== Abstract ==

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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. © 2009 Elsevier Ltd.

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== Original document ==

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The different versions of the original document can be found in:

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* [http://dx.doi.org/10.1016/j.trb.2009.12.002 http://dx.doi.org/10.1016/j.trb.2009.12.002]

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* [http://dx.doi.org/10.2139/ssrn.1143283 http://dx.doi.org/10.2139/ssrn.1143283]

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* [http://hdl.handle.net/10419/86804 http://hdl.handle.net/10419/86804]

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* [http://papers.tinbergen.nl/08056.pdf http://papers.tinbergen.nl/08056.pdf]

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* [https://research.vu.nl/en/publications/281a2faf-2913-4c38-85dc-b1e9e20f2c43 https://research.vu.nl/en/publications/281a2faf-2913-4c38-85dc-b1e9e20f2c43]

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* [https://research.vu.nl/en/publications/8a54c230-e37d-49ca-8d91-d0f5833ea37e https://research.vu.nl/en/publications/8a54c230-e37d-49ca-8d91-d0f5833ea37e]

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* [https://api.elsevier.com/content/article/PII:S0191261509001374?httpAccept=text/xml https://api.elsevier.com/content/article/PII:S0191261509001374?httpAccept=text/xml],

: [https://api.elsevier.com/content/article/PII:S0191261509001374?httpAccept=text/plain https://api.elsevier.com/content/article/PII:S0191261509001374?httpAccept=text/plain],

: [http://dx.doi.org/10.1016/j.trb.2009.12.002 http://dx.doi.org/10.1016/j.trb.2009.12.002] under the license https://www.elsevier.com/tdm/userlicense/1.0/

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* [https://www.sciencedirect.com/science/article/pii/S0191261509001374 https://www.sciencedirect.com/science/article/pii/S0191261509001374],

: [https://research.vu.nl/en/publications/pricing-capacity-and-long-run-cost-functions-for-first-best-and-s-2 https://research.vu.nl/en/publications/pricing-capacity-and-long-run-cost-functions-for-first-best-and-s-2],

: [https://trid.trb.org/view/920437 https://trid.trb.org/view/920437],

: [https://www.narcis.nl/publication/RecordID/oai%3Aresearch.vu.nl%3Apublications%2F8a54c230-e37d-49ca-8d91-d0f5833ea37e https://www.narcis.nl/publication/RecordID/oai%3Aresearch.vu.nl%3Apublications%2F8a54c230-e37d-49ca-8d91-d0f5833ea37e],

: [https://core.ac.uk/display/15454444 https://core.ac.uk/display/15454444],

: [https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1143283 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1143283],

: [https://ideas.repec.org/p/tin/wpaper/20080056.html https://ideas.repec.org/p/tin/wpaper/20080056.html],

: [http://eprints.whiterose.ac.uk/43640 http://eprints.whiterose.ac.uk/43640],

: [https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1143283_code356671.pdf?abstractid=1143283&mirid=1 https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1143283_code356671.pdf?abstractid=1143283&mirid=1],

: [https://econpapers.repec.org/RePEc:eee:transb:v:44:y:2010:i:7:p:870-885 https://econpapers.repec.org/RePEc:eee:transb:v:44:y:2010:i:7:p:870-885],

: [https://ssrn.com/abstract=1143283 https://ssrn.com/abstract=1143283],

: [https://academic.microsoft.com/#/detail/2143308456 https://academic.microsoft.com/#/detail/2143308456]

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DOIS: 10.2139/ssrn.1143283 10.1016/j.trb.2009.12.002

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