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Life span and the problem of optimal population size

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  • Raouf BOUCEKKINE

    ()
    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES), Center for Operations Research and Econometrics (CORE) and GREQAM, Université Aix-Marseille II)

  • Giorgio FABBRI

    ()
    (Dipartimento di Studi Economici S. Vinci, Università di Napoli Parthenope, Naples)

  • Fausto GOZZI

    ()
    (Dipartimento di Scienze Economiche ed Aziendali, Università LUISS - Guido Carli, Rome)

Abstract

We reconsider the optimal population size problem in a continuous time economy populated by homogenous cohorts with a fixed life span. Linear production functions in the labor input and standard rearing costs are also considered. First, we study under which conditions the successive cohorts will be given the same consumption per capita. We show that this egalitarian rule is optimal whatever the degree of altruism when life spans are infinite. However, when life spans are finite, this rule can only be optimal in the Benthamite case, i.e. when the degree of altruism is maximal. Second, we prove that under finite life spans 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 utility functions, it gives rise to two threshold lifetime values, say T0

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Bibliographic Info

Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2011018.

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Length: 41
Date of creation: 04 Apr 2011
Date of revision:
Handle: RePEc:ctl:louvir:2011018

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Keywords: Optimal population size; Benthamite Vs Millian criterion; finite lives; optimal extinction;

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References

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  1. Oded Galor & Omer Moav, 2000. "Natural Selection and the Origin of economic Growth," Working Papers 2000-18, Brown University, Department of Economics.
  2. Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 2000. "Vintage capital and the dynamics of the AK model," CEPREMAP Working Papers (Couverture Orange) 0003, CEPREMAP.
  3. 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.
  4. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  5. DE LA CROIX, David & DOTTORI, Davide, 2007. "Easter Island’s collapse: A tale of a population race," CORE Discussion Papers 2007001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Holger Strulik, 2005. "The Role of Human Capital and Population Growth in R&D-based Models of Economic Growth," Review of International Economics, Wiley Blackwell, vol. 13(1), pages 129-145, 02.
  7. Paul MAKDISSI, 2001. "Population, ressources naturelles et droits de propriété," Annales d'Economie et de Statistique, ENSAE, issue 61, pages 91-103.
  8. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  9. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2009. "Maintenance and investment: complements or substitutes? A reappraisal," Working Papers 2009_21, Business School - Economics, University of Glasgow.
  10. Asheim, Geir B., 1991. "Unjust intergenerational allocations," Journal of Economic Theory, Elsevier, vol. 54(2), pages 350-371, August.
  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. Alberto Bucci, 2007. "Population Growth in a Model of Economic Growth with Human Capital Accumulation and Horizontal R&D," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1049, Universitá degli Studi di Milano.
  13. Galor, Oded & Weil, David, 1999. "From Malthusian Stagnation to Modern Growth," CEPR Discussion Papers 2082, C.E.P.R. Discussion Papers.
  14. 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.
  15. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
  16. 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.
  17. 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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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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