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

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  • BOUCEKKINE, Raouf
  • RUIZ-TAMARIT, José Ramon

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 transition 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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File URL: http://dx.doi.org/10.1016/j.jmateco.2007.05.001
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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -2003.

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Handle: RePEc:cor:louvrp:-2003

Note: In : Journal of Mathematical Economics, 44, 33-54, 2008
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  1. Mulligan, C.B. & Sala-i-Martin, X., 1992. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," Papers 651, Yale - Economic Growth Center.
  2. BOUCEKKINE, Raouf & RUIZ TAMARIT, Ramon, . "Imbalance effects in the Lucas model: an analytical exploration," CORE Discussion Papers RP -1755, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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. Rivera-Batiz, Luis A & Romer, Paul M, 1991. "Economic Integration and Endogenous Growth," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 531-55, May.
  5. Eric W. Bond & Ping Wang & Chong K. Yip, 1993. "A general two-sector model of endogenous growth with human and physical capital: balanced growth and transitional dynamics," Research Paper 9324, Federal Reserve Bank of Dallas.
  6. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor & Francis Journals, vol. 18(3), pages 287-330.
  7. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, 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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