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 \(Q^{s}=2 / 3 P\), where \(Q^{s}\) is U.S. output in million ounces and \(P\) is the domestic price. The demand for the metal in the United States is \(Q^{\mathrm{D}}=40-2 P\), where \(Q^{\mathrm{D}}\) 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

a) Under a \$9 tariff, the U.S. domestic price of the metal was \$18. b) If the United States eliminates the tariff and the voluntary restraint agreement is approved, the U.S. domestic price of the metal will be \$13.

Step-by-step solution

Solve for Domestic Price Under \$9 Tariff

In this case, the price in the U.S. is the world price plus the tariff, which is \(\$9 + $9 = $18\). Therefore, the U.S. domestic price of the metal under a \$9 tariff is \$18 per ounce.

Calculate Demand and Supply Under \$9 Tariff

Now, let's calculate the U.S. domestic demand and supply at this price. Substituting \(P = 18\) into the supply equation, we get \(Q^{s}=2 / 3 * 18 = 12\) million ounces. Substituting \(P = 18\) into the demand equation, we get \(Q^{D} = 40 - 2 * 18 = 4\) million ounces.

Solve for Domestic Price after Removing Tariff and Approving Voluntary Restraint Agreement

In this case, the price in the U.S. will be equal to the world price, \$9. The supply is given by the equation \(Q^{s}=2 / 3 * 9 = 6\) million ounces. The voluntary restraint agreement limits imports to 8 million ounces, so the total supply is \(6 + 8 = 14\) million ounces. This will be equal to the U.S. demand. Therefore, we need to solve the equation \(14 = 40 - 2P\). Solving this for \(P\) gives the U.S. domestic price as \(P = 13\).

Key concepts

World Market Price

The world market price is a crucial element in understanding global trade dynamics. It is the price at which a good or service is traded internationally. When a country's domestic price for a product is higher than the world market price, as is often the case with commodities such as metals, it can lead to an increase in imports because it is cheaper to purchase the product from foreign producers.

However, domestic industries may struggle to compete with these lower prices, which is why some countries impose tariffs to protect local jobs and businesses. A tariff is effectively a tax on imports, designed to make them more expensive and less appealing when compared to locally produced items, shifting the demand back in favor of domestic producers. In our exercise, the removal of a tariff would typically result in the domestic price converging toward the world market price, assuming no other trade barriers are enacted.

Domestic Supply and Demand Equations

Understanding domestic supply and demand equations is key to predicting how changes in policy will affect a country's economy. These equations give us a mathematical model of how much of a good is produced and consumed within a country at different price levels.

In our exercise, domestic supply is modeled by the equation \(Q^{s}=\frac{2}{3}P\), and domestic demand by \(Q^{D}=40-2P\). Here, \(Q^{s}\) and \(Q^{D}\) represent the quantity supplied and demanded, respectively, and \(P\) is the price in dollars. By manipulating these equations, we can visualize the market's reaction to events like the introduction or removal of tariffs. A balanced domestic market is where supply equals demand, and that is where the price typically settles.

Voluntary Restraint Agreement

A Voluntary Restraint Agreement (VRA) is a trade pact between countries where an exporter agrees to limit the quantity of goods exported to a particular country. These are sometimes used as an alternative to tariffs and import quotas and can be a strategic decision to ease trade tensions or protect certain industries.

In our exercise, the United States is considering a VRA to limit the import of a metal to 8 million ounces per year. Unlike tariffs that affect the price, VRAs directly restrict the quantity, which can still have the effect of increasing the domestic price by limiting supply. This artificial scarcity means domestic producers can increase their prices as long as they remain competitive against the capped import supply.

Tariff Elimination Effects

The effects of tariff elimination can be wide-ranging, impacting domestic prices, production, and consumption patterns. When a tariff is removed, imported goods become cheaper, allowing them to more effectively compete with domestic goods. This can lead to a decrease in domestic prices, increased consumer choice, and potentially better prices due to competition.

In the context of the exercise, removing the \(\$9\) tariff would mean the domestic price would adjust closer to the world market price, all else being equal. However, the proposed VRA complicates this by retaining some level of protection for domestic producers. It illustrates how international trade policy can have complex effects on an economy, which is why these decisions are often the subject of intense debate and negotiation.