Question

1. We calculate the total welfare of having health insurance in one case. Suppose the price of hospitalization (i.e. impatient care) is p=500, and suppose the demand function for hospitalization with no insurance is written as q= -0.01p+6, where q is quantity and p is price of hospitalization. One illness might occur with probability of f (=0.4). Suppose one obtains health insurance with a coinsurance rate of 0.2 (no deductible, no stop-loss).

   1. 1) Without health insurance, what is the expected number of hospitalizations?

   2. 2) With health insurance, what is the expected number of hospitalizations?

   3. 3) What is the welfare loss form moral hazard?

   4. 4) What is the expected benefit to be paid by insurance company?

   5. 5) Suppose the loading fee is 20%. What is the insurance premium?

   6. 6) Suppose the risk premium for this risk is $300. How much is the consumer

      willing to pay for this insurance policy?

   7. 7) What is the gain for the consumer?

   8. 8) What is total net welfare (where the welfare gain is the risk reduction, and the welfare cost is moral hazard)? Is there a total net welfare gain or loss?

Answer 1

As per the given problem,

Price of hospitalization (P) = 500

Demand function for hospitalization without insurance is

q= -0.01P +6

this implies if the patient is not covered by health insurance and the illness occurs then q= 1 or else with no illness q=0.

The probability of getting the illnes is 40% and not getting the illness is 60%.

1. Therefore without insurance Expected no. of hospitalizations is -

E( q) = 40% of 1 + 60% of 0

or E(q) = 0.4

2. Now , if health insurance is taken then 20% or 0.2 (coinsurance rate)of the total medical bills has to be borne by the patient and the remaining 80% will be compensated by insurance program.

So assuming there is no insurance premium , the price paid by the patient in case of illness will be 20% of 500 = 100.

Therefore q = (-0.01) × 100 +6

or, q = 5.

Expected no. of hospitalizations will be -

E(q) = 40% of 5 + 60% of 0 = 2

3. When price of healthcare is reduced per patient due to insurance coverage then additional no. of healthcare is purchased. This is Moral hazard in health insurance markets.

Here in case of illness

Without insurance , cost of healthcare to patient = 1×500= 500

With insurance, and presence of coinsurance, cost of healthcare=5×100= 500

Therefore welfare loss from moral hazard is 500 -500=0.

4. In case of illness benefits paid by insurance company per hospitalization is = 80%of 500= 400

Without illness, benefits paid is 0.

with insurance, no. of hospitalizations (q) = 5

Therefore expected benefits is

= 40% of 5 × 400 + 60% of 5 ×0

= 800