A Characterization of Quasi-concave Function in View of the Integrability Theory
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 wordsIntegrability Inverse demand function Quasi-concavity Utility function
We are grateful to Shinichi Suda and Toru Maruyama for their helpful comments and suggestions.