Suggested Solutions to Assignment 2 (Optional)

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1 EC 239 Introduction to International Trade Instructor: Sharif F. Khan Department of Economics Wilfrid Laurier University Winter 2010 Suggested Solutions to Assignment 2 (Optional) Part B Short Questions B1. Question # 1 of Ch 2 (8 th ed. of the textbook) Canada and Australia are (mainly) English-speaking countries with populations that are not too different in size (Canada s is 60 percent larger). But Canadian trade is twice as large, relative to GDP, as Australia s. Why should this be the case? We saw that not only is GDP important in explaining how much two countries trade, but also, distance is crucial. Given its remoteness, Australia faces relatively high costs of transporting imports and exports, thereby reducing the attractiveness of trade. Since Canada has a border with a large economy (the U.S.) and Australia is not near any other major economy, it makes sense that Canada would be more open and Australia more selfreliant. B2. Question # 2 of Ch 2 (8 th ed. of the textbook) Mexico and Brazil have very different trading patterns. Mexico trades mainly with the United States, Brazil trades about equally with the United States and with the European Union; Mexico does much more trade relative to its GDP. Explain these differences using the gravity model. Mexico is quite close to the U.S., but it is far from the European Union (EU). So it makes sense that it trades largely with the U.S. Brazil is far from both, so its trade is split between the two. Mexico trades more than Brazil in part because it is so close to a major economy (the U.S.) and in part because it is a member of a free trade agreement with a large economy (NAFTA). Brazil is farther away from any large economy and is in a free trade agreement with relatively small countries. Page 1 of 11 Pages

2 B3. Question # 4 of Ch 2 (8 th ed. of the textbook) Over the past few decades, East Asian economies have increased their share of world GDP. Similarly, intra-east Asian trade that is, trade among East Asian nations has grown as a share of world trade. More than that, East Asian countries do an increasing share of their trade with each other. Explain why, using the gravity model. As the share of world GDP which belongs to East Asian economies grows, then in every trade relationship which involves an East Asian economy, the size of the East Asian economy has grown. This makes the trade relationships with East Asian countries larger over time. The logic is similar for why the countries trade more with one another. Previously, they were quite small economies, meaning that their markets were too small to import a substantial amount. As they became more wealthy and the consumption demands of their populace rose, they were each able to import more. Thus, while they previously had focused their exports to other rich nations, over time, they became part of the rich nation club and thus were targets for one another s exports. Again, using the gravity model, when South Korea and Taiwan were both small, the product of their GDPs was quite small, meaning despite their proximity, there was little trade between them. Now that they have both grown considerably, their GDPs predict a considerable amount of trade. B4. Question # 7 of Ch 3 (8 th ed. of the textbook) Japanese labor productivity is roughly the same as that of the United States in the manufacturing sector (higher in some industries, lower in others), while the United States is still considerably more productive in the service sector. But most services are nontraded. Some analysts have argued that this poses a problem for the United Sates, because our comparative advantage lies in things we cannot sell on world markets. What is wrong with this argument? The problem with this argument is that it does not use all the information needed for determining comparative advantage in production: this calculation involves the four unit labor requirements (for both the industry and service sectors, not just the two for the service sector). It is not enough to compare only service s unit labor requirements. If a * ls < als, Home labor is more efficient than Foreign labor in services. While this demonstrates that the United States has an absolute advantage in services, this is neither a necessary nor a sufficient condition for determining comparative advantage. For this determination, the industry ratios are also required. The competitive advantage of any industry depends on both the relative productivities of the industries and the relative wages across industries. Page 2 of 11 Pages

