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

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Stern, David I.

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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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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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Related research
Keywords: Microeconomics; production; substitution;

Find related papers by JEL classification:
D21 - Microeconomics - - Production and Organizations - - - Firm Behavior
B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
D24 - Microeconomics - - Production and Organizations - - - Production; Capital and Total Factor Productivity; Capacity

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  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, Blackwell Publishing, vol. 48(1), pages 147-58, January. [Downloadable!] (restricted)
  4. Kim, H Youn, 2000. "The Antonelli versus Hicks Elasticity of Complementary and Inverse Input Demand Systems," Australian Economic Papers, Blackwell Publishing, vol. 39(2), pages 245-61, June. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Stern, David I., 2009. "Interfuel Substitution: A Meta-Analysis," MPRA Paper 13734, University Library of Munich, Germany. [Downloadable!]
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