed in one of the industries in the Sraffa’s self-replacing system. To see this more clearly, let us reproduce here the examples used in the paper.

    The system in “equilibrium” is:
    280 qr. wheat + 12 t. iron right400 qr. wheat
    120 qr. wheat + 8 t. iron right20 t. iron

    In order for the system to reproduce itself at the self-replacing state the ratio of exchange between the two commodities has to be 1 ton of iron for 10 quarters of wheat.

    The system in “disequilibrium” is:
    350 qr. wheat + 15 t. iron right500 qr. wheat
    90 qr. wheat + 6 t. iron right15 t. iron

    Indeed, Sinha shows that, the industry in “excess supply” (wheat), having been left with a certain amount of wheat (410 quarters of wheat) after exchanging 90 quarters of wheat for 9 tons of iron (which is the surplus, measured in iron terms, of the iron industry), can combine 210 quarters of wheat with the 9 tons of iron to produce 300 quarters of wheat. But this is, as argued above, tantamount to assuming that constant returns prevail in the wheat industry, as indeed Sinha contends. In fact, Sinha performs the following mathematical transformation in the wheat industry:

    First, Sinha first takes:
    350 wheat + 15 iron right500 wheat

    then he expresses (although this is not written in the paper) the conditions of production in the wheat industry in terms of a unit of wheat produced. Hence:
    0.7 wheat + 0.03 iron right1 quarter of wheat

    Now it is straightforward to see that the wheat industry, which is left with 410 quarters of wheat and has 9 tons of iron to be employed as inputs, can combine the 9 tons of iron only with 210 quarters of wheat. But 210=(9*0.7)/0.03, so constant returns to scale are ruling in the wheat industry. Then, under constant returns, it is easy to check that 9 tons of iron combined with 210 quarters of wheat will produce 300 quarters of wheat, i.e., the amount of wheat necessary for the iron industry (90 quarters) plus the wheat necessary to produce wheat (210 quarters). Hence “Samuelson’s choice” of the example of subsistence economies for an attack that Sraffa does not make any assumptions regarding returns to scale is, according to Sinha, “misplaced”, because the self-replacement system “must be characterized by constant returns to scale” (p. 3, emphasis added).

    But the fact is that Sraffa does not assume constant returns to scale for any system, whether subsistence or surplus (Sraffa, 1960, p.v). The trick here is, in my opinion, that Sinha seems to accept that every time one can transform, by means of arithmetical operations, the production conditions so as to express inputs required per unit of output produced, then constant returns to scale will govern those production conditions. But, in my view, this is not the case.

    First, Sraffa’s system is a snapshot of the economy, or an ex-post description of it, as Sinha acknowledges in the paper. So, in the description of the production conditions, Sraffa is taking both the outputs and inputs (i.e., techniques) as given before determining prices. Now, in the equations, e.g., the fact that 5 quarters of wheat combined with 30 tons of iron produce 15 quarters of wheat does not mean, at any rate, that 0.33 quarter of wheat combined with exactly 2 tons of iron will produce exactly 1 quarter of wheat. The fact remains that only 5 qr. of wheat coupled with 30 tons of iron will produce 15 qr. of wheat. It is precisely the method adopted by Sraffa of computing the total inputs that entered the production of wheat and computing the total output at the end of the year that is represented in his equations. Indeed, this method does not allow that proportional changes in inputs will change output in the same proportions. In actual economies, indeed, there is no guarantee that, e.g., the first qr. of wheat entering the production process as input, coupled with 6 tons of iron, will produce 3 quarters of wheat because in the actual production process many other elements associated to the specific production process might be interrupting, either in a lesser or in a great extent, that which has been established arithmetically.

