For simplicity, throughout this problem, assume labor (L), capital (K ), and quantity pro- duced (Q) can be infinitely divided-that is, it is fine to hire 3.3 workers, rent 4.7 machines, and/or produce 134.2 units. Answer the following questions, assuming the production function for DurableTires Corp. is Q = L1/3K 1/2, where Q is the quantity of tires produced, L is the number of workers employed, and K is the number of machines rented.
a. What is the quantity of tires produced when the company employs 64 workers and 36 machines?
b. What are the average product of labor (L) and the average product of machines (K ) when the input mix is the one given above? Clearly and concisely, please explain how you would interpret these numbers.
c. Continue to assume the input mix given above: What is the marginal product of labor (L), if the number of workers is increased by 1 unit? What is the marginal product of cap- ital (K ), if the number of machines is increased by 1 unit, instead? Clearly and con- cisely, explain how you would interpret these numbers.
d. Does DurableTires' production function display increasing, decreasing, or constant returns to scale? Explain. Would your answer change, if the production function were Q = L 1/2K 1/2? How? Explain.
e. Does DurableTires' production function display increasing, decreasing, or constant returns to labor? Explain. Would your answer change, if the production function were Q = L 1/2K 1/2? How? Explain.