Choice Models for Budgeted Demand and Constrained Allocation

Utility maximization is implicit in models of consumer choice, learning, forward-looking behavior and substitution. It is a central feature of models of market competition built on the aggregation of individual choices, and is assumed in nearly all quantitative models of behavior. Yet, while the assumption of utility maximization is widely present in marketing analysis, it is rarely expressed in a way that constrains the choices that are made. Constrained utility maximization leads to richer tradeoffs among the choices when budgets and allocations are assigned non-trivial roles in the choice process. In this paper we develop alternative models of constrained maximization, and show that models of constrained choice significantly improve the in-sample and predictive fit to the data in two conjoint studies -- a pharmaceutical study of physician drug allocation and a conjoint study of volumetric demand. Inferences about the budget constraint, and extensions to non-conjoint applications, are discussed