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Suppose we have two firms in a market to which entry isrestricted. The inverse demand function facing these two firms isgiven by p = 130-2q, where q = q1 +q2. Both firms have the samecosts of production: C = 10q.
(a) Compute the best response functions and find the Cournotequilibrium. What would be aggregate output, price and profit foreach firm?
(b) Now suppose firm 1 gets to choose q1 before firm 2 chooses q2.Suppose also that firm 1 knows the best response function of firm2. What output should firm 1 produce to maximize profit? Whatoutput would firm 2 produce? What will be the price? What profitwill each firm make?
(c) If the manager of the firm 1 has an option of choosing before,simultaneously, or after firm 2, which will he choose?
(d) Now assume that owners of the firms decided to collude.Calculate symmetric collusive equilibrium. Are both firms betterthan in part a)?
(e) This collusion possibility is, however, discussed only andverbally agreed to it. Firm 1 however thinks that since this isonly verbal agreement, it could be violated. Would any of these twofirms violate the collusive agreement (assuming the other firmhonours the agreement)?Why yes or why not? What is the magnitude ofthe inducement to violate the collusive agreement?
(f) Show all your results in two graphs: (i) q-P plane (withdemand, marginal revenues, marginal cost curves) and (ii) q1-q2plane (with reaction functions, and isoprofit curves).