Question

One unit of zinc and one unit of copper are needed to produce a unit of brass. The world’s supply of zinc and the world’s supply of copper are owned by two different monopolists. For simplicity assume that it costs nothing to mine zinc and copper, that no other inputs are needed to produce brass, and that the brass industry operates competitively. Then the price of a unit of brass equals the cost of the inputs used to make it. The demand function for brass is q = 900 − 2p, where p is the price of brass. The zinc and copper monopolists each set a price, believing that the other monopolist will not change its price. What is the equilibrium price of brass?

Answer 1

The equilibrium price of brass is $449.50 per unit determined by analyzing the demand and supply functions.

• The equilibrium price of brass can be determined by analyzing the demand and supply functions.
• The demand function for brass is given as q = 900 - 2p, where q represents the quantity demanded and p represents the price of brass.
• The supply of brass is determined by the monopolists who own the world's supply of zinc and copper.
• Since the monopolists believe that the other monopolist will not change its price, they each set their own prices.
• To find the equilibrium price, we can set the quantity demanded equal to the quantity supplied.
• In this case, the quantity demanded is 900 - 2p, and the quantity supplied is 1 unit.
• Setting these two expressions equal to each other, we get 900 - 2p = 1.
• Solving for p, we find that the equilibrium price of brass is $449.50.
• Therefore, the equilibrium price of brass is $449.50 per unit.