Derivation of the Hicks Elasticity of Substitution from the Input Distance Function
AbstractThe 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 12414.
Date of creation: 30 Dec 2008
Date of revision:
Microeconomics; production; substitution;
Find related papers by 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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- 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.
- 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.
- 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.
- 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.
- 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.
Blog mentionsAs found by EconAcademics.org, the blog aggregator for Economics research:
- "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
- Paper Accepted at Economics Letters
by David Stern in Stochastic Trend on 2010-05-19 22:59:00
- Stern, David I, 2008.
"Elasticities of Substitution and Complementarity,"
12454, University Library of Munich, Germany.
- David I. Stern, 2009.
"Interfuel Substitution: A Meta-Analysis,"
Departmental Working Papers
2009-06, The Australian National University, Arndt-Corden Department of Economics.
- Stern, David I., 2009. "Interfuel Substitution: A Meta-Analysis," Research Reports 94882, Australian National University, Environmental Economics Research Hub.
- David I.Stern, 2009. "Interfuel Substitution: A Meta Analysis," Environmental Economics Research Hub Research Reports 0933, Environmental Economics Research Hub, Crawford School of Public Policy, The Australian National University.
- Stern, David I., 2009. "Interfuel Substitution: A Meta-Analysis," MPRA Paper 13734, University Library of Munich, Germany.
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