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Import Tariffs and Quotas Under Perfect Competition

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A Brief History of the World Trade Organization

The Gains from Trade

Import Tariffs for a Small Country

Import Tariffs for a Large Country

Import Quotas

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On September 11, 2009 President Barack Obama announced a tariff of 35% on imports of tires made in China. This tariff expired in September 27, 2012.

The tire tariff is an example of a trade policy, a government action meant to influence the amount of international trade.

Because the gains from trade are unevenly spread, industries and labor unions often feel that the government should do something to help limit their losses (or maximize their gains) from international trade.

That “something” is trade policy, which includes the use of import tariffs (taxes on imports), import quotas (quantity limits on imports), and exports subsidies.

Introduction

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In this chapter, we begin our investigation of trade policies by focusing on the effects of tariffs and quotas in a perfectly competitive industry.

Once the international context for setting trade policy has been established, the chapter examines in detail the most commonly used trade policy, the tariff.

A third purpose of the chapter is to examine the use of an import quota, which is a limit on the quantity of a good that can be imported from a foreign country.

Introduction

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1 A Brief History of the World Trade Organization

After World War II, the Allied countries met to discuss issues such as high trade barriers and unstable exchange rates.

In 1947 the General Agreement on Tariffs and Trade (GATT) was established to reduce barriers to trade between nations.

Some of the GATT’s main provisions are as follows:

A nation must extend the same tariffs to all trading partners that are WTO members.

Tariffs may be imposed in response to unfair trade practices such as dumping.

Recall that “dumping” is defined as the sale of export goods at a price less than that charged at home, or at a price less than costs of production and shipping.

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Some of the GATT’s main provisions are as follows:

Countries should not limit the quantity of goods and services that they import.

Countries should declare export subsidies provided to particular firms, sectors, or industries. Article XVI deals with export subsidies, and states that countries should notify each other of the extent of subsidies and discuss the possibility of eliminating them.

Countries can temporarily raise tariffs for certain products. Article XIX, called the safeguard provision or the escape clause, is our focus in this chapter.

1 A Brief History of the World Trade Organization

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Some of the GATT’s main provisions are as follows:

Regional trade agreements are permitted under Article XXIV of the GATT. The GATT recognizes the ability of blocs of countries to form two types of regional trade agreements:

free-trade areas, in which a group of countries voluntarily agree to remove trade barriers between themselves, and

(ii) customs unions, which are free-trade areas in which the countries also adopt identical tariffs between themselves and the rest of the world.

1 A Brief History of the World Trade Organization

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SIDE BAR

Key Provisions of the GATT
Article I General Most-Favoured-Nation Treatment
Article VI Anti-Dumping and Countervailing Duties
Article XI General Elimination of Quantitative Restrictions
Article XVI Subsidies
Article XIX Emergency Action on Imports of Particular Products
Article XXIV Territorial Application—Frontier Traffic—Customs Unions and Free-Trade Areas

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Consumer and Producer Surplus

FIGURE 7-1 (1 of 2)

In panel (a), the consumer surplus from purchasing quantity D1 at price P1 is the area below the demand curve and above that price. The consumer who purchases D2 is willing to pay price P2 but has to pay only P1. The difference is the consumer surplus and represents the satisfaction of consumers over and above the amount paid.

2 The Gains from Trade

Consumer and Producer Surplus

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Consumer and Producer Surplus

FIGURE 7-1 (2 of 2)

In panel (b), the producer surplus from supplying the quantity S1 at the price P1 is the area above the supply curve and below that price. The supplier who supplies unit S0 has marginal costs of P0 but sells it for P1. The difference is the producer surplus and represents the return to fixed factors of production in the industry.

2 The Gains from Trade

Consumer and Producer Surplus (continued)

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Home Welfare

FIGURE 7-2

The Gains from Free Trade at Home With Home demand of D and supply of S, the no-trade equilibrium is at point A, at the price PA producing Q0.

With trade, the world price is PW, so quantity demanded increases to D1 and quantity supplied falls to S1. Since quantity demanded exceeds quantity supplied, Home imports D1 – S1.

Consumer surplus increases by the area (b + d), and producer surplus falls by area b.

The gains from trade are measured by area d.

