Computer Science Department
School of Computer Science, Carnegie Mellon University


A Theory of Loss-leaders:
Making Money by Pricing Below Cost

Maria-Florina Balcan, Avrim Blum,
T-H. Hubert Chan, Mohammad Taghi Hajiaghai

July 2007


Keywords: Pricing below cost, unlimited supply, combinatorial auctions, single minded bidders, mechanism design, profit maximization

We consider the problem of assigning prices to goods of fixed marginal cost in order to maximize revenue in the presence of single-minded customers. We focus in particular on the question of how pricing certain items below their marginal costs can lead to an improvement in overall profit, even when customers behave in a fully rational manner. We develop two frameworks for analyzing this issue that we call the rebate and coupon models, and examine both fundamental "profitability gaps" (to what extent can pricing below cost help to improve profit) as well as algorithms for pricing in these models in a number of settings. To design our algorithms, we use several tools including a particular DAG representation and graph decomposition techniques which may be of independent interest.

19 pages

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