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Progreso técnico: una aproximación desde la Teoría de Grupos de Transformaciones de Lie = Technical Progress: an Approach from Lie Transformation Group Theory

Author

Listed:
  • Fedriani Martel, Eugenio M.

    () (Department of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide)

  • Tenorio Villalón, Ángel F.

    () (Department of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide)

Abstract

En la presente comunicación explicamos algunas de las herramientas de la Geometría Diferencial y, en concreto, de la Teoría de Lie con las que se trabaja actualmente en Economía. Se indican las condiciones que se exigen a las funciones de producción y la definición de un tipo de progreso técnico denominado de tipo Lie, consistente en exigir las tres propiedades que han de verificar los grupos de Lie. También se expone el uso del operador de Lie en interpretaciones económicas y en la cuantificación del impacto del progreso técnico. Dicho operador permite dar una respuesta a la Controversia Solow-Stigler. Por último, se indican varias aplicaciones de la Teoría de Lie en los estudios económicos, que permiten abrir futuras líneas de investigación, de las que se apuntan algunas. De este modo, nuestro objetivo principal es mostrar el uso, actual y futuro, de la Teoría de Lie en el campo de la Economía. = In this paper we explain some tools of Differential Geometry. In detail we deal with Lie Theory, which is currently being investigated in Economics. Firstly we indicate the conditions demanded to production functions in such studies, and the definition of a particular type of technical progress: the Lie type. For this type, the three properties of Lie groups have to be verified by the technical progress. We also show the use of Lie operator for economical interpretations, and for quantifying the impact of the technical progress. This operator allows us to answer Solow-Stigler Controversy. Finally we introduce some applications of Lie Theory in Economics, and suggest new future research lines they can generate. In this way, our main aim is to show the actual and future applications of Lie Theory in Economics

Suggested Citation

  • Fedriani Martel, Eugenio M. & Tenorio Villalón, Ángel F., 2006. "Progreso técnico: una aproximación desde la Teoría de Grupos de Transformaciones de Lie = Technical Progress: an Approach from Lie Transformation Group Theory," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 1(1), pages 5-24, June.
  • Handle: RePEc:pab:rmcpee:v:1:y:2006:i:1:p:5-24
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    Keywords

    cambio técnico; progreso técnico tipo Lie; holoteticidad; Technical change; Lie type of technical progress; holotheticity;

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General

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