Pareto-Improving and Self-Sustainable Pricing for the Morning Commute with Nonidentical Commuters

Congestion pricing, one of the effective tools to reduce congestion in a transportation network, may cause inequity among commuters if the differences in their value of time (VOT) are not properly taken into account. In this paper, we develop a bimodal competition model within the context of nonidentical commuters and departure time choice to study toll design, mode share, and benefit distribution problems. We first show that for a single bottleneck without schedule-late delay, commuters pass the bottleneck in increasing order of VOT under an optimal dynamic toll, and the optimal toll curve is strictly increasing and convex. Equipped with this result, we then derive the corresponding toll patterns, departure profiles, mode share, and user benefits in the morning commute under congestion tolls. We find that a queue-eliminating dynamic toll on the highway can drive the two-mode system to optimum, and it is Pareto improving. However, when a constant toll is used, commuters in the middle of the VOT distribution are possibly made worse off by the toll. By proposing a transit subsidy together with a toll charge on the highway, we obtain a core of feasible toll plus subsidy schemes that can simultaneously achieve three goals: driving the system toward optimum, benefiting every commuter, and financing itself without external investment. The results show that to be in this core, the toll charge can neither be too low nor too high.