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Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model

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  • Boucekkine, R.
  • Ruiz-Tamarit, J.R.

Abstract

The special functions are intensively used in mathematical physics to solve differential systems. We argue that their use should be most useful in economic dynamics, notably in the assessment of the transtion dynamics of endogenous growth models. We illustrate our argument on the Lucas-Uzawa model, which we solve by the means of Gaussian hypergeometric functions. We show how the use of Gaussian hypergeometric functions allows for an explicit representation of the equilibrium dynamics of the variables in level. In contrast to the preexisting approaches, our method is global and does not rely on dimension reduction

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 1 (January)
Pages: 33-54

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Handle: RePEc:eee:mateco:v:44:y:2008:i:1:p:33-54

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

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  1. 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.
  2. Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, Exeter University, Department of Economics.
  3. 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).
  4. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
  5. Luis A. Rivera-Batiz & Paul M. Romer, 1990. "Economic Integration and Endogenous Growth," NBER Working Papers 3528, National Bureau of Economic Research, Inc.
  6. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
  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. 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.
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