Auctions often involve the sale of many related goods: Treasury, spectrum, and electricity auctions are examples. In multi-unit auctions, bids for marginal units may affect payments for inframarginal units, giving rise to “demand reduction” and furthermore to incentives for shading bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings of the two formats are ambiguous.