The closed-form solution for a family of four-dimension nonlinear MHDS
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.
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- BOUCEKKINE, Raouf & RUIZ-TAMARIT, Ramon, 2004. "Imbalance effects in the Lucas model: an analytical exploration," CORE Discussion Papers 2004008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BOUCEKKINE, Raouf & RUIZ TAMARIT, Ramon, . "Imbalance effects in the Lucas model: an analytical exploration," CORE Discussion Papers RP -1755, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
- 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.
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- Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
- J. R. Ruiz-Tamarit & M. Ventura-Marco, . "Solution to Non-Linear MHDS arising from Optimal Growth Problems," Working Papers 2000-16, FEDEA.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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