ABSTRACT
A non-substitution theorem is a uniqueness theorem which asserts that under certain specified conditions an economy has one particular price structure for each admissible value of the rate of interest. The original formulations of the theorem assumed single production and therefore circulating capital only (see Arrow 1951; Georgescu-Roegen 1951; Koopmans 1951; Samuelson 1951).1 In all these formulations the rate of interest is assumed to be at a level lower than the maximum one, which is obtained at a wage rate equal to zero. The problem of whether the theorem holds good when wages are zero seems never to have been investigated. Although there is no particular economic motivation to study this situation, it is startling that a limiting case of a theorem which has been studied so extensively and is generally accepted in the scientific community has not been analysed. In this chapter the lacuna is made good. We first show in terms of a numerical example that, if wages are zero, then the theorem need not hold. Next we show that if there exists a commodity which is indispensable for the reproduction of all commodities, then the theorem does apply, i.e. uniqueness of prices obtains, even if wages are zero. The proof supplied offers also some insights into the formal structure of the nonsubstitution theorem.
