2. [10 points] Let us study a Cournot Oligopoly with the same market demand curve as in Question 1, namely: Q=12 - Pif0 12, where Q is the quantity demanded and P is the market price. The firms' production costs are also the same as before. But now there are N+1 firms. There are / 2 1 firms of type 1. Each one has marginal cost 4 and profit function III,; = P q1,i - 4 q1,i , for i = 1, 2, ..., N. (Here q1,; is the output, and III,; is the profit, of the it firm of type 1.) There is only one firm of type 2, with marginal cost 2 and profit II2 = P q2- 2 q2 when its output is q2. Again, each firm must decide on its own output level, simultaneously and independently of one another; and we regard this situation as a game in strategic form and investigate its Nash Equilibrium. Let Q1 = q1,1 + ... + qIN be the total output of the firms of type 1. (a) For any value of N, it is possible to have price P