No Trade, Free Trade for a Small Country, Gains from Trade

A small country is small in comparison with all the other countries buying and selling this product.

Rise in consumer surplus: + (b + d)

Fall in producer surplus: − b

Net effect on Home welfare: + d

2 The Gains from Trade

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JNB (J.Baker) - Suggest moving this to the notes portion underneath or deleting all together. This clutters the slide with too much information and distracts where the eye should focus which is on the figure.

Home Import Demand Curve

FIGURE 7-3

Home Import Demand With Home demand of D and supply of S, the no-trade equilibrium is at point A, with the price PA and import quantity Q0.

Import demand at this price is zero, as shown by the point A' in panel (b).

At a lower world price of PW, import demand is M1 = D1 – S1, as shown by point B.

Joining up all points between A' and B, we obtain the import demand curve, M.

The import demand curve shows the relationship between the world price of a good and the quantity of imports demanded by Home consumers.

2 The Gains from Trade

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Free Trade for a Small Country and Effect of the Tariff

FIGURE 7-4 (1 of 2)

Applying a tariff of t dollars will increase the import price from PW to PW + t. The domestic price of that good also rises to PW + t. This price rise leads to an increase in Home supply from S1 to S2, and a decrease in Home demand from D1 to D2, in panel (a).

3 Import Tariffs for a Small Country

Tariff for a Small Country

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Free Trade for a Small Country and Effect of the Tariff

FIGURE 7-4 (2 of 2)

Imports fall due to the tariff, from M1 to M2 in panel (b). As a result, the equilibrium shifts from point B to C.

3 Import Tariffs for a Small Country

Tariff for a Small Country (continued)

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FIGURE 7-5 (1 of 2)

The tariff increases the price from PW to PW + t. As a result, consumer surplus falls by (a + b + c + d). Producer surplus rises by area a, and government revenue increases by the area c.

3 Import Tariffs for a Small Country

Effect of Tariff on Welfare

Effect of the Tariff on Consumer Surplus, Producer Surplus, Government Revenue; Overall Effect of the Tariff on Welfare; Production Loss; Consumption Loss

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FIGURE 7-5 (2 of 2)

Therefore, the net loss in welfare, the deadweight loss to Home, is (b + d), which is measured by the two triangles b and d in panel (a) or the single (combined) triangle b + d in panel (b).

The triangle (b + d) is a deadweight loss, or a loss that is not offset by a gain elsewhere in the economy.

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Rise in government revenue: + c

Net effect on Home welfare: − (b + d)

3 Import Tariffs for a Small Country

Effect of Tariff on Welfare (continued)

Effect of the Tariff on Consumer Surplus, Producer Surplus, Government Revenue; Overall Effect of the Tariff on Welfare; Production Loss; Consumption Loss

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Effect of Tariff on Consumer Surplus, Producer Surplus, Government Revenue; Overall Effect of the Tariff on Welfare

The deadweight loss, triangles (b + d ), have the following interpretation:

The triangle b equals the increase in marginal costs for the extra units produced and can be interpreted as the production loss (or the efficiency loss) due to producing at marginal cost above the world price.

The triangle d can be interpreted as the drop in consumer surplus for those individuals who are no longer able to consume the units between D1 and D2 because of the higher price. We refer to this drop in consumer surplus as the consumption loss for the economy.

3 Import Tariffs for a Small Country

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Why and How Are Tariffs Applied?

If a small country suffers a loss when it imposes a tariff, why do so many have tariffs as part of their trade policies?

One answer is that a developing country does not have any other source of government revenue. Import tariffs are “easy to collect.”

A second reason is politics. The benefits to producers (and their workers) are typically more concentrated on specific firms and states than the costs to consumers, which are spread nationwide.

3 Import Tariffs for a Small Country

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SIDE BAR

Safeguard Tariffs

The U.S. Trade Act of 1974, as amended, describes conditions under which tariffs can be applied in the United States, and it mirrors the provisions of the GATT and WTO.

Section 201 allows the U.S. to impose safeguard tariffs if imports are a “substantial cause of serious injury, or the threat thereof, to the domestic industry.” Where the term “substantial cause” means a cause which is important and not less than any other cause.

Section 421 allows the U.S. to impose safeguard tariffs on China if imports from China “cause or threaten to cause market disruption to the domestic producers.”

