We examine the theoretical properties of the proposed auction format for Medicare Durable Medical Equipment. The format was used in a pilot auction in November 2009 covering nine cities and is planned for use in 100 cities in 2010. Two unusual features of the Medicare auction are 1) non-binding bids and 2) a median pricing rule in which winners are paid the median winning bid, rather than the clearing price where supply and demand balance. We show that these two features lead to complete market failure. Bidders in equilibrium submit low-ball bids resulting in a median below each bidder’s cost. As a result, bidders refuse to sign supply contracts and no quantity is supplied. In sharp contrast, the standard clearing-price auction has each bidder bid true costs as a dominant strategy, resulting in competitive equilibrium prices and full efficiency. Recent Caltech experiments (Kim et al. 2010) confirm these theoretical findings.