Bilateral Trade with Multiunit Demand and Supply

Simon Loertscher and Leslie M. Marx ()
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Leslie M. Marx: The Fuqua School of Business, Duke University, Durham, North Carolina 27708

Management Science, 2023, vol. 69, issue 2, 1146-1165

Abstract: 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.

Keywords: substitutes; complements; multiunit demand and supply; geometric utility; impossibility of efficient trade (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:69:y:2023:i:2:p:1146-1165

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