Basic Pricing Theory

  • Guillermo Gallego
  • Huseyin Topaloglu
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 279)


This chapter provides an introduction to multi-product monopoly pricing when the variable costs are linear. Profit maximization problems with linear variable costs arise from capacity constraints, where the firm maximizes the expected profit net of the opportunity costs of the capacities used. We argue that under mild assumptions, both the optimal profit function and the expected consumer surplus are convex functions of the variable costs. Consequently, when variable costs are random, both the firm and the representative consumer benefit from prices that dynamically respond to changes in variable costs. Randomness in variable cost is often driven by randomness in demand in conjunction with capacity constraints, and this accounts for some of the benefits of dynamic pricing. We explore conditions for the existence and uniqueness of maximizers of the expected profit and analyze in detail problems with capacity constraints both when prices are set for the entire sales horizon a priori, and when prices are allowed to change during the sales horizon. The firm’s problem is discussed in Sect. 8.2, while the representative consumer’s problem is presented in Sect. 8.3. The case with finite capacity is discussed in Sect. 8.4. Details about existence and uniqueness for single product problems are discussed in Sect. 8.5. This section also includes applications to priority pricing, social planning, multiple market segments, and peak-load pricing. Multi-product pricing problems are discussed in Sect. 8.6.


  1. T. Amornpetchkul, H.-S. Ahn, O. Sahin, Conditional promotions and consumer overspending. Prod. Oper. Manag. 27 (8), 1455–1475 (2018)Google Scholar
  2. S.P. Anderson, A. de Palma, J.G. Thisse, Discrete Choice Theory of Product Differentiation (MIT Press, Cambridge, 1992)Google Scholar
  3. A. Belkaid, V. Martinez-de-Albeniz, Here comes the sun: fashion goods retailing under weather shocks. Technical report, University of Navarra, Barcelona, Spain (2017)Google Scholar
  4. O. Besbes, R. Phillips, A. Zeevi, Testing the validity of a demand model: an operations perspective. Manuf. Serv. Oper. Manag. 12 (1), 162–183 (2010)Google Scholar
  5. T. Boyaci, Y. Akcay, Pricing when customers have limited attention. Manag. Sci. 64 (7), 2995–3014 (2018)Google Scholar
  6. G. Cachon, P. Feldman, Pricing services subject to congestion: charge per-use fees or sell subscriptions. Manuf. Serv. Oper. Manag. 13 (2), 244–260 (2011)Google Scholar
  7. G. Cachon, K.M. Daniels, R. Lobel, The role of surge pricing on a service platform with self-scheduling capacity. Manuf. Serv. Oper. Manag. 19 (3), 368–384 (2017)Google Scholar
  8. R. Caldentey, L.M. Wein, Revenue management of a make-to-stock queue. Oper. Res. 54 (5), 859–875 (2006)Google Scholar
  9. A. Caplin, B. Nalebuff, Aggregation and imperfect competition: on the existence of equilibrium. Econometrica 59(1), 25–59 (1991)Google Scholar
  10. J. Carrasco, J. de Ortuzar, Review and assessment of the nested logit model. Transp. Rev. 22 (2), 197–218 (2002)Google Scholar
  11. N. Chen, G. Gallego, Welfare analysis of dynamic pricing. Manag. Sci. 65 (1), 139–151 (2019)Google Scholar
  12. H. Chen, M. Hu, G. Perakis, Distribution-free pricing. Technical report, University of Toronto, Toronto, ON (2017a)Google Scholar
  13. M. Cohen, R.S. Pindyck, G. Perakis, Pricing with limited knowledge of demand. Technical report, MIT, Cambridge, MA (2017b)Google Scholar
  14. P. Courty, J. Nasiry, Loss aversion and the uniform pricing puzzle for media and entertainment products. Econ. Theory 66 (1), 105–140 (2018)Google Scholar
  15. Y. Cui, I. Duenyas, O. Sahin, Unbundling of ancillary service: how does price discrimination of main service matter? Manuf. Serv. Oper. Manag. 20 (3), 455–466 (2018)Google Scholar
  16. C. Du, W.L. Cooper, Z. Wang, Optimal pricing for a multinomial logit choice model with network effects. Oper. Res. 64 (2), 2016 (2016)Google Scholar
  17. C. Du, W.L. Cooper, Z. Wang, Optimal worst-case pricing for a logit demand model with network effects. Oper. Res. Lett. 46 (3), 2018 (2018)Google Scholar
  18. A.N. Elmachtoub, M.L. Hamilton, The power of opaque products in pricing. Technical report, Columbia University, New York, NY (2017)Google Scholar
  19. A.N. Elmachtoub, Y. Wei, Retailing with opaque products. Technical report, Columbia University, New York, NY (2015)Google Scholar
  20. A.N. Elmachtoub, V. Gupta, M.L. Hamilton, The value of personlized pricing. Technical report, Columbia University, New York, NY (2018)Google Scholar
  21. S.S. Eren, C. Maglaras, Monopoly pricing with limited demand information. J. Revenue Pricing Manag. 9 (1–2), 23–48 (2010)Google Scholar
  22. G. Gallego, O. Sahin, Revenue management with partially refundable fares. Oper. Res. 58 (4), 817–833 (2010)Google Scholar
