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Derivation of the Hicks Elasticity of Substitution from the Input Distance Function

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  • Stern, David I.

Abstract

The Hicks or direct elasticity of substitution is traditionally derived from the production function. This paper exploits duality theory to present a more general derivation from the input distance function, which is exactly dual to the Shadow Elasticity of Substitution. The new elasticity is more general than the traditional one as it can handle situations of technical inefficiency, nonseparability between inputs and outputs, and multiple outputs, but is equal to the traditional elasticity under the classical conditions. The new derivation is related to the Morishima and Antonelli Elasticities of Complementarity in the same way that the Shadow Elasticity of Substitution is related to the Morishima and Allen-Uzawa Elasticities of Substitution. Furthermore, distance (technical efficiency) is not constant for the Morishima and Antonelli Elasticities of Complementarity

Suggested Citation

  • Stern, David I., 2008. "Derivation of the Hicks Elasticity of Substitution from the Input Distance Function," MPRA Paper 12414, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:12414
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    File URL: https://mpra.ub.uni-muenchen.de/12414/1/MPRA_paper_12414.pdf
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    References listed on IDEAS

    as
    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. repec:bla:ausecp:v:39:y:2000:i:2:p:245-61 is not listed on IDEAS
    3. H. Youn Kim, 2000. "The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems," Australian Economic Papers, Wiley Blackwell, vol. 39(2), pages 245-261, June.
    4. Daniel McFadden, 1963. "Constant Elasticity of Substitution Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 73-83.
    5. Y. Mundlak, 1968. "Elasticities of Substitution and the Theory of Derived Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(2), pages 225-236.
    6. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    7. Kim, H Youn, 1992. "The Translog Production Function and Variable Returns to Scale," The Review of Economics and Statistics, MIT Press, vol. 74(3), pages 546-552, August.
    8. Hongil Lim & C. Richard Shumway, 1997. "Technical Change and Model Specification: U.S. Agricultural Production," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 79(2), pages 543-554.
    9. Berndt, Ernst R & Wood, David O, 1975. "Technology, Prices, and the Derived Demand for Energy," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 259-268, August.
    10. 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.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Paper Accepted at Economics Letters
      by David Stern in Stochastic Trend on 2010-05-20 03:59:00
    2. "Elasticities of Substitution and Complementarity" to be published in Journal of Productivity Analysis
      by David Stern in Stochastic Trend on 2010-12-09 03:02:00

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    Cited by:

    1. Sanzidur Rahman, 2010. "Women’s Labour Contribution to Productivity and Efficiency in Agriculture: Empirical Evidence From Bangladesh," Journal of Agricultural Economics, Wiley Blackwell, vol. 61(2), pages 318-342, June.
    2. David I. Stern, 2012. "Interfuel Substitution: A Meta‐Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 307-331, April.
    3. David Stern, 2011. "Elasticities of substitution and complementarity," Journal of Productivity Analysis, Springer, vol. 36(1), pages 79-89, August.

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    More about this item

    Keywords

    Microeconomics; production; substitution;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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