Question

3. Cost Minimization and Input Substitution

Monique just started managing a primary care center that currently employs both physicians and nurses. The current market salary of a nurse is $65,000 and the current market salary of a physician is $195,000. Assume the center’s goal is to minimize costs.

a) If the center is paying its staff the market salaries, what should be true about the rate at which physicians and nurses can substitute for one another in the production of health care at the center (in order for the center to be using the cost-minimizing combination of physicians and nurses)?

b) Monique conducts a study using the center’s own data and finds that nurse-led care is comparable (in terms of patient satisfaction, health outcomes, etc.) to physician-led care. Therefore, she concludes that, given the current staff, one physician can substitute for one nurse at the clinic. She sets out to use this information to adjust the ratio of nurses and physicians at the center. What should she do? Explain.

Answer 1

A. For the centre to be using cost minimizing combination of physicians and nurses, the rate of substitution between physicians and nurse should be equal to the ratio of salary paid to physians and nurses.

The rate of substitution between physicians and nurses = Marginal product of physicians(MPp) /Marginal product of nurse(MPn)

Ratio of salary to physicians and nurses = Salary of physicians /salary of nurses = 195,000/65,000 = 3

Thus, rate of substitution between physicians and nurses =3.

This means that 1 physician can substitute for 3 nurses.

B. If Monique believes that nurses and physicians are perfectly substitutable, that is one physician can substitute for one nurse at hospital. It means that her production function is of kind: Q(P, N) = P+ N.

Thus, she should use the input(here the doctors or nurses) which is cheaper. Since nurses are cheaper/less paid than physicians, she should fire all physicians and employ only nurses.