Suppose in an economy there are two types of consumers, young and old. The

young people have a probability 0.25 of being sick and the old people has a prob-

ability of 0.45 of being sick. Both types have an income 100 in good state and 80

in bad state, because they have to pay for the hospitalization cost when they fall

ill. Suppose, an insurance company is offering a premium of 0.5 per dollar.

(a) (15 points) Show that the young people will not buy non-zero amount of

insurance (we assume that the young and the old agents cannot sell insurance).

(b) (15 points) Solve for the optimal insurance decision of the old people.