Second-best Pricing for Imperfect Substitutes in Urban Networks

This paper considers second-best pricing as it arises through incomplete coverage of full networks. The main principles are first reviewed by considering the classic two-route problem and some extensions that have been studied more recently. In most of these studies the competing routes are assumed to be perfect substitutes, which is probably not the case for most parallel roads in reality, and even less likely for the case where competing connections represent different transport modes. In this paper a modelling framework in which the alternatives are imperfect substitutes is developed and numerical results for two roads and two modes are presented. In the model, trip generation and trip distribution are distinguished in a way that is consistent with economic theory. The model is used to consider situations in which one route or mode cannot be tolled. Simulation results show that, for the chosen parameter values, there is a substantial difference between the effec!tiveness of policies in which the capacities have to be taken as given, and those in which capacity of at least one mode can be changed. A striking feature of the policy in which the capacities of both modes/routes and the railway fare/toll on one road can be used as policy instruments is the existence of two equilibria for a range of values of â. In one equilibrium there are substantial numbers of users of both modes, whereas in the other use of one mode is negligible.