今天要和大家讨论的是一个关于靠脸吃饭的和靠能力吃饭的人应在多大年纪结婚的模型。

我们这里首先做以下简单假设:
1. 靠脸吃饭的人没有真才实学,或者说,我们在此讨论中姑且不考虑既有真才实学,同时还貌比潘安、赛貂蝉的人。
2. 靠能力吃饭的人相貌平平，或者说他或她的长相不能给自己带来任何的附加价值。我们不考虑既有事业,又很帅又幽默的男性或女性,因为其数量也很少,比如我。(床板儿大的砖头向我飞来@$!%#^#*&!$_*(@!)
3. 人的一生效用最大值100,假设靠脸吃饭的人之间无差异,靠能力吃饭的人之间也无差异。
各位亲爱的读者，如果你同意我以上的假设并且具备了基本的微积分知识，那么希望你能有耐心的读完本文。感谢您的配合。

基于以上假设,我们可以分别划出靠脸吃饭的人和靠能力吃饭的人的价值随年龄变化的曲线 U=f(y)。U为效用，Y为年龄。
 
由此图我们可以看出，靠脸吃饭的人的价值在18-24岁急速上升，26岁达到顶点，28岁后迅速下跌。而靠能力吃饭的人的价值则在22-30岁稳步上升，且升至最大值后下降缓慢。此理论非我独创，参见Rob Campbell (J.P.Morgan, Diversified Industrials Investment Banking) 的留言。（详见本文最下方的引文）

根据统计数据及线形回归，先做出两条平滑曲线：“靠脸吃饭”“靠能力吃饭”。
两条曲线相交于K点（28，78），其含义是靠能力吃饭的人在28岁时价值（财富及社会地位）等于靠脸吃饭的人在28岁的价值（美貌）。
好的，那么很多人会得出一个结论，靠能力吃饭的人和靠脸吃饭的人最适合结婚的年龄是在他们28岁那一年。因为他们的“价值”相等。
而现实中这种情况很少发生，为什么呢？根据Rob Campbell先生的留言我们可以清楚地明白，28岁的女性是一个贬值资产，而28岁的男性是一项升值资产。（很多女性看到这里又会心存不满，请见谅。本人坚持认为男女是平等的，男性中也存在大量靠脸吃饭的人，反之亦然。何况随着人口比例失衡，女权社会即将到来。）
至于靠脸吃饭的人是贬值资产，靠能力吃饭的人是增值资产这一论断我们也可以从该曲线在K点的切线斜率看出来：“靠能力吃饭”曲线在K点的斜率经测算为0.9，“靠脸吃饭”曲线在K点的斜率经测算为：-1.2。（计算方法由MATLAB进行线形回归得出曲线方程并求一阶倒数，过程繁琐在此不赘述。并且由于统计样本数量偏少，曲线图和函数事实上并不一致，因此暂不将原始数据和函数表达式公布）
之所以大多数人会犯以上错误（28岁的靠脸吃饭的人和靠能力吃饭的人结合），因为他们将该图形默认为了“数量-价格”曲线，而事实上，上图为“年龄-价值”曲线。
 “年龄-价值”不同于“数量-价格”曲线的最大之处在于后者必须在买卖双方给出相同的数量价格才能成交，而男女之间结婚显然并不要求年龄一样。

那么，究竟这两种人最适宜结婚的时间是何时呢？
根据我们之前的讨论，或许各位已经想到，那就是双方价值的增长速度——曲线切线的斜率——最大的时候，因为此时价值增值最快。
根据对曲线进行一阶求导以及根据中国大陆《婚姻法》对男女结婚年龄的限制，我们得出以下两条切线：
 
两条切线分别切两条曲线于P₁和P₂两点，且该两条曲线在该两点斜率相同。因此两类人最适合谈恋爱的年纪分别为22岁和25岁。
各位靠脸吃饭的朋友可能会有异议，此时你们价值约为76，而靠能力吃饭的人价值只有50。作为靠脸吃饭的你是否会心存不甘？
但请注意，Y=25时，“靠能力吃饭”曲线不仅有很高的增长速度（一阶倒数最大），更重要的是，此时该曲线的二阶倒数为零，也就是说，这是该曲线的一个拐点，该曲线速度将加速上升，即靠能力吃饭的人价值将加速升值。
而现实中的确存在大量的靠能力吃饭的人比靠脸吃饭的人配偶年龄稍大的现象，例如事业有成的男人和年轻小姑娘，再例如富婆和小白脸。这些现象与我们的模型吻合。

为了进一步说服各位朋友该模型的重要性和准确性,我将证明以下观点:
22岁的靠脸吃饭的朋友和25的靠能力吃饭的朋友谈恋爱并不吃亏,尽管该瞬间靠脸吃饭的人的价值大于男性靠能力吃饭的人.
证明过程请先看下图:
 
上图中,左边蓝色阴影部分面积S₁=∫[U(靠脸吃饭)-U(靠能力吃饭)]，也就是一个22岁靠脸吃饭的人在和25岁靠能力吃饭的人恋爱后，靠能力吃饭的人从靠脸吃饭的人那里得到的净价值，俗话称之为“占的便宜”。
而右边红色阴影部分面积S₂=∫[U(靠能力吃饭)-U(靠脸吃饭)]，即28岁后，原先的22岁靠脸吃饭的人从其原先25岁靠能力吃饭的人处得到的净价值。显然，S₂>S₁。各位靠脸吃饭的人总得为将来着想吧。

因此各位靠脸吃饭的朋友在一生最美好的时间中切莫因小失大,切莫过于自信,把握好自己的幸福.

