Congestion Pricing with Continuously Distributed Values of Time

We develop a model for steady-state congestion pricing in which the value of time has a continuous distribution. Extensions of the usual formula for the toll that maximises the social benefit are found. Different optimal tolls are found depending on whether the social welfare function is measured in money or time units, and whether toll revenue is or is not included as part of the benefit. Distribution effects among the population are examined. Ranges of Pareto efficient tolls under different assumptions concerning the distribution of toll revenue are identified.