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Life span and the problem of optimal population size

Author

Listed:
  • Raouf Boucekkine

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

  • Giorgio Fabbri

    (Dipartimento Matematica e statistica - Université de Naples)

  • Fausto Gozzi

    (Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

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://shs.hal.science/halshs-00536073v1
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    Cited by:

    1. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2011. "Revisiting the Optimal Population Size Problem under Endogenous Growth: Minimal Utility Level and Finite Life," Asia-Pacific Journal of Accounting & Economics, Taylor & Francis Journals, vol. 18(3), pages 287-305.

    More about this item

    Keywords

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    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
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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