The natural projection approach to the infinite-horizon model

Abstract

We extend the approach through the natural projection to the infinite-horizon general equilibrium model with smooth, discounted utility functions. We show that the natural projection is a smooth, proper Fredholm map of index zero. This enables us to define its Brouwer degree. We then show that this degree is equal to one, which yields an alternative proof of the existence of equilibria. A variant of Smale's infinite dimensional extension of Sard's theorem implies that the set of regular economies is open and dense.