Exercises Lecture 8: Trade policies


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1 Exercises Lecture 8: Trade policies Exercise 1, from KOM 1. Home s demand and supply curves for wheat are: D = S = Derive and graph Home s import demand schedule. What would the price of wheat be in the absence of trade?. Now add Foreign, which has a demand curve and a supply curve D = 80 0 S = Derive and graph Foreign s export supply curve and find the price of wheat that would prevail in Foreign in the absence of trade 3. Now allow Foreign and Home 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? 4. Assume that Home imposes a specific tariff t = 0.5 on wheat imports. (a) Determine and graph the effects of the tariff on the following: (i) the price of wheat in each country; (ii) the quantity of wheat supplied and demanded in each country; (iii) the volume of trade. (b) Determine the effect of the tariff on the welfare of each of the following groups: (i) Home importcompeting producers; (ii) Home consumers; (iii) the Home government. (c) Show graphically and calculate the terms of trade gain, the efficiency loss, and the total effect on welfare of the tariff. 1
2 Exercise, from KOM Suppose that Foreign had been a much larger country, with domestic demand and supply D = S = Notice that this assumption implies that the Foreign price of wheat in the absence of trade would have been the same as in the previous problem. 1. Recalculate the free trade equilibrium and the effects of a 0, 5 specific tariff by Home.. Relate the difference in results to the discussion of the small country case in the text. Exercise 3 Consider Fig. 1 and answer to the following questions. 14 S 8 6 World price + tariff 3 World price D Figure 1
3 1. In the absence of Trade how many units of the good does this country produce and consume?. In the absence of trade what is the country s consumer plus producer surplus? 3. With free trade and no tariffs, what is the amount of the good imported? 4. With a specific tariff t = 3 per unit, what is the amount of the good imported? 5. What is the effect of the tariff on the welfare of producers, consumers and government? Exercise 4, from KOM The nation of Acirema is small and unable to affect world prices. It imports peanuts at the price of $10 per bag. The demand and supply curves are: D = S = Determine the free trade equilibrium. Then calculate and graph the following effects of an import quota that limits imports to 50 bags. 1. The increase in the domestic price.. The quota rents. 3. The consumption distortion loss. 4. The production distortion loss. 3
4 Solutions Exercise 1 1. Home s import demand schedule MD is given by: MD = D S = = and graphically it is given by: HOME 5 S 1,75 1,5 1 D ,75 1,5 1 MD Figure. Home s Import Demand Curve The price of wheat be in the absence of trade is given by the intersection of the curves D and S and it equal to =. Algebraically, it is obtained from D = S (or MD = 0), hence: = 0 = 4
5 . Foreign s export supply curve XS is given by: XS = S D = = and graphically it is given by: FOREIGN XS 4 S D Figure 3. Foreign s export supply curve As previously, the price of wheat be in the absence of trade is given by the intersection of the curves D and S and it equal to = 1. Algebraically, it is obtained from D = S (or XS = 0), hence: = 0 = 1 5
6 3. The equilibrium under free trade is given by MD = XS, that is: = = 80 W = 1, 5 To find the volume of trade, it suffices to substitute the world price W into either the MD or the XS, so as to obtain: , 5 = 0 = Volume of trade without tariff (free trade) Graphically, it is represented in Fig. 4 WORLD EUILIBRIUM XS t { 1,75 1,5 1,5 1 MD Figure 4. World equilibrium 4. (a) When Home imposes a tariff t = 0.5 on wheat imports, only the MD modifies (the XS remains unchanged), and becomes: MD = ( + t) = 80 40( + 0, 5) = = } {{ } T 6
7 hence the new price, namely T, is given by: MD = XS = T = 1, 5 while the price in Home, T is given by T = T + t = 1, 5 + 0, 5 = 1, 75 To determine the the quantity of wheat supplied and demanded in each country as well as the new volume of trade, it suffices to substitute the correct price, either T or T in the demand and supply functions. Hence, substituting T in D and S you obtain, for Home: D = , 75 = 65 S = , 75 = 55 while, by substituting T in D and S you obtain, for Foreign: D = , 5 = 55 S = , 5 = 65 where it should be clear that the new volume of trade is equal to 10, as shown by Fig. 4. (b) To determine the effect of the tariff on the welfare of the different groups, refer to Fig. 5. where the areas a, b, c, d and e are given by: a = ( ) 0.5 = 13, 15 b = d = = 0, 65 c = e = =, 5 The reduction in consumers surplus is equal to a + b + c + d, hence it is equal to 16,875. 7
