DEPARTMENT OF ECONOMICS
Answers to Problem Set #9
P&R, page 431, #10:
As the owner of the only tennis club in an isolated wealthy community, you must decide on
membership dues and fees for court time. There are two types of tennis players. "Serious" players
is court hours per week and P is the fee per hour for each individual player. There are also
"occasional" players with demand
Assume that there are 1,000 players of each type. Because you have plenty of courts, the marginal
cost of court time is zero. You have fixed costs of $10,000 per week. Serious and occasional players
look alike, so you must charge them the same prices.
.Suppose that to maintain a "professional" atmosphere, you want to limit membership to
serious players. How should you set the
membership dues and court fees (assume 52
weeks per year) to maximize profits, keeping in mind the constraint that only serious players
choose to join? What would profits be (per week)?
In order to limit membership to serious players, the club owner should charge an entry
equal to the total consumer surplus ofserious players. With individual demands
individual consumer surplus is equal to:
(0.5)(10 . 0)(10 . 0)
$2600 per year.
entry fee of $2600 maximizes profits by capturing all consumer surplus. The profit-
maximizing court fee is set to zero, because marginal cost is equal to zero. The entry fee
of $2600 is higher than the occasional players are willing to pay (higher than their
consumer surplus at a court fee of zero); therefore, this strategy will limit membership
to the serious player. Weekly profits would be
(50)(1,000) - 10,000
A friend tells you that you could make greater profits by encouraging both types of players to
join. Is the friend right? What annual dues and court fees would maximize weekly profits?
What would these profits be?
When there are two classes of customers, serious and occasional players, the club owner
maximizes profits by charging court fees above marginal cost and by setting the entry
fee (annual dues) equal to the remaining consumer surplus of the consumer with the
lesser demand, in this case, the occasional player. The entry fee,
is equal to the
consumer surplus remaining after the court fee is assessed:
= 32 -