3 B5. Question # 8 of Ch 3 (8 th ed. of the textbook) Anyone who has visited Japan know it is an incredibly expensive place; although Japanese workers earn about the same as their U.S. counterparts, the purchasing power of their incomes is about one-third less. Extend your discussion from question 7 (of Chapter 3) to explain this observation. (Hint: Think about wages and the implied prices of nontraded goods.) While Japanese workers may earn the equivalent wages of U.S. workers, the purchasing power of their income is one-third less. This implies that although w = w * (more or less), p < p * (since 3p = p * ). Since the United States is considerably more productive in services, service prices are relatively low. This benefits and enhances U.S. purchasing power. However, many of these services cannot be transported and hence, are not traded. This implies that the Japanese may not benefit from the lower U.S. services costs, and do not face an international price which is lower than their domestic price. Likewise, the price of services in United States does not increase with the opening of trade since these services are non-traded. Consequently, U.S. purchasing power is higher than that of Japan due to its lower prices on non-traded goods. B6. Question # 9 of Ch 3 (8 th ed. of the textbook) How does the fact that many goods are nontraded affect the extent of possible gains from trade? Gains from trade still exist in the presence of non-traded goods. The gains from trade decline as the share of non-traded goods increases. In other words, the higher the portion of goods which do not enter the international marketplace, the lower the potential gains from trade. If transport costs were high enough so that no goods were traded, then, obviously, there would be no gains from trade. B7. Question # 1 of Ch 4 (8 th ed. of the textbook) In the United States where land is cheap, the ratio of land to labor used in cattle raising is higher than that of land used in wheat growing. But in more crowded countries, where land is expensive and labor is cheap, it is common to raise cows by using less land and more labor than Americans use to grow wheat. Can we still say that raising cattle is land-intensive compared with farming wheat? Why or why not? The definition of cattle growing as land intensive depends on the ratio of land to labor used in production, not on the ratio of land or labor to output. The ratio of land to labor in cattle exceeds the ratio in wheat in the United States, implying cattle is land intensive in the United States. Cattle is land intensive in other countries as well if the ratio of land to labor in cattle production exceeds the ratio in wheat production in that country. Comparisons between another country and the United States is less relevant for this purpose. Page 3 of 11 Pages

4 B8. Question # 3 of Ch 4 (8 th ed. of the textbook) The world s poorest countries cannot find anything to export. There is no resource that is abundant certainly not capital or land, and in small poor nations not even labor is abundant. Discuss. What matters is not the absolute abundance of factors, but their relative abundance. Poor countries have an abundance of labor relative to capital when compared to more developed countries. B9. Question # 4 of Ch 4 (8 th ed. of the textbook) The U.S. labor movement which mostly represents blue-collar workers rather than professionals and highly educated workers has traditionally favored limits on imports from less-affluent countries. Is this a shortsighted policy or a rational one in view of the interests of union members? How does the answer depend on the model of trade? In the Ricardian model, labor gains from trade through an increase in its purchasing power. This result does not support labor union demands for limits on imports from less affluent countries. The Heckscher-Ohlin model directly addresses distribution by considering the effects of trade on the owners of factors of production. In the context of this model, unskilled U.S. labor loses from trade since this group represents the relatively scarce factors in this country. The results from the Heckscher-Ohlin model support labor union demands for import limits. In the short run, certain unskilled unions may gain or lose from trade depending on in which sector they work, but in theory, in the longer run, the conclusions of the Heckscher-Ohlin model will dominate. B10. Question # 6 of Ch 4 (8 th ed. of the textbook) Explain why the Leontief paradox and the more recent Bowen, Leamer, and Sveikaukas results reported in the text contradict the factor-proportions theory. The factor proportions theory states that countries export those goods whose production is intensive in factors with which they are abundantly endowed. One would expect the United States, which has a high capital/labor ratio relative to the rest of the world, to export capital-intensive goods if the Heckscher-Ohlin theory holds. Leontief found that the United States exported labor-intensive goods. Bowen, Leamer and Sveikauskas found for the world as a whole the correlation between factor endowment and trade patterns to be tenuous. The data do not support the predictions of the theory that countries exports and imports reflect the relative endowments of factors. Page 4 of 11 Pages

