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

Expert verified
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

01

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.
02

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.
03

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 \(P = 13\).

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Key Concepts

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

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.

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Most popular questions from this chapter

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?

Among the tax proposals regularly considered by Congress is an additional tax on distilled liquors. The tax would not apply to beer. The price elasticity of supply of liquor is \(4.0,\) and the price elasticity of demand is \(-0.2 .\) The cross-elasticity of demand for beer with respect to the price of liquor is 0.1 a. If the new tax is imposed, who will bear the greater burden-liquor suppliers or liquor consumers? Why? b. Assuming that beer supply is infinitely elastic, how will the new tax affect the beer market?

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 free-market equilibrium price and quantity. b. Now suppose the government wants to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars-hence 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?

About 100 million pounds of jelly beans are consumed in the United States each year, and the price has been about 50 cents per pound. However, jelly bean producers feel that their incomes are too low and have convinced the government that price supports are in order. The government will therefore buy up as many jelly beans as necessary to keep the price at \(\$ 1\) per pound. However, government economists are worried about the impact of this program because they have no estimates of the elasticities of jelly bean demand or supply. a. Could this program cost the government more than \(\$ 50\) million per year? Under what conditions? Could it cost less than \(\$ 50\) million per year? Under what conditions? Illustrate with a diagram. b. Could this program cost consumers (in terms of lost consumer surplus) more than \(\$ 50\) million per year? Under what conditions? Could it cost consumers less than \(\$ 50\) million per year? Under what conditions? Again, use a diagram to illustrate.

You know that if a tax is imposed on a particular product, the burden of the tax is shared by producers and consumers. You also know that the demand for automobiles is characterized by a stock adjustment process. Suppose a special 20 -percent sales tax is suddenly imposed on automobiles. Will the share of the tax paid by consumers rise, fall, or stay the same over time? Explain briefly. Repeat for a 50 -centsper-gallon gasoline tax.
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