Suppose that there are only three types of consumers and consider a one period insurance choice problem in which there is only one health plan, and it offers full insurance.

Expected cost to the insurer

Healthy, Low cost (L): $1000

Medium Cost sick (M): $3000

High Cost (H): $5000

b) Assume an actuarial fair insurance is charged, and that each type is risk neutral and hence only values health care spending at its expected cost to the health plan

What will happen if the health plan offers to insure the full population at the actuarially fair premium and consumers are allowed to not buy insurance? What will be the market equilibrium if only full insurance is allowed.

c) Now assume that consumers are risk averse, and are willing to pay 50% more than the expected value of their expected health insurance cost as the premium. Calculate the willingness to pay for insurance for each of these three types of consumers.

What happens in this scenario if a health plan attempts to offer insurance at an actuarially fair premium? What is the equilibrium.

d) Now assume that in addition to having risk averse consumers, there are administrative costs equal to 20% of the expected costs. (This is a typical rate for small plans in the US.) In this scenario, the health plan is not willing to offer actuarially fair insurance, but instead will add these costs onto the premium offer. Note that this administrative cost/profit does not affect the value of the insurance to consumers, only affects premiums.

What happens in this scenario with risk averse consumers? What is the equilibrium.

e) Continuing to assume administrative costs, how much of a penalty (or tax) on those not buying insurance will the government have to charge in order to make all three of the risk averse groups willing to buy insurance and result in an equilibrium in which everyone is insured?

f) Comment on how this problem is related to the uninsurance problem in the US?