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Revisiting the Optimal Population Size Problem under Endogenous Growth: Minimal Utility Level and Finite Life

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  • Raouf Boucekkine
  • Giorgio Fabbri
  • Fausto Gozzi

Abstract

In this paper, we devise a social criterion in the spirit of the critical utility level of Blackorby-Donaldson (1984) to study an optimal population size problem in an endogenously growing economy populated by workers living a fixed amount of time and without capital accumulation. Population growth is endogenous. The problem is analytically solved, yielding closed-form solutions to optimal demographic and economic dynamics. It is shown that provided the economy is not driven to optimal finite time extinction, the optimal solution is egalitarian for appropriate choices of the critical utility levels: all individuals of any cohort are given the same consumption. The results obtained do not require any priori restriction of the values of the elasticity of intertemporal substitution unlike in several related papers.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:raaexx:v:18:y:2011:i:3:p:287-305
    DOI: 10.1080/16081625.2011.9720885
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    1. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    2. 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.
    3. Palivos, Theodore & Yip, Chong K., 1993. "Optimal population size and endogenous growth," Economics Letters, Elsevier, vol. 41(1), pages 107-110.
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    7. 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.
    8. Ng, Yew-Kwang, 1986. "Social criteria for evaluating population change: An alternative to the Blackorby-Donaldson criterion," Journal of Public Economics, Elsevier, vol. 29(3), pages 375-381, April.
    9. Marc Nerlove & Assaf Razin & Efraim Sadka, 1985. "Population Size: Individual Choice and Social Optima," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(2), pages 321-334.
    10. Palivos, Theodore, 2001. "Social norms, fertility and economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1919-1934, December.
    11. 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.
    12. Raouf Boucekkine & Giorgio Fabbri & Fausto Gozzi, 2010. "Life span and the problem of optimal population size," Working Papers halshs-00536073, HAL.
    13. Blackorby, Charles & Donaldson, David, 1984. "Social criteria for evaluating population change," Journal of Public Economics, Elsevier, vol. 25(1-2), pages 13-33, November.
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    Cited by:

    1. Kohei Kamaga, 2016. "Infinite-horizon social evaluation with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 207-232, June.

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