On the "Law of Demand"
[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 ρ, with ρ(O) extgreater 0, then we show that the market demand function F(p) = ∫f(p, w)ρ(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.]