3. Second Degree Price Discrimination
Suppose that you are the CEO of Cellco, a wireless communications company located in
Valleytown. Since Valleytown is surrounded by mountains from all sides, only your company
can provide cellular phone service for the local consumers. Assume the cost of serving each
customer is 0.
There are two types of customers: business customers (B) who value each minute of
communication at $U_B = $0:15$, and personal use customers (P) who value each minute of
communication at $U_P = $0.10$. That is, customers of type B and P have the following utilities:
$U_B = 0.15q - p$
$U_P = 0.10q - p$
You do not know which customer is which type and would like to offer two different plans:
a business plan with $q_B = 1200$ included minutes for the at monthly fee $p_B$ and a personal
use plan with $q_P = 800$ included minutes for the at monthly fee $p_P$. You want each type of
customer to take the plan designed for this type. For simplicity, assume that your customers
never want extra minutes.
a. Your marketing manager proposes to charge business customers $p_B = $180$ and per-
sonal use customers $p_P = $80$. Will it work? Why or why not?
b. Can you find the profit-maximizing way to price the two plans, so that each type of
customer takes the plan designed for this type?
c. Flipping through the Valleytown Yellow Pages, you realize that you have $n_B = 100$
business customers. What is the minimum number of personal use customers that you need
to have in order to prefer to offer two different plans as opposed to just a business plan?
