Behavioral Heterogeneity: Pareto Distributions of Homothetic Preference Scales and Aggregate Expenditures Income Elasticities

We evaluate the income elasticity of the aggregate budget share spent on a sub-group of commodities, in a competitive framework, by a continuum of agents having the same income, but heterogeneous behavior described by an "homothetic preferences scaling factor" having a bounded Pareto distribution in the population. If individual budget share increases globally significantly in the limit from low to large incomes, aggregate budget share is locally increasing with medium range incomes when the logarithm of the heterogeneity factor has an increasing (exponential) density with a large support. Aggregate income elasticity converges to that exponential density parameter when its support becomes infinitely large. Symmetric results hold in the decreasing case. Applications are made to market expenditures, wealth effects on portfolio choice with many risky assets, concave expenditures, that are compatible with standard (expected) utility maximization or other "behavioral" decision making processes.