Abstract
This paper develops a model of nonlinear pricing with competition. The novel element is that each consumer's willingness to pay for quality is private information and is allowed to differ across brands. The consumer's preferences are represented by a multidimensional type containing the marginal value of quality for different products. Buyers with high willingness to pay for quality also display strong preferences for particular brands, and require higher discounts in order to switch away from their favorite product. Therefore, competition is fiercer for buyers with lower tastes for quality, and hence more elastic demands. This is in sharp contrast to earlier models in which competition is fiercer for higher-taste, more valuable buyers. In equilibrium, firms either compete intensively for the entire market (providing strictly positive rents to all consumers) or shut down the least profitable segment of the market. Quality levels are distorted downwards for all buyers, except for those with the highest type. The number of competing firms and the degree of correlation across brand preferences enhance the efficiency of the allocation.
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