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Life span and the problem of optimal population size

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  • Raouf Boucekkine

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • 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

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Paper provided by HAL in its series Working Papers with number halshs-00536073.

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Date of creation: 2010
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Handle: RePEc:hal:wpaper:halshs-00536073

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

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  1. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2002. "Vintage Human Capital, Demographic Trends, and Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 104(2), pages 340-375, June.
  2. Paul MAKDISSI, 2001. "Population, ressources naturelles et droits de propriété," Annales d'Economie et de Statistique, ENSAE, issue 61, pages 91-103.
  3. Bucci, Alberto, 2008. "Population growth in a model of economic growth with human capital accumulation and horizontal R&D," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1124-1147, September.
  4. Raouf BOUCEKKINE & Giorgio FABBRI & Fausto GOZZI, 2009. "Maintenance and investment : Complements or Substitutes ? A Reappraisal," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2009010, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  5. 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, vol. 120(1), pages 39-72, January.
  6. Galor, Oded & Moav, Omer, 2001. "Natural Selection and the Origin of Economic Growth," CEPR Discussion Papers 2727, C.E.P.R. Discussion Papers.
  7. Asheim, Geir B., 1991. "Unjust intergenerational allocations," Journal of Economic Theory, Elsevier, vol. 54(2), pages 350-371, August.
  8. 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.
  9. Strulik, Holger, 2002. "The Role of Human Capital and Population Growth in R&D-Based Models of Economic Growth," Royal Economic Society Annual Conference 2002 170, Royal Economic Society.
  10. Arnaud CHÉRON, 2001. "Risque de chômage, assurance complète et choix des ménages dans les modèles dynamiques," Annales d'Economie et de Statistique, ENSAE, issue 61, pages 105-118.
  11. 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.
  12. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  13. David, DE LA CROIX & Davide, DOTTORI, 2007. "Easter Island’s Collapse : A Tale of a Population Race," Discussion Papers (ECON - Département des Sciences Economiques) 2007005, Université catholique de Louvain, Département des Sciences Economiques.
  14. Galor, Oded & Weil, David, 1999. "From Malthusian Stagnation to Modern Growth," CEPR Discussion Papers 2082, C.E.P.R. Discussion Papers.
  15. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
  16. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
  17. Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, MIT Press, vol. 100(2), pages 321-34, May.
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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 lives," Working Papers halshs-00599084, HAL.

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