IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-06c60007.html
   My bibliography  Save this article

The Ramsey model with logistic population growth

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/pubs/EB/2007/Volume3/EB-06C60007A.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 5, Elsevier.
    2. Kazumi Asako, 1979. "Environmental Pollution in an Open Economy," The Economic Record, The Economic Society of Australia, vol. 55(4), pages 359-367, December.
    3. Jean-Bernard Chatelain & Kirsten Ralf, 2024. "Wealth in the Quadratic Loss Function of the Ramsey Malinvaud Cass Koopmans Model of Optimal Savings," Revue d'économie politique, Dalloz, vol. 134(3), pages 371-390.
    4. Gordon Cordina, 2004. "Economic Vulnerability And Economic Growth: Some Results From A Neo-Classical Growth Modelling Approach," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 29(2), pages 21-39, December.
    5. Andersson, Fredrik N.G. & Edgerton, David L. & Opper, Sonja, 2013. "A Matter of Time: Revisiting Growth Convergence in China," World Development, Elsevier, vol. 45(C), pages 239-251.
    6. Alexander Beames & Mariano Kulish & Nadine Yamout, 2022. "Fiscal Policy and the Slowdown in Trend Growth in an Open Economy," Working Papers 143, Red Nacional de Investigadores en Economía (RedNIE).
    7. Axel Börsch‐Supan & Alexander Ludwig & Joachim Winter, 2006. "Ageing, Pension Reform and Capital Flows: A Multi‐Country Simulation Model," Economica, London School of Economics and Political Science, vol. 73(292), pages 625-658, November.
    8. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    9. George Halkos & Iacovos Psarianos, 2016. "Exploring the effect of including the environment in the neoclassical growth model," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 18(3), pages 339-358, July.
    10. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
    11. I. Hakan Yetkiner, 2006. "Saglik ile Buyume," Ege Academic Review, Ege University Faculty of Economics and Administrative Sciences, vol. 6(2), pages 83-91.
    12. Rao Aiyagari, S., 1988. "Nonmonetary steady states in stationary overlapping generations models with long lived agents and discounting: Multiplicity, optimality, and consumption smoothing," Journal of Economic Theory, Elsevier, vol. 45(1), pages 102-127, June.
    13. Andrés Fernández & Ayşe İmrohoroğlu & Cesar E. Tamayo, 2019. "Saving Rates in Latin America: A Neoclassical Perspective," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 67(4), pages 791-823, December.
    14. ?gel de la Fuente, "undated". "Convergence Across Countries And Regions: Theory And Empirics," UFAE and IAE Working Papers 447.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    15. Li, Defu & Bental, Benjamin, 2023. "What determines the Direction of Technological Progress(2023.11.16)?," MPRA Paper 119211, University Library of Munich, Germany, revised 16 Nov 2023.
    16. Pozzolo, Alberto Franco, 2004. "Endogenous Growth in Open Economies - A Survey of Major Results," Economics & Statistics Discussion Papers esdp04020, University of Molise, Department of Economics.
    17. Matthew Higgins & Daniel Levy & Andrew T. Young, 2003. "Growth and Convergence across the US: Evidence from County-Level Data," Working Papers 2003-03, Bar-Ilan University, Department of Economics.
    18. J. Subrick & Andrew Young, 2010. "Nobelity and novelty: Finn Kydland and Edward Prescott’s contributions viewed from Vienna," The Review of Austrian Economics, Springer;Society for the Development of Austrian Economics, vol. 23(1), pages 35-53, March.
    19. Carlos Mendez & Mitsuhiko Kataoka, 2021. "Disparities in regional productivity, capital accumulation, and efficiency across Indonesia: A club convergence approach," Review of Development Economics, Wiley Blackwell, vol. 25(2), pages 790-809, May.
    20. Francisco J. Buera & Joseph P. Kaboski & Martí Mestieri & Daniel G. O'Connor, 2020. "The Stable Transformation Path," NBER Working Papers 27731, National Bureau of Economic Research, Inc.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-06c60007. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.