Market size, entry costs and free entry Cournot equilibrium

We consider a free entry, symmetric cost, Cournot equilibrium in a homogeneous product market. There is a parameter A which is the index of the "market size" . If a firm decides to enter, it must incur set-up costs of F. We explore the following question: How do the number of firms, individual output and total output in a free entry equilibrium change with an increase in the market size and entry cost? Conventional wisdom suggests that these should increase with A and decrease with F. However, we show this may not be true. We use the implicit function theorem to provide a complete characterization. We also illustrate our results with specific examples.