1) Suppose Al has an income of $25,000 and faces a 20% chance of having a serious medical problem that requires $15,000 worth of medical care. Al's utility function is U(1) = 10.5 [or square root of income]. There are two possible health insurance plans available. The first has 25% coinsurance and has a premium of $2500. The second plan has a $1500 deductible then 25% coinsurance and has a premium of $2200. Which plan would Al choose, if any? What is the AFP for each plan? What is the loading factor for each plan? (loading factor is % by which premium exceeds the AFP)
1) Suppose Al has an income of $25,000 and faces a 20% chance of having a serious medical problem that requires $15,000 worth of medical care. Al's utility function is U(1) = 10.5 [or square root of income]. There are two possible health insurance plans available. The first has 25% coinsurance and has a premium of $2500. The second plan has a $1500 deductible then 25% coinsurance and has a premium of $2200. Which plan would Al choose, if any? What is the AFP for each plan? What is the loading factor for each plan? (loading factor is % by which premium exceeds the AFP)
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.15P
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Question
![Insurance Example
o Initial income = $15,000
o Risk averse consumer faces 20% chance of losing
$10,000
o Actuarially fair insurance premium (AFP) for
covering this risk equals the expected value of
the loss (.2x$10,000 = $2000)
%3D
Question
1) Suppose Al has an income of $25,000 and faces a 20% chance of having a serious medical problem
that requires $15,000 worth of medical care. Al's utility function is U(I) = 10.5 [or square root of income].
There are two possible health insurance plans available. The first has 25% coinsurance and has a
premium of $2500. The second plan has a $1500 deductible then 25% coinsurance and has a premium of
$2200. Which plan would Al choose, if any?
What is the AFP for each plan?
What is the loading factor for each plan? (loading factor is % by which premium exceeds the AFP)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa27e55af-6dbc-4115-b58e-172510316635%2Fcb8c5ed0-539b-4b1c-8070-5f901442c332%2Ffss5r5a_processed.png&w=3840&q=75)
Transcribed Image Text:Insurance Example
o Initial income = $15,000
o Risk averse consumer faces 20% chance of losing
$10,000
o Actuarially fair insurance premium (AFP) for
covering this risk equals the expected value of
the loss (.2x$10,000 = $2000)
%3D
Question
1) Suppose Al has an income of $25,000 and faces a 20% chance of having a serious medical problem
that requires $15,000 worth of medical care. Al's utility function is U(I) = 10.5 [or square root of income].
There are two possible health insurance plans available. The first has 25% coinsurance and has a
premium of $2500. The second plan has a $1500 deductible then 25% coinsurance and has a premium of
$2200. Which plan would Al choose, if any?
What is the AFP for each plan?
What is the loading factor for each plan? (loading factor is % by which premium exceeds the AFP)
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