Suppose individuals have a utility function given by () = . All individuals have the same utility function but have different probabilities of having an accident. Assume group 1 individuals start with a wealth of $100 and face a .5 probability of having an accident. Assume group 2 individuals start with a wealth of $100 and face a .2 probability of having an accident. If an accident occurs both groups will lose $36.

2 Suppose there were very few high-risk individuals in the economy but the insurance company was totally unaware that the high risk population existed. Assume also that there is only one insurance company (so no competition and thus the insurance company offers a full-insurance coverage contract to the low risk individuals and charges premiums to low risk consumers that extract their full willingness to pay for this contract). a) (10 points) What would the premium be to the low risk consumer? b) (10 points) How much would the insurance company make on each low-risk consumer? c) (10 points) How much would the insurance company lose on each high-risk consumer? d) (20 points) Show, using he diagram that we utilized in class (where the horizontal axis is wealth in the non-accident state and the vertical axis is wealth in the accident state) the iso-expected utility curve for the low and high risk person through the contract purchased by the low risk consumers. Include the EL line we used in class to show that the insurance company makes money on a low risk consumer.