Step by Step: Revisiting Step Tolling in the Bottleneck Model

Tinbergen Institute Discussion Paper 10-118/3

41 Pages Posted: 4 Dec 2010 Last revised: 8 May 2012

See all articles by Robin Lindsey

Robin Lindsey

affiliation not provided to SSRN

Vincent A.C. van den Berg

VU University Amsterdam; Tinbergen Institute

Erik T. Verhoef

VU University Amsterdam - Department of Spatial Economics; Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Date Written: November 29, 2010

Abstract

In most dynamic traffic congestion models, congestion tolls must vary continuously over time to achieve the full optimum. This is also the case in Vickrey's (1969) 'bottleneck model'. To date, the closest approximations of this ideal in practice have so-called 'step tolls,' in which the toll takes on different values over discrete time intervals, but is constant within each interval. Given the prevalence of step tolling schemes they have received surprisingly little attention in the literature. This paper compares two step-toll schemes that have been studied using the bottleneck model by Arnott, de Palma and Lindsey (1990) and Laih (1994). It also proposes a third scheme in which late in the rush hour drivers slow down or stop just before reaching a tolling point, and wait until the toll is lowered from one step to the next step. Such behaviour has indeed been observed in reality. Analytical derivations and numerical modelling show that the three tolling schemes have different optimal toll schedules and reduce total social costs by different percentages. These differences persist even in the limit as the number of steps approaches infinity. Braking lowers the welfare gain from tolling by 14% to 21% in the numerical example. Therefore, preventing or limiting braking seems important in designing step-toll systems.

Keywords: Congestion pricing, step tolls, bottleneck model, Vickrey model, departure time choice, braking

JEL Classification: D62, R41, R48

Suggested Citation

Lindsey, Robin and van den Berg, Vincent A.C. and Verhoef, Erik T., Step by Step: Revisiting Step Tolling in the Bottleneck Model (November 29, 2010). Tinbergen Institute Discussion Paper 10-118/3, Available at SSRN: https://ssrn.com/abstract=1717654 or http://dx.doi.org/10.2139/ssrn.1717654

Robin Lindsey (Contact Author)

affiliation not provided to SSRN

Vincent A.C. van den Berg

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

HOME PAGE: http://www.feweb.vu.nl/nl/afdelingen-en-instituten/spatial-economics/staff/v-berg/index.asp

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Erik T. Verhoef

VU University Amsterdam - Department of Spatial Economics ( email )

De Boelelaan 1105
1081HV Amsterdam
Netherlands
+31 020 4446094 (Phone)
+31 020 4446004 (Fax)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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