Buyer's preferences over auctions depend on their measure of absolute risk aversion. If it is constant and they have independent private values, they are indifferent between a first-price auction (FPA), a second-price auction (SPA), and a first-price auction in which the number of bidders is revealed before bids are taken (FPA- R). If they have decreasing absolute risk aversion, they prefer the SPA to the FPA-R to the FPA. Their preference for the SPA is diminished to the extent that their values are affiliated. Affiliation also causes them to prefer the number of bidders to be revealed, whereas the seller then prefers to keep it secret.

We address the monopoly problem of designing and pricing a product line of goods distinguished by different quality and warranty levels. Consumers vary in their evaluations of these attributes, so that the problem is one of screening. It is sufficiently complex that the local approach commonly used does not work. Instead, we use new techniques for dealing with incentive constraints between nonadjacent consumer types. These techniques allow us to characterize optimal allocations that may not be monotonic. In particular, although the more eager types of buyer do pay higher prices and yield the monopoly higher profit, they may receive lower quality or lower warranty coverage. We find preference restrictions that restore monotonicity: concave risk tolerance implies that warranty coverage increases in type, and constant absolute risk aversion implies that quality increases in type.