Hotelling Models with Price-Sensitive Demand and Asymmetric Transport Costs: An Application to Public Transport Scheduling

Tinbergen Institute Discussion Paper 12-119/VIII

18 Pages Posted: 9 Nov 2012

See all articles by Adriaan van der Weijde

Adriaan van der Weijde

Vrije Universiteit Amsterdam, School of Business and Economics

Erik T. Verhoef

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

Vincent A.C. van den Berg

VU University Amsterdam; Tinbergen Institute

Date Written: November 8, 2012

Abstract

We formulate a horizontal differentiation model with price-sensitive demand and asymmetric transport costs, in the context of transport scheduling. Two competitors choose fares and departure times in a fixed time interval. Consumers are distributed uniformly along the interval; their location indicates their desired departure time. In a standard Hotelling model, locations are chosen before prices. In our context, the opposite order is also conceivable, but we show that it does not result in a Nash equilibrium; the same is true for a game in both variables are chosen simultaneously. We also discuss Stackelberg game structures and second-best regulation.

We conclude that the addition of price-sensitive demand results in equilibria in the traditional Hotelling model with price setting; there, services are scheduled closer together than optimal. We also show that it is possible to include asymmetric schedule delay functions. Our results show that departure times can be strategic instruments. Optimal regulatory strategies depend on the value of schedule delay, and on whether the regulator can commit.

Keywords: horizontal differentiation, scheduling, transport

JEL Classification: L11, L51, L91, R40

Suggested Citation

van der Weijde, Adriaan and Verhoef, Erik T. and van den Berg, Vincent A.C., Hotelling Models with Price-Sensitive Demand and Asymmetric Transport Costs: An Application to Public Transport Scheduling (November 8, 2012). Tinbergen Institute Discussion Paper 12-119/VIII, Available at SSRN: https://ssrn.com/abstract=2172840 or http://dx.doi.org/10.2139/ssrn.2172840

Adriaan Van der Weijde (Contact Author)

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

De Boelelaan 1105
Amsterdam, 1081HV
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

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

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