5 B11. Question # 7 of Ch 4 (8 th ed. of the textbook) In the discussion of empirical results on the Heckscher-Ohlin model, we noted that recent work suggests that the efficiency of factors of production seems to differ internationally. Explain how this would affect the concept of factor-price equalization. If the efficiency of the factors of production differs internationally, the lessons of the Heckscher-Ohlin theory would be applied to effective factors which adjust for the differences in technology or worker skills or land quality (for example). The adjusted model has been found to be more successful than the unadjusted model at explaining the pattern of trade between countries. Factor-price equalization concepts would apply to the effective factors. A worker with more skills or in a country with better technology could be considered to be equal to two workers in another country. Thus, the single person would be two effective units of labor. Thus, the one high-skilled worker could earn twice what lower-skilled workers do, and the price of one effective unit of labor would still be equalized. B12. A good cannot be both land and labor-intensive. Discuss. In a two good, two factor model, such as the original Heckscher-Ohlin framework, the factor intensities are relative intensities. Hence, the relevant statistic is either workers per acre (or acres per worker); or wage per rental unit (or rental per wage). In order to illustrate the logic of the statement above, let us assume that the production of a broom requires 4 workers and 1 acre. Also, let us assume that the production of one bushel of wheat requires 40 workers and 80 acres. In this case the acres per person required to produce a broom is one quarter, whereas to produce a bushel of wheat requires 2 acres per person. The wheat is therefore (relatively) land intensive, and the broom is (relatively) labor intensive. B13. No country is abundant in everything. Discuss. The concept of relative (country) factor abundance is (like factor intensities) a relative concept. When we identify a country as being capital intensive, we mean that it has more capital per worker than does the other country. If one country has more capital worker than another, it is an arithmetic impossibility that it also has more workers per unit capital. Page 5 of 11 Pages

6 B14. Countries do not in fact export the goods the H.O. theory predicts. Discuss. This statement is not true. Although one may find many cases where it seems to be true (e.g. the Leontieff Paradox), all one needs to do in order to render the above statement not (generally) true is to find one counter example. In fact, one can find large subsets of agricultural and commodity products in which the H.O predictions are generally fulfilled. Labor-intensive countries such as Bangladesh do in fact export relatively labor-intensive goods. Capital-intensive countries such as Germany do in fact export capital-intensive products (at least to South countries). Countries such as Costa Rica ("sunshine abundant") tend to export bananas (sunshine-intensive products). The U.S. (a wheat-landabundant country) does indeed export wheat (a wheat-land intensive product). In fact, since the early 1980s, the Leontieff Paradox was not found to describe the U.S. trade data (hence ratifying the H.O. theory). Part C Problem Solving Questions Read each part of the question very carefully. Show all the steps of your calculations to get full marks. C1. Question # 3 of Ch 2 (8 th ed. of the textbook) Equation (2.1) says that trade between any two countries is proportional to the product of their GDPs. Does this mean that if the GDP of every country in the world doubled, world trade would quadruple? Analyze this question using the simple example shown in Table 2-2. No, if every country s GDP were to double, world trade would not quadruple. One way to see this using the example from Table 2-2 would simply be to quadruple all the trade flows in 2-2 and also double the GDP in 2-1. We would see that the first line of Table 2-2 would be, 6.4, 1.6, 1.6. If that were true, Country A would have exported $8 trillion which is equal to its entire GDP. Likewise, it would have imported $8 trillion, meaning it had zero spending on its own goods (highly unlikely). If instead we filled in Table 2-2 as before, by multiplying the appropriate shares of the world economy times a country s GDP, we would see the first line of Table 2-2 reads, 3.2, 0.8, 0.8. In this case, 60% of Country A s GDP is exported, the same as before. The logic is that while the world GDP has doubled, increasing the likelihood of international trade, the local economy has doubled, increasing the likelihood of domestic trade. The gravity equation still holds. If you fill in the entire table, you will see that where before the equation was 0.1 GDP i GDP j, it now is 0.05 GDP i GDP j. The coefficient on each GDP is still one, but the overall constant has changed. Page 6 of 11 Pages

