IDEAS home Printed from
   My bibliography  Save this paper

Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand


  • Paul Koster
  • Erik T. Verhoef

    (VU University Amsterdam, the Netherlands)

  • Simon Shepherd
  • David Watling

    (University of Leeds, United Kingdom)


This paper deals with first-best and second-best congestion pricing of a stylised two-link network with probabilistic route choice of travellers. Travellers may have heterogeneous values of travel times and may differ in their idiosyncratic route preferences. We derive first-best and second-best tolls taking into account how the overall network demand responds to generalized costs including the tolls that are levied. We show that with homogeneous values of times the welfare losses of second-best pricing, of one link only, may be smaller if route choice is probabilistic. Furthermore, we show that with heterogeneous values of times, common second-best tolls and group-differentiated tolls can be very close when route choice is governed by random utility maximisation, leading to low welfare losses from the inability to differentiate tolls.

Suggested Citation

  • Paul Koster & Erik T. Verhoef & Simon Shepherd & David Watling, 2014. "Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand," Tinbergen Institute Discussion Papers 14-078/VIII, Tinbergen Institute, revised 13 Nov 2014.
  • Handle: RePEc:tin:wpaper:20140078

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. van den Berg, Vincent & Verhoef, Erik T., 2011. "Congestion tolling in the bottleneck model with heterogeneous values of time," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 60-78, January.
    3. Small, Kenneth A & Rosen, Harvey S, 1981. "Applied Welfare Economics with Discrete Choice Models," Econometrica, Econometric Society, vol. 49(1), pages 105-130, January.
    4. Huang, Hai-Jun & Li, Zhi-Chun, 2007. "A multiclass, multicriteria logit-based traffic equilibrium assignment model under ATIS," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1464-1477, February.
    5. H C W L Williams, 1977. "On the formation of travel demand models and economic evaluation measures of user benefit," Environment and Planning A, Pion Ltd, London, vol. 9(3), pages 285-344, March.
    6. Verhoef, Erik & Nijkamp, Peter & Rietveld, Piet, 1996. "Second-Best Congestion Pricing: The Case of an Untolled Alternative," Journal of Urban Economics, Elsevier, vol. 40(3), pages 279-302, November.
    7. Parry, Ian W.H., 2008. "How should heavy-duty trucks be taxed?," Journal of Urban Economics, Elsevier, vol. 63(2), pages 651-668, March.
    8. H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
    9. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1992. "Route choice with heterogeneous drivers and group-specific congestion costs," Regional Science and Urban Economics, Elsevier, vol. 22(1), pages 71-102, March.
    10. van den Berg, Vincent & Verhoef, Erik T., 2011. "Winning or losing from dynamic bottleneck congestion pricing?: The distributional effects of road pricing with heterogeneity in values of time and schedule delay," Journal of Public Economics, Elsevier, vol. 95(7-8), pages 983-992, August.
    11. Small, Kenneth A. & Yan, Jia, 2001. "The Value of "Value Pricing" of Roads: Second-Best Pricing and Product Differentiation," Journal of Urban Economics, Elsevier, vol. 49(2), pages 310-336, March.
    12. Lei Zhang & David M. Levinson & Shanjiang Zhu, 2008. "Agent-Based Model of Price Competition, Capacity Choice, and Product Differentiation on Congested Networks," Journal of Transport Economics and Policy, University of Bath, vol. 42(3), pages 435-461, September.
    13. Light, Thomas, 2009. "Optimal highway design and user welfare under value pricing," Journal of Urban Economics, Elsevier, vol. 66(2), pages 116-124, September.
    14. de Palma, André & Kilani, Moez & Lindsey, Robin, 2008. "The merits of separating cars and trucks," Journal of Urban Economics, Elsevier, vol. 64(2), pages 340-361, September.
    15. Vincent van den Berg & Erik T. Verhoef, 2011. "Congesting Pricing in a Road and Rail Network with Heterogeneous Values of Time and Schedule Delay," Tinbergen Institute Discussion Papers 11-059/3, Tinbergen Institute, revised 24 May 2012.
    16. Small, Kenneth A., 2012. "Valuation of travel time," Economics of Transportation, Elsevier, vol. 1(1), pages 2-14.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Ioannis Tikoudis, 2015. "Congestion Pricing in Urban Polycentric Networks with Distorted Labor Markets: A Spatial General Equilibrium Model for the Area Randstad," Tinbergen Institute Discussion Papers 15-085/VIII, Tinbergen Institute, revised 26 Oct 2017.

    More about this item


    Stochastic User Equilibrium; Second-best Congestion Pricing; Preference Heterogeneity; Scale Heterogeneity; Probabilistic Choice;

    JEL classification:

    • R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise
    • R48 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Government Pricing and Policy

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20140078. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tinbergen Office +31 (0)10-4088900). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.