Demand: P=10-1/4Q

4. (Collusion) Now suppose firms face the same market demand as in Problem 3. But now there are three firms (firm 1, firm 2, and firm 3) where Q = q1 + q2 + q3. All of them bear the same production marginal cost of c1 = C2 = C3 = 4 per one gallon of water. Lastly, the game among these firms is repeated indefinitely in each period t = 1, 2, 3, ... . Let 6 E (0, 1) denote the firms common time discount factor. (a) Find the static (joint) monopolist's quantity, price and profit when they collude. (b) Solve the static Cournot game. That is, find q1*, q2*, q3*, p*, m1*, 2", 13*. (c) Now find the static profit of firm 1 when he solely deviates from collusion.(d) Calculate the lifetime value of firm 1 when all of the firms maintain collusion forever (Vast). Also find the lifetime value of firm 1 when he solely betrays at t = 1 and is detected by others at t = 2 (Villa)- (e) Compute the minimum threshold value of 6 that would make collusion sustainable