Is Private Tolling Efficient?

Is Private Tolling Efficient?


N Wagner, Universite Paris-Est, LVMT


We study the impact of heterogeneity in the value of time in a tolling scheme. It is shown that when congestion is modeled dynamically and the tolls are flat, the efficiency of private tolling increases with the level of heterogeneity.


Facing ever rising levels of traffic congestion, many local authorities have given serious consideration to road pricing. Among the existing schemes, value pricing has enjoyed a reasonable success especially in the US. A famous instance is the one currently operating on the SR91 in California. In a value pricing scheme, travelers choose between two roadways: one is free but congested, while the other one is priced but free owing.

An important literature has already explored the design and the assessment of value pricing. It has mainly focused on two features of the problem.

On one hand, it has been pointed out that the welfare gain is highly affected by the level of heterogeneity among the travelers, especially regarding their value of time (e.g. Papon, 1992; Verhoef and Small, 1999; Small and Yan, 2001). These results have been achieved using static models, thus neglecting the time-varying nature of congestion and the possibility for travelers to adjust their departure time, e.g. by leaving earlier than preferred to avoid traffic jams. On the other hand, dynamic models of congestion, most of them inspired by Vickrey's bottleneck model, have been used to assess value pricing. Most of these works tend to neglect the heterogeneity among travelers, or to have a crude representation of it, for instance by considering only two possible values of times (e.g. De Palma and Lindsey, 2002). Papers accounting for both aspects are very rare.

A notable exception is van den Berg and Verhoef (2010) who considered a bottleneck model with two routes, where heterogeneity is represented by a continuum of values of time. Under this framework, they assessed two pricing policies. In both of them a time-varying and queue clearing toll is set on one roadway, while the other one is untolled. However in the first policy the toll is set to maximize revenue while in the second it is set to maximize the welfare gains. This gives interesting results: as in the static case, the level of heterogeneity impacts the welfare gains of both schemes but in an adverse way. In the static case the relative efficiency of a private pricing scheme decreases with heterogeneity. With a bottleneck model, it is the contrary. This is saying that changing the representation of congestion from a static to a dynamic framework leads to radically different results when it comes to the impact of heterogeneity.

Our methodological approach is the following. A bottleneck model with two routes and continuous heterogeneity in the value of time is exposed. It is shown that the problem can be reduced to the resolution of a differential equation and examples of resolution are given in the case of a uniform distribution of the values of time. The results are exploited to assess a value pricing scheme under two ownership regimes. In the first case the priced roadway is publicly owned and the toll is set to maximise the welfare gains; in the second one, it is privately owned and the toll is set to maximise profits.


Association for European Transport