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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.
    3. Guy Dumais & Glenn Ellison & Edward L. Glaeser, 2002. "Geographic Concentration As A Dynamic Process," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 193-204, May.
    4. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    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.
    9. K.H. Midelfart & H.G. Overman & S.J. Redding & A.J. Venables, 2000. "The location of European industry," European Economy - Economic Papers 2008 - 2015 142, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    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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    1. 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.
    2. 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.
    3. 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.
    4. Bosi, Stefano & Camacho, Carmen & Ha-Huy, Thai, 2023. "Balanced growth and degrowth with human capital," Economics Letters, Elsevier, vol. 232(C).
    5. 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).
    6. 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.
    7. 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.
    8. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    9. 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.
    10. Wei Jin & ZhongXiang Zhang, 2018. "Capital Accumulation, Green Paradox, and Stranded Assets: An Endogenous Growth Perspective," Working Papers 2018.33, Fondazione Eni Enrico Mattei.
    11. 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.
    12. 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.
    13. Jin, Wei & Shi, Xunpeng & Zhang, Lin, 2021. "Energy transition without dirty capital stranding," Energy Economics, Elsevier, vol. 102(C).
    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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