Threshold Utility Model with Applications to Retailing and Discrete Choice Models

49 Pages Posted: 16 Jul 2019 Last revised: 30 Mar 2020

See all articles by Guillermo Gallego

Guillermo Gallego

HKUST

Ruxian Wang

Johns Hopkins University - Carey Business School

Date Written: July 6, 2019

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.

Keywords: Threshold Choice Model, Utility Maximization, Multiple Purchases, Pricing Analytics, Assortment Planning

Suggested Citation

Gallego, Guillermo and Wang, Ruxian, Threshold Utility Model with Applications to Retailing and Discrete Choice Models (July 6, 2019). Available at SSRN: https://ssrn.com/abstract=3420155 or http://dx.doi.org/10.2139/ssrn.3420155

Ruxian Wang

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

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