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Chapter 9: Problem 8

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 \(Q^{D}=40-2 P,\) 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

Expert verified
The U.S. domestic price of the metal with the $9 tariff was $27 per ounce. Eliminating this tariff and introducing a voluntary restraint agreement, caused the U.S. domestic price to drop to $11 per ounce.

Step by step solution

01

Calculate the U.S. domestic price under the $9 tariff

With the $9 tariff, the world price of the metal goes up to $18 per ounce. Using the supply equation \(Q^{S}=2 / 3 P\), we need to find the value of 'P' (price) when the tariff is applied. To do that, we equate \(Q^{S}\) to the amount of metal supplied at that price. We set \(Q^{S}=2 / 3 P\) to 18, the increased world price and solve for 'P'. We get 'P' as \(27$ per ounce.
02

Determine the U.S. domestic price without the tariff

The exercise asks us to figure out what the domestic (U.S.) Price (P) would be if tariffs were eliminated and a voluntary restraint agreement caps imports to 8 million ounces yearly. We know that the world price is $9 and the limited import quantity is 8 million ounces. Consequently, the metal supply is then shared by both local production:(\(Q^{S}=2 / 3 P\)) and import (set at 8 million ounces). So, the Demand equation \(Q^{D}=40-2P\) becomes \(Q^{D}=Q^{S}+8=40-2P\). Solving this equation for 'P' will give us the U.S. domestic price of the metal without the tariff.
03

Substitute and solve

Substitute \(Q^{S}\) in the equation to get the equation as \(2 / 3 P + 8 = 40 - 2P\). Solving this linear equation will give the new value of 'P' which turns out to be \($11) per ounce

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the World Market Price
The concept of world market price is a critical component in international trade economics. It represents the price at which goods or commodities are traded globally, and it serves as a benchmark for domestic markets.

For instance, if a particular metal is traded on the world market at \(9 per ounce, this price is available to any country willing to engage in trade. This price does not account for additional costs such as transportation or tariffs imposed by importing countries. When a country like the United States decides to import this metal, the world market price serves as the base price before domestic considerations like supply and demand or governmental policies come into play.

Using our exercise example, unlimited quantities of metal could be imported into the United States at the world market price of \)9 per ounce, which significantly influences the U.S. domestic market for this metal.
Domestic Supply and Demand Dynamics
The domestic supply and demand for a commodity can be quite different from its international dynamics. In the context of the textbook exercise, the supply from domestic U.S. mines can be denoted by the equation QS = 2/3 P, where the supply quantity QS is influenced by the domestic price level, P. Conversely, the demand for this metal in the U.S. follows the equation QD = 40 - 2P, showcasing that demand decreases as the price increases.

Therefore, the balance between the domestic supply and demand primarily determines the domestic price level. Without any external influences, such as tariffs or trade agreements, the domestic market would reach an equilibrium where the amount supplied by domestic producers matches the quantity demanded by consumers at a certain price. The intersection of these two equations reflects the domestic market's natural equilibrium state.
Tariff Impact on Domestic Prices
The impact of a tariff, which is essentially a tax imposed on imported goods, can have significant effects on domestic markets. By increasing the cost of imports through a tariff, a government can make imported goods less competitive compared to domestic products. This helps protect local industries from foreign competition.

In our exercise, the U.S. had a tariff of \(9 per ounce on the metal, making the effective price for imported metal \)18 per ounce. This tariff shielded U.S. producers by elevating the domestic price, which, according to the solution, increased to $27 per ounce.

If the tariff is removed, the domestic price would shift again. The new price without the tariff needs to consider the voluntary restraint agreement limiting imports to 8 million ounces per year. This external constraint can alter supply-and-demand dynamics, leading to a new domestic price that could potentially be lower than the tariff-inflated price but still above the world market price due to the import limitation.

