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Pricing, Capacity and Long-run Cost Functions for First-best and Second-best Network Problems

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Author Info
Erik T. Verhoef () (VU University Amsterdam)
Andrew Koh () (University of Leeds)
Simon Shepherd () (University of Leeds)

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Abstract

This paper considers the use of ‘long-run cost functions’ for congested networks in solving second-best network problems, in which capacity and tolls are instruments. We derive analytical results both for general cost and demand functions and for specific functional forms, namely Bureau of Public Roads cost functions and constant-elasticity demand functions. The latter are also used in a numerical simulation model. We consider second-best cases where only a subset of links in a network is subject to tolling and/or capacity choice, and cases with and without a self-financing constraint imposed. We will demonstrate that, under certain assumptions, second-best long-run cost (or actually: generalized price) functions can be derived for most of the cases of interest, which can be used in an applied network model as a substitute for the conventional short-run user cost functions. Doing so reduces the dimensionality of the problem and should therefore be helpful in speeding up procedures for finding second-best optima.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-056/3.

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Date of creation: 05 Jun 2008
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Handle: RePEc:dgr:uvatin:20080056

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Traffic congestion; Road pricing; Road capacity choice; Second-best; Networks;

Find related papers by JEL classification:
R41 - Urban, Rural, and Regional Economics - - Transportation Systems - - - Transportation: Demand, Supply, and Congestion
R48 - Urban, Rural, and Regional Economics - - Transportation Systems - - - Government Pricing; Regulatory Policies
D62 - Microeconomics - - Welfare Economics - - - Externalities

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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. Verhoef, Erik T., 2007. "Second-best road pricing through highway franchising," Journal of Urban Economics, Elsevier, vol. 62(2), pages 337-361, September. [Downloadable!] (restricted)
    Other versions:
  2. 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)
  3. 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)
  4. 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)
  5. Erik T. Verhoef & Herbert Mohring, 2007. "Self-Financing Roads," Tinbergen Institute Discussion Papers 07-068/3, Tinbergen Institute. [Downloadable!]
  6. Verhoef, Erik T., 2002. "Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 707-729, September. [Downloadable!] (restricted)
  7. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May. [Downloadable!] (restricted)
  8. Small, K.A. & Gomez-Ibanez, J.A., 1996. "Urban Transportation," Papers 95-96-4, California Irvine - School of Social Sciences.
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  9. Erik T. Verhoef & Jan Rouwendal, 2004. "Pricing, Capacity Choice, and Financing in Transportation Networks," Journal of Regional Science, Blackwell Publishing, vol. 44(3), pages 405-435. [Downloadable!] (restricted)
    Other versions:
  10. Erik T. Verhoef & Kenneth A. Small, 2004. "Product Differentiation on Roads," Journal of Transport Economics and Policy, London School of Economics and University of Bath, vol. 38(1), pages 127-156, January. [Downloadable!] (restricted)
  11. 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)
  12. Sumalee, Agachai & May, Tony & Shepherd, Simon, 2005. "Comparison of judgmental and optimal road pricing cordons," Transport Policy, Elsevier, vol. 12(5), pages 384-390, September. [Downloadable!] (restricted)
  13. Yang, Hai & Huang, Hai-Jun, 1998. "Principle of marginal-cost pricing: how does it work in a general road network?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 45-54, January. [Downloadable!] (restricted)
  14. 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. [Downloadable!]
  15. Verhoef, Erik T., 2002. "Second-best congestion pricing in general static transportation networks with elastic demands," Regional Science and Urban Economics, Elsevier, vol. 32(3), pages 281-310, May. [Downloadable!] (restricted)
    Other versions:
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Cited by:
(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. Andrew Koh & Simon Shepherd & Agachai Sumalee, 2009. "Second best toll and capacity optimisation in networks: solution algorithm and policy implications," Transportation, Springer, vol. 36(2), pages 147-165, March. [Downloadable!] (restricted)
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