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Chapter 9: Problem 6

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?

Short Answer

Expert verified
Demand curve is \(Q_D = 40 - 2P\), and supply curve is \(Q_S = 2/3P\). Without trade restrictions, imports would be 16 million pounds. With a 3 dollar tariff, the domestic price becomes 12 dollars, imports become 8 million pounds, and the government earns 24 million dollars. The deadweight loss can be calculated as described. If a quota of 8 million pounds were imposed instead, the domestic price would increase to about 13 dollars, and the cost to consumers and gain for producers can be calculated as described.

Step by step solution

01

Confirming the Demand and Supply Curves

By tracking changes in quantity demanded or supplied when prices change in the table, the curves' function can be constructed. For the demand curve, a price increase by 3 leads to a decrease in demand by 6 million pounds, making the coefficient -2. The equation for the demand curve is hence \(Q_D = 40 - 2P \). For the supply curve, a similar calculation shows a coefficient of 2/3, hence the supply curve is \(Q_S = 2/3 P \)
02

Calculate the No-Trade Import Quantity

If there were no restrictions on trade, the quantity imported to the US would be the difference between quantity demanded at the world price and quantity supplied at the world price. From the table, at a world price of $9, quantity demanded is 22 million pounds, and quantity supplied is 6 million pounds. The difference is hence 16 million pounds, which concludes that the US would import 16 million pounds.
03

Calculate Effects of Tariff

When a tariff of $3 per pound is imposed, the price domestically effectively becomes $12 per pound (9+3). At this price, quantities demanded and the quantities supplied domestically can be obtained by plugging 12 into the respective demand and supply functions, resulting in 16 million pounds and 8 million pounds respectively. Imports become 8 million pounds (16 - 8). Government revenue is then the tariff amount times imports, equalling 24 million dollars ($3/pound * 8 million pounds). The Deadweight loss can be calculated by finding the area of the triangle formed by the supply curve at 9 and 12 dollars, and the demand curve at those prices.
04

Calculate Effects of Import Quota

A quota limits imports to 8 million pounds. To find the resulting domestic price, solve for P when \(Q_D = Q_S + Quota\), which yields a price of about 13 dollars. At that price, consumers pay more than the world price, and producers gain more. The cost to consumers is the difference in consumer surplus - the area under the demand curve above price, whereas the gain for producers is the increase in producer surplus, area above the supply curve below the price.

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Most popular questions from this chapter

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?

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