We consider N identical firms that compete à la Cournot. Each firm incurs a constant marginal cost c. The demand for the homogenous good is given by the following function: Q = 1 - P where P denotes the unit price of the good.

1. Determine the Nash equilibrium of the Cournot game. Deduce the profit of each firm at the equilibrium. Express the total surplus at the equilibrium We introduce an entry stage in the game. The game becomes the following:

Stage 1: firms decide simultaneously to enter the market. Entry has a fixed cost F.

Stage 2: the firms compete à la Cournot

2. Determine the free entry number of firms, i.e. the number of firms such that an additional entry would not be profitable (ignore the integer problem).

3. Express the total surplus if N firms enter the market at stage 1. Deduce the optimal number of firms. Can we say that at the equilibrium too many firms enter on the market? Explain.