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The closed-form solution for a family of four-dimension nonlinear MHDS

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  • Ruiz-Tamarit, José Ramón

Abstract

In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externality, the socially optimal short-run trajectory is unique.

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  • Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    • Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:1000-1014
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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. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
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    5. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    6. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    7. 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.
    8. Marius Brülhart, 2001. "Evolving geographical concentration of European manufacturing industries," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 137(2), pages 215-243, June.
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    10. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    2. Antony, Jürgen & Klarl, Torben, 2019. "Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203640, Verein für Socialpolitik / German Economic Association.
    3. Wei Jin & ZhongXiang Zhang, 2018. "Capital Accumulation, Green Paradox, and Stranded Assets: An Endogenous Growth Perspective," Working Papers 2018.33, Fondazione Eni Enrico Mattei.
    4. Hiraguchi, Ryoji, 2009. "A note on the closed-form solution to the Lucas-Uzawa model with externality," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1757-1760, October.
    5. C. Chilarescu & I. Viasu, 2019. "Uniqueness and Multiple Trajectories for the Case of Lucas Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1157-1177, October.
    6. Constantin Chilarescu & Ioana Viasu, 2016. "A Closed-form Solution of a Two-sector Endogenous Growth Model with Habit Formation," Australian Economic Papers, Wiley Blackwell, vol. 55(2), pages 112-127, June.
    7. 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.
    8. Bosi, Stefano & Camacho, Carmen & Ha-Huy, Thai, 2023. "Balanced growth and degrowth with human capital," Economics Letters, Elsevier, vol. 232(C).
    9. Stefano Bosi & Carmen Camacho & Thai Ha-Huy, 2023. "On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988)," PSE Working Papers halshs-03920386, HAL.
    10. Jin, Wei & Shi, Xunpeng & Zhang, Lin, 2021. "Energy transition without dirty capital stranding," Energy Economics, Elsevier, vol. 102(C).
    11. Antony, Jürgen & Klarl, Torben, 2023. "Subsistence consumption and natural resource depletion: Can resource-rich low-income countries realize sustainable consumption paths?," Journal of Macroeconomics, Elsevier, vol. 77(C).
    12. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    13. Jung Young-Cheol & Quyen Nguyen V., 2012. "The Global Transmission of Government Debt," The B.E. Journal of Macroeconomics, De Gruyter, vol. 12(1), pages 1-24, July.
    14. Jürgen Antony & Torben Klarl, 2019. "Non-Renewable Resources in a Ramsey Economy with Subsistence Consumption, Human and Physical Capital Accumulation: A full Characterization," Bremen Papers on Economics & Innovation 1904, University of Bremen, Faculty of Business Studies and Economics.
    15. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
    16. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 26(1), pages 135-138, January.
    17. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).

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