IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v32y2023i4p1223-1242.html
   My bibliography  Save this article

Product‐line pricing with dual objective of profit and consumer surplus

Author

Listed:
  • Woonghee T. Huh
  • Hongmin Li

Abstract

In many settings, consumer surplus directly impacts a firm or organization's objective, and the profit‐only objective becomes inadequate. Our paper is the first to consider the dual objective of profit and consumer surplus in multi‐product pricing under the multinomial logit demand, where the prices are continuously set. We define a firm's marginal consumer surplus as its marginal contribution to the expected customer utility transformed into monetary unit. Although the profit is concave in the choice probability space, the marginal consumer surplus is convex, complicating the analysis. We identify the optimal monopoly pricing solution and develop solution approaches for the equilibrium solutions of both price‐competition and quantity‐competition oligopolies. In the monopolistic setting, we solve the optimal solution in a near‐closed‐form expression, and show that the firm's markup and profit decline as its emphasis for marginal consumer surplus increases and eventually drops to zero when the firm turns into a social welfare maximizer. Therefore, social welfare is maximized only when the monopolist is willing to endure zero profit. In competitive settings, if one firm's emphasis on marginal consumer surplus increases, then the improvement in marginal consumer surplus can magnify through competitive forces, reflected in reduced equilibrium prices for all firms. Moreover, we find that, while the overall marginal consumer surplus always increases with any firm's weight on marginal consumer surplus in its objective (referred to as the CS weight), a firm's marginal consumer surplus increases in its own CS weight but decreases in other firms' CS weight. Finally, we prove that, all else equal, a firm with a higher CS weight can earn a higher profit than its profit‐maximizing competitors, which is counterintuitive. In the quantity competition, a firm may even increase its absolute profit level by increasing its CS weight.

Suggested Citation

  • Woonghee T. Huh & Hongmin Li, 2023. "Product‐line pricing with dual objective of profit and consumer surplus," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1223-1242, April.
  • Handle: RePEc:bla:popmgt:v:32:y:2023:i:4:p:1223-1242
    DOI: 10.1111/poms.13922
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.13922
    Download Restriction: no

