Efficient Propagation of Shocks and the Optimal Return of Money

We show that price stickiness is predicted by the theory of second best, applied to a random- matching model of money. The economy is hit with iid, aggregate, preference shocks, and allocations are allowed to be history dependent. Due to individual anonymity and lack of commitment, implementable allocations must satisfy participation constraints. Price stickiness becomes necessary for optimality, in terms of average, ex-ante welfare, when aggregate uncen- tainty is present but not too severe, and the degree of patience is neither too low or too high. By applying mechanism design to an alternative economy with centralized markets, we also find important that macroeconomic policies, such as the taxation of money holdings, are unable to implement the first best for price stckiness to have a social role