Optimal monetary policy with state-dependent pricing

We study optimal monetary policy from the timeless perspective in a general state-dependent pricing framework. Firms are monopolistic competitors and are subject to idiosyncratic menu cost shocks. We find that, under isoelastic preferences and no government spending, strict price stability 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 therefore has no effect on the rate of price adjustment. We offer an analytic solution which does not rely on local approximation or efficiency of the steady-state.