Optimal Link Tolls for Multi-node and Multi-link Transportation Networks Taking into Account the Welfare Cost of Fund Procurement

Abstract

This study discusses the optimal link toll, which maximizes social surplus under a user equilibrium condition, with imperfect substitution assumption for route choice in a transportation network with many nodes and links, as well as taking into account the welfare cost of funds procurement. In contrast to previous studies, this study formulates optimal link tolls, taking into account the marginal cost of public funds (MCF), which is the marginal welfare loss of taxpayers due to a marginal tax raise. The formula for optimal tolls on links is derived from the following conditions. One is MCF classified into two, not taking into account funding (MCF equal to -1) and pricing for funding (MCF does not equal -1). Another is tolls classified into two, pricing on all links (full link pricing), and pricing on a specific link (partial link pricing). Following the above conditions, this study succeeds in deriving the formula for optimal tolls on a full network with many links and nodes. Furthermore, this study indicates two calculation methods: one is to solve analytically or numerically for when the functional form of link flow demand is known. When the functional form is unknown, such as a perfect substitution case, it is necessary to carry out iteration until convergence: with the traffic assignment given the price level and with a change in price level based on the traffic assignment.