    File URL: https://libkey.io/10.1111/poms.13922?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Peter M. Guadagni & John D. C. Little, 1983. "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, INFORMS, vol. 2(3), pages 203-238.
    2. A. Gürhan Kök & Yi Xu, 2011. "Optimal and Competitive Assortments with Endogenous Pricing Under Hierarchical Consumer Choice Models," Management Science, INFORMS, vol. 57(9), pages 1546-1563, February.
    3. Mika Sumida & Guillermo Gallego & Paat Rusmevichientong & Huseyin Topaloglu & James Davis, 2021. "Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints," Management Science, INFORMS, vol. 67(5), pages 2845-2869, May.
    4. Woonghee Tim Huh & Hongmin Li, 2015. "Technical Note—Pricing Under the Nested Attraction Model with a Multistage Choice Structure," Operations Research, INFORMS, vol. 63(4), pages 840-850, August.
    5. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    6. Hongmin Li & Woonghee Tim Huh, 2011. "Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 549-563, October.
    7. Anderson, Simon P. & Renault, Regis, 2003. "Efficiency and surplus bounds in Cournot competition," Journal of Economic Theory, Elsevier, vol. 113(2), pages 253-264, December.
    8. Amr Farahat & Woonghee Tim Huh & Hongmin Li, 2019. "On the Relationship Between Quantity Precommitment and Cournot Games," Operations Research, INFORMS, vol. 67(1), pages 109-122, January.
    9. Small, Kenneth A & Rosen, Harvey S, 1981. "Applied Welfare Economics with Discrete Choice Models," Econometrica, Econometric Society, vol. 49(1), pages 105-130, January.
    10. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    11. Aydın Alptekinoğlu & John H. Semple, 2021. "Heteroscedastic Exponomial Choice," Operations Research, INFORMS, vol. 69(3), pages 841-858, May.
    12. Alice Paul & Jacob Feldman & James Mario Davis, 2018. "Assortment Optimization and Pricing Under a Nonparametric Tree Choice Model," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 550-565, July.
    13. Srikanth Jagabathula & Paat Rusmevichientong, 2017. "Nonparametric Joint Assortment and Price Choice Model," Management Science, INFORMS, vol. 63(9), pages 3128-3145, September.
    14. Jose Blanchet & Guillermo Gallego & Vineet Goyal, 2016. "A Markov Chain Approximation to Choice Modeling," Operations Research, INFORMS, vol. 64(4), pages 886-905, August.
    15. Panos Kouvelis & Yixuan Xiao & Nan Yang, 2015. "PBM Competition in Pharmaceutical Supply Chain: Formulary Design and Drug Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 511-526, October.
    16. Chenhao Du & William L. Cooper & Zizhuo Wang, 2016. "Optimal Pricing for a Multinomial Logit Choice Model with Network Effects," Operations Research, INFORMS, vol. 64(2), pages 441-455, April.
    17. Anderson, Simon P & De Palma, Andre, 1992. "The Logit as a Model of Product Differentiation," Oxford Economic Papers, Oxford University Press, vol. 44(1), pages 51-67, January.
    18. Hongmin Li & Scott Webster & Nicholas Mason & Karl Kempf, 2019. "Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand," Service Science, INFORMS, vol. 21(1), pages 14-28, January.
    19. James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    20. Hongmin Li, 2020. "Optimal Pricing Under Diffusion-Choice Models," Operations Research, INFORMS, vol. 68(1), pages 115-133, January.
    21. James Dong & A. Serdar Simsek & Huseyin Topaloglu, 2019. "Pricing Problems under the Markov Chain Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 28(1), pages 157-175, January.
    22. W. Zachary Rayfield & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "Approximation Methods for Pricing Problems Under the Nested Logit Model with Price Bounds," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 335-357, May.
    23. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    24. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    25. Ruxian Wang & Ozge Sahin, 2018. "The Impact of Consumer Search Cost on Assortment Planning and Pricing," Management Science, INFORMS, vol. 64(8), pages 3649-3666, August.
    26. Aydın Alptekinoğlu & John H. Semple, 2016. "The Exponomial Choice Model: A New Alternative for Assortment and Price Optimization," Operations Research, INFORMS, vol. 64(1), pages 79-93, February.
    27. Ningyuan Chen & Guillermo Gallego, 2019. "Welfare Analysis of Dynamic Pricing," Management Science, INFORMS, vol. 65(1), pages 139-151, January.
    28. McConnell K. E., 1995. "Consumer Surplus from Discrete Choice Models," Journal of Environmental Economics and Management, Elsevier, vol. 29(3), pages 263-270, November.
    29. Hongmin Li & Scott Webster & Gwangjae Yu, 2020. "Product Design Under Multinomial Logit Choices: Optimization of Quality and Prices in an Evolving Product Line," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1011-1025, September.
    30. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    31. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    32. Hongmin Li & Scott Webster, 2017. "Optimal Pricing of Correlated Product Options Under the Paired Combinatorial Logit Model," Operations Research, INFORMS, vol. 65(5), pages 1215-1230, October.
    33. Ruxian Wang & Zizhuo Wang, 2017. "Consumer Choice Models with Endogenous Network Effects," Management Science, INFORMS, vol. 63(11), pages 3944-3960, November.
    34. Amr Farahat & Georgia Perakis, 2011. "TECHNICAL NOTE---A Comparison of Bertrand and Cournot Profits in Oligopolies with Differentiated Products," Operations Research, INFORMS, vol. 59(2), pages 507-513, April.
    35. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hongmin Li & Scott Webster & Gwangjae Yu, 2020. "Product Design Under Multinomial Logit Choices: Optimization of Quality and Prices in an Evolving Product Line," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1011-1025, September.
    2. Hongmin Li & Scott Webster & Nicholas Mason & Karl Kempf, 2019. "Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand," Service Science, INFORMS, vol. 21(1), pages 14-28, January.
    3. Ruben van de Geer & Arnoud V. den Boer, 2022. "Price Optimization Under the Finite-Mixture Logit Model," Management Science, INFORMS, vol. 68(10), pages 7480-7496, October.
    4. Strauss, Arne K. & Klein, Robert & Steinhardt, Claudius, 2018. "A review of choice-based revenue management: Theory and methods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 375-387.
    5. Rui Chen & Hai Jiang, 2020. "Capacitated assortment and price optimization under the nested logit model," Journal of Global Optimization, Springer, vol. 77(4), pages 895-918, August.
    6. Hongmin Li, 2020. "Optimal Pricing Under Diffusion-Choice Models," Operations Research, INFORMS, vol. 68(1), pages 115-133, January.
    7. Hongmin Li & Scott Webster, 2017. "Optimal Pricing of Correlated Product Options Under the Paired Combinatorial Logit Model," Operations Research, INFORMS, vol. 65(5), pages 1215-1230, October.
    8. Mika Sumida & Guillermo Gallego & Paat Rusmevichientong & Huseyin Topaloglu & James Davis, 2021. "Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints," Management Science, INFORMS, vol. 67(5), pages 2845-2869, May.
    9. Ruxian Wang, 2018. "When Prospect Theory Meets Consumer Choice Models: Assortment and Pricing Management with Reference Prices," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 583-600, July.
    10. Xiaobo Li & Hailong Sun & Chung Piaw Teo, 2022. "Convex Optimization for Bundle Size Pricing Problem," Management Science, INFORMS, vol. 68(2), pages 1095-1106, February.
    11. Zhenzhen Yan & Karthik Natarajan & Chung Piaw Teo & Cong Cheng, 2022. "A Representative Consumer Model in Data-Driven Multiproduct Pricing Optimization," Management Science, INFORMS, vol. 68(8), pages 5798-5827, August.
    12. Ruxian Wang & Zizhuo Wang, 2017. "Consumer Choice Models with Endogenous Network Effects," Management Science, INFORMS, vol. 63(11), pages 3944-3960, November.
    13. James M. Davis & Huseyin Topaloglu & David P. Williamson, 2017. "Pricing Problems Under the Nested Logit Model with a Quality Consistency Constraint," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 54-76, February.
    14. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    15. Qi Feng & J. George Shanthikumar & Mengying Xue, 2022. "Consumer Choice Models and Estimation: A Review and Extension," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 847-867, February.
    16. Sentao Miao & Xiuli Chao, 2021. "Dynamic Joint Assortment and Pricing Optimization with Demand Learning," Manufacturing & Service Operations Management, INFORMS, vol. 23(2), pages 525-545, March.
    17. Srikanth Jagabathula & Paat Rusmevichientong, 2017. "Nonparametric Joint Assortment and Price Choice Model," Management Science, INFORMS, vol. 63(9), pages 3128-3145, September.
    18. Ruxian Wang & Maqbool Dada & Ozge Sahin, 2019. "Pricing Ancillary Service Subscriptions," Management Science, INFORMS, vol. 65(10), pages 4712-4732, October.
    19. Kameng Nip & Zhenbo Wang & Zizhuo Wang, 2021. "Assortment Optimization under a Single Transition Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2122-2142, July.
    20. Aydın Alptekinoğlu & John H. Semple, 2021. "Heteroscedastic Exponomial Choice," Operations Research, INFORMS, vol. 69(3), pages 841-858, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:popmgt:v:32:y:2023:i:4:p:1223-1242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.