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WELLESLEY COLLEGE DEPARTMENT OF ECONOMICS ECONOMICS 201-03 JOHNSON Answers to Problem Set #9 1. 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 have demand where Q 1 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. a. .Suppose that to maintain a "professional" atmosphere, you want to limit membership to serious players. How should you set the annual 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 fee, T, equal to the total consumer surplus ofserious players. With individual demands of Q1 = 10 . P, individual consumer surplus is equal to: (0.5)(10 . 0)(10 . 0) = $50, or (50)(52) = $2600 per year. An 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 11: = (50)(1,000) - 10,000 = $40,000. b. 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: T= (Q2 - 0)(16 -P)(l/2), Q2 =4 - (l/4)P, or T= (1/2)(4 - (1I4)P)(l6 - P) = 32 - 4P + P/8.
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- - Entry fees for all players would be 2000(32 - 4P + p2/8). Revenues from court fees equals P(QI + Q2) = P[1000(lO - P) + 1000(4 - P/4)] = 14,000P - 1250p2. Then total revenue = TR = 64,000 - 6000P - 1000p2. ,'-'\ L;; ~ 1 l[ t~~~ ~~o-\s> l'Cl 'M~ \ ~\)e.- 1\/ S~" - ~~ ? '0\ -- - bOIlC> - 211~ \' ~ "tl , , p? ~l>%~llll ~"3 7'h.t'] Total revenue is equal to $73,000. Total cost is equal to ftxed costs of$lO,OOO. So proftt is $63,000 per week, which is greater than the $40,000 when only serious players become members. c. Suppose that over the years young, upwardly mobile professionals move to your community, all of whom are serious players. You believe there are now 3,000 serious players and 1,000 occasional players. Would it still be profitable to cater to the occasional player? What would be the profit-maximizing annual dues and court fees? What would profits be per week? An entry fee of $50 per week would attract only serious players. With 3,000 serious
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This note was uploaded on 06/15/2010 for the course ECON 201 taught by Professor Johnson during the Fall '08 term at Wellesley College.

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