Determinacy in Infinite Horizon Exchange Economies

Infinite horizon economies and other models which naturally require an infinite number of commodities, such as product differentiation models and financial markets models with an infinite number of states, have become increasingly important for studying a wide array of economic problems. Although the existence and optimality of equilibria in such models have been studied in depth, almost nothing is known about qualitative properties of equilibria such as determinacy in general infinite horizon or infinite-dimensional economies. Moreover, resolving issues such as determinacy is crucial before such models can be used as the basis for any robust comparative statics analysis or for drawing any meaningful policy conclusions, as if equilibria are indeterminate, slight measurement error or variations in initial conditions can result in drastically different equilibria, and hence drastically different conclusions about the effects of changes in parameters or policies. This paper provides a framework for establishing the determinacy of equilibria in general infinite horizon models, establishes a meaningful notion of regular economy for such models, and gives sufficient conditions for regular infinite horizon economies to have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, as well as for regular economies to be generic.