(5) (40 points) Suppose two oligopolists face the following inverse demand curve p(y) = 1000 - 2y. The cost function of firm i is ;(y;) = 100y; + $y7, for i=1,2 {a) (1 points) Assume firms set quantities simultaneously (Cournot competition). Write the profit maximization problem of each firm (b) (6 points) Find the best response function of each firm (c) (6 points) Find the chosen production levels y; and y, {(d) (4 points) What is the total production in this market, and the resulting equilibrium price? (z) (1 points) Now assume the firms set prices sequentially (Stackelberg competition). Firm 1 is the leader and firm 2 is the follower. Write the profit maximization problem of each firm (h) (6 points) Find the chosen production levels y; and y; in this case (i) (4 points) What is the total production in the market and the equilibrium price in this case