$7\mathrm{.}5.$ Bay Pines Medical Center estimates that a capitated population of

$50,000$ would have the following base case utilization and total cost

characteristics:

In addition to medical costs, Bay Pines allocates $10$ percent of

the total premium $($total capitated revenue$)$ for administration$/$

reserves.

a$.$ What is the PMPM rate that Bay Pines must set to cover medical

costs plus administrative expenses?

b$.$ What would be the rate if a utilization management program

were to reduce utilization within each patient service category by

$10$ percent? By $20$ percent?

c$.$ Return to the initial base case utilization assumption. What rate

would be set if the average cost on each service were reduced by

$10$ percent?

d$.$ Assume that both utilization and cost reductions were made.

What would the premium hes