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The Solow growth model with a CES production function and declining population

Author

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  • Hiroaki Sasaki

    (Graduate School of Economics, Kyoto University)

Abstract

This study investigates the relationship between per capita output growth and population growth using the Solow growth model when population growth is negative. When the Cobb-Douglas production function is used, the per capita output growth rate can be positive even if the technological progress rate is zero. In contrast, when the CES production function is used, the per capita output growth rate is zero if the technological progress rate is zero and the elasticity of substitution between capital and labor is less than unity.

Suggested Citation

  • Hiroaki Sasaki, 2019. "The Solow growth model with a CES production function and declining population," Economics Bulletin, AccessEcon, vol. 39(3), pages 1979-1988.
    • Handle: RePEc:ebl:ecbull:eb-19-00417
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    References listed on IDEAS

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    1. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    2. Robert J. Barro & Xavier Sala-i-Martin, 2003. "Economic Growth, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262025531, December.
    3. Sasaki, Hiroaki & Hoshida, Keisuke, 2017. "The Effects Of Negative Population Growth: An Analysis Using A Semiendogenous R&D Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 21(7), pages 1545-1560, October.
    4. Rowthorn, Robert, 1999. "Unemployment, Wage Bargaining and Capital-Labour Substitution," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 23(4), pages 413-425, July.
    5. Charles I. Jones, 1999. "Growth: With or Without Scale Effects?," American Economic Review, American Economic Association, vol. 89(2), pages 139-144, May.
    6. Thomas Christiaans, 2011. "Semi-endogenous growth when population is decreasing," Economics Bulletin, AccessEcon, vol. 31(3), pages 2667-2673.
    7. Rainer Klump & Peter McAdam & Alpo Willman, 2007. "Factor Substitution and Factor-Augmenting Technical Progress in the United States: A Normalized Supply-Side System Approach," The Review of Economics and Statistics, MIT Press, vol. 89(1), pages 183-192, February.
    8. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    9. World Bank, 2013. "World Development Indicators 2013," World Bank Publications - Books, The World Bank Group, number 13191, October.
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    Citations

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    Cited by:

    1. Yasutaka Niisato, 2025. "Harrod–Okishio investment function, business cycle, and decreasing population," Evolutionary and Institutional Economics Review, Springer, vol. 22(1), pages 155-175, April.
    2. Połeć, Anna & Matsumoto, Akio, 2026. "The delay Solow model with the Lambert W function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 155-174.
    3. Hiroaki Sasaki & Noriki Fukatani & Daisuke Imai & Yusuke Kamanaka, 2025. "Sustainable Economic Growth in an Economy With Exhaustible Resources and a Declining Population Under the Balance‐of‐Payments Constraint," Bulletin of Economic Research, Wiley Blackwell, vol. 77(3), pages 328-345, July.
    4. Sasaki, Hiroaki & Mino, Kazuo, 2024. "Effects of exhaustible resources and declining population on economic growth with Hotelling’s rule," International Review of Economics & Finance, Elsevier, vol. 94(C).
    5. Yang, Jun & Yang, Dingjian, 2025. "Data factors and high-quality population development: A theoretical study incorporating data as a production factor," Economic Analysis and Policy, Elsevier, vol. 88(C), pages 1185-1236.
    6. Bucci, Alberto, 2023. "Can a negative population growth rate sustain a positive economic growth rate in the long run?," Mathematical Social Sciences, Elsevier, vol. 122(C), pages 17-28.
    7. Fernández-Villaverde, Jesús & Ventura, Gustavo & Yao, Wen, 2025. "The wealth of working nations," European Economic Review, Elsevier, vol. 173(C).
    8. Hellwagner, Timon & Weber, Enzo, 2021. "Labour Market Adjustments to Population Decline," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242455, Verein für Socialpolitik / German Economic Association.
    9. Sasaki, Hiroaki, 2023. "Growth with automation capital and declining population," Economics Letters, Elsevier, vol. 222(C).
    10. Ichiroh DAITOH & Hiroaki SASAKI, 2023. "At the Right Time:Ramsey-Cass-Koopmans Model with Declining Population," Discussion papers e-23-002, Graduate School of Economics , Kyoto University.

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    More about this item

    Keywords

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    JEL classification:

    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment

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