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Life span and the problem of optimal population size

Author

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  • Raouf Boucekkine

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

  • Giorgio Fabbri

    () (Dipartimento Matematica e statistica - Université de Naples)

  • Fausto Gozzi

    () (Dipartimento di Scienze Economiche e Aziendali - Libera Università INTERNAZIONALE DEGLI STUDI SOCIALI G. CARLI)

Abstract

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. This assumption is combined with a linear production function in the labor input and standard rearing costs. A general social welfare function is specified, admitting the Millian and Benthamite cases as polar parameterizations. It is shown that if the lifetime is low enough, population is asymptotically driven to extinction whatever the utility function and the level of inter-generational altruism. Moreover, population is driven to extinction at finite time whatever the values of lifetime and altruism provided the utility function is negative. When the utility function is positive, it is shown that the Millian welfare function leads to optimal extinction at finite time whatever the lifetime. In contrast, the Benthamite case is much more involved: for isoelastic positive utility functions, it gives rise to two threshold lifetime values, say T_0

Suggested Citation

  • Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00536073 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00536073
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    References listed on IDEAS

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    1. Oded Galor & Omer Moav, 2002. "Natural Selection and the Origin of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, pages 1133-1191.
    2. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    3. David Croix & Davide Dottori, 2008. "Easter Island’s collapse: a tale of a population race," Journal of Economic Growth, Springer, vol. 13(1), pages 27-55, March.
    4. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, pages 333-348.
    5. Raouf Boucekkine & Giorgio Fabbri, 2010. "Assessing the Parfit's Repugnant Conclusion within a canonical endogenous growth set-up," Working Papers 2010_20, Business School - Economics, University of Glasgow.
    6. Asheim, Geir B., 1991. "Unjust intergenerational allocations," Journal of Economic Theory, Elsevier, vol. 54(2), pages 350-371, August.
    7. repec:adr:anecst:y:2001:i:61:p:07 is not listed on IDEAS
    8. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, pages 39-72.
    9. David N. Weil & Oded Galor, 1999. "From Malthusian Stagnation to Modern Growth," American Economic Review, American Economic Association, pages 150-154.
    10. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, pages 340-375.
    11. Arrow, Kenneth J. & Bensoussan, Alain & Feng, Qi & Sethi, Suresh P., 2008. "The Genuine Saving Criterion and the Value of Population in an Economy with Endogenous Population Changes," MPRA Paper 14622, University Library of Munich, Germany.
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    14. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, pages 331-373.
    15. Bucci, Alberto, 2008. "Population growth in a model of economic growth with human capital accumulation and horizontal R&D," Journal of Macroeconomics, Elsevier, pages 1124-1147.
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    Cited by:

    1. Raouf Boucekkine & David de la Croix & Omar Licandro, 2011. "Vintage capital growth theory: Three breakthroughs," UFAE and IAE Working Papers 875.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    2. repec:taf:raaexx:v:18:y:2011:i:3:p:287-305 is not listed on IDEAS

    More about this item

    Keywords

    Optimal population size; Benthamite Vs Millian criterion; finite lives; optimal extinction; optimal control of infinite dimensioned problems;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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