A large share of the world supply of bauxite (used for aluminum) comes from Australia and China

a. Finding the competitive price and quantity

On a market with many suppliers and free entry and exit, the price will be always equal to the marginal cost, i.e., P = $1,000. Then, we can find the quantity from the demand function as 1,000 = 15,000 - Q, and hence, Q = 14,000

b. Finding the monopoly price and quantity

The monopoly maximizes its profit at such a quantity that the marginal cost equals the marginal revenue, i.e., 1,000 = 15,000 - 2Q, and hence, Q = 7,000

The monopoly will charge the price that the market is ready to pay at the optimal quantity, i.e., P = 15,000 - Q = 15,000 - 7,000 = $8,000

c. Finding the cartel price and quantity

If several firms (or countries) form a cartel, they will coordinate to maximize their joint profits. This is achieved at the monopoly price and quantity. Hence, P = $8,000 and Q = 7,000