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Pareto-Efficiency and Endogenous Fertility: A Simple Model

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  • PHILIPPE MICHEL
  • BERTRAND WIGNIOLLE

Abstract

Pareto-efficiency of the competitive equilibrium is studied for a simple economy with overlapping generations and endogenous fertility. For CES utility and production functions, the properties of the economy are closely related to the two elasticities of substitution. The competitive equilibrium exists and is unique if the sum of the two elasticities is not less than one. For certain parameters, the equilibrium is both in under-accumulation and inefficient. When the sum of the two elasticities is greater than two, an equilibrium converging in under-accumulation is Pareto-efficient.

Suggested Citation

  • Philippe Michel & Bertrand Wigniolle, 2009. "Pareto-Efficiency and Endogenous Fertility: A Simple Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(1), pages 36-59.
  • Handle: RePEc:taf:mpopst:v:16:y:2009:i:1:p:36-59
    DOI: 10.1080/08898480802619587
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    References listed on IDEAS

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    1. Michel, Philippe & Pestieau, P, 1993. "Population Growth and Optimality: When Does Serendipity Hold?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 6(4), pages 353-362, November.
    2. Mikhail Golosov & Larry E. Jones & Michèle Tertilt, 2007. "Efficiency with Endogenous Population Growth," Econometrica, Econometric Society, vol. 75(4), pages 1039-1071, July.
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    5. Willis, Robert J, 1973. "A New Approach to the Economic Theory of Fertility Behavior," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 14-64, Part II, .
    6. Philippe Michel & Bertrand Wigniolle, 2007. "On Efficient Child Making," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 307-326, May.
    7. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
    8. J. Ignacio Conde-Ruiz & Eduardo L. Giménez & Mikel Pérez-Nievas, 2010. "Millian Efficiency with Endogenous Fertility," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 154-187.
    9. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
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    12. Gary S. Becker, 1960. "An Economic Analysis of Fertility," NBER Chapters,in: Demographic and Economic Change in Developed Countries, pages 209-240 National Bureau of Economic Research, Inc.
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    Cited by:

    1. Thomas Baudin, 2012. "The Optimal Trade-Off Between Quality and Quantity with Unknown Number of Survivors," Mathematical Population Studies, Taylor & Francis Journals, vol. 19(2), pages 94-113, April.
    2. Schoonbroodt, Alice & Tertilt, Michèle, 2014. "Property rights and efficiency in OLG models with endogenous fertility," Journal of Economic Theory, Elsevier, vol. 150(C), pages 551-582.

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    Keywords

    endogenous fertility; Pareto-efficiency;

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