Journal
JOURNAL OF MATHEMATICAL ECONOMICS
Volume 44, Issue 1, Pages 33-54Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jmateco.2007.05.001
Keywords
special functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics
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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 economic growth models. We illustrate our argument on the famous 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 all variables in level. The parameters of the involved hypergeometric functions are identified using the Pontryagin conditions arising from the underlying optimization problems. In contrast to the pre-existing approaches, our method is global and does not rely on dimension reduction. (c) 2007 Elsevier B.V. All rights reserved.
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