Question

Textbook Exercise # 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 Q 12-P each individual player. There are also "occasional" players with demand where Q, is court hours per week and P is the fee per hour Q2 4-0.25P Assume that there are 1,000 players of each type. Because you have plenty of courts, the marginal cost of court time is S0. You have fixed costs of $12,000 per week. Serious and occasional players look alike, so you must charge them the same prices. a. Suppose f be fne wk n i b os players. How should you set the annual membership dues and court fees (assume S 2 weeks per year) to maximize profits, keeping in mind the constraint that only serious The annual membership fee is S The court fee is s Weekly profit is encouraging both types of players to join. Is your friend right? What annual dues and court fees would maximize weekly profits? What would these profits be? (round your answers b.A friend tells you that you could make greater profits b two decimal places) The annual membership fee is S The court fee is s Weekly profit is s

Answer 1

Solutron: Given Q1-P -4-0-2SP There players of Cach dype are 1000 Mc-to Fc = 2000 per Week profers fonal atnasphere praf TO maintaih a Calcolation: players in tHe cout) arallowed Cony Senou changed annual manbashipte CS actP =o Fo Courtee o, 1=18-o t 2 C C.S 7a wesfs MC-o

: Anual mombership fee is =48,Xs& 3-344 and courtPee = 0 wecly proft: Sourte ofrevenue entry frembevshipfe) players Cla0o *12FC Doo Senous - 1200D Cnourag ing bath dy pa af players t join n tte valwej art Now ce Set fhe entry fee yval fptte Gonfunex Suplus player ypeith cer demand whan two clasel of customerr are and oceas fon al players, Je club owner naxinxe the Profrt bcharg ng Coustfee above marghal costCH)

and by pelbing enty te CS oemainihg) So hare T QC16-P) ufere 2 -0.35p 05(4-0.35PC6-p) Theredare TOS = 32-up-t o- | 2572 total enty pees paid hy all playeyy cod be 2o0o T= 2000 ( 32 -4P+012p) Poop tasop2 Roverve from Goutfe eapal Pt0001-t1000 1a000p-o00p + yo0op PCto0o tto002) asop 16000P-asop 2 Tutal evenue TR D+

Pooof280p 64000- 6000-12p2 Guo008000p-loo0p . <TR marg inal cost i'? 2em, 8o ce want do maximise tota evenue . qo do this drferentratng TR with Pnre go00 dp Z000P80UD 18 re get a1=12 - Cwe and 2=4-0.as)

TR 6u000 8ooo(4)loso(4) 000 Gu00o t 320o0 96000-16000 TR= 80 000 Predit go000 1000 qreader than Gecoorodt oten only players become ramor. Ore denau pretableto dightitnare :. Hence end is enlourag e both typel af- players tJoin