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]
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AEM230_Prob_Set__2___Fall_2007_Solution_Key - AEM/ECON 230...

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