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Solution to Non-Linear MHDS arising from Optimal Growth Problems

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

Abstract

In this paper we propose a method for solving in closed form a general class of non-linear modified Hamiltonian dynamic systems (MHDS). This method may be used to analyze some intertemporal optimization problems With a predetermined structure involving unbounded technological constraints. The method seems specially well designed to study endogenous growth models With two controls and one state variable. We use the closed form solutions to Study either unicity or indeterminacy of the non-explosive paths in a Context charaterized by the lack of a well defined isolated steady state. Moreover, in this way we can avoid both the reduction of dimension and the linearization process even when the dynamic system offers a continuum of steady states or no steady stateat all.

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Paper provided by FEDEA in its series Working Papers with number 2000-16.

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Handle: RePEc:fda:fdaddt:2000-16

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  1. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  2. 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.
  3. Casey B. Mulligan & Xavier Sala-i-Martin, 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," NBER Working Papers 3986, National Bureau of Economic Research, Inc.
  4. 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.
  5. Sergio Rebelo, 1999. "Long Run Policy Analysis and Long Run Growth," Levine's Working Paper Archive 2114, David K. Levine.
  6. 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.
  7. 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.
  8. 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.
  9. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
  10. 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.
  11. 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.
  12. Lans Bovenberg, A. & Smulders, Sjak, 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Journal of Public Economics, Elsevier, vol. 57(3), pages 369-391, July.
  13. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  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. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
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Cited by:
  1. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
  2. 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.
  3. 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.
  4. 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.
  5. 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).
  6. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA.

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