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Bilateral Trade with Multiunit Demand and Supply

Author

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  • Simon Loertscher

    (Department of Economics, University of Melbourne, Melbourne, Victoria 3010, Australia)

  • Leslie M. Marx

    (The Fuqua School of Business, Duke University, Durham, North Carolina 27708)

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.

Suggested Citation

  • Simon Loertscher & Leslie M. Marx, 2023. "Bilateral Trade with Multiunit Demand and Supply," Management Science, INFORMS, vol. 69(2), pages 1146-1165, February.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:2:p:1146-1165
    DOI: 10.1287/mnsc.2022.4399
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    References listed on IDEAS

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    8. Simon Loertscher & Leslie M. Marx, 2022. "Incomplete Information Bargaining with Applications to Mergers, Investment, and Vertical Integration," American Economic Review, American Economic Association, vol. 112(2), pages 616-649, February.
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    13. Delacrétaz, David & Loertscher, Simon & Marx, Leslie M. & Wilkening, Tom, 2019. "Two-sided allocation problems, decomposability, and the impossibility of efficient trade," Journal of Economic Theory, Elsevier, vol. 179(C), pages 416-454.
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    Cited by:

    1. Gal Danino & Moran Koren & Omer Madmon, 2023. "The Multi-BMBY Mechanism: Proportionality-Preserving and Strategyproof Ownership Restructuring in Private Companies," Papers 2311.06780, arXiv.org, revised Oct 2024.

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