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

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

Where did the 45 come from…

Solve for Q when P = 0.

How come we need to find the area for Triangle A? I understand that Triangle A is the consumer surplus, but can someone explain why we’re using the consumer surplus to determine how much to charge?

Because that’s the amount of additional value that consumers receive because the demand curve slopes downward and everyone is charged the same (equilibrium) price per match. You don’t want the members to enjoy that additional value; you want to capture it for yourself.

The tough part is that not every member will be willing to pay the same membership fee; the only way to capture the full value of the consumer surplus is through discriminatory pricing.