6533b82bfe1ef96bd128df09

RESEARCH PRODUCT

The closed-form solution for a family of four-dimension nonlinear MHDS

José Ramón Ruiz-tamaritJosé Ramón Ruiz-tamarit

subject

Economics and EconometricsNonlinear systemState variableMathematical optimizationControl and OptimizationEndogenous growth theoryApplied MathematicsIntertemporal optimizationClosed-form expressionMathematical economicsExternalityHamiltonian (control theory)Mathematics

description

In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externality, the socially optimal short-run trajectory is unique. (C) 2007 Elsevier B.V. All rights reserved.

yearjournalcountryeditionlanguage
2008-03-01Journal of Economic Dynamics and Control
https://doi.org/10.1016/j.jedc.2007.03.008