The Spring of Sraffa’s Equations: The “absolutely necessary commodity” and the “community that produces just what is sufficient to keep it going”

In order to start our discussion of how the exploration of the reduction of the inputs of a given production process to an absolutely necessary commodity may have led Sraffa to write his equations, the part of the prelectures that contains the relevant sentences must be quoted in full:⁹

Physical real costs

This conception would be tenable only if all the commodities considered (or at least one of them) had, each of them, no possible substitute (and therefore were absolute necessaries, since luxuries are naturally substitutes among themselves).

There is however something to be said for this conception of real cost. It is true that there is an infinite number of combinations of commodities which would be “the minimum” necessary to support permanently a labourer working 8 hours a day at a given standard of efficiency. But this difficulty arises only in so far as we abstain from using a unit of measure for the different commodities, and simply say that the real cost of producing a given article is a given set of diverse commodities—and this would be an “ultimate” conception if there were no possible substitutes for those commodities. This not being the case, we must find a unit of measure for cost: the necessity for this unit arises, not from a desire of actually measuring—it is prior to it, and is required even for thinking of cost. The best measure available is the amount of various commodities that is required to support during an hour, or day or year a average common labourer: if there are many of such sets of commodities, we can choose the one that can be produced with a minimum of labour (this is ambiguous!). Of course, not all individuals in one trade require the same amount of necessaries, and persons in different trades require different amounts— and to this extent our measurement is inexact, and real cost is slightly different (in excess or deficiency) from number of hours of labour. I contend however that the amount of necessar­ies varies much less between different workers, than vary a) their disutilities, b) their wages.

Thus to Ricardo’s T. V..^l'^, based on amount of labour, two interpretations can be given: 1) the subjective psycholog., disutility one, 2) the objective physical, necessaries of existence one. He probably had not always clear in mind the distinction, but I believe that the latter is the one that underlies his T V (Sraffa Papers, D3/12/3/44-47 [A4/ 16iii-vi]; spelling and words underlined or crossed out as in original manuscript; smaller case indicates words Sraffa inserted above the line; sentences within square brackets were written by Sraffa, within square brackets, on the left hand margin of the sheet; emphasis added)

The passages we have just reproduced appear in the prelectures at a point where Sraffa had already recognized that also more recent theories of value must rely upon an ulti­mate standard and had already criticized the possibility of employing to such an effect either Leon Walras’s, Carl Menger’s and William Jevons’s utility or Marshall’s real costs. Here Sraffa considers an alternative conception: physical real costs. The relevant pas­sages, however, even though opening as if something had already been said about such an alternative conception, are not preceded by any real introduction nor contain it them­selves, and no author is mentioned as proponent of the conception. Nevertheless, it can clearly be gathered that physical real costs are opposed to what Sraffa had just described as psychological standards (“All the ultimate standards we have considered up to this point are psychological,” Sraffa Papers, D3/12/3/42 [A4/16i]). On the contrary, as the text soon reveals, physical real costs refer to a conception that describes production processes as sets of commodity inputs—and, to do this, also labor inputs have to be expressed as a set of commodities “which satisfy the condition of maintaining life and efficiency of the producers” (Sraffa Papers, D3/12/3/44 [A4/16iii]).¹¹ The latter set is described as an absolutely necessary commodity, and, as Sraffa put it, once such a com­modity had been identified,

it would be easy to find the cost of all the other things in terms of the necessary one, and thus by going back enough in the genealogy of production (and stopping along each branch so soon as we have resolved it into our necessary commodity) we might find exactly the total amount of corn (if this were the ideal necessary commodity, which it is not) that has actually entered into the production of, say, this book, and covers entirely its cost of production, at the exclusion of any other commodity.

This would answer the question of the existence of an ultimate standard or of a common measure of value, and would allow to express the value of any commodity by a definite magnitude.

We might try and identify the sources of this conception (see, for instance, docu­ments kept in folders D3/12/2, D3/12/42 and D2/4), but what we wish to stress is that, according to Sraffa, an obstacle would stand against the possibility of reaching a general solution by this route: the existence of substitutes would make it impossible to identify an absolutely necessary commodity and would imply that the physical real costs conception, in Sraffa’s words, is not tenable (Sraffa Papers, D3/12/3/44 [A4/ 16iii]). Sraffa, however, suggests that this outcome could be avoided by confining the analysis within a special case or by pursuing an approximate solution. In general, a bundle of commodities could be used to the same purpose that should have been served by the absolutely necessary commodity. This would allow us to obtain an approximate solution, and, according to Sraffa, even though not exact, this solution would be more precise than any measures of value based on disutility or wages. The special case, in contrast, is outlined by Sraffa in the note appended on the left-hand margin of sheet D3/12/3/44 [A4/ 16iii]: within the boundaries of “a community that produces just what is sufficient to keep it going,”¹² the problems posed by the existence of substitutes could be sidestepped and the physical real costs approach could lead to an exact determination of the value of individual commod­ities by reducing their inputs to different amounts of the absolutely necessary commodity.

If this can be taken to be the stage reached by Sraffa in the summer of 1927 in terms of positive explanation of the values of individual commodities,¹³ we may stress that it contains elements pointing toward three crucial directions: (1) the description of production processes as lists, as we may call them, or sets, as Sraffa put it, of quantities of diverse commodities representing the real cost of producing a given article; (2) the identification of the case of an economy that barely “keeps going”—that is, an economy that produces no surplus above the replacement of the means of production it employs; (3) the reduction of the production process of any individual commodity to a hypothetical absolutely necessary commodity.

The importance we attribute to these three elements, or directions, stems from their similarity with two features of Production of Commodities: the way industries, or production processes, are described and the distinction between production for subsistence and pro­duction with a surplus. On this basis, it may be natural to conclude that Sraffa’s equations and the schemes that characterize Production of Commodities may be seen as an evolution from the prelectures.

But recording these similarities does not necessarily have to mark the end of our inquiry into the origins of Sraffa’s equations: a more detailed conjecture concerning the line in the development of Sraffa’s thought from the prelectures to the early formulations of his equations may be put forward. More precisely, we consider information on how, starting from the identification of a physical real costs approach and from the three ele­ments mentioned above, Sraffa may have moved toward the definition of a system of simultaneous equations whose solution would have allowed him to determine exchange values, as in Production of Commodities, with no need to reduce the production process of each commodity to a hypothetical absolutely necessary commodity.

The importance of the third element is notable because we expect it to indicate the precise analytical direction taken by Sraffa in November 1927: in order to reduce pro­duction processes to a hypothetical absolutely necessary commodity, he most likely could have tried to describe them analytically, following the idea that they could be seen as sets of inputs. And he could have done this for the special case of an economy that barely keeps going. Indeed, it is reasonable to say that if he had not identified a case within whose boundaries the problems posed by the existence of substitutes could have been

sidestepped, he would have had little or no incentive to pursue the reduction of the production process of an individual commodity to a hypothetical absolutely necessary commodity—a direction that he had otherwise described as untenable.¹⁴

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