平狄克微经第六版习题求助~~~

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平狄克、鲁宾费尔德的《微观经济学》第六版（就是红皮的那本）第11章课后习题第10题第二问（P422），是一道关于两步收费的问题。已知“热衷”的网球手的需求为：Q=10-P，“偶尔为之”的网球手的需求为：Q=4-0.25P，Q为每周用场地的时间，两种网球手数量相同，问为使利润最大化网球场的会员费和场地费各是多少？
       这一问的答案是每周的场地费为3.75美元每小时，中间有一点不明白，他计算会员费T=（4-0.25P）*（10-P）/2，为什么是（10-P）而不是（16-P）呢？搞不懂，按16-P算出来场地费应该是3美元每小时。求助达人~~~

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关键词：习题求助 平狄克 利润最大化 微观经济学 鲁宾费尔德 求助 微观经济学 平狄克 两步收费

为什么是16-P呢？我没有他的书，只是做一个简单分析。

2# nlm0402
    你把两条需求曲线画出来，“偶尔为之”的网球手的需求曲线跟纵轴交点是16，所以我觉得入门费应该是“偶尔为之”的网球手的消费者剩余，算起来应该是用（16-P）而不是（10-P）

是楼主看错了吧。Q=10-P不是表示“偶尔为之”的，而是表示热衷的，Q=4-0.25P才是表示“偶尔为之”的。

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.

这里的答案场地费确实是3美元没错，用答案求导做出来的。

4# jafe002
没写错，确实是“热衷”的网球手需求为Q=10-P，“偶尔为之”的是Q=4-0.25P，虽然我很好奇后者的弹性为何更小……

8# jafe002
哇~~~太给力了~多谢了~为这个问题郁闷两天了~原来是我那本中文的答案错了！！！