Mergers for market power in a cournot setting and merger guidelines

The US Merger Guidelines consider that the anticompetitive effect of a horizontal merger is increasing in the initial market concentration and decreasing in the elasticity of demand. These ideas are studied in a setting where identical firms compete à la Cournot and marginal cost is constant. The former relationship holds if demand is convex, but it may fail to be true if demand is concave. The latter one only holds if the elasticity of demand is increasing in the degree of concavity. This condition is satisfied by linear demands, constant elasticity demands and demands that are log -linear in price.Mergers, market power, antitrust