Regularity in overlapping generations exchange economies

Abstract

In this paper we develop a regularity theory for stationary overlapping generations economies. We show that generically there is an odd number of steady states in which a non-zero amount of nominal debt (fiat money) is passed from generation to generation and an odd number in which there is no nominal debt. We are also interested in non-steady state perfect foresight paths. As a first step in this direction we analyze the behavior of paths near a steady state. We show that generically they are given by a second order difference equation that satisfies strong regularity properties. Economic theory alone imposes little restriction on those paths: With n goods and consumers who live for m periods, for example, the only restriction on the set of paths converging to the steady state is that they form a manifold of dimension no less than one, no more than 2 nm.