PS05__Answers_ - EC 340 Spring 2011 Problem Set 5 Suppose...

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Unformatted text preview: EC 340 Spring 2011 Problem Set 5 Suppose that the Home imports electrical cable from Foreign. Further suppose that Home levies a $7 specific tariff on imports of cable. Use this information, along with the information in the diagram to the left to answer questions 1 – 5. 1. Is Home a large or small country (in the technical sense)? How do you know? The Home country is large because the export supply curve is upward sloping. This means that by restricting imports, the Home is able to force down the price of the product that the Foreign country receives. If Home were small, the export supply curve would be horizontal. 2. What is the value of the terms of trade gain/loss for Home? Use the diagram to find out what the tariff‐distorted prices will be in the importing and exporting countries. These prices have to satisfy the relationship that export country’s price _ tariff = import country’s price. Since the tariff is $7, this means that the two prices have to be $7 apart. This happens when the quantity of trade (Home imports = Foreign exports) is 20. At this level of trade, the price in the export country is $18 and the price in the import country is $25. The latter price can be determined by noticing that every 10 unit increase/decrease in the quantity of trade corresponds to a decrease/increase of the price of the product in the import country. Next, the terms of trade gain for Home is (Free‐trade‐price – Tariff‐distorted export price) * quantity of trade = ($24 ‐ $18)*20 = $120. 3. Relative to free trade, what is the net welfare effect for Home of the import tariff? The net effect on Home welfare = Terms of trade gain – Deadweight loss. The terms of trade gain was derived above. The deadweight loss is the area of a triangle in the above diagram, the 4. 5. height of which is the difference between the tariff‐distorted price in the Home (importing) country minus the free‐trade pric, ($25 ‐ $24) and the base of which is the reduction in the volume of imports (30 – 20). In this case, the deadweight loss is then ½ * $1 * 10 = $5. So the net welfare effect is $120 ‐ $5 = $115. Relative to free trade, what is the net welfare effect for the entire world of the import tariff? Home’s terms of trade gain is a terms of trade loss to Foreign, so these just cancel each other (when considering the world as a whole). What remains is the deadweight loss in the two countries. We calculated Home’s deadweight loss in answering question 3. Foreign’s deadweight loss is similar. It is the area of a triangle where the height is the difference between the free trade price and the tariff‐distorted export price ($24 ‐ $18) and base is the reduction in the quantity of exports (10). So the Foreign deadweight lossis ½ * $6 * 10 = $30. Deadweight loss for the world as a whole is then $5 + $30 = $35. This is the net loss for the world as a whole. Home is thinking about increasing its tariff to $14. Would this increase Home’s welfare or decrease Home’s welfare? How do you know? To answer this question, figure out the net welfare effect (compared with free trade) on Home of a $14 tariff. In this case, the quantity of trade falls to 10 units, the export price is $12, the price in the importing (Home) country is $26. The resulting terms of trade gain is ($24 ‐ $12) * 10 = $120, and the deadweight loss is ½ * ($26 ‐ $24) * 20 = $40. The net welfare gain (relative to free trade) is then $120 ‐ $40 = $80. This is less than the net welfare gain with the $7 tariff (that was $115), so the $14 tariff leads to lower welfare than the $7 tariff. North imports sugar from South. With free trade, the price of sugar is $6 per pound. North levies a specific import tariff of $2 per pound on sugar. The price of sugar in North rises to $8. The demand and supply diagram to the right illustrates North’s market for sugar. Use this information to answer questions 6 – 10. 6. Is North a small country or a large country (in the technical sense)? How do you know? North is small in the technical sense since the tariff‐distorted price of sugar in North increases by the full amount of the tariff. There is no effect on the price of sugar in South. 7. What is the value of the production distortion in North that is created by the tariff? The production distortion is represented by the area of a triangle. The height of the triangle is the Tariff‐distorted price – Free‐trade price ($8 ‐ $6 = $2). The base of the triangle is the increased quantity supplied. In this case, the quantity supplied is 20 when the price is $6, and 40 when the price is $8, so the increase is 20 units. The triangle then has an area equal to ½ * $2 * 20 = $20. 8. What is the value of the consumption distortion in North that is created by the tariff? The consumption distortion is represented by the area of a triangle. The height of the triangle is the Tariff‐distorted price – Free‐trade price ($8 ‐ $6 = $2). The base of the triangle is the reduced quantity demanded. In this case, the quantity demanded is 90 when the price is $6, and 75 when the price is $8 (note that the slope of the demand curve is such that every $4 change in price leads to a 30 unit change in quantity), so the decrease is 15 units. The triangle then has an area equal to ½ * $2 * 15 = $15. 9. What is the terms of trade gain/loss for North that is created by the tariff? Since North is a small country, there is no terms of trade gain or loss. 10. 11. What is the total deadweight loss in North created by the tariff? The total deadweight loss is the sum of the production and consumption distortions. In this case, that is $20 + $15 = $35. Compared with free trade, what is the net welfare effect of the tariff on North? The net welfare effect equals the terms of trade gain minus deadweight loss: 0 ‐ $35 = ‐$35. ...
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