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Second-Best Congestion Pricing in General Networks - Algorithms for Finding Second-Best Optimal Toll Levels and Toll Points

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Author Info
Erik T. Verhoef () (Vrije Universiteit Amsterdam)

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Abstract

This paper considers the second-best problem where not all links of a congested transportation network can be tolled. The paper builds on earlier work, in which the second-best tax rule for this problem was derived for general static networks, so that the solution presented is valid for any graph of the network, and for any set of tolling points available on that network. An algorithm is presented for finding second- best tolls, based on this general solution. A simulation model is used for studying its performance for various archetype pricing schemes: a toll-cordon, area licences, parking policies in the city centre, pricing of a single major highway, and pay-lanes and 'free-lanes' on major highways. Furthermore, an exploratory analysis is given of a method for selecting the optimal location of toll points in case not all links can be tolled.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-084/3.

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Date of creation: 23 Oct 2000
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Handle: RePEc:dgr:uvatin:20000084

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  1. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September. [Downloadable!] (restricted)
  2. Verhoef Erik T., 1997. "Externalities," Serie Research Memoranda 0031, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics. [Downloadable!]
  3. Braid, Ralph M., 1989. "Uniform versus peak-load pricing of a bottleneck with elastic demand," Journal of Urban Economics, Elsevier, vol. 26(3), pages 320-327, November. [Downloadable!] (restricted)
  4. AndrÊ de Palma & Robin Lindsey, 2000. "Private toll roads: Competition under various ownership regimes," The Annals of Regional Science, Springer, vol. 34(1), pages 13-35. [Downloadable!] (restricted)
  5. Braid, Ralph M., 1996. "Peak-Load Pricing of a Transportation Route with an Unpriced Substitute," Journal of Urban Economics, Elsevier, vol. 40(2), pages 179-197, September. [Downloadable!] (restricted)
  6. Liu, Louie Nan & McDonald, John F., 1998. "Efficient Congestion Tolls in the Presence of Unpriced Congestion: A Peak and Off-Peak Simulation Model," Journal of Urban Economics, Elsevier, vol. 44(3), pages 352-366, November. [Downloadable!] (restricted)
  7. de PALMA, AndrŽ & NESTEROV, Yurii, 1998. "Optimization formulations and static equilibrium in congested transportation networks," CORE Discussion Papers 1998061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  8. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January. [Downloadable!] (restricted)
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  9. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May. [Downloadable!] (restricted)
  10. Erik T. Verhoef, 2000. "Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demands," Tinbergen Institute Discussion Papers 00-078/3, Tinbergen Institute. [Downloadable!]
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  11. Liu, Louie Nan & McDonald, John F., 1999. "Economic efficiency of second-best congestion pricing schemes in urban highway systems," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 157-188, April. [Downloadable!] (restricted)
  12. Verhoef, Erik T., 1999. "Time, speeds, flows and densities in static models of road traffic congestion and congestion pricing," Regional Science and Urban Economics, Elsevier, vol. 29(3), pages 341-369, May. [Downloadable!] (restricted)
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  13. Verhoef, E.T. & Small, K.A., 1999. "Product Differentiation on Roads Second-Best Congestion Pricing with Heterogeneity under Public and Private Ownership," Papers 99-00-01, California Irvine - School of Social Sciences.
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  14. Glazer, Amihai & Niskanen, Esko, 1992. "Parking fees and congestion," Regional Science and Urban Economics, Elsevier, vol. 22(1), pages 123-132, March. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. May, A. D. & Milne, D. S., 2000. "Effects of alternative road pricing systems on network performance," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(6), pages 407-436, August. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. De Borger Bruno & Mayeres Inge, 2004. "Taxation of car ownership, car use and public transport: insights derived from a discrete choice numerical optimisation model," Energy, Transport and Environment Working Papers Series ete0413, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Energy, Transport and Environment. [Downloadable!]
    Other versions:
  2. Yannick Gabuthy & Matthieu Neveu & Laurent Denant-Boemont, 2006. "The Coordination Problem in a Structural Model of Peak-Period Congestion: An Experimental Study," Review of Network Economics, Concept Economics, vol. 5(2), pages 273-298, June. [Downloadable!]
  3. Richard Arnott & Elizaveta Shevyakhova, 2007. "Tenancy Rent Control and Credible Commitment in Maintenance," Boston College Working Papers in Economics 661, Boston College Department of Economics. [Downloadable!]
    Other versions:
  4. Simon Shepherd, 2008. "The effect of complex models of externalities on estimated optimal tolls," Transportation, Springer, vol. 35(4), pages 559-577, July. [Downloadable!] (restricted)
  5. Erik T. Verhoef & Peter Nijkamp, 2003. "Externalities in the Urban Economy," Tinbergen Institute Discussion Papers 03-078/3, Tinbergen Institute. [Downloadable!]
  6. Parry, Ian & Harrington, Winston & Nelson, Per-Kristian & Safirova, Elena & Mason, Dave & Gillingham, Kenneth, 2003. "Welfare and Distributional Effects of Road Pricing Schemes for Metropolitan Washington, DC," Discussion Papers dp-03-57, Resources For the Future. [Downloadable!]
    Other versions:
  7. Lei Zhang & David Levinson & Shanjiang Zhu, 2007. "Agent-Based Model of Price Competition and Product Differentiation on Congested Networks," Working Papers 200809, University of Minnesota: Nexus Research Group. [Downloadable!]
  8. Erik T. Verhoef & Andrew Koh & Simon Shepherd, 2008. "Pricing, Capacity and Long-run Cost Functions for First-best and Second-best Network Problems," Tinbergen Institute Discussion Papers 08-056/3, Tinbergen Institute. [Downloadable!]
  9. Erik T. Verhoef, 2000. "Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demands," Tinbergen Institute Discussion Papers 00-078/3, Tinbergen Institute. [Downloadable!]
    Other versions:
  10. Takamasa Akiyama & Se-Il Mun & Masashi Okushima, 2004. "Second-Best Congestion Pricing in Urban Space: Cordon Pricing and Its Alternatives," Review of Network Economics, Concept Economics, vol. 3(4), pages 401-414, December. [Downloadable!]
  11. Richard Arnott & John Rowse, 2007. "Downtown Parking in Auto City," Boston College Working Papers in Economics 665, Boston College Department of Economics. [Downloadable!]
    Other versions:
  12. Safirova, Elena A. & Houde, Sébastien & Lipman, D. Abram & Harrington, Winston & Bagliano, Andrew D., 2006. "Congestion Pricing: Long-Term Economic and Land-Use Effects," Discussion Papers dp-06-37, Resources For the Future. [Downloadable!]
  13. Richard Arnott, 2007. "Congestion Tolling with Agglomeration Externalities," Boston College Working Papers in Economics 660, Boston College Department of Economics. [Downloadable!]
    Other versions:
  14. Erik T. Verhoef, 2005. "Second-best Road Pricing Through Highway Franchising," Tinbergen Institute Discussion Papers 05-082/3, Tinbergen Institute. [Downloadable!]
    Other versions:
  15. Safirova, Elena A. & Houde, Sébastien & Coleman, Conrad T. & Harrington, Winston & Lipman, D. Abram, 2006. "Long-Term Consequences of Congestion Pricing: A Small Cordon in the Hand Is Worth Two in the Bush," Discussion Papers dp-06-42, Resources For the Future. [Downloadable!]
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