Determinacy of Competitive Equilibria in Economies with Many Commodities

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. The paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. For the case of sequence economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, the paper develops sufficient conditions on preferences and technologies for these generic determinacy conclusions to hold. These arguments build on the intuition that these economies can be thought of as the limit of economies with a large finite number of commodities, and conclude that the sharp predictions of generic determinacy in economies with finitely many commodities carry over to economies with countably many commodities under one additional assumption, which prohibits goods from becoming perfect substitutes asymptotically.