We consider the problem of a monopolist with an object to sell before some deadline, facing n buyers with independent private values. The monopolist posts prices but has no commitment power. We show that the monopolist can always secure at least the larger of the static monopoly profit and the revenue from a Dutch auction with a zero reserve price. When there are only a few buyers, her profits are higher than this bound, and she essentially posts unacceptable prices up to the very end, at which point prices collapse to a “reservation price” that exceeds marginal cost. When there are many buyers, the seller abandons this reservation price in order to more effectively screen buyers. Her optimal policy then replicates a Dutch auction, with prices decreasing continuously over time. With more units to sell, prices jump up after each sale.
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 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.