We study optimal monetary policy in a heterogeneous agent new Keynesian economy. A utilitarian planner seeks to reduce consumption inequality, in addition to stabilizing output gaps and inflation. The planner does so both by reducing income risk faced by households, and by reducing the pass-through from income to consumption risk, trading off the benefits of lower inequality against productive inefficiency and higher inflation. When income risk is countercyclical, policy curtails the fall in output in recessions to mitigate the increase in inequality. We uncover a new form of time inconsistency of the Ramsey plan—the temptation to exploit households' unhedged interest rate exposure to lower inequality.