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Solution to nonlinear MHDS arising from optimal growth problems

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  • 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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/505565

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Keywords: Nonlinearity Hamiltonian Closed form Growth Transitional dynamics;

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References

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  1. 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.
  2. Mulligan, C.B. & Sala-i-Martin, X., 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," Papers 651, Yale - Economic Growth Center.
  3. 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.
  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. BENCHEKROUN, Hassan & WITHAGEN, Cees, 2010. "The Optimal Depletion of Exhaustible Resources : A Complete Characterization," Cahiers de recherche 04-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  7. Smulders, J.A., 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153411, Tilburg University.
  8. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
  9. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2008. "Note on global dynamics and imbalance effects in the Lucas-Uzawa model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 503-518.
  10. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
  11. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
  12. 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.
  13. 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.
  14. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
  15. Russell, Thomas & Zecevic, Aleksandar, 2000. "Indeterminate growth paths and stability," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 39-62, January.
  16. 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.
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Citations

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Cited by:
  1. 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).
  2. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  3. J.Aznar-Márquez & J.R. Ruiz-Tamarit, 2004. "Non-Catastrophic Endogenous Growth with Pollution and Abatement," Economic Working Papers at Centro de Estudios Andaluces E2004/80, Centro de Estudios Andaluces.
  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-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  6. 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.

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