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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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    References listed on IDEAS

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    1. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    2. Raouf BOUCEKKINE & Blanca MARTINEZ & José Ramon RUIZ-TAMARIT, 2013. "Optimal sustainable policies under pollution ceiling: the demographic side," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2013028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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    Cited by:

    1. Ziesemer, Thomas, 2018. "The serendipity theorem for an endogenous open economy growth model," MERIT Working Papers 001, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    2. F. J. Escribá-Pérez & M. J. Murgui-García & J. R. Ruiz-Tamarit, 2017. "Economic and Statistical Measurement of Physical Capital with an Application to the Spanish Economy," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017020, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • J1 - Labor and Demographic Economics - - Demographic Economics
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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