IDEAS home Printed from
   My bibliography  Save this article

The Ramsey model with a bounded population growth rate


  • Guerrini, Luca


This paper presents an extension of the canonical Ramsey growth model of optimal capital accumulation by departing from the standard assumption of constant population growth rate. More concretely, this rate is assumed to be variable over time, subject only to be between prescribed upper and lower limits. In this kind of setup, the model is represented by a two dimensional dynamical system, which happens to be non-autonomous. In contrast to the Ramsey model, the linearization method cannot be used. It will be necessary to use different techniques to derive the dynamic properties of the model's solution, as well as investigate its long-run growth and asymptotic stability. This will be done using the method proposed by Guerrini (2006), when studying the Solow model with a variable population growth rate. The paper also shows that closed-form analytic solutions can always be derived for the model, when capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.

Suggested Citation

  • Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
  • Handle: RePEc:eee:jmacro:v:32:y:2010:i:3:p:872-878

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
    2. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    3. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
    4. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. repec:eee:apmaco:v:253:y:2015:i:c:p:262-273 is not listed on IDEAS
    2. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
    3. 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.
    4. 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.


    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:eee:jmacro:v:32:y:2010:i:3:p:872-878. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.