Question

A nightclub manager realizes that demand for drinks is more elastic among students and tries to determine the optimal pricing schedule. Specifically, he estimates that the demand functions are given by q1 = 30 − 6p1 for students and q2 = 24 − 4p2 for non-students. Assume that drinks cost the nightclub $2 each.

A. If the market cannot be segmented, what is the uniform monopoly price?

(a) $3.10 (b) $3.30 (c) $3.50 (d) $3.70 (e) $4.20

B. If the nightclub can charge according to whether or not the customer is a student but is limited to linear pricing, what price (per drink) should be set for students?

(a) $3.10 (b) $3.25 (c) $3.40 (d) $3.50 (e) $3.80

C. Under the same conditions of B, what price (per drink) should be set for non-students?

(a) $3.80 (b) $4.00 (c) $4.30 (d) $4.60 (e) $5.20

Answer 1

The correct answers of the questions are given below:-

1)
Uniform Monopoly Price is P= p1= p2

Aggredate Demand is Q= q1 + q2 =(30-6P) + (24-4P)

= 54-10P

Inverse demand is P= 54/10 - Q/10

Marginal revenue is MR= 54/10 - 2Q/10

MR=MC, that is 54/10 - 2Q/10 = 2

Q=17

Hence, P= 54/10-17/10

=37/10 = 3.7

And (d)$3.70

2)
Demand for students q1=30-6p1

p1=30/6-q1/6

If the club owner can price discriminate, he will equate marginal revenue and marginal cost for students

that is, 30/6-2(q1)/6=2

30-2(q1)= 12

q1=9

Hence p1 = 30/6-9/6

= 3.5

Ans (d) $3.50

3)
Demand for non students q2=24-4p2

p2=24/4-(q2)/4

If the club owner can price discriminate, he will equate marginal revenue and marginal cost for non students

that is, 24/4-2(q2)/4 = 2

24-2(q2) = 8

q2=8

Hence p2 = 24/4-8/4

= 4

Ans (b) $4.00

Therefore the correct choices are

Q1) Option D

Q2) Option D

Q3) Option B