# Mathematical principles of road congestion pricing

The original publication is available at http://orion.journals.ac.za/pub

Journal Article

This paper briefly considers the objectives of road congestion pricing and identifies prereq- uisites to the successful application of such a pricing scheme. The paper is divided into two sections. In the first section, a mathematical analysis of the constituents of an optimal road congestion price is offered. The eliminated inefficiency loss achieved by the introduction of a congestion levy is usually evaluated by means of an integral involving marginal trip cost, travel demand and average trip cost in two-dimensional (travel time, traffic flow)-space. In this section we show that this loss may, in fact, be evaluated more easily for a general marginal trip cost function and a linear demand function as the difference between the areas of a rectangle (representing the part of road agency revenue that lies below the original trip cost) and a triangle (representing the loss of consumer surplus of the reduced traffic) in (travel time, traffic flow)-space, eliminating the need to use integration. The next section deals with the application of the illustrated mathematical principles and proofs to a hypothetical case study relating to road congestion pricing in Cape Town.