Question

You are a researcher traveling overseas, where you face a 10% chance of contracting a serious, but treatable illness. Treatment for this illness is $40,000, and allows for a complete recovery. Your health insurance is provided by your employer, but your insurance will not cover treatment for this particular disease. You can purchase additional health insurance coverage that will cover the costs of treatment for this disease. This additional insurance will cost $5,000. Assume your annual income is $80,000. If you purchase this insurance, you will have $75,000 in wealth, and the utility of your income will be diminished from 100 to 98. If you do not purchase this insurance, your wealth will be reduced to $40,000, with a utility of 52. a. Using the formulas covered in the text, will you decide to purchase insurance? Why or why not? (SHOW YOUR CALCULATIONS.) b. If the cost of treatment were $10,000, reducing the utility of your wealth with insurance to 94, would you purchase insurance? Why or why not? (SHOW YOUR CALCULATIONS.) c. If the risk of the disease were 0.01 (1%), instead of 0.10 (10%), and the cost of insurance is $5,000, would you purchase insurance? Why or why not? (SHOW YOUR CALCULATIONS.)

Answer 1

a)

Let us first calculate the expected utility in case of no insurance.

Probability of illness=p=0.10

Probability of no illness=1-p=1-0.10=0.90

Wealth in case of illness=80000-40000=$40000

Wealth in case of no illness=80000-0=$80000

Given

U(80000)=100

U(40000)=52

U(75000)=98

Expected utility=p*U(40000)+(1-p)*U(80000)

Expected utility=0.10*52+0.90*100=95.20

In case of insurance expected utility is U(80000-5000)=U(75000)=98

Expected utility is higher in case of insurance. Researcher would go for insurance.

b)

If cost of insurance is $10,000

In case In case of insurance expected utility is U(80000-10000)=U(70000)=94

Expected utility is lower in case of insurance. Researcher would not go for insurance.

c)

Let us first calculate the expected utility in case of no insurance.

Probability of illness=p=0.01

Probability of no illness=1-p=1-0.01=0.99

Wealth in case of illness=80000-40000=$40000

Wealth in case of no illness=80000-0=$80000

Given

U(80000)=100

U(40000)=52

U(75000)=98

Expected utility=p*U(40000)+(1-p)*U(80000)

Expected utility=0.01*52+0.99*100=99.52

In case of insurance expected utility is U(80000-5000)=U(75000)=98

Expected utility is lower in case of insurance. Researcher would not go for insurance.