Pricing Policies for Selling Indivisible Storable Goods to Strategic Consumers

TL;DR

This paper compares preannounced and contingent pricing policies for selling indivisible storable goods, showing that contingent policies can be more profitable, lower prices, and increase consumer surplus, contrary to divisible goods cases.

Contribution

It provides a polynomial-time method to compute optimal preannounced policies and quantifies the potential revenue gains of contingent policies in the indivisible goods setting.

Findings

Contingent policies can yield higher revenues than preannounced policies.

Consumers do not need to store units under optimal preannounced policies.

Contingent policies can be up to logarithmic in the number of consumers more profitable.

Abstract

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. (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.