A massage parlor recognizes that it serves two different types of customers: old

Question

A massage parlor recognizes that it serves two different types of customers: old people and young people, and that old people have demand massages given by Qold (Pold) = 60 ? P old , while young people have demand for massages given by Q young (P young) = 120 ? P young , where Q group is the demand for massages for people in that group, and P group is the price charged to people in that group. The massage parlor’ s cost function is given by Tc(Q) = 20Q , regardless of whether the massage is sold to an old person or a young person. Assume that the massage parlor can verify whether a person is old or young by checking their ID and defining “old” as anyone over 65 years of age.
11. What price will the massage parlor charge to old people? 12. What price will the massage parlor charge to young people?

Explanation / Answer

MC = dTC/dQ = 20

In presence of correct segmentation, profit is maximized when MRold = MC and MRyoung = MC.

For old segment,

Qold = 60 - Pold

Pold = 60 - Qold

Total revenue (TR) = Pold x Qold = 60Qold - Qold2

MRold = dTR/dQold = 60 - 2Qold

Equating with MC,

60 - 2Qold = 20

2Qold = 40

Qold = 20

Pold = 60 - 20 = 40

For young segment,

Qyoung = 120 - Pyoung

Pyoung = 120 - Qyoung

Total revenue (TR) = Pyoung x Qyoung = 120Qyoung - Qyoung2

MRyoung = dTR/dQyoung = 120 - 2Qyoung

Equating with MC,

120 - 2Qyoung = 20

2Qyoung = 100

Qyoung = 50

Pyoung = 120 - 50 = 70

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