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Journal of Convex Analysis 12 (2005), No. 2, 431--446
Copyright Heldermann Verlag 2005

Integrability of Pseudomonotone Differentiable Maps and the Revealed Preference Problem

Jean-Pierre Crouzeix
LIMOS, CNRS-UMR 6158, Université Blaise Pascal, 63177 Aubičre, France

Tamás Rapcsák
Computer and Automation Institute, Hungarian Academy of Sciences, 1518 Budapest, Hungary


\newcommand{\R}{{\mathbb R}} \newcommand{\norm}{\vert\vert} The problem considered is as follows: given $C\subset \R^n$ and $F:C\rightarrow \R^n$ differentiable, find $f:C\rightarrow \R$ differentiable such that $\norm \nabla f(x)\norm^{-1} \nabla f(x) = \norm F(x) \norm^{-1}F(x)$ for all $x\in C$. Conditions for $f$ to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.

Keywords: Generalized convexity, generalized monotonicity, consumer theory, direct and indirect utility functions, revealed preference theory.

MSC: 90A40, 90C26; 52A41, 47N10, 47H05

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