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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.

Suggested Citation

  • Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
    • Handle: RePEc:eee:matsoc:v:61:y:2011:i:2:p:86-96
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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". "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA.
    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. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    6. 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).
    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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    More about this item

    Keywords

    Nonlinearity Hamiltonian Closed form Growth Transitional dynamics;

    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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