A monopolist sells to two consumer groups, students and non-students. Demand for students: Q =...
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.
Homework Answers
Market for students
Profit = revenue - cost
πstudents = (p - c)q
= (p - 20)(500 - 0.5p)
= 500p - 1000 - 0.5p^2 + 10p
= 510p - 0.5p^2 - 1000
Profit is maximum when π'(p) = 0
510 - p = 0
p = $510
q = 500 - 510/2 = 245 units
Hence, profit-maximizing price/quantity combination in market for students is P = $510 and Q = 245 units
Market for non students
Profit = revenue - cost
πnon-students = (p - c)q
= (p - 20)(750 - 2p)
= 750p - 1500 - 2p^2 + 40p
= 790p - 2p^2 - 1500
Profit is maximum when π'(p) = 0
790 - 4p = 0
p = $197.50
q = 750 - 197.50*2 = 355 units
Hence, profit-maximizing price/quantity combination in market for non students is P = $197.50 and Q = 355 units
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A monopolist sells to
two consumer groups, students and non-students.
Demand
for students: Q =...
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