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Human capital and welfare

Author

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  • Stefano Bosi

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay, Université Paris-Saclay, UEVE - Université d'Évry-Val-d'Essonne)

  • 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

We introduce the Human Development Index (HDI) in a growth model to show that if households cared about human capital, even if infinitesimally, then human capital would increase forever protecting economies indirectly. Here, human capital will have an additional positive effect on social welfare through the quality of individual health and education. In a simple economy with a Cobb–Douglas technology and logarithmic preferences, we provide the explicit trajectories for human capital, consumption, and the HDI, which correspond to the balanced growth path (BGP). Using a two-step maximization strategy, we compute the optimal initial value of the control variable, in this case, the initial optimal labour supply. In other words, we prove the optimality of the BGP. We highlight a HDI crossing property: the propensity to consume has a positive effect on the HDI in the short run, but negative in the long run.

Suggested Citation

  • Stefano Bosi & Carmen Camacho & David Desmarchelier, 2023. "Human capital and welfare," Post-Print halshs-03920429, HAL.
    • Handle: RePEc:hal:journl:halshs-03920429
    DOI: 10.1093/oep/gpac020
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03920429v3
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