  23. G. Gallego, R. Wang, Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62 (2), 450–461 (2014)Google Scholar
  24. T.-H. Ho, C.S. Tang, D.R. Bell, Rational shopping behavior and the option value of variable pricing. Manag. Sci. 44 (12–2), S145–S160 (1998)Google Scholar
  25. Z. Hu, J. Nasiry, Are markets with loss-averse consumers more sensitive to losses? Manag. Sci. 64 (3), 1384–1395 (2018)Google Scholar
  26. M. Hu, M. Pavlin, M. Shi, When gray markets have silver linings: all-unit discounts, gray markets, and channel management. Manuf. Serv. Oper. Manag. 15 (2), 250–262 (2013a)Google Scholar
  27. C.R. Johnson, Positive definite matrices. Am. Math. Mon. 77 (3), 259–264 (1970)Google Scholar
  28. P.W. Keller, R. Levi, G. Perakis, Efficient formulations for pricing under attraction demand models. Math. Program. 14 (1–2), 223–261 (2014)Google Scholar
  29. V. Kostami, D. Kostamis, S. Ziya, Pricing and capacity allocation for shared services. Manuf. Serv. Oper. Manag. 19 (2), 230–245 (2017)Google Scholar
  30. M.A. Larriviere, E.L. Porteus, Selling to the newsvendor: an analysis of price-only contracts. Manuf. Serv. Oper. Manag. 3 (4), 293–305 (2001)Google Scholar
  31. H. Li, W.T. Huh, Pricing multiple products with the multinomial logit and nested logit models: concavity and implications. Manuf. Serv. Oper. Manag. 13 (4), 546–563 (2011)Google Scholar
  32. Y. Lu, D. Simchi-Levi, On the unimodality of the profit function of the pricing newsvendor. Prod. Oper. Manag. 22 (3), 615–625 (2013)Google Scholar
  33. W. Ma, D. Simchi-Levi, Learning valuation distributions from bundle sales. Technical report, MIT, Cambridge, MA (2018)Google Scholar
  34. C. Maglaras, A. Zeevi, Pricing and design of differentiated services: approximate analysis and structural insights. Oper. Res. 53 (2), 242–262 (2005)Google Scholar
  35. P.R. McAfee, Coarse matching. Econometrica 75 (5), 2025–2034 (2004)Google Scholar
  36. D. McFadden, Conditional logit analysis of qualitative choice behavior, in Frontiers in Econometrics, ed. by P. Zarembka (Academic, New York, 1974), pp. 105–142Google Scholar
  37. N.C. Petruzzi, M. Dada, Pricing and the newsvendor problem: a review with extensions. Oper. Res. 47 (2), 183–194 (1999)Google Scholar
  38. R. Phillips, Optimizing prices for consumer credit. J. Revenue Pricing Manag. 12 (4), 360–377 (2013)Google Scholar
  39. I.P.L. Png, Reservations: customer insurance in the marketing of capacity. Mark. Sci. 8 (3), 248–264 (1989)Google Scholar
  40. W.Z. Rayfield, P. Rusmevichientong, H. Topaloglu, Approximation methods for pricing problems under the nested logit model with price bounds. INFORMS J. Comput. 27 (2), 335–357 (2015)Google Scholar
  41. P. Rusmevichientong, B. Van Roy, P.W. Glynn, A nonparametric approach to multiproduct pricing. Oper. Res. 54 (1), 82–98 (2006)Google Scholar
  42. S. Shugan, J. Xie, Advance pricing of services and other implications of separating purchase and consumption. J. Serv. Res. 2 (3), 227–239 (2000)Google Scholar
  43. C.S. Tang, R. Yin, Joint ordering and pricing strategies for managing substitutable products. Prod. Oper. Manag. 16 (1), 138–153 (2007)Google Scholar
  44. C.S. Tang, K. Rajaram, A. Alptekinoglu, J. Ou, The benefits of advance booking discount programs: model and analysis. Manag. Sci. 50 (4), 465–478 (2004)Google Scholar
  45. G.J. van den Berg, On the uniqueness of optimal prices set by monopolistic sellers. J. Econ. 141 (2), 482–491 (2007)Google Scholar
  46. X. Vives, Oligopoly Pricing: Old Ideas and New Tools (MIT Press, Cambridge, 2001)Google Scholar
  47. R. Wang, When prospect theory meets consumer choice models: assortment and pricing management with reference prices. Manuf. Serv. Oper. Manag. 20 (3), 583–600 (2018b)Google Scholar
  48. R. Wang, Z. Wang, Consumer choice models with endogenous network effects. Manag. Sci. 63 (11), 3944–3960 (2017)Google Scholar
  49. R. Wang, M. Dada, O. Sahin, Pricing ancillary service subscriptions. Manag. Sci. (2019, forthcoming)Google Scholar
  50. J. Xie, S. Shugan, Electronic tickets, smart cards, and online prepayments: when and how to advance sell. Mark. Sci. 20, 219–243 (2001)Google Scholar
  51. Z. Yan, C. Cheng, K. Natarajan, C.-P. Teo, Marginal estimation price optimization: data driven multi-product pricing problem. Technical report, Singapore University of Technology and Design, Singapore (2017)Google Scholar
  52. H. Zhang, P. Rusmevichientong, H. Topaloglu, Technical note – multiproduct pricing under the generalized extreme value models with homogeneous price sensitivity parameters. Oper. Res. 66 (6), 1559–1570 (2018)Google Scholar
  53. S. Ziya, H. Ayhan, R.D. Folley, Relationships among three assumptions in revenue management. Oper. Res. 52 (5), 804–809 (2004)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Guillermo Gallego
    • 1
  • Huseyin Topaloglu
    • 2
  1. 1.Clearwater BayHong Kong
  2. 2.ORIECornell UniversityNew YorkUSA

Personalised recommendations