Annals of Operations Research

, Volume 274, Issue 1–2, pp 131–154 | Cite as

Pricing policies for selling indivisible storable goods to strategic consumers

  • Gerardo BerbegliaEmail author
  • Gautam Rayaprolu
  • Adrian Vetta
Original Research


We study the dynamic pricing problem faced by a monopolistic retailer who sells a storable product to forward-looking consumers. In this framework, the two major pricing policies (or mechanisms) studied in the literature are the preannounced (commitment) pricing policy and the contingent (threat or history dependent) pricing policy. We analyse and compare these pricing policies in the setting where the good can be purchased along a finite time horizon in indivisible atomic quantities. First, we show that, given linear storage costs, the retailer can compute an optimal preannounced pricing policy in polynomial time by solving a dynamic program. Moreover, under such a policy, we show that consumers do not need to store units in order to anticipate price rises. Second, under the contingent pricing policy rather than the preannounced pricing mechanism, (i) prices could be lower, (ii) retailer revenues could be higher, and (iii) consumer surplus could be higher. This result is surprising, in that these three facts are in complete contrast to the case of a retailer selling divisible storable goods (Dudine et al. in Am Econ Rev 96(5):1706–1719, 2006). Third, we quantify exactly how much more profitable a contingent policy could be with respect to a preannounced policy. Specifically, for a market with N consumers, a contingent policy can produce a multiplicative factor of \(\Omega (\log N)\) more revenues than a preannounced policy, and this bound is tight.


Price optimization Storable goods Monopoly Price discrimination Price commitment Dynamic programming Profit bounds 



The authors would like to thank to Gustavo Vulcano and Jun Xiao for helpful discussions.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Melbourne Business SchoolUniversity of MelbourneParkvilleAustralia
  2. 2.McGill UniversityMontrealCanada

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