A buyer with downward sloping demand faces a number of unit-supply sellers. This paper characterizes optimal auctions in this setting. For the symmetric case, a uniform auction (with price equal to lowest rejected offer) is optimal whencomplemented with reserve prices for different quantities acquired. For asymmetric sellers, the optimal distortions are familiar.

The problem is similar to the third-degree discriminating monopsonist problem, just as in the unit (flat) demand case (Bulow-Roberts, 1989), and when the number of sellers (and the demand) grows their outcomes approach at the speed of the law of large numbers.