When each bidder can buy at most one unit and the objects auctioned don't have secondary markets, the multi-unit auction has the following characteristics: (i) Under the competitive auction, the optimal bidding price equals the bidder's reservation price, but under the discriminative auction, the optimal bidding price is lower than the bidder's reservation price. (ii) Whether the bidder's expected utility is greater under the competitive auction than under the discriminative auction, or vice versa, depends on the bidder's utility function and risk attitude. (iii) Not until the auction is finished can the seller make sure whether the competitive auction or the discriminative auction brings him more expected revenues.