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

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Author Info
BOUCEKKINE, Raouf
RUIZ-TAMARIT, Ramon

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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 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.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2004084.

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Date of creation: 01 Dec 2004
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Handle: RePEc:cor:louvco:2004084

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Related research
Keywords: special functions; hypergeometric functions; optimal control; Lucas-Uzawa model; economic dynamics;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

References listed on IDEAS
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  1. Karim Abadir, 1999. "An introduction to hypergeometric functions for economists," Econometric Reviews, Taylor and Francis Journals, vol. 18(3), pages 287-330. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
  3. Raouf, BOUCEKKINE & Ramon, RUIZ-TAMARIT, 2004. "Imbalance effects in the Lucas model : An analytical exploration," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004005, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
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  4. 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. [Downloadable!] (restricted)
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  5. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Agustin, PEREZ BARAHONA, 2007. "Capital Accumulation and Non-Renewable Energy Resources : a Special Functions Case," Discussion Papers (ECON - Département des Sciences Economiques) 2007008, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
  2. Raouf Boucekkine & Natali Hritonenko & Yuri Yatsenko, . "Optimal Firm Behavior under Environmental Constraints," Working Papers 2008_11, Department of Economics, University of Glasgow. [Downloadable!]
    Other versions:
  3. repec:bep:maccon:v:7:y:2007:i:1:p:1524-1524 is not listed on IDEAS
  4. Raouf Boucekkine & B. Martínez & J. R. Ruiz-Tamarit, 2007. "A note on global dynamics and imbalance effects in the Lucas-Uzawa model," Working Papers 2007_26, Department of Economics, University of Glasgow. [Downloadable!]
    Other versions:
  5. Raouf, BOUCEKKINE & Bity, DIENE & Theophile, AZOMAHOU, 2006. "The Growth economics of epidemics," Discussion Papers (ECON - Département des Sciences Economiques) 2006021, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
  6. G. Mingari Scarpello & A. Palestini & D. Ritelli, 2009. "Closed form solutions to generalized logistic-type nonautonomous systems," Working Papers 654, Dipartimento Scienze Economiche, Universita' di Bologna. [Downloadable!]
  7. Rauf, BOUCEKKINE & Blanca, MARTINEZ & Jose R., RUIZ-TAMARIT, 2007. "Global dynamics and imbalance effects in the Lucas Uzawa model : further results," Discussion Papers (ECON - Département des Sciences Economiques) 2007018, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
    Other versions:
  8. repec:bep:maccon:v:6:y:2006:i:1:p:1356-1356 is not listed on IDEAS
  9. Privileggi, Fabio, 2008. "On the transition dynamics in endogenous recombinant growth models," P.O.L.I.S. department's Working Papers 120, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
  10. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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