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

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  • BOUCEKKINE, Raouf
  • RUIZ-TAMARIT, José Ramon

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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Suggested Citation

  • BOUCEKKINE, Raouf & RUIZ-TAMARIT, José Ramon, 2009. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," LIDAM Reprints CORE 2003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2003
    DOI: 10.1016/j.jmateco.2007.05.001
    Note: In : Journal of Mathematical Economics, 44, 33-54, 2008
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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