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The Ramsey model with logistic population growth

Author

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  • Juan Gabriel Brida

    (Free University of Bolzano)

  • Elvio Accinelli

    (Universidad Autonoma Metropolitana, Mexico)

Abstract

In standard economic growth theory it is assumed that labor force follows exponential growth, a not realistic assumption. As described in Maynard Smith (1974), the growth of natural populations is more accurately depicted by a logistic growth law. In this paper we analyze how the Ramsey growth model is affected by logistic growth of population, comparing it with the classic Ramsey model. We show that there is a unique nontrivial steady state of the model and that the parameters of the logistic equation play no role in determining long run equilibrium per worker level of consumption and capital. In addition, we study the stability of the model showing that its nontrivial equilibrium is a saddle point.

Suggested Citation

  • Juan Gabriel Brida & Elvio Accinelli, 2007. "The Ramsey model with logistic population growth," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    • Handle: RePEc:ebl:ecbull:eb-06c60007
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    References listed on IDEAS

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    1. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
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    Cited by:

    1. Fosu, Gabriel Obed & Gogovi, Gideon & Appati, Justice & Bondzie, Eric Amoo, 2013. "Comparability of the Neoclassical Economic Growth models: The Ramsey Models in Perspective," MPRA Paper 69284, University Library of Munich, Germany.
    2. Guerrini, Luca, 2010. "Transitional dynamics in the Ramsey model with AK technology and logistic population change," Economics Letters, Elsevier, vol. 109(1), pages 17-19, October.
    3. 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.
    4. Guerrini, Luca, 2010. "The Ramsey model with AK technology and a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1178-1183, December.
    5. Growiec, Jakub, 2010. "Knife-edge conditions in the modeling of long-run growth regularities," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1143-1154, December.
    6. Roman G. Smirnov & Kunpeng Wang, 2017. "In search of a new economic model determined by logistic growth," Papers 1711.02625, arXiv.org, revised Oct 2018.
    7. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
    8. Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    9. Marsiglio, Simone & La Torre, Davide, 2012. "Population dynamics and utilitarian criteria in the Lucas–Uzawa Model," Economic Modelling, Elsevier, vol. 29(4), pages 1197-1204.
    10. Iulia PARA & Ioana VIASU, 2018. "On the Solutions to the Ramsey Model with Logistic Population Growth via the Partial Hamiltonian Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 142-150, December.
    11. Fabio Tramontana & Viktor Avrutin, 2014. "Complex endogenous dynamics in a one-sector growth model with differential savings," DEM Working Papers Series 078, University of Pavia, Department of Economics and Management.
    12. Guerrini, Luca, 2010. "A closed-form solution to the Ramsey model with logistic population growth," Economic Modelling, Elsevier, vol. 27(5), pages 1178-1182, September.

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    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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