Stability of Pure Trade Equilibrium with Externalities

Abstract

Sufficient conditions for the stability of competitive equilibrium in a pure trade economy with externalities are developed in this paper. Externalities are introduced through the assumption that each individual's utility depends on the consumption of every other individual. A two-level adjustment process is postulated. At fixed prices, individual strategies must be made mutually consistent. Each individual's strategy is stated as a relation which maps prices and the demands of all other individuals into the demand of that individual. The equilibrium of the externality adjustment process is a demand allocation, depending on price, which is feasible and maximizes utility for each individual at given prices. Sufficient conditions for stability of the externality adjustment process are proved and interpreted. The equilibrium demand functions are then used in a tatonnement process to investigate the stability of competitive equilibrium. All the standard theorems on excess demand functions which give sufficient conditions for stability apply to the equilibrium demand functions of an economy with externalities. It is established that the stability properties of an economy without externalities possess a certain type of continuity. Any sequence of economies with externalities which converges in the proper sense to an economy without externalities characterized by gross substitutability has the property that for all t > T the competitive equilibrium of the economy with externalities is stable. Weaker stability conditions on the limit economy can make this theorem fail.

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