Equilibrium analysis of the infinite horizon model with smooth discounted utility functions

Abstract

Abstract The equilibrium set and the natural projection are studied within the setup of the pure exchange infinite-horizon model with a finite number of infinitely lived agents, utility functions belonging to the smooth discounted variety, and individual endowments being variable. We show that the equilibrium set has convex fibers, which implies arc-connectedness and, more generally, contractibility. We also show that the sets of regular equilibria and of regular economies are open and dense for the product topology. Therefore, it is generically true that the equilibria of infinite-horizon economies with smooth discounted utility functions can be approximated by those of finite-horizon truncated economies.