# The Impact of Competition on Prices with Numerous Firms

*Xavier Gabaix*,
*David Laibson*,
*Deyuan Li* (),
*Hongyi Li*,
*Sidney Resnick* () and
*Casper de Vries*

Additional contact information

Deyuan Li: Fudan University

Sidney Resnick: Cornell University

Working Papers from Chapman University, Economic Science Institute

**Abstract:**
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.

**Pages:** 74 pages

**Date:** 2013

**New Economics Papers:** this item is included in nep-bec, nep-com and nep-ind

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**Citations:** View citations in EconPapers (18)

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http://www.chapman.edu/research-and-institutions/e ... t-of-competition.pdf

**Related works:**

Journal Article: The impact of competition on prices with numerous firms (2016)

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**Persistent link:** https://EconPapers.repec.org/RePEc:chu:wpaper:13-07

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