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

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  • Raouf, BOUCEKKINE

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

  • José R. , RUIZ-TAMARIT

    (Universitat de Valencia (Spain))

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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Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 2004026.

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Date of creation: 01 Oct 2004
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Handle: RePEc:ctl:louvir:2004026

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Keywords: Special functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics;

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  1. Danyang Xie, 2002. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," GE, Growth, Math methods 0210002, EconWPA.
  2. 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.
  3. 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).
  4. 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.
  5. Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, Exeter University, Department of Economics.
  6. 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.
  7. 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.
  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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