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Hotelling was right with decreasing returns to scale and a coalition-proof refinement

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  • Chia-Hung Sun

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  • Fu-Chuan Lai

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    Abstract

    This paper provides a simple, realistic, and very slightly modified version of the production technology in Hotelling’s (Econ J 39:41–57, 1929 ) spatial model with linear transportation costs to overcome the nonexistence problem of equilibrium—decreasing returns to scale. It is shown that a pure strategy Nash equilibrium in price competition always exists for all location pairs and guarantees uniqueness if we utilize a coalition-proof refinement introduced by Bernheim et al. (J Econ Theory 42:1–12, 1987 ). Decreasing returns to scale reduce the profit a firm can capture through price undercutting and stabilize the price equilibrium due to the increasing average production cost of firms. As a consequence, duopoly firms agglomerating at the center of a line are shown to be at the unique location equilibrium. This paper confers a new validity to the so-called principle of minimum differentiation, in some sense, with the least deviation from the original Hotelling (Econ J 39:41–57, 1929 ) model. Copyright Springer-Verlag 2013

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    Bibliographic Info

    Article provided by Springer in its journal The Annals of Regional Science.

    Volume (Year): 50 (2013)
    Issue (Month): 3 (June)
    Pages: 953-971

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    Handle: RePEc:spr:anresc:v:50:y:2013:i:3:p:953-971

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    1. Takanori Ago, 2008. "Central agglomeration of monopolistically competitive firms," Journal of Economic Geography, Oxford University Press, vol. 8(6), pages 811-823, November.
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    12. Economides, Nicholas, 1984. "The principle of minimum differentiation revisited," European Economic Review, Elsevier, vol. 24(3), pages 345-368, April.
    13. Dixon, Huw, 1990. "Bertrand-Edgeworth Equilibria when Firms Avoid Turning Customers Away," Journal of Industrial Economics, Wiley Blackwell, vol. 39(2), pages 131-46, December.
    14. Jehiel, Philippe, 1992. "Product differentiation and price collusion," International Journal of Industrial Organization, Elsevier, vol. 10(4), pages 633-641, December.
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