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TABLE 7-1

APPLICATION

U.S. Tariffs on Steel and Tires

U.S. ITC Recommended and Actual Tariffs for Steel Shown here are the tariffs recommended by the U.S. International Trade Commission for steel imports, and the actual tariffs that were applied in the first year.

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Deadweight Loss Due to the Steel Tariff

The deadweight loss relative to the value of imports equals:

U.S. Tariffs on Steel and Tires

APPLICATION

Oliphant Universal Press Syndicate

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Response of the European Countries

The countries in the European Union (EU) took action by bringing the case to the WTO. The WTO ruling entitled the European Union and other countries to retaliate against the United States by imposing tariffs of their own against U.S. exports.

The use of tariffs by an importer can easily lead to a response by exporters and a tariff war.

U.S. Tariffs on Steel and Tires

The WTO has a dispute settlement procedure under which countries can bring their complaint and have it evaluated.

APPLICATION

Oliphant Universal Press Syndicate

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Tariff on Tires

U.S. Tariffs on Steel and Tires

The tariff on tires imported from China, announced by President Obama on September 11, 2009, was filed under Section 421 of U.S. trade law.

The tire tariff was applied to imports from a single country—China—under Section 421, whereas the steel tariff was applied against many countries under Section 201.

For this reason we will refer to the tariff on tires applied against China as a discriminatory tariff.

APPLICATION

©2009 Jianping Fan, and PoliticalCartoons.com

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A Discriminatory Tariff

APPLICATION

U.S. Tariffs on Steel and Tires

FIGURE 7-6

Effect of the Tariff on Tires The tariff on tires increases the price of tires from China from PW to PW + t. The supply from the United States is shown by S, and the supply from other exporting countries by X*.

As a result of the tariff, these two sources of supply increase from S1 + X*1 to S2 + X*2; China supplies the rest of the market up to demand D1.

Because the other exporting countries do not face the tariff, they collect area e from the higher prices charged in the U.S. market. Therefore, the deadweight loss from the tariff is (b + d + e).

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Deadweight Loss Due to the Tire Tariff

APPLICATION

U.S. Tariffs on Steel and Tires

FIGURE 7-7

U.S. Imports of Tires

U.S. Imports of Tires The tariff applied to U.S. imports of tires began in the fourth quarter of 2009 and ended in the third quarter of 2012. The value of imports from China fell from about 33% of overall imports to 15% when the tariff began, and rose from about 12% of overall imports to 22% when the tariff ended. This decline in imports from China was substantially made up by increased imports from other Asian countries and Mexico, which exported more to the United States.

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Deadweight Loss Due to the Tire Tariff

APPLICATION

U.S. Tariffs on Steel and Tires

Figure 7-7 shows that the decline in imports from China was made up for by increased imports from other Asian countries and Mexico, which exported more to the United States.

These other exporters were also able to charge higher prices. For car tires, the average price charged by countries other than China increased from $54 to $64 during the times of the tariff.

An estimate of the area e—the total increase in the amount paid to tire exporters other than China—is $817 million per year, which substantially exceeds the deadweight loss for the steel tariff at $185 million per year.

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Foreign Export Supply

FIGURE 7-8 (1 of 3)

In panel (a), with Foreign demand of D* and Foreign supply of S*, the no-trade equilibrium in Foreign is at point A*, with the price of PA*.

At this price, the Foreign market is in equilibrium and Foreign exports are zero—point A* in panel (a) and point A* in panel (b), respectively.

4 Import Tariffs for a Large Country

Foreign Export Supply

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If we consider a large enough importing country or a large country, we might expect that its tariff will change the world price.

Foreign Export Supply

FIGURE 7-8 (2 of 3)

When the world price, PW, is higher than Foreign’s no-trade price, the quantity supplied by Foreign, S*1, exceeds the quantity demanded by Foreign, D*1, and Foreign exports X*1 = S*1 – D*1.

In panel (b), joining up points A* and B*, we obtain the upward-sloping export supply curve X*.

4 Import Tariffs for a Large Country

Foreign Export Supply (continued)

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If we consider a large enough importing country or a large country, we might expect that its tariff will change the world price.

Foreign Export Supply

FIGURE 7-8 (3 of 3)

With the Home import demand of M, the world equilibrium is at point B*, with the price PW.

