Problem 3 Consider an innitely repeated Cournot duopoly with discount factor i'b' = 0.9. unit costs of (z = (J, and an inverse demand function [)(Q) = 10 Q Firm 1 is more powerful than rm 2 such that in any collusive agreement. rm 1 can choose each rm's quantity. Specically, let (1,,\" be the monopoly quantity. Usually we assume that (11,, = (m = \"'7 but now we Will assume that (11: = oqm and (12$ = (1 am,\" where rm 1 chooses or 6 [0,1]. You may assume all collusive agreements entail each rm producing its assigned quantity, but if any rm deviates. the rms shift to a Cournot equilibrium for all remaining periods. A. E. Find each rm's (perperiod) prots under collusion. as a function of (i. Find each rm's (perperiod) prots under a Cournot equilibrium. Suppose rm 1 deviates from the agreement. \"'hat is its deviation quantity and prot, as a function of of? Suppose rm 2 deviates from the agreement. \"hat is its deviation quantity and prot, as a function of o? . Write down the inequalities that must hold for a collusive agreement to be sustainable. You should have two inequalities. one per rm. Find the range of 0: under which collusion is sustainable. \"That. value of (r maximizes rm 1's prots under collusion? \"'hat value of o maximizes rm 2's prots under collusion