Question

1. A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that the mar- ginal cost of mining diamonds is constant at $1,000 per diamond and the demand for diamonds is described by the following schedule:

Price Quantity

$8,000 5,000 diamonds 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

a. If there were many suppliers of diamonds, what would be the price and quantity?

b. If there were only one supplier of diamonds, what would be the price and quantity?

c. If Russia and South Africa formed a cartel, what would be the price and quantity? If the countries split the market evenly, what would be South Africa’s production and profit? What would hap- pen to South Africa’s profit if it increased its pro- duction by 1,000 while Russia stuck to the cartel agreement?

d. Use your answers to part (c) to explain why cartel agreements are often not successful.

Answer 1

Price, P	Quantity, Q	TR=P*Q	Marginal Revenue, MR=Change in TR/Change in Q
8000	5000	40000000
7000	6000	42000000	2000
6000	7000	42000000	0
5000	8000	40000000	-2000
4000	9000	36000000	-4000
3000	10000	30000000	-6000
2000	11000	22000000	-8000
1000	12000	12000000	-10000

a)

If there are many suppliers of diamonds, market is likely to behave as perfectly competitive market. Each competitive firm sets its output such that Price equals marginal cost to maximize profit. So.

Market price=$1000

Output=Quantity demanded at a price of $1000=12000

b)

Single supplier will behave like a monopolist. A monopolist will increase the output as long as MR>MC or MR=MC to maximize profit.

In this case MR>MC for a output level of 6000 but MR<MC for a output level of 7000. So,

Optimal output=6000

Market Price=Price at which quantity demanded is 6000=$7000

c)

Cartel behaves like a monopolist. So, (Refer part b)

Optimal output=6000

Market Price=Price at which quantity demanded is 6000=$7000

Output of South Africa=q=Q/2=6000/2=3000

Profit of South Africa=(P-AC)*q=(P-MC)*q=(7000-1000)*3000=$18,000,000

If South Africa breaks the cartel agreement and increases its out by 1000 units.

Output of South Africa=4000

Output of Russia=3000

Total Output =4000+3000=7000

Market Price=Price at which quantity demanded is 7000=$6000

Profit of South Africa=(P-AC)*q=(P-MC)*q=(6000-1000)*4000=$20,000,000

South Africa's profit will increase bt $2 million

d)

We can see that market price declines as a result of cartel failure but profit of deviating country has increased. This increase in profit acts as an incentive for cartel failure.