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

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  • Adriaan Hendrik van der Weijde

    (VU University Amsterdam)

  • Erik T. Verhoef

    (VU University Amsterdam)

  • Vincent A. C. van den Berg

    (VU University Amsterdam)

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-119/VIII.

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Date of creation: 08 Nov 2012
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Handle: RePEc:dgr:uvatin:20120119

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Web page: http://www.tinbergen.nl

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Keywords: horizontal differentiation; scheduling; transport;

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  1. Cancian, Maria & Bills, Angela & Bergstrom, Theodore, 1995. "Hotelling Location Problems with Directional Constraints: An Application to Television News Scheduling," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 121-24, March.
  2. d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "On Hotelling's "Stability in competition"," CORE Discussion Papers RP -385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Gu Yiquan & Wenzel Tobias, 2012. "Price-Dependent Demand in Spatial Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-26, March.
  4. Peran van Reeven & Maarten C. W. Janssen, 2006. "Stable Service Patterns in Scheduled Transport Competition," Journal of Transport Economics and Policy, London School of Economics and University of Bath, vol. 40(1), pages 135-160, January.
  5. Helge Sanner, 2005. "Instability in Competition: Hotelling Re-reconsidered," Volkswirtschaftliche Diskussionsbeiträge 79, Universität Potsdam, Wirtschafts- und Sozialwissenschaftliche Fakultät.
  6. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-79, June.
  7. Tönu Puu, 2002. "Hotelling's "Ice cream dealers" with elastic demand," The Annals of Regional Science, Springer, vol. 36(1), pages 1-17.
  8. Stefano Colombo, 2011. "Spatial price discrimination in the unidirectional Hotelling model with elastic demand," Journal of Economics, Springer, vol. 102(2), pages 157-169, March.
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