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

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  • Ruiz-Tamarit, José Ramón

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 3 (March)
Pages: 1000-1014

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:3:p:1000-1014

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References

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  1. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
  2. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  3. Raouf, BOUCEKKINE & Ramon, RUIZ-TAMARIT, 2004. "Imbalance effects in the Lucas model : An analytical exploration," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004005, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  4. 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.
  5. Guy Dumais & Glenn Ellison & Edward L Glaeser, 1998. "Geographic Concentration as a Dynamic Process," Working Papers 98-3, Center for Economic Studies, U.S. Census Bureau.
  6. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  7. Casey B. Mulligan & Xavier Sala-i-Martin, 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," NBER Working Papers 3986, National Bureau of Economic Research, Inc.
  8. 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.
  9. Marius Brülhart, 2001. "Evolving geographical concentration of European manufacturing industries," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 137(2), pages 215-243, June.
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Cited by:
  1. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 26(1), pages 135-138, January.
  2. 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.
  3. Hiraguchi, Ryoji, 2009. "A note on the closed-form solution to the Lucas-Uzawa model with externality," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1757-1760, October.
  4. Olaf Posch & Timo Trimborn, 2011. "Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty," DEGIT Conference Papers c016_044, DEGIT, Dynamics, Economic Growth, and International Trade.
  5. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.

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