Intensity of Competition and the Number of Competitors

We setup a model of competitive interaction among symmetric firms producing a homogeneous good that includes both Bertrand and Cournot competition as special cases. In our model the intensity of competition is captured by a single parameter - the perceived slope of competitors' sup- ply functions. We show when the number of firms is fixed, total welfare increases monotonically with the degree of competition. We then exam- ine how the intensity of competition affects the gains from changing the number of competitors. For very intense competition, most of the gains from extra competition are captured with the entry of a small number of firms and subsequent gains from entry are small. Conversely, when the intensity of competition is small, a reduction in the number of firms can have a large impact on welfare. We also examine the case when the in- tensity of competition is a function of the number of firms in the market and provide a sufficient condition for mergers to be profitable.