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

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  • Hiraguchi, Ryoji

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jedc

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Keywords: Endogenous growth Closed-form solution;

References

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  1. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
  2. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
  3. 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.
  4. 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.
  5. 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.
  6. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
  7. 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.
  8. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  9. Campbell Leith & Jim Malley, 2002. "Estimated General Equilibrium Models for the Evaluation of Monetary Policy in the US and Europe," CESifo Working Paper Series 699, CESifo Group Munich.
  10. 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.
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Citations

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Cited by:
  1. 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.
  2. OA. Carboni & P. Russu, 2012. "A Model of Economic Growth with Public Finance: Dynamics and Analytic Solution," Working Paper CRENoS 201229, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  3. 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.
  4. Carboni, Oliviero & Russu, Paolo, 2011. "The Conditions for a Balanced Growth in a Model with Public Finance: an Analytic Solution," MPRA Paper 36600, University Library of Munich, Germany.

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