2. You are deciding whether or not to purchase insurance. Your income is $100,000 and the chance of you getting sick is 30%. The insurance company is offering you a coinsurance rate of 0.15 and the utility that you get from your disposable income is U = √Y. If you get sick, your medical bills add up to $80,000. Assume that the insurance company charges the actuarially fair premium, and assume that you would purchase the same amount of medical care whether you are insured or not (i.e. M³ = M¹ = M*). Economic theory predicts that you will purchase insurance if the expected gain in utility from receiving the insurance payout when you are sick is greater than the expected loss in utility from paying the premium and remaining healthy. a. Using an expected utility diagram, show your decision process regarding whether to buy insurance or not. Calculate and then show on the diagram the following: i. Disposable income if you remain healthy and do not purchase insurance Disposable income if you are healthy and have purchased insurance iii. Disposable income if you become ill and have purchased insurance ii.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2. You are deciding whether or not to purchase insurance. Your income is $100,000 and the chance of
you getting sick is 30%. The insurance company is offering you a coinsurance rate of 0.15 and the
utility that you get from your disposable income is U = VY. If you get sick, your medical bills add up
to $80,000. Assume that the insurance company charges the actuarially fair premium, and assume that
you would purchase the same amount of medical care whether you are insured or not (i.e. Mi = M¹ =
M*). Economic theory predicts that you will purchase insurance if the expected gain in utility from
receiving the insurance payout when you are sick is greater than the expected loss in utility from paying
the premium and remaining healthy.
a.
Using an expected utility diagram, show your decision process regarding whether to buy
insurance or not. Calculate and then show on the diagram the following:
i. Disposable income if you remain healthy and do not purchase insurance
ii.
Disposable income if you are healthy and have purchased insurance
iii. Disposable income if you become ill and have purchased insurance
iv. Disposable income if you become ill and have not purchased insurance
b. Calculate and then show on the diagram:
i. Utility if you remain healthy and have not purchased insurance
ii.
Utility if you are healthy and have purchased insurance
iii.
Utility if you become ill and have purchased insurance
iv. Utility if you become ill and have not purchased insurance
What is the expected decrease in your utility from buying insurance? What is the expected increase
in your utility from buying insurance?
d. Should you purchase insurance? Why or why not?
C.
Transcribed Image Text:2. You are deciding whether or not to purchase insurance. Your income is $100,000 and the chance of you getting sick is 30%. The insurance company is offering you a coinsurance rate of 0.15 and the utility that you get from your disposable income is U = VY. If you get sick, your medical bills add up to $80,000. Assume that the insurance company charges the actuarially fair premium, and assume that you would purchase the same amount of medical care whether you are insured or not (i.e. Mi = M¹ = M*). Economic theory predicts that you will purchase insurance if the expected gain in utility from receiving the insurance payout when you are sick is greater than the expected loss in utility from paying the premium and remaining healthy. a. Using an expected utility diagram, show your decision process regarding whether to buy insurance or not. Calculate and then show on the diagram the following: i. Disposable income if you remain healthy and do not purchase insurance ii. Disposable income if you are healthy and have purchased insurance iii. Disposable income if you become ill and have purchased insurance iv. Disposable income if you become ill and have not purchased insurance b. Calculate and then show on the diagram: i. Utility if you remain healthy and have not purchased insurance ii. Utility if you are healthy and have purchased insurance iii. Utility if you become ill and have purchased insurance iv. Utility if you become ill and have not purchased insurance What is the expected decrease in your utility from buying insurance? What is the expected increase in your utility from buying insurance? d. Should you purchase insurance? Why or why not? C.
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