Problem set week 3 (8) + answers BB PDF

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Week 3 (8) International Trade and Income Distribution Chapters 4, 5Specific Factors ModelHeckscher – Ohlin ModelProblem setExercise 3. An economy can produce good 1 using labor and capital and good 2 using labor and land. The total supply of labor is 100 units. Given the supply of capital and land,...

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Week 3 (8) International Trade and Income Distribution Specific Factors Model Heckscher – Ohlin Model

Chapters 4, 5

Problem set

Exercise 3.1 An economy can produce good 1 using labor and capital and good 2 using labor and land. The total supply of labor is 100 units. Given the supply of capital and land, the outputs of the two goods depend on labor input as follows: Labor input Output of to good 1 good 1

Labor input to good 2

Output of good 2

0 10 20 30 40 50 60 70 80 90 100

0 10 20 30 40 50 60 70 80 90 100

0.0 39.8 52.5 61.8 69.3 75.8 81.5 86.7 91.4 95.9 100

0.0 25.1 38.1 48.6 57.7 66.0 73.6 80.7 87.4 93.9 100

a. Graph the production functions for good 1 and good 2. b. Graph the production possibility frontier. Why is it curved? a .

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b.

Because of diminishing returns (or increasing opportunity costs), the PPF is a bowed-out curve.

Exercise 3.2 The marginal product op labor curves corresponding to the production functions in exercise 2.1 are as follows: Workers Employed

MPL in Sector 1

MPL in Sector 2

10 20 30 40 50 60 70 80 90 100

15.1 11.4 10.0 8.7 7.8 7.4 6.9 6.6 6.3 6.0

15.9 10.5 8.2 6.9 6.0 5.4 5.0 4.6 4.3 4.0

a. Suppose that the price of good 2 relative to that of good 1 is 2. Determine graphically the wage rate and the allocation of labor between the two sectors. Answer: Draw the marginal product of labor times the price for each sector given that the total labor allocated between these sectors must sum to 100. Thus, if there are 10 workers employed in Sector 1, then there are 90 workers employed in Sector 2. If there are 50 workers employed in Sector 1, then there are 50 workers employed in Sector 2. For simplicity, define P1  1 and P2  2 (it does not matter what the actual prices are in determining the allocation of labor, only that the relative price P2/P1  2).

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NB: curves are switched: P1xMPL1 actually is P2xMPL2 In competitive labor markets, the wage is equal to price times the marginal product of labor. With mobile labor between sectors, the wage rate must be equal between sectors. Thus, the equilibrium wage is determined by the intersection of the two P  MPL curves. Looking at the diagram above, it appears that this occurs at a wage rate of 10 and a labor supply of 30 workers in Sector 1 (70 workers in Sector 2). b. Using the graphs drawn for exercise 3.1or the table, determine the output of each sector. Then confirm graphically that the slope of the production possibility frontier at that point equals the relative price.

Answer: From part (a), we know that 30 units of labor are employed in Sector 1 and 70 units of labor are employed in Sector 2. Looking at the table in exercise 2.1, we see that these labor allocations will produce 48.6 units of good 1 and 86.7 units of good 2. At this production point (Q1  48.6, Q2  86.7), the slope of the PPF must be equal to P1/P2, which is ½. Looking at the PPF in exercise 2.1, we see that it is roughly equal to ½.

c. Suppose that the relative price of good 2 falls to 1.3. Repeat (a) and (b).

Answer: If the relative price of good 2 falls to 1.3, we simply need to redraw the P  MPL diagram with P1  1 and P2  1.3.

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NB: curves are switched: P1xMPL1 actually is P2xMPL2

The decrease in the price of good 2 leads to an increase in the share of labor accruing to Sector 1. Now, the two sectors have equal wages (P  MPL) when there are 50 workers employed in both sectors. Looking at the table in exercise 3.1, we see that with 50 workers employed in both Sectors 1 and 2, there will be production of Q1  66 and Q2  75.8. The PPF at the production point Q1  66, Q2  75.78 must have a slope of P1/P2  1/1.3  0.77. d. Discuss the effects of the price change from 2 to 1.3 on the income of the specific factors in sector 1 and sector 2.

