Question

Consider the following scenario: Joe’s initial income Y is $10,000. Joe experiences illness with a probability of 20%. Joe’s total medical costs associated with the illness are $1000.
A. What is the amount of medical coverage he should buy?
B. If Joe must pay a premium of $300 for insurance (i.e., 0% coinsurance rate, no deductible), what is the loading fee?

Answer 1

A. Joe’s expected loss is the difference between his income if he has insurance and his income if he does not.

His expected income without insurance is $9,800.

E(I) = 0.8*10 000 + 0.2*(10000-1000) = 8 000 + 1 800 = 9 800

His expected income with insurance is $10,000.

He has an expected loss of $200.

B. Expected value = (0.2)(1,000) + (0.8)(−300) = − $40.00