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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

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 12414.

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Date of creation: 30 Dec 2008
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Handle: RePEc:pra:mprapa:12414

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Keywords: Microeconomics; production; substitution;

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References

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  1. 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.
  2. Kim, H Youn, 2000. "The Antonelli versus Hicks Elasticity of Complementary and Inverse Input Demand Systems," Australian Economic Papers, Wiley Blackwell, vol. 39(2), pages 245-61, June.
  3. Blackorby, Charles & Russell, R Robert, 1981. "The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and Its Relationship to the Hicks and Allen Elasticities," Review of Economic Studies, Wiley Blackwell, vol. 48(1), pages 147-58, January.
  4. 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 546-52, August.
  5. 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 882-88, September.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. "Elasticities of Substitution and Complementarity" to be published in Journal of Productivity Analysis
    by David Stern in Stochastic Trend on 2010-12-08 21:02:00
  2. Paper Accepted at Economics Letters
    by David Stern in Stochastic Trend on 2010-05-19 22:59:00
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Cited by:
  1. Stern, David I., 2009. "Interfuel Substitution: A Meta-Analysis," Research Reports 94882, Australian National University, Environmental Economics Research Hub.
  2. Stern, David I, 2008. "Elasticities of Substitution and Complementarity," MPRA Paper 12454, University Library of Munich, Germany.

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