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Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demands

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  • Erik T. Verhoef

    ()
    (Vrije Universiteit Amsterdam)

Abstract

This paper studies the second-best problem where not all links of a congestedtransportation network can be tolled. The second-best tax rule for thisproblem is derived for general static networks, so that the solution presentedis valid for any graph of the network and any set of tolling points available.A number of known second-best tax rules are shown to be special cases of thegeneral solution presented. It is further demonstrated that, for instance byusing the concept of 'virtual links', the same method can be applied to abroader class of second-best problems in static networks. Finally, a smallnetwork is used to demonstrate numerically that an interior second-bestoptimum need not always be unique, and need not always exist. However, bothexamples require extreme differences in marginal external costs across links,and a non-optimal toll-point to be used, which casts doubt on the practicalrelevance of this complication.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 00-078/3.

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Date of creation: 26 Sep 2000
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Handle: RePEc:dgr:uvatin:20000078

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  1. Erik Teodoor Verhoef, 1998. "Time, speeds, flows and densities in static models of road traffic congestion and congestion pricing," ERSA conference papers ersa98p156, European Regional Science Association.
  2. Verhoef Erik T., 1997. "Externalities," Serie Research Memoranda 0031, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  3. de PALMA, André & 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).
  4. Glazer, Amihai & Niskanen, Esko, 2001. "Parking fees and congestion," University of California Transportation Center, Working Papers qt9h51t02k, University of California Transportation Center.
  5. Arnott, Richard J., 1979. "Unpriced transport congestion," Journal of Economic Theory, Elsevier, vol. 21(2), pages 294-316, October.
  6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  7. 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.
  8. Sullivan, Arthur M., 1983. "Second-best policies for congestion externalities," Journal of Urban Economics, Elsevier, vol. 14(1), pages 105-123, July.
  9. Richard Arnott & Andre de Palma & Robin Lindsey, 1985. "Economics of a Bottleneck," Working Papers 636, Queen's University, Department of Economics.
  10. Erik T. Verhoef & Kenneth A. Small, 1999. "Product Differentiation on Roads: Second-Best Congestion Pricing with Heterogeneity under Public and Private Ownership," Tinbergen Institute Discussion Papers 99-066/3, Tinbergen Institute.
  11. 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.
  12. Verhoef, Erik T. & Emmerink, Richard H. M. & Nijkamp, Peter & Rietveld, Piet, 1996. "Information provision, flat and fine congestion tolling and the efficiency of road usage," Regional Science and Urban Economics, Elsevier, vol. 26(5), pages 505-529, August.
  13. 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.
  14. 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.
  15. Erik T. Verhoef, 2000. "Second-Best Congestion Pricing in General Networks - Algorithms for Finding Second-Best Optimal Toll Levels and Toll Points," Tinbergen Institute Discussion Papers 00-084/3, Tinbergen Institute.
  16. 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.
  17. Small, Kenneth A. & Gomez-Ilbanez, Jose A., 1998. "Road Pricing for Congestion Management: The Transition from Theory to Policy," University of California Transportation Center, Working Papers qt8kk909p1, University of California Transportation Center.
  18. Wilson, John D., 1983. "Optimal road capacity in the presence of unpriced congestion," Journal of Urban Economics, Elsevier, vol. 13(3), pages 337-357, May.
  19. 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.
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