Question

You are a competitive athlete, and will earn $4,000,000 if you play for the entire season. If you are injured before the season starts, you will earn only $40,000. Your utility function is U = I n c o m e. There is a 5% probability that you will be injured, and a 95% probability that you will not be injured.

(a) What is your expected income for the year?

(b) What is your expected utility for the year?

(c) An insurance company offers you a policy that will fully insure your income. What is the maximum price you are willing to pay for this policy?

(d) A second insurance company offers you a policy that will partially compensate you, but not fully insure you. This second company offers a $3,000,000 payout in the event of an injury, and charges a fee of $40,000. If the first insurance company charges a fee of $100,000 for full insurance, which insurance policy do you buy? Why?

Answer 1

a) expected income is 95% of 400000

as there are 95% chances so on an average we get 95% that is 398000

b) expected ultility is also 398000

as utility = income

c)minimum price i would like to pay is $40000 as in injury he will be getting this in any case

d) above comparing both offers we will accept

first because

we get 400000 but paid 100000 therefore profit of 300000+40000 get after injury

but in second

we pay 40000 and get 300000 therefore profit of 260000+40000 grt on injury