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We analyze third degree price discrimination by an upstream monopolist to a continuum of heterogeneous downstream firms. The novelty of our approach is to recognize that customizing prices may be costly. As a consequence, partial price discrimination arises in equilibrium; in particular, we show that inefficient downstream firms receive personalized prices whereas efficient firms are charged a uniform price. The extreme cases of complete price discrimination and uniform price arise in our setting as particular cases, depending on the cost of customizing prices.

We analyze third degree price discrimination by an upstream monopolist to a continuum of heterogeneous downstream firms. The novelty of our approach is to recognize that customizing prices may be costly. As a consequence, partial price discrimination arises in equilibrium; in particular, we show that inefficient downstream firms receive personalized prices whereas efficient firms are charged a uniform price. The extreme cases of complete price discrimination and uniform price arise in our setting as particular cases, depending on the cost of customizing prices.