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
Date Written: December 2004
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: Suggested Citation