Memory and the Limits of Money

I study a simplified version of Trejos and Wright’s (1995) random matching environment. If histories are observable, then full efficiency is achievable in equilibrium in the limit as agents become patient. In contrast, if histories are not observed, then payoffs in any monetary equilibrium (one in which agents exchange a good for an indivisible unit of fiat money) with a fixed stock of money are bounded away from efficiency. The gap disappears as the stock of money grows, but for any fixed level of patience, efficiency falls to zero if the stock of money is too high. The key insight is that the fraction of agents with zero money holdings in steady state converges to a positive level as patience increases.