Market size and competition: A “hump-shaped” result

An active empirical literature estimates entry threshold ratios (ETRs), introduced by Bresnahan and Reiss (1991), to learn about the impact of firm entry on competition. We show that in the standard homogeneous goods oligopoly model, there is no monotonic relationship with the price-cost margin, one measure for the strength of competition. Regardless of the shape of demand, the ETR is hump-shaped in the number of active firms. It can also increase with entry in the Salop model of product differentiation or in a game of repeated interactions where collusion is possible. Empirical applications should use caution and only interpret changes in the ratio as indicative of a change in competition when the number of firms is sufficiently large.