How long should the COVID-19 lockdown continue?

Nations struggled to decide when and how to end COVID-19 inspired lockdowns, with sharply divergent views between those arguing for a resumption of economic activity and those arguing for continuing the lockdown in some form. We examine the choice between continuing or ending a full lockdown within a simple optimal control model that encompasses both health and economic outcomes, and pays particular attention to when need for care exceeds hospital capacity. The model shows that very different strategies can perform similarly well and even both be optimal for the same relative valuation on work and life because of the presence of a so-called Skiba threshold. Qualitatively the alternate strategies correspond to trying essentially to eradicate the virus or merely to flatten the curve so fewer people urgently need healthcare when hospitals are already filled to capacity.