Econ 441 Alan Deardorff Summer Term 2002 Midterm Exam No. 2 - Answers Page 1 of 13 Midterm Exam No. 2 - Answers July 29, 2002 Answer all questions, in blue book. Plan ahead and budget your time. The questions are worth a total of 60 points, as indicated. You will have 80 minutes to complete the exam. 1. [19 points] In the diagram on page 2 are drawn unit-value isoquants for a world that produces three goods, X1, X2, and X3, using two factors, K and L, at free trade prices p1, p2, and p3 measured in dollars. To assist you, I have drawn two straight lines tangent to pairs of the isoquants, showing the points of tangency as open dots, and also drawing the rays from the origin through these points of tangency. Factor endowments are shown for seven countries, represented by the solid dots labeled E1,…,E7. Answer the following questions about these countries. Feel free to tear off this front page of the exam so that you can look at it and the diagram together. a. (4 points) Which country (or countries, if there are ties) has the largest absolute stock of capital? Which has the most labor? Which countries have the largest and the smallest ratios of capital to labor in their endowments? Country 2 has the largest capital stock, K2. Country 7 has the largest labor force, L7. Country 1 has the largest capital-labor ratio, k1 = K1/L1 (since it is to the left of the steepest ray drawn, and all other countries are to the right of that). Country 7 has the smallest capital-labor ratio. b. (4 points) Which country (or countries) has the highest rental price of capital? Which has the lowest? Which pairs or groups of countries, if any, have the same wage rate of labor? Countries 6 and 7 both have the highest rental price of capital, r6=r7. Country 1 has the lowest rental price of capital, r1. Factor price equalization holds in the two cones, and therefore countries 2 and 4 have the same wage of labor, w2=w4, and so do countries 6 and 7, w6=w7 (<w2). c. (2 points) Which country produces the most good 1? Which produces the most good 3? Only country 7 produces good 1 at all, so it must produce the most. (It employs the vector of factors 71v in producing good 1.) Countries 1, 2, and 4 all produce good 3, country 1 producing only that, while countries 2 and 4 produce both good 3 and good 2. They employ vectors 23v and 43v in producing good 3. Clearly, country 2 employs more of both factors in the sector than either of the other countries, so it produces the most good 3.Econ 441 Alan Deardorff Summer Term 2002 Midterm Exam No. 2 - Answers Page 2 of 13 d. (4 points) What does country 6 produce, what does it export and import, and how do its factor prices compare to factor prices in the other countries? Country 6 on the edge of a cone. It produces only good 2 (since to produce any of good 1 would leave it the wrong amount of factors to fully employ in good 2). It therefore exports good 2, while it imports goods 1 and 3. Its factor prices are the same as country 7’s, r7 and w7, and thus its wage is lower than in all of countries 1-5 and its rental on capital is higher than in countries 1-5. e. (2 points) In what industry does country 7 employ the largest fraction of its total labor force? Is country 7’s output of good 1 worth more than $1, less than $1, or exactly $1? Country 7 employs vector 72v in sector 2 and 71v in sector 1, from which it employs more labor in sector 2 than in sector 1, hence a larger fraction of its labor force. Country 7’s inputs to sector 1 lie well inside its unit isocost line (the straight line from 1/r7 to 1/w7, and therefore these inputs, and also its output, are worth less than $1 f. (3 points) Which country or countries (if any) produce all three goods? In what direction would the price of good 2 have to change (holding the prices of goods 1 and 3 constant) in order to make it possible for some country that currently does not produce all three goods to do so? If that price change happened, would factor prices then be equal in all seven countries? No country produces all three goods. In a 2-cone equilibrium such as this, prices are such that no country can produce all three goods in free trade. To change that, all three unit-value isoquants would have to be tangent to a single straight line. To achieve that by changing only p2, we would need to reduce p2 until its unit-value isoquant had shifted out to the new position shown in the lower diagram below. There would then be the single cone shown, instead of two cones, and countries 1 and 2 would lie outside of it. So factor prices would not be equal across all seven countries. (Indeed, factor prices in country 1 would continue to be what they were before.)Econ 441 Alan Deardorff Summer Term 2002 Midterm Exam No. 2 - Answers Page 3 of 13 K L E1 X1=1/p1 X2=1/p2 X3=1/p3 E2 E3 E4 E5 E6 E7 1/r6=1/r7 1/w6 = 1/w7 1/w2 = 1/w4 1/r1 1v 43v 23v 72v K2 k1 L7 K L E1 X1=1/p1 X2=1/p2 X3=1/p3 E2 E3 E4 E5 E6 E7 X2=1/p2'Econ 441 Alan Deardorff Summer Term 2002 Midterm Exam No. 2 - Answers Page 4 of 13 2. [8 points] As a start toward learning how economic development may affect the world economy, analyze the effect of capital accumulation in labor-abundant countries on world output of goods, as follows: Suppose that the world economy is characterized by free trade in either the 2-good-1-cone HO model or the 3-good-2-cone HO model, as indicated below, with the factor endowments of various countries ranging from least developed, with very little capital per worker, to most developed, with a lot of capital per worker. Then determine the effect, at constant prices, of a developing country in the stated situation increasing its capital stock while holding its labor force constant. What will happen, as a result, to that country’s outputs (and therefore the world’s outputs) of each of the goods in the model? (Assume that capital accumulation is not enough to change the country’s pattern of specialization.) a. (2 points) The 2-good-1-cone HO model: capital accumulation in a country that produces both goods – labor-intensive X1 and capital-intensive X2 – and that exports X1. This is the standard Rybczynski result that, as shown below, capital accumulation at constant prices causes the output of the capital-intensive good to increase and that of the labor-intensive good to decrease. Thus output of