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


  • Guerrini, Luca


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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    References listed on IDEAS

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    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. Elshennawy, Abeer & Robinson, Sherman & Willenbockel, Dirk, 2016. "Climate change and economic growth: An intertemporal general equilibrium analysis for Egypt," Economic Modelling, Elsevier, vol. 52(PB), pages 681-689.
    3. Jevgenijs Steinbuks & Thomas W. 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. repec:eee:apmaco:v:253:y:2015:i:c:p:262-273 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. 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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