$3-23$ In Problem $3-22,$ you helped Allen Young determine the best investment strategy. Now, Allen is thinking about paying for a stock market newsletter. A friend of Allen said that these types of letters could predict very accurately whether the market would be good, fair, or poor. Then, based on these predictions, Allen could make better investment decisions.

a$.$ What is the most that Allen would be willing to pay for a newsletter?

b$.$ Allen now believes that a good market will give a return of only $11\%$ instead of $14\%.$ Will this information change the amount that Allen would be willing to pay for the newsletter? If your answer is yes, determine the most that Allen would be willing to pay, given this new information.