3. Suppose there is a duopoly of two identical firms, A and B, facing the inverse demand P=320-2Q, and cost functions are CA=20QA and CB=200B respectively. a) Find the Cournot-Nash equilibrium quantities, price, and profits for each firm. b) Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective prices, quantities, and profits of each firm now? c) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? d) Show that firms have selfish incentives to deviate from the collusive outcome. e) Show the Cournot, Stackelberg and cartel outcomes on the inverse demand function, and calculate consumer surplus and deadweight loss in each case. 4 P= 320- 2(Qut2b) Ty (320- 2Qu-2 2b) Qu 320 Qu- 2Qu- 2abQu 320 2b-2QuQb-2262 MR = 320- 420- 22b=0 MR= 320- 2Qa- 42b=0 320 - 22b = 4Qu 320 - 2 26 = 42b 80 - zQasab Brl 60 - 2 ( 80 - 2Q ) = Qu 80- 40 +4Qu = Qu 40 = Z Q9