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

Author

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  • Raouf Boucekkine

    (IMéRA - Institute for Advanced Studies - Aix-Marseille University, GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Blanca Martínez

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

  • José Ramón Ruiz-Tamarit

    (Department of Economic Analysis, Universitat de Valencia - UV - Universitat de València, IRES Department of Economics, 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 & José Ramón Ruiz-Tamarit, 2017. "Optimal Population Growth as an Endogenous Discounting Problem: The Ramsey Case," Working Papers halshs-01579155, HAL.
    • Handle: RePEc:hal:wpaper:halshs-01579155
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01579155
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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).
    3. Kenneth Arrow & Partha Dasgupta & Lawrence Goulder & Gretchen Daily & Paul Ehrlich & Geoffrey Heal & Simon Levin & Karl-Göran Mäler & Stephen Schneider & David Starrett & Brian Walker, 2004. "Are We Consuming Too Much?," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 147-172, Summer.
    4. Marín-Solano, Jesús & Navas, Jorge, 2009. "Non-constant discounting in finite horizon: The free terminal time case," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 666-675, March.
    5. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
    6. Le Kama, Alain Ayong & Schubert, Katheline, 2007. "A Note On The Consequences Of An Endogenous Discounting Depending On The Environmental Quality," Macroeconomic Dynamics, Cambridge University Press, vol. 11(02), pages 272-289, April.
    7. Barro, Robert J & Becker, Gary S, 1989. "Fertility Choice in a Model of Economic Growth," Econometrica, Econometric Society, vol. 57(2), pages 481-501, March.
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    9. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2008. "Note on global dynamics and imbalance effects in the Lucas-Uzawa model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 503-518.
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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).
    3. repec:eee:ecmode:v:75:y:2018:i:c:p:246-255 is not listed on IDEAS

    More about this item

    Keywords

    population ethics; optimal growth; optimal population size; endogenous discounting; optimal demographic transitions;

    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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