PROBLEMS

1. In the short-run specific-factors model, examine the impact on a small country following a natural disaster that decreases it population. Assume that land is specific to agriculture and capital is specific to manufacturing, whereas labor is free to move between the two sectors.

   1. Question

      In a diagram similar to Figure 5-2, determine the impact of the decrease in the workforce on the output of each industry and the equilibrium wage.

      Prob 5 1a. In a diagram similar to Figure 5-2, determine the impact of the decrease in the workforce on the output of each industry and the equilibrium wage.

   2. Question

      What happens to the rentals on capital and land?

      Prob 5 1b. What happens to the rentals on capital and land?

2. Question

   How would your answer to Problem 1 change if instead we use the long-run model, with shoes and computers produced using labor and capital?

   Prob 5 2. How would your answer to Problem 1 change if instead we use the long-run model, with shoes and computers produced using labor and capital?

3. Question

   Consider an increase in the supply of labor due to immigration, and use the long-run model. Figure 5-8 shows the box diagram and the left-ward shift of the origin for the shoe industry. Redraw this diagram but instead shift to the right the origin for computers. That is, expand the labor axis by the amount ΔL but shift it to the right rather than to the left. With the new diagram, show how the amount of labor and capital in shoes and computers is determined, without any change in factor prices. Carefully explain what has happened to the amount of labor and capital used in each industry and to the output of each industry.

   Prob 5 3. Consider an increase in the supply of labor due to immigration, and use the long-run model. Figure 5-8 shows the box diagram and the left-ward shift of the origin for the shoe industry. Redraw this diagram but instead shift to the right the origin for computers. That is, expand the labor axis by the amount ΔL but shift it to the right rather than to the left. With the new diagram, show how the amount of labor and capital in shoes and computers is determined, without any change in factor prices. Carefully explain what has happened to the amount of labor and capital used in each industry and to the output of each industry.
4. In the short-run specific-factors model, consider a decrease in the stock of land. For example, suppose a natural disaster decreases the quantity of arable land used for planting crops.

   1. Question

      Redraw panel (a) of Figure 5-11 starting from the initial equilibrium at point A.

      Prob 5 4a. Redraw panel (a) of Figure 5-11 starting from the initial equilibrium at point A.

   2. Question

      What is the effect of this change in land on the quantity of labor in each industry and on the equilibrium wage?

      Prob 5 4b. What is the effect of this change in land on the quantity of labor in each industry and on the equilibrium wage?

   3. Question

      What is the effect on the rental on land and the rental on capital?

      Prob 5 4c. What is the effect on the rental on land and the rental on capital?

   4. Question

      Now suppose that the international community wants to help the country struck by the natural disaster and decides to do so by increasing its level of FDI. So the rest of the world increases its investment in physical capital in the stricken country. Illustrate the effect of this policy on the equilibrium wage and rentals.

      Prob 5 4d. Now suppose that the international community wants to help the country struck by the natural disaster and decides to do so by increasing its level of FDI. So the rest of the world increases its investment in physical capital in the stricken country. Illustrate the effect of this policy on the equilibrium wage and rentals.

5. Question

   According to part A of Table 5-1, what education level loses most (i.e., has the greatest decrease in wage) from immigration to the United States? Does this result depend on keeping the rental on capital constant? Explain why or why not.

   Prob 5 5. According to part A of Table 5-1, what education level loses most (i.e., has the greatest decrease in wage) from immigration to the United States? Does this result depend on keeping the rental on capital constant? Explain why or why not.
6. Suppose that computers use 2 units of capital for each worker, so that K_C = 2 · L_C, whereas shoes use 0.5 unit of capital for each worker, so that K_S = 0.5 · L_S. There are 100 workers and 100 units of capital in the economy.

   1. Question

      Solve for the amount of labor and capital used in each industry.
      Hint: The box diagram shown in Figure 5-7 means that the amount of labor and capital used in each industry must add up to the total for the economy, so that
      K_C + K_S = 100 and L_C + L_S = 100
      Use the facts that K_C = 2 · L_C and K_S = 0.5 · L_S to rewrite these equations as
      2 · L_C + 0.5 · L_S = 100 and L_C + L_S = 100
      Use these two equations to solve for L_C and L_S, and then calculate the amount of capital used in each industry using K_C = 2 · L_C and K_S = 0.5 · L_S.