7 C2. Question # 1, 2, 3, 4 and 5 of Ch 3 (8 th ed. of the textbook) 1. Home has 1,200 units of labor available. It can produce two goods, apples and bananas. The unit labor requirement in apple production is 3, while in banana production it is 2. a. Graph Home s production possibility frontier. The production possibility curve is a straight line that intercepts the apple axis at 400 (1200/3) and the banana axis at 600 (1200/2). See Figure C2_1a. b. What is opportunity cost of apples in terms of bananas? The opportunity cost of apples in terms of bananas is 3/2. It takes three units of labor to Harvest an apple but only two units of labor to harvest a banana. If one foregoes harvesting an apple, this frees up three units of labor. These 3 units of labor could then be used to harvest 1.5 bananas. c. In the absence of trade, what would the price of apples in terms of bananas be? Why? Labor mobility ensures a common wage in each sector and competition ensures the price of goods equals their cost of production. Thus, the relative price equals the relative costs, which equals the wage times the unit labor requirement for apples divided by the wage times the unit labor requirement for bananas. Since wages are equal across sectors, the price ratio equals the ratio of the unit labor requirement, which is 3 apples per 2 bananas. 2. Home is as described in problem 1 (of Chapter 3). There is now also another country, Foreign, with a labor force of 800. Foreign s unit labor requirement in apple production is 5, while in banana production it is 1. a. Graph Foreign s production possibility frontier. The production possibility curve is linear, with the intercept on the apple axis equal to 160(800/5) and the intercept on the banana axis equal to 800(800/1). See Figure C2_2a. Page 7 of 11 Pages

8 b. Construct the world relative supply curve. The world relative supply curve is constructed by determining the supply of apples relative to the supply of bananas at each relative price. The lowest relative price at which apples are harvested is 3 apples per 2 bananas. The relative supply curve is flat at this price. The maximum number of apples supplied at the price of 3/2 is 400 supplied by Home while, at this price, Foreign harvests 800 bananas and no apples, giving a maximum relative supply at this price of 1/2. This relative supply holds for any price between 3/2 and 5. At the price of 5, both countries would harvest apples. The relative supply curve is again flat at 5. Thus, the relative supply curve is step shaped, flat at the price 3/2 from the relative supply of 0 to 1/2, vertical at the relative quantity 1/2 rising from 3/2 to 5, and then flat again from 1/2 to infinity. See Figure C2_2b. 3. Now suppose world relative demand takes the following form: Demand for apples/demand for bananas = price of bananas/price of apples. a. Graph the relative demand curve along with the relative supply curve. The relative demand curve includes the Points (1/5, 5), (1/2, 2), (1, 1), (2, 1/2). See Figure C2_3. b. What is the equilibrium relative price of apples? The equilibrium relative price of apples is found at the intersection of the relative demand and relative supply curves. This is the Point (1/2, 2), where the relative demand curve intersects the vertical section of the relative supply curve. Thus the equilibrium relative price is 2. c. Describe the pattern of trade. Home produces only apples, Foreign produces only bananas, and each country trades some of its product for the product of the other country. d. Show that both Home and Foreign gain from trade. In the absence of trade, Home could gain three bananas by foregoing two apples, and Foreign could gain by one apple foregoing five bananas. Trade allows each country to trade two bananas for one apple. Home could then gain four bananas by foregoing two apples while Foreign could gain one apple by foregoing only two bananas. Each country is better off with trade. Page 8 of 11 Pages

