A theory of clearance sales

Abstract

Clearance sales are widely used by firms as an intertemporal selling policy, in particular in markets where firms face demand uncertainty and need to choose capacity in advance. Clearance sales consist in charging a high price initially but then lowering the price in the sales period. High-valuation consumers purchase the good at the high initial price so as to avoid rationing at the low price, while low-valuation consumers wait for the price to drop. We develop a simple model of intertemporal monopoly pricing under demand uncertainty, and show that clearance sales may be the optimal intertemporal selling policy. In this article, we derive the optimal selling policy of a monopolist who faces uncertainty about the level of demand. In contrast to much of the literature, we show that uniform pricing is not necessarily optimal. The optimal selling policy may instead involve clearance sales: the monopolist commits to supply only a limited quantity, and then charge a high price in the first period (palatable to high-valuation consumers) and a low price (affordable to low-valuation consumers) in the last period. The premium associated with the rent offered to consumers that buy at the high price and the probability of being rationed at the low price induce all high-valuation consumers to separate themselves and purchase the good in the first period. In contrast, lowvaluation consumers purchase the good in the last period but are rationed with an optimally determined probability.