Firms A and B make up a cartel that monopolizes the market for a scarce natural resource. The firms’ marginal costs are MCa = 6+2Qa and MCb = 18+Qb respectively. The firms seek to maximize the cartel’s total profit.
a. The firms have decided to limit their total output to Q = 18. What outputs should the firms produce to achieve this level of output at minimum total cost? What is each firm’s marginal cost?
b. The market demand curve is P = 86 − Q, where Q is the total output of the cartel. Show that the cartel can increase its profit by expanding its total output. (Hint: Compare MR to MC at Q = 18.)
c. Find the cartel’s optimal outputs and optimal price. (Hint: At the optimum, MR = MCA = MCB.)