Discrete-Choice Models and Representative Consumer Theory

We establish the Hurwicz-Uzawa integrability of the broad class of discrete-choice additive random-utility models of individual consumer behavior with perfect substitutes preferences and divisible goods. We derive the corresponding indirect uility function and then establish a representative consumer formulation for this entire class of models. The representative consumer is always normative, facilitating aggregate welfare analysis. These findings should be of interest to the literatures in macro, trade, industrial organization, labor and ideal price index measurement that use representative consumer models, such as CES and its variants. Our results generalize such representative consumer formulations to the broad, empirically-relevant class of models of behavior that are routinely used in the discrete-choice analysis of micro data, including specifications that do not suffer from the IIA property and that allow for heterogeneous consumer preferences and incomes. When products are indivisible, we show that Hurwicz-Uzawa integrability fails; although some model variants might satisfy a stronger version of quasi-linear integrability.