On the Optimum Distribution of Money∗

Although the quantity of money is a concept deeply rooted in the history of economic thought, the truth is that money balances tend to disperse in models with idiosyncratic shocks, except when strong assumptions are imposed. This is so because monetary allocations are poor substitutes for perfect insurance. In this paper, we design the optimum money distribution when trade takes place according to sim-ple pairwise meetings. The bad news is that the dimensionality of the problem is intimidating. The good news is that it is a common-sense generalization of the Ramsey problem in mainstream macroeconomics. The results are two: temporary incentive constraints suffice for defin-ing the recursive problem without prior computation of the set of admissible states, and the optimum is attained when money holdings and aggregate shocks are discrete.