Question 3 (45 pts): Let's consider a market in which there are only two firms that produce an identical product. The two firms face the market demand curve given by Q=1502p, where Q=q1+q2 and that qi is the output of firm i,i=1,2. The two firm's cost functions are given as C1=10q1 and C2=20q2 a. (15 pts) Assume that the two firms are independent of each other and that they choose their outputs simultaneously i. (10 pts) Derive the output reaction of each firm ii. (5 pts) Determine the Cournot equilibrium output of each firm and the market price b. ( 10 pts) Suppose that Firm 2 decides it wants to be a leader and that Firm 1 will follow suit. Determine the Stackelberg equilibrium of each firm and the market price. c. (20 pts) Compared to the case in (a), what is the effect of Firm 2's ability to be the quantity leader on the: i. (5 pts) Profit of each firm under each equilibrium ii. (5 pts) The producer surplus under each equilibrium iii. (10 pts) The consumer surplus and the total welfare. Which scenario (Stackelberg vs Cournot) would be the better case for the society? Question 3 (45 pts): Let's consider a market in which there are only two firms that produce an identical product. The two firms face the market demand curve given by Q=1502p, where Q=q1+q2 and that qi is the output of firm i,i=1,2. The two firm's cost functions are given as C1=10q1 and C2=20q2 a. (15 pts) Assume that the two firms are independent of each other and that they choose their outputs simultaneously i. (10 pts) Derive the output reaction of each firm ii. (5 pts) Determine the Cournot equilibrium output of each firm and the market price b. ( 10 pts) Suppose that Firm 2 decides it wants to be a leader and that Firm 1 will follow suit. Determine the Stackelberg equilibrium of each firm and the market price. c. (20 pts) Compared to the case in (a), what is the effect of Firm 2's ability to be the quantity leader on the: i. (5 pts) Profit of each firm under each equilibrium ii. (5 pts) The producer surplus under each equilibrium iii. (10 pts) The consumer surplus and the total welfare. Which scenario (Stackelberg vs Cournot) would be the better case for the society