THE GEOMETRIC STRUCTURE OF SOME SYSTEMS OF DEMAND EQUATIONS

Consider the income compensation function Y = phi(p, y; p0) where Y, y is-an-element-of R are income levels and p, p0 is-an-element-of R(n) are prices. By holding po fixed we may interpret this as an n-paramete r transformation of R to R. With this interpretation we show that a sy stem of demand functions is additively separable in income and prices if and only if phi is a Lie transformation group on R. Sophus Lie's 18 88 classification of such groups into three fundamental types provides an alternative derivation of both the rank 3 condition of Gorman and the additively separable functional forms found by him.