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.
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.
Auteur(s)
Stefano Bosi1
, Carmen Camacho2, 3
, David Desmarchelier4
1
EPEE -
Centre d'Etudes des Politiques Economiques
( 1042269 )
- 4, boulevard François Mitterrand, 91025 EVRY CEDEX
- France
Université d'Évry-Val-d'Essonne EA 2177 ( 300306 )
;
Université Paris-Saclay ( 419361 )
2
PSE -
Paris School of Economics
( 301309 )
- 48 boulevard Jourdan 75014 Paris
- France
Université Paris 1 Panthéon-Sorbonne ( 7550 )
;
École normale supérieure - Paris ( 59704 )
;
Université Paris Sciences et Lettres ( 564132 )
;
École des hautes études en sciences sociales ( 99539 )
;
École des Ponts ParisTech ( 301545 )
;
Centre National de la Recherche Scientifique ( 441569 )
;
Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement ( 577435 )
3
PJSE -
Paris Jourdan Sciences Economiques
( 578027 )
- 48 boulevard Jourdan 75014 Paris
- France
Université Paris 1 Panthéon-Sorbonne UMR8545 ( 7550 )
;
École normale supérieure - Paris ( 59704 )
;
Université Paris Sciences et Lettres ( 564132 )
;
École des hautes études en sciences sociales ( 99539 )
;
École des Ponts ParisTech ( 301545 )
;
Centre National de la Recherche Scientifique ( 441569 )
;
Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement UMR1393 ( 577435 )
4
BETA -
Bureau d'Économie Théorique et Appliquée
( 1001961 )
- Université de Lorraine, UFR Droit Sciences Economiques et Gestion, 13 place Carnot CO 70026, 54035 Nancy Cedex
Université de Strasbourg, Faculté des Sciences Economiques et de Gestion, 61 avenue de la Forêt Noire 67085 Strasbourg Cedex
- France