Suppose Audrey and Nicky are cousins with a destructive streak. Audrey is 1 year old and has a 10% chance of creating substantial damage in the next year, in which case the expected cost is $2000. Nicky is 2 years old and has a 5% chance of creating substantial damage in the next year, in which case the expected cost is $3000. In both cases their parents would be responsible for the damage, and their parents are risk averse
a) If the insurance company were able to differentiate based on age, and offered actuarially fair insurance, how much would they charge Audrey’s parents and Nicky’s parents for insurance?
b) Once Nicky’s parents have bought insurance, how is their behavior likely to change compared with when they did not have insurance? What is this called?.
c) Suppose Nicky’s parents have $10,000 of wealth initially, but their wealth increases to $20,000 due to a bequest. Find the effect of this change in initial wealth on their maximum willingness to pay for insurance if their utility function is where c is their total wealth.