Demand

[archived_user]

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

 

[archived_user]

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