Monopoly pricing when customers queue

It takes time to process purchases and as a result a queue of customers may form. The pricing and capacity (service rate) decision of a monopolist who must take this into account are characterized. We find that an increase in the average number of customers arriving in the market either has no effect on the price, or else causes the firm to reduce the prince in the short run. In the long run the firm will increase capacity and raise the price. When customer preferences are linear, the equilibrium is socially efficient. When preferences are not linear, the equilibrium will not normally be socially efficient.