Calculation of resulting income from full insurance.
Let's say you live in Montana and you like to ride mechanical bulls in bars on Friday nights. You estimate over next year there's a 4% probability you will incur medical bills of $20,000, which is equal to your salary as a philosophy professor. Let's assume there's a 96% chance that you won't be injured from flying off the bull over the course of a year. Suppose that your utility depends only on your consumption/income in either possible outcome.
(a) If you buy full insurance (b = D) at an actuarially fair premium (AFP), what would be your resulting income if you're injured?
(b) If you are not injured?
(c) If you buy partial insurance, can your resulting income ever be more when you're injured than when you're not injured?