Three oligopolists, A, B and C, produce an identical product, Q. Q is produced under conditions of constant costs, that is, AC = MC = $100. The market demand schedule for Q is:

Price                         Quantity demand                     TR                       MR

$1000                              0                                                     

950                                 25

900                                  50

850                                  75

800                                 100

750                                 125

700                                150

650                                175

600                                200

550                                225

500                               250

450                               275

400                              300

a). A, B, and C decide to act illegally as a cartel, to divide the market equally among the three of them, and to set the price and output that will maximize their total profits. What price and output do they set? What is the output level that each of the firms agrees to? What profit is earned by each firm and by the three firms together? 

b). A is impressed with the honesty of B and C, and believes they will keep to their agreements. They do, and A cheats by increasing output by 25 units. What is the new market price? How have the profit levels of A, B, and C changed? How have total profits in the industry changed? 

c). What actions are B and C likely to take in retaliation? Show how these actions will affect the market price, and the profit levels of the three firms. d) What can you learn from this problem about the likely stability of a cartel?