A person's utility function is U = C1/2 . C is the amount of consumption they...
A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year.
a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium?
b. What is the most you would be willing to pay for insurance, given your utility function?
Homework Answers
a)
Actuarially fair insurance premium=Probability of loss (accident)*Loss Amount=0.02*30000=$600
Probability of accident=p=0.02
Probability of no accident=1-p=1-0.02=0.98
If insurance is bought at actuarially fair insurance premium
Utility in case of accident=U(40000-30000+30000-600)=U(39400)=394001/2=198.49 utils
Utility in case of no accident=U(40000-600)=U(39400)=394001/2=198.49 utils
Expected utility=p*U(39400)+(1-p)*U(39400)=0.02*198.49+0.98*198.49=198.49
b)
Probability of accident=p=0.02
Probability of no accident=1-p=1-0.02=0.98
Utility in case of accident=U(40000-30000)=U(10000)=100001/2=100 utils
Utility in case of no accident=U(40000)=U(40000)=400001/2=200 utils
Expected utility in case of no insurance=p*U(10000)+(1-p)*U(40000)
Expected utility in case of no insurance=0.02*100+0.98*200=198 utils
If agent is willing to pay a maximum of amount X towards insurance,
Expected utility in case of insurance=U(40000-X)
Put
Expected utility in case of insurance=expected utility in case of no insurance
U(40000-X)=198
(40000-X)1/2=198
40000-X=39204
X=40000-39204=$794
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