Answer: The decrease in the relative price of good 2 led to an increase in production of good 1 and a decrease in the production of good 2. The expansion of Sector 1 increases the income of the factor specific to Sector 1 (capital). The contraction of Sector 2 decreases the income of the factor specific to Sector 2 (land).

Exercise 3.3 Consider two countries (Home and Foreign) that produce good 1 (with labor and capital) and good 2 (with labor and land) according to the production functions described in exercise 3.1 and 3.2. Initially, both countries have the same supply of labor (100 units), capital, and land. The capital stock of Home then grows. This change shifts out both the production curve for good 1 and associated marginal product of labor curve . Nothing happens to the production and marginal product curves for good 2. a. Show how the increase in the supply of capital for Home affects its production possibility frontier.

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Answer: The increase in the capital stock in Home will increase the possible production of good 1, but have no effect on the production of good 2, since good 2 does not use capital in production. As a result, the PPF shifts out to the right, representing the greater quantity of good 1 that Home can now produce.

b. Draw the relative supply curve for both the Home and the Foreign economy.

Answer: Given the increased production possibility for Home, the relative supply of home (defined as Q1/Q2) is further to the right than the relative supply for Foreign. As a result, the relative price of good 1 is lower in Home than it is in Foreign. c. If those two economies open up to trade, what will be the pattern of trade (i.e. which country exports which good)? Answer: If both countries open to trade, Home will export good 1 and Foreign will export good 2. d. Describe how opening up to trade affects all three factors (labor, capital, land) in both countries. Answer: Owners of capital in Home and owners of land in Foreign will benefit from trade, while owners of land in Home and owners of capital in Foreign will be hurt. The effects on labor will be ambiguous since the real wage in terms of good 1 will fall (rise) in Home (Foreign) and the real wage in terms of good 2 will rise (fall) in Home (Foreign). The net welfare effect for labor will depend on preferences in each country. For example, if labor in Home consumes relatively more of good 2, they will gain from trade. If labor in Home consumes relatively more of good 1, they will lose from trade.

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Exercise 3.4 There are two countries, A and B, that both produce two goods, namely X and Y. For the production of both goods, both labor and capital are used, however, the production of X is relatively capital-intensive, while that of Y is relatively labour-intensive. A further given is that country A has a relatively large amount of labour available while country B has a relatively large amount of capital. Use the Heckscher – Ohlin model to answer the following questions. a. Draw the production possibility curve of country A and B and explain why they look the way they do. b. Imagine the relative demand for both products is equal in the two countries and that there is no trade between the countries. Will the relative price of product X compared to product Y be different between the countries? What will be the relative earnings of the production factors in both countries? c. Now the countries start trading. Which product will each country export? And what are the consequences of trade in terms of the distribution of income? Answers a. Y

Y

Country A

X

Country B

X

In country A labor is relatively abundant. Country A can produce relatively more of the labor intensive good Y. The production possibilities curve is biased towards Y. Capital is relatively abundant in country B. The ppf is therefore biased towards the production of good X. b. Country A produces relatively more Y, country B produces relatively more X. In case the relative demand is the same in both countries, the relative price of X is higher is country a and lower in country B. In country A wages are relatively low (labour is the relative abundant factor) and earnings of the factor capital are relatively high (capital is the relatively scarce factor). In country B wages are relatively high, and earnings of factor capital are relatively low. c. In case of trade, relative prices of X converge. One world relative price for good X (somewhere between the two autartic relative prices). For country A, the relative price of X falls and production of X falls. The relative price of Y rises and the production of Y rises. Demand for Y falls and demand for X increases. Country A will export Y and import X. For country B, the relative price of X rises, production of X increases, demand for X falls. Country B will export good X and import good Y.

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The increase in production of the labour intensive good Y in country A will increase demand for labour and lower demand for capital: ratio w/r rises. In country B: more production of Y, more demand for capital and less demand for labour: w/r ratio falls. Relative abundant factor gains from trade, relative scarce factor looses.

