In a market there are two identical firms, i = 1, 2 that supply a product. The total cost is given by Ci(qi) = 240qi , where qi is the output supplied by firm i = 1, 2. The inverse demand function in this market is given by:

p = 600 2Q (1) where Q = q1 + q2.

(i) Find the equilibrium in this market if firms simultaneously and non-cooperatively choose the quantities they produce. Briefly but clearly show your derivations. Compute the equilibrium profits of firms 1 and 2 respectively.

[10 marks]

(ii) The owners of Firm 1 turn you down as manager and prefer to run their firm alone as before, while the owners of firm 2 appoint you as manager. You are interested in sales as well as profits so your managerial objective is to maximize M2(q1, q2) = 2(q1, q2) + (3 s)q2 where 2(q1, q2) is the profit of firm 2 and s=9. Compute the equilibrium in this case and (a) Justify whether or not your appointment was a wise decision for the owners of firm 2. (b) Justify whether or not the decision of the owners of firm 1 to turn you down was wise, given that you were finally appointed by firm 2.

[15 marks]

(iii) As manager of firm 2, having the same objective as in (ii), you face the following situation: Before production decisions, firm 2 has the opportunity to invest in a new technology that will reduce its marginal cost to c2 = 180. This new technology requires payment of a fixed installation cost F = 2170, so the total cost of firm 2 would become C2(q2) = 180q2 + 2170. Your decision whether or not to install the new technology will be known by firm 1 before its output decision. If you do not invest in the new technology, the competition will be in the same terms as in (ii). If you invest, the installation of the new technology will cause delays in your output decision of firm 2 and meanwhile firm 1 will announce its output decision first, i.e., firm 1 will move first. Explain whether or not you would install the new technology.

[25 marks]