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- Title
Functional Separability and Partial Elasticities of Substitution.
- Authors
Russell, R. Robert
- Abstract
Theorems 3 and 4 of the recent paper by Berndt and Christensen [1] relate weak and strong separability [14] of a production function to certain equality restrictions on the partial elasticities of substitution. Both theorems are local. Also, homotheticity of the production function is a condition of both theorems but is not included in either set of necessary conditions. This note extends and strengthens the Berndt-Christensen results. First, Theorem 1 and Corollary 1 generalize Theorems 3 and 4 of Berndt and Christensen by showing that the relations hold globally (once certain details regarding differentiability are taken into account). Second, Theorem 2 and Corollary 2 strengthen the Berndt-Christensen results by showing that homotheticity of the specific aggregator functions (homothetic separability [2, 10]), but not necessarily of the production function itself, is sufficient for separability to induce the appropriate restrictions on the partial elasticities of substitution. Third, Theorem 3 and Corollary 3.1 show that homotheticity of the specific aggregator functions is a necessary condition for weak, and hence strong, separability together with equality restrictions on the partial elasticities of substitution. Finally, three additional corollaries (1.2, 2.2 and 3.2) of this note relate the partial elasticity of substitution restrictions to homothetically recursive production functions [3].
- Subjects
PRODUCTION functions (Economic theory); SUBSTITUTION (Economics); ECONOMICS; ELASTICITY (Economics); ECONOMIC models; PRODUCTION (Economic theory); ECONOMIES of scale; CAPITAL productivity
- Publication
Review of Economic Studies, 1975, Vol 42, Issue 1, p79
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2296821