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 Demanded
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?