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

Yu (Marco) Nie*, Yang Liu

*Corresponding author for this work

Research output: Contribution to journalArticle

58 Scopus citations


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. Our 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, we 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 our 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.

Original languageEnglish (US)
Pages (from-to)39-51
Number of pages13
JournalTransportation Research Part A: Policy and Practice
Issue number1
StatePublished - Jan 1 2010


  • Congestion pricing
  • Log-normal
  • Pareto-improving
  • Self-financing
  • Value of time

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation
  • Management Science and Operations Research

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