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The Downs–Thomson paradox with imperfect mode substitutes and alternative transit administration regimes


  • Zhang, Fangni
  • Lindsey, Robin
  • Yang, Hai


The Downs–Thomson paradox (D–T paradox) occurs when expansion of a congested and untolled highway undermines scale economies of a competing transit service, leaving users of both modes worse off. The standard analysis of the D–T paradox is based on several stringent assumptions: fixed total travel demand, perfect substitutability between automobile and transit trips, and no transit crowding. This paper re-examines the paradox when these assumptions are relaxed while retaining the usual assumption that there is no congestion interaction between the modes. It also broadens consideration to alternative transit administration regimes. In the standard treatment the transit operator is obliged to cover its costs. In this paper we also study two other regimes: transit profit maximization, and system-wide welfare maximization with no financing constraint. We examine how the transit system operator responds to highway capacity expansion in each regime, and how this affects welfare for drivers and transit users. We show that in all regimes the full price of transit declines only if the full price of driving falls as well. Thus, drivers are more likely to benefit from highway expansion than transit riders. The D–T paradox cannot occur in the profit maximization or unconstrained welfare maximization regimes. In the traditional self-financing regime transit service deteriorates, but the D–T paradox is not inevitable. Numerical analysis suggests that it can occur only when automobile and transit trips are nearly perfect substitutes.

Suggested Citation

  • Zhang, Fangni & Lindsey, Robin & Yang, Hai, 2016. "The Downs–Thomson paradox with imperfect mode substitutes and alternative transit administration regimes," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 104-127.
  • Handle: RePEc:eee:transb:v:86:y:2016:i:c:p:104-127
    DOI: 10.1016/j.trb.2016.01.013

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    Cited by:

    1. Wang, Wei (Walker) & Wang, David Z.W. & Zhang, Fangni & Sun, Huijun & Zhang, Wenyi & Wu, Jianjun, 2017. "Overcoming the Downs-Thomson Paradox by transit subsidy policies," Transportation Research Part A: Policy and Practice, Elsevier, vol. 95(C), pages 126-147.
    2. Li, Chuanyao & Huang, Haijun, 2019. "Analysis of bathtub congestion with continuous scheduling preference," Research in Transportation Economics, Elsevier, vol. 75(C), pages 45-54.
    3. Liu, Wei & Geroliminis, Nikolas, 2017. "Doubly dynamics for multi-modal networks with park-and-ride and adaptive pricing," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 162-179.
    4. van den Berg, Vincent A.C. & Verhoef, Erik T., 2016. "Autonomous cars and dynamic bottleneck congestion: The effects on capacity, value of time and preference heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 43-60.
    5. Liu, Wei & Geroliminis, Nikolas, 2016. "Modeling the morning commute for urban networks with cruising-for-parking: An MFD approach," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 470-494.
    6. Zhang, Fangni & Liu, Wei & Wang, Xiaolei & Yang, Hai, 2017. "A new look at the morning commute with household shared-ride: How does school location play a role?," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 198-217.
    7. Liu, Wei & Zhang, Fangni & Yang, Hai, 2017. "Modeling and managing morning commute with both household and individual travels," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 227-247.
    8. Zhang, Junlin & Lindsey, Robin & Yang, Hai, 2018. "Public transit service frequency and fares with heterogeneous users under monopoly and alternative regulatory policies," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 190-208.
    9. Wang, Jing & Zhang, Xiaoning & Wang, Hua & Zhang, Michael, 2019. "Optimal parking supply in bi-modal transportation network considering transit scale economies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 207-229.


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