An axiomatic analysis of Piero Sraffa's "Production of commodities by means of commodities" within the context of joint production

Abstract

Since the publication in 1960 of Piero Sraffa's slim volume many mathematical analyses of single commodity production, using the Perron-Frobenius Theorems, have been published. Little, however, has been published that extends these analyses to the more general case of joint production, for which these theorems are no longer applicable. In this Thesis several of the main concepts in Sraffa's work are defined and analysed, for the general case of joint production, within an explicity developed axiomatic structure (Chapter (2)). It is shown that certain propositions that are true in special cases of single commodity production (often due to the above theorems) cease to be so when the analysis is extended to joint production. Firstly, the two disjoint and exhaustive sets of basic and non-basic products are defined and examined. A basic system is then defined and shown to be, in general, non-unique. However, for the purposes of Sraffa's analysis every basic system has the same set of relevant properties and so a basic system can be treated as though it were unique (Chapters (4) - (6)). Secondly, a standard commodity is defined and its role as a numeraire of the economic system investigated. It is shown that a standard commodity is not necessarily an economically meaningful numeraire. Two alternative definitions of a standard commodity are then constructed that are superior to the original in that every standard commodity, by definition, is an economically meaningful numeraire (Chapters (7) - (12)). Finally, some asserted properties of a standard commodity are examined, especially in the light of Sraffa's role as the editor of Ricardo's "Works" (Chapters (13) and (14)).