A private clinic offers optional MRI scans with two levels of service speed: urgent and routine.

Both levels provide equally good medical information; they differ only in their speed. Urgent

scans are given priority for scheduling, so they are guaranteed to be performed within one week

of the patient's request; by contrast, routine scans are only guaranteed to be performed within

one month of the request. The clinic can serve up to 40 patients per week.

The clinic believes there are three main categories of patients.

Premium patients are willing to pay up to $1000 to get a scan done within one week, or

$500 for scans done within one month. 5 potential patients per week are in this category.

Professional patients are willing to pay $600 for scans within one week or $450 for scans

within one month. 15 potential patients per week are in this category.

Ordinary patients are willing to pay $240 for scans within one week or $210 for scans

within one month. 20 potential patients per week are in this category.

The clinic wants to maximize its weekly revenue but does not know the category of any

individual patient. So, it plans to charge different prices for different service speeds. Questions

Treat this situation as a sequential-move game that you need to model, analyze, and interpret.

The clinic moves first by choosing the prices to charge for urgent and routine services. Nature

moves second by determining which category of patient contacts the clinic. Patients move third

by deciding whether to use the urgent service, the routine service, or neither service.

1. Suppose the clinic only offers the routine service level. What would be the one best price to

charge, who would use the service, and what would be the clinic's weekly revenue? (Hint: You

can solve this "warm-up" question by careful thinking, or by defining one DV and 3 PCs.)

2. Suppose the clinic wants premium patients to use the urgent service, professional patients to

use the routine service, and ordinary patients to not use these services at all. What two prices

should it charge, and what would be its average weekly revenue? (Hint: You will need to define

2 DVs, 2 PCs, and 2 ICCs for this question.)