## Whose fatal error? Sraffa and Samuelson on Marshall’s partial equilibria method

When in 1990 Samuelson examined Sraffa’s overall theoretical contribution to economics in “Revisionist Findings on Sraffa”, he defined the results achieved by the latter in the first part of the 1926 Economic Journal paper as Sraffa’s fatal error. That is the more surprising since Eatwell (1990), Garegnani (1990) and Schefold (1990) commenting on Samuelson’s revisionist findings pointed out that Samuelson’s analysis of the same issue as developed in a section of Samuelson 1971 paper on “An exact Hume-Ricardo-Marshall model of international trade” is identical to that of Sraffa 1925. Indeed, it is possible to argue that Samuelson’s analysis is even more devastating than Sraffa’s in terms of his negative assessment of the theoretical domain of the Marshallian model of partial equilibrium. The questions set by Sraffa and Samuelson are very similar: Sraffa’s analysis is specifically devoted to reconstructing the partial equilibrium model in a logically coherent way; Samuelson’s analysis is specifically devoted to identifying the conditions in which a partial equilibria model delivers exactly the same results as a general equilibrium model (the latter considered as the benchmark model as far as logically consistency is concerned). But the two analyses have opposite aims: Sraffa wants to accurately identify the boundaries of partial equilibrium empirical domain, that is, the set of empirical situations that are logically analyzable within that model; Samuelson wants to identify the “needed mathematical foundations for the rigorous partial-equilibrium handling of general equilibrium”. Also Sraffa’s and Samuelson’s final verdict on Marshall is different: as is well-known, Sraffa was of the opinion that “it is Marshall’s theory that should be discarded” (Sraffa 1930, 93). Samuelson, on the contrary, stated: “A rigorous model has been presented here. No attempt has been made to lighten the strong assumptions needed […]. Although all the strong assumptions made here are needed if the partial-equilibrium diagrams are to be valid, many of the properties of the classical model […] will be valid in much more general models that dispense with simple graphs and are definable by simultaneous equations”. ([1971] 1972, p. 373). Hence, granted that Sraffa’s and Samuelson’s analyses of the hits and misses of Marshall’s partial equilibrium model are almost indistinguishable how is possible that the two authors reach different conclusions on the fruitfulness of Marshall’s method? Whose fatal error is it? Our paper is devoted to analyze these facts and to investigate the methodological issues that are on the back of Sraffa’s and Samuelson’s reasonings.

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Keywords: Sraffa, Samuelson, long period, partial equilibrium

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