IDEAS home Printed from https://ideas.repec.org/p/ajk/ajkdps/191.html
   My bibliography  Save this paper

A Dynamic Theory of Random Price Discounts

Author

Listed:
  • Francesc Dilmé

    (University of Bonn)

  • Daniel Garrett

    (Toulouse School of Economics)

Abstract

A seller with commitment power sets prices over time. Risk-averse buyers arrive to the market and decide when to purchase. We obtain that the optimal price path is a “regular” price, with occasional episodes of sequential discounts that occur at random times. The optimal price path has the property that the price a buyer ends up paying is independent of his arrival and purchase times, and only depends on his valuation. Our theory accommodates empirical findings on the timing of discounts.

Suggested Citation

  • Francesc Dilmé & Daniel Garrett, 2022. "A Dynamic Theory of Random Price Discounts," ECONtribute Discussion Papers Series 191, University of Bonn and University of Cologne, Germany.
    • Handle: RePEc:ajk:ajkdps:191
    as

    Download full text from publisher

    File URL: https://www.econtribute.de/RePEc/ajk/ajkdps/ECONtribute_191_2022.pdf
    File Function: First version, 2022
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kehoe, Patrick & Midrigan, Virgiliu, 2015. "Prices are sticky after all," Journal of Monetary Economics, Elsevier, vol. 75(C), pages 35-53.
    2. Gautam Gowrisankaran & Marc Rysman, 2012. "Dynamics of Consumer Demand for New Durable Goods," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1173-1219.
    3. Rabin, Matthew, 2000. "Diminishing Marginal Utility of Wealth Cannot Explain Risk Aversion," Department of Economics, Working Paper Series qt61d7b4pg, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    4. Simon Board, 2008. "Durable-Goods Monopoly with Varying Demand," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(2), pages 391-413.
    5. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    6. Qian Liu & Garrett J. van Ryzin, 2008. "Strategic Capacity Rationing to Induce Early Purchases," Management Science, INFORMS, vol. 54(6), pages 1115-1131, June.
    7. Simon Board & Andrzej Skrzypacz, 2016. "Revenue Management with Forward-Looking Buyers," Journal of Political Economy, University of Chicago Press, vol. 124(4), pages 1046-1087.
    8. Février, Philippe & Wilner, Lionel, 2016. "Do consumers correctly expect price reductions? Testing dynamic behavior," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 25-40.
    9. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 267-289.
    10. Igal Hendel & Aviv Nevo, 2013. "Intertemporal Price Discrimination in Storable Goods Markets," American Economic Review, American Economic Association, vol. 103(7), pages 2722-2751, December.
    11. John Conlisk & Eitan Gerstner & Joel Sobel, 1984. "Cyclic Pricing by a Durable Goods Monopolist," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(3), pages 489-505.
    12. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
    13. Francesc Dilmé & Fei Li, 2019. "Revenue Management without Commitment: Dynamic Pricing and Periodic Flash Sales," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1999-2034.
    14. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    15. Tao Chen & Ajay Kalra & Baohong Sun, 2009. "Why Do Consumers Buy Extended Service Contracts?," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 36(4), pages 611-623, December.
    16. Shilony, Yuval, 1977. "Mixed pricing in oligopoly," Journal of Economic Theory, Elsevier, vol. 14(2), pages 373-388, April.
    17. Moore, John, 1984. "Global Incentive Constraints in Auction Design," Econometrica, Econometric Society, vol. 52(6), pages 1523-1535, November.
    18. Budish, Eric B. & Takeyama, Lisa N., 2001. "Buy prices in online auctions: irrationality on the internet?," Economics Letters, Elsevier, vol. 72(3), pages 325-333, September.
    19. Fershtman, Chaim & Fishman, Arthur, 1992. "Price Cycles and Booms: Dynamic Search Equilibrium," American Economic Review, American Economic Association, vol. 82(5), pages 1221-1233, December.
    20. Martin Pesendorfer, 2002. "Retail Sales: A Study of Pricing Behavior in Supermarkets," The Journal of Business, University of Chicago Press, vol. 75(1), pages 33-66, January.
    21. Judith Chevalier & Austan Goolsbee, 2009. "Are Durable Goods Consumers Forward-Looking? Evidence from College Textbooks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(4), pages 1853-1884.
    22. Martin Eichenbaum & Nir Jaimovich & Sergio Rebelo, 2011. "Reference Prices, Costs, and Nominal Rigidities," American Economic Review, American Economic Association, vol. 101(1), pages 234-262, February.
    23. Nancy L. Stokey, 1979. "Intertemporal Price Discrimination," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 355-371.
