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Selling two complementary goods

Author

Listed:
  • Komal Malik

    (Indian Statistical Institute, Delhi)

  • Kolagani Paramahamsa

    (Indian Statistical Institute, Delhi)

Abstract

A seller is selling a pair of complementary goods to an agent. The agent consumes the goods only in a certain ratio and freely disposes of excess in either of the goods. The value of the bundle and the ratio are private information of the agent. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price mechanism for a class of distributions; that is, it has a di↵erent posted price for each ratio report. We identify additional sufficient conditions on the joint distribution for a posted price to be an optimal mechanism. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio types are independently distributed.

Suggested Citation

  • Komal Malik & Kolagani Paramahamsa, 2021. "Selling two complementary goods," Discussion Papers 21-01, Indian Statistical Institute, Delhi.
    • Handle: RePEc:alo:isipdp:21-01
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    File URL: https://www.isid.ac.in/~epu/dispapers/dp21_01.pdf
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    optimal mechanism; complementary goods; multidimensional private information; posted-price mechanism;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly

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