This paper considers coarse tolling of congestion under heterogeneous preferences, and especially the distributional effects of such tolls. With coarse tolling, the toll equals a fixed value during the centre of the peak; outside this period, it is zero. This paper investigates three dimensions of heterogeneity. With the first, all values of time and schedule delay vary in fixed proportions, and this heterogeneity may stem from income differences. The second has differences in flexibility of users when to arrive. The third captures differences in willingness to arrive before or after the preferred arrival time. The paper uses three models of coarse tolling: the Laih, ADL, and Braking model. All three dimensions affect the welfare gain of coarse tolling. In the Laih model, the generalised price with coarse tolling is in between the no-toll and first-best one. In the other models this is not so, and distributional effects may be non-monotonic and very different from the first-best toll's effects. In the Braking model, the capacity goes unused for some time during the tolled period. Compared with in the Laih model, this raises total cost, and it is most harmful for users with low values and difficulty to arrive late: e.g. low-income users with a strict work start time or a trip to the doctor.
Coarse tolling heterogeneous preferences distributional effects bottleneck model proportional heterogeneity