The company Toilet Paper Empire (TPE) has a monopoly on toilet paper production. It offers its product in three different sizes: a small (S) package which contains 4 rolls, a medium (M) package which contains 8 rolls, and a large (L) package which contains 12 rolls.

There are two types of consumers in the market: type A consumers and type B consumers. The willingness-to-pay (WTP) for each type of toilet paper package for each type of consumer is detailed in the table below (in dollar amounts):

(a) Suppose that TPE adopts a linear pricing strategy, where the price per roll is$1, regardless of the size of the package. In other words, the S package is priced at$4, the M package is priced at$8, and the L package is priced at$12. What type of package will type A consumers buy? What type of package will type B consumers buy?

(b) If there are 500 type-A consumers in the economy, and 500 type-B consumers, how much will TPE's total sales be?

(c) Suppose that TPE now offers better prices for people buying larger packages of toilet paper. Specifically, while the price of the S package remains at$4, the M package will now be sold for$6.40 and the L package will now be sold for $9. How does this affect the consumption decisions of each type of consumer? How does it impact TPE's total revenues?

(d) TPE is considering discontinuing sales of the M packages, and selling only S or L packages (maintaining the same pricing strategy as in part c). If TPE's goal is to maximize their revenues, would this be a good strategy for them? Explain why or why not.