Can you please help me answer 8, 9, 10. I don't need for 7. I will rate you when I get answers. Thank you!

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

a) 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 could occur with the same prices for goods. Hint:You can refer to Figure 5-9 to see the effect of immigration on the PPF,

b) 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 salne 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.

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

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:

a. 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?

b. 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?

142 PART 2 PATTERNS OF INTERNATIONAL TRADE FIGURE 5-9 Output of shoes, Qs Relative price of computers, P/PS The Long-Run Effect on Industry Outputs of an Increase in Home Labor With an increase in the amount of labor at Home, the PPF shifts outward. The output of shoes increases, while the output of computers declines as the equilibrium moves from point A to B. The prices of goods have not changed, so the slopes of the PPFs at points A and B (i.e., the relative price of computers) are equal. Shift in Home PPF due to immigration An increase of both labor and capital in shoe production causes an increase in shoe output and a decrease in computer output Output of computers, QC FIGURE 4-3 (a) Home Country (b) International Market Output of shoes, as Relative price of computers, Pc/Ps Home export supply curve for computers Home consumption Qs3 (PIP)" Home production Shoe imports D (PC/Ps). sz B World price line, slope = (PC/P>)" Qc3 Qcz Qcz - Qo Output of computers, Qc Quantity of computers Computer exports International Free-Trade Equilibrium at Home At the free-trade world relative price of computers, (PC/Ps)", Home produces at point B in panel (a) and consumes at point , exporting computers and importing shoes. (Point A is the no-trade equilibrium.) The "trade triangle" has a base equal to the Home exports of computers (the difference between the amount produced and the amount consumed with trade, Qcz - Qc3). The height of this triangle is the Home imports of shoes (the difference between the amount consumed of shoes and the amount produced with trade, Qs3 - Qsz). In panel (b), we show Home exports of computers equal to zero at the no-trade relative price, (PC/Ps)", and equal to (Qcz - Qc3) at the free-trade relative price, (Pc/Ps)". FIGURE 4-2 (b) Foreign Output of (a) Home Relative price of computers, slope = (PC/Ps) Output of shoes, as shoes, Q* Foreign PPF asi Qs1 U* U Relative price of computers, slope = (P/P3) Output of computers, Q* Home PPF Output of computers, QC Qg QCM No-Trade Equilibria in Home and Foreign The Home production possibilities frontier (PPF) is shown in panel (a), and the Foreign PPF is shown in panel (b). Because Home is capital- abundant and computers are capital-intensive, the Home PPF is skewed toward computers. Home preferences are summarized by the indifference curve, U, and the Home no-trade (or autarky) equilibrium is at point A, with a low relative price of computers, as indicated by the flat slope of (PC/Ps)". Foreign is labor- abundant and shoes are labor-intensive, so the Foreign PPF is skewed toward shoes. Foreign preferences are summarized by the indifference curve, U, and the Foreign no-trade equilibrium is at point A, with a higher relative price of computers, as indicated by the steeper slope of (PC/P3). TABLE 5-2 Real Rental and Wages in Singapore This table shows the growth rate in the real rental and real wages in Singapore, depending on the method used to construct these factor prices. In part A, a production function approach is used to construct the factor prices, and the real rental falls over time because of the growth in capital. As a result, implied productivity growth is negative. In part B, the rental and wages are constructed from data on payments to capital and labor in Singapore, and real wages grow over time, while the real rental either grows or falls slightly. As a result, implied productivity growth is positive. ANNUAL GROWTH RATE (%) Real Rental Real Wages Implied Productivity Part A: Using Production Function and Marginal Products Time Period: 1970-1980 -5.0 2.6 -1.5 1980-1990 -1.9 0.5 -0.7 1970-1990 -3.4 1.6 -1.1 Part B: Using Calculated Rental and Actual Wages Interest Rate Used and Time Period: Bank lending rate (1968-1990) 2.7 2.2 Return on equity (1971-1990) -0.2 3.2 1.5 Earnings-price ratio (1973-1990) -0.5 3.6 1.6 1.6 Sources: Part A from Alwyn Young, 1995, "The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience." Quarterly Journal of Economics, 110(3), August. 