Price Discrimination with Fairness Constraints

54 Pages Posted: 3 Oct 2019 Last revised: 28 Sep 2021

See all articles by Maxime C. Cohen

Maxime C. Cohen

Desautels Faculty of Management, McGill University

Adam N. Elmachtoub

Department of Industrial Engineering and Operations Research & Data Science Institute, Columbia University

Xiao Lei

HKU Business School, The University of Hong Kong

Date Written: September 24, 2019

Abstract

Price discrimination strategies, which offer different prices to customers based on differences in their valuations, have become common practice. While it allows sellers to increase their profits, it also raises several concerns in terms of fairness, e.g., by charging higher prices (or denying access) to protected minorities in case they have higher (or lower) valuations than the general population. This topic has received extensive attention from media, industry, and regulatory agencies. In this paper, we consider the problem of setting prices for different groups under fairness constraints. We first propose four definitions: fairness in price, demand, consumer surplus, and no-purchase valuation. We prove that satisfying more than one of these fairness constraints is impossible even under simple settings. We then analyze the pricing strategy of a profitmaximizing seller and the impact of imposing fairness on the seller’s profit, consumer surplus, and social welfare. Under a linear demand model, we find that imposing a small amount of price fairness increases social welfare, whereas too much price fairness may result in a lower welfare relative to imposing no fairness. On the other hand, imposing fairness in demand or consumer surplus always decreases social welfare. Finally, no-purchase valuation fairness always increases social welfare. We observe similar patterns under several extensions and for other common demand models numerically. Our results and insights provide a first step in understanding the impact of imposing fairness in the context of discriminatory pricing.

Keywords: pricing, fairness, social welfare

Suggested Citation

Cohen, Maxime C. and Elmachtoub, Adam and Lei, Xiao, Price Discrimination with Fairness Constraints (September 24, 2019). Available at SSRN: https://ssrn.com/abstract=3459289 or http://dx.doi.org/10.2139/ssrn.3459289

Maxime C. Cohen

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Adam Elmachtoub

Department of Industrial Engineering and Operations Research & Data Science Institute, Columbia University ( email )

535F S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

HOME PAGE: http://www.columbia.edu/~ae2516/

Xiao Lei (Contact Author)

HKU Business School, The University of Hong Kong ( email )

Hong Kong
China

HOME PAGE: http://www.xiao-lei.org

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
1,583
Abstract Views
4,939
rank
16,665
PlumX Metrics