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6. (4p) Consider a Heckscher-Ohlin model with two countries, Home and Foreign, and two factors of production, land (T) and labor (L). Land and labor are used to produce two goods, gadgets and widgets. The two countries have the same homothetic preferences. There are no factor intensity reversals. Endowments and production technologies are such that with trade, both countries produce both goods. Home is endowed with 400 units of land (T) and 200 units of labor (L). 3 Sample Midterm 1 Answer Key ECON203 Foreign's endowments are T*=500, L*=400. Gadget is the relatively labor-intensive good and widget is the relatively land-intensive good. Both countries produce both goods. Which of the following is true? (Two (2) answers are correct, indicate both.) A. Foreign widget production uses more labor relative to land than Home widget production. B. Foreign widget production uses less labor relative to land than Home widget production. C. Home and Foreign use the same amount of labor relative to land in widget production. D. Foreign gadget production uses more labor relative to land than Home gadget production. E. Foreign gadget production uses less labor relative to land than Home gadget production. F. Home and Foreign use the same amount of labor relative to land in gadget production.6. (4p) Consider a Heckscher-Ohlin model with two countries, Home and Foreign, and two factors of production, land (T) and labor (L). Land and labor are used to produce two goods, gadgets and widgets. The two countries have the same homothetic preferences. There are no factor intensity reversals. Endowments and production technologies are such that with trade, both countries produce both goods. Home is endowed with 400 units of land (T) and 200 units of labor (L). 3 Sample Midterm 1 Answer Key ECON203 Foreign's endowments are T*=500, L*=400. Gadget is the relatively labor-intensive good and widget is the relatively land-intensive good. Both countries produce both goods. Which of the following is true? (Two (2) answers are correct, indicate both.) A. Foreign widget production uses more labor relative to land than Home widget production. B. Foreign widget production uses less labor relative to land than Home widget production. C. Home and Foreign use the same amount of labor relative to land in widget production. D. Foreign gadget production uses more labor relative to land than Home gadget production. E. Foreign gadget production uses less labor relative to land than Home gadget production. F. Home and Foreign use the same amount of labor relative to land in gadget production.( Heckscher-Ohlin Model) There are two economies, Home and Foreign producing 2 goods, furniture (F) and cosmetics (C), using capital (K ) and labor (L). Furni- ture production is relatively more capital intensive than the production of cosmetics. The production functions for both goods satisfy the assumptions of constant returns to scale and diminishing returns to a single factor. Both economies share the same production technologies and consumers in all countries have identical homothetic pref- erences. Home has 600 units of capital and 400 units of labor while Foreign is endowed with 100 units of capital and 300 units of labor. Both factors can move freely across sectors. The world economy is currently under autarky. (a) Characterize an autarky equilibrium for Home. (b) Which country is relatively more labor-abundant?( Heckscher-Ohlin Model) There are two economies, Home and Foreign producing 2 goods, furniture (F) and cosmetics (C), using capital (K ) and labor (L). Furni- ture production is relatively more capital intensive than the production of cosmetics. The production functions for both goods satisfy the assumptions of constant returns to scale and diminishing returns to a single factor. Both economies share the same production technologies and consumers in all countries have identical homothetic pref- erences. Home has 600 units of capital and 400 units of labor while Foreign is endowed with 100 units of capital and 300 units of labor. Both factors can move freely across sectors. The world economy is currently under autarky. (a) Characterize an autarky equilibrium for Home. (b) Which country is relatively more labor-abundant?C. Heckscher-Ohlin Model. Suppose all the assumptions behind the model apply: 2 countries (Home and Foreign), 2 goods (food and cloth), 2 factors of production (labor and land), and each country has the same tastes, the same technology, and increasing costs of production. Also there are competitive markets in each country and industry and the supply of factors are fixed for each country. Moreover, assume the following: (1.) The land-labor ratio to produce a unit if food (to = , / L, ) is greater than it is to produce a unit of cloth (to = T / Le ) in both countries, (T, / L. > T/ L , i.e., food is land intensive and cloth labor intensive) and (2.) The ratio of total land to total labor (f = 7 / L ) in the Home country is greater than it is in the foreign country (7* ), that is Home is land abundant and the foreign country is labor abundant (T / L > T* /[* ). Given the above information, answer the following questions.C. Heckscher-Ohlin Model. Suppose all the assumptions behind the model apply: 2 countries (Home and Foreign), 2 goods (food and cloth), 2 factors of production (labor and land), and each country has the same tastes, the same technology, and increasing costs of production. Also there are competitive markets in each country and industry and the supply of factors are fixed for each country. Moreover, assume the following: (1.) The land-labor ratio to produce a unit if food (to = , / L, ) is greater than it is to produce a unit of cloth (to = T / Le ) in both countries, (T, / L. > T/ L , i.e., food is land intensive and cloth labor intensive) and (2.) The ratio of total land to total labor (f = 7 / L ) in the Home country is greater than it is in the foreign country (7* ), that is Home is land abundant and the foreign country is labor abundant (T / L > T* /[* ). Given the above information, answer the following questions.