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

Author

Listed:
  • Saad Labyad

    (University of Oxford)

  • Mehdi Senouci

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

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.

Suggested Citation

  • Saad Labyad & Mehdi Senouci, 2018. "Deriving multiple-input production and utility functions from elasticities of substitution functions ," Working Papers hal-01866275, HAL.
    • Handle: RePEc:hal:wpaper:hal-01866275
    Note: View the original document on HAL open archive server: https://hal.science/hal-01866275
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    References listed on IDEAS

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    Keywords

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