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The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS

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  • José Ramón Ruiz-Tamarit

Abstract

In this paper I propose a method for solving in closed form a general class of four-dimension non-linear modified Hamiltonian dynamic systems. This method may be used to study several intertemporal optimization problems with a predetermined structure, involving unbounded technological constraints as well as multiple controls and state variables. The method is developed here by solving the first order conditions corresponding to the socially optimal solution to the Lucas (1988) two-sector model of endogenous growth

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Paper provided by FEDEA in its series Working Papers with number 2002-18.

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Handle: RePEc:fda:fdaddt:2002-18

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  1. Guy Dumais & Glenn Ellison & Edward L. Glaeser, 2002. "Geographic Concentration As A Dynamic Process," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 84(2), pages 193-204, May.
  2. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, De Gruyter, vol. 4(1), pages 1-19, December.
  3. Marius Brülhart, 2001. "Evolving geographical concentration of European manufacturing industries," Review of World Economics (Weltwirtschaftliches Archiv), Springer, Springer, vol. 137(2), pages 215-243, June.
  4. Mulligan, Casey B & Sala-i-Martin, Xavier, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 108(3), pages 739-73, August.
  5. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, Elsevier, vol. 61(2), pages 86-96, March.
  6. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 99(3), pages 483-99, June.
  7. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods, EconWPA 0210002, EconWPA.
  8. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, Elsevier, vol. 22(1), pages 3-42, July.
  9. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, Elsevier, vol. 63(1), pages 113-142, June.
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Cited by:
  1. Olaf Posch & Timo Trimborn, 2011. "Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty," DEGIT Conference Papers, DEGIT, Dynamics, Economic Growth, and International Trade c016_044, DEGIT, Dynamics, Economic Growth, and International Trade.
  2. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, Elsevier, vol. 26(1), pages 135-138, January.
  3. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, Elsevier, vol. 25(6), pages 1175-1182, November.
  4. Hiraguchi, Ryoji, 2009. "A note on the closed-form solution to the Lucas-Uzawa model with externality," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(10), pages 1757-1760, October.
  5. J. R. Ruiz-Tamarit & M. Ventura-Marco, . "Solution to Non-Linear MHDS arising from Optimal Growth Problems," Working Papers, FEDEA 2000-16, FEDEA.

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