To to get the COVID-19 virus under control, many countries have shut down parts 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. 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 by 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 through taxes and transfers, but where taxation distorts labor supply and output. Optimal redistribution and mitigation policies interact, and more modest shutdowns are optimal when redistribution creates tax distortions. A harder but shorter shutdown is preferred as vaccines become available in the first half of 2021.