      Prob 5 6a. Solve for the amount of labor and capital used in each industry.Hint: The box diagram shown in Figure 5-7 means that the amount of labor and capital used in each industry must add up to the total for the economy, so thatK_C + K_S = 100 and L_C + L_S = 100Use the facts that K_C = 2 · L_C and K_S = 0.5 · L_S to rewrite these equations as2 · L_C + 0.5 · L_S = 100 and L_C + L_S = 100Use these two equations to solve for L_C and L_S, and then calculate the amount of capital used in each industry using K_C = 2 · L_C and K_S = 0.5 · L_S.

   2. Question

      Suppose that the number of workers increases to 125 due to immigration, keeping total capital fixed at 100. Again, solve for the amount of labor and capital used in each industry. Hint: Redo the calculations from part (a), but using L_C + L_S = 125.

      Prob 5 6b. Suppose that the number of workers increases to 125 due to immigration, keeping total capital fixed at 100. Again, solve for the amount of labor and capital used in each industry. Hint: Redo the calculations from part (a), but using L_C + L_S = 125.

   3. Question

      Suppose instead that the amount of capital increases to 125 due to FDI, keeping the total number of workers fixed at 100. Again solve for the amount of labor and capital used in each industry. Hint: Redo the calculations from part (a), using K_C + K_S = 125.

      Prob 5 6c. Suppose instead that the amount of capital increases to 125 due to FDI, keeping the total number of workers fixed at 100. Again solve for the amount of labor and capital used in each industry. Hint: Redo the calculations from part (a), using K_C + K_S = 125.

   4. Question

      Explain how your results in parts (b) and (c) are related to the Rybczynski theorem.

      Prob 5 6d. Explain how your results in parts (b) and (c) are related to the Rybczynski theorem.

Questions 7 and 8 explore the implications of the Rybczynski theorem and the factor price insensitivity result for the Heckscher-Ohlin model from Chapter 4.

7. In this question, we use the Rybczynski theorem to review the derivation of the Heckscher-Ohlin theorem.

   1. Question

      Start at the no-trade equilibrium point A on the Home PPF in Figure 4-2, panel (a). Suppose that through immigration, the amount of labor in Home grows. Draw the new PPF, and label the point B where production would occur with the same prices for goods. Hint: You can refer to Figure 5-9 to see the effect of immigration on the PPF.

      Prob 5 7a. Start at the no-trade equilibrium point A on the Home PPF in Figure 4-2, panel (a). Suppose that through immigration, the amount of labor in Home grows. Draw the new PPF, and label the point B where production would occur with the same prices for goods. Hint: You can refer to Figure 5-9 to see the effect of immigration on the PPF.

   2. Question

      Suppose that the only difference between Foreign and Home is that Foreign has more labor. Otherwise, the technologies used to produce each good are the same across countries. Then how does the Foreign PPF compare with the new Home PPF (including immigration) that you drew in part (a)? Is point B the no-trade equilibrium in Foreign? Explain why or why not.

      Prob 5 7b. Suppose that the only difference between Foreign and Home is that Foreign has more labor. Otherwise, the technologies used to produce each good are the same across countries. Then how does the Foreign PPF compare with the new Home PPF (including immigration) that you drew in part (a)? Is point B the no-trade equilibrium in Foreign? Explain why or why not.

   3. Question

      Illustrate a new point A* that is the no-trade equilibrium in Foreign. How do the relative no-trade prices of computers compare in Home and Foreign? Therefore, what will be the pattern of trade between the countries, and why?

      Prob 5 7c. Illustrate a new point A* that is the no-trade equilibrium in Foreign. How do the relative no-trade prices of computers compare in Home and Foreign? Therefore, what will be the pattern of trade between the countries, and why?
8. Continuing from Problem 7, we now use the factor price insensitivity result to compare factor prices across countries in the Heckscher-Ohlin model.

   1. Question

      Illustrate the international trade equilibrium on the Home and Foreign production possibilities frontiers. Hint: You can refer to Figure 4-3 to see the international trade equilibrium.

      Prob 5 8a. Illustrate the international trade equilibrium on the Home and Foreign production possibilities frontiers. Hint: You can refer to Figure 4-3 to see the international trade equilibrium.

   2. Question

      Suppose that the only difference between Foreign and Home is that Foreign has more labor. Otherwise, the technologies used to produce each good are the same across countries. Then, according to the factor price insensitivity result, how will the wage and rental compare in the two countries?

      Prob 5 8b. Suppose that the only difference between Foreign and Home is that Foreign has more labor. Otherwise, the technologies used to produce each good are the same across countries. Then, according to the factor price insensitivity result, how will the wage and rental compare in the two countries?

