A Simple Planning Problem for COVID-19 Lock-down, Testing, and Tracing

We study the optimal lock-down for a planner who controls the fatalities of COVID-19 while minimizing the output costs of the lockdown. The policy prescribes a severe lock-down beginning a few weeks after the outbreak, covering almost 50 percent of the population after a month, with a total duration shy of 4 months. The intensity of the optimal lock-down depends on the gradient of the fatality rate with respect to the infected and the availability of antibody testing, which yields a welfare gain of 2 percent of GDP. We also study test-tracing-quarantine, which we show to be complementary to lock-down.