# Mathematicians Have Perfect Marriages

It seems none of the guys I know who are married, have proposed marriage by picking a romantic evening, kneeling in front of his girlfriend as in the movie, and slipping a ring on her finger provoking happy tears. In contrast, almost all of them were backed into a corner by their girlfriends, a knife held to their throats, and consented to the marriage mopishly.

Is it because they do not love their girlfriends? No. Look at those trustworthy guys, they have a sense of responsibility, monogomy, and romance and will fight with anyone who wants to get his hands on their wife. But why are they afraid to get married? One friend told me the answer—too expensive.

A funny guy made an “unofficial” report, analyzing the cost of getting a wife in Nanjing, a Middle-income city in China:

1. A house (80 square meters, urban district), 480,000 RMB;
2. Interior decoration, 50,000 RMB;
3. Appliances and furnitures, 30,000 RMB;
4. An ordinary car. 100,000 RMB;
5. Honeymoon trip. 16,000 RMB;
6. Other expenses: 24,000 RMB;
(Total amount: 700,000 RMB)

Suppose the guy’s annual income is 50,000 RMB; and his parents can afford 200,000 RMB for him, (70-20)/5=10 —The guy has to work without eating or drinking for 10 years.

Comes to the situations in other cities in China:

 Total expense (10 thousands RMB) years Najing 70 10 Beijing 103.8 12 Shanghai 140.02 15 Shenzhen 85.8 14 Guangzhou 104.8 12 Hangzhou 127.8 16.67 Suzhou 74.95 7.5 Wuhan 20.2 3.5 Taizhou 46.4 15.5

And there is something worse. According to the China Teenage Research center and the research center of population and development at Renmin University, the ratio of females to males now in China is 100:119.58, which means 10% men will not be able to find a wife—it is an issue that threatens the sustainable development and social harmony of the country!

Now just let’s put the “country first” aside but just think about the “change we need”. A blogger built a “”Beauty and the Geek mathematical model”, trying to find the prefect age for getting married. He referred Mr. Rob Campbell (J.P.Morgan, Diversified Industrials Investment Banking)‘s theory, which rests on the following assumption:
1. Women’s value lies in their appearance;
2. Men’s value lies in their achievement;
3. The life span of both men and women is 100 years;

So the following Curve shows the change of value with age: U=f(y); U=Value, Y=age

From the graph, we can see women’s value increases steeply between 18-24 years old, and reaches the summit at 26 years old; but begins to plunge at 28 years old. On the other hand, men’s value begins to increase from 22 years old on, and remains high after it has reached the peak.

The two curves cross at K (28,78,), which means at 28 years old, the values of men and women are same. So, many people will think 28 is the perfect age to get married, — which is wrong.

The problem is, a 28 years old woman is a distressed asset; and a 28 years old man is an appreciable asset.

So the prefect age should be the time that the increasing speed of the two people is fastest, which means, the slope of the tangents of curves are biggest. Look at the following graph:

On P₁ and P₂, the tangents of two curves are same. So the prefect age to get marry is: 25 (man) and 22 (woman)

Although at the moment women’s value is bigger than men’s value. Women will not suffer losses, because:

The area of blue part S₁=∫[U(women)-U(men)], which means the benefits a man get form the women;

The area of blue part S₂=∫[U(men)-U(women)], which means the benefits a woman get form the men;

Apparently, S₂>S₁

What do you think?