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+Q, 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 MC = MCB.)