Question

With 5% probability, Jose will get sick and demand a quantity Q = 60 − 3P of medicine.

(a) If the unit price of medicine is $15, what quantity will Jose demand if he gets sick? How much will that cost him?

(b) From Jose’s perspective, what is his expected loss from sickness?

(c) Suppose Jose gets an insurance policy with 0% coinsurance. If he gets sick while he has this policy, what quantity of medicine will Jose demand? How much will that cost?

(d) From the insurance company’s perspective, what is the expected loss from Jose’s sickness?

(e) How likely is it that Jose will choose to purchase the insurance policy described in part (c)? Is there a different kind of insurance policy he may be more likely to purchase?

Answer 1

Given, Qty. Demand function of medicine => Qd = 60 - 3P

therefore, at Price = $ 15 , Qty. Demand of Medicine = 60 - 30(15) = 15 units.

and, so, Total Cost = Qty. purchased x Price per unit medicine

= 15 x 15 = $ 225.

Now, Expected loss from sickness = Probability of getting sick x Total Cost

= 0.05 x $ 225 = $ 11.25.

If Jose gets an insurance policy with 0% coinsurance and if he gets sick , then, it means he has to pay 0% of health care costs after deductible or full cost will be beared by the insurance irrespective of qty. demanded.

Therefore, in case of co-insurance the whole cost will beared by insurance company and so, loss of insurance company equals the amt. that it has to pay on the behalf of insured will $ 225.

There is Copay insurance policy that he may like to purchase in which an insured person will have to pay just a fixed amout of fees irrespective of the cost of that service availed.