8 S 1,75 1,5 1,5 a b c e d D Figure 5. Welfare, efficiency loss and terms of trade gain. roducers gain the area a, which is equal to 13,15. Government revenue is equal to the area c, hence it is equal,5. (c) The efficiency loss is equal to b + d = 0, 65 = 1, 5 The terms of trade gain is equal to e =, 5 The total effect on welfare of the tariff is positive and equal to (b + d) + e = 1, 5 +, 5 = 1, 5. 8
9 Solutions Exercise To recalculate the free trade equilibrium and the effects of a 0, 5 specific tariff by Home you need to determine the new XS, given by: XS = S D = = The free trade equilibrium is given by the intersection of the XS with the MD as follows: MD = XS : = W = 1, 09 The equilibrium with a tariff t = 0, 5 imposed by Home is given instead by: MD = XS : = T = 1, 045 while the price in Home, T : T + t = 1, , 5 = 1, 545 By following the same reasoning as the previous exercise, the volume of trade with no tariff ( = 1, 09) is therefore equal to 36,4 (you just need to substitute the price into either the MD or the XS), while the volume of trade with the tariff is equal to 18, (in this case either you plug T into the MD or T into the XS). Notice that there is already an important difference in comparison to Exercise 1. When Home is relatively small, the effect of a tariff on world price is much smaller than when Home is relatively large. When Foreign and Home were closer in size, as in Exercise 1, a tariff of 0, 5 imposed by Home lowered world price from 1, 5 to 1, 5, whereas in this case the same tariff lowers world price only from 1, 09 to 1, 045. There are important differences also when it comes to analyze welfare, as Fig. 6 shows. The areas now are given by: a = (50, , 8) 0, 455 = 1, 089 b = d = 9.1 0, 455 =, 07 c = 18, 0, 455 = 8, 8 9
10 e = 18, 0, 045 = 0, 819 where a represent the increase in producers surplus, a + b + c + d = 33,51 the reduction in consumers surplus and c the government s revenue. It is important to underline that  given the assumptions of the exercise  now the efficiency loss, b + d = 4, 14 is much bigger in comparison to the terms of trade gain, equal to e = 0, 819, as a consequence of the different variation of prices. This small country example where the distortionary losses from the tariff overcome the terms of trade gains should then make it clear that the smaller the economy, the larger the losses from a tariff due to smaller terms of trade gains. Solutions Exercise S 1,545 1,09 1,045 a b c e d 41,8 50,9 69,1 78, Figure 6. Welfare, efficiency loss and terms of trade gain. D 10
11 . The consumers surplus is equal to 6 60 = 180, which is also equal to producers surplus. Hence the total surplus (consumers + producers) is equal to With free trade, you have to consider the world price W = 3, thus the amount of good imported is equal to = With a specific tariff t = 3 per unit the amount of good imported is equal to = The variation in consumers surplus can be calculated by considering the initial surplus  the surplus with the tariff, that is: 100 (14 3) 80 (14 6) = = = 30 By the same reasoning, the variation in producers surplus is: 40 (6 ) 10 (3 ) = 80 5 = 75 Finally, the revenue for the government is given by: amount imported amount of the tariff = 40 3 = 10 Solutions Exercise 4 1. To determine the free trade equilibrium, you just have to substitute the price W = 10 into the demand and supply functions as follows: D = = 300 S = = 100. Hence the MD is MD = D S = = 00 which defines total imports of Acirema. 11
12 With a quota which limits imports to 50 bags, the increase in the domestic price can be identified by equating the demand to the domestic supply + the quota, that is: D = S + quota : = }{{} quota = 0 Hence, graphically, the equilibrium is as in Fig. 7: S 3, a b D Figure 7. uota rents are therefore given by (0 10) quota = = The consumption distortion loss is given by the area b, where b = = 500 1
13 4. The production distortion loss is given by the area a, where a = = 50 13
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