Firm 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. The firms seek to maximize the cartels total profit.
a) the firm have decided to limit their total output to Q+ 18. What output should firm produce to archieve this level of output a minimum total cost? What is each firms 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 profits by expanding its total output.( hint compare MR to MC at Q=18)
c) Find the cartel optimal output and optimal price. ( hint : At the optimum, MR= MCa=MCb)