Consider an oligopoly with three rms. Firms 1 and 2 face marginal costs

c = 40 while rm 3 faces marginal cost k = 20. Demand is p = 120 Q,

where Q = q1 + q2 + q3.

(a) Write down the prot functions and the rst-order-necessary-conditions

if each rm, i = 1; 2; 3, were to maximize its prots.

(b) Assuming that q1 = q2, nd the Cournot equilibrium output levels

q

1 = q

2, q

3, and Q, and price p, and profits to each firm,

1 =

2

and

3 and show these on a graph (with production of rm 1 at left

and rm 3 at right).

(c) Suppose rm 1 and rm 2 merge, and that their marginal costs re-

main at c = 40. Find the duopoly equilibrium quantities q

12 , q

3 , and

Q, and price p, and show these on your graph (with production

of rm `12' at left and rm 3 at right). Explain whether society is

better o or worse o as a result of the merger.