Collaborative Research: Revenue Maximization in Multi-Object Sales

University Of Maryland, College Park, College Park MD

Investigators

Abstract

Consider a monopolist who intends to maximize her revenue from selling several objects but does not know the potential buyers' exact valuations for those objects. Situations of this sort are common -- a government agency selling spectrum licenses to one or many potential buyers, an automotive firm pricing a variety of options for its new models, an art collector deciding whether to sell all or part of the collection. When the seller only has a single object to sell, it is well known how the sale should be conducted to maximize revenue. When the seller has two or more objects to sell, it is not known in general how the sale should be conducted in order to maximize revenue. The project addresses this question in three related parts. First, the study investigates the properties of all trading institutions that may be revenue maximizing. Second, it examines the optimality of a very simple and commonly used institution, "bundling," the posting of a price for each sub-collection or bundle of goods. The study offers conditions under which bundling is optimal. Finally, it explores the relationship between optimal pricing schedules in the monopolist problem and the determination of optimal reserve prices in multi-unit auctions. The project contributes to our understanding in several related areas -- multi-dimensional mechanism design, multi-unit auctions, and price discrimination and bundling. Firms and governments frequently must buy or sell many goods profitably. The project offers answers to how this may be achieved. It also provides guidance to antitrust enforcement. The bundling of products to raise revenues often implies some loss in social efficiency. An understanding of the nature of revenue-maximizing schemes is necessary in order to evaluate the social costs of this behavior.