由于本人时间有限，此模型暂告一段落。祝各位年轻读者早成眷属，白头偕老。

版权所有，欢迎转载
现实社会纷繁复杂，请各位切勿对号入座

                                               里奥.XU
                                                        2008/2/29 于松园

附录：Campbell先生及Pers小姐对话及读者评价
25 Year-Old Beauty Seeks Rich Banker

The following exchange took place on Craigslist - the investment banker's response is a classic!

'What am I doing wrong?

Okay, I’m tired of beating around the bush. I’m a beautiful (spectacularly beautiful) 25 year old girl. I’m articulate and classy. I’m not from New York. I’m looking to get married to a guy who makes at least half a million a year. I know how that sounds, but keep in mind that a million a year is middle class in New York City, so I don’t think I’m overreaching at all.

Are there any guys who make 500K or more on this board ? Any wives ? Could you send me some tips ? I dated a business man who made an average of around 200 - 250K. But that’s where I seem to hit a roadblock. $250,000 won’t get me to Central Park West. I know a woman in my yoga class who was married to an investment banker, and lives in Tribeca. She’s not as pretty as I am, nor is she a great genius. So what is she doing right ? How do I get to her level ?

Here are my questions specifically:

- Where do you single rich men hang out ? Give me specifics - bars, restaurants, gyms

- What are you looking for in a mate? Be honest guys, you won’t hurt my feelings

- Is there an age range I should be targeting ?

- Why are some of the women living lavish lifestyles on the Upper East Side so plain? I’ve seen really ‘Plain Jane’ boring types, who have nothing to offer incredibly wealthy guys. Then I’ve seen drop dead gorgeous girls in singles bars in the East Village. What’s the story there ?

- Lawyers, investment bankers, doctors. How much do those guys really make ? And where do the hedge fund guys hang out ?

- How do you rich guys decide on marriage vs. just a girlfriend ? I am looking for MARRIAGE ONLY.

Please hold your insults - I’m putting myself out there in an honest way. Most beautiful women are superficial - at least I’m being up front about it. I wouldn’t be searching for these kind of guys if I wasn’t able to match them - in looks, culture, sophistication, and keeping a nice hearth and home'.

An Investment Banker's Response:

Dear Pers-431649184:

'I read your posting with great interest and have thought meaningfully about your dilemma. I offer the following analysis of your predicament.

Firstly, I’m not wasting your time. I qualify as a guy who fits your bill - that is, I make more than $500K per year. That said, here’s how I see it:

Your offer, from the prospective of a guy like me, is a plain and simple crappy business deal. Here’s why. Cutting through all the B.S., what you suggest is a simple trade: you bring your looks to the party and I bring my money. Fine, simple. But here’s the rub, your looks will fade and my money will likely continue into perpetuity - in fact, it is very likely that my income will increase, but it is an absolute certainty that you won’t be getting any more beautiful!

So, in economic terms, you are a depreciating asset. Not only are you a depreciating asset, however, your depreciation accelerates! Let me explain - you’re 25 now and will likely remain pretty hot for the next 5 years, but less so each year. Then the fade begins in earnest. By 35 - stick a fork in you!

So, in Wall Street terms, we'd call you a trading position - not a buy and hold…hence the rub…marriage. It doesn’t make good business sense to 'buy you' (which is what you’re asking) - so I’d rather lease. In case you think I’m being cruel, I would say the following: if my money were to go away, so would you - so when your beauty fades I need an out too. It’s as simple as that. So the deal that makes sense for me is dating, not marriage.

Separately, I was taught early in my career about efficient markets. So, I wonder why a girl as 'articulate, classy and spectacularly beautiful' as you has been unable to find your sugar daddy. I find it hard to believe that, if you are as gorgeous as you say you are, your $500K man hasn’t found you - if only for a tryout.

By the way, you could always find a way to make your own money - and then we wouldn’t need to have this difficult conversation.

With all that said, I must say you’re going about it the right way. Classic 'pump and dump'. I hope this is helpful, and if you want to enter into some sort of lease, please let me know'.

Reader Comment:

1. If she piles on the weight, it's likely to be 'plump and dump!'

2. 'The Investment Banker's response is correct if you see the gold digger as providing only companionship, looks and sophistication.

However, some Investment Bankers may wish to have offspring carrying their genes into the next generation. This is a long-term contract, and you have to 'buy and hold' rather than 'lease'. Therefore this 25 year-old beauty should change her sales pitch to: 'I'll give you nice children AND I'll let you do whatever else you want on the side as long as you're discreet'.

3. 'I hate to say it but, in the current environment, this Master of the Universe should ship her in asap. Then at least he'll have a nice shoulder to cry on when he gets canned. We're ALL depreciating assets these days. At least this young lady has some gumption as well as those spectacular good looks and style to fall back on'.

4. Response to investment banker: 'Ah! But I am an depreciating asset all right (for that matter, you are too - but your cash flow stream more than overcompensates for the toxicity of the future tummy expansion, and contraction of the hair). But the depreciating asset is a convertible one with two embedded options:

The first option is for conversion to a wife, preferably before the day that the hair / tummy factor becomes less than positive and cashflow benefits become more important. If you do not take up that wife-conversion option, then the expanding gut and thinning hair will require a constantly and exponentially increasing stream of invested earnings to attract young chicks.

The second option is that you have a put option on a baby (which is preferably contingent on the first option being exercised), safe in the knowledge that good genes will be passed on. You have to admit, the main reason why you investment bankers are so attractive is because you can make money. However, we have established information that those money-making genes do not travel very well. My good looks will probably be passed on though.

So, for an upfront investment in this depreciating asset will, in the long run, make your overall yield curve positive.
Rob Campbell
J.P.Morgan
Diversified Industrials Investment Banking
277 Park Avenue , 16/F, New York, NY 10172