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Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications

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  • Hongmin Li

    (W.P. Carey School of Business, Arizona State University, Tempe, Arizona 85287)

  • Woonghee Tim Huh

    (Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada)

Abstract

We consider the problem of pricing multiple differentiated products with the nested logit model and, as a special case, the multinomial logit model. We prove that concavity of the total profit function with respect to market share holds even when price sensitivity may vary with products. We use this result to analytically compare the optimal monopoly solution to oligopolistic equilibrium solutions. To demonstrate further applications of the concavity result, we consider several multiperiod dynamic models that incorporate the pricing of multiple products in the context of inventory control and revenue management, and establish structural results of the optimal policies.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormsom:v:13:y:2011:i:4:p:549-563
    DOI: 10.1287/msom.1110.0344
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    as
    1. Wallace J. Hopp & Xiaowei Xu, 2008. "A Static Approximation for Dynamic Demand Substitution with Applications in a Competitive Market," Operations Research, INFORMS, vol. 56(3), pages 630-645, June.
    2. Guillermo Gallego & Garrett van Ryzin, 1997. "A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management," Operations Research, INFORMS, vol. 45(1), pages 24-41, February.
    3. Anderson, Simon P & de Palma, Andre, 1992. "Multiproduct Firms: A Nested Logit Approach," Journal of Industrial Economics, Wiley Blackwell, vol. 40(3), pages 261-276, September.
    4. Greene, David L, 1991. "Short-run Pricing Strategies to Increase Corporate Average Fuel Economy," Economic Inquiry, Western Economic Association International, vol. 29(1), pages 101-114, January.
    5. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    6. David Besanko & Jean-Pierre Dubé & Sachin Gupta, 2003. "Competitive Price Discrimination Strategies in a Vertical Channel Using Aggregate Retail Data," Management Science, INFORMS, vol. 49(9), pages 1121-1138, September.
    7. McFadden, Daniel, 1980. "Econometric Models for Probabilistic Choice among Products," The Journal of Business, University of Chicago Press, vol. 53(3), pages 13-29, July.
    8. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    9. Fernando Bernstein & Awi Federgruen, 2004. "A General Equilibrium Model for Industries with Price and Service Competition," Operations Research, INFORMS, vol. 52(6), pages 868-886, December.
    10. David Besanko & Sachin Gupta & Dipak Jain, 1998. "Logit Demand Estimation Under Competitive Pricing Behavior: An Equilibrium Framework," Management Science, INFORMS, vol. 44(11-Part-1), pages 1533-1547, November.
    11. Kyle D. Chen & Warren H. Hausman, 2000. "Technical Note: Mathematical Properties of the Optimal Product Line Selection Problem Using Choice-Based Conjoint Analysis," Management Science, INFORMS, vol. 46(2), pages 327-332, February.
    12. Goldberg, Pinelopi Koujianou, 1995. "Product Differentiation and Oligopoly in International Markets: The Case of the U.S. Automobile Industry," Econometrica, Econometric Society, vol. 63(4), pages 891-951, July.
    13. Kenneth E. Train & Daniel L. McFadden & Moshe Ben-Akiva, 1987. "The Demand for Local Telephone Service: A Fully Discrete Model of Residential Calling Patterns and Service Choices," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 109-123, Spring.
    14. 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.
    15. Gérard P. Cachon & A. Gürhan Kök, 2007. "Category Management and Coordination in Retail Assortment Planning in the Presence of Basket Shopping Consumers," Management Science, INFORMS, vol. 53(6), pages 934-951, June.
    16. Yalç{i}n Akçay & Harihara Prasad Natarajan & Susan H. Xu, 2010. "Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice," Management Science, INFORMS, vol. 56(8), pages 1345-1361, August.
    17. 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.
    18. 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.
    19. Jeffrey A. Dubin, 1986. "A Nested Logit Model of Space and Water Heat System Choice," Marketing Science, INFORMS, vol. 5(2), pages 112-124.
    20. 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.
    21. Daniel McFadden, 1986. "The Choice Theory Approach to Market Research," Marketing Science, INFORMS, vol. 5(4), pages 275-297.
    22. Wallace J. Hopp & Xiaowei Xu, 2005. "Product Line Selection and Pricing with Modularity in Design," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 172-187, August.
    23. Lan Luo & P. K. Kannan & Brian T. Ratchford, 2007. "New Product Development Under Channel Acceptance," Marketing Science, INFORMS, vol. 26(2), pages 149-163, 03-04.
    24. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    25. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    26. James W. Friedman, 1988. "On the Strategic Importance of Prices versus Quantities," RAND Journal of Economics, The RAND Corporation, vol. 19(4), pages 607-622, Winter.
    27. Guillermo Gallego & Woonghee Tim Huh & Wanmo Kang & Robert Phillips, 2006. "Price Competition with the Attraction Demand Model: Existence of Unique Equilibrium and Its Stability," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 359-375, June.
    28. P. K. Kannan & Gordon P. Wright, 1991. "Modeling and Testing Structured Markets: A Nested Logit Approach," Marketing Science, INFORMS, vol. 10(1), pages 58-82.
    29. Goker Aydin & Evan L. Porteus, 2008. "Joint Inventory and Pricing Decisions for an Assortment," Operations Research, INFORMS, vol. 56(5), pages 1247-1255, October.
    30. Woonghee Tim Huh & Ganesh Janakiraman, 2008. "( s, S ) Optimality in Joint Inventory-Pricing Control: An Alternate Approach," Operations Research, INFORMS, vol. 56(3), pages 783-790, June.
    31. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    32. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    33. Constantinos Maglaras & Joern Meissner, 2006. "Dynamic Pricing Strategies for Multiproduct Revenue Management Problems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 136-148, July.
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