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Pareto-efficiency and endogenous fertility: a simple model

  • Philippe Michel

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales - Université Paul Cézanne - Aix-Marseille 3 - Université de la Méditerranée - Aix-Marseille 2 - CNRS - Centre National de la Recherche Scientifique)

  • Bertrand Wigniolle

    ()

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

This article is devoted to the study of the Pareto-efficiency of the competitive equilibrium for a simple overlapping generations economy with endogenous fertility. For CES utility and production functions, it is proved that the economic properties of the economy are closely related to the two elasticitiesof substitution. First, the competitive equilibrium exists and is unique if the sum of the two elasticities is not smaller than one. Secondly, a set of parameters is provided such that the equilibrium is both in under-accumulation and inefficient. Thirdly, a sufficient condition is proved that ensures that an equilibrium converging in under-accumulation is Pareto-efficient: the sum of the two elasticities must not be greater than two.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00306463.

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Date of creation: Jan 2009
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Publication status: Published in Mathematical Population Studies, Taylor & Francis (Routledge), 2009, 16 (1), pp.36-59. <10.1080/08898480802619587>
Handle: RePEc:hal:cesptp:halshs-00306463
DOI: 10.1080/08898480802619587
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00306463
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  1. MICHEL, Philippe & PESTIEAU, Pierre, . "Population growth and optimality. When does serendipity hold?," CORE Discussion Papers RP 1072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Mikel Perez-Nievas & Eduardo L. Gimenez & J. Ignacio Conde-Ruiz, 2007. "Millian efficiency with endogenous fertility," 2007 Meeting Papers 338, Society for Economic Dynamics.
  3. Mikhail Golosov & Larry E. Jones & Michele Tertilt, 2004. "Efficiency with Endogenous Population Growth," NBER Working Papers 10231, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
  7. Razin, Assaf & Ben-Zion, Uri, 1975. "An Intergenerational Model of Population Growth," American Economic Review, American Economic Association, vol. 65(5), pages 923-33, December.
  8. Jeremy Greenwood & Ananth Seshadri & Guillaume Vandenbroucke, 2005. "The Baby Boom and Baby Bust," American Economic Review, American Economic Association, vol. 95(1), pages 183-207, March.
  9. 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 S14-64, Part II, .
  10. Birdsall, Nancy, 1988. "Economic approaches to population growth," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 1, chapter 12, pages 477-542 Elsevier.
  11. 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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