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Solution to nonlinear MHDS arising from optimal growth problems

Author Info

  • Ruiz-Tamarit, J.R.
  • Ventura-Marco, M.

Abstract

In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 61 (2011)
Issue (Month): 2 (March)
Pages: 86-96

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Handle: RePEc:eee:matsoc:v:61:y:2011:i:2:p:86-96
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

Keywords: Nonlinearity Hamiltonian Closed form Growth Transitional dynamics;

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Find related papers by JEL classification:
  • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
  • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
  • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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  1. Smith William T, 2007. "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-33, August.
  2. 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.
  3. Bovenberg, A.L. & Smulders, J.A., 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Other publications TiSEM 6784bb12-71fb-45a5-bf7e-8, Tilburg University, School of Economics and Management.
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  5. M. Kurz, 1968. "The General Instability of a Class of Competitive Growth Processes," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 155-174.
  6. Benchekroun, Hassan & Withagen, Cees, 2011. "The optimal depletion of exhaustible resources: A complete characterization," Resource and Energy Economics, Elsevier, vol. 33(3), pages 612-636, September.
  7. Raouf Boucekkine & B. Martínez & J. R. Ruiz-Tamarit, 2007. "A note on global dynamics and imbalance effects in the Lucas-Uzawa model," Working Papers 2007_26, Business School - Economics, University of Glasgow.
  8. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
  9. Sergio Rebelo, 1999. "Long Run Policy Analysis and Long Run Growth," Levine's Working Paper Archive 2114, David K. Levine.
  10. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  11. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
  12. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  13. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
  14. Russell, Thomas & Zecevic, Aleksandar, 2000. "Indeterminate growth paths and stability," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 39-62, January.
  15. 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.
  16. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  17. 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.
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Cited by:

  1. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  2. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  3. J., AZNAR-MARQUEZ & Jose-Ramon, RUIZ-TAMARIT, 2005. "Demographic Transition Environmental Concern and the Kuznets Curve," Discussion Papers (ECON - Département des Sciences Economiques) 2005001, Université catholique de Louvain, Département des Sciences Economiques.
  4. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA.
  5. J., AZNAR-MARQUEZ & José Ramon, RUIZ-TAMARIT, 2005. "Non Catastrophic Endogenous Growth with Pollution and Abatment," Discussion Papers (ECON - Département des Sciences Economiques) 2005002, Université catholique de Louvain, Département des Sciences Economiques.
  6. Juana AZNAR-MARQUEZ & Jose-Ramon RUIZ-TAMARIT, 2012. "Sufficient and Necessary Conditions for Non-Catastrophic Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2012027, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Aznar-Márquez, J. & Ruiz-Tamarit, J.R., 2016. "Environmental pollution, sustained growth, and sufficient conditions for sustainable development," Economic Modelling, Elsevier, vol. 54(C), pages 439-449.

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