13 Question (5 points) An economic analysis of the production of laptop computers concludes that the function $f(K, L)=K^{\frac{2}{3}} L^{\frac{2}{3}}$ is a good approximation of actual production. Let $K$ represent all capital used in production while $L$ represents hours of labor. 20th attempt Part 1 (2 points) See Hint What are the returns to scale in laptop computer production? Choose one: A. increasing B. decreasing C. constant D. The returns to scale vary with different combinations of inputs. Suppose that, in the short run, a firm has 27 units of capital. What can we conclude about the marginal product of labor? Choose one:
Suppose that, in the short run, a firm has 27 units of capital. What can we conclude about the marginal product of labor? Choose one: A. The marginal product of labor is increasing because the returns to scale are increasing. B. The marginal product of labor is decreasing, which can be true regardless of the returns to scale. C. The marginal product of labor is constant. D. The marginal product of labor is decreasing because the returns to scale are decreasing. E. The marginal product of labor is increasing, which can be true regardless of the returns to scale.
Part 2 (1 point) See Hint Suppose that capital is still fixed at 27 units and that the prevailing wage is $\$ 45.00$ while the rental rate for capital is $\$ 5.00$. In the boxes below, sort the short-run total, average, and marginal cost functions into their correct categories. (Note that you will not use all available functions; you can use the scroll bar to see all of them). Items (8 items) (Drag and drop into the appropriate area below) $30.00 y^{\frac{3}{4}}+\frac{30.00}{y}$ $30.00 y^{\frac{1}{4}}+30.0$ $22.50 y^{-\frac{1}{4}}$ Categories SR Marginal Cost $2.50 y^{\frac{1}{2}}$
Part 3 (1 point) Now consider the long-run problem where capital and labor are both variable. With wages of $\$ 45.00$ and a rental rate on capital of $\$ 5.00$, sort the long-run total, average, and marginal costs into their correct boxes below. Use the scroll bar to see all answer choices. Items (8 items) (Drag and drop into the appropriate area below) $1.67 y^{\frac{3}{2}}+135.0$ $30.00 y^{\frac{1}{2}}$ $1.67 y^{\frac{1}{2}}+\frac{135.00}{y}$ $2.50 y^{\frac{1}{2}}$ $30.00 y^{\frac{1}{2}}+\frac{22.50}{y}$ Categories LR Total Cost $30.00 y^{\frac{3}{4}}$ LR Average Total Cost $30.00 y^{-\frac{1}{4}}$ LR Marginal Cost $22.50 y^{-\frac{1}{4}}$
Part 4 (1 point) $\quad$ Feedback See Hint Based on your answers from Parts 2 and 3, what can you conclude? * Choose one or more: A. In both the short and long run, there exists a level of production that minimizes average total cost. It is found at lower output in the short run. B. In the short run, there exists a level of production that minimizes average total cost. In the long run, production always gets more efficient as output increases. C. In the long run, there exists a level of production that minimizes average total cost. In the short run, production always gets more efficient as output increases. D. In both the short run and the long run, production continues to become more efficient as output increases. There is no level of output that minimizes average total cost in either case. E. In both the short run and the long run, marginal cost is increasing, which results in average cost increasing with output as well. F. In the short run, marginal and average costs are increasing with output, but in the long run, both are decreasing with output. G. In the short run, both marginal and average costs are decreasing with output, but in the long run, both are increasing. H. In both the short and long run, marginal cost and average cost are decreasing with output.