9 4. Suppose that instead of 1,200 workers, Home had 2,400. Find the equilibrium relative price. What can you say about the efficiency of world production and the division of the gains from trade between Home and Foreign in this case? The increase in the number of workers at Home shifts out the relative supply schedule such that the corner Points are at (1, 3/2) and (1, 5), instead of (1/2, 3/2) and (1/2, 5). The intersection of the relative demand and relative supply curves is now in the lower horizontal section, at the Point (2/3, 3/2). In this case, Foreign still gains from trade but the opportunity cost of bananas in terms of apples for Home is the same whether or not there is trade, so Home neither gains nor loses from trade. See Figure C2_4. 5. Suppose that Home has 2400 workers, but they are only half as productive in both industries as we have been assuming. Construct the world relative supply curve and determine the equilibrium relative price. How do the gains from trade compare with those in the case described in problem 4 (of Chapter 3)? This answer is identical to that in problem 3 (of Chapter 3). The amount of effective labor has not changed since the doubling of the labor force is accompanied by a halving of the productivity of labor. C3. Question # 2 of Ch 4 (8 th ed. of the textbook) Suppose that at current factor prices cloth is produced using 20 hours of labor for each acre of land, and food is produced using only 5 hours of labor per acre of land. a. Suppose that the economy s total resources are 600 hours of labor and 60 acres of land. Use a diagram to determine the allocation of resources. The box diagram has 600 as the length of two sides (representing labor) and 60 as the length of the other two sides (representing land). There will be a ray from each of the two corners representing the origins. To find the slopes of these rays we use the information from the question concerning the ratios of the production coefficients. The question states that alc/atc = 20 and alf/atf = 5. Since alc/atc = (LC/QC)/(TC/QC) = LC/TC we have LC = 20TC. Using the same reasoning, alf/atf = (LF/QF)/(TF/QF) = LF/TF and since this ratio equals 5, we have LF = 5TF. We can solve this algebraically since L = LC + LF = 600 and T = TC + TF = 60. The solution is LC = 400, TC = 20, LF = 200 and TF = 40. See Figure C3_a. Page 9 of 11 Pages

10 b. Now suppose that the labor supply increases first to 800, then 1,000, then 1,200 hours. Using a diagram like Figure 4-9, trace out the changing allocation of resources. The dimensions of the box change with each increase in available labor, but the slopes of the rays from the origins remain the same. The solutions in the different cases are as follows (Note: Follow the same method which is described in the solution to part a). L = 800: TC = 33.33, LC = , TF = 26.67, LF = L = 1000: TC = 46.67, LC = , TF = 13.33, LF = L = 1200: TC = 60, LC = 1200, TF = 0, LF = 0. (complete specialization). See Figure C3_b(i), Figure C3_b(ii) and Figure C3_b(iii). c. What would happen if the labor supply were to increase even further? At constant factor prices, some labor would be unused, so factor prices would have to change, or there would be unemployment. C4. Consider the following data on the factor endowments of two countries, A and B: Factor Endowments Country A Country B Labor force ( in millions of workers) Capital stock (in thousands of machines) a) Which country is relatively capital abundant? Country B is relatively capital abundant because (K/L) B = 10/20 = ½ > (K/L) A =15/45 = 1/3. b) Which country is relatively labor abundant? Country A is relatively labor abundant because (L/K) A = 45/15 = 3> (L/K) B =20/10 = 2. Page 10 of 11 Pages

11 c) Suppose that good S is capital intensive relative to good T, which country will have comparative advantage in the production of S? Explain. Assume that the standard assumptions of the Heckscher-Ohlin model holds for country A and B. According to the H-O model, the relatively capital abundant country A will have comparative advantage in the production of S which uses capital intensively. The intuitive explanation for this result is given below. Since country A is relatively capital abundant, it will produce relatively more of good S which uses capital intensively. On the other hand, since country B is relatively labor abundant, it will produce relatively more of good T which uses labor intensively. So, for any given relative price of good S, the relative supply of good S will be higher in country A than it will be in country B. Since the relative demand of good S is same in both countries, the autarky (in the absence of trade) equilibrium relative price of good S will be lower in country A than it is country B. It implies that country A will have comparative advantage in the production of S. Page 11 of 11 Pages

industry depends on both the relative productivities of the industries and the relative wages across industries.

industry depends on both the relative productivities of the industries and the relative wages across industries. 1. a. The production possibility curve is a straight line that intercepts the apple axis at 400 (1200/3) and the banana axis at 600 (1200/2). b. The opportunity cost of apples in terms of bananas is 3/2.

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