The system of inequalities ars > Xr—Xs

Abstract

In the investigation of preference orders which are explanations of expenditure data which associates a quantity vector xr with a price vector pr (r = 1, …, k), in respect to some n goods, there is considered the class of functions φ, with gradient g, which are increasing and convex in some convex region containing the points xr, such that gr = g(xr) has the direction of pr. † Let ur = pr/er, where so that