Friedman meets Hosios : efficiency in search models of money

This article studies optimal monetary policy in an economy with endogenous search decisions. We show that the same frictions that give fiat money a positive value generate an inefficient quantity of goods in each trade and an inefficient number of trades. The Friedman rule eliminates the first inefficiency and the Hosios rule the second. A monetary equilibrium attains the social optimum if and only if both rules are satisfied. When they cannot be satisfied simultaneously, optimal monetary policy achieves only the second best. We analyse the conditions under which the second-best monetary policy exceeds the Friedman rule.