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ps4ans - ECONOMICS 450 INTERNATIONAL TRADE FALL 2011 MARK...

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ECONOMICS 450: INTERNATIONAL TRADE FALL 2011 MARK MOORE PROBLEM SET 4: SOLUTIONS A. CHAPTER 5 PROBLEMS. 1. a. The first step is to compute the opportunity cost of both cloth and food. We are given the following resource constraints: a KC = 2 , a LC = 2 , a KF = 3 , a LF = 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: 2 Q C + Q F 2,000 Labor constraint 2 Q C + 3 Q F 3,000 Capital constraint Solve these two constraints for the quantity of food produced: Q F 2,000 - 2 Q C Q F 1,000 - 2/3 Q C 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. 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.
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Q C = 2 K + 2 L P C = 2 r + 2 w Q F = 3 K + L P F = 3 r + w This gives us two equations and two unknowns ( r and w ). Solve for the factor prices: w = P F - 3 r P C = 2 r + 2( P F - 3 r ) = 2 r + 2 P F - 6 r = 2 P F - 4 r r = (2 P F - P C )/4 w = (3 P C - 2 P F )/4 c. Looking at the two expressions above, 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.
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