Does a pure exchange economy with an infinite time horizon have determinate perfect foresight equilibria? When there is a finite number of infinitely lived agents equilibria are generically determinate. This is not true with overlapping generations of finitely lived agents. We 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 continua 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 and whether or not the equilibria are Pareto efficient.