Discrete/continuous choice models and representative consumer theory

We establish the integrability of demand for a broad class of discrete/continuous choice, additive, homothetic random-utility models of individual consumer behavior with perfect substitutes preferences (linear indifference curves) 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 literature 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/continuous 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/continuous 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 and integrability no longer holds. If we relax homotheticity, we find that integrability generically fails to hold except in the special case of IIA preferences.