Econometrica Vol. 3 No. 4 1935
Demand in Relation to the Income Curve
Abstract
1. General notions.-Assume that we have to do with a homogeneous population, whose distribution with respect to the individual (or per family) income x is described by the function y(x). For a price of a commodity A, the total expenditure of a person for this commodity is a function of his income WA(X), making the total expenditure of the population fxoo WA(x)y(x)dx, xO being the minimum income. It should be noted that (1) w is really a regression function, although for theoretical purposes we shall regard it as a function proper; (2) the commodity A may be a one-price commodity, such as crystalline sugar, or a manypriced one, such as cigarettes; in the latter case, when speaking of a given price, we really think of a price system. The function w, which we may call-according to Frisch's proposal -an Engel function, is, of course, limited in value by the inequality 0_ WA (x) <x. As x increases, WA(X) may increase in proportion to x, more slowly than x, or faster than x. Accordingly, we shall say that the elasticity of expenditure for A with respect to income is equal to, less, or greater than, unity, the elasticity being defined as follows:
- DOI
- 10.2307/1905632
- Volume
- 3
- Issue
- 4
- Pages
- 411
- Sources
- openalex crossref