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A mathematical reformulation of the reference price

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  • Kevin Dayaratna
  • P. Kannan

Abstract

Reference prices have long been studied in applied economics and business research. One of the classic formulations of the reference price is in terms of an iterative function of past prices. There are a number of limitations of such a formulation, however. Such limitations include burdensome computational time to estimate parameters, an inability to truly account for customer heterogeneity, and an estimation procedure that implies a misspecified model. Managerial recommendations based on inferences from such a model can be quite misleading. We mathematically reformulate the reference price by developing a closed-form expansion that addresses the aforementioned issues, enabling one to elicit truly meaningful managerial advice from the model. We estimate our model on a real world data set to illustrate the efficacy of our approach. Our work is not only important from a modeling perspective, but also has valuable behavioral and managerial implications, which modelers and non-modelers alike should find useful. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Kevin Dayaratna & P. Kannan, 2012. "A mathematical reformulation of the reference price," Marketing Letters, Springer, vol. 23(3), pages 839-849, September.
    • Handle: RePEc:kap:mktlet:v:23:y:2012:i:3:p:839-849
    DOI: 10.1007/s11002-012-9192-3
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    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. Kamins, Michael A & Dreze, Xavier & Folkes, Valerie S, 2004. "Effects of Seller-Supplied Prices on Buyers' Product Evaluations: Reference Prices in an Internet Auction Context," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 30(4), pages 622-628, March.
    3. Timothy B. Heath & Subimal Chatterjee & Karen R. France, 1995. "Mental Accounting and Changes in Price: The Frame Dependence of Reference Dependence," Post-Print hal-00670476, HAL.
    4. Heath, Timothy B & Chatterjee, Subimal & France, Karen Russo, 1995. "Mental Accounting and Changes in Price: The Frame Dependence of Reference Dependence," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 22(1), pages 90-97, June.
    5. Marcus Cunha Jr. & Jeffrey D. Shulman, 2011. "Assimilation and Contrast in Price Evaluations," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 37(5), pages 822-835.
    6. Briesch, Richard A, et al, 1997. "A Comparative Analysis of Reference Price Models," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 24(2), pages 202-214, September.
    7. Wolfgang Jank & P. K. Kannan, 2005. "Understanding Geographical Markets of Online Firms Using Spatial Models of Customer Choice," Marketing Science, INFORMS, vol. 24(4), pages 623-634, December.
    8. 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.
    9. Praveen K. Kopalle & Ambar G. Rao & João L. Assunção, 1996. "Asymmetric Reference Price Effects and Dynamic Pricing Policies," Marketing Science, INFORMS, vol. 15(1), pages 60-85.
    10. Grewal, Dhruv & Janakiraman, Ramkumar & Kalyanam, Kirthi & Kannan, P.K. & Ratchford, Brian & Song, Reo & Tolerico, Stephen, 2010. "Strategic Online and Offline Retail Pricing: A Review and Research Agenda," Journal of Interactive Marketing, Elsevier, vol. 24(2), pages 138-154.
    11. Kopalle, Praveen K. & Kannan, P.K. & Boldt, Lin Bao & Arora, Neeraj, 2012. "The impact of household level heterogeneity in reference price effects on optimal retailer pricing policies," Journal of Retailing, Elsevier, vol. 88(1), pages 102-114.
    12. Bruce G. S. Hardie & Eric J. Johnson & Peter S. Fader, 1993. "Modeling Loss Aversion and Reference Dependence Effects on Brand Choice," Marketing Science, INFORMS, vol. 12(4), pages 378-394.
    13. Winer, Russell S, 1986. "A Reference Price Model of Brand Choice for Frequently Purchased Products," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 13(2), pages 250-256, September.
    14. Kalyanaram, Gurumurthy & Little, John D C, 1994. "An Empirical Analysis of Latitude of Price Acceptance in Consumer Package Goods," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 21(3), pages 408-418, December.
    15. Janiszewski, Chris & Lichtenstein, Donald R, 1999. "A Range Theory Account of Price Perception," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 25(4), pages 353-368, March.
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    5. Kevin Dayaratna & Jesse Crosson & Chandler Hubbard, 2022. "Closed Form Bayesian Inferences for Binary Logistic Regression with Applications to American Voter Turnout," Stats, MDPI, vol. 5(4), pages 1-21, November.

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