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Prof. Dr. Georgeta Auktor

Principles of international economics Problems for exam preparation

The Ricardian model

Problem 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. b. What is the opportunity cost of apples in terms of bananas? c. In the absence of trade, what would be the price of apples in terms of bananas? Why? Answer The production possibility curve is a straight line that intercepts the apple axis at 400 (1,200/3) and the banana axis at 600 (1,200/2).

b. The opportunity cost of apples in terms of bananas is 3/2. It takes 3 units of labor to harvest an apple but only 2 units of labor to harvest a banana. If one forgoes harvesting an apple, this frees up 3 units of labor. These 3 units of labor could then be used to harvest 1.5 bananas. c. Labor mobility ensures a common wage in each sector, and competition ensures the price of goods equals their cost of production. => relative prices = the relative costs = (w * aLA ) / (w * aLB ) Because wages are equal across sectors, the price ratio equals the ratio of the unit labor requirement, which is 3 apples per 2 bananas. P=aLA / aLB = 3/2

Problem 2 Home is described in problem 1. 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. 1

Prof. Dr. Georgeta Auktor a. Graph Foreign’s production possibility frontier. b. Construct the world relative supply curve. Answer 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).

b. 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.

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Prof. Dr. Georgeta Auktor

Problem 3 Now suppose world relative demand takes the following form: Demand for apples / demand for bananas = price of bananas / price of apples. a. b. c. d.

Graph the relative demand curve along with the relative supply curve. What is the equilibrium relative price of apples? Describe the pattern of trade. Show that both Home and Foreign gain from trade.

Answer a. The relative demand curve includes the points (1/5, 5), (1/2, 2), (2/3, 3/2), (1, 1), (2, 1/2). (see the world relative demand equation above)

b. 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. Home produces only apples, Foreign produces only bananas, and each country trades some of its product for the product of the other country. d. In the absence of trade, Home could gain 3 bananas by forgoing 2 apples, (from the labor unit requirements) (2 apples free up 6 units of labor, which enable the production of 3 bananas) and Foreign could gain by 1 apple forgoing 5 bananas. Trade allows each country to trade 2 bananas for 1 apple. Home could then gain 4 bananas by forgoing 2 apples, while Foreign could gain 1 apple by forgoing only 2 bananas. Each country is better off with trade.

Problem 4 Suppose an hour’s labor produces 10 kg of rice and 5 meter of cloth in India, and 5 kg and 2 meter in Thailand. Using opportunity costs, explain which country will export cloth and which will export paddy in trade. 3

Prof. Dr. Georgeta Auktor Answer India’s opportunity cost of producing rice = 5/10=0.5 Thailand’s opportunity cost of producing rice = 2/5 = 0.4 To produce one kg of rice, India must give up 0.5 meter of cloth and Thailand 0.4 meter of cloth. Thus, India will export cloth and Thailand will export rice.

Problem 5 “Chinese workers earn only $0.75 an hour; if we allow China to export as much as it likes, our workers will be forced down to the same level. You can’t import a $10 shirt without importing the $0.75 wage that goes with it.” Discuss. Answer This statement is just an example of the pauper labor argument. The point is that relative wage rates do not come out of thin air; they are determined by comparative productivity and the relative demand for goods. We have seen that wages and productivity are strongly correlated. China’s low wage presumably reflects the fact that China is less productive than Germany in most industries. As we have seen in theory, a highly productive country that trades with a less productive, low-wage country will raise, not lower, its standard of living.

Problem 6 The Ricardian model demonstrates that: A) trade between two countries will benefit both countries. B) trade between two countries may benefit both regardless of which good each exports. C) trade between two countries may benefit both if each exports the product in which it has a comparative advantage. D) trade between two countries may benefit one but harm the other. E) trade between two countries always benefits the country with a larger labor force. Answer: C Problem 7 Use the information in the table below to answer the following questions.

