Optimal capacity allocation in a vertical industry

We examine how a social planner should allocate productive capacity in a downstream industry when, upstream, there is an efficient supplier and a set of less efficient suppliers of an essential input. We show that optimal allocation consists of setting a large quota and small quotas for the remaining capacity. This allows the planner, without necessarily harming consumers, to reap licensing rents above those that would be obtained in a competitive downstream market or under public management of capacity. We also discuss circumstances under which a use-or-lose requirement for the large quota is welfare enhancing or welfare reducing, and under which banning price discrimination in the intermediate market may be socially optimal.