Optimal lockdown in altruistic economies

Stefano Bosi (), Carmen Camacho () and David Desmarchelier
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Stefano Bosi: EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay
Carmen Camacho: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: 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.

Keywords: Optimal lockdown; SIS model; Ramsey model; COVID-19 (search for similar items in EconPapers)
Date: 2021-03
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03231030v2
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Citations: View citations in EconPapers (32)

Published in Journal of Mathematical Economics, 2021, 93, pp.16. ⟨10.1016/j.jmateco.2021.102488⟩

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Journal Article: Optimal lockdown in altruistic economies (2021)
Working Paper: Optimal lockdown in altruistic economies (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03231030

DOI: 10.1016/j.jmateco.2021.102488

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