Production functions having the CES property

Losonczi, László (2010) Production functions having the CES property. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 26 (1). pp. 113-125. ISSN 0866-0182

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Abstract

To what measure does the CES (constant elasticity of substitution) property determine production functions? We show that it is not possible to find explicitely all two variable production functions f(x; y) having the CES property. This slightly generalizes the result of R. Sato [16]. We show that if a production function is a quasi-sum then the CES property determines only the functional forms of the inner functions, the outer functions being arbitrary (satisfying some regularity properties). If in addition to CES property homogeneity (of some degree) is required then the (twovariable) production function is either CD or ACMS production function. This generalizes the result of [4] and also makes their proof more transparent (in the special case of degree 1 homogeneity).

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