Pricing with Fairness

33 Pages Posted: 3 Oct 2019

See all articles by Maxime Cohen

Maxime Cohen

Desautels Faculty of Management, McGill University

Adam N. Elmachtoub

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

Xiao Lei

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: September 24, 2019

Abstract

Discriminatory pricing -- offering different prices to different customers -- has become common practice. While it allows sellers to increase their profits, it also raises several concerns in terms of fairness. This topic has received extensive attention from both the media and regulatory agencies. In this paper, we consider the problem of pricing to different groups under fairness constraints. We first propose four definitions: fairness in price, demand, consumer surplus, and no-purchase valuation. We then analyze the pricing strategy of a profit-maximizing seller, and the impact of imposing fairness on the seller's profit, consumer surplus, and social welfare. Under linear or exponential demand, we show that imposing a small amount of fairness in price or no-purchase valuation increases social welfare, whereas fairness in demand or surplus reduces social welfare. We fully characterize the impact of imposing different types of fairness for linear demand. We also discover that imposing too much price fairness may result in a lower social welfare relative to imposing no price fairness. We then show computationally that most of our findings continue to hold for three common non-linear demand models: exponential, logistic, and log-log. Our results and insights provide a first step in understanding the impact of imposing fairness in the context of pricing.

Keywords: pricing, fairness, social welfare

Suggested Citation

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

Maxime 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)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

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

HOME PAGE: http://www.columbia.edu/~xl2625/

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