Peak-load pricing of a transportation route with an unpriced substitute

This paper considers two routes to work, which could be two bridges, a freeway and a tollroad, or roadway travel and subway travel. Both routes are subject to pure bottleneck-and-queue congestion. If peak-load pricing can be imposed on both routes, the first-best solution is attained. However, if one route is unpriced, then the other route should have a second-best time-varying toll that is negative at the tails of the rush hour, positive near the peak of the rush hour, and zero on average. If the two routes have the same capacities, and if the parameter g is 1, then two-thirds of the total traffic should use the priced route, and the efficiency gain of second-best pricing is two-thirds of the efficiency gain of first-best pricing. (C) 1996 Academic Press, Inc.