The same the up-and-coming Vice President of Marketing at FW suggests that this “two-tiered pricing” is a great marketing strategy but wonders if it could be improved even more. Instead of charging the initial monopoly profit-maximizing price p⇤ and then charging the second price ˆp, why not plan in advance to choose two prices p1, p2: first charge the price p1, and sell as many units as possible at the price p1; then lower the price to p2 and sell as many more units as possible at the lower price? [Of course this marketing strategy would have to be kept secret; otherwise no one would buy at the price p1 but instead wait for the lower price p2.] If FW had adopted this strategy:

(a) For each pair of prices p1, p2, how many units would FW have sold at each price? (Remember that, when the price is lowered to p2, all the customers who were willing to pay p1 would have already done so and would not buy again.)

(b) For each pair of prices p1, p2, what would FW’s profit be?