Question

There is a 1 percent chance (0.01) that you will have a medical bill of $100,000; 19 percent chance (0.19) that you will have a medical bill of $10,000; 60 percent chance (0.6) that you will have a medical bill of $500; and 20 percent chance (0.2) that you will have a medical bill of $0.

A) What is your expected medical spending, without any insurance?

B) If you have complete insurance (i.e. zero deductible, zero copay), what is your expected out of pocket medical spending (EXCLUDING PREMIUM COST)? What is expected benefit (i.e. the expected value of the amount of money that the insurance company is going to PAY FOR YOU) you get from this insurance policy?

C) For the complete insurance policy above, will you be willing to pay a premium of $3712? Explain.

D) Now, assume you have an insurance policy with $5000 deductible, but still zero copay, what is the expected out of pocket medical spending (EXCLUDING PREMIUM COST)? What is the expected benefit you get from this insurance policy?

E) Now, assume the insurance policy in D) is sold at 116 percent (1.16 times) of the expected benefit, do you prefer this policy or the policy from B) with a premium of $3712? Explain.

Answer 1

a)

Expected medical spending is given by

E(X) = ΣΡ και X

E(x)=0.01*100000+0.19*10000+0.60*500+0.2*0=$3200

b)

In case of complete insurance,

Expected out of pocket medical spending=E(X)=0 (All is paid by insurance company)

Expected benefit=Savings of amount equal to expected cost without insurance=$3200

c)

A premium of $3712 will not be aceptable to a risk neutral person as it is higher than the expected medical expense.

A risk averse peson may pay the premium of higher than expected cost but that depends upon his preferences towards risk or say utility function. It is undeterminate if he will pay or not.

d)

Out of pocket expense in case of medical bills being $100000=$5000

Out of pocket expense in case of medical bills being $10000=$5000

Out of pocket expense in case of medical bills being $500=$500

Out of pocket expense in case of medical bills being $0=0

Expected out of pocket medical spending is given by

E(X) = ΣΡ και X

E(x)=0.01*5000+0.19*5000+0.60*500+0.2*0=$1300

Expected benefit=3200-1300=$1900

d)

Fair Premiun=expected benefit*116%=1900*116%=$2204

A premium of $3712 is much higher than $2204. I shall not prefer it.