Chap 5 ans - IE Chap 5 PDF

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Go back to the numerical example with no factor substitution that leads to the production possibility frontier in Figure 5-1. (Question 1, Chapter 5) a. What is the range for the relative price of cloth such that the economy produces both cloth and food? Which good is produced if the relative price ...

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1. Go back to the numerical example with no factor substitution that leads to the production possibility frontier in Figure 5-1. (Question 1, Chapter 5) a. What is the range for the relative price of cloth such that the economy produces both cloth and food? Which good is produced if the relative price is outside of this range? For parts (b) through (f), assume the price range is such that both goods are produced. 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 = 2000; 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 ≤ 2000 ➔ Labor constraint 2QC + 3QF ≤ 3000 ➔ Capital constraint Solve these two constraints for the quantity of food produced: QF ≤ 2000 − 2QC QF ≤ 1000 − 2/3Q 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, 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. 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 workshop, 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. 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 = 2 K + 2 L ➔ PC = 2r + 2w QF = 3 K + 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 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? 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. Now assume the economy's supply of machine-hours increases from 3,000 to 4,000. Derive the new production possibility frontier. 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 ≤ 1333 − 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, the new production possibilities frontier will intercept the x-axis at 2,000 instead of 1,500. e. How much cloth and food will the economy produce after this increase in its capital supply? 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. f. Describe how the allocation of machine-hours and work hours between the cloth and food sectors changes. Do those changes conform with the changes described for the case with factor substitution? 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. 2. In the United States, where Internet services are cheap, the ratio of capital to labor used is higher than that of capital used in accounting services. But in other

countries, where Internet services are expensive and labor is cheap, it is common to use less capital and more labor than in the United States. Can we still say that Internet services are capital intensive compared to accounting services? Why or why not? (Question 2, Chapter 5) The definition of Internet services as capital intensive depends on the ratio of capital to labor used in production, not on the ratio of capital or labor to output. The ratio of capital to labor in Internet services exceeds the accounting services in United States, implying that Internet services are capital intensive in the United States. Internet services are capital intensive in other countries as well if the ratio of capital to labor in Internet services exceeds the ratio in accounting services in that country. Comparisons between another country and the United States are less relevant for this purpose. 3. “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. (Question 3, Chapter 5) This question is similar to an issue discussed in Chapter 4. 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. For example, consider a large, rich country like the United States and a small, poor country like Guatemala. Though the United States has more land, natural resources, capital, and labor than Guatemala, what matters for trade is the relative abundance of these factors. The ratio of labor to capital is likely to be much higher in Guatemala than in the United States, reflecting a relative scarcity of capital in Guatemala and abundance in the United States. This makes labor relatively cheaper and capital more expensive in Guatemala than in the United States. Notice that this difference in factor prices is not driven by how much labor Guatemala has compared to the United States, but by the proportion of labor to other factors within each country. 4. Most U.S. immigrants are represented by Mexican blue-collar workers that are more likely to work in risky jobs than U.S. –born workers with positive effect on productivity. Limiting immigration is a short sighted or a rational policy in view of the interests of union members? How does the answer depend on the model of trade? (Question 4, Chapter 5) Limiting immigration is a short-sighted policy, as labor unions representing unskilled workers are not directly hurt by the immigration of Mexican blue-collar workers. This is because the US-born workers are not willing to work in risky jobs, but they may consider to be hurt directly by trade that favors the export of skill-intensive goods (and import of low-skill goods). However, the unions may be better served lobbying for resources to increase skill levels among its membership, given that the gains from trade overall will exceed the losses in a particular sector. 5. Will free trade and perfect competition lead to an equalization of wage rate internationally? Explain. Why would the wage rate greatly vary between developed and developing countries, in the same sector in a real world situation, even after the adoption of free trade? (Question 7, Chapter 5) The factor-price equalization is based on the fact that free trade would lead to the convergence of wages between these countries. The theory says that when trade

between two countries resumes, the relative prices of the goods converge. This converge in turn, causes the convergence of the relative prices of capital and labor. This means that when two countries are engaged in trading of goods, in an indirect way these two countries are in effect trading the factors of production. In other words, a country abundant in labor is trading the goods produced in high ratio of labor to capital for goods produced with a low labor capital ratio. That means the country is exporting labor and importing the capital. Hence, trade leads to equalization of factor prices of the two countries. However, in the real world, factor prices are not equalized. Mainly, the wage rates in the developing countries are substantially lower than that of the developed countries. This may be due to various reasons. First, the difference is may be due to the dissimilarity in the quality of labor. Second, the countries operate in different technologies of production even for the same products. Third, in the real world the prices are not fully equalized by international trade. Fourth, many countries do not involve sufficiently in the production, which relatively involves more abundant factors. Some countries even with higher labor to capital ratio involve more in the capital-intensive technology. The factor price equalization does not occur if the countries involved in trading of their relative scarce resource used products. In the real world situation one or more of these factors mentioned above arises in international trade, hence the difference in wages across countries....