Optimal random monetary policy with nominal rigidity

This paper studies a money-in-the-utility function model with imperfect competition and one-period ahead nominal price setting. Under standard assumptions on preferences, Friedman's rule—setting the money growth rate equal to the household time discount factor—generates an equilibrium that is optimal within the class of deterministic policies. We then provide conditions under which a random monetary policy increases ex ante expected welfare relative to Friedman's rule. The result obtains because random policy can reduce the distortion associated with imperfect competition. Our result exhibits original features relative to existing cases of welfare-improving random monetary policy, such as Polemarchakis and Weiss (J. Econom. Theory 15 (1977) 345).