Existence of self-financing and Pareto-improving congestion pricing: Impact of value of time distribution

Document Type

Journal Article

Publication Date


Subject Area

operations - traffic, policy - congestion, economics - pricing, economics - value of time, organisation - management


Value of time, Traffic management (Physical distribution), Self-financing, Refunds, Physical distribution, Pareto method, Mathematical models, Distribution, Congestion pricing


This paper considers a static congestion pricing model in which travelers select a mode from either, driving on highway or taking public transit, to minimize a combination of travel time, operating cost and toll. The focus is to examine how travelers' value of time (VOT), which is continuously distributed in a population, affects the existence of a pricing-refunding scheme that is both self-financing (i.e. requiring no external subsidy) and Pareto-improving (i.e. reducing system travel time while making nobody worse off). A condition that insures the existence of a self-financing and Pareto-improving (SFPI) toll scheme is derived. The authors' derivation reveals that the toll authority can select a proper SFPI scheme to distribute the benefits from congestion pricing through a credit-based pricing scheme. Under mild assumptions, the authors prove that an SFPI toll always exists for concave VOT functions, of which the linear function corresponding to the uniform distribution is a special case. Existence conditions are also established for a class of rational functions. These results can be used to analyze more realistic VOT distributions such as log-normal distribution. A useful implication of study analysis is that the existence of an SFPI scheme is not guaranteed for general functional forms. Thus, external subsidies may be required to ensure Pareto-improving, even if policy-makers are willing to return all toll revenues to road users.


Transportation Research Part A Home Page: http://www.sciencedirect.com/science/journal/09658564