A nightclub manager realizes that demand for drinks is more elastic among studen

Question

A nightclub manager realizes that demand for drinks is more elastic among students, and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demands:

Under 25: qs = 18 – 5p
Over 25: qa = 10 – 2p
The two age groups visit the night club in equal numbers on average. Assume that drinks cost the nightclub $2 each.

a) If the market cannot be segmented, what is the uniform monopoly price?
b) If the night club 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 each group?

Explanation / Answer

a. combine the two demand function into:
q=28-7p

since costs are a function of q, we change the demand function into a function of q.
p=-(q/7) +(28/7)

TR is given by
pq=-(q^2/7) +4q

then MR= -(2/7)q +4
setting this equal to MC we get q=7
substituting this into our demand function above we get
7=28-7p, from which it follows that p=3

b.

Here we calculate the profit maximizing level of p for both groups.

for students:

p=-(q/5) +(18/5)

MR=-(2/5)q+(18/5)

setting this equal to MC gives q=4

substituting this into our demand function above we get
4=18-5p, from which it follows that p=2.8

For older people:

p=-(q/2) +(10/2)

MR=-q+5

setting this equal to MC gives q=4

substituting this into our demand function above we get
4=10-2p, from which it follows that p=3

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