Question

There are two types of potential members for a new gym—students and adults. The new gym owner would like to give students a discounted price in order to attract more students to her gym. The gym’s MC=4. Which of the following sets of demand curves for students (S) and adults (A) would allow the gym owner to engage in third-degree price discrimination and charge a lower price to the students?

Group of answer choices

None of the other answers is correct.

pa = 40 - 2qa, ps = 40 - 4qs

pa = 20 - 4qa,ps = 20 - 2qs

pa=20 - 2qa, ps = 36- 2qs

_{pa = 25 - 3qa, ps = 30 - 3qs}

None of the other answers is correct.

None of the other answers is correct.

Answer 1

None of the other answers is correct.

The first two functions give the same ticket price for both the adults and students, while the nestxt two give higher price for studens.

calculation:

For a monopolist, MC=MR for quantity; then plug in q in demand function for price.

option 1:

pa = 40 - 2qa, ps = 40 - 4qs
so, MR: pa = 40 - 4qa, ps = 40 - 8qs
MC = MR: 40 - 4qa = 4 , 40 - 8qs = 4
So, qa = 9; qs = 4.5; plugging in q in demand fuction:
40 - 2*9 = 22; 40 - 4*4.5 = 22

So, pa = 22; ps = 22

option 2:

pa = 20 - 4qa, ps = 20 - 2qs
so, MR: pa = 20 - 8qa, ps = 20 - 4qs
MC = MR: 20 - 8qa = 4 , 20 - 4qs = 4
So, qa = 2; qs = 4; plugging in q in demand fuction:
20 - 4*2 = 12; 40 - 2*4 = 12

So, pa = 12; ps = 12

option 3:

pa = 20 - 2qa, ps = 36 - 2qs
so, MR: pa = 20 - 4qa, ps = 36- 4qs
MC = MR: 20 - 4qa = 4 , 36 - 4qs = 4
So, qa = 4; qs = 8; plugging in q in demand fuction:
20 - 2*4 =12 ; 40 - 2*8 = 20

So, pa = 12; ps = 20

option 4:

pa = 25 - 3qa, ps = 30 - 3qs
so, MR: pa = 25 - 3qa, ps = 30 - 3qs
MC = MR: 25 - 6qa = 4 , 30 - 6qs = 4
So, qa = 3.5; qs = 4.67; plugging in q in demand fuction:
25 - 3*3.5 = 14.5 30 - 3*4.67 = 16

So, pa = 14.5; ps = 16

None of these allow lower ticket price for students.