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Unformatted text preview: Prof. Anca Cristea EC 481/581 Winter 2011 Answers: Problem Set 3 1. For this problem, assume that Foreign is a labor abundant country and that it produces two goods: shoes, which are labor intensive, and computers, which are capital intensive. Using a diagram representing the economy
wide relative demand for labor (similar to Figure 4.8 on page 112 in the textbook), show the effect of a decrease in the relative price of computers in the Foreign country. What happens to the wage relative to the rental ratio? Is there an increase in the labor
capital ratio in each industry? Explain. 2. Suppose there are two countries U.S. and Mexico. Two goods: iPhones (P) and surfboards (S), which are produced in both countries using capital (K) and labor (L). In both countries it takes: 4 units of labor and 1 unit of capital to make one surfboard; and it takes 1 unit of labor and 2 units of Prof. Anca Cristea EC 481/581 Winter 2011 capital to make one iPhone. U.S. has 60 units of labor and 80 units of capital, while Mexico has 40 units of labor and 40 units of capital. In summary, we have the following information: Technology: Factor Endowments: aLS = 4 aKS = 1 U.S.: L = 60; K = 80 aLP = 1 aKP = 2 Mexico: L* = 40; K* = 40 a. Given the information above, show which country is capital abundant relative to the other country; show which good is capital intensive. K 80 U.S.: = = 4 / 3 > 1 L 60 Because K/L ratio in U.S. is greater than the K*/L* ratio in Mexico => U.S. is the capital abundant country. K * 40 Mexico: * = = 1 L 40 € Surfboard: €
K s aKS QS aKS 1 = = = Ls aLS QS aLS 4
iPhone: K P aKP QP aKP 2 = = = LP aLP QP aLP 1 Because K/L ratio used in the production of surfboards is lower than the K/L ratio used in the production of iPhones => iPhones are capital intensive. € € b. According to the Heckscher
Ohlin theorem, which product will the U.S. export and which product will Mexico export? Explain why. U.S. is capital abundant, so it exports the capital intensive good, iPhones. Mexico is labor abundant and so it exports the labor intensive good, surfboards. c. Suppose that the price of iPhones is $18 and the price of surfboards is $11. Solve for the wage (w) and rental rate on capital (r) in the U.S. (Hint: use the two equations that show that unit prices must be equal to unit costs for each good). Because goods markets are perfectly competitive, the cost of producing one unit of a good must equal its price. Thus: Ⱥ aLS w + aKS r = pS Ⱥ Ⱥ aLP w + aKP r = pP => Ⱥ 4 w + r = 11 Ⱥ Ⱥ w + 2 r = 18 € This is a system with 2 equations and two unknowns. One way to solve for it is to multiply the top equation by (
2) and then add the two equations together to get:
8w
2r + w + 2r =
22 +28 => w=4/7 € Substituting w=4/7 into the first equation and solving for r we get: r=11
16/7 = 61/7. d. According to the Stolper
Samuelson theorem, when the U.S. open up to international trade, who benefits and who loses from trade (among capital owners and workers)? Since the U.S. exports the capital intensive good, iPhones, the relative price for iPhones increases after trade, and as a result of that the factor used intensively in the iPhone sector, capital, gains from trade. At the same time, the factor used intensively in the import competing sector, labor, looses from opening to trade. Prof. Anca Cristea EC 481/581 Winter 2011 3. Suppose when Russia opens to trade, it imports automobiles, a capital intensive good. a. According to the Heckscher
Ohlin theorem, is Russia a capital
abundant or a labor
abundant country? Explain. b. What is the impact of opening trade on the real wage in Russia? c. What is the impact of opening trade on the real rental rate of capital? d. Which group, capital owners or labor, would support policies to limit free trade? Briefly explain. 4. In 2001 China successfully negotiated terms to become a member of the WTO. Consequently, countries such as the United States are shifting toward free trade with China. What does the Stolper
Samuelson theorem predict about the impact of this shift on the real wage of unskilled labor in the United States? In China? Prof. Anca Cristea EC 481/581 Winter 2011 5. In the 1980s the U.S. received large amounts of foreign direct investments (FDI) from Japan, especially in the automotive industry (several Japanese car factories were built throughout the U.S.). Assuming that the U.S. produces only cars and t
shirts, and that cars are capital intensive while t
shirts are labor intensive, show with the help of a Box diagram (similar to the one drawn in class) how this increase in total capital stock in the U.S. affects total production of cars compared to the production of t
shirts. Clearly indicate how the equilibrium allocation of capital and labor changes across the two industries. What happens to the nominal earnings of workers and capital
owners? Why? Are the results consistent with the Rybczynski theorem and ‘factor price insensitivity’? Let’s label cars by ‘c’ and t
shirts by ‘s’. As more capital tarts flowing into the U.S., it first gets employed in the capital
intensive sector, cars. But to increase the production of cars, firms in the automotive sector need additional workers. Since the demand for workers is stronger in the car sector, workers start leaving the t
shirt industry. This leads to a drop in output of t
shirts, triggering a release of capital as well (however, more labor than capital is released from the textile sector since t
shirts are labor intensive). In the graphs below, an increase in capital due to FDI is represented by an increase in the height of the box, shifting the origin for cars to Oc’. The new allocation of capital and labor across the two sectors is given by point B: OsL’ units of labor and OsK’ units of capital used in the t
shirt sector; and Oc’L’ units of labor and Oc’K’ units of capital used in the t
shirt sector. Because Ls and Ks decrease, output in the t
shirt sector shrinks, while output in the car sector increases given the increase in Lc and Kc. Since the relative price of cars (Pc/Ps) does not change, neither do the nominal wage and rental ratio. Because of this “factor price insensitivity”, the K/L ratio must stay constant in both sectors; on the graph, a constant K/L ratio implies that the line starting from the new origin Oc’ must have the same slope as the previous line originating in Oc. (Notice that the level of K and L used in each sector changes, however it changes in equal proportions such that the ratio stays the same). The fact that in the Heckscher
Ohlin model, an increase in capital due to FDI does not change the nominal wage
rental ratio but only the output of the two sectors, is exactly what the Rybczynski Theorem states. ...
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 Spring '11
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