Demand Dispersion, Metonymy and Ideal Panel Data

In a generic competitive distribution economy with "increasing disper- sion," market demand satisfies the weak axiom of revealed preference and equilib- rium is unique. Increasing dispersion requires, roughly, that when the households' incomes rise slightly their demand vectors move apart. We show how to test for it using panel data with fixed relative prices under a "structural stability" hypothesis (10). We also show how to test for it using cross section data if the households' de- mand functions and incomes are independently distributed, or under a much weaker assumption that is implied by "metonymy." Metonymy, introduced in (6), relates the demand distribution of households with income x to the demand distribution that slightly poorer households would have if their incomes rose to x. We show that metonymy for a single population is untestable—even with ideal panel data that allow a direct test of increasing dispersion. Thus, cross section tests of increasing dispersion rely on an assumption that is not potentially falsifiable.