×
Boucekkine, R.; Ruiz-Tamarit, J. R.

Special functions for the study of economic dynamics: the case of the Lucas-Uzawa model. (English) Zbl 1141.91604

J. Math. Econ. 44, No. 1, 33-54 (2008).
Summary: The special functions are intensively used in 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 . 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.
© Elsevier B.V.

Cited in 2 Reviews
Cited in 34 Documents

MSC:

91B62 Economic growth models

Keywords:

special functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics
Cite Review PDF
Full Text: DOI Link

References:

[1] Abadir, K. M., An introduction to hypergeometric functions for economists, Econometric Reviews, 18, 287-330, 1999 · Zbl 1073.91526
[2] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions, 1972, Dover Publications: Dover Publications New York · Zbl 0543.33001
[3] Andrews, G.; Askey, R.; Roy, R., Special Functions, 1999, Cambridge University Press: Cambridge University Press Cambridge · Zbl 0920.33001
[4] Becken, W.; Schmelcher, P., The analytic continuation of the Gaussian hypergeometric function \( {}_2F_1 ( a , b \text{;} c \text{;} z )\) for arbitrary parameters, Journal of Computational and Applied Mathematics, 126, 449-478, 2000 · Zbl 0976.33003
[5] Benhabib, J.; Perli, R., Uniqueness and indeterminacy: on the dynamics of endogenous growth, Journal of Economic Theory, 63, 113-142, 1994 · Zbl 0803.90023
[6] Boucekkine, R., Ruiz-Tamarit, J.R. 2004. Imbalance effects in the Lucas Model: an analytical exploration. Berekeley Electronic Journals in Macroeconomics/Topics in Macroeconomics (Article 15).
[7] Caballé, J.; Santos, M. S., On endogenous growth with physical and human capital, Journal of Political Economy, 101, 1042-1067, 1993
[8] Goursat, M., Sur l’équation différentielle linéaire qui admet pour intégrale la série hypergéométrique, Annales de l’Académie des Sciences et de l’École Normale Supérieure, 10, S3-S142, 1881 · JFM 13.0267.01
[9] Kummer, E., Uber die hypergeometrische reihe, Journal of Reine Angewandte Mathematics, 15, 39-83, 1836, (127–172) · ERAM 015.0533cj
[10] Luke, Y., The Special Functions and their Approximations, 1969, Academic Press: Academic Press New York · Zbl 0193.01701
[11] Mulligan, C. B.; Sala-i-Martín, X., Transitional dynamics in two sector models of endogenous growth, Quarterly Journal of Economics, 108, 739-773, 1993
[12] Rivera-Batiz, L.; Romer, P., Economic integration and endogenous growth, Quarterly Journal of Economics, 106, 531-556, 1991
[13] Temme, N. M., Special Functions. An Introduction to the Classical Functions of Mathematical Physics, 1996, Wiley · Zbl 0856.33001
[14] Temme, N. M., Large parameter cases of the Gauss hypergeometric function, Journal of Computational and Applied Mathematics, 153, 441-462, 2003 · Zbl 1019.33003
[15] Xie, D., Divergence in economic performance: transitional dynamics with multiple equilibria, Journal of Economic Theory, 63, 97-112, 1994 · Zbl 0803.90037
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.