AEC 311 Assignment 5 Name: - 40 points max - 6 analytical questions: 25 points altogether - 5 multiple choice; 3 points each I On analytical questions, points may be deducted if you get the correct answer but make no effort to explain how you got it, of if your general process was correct but you got the wrong nal answer. Problems 1-3 concern cotton, which can be produced all over the world using the same basic long-run production function: q = LIISKCFJ where q is output, I. is labor, and K is capital. For example, labor is relatively inexpensive in India, and cotton is produced with this combination of inputs: L = 36 and K = 9. In the United States, labor is relatively lm and it produces cotton with this combination of inputs: L = 4 and K = 81. 1:45 points) If we were to map this production function using isoquants, is it possible for India and the United States to be on the same isoquant? 2:9! points) Based on how much L and K they actually use, do India and the United States have the same marginal rate of technical substitution? Calculate them based on the formula that we went through in class. 3. (4 M the price of capital (K) in each country is 50, what does this imply that the cost of labor is in each country if cotton producers are minimizing costs in each country? Solve for wage (w) in each country, the units of which are in dollars per week. Problems 4-6 concern a dairy operation that is trying to determine the optimal number of workers per day (L). It wants to hire workers up to the point where the extra output from hiring workers achieves its maximum. If q is the amount of milk produced per day and K is the number of cows, the amount of milk produced is: g = 600K212? K3123 g 4. (4 M the short run, the number of cows (K) is xed at 10, but the operation can vary (L) how many hours its employees work. Write the formula for the short-run production function by replacing K with its fixed short run value (10). 5. (4 points) A graph of this short run production function will show it to be shaped like an m U. We want to nd the number of workers (L) that will maximize output. Before this maximum, each additional worker will provide more output than the previous worker did. But alter this point, each additional worker makes output 9 decline. Start by finding the slope of the production function, which is 114}: or marginal product of labor. 6. (4 points) Output is maximized at the very top of the inverted gag production function. This is where the slope of the production function is zero, that is, where JMPL = 0. With this information, nd the number of workers (L) that gives the maximum amount of output 'om the last worker. Multiple choice: In the remaining questions, indicate which letter has the best answer. (3 points each) 7. 6) Automobile manufacturers view the assembly-line workers as A) capital services. B) labor services. C) materials. D) none of above. 8. Fixed costs are A) a production expense that does not vary with output. B) a production expense that changes with the quantity of output produced. C) equal to total cost divided by the units of output produced. D) the amount by which a rm's cost changes if the firm produces one more unit of output. 9. Variable costs are A) a production expense that does not vary with output. B) a production expense that changes with the quantity of output produced. C) equal to total cost divided by the units of output produced. D) the amount by which a rm's cost changes if the firm produces one more unit of output. 10. A rm's marginal cost can always be thought of as the change in total cost if A) the rm produces one more unit of output. B) the rm buys one more unit of capital. C) the rm's average cost increases by $1. D) the rm moves to the next highest isoquant. 11. The slope of an isoquant tells us A) how much output increases when both inputs are increased. B) the increase in MPL when capital increases. C) the decrease in capital necessary to keep output constant when labor increases by one unit. D) the decrease in capital necessary to keep MPL constant when labor increases by one unit