Suppose that upon graduating, you accept a position in hospital administration at a large urban hospital. Specifically, your initial job is to allocate resources across two disparate divisions within the hospital: the OB/GYN service and the Psychology Clinic. These two divisions have very little overlap, so $1 invested in the Psychology Clinic has no direct effect on the OB/GYN service. Suppose you are given a fixed amount of money to hire new physician assistants.

1. Draw a production function for each division (two graphs) of output (number of patients seen) as a function of physician assistants. Assume that capital (i.e., the facility size) is fixed and that both divisions are operating in a productively efficient manner.
2. Referring to your graphs, describe the opportunity cost of devoting $1 to the Psychology Clinic.
3. Demonstrate on your graphs a set of points (one for each division) that would be allocatively efficient. Explain why you chose these points.
4. Suppose a new technology arises that complements physician assistants in the production of OB/GYN cases. Redraw both production functions. How does the opportunity cost of $1 of investment in the Psychology Clinic change? Explain. If the answer is ambiguous, describe the factors that would be important in the answer.