Question

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

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

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 \(Q_S = 2/3 P \)

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.

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.

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.

Key concepts

Demand and Supply Curves

Demand and supply curves are fundamental elements in understanding international trade. They illustrate how much of a product consumers are willing to purchase at each price, and how much producers are willing to sell, respectively. In this specific exercise, the demand curve is represented by the equation \(Q_D = 40 - 2P\), where \(Q_D\) is the quantity demanded in million pounds and \(P\) is the price per pound in dollars. As the price increases, the quantity demanded decreases, which is typical for most goods.

On the other hand, the supply curve is given by \(Q_S = \frac{2}{3}P\). This relationship indicates that as prices rise, suppliers are willing to offer more of the product for sale. These graphical representations help us understand the quantity of a product that the market demands and supplies at various prices. This balance, or equilibrium, is where the supply and demand intersect, directly influencing international trade dynamics by determining prices and quantities in the market.

Tariff Effects

Tariffs are taxes imposed on imported goods and have several effects on the domestic market. In this scenario, a tariff of \(\\(3\) per pound is applied to the imported vegetable fiber. This levy directly increases the cost of imported goods, making them more expensive for domestic consumers. As a result, the domestic price for the fiber becomes \(\\)12\) per pound, compared to the initial world price of \(\\(9\).

This price rise causes a decrease in quantity demanded domestically. With the higher price, the domestic supply increases to a certain extent. However, imports decrease to 8 million pounds, as calculated by the new quantities demanded and supplied. The government also generates revenue from this tariff, which amounts to \(24\) million dollars (calculated as \(\\)3\) multiplied by \(8\) million pounds of imports).

• Imports become more expensive.
• Domestic producers increase output.
• Government earns revenue from tariffs.

This policy tends to provide protection for domestic industries but can burden consumers with higher prices while also inducing inefficiencies in the market.

Import Quota

An import quota sets a physical limit on the quantity of goods that can be imported. In this situation, the United States implements a quota for 8 million pounds of vegetable fiber imports, directly restricting the amount entering the market. Consequently, quotas can impact the domestic market quite similarly to tariffs by pushing up domestic prices and lowering imports.

With the set quota, the equilibrium price increases to around \(\$13\) per pound. This change causes an increase in consumer costs since they now pay more for the fiber than at the previous world price. On the other side, domestic producers benefit from a higher price, which potentially increases their revenue and business growth.

• Restricts imports to a specific quantity.
• Increases domestic prices.
• Benefits domestic producers at consumers' cost.

While the quota may help shield domestic industries, the trade-off is clear: consumers face higher prices, leading to a decrease in consumer surplus. The balance between benefiting producers and protecting consumer interests becomes critical in discussing and designing trade policies.

Deadweight Loss

Deadweight loss refers to the loss of economic efficiency in a market, typically due to policy interventions such as tariffs and quotas. This exercise highlights how such interventions can result in a net loss to society, even when some groups may benefit.

When a tariff is imposed, some potential transactions do not occur due to increased prices. For instance, consumers may find the new price too high, reducing their purchases, and some producers may not be able to compete even at the increased price level. This results in a deadweight loss, represented graphically by a triangle between the demand and supply curves, encompassing the difference between the price consumers are willing to pay and the price producers receive.

• Occurs due to market inefficiencies.
• Represents lost consumer and producer surplus.
• Caused by interventions like tariffs and quotas.

Understanding deadweight loss is essential for analyzing trade policies since it helps policymakers weigh the benefits against the societal costs, aiming for the most beneficial economic outcomes with the least unintended consequences.