(a) (b) (c) (d)

Does either country have an absolute advantage in the production of wheat or beef? Explain. What is the opportunity cost of wheat in each country? What is the opportunity cost of beef in each country? Analyze comparative advantage and opportunities for trade between the U.S. and Argentina. 4

Prof. Dr. Georgeta Auktor

Answer (a) The U.S. has an absolute advantage in the production of both wheat and beef because labor productivity in the U.S. exceeds labor productivity in Argentina for both products. (b) In the U.S., the opportunity cost of wheat is 100/300 or 0.33 units of beef. In Argentina, the opportunity cost of wheat is 20/20 or 1.0 unit of beef. (c) In the U.S., the opportunity cost of beef is 300/100 or 3.0 units of wheat. In Argentina, the opportunity cost of beef is 20/20 or 1.0 unit of wheat. (d) The U.S. has a comparative advantage in wheat production and Argentina has a comparative advantage in beef production. If the U.S. can trade wheat to Argentina at a rate of more than 0.33 units of beef per unit of wheat, then the U.S. will benefit. If Argentina can trade beef to the U.S. at a rate of more than one unit of wheat per unit of beef, then Argentina will benefit. Problem 8 In a two product two country world, international trade can lead to increases in: a. consumer welfare only if output of both products is increased. b. output of both products and consumer welfare in both countries. c. total production of both products but not consumer welfare in both countries. d. consumer welfare in both countries but not total production of both products. e. prices of both goods in both countries.

Answer: B

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Prof. Dr. Georgeta Auktor

Specific factors and income distribution

Problem 1 In Home and Foreign, there are two factors of production, land and labor, used to produce only one good. The land supply in each country and the technology of production are exactly the same. The marginal product of labor in each countries depends on employment as follows: Number of workers employed Marginal product of last worker 1 20 2 19 3 18 4 17 5 16 6 15 7 14 8 13 9 12 10 11 11 10 Initially there are 11 workers employed in Home, but only 3 workers in Foreign. Find the effect of free movement of labor from Home to Foreign on employment, production, real wages, and the income of landowners in each country. Answer The real wage in Home is 10, while real wage in Foreign is 18. If there is free movement of labor, then workers will migrate from Home to Foreign until the real wage is equal in each country. If 4 workers move from Home to Foreign, then there will be 7 workers employed in each country, earning a real wage of 14 in each country. We can find total production by adding up the marginal product of each worker. After trade, total production is 20 + 19 + 18 + 17 + 16 + 15 + 14 = 119 in each country for total world production of 238. Before trade, production in Home was 20 + 19 + 18 = 57. Production in Foreign was 20 + 19 + … + 10 =165. Total world production before trade was 57 + 165 = 222. Thus, trade increased total output by 16. Workers in Home benefit from migration, while workers in Foreign are hurt. Landowners in Home are hurt by migration (their costs rise), while landowners in Foreign benefit.

Problem 2 Using the numerical example in problem 1, assume now that Foreign limits immigration so that only 2 workers can move there from Home. Calculate how the movement of these two workers affects the income of five different groups: a. b. c. d. e.

Workers who were originally in Foreign. Foreign landowners. Workers who stay in Home Home landowners The workers who do move. 6

Prof. Dr. Georgeta Auktor Answer If only 2 workers can move from Home to Foreign, there will be a real wage of 12 in Home and a real wage of 16 in Foreign. a. Workers in Foreign are hurt as their wage falls from 18 to 16. b. Landowners in Foreign benefit as their costs fall by 2 for each worker employed. c. Workers who stay at home benefit as their wage rises from 10 to 12. d. Landowners in Home are hurt as their costs rise by 2 for each worker employed. e. The workers who do move benefit by seeing their wages rise from 10 to 16.

