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Dynamic Pricing Strategies with Reference Effects


  • Ioana Popescu

    () (Decision Sciences Area, INSEAD, Boulevard de Constance, 77300 Fontainebleau, France)

  • Yaozhong Wu

    () (Department of Decision Sciences, NUS Business School, National University of Singapore, Singapore 117592)


We consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions, where demand is sensitive to the firm’s pricing history. Consumers have memory and are prone to human decision-making biases and cognitive limitations. As the firm manipulates prices, consumers form a reference price that adjusts as an anchoring standard based on price perceptions. Purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory.We prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount, respectively surcharge, relative to their expectations. The effect is that of a skimming or penetration strategy. The firm’s optimal pricing path is monotonic on the long run, but not necessarily at the introductory stage. If consumers are loss averse, we show that optimal prices converge to a constant steady-state price, characterized by a simple implicit equation; otherwise, the optimal policy cycles. The range of steady states is wider the more loss averse consumers are. Steady-state prices decrease with the strength of the reference effect and with customers’ memory, all else equal. Offering lower prices to frequent customers may be suboptimal, however, if these are less sensitive to price changes than occasional buyers.If managers ignore such long-term implications of their pricing strategy, the model indicates that they will systematically price too low and lose revenue. Our results hold under very general reference dependent demand models.

Suggested Citation

  • Ioana Popescu & Yaozhong Wu, 2007. "Dynamic Pricing Strategies with Reference Effects," Operations Research, INFORMS, vol. 55(3), pages 413-429, June.
  • Handle: RePEc:inm:oropre:v:55:y:2007:i:3:p:413-429

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    References listed on IDEAS

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    Cited by:

    1. Grigoriev Alexander & Hiller Benjamin & Marbán Sebastián & Vredeveld Tjark & Zwaan Ruben van der, 2010. "Dynamic Pricing Problems with Elastic Demand," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Ahrens, Steffen & Pirschel, Inske & Snower, Dennis J., 2017. "A theory of price adjustment under loss aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 78-95.
    3. repec:eee:ejores:v:263:y:2017:i:2:p:596-610 is not listed on IDEAS
    4. Shi, Ye & Yu, Yugang & Wang, Lizhi, 2015. "Operational impact on the environment: Managing service systems with environmental deterioration," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 310-320.
    5. Jie Xu & Nan Liu, 2017. "Research on closed loop supply chain with reference price effect," Journal of Intelligent Manufacturing, Springer, vol. 28(1), pages 51-64, January.
    6. repec:spr:jbecon:v:87:y:2017:i:6:d:10.1007_s11573-016-0839-z is not listed on IDEAS
    7. repec:kap:expeco:v:20:y:2017:i:3:d:10.1007_s10683-016-9501-4 is not listed on IDEAS
    8. Han Wang & Damien Fay & Kenneth N. Brown & Liam Kilmartin, 2016. "Modelling revenue generation in a dynamically priced mobile telephony service," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(4), pages 711-734, August.
    9. repec:gam:jsusta:v:10:y:2018:i:1:p:157-:d:126565 is not listed on IDEAS
    10. repec:eee:ejores:v:262:y:2017:i:1:p:136-150 is not listed on IDEAS


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