Jannah1721

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!