Walrasian equilibrium as limit of competitive equilibria without divisible goods

Abstract

This paper investigates the limit properties of a sequence of competitive outcomes existing for economies where all commodities are indivisible, as indivisibility vanishes. The nature of this limit depends on whether the “strong survival assumption” is assumed or not in the limit economy, a standard “convex economy”. If this condition holds, then the equilibrium sequence converges to a Walras equilibrium for the convex economy; otherwise it converges to a hierarchic equilibrium, a competitive outcome existing in this economy despite the fact that a Walras equilibrium might not exist.