The Law of Demand When Income Is Price Dependent

We identify sufficient conditions which guarantee that aggregate demand is approximately linear in income and satisfies a restricted form of the law of demand in a market where income is price dependent. The conditions involve the way preferences are distributed: loosely speaking, preferences have to be sufficiently heterogeneous. The definition of heterogeneity we use is similar to Grandmont (1992) but it is applied to homothetic transformations as introduced in Jerison (1982) and Grandmont (1987) and allows for the possibility of atoms. Another condition is that the distributions of preferences and income are independent. In exchange and production economies, our result guarantees the uniqueness of the price equilibrium and its stability under the Walras' tatonnement.