To slow the spread of COVID-19, many countries are shutting down non-essential sectors of the economy. Older individuals have the most to gain from slowing virus diffusion. Younger workers in sectors that are shuttered have the 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 and retired), by sector (basic and luxury), and by health status. Disease transmission occurs in the workplace, in consumption activities, at home, and in hospitals. We study the optimal economic mitigation policy of a utilitarian government that can redistribute across individuals, but where such redistribution is costly. We show that optimal redistribution and mitigation policies interact, and reflect a compromise between the strongly diverging preferred policy paths of different subgroups of the population. We find that the shutdown in place on April 12 is too extensive, but that a partial shutdown should remain in place through the fall. People prefer deeper and longer shutdowns if a vaccine is imminent, especially the elderly.