Aunt Jane\'s Fitness Center is planning to utilize price discrimination to set i
ID: 1245979 • Letter: A
Question
Aunt Jane's Fitness Center is planning to utilize price discrimination to set its family and corporate rates. For a family membership, it's estimated demand curve is Qf = 984 - 20Pf For the corporate market its estimated demand curve is Qc = 2,070 - 50Pc In both equations, Q represents the quantity of members and P represents the monthly membership fee. The center's weekly total cost is TC = 12,000 + 10Q, where Q is total number of members (Qf + Qc) a. With price discrimination, how many memberships will be sold in each market? b. What price will Aunt Jane's charge in each market? c. What will be the center's monthly profit?Explanation / Answer
Given
Qf= 984- 20 Pf ==> Pf= (984-Qf)/20
Qc= 2070 - 50Pc ==> Pc= (2070- Qc)/50
And TC= 12,000 +10(Qf+Qc)
Revenue from family membership will be = Qf.Pf = (984Qf - Qf2)/20
Revenue from corporate membership = Qc.Pc = (2070Qc- Qc2)/50
Profits = Total revenue - Total cost
= [(984Qf- Qf2)/20] + [(2070Qc - Qc2)/50] - 12,000 - 10(Qf+ Qc)
/Qf = [(984 - 2Qf)/20] - 10 = 0
Solving for Qf, we get
984 - 2Qf= 200
==> (984-200)/2 = Qf* = 392
/Qc = [(2070-2Qc)/50] - 10 = 0
Solvinf gor Qc, we get
2070 - 2Qc= 500
(2070-500)/2 = Qc* = 785
a) So 392 memberships will be solf in family market and 785 in corporate market
b) Pf = (984- Qf)/20 = (984- 392)/20 = $29.6
Pc = (2070-Qc)/50 = (2070-785)/50 = $25.7
c) Profits, = Pf.Qf + Pc.Qc - TC
=(29.6)(392) + (25.7)(785) - 12000 - 10(392 + 785)
= 11603.2 + 20174.5 - 12,000- 11770
= $8007.7
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.