We present models in which price discrimination in the context of a two-part price can occur in some competitive markets. Purchases take place in groups, which choose which firms to patronize. While firms are perfectly competitive with respect to groups, they have some market power over individual consumers, who are constrained by their groups' choices. We find that firms will charge an entry fee that is below marginal cost, and the second part of the price is marked up above marginal cost. The markup not only is positive but increases with the quality of the product.