1. a. Suppose you are a risk adverse individual who is sick with probability 20%. You get income I_H when healthy and income I_S when sick. On a graph draw your utility function. On the axes mark income when sick and healthy and utility when sick and healthy.

b. On the graph in Part A illustrate your expected income and expected utility.

c. On the same graph indicate how much better off insurance could make you.

d. On the same graph indicate how much you would be willing to pay for full insurance. (Indicate the size of the premium, not just the insurance company's profit.)

e. Suppose you are offered an actuarially fair, partial insurance contract. Write a single equation for r in terms of probability of sickness and your two incomes.

f.Suppose that instead you are offered two other contracts. One where the insurance is full but unfair. And a second where the insurance is fair but partial.You find that you prefer the fair but partial contract. Illustrate this on a new graph.