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) If the market cannot be segmented, then combine both the demand curve. i.e. aggregate demand curve. Therefore, qs+qa= 28-7p. ( it helps if u graph this out). The new demand curve is Q=28-7p. The monopoly quantity to produe is where marginal cost (2)= marginal revenue for Q. The marginal revenue curve,MRQ is twice steeper than the new demand curve Q. MRQ= 14- 7/2(p). At $2, the monopoly quantity to produce when the market is aggregated is 7 units. At 7 units, the uniform price is 3 dollars. b). If the club can segment the market and charge both groups at different price, then lets find each marginal revenue curves for both qs and qa. Qs= 18-5p. Therefore, MRQs= 9-5/2p. If it cost $2 to produce each drink, then MRQ= 4 units. At 4 units, the price to charge those under 25 years of age is 4= 18-5p. P= 2.80. Likewise, do the same for Qa. You will find that the mx profit quantity to produce is 3. At this quantity, the price to charge for those over 25 is $3.50.

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