Optimal Monetary Policy with State-Dependent Pricing

This paper studies optimal monetary policy from the timeless perspective in a general model of state-dependent pricing. Firms are modeled as monopolistic competitors subject to idiosyncratic menu cost shocks. We find that, under certain conditions, a policy of zero inflation is optimal both in the long run and in response to aggregate shocks. Key to this finding is an "envelope" property: at zero inflation, a marginal increase in the rate of inflation has no effect on firms' profits and hence on their probability of repricing. We offer an analytic solution that does not require local approximation or e¢ ciency of the steady state. Under more general conditions, we show numerically that the optimal commitment policy remains very close to strict inflation targeting.