Problem 3 A country produces two crops- paddy and wheat. Given the price of Paddy (Pp) and wheat (Pw), the relationship of labor allocation is shown as MLPp*Pp=MLPw*Pw=w, where MLPp and MLPw are marginal products of labor for the two. If wheat’s price increases by 10% with no changes in paddy prices, what will happen to labor demand for what production, and the market wage rate? Answer Wage rate raises less than proportionally. • • • •

Labor demand for wheat increases (shifts from paddy to wheat= Wage rate increases less than proportionately Output for wheat increases Output for paddy decreases

Problem 4 The effect of trade on specialized employees of exporting industries will be ________ jobs and ________ pay because they are relatively ________. A) more; higher; immobile B) fewer; lower; immobile C) fewer; lower; mobile D) more; lower; immobile E) more; higher; mobile Answer: A

Problem 5 The relative price of a unit of cloth in the small isolated country of Moribundia is 5 units of food. When then central city, Mudhole, puts in an airstrip, the country is able to engage in trade. If the relative price of cloth in the outside world is 8 units of food, then Moribundia will export ________ and ________ factors used in the production of ________ will benefit. A) cloth; immobile; cloth B) food; immobile; food C) food; mobile; food D) cloth; mobile; cloth E) cloth; immobile; food 7

Prof. Dr. Georgeta Auktor

Answer: A Problem 6 In the specific factors model, a 5% increase in the price of food accompanied by a 1% increase in the price of cloth will cause ________ in the welfare of labor, ________ in the welfare of the fixed factor in the production of food, and ________ in the welfare of the fixed factor in the production of cloth. A) an ambiguous change; an increase; a decrease B) an ambiguous change; a decrease; an increase C) an ambiguous change; an ambiguous change; an ambiguous change D) a decrease; an ambiguous change; an ambiguous change E) an increase; a decrease; an increase Answer: A

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Prof. Dr. Georgeta Auktor

The Hechscher-Ohlin Model

Problem 1 Production of one yard of cloth requires a combination of 2 work-hours and 2 machine-hours. The production of food is more automated; as a result, production of one calorie of food requires 1 workhour along with 3 machine-hours. Thus all the unit input requirements are fixed and there is no possibility of substituting labor for capital or vice versa. Assume also that an economy is endowed with 3,000 units of machine-hours along with 2,000 units of work-hours. a. What is the range of for the relative price of cloth such that the economy produces both cloth and good? Which good is produced if the relative price is outside of this range? (assuming that both goods are produced) b. Write down the unit cost of producing one yard of cloth and one calorie of food as a function of the price of one machine-hour r, and one work-hour, w. In a competitive market, those costs will be equal to the prices of cloth and food. Solve for the factor prices r and w. c. What happens to those factor prices when the price of cloth rises? Who gains and who loses from this change in the price of cloth? Why? Do those changes conform to the changes described for the case with factor substitution? d. Now assume the economy’s supply of machine-hours increases from 3,000 to 4,000. Derive the new PPF. e. How much cloth and food will the economy produce after this increase in its capital supply? f.

Describe how the allocation of machine-hours and work-hours between the cloth and food sectors changes. Do these changes conform with the changes described for the case with factor substitution?

Answer a. The first step is to compute the opportunity costs of both cloth and food. We are given the following resource constraints: aKC = 2, aLC = 2, aKF =฀ 3, aLF = 1 L =฀ 2,000; K = 3,000 Each unit of cloth is produced with 2 units of capital and 2 units of labor. Each unit of food is produced with 3 units of capital and 1 unit of labor. Furthermore, the economy is endowed with 2,000 units of labor and 3,000 units of capital. Given these values, we can define the following resource constraints: 2QC + QF ≤ 2,000  Labor constraint 2QC + 3QF ≤ 3,000  Capital constraint Solve these two constraints for the quantity of food produced: QF ≤ 2,000 - 2QC QF ≤ 1,000 - 2/3QC 9

