The authors explore the properties of various types of public and private pricing on a congested road network, with heterogeneous users, and allowing for elastic demand. The network allows them 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. They find that revenue-maximising pricing is much less efficient than welfare-maximising pricing, but this difference is mitigated by the product differentiation made possible with heterogeneous users. Ignoring heterogeneity causes the welfare benefits of a policy of current interest, namely second-best pricing of one of two parallel links, to be dramatically underestimated. Unlike first-best policies, secondbest policies are in danger of losing much of their potential effectiveness if heterogeneity is ignored when setting toll levels.
Verhoef et al. (Thu,) studied this question.