Question 3. (7 points) Consider two firms that produce identical output and face the market demand p=100q, where q=q1+q2 is the total output produced by the two firms, and qi(i{1,2}) is the output of firm i. The cost function of firm 1 is C1(q1)=6q1, and the cost function of firm 2 is C2(q2)=20q2. (a) Suppose that the firms decide how much to produce simultaneously. Find the Cournot-Nash equilibrium in this quantity competition 3 game. Be careful writing the optimization problem for each firm and finding best responses. (b) What is the equilibrium price per unit of output? What are the profits of each firm? (c) Suppose now that the same firms set prices p1 and p2 simultaneously. Assume that if a firm is indifferent between producing and non-producing it will not produce. Find the Bertrand-Nash equilibrium in this price competition game. (d) What are the equilibrium quantities produced by each firm? What are the profits of each firm? Question 3. (7 points) Consider two firms that produce identical output and face the market demand p=100q, where q=q1+q2 is the total output produced by the two firms, and qi(i{1,2}) is the output of firm i. The cost function of firm 1 is C1(q1)=6q1, and the cost function of firm 2 is C2(q2)=20q2. (a) Suppose that the firms decide how much to produce simultaneously. Find the Cournot-Nash equilibrium in this quantity competition 3 game. Be careful writing the optimization problem for each firm and finding best responses. (b) What is the equilibrium price per unit of output? What are the profits of each firm? (c) Suppose now that the same firms set prices p1 and p2 simultaneously. Assume that if a firm is indifferent between producing and non-producing it will not produce. Find the Bertrand-Nash equilibrium in this price competition game. (d) What are the equilibrium quantities produced by each firm? What are the profits of each firm