# Suggested Solutions to Assignment 2 (Optional)

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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

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

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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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