Is the Service Quality of Private Roads too Low, too High, or Just Right When Firms Compete Stackelberg in Capacity?

Tinbergen Institute Discussion Paper No. 2011-079/3

1 Pages Posted: 24 May 2011

See all articles by Vincent A.C. van den Berg

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: May, 16 2011

Abstract

We study road supply by competing firms between a single origin and destination. In previous studies, firms simultaneously set their tolls and capacities while taking the actions of the others as given in a Nash fashion. Then, under some widely used technical assumptions, firms set a volume/capacity ratio that is socially optimal, and thus the level of travel time or service quality is socially optimal. We find that this result does not hold if capacity and toll setting take place in separate stages, as then firms want to limit the toll competition by setting lower capacities; or when firms set capacities one after another in a Stackelberg fashion, as then firms want to limit their competitors' capacities by setting higher capacities. In our Stackelberg competition, the firms that act last have few if any capacity decisions to influence. Hence, they are more concerned with the toll-competition substage, and set a higher volume/capacity ratio than socially optimal. The firms that act first care more about their competitors' capacities that they can influence: they set a lower volume/capacity ratio. So the first firms to enter have a too short travel time from a social perspective, and the last firms a too long travel time. The average private travel time is shorter than socially optimal. Still, in our numerical model, for three or more firms, welfare is higher under Stackelberg competition than under Nash competition, because of the larger total capacity and lower tolls.

Keywords: Private road supply, oligopoly, Nash Competition, Stackelberg Competition, service quality, volume/capacity ratio, traffic congestion, congestion pricing

JEL Classification: D62, L13, R41, R42, R48

Suggested Citation

van den Berg, Vincent A.C. and Verhoef, Erik T., Is the Service Quality of Private Roads too Low, too High, or Just Right When Firms Compete Stackelberg in Capacity? (May, 16 2011). Tinbergen Institute Discussion Paper No. 2011-079/3 , Available at SSRN: https://ssrn.com/abstract=1843102 or http://dx.doi.org/10.2139/ssrn.1843102

Vincent A.C. van den Berg (Contact Author)

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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