Problem Set 1: Tariffs and Quotas (Solutions) Universidad Carlos III de Madrid Economics of European Integration TA: Victor Troster Fall 2012 Problem 1 Suppose there are only two countries in the world (ome and Rest of the World) which produce and consume wheat. The price of wheat in Rest of the World is equal to 2 (P RW = 2) and ome is a small country with the following demand and supply functions for wheat: D = 50 10P S = 30 + 10P (a) Compute and graph the equilibrium in absence of trade. What would be the consumer and producer surplus? The market clearing condition implies that D = S 50 10P = 30 + 10P 20 = 20P. p = 1 q = 40. Then the consumer and producer surplus are CS = (5 1)40 = 160 2 2 = 80 P S = (40 30)1 40 = 35. 2 (b) Now allow ome and Rest of the World to trade, assuming zero transportation cost. Find and graph the equilibrium under free trade. What would be the consumer and producer surplus changes? Since the home price is less than the international price, under free trade the home country exports. The equilibrium conditions are D = S X p = p RW = 2, 1
where X are exports from ome. and the equilibrium consists of the following objects: 50 10 (2) = 30 + 10 (2) X 50 20 = 30 + 20 X p = 2 X = 20 qd = 30; qs = 50. (5 2)30 CS = C = 80 = 45 80 = 35 2 [ P S = A + B = 40 + 10 ] = 45. 2 ome country imposes a tariff of 20% (0.2) on wheat exports. (c) Determine and show graphically the effects of the tariff on: (1) The price of wheat in each country; (2) the quantity of wheat supplied and demanded in ome. The equilibrium conditions are D = S X p = p RW (1 + t). p RW = 2. and the equilibrium is p T = p RW (1 + 0.2) = 2 1.2 = 1.67 50 10(1.67) = 30 + 10(1.67) X, X T = 13.4 qd T = 33.3; qs T = 46.7. (d) Determine the effect of the tariff on the welfare of each of the following groups: (1) ome exporting producers; (2) ome consumers; (3) ome government. 2
(1) ome exporting producers: Since the price now is lower, the home-exporting producer faces a decrease in his surplus: p =2 P S = (b + c + d) = (30 + 10p )dp = (30p + 5p 2 ) 2 1.67 = (80 64.05) = 15.95. p =1.67 (2) ome consumers: Since the price now is lower, the home-consumers faces an increase in his surplus: CS = b = (3) ome government: p =2 p =1.67 (50 10p )dp = (50p 5p 2 ) 2 1.67 = 80 69.55 = 10.45. GovT axincome = (1 + t) X T = 1.2 13.4 = 16.08. (e) Show graphically and calculate the efficiency loss due to the tariff. The loss is EfficiencyLoss = P S + CS + GovT axincome = 15.95 + 10.45 + 32.16 = 26.66 ome introduces an export quota of 10 units of wheat. (f) Determine and show graphically the effects of the export quota on: (1) the price of wheat in each country; (2) the quantity of wheat supplied and demanded in ome. 3
The equilibrium conditions are D = S X X = 10. 50 10p q = 30 + 10pq 10 30 = 20p q and the equilibrium is p q = 1.5; pq RW = 1.5 X q = 10 q q D = 35; q q S = 45. (g) Determine the effect of the export quota on the welfare of each of the following groups: (1) ome export-competing producers; (2) ome consumers; (3) ome government. (1) ome export-competing producers: Since the price now is lower than under free-trade, the home-exporting producer faces a decrease in his surplus: P S = (b + e + c + d) = p =2 p =1.5 (30 + 10p )dp = (30p + 5p 2 ) 2 1.5 = (80 56.25) = 23.75. (2) ome consumers: Since the price now is lower, the home-consumers faces an increase in his surplus: CS = b = p =2 p =1.5 (50 10p )dp = (50p 5p 2 ) 2 1.5 = 80 63.75 = 16.25. (3) ome government: Since it is an export quota, it does not generate any revenue to the Government. So, GovT axincome = 0. (h) Show graphically and calculate the efficiency loss due to the export quota. The efficiency loss is EfficiencyLoss = (b + e + c + d) + b = 23.75 + 16.25 + 0 = 7.5. 4
