Question

Henni runs a hip hairdressing business. Two types of customers come to see Henni - women and men. The demand for haircuts by men is given by QDM = 10 - P, while the demand for haircuts by women is given by QDW = 102 - P. Assume that the marginal cost of haircuts is constant at $2 and is the same for both women and men.

If Henni operates as a monopolist in her neighborhood and can price discriminate between males and females.

1. What is social welfare under Henni's discriminatory regime?

Answer 1

With price discrimination, profit is maximized when MRm = MC and MRw = MC.

For men,

QDM = 10 - P

P = 10 - QDM

TR = P x QDM = 10QDM - QDM2

MR = dTR/dQDM = 10 - 2QDM

10 - 2QDM = 2

2QDM = 8

QDM = 4

P = 10 - 4 = 6

From demand function, when QDM = 0, P = 10 (vertical intercept)

Consumer surplus (CSM) = Area between demand curve and price = (1/2) x (10 - 6) x 4 = 2 x 4 = 8

Producer surplus (PSM) = Area between MC curve and price = (6 - 2) x 4 = 4 x 4 = 16

Total surplus (TSM) = CSM + PSM = 8 + 16 = 24

For women,

QDW = 102 - P

P = 102 - QDW

TR = P x QDW = 102QDW - QDW²

MR = dTR/dQDW = 102 - 2QDW

102 - 2QDW = 2

2QDW = 100

QDW = 50

P = 102 - 50 = 52

From demand function, when QDW = 0, P = 102 (vertical intercept)

Consumer surplus (CSW) = Area between demand curve and price = (1/2) x (102 - 52) x 50 = 25 x 50 = 1250

Producer surplus (PSW) = Area between MC curve and price = (52 - 2) x 50 = 25 x 50 = 1250

Total surplus (TSW) = CSW + PSW = 1250 + 1250 = 2500

Therefore,

Total social surplus = TSM + TSW = 24 + 2500 = 2524