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Solution to Non-Linear MHDS arising from Optimal Growth Problems

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Author Info
J. R. Ruiz-Tamarit
M. Ventura-Marco

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

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  1. Gary D. Hansen & Edward C. Prescott, 1992. "Recursive methods for computing equilibria of business cycle models," Discussion Paper / Institute for Empirical Macroeconomics 36, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
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  3. Bovenberg, A.L. & Smulders, S., 1993. "Environmental Quality and Pollution-Saving Technological Change in Two- Sector Endogenous Growth Model," Papers 9321, Tilburg - Center for Economic Research.
  4. 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. [Downloadable!] (restricted)
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  5. Russell, Thomas & Zecevic, Aleksandar, 2000. "Indeterminate growth paths and stability," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 39-62, January. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. José Julián Escario & José Alberto Molina, . "Do tobacco taxes reduce lung cancer mortality?," Working Papers 2000-17, FEDEA. [Downloadable!]
  2. Simón Sosvilla-Rivero, . "La política macroeconómica en economías interdependientes," Working Papers 2001-03, FEDEA. [Downloadable!]
  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. [Downloadable!]
  4. J. Aznar-Márquez & J. R. Ruiz-Tamarit, . "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA. [Downloadable!]
  5. J., AZNAR-MARQUEZ & JosŽ 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. [Downloadable!]
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  6. Juan J. Dolado & Florentino Felgueroso & Juan F. Jimeno, . "Female Employment and Occupational Changes in the 1990s: How is the EU Performing Relative to the US?," Working Papers 2000-18, FEDEA. [Downloadable!]
    Other versions:
  7. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA. [Downloadable!]
    Other versions:
  8. J. Aznar-Marquez & J.R. Ruiz-Tamarit, 2001. "Endogenous Growth, Capital Utilization and Depreciation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001037, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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