A characterization of monotone individual demand functions (Q1121754)

\textit{L. G. Mityushin} and \textit{W. M. Polterovich} [Ekonom. Mat. Metody 14, 122-128 (1978; Zbl 0408.90009)] have obtained a condition for the monotonicity of the demand function of an individual possessing a twice continuously differentiable utility function and involving such a utility function. Here monotonicity is characterized by means of differential geometric properties of the indifference surfaces and of the Engel curves. It turns out that those necessary and sufficient conditions can be regarded as a variant of the Mityushin-Polterovich condition specialized to a least concave utility function [see \textit{G. Debreu}, ibid. 3, 121-129 (1976; Zbl 0361.90007); and the author, ibid. 4, 1-56 (1977; Zbl 0361.90008)]. The results are extended to points where demand is not differentiable.