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Most popular questions from this chapter

The United States currently imports all of its coffee. The annual demand for coffee by U.S. consumers is given by the demand curve \(Q=250-10 P,\) where \(Q\) is quantity (in millions of pounds) and \(P\) is the market price per pound of coffee. World producers can harvest and ship coffee to U.S. distributors at a constant marginal (= average) cost of \$8 per pound. U.S. distributors can in turn distribute coffee for a constant \(\$ 2\) per pound. The U.S. coffee market is competitive. Congress is considering a tariff on coffee imports of \(\$ 2\) per pound. a. If there is no tariff, how much do consumers pay for a pound of coffee? What is the quantity demanded? b. If the tariff is imposed, how much will consumers pay for a pound of coffee? What is the quantity demanded? c. Calculate the lost consumer surplus. d. Calculate the tax revenue collected by the government. e. Does the tariff result in a net gain or a net loss to society as a whole?

In \(1983,\) the Reagan administration introduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let's consider the wheat market: a. Suppose the demand function is \(Q^{D}=28-2 P\) and the supply function is \(Q^{S}=4+4 P\), where \(P\) is the price of wheat in dollars per bushel, and \(Q\) is the quantity in billions of bushels. Find the freemarket equilibrium price and quantity. b. Now suppose the government wants to lower the supply of wheat by 25 percent from the freemarket equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollarshence the name of the program. The wheat comes from vast government reserves accumulated from previous price support programs. The amount of wheat paid is equal to the amount that could have been harvested on the land withdrawn from production. Farmers are free to sell this wheat on the market. How much is now produced by farmers? How much is indirectly supplied to the market by the government? What is the new market price? How much do farmers gain? Do consumers gain or lose? c. Had the government not given the wheat back to the farmers, it would have stored or destroyed it. Do taxpayers gain from the program? What potential problems does the program create?

In Exercise 4 in Chapter 2 (page 84 ), we examined a vegetable fiber traded in a competitive world market and imported into the United States at a world price of \(\$ 9\) per pound. U.S. domestic supply and demand for various price levels are shown in the following table $$\begin{array}{|ccc|} \hline & \text { U.S. SUPPLY } & \text { U.S. DEMAND } \\ \text { PRICE } & \text { (MILLION POUNDS) } & \text { (MILLION POUNDS) } \\ \hline 3 & 2 & 34 \\ \hline 6 & 4 & 28 \\ \hline 9 & 6 & 22 \\ \hline 12 & 8 & 16 \\ \hline 15 & 10 & 10 \\ \hline 18 & 12 & 4 \\ \hline \end{array}$$ Answer the following questions about the U.S. market: a. Confirm that the demand curve is given by \(Q_{D}=40-2 P,\) and that the supply curve is given by \(Q_{s}=2 / 3 P\) b. Confirm that if there were no restrictions on trade, the United States would import 16 million pounds. c. If the United States imposes a tariff of \(\$ 3\) per pound, what will be the U.S. price and level of imports? How much revenue will the government earn from the tariff? How large is the deadweight loss? d. If the United States has no tariff but imposes an import quota of 8 million pounds, what will be the U.S. domestic price? What is the cost of this quota for U.S. consumers of the fiber? What is the gain for U.S. producers?

Suppose the market for widgets can be described by the following equations: \\[ \begin{array}{cl} \text { Demand: } & P=10-Q \\ \text { Supply: } & P=Q-4 \end{array} \\] where \(P\) is the price in dollars per unit and \(Q\) is the quantity in thousands of units. Then: a. What is the equilibrium price and quantity? b. Suppose the government imposes a tax of \(\$ 1\) per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive? c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of \(\$ 1\) per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government?

Japanese rice producers have extremely high production costs, due in part to the high opportunity cost of land and to their inability to take advantage of economies of large-scale production. Analyze two policies intended to maintain Japanese rice production: (1) a per-pound subsidy to farmers for each pound of rice produced, or (2) a per-pound tariff on imported rice. Illustrate with supply-and-demand diagrams the equilibrium price and quantity, domestic rice production, government revenue or deficit, and deadweight loss from each policy. Which policy is the Japanese government likely to prefer? Which policy are Japanese farmers likely to prefer?
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