Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. She has estimated demand for her work to be:

where Q is the number of nose operations performed monthly and P is the price of a nose operation.

a. What is the inverse demand function for Dr. Williams' services?

b.What is the marginal revenue function?

The average variable cost function for reconstructive nose surgery is estimated to be:

where AVC is the average variable cost (measured in dollars), and Q is the number of operations per month. The doctor's fixed cost per month is $8,000.

c. If the doctor wishes to maximize her profit, how many nose operations should she perform each month?

d.What price should Dr. Williams charge to perform a nose operation?

e.How much profit does she earn each month?