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Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case

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  • Raouf Boucekkine

    () (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Blanca Martínez

    ()

  • José Ramón Ruiz-Tamarit

Abstract

This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.

Suggested Citation

  • Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Post-Print hal-01825912, HAL.
  • Handle: RePEc:hal:journl:hal-01825912
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01825912
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