Monotonic assignment rules and common pricing

In this paper we study the production and pricing of a good by a single supplier (such as a monopolist or government) under some given optimality criterion—for example, profit maximization or social benefit maximization. In general, this may require discriminatory pricing. The primary focus here is on the pricing policy and whether it is possible to achieve the same objective value with common pricing—where each individual acquiring the good pays the same price. We consider the case of declining (marginal) cost and show that for a large class of problems, optimality is achievable with common pricing. Because the environment is one of incomplete information, incentive and participation constraints are important restrictions on the problem. We frame the discussion in terms of interim expected utility. When ex post restrictions are considered, the problem is altered substantially, and the value of the objective may be lower under common pricing.