Microeconomics Homework Assignment # 12 Part 1. Short questions. For each question, provide both answer and explanation. I. A rm is using 400 units of capital and 200 units of labor to produce 20,000 units of output. Capital costs $80 per unit and labor $20 per unit. The last unit of capital added 100 units of output, while the last unit of labor added 30 units of output. Is the rm using optimal (cost minimizing) quantities of inputs? If not, what should the rm do in order to be productively efcient? 2. The production function is given by F(L) = 6Lm. Assuming that each unit of labor services costs $12 and the price of output is $6, how many units of labor will the rm hire? 3. Suppose a rm has a market power in the labor market, but sells its output in a perfectly competitive market. Also suppose that its capital stock is xed in the short run, and the law of diminishing marginal returns applies. Can you draw the rm's demand for labor curve? If yes, draw it. If no, explain why you cannot do it. Part II. Longer questions. 1. A producer of widgets pays $5 for each day of labor and $15 for each day of capital employed. The table below describes the marginal products of each at various levels of employment. If you must produce Q : 920 widgets, nd the least-cost combination of labor and capital. 2. You are given the following information on the operations of a perfectly competitive widget shop that sells wid e nerda is $200. Revenue Cost Prot (Number of (Number of workers) widgets per ___ ___ A. Fill in the column for the marginal product of labor. In what units in the marginal product expressed? Does the data obey the law of diminishing marginal returns and why? B. Fill in the column for the marginal value product of labor. In what units is it expressed? C. Suppose that the market wage is $20 per day. How many workers should the shop hire per day and why? D. Fill in the columns for revenue, cost, and prot. In the long run, should this rm change the amount of capital it is using