The impact of competition on prices with numerous firms

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 are proportional to 1 ¡  0 £ −1 (1− 1)¤¢, where  is the random utility noise distribution and  is the number of firms. This implies prices are pinned down by the tail properties of the noise distribution and that 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 1 √ ln, 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. ∗Gabaix: NYU Stern, CEPR and NBER, [email protected]; Laibson: Harvard University and NBER, [email protected]; D. Li: Fudan University, [email protected]; H. Li: University of New South Wales, [email protected]; Resnick: Cornell, [email protected]; de Vries: Erasmus University Rotterdam, Tinbergen Institute and Chapman University, [email protected]. We thank Timothy Armstrong, Jeremy Bulow, Thomas Chaney, Victor Chernozhukov, Robert Hall, Rustam Ibragimov, Paul Klemperer, Johan Walden and Glen Weyl for helpful conversations and seminar participants at the AEA, Chicago, MIT, NYU and SITE for useful comments. This research was partially supported by the NSF and the Swiss National Science foundation. D. Li’s research was partially supported by NNSFC Grant 11171074.