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Closed‐Form Solutions to Bundling Problems

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  • John C. Eckalbar

Abstract

This paper investigates the case of a monopolist selling two distinct goods to a group of m traders who are characterized by their reservation prices, which are drawn independently from uniform distributions over the intervals [ 0, R1] and [ 0, R2]. Closed‐form solutions are derived for optimal prices, quantities, profits, and consumers' surplus under situations of separate sales, pure bundling, and mixed bundling. This allows a clear comparison of the price, output, and welfare effects of various forms of bundling. We further investigate situations of positive marginal cost, positive and negative correlation of reservation values, and substitutes and complements.

Suggested Citation

  • John C. Eckalbar, 2010. "Closed‐Form Solutions to Bundling Problems," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 19(2), pages 513-544, June.
    • Handle: RePEc:bla:jemstr:v:19:y:2010:i:2:p:513-544
    DOI: 10.1111/j.1530-9134.2010.00260.x
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chakravarty, A. & Mild, A. & Taudes, A., 2013. "Bundling decisions in supply chains," European Journal of Operational Research, Elsevier, vol. 231(3), pages 617-630.
    2. Andrea Mantovani, 2013. "The Strategic Effect of Bundling: A New Perspective," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 42(1), pages 25-43, February.
    3. Zhaolin Li & Artem Prokhorov, 2024. "Improved Semi-Parametric Bounds for Tail Probability and Expected Loss: Theory and Applications," Papers 2404.02400, arXiv.org, revised May 2024.
    4. Takanori Adachi & Takeshi Ebina & Makoto Hanazono, 2017. "Endogenous Product Boundary," Manchester School, University of Manchester, vol. 85(1), pages 13-40, January.
    5. Banciu, M. & Ødegaard, F., 2016. "Optimal product bundling with dependent valuations: The price of independence," European Journal of Operational Research, Elsevier, vol. 255(2), pages 481-495.
    6. Terrence August & Duy Dao & Kihoon Kim, 2019. "Market Segmentation and Software Security: Pricing Patching Rights," Management Science, INFORMS, vol. 65(10), pages 4575-4597, October.
    7. Alexei Alexandrov & Özlem Bedre-Defolie, 2014. "The Equivalence of Bundling and Advance Sales," Marketing Science, INFORMS, vol. 33(2), pages 259-272, March.
    8. Girju, Marina & Prasad, Ashutosh & Ratchford, Brian T., 2013. "Pure Components versus Pure Bundling in a Marketing Channel," Journal of Retailing, Elsevier, vol. 89(4), pages 423-437.
    9. Ritwik Raj & Mark H. Karwan & Chase Murray & Lei Sun, 2022. "Itemized pricing in B2B bundles with diminishing reservation prices and loss averse customers," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(4), pages 375-392, August.
    10. Liu Weihua & Yu Hui, 2017. "Pure Components VS Full Mixed Bundling When Stackelberg Pricing," Journal of Systems Science and Information, De Gruyter, vol. 5(5), pages 435-445, October.
    11. Masoud Talebian & Zhaolin Li & Qiang Lu, 2020. "Pricing and inventory management for mixed bundled products with stochastic demand," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 19(6), pages 401-410, December.
    12. Hemant K. Bhargava, 2013. "Mixed Bundling of Two Independently Valued Goods," Management Science, INFORMS, vol. 59(9), pages 2170-2185, September.
    13. Chen, Bo & Ni, Debing, 2017. "Optimal bundle pricing under correlated valuations," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 248-281.
    14. Takanori Adachi & Takeshi Ebina & Makoto Hanazono, 2011. "Option Package Bundling," KIER Working Papers 785, Kyoto University, Institute of Economic Research.
    15. Sheikhzadeh, Mehdi & Elahi, Ehsan, 2013. "Product bundling: Impacts of product heterogeneity and risk considerations," International Journal of Production Economics, Elsevier, vol. 144(1), pages 209-222.
    16. Sreya Kolay & Rajeev K. Tyagi, 2022. "Optimal Bundling of Events," Marketing Science, INFORMS, vol. 41(2), pages 380-400, March.
    17. Sobolewski, Maciej & Kopczewski, Tomasz, 2017. "Estimating demand for fixed-line telecommunication bundles," Telecommunications Policy, Elsevier, vol. 41(4), pages 227-241.
    18. Marjan Izadpanah & Ali Vaezi, 2023. "A Bundle Pricing Approach for Mobile Telecommunication Services: Method and Data Analysis," Journal of Emerging Trends in Marketing and Management, The Bucharest University of Economic Studies, vol. 1(3), pages 7-25, September.
    19. Kopczewski, Tomasz & Sobolewski, Maciej & Miernik, Ireneusz, 2018. "Bundling or unbundling? Integrated simulation model of optimal pricing strategies," International Journal of Production Economics, Elsevier, vol. 204(C), pages 328-345.

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