4 Import Tariffs for a Large Country

Foreign Export Supply (continued)

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Effect of the Tariff

FIGURE 7-9

Tariff for a Large Country

The tariff shifts up the export supply curve from X* to X*+ t.

As a result, the Home price increases from PW to P* + t, and the Foreign price falls from PW to P*.

The deadweight loss at Home is the area of the triangle (b + d), and Home also has a terms-of-trade gain of area e.

Foreign loses the area (e + f), so the net loss in world welfare is the triangle (b + d + f). Area e is a measure of the terms-of-trade gain for the importer.

Terms of Trade, Home Welfare, Foreign and World Welfare

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Rise in government revenue: + (c + e)

Net effect on Home welfare: e − (b + d)

The terms of trade for a country as the ratio of export prices to import prices.

4 Import Tariffs for a Large Country

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Foreign Export Supply

Optimal Tariff for a Large Importing Country

FIGURE 7-10

Tariffs and Welfare for a Large Country For a large importing country, a tariff initially increases the importer’s welfare because the terms-of-trade gain exceeds the deadweight loss. So the importer’s welfare rises from point B. Welfare continues to rise until the tariff is at its optimal level (point C). After that, welfare falls. If the tariff is too large (greater than at B), then welfare will fall below the free-trade level. For a prohibitive tariff, with no imports at all, the importer’s welfare will be at the no-trade level, at point A.

Optimal Tariff Formula The formula depends on the elasticity of Foreign export supply, which we call E*X:

4 Import Tariffs for a Large Country

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APPLICATION

U.S. Tariffs on Steel Once Again

Optimal Tariffs for Steel

TABLE 7-2

Optimal Tariffs for Steel Products This table shows optimal tariffs for steel products, calculated with the elasticity formula.

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On January 1, 2005, China was poised to become the world’s largest exporter of textiles and apparel. On that date, a system of worldwide import quotas known as the Multifibre Arrangement (MFA) was abolished.

Besides the MFA, there are many other examples of import quotas.

For example, since 1993 Europe had a quota on the imports of bananas that allowed for a greater number of bananas to enter from its former colonies in Africa than from Latin America.

Another example is the quota on U.S. imports of sugar, which is still in place despite calls for its removal.

5 Import Quotas

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Banana Wars

HEADLINES

This article discusses a well-known example of a quota that applied to European imports of bananas. The quota and discriminatory tariff on bananas from Latin America finally ended in late 2009.

Sugar Could Sweeten U.S. Australia Trans-Pacific Trade Talks

HEADLINES

This article discusses the reasons for a sugar quota in the United States, which has been in place since before World War II. Under current negotiations for the Trans-Pacific Partnership, Australia has asked the United States to reconsider this quota and allow more exports from Australia.

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Import Quota in a Small Country

Free-Trade Equilibrium, Effect of the Quota, Effect on Welfare

FIGURE 7-11

Quota for a Small Country Under free trade, the Foreign export supply curve is horizontal at the world price PW, and the free-trade equilibrium is at point B with imports of M1. Applying an import quota of M2 < M1 leads to the vertical export supply curve —with the equilibrium at point C. The quota increases the import price from PW to P2. There would be the same impact on price and quantities if instead of the quota, a tariff of t = P2 – PW had been used.

For every level of the import quota, there is an equivalent import tariff that would lead to the same Home price and quantity of imports.

5 Import Quotas

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Import Quota in a Small Country

5 Import Quotas

FIGURE 7-11 (revisited)

The quota and tariff differ in terms of area c, in Figure 8-9, which would be collected as government revenue under a tariff.

Under the quota, this area equals the difference between the domestic price P2 and the world price PW, times the quantity of imports M2.

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Import Quota in a Small Country

Whoever is actually importing the good will be able to earn the difference between the world price PW and the higher Home price P2 by selling the imports in the Home market.

We call the difference between these two prices the rent associated with the quota, and hence the area c represents the total quota rents.

Next we examine the four possible ways that these quota rents can be allocated.