    Secondly, what exactly happens in the actual production process cannot, I think, be exactly represented by Sraffa’s price equations or by any other theory of value. Indeed, as argued above, what actually happens in production processes involves a myriad of factors and elements which the theory cannot systematically deal with them all in a satisfactory way. How could any theory of value predict exactly the effects on prices if that theory considered too many a factor influencing the former, such as weather conditions, business strategies, macroeconomic policies, industrial policies, market structure, institutions, labour unions’ demands, and so on? So, in the best of the cases, the theory will be able to isolate the main causes of value and then lay out in very basic terms the effects of those causes on the matter under study. Thus, the production conditions as represented by Sraffa’s equation systems cannot refer to actually observable magnitudes; rather, they have to be viewed as rough approximations of the representation of the production conditions, i.e., gross inputs and gross outputs computed at the end of the year. In this respect, I think that it might be useful to recall the basic elements in the method of economic analysis for choosing the data:

    “An economic datum is not, however, absolutely fixed like a natural constant. Rather it is to be viewed as being determined by other causes: The supply behaviour of firms is influenced by their strategies and the technological conditions under which they operate. (…) Again, these are not ultimate data since technologies are subject to various influences and might change over time. Hence economic data are typically only of a provisional nature.” (Schlicht, 1985, p. 2)

    So the datum referring to “technologies” is of course subject to changes over time, but:

    “We will be unable to predict the development of all those influences subject to technical change, since we cannot predict still unknown future inventions with accuracy. Hence those data describing technology are provisional by necessity, and the provisional nature of economic data cannot be avoided in this respect, at least. Since technological change is of paramount importance in economics, we have to face this difficulty. The provisional nature of our data leads to a particular problem: What is to be considered as variable, and what is to be considered as fixed if everything is floating? What are the requirements which are to be met by those factors which we take as data of our analysis?” (Schlicht, 1985, pp. 2-3, emphasis added)

    As Schlicht makes it clear, at a certain stage the problem for building around a sound theory is to satisfactorily choose the data, but what data can we choose is “everything is floating”?

    “In freezing some factors, we transform them into data of our analysis. The choice of these data is not, however, simply a matter of caprice if the isolation is intended to be of substantive relevance. A substantive isolation requires those factors transformed into data have to be sufficiently stable with regard to the processes we want to explain such that the movements of the data do not destroy or supersede the relations we are studying in our model. This is the isolation principle. If it is satisfied, the results obtained in a partial model will continue to hold approximately true even if we make allowance for these movements.” (Schlicht, 1985, p. 19, emphasis added)

    So the inputs and outputs taken as data in Sraffa’s equations can, from this methodological perspective, undergo changes subject to the condition that they be sufficiently stable with regard to the problem at hand, i.e., the velocity of changes in production conditions is lower than the speed of adjustment of prices when production conditions varies. If the determination of the data is intended to be relevant (i.e., we cannot take the whole infinite factors determining value at every instant so we centred on a few causes of value), then the determination of prices will roughly hold true if the very data we choose do change while determining prices as they in fact do in the realm of pure theory.

    Now Sinha dismissed Samuelson choice of the self-replacing system to attack on the alleged missing constant returns to scale hypothesis in Sraffa as misplaced but this is done, in my opinion, by actually accepting that constant returns to scale prevail in Sraffa’s self-replacing system. However, Sinha (p. 3) refers readers to a previous article of his (Sinha, 2007) “for a more detailed response to Samuelson on this point”. One can read there, on the other hand, quite different an argument to rebut Samuelson, and indeed, in my opinion, quite in the lines followed by Garegnani actually. Suffice it to compare Sinha (2007, p. 63, emphasis in original)’s argument which reads: “any system of production, if it is of the type that depicts production for subsistence, ‘is capable of being brought to such a state [self-replacing state] merely by changing the proportions in which individual equations enter it.’ Clearly the remark in the footnote is a remark about the logical necessity of a system of a particular type and not about any given empirical system” to Garegnani’s rebuttal of Samuelson (see above, and p. 3 of Sinha’s present paper). Moreover, in rejecting Samuelson’s criticism that constant returns to scale have to be assumed in Sraffa’s system, Sinha (2007, p. 69) concludes that paper by citing from Garegnani (2005) one Sraffa’s exam question to his 1928-31 Cambridge students as a clear-cut instance to dismiss Samuelson critique altogether. Do not Sinha’s 2007 and Garegnani’s argument have some commonality?

