The Law of Demand When Income Is Price Dependent
找到了保证总需求近似线性于收入并满足需求定律的充分条件，要求偏好足够异质且偏好与收入分布独立，这确保了价格均衡的唯一性和稳定性。
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.