2) Let the inverse demand function and the cost function be given by P = 50 − 2Q and C = 10 + 2q respectively, where Q is total industry output and q is the firm’s output.
a) First consider first the case of uniform-pricing monopoly, as a benchmark. Then in this case Q = q. Find out the firm’s profit, price and quantity. (10p)
b) Now let us consider the case of two firms, or duopoly. Let q1 be the output of firm 1 and q2 the output of firm 2. Then Q = q1 + q2. Suppose the firms make their price choices simultaneously. Find both firms’ profits, prices and quantities. (Hint: Use Cournot Solution) (10p)