Please only do part b.

2. Consider an individual with utility function u(w) = wa, a

2. Consider an individual with utility function u(w) = wa, a < 1. (a) Suppose this individual with initial wealth w risks losing D dollars given a health emergency, which occurs with probability p. One unit of insurance is offered at the actuarially fair price and pays out 1 dollar given a health emergency. Show that the consumer insures fully and derive expected utility and expected wealth. (b) Set up an equality that could be used to derive the individual's maximum willingness to pay for full insurance as compared to no insurance (you can leave willingness to pay as an implicit function). Then, determine how the individual's Arrow-Pratt measure of absolute risk aversion varies with a and explain what (if anything) Pratt's Theorem tells us about how willingness to pay for full insurance as compared to no insurance varies with a.