Question

The Mount Sunburn Athletic Club has two kinds of tennis players, Acers and Netters, in its membership. A typical Ace has a weekly demand for hours of QA = 6 − P .
A typical Netter has a weekly demand of QN = 3 − P/2.

The marginal cost of a court is zero and there are one thousand players of each type. If the MSAB charges the same price per hour regardless of who plays, what price should it charge if it wishes to maximize club revenue?

Answer 1

In MSAB,

Demand for Acer: QA = 6 - P ........................................................... (i)

Demand for Netter QN = 3 - P/2 .....................................................(ii)

MC = 0

Number of Players of Each Type = 1000

LET, QA + QN = Q

Therefore, from equation i and ii we have:

(6 - P) + (3 - P/2) = Q

   9 - 3P/2 = Q

   18 -3P = 2Q

   P = 6 - 2Q/3 ................................................... (iii)

Now, Revenue = PQ

Revenue = PQ = (6 - 2Q/3)Q

PQ = 6Q - 2Q²/3

Now, For maximizing the revenue, we differentiate the Revenue i.e. PQ with respect to Q

  

For maximization, we set

  

  

Now, Putting Q = 4.5 in equation (iii) we have,

  

  

  

Revenue maximizing Price is equal to 3