Consider a person with constant relative risk aversion p.
(a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. Calculate the amount he would pay to avoid the gamble, for various values of p (say, between 0.5 and 40), and for x=100, x=1000, x=10,000 and x= 25000. For large gambles, do large values of p seem reasonable? What about small gambles?
(b) Suppose p > 1 and the person has wealth w. Suppose he is offered a gamble in which he loses x or wins y with equal probabilities. Show that he will reject the gamble no matter how large y is if p >= (log(0.5)+log(1-x/w))/log(1-x/w).
I'm not sure where to start with this. Am I solving for the risk premium and multiplying by w?
I know that for someone with CRRA utility u(w)= (1/(1-p))w^(1-p) and that an individual will pay pi(w) to avoid the gamble if u((1-pi)w)=E[u(1+epsilon tilda)w)]. But I'm not sure how to apply this information to solve the question. Any help is appreciated.