Digitized by the Internet Archive in 2011 with Funding from Boston Library Consortium Iviember Libraries Working Paper Department of Economics Comparative Statics and Perfect Foresight in Infinite Horizon Economies

This paper considers whether infinite horizon economies have determinate perfect foresight equilibria. ¥e consider stationary pure exchange economies with both finite and infinite numbers of agents. When there is a finite number of infinitely lived agents, we argue that equilibria are generically determinate. This is because the number of equations determining the equilibria is not infinite, but is equal to the number of agents minus one and must determine the marginal utility of income for all but one agent. In an overlapping generations model with infinitely many finitely lived agents, this reasoning breaks down. ¥e ask whether the initial conditions together with the requirement of convergence to a steady state locally determine an equilibrium price path. In this framework there are many economies with isolated equilibria, many with continue of equilibria, and many with no equilibria at all. With two or more goods in every period not only can the price level be indeterminate but relative prices as well. Furthermore, such indeterminacy can occur whether or not there is fiat money in the economy. Equilibria may be pareto efficient or inefficient regardless of whether they are determinate or not. Comparative Statics and Perfect Foresight in Infinite Horizon Economies by Timothy J. Kehoe and David K. Levine* 1 . INTRODUCTION Finite economies have the same number of equations as unknowns. Imposing assumptions of differentiability on such economies allows us to do regularity analysis. Almost all economies have equations that are locally independent at equilibria. This is important because it enables us to do comparative statics: First, equilibria are locally determinate. Second, small perturbations in the underlying parameters of the economy displace an equilibrium only slightly, and the displacement can be approximately computed by inverting a matrix of partial derivatives. This paper considers whether infinite horizon economies have determinate perfect foresight equilibria. This question is of crucial importance. If instead equilibria are locally indeterminate, not only are we unable to make comparative static predictions, but the agents in the model are unable to determine the consequences of unanticipated shocks. The idea underlying perfect foresight is that agents' expectations should be the actual future sequence predicted by the model; if the model does not make determinate predictions, the concept of perfect foresight is meaningless . * We are grateful to David Backus, Drew Fudenberg, J.S. Jordan, Andreu Kas-Colell, Herbert Scarf, and participants in seminars at M.I.T., U.C. Berkeley, U.C San Diego, U.C.L.A., McMaster University, the Federal Reserve Bank of Minneapolis, the NBER General Equilibrium Conference, Northwestern University, March 1982, and the Latin American Econometric Society Meetings, Mexico City, July 1982, for helpful comments and suggestions.