This paper characterizes optimal redistribution for a social planner with three instruments: labor income taxes and transfers, corporate income taxes, and a minimum wage. The modeled economy features search-and-matching frictions, generates positive firm profits in equilibrium, and accommodates empirically relevant effects of the minimum wage such as wage spillovers and reallocation effects. I find that minimum wages are more likely to be desirable when corporate taxes are low because minimum wages generate corporate revenue losses and redistribute from capitalists to low-skill workers.Minimum wages can improve welfare even under optimal income taxes by shifting tax incidence when wages bunch at the minimum. I estimate the sufficient statistics that guide the welfare analysis using state-level variation in minimum wages. I find that minimum wages have increased low-skill workers' welfare with null effects on high-skill workers and negative effects on capitalists. Results suggest that, under current corporate tax rates, weak social preferences for redistribution toward low-skill workers would justify small state-level minimum wages increases.