Question

A particular metal is traded in a highly competitive world market at a world price of \(9 per ounce.

Unlimited quantities are available for import into the United States at this price. The supply of this metal from domestic U.S. mines and mills can be represented by the equation QS = 2/3P, where QS is U.S. output in million ounces and P is the domestic price.

The demand for the metal in the United States is QD = 40 - 2P, where QD is the domestic demand in million ounces.

In recent years the U.S. industry has been protected by a tariff of \)9 per ounce. Under pressure from other foreign governments, the United States plans to reduce this tariff to zero. Threatened by this change, the U.S. industry is seeking a voluntary restraint agreement that would limit imports into the United States to 8 million ounces per year.

a. Under the $9 tariff, what was the U.S. domestic price of the metal?

b. If the United States eliminates the tariff and the voluntary restraint agreement is approved, what will be the U.S. domestic price of the metal?

Short answer

1. The U.S. domestic price of the metal is $18 per ounce.

2. The new U.S. domestic price of the metal will be $12 per ounce.

Step-by-step solution

Step 1. Determining the U.S. domestic price of the metal

The U.S. domestic price of the metal will be the sum of the world price and the tariff price. The domestic price of the metal is calculated below:

$$\begin{gathered} Priceofmetal=Worldprice+Tariff \\ =\$9+\$9 \\ =\$18 \end{gathered}$$

The domestic price of the metal in the U.S. market would be $18 per ounce.

Step 2. Determining the U.S. domestic price of metal after the implementation of quota policy

The quota will restrict the quantity of imports to 8 million ounces per year. Since quantity import is equivalent to the quantity of imports, the difference between the quantity demanded and quantity supplied will be the quantity of import.

Import = Quantity demanded (QD) –Quantity supplied (QS). Putting the values of import, QD, and QS, the new price after the quota policy is calculated below:

$$\begin{gathered} Import=QD-DS \\ 8=\left(40-2P\right)-\left(\frac{2}{3}P\right) \\ 40-8=2P+\frac{2}{3}P \\ P=12 \end{gathered}$$

Thus, the new U.S. domestic price for the metal after implementing the quota policy will be $12 per pound.