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

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  • Atanas Christev
  • Allen Featherstone

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, the Allen-Uzawa partials allow for the verification of curvature properties.

Suggested Citation

  • Atanas Christev & Allen Featherstone, 2005. "A Note on Allen-Uzawa Partial Elasticities of Substitution: The Case of the Translog Cost Function," Working Papers E03, Department of Economics, School of Management and Languages, Heriot Watt University.
    • Handle: RePEc:hwe:hwecwp:2005-e03
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    5. 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.
    6. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

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    3. Dogan, Can & Akay, Gokhan H., 2016. "Multi-sector specific factors model with two mobile factors," International Review of Economics & Finance, Elsevier, vol. 46(C), pages 136-147.

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    More about this item

    Keywords

    Elasticity of Substitution; Translog Cost Function; 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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