A NOTE ON PARETO LAWS

1. ESTEBAN [1986] launches the Weak-Weak Pareto Law (WWPL) for a set 'S- of densities f characterized by, among other things, finite means. He claims that a.) for all f e 7 this law is weaker than the Weak Pareto Law of MANDELBROT [1960] and b.) the subset P of ^ of densities satisfying this law together with two additional conditions, viz. mode existence and a constant declining ra te of income elasticity, coincides with ïï, the class of generalized gamma densities. This note shows that: (I) There exists a class of functions Z largely overlapping with!F in which WWPL is stronger than WPL: (Z n WWPL) c WPL. Z includes both functions with and functions without a finite mean. (II) There are no densities with a constant declining ra te of elasticity. As a result, <F is empty. 2. The Pareto distribution defined as: (1) F(x) = 1- (x/x f " x s = x, a>