In Equation 7.30 we showed that the amount an individual is willing to pay to avoid a fair gamble (h) is given by p = 0.5E(h ² ) r(W), where r(W) is the measure of absolute risk aversion at this person's initial level of wealth. In this problem we look at the size of this payment as a function of the size of the risk faced and this person's level of wealth.

a. Consider a fair gamble (v) of winning or losing $1, For this gamble, what is E (v ² )?

b. Now consider varying the gamble in part (a) by multiplying each prize by a positive constant k. Let h = kv. What is the value of E (h ² )?

c. Suppose this person has a logarithmic utility function U (W) = In W. What is a general expression for r (W)?

p=- KU" (W) U'(W) = kr(W).