Bilateral Trade with Multiunit Demand and Supply

• 成果类型: Article
• 署名作者: Loertscher, Simon; Marx, Leslie M.
• 署名单位: University of Melbourne; Duke University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2022.4399
• 发表日期: 2023
• 页码: 1146-1165
• 关键词: Substitutes; complements; multiunit demand and supply; geometric utility; impossibility of efficient trade

摘要

We study a bilateral trade problem with multiunit demand and supply and one-dimensional private information. Each agent geometrically discounts additional units by a constant factor. We show that when goods are complements, the incentive problem measured as the ratio of second-best to first-best social surplus-becomes less severe as the degree of complementarity increases. In contrast, if goods are substitutes and each agent's distribution exhibits linear virtual types, then this ratio is a constant. If the bilateral trade setup arises from prior vertical integration between a buyer and a supplier, with the vertically integrated firm being a buyer facing an independent supplier, then the ratio of second-best to first-best social surplus is, in general, not monotone in the degree of complementarity when products are substitutes and is increasing when products are complements. Extensions to profit maximization by a market maker and a discrete public good problem show that the broad insight that complementarity of goods mitigates the incentive problem generalizes to these settings.