5 Import Quotas

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Import Quota in a Small Country

Giving the Quota to Home Firms

Quota licenses (i.e., permits to import the quantity allowed under the quota system) can be given to Home firms: With home firms earning the rents c, the net effect of the quota on Home welfare is

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Quota rents earned at Home + c

Net effect on Home welfare: − (b + d)

5 Import Quotas

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Import Quota in a Small Country

Rent Seeking

If licenses for the imported chemicals are allocated in proportion to each firm’s production of batteries in the previous years, then the Home firms will likely produce more batteries than they can sell (and at lower quality) just to obtain the import licenses for the following year.

Alternatively, firms might engage in bribery or other lobbying activities to obtain the licenses.

These kinds of inefficient activities done to obtain quota licenses are called rent seeking. If rent seeking occurs, the welfare loss due to the quota would be

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Net effect on Home welfare: − (b + c + d)

5 Import Quotas

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Import Quota in a Small Country

3. Auctioning the Quota

A third possibility for allocating the rents that come from the quota is for the government of the importing country to auction off the quota licenses.

In a well-organized, competitive auction, the revenue collected should exactly equal the value of the rents, so that area c would be earned by the Home government.

Using the auction method to allocate quota rents, the net loss in domestic welfare due to the quota becomes

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Auction revenue earned at Home + c

Net effect on Home welfare: − (b + d)

5 Import Quotas

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Import Quota in a Small Country

4. “Voluntary” Export Restraint

The final possibility for allocating quota rents is for the government of the importing country to give authority for implementing the quota to the government of the exporting country.

Because the exporting country allocates the quota among its own producers, this is sometimes called a “voluntary” export restraint (VER), or a “voluntary” restraint agreement (VRA).

In the 1980s the United States used this type of arrangement to restrict Japanese automobile imports.

In this case, the quota rents are earned by foreign producers, so the loss in Home welfare equals

Fall in consumer surplus: − (a + b + c + d)

Rise in producer surplus: + a

Net effect on Home welfare: − (b + c + d)

5 Import Quotas

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Import Quota in a Small Country

Costs of Import Quotas in the United States

TABLE 7-3

Annual Cost of U.S. Import Protection ($ billions) Shown here are estimates of the dead weight losses and quota rents due to U.S. import quotas in the 1980s, for the years around 1985. Many of these quotas are no longer in place today.

5 Import Quotas

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APPLICATION

China and the Multifibre Arrangement

One of the founding principles of GATT was that countries should not use quotas to restrict imports.

The Multifibre Arrangement (MFA), organized under the auspices of the GATT in 1974, was a major exception to that principle and allowed the industrial countries to restrict imports of textile and apparel products from the developing countries.

Importing countries could join the MFA and arrange quotas bilaterally (i.e., after negotiating with exporters) or unilaterally (on their own).

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APPLICATION

China and the Multifibre Arrangement

Growth in Exports from China

The MFA expired on January 1, 2005. The biggest potential supplier of textile and apparel products was China. Immediately, exports of textiles and apparel from China grew rapidly.

Welfare Cost of MFA

Given the drop in prices in 2005 from countries selling to the United States, it is possible to estimate the welfare loss due to the MFA.

The United States did not auction the quota licenses for textiles and apparel so the quota rents were earned by foreign exporting firms.

That means the welfare loss for the United States due to the MFA is the area (b + c + d) in Figure 7-11.

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China and the Multifibre Arrangement

Import Quality

The prices of textile and apparel products dropped the most (in percentage terms) for the lower-priced items.

So an inexpensive T-shirt coming from China and priced at $1 had a price drop of more than 38% (more than 38¢), whereas a more expensive item priced at $10 experienced a price drop of less than 38% (less than $3.80).

As a result, U.S. demand shifted toward the lower-priced items imported from China: there was “quality downgrading” in the exports from China.

APPLICATION

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China and the Multifibre Arrangement

Reaction of the United States and Europe

The European Union threatened to impose new quotas on Chinese exports, and in response, China agreed on June 11, 2005, to “voluntary” export restraints.

Due to the worldwide recession, Chinese exports in this industry were much lower in 2009 than they had been in earlier years.

China indicated that it would not accept any further limitation on its ability to export textile and apparel products to the United States and to Europe, and both these quotas expired.

APPLICATION

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China and the Multifibre Arrangement

FIGURE 7-12 (1 of 2)

After the expiration of the Multifibre Arrangement (MFA), the value of clothing and textiles exports from China rose dramatically, as shown in panel (a). This reflects the surge in the quantity of exports that were formerly constrained under the MFA as well as a shift to Chinese exports from other, higher-cost producers such as Hong Kong, Taiwan, and South Korea.

