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 rms is large, markups are proportional to 1= (nF' [F^-1 (1- 1/n)], where F is the random utility noise distribution and n is the number of rms. 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 rms 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 rms. For example, for the Gaussian case asymptotic markups are proportional to 1=pln n, implying a zero asymptotic elasticity of the markup with respect to the number of rms. Thus competition only exerts weak pressure on prices. We also study applications of the model, including endogenizing the level of noise.
Gabaix, X., Laibson, D., Li, D., & Li, H. (2013). The impact of competition on prices with numerous firms. ESI Working Paper 13-07. Retrieved from http://digitalcommons.chapman.edu/esi_working_papers/51