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U-M ECON 441 - Problem Set 6 Tariffs Answers

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Econ 441 Alan Deardorff Fall Term 2008 Problem Set 6 - Answers Page 1 of 15 Problem Set 6 Tariffs - Answers 1. The graph below shows domestic supply and demand for a good in a small country. Suppose that it faces a world price of the good of $4 per pound. Show the effects on this market of a 25% ad valorem tariff on the good by drawing the equilibria with and without the tariff, then using the grid lines in the figure to calculate the changes in quantities supplied, demanded, and imported, and the welfare effects of the tariff on suppliers, demanders, government, and the country as a whole. Reading from the figure, quantity supplied rises from 2000 to 4000 pounds, quantity demanded falls from 9500 to 9000 pounds, quantity imported falls from 7500 to 5000 pounds. Suppliers gain area “a”, which is $3000, demanders lose area “a+b+c+d”, which is $9250, government gains revenue of area “c”, which is $5000, and the country as a whole therefore loses (9250–3000–5000) = –$1250.Econ 441 Alan Deardorff Fall Term 2008 Problem Set 6 - Answers Page 2 of 15 2. Use the partial equilibrium, small-country model of a tariff to work out the effects of an increase in a tariff that was already positive. For each case below, find the effects on domestic price, domestic quantities supplied and demanded, quantity of imports, and the welfare of suppliers, demanders, government, and the country as a whole. Also note, by comparing with your notes from class, whether any of these results differ from the effects of a positive tariff starting from a zero tariff. a. A tariff increase that is small enough so that the quantity of imports remains positive. Since this is a small country, the domestic price rises from p*+t to p*+t'. Supply increases from S1 to S2; demand decreases from D1 to D2; and imports decrease from M1 to M2. Suppliers gain area “a”, demanders lose area “a+b+c+d” and the government’s tariff revenue changes from “e+f+g” to “c+f”, the change therefore being “+c–e–g”. This may be an increase or a decreases in revenue, depending on the sizes of these areas. If the initial and new tariffs are both not too high (below the revenue-maximizing tariff), then the tariff increase will increase revenue. Otherwise, the higher are these tariffs, the more likely it is for the revenue to fall. For the country as a whole, the net effect on welfare is a loss of “b+d+e+g”. It is the possibility of lost tariff revenue that is the main difference in these effects as compared to levying a tariff starting from zero, and also the portion of that loss, “e+g”, that is an addition to the net loss to the country, since it is a loss to government that is not a gain to anybody else.Econ 441 Alan Deardorff Fall Term 2008 Problem Set 6 - Answers Page 3 of 15 b. A tariff increase that is large enough to reduce the quantity of imports to zero. The price now rises to the level where domestic supply and demand are equal, pA, for any t'' such that p*+ t''>pA. In the diagram below, quantities supplied and demanded rise and fall respectively to S2=D2, which are their levels in autarky. Quantity of imports falls to zero. Suppliers gain area “a”, demanders lose area “a+b+c”, and the government loses its entire initial tariff revenue, “d+e”. The country as a whole therefore loses “b+c+d+e”. Compared to the case of a tariff starting from zero, the main difference is this extra and now necessary loss of tariff revenue. 3. Suppose that, in a partial equilibrium model, a country’s autarky price is $10, while its price with free trade is $8. What will be the domestic price if the country levies a specific tariff of $3 and the country is a. Small? In a small country, this greater-than-prohibitive tariff will just raise domestic price to its autarky level, $10, much as in the figure above for tariff t''. b. Large? In a large country, since the tariff pushes down the world price, it may achieve equilibrium without eliminating trade. The figure below, showing just the market for imports, shows such a case:Econ 441 Alan Deardorff Fall Term 2008 Problem Set 6 - Answers Page 4 of 15 Here, the $3 tariff pushes the domestic price up only to $9, while lowering the foreign price to $6. For a tariff in a large country to be prohibitive, it would have to be at least equal to the difference between the two countries’ autarky prices, in this case $10 – $4 = $6. 4. In the partial equilibrium, large-country model, show how the import supply curve can be derived as the excess supply in the Foreign country’s domestic market. Then use this to show how a tariff levied by the Home country affects prices, quantities, and welfare (of Foreign suppliers, demanders, and government) in the Foreign economy. The supply of imports curve on the right is derived as the horizontal distance between the Foreign country’s domestic supply, S*, and its domestic demand, D*. When the Home country, whose demand for imports is shown as Dm, levies a tariff, t, this drives a wedge between its domestic price, pt, and the Foreign country’s domestic price, pt*, such that pt − pt* = t, and such that the quantities supplied and demanded of imports are the same. That is, we look for a place where the Dm curve is above the Sm curve by the distance t. This pushes the price in Foreign down, from p0* to pt*. Within the Foreign country, demanders gain from this fall in price, an increase in consumer surplus equal to “a+b”. Suppliers lose, however, a loss of producerEcon 441 Alan Deardorff Fall Term 2008 Problem Set 6 - Answers Page 5 of 15 surplus equal to “a+b+c+d+e,” for a net loss to the country of “c+d+e,” which is also shown as the area to the left of the Sm supply curve on the right. This net loss by the Foreign country is due to the worsening of its terms of trade. The Foreign government is not involved, since it is not taxing anything. 5. Using the partial equilibrium model of a large importing country, suppose that the country is initially in equilibrium with a certain non-prohibitive tariff. a. Assuming that the tariff is a specific tariff and that its size does not change, what will be the effects on prices, quantities, and welfare of i. A shift to the right in the domestic demand curve (more of the good demanded at each price). The initial equilibrium has domestic price pt=pt*+t. The shift to


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