Gross substitutability of point-to-set correspondences

Abstract

In this paper the notion of gross substitutability for the multi-valued case is studied. It is proved that, if in a pure exchange equilibrium model gross substitutability and some auxiliary conditions prevail, then (a) the set of equilibria is a Cartesian product of a convex set of equilibrium resource allocations and a convex cone of equilibrium prices; hence all equilibria are equiadvantageous for every trader; (b) the weak axiom of revealed preference holds in any equilibrium; (c) any equilibrium is stable with respect to reallocations of initial resources. Some situations in which Walras' law does not hold are considered as well. © 1983.