Bosi Stefano, Camacho Carmen, Desmarchelier David
Université Paris-Saclay, Univ Evry, EPEE, 91025, Evry-Courcouronnes, France.
PJSE (UMR 8545), PSE, France.
J Math Econ. 2021 Mar;93:102488. doi: 10.1016/j.jmateco.2021.102488. Epub 2021 Feb 3.
The recent COVID-19 crisis has revealed the urgent need to study the impact of an infectious disease on market economies and provide adequate policy recommendations. The present paper studies the optimal lockdown policy in a dynamic general equilibrium model where households are altruistic and they care about the share of infected individuals. The spread of the disease is modeled here using SIS dynamics, which implies that recovery does not confer immunity. To avoid non-convexity issues, we assume that the lockdown is constant in time. This strong assumption allows us to provide analytical solutions. We find that the zero lockdown is efficient when agents do not care about the share of infected, while a positive lockdown is recommended beyond a critical level of altruism. Moreover, the lockdown intensity increases in the degree of altruism. Our robust analytical results are illustrated by numerical simulations, which show, in particular, that the optimal lockdown never trespasses 60% and that eradication is not always optimal.
近期的新冠疫情危机凸显了研究传染病对市场经济的影响并提供适当政策建议的迫切需求。本文在一个动态一般均衡模型中研究最优封锁政策，在该模型中家庭是利他的，且他们关心感染个体的比例。这里使用易感-感染-易感（SIS）动态模型来模拟疾病传播，这意味着康复后不会获得免疫力。为避免非凸性问题，我们假设封锁在时间上是恒定的。这个强假设使我们能够提供解析解。我们发现，当个体不关心感染比例时，零封锁是有效的，而当利他主义超过临界水平时，建议进行积极的封锁。此外，封锁强度会随着利他主义程度的增加而增加。我们稳健的解析结果通过数值模拟得到说明，数值模拟特别表明，最优封锁从不超过60%，而且根除并不总是最优的。
