Question

1. This question is to review what we have studied and illustrate the issues with cartels. Suppose, for simplicity, that the marginal cost of mining diamonds is a constant $1000 per diamond and all diamonds are the same. The demand for diamonds is described by the following demand schedule:

Price	Quantity (diamonds)
$8,000	5,000
$7,000	6,000
$6,000	7,000
$5,000	8,000
$4,000	9,000
$3,000	10,000
$2,000	11,000
$1,000	12,000

1. If there were many suppliers of diamonds (perfect competition), what would be the price and quantity in the market?
2. If there was only one supplier of diamonds in the world, what price and quantity would they choose? [Hint: find marginal revenue and compare to marginal cost]
3. Imagine that Russia and South Africa are the only producers of diamonds. They agree to form a cartel, split the market, and restrict production. What quantity should they produce and what will the market price of diamonds be?
4. Suppose that Russia and South Africa each get half of the market. Assume there are no fixed costs. If they produce the quantity discussed in part c, what are South Africa’s profits?
5. What happens to South Africa’s profits if it increases production by 1,000 while Russia sticks to the cartel agreement?
6. Use you answer in part e to discuss why cartel agreements are often not successful.

Answer 1

P	Q	TC	TR	MR	MC
8000	5000	5000000	40000000
7000	6000	6000000	42000000	2000	1000
6000	7000	7000000	42000000	0	1000
5000	8000	8000000	40000000	-2000	1000
4000	9000	9000000	36000000	-4000	1000
3000	10000	10000000	30000000	-6000	1000
2000	11000	11000000	22000000	-8000	1000
1000	12000	12000000	12000000	-10000	1000

a) If there are many suppliers, it will set P=MC so Price = 1000 and quantity = 12000

b) If there were one supplier, it will set MC=MR so Price = 7000 and quantity = 6000

c) If they form a cartel they will act like a monopolist so price = 7000 and quantity = 6000 where each will produce 6000/2 = 3000 units

d) South Africa's profit = 3000*7000 - 3000*1000 = 18 million

e) South Africa increasing production will increase total output to 7000 which will decrease the price to 6000 so SA profit = 4000*6000 - 4000*1000 = 20 million, therefore, the profits increases by 2 million

f) Cartels are not successful because one party always has an incentive to cheat on its partner to increase its profits