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

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  • Erik T. Verhoef

    ()
    (VU University Amsterdam)

  • Andrew Koh

    ()
    (University of Leeds)

  • Simon Shepherd

    ()
    (University of Leeds)

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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Bibliographic 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

Related research

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

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References

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  1. 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.
  2. Erik T. Verhoef & Herbert Mohring, 2007. "Self-Financing Roads," Tinbergen Institute Discussion Papers 07-068/3, Tinbergen Institute.
  3. Erik T. Verhoef & Jan Rouwendal, 2004. "Pricing, Capacity Choice, and Financing in Transportation Networks," Journal of Regional Science, Wiley Blackwell, Wiley Blackwell, vol. 44(3), pages 405-435.
  4. Erik T. Verhoef, 1998. "Second-Best Congestion Pricing in General Static Transportation Networks with Elastic Demand," Tinbergen Institute Discussion Papers 98-086/3, Tinbergen Institute.
  5. DE BORGER, Bruno & PROOST, Stef & VAN DENDER, K., . "Congestion and tax competition in a parallel network," Working Papers 2004003, University of Antwerp, Faculty of Applied Economics.
  6. Erik T. Verhoef, 2005. "Second-best Road Pricing Through Highway Franchising," Tinbergen Institute Discussion Papers 05-082/3, Tinbergen Institute.
  7. AndrÊ de Palma & Robin Lindsey, 2000. "Private toll roads: Competition under various ownership regimes," The Annals of Regional Science, Springer, Springer, vol. 34(1), pages 13-35.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Small, Kenneth A. & Gomez-Ibanez, Jose A., 1999. "Urban transportation," Handbook of Regional and Urban Economics, Elsevier, in: P. C. Cheshire & E. S. Mills (ed.), Handbook of Regional and Urban Economics, edition 1, volume 3, chapter 46, pages 1937-1999 Elsevier.
  14. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  15. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-79, March.
  16. 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.
  17. 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.
  18. Yang, Hai & Meng, Qiang & Lee, Der-Horng, 2004. "Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions," Transportation Research Part B: Methodological, Elsevier, vol. 38(6), pages 477-493, July.
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Citations

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Cited by:
  1. Wu, Di & Yin, Yafeng & Lawphongpanich, Siriphong, 2011. "Optimal selection of build–operate-transfer projects on transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1699-1709.
  2. Andrew Koh & Simon Shepherd & Agachai Sumalee, 2009. "Second best toll and capacity optimisation in networks: solution algorithm and policy implications," Transportation, Springer, Springer, vol. 36(2), pages 147-165, March.

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