To slow COVID-19, many countries have shut down part of the economy. Older individuals have the most to gain from slowing virus diffusion. Younger workers in sectors that are shuttered have most to lose. In this paper, we build a model in which economic activity and disease progression are jointly determined. Individuals differ by age (young, retired), by sector (basic, luxury), and health status. Disease transmission occurs in the workplace, through consumption, at home, and in hospitals. We study the optimal economic mitigation policy for a government that can redistribute across individuals, but where redistribution is costly. Optimal redistribution and mitigation policies interact, and more modest shutdowns are optimal when redistribution is more costly. We find that the shutdowns that were implemented in mid-April were too extensive, but a partial shutdown should remain in place through the fall. A deeper and longer shutdown is preferred if a vaccine is imminent.