Screening with tolls and damages

A welfare-maximizing designer allocates two kinds of goods using two screening instruments: tolls, whose costs are separable from agents' values, and damages, which are more costly to agents whose values for the goods are higher. Tolls include payments, queues, and administrative burdens; damages include quality reductions, delays, and restrictions on use. When agents differ only in their value for one type of good, the designer can never gain from damaging it. However, using damages can be optimal when valuations for both goods are heterogeneous, as the two instruments can ``sort'' agents across the available options in different ways. I provide conditions under which the optimal mechanism includes a damaged option, as well as sufficient conditions under which it does not; in the latter case, the optimal mechanism posts ``market-clearing'' tolls for each good. Intuitively, damages are more likely to be optimal when values for the two goods are positively affiliated, and less likely when high value for one good predicts low value for the other.