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A Characterization of Quasi-concave Function in View of the Integrability Theory

  • Yuhki Hosoya
Chapter
Part of the Advances in Mathematical Economics book series (MATHECON, volume 18)

Abstract

Let g and u be C 1-class real-valued functions that satisfy the Lagrange multiplier condition Du = λ g and Du ≠ 0. In this paper, we show that u is quasi-concave if and only if g satisfies an inequality which is related to the Bordered Hessian condition even if both of u and g are C 1 rather than C 2.

Key words

Integrability Inverse demand function Quasi-concavity Utility function 

Notes

Acknowledgements

We are grateful to Shinichi Suda and Toru Maruyama for their helpful comments and suggestions.

References

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    Hosoya, Y.: Elementary form and proof of the Frobenius theorem for economists. Adv. Math. Econ. 16, 39–52 (2012)CrossRefMathSciNetGoogle Scholar
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    Otani, K.: A characterization of quasi-concave functions. J. Econ. Theory 31, 194–196 (1983)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Graduate School of EconomicsKeio UniversityTokyoJapan

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