ps2_solutions.pdf

FEB13085: International Trade Policy FEB13085: International Trade Policy Problem Set 2 Solutions Lecturer: Dr. Aksel Erbahar Teaching Assistant: Elizabeth Oluwajimi Trade Policy 1. We know that the optimal percentage tariff (with a specific tariff t) of a large country with perfect competition can...

FEB13085: International Trade Policy FEB13085: International Trade Policy Problem Set 2 Solutions Lecturer: Dr. Aksel Erbahar Teaching Assistant: Elizabeth Oluwajimi Trade Policy 1. We know that the optimal percentage tariff (with a specific tariff t) of a large country with perfect competition can be shown as:  dp∗ m . dm dp  t∗ = , p∗ dt p∗ dp dt (1) where p is domestic price, p∗ is world price, and m is imports. (a) Assume that a large country’s demand curve for a good is D = 200 − 4P. This country does not have any production of this good and imports it from a foreign monopolist (there are no other foreign producers) who has a marginal cost of 10 and serves the home country only. With free trade, what is the import demand elasticity of this good? Solution: The inverse import demand function of the home country is P = 50 − D/4 since there is no home production. The monopolist maximizes its profits by equating marginal revenue to marginal cost: 50 − D/2 = 10, which results in exports of 80 units. This means that the price charged by the monopolist is 30. In this free trade equilibrium,  dm p  the import demand elasticity − is 1.5. dp m (b) What is the optimal percentage tariff for the home country? Solution: Equation (1) can be rewritten as (see lecture slides): t∗  dm p −1  dp∗ dp  = / , p dp m dt dt (2) which means that the optimal tariff equals the inverse of the elasticity of import demand, times the ratio of the change in the relative foreign and domestic price of imports (note how we replaced p∗ with p, but we don’t need to if we start from free trade where p∗ = p). Now, the marginal cost of the monopolist has increased to 10 + t, this means that profit maximization occurs when: 50 − D/2 = 10 + t =⇒ D = 80 − 2t. Plugging this in the inverse demand function, we get P = 30 + t/2. Using this, we can find that dp/dt = 1/2, 1 FEB13085 Problem Set 2 which implies that dp∗ /dt = −1/2 since p = p∗ + t. Plugging these figures and the negative of the inverse import demand elasticity we found in part (a) in equation (2), we find that the optimal percentage tariff is 2/3 or ≈ 67%. (c) Redo parts (a) and (b) assuming instead that the demand curve is D = 200−2P. Discuss intuitively the relationship between protectionism and import demand elasticities. Solution: With this demand curve, the monopolist maximizes profits at: 100 − D = 10, resulting in 90 units of imports with price 55. This implies that the import demand elasticity is approximately 1.22, lower than what we found in part (a). With a tariff, the monopolist’s marginal cost is higher and thus exports D = 90 − t with price P = 55 + t/2. This means that dp/dt = 1/2 and dp∗ /dt = −1/2 as before (note that this is due to the monopolist facing a linear demand curve). Plugging in the numbers, we find that the optimal percentage tariff is 1/1.22 or ≈ 82%. This result indicates that we should tend to see countries have higher protection on goods that have lower import demand elasticities. Intuitively, a lower import demand elasticity would result in a relatively lower reduction of imports due to a tariff because of the importer’s market power and ability to influence world prices. This means that tariffs on more inelastic goods would generate relatively larger terms-of-trade gains as well as lower deadweight losses (this can also be shown graphically). 2. Indonesia’s demand and supply curves for pineapples are given by: D = 100 − 20p and S = 20 + 20p respectively. (a) Derive and graph Indonesia’s import demand schedule. What would the price of pineapples be in the absence of trade? Solution: Import demand is given by the equation M (p) = D(p) − S(p) = 80 − 40p. The absence of trade is the equivalent to import demand being zero, which happens at p = 2. See Figure 1. (b) Now, add another country, Thailand, whose demand and supply curves are given by: D∗ = 80 − 20p and S ∗ = 40 + 20p respectively. Derive and graph Thailand’s export supply curve and find the price of pineapples that would prevail in Thailand in the absence of trade. Solution: Thailand’s export supply curve is given by: X ∗ (p) = S ∗ (p) − D∗ (p) = −40 + 40p. The absence of trade is equivalent to export supply being zero, which occurs at p∗ = 1. See Figure 1. (c) Now allow Indonesia and Thailand to trade with each other, at zero transportation cost. Find and graph the equilibrium under free trade. What is the world price? What is the volume of trade? 