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Endogenous Fertility Waves and the Dynamics of Utility in an Overlapping Generations Model

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  • Wolfgang Kuhle

Abstract

This paper investigates the conditions under which the Easterlin hypothesis holds within a neoclassical overlapping generations model with endogenous capital accumulation, wages, interest rates, and fertility. We develop a tractable analytical framework that maps economic transitions into utility space via a continuously differentiable first-order difference equation for cohort lifetime utilities. This reformulation allows for a transparent normative evaluation of non-steady-state paths without requiring explicit solutions to the underlying nonlinear system. Within this framework, we show that when fertility cycles emerge and children are normal goods, the utility of small cohorts strictly exceeds that of large cohorts. Crucially, this cohort-welfare asymmetry is driven by fertility preferences and is independent of the economy's position relative to the golden rule.

Suggested Citation

  • Wolfgang Kuhle, 2026. "Endogenous Fertility Waves and the Dynamics of Utility in an Overlapping Generations Model," Papers 2606.02362, arXiv.org.
    • Handle: RePEc:arx:papers:2606.02362
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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. de la Croix, David & Ponthiere, Gregory, 2010. "On the Golden Rule of capital accumulation under endogenous longevity," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 227-238, March.
    3. Alexander Ludwig & Edgar Vogel, 2020. "Correction to: Mortality, fertility, education and capital accumulation in a simple OLG economy," Journal of Population Economics, Springer;European Society for Population Economics, vol. 33(1), pages 389-389, January.
    4. David Croix & Pierre Pestieau & Grégory Ponthière, 2012. "How powerful is demography? The Serendipity Theorem revisited," Journal of Population Economics, Springer;European Society for Population Economics, vol. 25(3), pages 899-922, July.
    5. Galor, Oded & Ryder, Harl E., 1989. "Existence, uniqueness, and stability of equilibrium in an overlapping-generations model with productive capital," Journal of Economic Theory, Elsevier, vol. 49(2), pages 360-375, December.
    6. Klaus Jaeger & Wolfgang Kuhle, 2009. "The optimum growth rate for population reconsidered," Journal of Population Economics, Springer;European Society for Population Economics, vol. 22(1), pages 23-41, January.
    7. de la Croix,David & Michel,Philippe, 2002. "A Theory of Economic Growth," Cambridge Books, Cambridge University Press, number 9780521806428, August.
    8. Alexander Ludwig & Thomas Schelkle & Edgar Vogel, 2012. "Demographic Change, Human Capital and Welfare," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(1), pages 94-107, January.
    9. Stefan Felder, 2016. "“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)," Journal of Population Economics, Springer;European Society for Population Economics, vol. 29(3), pages 957-967, July.
    10. Kuhle, Wolfgang, 2014. "The dynamics of utility in the neoclassical OLG model," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 81-86.
    11. Ludwig, Alexander, 2007. "The Gauss-Seidel-quasi-Newton method: A hybrid algorithm for solving dynamic economic models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1610-1632, May.
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