We characterize optimal monetary policy under state-dependent pricing. The framework gives rise to nonlinear inflation dynamics: The flexibility of the price level increases after large shocks due to an endogenous rise in the frequency of price changes. In response to large cost-push shocks, optimal policy leverages the lower sacrifice ratio to curb inflation. When faced with total factor productivity shocks, an efficient disturbance, the optimal policy commits to strict price stability. The optimal long-run inflation rate is just above zero.
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