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A closed-form solution to the Ramsey model with logistic population growth

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  • Guerrini, Luca

Abstract

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb-Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.

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  • 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.
    • Handle: RePEc:eee:ecmode:v:27:y:2010:i:5:p:1178-1182
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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.
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    3. Jevgenijs Steinbuks & Thomas Hertel, 2016. "Confronting the Food–Energy–Environment Trilemma: Global Land Use in the Long Run," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(3), pages 545-570, March.
    4. Borissov, Kirill & Dubey, Ram Sewak, 2020. "Growth with many agents and wages paid ex ante," Economic Modelling, Elsevier, vol. 89(C), pages 101-107.
    5. 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.
    6. 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.
    7. Cai, Yongyang & Steinbuks, Jevgenijs & Elliott, Joshua & Hertel, Thomas W., 2014. "The effect of climate and technological uncertainty in crop yields on the optimal path of global land use," Policy Research Working Paper Series 7009, The World Bank.
    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. Kajanovičová, Viktória & Novotný, Branislav & Pospíšil, Michal, 2020. "Ramsey model with non-constant population growth," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 40-46.
    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. Hofstad, Ole & Araya, Meley Mekonen, 2015. "Optimal wood harvest in miombo woodland considering REDD+payments — A case study at Kitulangalo Forest Reserve, Tanzania," Forest Policy and Economics, Elsevier, vol. 51(C), pages 9-16.

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