A limit theorem on the core of an economy

Abstract

In his Mathematical Psychics [5], Edgeworth presented a remarkable study of the exchanges of two commodities that might arise in an economy with two types of consumers. The first case that he considers concerns two individuals each of whom initially possesses certain quantities of each commodity. The result of trading consists of a reallocation of the total amounts of the two commodities and may, therefore, be described geometrically by a point in the Edgeworth box corresponding to that economy. Edgeworth confines his attention to those exchanges which are Pareto optimal, i.e., those which cannot yield greater satisfaction for one consumer without impairing that of the other by means of additional trade. He further restricts the admissible final allocations to those which are at least as desired by both consumers as the allocation prevailing before trading. Those allocations which are not ruled out by either of these considerations constitute the "contract curve."

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