A large share of the world's supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is $1000 per diamond, and the demand for diamonds is described by the following schedule: Price($): 8000, 7000, 6000, 5000, 4000, 3000, 2000 Quantity: 5000, 6000, 7000, 8000, 9000, 10000, 11000 a) If there were many suppliers of diamonds, what would be the price and quantity? b) If there was 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 happen to South Africa's profit if it increased its production by 1000 while Russia stuck to the cartel agreement? d) Use your answer to part (c) to explain why cartel agreements are often not successful.

a) If there were many suppliers of diamonds, the price would be determined by the marginal cost of production, which is $1000 per diamond. The quantity would be determined by the demand at that price. Looking at the demand schedule, we see that at a price of$2000, the quantity demanded is 11000 diamonds. Therefore, if there were many suppliers, the price would be $2000 and the quantity would be 11000 diamonds.

b) If there was only one supplier of diamonds, they would act as a monopolist and set the price to maximize their profit. The monopolist would choose the price and quantity where marginal cost equals marginal revenue. Looking at the demand schedule, we see that the highest price that can be charged is $8000 for 5000 diamonds. Therefore, if there was only one supplier, the price would be$8000 and the quantity would be 5000 diamonds.

c) If Russia and South Africa formed a cartel, they would act like a monopolist and set the price to maximize their joint profit. Assuming they split the market evenly, each country would produce half of the total quantity. Looking at the demand schedule, we see that the highest price that can be charged is $8000 for 5000 diamonds. Therefore, if Russia and South Africa formed a cartel, the price would be$8000 and the total quantity would be 5000 diamonds. Each country would produce 2500 diamonds. South Africa's profit would be the total revenue minus the total cost, which is ($8000 * 2500) - ($1000 * 2500) = $17,500,000. If South Africa increased its production by 1000 while Russia stuck to the cartel agreement, it would increase the total quantity to 6000 diamonds, which would decrease the price to$7000 according to the demand schedule. South Africa's new profit would be ($7000 * 3500) - ($1000 * 3500) = $21,000,000.

d) Cartel agreements are often not successful because each member of the cartel has an incentive to cheat and increase their production to increase their profit, as we saw with South Africa in part (c). This increases the total quantity and decreases the price, which hurts the other members of the cartel. This creates a tension between cooperation and self-interest, which often leads to the breakdown of the cartel agreement.