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The Impact of Competition on Prices with Numerous Firms

  • Xavier Gabaix

    ()

    (NYU Stern, CEPR and NBER)

  • David Laibson

    ()

    (Harvard University and NBER)

  • Deyuan Li

    ()

    (Fudan University)

  • Hongyi Li

    ()

    (University of New South Wales)

  • Sidney Resnick

    ()

    (Cornell University)

  • Casper G. de Vries

    ()

    (Economic Science Institute, Chapman University, Erasmus University Rotterdam, Tinbergen Institute)

We use extreme value theory (EVT) to develop insights about price theory. Our analysis reveals "detail-independent" equilibrium properties that characterize a large family of models. We derive a formula relating equilibrium prices to the level of competition. When the number of firms is large, markups and prices are pinned down by the tail properties of the noise distribution and prices are independent of many other institutional details. The elasticity of the markup with respect to the number of firms is shown to be the EVT tail exponent of the distribution for preference shocks and in most leading cases is relatively insensitive to the number of firms. For example, for the Gaussian case asymptotic markups are proportional to one over the square root of log n, implying a zero asymptotic elasticity of the markup with respect to the number of firms. Thus competition only exerts weak pressure on prices. We also study applications of the model, including endogenizing the level of noise.

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Paper provided by Chapman University, Economic Science Institute in its series Working Papers with number 13-07.

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Length: 74 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:chu:wpaper:13-07
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