Question

In: Economics

Susan is a self-employed consultant, earning $80,000 annually. She does not have health insurance but knows...

Susan is a self-employed consultant, earning $80,000 annually. She does not have health insurance but knows that, in a given year, there is a 5 percent probability she will develop a serious illness. If so, she could expect medical bills to be as high as $25,000. Susan derives utility from her income according to the following formula:

U = Y^(0.3), (i.e. Y raised to the 0.3 power), where Y is annual income.

a) What is Susan's expected utility?

b) What is her maximum willingness to pay for health insurance?

Solutions

Expert Solution

a)

Probability of illness=p=0.05

Income in case of illness=Yi=80000-25000=$55000

Utility in case of illness=U(55000)=Y0.3=550000.3=26.43071

Probability of no illness=1-p=1-0.05=0.95

Income in case of no illness=Yn=$80000

Utility in case of no illness=U(80000)=Y0.3=800000.3=29.57515

Expected Utility=p*U(55000)+(1-p)*U(80000)

Expected Utility=0.05*26.43071+0.95*29.57515=29.41793 utils

b)

Utility in case Susan is willing to pay a maximum of $X towards insurance=U(80000-X)

We know that in order to be indifferent

Expected Utility in case of insurance=Utility in case of insurance

U(80000-X)=29.41793

(80000-X)0.3=29.417928

80000-X=78591.14

X=80000-78591.14=$1408.86

Maximum willingness to pay for insurance=$1408.86

Rahul Sunny answered 2 years ago
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