The Geometric Structure of Some Systems of Demand Equations

Document Type

Article

Publication Date

1993

Publisher

Elsevier B.V.

Abstract

Consider the income compensation function Y = φ(p, y; p0) where Y, y ∈ R are income levels and p, p0 ∈ Rn are prices. By holding p0 fixed we may interpret this as an n-parameter transformation of R to R. With this interpretation we show that a system of demand functions is additively separable in income and prices if and only if φ is a Lie transformation group on R. Sophus Lie's 1888 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.

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