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- Title
A Note on Elasticity of Substitution Functions.
- Authors
Lau, Lawrence J.
- Abstract
The article shows that the factor cost function up to m arbitrary functions of output. In the case of homotheticity, the set of elasticity of substitution functions characterize the cost function up to one arbitrary function of output and m−1 arbitrary constants. In the case of constant returns, the set of elasticity of substitution functions characterizes the cost function up to m arbitrary constants. Because of the duality between cost functions and production functions, this implies that the technology is characterized by the set of elasticity of substitution functions up to in arbitrary functions of output in general, up to one arbitrary function of output and m−1 arbitrary constants in the case of homotheticity and up to in arbitrary constants in the case of constant returns. The method used in the article is perfectly general and may be used to prove similar results for other definitions of elasticity of substitution, including, for instance, the direct elasticity of substitution and the shadow elasticity of substitution. In all of these cases it can be shown that the technology is characterized by the respective set of elasticity of substitution functions up to m arbitrary functions of one variable. The argument used here depends on the assumption of analyticity. It may be useful to investigate the effect of a weakening of the analyticity assumption.
- Subjects
PRODUCTION functions (Economic theory); ELASTICITY (Economics); SUBSTITUTION (Economics); CONSUMPTION (Economics); COST; ECONOMIES of scale; FUNCTIONAL analysis
- Publication
Review of Economic Studies, 1976, Vol 43, Issue 2, p353
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2297330