Suppose that the demand equations of women and men for admission to basketball g

Question

Suppose that the demand equations of women and men for admission to basketball games are given by Pw=6 - (1/8000)qw where Pw is price charged to women and Pm= 10-(1/8000)qm where pm is the price charged to men qw, qm: quantity of tickets for women, men respectively. Moreover, suppose that the total seating capacity of Madison Square Garden is fixed at 56000.

If the ticket seller practice third degree price discrimination and would like to fill the garden

a. what price should men and women be charged for a ticket?

b. can you determine the elasticity of demand for each market?

Explanation / Answer

Pw = 6 - (1/8000)qw

Pm = 10 - (1/8000)qm

qw + qm = 56,000

Total revenue for women, TRw = Pw x qw = 6qw - (1/8000)qw2

Marginal revenue, MRw = dTRw / dqw = 6 - (1/4000)qw

Total revenue for men, TRm = Pm x qm = 10qm - (1/8000)qm2

Marginal revenue, MRm = dTRm / dqm = 10 - (1/4000)qm

(a) Third degree discrimination maximizes profits when MRw = MRm

6 - (1/4000)qw = 10 - (1/4000)qm

(1/4000)qm - [(1/4000) x (56,000 - qm] = 10 - 6 = 4 [Since qw = 56,000 - qm]

(1/4000)qm - 14,000 + (1/4000)qm = 4

(1/2000)qm = 14,004

qm = 14,004 x 2000 = 28,008,000

NOTE: This answer cannot be correct because maximum capcity is fixed at 56,000. Please cross-check your data (demand functions for Pw & Pm). Incorrect demand functions will give wrong results as this.

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