A person's utility function is U = C1/2 . C is the amount of consumption they...

A person's utility function is U = C^1/2 . 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. What is their expected utility?

b. Calculate the actuarially fair insurance premium.

c. What would their expected utility be if they purchased the actuarially fair insurance premium?

Solutions

Expert Solution

U=C^1/2

In case of no insurance

Probability of accident=p=0.02

Consumption in case of accident=C=40000-30000=$10000

Utility in case of accident=U(10000)=10000^1/2=100 utils

Probability of no accident=1-p=1-0.02=0.98

Consumption in case of no accident=C=40000

Utility in case of no accident=U(40000)=40000^1/2=200 utils

Expected utility=p*U(10000)+(1-p)*U(40000)=0.02*100+0.98*200=198 utils

Actuarially fair insurance premium=Probability of accident*Loss in case of accident

Actuarially fair insurance premium=0.02*30000=$600

In case of insurance purchased at $600

Probability of accident=p=0.02

Consumption in case of accident=C=40000-30000+30000-600=$39400

Utility in case of accident=U(10000)=10000^1/2=198.49 utils

Probability of no accident=1-p=1-0.02=0.98

Consumption in case of no accident=C=40000-600=$39400

Utility in case of no accident=U(39400)=39400^1/2=198.49 utils

Expected utility=p*U(39400)+(1-p)*U(39400)=0.02*198.49+0.98*198.49=198.49 utils

Rahul Sunny answered 1 year ago

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