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Optimal population growth as an endogenous discounting problem: The Ramsey case

Author

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  • Raouf BOUCEKKINE

    (Aix-Marseille University, CNRS, EHESS, Centrale Marseille, AMSE and IMRA)

  • Blanca MARTINEZ

    (Department of Economics, Universidad Complutense de Madrid, Spain and Instituto Complutense de Analisis Economico (ICAE))

  • J.R. RUIZ-TAMARIT

    (Department of Economic Analysis, Universitat de Valencia, Spain, and IRES Department of Economics, Universite Catholique de Louvain)

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 MARTINEZ & J.R. RUIZ-TAMARIT, 2017. "Optimal population growth as an endogenous discounting problem: The Ramsey case," LIDAM Discussion Papers IRES 2017013, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    • Handle: RePEc:ctl:louvir:2017013
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    2. de la Croix, David & Doepke, Matthias, 2021. "A soul’s view of the optimal population problem," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 98-108.
    3. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2021. "SIR economic epidemiological models with disease induced mortality," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    4. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle, 2021. "Optimal prevention and elimination of infectious diseases," Journal of Mathematical Economics, Elsevier, vol. 93(C).
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    6. 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," LIDAM Discussion Papers IRES 2017020, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).

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    More about this item

    Keywords

    Optimal population size; Population ethics; Optimal growth; Endogenous discounting; Optimal demographic transitions;
    All these keywords.

    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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