    Sinha then proceeds (p. 4) to discuss Samuelson’s criticism on constant returns for systems with a surplus. According to Samuelson, Sraffa’s surplus system has to be in a steady or stationary state. Here Sinha’s argument against the critique centred on a stationary state is reasonably persuasive; pointing out that in Sraffa’s book there is no analytical element to support Samuelson’s reading. However, the author again goes on (pp. 4-8) to criticise Garegnani for his not having specifically disputed that Sraffa’s system is in “equilibrium”. Indeed, as Sinha himself acknowledges, Garegnani sees Sraffa’s equality of inputs and outputs prices as being of a different nature than the stationary or steady state. As is well known, Garegnani’s reconstruction of classical theory relies on a clear distinction between the data taken as given for the determination of prices and the non-given distributive variables and the data which marginalist theory takes as given for the simultaneous determination, by means of supply and demand functions, of output, prices and distribution. So underlying the discrepancies between Samuelson and Garegnani is the fact that the former has never acknowledged the existence of an alternative theory to orthodox thinking. Now Sinha seems to underplay in his paper this radical dichotomy which characterizes the two different approaches in economic theory. Although Sinha discusses, too extensively in my opinion, all the data for determining prices and the non-given distributive variable in Garegnani’s reconstruction of classical economics, he fails to grasp the radically different nature of the role played by these data for the classical theory of value with respect to the role played by the given data in marginalist theory. The fact that in Garegnani’s “core” techniques, output and, say, real wages are taken as given for determination of prices and the profit rate does not mean in the least that techniques, output and wages are not also object of investigation for classical economics. However, these data are determined separately from the determination of prices and the profit rate. This separation, according to Garegnani, is rooted in the fact that, on the one hand, within the core, one can draw general and quantitative properties by the price relations of this core thanks to the competitive tendency of profits, rents and wages to uniformity. Indeed within the core it seems possible to apply a purely deductive method at a level of generality provided there is a competitive tendency towards uniformity in distributive variables (i.e., to investigate the behaviour of prices and the profit rate through price equations). On the other hand, because of the very nature of techniques, outputs and wages these variables cannot be determined with that level of generality allowed by deductive methods as in the case of prices and the rate of profits. This is so because there is a multiplicity and variability of factors affecting these three circumstances which cannot be generally represented by mathematical or arithmetical apparatuses. That is why Garegnani calls these circumstances as intermediate data. So once this separation is understood it will be clear that in the classical theory there cannot be space for a simultaneous determination of prices, distribution and outputs, as is the case in marginalist theory (for a detailed and thorough explanation of this method, see Garegnani, 2003b, pp. 10-11). Again, it might be useful to remind ourselves of the economic method as analyzed by Schlicht (1985, p.3):

    “Economic data are not ultimate data, like the speed of light in physics. Rather they are provisional in nature. All factors not explicitly considered as variables are assumed to be fixed within an argument.”

    Sinha criticises Garegnani’s arguments because, for Sinha, a gravitational mechanism that guarantees uniformity in the distributive variables and prices cannot be conceived as being independent of the system of production. In the same vein, Sinha’s critique of both Garegnani’s treatment of effectual demand (pp. 4-5) and Garegnani’s position with respect to the analysis of the effects on prices due to changes in effectual demand (p.12), is rooted in the same misreading of the above explained separability that characterises Garegnani’s method. Sure, if the above mentioned separability in the method is not fully taken as an alternative to the general equilibrium approach of marginalist theory, then it will be easy to claim that in Garegnani’s reconstruction of Sraffa’s system the gravitation adjustment needs assuming constant returns to scale (p. 6) and hence the unsatisfactory response to Samuelson. In effect, Sinha’s (p. 5) interpretation of the separability of Garegnani’s method is, in my opinion, misunderstood as the author claims that such separability would rule out any possibility of classical gravitation; in other words, he claims for a general deductive method encompassing both adjustment in prices and quantities of both inputs and outputs produced.

    On pp. 12-13 Sinha charges Garegnani with having attributed to Sraffa’s prices the classical long-term equilibrium nature. For Sinha (p.12, emphasis added), instead, “At any moment, prices are determined by the empirical input-output data with the additional knowledge of ‘money wages’ in terms of the Standard commodity irrespective of demand considerations. If, however, changes in demand patterns affect changes in outputs that change the equations then prices would change but those prices can again be determined by the given input-output data along with the knowledge of the ‘money wages’ at that moment”. It would thus seem that Sinha takes Sraffa’s prices as being variables which could be determinate at any moment empirically. One of the strongest arguments to maintain Sinha’s point is that he has argued that in Sraffa (1960) there is no reference to mechanisms or processes through which a uniform rate of profit is ascertained so the gravitational mechanism would be ruled out and, with it, any conceivable reference in Sraffa (1960) to classical long-term equilibrium prices (see Sinha, 2011, which however is not quoted in the paper). Despite the challenging nature of his position, Sinha does not develop this argument in full in the paper, which, I think, is the ultimate reason for discrepancies with Garegnani.

