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Demand

The monthly demand curve for playing tennis at a particular club is given by the following equation: PTennis Match = 9 − 0.20 × QTennis Match. The club currently charges members $4.00 to play a match but is considering adding a membership fee. If the club continues to charge the same per play charge, the most that it will be able to charge as a membership fee is closest to:

  1. $62.50.
  2. $162.50.
  3. $40.00.

Solution

A is correct. On rearrangement, the demand function is:

QTennis Match = 45 − 5.0 × PTennis Match

The number of matches played per month at $4.00/match = 45 − 5.0 × 4.00 = 25

The y-intercept of the demand curve occurs when Q = 0: P = 9

The x-intercept of the demand curve occurs when P = 0: Q = 45

In addition to the per play charge, the club will be able to charge the consumer surplus: the area under the demand curve above the current price per match to a total of 25 matches: *0.5* × ($9.00 − $4.00) × 25 = $62.50.

This is illustrated in the diagram as triangle A.

EC_Fa_1.PNG

I did not understand from where did the 0.5 come??

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Right angled triangle

Solve for 

area

Area in right angled triangle

if a and b are two of the right sides of the triangle

in this case a= 5

b = 25

The Area os given by

Area = a*b /2

=5* 25 /2 = 62.5