Andrei Bazhanov

Quantity Premiums and Discounts in Dynamic Pricing

We consider a dynamic pricing problem for a monopolistic company selling a perishable product when customer demand is both uncertain and occurs in batches that must be fulfilled as a whole. The seller can price-discriminate between different sized batches by setting different unit prices. The problem is modeled as a stochastic optimal control problem to find an inventory-contingent dynamic pricing policy that maximizes the expected total revenues. We find the optimal pricing policy and prove several monotonicity results. First, we establish stochastic order conditions on the unit willingness-to-pay distributions that determine when quantity discounts or premiums take place for a batch purchase compared to a rapid sequence of purchases with the same total size. Second, we give sufficient conditions for prices to be monotonically decreasing or increasing in inventory. Third, we characterize the conditions for the perceived quantity discounts and premiums that result from comparing unit prices for different batch sizes under a particular inventory level.

Quantity Competition in the Presence of Strategic Consumers

Oligopolistic retailers decide on the initial inventories of an undifferentiated limited-lifetime product offered to strategic consumers. A manufacturer sets the first-period (full) price, while the second-period (clearance) price is determined by a market clearing process. The resulting symmetric pure-strategy equilibria may lead to no sales in the first or second period (Cournot outcome versus collusion), and sales in both periods with the clearance price above or at the salvage value. The equilibria possess a comprehensive set of monotonic properties. In particular, increasing strategic behavior can benefit retailers and hurt consumers, increasing competition may harm the local economy, and high levels of strategic behavior may insure against oversupply that leads to clearance sales at the salvage value. The welfare-optimal number of retailers can lead to the above-cost clearance price.