    On the issue of the Standard commodity I think that, on the whole, Sinha’s argument is fairly persuasive and indeed complementary, rather than radically opposite, to Garegnani’s own rebuttal of Samuelson’s criticism of an allegedly irrelevance of the standard commodity. However, Samuelson also raised doubts about the existence of basic goods and on this score, again, Sinha (p. 11) seems to be at loggerheads with Garegnani. The point here concerns actually what would come to happen on the economic system if we were to ignore the basic role of workers necessaries, i.e., to accept Samuelson’s misgivings. Garegnani (p. 66, in Kurz, 2013) argues that the very existence of a maximum rate of profits would be put at serious risk. Sinha disputes Garegnani’s contention, and argues (p. 11) that “Now, as far as the existence of ‘a maximum rate of profits’ is concerned, Garegnani’s above contention seems to be incorrect. One does not need existence of a basic good to show that a maximum rate of profits must exist. Its existence depends on the fact that production requires some produced means of production. In other words, capital can never be completely reduced to only ‘variable capital’, to use Marx’s terminology. But the existence of constant capital as such in the production process does not mean that it must be a ‘basic’ good.” However, in my opinion, this disputation is groundless. Indeed, in order to achieve a maximum rate of profits entirely in terms of the production conditions one has to show the existence of the standard commodity, as Sraffa performed. So, if we do not have at least one basic commodity, i.e., at least one commodity that enter directly and indirectly the production of all the commodities, how a standard commodity could be constructed? As is well known, the Standard commodity is a composite commodity which is built on the basis of considering all basic commodities of the system, combined in such proportions so as to make the standard commodity independent of changes in distribution. I think, after all, that Sinha’s contention on this very specific point does not better off his own criticism of Samuelson, which, again, seems to me to be persuasive.

    Finally I would like to raise my big doubt I find in Sinha’s paper: why, if Sraffa’s framework were more compatible to Sinha’s own reconstruction, would that framework necessarily be totally incompatible with the gravitation mechanisms and hence with classical long-period “equilibrium” prices? This, I think, is far from settled in Sinha’s paper. And, indeed, instances that Sraffa’s system is compatible to the reconstruction championed by Garegnani can be traced both to his unpublished manuscripts as well as to Sraffa (1960). Thus Sraffa himself wrote about the meaning of his equations in the late 1920s when he started developing what eventually end up being Sraffa (1960)’s price equations:

    “Ratio of solutions are ‘‘absolute value’’. It is not contended that they are actual exchange values (this depends on institutions) which is [sic] indeterminate’ (D3/12/6: CXVI.3.i)” (quoted by Garegnani, 2005, p. 474).

    Now if we recall that Sraffa (1960, p. 9) himself explicitly mentions that his prices in the equations are not meant to be market values and that, instead, “necessary price”, “natural prices” or “production prices” would meet the case, then how could it be argued that Sraffa’s system is inhospitable to classical gravitation?

    It is the opinion of this reviewer that Sinha’s paper has a constructive part, which is actually his own reconstruction of Sraffa’s system and which he deploys to counter Samuelson’s attacks on Sraffa but also to criticise Garegnani to the extent of concluding that Gareganani’s responses to Samuelson are, overall, unsatisfactory. However, as pointed out above, one drawback in Sinha’s paper is that actually his own reconstruction of Sraffa does not appear systematically dealt with throughout, but perhaps this had to do with the type of arrangements he might have chosen for a better adaptation of the structure of his reflection on the Samuelson-Garegnani debate. The second drawback which I see is the excessive criticism used in his attempt to “reflect” on Garegnani’s position in this debate. I think that such criticism in most cases is unjustified and originates in a misreading of Garegnani’s own reconstruction of Sraffa along classical lines. In fact much of Sinha’s own reconstruction of Sraffa is actually used to refute Garegnani. However, as I commented above, it seems that on the issues of both Samuelson’s attack regarding constant returns and the alleged irrelevancy of the standard commodity, Sinha and Garegnani may find some commonality, and therefore, it would thus seem, no need for a long and excessive critical excursus on Garegnani.

