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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. Irmen, Andreas & Thisse, Jacques-Francois, 1998. "Competition in Multi-characteristics Spaces: Hotelling Was Almost Right," Journal of Economic Theory, Elsevier, vol. 78(1), pages 76-102, January.
    2. Konishi, Hideo, 2005. "Concentration of competing retail stores," Journal of Urban Economics, Elsevier, vol. 58(3), pages 488-512, November.
    3. 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.
    4. 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.
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    Cited by:

    1. Lamarche-Perrin, Alex & Orléan, André & Jensen, Pablo, 2018. "Coexistence of several currencies in presence of increasing returns to adoption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 612-619.
    2. Zhang, Peng & He, Yong & Zhao, Xuan, 2019. "“Preorder-online, pickup-in-store” strategy for a dual-channel retailer," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 27-47.
    3. Stefano Colombo & Noriaki Matsushima, 2020. "Competition Between Offline and Online Retailers with Heterogeneous Customers," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 57(3), pages 647-664, November.
    4. Pu-Yan Nie, 2013. "Innovation Under Spatial Duopoly," Prague Economic Papers, Prague University of Economics and Business, vol. 2013(4), pages 474-486.
    5. 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.
    6. repec:prg:jnlpep:v:preprint:id:712:p:1-16 is not listed on IDEAS
    7. Alex Lamarche-Perrin & André Orléan & Pablo Jensen, 2018. "Coexistence of several currencies in presence of increasing returns to adoption," Post-Print hal-01531277, HAL.
    8. Alex Lamarche-Perrin & André Orléan & Pablo Jensen, 2018. "Coexistence of several currencies in presence of increasing returns to adoption," PSE-Ecole d'économie de Paris (Postprint) hal-01531277, HAL.
    9. Alex Lamarche-Perrin & André Orléan & Pablo Jensen, 2017. "A simplistic model of the emergence of money," Working Papers halshs-01531274, HAL.
    10. Harold Houba & Evgenia Motchenkova & Hui Wang, 2022. "Personalized Pricing, Competition and Welfare," Tinbergen Institute Discussion Papers 22-020/VII, Tinbergen Institute.
    11. Yong-Cong Yang & Pu-Yan Nie & Zhao-Hui Wang & Tan Zheng-Xun, 2019. "Spatial Monopoly with Upgrades of Durable Goods," Prague Economic Papers, Prague University of Economics and Business, vol. 2019(5), pages 516-531.

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