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A solution to the Lucas-Uzawa model with increasing returns to scale: Note

  • Hiraguchi, Ryoji

Chilarescu [2008, An analytical solutions for a model of endogenous growth, Economic Modelling.] claims that he determines a solution path to the Lucas-Uzawa model with increasing returns to scale. However, the path is not a closed-form since it depends on the initial consumption and the initial time for goods production, that are unknown. Moreover, the production function is nonconcave and then the first order conditions and the transversality conditions are not sufficient for the optimality. This note converts the model to a problem in which the Hamiltonian is available and derives a fully-closed form solution.

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Article provided by Elsevier in its journal Economic Modelling.

Volume (Year): 26 (2009)
Issue (Month): 5 (September)
Pages: 831-834

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Handle: RePEc:eee:ecmode:v:26:y:2009:i:5:p:831-834
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  1. Raouf, BOUCEKKINE & José R. , RUIZ-TAMARIT, 2004. "Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  2. 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.
  3. 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.
  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, vol. 33(10), pages 1757-1760, October.
  5. Chilarescu, Constantin, 2008. "An analytical solutions for a model of endogenous growth," Economic Modelling, Elsevier, vol. 25(6), pages 1175-1182, November.
  6. 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).
  7. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  8. 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.
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