Many suppliers prefer to ration products than to raise prices to clear the market, as for example when restaurants, cinemas and sports events turn away the last customers to arrive rather than inviting bids for seats. In Discussion Paper No. 805, Richard Gilbert and Research Fellow Paul Klemperer propose that they may be rational to set prices that create excess demand and ration output if consumers incur sunk costs specific to the seller before using its product. Rationing remains inefficient ex post, but it may be rational for the seller if rationing in some states of demand allows higher prices and profits in others. Setting prices to clear the market requires high (low) prices when demand is high (low) for consumers to cover their sunk costs, which favours those in the market when demand is low. If marginal consumers are unlikely to be in the market then, sellers will incur costs by charging low prices and they may do better to attract them at lower cost by charging less than market-clearing prices under high demand. This model may also account for employers' setting wages that create an excess supply of labour and also for `second-sourcing' buyers' purchase of some inputs from an inferior, e.g. more costly, supplier.

Gilbert and Klemperer then extend their model to show that rationing is potentially even more profitable when resale among buyers is permitted. Practices such as airlines' buy-backs of tickets that are overbooked can be viewed as a means to exclude third parties who might otherwise enter the market solely for arbitrage. It may also be optimal for a seller to commit both to a future price that may involve rationing and to a rationing rule that favours past purchasers. Sellers' targeting of subsidies on key customers may also account for phenomena such as apparently discriminatory refusals to trade. Sellers who allocate to all customers that have previously made seller-specific investments guarantee them a positive surplus ex post, which induces them to make the desired investments ex ante.

An Equilibrium Theory of Rationing
Richard J Gilbert and Paul Klemperer

Discussion Paper No. 805, July 1993 (AM)