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

In: Control Systems and Mathematical Methods in Economics

Author

Listed:
  • Raouf Boucekkine

    (CNRS, EHESS, Centrale Marseille, AMSE and IMRA
    Senior member, IUF)

  • Blanca Martínez

    (Universidad Complutense de Madrid
    Instituto Complutense de Análisis Económico (ICAE))

  • J. Ramon Ruiz-Tamarit

    (Universitat de València
    Université 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 Martínez & J. Ramon Ruiz-Tamarit, 2018. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Lecture Notes in Economics and Mathematical Systems, in: Gustav Feichtinger & Raimund M. Kovacevic & Gernot Tragler (ed.), Control Systems and Mathematical Methods in Economics, pages 321-347, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-75169-6_16
    DOI: 10.1007/978-3-319-75169-6_16
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    References listed on IDEAS

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    3. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle, 2021. "Optimal prevention and elimination of infectious diseases," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    4. Ziesemer, Thomas, 2018. "The serendipity theorem for an endogenous open economy growth model," MERIT Working Papers 2018-001, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
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    6. Escribá-Pérez, F.J. & Murgui-García, M.J. & Ruiz-Tamarit, J.R., 2018. "Economic and statistical measurement of physical capital: From theory to practice," Economic Modelling, Elsevier, vol. 75(C), pages 246-255.

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    • 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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