There are 3 identical firms that mine bauxite in Australia. The cost curve of each individual firm
Question:
There are 3 identical firms that mine bauxite in Australia. The cost curve of each individual firm is given by Cj(Qj) = 9Qj2+12Qj for j = 1,2,3. Q is measured in tons. Suppose that these are the only 3 firms in Australia and they form a cartel.
a) Show that the marginal cost of the cartel is given by MC = 6QTotal + 12 where QTotal is the sum of the three firms production. The cartel is the unique supplier of bauxite in Australia and the inverse market demand is given by P(Q) = 912 - 7Q where P is measured in dollars per ton.
b) How many tons of bauxite will the cartel sell in the Australia? At what price will it sell bauxite? Illustrate your answer in a diagram. Be sure to indicate in your diagram the total quantity sold and the price at which it is sold.
c) How much does each individual firm sell at this price? What are the profits of an individual firm at this price and quantity?
d) Show that firm 1 can earn higher profits by increasing the quantity it sells by 1 ton. Briefly explain your answer. For the remainder of the question, assume that no firm in the cartel cheats on the cartel agreement. Bauxite is also sold on the world market which is perfectly competitive. The current world market price for Australian bauxite is $408 per ton. All shipping costs are paid by the buyers so the cartel gets $408 per ton.
e) Why would the cartel be willing sell bauxite in the world market at a price lower than the Australian price? Briefly explain your answer.
f) At the world price of $408 how many tons will the cartel sell on the world market? How many tons will it sell in the Australia? What will be the price of bauxite in the Australia? Illustrate your answer in your diagram.