    If these drawbacks could be overcome, and the abovementioned big doubt properly addressed, we may perhaps have a more balanced paper.

    [1] Garegnani, P. (1966). “Switching of Techniques”. Quarterly Journal of Economics, 80, pp. 554-567.
    [2] Garegnani, P. (1970). “Heterogeneous Capital, the Production Function and the Theory of Distribution”. Review of Economic Studies, 37, pp. 407-436.
    [3] Garegnani, P. (2000). “Savings, investment and capital in a system of general intertemporal equilibrium”. In: Critical essays on Piero Sraffa’s legacy in economics, ed. H. D. Kurz. Cambridge: Cambridge University Press.
    [4] Garegnani, P. (2003). “Savings, investment and capital in a system of general intertemporal equilibrium”. In: General equilibrium: Problems and prospects, eds. F. Petri and F. Hahn. London: Routledge.
    [5] Garegnani, P. (2003b). “Professor Blaug on Understanding Classical Economics”. Quaderno di Ricerca del Centro di Ricerche e Documentazione Piero Sraffa, n.3, Rome: Aracne editrice.
    [6] Garegnani, P. (2005). “On a turning point in Sraffa’s theoretical and interpretative position in the late 1920s”, European Journal of the History of Economic Thought, September.
    [7] Garegnani, P. (2005b). “Capital and Intertemporal Equilibria: A Reply to Mandler”,. Metroeconomica, 56, pp. 411-437.
    [8] Hahn, F.H. (1982). “The Neo-Ricardians”. Cambridge Journal of Economics, 6, pp. 353-374.
    [9] Harcourt, G.C. (1972). Some Cambridge Controversies in the Theory of Capital. Cambridge University Press, Cambridge.
    [10] Kurz, H.D (ed.) (2013). The Theory of Value and Distribution in Economics Discussions between Pierangelo Garegnani and Paul Samuelson, Routledge: London.
    [11] Lazzarini, A. (2015). “Some Unsettled Issues in a Second Phase of the Cambridge-Cambridge Controversy”, Review of Radical Political Economics. (Forthcoming).
    [12] Mandler, M. (2002). “Classical and neoclassical indeterminacy in one-shot versus ongoing equilibria” Metroeconomica 53 (3): 203-222.
    [13] Parrinello, S. (2005). “Intertemporal Competitive Equilibrium, Capital and the Stability of the Tâtonnement Pricing Revisited”. Metroeconomica, 56, pp. 514-531.
    [14] Petri, F. (2009). “On the recent debate on capital theory and general equilibrium” Quaderni del Dipartimento di Economia Politica dell’Università degli Studi di Siena n. 568.
    [15] Samuelson, P.A. (1962). “Parable and Realism in Capital Theory: The Surrogate Production Function”. Review of Economic Studies, 29, pp. 193-206.
    [16] Samuelson, P.A. (1966). “A Summing Up”. Quarterly Journal of Economics, 80, pp. 568-583.
    [17] Schlicht, E. (1985). Isolation and aggregation in economics. Springer-Verlag: Berlin.
    [18] Sinha, A. (2007). “Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula”, Contributions to Political Economy, 26, pp. 61-70.
    [19] Sinha, A. (2011). “Listen to the Silences: A New Interpretation of Sraffa’s Production of Commodities”, Indira Gandhi Institute of Development Research, Mumbai, India.
    [20] Sraffa, P. (1960). Production of Commodities by means of Commodities: Prelude to a Critique of Economic Theory. Cambridge University Press, Cambridge.

    • Ajit Sinha says:

      I thank Dr. Lazzarini for his detailed and careful comments on my obviously controversial paper. Since his comments are rather long, I will not take space to either summarise or extensively quote from it. I will simply respond to what I think are the relevant arguments made by Lazzarini by referring to the numbers of his sections.

