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On two theories of value and distribution

Naqvi, Nadeem (2011): On two theories of value and distribution.

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Abstract

This paper compares the theory of value and distribution of Arrow and Debreu [1954] with that of Sraffa [1960]. I consider such versions of the two models that capture their salient features, without aiming at the greatest possible generality, so as to isolate the precise nature of the differences between the two conceptions of the same economic reality, and inter alia, to quarantine both the sources and the entailments of the differences in the two theories that respectively purport to determine the values of commodities and distribution of income in society. Both theories are complete and consistent. Sraffa’s model is based exclusively on factual information, so it achieves less in terms of determining endogenous variables. The Arrow-Debreu is based on counterfactual information regarding additional production scenarios that are unobserved, in addition to the factual information that Sraffa has, so it achieves more by way of determination of endogenous variables. In terms of entailments, in Sraffa's theory there is an insufficiency of determinants in the economic grounds of society, thereby requiring the political component of society to also play an influential role in the joint determination of values and distribution. In the Arrow-Debreu model this determination is made complete solely in the economic sphere of society, rendering this theory purely economic, rather than political-economic, as in Sraffa. Both the information content difference at source, and the purely-economic versus political-economic difference in the entailments of what it takes to determine values and distribution, render the two theories radically different. In addition, (1) the prices in the two theories are different both in terms of definitions and values, and (2) since Sraffa’s model has only one set of numbers on the observed production of commodities by means of commodities and labor for a single year, it is impossible to define constant returns to scale, while in the Arrow-Debreu model, this property is admissible, and possible to define, because their model’s information base is sufficiently larger than Sraffa’s. Further, Sraffa’s theory is invariant to (a) the interpretation of prices – market-clearing, long-period, or whatever, (b) multiplicity of profit rates across industries, instead of a uniform rate of profit, and (c) presence or absence of general aggregate demand functions for commodities, and is (d) more general than the Arrow-Debreu theory because it is based on weaker assumptions, in the sense of a strictly smaller information set, so that it is only to be expected that the Arrow-Debreu theory would be capable of determining more endogenous variables in the model of an economy. (416 words)

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