Revenue and Efficiency in Multi-Unit Uniform-Price Auctions

I show that in a private value multi-unit uniform-price auction, the reservation price increases both the efficiency and revenue. In equilibrium the difference between the true value of a unit and the submitted bid (shading) is different for each unit; therefore, the seller cannot allocate units efficiently, i.e., to those who value them the most. When the seller increases the reservation price, the bidders increase their bids on the units with greater shading. Then more often the units are allocated among those who have higher values for them, that is, efficient, although some bidders with a low value do not participate in the auction. In contrast to some other auction formats, for a low range of reservation prices, the higher the reservation price, the higher is both the expected efficiency and revenue