question 1, Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U' > 0) and (U'' < 0).

a, Draw a utility function in U- I space that fits this description.

b, Explain the connection between U'' and risk aversion.

question 2, Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I and is concave (in other words, our basic assumptions throughout this chapter). Let IS = 0 be this person's income if he is sick, let IH > 0 be his income if he is healthy, let p be his probability of being sick, let E[I] be expected income, and let E[U] be his expected utility when he has no insurance.

a, Write down algebraic expressions for both E[I] and E[U] in terms of the other parameters of the model

question 3, Health insurance is normally seen as a good that is most valuable to sick people, since health expenditures are highest for the sick. Yet, in the basic insurance model discussed in this chapter, actuarially-fair health insurance is worth nothing to people who are certain to become sick

(p = 1). Why does the standard model produce this result? How is this different from the way real-world insurance markets work?