Product Differentiation on Roads: Constrained Congestion Pricing with Heterogeneous Users

We explore the properties of various types of public and private pricing on a congested road network, with heterogeneous users and allowing for elastic demand. Heterogeneity is represented by a continuum of values of time. The network allows us to model certain features of real-world significance: pricing restrictions on either complementary or substitute links, as well as interactions between different user groups on shared links (e.g. in city centers). We find that revenue-maximizing pricing, whether restricted or unrestricted; but this difference is mitigated by the product differentiation made possible with heterogeneous users. Product differentiation also produces some unexpected distributional effects: those hurt most by pricing may be people with moderate rather than low values of time, and first-best pricing can cause congestion levels to increase for some users compared to no pricing. Ignoring heterogeneity causes the welfare benefits of a policy close to one currently being used, namely second-best pricing of one of two parallel links, to be dramatically underestimated. Unlike first-best policies, second-best policies are in danger of losing much of their potential effectiveness if heterogeneity is ignored when setting toll levels.