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AEM230_Prob_Set__2___Fall_2007_Solution_Key

# AEM230_Prob_Set__2___Fall_2007_Solution_Key - AEM/ECON 230...

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AEM/ECON 230 Prof. David Lee International Trade and Finance Fall 2007 Problem Set #2 (Solution Key) Question 1: Gains from Trade [40 points] An economist from the United States Department of Agriculture (USDA) collected the following information on the sugar markets in the U.S. and in the rest of the world (ROW): Supply and demand curves are linear in both the U.S. and the ROW. At prices 20 \$ 1 = P per ton and 30 \$ 2 = P per ton, quantities demanded and supplied in each market are indicated in Table I: Table I: Supply and Demand for Sugar for Selected Price Levels (US and ROW) United States Rest of the World (ROW) Price (\$ per ton) Demand (tons) Supply (tons) Demand (tons) Supply (tons) 20 1 = P 40 1 = US D 10 1 = US S 25 1 = ROW D 60 1 = ROW S 30 2 = P 30 2 = US D 15 2 = US S 20 2 = ROW D 90 2 = ROW S (a) Derive the demand and supply equations for each market (U.S. and ROW). [4 points] The demand and supply equations have the linear form y = Ax + B, where A is the slope and B is the y-intercept. From Table I, we obtain the following: Demand in the US : Supply in the US : P = A D US + B P = A S US + B A = [(30 – 20) / (30 – 40)] = (10/–10) = –1 A = [(30 – 20) / (15 – 10)] = (10/5) = 2 20 = –1 (40) + B B = 20 + 40 = 60 20 = 2(10) + B B = 20 – 20 = 0 P = –D US + 60 P = 2S US Demand in the ROW : Supply in the ROW: P = A D ROW + B P = A S ROW + B A = [(30 – 20) / (20 – 25)] = (–10/5) = –2 A = [(30 – 20) / (90 – 60)] = (10/30) = 1/3 20 = (–2* 25) + B B = 20 + 50 = 70 20 =[ (1/3)*60] + B B = 20 – 20 = 0 P = –2D ROW + 70 P = (1/3) S ROW (b) Determine the autarky equilibrium price and quantity in the U.S. and in the ROW. [4 points] In equilibrium, D US = S US = US Q Thus, US Q + 60 = 2 US Q 3 Q US = 60 autarky US Q = 20 autarky US P = 2 autarky US Q = 2* 20 = 40 (alternatively, autarky US P = – autarky US Q + 60 = – 20 + 60 = 40)

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In equilibrium, D ROW = S ROW = Q ROW Thus, – 2Q ROW + 70 = (1/3)Q ROW [(1/3) + 2] Q ROW = 70 (7/3) Q ROW = 70 Q ROW = (70*3)/7 = 210/7 autarky ROW Q = 30 autarky ROW P = (1/3) autarky ROW Q = (1/3)*30 = 10 [1 point] (alternatively, autarky ROW P = – 2 autarky ROW Q + 70 = – 60 + 70 = 10) (c) Calculate the consumer surplus (CS) and the producer surplus (PS) under autarky in each market. (Hint: Graphs may be helpful.) [6 points] autarky US CS = (1/2)*(60 – 40)*(20 – 0) = 200 autarky US PS = (1/2)*(40 – 0)*(20 – 0) = 400 autarky ROW CS = (1/2)*(70 – 10)*(30 – 0) = 900 autarky ROW PS = (1/2)*(10 – 0)*(30 – 0) = 150 (d) Suppose that the U.S. and the ROW engage in free trade in sugar. Determine the world free trade equilibrium price and quantity traded ( Hint: first determine the equations for ES and ED ). Assume that the U.S. and the ROW are large countries. [6 points] First, find Excess Supply (ES) and Excess Demand (ED). ES is obtained from the supply and demand functions of the exporting country: ES = S ROW – D ROW = 3P – (35 – 0.5P) = 3P – 35 + 0.5P = 3.5P – 35 ED is obtained from the supply and demand functions of the importing country: ED = D US – S US = 60 – P – 0.5P = 60 – 1.5P Second, let ES = ED in equilibrium: 3.5P – 35 = 60 – 1.5P 5P = 95 P = (95/5) FreeTrade w P = 19 Finally, ES = ED = 60 – 1.5P = 60 – 28.5 = 31.5 (e) Use a 3-panel graph (ROW, World, U.S.) to illustrate the free trade supply and demand schedules in each market. Clearly label supply and demand curves for each country, as well as excess supply and excess demand curves in the international market. [6 points] See attachment.
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