03 May The human resource manager of the XYZ Compa
The human resource manager of the XYZ Company makes the following claim: “Our workers make an average of $500 per week. We produce $6000 worth of output each week using only 10 workers. That averages out to $600 per worker per week. We should therefore hire more people as long as the wage is $500 per week.” Assess this claim – is the reasoning solid or do you disagree? (2 points) 2. Consider a firm that uses both labor and capital in production. The price of capital is $20 per unit and the wage rate is $10 per hour. • Draw the firm’s isocost line assuming a total production cost of $100. How steep is this line (that is, what is its slope)? Be sure to clearly label the axes. (3 points) • Suppose the wage drops to $5 per unit. In which direction does the substitution effect change the firm’s demand for labor and capital? In which direction does the scale effect change the firm’s demand for labor and capital? (2 points) • If the firm chooses its labor and capital combination to minimize its production costs, will the marginal product of labor be higher than, lower than, or equal to the marginal product of capital? Why? (Assume that the price of labor and capital are those given in part b.) (2 points) 3. Consider a firm that uses two inputs: skilled workers and computers. Explain what it means if skilled workers and computers are complements in production. If the price of computers falls, and skilled workers and computers are complements, will the firm want to hire more or fewer skilled workers? (2 points) 4. Suppose the hourly wage is $20, the price of each unit of capital is $25, and the price of output is $50 per unit. Assume that the firm cannot affect any of these prices. The production function of the firm is , so that the marginal product of labor is . • If the current capital stock is fixed at 1,600 units, how many hours of labor should the firm hire in the short run (i.e., what should E be)? How much profit will the firm earn (hint: remember that profit is just price×output – wage×E – price of capital×K)? (3 points total: 2 for the value of E and 1 for the profit). • Now let’s think about the long run, in which the firm can freely choose both labor and capital. Based on the production function, the marginal product of capital can be written as (the fact that we’re telling you what MPK is in this part is a big hint). If the firm is maximizing profits, what must the ratio of MPE to MPK be? What must the ratio of E to K be? (2 points)
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