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Optimal selling mechanisms for multiproduct monopolists : incentive compatibility in the presence of budget constraints

Author

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  • KLINGER MONTEIRO , Paulo

    (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

  • PAGE, Frank H. Jr.

    (Department of Finance, University of Alabama, Tuscaloosa, US)

Abstract

We demonstrate the existence of an optimal, individually rational, and incentive compatible selling mechanism for a multiproduct monopolist facing a market populated by consumers with budget constraints. Our main contribution is to show that, in general, when facing consumers with budget constraints the monopolist is able to maximize profits over the set of individually rational and incentive compatible selling mechanisms only if other goods are available and only if the monopolist’s goods are nonessential relative to other goods.

Suggested Citation

  • KLINGER MONTEIRO , Paulo & PAGE, Frank H. Jr., 1997. "Optimal selling mechanisms for multiproduct monopolists : incentive compatibility in the presence of budget constraints," LIDAM Discussion Papers CORE 1997011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1997011
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    2. Didier Laussel & Joana Resende, 2020. "Complementary Monopolies with asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 943-981, November.
    3. Shin‐kun Peng, 2004. "Spatial Monopoly with Product Differentiation," Southern Economic Journal, John Wiley & Sons, vol. 70(3), pages 646-660, January.
    4. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    5. Carlier, Guillaume & Zhang, Kelvin Shuangjian, 2020. "Existence of solutions to principal–agent problems with adverse selection under minimal assumptions," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 64-71.
    6. Naoki Kojima, 2014. "Mechanism design to the budget constrained buyer: a canonical mechanism approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 693-719, August.
    7. Carlier, Guillaume, 2001. "A general existence result for the principal-agent problem with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 129-150, February.
    8. Kelvin Shuangjian Zhang, 2017. "Existence in Multidimensional Screening with General Nonlinear Preferences," Papers 1710.08549, arXiv.org, revised Dec 2018.
    9. PAGE, Frank, 2000. "Competitive selling mechanisms: the delegation principle and farsighted stability," LIDAM Discussion Papers CORE 2000021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Pass, Brendan, 2012. "Convexity and multi-dimensional screening for spaces with different dimensions," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2399-2418.
    11. Guillaume Carlier & Kelvin Shuangjian Zhang, 2019. "Existence of solutions to principal-agent problems with adverse selection under minimal assumptions," Papers 1902.06552, arXiv.org, revised Mar 2020.
    12. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    13. Gautier, Axel & Mitra, Manipushpak, 2002. "Financing Infrastructure under Budget Constraint," Bonn Econ Discussion Papers 15/2002, University of Bonn, Bonn Graduate School of Economics (BGSE).
    14. Kelvin Shuangjian Zhang, 2019. "Existence in multidimensional screening with general nonlinear preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 463-485, March.
    15. Aloisio Araujo & Sergei Vieira & Braulio Calagua, 2022. "A necessary optimality condition in two-dimensional screening," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 781-806, April.
    16. Rosario Maggistro & Paolo Pellizzari & Elena Sartori & Marco Tolotti, 2022. "Dangerous tangents: an application of $$\Gamma $$ Γ -convergence to the control of dynamical systems," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 451-480, December.

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