   3. Question

      Call the result in part (b) “factor price equalization.” Is this a realistic result? Hint: You can refer to Figure 4-9 to see wages across countries.

      Prob 5 8c. Call the result in part (b) “factor price equalization.” Is this a realistic result? Hint: You can refer to Figure 4-9 to see wages across countries.

   4. Question

      Based on our extension of the Heckscher-Ohlin model at the end of Chapter 4, what is one reason why the factor price equalization result does not hold in reality?

      Prob 5 8d. Based on our extension of the Heckscher-Ohlin model at the end of Chapter 4, what is one reason why the factor price equalization result does not hold in reality?

9. Question

   Recall the formula from the application “The Effect of FDI on Rentals and Wages in Singapore.” Give an intuitive explanation for this formula for the rental rate. Hint: Describe one side of the equation as a marginal benefit and the other as a marginal cost.

   Prob 5 9. Recall the formula from the application “The Effect of FDI on Rentals and Wages in Singapore.” Give an intuitive explanation for this formula for the rental rate. Hint: Describe one side of the equation as a marginal benefit and the other as a marginal cost.
10. In Table 5-2, we show the growth in the real rental and real wages in Singapore, along with the implied productivity growth. One way to calculate the productivity growth is to take the average of the growth in the real rental and real wage. The idea is that firms can afford to pay more to labor and capital if there is productivity growth, so in that case real factor prices should be growing. But if there is no productivity growth, then the average of the growth in the real rental and real wage should be close to zero.
    
    To calculate the average of the growth in the real factor prices, we use the shares of GDP going to capital and labor. Specifically, we multiply the growth in the real rental by the capital share of GDP and add the growth in the real wage multiplied by the labor share of GDP. Then answer the following:

    1. Question

       For a capital-rich country like Singapore, the share of capital in GDP is about one-half and the share of labor is also one-half. Using these shares, calculate the average of the growth in the real rental and real wage shown in each row of Table 5-2. How do your answers compare with the productivity growth shown in the last column of Table 5-2?

       Prob 5 10a. For a capital-rich country like Singapore, the share of capital in GDP is about one-half and the share of labor is also one-half. Using these shares, calculate the average of the growth in the real rental and real wage shown in each row of Table 5-2. How do your answers compare with the productivity growth shown in the last column of Table 5-2?

    2. Question

       For an industrialized country like the United States, the share of capital in GDP is about one-third and the share of labor in GDP is about two-thirds. Using these shares, calculate the average of the growth in the real rental and real wage shown in each row of Table 5-2. How do your answers now compare with the productivity growth shown in the last column?

       Prob 5 10b. For an industrialized country like the United States, the share of capital in GDP is about one-third and the share of labor in GDP is about two-thirds. Using these shares, calculate the average of the growth in the real rental and real wage shown in each row of Table 5-2. How do your answers now compare with the productivity growth shown in the last column?
11. Figure 5-14 is a supply and demand diagram for the world labor market. Starting at points A and A*, consider a situation in which some Foreign workers migrate to Home but not enough to reach the equilibrium with full migration (point B). As a result of the migration, the Home wage decreases from W to W″ > W′, and the Foreign wage increases from W* to W^** < W′.

    1. Question

       Are there gains that accrue to the Home country? If so, redraw the graph and identify the magnitude of the gains for each country. If not, say why not.

       Prob 5 11a. Are there gains that accrue to the Home country? If so, redraw the graph and identify the magnitude of the gains for each country. If not, say why not.

    2. Question

       Are there gains that accrue to the Foreign country? If so, again show the magnitude of these gains in the diagram and also show the world gains.

       Prob 5 11b. Are there gains that accrue to the Foreign country? If so, again show the magnitude of these gains in the diagram and also show the world gains.
12. A housekeeper from the Philippines is contemplating immigrating to Singapore in search of higher wages. Suppose the housekeeper earns approximately $2,000 annually and expects to find a job in Singapore worth approximately $5,000 annually for a period of three years. Furthermore, assume that the cost of living in Singapore is $500 more per year than at home.

    1. Question

       What can we say about the productivity of housekeepers in Singapore versus the Philippines? Explain.

       Prob 5 11a. What can we say about the productivity of housekeepers in Singapore versus the Philippines? Explain.

    2. Question

       What is the total gain to the housekeeper from migrating?

       Prob 5 11b. What is the total gain to the housekeeper from migrating?

    3. Question

       Is there a corresponding gain for the employer in Singapore? Explain.

       Prob 5 11c. Is there a corresponding gain for the employer in Singapore? Explain.