3. (16 points) Consider an industry with 2 rms producing homogeneous product. The cost function for rm 1 and rm 2 are c1(y1) = a+by1+cy% and c2(yg) = a'+b'y2+c'y, respectively. y1, y2 are outputs of firm 1 and rm 2, and others are parameters which are all positive. The market demand is P(y) = 100 2(y1 + m). Suppose rm 1 is the quantity leader. It decides and announces its output yl rst; rm 2 then observes yl and chooses its output. (a) (5 points) Suppose a = 1, b = 3,c 2 La" 2 2, b' = 2, c' = 1. What are the equilibrium price, outputs, and prots for each rm? Page 5 out of 6 (b) (6 points) Suppose the rms are operating in a country with loose anti-trust law, and the two rms realize that collusion may increase total prots. i. Solve for the collusion price and outputs for each rm. Given the outputs and price, how much is the total prots and prots for each rm? ii. Is the collusion result stable? Explain why. (0) (5 points] Does rm 1 have incentive to become the quantity leader, compared with being the quantity follower and Cournot competitor? You don't need to solve the problem numerically. Just use a graph to explain your answer clearly