2 FEB13085 Problem Set 2 Solution: When they are allowed to trade, there is no distortion in prices so we have a common world price of pw = p = p∗. In order to find equilibrium, we set import demand equal to export supply giving: M D(p) = XS ∗ (p∗ ) ⇒ 80 − 40pw = −40 + 40pw ⇒ pw = 1.5. At this world price we have M (1.5) = X ∗ (1.5) = 20. See Figure 1. (d) Determine and graph the effects of a 0.5 tariff imposed by Indonesia on the following: (1) the price of pineapples in each country; (2) the quantity of pineapples supplied and demanded in each country; (3) the volume of trade. Solution: The tariff causes a wedge to be placed between prices seen between the two countries, so we now have p = p∗ + 0.5. Setting export supply equal to import demand, we get: M (p∗ ) = X ∗ (p∗ + 0.5) ⇒ 80 − 40p∗ = −40 + 40(p∗ + 0.5) ⇒ p∗ = 1.25 ⇒ p = 1.75. At these prices, Indonesia produces 55 and demands 65, Thailand produces 65 and demands 55. The volume of trade is thus exports of 10 from Thailand to Indonesia. See Figure 2. (e) Show graphically and calculate the terms of trade gain, the efficiency loss, and the total effect on welfare due to the tariff imposed by Indonesia. Solution: See Figure 3. Producers gain area a, consumers lose areas a, b, c, d, and the government receives c and e. We can calculate the areas with some simple geometry. Recall, before the tariff, total trade was 20, but now it is 10. Also, notice the height of both triangles b and d is 0.25. Therefore, we have: b+d = 1/2 × (20 − 10) × 0.25 = 1.25 e = 10 × 0.25 = 2.5 ⇒ e − b − d = 1.25. 3. In July 2016, the US filed a complaint at the WTO against China’s export taxes on raw materials such as antimony, cobalt, copper, graphite, lead, magnesia, talc, tantalum, and tin. (a) Assuming that the Chinese government owns the production of all these raw materials, explain with graphs the welfare effect of China’s export taxes on these goods for China (large country). What is the effect on the US? What’s the change in world welfare? Can you think of any other reasons as to why China would want to impose these taxes? 3 FEB13085 Problem Set 2 Solution: Figure 4 depicts the welfare effects of an export tax imposed by a large country. An export tax shifts the export supply curve to the left, increasing the world price from p∗ to pX. Since exporters in China now have to pay the tax (s), the domestic price must go down to pX − s = pD. Domestic consumption rises, domestic production falls, and thus exports decrease. Consumers in China gain e, government (who owns production) gains c − e − f − h, and hence China as a whole gains c − f − h where f + h are the deadweight losses (DWL). Area c is the terms-of-trade (ToT) gain for China as its exports are now more expensive in the world market. The effect of this export tax is simply a rise in US import prices. Theoretically, this is just like imposing a tariff from a small country perspective (producers gain, consumers lose), except now there are no government revenues, so the country as a whole loses (looking at the lecture slides, the loss would be b + c + d). From the world’s perspective, China’s ToT gain will be a ToT loss for the rest of the world (RoW). This means that the world as whole will lose due to DWLs generated by both China and the RoW (assuming US is the only importer would mean that the world as a whole loses b + d + f + h). In addition to the ToT gains, China might want to impose these taxes to gain competitiveness in sectors that use these raw materials such as aerospace, automotive, and electronics, since now the key inputs would be relatively cheaper for domestic downstream producers. Officially, China argued that it had imposed some of these export restrictions due to environmental concerns. (b) Suppose that Cambodia imposes an export tax on rice. Explain with graphs the welfare effect of this policy on Cambodia (small country). Why do you think Cambodia would implement such a policy? Would you expect any country to challenge this policy at the WTO? Solution: Figure 5 depicts the welfare effects of an export tax imposed by a small country. Here, since the import demand facing Cambodia is perfectly elastic, the leftward shift in the export supply curve does not change world prices. This means that the domestic price must go down to p∗ − s = pD. Consumers gain a, producers lose a + b + c + d, the government gains c, so the country as a whole loses b + d. One reason as to why Cambodia might want to implement this policy is to make rice relatively cheaper for its inhabitants. Since there is no effect on world prices, we would not expect any country to challenge this policy at the WTO. 4 FEB13085 Problem Set 2 Multiple Choice Questions 1. Which of the following is likely to happen when a large country levies a tariff and would not happen if a small country did the same? a. Domestic output of the protected good rises. b. Domestic demand for the protected good rises. c. Domestic price of the protected good rises. d. World price of the protected good falls. e. Government collects tariff revenue. 