9 - On the probability of re-switching and capital reversing in a two-sector Sraffian model

Summary

Introduction

In his classic Production of Commodities by Means of Commodities (1960), Piero Sraffa claimed (in Chapter XII) that a technique of production which was most profitable at one rate of profit (interest) could become inferior to another technique at a higher rate and then reappear as the most profitable at a yet higher rate. This phenomenon, known as the ‘re-switching’ of techniques, has profound implications for the logic of using aggregate concepts of capital and the standard monotonic relationships between ‘factor’ quantities and prices derived there from (see Harcourt, 1972, and, for a recent exposition, Ahmad, 1991). Sraffa's claim was the subject of intense debate in a symposium (1966) in the Quarterly Journal of Economics, and subsequently in papers by Galloway and Shukla (1974), Garegnani (1970, 1976), Sato (1976) and Laibman and Nell (1977). The outcome established categorically the possibility of re-switching in general multisector models of production, but despite these demonstrations of ‘possibility’, the question of ‘probability’ has received far less attention.

Apart from some early statements of (generally quite weak) sufficiency conditions for non-re-switching (e.g. Bruno, Burmeister and Sheshinski, 1966, p. 544), there have been few explicit attempts in the theoretical literature to deal with this question. One of the first was by Eltis (1973, Chap. 5), who considered the matter in relation to the two-sector model of Hicks (1965) and to his own particular variant of the model.