State Dependent Pricing with a Queue

Existing studies of pricing when customers queue, assume that the firm cannot adjust the price to the state of demand. In most applications this assumption is false. We adapt the classic model of Naor (1969) to allow the firm to adjust the price to the state of demand. When customers are homogeneous the firm's pricing rule maximizes social welfare. When customers are unobservably heterogenous, the firm's pricing rule does not maximize social welfare. We find that the firm may not always attract customers even when it is technically and economically feasible to do so. This is interpreted as an option effect. The effects of changes to the basic parameters, on the queue length are presented.