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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

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.

Suggested Citation

  • Larralde, Hernn & Stehl, Juliette & Jensen, Pablo, 2009. "Analytical solution of a multi-dimensional Hotelling model with quadratic transportation costs," Regional Science and Urban Economics, Elsevier, vol. 39(3), pages 343-349, May.
  • Handle: RePEc:eee:regeco:v:39:y:2009:i:3:p:343-349
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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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    Cited by:

    1. Alex Lamarche-Perrin & André Orléan & Pablo Jensen, 2018. "Coexistence of several currencies in presence of increasing returns to adoption," Working Papers hal-01531277, HAL.
    2. Alex Lamarche-Perrin & Andr'e Orl'ean & Pablo Jensen, 2018. "Coexistence of several currencies in presence of increasing returns to adoption," Papers 1801.04218, arXiv.org.
    3. Alex Lamarche-Perrin & André Orléan & Pablo Jensen, 2017. "A simplistic model of the emergence of money," Working Papers halshs-01531274, HAL.

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