The Review of Economics and Statistics Vol. 53 No. 3 1971
A Production Model with Two Labor Inputs: A Comment
Abstract
V faL-e + [p(L1 K) -e]K-e} -l/e (1) where 4 is an arbitrary function. In the particular case where 4' 4 (L11K) is constant and e--O, the production function becomes V = r1 KA L1(L1/L)X. (2) While testing the ability of the production function (2) to explain the international pattern of labor productivity and wages, Mitchell does not present all properties of that function. Indeed, one special feature of the function (2) is to be easily workable for empirical purposes, if we have statistical data on physical quantities of the inputs and output, or on relative shares. Another main feature lies in the properties of that function, concerning the partial elasticities of substitution between pairs of inputs. This note considers those two points, with emphasis laid on the second one. We show that some of these partial elasticities of substitution are not constant. Uzawa [6] has characterized the class of constant Allen elasticity of substitution production functions (CAES), and McFadden [3] the class of constant direct partial elasticity of substitution production functions (CDES) as well as the class of constant shadow partial elasticity of substitution production functions. The function (2) is neither of the CAES class, nor of the CDES class. Hence, we must calculate the partial elasticities of substitution, according to each of the two conventional definitions. We begin with the Allen partial elasticity of substitution, as reformulated by Uzawa [6, p. 293] c a2 C
- DOI
- 10.2307/1937974
- Volume
- 53
- Issue
- 3
- Pages
- 288
- Sources
- openalex crossref