Suppose there are 10,000 individuals facing an identical risk of illness (say 10%). If fell ill, without insurance, an individual is expected to incur $20,000 in health care expenditures. If they are risk averse, each would prefer to pay a $2000 premium and be compensated in case they fall ill. Ignoring administrative costs, an insurance agency would break-even charging each individual a premium of $2000. But suppose that, once they have full insurance coverage and no longer have to pay any out-of pocket health care costs, each of those who
fall ill consume $25,000 in health care.

a) Did the insurer make any profit? Why or Why not?

b) If, anticipating this behavioural change, the insurer charges a premium of $2500. Would it be profitable for the insurer? Why or Why not?

c) Instead of each of the 10,000 individuals facing an identical risk of illness (10%), suppose that for one-quarter of them the risk of illness is 5%, for one quarter the risk is 15%, and for one-half it remains 10%. The total expected losses remain $20 million. Suppose that the insurer still charges everyone the same premium of $2000 as he is not able to identify which individuals face a risk of 5%, 10%, and 15%. What will happen under such scenario?