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A note on the closed-form solution to the Lucas-Uzawa model with externality

  • Hiraguchi, Ryoji

Ruiz-Tamarit [2008. The closed-form solution for a family of four-dimension nonlinear MHDS. Journal of Economic Dynamics and Control 32, 1000-1014] provides a closed-form solution to the two-sector model of endogenous growth with externalities. He assumes that the coefficient of the relative risk aversion is equal to the physical capital share, but this assumption is empirically and theoretically implausible. This note uses the result of Boucekkine and Ruiz-Tamarit [2008. Special functions for the study of economic dynamics: the case of the Lucas-Uzawa model. Journal of Mathematical Economics 44, 33-54] and derives a closed-form solution without setting the parametric assumption. The solution path is expressed in terms of the Gauss hypergeometric functions.

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

Volume (Year): 33 (2009)
Issue (Month): 10 (October)
Pages: 1757-1760

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Handle: RePEc:eee:dyncon:v:33:y:2009:i:10:p:1757-1760
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Leith, Campbell & Malley, Jim, 2005. "Estimated general equilibrium models for the evaluation of monetary policy in the US and Europe," European Economic Review, Elsevier, vol. 49(8), pages 2137-2159, November.
  2. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  3. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  4. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
  5. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
  6. 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.
  7. Cysne, Rubens Penha, 2006. "A note on the non-convexity problem in some shopping-time and human-capital models," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2737-2745, October.
  8. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-67, December.
  9. Hiraguchi, Ryoji, 2009. "Non-concavity problems in the dynamic macroeconomic models: A note," Journal of Banking & Finance, Elsevier, vol. 33(3), pages 568-572, March.
  10. Hiraguchi, Ryoji, 2009. "A solution to the Lucas-Uzawa model with increasing returns to scale: Note," Economic Modelling, Elsevier, vol. 26(5), pages 831-834, September.
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