Deriving multiple-input production and utility functions from elasticities of substitution functions *

Saad Labyad and Mehdi Senouci
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Saad Labyad: University of Oxford

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Abstract: For each production or utility function, we can define the corresponding elasticities of substitution functions; but is the reverse true? This paper shows that yes, and that this link is fruitful. By inverting the system of partial differential equations defining the elasticities of substitution functions, we uncover an analytical formula which encompasses all production and utility functions that are admissible in Arrow-Debreu equilibria. We highlight the "Constant Elasticities of Substitution Matrix" (CESM) class of functions which, unlike the CES functions, does not assume uniform substitutability among all pairs of goods. A shortcoming of our method is that it permits only to control for local concavity while it is difficult to control for global concavity.

Keywords: Production functions; Utility functions; Elasticity of substitution; Marginal productivity; Marginal utility; Factor shares (search for similar items in EconPapers)
Date: 2018-09-03
New Economics Papers: this item is included in nep-upt
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