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We analyze the problem of a seller of multiple identical units of a good who faces a set of buyers with unit demands, private information, and identity‐dependent externalities. We derive the seller's optimal mechanism and characterize its main properties. We show that the probability that a buyer obtains a unit is an increasing function of the externalities he generates and enjoys. Also, the seller's allocation of the units of the good need not be ex post efficient. As an illustration, we apply the model to the problem faced by a developer of a shopping mall who wants to allocate and price its retail space among anchor and non‐anchor stores. We show that a commonly used sequential mechanism is not optimal unless externalities are large enough.