Find the price of actuarially fair insurance

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Reference no: EM13198989

Although self-employed workers have the option to purchase private health insurance, many do not, due to adverse selection. Suppose half the population is healthy and half is unhealthy. The cost of getting sick is $1000 for the healthy and $10,000 for the unhealthy. An individual becomes sick with probability 0.4, regardless of health. The utility of wealth is U(Y) = Y^0.5 for everyone. Although an individual knows whether he is healthy or not, the insurance company does not. Everyone is offered the same insurance premium. Assume insurance companies must make zero expected profits.
a. Find the premium corresponding to actuarially fair insurance when everyone purchases insurance. Is it different from the price an insurance company that makes zero expected profits offers?
b. If the price determined in a. is offered to the healthy people, do they buy insurance? Explain.
c. Find the price of actuarially fair insurance if only unhealthy people purchase insurance.
d. If the price determined in part c. is offered to them, do unhealthy people buy insurance? Explain.
e. Given your analysis above, what happens in the market for insurance? In particular, since each person decides whether to purchase insurance or not, find the price of insurance and who buys it.

Reference no: EM13198989

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