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Optimal lockdown in altruistic economies

Author

Listed:
  • 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 des Ponts ParisTech - 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 des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • David Desmarchelier

    (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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.

Suggested Citation

  • Stefano Bosi & Carmen Camacho & David Desmarchelier, 2021. "Optimal lockdown in altruistic economies," PSE-Ecole d'économie de Paris (Postprint) halshs-03231030, HAL.
    • Handle: RePEc:hal:pseptp:halshs-03231030
    DOI: 10.1016/j.jmateco.2021.102488
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03231030v2
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    Cited by:

    1. Pierre Pestieau & Gregory Ponthiere, 2022. "Optimal lockdown and social welfare," Journal of Population Economics, Springer;European Society for Population Economics, vol. 35(1), pages 241-268, January.
    2. Luciana BARTOLINI & Francesco MAGRIS, 2022. "Growth, Lockdown and the Dynamics of the Covid-19 Pandemic," LEO Working Papers / DR LEO 2935, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    3. Caulkins, J.P. & Grass, D. & Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Kuhn, M. & Prskawetz, A. & Sanchez-Romero, M. & Seidl, A. & Wrzaczek, S., 2023. "The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?," European Journal of Operational Research, Elsevier, vol. 311(1), pages 233-250.
    4. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2023. "Optimal interventions in networks during a pandemic," Journal of Population Economics, Springer;European Society for Population Economics, vol. 36(2), pages 847-883, April.
    5. Carmen Camacho & Chrysovalantis Vasilakis, 2023. "Antivax and inequality," Working Papers hal-03693126, HAL.
    6. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    7. Bambi, Mauro & Ghilli, Daria & Gozzi, Fausto & Leocata, Marta, 2024. "Habits and demand changes after COVID-19," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    8. Carmen Camacho & Rodolphe Desbordes & Davide Torre, 2022. "A Time-Space Integro-Differential Economic Model of Epidemic Control," Working Papers hal-03693086, HAL.
    9. Camacho, Carmen & Vasilakis, Chrysovalantis, 2023. "Transmissible Diseases, Vaccination and Inequality," IZA Discussion Papers 16504, Institute of Labor Economics (IZA).
    10. Thomas Hellmann & Veikko Thiele, 2022. "A theory of voluntary testing and self‐isolation in an ongoing pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 873-911, October.
    11. David Desmarchelier & Thomas Lanzi, 2023. "Opinion Dynamics and Political Persuasion," Post-Print hal-04711036, HAL.
    12. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    13. David Desmarchelier & Thomas Lanzi, 2022. "Opinion Dynamics and Political Persuasion," Working Papers of BETA 2022-33, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    14. Pongou, Roland & Tchuente, Guy & Tondji, Jean-Baptiste, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," GLO Discussion Paper Series 957, Global Labor Organization (GLO).
    15. Jacek Rothert, 2021. "Optimal federal transfers during uncoordinated response to a pandemic," GRAPE Working Papers 58, GRAPE Group for Research in Applied Economics.
    16. Hubert Kempf & stéphane Rossignol, 2023. "Lockdown policies and the dynamics of a pandemic: foresight, rebounds and optimality," Documents de recherche 23-06, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    17. David Desmarchelier & Magali Jaoul-Grammare & Guillaume Morel & Thi Kim Cuong Pham, 2021. "Infectious disease and endogenous cycles: lockdown hits two birds with one stone," Working Papers of BETA 2021-23, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    18. Stefano Bosi & Carmen Camacho & David Desmarchelier, 2023. "On human capital accumulation in times of epidemic," PSE Working Papers halshs-04164371, HAL.
    19. Jacek Rothert, 2022. "Optimal federal transfers during uncoordinated response to a pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1124-1153, October.
    20. Chohan, Usman W., 2022. "Analyzing sound COVID-19 policy responses in developing countries: the case study of Pakistan," Studia z Polityki Publicznej / Public Policy Studies, Warsaw School of Economics, vol. 9(2), pages 1-22, August.
    21. Keiichi Morimoto & Shiba Suzuki, 2022. "Ambiguity in a pandemic recession, asset prices, and lockdown policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1039-1070, October.
    22. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.
    23. Wilson, Matthew S., 2023. "Social contact in a pandemic: Rationality vs. heuristics," Research in Economics, Elsevier, vol. 77(1), pages 159-177.
    24. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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