🤖 AI Summary
This study investigates the stability and uniqueness of general equilibrium in economies characterized by a large number of goods and highly patient consumers. By constructing a finite-horizon exchange economy through truncation of an infinite-horizon discounted additive utility model, the paper examines how the effective number of goods influences the relative growth rates of substitution and income effects. The analysis demonstrates that, under sufficiently patient consumers and preferences satisfying a proposed “preference diversification” condition, an increase in the number of goods amplifies aggregate substitution effects while attenuating income effects. This mechanism guarantees that all equilibria are locally tâtonnement stable, which in turn implies equilibrium uniqueness. The work thus provides a novel microeconomic foundation for well-behaved equilibria in high-dimensional commodity spaces.
📝 Abstract
We show that a large effective number of commodities can be a source of equilibrium stability and uniqueness: expanding substitution opportunities strengthens aggregate substitution effects. We study finite dated-commodity exchange economies obtained by truncating a countably infinite-horizon environment with discounted, additively separable utilities. In this setting, the effective number of commodities is the discounted count of dated commodities, so greater patience makes distant commodities more relevant. With an appropriate normalization, equilibrium substitution effects accumulate at the rate of the effective number of commodities. When a preference diversification condition holds, equilibrium income effects grow at a lower rate. The condition is satisfied, for example, when agents have sparse or localized taste differences across commodities, or when their taste profiles become sufficiently heterogeneous as the commodity space expands. Hence, whenever the effective number of commodities is sufficiently large, every equilibrium is locally tâtonnement stable, which in turn implies equilibrium uniqueness.