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Concavity of the CES function via the power mean inequality

Author

Listed:
  • Vittorio Larocca
  • Luca Panaccione

Abstract

This note analyses the concavity and convexity of the constant elasticity of substitution function by means of the power mean inequality. The paper provides a straightforward proof based on the gradient inequality that characterizes concave and convex functions. The approach avoids the standard procedure based on checking the semidefiniteness of the Hessian matrix, which can become cumbersome when the number of commodities is large. The argument also generalizes Afriat's proof for the Cobb-Douglas function to the case of the CES function.

Suggested Citation

  • Vittorio Larocca & Luca Panaccione, 2023. "Concavity of the CES function via the power mean inequality," CIMEO Working Paper Series 172, Centre for Investigation and Modelling of Experimental Observations (CIMEO).
    • Handle: RePEc:ter:wpaper:00172
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    Keywords

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    JEL classification:

    • D10 - Microeconomics - - Household Behavior - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General

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