641-680. Part 8 from Chang-Tai Hsieh, 2002, "What Explains the Industrial Revolution in East Asia? Evidence from the Factor Markets." American Economic Review, 92(3), 502-526. 142 PART 2 PATTERNS OF INTERNATIONAL TRADE FIGURE 5-9 Output of shoes, Qs Relative price of computers, P/PS The Long-Run Effect on Industry Outputs of an Increase in Home Labor With an increase in the amount of labor at Home, the PPF shifts outward. The output of shoes increases, while the output of computers declines as the equilibrium moves from point A to B. The prices of goods have not changed, so the slopes of the PPFs at points A and B (i.e., the relative price of computers) are equal. Shift in Home PPF due to immigration An increase of both labor and capital in shoe production causes an increase in shoe output and a decrease in computer output Output of computers, QC FIGURE 4-3 (a) Home Country (b) International Market Output of shoes, as Relative price of computers, Pc/Ps Home export supply curve for computers Home consumption Qs3 (PIP)" Home production Shoe imports D (PC/Ps). sz B World price line, slope = (PC/P>)" Qc3 Qcz Qcz - Qo Output of computers, Qc Quantity of computers Computer exports International Free-Trade Equilibrium at Home At the free-trade world relative price of computers, (PC/Ps)", Home produces at point B in panel (a) and consumes at point , exporting computers and importing shoes. (Point A is the no-trade equilibrium.) The "trade triangle" has a base equal to the Home exports of computers (the difference between the amount produced and the amount consumed with trade, Qcz - Qc3). The height of this triangle is the Home imports of shoes (the difference between the amount consumed of shoes and the amount produced with trade, Qs3 - Qsz). In panel (b), we show Home exports of computers equal to zero at the no-trade relative price, (PC/Ps)", and equal to (Qcz - Qc3) at the free-trade relative price, (Pc/Ps)". FIGURE 4-2 (b) Foreign Output of (a) Home Relative price of computers, slope = (PC/Ps) Output of shoes, as shoes, Q* Foreign PPF asi Qs1 U* U Relative price of computers, slope = (P/P3) Output of computers, Q* Home PPF Output of computers, QC Qg QCM No-Trade Equilibria in Home and Foreign The Home production possibilities frontier (PPF) is shown in panel (a), and the Foreign PPF is shown in panel (b). Because Home is capital- abundant and computers are capital-intensive, the Home PPF is skewed toward computers. Home preferences are summarized by the indifference curve, U, and the Home no-trade (or autarky) equilibrium is at point A, with a low relative price of computers, as indicated by the flat slope of (PC/Ps)". Foreign is labor- abundant and shoes are labor-intensive, so the Foreign PPF is skewed toward shoes. Foreign preferences are summarized by the indifference curve, U, and the Foreign no-trade equilibrium is at point A, with a higher relative price of computers, as indicated by the steeper slope of (PC/P3). TABLE 5-2 Real Rental and Wages in Singapore This table shows the growth rate in the real rental and real wages in Singapore, depending on the method used to construct these factor prices. In part A, a production function approach is used to construct the factor prices, and the real rental falls over time because of the growth in capital. As a result, implied productivity growth is negative. In part B, the rental and wages are constructed from data on payments to capital and labor in Singapore, and real wages grow over time, while the real rental either grows or falls slightly. As a result, implied productivity growth is positive. ANNUAL GROWTH RATE (%) Real Rental Real Wages Implied Productivity Part A: Using Production Function and Marginal Products Time Period: 1970-1980 -5.0 2.6 -1.5 1980-1990 -1.9 0.5 -0.7 1970-1990 -3.4 1.6 -1.1 Part B: Using Calculated Rental and Actual Wages Interest Rate Used and Time Period: Bank lending rate (1968-1990) 2.7 2.2 Return on equity (1971-1990) -0.2 3.2 1.5 Earnings-price ratio (1973-1990) -0.5 3.6 1.6 1.6 Sources: Part A from Alwyn Young, 1995, "The Tyranny of Numbers: Confronting the Statistical Realities of the East Asian Growth Experience." Quarterly Journal of Economics, 110(3), August. 641-680. Part 8 from Chang-Tai Hsieh, 2002, "What Explains the Industrial Revolution in East Asia? Evidence from the Factor Markets." American Economic Review, 92(3), 502-526