Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model

CORE Discussion Paper No. 2004/84

43 Pages Posted: 15 Apr 2005

See all articles by Raouf Boucekkine

Raouf Boucekkine

Universite Catholique de Louvain

J. R. Ruiz Tamarit

University of Valencia - Department of Economic Analysis; Universite Catholique de Louvain - Institut de Recherches Economiques et Sociales

Date Written: December 2004

Abstract

The special functions are intensively used in mathematical physics to solve differential systems. We argue that they 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.

Keywords: special functions, hypergeometric functions, optimal control, Lucas-Uzawa model, economic dynamics

JEL Classification: C61, C62, O41

Suggested Citation

Boucekkine, Raouf and Ruiz Tamarit, José Ramón, Special Functions for the Study of Economic Dynamics: The Case of the Lucas-Uzawa Model (December 2004). CORE Discussion Paper No. 2004/84. Available at SSRN: https://ssrn.com/abstract=688904 or http://dx.doi.org/10.2139/ssrn.688904

Raouf Boucekkine (Contact Author)

Universite Catholique de Louvain ( email )

3, Place Montesquieu
Institut de Recherches Economiques et Sociales (IRES)
1348 Louvain-la-Neuve
Belgium
+32 10 47 38 48 (Phone)
+32 10 47 39 45 (Fax)

José Ramón Ruiz Tamarit

University of Valencia - Department of Economic Analysis ( email )

Av. dels Tarongers s/n
46022 Valencia
Spain
34 96 3828250 (Phone)
34 96 3828249 (Fax)

Universite Catholique de Louvain - Institut de Recherches Economiques et Sociales ( email )

3, Place Montesquieu
1348 Louvain-la-Neuve
Belgium

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