      My Response to §1:
      I may point out that the re-switching proposition as presented in Sraffa (1960) is not Sraffa’s discovery. Sraffa was actually expecting the two techniques to be represented by two straight lines superimposed on each other. It was Besicovitch who pointed out to Sraffa that the w-r relationship for the second technique must be non-linear if measured by the Standard commodity of the first technique and therefore they may cut each other at several points. To quote Sraffa:

      My suggestion was that, in the case of several intersections of the prices from 2 alternative methods, the two systems resulting must have the same value of R. The reason given being that the connection between w and r in the two systems being linear, the two straight lines cannot intersect more than once; and if they must have several points in common, the lines must coincide, and therefore also coincide with R.

      B’s answer is that they are straight lines if each is in its own standard unit: but then they cannot be compared. Here they are both taken in the unit of one of the two systems: that one is a straight line, but (in that unit) the other is a curve – so, many intersections are possible.’ (Sraffa Papers, file #: D3/12/37, p. 11, dated 14.6.44).

      Sraffa’s criticism of the marginal product theory of capital was not based on his ‘re-switching proposition’ but rather on his proposition that the maximum rate of profits R must remain constant with respect to changes in the rate of profits r. This is what he called ‘My Hypothesis’ in 1942 and kept working on to prove it till September 1944. This is achieved by the end of the Part 1 of the book (Sraffa 1960). Both Part II and Part III of the book are devoted to relaxing the assumptions of Part I to see if the main propositions established in Part 1 still hold. Part II introduces fixed capital, joint production and land in the system. Part III relaxes the assumption of only one technique available for production. By the way, re-switching is nothing but substitution of one technique for another given changes in wages or the rate of profits. Sraffa thought that this was important in understanding accumulation and Marx’s proposition regarding ‘falling rate of profits’ (on this, see Sinha 2014). Thus it would be a mistake to interpret the nature of Sraffa’s critique of the ‘marginist’ theory to be based on his re-switching proposition. I might also add here that in the ‘Preface’ to the Production of Commodities by Means of Commodities Sraffa wrote:

      While the central propositions had taken shape in the late 1920’s, particular points, such as the Standard commodity, joint products and fixed capital, were worked out in the ‘thirties and early ‘forties. In the period since 1955, while these pages were being put together out of a mass of old notes, little was added, apart from filling gaps which had become apparent in the process (such as the adapting of the distinction of ‘basics’ and ‘non-basics’ to the case of joint products). (1960: vi).

      Interestingly, the proposition regarding re-switching of techniques is not even mentioned. Surely, this could not have been just a slip on Sraffa’s part.

      On the question of Garegnani’s (2003), the best I can do here is to refer Lazzarini to Schefold (2007). But I am glad that Lazzarini has added some of the references to this literature for reader’s benefit.

      My Response to §2:
      This section does not require any response.

      Response to §3:
      Unfortunately, I think lazzarini has completely misunderstood my argument. In my example of a readjustment of a subsistence system in disequilibrium, I do not assume constant returns. What I show is that the industry which must contract can show only three possible outcomes. Either its total output is larger than 300 or smaller than 300 or equal to 300. If it is larger than 300 then the industry must be characterised as ‘diminishing returns’ industry. And if that is the case then the system would turn into a ‘surplus’ system and no longer remain a subsistence system. Sraffa in the parenthesis of the foot note goes on to add that he discusses such systems in §4ff of the book. If the total output turns out to be less than 300 then the industry must be characterised as ‘increasing returns’ industry. In this case the system must turn into a ‘deficit system’, which will not have any historical viability and so Sraffa in the parenthesis of the foot note clarifies that that is why he does not discuss such cases. It is only when the output turns out to be 300, which is the case of ‘constant returns’, that the system can revert back to being a subsistence system. Hence systems of this type, i.e., the subsistence systems, must be characterised by constant returns otherwise a slight vibration in the system would turn it into either surplus or deficit system for ever, i.e., the system will not have historical viability as a subsistence system. My interpretation gets further support from a draft of the foot note written by Sraffa in March 1956:

      ‘Note to p. 4 The statement in this form applies only to a system which is in a self-replacing state. But any system, to be consistent, must be capable of being brought to such a state merely by changing the proportions in which the several equations enter it. If this is not possible there may be a deficit or a surplus, but no equality.’ (D3/12/71: 5).

