On the structure of the equilibrium price set of overlapping-generations economies

This paper is concerned with generic properties of the set of price equilibria of overlapping-generations economies that include money. It is shown (in a C¹ topology) that if generations live for m periods and if there are n goods available in each period, then most economies will feature equilibrium price sets of dimension at most (m-1)n. It is likewise shown that for every k that ranges between 0 and (m-1)n there are open sets of economies which possess locally k-dimensional, C¹ manifolds of equilibria. In the process of establishing these facts, a transversality theorem is proved which applies to maps, not necessarily Fredholm, between open subsets of non-separable, infinite-dimensional spaces.