A monopolist sells to two consumer groups, students and non-students.

A monopolist sells to two consumer groups, students and non-students.

Demand for students: Q = 500 – 1/2P
Demand for non-students: Q = 750 – 2P
MC = 20

Find the profit-maximizing price/quantity combination in each market if the groups can be separated.

ANSWER

Students:
P = 1000 – 2Q
MR = 1000 – 4Q
Set MR = MC. 20 = 1000 – 4Q
245 = Q, P = $510

Non-students:
P = 375 – 1/2 Q
MR = 375 – Q
Set MR = MC. 20 = 375 – Q
355 = Q, P = $197.50