Beschreibung:
We consider if a road is self-financing under flat or step tolling and optimized capacity while incorporating preference heterogeneity, bottleneck congestion and linear capacity cost. Previous work has shown that a sufficient condition for the toll revenue to equal the capacity cost is that the toll to equals the marginal external costs (MECs) of all types of user at all moments when their users travel. However, under 'ratio heterogeneity' between values of time (VOT) and schedule delay, an anonymous second-best coarse toll must differ from the heterogeneous MECs. This paper derives that this toll will be a weighted average of the MECs with the weights depending on the derivatives of the demand and travel cost functions. 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 was ignored in previous work and makes selffinancing less likely than previously thought, but it can still occur if Low-VOT users are much more price sensitive than High-VOT users, as this raises the toll. In our numerical model, the Low-VOT type must be almost twice as price sensitive than the High-VOT type for there not to be loss; and, typically, there is a 5% to 15% loss. Imposing self-financing only causes a small welfare loss of 0% to 1.5%. We also analyze other forms of heterogeneity: proportional heterogeneity, heterogeneity in the preferred arrival time and heterogeneity between values of schedule delay early and late.