This is a four part question based on the scenario below:

A health system owns one large hospital and a network of physicians (both primary care and specialty care). It produces inpatient care by using physicians and nurses, measured in days, as well as other services:

Q(D,N,T) = output of inpatient care (measured in inpatient days).

In the above notation, Q is the amount of output measured by total number of days hospital stays; D is the total number of physician-days; N is the total number of nurse-days; and T is the total units of other services In the current market, the average physician salary is about $700 per day; the average salary of nurses is $200 per day; and the average daily cost of providing other services (e.g. lab tests, etc), including maintain beds, is $300. Throughout this exercise, assume the total number of beds is fixed, and thus, it will NOT be part of your consideration.

A. If the hospital is already running efficiently right now (i.e. with minimum cost) and providing 30,000 inpatient-days per year, what would be the ratio(s) of marginal products of the three inputs? (Hint, you do not need to know the actual inputs to answer this question.)

B. As the chief operating officer, you have proposed to increase the capacity of the hospital to provide 40,000 inpatient-days per year, and you believe there is sufficient demand for this and the hospital has enough beds. However, within the next year, it will be difficult to add new physicians. If you want to reach this new goal by the end of next year, what would be the ratio(s) of marginal products of the three inputs at the new production level? (Again, you don't need the exact units of input to answer this question. You can answer this in relation to part A and simply state what you expect to be the case.)

C. You also plan to start recruiting new doctors for the health system in the second year (right after the increased goal is reached), and expect to "stabilize" the increased level of capacity in 3 years. If everything goes as you planned, by the end of the third year, what should be the ratio(s) of marginal products of the three inputs at that point, with the expanded production?

D. Without calculating any specific numbers, comparing C to B, what would you expect in terms of the total cost of production after expansion in these two scenarios?