2. Consider the following two-stage model of entry in a Cournot setting. In the first stage, a large number of potential entrants decide whether to pay the fixed cost F (which is then sunk) in order to enter the market. In the second stage, the N firms that entered in the first stage choose quantities simultaneously. The market demand curve is given by P = 100 - Q. Each firm i has a total cost function, if it chooses to enter, given by C(q) = qt - F. (a) Supposing N firms have entered in the first stage, solve for the symmetric second stage Cournot Nash equilibrium. (b) Derive a formula determining how many firms will enter the market, as a function of F. How many firms will enter if F equals (i) 800 or (ii) 400?