(2) Now suppose Foreign shares the same technology with Home (i.c., ajg = 1, alp = 4, "ko =2, app = 2). The endowments of Foreign are given by: Factor endowments Labor Capital Foreign 2,800 2,000 Two countries engage in free trade. The world relative price of clothing is given by Po/ Pp = 1/2. (1 point) a. Which country is relatively labor abundant and which capital abundant? (1 point) b. Describe the pattern of trade between Home and Foreign. (2 points) c. Show graphically the production and consumption of Home under free trade. (1 points) d. Do both Home and Foreign benefit from trade? If not, which country gets worse off? (1 points) e. Does everyone in Foreign benefit from trade? If not, which group (workers or capital owners) gets worse off? (1 point) f. In which country are wages higher?(2) Now suppose Foreign shares the same technology with Home (i.c., ajg = 1, alp = 4, "ko =2, app = 2). The endowments of Foreign are given by: Factor endowments Labor Capital Foreign 2,800 2,000 Two countries engage in free trade. The world relative price of clothing is given by Po/ Pp = 1/2. (1 point) a. Which country is relatively labor abundant and which capital abundant? (1 point) b. Describe the pattern of trade between Home and Foreign. (2 points) c. Show graphically the production and consumption of Home under free trade. (1 points) d. Do both Home and Foreign benefit from trade? If not, which country gets worse off? (1 points) e. Does everyone in Foreign benefit from trade? If not, which group (workers or capital owners) gets worse off? (1 point) f. In which country are wages higher?Problem 4 (23 points) Firm X has the following production function (K, I) = (1 + K2/3). 1. (6 points) Find the marginal product of labor and capital and the marginal rate of technical substitution, and state if the returns to capital and labor are increasing, decreasing or constant. Explain what is " weird" about this MRTS. 2. (8 points) Graph the isoquants of the production function and state whether the production function exhibits constant, increasing or decreasing returns to scale. 3. (9 points) Now suppose that the production function is f( K, L) = exp(2t) (1 + K2/3) where t measures years. How does this affect the marginal products of labor and capital, the returns to scale and the MRTS? What is the rate of productivity increase over time? Graph the isoquants for q = 100 for * = 1, 2. Explain.(1) Consider Home produces clothing (C) and food (F) using labor (L) and capital (C). We assume there are constant returns to scale. The unit factor requirements for two goods are given by: GLC = 1, app =4, agc = 2, opp = 2. The endowments of Home are as follows: Factor endowments Labor Capital Home | 2,500 2,000 (1 point) a. Which good is relatively labor intensive? Which good is relatively capital intensive? (2 points) b. Find the equation(s) of Home's PPF and graph the PPF (You can place QC on the horizontal axis and Qp on the vertical axis). At which point on the PPF are both factors fully employed? (2 points) c. Suppose Home produces at the point that you find in b. According to Ry- bezynski theorem, what happens to the output mix if the total capital stock increases? (1 point) d. Suppose the autarky prices are given by Po = 10, Pp = 20. At which point on the PPF does Home produce? (2) Now suppose Foreign shares the same technology with Home (i.e., alg = 1, ajg = 4, "ko =2. okp = 2). The endowments of Foreign are given by: Factor endowments Labor | Capital Foreign 2,800 2,000 Two countries engage in free trade. The world relative price of clothing is given by Po/Pp = 1/2. (1 point) a. Which country is relatively labor abundant and which capital abundant? (1 point) b. Describe the pattern of trade between Home and Foreign. (2 points) c. Show graphically the production and consumption of Home under free trade. (1 points) d. Do both Home and Foreign benefit from trade? If not, which country gets worse off? (1 points) e. Does everyone in Foreign benefit from trade? If not, which group (workers or capital owners) gets worse off? (1 point) f. In which country are wages higher?(1) Consider Home produces clothing (C) and food (F) using labor (L) and capital (C). We assume there are constant returns to scale. The unit factor requirements for two goods are given by: GLC = 1, app =4, agc = 2, opp = 2. The endowments of Home are as follows: Factor endowments Labor Capital Home | 2,500 2,000 (1 point) a. Which good is relatively labor intensive? Which good is relatively capital intensive? (2 points) b. Find the equation(s) of Home's PPF and graph the PPF (You can place QC on the horizontal axis and Qp on the vertical axis). At which point on the PPF are both factors fully employed? (2 points) c. Suppose Home produces at the point that you find in b. According to Ry- bezynski theorem, what happens to the output mix if the total capital stock increases? (1 point) d. Suppose the autarky prices are given by Po = 10, Pp = 20. At which point on the PPF does Home produce? (2) Now suppose Foreign shares the same technology with Home (i.e., alg = 1, ajg = 4, "ko =2. okp = 2). The endowments of Foreign are given by: Factor endowments Labor | Capital Foreign 2,800 2,000 Two countries engage in free trade. The world relative price of clothing is given by Po/Pp = 1/2. (1 point) a. Which country is relatively labor abundant and which capital abundant? (1 point) b. Describe the pattern of trade between Home and Foreign. (2 points) c. Show graphically the production and consumption of Home under free trade. (1 points) d. Do both Home and Foreign benefit from trade? If not, which country gets worse off? (1 points) e. Does everyone in Foreign benefit from trade? If not, which group (workers or capital owners) gets worse off? (1 point) f. In which country are wages higher?Problem 2 (35 points) Anne consumes only books (a) and video games (y) . Her preferences can be represented by the following utility function: U = ry. The price of books is p,, the price of video games is py, and Anne has an income of m dollars. 