Suppose individuals have utility function given by U(W)=W (Utility is equal to the square root of Wealth) and is thinking about buying health insurance. Individuals start with a wealth of $100 and face a 20% probability of getting ill. If they do get ill, they suffer losses $36. Suppose there is an insurance company that is willing to offer full insurance to the consumer (they will cover all the losses from illness if the consumer does gets ill).

Now however there happens to exist high risk individuals in the community that the insurance company did not know existed. They have the same exact utility function as the previous consumers but have a much higher probability of an accident. These higher risk individuals have a 50% probability of having an accident. There is still a $36 loss to the consumer if an accident occurs.

c) (10 points) Would the high-risk person want to buy the contract? If they do, will the insurance company lose money for each high-risk person buying it? (recall that they made money when low risk people purchased the contract).

d) (20 points) Use the graph structure (with Wealth if there is an accident on the vertical axis and Wealth without an accident on the horizontal axis) to show why the high-risk person would be so attracted to this contract (that they get on a higher indifference curve when buying this insurance contract versus not buying insurance.

e) (10 points) Now suppose the insurance company realizes that they are losing lots of money because there are two types of consumers but still cannot determine which consumers are high-risk and which consumers are low-risk. Explain in words how the insurance company is likely to respond to this situation.