This paper quantitatively analyzes how policy responses to the COVID-19 pandemic should differ in developing countries. To do so we build an incomplete-markets macroeconomic model with heterogeneous agents and epidemiological dynamics that features several of the key distinctions between advanced and developing economies germane to the pandemic. We focus in particular on differences in: age structure, fiscal capacity, healthcare capacity, informality, and the frequency of contacts between individuals at home, work, school and other locations. The model predicts that blanket lockdowns are less effective in developing countries, saving fewer lives per unit of lost GDP. In contrast, age-specific policies are even more effective, since they focus scarce public funds on shielding the smaller population of older individuals. School closures are also more effective at saving lives in developing countries, providing a greater reduction in secondary transmissions between children and older adults at home.