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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.

Suggested Citation

  • J. R. Ruiz-Tamarit & M. Ventura-Marco, "undated". "Solution to Non-Linear MHDS arising from Optimal Growth Problems," Working Papers 2000-16, FEDEA.
    • Handle: RePEc:fda:fdaddt:2000-16
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    10. 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.
    11. 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, December.
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    13. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
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    16. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    17. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
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    Cited by:

    1. 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.
    2. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    3. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA.
    4. 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.
    5. 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.
    6. 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.
    7. Juana AZNAR-MARQUEZ & Jose-Ramon RUIZ-TAMARIT, 2012. "Sufficient and Necessary Conditions for Non-Catastrophic Growth," LIDAM Discussion Papers IRES 2012027, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).

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    More about this item

    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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