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Pricing, capacity and long-run cost functions for first-best and second-best network problems

  • Verhoef, Erik T.
  • Koh, Andrew
  • Shepherd, Simon

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 sub-set 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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Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 44 (2010)
Issue (Month): 7 (August)
Pages: 870-885

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Handle: RePEc:eee:transb:v:44:y:2010:i:7:p:870-885
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  1. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  2. 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.
  3. 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.
  4. Erik T. Verhoef & Jan Rouwendal, 2004. "Pricing, Capacity Choice, and Financing in Transportation Networks," Journal of Regional Science, Wiley Blackwell, vol. 44(3), pages 405-435.
  5. 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.
  6. Bruno De Borger & Stef Proost & Kurt Van Dender, 2003. "Congestion and tax competition in a parallel network," Energy, Transport and Environment Working Papers Series ete0309, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, Energy, Transport and Environment.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Verhoef, Erik T., 2007. "Second-best road pricing through highway franchising," Journal of Urban Economics, Elsevier, vol. 62(2), pages 337-361, September.
  13. 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.
  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.
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