A property of the demand correspondence of a concave utility function

This paper establishes that the concavity of a consumer's utility function restricts the way in which the demand correspondence can fail to be lower semi-continuous. Two demand theoretic implications are drawn, one of which is that for a fixed endownment the demand correspondence is single-valued except on a set of prices having Lebesgue measure zero. There exist continuous, strictly monotone, and convex but not concavifiable preferences which violate this property.