The typical approach in the epidemiology literature is to study the dynamics of the pandemic–for infected, deaths, and recovered–as functions of some exogenously chosen diffusion parameters, which are in turn related to various policies, such as the partial lockdown of schools, businesses, and other measures of diffusion mitigation. We use a simplified version of these models to analyze how to optimally balance the fatality induced by the epidemic with the output costs of the lockdown policy. The planner’s objective is to minimize the present discounted value of fatalities while also trying to minimize the output costs of the lockdown policy.
In our baseline parameterization, conditional on a 1% fraction of infected agents at the outbreak, the possibility of testing and no cure for the disease, the optimal policy prescribes a lockdown starting two weeks after the outbreak, covering 60% of the population after one month. The lockdown is kept tight for about a full month, and is subsequently gradually withdrawn, covering 20% of the population three months after the initial outbreak. The output cost of the lockdown is high, equivalent to losing 8% of one year’s GDP (or, equivalently, a permanent reduction of 0.4% of output). The total welfare cost is almost three times bigger due to the cost of deaths. The intensity of the lockdown depends on the gradient of the fatality rate as a function of the infected, the value of a statistical life, and the availability of testing. We find that an antibody test, which allows to avoid lockdown of those immune, improves welfare by about 2% of one year’s GDP.