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

We consider the problem of assigning prices to goods of fixed marginal cost in order to maximize revenue in the presence of singleminded 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 discount and the 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 considered previously in the literature.