Optimal Lockdown and Social Welfare

Abstract

This paper reexamines the design of the optimal lockdown strategy by paying attention to its robustness to the postulated social welfare criterion. We first characterize optimal lockdown under utilitarianism, and we show that this social criterion can, under some conditions, imply a COVID19 variant of Parfit’s (1984) Repugnant Conclusion: for any non-maximal lockdown saving lives at the cost of reducing average utility at a given period, there exists always a stricter lockdown, which further reduces average utility, but leads to a larger aggregate welfare. The optimal lockdown under utilitarianism is also shown to deteriorate the situation of the worst-off, against Hammond Equity. In order to do justice to Hammond Equity, we characterize optimal lockdown under the ex post egalitarian criterion, which gives absolute priority to the worst-o¤ ex post. Under general conditions, the ex post egalitarian optimum involves a zero lockdown. Varying between zero and its maximal level, the optimal lockdown policy is not robust to the postulated ethical criterion.

Keywords: Covid-19, lockdown, optimal policy, social welfare

JEL Classification: I180, I310, J180