Prof. Dr. Georgeta Auktor This gives us two budget constraints for food production that must both be met. The production possibilities frontier traces out these budget constraints for food and cloth production. Looking at the diagram (see Chapter 5, Figure 5-1 in Krugman textbook), we see that production of both food and cloth will take place when the relative price of cloth is between the two opportunity costs of cloth. The opportunity cost of cloth is given by the slopes of the two components of the production possibilities frontier above, 2/3 and 2. When cloth production is low, the economy will be using relatively more labor to produce cloth, and the opportunity cost of cloth is 2/3 a unit of food. However, as cloth production rises, the economy runs scarce on labor and must take capital away from food production, raising the opportunity cost of cloth to 2 units of food. As long as the relative price of cloth lies between 2/3 and 2 units of food, the economy will produce both goods. If the price of cloth falls below 2/3, then the economy should completely specialize in food production (too low a compensation for producing cloth). If the price of cloth rises above 2, complete specialization in cloth will occur (too low a compensation for producing food). b. Note the input requirements for each good. One unit of cloth can be produced using 2 units of capital and 2 units of labor. One unit of food is produced using 3 units of capital and 1 unit of labor. In a competitive market, the unit cost of each good must be equal to the output price. QC = 2K + 2L  PC = 2r + 2w QF = 3K + L  PF = 3r + w This gives us two equations and two unknowns (r and w). Solve for the factor prices: w = PF - 3r PC = 2r + 2(PF - 3r) = 2r + 2PF - 6r = 2PF - 4r *** r = (2PF - PC)/4 *** w = (3PC - 2PF)/4 c.

Looking at the two expressions in part (b), we see that an increase in the price of cloth will cause the rental rate of capital to fall and the wage rate to laborers to rise. This makes sense, as cloth is a labor-intensive good. An increase in its price will lead to greater production of cloth and an increase in demand for the factor it uses intensively—labor. d. The capital stock increases to 4,000. The labor constraint will remain unchanged, keeping the maximum price of cloth at 2 units of food. The new capital constraint is given by: 2QC + 3QF ≤ 4,000 Solving for QF yields: QF ≤ 1,333 - 2/3QC Thus, the minimum price of cloth is also unchanged at 2/3 units of food. The only difference now is that the production possibilities frontier will have a larger horizontal intercept (if cloth is on the horizontal axis). Compared to Figure 5-1 in the textbook, the new production possibilities frontier will intercept the x-axis at 2,000 instead of 1,500. e. The actual production point for cloth and food will depend on the relative prices of cloth and food. If we assume that the economy is producing at a point such that all resources are being utilized (point 3 in Figure 5-1), then we can compute the quantities of cloth and food by setting the resource constraints equal to one another: QF = 1,333 - 2/3QC =2,000 - 2QC 2QC - 2/3QC = 2,000 - 1,333 4/3QC = 667 QC = 500 QF = 1,333 - 2/3 × 500 = 1,000 10

Prof. Dr. Georgeta Auktor f.

Prior to the expansion of the capital stock, the economy was producing 750 units of cloth and 500 units of food. After the expansion, cloth production fell to 500, while food production increased to 1,000. This is precisely what the Rybczynski effect predicts will happen.

Problem 2 “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 countries not even labor is abundant.” Discuss. Answer What matters is not the absolute advantage of factors but their relative abundance. Poor countries have an abundance of labor relative to capital when compared to more developed countries, For example, consider a large, rich country like Canada, and a small, poor country like Guatemala. Though Canada has more land, natural resources, capital, and labor than Guatemala, what matters for trade is the relative abundance of these factors. The ratio of L (labor) to K (capital) is likely to be much higher in Guatemala than in Canada, reflecting a relative scarcity of capital in Guatemala and abundance in Canada. This makes L relatively cheaper and K more expensive in Guatemala than in Canada. Notice that this difference in factor prices is not driven by how much L Guatemala has compared to Canada, but by the proportion of L to other factors within each country.

Problem 3 The US 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. a. Is this a shortsighted policy or a rational one in view of the interests of union members? b. How does the answer depend on the model of trade? Answer a. On surface it might appear rational from the point of view of union members. But….. b. In the Ricardian model, labor gains from trade through an increase in its productivity (and thus purchasing power). This result does not support labor union demands for limits on imports from less affluent countries. H-O model directly addresses distribution effets by considering how trade impacts the own...