3. An investor with a total wealth of $100 is faced with the following opportunities. First, he may invest $100 now and receive $144 if there are good times, but receive $64 if there are bad times. The investor estimates that good times happen with 50% probability.He can also buy an investor newsletter whether good times or bad times with occur.

(a) Draw the decision tree that illustrates the options available to the investor and the payoffs to the different options. Define P as the price of the newsletter.

(b) If the investor is risk-neutral with U(M) = M, where M is income, how much would he be willing to pay for the subscription to the newsletter?

(c) If the investor is risk-averse with utility U(M) = M0.5 , where M is income, how much would this investor be willing to pay for the subscription to the newsletter?

(d) Suppose that the owner of the newsletter estimates that there are 75 risk-averse investors like those of part (c) and 25 investors like those of part(b). If it costs zero to produce the newsletter, how should the newsletter be priced assuming (i) that the owner wishes to maximize the profits of the news letter and (ii) that this is the only newsletter available to investors.