Concavity of the CES function via the power mean inequality

Vittorio Larocca and Luca Panaccione

No 172, CIMEO Working Paper Series from Centre for Investigation and Modelling of Experimental Observations (CIMEO)

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.

Keywords: CES function; concavity; convexity; gradient inequality; power mean inequality (search for similar items in EconPapers)
JEL-codes: D10 D20 (search for similar items in EconPapers)
Date: 2023-05
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.dipecodir.it/wpcom/data/wp_no_172_2023.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ter:wpaper:00172

Access Statistics for this paper

More papers in CIMEO Working Paper Series from Centre for Investigation and Modelling of Experimental Observations (CIMEO) Contact information at EDIRC.
Bibliographic data for series maintained by Giovanni Di Bartolomeo ().