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Optimal Selling Mechanisms for Multiproduct Monopolists: Incentive Compatibility in the Presence of Budget Constraints

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  • Paulo Klinger Monteiro

    (Impa)

  • Frank H. Page Jr.

    (University of Alabama)

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 via examples and our existence result 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

  • Paulo Klinger Monteiro & Frank H. Page Jr., 1996. "Optimal Selling Mechanisms for Multiproduct Monopolists: Incentive Compatibility in the Presence of Budget Constraints," Microeconomics 9610002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpmi:9610002
    Note: Type of Document - Latex; prepared on Textures; to print on PostScript; pages: 18
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    1. I. V. Evstigneev, 1976. "Measurable Selection and Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 267-272, August.
    2. Artstein, Zvi, 1979. "A note on fatou's lemma in several dimensions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 277-282, December.
    3. Monteiro, Paulo Klinger, 1996. "A new proof of the existence of equilibrium in incomplete market economies," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 85-101.
    4. Page, F H, Jr, 1991. "Optimal Contract Mechanisms for Principal-Agent Problems with Moral Hazard and Adverse Selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 323-338, October.
    5. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    6. Leonard J. Mirman & David Sibley, 1980. "Optimal Nonlinear Prices for Multiproduct Monopolies," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 659-670, Autumn.
    7. Page, Frank H, Jr, 1992. "Mechanism Design for General Screening Problems with Moral Hazard," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 265-281, April.
    8. Wilson, Robert, 1996. "Nonlinear pricing and mechanism design," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 5, pages 253-293, Elsevier.
    9. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    10. Spulber Daniel F., 1993. "Monopoly Pricing," Journal of Economic Theory, Elsevier, vol. 59(1), pages 222-234, February.
    11. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    12. Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
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    Citations

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    Cited by:

    1. Shin‐kun Peng, 2004. "Spatial Monopoly with Product Differentiation," Southern Economic Journal, John Wiley & Sons, vol. 70(3), pages 646-660, January.
    2. 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.
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    9. 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.
    10. 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.
    11. Kelvin Shuangjian Zhang, 2017. "Existence in Multidimensional Screening with General Nonlinear Preferences," Papers 1710.08549, arXiv.org, revised Dec 2018.
    12. 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).
    13. Pass, Brendan, 2012. "Convexity and multi-dimensional screening for spaces with different dimensions," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2399-2418.
    14. 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.
    15. 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.

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    More about this item

    Keywords

    nonlinear pricing; budget constraints; multi-product;
    All these keywords.

    JEL classification:

    • D - Microeconomics

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