The aggregation problem in demand analysis and exchange equilibrium is studied by putting restrictions on the shape of the distribution of the agents’ characteristics. This is done by exploiting the ﬁnite dimensional linear structure induced on demand functions by aﬀine transformations of the commodity space (or household equivalence scales). Increasing the degree of behavioral heterogeneity in the household sector or more speciﬁcally, making the conditional distributions in each equivalence class of demand functions ﬁat enough, has an important regularizing influence on aggregate budget shares: market demand has a negative dominant diagonal Jacobian matrix, aggregate excess demand has the gross substitutability property, on a large set of prices. These facts have strong consequences for the unicity and stability of equilibrium as well as for the prevalence of the weak axiom of revealed preference in the aggregate in a private ownership Walrasian exchange model.
Grandmont, Jean-Michel, "Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem" (1991). Cowles Foundation Discussion Papers. 1230.