1. (5 points) Write down Anne's budget constraint, calculate the Marginal Rate of Substitution (at an arbitrary bundle (z, y)) and compute her demand for books and video games (as a function of Pr+Py and m). 2. (5 points) Compute the price elasticity of the demand for books. Compute the cross-price elasticity of the demand for books with respect to the price of video games. (The cross-price elasticity measures the change of the quantity demanded for a good in response to a change in the price of another good, holding everything else constant. It is measured as the percentage change in quantity demanded for the first good divided by the percentage change in price of the second good.) 3. (5 points) Draw the Engel curve for video games. Are video games an inferior or a normal good? Explain. 4. (5 points) Suppose that initially the prices are pr = Py = 1 and income is m = 90. How many books does Anne buy? Now suppose that the price of books increases to pr = 2, how many books will she buy now? How much of the drop in demand for books is due to the substitution effect and how much is due to the income effect? Calculate this numerically and show it in a graph. 5. (15 points) Suppose that her utility function were u(r, y) = x1/2 + y instead. Also suppose that the prices are now P, = 1, py = 10 and her income is m = 50. (i) Calculate her demand for books and video games in this case. (ii) Now suppose that the price of video games increases to py = 15 how many books and video games will she buy now? What is different in this case compared to question 2.4. Explain. (ini) How much of the drop in demand for video games is due to the substitution effect and how much is due to the income effect? Calculate this numerically and show it in a graph. Problem 3 (18 points) For each of the following production functions: (a) F(L, K) = D'KI (b) F ( L, K ) = L+DOR! (c) F(L, K) = 2L + K 1. (2 points, per production function) Find the marginal product of labor and capital, and state if the returns to capital and labor are increasing, decreasing or constant. 2. (2 points, per production function) Find the marginal rate of technical substitut tion. 3. (2 points, per production function) State whether the production function exhibits constant, increasing or decreasing returns to scale.Problem 2 (35 points) Anne consumes only books (a) and video games (y) . Her preferences can be represented by the following utility function: U = ry. The price of books is p,, the price of video games is py, and Anne has an income of m dollars. 1. (5 points) Write down Anne's budget constraint, calculate the Marginal Rate of Substitution (at an arbitrary bundle (z, y)) and compute her demand for books and video games (as a function of Pr+Py and m). 2. (5 points) Compute the price elasticity of the demand for books. Compute the cross-price elasticity of the demand for books with respect to the price of video games. (The cross-price elasticity measures the change of the quantity demanded for a good in response to a change in the price of another good, holding everything else constant. It is measured as the percentage change in quantity demanded for the first good divided by the percentage change in price of the second good.) 3. (5 points) Draw the Engel curve for video games. Are video games an inferior or a normal good? Explain. 4. (5 points) Suppose that initially the prices are pr = Py = 1 and income is m = 90. How many books does Anne buy? Now suppose that the price of books increases to pr = 2, how many books will she buy now? How much of the drop in demand for books is due to the substitution effect and how much is due to the income effect? Calculate this numerically and show it in a graph. 5. (15 points) Suppose that her utility function were u(r, y) = x1/2 + y instead. Also suppose that the prices are now P, = 1, py = 10 and her income is m = 50. (i) Calculate her demand for books and video games in this case. (ii) Now suppose that the price of video games increases to py = 15 how many books and video games will she buy now? What is different in this case compared to question 2.4. Explain. (ini) How much of the drop in demand for video games is due to the substitution effect and how much is due to the income effect? Calculate this numerically and show it in a graph. Problem 3 (18 points) For each of the following production functions: (a) F(L, K) = D'KI (b) F ( L, K ) = L+DOR! (c) F(L, K) = 2L + K 1. (2 points, per production function) Find the marginal product of labor and capital, and state if the returns to capital and labor are increasing, decreasing or constant. 2. (2 points, per production function) Find the marginal rate of technical substitut tion. 3. (2 points, per production function) State whether the production function exhibits constant, increasing or decreasing returns to scale