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The Ramsey model with a bounded population growth rate

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  • Guerrini, Luca
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Macroeconomics.

    Volume (Year): 32 (2010)
    Issue (Month): 3 (September)
    Pages: 872-878

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    Handle: RePEc:eee:jmacro:v:32:y:2010:i:3:p:872-878

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    Web page: http://www.elsevier.com/locate/inca/622617

    Related research

    Keywords: Ramsey Bounded population growth rate Closed-form solution;

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    1. BOUCEKKINE, Raouf & RUIZ TAMARIT, Ramon, . "Imbalance effects in the Lucas model: an analytical exploration," CORE Discussion Papers RP -1755, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    3. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
    4. repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
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    Cited by:
    1. J. R. Ruiz-Tamarit & M. Ventura-Marco, . "Solution to Non-Linear MHDS arising from Optimal Growth Problems," Working Papers 2000-16, FEDEA.
    2. 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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