Tolls vs tradable permits for managing travel on a bimodal congested network with variable capacities and demands

Congestion pricing has long been considered an efficient tool for tackling road traffic congestion, but tolls are generally unpopular. Interest is growing in tradable permits as an alternative. Tolls and tradable permits are interchangeable if travel conditions are unchanging, but not if conditions vary and tolls and permit quantities are inflexible and cannot be adapted to current conditions. We compare the allocative efficiency of tolls and tradable permits on a bimodal network under uncertainty. Road links are congestion prone and public transit may be crowded. Road traffic entering a cordon area around the downtown is controlled using either a toll or a tradable permit. Two groups of travelers can drive or take transit. Group 1 travels downtown, and if it drives it must either pay the toll or use a permit. Group 2 travels to a suburb, and can avoid the cordon by taking a bypass. All demand and cost parameters of the model can vary, either systematically or irregularly. Each parameter combination constitutes a state. Travelers learn the state in advance, and adapt their mode and route choices accordingly. A planner minimizes expected total travel costs by either setting the level of the toll or choosing the quota of permits to distribute. Two cases are considered. In the first, the toll and quota are flexible and can be adjusted to daily travel conditions. In the second, the instruments are inflexible and must be set at the same level regardless of the state. If travelers have identical preferences, the optimal flexible toll is invariant to the numbers of travelers in each group and the capacity of the link entering the cordon. The toll is robust in the sense that inflexibility causes no welfare loss if these parameters vary. By contrast, the quota is not robust. We derive a general rule for ranking the efficiency of a fixed toll and fixed quota. We then explore a numerical example. In most instances, the fixed toll outperforms the fixed quota by a significant margin although the quota can do better in some states. We also compare the welfare-distributional effects of tolls and permits, and find that suburban travelers fare better than downtown travelers from both forms of regulation.