PS04a-2CG - Econ 441 Summer Term 2002 Alan Deardorff...

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Econ 441 Alan Deardorff Summer Term 2002 Problem Set 4 - Answers Page 1 of 12 Problem Set 4 - Answers Two-Cone Model and Gains from Trade 1. The graph below shows unit value isoquants for three goods, X 1 , X 2 , and X 3 , based on prices that are assumed to prevail throughout a world of many countries with free trade. Also shown are points representing the factor endowments of several countries, E 1 , E 2 , etc. Complete the two-cone Lerner diagram to identify the factor prices, factor ratios, and vectors of factors that will be employed in each sector by each country, and use these to answer the following questions: K L E 3 E 6 E 4 E 1 E 2 E 5 X 1 =1/ p 1 X 2 =1/ p 2 X 3 =1/ p 3
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Econ 441 Alan Deardorff Summer Term 2002 Problem Set 4 - Answers Page 2 of 12 a. In which country or countries will the wage in units of good X 1 , be highest, and in which will it be lowest? Would the answer be any different for the wage in units of goods X 2 or X 3 ? Drawing the tangencies to pairs of adjacent isoquants we find the two cones of this equilibrium. Countries 1 and 2 are in the labor-intensive cone with identical nominal wages, and countries 3 and 6 are in the capital-intensive cone also with identical, but higher, wages. Countries 4 and 5 are not in either cone, and they therefore will specialize in goods 1 and 2 respectively. To find their factor prices, we draw rays from the origin through their endowment points and find the isocost lines tangent to their respective isoquants where they cross these rays. This gives us the wages shown as w 4 and w 5 . Reading from these, we see that the lowest nominal wage is in country 5, while the highest is in both country 3 and country 6. Since prices of goods are the same for all countries, these are the lowest and highest respectively in terms of good 1 or any other good. K L E 3 E 6 E 4 E 1 E 2 E 5 X 1 =1/ p 1 X 2 =1/ p 2 X 3 =1/ p 3 1/ w 3 =1/ w 6 1 /w 4 1/ w 1 =1/ w 2 1 /w 5
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Econ 441 Alan Deardorff Summer Term 2002 Problem Set 4 - Answers Page 3 of 12 b. Which country will produce the largest quantity of each good? For the four countries inside cones, the parallelogram construction identifies the vectors of factors they employ in each of the two goods that they produce, 1 1 v and 1 2 v for goods 1 and 2 in country 1, for example. For countries 4 and 5, which completely specialize, their endowment points are themselves the vectors of factors they employ in their only sector. Comparing these vectors, we can observe that country 2 employs more factors in producing good 1 than countries 1 and 5 (the only other countries that produce it), and therefore country 2 has the largest output of good 1. Similarly, country 1 produces the most of good 2 (which is produced by all countries except 5), and country 3 produces the most of good 3. c. Which country will produce the largest
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This note was uploaded on 04/15/2009 for the course ACCOUNTING BUSI0027 taught by Professor Guan during the Spring '09 term at HKU.

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PS04a-2CG - Econ 441 Summer Term 2002 Alan Deardorff...

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