Optimal Monetary Policy with Redistribution

We study optimal monetary policy in a general equilibrium economy with heterogeneous agents and nominal rigidities. Households differ in type-specific, state-contingent labor productivity and initial firm ownership, yet markets are complete. The fiscal authority has access to a linear tax schedule with non-state-contingent tax rates and uniform, lump-sum taxes (or transfers). We derive sufficient conditions under which implementing flexible-price allocations is optimal. We then show that when there are fluctuations in relative labor productivity across households, it is optimal for monetary policy to abandon the flexible-price benchmark and target a state-contingent markup. The optimal markup covaries positively with a sufficient statistic for labor income inequality. In a calibrated version of the model, countercyclical earnings inequality implies countercyclical optimal markups.