My Math Forum Regarding mergers

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 December 2nd, 2014, 09:15 AM #1 Newbie   Joined: Oct 2014 From: Korea Posts: 4 Thanks: 0 Regarding mergers Hye guys! I'm wondering on how to solve these qs: Question 1: There are three fi rms producing a homogenous product. Let qi be the output level of firm i E {1,2,3} and let Q be the aggregate output level, that is, Q = q1 + q2 + q3. The aggregate demand is P = 50-2Q. Firms' cost functions are C(qi) = 2qi. Solve the following problems: (1) Find the Cournot equilibrium output and pro fit level of each fi rm. (2) Now suppose that fi rm 2 and 3 merge into a single firm. Calculate the profi t level of this merged fi rm under a Cournot market structure. (3) Do firm 2 and 3 benefi t from this merger? Are consumers better off ? Question 2: Consider a repeated game with an in finite time horizon. There are N(>2) fi rms producing a homogeneous product. These firms compete a la Bertrand every period. The aggregate demand function in each period is P = 54􀀀-3Q. Each fi rm has a cost function of C(q) = 6q. Firms' discount factor is B(beta) . Let QM be total output in a period under monopoly and let qM = QM/N . Suppose the firms use the following trigger strategies. Each firm i chooses qM in the first period. It further chooses qM in subsequent periods if no deviation from qM has been observed. Otherwise it competes in Bertrand fashion. The technology of detecting a deviation from qM is not perfect: there is a time lag of T periods before fi rms observe other players' previous choices. For example, if a fi rm chooses something other than qM in period 1, the punishment for this deviation will take place in period T + 2 instead of in period 2. Under what conditions on B , T, and N, can this trigger strategy support the monopoly allocation? Does a higher make this tacit collusion easier to sustain? Does a higher T make it easier? What about N? Hope you guys can help me with these. Thank you very much!

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