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A Note on Allen-Uzawa Partial Elasticities of Substitution: The Case of the Translog Cost Function

Author

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  • Christev, Atanas

    (Heriot-Watt University, Edinburgh)

  • Featherstone, Allen

    (Kansas State University)

Abstract

This note provides a useful property of the Allen-Uzawa partials for the translog cost function. It also suggests how the main results extend to any functional form with certain properties. The curvature of the Allen-Uzawa matrix is the same as the curvature of the Hessian matrix. Intuitively and empirically, the Allen-Uzawa partials allow for the verification of curvature properties.

Suggested Citation

  • Christev, Atanas & Featherstone, Allen, 2007. "A Note on Allen-Uzawa Partial Elasticities of Substitution: The Case of the Translog Cost Function," IZA Discussion Papers 2712, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp2712
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    References listed on IDEAS

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    1. Charles Blackorby & R. Robert Russell, 1981. "The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and its Relationship to the Hicks and Allen Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 147-158.
    2. Ryan, David L & Wales, Terence J, 1998. "A Simple Method for Imposing Local Curvature in Some Flexible Consumer-Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 331-338, July.
    3. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    4. Allen M. Featherstone & Charles B. Moss, 1994. "Measuring Economies of Scale and Scope in Agricultural Banking," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(3), pages 655-661.
    5. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    6. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    7. Ryan, David L. & Wales, Terence J., 2000. "Imposing local concavity in the translog and generalized Leontief cost functions," Economics Letters, Elsevier, vol. 67(3), pages 253-260, June.
    8. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    9. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 291-299.
    10. Anderson, R. K. & Moroney, J. R., 1993. "Morishima elasticities of substitution with nested production functions," Economics Letters, Elsevier, vol. 42(2-3), pages 159-166.
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    Cited by:

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    3. Elisa Meneghello & Martina Menon & Federico Perali & Furio Rosati, 2022. "The Shadow Wage of Child Labor: An application to Nepal," Working Papers 8, SITES.

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    More about this item

    Keywords

    translog cost function; elasticity of substitution; concavity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D20 - Microeconomics - - Production and Organizations - - - General

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