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Solution to Non-Linear MHDS arising from Optimal Growth Problems

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

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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  17. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  18. 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.
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