Problem:

Let’s say you live in the Montana and you like to ride mechanical bulls in bars on Friday nights. You estimate which over the upcoming year there's a 4% probability you will acquire medical bills of $20,000, which is equivalent to your salary as a philosophy professor. Let’s suppose there's a 96% chance that you won’t be injured from flying off the bull over the course of year. Suppose also that your utility depends only on your consumption or income in either probable outcome.

Required:

a) If you buy full insurance (b = D) at the actuarially fair premium (AFP), what would be your resulting income if you're injured?

b) If you’re not injured?

c) If you purchase partial insurance, can your resulting income ever be more when you’re injured than when you’re not damaged?