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

Saad Labyad (1) , Mehdi Senouci (2)

1 University of Oxford
2 LGI - Laboratoire Génie Industriel - EA 2606

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.

Mots clés: Production functions; Utility functions; Elasticity of substitution; Marginal productivity; Marginal utility; Factor shares

Domaines: Economies et finances

Saad Labyad, Mehdi Senouci. Deriving multiple-input production and utility functions from elasticities of substitution functions *. 2018. ⟨hal-01866275⟩