唉，楼主应该把整到题目传上来的。
刚刚翻了一下英文版的微观（手头没有中文的），发现这道题有三个小问，楼主问的是第一小问，我把英文版的题目抄上来吧。
Question: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 Q1=10-P,where Q1 is crout hours per week and P is the fee per hour for each individual player.
There are also "occasional" players with demand Q2=4-0.25P
Assume that there are 1000 players of each type.Because you have plenty pf courts,the marginal cost of time is zero.You have fixed costs of 10,000 doisllars per week.Serious and occasional players look alike,so you must charge them the same prices.Soppose that to maintain a "professional" atmosphere,you want to limit membership to serious players.How should you set the annual membership dues and courts fees(assume 52 weeks per year) to maximize profits,keeoing in mind the constraint that only serious players choose to join?What would profits be(pre week)?
OH,楼主说了是第二问，我看漏了。。。。
第二问(接so you must charge them the same prices)：A friend tells you that you could make greater profits by encouraging both types of players to join.Is your friend right?What annual dues and court fees woud maxmize weekly profits?What would these profits be?
答案和解析也传上来吧，没详细看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, T, is equal to the consumer surplus remaining after the court fee is assessed:
T = (Q2 – 0)(16 – P)(1/2),
where
Q2 = 4 – (1/4)P, or T = (1/2)(4 – (1/4)P)(16 – P) = 32 – 4P + P2/8.
Entry fees for all players would be
2000(32 – 4P + P2/8).
Revenues from court fees equals
P(Q1 + Q2) = P[1000(10 – P) + 1000(4 – P/4)] = 14,000P – 1250P2.
Then total revenue = TR = 64,000 – 6000P – 1000P2.
Marginal cost is zero and marginal revenue is given by the slope of the total revenue curve:
∆TR/∆P = 6000 – 2000P.
Equating marginal revenue and marginal cost implies a price of $3.00 per hour. Total revenue is equal to $73,000. Total cost is equal to fixed costs of $10,000. So profit is $63,000 per week, which is greater than the $40,000 when only serious players become members.
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