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

Verhoef, ET, Koh, Andrew and Shepherd, SP (2010) Pricing, capacity and long-run cost functions for first-best and second-best network problems. Transportation Research Part B: Methodological, 44 (7). 870 - 885 . ISSN 0191-2615


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.

Item Type: Article
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 30 Jan 2012 11:42
Last Modified: 04 Mar 2015 10:08
Published Version: http://dx.doi.org/10.1016/j.trb.2009.12.002
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.trb.2009.12.002
URI: http://eprints.whiterose.ac.uk/id/eprint/43640

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