In: Economics
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?
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