    24. Daniel F. Garrett, 2016. "Intertemporal Price Discrimination: Dynamic Arrivals and Changing Values," American Economic Review, American Economic Association, vol. 106(11), pages 3275-3299, November.
    25. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1415-1464.
    26. Sobel, Joel, 1991. "Durable Goods Monopoly with Entry of New Consumers," Econometrica, Econometric Society, vol. 59(5), pages 1455-1485, September.
    27. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    28. Ortner, Juan, 2017. "Durable goods monopoly with stochastic costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    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. Maxim Sinitsyn, 2017. "Pricing with Prescheduled Sales," Marketing Science, INFORMS, vol. 36(6), pages 999-1014, November.
    2. Hao Lan & Tim Lloyd & Wyn Morgan & Paul W. Dobson, 2022. "Are food price promotions predictable? The hazard function of supermarket discounts," Journal of Agricultural Economics, Wiley Blackwell, vol. 73(1), pages 64-85, February.
    3. Hinnosaar, Toomas, 2017. "Calendar mechanisms," Games and Economic Behavior, Elsevier, vol. 104(C), pages 252-270.
    4. Benjamin Eden, 2018. "Price Dispersion And Demand Uncertainty: Evidence From U.S. Scanner Data," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1035-1075, August.
    5. Février, Philippe & Wilner, Lionel, 2016. "Do consumers correctly expect price reductions? Testing dynamic behavior," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 25-40.
    6. Benjamin Eden & Maya Eden & Jonah Yuen, 2016. "Inside The Price Dispersion Box: Evidence From Us Scanner Data," Vanderbilt University Department of Economics Working Papers 16-00017, Vanderbilt University Department of Economics.
    7. Kevin R. Williams, 2017. "The Welfare Effects of Dynamic Pricing: Evidence from Airline Markets," Cowles Foundation Discussion Papers 2103R2, Cowles Foundation for Research in Economics, Yale University, revised Jun 2021.
    8. Vibhanshu Abhishek & Mustafa Dogan & Alexandre Jacquillat, 2021. "Strategic Timing and Dynamic Pricing for Online Resource Allocation," Management Science, INFORMS, vol. 67(8), pages 4880-4907, August.
    9. Holzer, Patrick Sebastian, 2020. "The effect of time-varying factors on promotional activity in the German milk market," Journal of Retailing and Consumer Services, Elsevier, vol. 55(C).
    10. Omar Besbes & Ilan Lobel, 2015. "Intertemporal Price Discrimination: Structure and Computation of Optimal Policies," Management Science, INFORMS, vol. 61(1), pages 92-110, January.
    11. Kevin R. Williams, 2022. "The Welfare Effects of Dynamic Pricing: Evidence From Airline Markets," Econometrica, Econometric Society, vol. 90(2), pages 831-858, March.
    12. Shi, Shouyong, 2016. "Customer relationship and sales," Journal of Economic Theory, Elsevier, vol. 166(C), pages 483-516.
    13. Nakamura, Emi & Steinsson, Jón, 2011. "Price setting in forward-looking customer markets," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 220-233.
    14. Berck, Peter & Brown, Jennifer & Perloff, Jeffrey M. & Villas-Boas, Sofia Berto, 2008. "Sales: Tests of theories on causality and timing," International Journal of Industrial Organization, Elsevier, vol. 26(6), pages 1257-1273, November.
    15. Daniel F. Garrett, 2019. "Fake Sales: A Dynamic Pricing Perspective," The Japanese Economic Review, Springer, vol. 70(3), pages 375-382, September.
    16. Paul Heidhues & Botond Köszegi, 2004. "The Impact of Consumer Loss Aversion on Pricing," CIG Working Papers SP II 2004-17, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG).
    17. Ken Moon & Kostas Bimpikis & Haim Mendelson, 2018. "Randomized Markdowns and Online Monitoring," Management Science, INFORMS, vol. 64(3), pages 1271-1290, March.
    18. Fabio Antoniou & Raffaele Fiocco, 2023. "Storable Good Market With Intertemporal Cost Variations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(1), pages 361-385, February.
    19. Fertő, Imre & Bakucs, Lajos Zoltán, 2009. "Árleszállítások és a kiskereskedelmi árak változása a tejtermékek piacán [Sales and retail price patterns on the market for milk products]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 634-647.
    20. P. Février & L. Wilner, 2012. "Do Consumers Correctly Expect Price Reductions? Testing Dynamic Behavior," Documents de Travail de l'Insee - INSEE Working Papers g2012-03, Institut National de la Statistique et des Etudes Economiques.

    More about this item

    Keywords

    dynamic pricing; sales; random mechanisms;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ajk:ajkdps:191. 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: ECONtribute Office (email available below). General contact details of provider: https://www.econtribute.de .

    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.