Threshold Utility Model with Applications to Retailing and Discrete Choice Models

Abstract

We propose and study a threshold utility model (TUM) where consumers buy any product whose net utility exceeds a non-negative, product-specific threshold. The thresholds are selected to maximize the expected surplus of the representative consumer subject to a bound on the expected number of selected products. We show that at optimality the thresholds are product-invariant and that the generalized extreme value (GEV) model is a special case of the TUM. The TUM is shown to yield higher consumer surplus than observing all the products' utilities and selecting the best when the bound is an integer. The model can also be applied with proxy utilities as in on-line shopping, and portfolio management. Comparative statics are applied to the threshold, the purchase probabilities and the expected surplus. Extensions to multi-unit TUM, weighted TUM, multiplicative TUM, discontinuous utility and bound-induced copulas are also considered. We also provide solutions to pricing and assortment optimization problems under the TUM.