8. (20 points)(Oligopolies) Two large firms compete in a market. These two firms produce a homogeneous product and decide their production quantities. Firm 1 decides its quantity first, then Firm 2 decides its quantity after observing Firm 1's decision. Firm 1 has the cost function of ;(y;) = y?, and Firm 2 has the cost function of 3(y;) = y3. The market demand function is linear, and it is D(p) = 1500 2p. (a) Write down Firm 2's optimization problem and derive Firm 2's response function by treating y; as a constant. (b) Solve Firm 1's optimization problem and find both firms' optimal production levels and the equilibrium market price (%, ckemerg)- (c) Suppose these two firms merge. They merge in the sense that one firm completely ceases operation, so the merged firm's profit function is 7(y) = py y%. Explain whether consumers would prefer the Stackelberg duopolies or the merged firm. (d) Now, suppose both firms move simultaneously, not sequentially. Solve both firms' optimal quantity levels and the resulting equilibrium market price (Cournot-Nash equilibrium). (-3 points if your answer sheets are not stapled or clipped). End. . + . \"Hint: Express the profit in terms of y and k only. WHint: Find the inverse demand function of the downstream firm first. That is, express k in terms of x. HNote: All these values are functions of z. 12 int: Fi * Aod ; ; aie Cha s * ) . ok \" 3 Thic Hint: Find Prmerged and Ymerged and compare them with Pitackelbaig and ym"_;'.t,m(,?.y( yi +v3 in (b)). Which market do you wish to be in