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 (linear indifference) preferences and divisible goods. We derive the corresponding indirect utility 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. These flexible discrete-choice formulations also overcome many of the known limitations of CES and its variants for equilibrium prices and markups, trade liberalization effects and welfare analysis. We also discuss quasi-linear integrability in the case where products are indivisible.