The monthly demand curve for playing tennis at a particular club is given by the following equation: *P*_{Tennis Match} = 9 − 0.20 × *Q*_{Tennis 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:

- $62.50.
- $162.50.
- $40.00.

Solution

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

*Q*_{Tennis Match }= 45 − 5.0 × *P*_{Tennis 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??