Revenue management without commitment: Dynamic pricing and periodic fire sales

Hosted by Claudio Mezzeti

We consider a market with a profit-maximizing monopolist seller who has K identical goods to sell before a deadline. At each point of time, the seller posts a price and the quantity available but cannot commit to future offers. Over time, potential buyers with different reservation values enter the market. Buyers strategically time their purchases, trading off:

1. the current price without competition and
2. a possibly lower price in the future with the risk of being rationed.

We analyze equilibrium price paths and buyers' purchases behavior in which prices decline smoothly over the time period between sales and jump up immediately after a transaction occurs. In equilibrium, high-value buyers purchasing on arrival. Crucially, the seller may periodically liquidate part of his stock via fire sales before the deadline in order to secure a higher price in the future. Intuitively, these sales allow the seller to 'commit' to high prices going forward.

The possibility of fire sales before the deadline implies that the allocation may be inefficient. The inefficiency arises from the scarce good being misallocated to low-value buyers, rather than the withholding inefficiency that is normally seen with a monopolist seller.