Pareto-improving toll and subsidy scheme on transportation networks

This paper presents an original study on the economics of a link-based Toll and Subsidy Scheme (TSS) on a general transportation network. Different from a traditional congestion pricing scheme, the combination of toll and subsidy is found to be able to serve more planning purposes simultaneously, such as efficiency, fairness, and public acceptance. We first demonstrate that on a one-origin or one-destination network, a pareto-improving, system-optimal and revenue-neutral TSS always exists and can be obtained by solving a set of linear equations. Recognizing that such a scheme may not always exist for a multi-origin network, we then define the maximum-revenue problem with pareto-improving constrains to find the maximum possible revenue collected by the toll and subsidy scheme with optimal arc flows and non-increasing origin-destination travel costs. We discover that the problem is actually the dual problem of a balanced transportation problem, which can thus be solved efficiently by existing algorithms. At the end of the paper, a numerical example with a small synthetic network is provided for the comparison of toll and subsidy scheme with other existing toll schemes in terms of OD travel disutilities.