Two Concepts of Basic Commodities for Joint Production Systems

Abstract

The concept of a basic commodity as introduced in Sraffa’s (1960) well-known book: ‘The Production of Commodities by Means of Commodities’ has often been treated and reformulated in the literature under the presupposition of a square single-product system. Its various formulations in terms of direct and indirect – or solely in terms of direct – relationships between the production accounts of the commodities produced can be easily understood from a mathematical as well as from an economic point of view. This situation, however, changes drastically once joint products are taken into account. In this general case the various definitions at hand not only lose their equivalence, but are – following a proposal made by Sraffa (1960, 60) and formalized by Manara (1980) – in fact replaced by a new and much more complicated definition, which, in addition, does not give a complete generalization of the original concept of basic commodities (as we shall see in Sect. 9.4). The proposed new formulation of basic commodities for joint production systems is based on linear combinations of the direct relationships which describe the production of commodities by means of commodities for this case, and Sraffa (1960, 57) explicitly states that ‘the criterion previously adopted…(in terms of direct and indirect relationships, P.F.) now fails, …’. It is the aim of the present chapter to demonstrate that this view need not be conclusive. In fact, we shall see in Sect. 9.2 that our four equivalent ways of generalizing the single product approach to the case of joint production (among them one which generalizes this approach in a very natural way), give rise to a concept of ‘basics’ which differs from the Sraffian one. Section 9.3 presents several properties of this alternative notion of basics and it also provides a motivation for their denomination: Leontief-basics, to be suggested in this chapter. In Sect. 9.4 we shall then briefly consider their known alternative, the Sraffa-basics, by utilizing two simplifications of their original definition which have been provided by Steedman (1980) and Pasinetti (1980). This section also completes their up to now incomplete characterization if the set of singular output matrices is excluded from consideration.