2. According to the “optimal tariff argument”, a. A tariff is the easiest way for a government to raise revenue. b. A tariff can benefit a large country by causing the world price of imports to fall. c. The optimal tariff raises the cost of imported goods to equal the cost of domestically produced goods. d. The best time to levy a tariff is shortly after consumers have come to depend on imports. e. Workers should be given extended unemployment compensation if they lose their jobs because of competition from imports. 3. With free trade, Albania, a small country, imports 70 tons of steel at a world price of $4 per ton. It then imposes an import quota permitting only 30 tons of steel to be imported. In response, the price of steel inside Albania rises by $2 to $6 per ton. The total quota rent is: a. $2 b. $60 c. $80 d. $120 e. $180 4. Suppose you know that, in a small country, a 3% tariff on imported beer would cause a deadweight loss of $12,000. Which of the following would be the most plausible deadweight loss due to a 6% tariff on beer, in the same country? a. $6,000 b. $12,000 c. $24,000 d. $36,000 e. $48,000 5 FEB13085 Problem Set 2 5. If the US subsidizes exports of corn, who is hurt? a. US corn farmers. b. Consumers of corn in the US. c. Consumers of corn in foreign countries that import corn. d. The importing-country government. e. None of the above. 6. Suppose that Thailand is a small country that imports computers, which it also produces itself under free trade. If Thailand levies a tariff on imports of computers, then: a. The price of computers on the world market will fall. b. The price of computers in Thailand will fall. c. Consumers in Thailand will buy a larger total quantity of computers. d. Consumers in Thailand will buy more computers from producers in Thailand. e. Computer producers in Thailand will have to pay the tariff. 7. A specific tariff is: a. An import tax that must be paid in kind (i.e. giving the government the good itself). b. Any tax on a particular imported good (as opposed to one on all imports). c. A requirement to pay the government a specified fraction of the monetary value of an imported good. d. A tax on imports defined as an amount of currency per unit of the good. e. The revenue that the government earns by auctioning off import quotas. 8. The main difference between a tariff and a quota is that: a. A quota reduces the quantity of imports more than a tariff. b. A tariff raises the price of imports more than a quota. c. A quota does not harm domestic consumers. d. A tariff does not harm foreign producers. e. A tariff generates government revenue, while a quota, unless it is sold, does not. 9. The figure below shows domestic supply and demand for a good in a small country that faces the world price Pw. Suppose that instead of trading freely at that price, the country is imposing an import quota in the amount of q. Which of the following will happen if the world price of the good falls below Pw ? a. The domestic price of the good will fall. 6 FEB13085 Problem Set 2 b. The quantity of imports of the good will increase. c. The total value of the quota rents will increase. d. Domestic supply of the good will decrease. e. All of the above. 10. Which of the following is an example of Strategic Trade Policy? a. A subsidy to a domestic manufacturer of airplanes so that it can steal market share from a foreign manufacturer of airplanes. b. A countervailing duty. c. Use of a tariff by a large country to improve its terms of trade. d. Negotiation of a free trade agreement. e. A subsidy to farmers in a rich country that lowers the world price of their agricultural exports and impoverishes foreign farmers in poor countries. 7 FEB13085 Problem Set 2 List of figures Figure 1: Import demand and export supply Figure 2: The effect of a tariff 8 FEB13085 Problem Set 2 Figure 3: Welfare changes Figure 4: Export taxes from a large country perspective 9 FEB13085 Problem Set 2 Figure 5: Export taxes from a small country perspective 10