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

12 Pages Posted: 12 Jan 2009  

David I. Stern

Australian National University (ANU) - Crawford School of Public Policy

Date Written: January 12, 2009

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, non-separability 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.

Keywords: Microeconomics, production, substitution

JEL Classification: B21, D24

Suggested Citation

Stern, David I., Derivation of the Hicks Elasticity of Substitution from the Input Distance Function (January 12, 2009). Available at SSRN: https://ssrn.com/abstract=1326287 or http://dx.doi.org/10.2139/ssrn.1326287

David I. Stern (Contact Author)

Australian National University (ANU) - Crawford School of Public Policy ( email )

ANU College of Asia and the Pacific
J.G. Crawford Building, #132, Lennox Crossing
Canberra, Australian Capital Territory 0200
Australia

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