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 2nm.
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*We are grateful to David Backus, Drew Fudenberg, J.S. Jordan, Andreu Mas-Colell, an anonymous referee and seminar participants at U.C. Berkeley, M.I.T., U.C.L.A., the University of Pennsylvania, U.C. San Diego, Yale, the Federal Reserve Bank of Minneapolis, and the NBER General Equilibrium Conference at Northwestern University, March 1982, for helpful comments and suggestions. The work of the first author was supported by the National Science Foundation under Grant no. SES-8209778.