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Analytical solution of a multi-dimensional Hotelling model with quadratic transportation costs

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  • Larralde, Hernn
  • Stehl, Juliette
  • Jensen, Pablo
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    Abstract

    We present an analytical solution to the two-dimensional two-stage Hotelling model with quadratic transportation costs. We assume that consumers' choice is tempered by a logit function, which characterizes consumers' heterogeneity. As in the one-dimensional case, stores aggregate spatially when consumers' heterogeneity is strong enough. When it decreases, we show that stores differentiate in only one dimension. The analytical solution allows us to give a precise interpretation of this effect through the comparison of consumers' elasticity under differentiation along one or two characteristics. Finally, we extend our results to a hypercube of any dimension.

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    Bibliographic Info

    Article provided by Elsevier in its journal Regional Science and Urban Economics.

    Volume (Year): 39 (2009)
    Issue (Month): 3 (May)
    Pages: 343-349

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    Handle: RePEc:eee:regeco:v:39:y:2009:i:3:p:343-349

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    Related research

    Keywords: Spatial competition Minimum differentiation Consumer heterogeneity Analytical solution;

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    1. Tabuchi, Takatoshi, 1994. "Two-stage two-dimensional spatial competition between two firms," Regional Science and Urban Economics, Elsevier, vol. 24(2), pages 207-227, April.
    2. Veendorp, E. C. H. & Majeed, Anjum, 1995. "Differentiation in a two-dimensional market," Regional Science and Urban Economics, Elsevier, vol. 25(1), pages 75-83, February.
    3. Konishi, Hideo, 2005. "Concentration of competing retail stores," Journal of Urban Economics, Elsevier, vol. 58(3), pages 488-512, November.
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