We consider the problem of a monopolist who must sell her inventory before some deadline, facing n buyers with independent private values. The monopolist posts prices but has no commitment power. The seller faces a basic trade-off between imperfect price discrimination and maintaining an effective reserve price. When there is only one unit and only a few buyers, the seller essentially posts unacceptable prices up to the very end, at which point prices collapse in a series of jumps to a "reserve

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... price" that exceeds marginal cost. When there are many buyers, the seller abandons this reserve price in order to more effectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time.