This article considers advance selling problems. It explains why some goods (e.g. airline tickets) are sold cheap to early buyers, while others (e.g. theatre tickets) offer discounts to those who buy late. We derive the profit maximising selling strategy for a monopolist when aggregate demand is certain but buyers face uncertainty about their individual demands. When aggregate demand exceeds capacity, both Advance Purchase Discounts as well as Clearance Sales might be optimal. We determine how the comparison of these price discrimination strategies depends on the rationing rule, capacity costs and the availability of temporal capacity limits, price commitment and resale.
In this article we consider products that can be purchased in advance, i.e. long before their actual date of consumption. Common examples are airline travel, theatre tickets, the right to participate in conferences or sports events and seasonal products like the newest skiing equipment. In these examples consumers face a trade-off between buying early and buying late. By delaying their purchase consumers may get a better picture about their personal fit with the product but increase their risk to become rationed. This trade-off influences the way in which prices change over time.
To see this consider the extreme case where consumers face individual demand uncertainty but rationing risks are negligible. For example, potential participants of a conference or sports event are typically uncertain about their ability to attend but the maximum number of participants might be unlikely to be reached. In this case it is clear that consumers prefer to buy late rather than early since buying late maximises their available information. A profit maximising monopolist can therefore charge an information premium to those consumers that buy late and prices will increase over time. Hence those products for which consumers face individual demand uncertainty but rationing risks are absent will offer Advance Purchase Discounts. Now consider the opposite case where consumers are certain about their personal fit with the product but face a positive risk of becoming rationed. For example, consumers typically know their valuation of a new pair of skis but skis may not be available at the end of the season. In this case consumers prefer to buy early rather than late since buying early minimises their risk of becoming rationed. As a consequence, a profit maximising seller may charge a supply security premium to those consumers who buy early and prices will decrease over time. Hence those products for which individual demand uncertainty is absent but rationing risks exist will be sold by use of a Clearance Sale.