This question is motivated by the example of non-linear pricing that we dis- cussed in class. A cellular phone company offers data plans and wants to determine a pricing strategy that maximizes revenue.

(a) Suppose that there are 100 consumers who all have the same preferences. An individual consumer's willingness to pay for the first GB of data is $20, for the second GB it is $15, for the third $5, and for the fourth and fifth it is $2. For simplicity we assume that nobody wants to use more than 5 GB.

First determine a price per unit (i.e., per GB of data) that maximizes the firm's revenue. Then suppose that the firm wants to charge a fixed fee, F, that allows unlimited data use. Determine the value F that maximizes the firm's revenue.