p.997

On the "Law of Demand"

Werner Hildenbrand

Abstract

If all individuals of a given group have the same consumption behavior described by a common demand function f(p,w), which is assumed to satisfy the weak axion of revealed preference, and if the distribution of individual total expenditure w is given by a decreasing density p, with p(O) > 0, then we show that the market demand function F(p) = 2ff(p,w)p(w) dw is monotone, i.e., for any two price vectors p and q one has (q - p). (F(q) - F(p)) @<0. Thus, all partial market demand curves are decreasing. Furthermore, if the expansion paths of f for two different price vectors are different then we show that F is strictly monotone, which implies that the market demand function F satisfies the weak axiom of revealed preference. The result is applied to prove uniqueness and global stability in distribution economies and special exchange economies.