6533b81ffe1ef96bd1276f4b

RESEARCH PRODUCT

Solution to nonlinear MHDS arising from optimal growth problems

José Ramón Ruiz-tamaritJosé Ramón Ruiz-tamaritManuel Ventura-marco

subject

Mathematical optimizationState variableSteady state (electronics)Sociology and Political ScienceGeneral Social SciencesReduction (complexity)Nonlinear systemLinearizationPath (graph theory)UniquenessStatistics Probability and UncertaintyGeneral PsychologyHamiltonian (control theory)Mathematics

description

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.

yearjournalcountryeditionlanguage
2011-03-01Mathematical Social Sciences
https://doi.org/10.1016/j.mathsocsci.2011.01.001