APPLICATION

Changes in Clothing and Textile Exports to the United States after the MFA, 2004-2005

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China and the Multifibre Arrangement

FIGURE 7-12 (2 of 2)

In panel (b), we see that the prices of goods constrained by the MFA typically fell by more than the average change in export prices after the MFA’s expiry. This is exactly what our theory of quotas predicts: the removal of quotas lowers import prices for consumers.

APPLICATION

Changes in Clothing and Textile Exports to the United States after the MFA, 2004-2005 (continued)

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1. The government of a country can use laws and regulations, called “trade policies,” to affect international trade flows. An import tariff, which is a tax at the border, is the most commonly used trade policy.

K e y T e r m

KEY POINTS

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2. The rules governing trade policies in most countries are outlined by the General Agreement on Tariffs and Trade (GATT), an international legal convention adopted after World War II to promote increased international trade. Since 1995 the new name for the GATT is the World Trade Organization (WTO).

K e y T e r m

KEY POINTS

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3. In a small country, the quantity of imports demanded is assumed to be very small compared with the total world market. For this reason, the importer faces a fixed world price. In that case, the price faced by consumers and producers in the importing country will rise by the full amount of the tariff.

K e y T e r m

KEY POINTS

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4. The use of a tariff by a small importing country always leads to a net loss in welfare. We call that loss the “deadweight loss.”

K e y T e r m

KEY POINTS

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5. In a large country, the decrease in imports demanded due to the tariff causes foreign exporters to lower their prices. Consumer and producer prices in the importing country still go up, since these prices include the tariff, but they rise by less than the full amount of the tariff (since the exporter price falls).

K e y T e r m

KEY POINTS

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JNB (J.Baker) - Skipped actual Key point #5. This one is #6 as listed in the text, so there should be 11 Key points in total.

6. The use of a tariff for a large country can lead to a net gain in welfare because the price charged by the exporter has fallen; this is a terms-of-trade gain for the importer.

K e y T e r m

KEY POINTS

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7. The “optimal tariff” is the tariff amount that maximizes welfare for the importer. For a small country, the optimal tariff is zero since any tariff leads to a net loss. For a large country, however, the optimal tariff is positive.

K e y T e r m

KEY POINTS

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8. The formula for the optimal tariff states that it depends inversely on the foreign export supply elasticity. If the foreign export supply elasticity is high, then the optimal tariff is low, but if the foreign export supply elasticity is low, then the optimal tariff is high.

K e y T e r m

KEY POINTS

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9. “Import quotas” restrict the quantity of a particular import, thereby increasing the domestic price, increasing domestic production, and creating a benefit for those who are allowed to import the quantity allotted. These benefits are called “quota rents.”

K e y T e r m

KEY POINTS

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10. Assuming perfectly competitive markets for goods, quotas are similar to tariffs since the restriction in the amount imported leads to a higher domestic price. However, the welfare implications of quotas are different from those of tariffs depending on who earns the quota rents. These rents might be earned by firms in the importing country (if they have the licenses to import the good), or by firms in the exporting country (if the foreign government administers the quota), or by the government in the importing country (if it auctions off the quota licenses). The last case is most similar to a tariff, since the importing government earns the revenue.

K e y T e r m

KEY POINTS

© 2014 Worth Publishers International Economics, 3e | Feenstra/Taylor

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trade policy

import tariff

import quota

dumping

export subsidies

safeguard provision

escape clause

regional trade agreements

free-trade areas

customs unions

consumer surplus

K e y T e r m

KEY TERMS

producer surplus

small country

import demand curve

deadweight loss

production loss

consumption loss

dispute settlement procedure

tariff war

large country

terms of trade

terms-of-trade gain

optimal tariff

Multifibre Arrangement (MFA)

equivalent import tariff

quota rents

quota licenses

rent seeking

“voluntary” export restraint (VER)

“voluntary” restraint agreement (VRA)

© 2014 Worth Publishers International Economics, 3e | Feenstra/Taylor

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*

1

tariff

Optimal

X

E

=

*

1

tariff

Optimal

X

E

=