Self-financing roads under coarse tolling and preference heterogeneity

We consider whether a road is self-financing under flat or step tolling and optimized bottleneck capacity while incorporating preference heterogeneity and price-sensitive demand. Previous work has shown that a sufficient condition for the toll revenue to equal the capacity cost is that the toll equals the marginal external costs (MECs) of all types of users at all their travel moments. However, under 'ratio' heterogeneity between the value of time (VOT) and values of schedule delay, a coarse toll must differ from the heterogeneous MECs. We expand the literature by showing that the capacity rule also has a second-best correction: the capacity is set higher than following the first-best rule to reduce the distortion from overpricing High-VOT users. This issue has been ignored in previous work and makes self-financing less likely than previously thought, but it can still occur if Low-VOT users are much more price sensitive than High-VOT users. In our numerical model, the Low-VOT type must be almost twice as price sensitive as the High-VOT type for there not to be a loss, and, typically, there is a 0 % to 10 % loss. Nevertheless, imposing self-financing only causes a tiny welfare loss. We also discuss other forms of heterogeneity. Under proportional heterogeneity, the self-financing result holds as the coarse toll equals the homogeneous MEC. Under heterogeneity in the preferred arrival time, the self-financing typically also holds.