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Equilibrium and Optimal Fertility with Increasing Returns to Population and Endogenous Fertility

Listed author(s):
  • Cuberes, David
  • Tamura, Robert

We present a general equilibrium dynamic model that characterizes the gap between optimal and equilibrium fertility and investment in human capital. In the model, the aggregate production function exhibits increasing returns to population arising from specialization but households face the standard quantity-quality trade-off when deciding how many children they have and how much education these children receive. In the benchmark model, we solve for the equilibrium and optimal levels of fertility and investment per child and show that competitive fertility is too low and investment per child too high. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment raises the likelihood that a child survives to the next generation. In this setup, the model endogenously generates a demographic transition but, since households do not internalize the positive effects of a larger population on productivity and the negative effects of human capital on mortality, both the industrial revolution and the demographic transition take place much later than it would have been optimal. Our model can be interpreted as a bridge between the literature on endogenous demographic transitions and papers that study welfare issues associated with fertility and human capital decisions.

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File URL: https://mpra.ub.uni-muenchen.de/80585/8/MPRA_paper_80585.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 57063.

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Date of creation: 02 Jul 2014
Handle: RePEc:pra:mprapa:57063
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  1. Oded Galor & Omer Moav, 2002. "Natural Selection and the Origin of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 117(4), pages 1133-1191.
  2. Gary Anthony Gigliotti, 1983. "Total Utility, Overlapping Generations and Optimal Population," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 71-86.
  3. Jones Charles I., 2001. "Was an Industrial Revolution Inevitable? Economic Growth Over the Very Long Run," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(2), pages 1-45, August.
  4. Becker, Gary S & Lewis, H Gregg, 1973. "On the Interaction between the Quantity and Quality of Children," Journal of Political Economy, University of Chicago Press, vol. 81(2), pages 279-288, Part II, .
  5. Kalemli-Ozcan, Sebnem, 2002. "Does the Mortality Decline Promote Economic Growth?," Journal of Economic Growth, Springer, vol. 7(4), pages 411-439, December.
  6. Sah, Raaj Kumar, 1991. "The Effects of Child Mortality Changes on Fertility Choice and Parental Welfare," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 582-606, June.
  7. Rodrigo R. Soares, 2005. "Mortality Reductions, Educational Attainment, and Fertility Choice," American Economic Review, American Economic Association, vol. 95(3), pages 580-601, June.
  8. David N. Weil, 2005. "Accounting for the Effect of Health on Economic Growth," NBER Working Papers 11455, National Bureau of Economic Research, Inc.
  9. Galor, Oded & Weil, David N, 1996. "The Gender Gap, Fertility, and Growth," American Economic Review, American Economic Association, vol. 86(3), pages 374-387, June.
  10. Barro, Robert J & Becker, Gary S, 1989. "Fertility Choice in a Model of Economic Growth," Econometrica, Econometric Society, vol. 57(2), pages 481-501, March.
  11. Matthias Doepke & Michèle Tertilt, 2009. "Women's Liberation: What's in It for Men?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1541-1591.
  12. David N. Weil & Oded Galor, 1999. "From Malthusian Stagnation to Modern Growth," American Economic Review, American Economic Association, vol. 89(2), pages 150-154, May.
  13. Tamura, Robert, 2006. "Human capital and economic development," Journal of Development Economics, Elsevier, vol. 79(1), pages 26-72, February.
  14. Samuelson, Paul A, 1975. "The Optimum Growth Rate for Population," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(3), pages 531-538, October.
  15. Tamura, Robert, 1996. "From decay to growth: A demographic transition to economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1237-1261.
  16. Michele Tertilt, 2005. "Polygyny, Fertility, and Savings," Journal of Political Economy, University of Chicago Press, vol. 113(6), pages 1341-1370, December.
  17. Tamura, Robert, 2002. "Human capital and the switch from agriculture to industry," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 207-242, December.
  18. Eckstein, Zvi & Wolpin, Kenneth I., 1985. "Endogenous fertility and optimal population size," Journal of Public Economics, Elsevier, vol. 27(1), pages 93-106, June.
  19. Matthias Doepke, 2005. "Child mortality and fertility decline: Does the Barro-Becker model fit the facts?," Journal of Population Economics, Springer;European Society for Population Economics, vol. 18(2), pages 337-366, 06.
  20. David N. Weil & Oded Galor, 2000. "Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and Beyond," American Economic Review, American Economic Association, vol. 90(4), pages 806-828, September.
  21. Nerlove, Marc & Razin, Assaf & Sadka, Efraim, 1982. "Population size and the social welfare functions of Bentham and Mill," Economics Letters, Elsevier, vol. 10(1-2), pages 61-64.
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