Exercise 3.5 The trade theory of Heckscher & Ohlin assumes a two-country world, which can produce two goods by means of two production factors. Although the overall pattern of international trade does not seem to be very well accounted for by a pure Heckscher-Ohlin model, North-South trade in manufactures seems to fit the theory much better, according to Krugman and Obstfeld. The Heckscher-Ohlin model is therefore often used in the globalization debate. a.

Assume that high-skilled labour is the relative abundant factor in North (OECD countries), while low-skilled labour is relatively abundant in South (Emerging Economies or NICs). The production of chemicals is relatively high-skilled intensive, and the production of clothing is relatively low-skilled intensive. Use the Heckscher-Ohlin theory of international trade (especially the StolperSamuelson Theorem) to illustrate the adverse effects of North-South trade on the position of low-skilled labour in the OECD countries. According to Heckscher and Ohlin, North has a comparative advantage in the production of chemicals, while South has a comparative advantage in the production of clothing. In the absence of trade, the relative price of chemicals will be lower in North than in South. Trade leads to a convergence of relative prices, so international trade will raise the relative price of chemicals in North (and lower the relative price of the low-skill intensive good). Changes in relative prices have strong effects on the relative factor earnings: if the relative price of a good increases, then the nominal and real return to the factor used intensively in the production of that good increases, while the nominal and real return to the other factor decreases (Stolper-Samuelson Theorem). Thus, the increase in the relative price of chemicals will raise the real income of high-skilled labour in the OECD (relative abundant factor) and will lower the real income of low-skilled labour in the OECD (relative scarce factor).

b. However, many economists do not agree with this outcome of the Heckscher-Ohlin model. In their view, technology and not trade is the main cause of the worsened position of low-skilled labour in the OECD. Discuss the real-world significance of the main implications of the Heckscher-Ohlin model, and argue how technology affects the relative demand for low-skilled labour and/or the relative supply of low-skilled labour.

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- According to HO, trade will lower the relative price of the low-skill intensive good in the OECD. However, influencial studies do not on average find such a decrease in relative prices, and in some instances even a rise in the relative price of low-skill intensive goods is found (GPdV, p98). For Germany H and S show that there has been no systematic decline of relative prices in labour-intensive industries (HS, p.1493). - The Stolper-Samuelson Theorem indicates that the trade pattern decreases the relative real wages of low-skilled labour in the OECD. However, there is no evidence that the relative wages of low-skilled labour in the EU have fallen (GPdV, p.98). In Germany, relative wages of low-skilled employees increased in the period 1970-1995 (HS, p.1495, 1496). However, the relatively high low-skill unemployment in Europe can be taken as a manifestation of the Stolper-Samuelson theorem in the presence of wage rigidities (GPdV, p.98; HS, pp. 1486-1489). - Technical change is typically skill-biased. In general, skill-biased technical change leads to an increase in the demand for skilled workers and a decrease in the demand for low-skilled workers (GPdV, p.100; HS, p.1484-1486). In the empirical literature, there is a wide consensus that skill-biased technical change drives the skill composition in industrial countries (HS, p.1485).

Exercise 3.6 Leontief (1953) tested the Heckscher-Ohlin-Samuelson (HOS) factor abundance model. What he found was remarkable: HOS does not work in practice, at least for the US. What he did was the following. He calculated the amounts of capital and labour used in each industry, and the amounts of capital and labour in US exports and imports. He found that the capital/per capita in exports - $13,700 - was lower(!) than capital/per capita in imports - $18,200. But the US is a relatively capital-rich country, so this finding runs against the HOS model. Can you think of explanations of Leontief’s findings? In the literature this is known as the Leontief paradox. (Hint; most people try to find reasons what he did wrong.) Answer The so-called Leontief paradox has created a whole library of papers that discuss the reasons why it might occur. Among the valid criticisms of his work are the following. He tested it for 1947, an unusual year for the US directly after the war. He ignored other production factors, such as land. He ignored the fact that the US was not engaged in free trade. He should have distinguished between high-skilled and low-skilled labour. More fundamental criticism came from Edward Leamer. His analysis is beyond the scope of this book, but his criticism stresses the fact that a correct test should incorporate three elements: the factor content of trade, the factor intensity of production, and the factor endowments of a country. The HOS model is about these three(!) elements, and not only about the factor content of trade, as was analyzed by Leontief.

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