On optimal congestion

A number of classic papers conclude that if a congestible facility is the property of a profit maximizing entrepreneur, he will impose a charge for use that induces the socially optimal level of use and congestion. All these papers happen to deal with a special case in which that conclusion holds, but it is not true in general. In general, the socially optimal level of use of a congestible facility is the level at which the marginal cost of providing the service is equal to the sum of the decreases in the users' willingnesses to pay for a unit of service when the level of congestion is optimal, and need not coincide with the level resulting from a profit-maximizing charge. This sum is derived from the integral under a fictitious demand curve constructed by imagining that the level of congestion is the same (and optimal) at all levels of the use-charge.