Problem 2 Suppose ome is not anymore a small country and the Rest of the World (which is also a large country) exhibits the following demand and supply curves for wheat: D RW = 80 40P S RW = 40 + 40P (a) Derive and graph ome s import demand curve and Rest of the World s export supply curve. What would be the price of wheat in each country in absence of trade? ome s import demand curve is Rest of the World s export supply curve is M = D S M = 20 20p. X RW = S RW D RW X RW = 80p RW 40. M = 0 p = 1; q = 40 X RW = 0 p RW = 0.5; q RW = 60. (b) Now allow Foreign and ome to trade with each other, assuming zero transportation cost. Find and graph the equilibrium under free trade. What is the world price? What is the volume of trade? The equilibrium conditions are M = X RW p = p RW = p W. That is, 20 20p W = 80p W 40, 5
which leads to the following equilibrium p W = 0.6 M = XRW = 8 qd = 44; qs = 36 qd RW = 56; qs RW = 64. ome imposes a tariff of 0.5 on wheat imports. (c) Determine and show graphically the effects of the tariff on the following: (1) the price of wheat in each country; (2) the quantity of wheat supplied and demanded in each country; (3) the volume of trade. Equilibrium conditions: which leads to the following equilibrium: M = X RW p = p RW + t. 20 20(p RW + 0.5) = 80p RW 40, p T RW = 0.5; p T = 1 M T = XRW T = 0 No trade! qd T = 40; qs T = 40 q T D RW = 60; q T S RW = 60. (d) Determine the effect of the tariff on the welfare of each of the following groups: (1) ome importcompeting producers; (2) ome consumers; (3) the ome government. (1) ome import-competing producers: P S = (2) ome consumers: CS = (3) ome government: p =1 p =0.6 p =1 p =0.6 (30 + 10p )dp = (30p + 5p 2 ) p =1 p =0.6 (50 10p )dp = (50p 5p 2 ) p =1 p =0.6 GovT axincome = (1 + t) M T = t 0 = 0. (e) Show graphically and calculate the efficiency gain/loss of the tariff in ome. The efficiency gain is = 35 19.8 = 15.2 = (45 28.2) = 16.8 SW = P S + CS + GovT axincome = 15.2 16.8 + 0 = 1.6. 6
Problem 3 Suppose now that the Rest of the World is a much larger economy, with the following demand and supply curves for wheat: D RW = 800 400P S RW = 400 + 400P Note: This implies that the Rest of the World price of wheat in the absence of trade is the same as in Problem 2, (a). Recalculate the free trade equilibrium and the effects of a 0.5 specific import tariff imposed by ome. Compare your results with those you got in the case in which ome was a small country (Problem 1). ome s import demand curve and Rest of the World s export supply curve are The equilibrium in absence of trade is M = D S M = 20 20p X RW = S RW D RW X RW = 800p RW 400. M = 0 p = 1; q = 40 X RW = 0 p RW = 0.5; q RW = 600. When free trade is introduced, the equilibrium conditions are M = X RW p = p RW = p W. and the equilibrium is 20 20p W = 800p W 400, p W = 0.512 (0.6 in Problem 2) M = X RW = 9.75 (8 in Problem2) q D = 44.88; q S = 35.12 q D RW = 595.12; q S RW = 604.88. The tariff of 0.5 leads to the following equilibrium conditions, which leads to the following equilibrium, The welfare effects of the tariff here are (1) ome import-competing producers: P S = p =1 p =0.512 M = X RW p = p RW + t. 20 20(p RW + 0.5) = 800p RW 400, p T RW = 0.5; p T = 1 ( same as in Problem 2 ) M T = XRW T = 0 ( same as in Problem 2 ) qd T = 40; qs T = 40 q T D RW = 600; q T S RW = 600. (30 + 10p )dp = (30p + 5p 2 ) p =1 7 p =0.512 = 35 16.67 = 18.33 (15.2 in Problem 2)
(2) ome consumers: p =1 CS = (50 10p )dp = (50p 5p 2 ) p =1 p =0.512 = (45 24.3) = 20.7 ( 16.8 in Problem 2) p =0.512 (3) ome government: Finally, the loss of efficiency here is GovT axincome = (1 + t) M T = 0 ( same as in Problem 2). SW = P S + CS + GovT axincome = 18.33 20.7 + 0 = 2.37 ( 1.6 in Problem 2). 8