Quasiconcavity of a separable product of utility functions

ABSTRACT

The nontrivial problem of the quasiconcavity of a separable sum of utility functions has been studied and solved by Debreu-Koopmans and Crouzeix-Lindberg via the introduction of convexity indices. This paper studies the equivalent problem of the quasiconcavity of a separable products. This approach makes the proofs easier.

KEYWORDS:

• Utility functions
• log-concave functions
• additive and multiplicative separability
• additive and multiplicative concavity indices

Acknowledgements

The authors are grateful to two anonymous referees and the handling Editor for their valuable comments, which allowed us to improve the original presentation. They also express their special thanks to Professor Jean-Pierre Crouzeix for his private communication and his precious remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.