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The Ramsey model with a bounded population growth rate

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  • Guerrini, Luca

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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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    4. Guerrini, Luca, 2006. "The Solow-Swan model with a bounded population growth rate," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 14-21, February.
    5. 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.
    6. Juan Gabriel Brida & Elvio Accinelli, 2007. "The Ramsey model with logistic population growth," Economics Bulletin, AccessEcon, vol. 3(15), pages 1-8.
    7. repec:ebl:ecbull:v:3:y:2007:i:15:p:1-8 is not listed on IDEAS
    8. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
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    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. 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.
    3. 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.
    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. 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.
    6. 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.
    7. Kajanovičová, Viktória & Novotný, Branislav & Pospíšil, Michal, 2020. "Ramsey model with non-constant population growth," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 40-46.
    8. 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.
    9. 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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