      Now, what could the phrase, ‘If this is not possible’, mean? If Garegnani’s interpretation is correct then the question of it being not possible does not arise—it has to be always possible. But Sraffa’s point is that the system may not revert back to a subsistence system if the industries were not characterised by constant returns. It is my understanding that there has been no change in my interpretation on this point since Sinha (2007), though I was not aware of the above mentioned note when I wrote Sinha (2007).

      My Response to §4
      My discussion of Garegnani’s ‘core’, which Lazzarini describes as ‘too extensive’, is designed to show that it does not constitute a coherent ‘alternative theory’. It is the notion of equilibrium, which requires the assumption of constant returns along with no substitution of factors, in Garegnani’s interpretation of Sraffa’s system that destroys his attempt to constitute it as a radically different theory. On the other hand, it is my interpretation of Sraffa’s system of equations, which does away with the notion of equilibrium and hence any assumption regarding returns to scale, that provides a radical alternative to the orthodox general equilibrium theory. Dr. Lazzarini needs to take up my criticisms of Garegnani’s ‘givens’ of the ‘core’ rather than paraphrase the same old assertions of Garegnani and his followers. Assertions cannot substitute arguments.

      My Response to §5
      Lazzarini is right that the question of whether Sraffa assumes equilibrium condition for his prices or not lies at the core of the difference between Garegnani’s understanding of Sraffa’s theory and mine. Though Sinha (2011) is not cited in my paper, many other published papers of mine are cited that deal with the question of uniformity of the industrial rates of profits in Sraffa’s system not being based on the assumption of equilibrium of quantity supplied and the effectual demand. I thought that this was not the occasion to develop that argument. This argument, however, would be reinforced by supportive evidence from Sraffa’s archives in my forthcoming book on Sraffa.

      On the question of the requirement of the Standard commodity for the determination of the maximum rate of profits, I disagree with Lazzarini. Yes, you need the Standard commodity to prove that the maximum rate of profits R remains constant with respect to changes in the rate of profits r. But this is an entirely different matter than the determination of r when w = 0.

      My Response to §6
      The classical centre of gravitation argument requires the assumption of constant returns to scale—there is no way around it. An assumption of constant returns to scale in Sraffa’s system turns it into a special case of general equilibrium. Sraffa knew it well. That’s why in the very first statement of the ‘Preface’ to the book he warned his readers not to bring the baggage of ‘equilibrium’ to his book, as the assumption of equilibrium would logically imply constant returns assumption. Sraffa was warned of this not only by Keynes to whom he refers in the Preface but also by Pigou in January 1928. Sraffa’s theory eschews all reference to equilibrium and therefore the classical notion of centre of gravitation. This paper was not the appropriate forum to develop these ideas as they are developed by me in other places. No one denies that an empirical system may turn out to be in equilibrium by a fluke but barring such flukes the empirical system or the ‘system of observation’, as Sraffa puts it, would not be at the centre of gravitation and Sraffa’s prices refer to the prices that would prevail in such systems of observations if either the rate of profits or the wages in terms of the Standard commodity were given from outside the system of equations. By the way, the 1927 quotation from Sraffa presented by Lazzarini refers to a subsistence system and it is irrelevant to the problem of equality of the rate of profits and the question of centre of gravitation. Furthermore, by ‘natural prices’ Sraffa does not mean the centre of gravitation or long-term prices. In 1928, Sraffa wrote: ‘When A. Smith etc. said ‘natural’ he did not in the least mean the ‘normal’ or the ‘average’ nor the ‘long run’ value. He meant that physical, truly natural relations between commodities, that is determined by the equations…’ (D3/12/11: 83). Furthermore, in the quotation offered by Lazzarini from page 9 of Sraffa’s book (1960), Sraffa clearly tells us that ‘the present context’, i.e., the context of the determination of prices by adding a uniform rate of profits, does not contain any reference to ‘market prices’. Now, the classical notion of center of gravitation, of course, contains a reference to ‘market prices’, as it is supposed to be the center of gravitation of nothing else but ‘market prices’. It is the notion of ‘effectual demand’ of classical economics that calls forth the notion of ‘market prices’. Sraffa’s parenthetical remark suggest that his context of price determination has no room for the notion of ‘effectual demand’.


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