Advances in Mathematical Economics Volume 18 pp 135-140

Part of the Advances in Mathematical Economics book series (MATHECON, volume 18) | Cite as

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



Let g and u be C1-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 C1 rather than C2.

Key words

Integrability Inverse demand function Quasi-concavity Utility function 


  1. 1.
    Debreu, G.: Smooth preferences, a corrigendum. Econometrica 44, 831–832 (1976)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Hosoya, Y.: Elementary form and proof of the Frobenius theorem for economists. Adv. Math. Econ. 16, 39–52 (2012)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Otani, K.: A characterization of quasi-concave functions. J. Econ. Theory 31, 194–196 (1983)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Graduate School of EconomicsKeio UniversityTokyoJapan

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