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Production functions having the CES property. (English) Zbl 1224.62143

Summary: To what extent does the CES (constant elasticity of substitution) property determine production functions. We show that it is not possible to find explicitly all two-variable production functions \(f(x, y)\) having the CES property. This slightly generalizes a result of R. Sato [Econometrica 43, 999–1003 (1975; Zbl 0328.90020)]. We show that if a production function is a quasi-sum then the CES property determines only the functional form of the inner functions, the outer functions being arbitrary (satisfying some regularity properties). If in addition to the CES property homogeneity (of some degree) is required, then the (two-variable) production function is either a CD or ACMS production function. This generalizes a result of K.J. Arrow et al. [Capital-labor substitution and economic efficiency. Rev. Econom. Stat. 43, No. 3, 225–250 (1961)] and also makes their proof more transparent (in the special case of degree 1 homogeneity).

MSC:

62P20 Applications of statistics to economics
91B38 Production theory, theory of the firm
90B30 Production models

Keywords:

elasticity

Citations:

Zbl 0328.90020
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