Revisiting the Marriage Supermarket

by on February 7, 2010 at 7:41 am in Books, Economics | Permalink

In comments to yesterday's post on the effects on dating style of a declining number of university men a number of people asked why a relatively small change in the sex ratio (m:w) from 50:50 to say 40:60 should make such a big difference.  In the Logic of Life, Tim Harford gave a characteristically excellent explanation.

Imagine, says Tim, a marriage supermarket.  In this supermarket any man and woman who pair up get $100 to split between them.  Suppose 20 men and 20 women show up at the supermarket, it's pretty clear that all the men and women will pair up and split the $100 gain about equally, $50,$50.  Now imagine that the sex ratio changes to 19 men and 20 women.  Surprisingly, a tiny change in the ratio has a big effect on the outcome.

Imagine that 19 men and women have paired up splitting the gains $50:$50 but leaving one woman with neither a spouse nor any gain.  Being rational this unmatched woman is unlikely to accede to being left with nothing and will instead muscle in on an existing pairing offering the man say a $60:$40 split.  The man being rational will accept but this still leaves one women unpaired and she will now counter-offer $70:$30.  And so it goes.

If you follow through on the logic it becomes clear that in the final equilibrium no married (paired) woman can be significantly better off than the unmarried woman (otherwise the unmarried woman would have an incentive to muscle in with a better deal) and so because the unmarried woman gets nothing the married women can't get much more nothing.  Thus when the sex ratio is 20:20 the split is $50:$50 and when the sex ratio is 19:20 the split is more like to $99:$1 in favor of the men.

The key simplification of the marriage supermarket is that the next best option to marriage (pairing) is worth $0–thus there is a long way to fall from the equal sex ratio equilibrium of $50.  If the outside option is worth more then changes in the sex ratio will have smaller effects.  Nevertheless, the logic of the marriage supermarket explains why a relatively small change in the sex ratio can lead to a large change in sexual and other mores affecting the marriage equilibrium.

1 E. Barandiaran February 7, 2010 at 7:50 am

Alex, thanks for reminding me why I didn’t buy TH’s book and why it should not be used to teach economics.

2 Brock February 7, 2010 at 8:02 am

Well, we should see interesting things in China pretty soon then.

3 Slocum February 7, 2010 at 8:20 am

Except, of course, in the university context (unlike China), the sex ratios have not really changed because the women are not obligated to shop for men at the the supermarket (university) exclusively.

Here’s a bit of conjecture. Among high-school aged friends of my own kids, I’ve noticed a more common desire among the girls, but not really the boys, to go to a school in a big city. This, of course, would make it much easier to date ‘outside’ than would attending a small college or even a state university in a more isolated area. I wonder…

4 Gary Arndt February 7, 2010 at 8:46 am

A better option would be to change the rules of the game to let women share. If in the above example 2 women can team up to share a man, then the distribution would still be tilted towards men, but not quite so far.

Polygamy has economic roots.

5 Andrew February 7, 2010 at 9:33 am

Some ironies:

If a female goes into a male dominated major, she will end up in a male-dominated profession and vice-versa.

If a university environment favors women (sitting for hours staring doe-eyed at the pinhead at the head of a classroom, or writing long reports dotting every i and crossing every t for example), then women become the majority. Then, unless the U does “affirmative action,” they will even further tailor their environment to their current customers. Btw, I just have to say that if a U is not serving the needs of future male workers, to serve those needs is not really affirmative action, anywhere else it is called marketing.

6 dearieme February 7, 2010 at 11:38 am

At Oxford and Cambridge there are no longer any all-male Colleges, but there are still all-female Colleges. Which only goes to show.

7 j February 7, 2010 at 12:43 pm

Why these idle speculations? Why not watch what is happening in the real world? For example: after WWII, there was a general surplus of fertile females in almost all European countries that participated in the fight. What happened for example in Germany in the fifties? In Russia? Apparently nothing, the people adapted to the situation.

8 knb February 7, 2010 at 12:52 pm

The other commenters have apparently never heard of a “thought experiment” before. It illustrates a concept: in a skewed marriage market the more abundant sex must make a lot more concessions to the scarce sex.

It is true: in countries where the men leave to make more money (Baltic states), women “sweeten the pot” to a much greater extent than women in the US. And African-American women compete hard for the relatively scarce Black male who hasn’t been murdered or imprisoned (or married a white girl).

9 Helen DeWitt February 7, 2010 at 1:09 pm

Ignores cost of full-time relationships to women. Men are high-maintenance. A woman who shares a good lover with 1+ other women will have a startling professional advantage over women with a realio-trulio full-time SO and will compete with men on a level playing field. The hypothesis is that women who have brushed shoulders with economics will double up with women with a similar advantage, while uneconomically-inclined women will seek monogamy on increasingly silly terms. The hypothesis is that a man who has immersed himself in economics will disregard maintenance costs.

10 Helen DeWitt February 7, 2010 at 1:09 pm

Ignores cost of full-time relationships to women. Men are high-maintenance. A woman who shares a good lover with 1+ other women will have a startling professional advantage over women with a realio-trulio full-time SO and will compete with men on a level playing field. The hypothesis is that women who have brushed shoulders with economics will double up with women with a similar advantage, while uneconomically-inclined women will seek monogamy on increasingly silly terms. The hypothesis is that a man who has immersed himself in economics will disregard maintenance costs.

11 kevincure February 7, 2010 at 2:24 pm

1) The same idea might explain high Chinese savings: http://www.voxeu.org/index.php?q=node/4568

2) In cooperative game theory, this is sometimes (half-jokingly) called the “Marxism Game”! Let the value of a coalition of capital and labor be min{capital,labor}. Then if labor is receiving any positive amount, the capital in that coalition can offer less money to any of the labor that is left out, down to the point where labor is paid only what it could make by working by itself. Sometimes this is called “Left-Glove, Right-Glove”, also.

12 Doug February 7, 2010 at 2:47 pm

The split would not start at $50 $50.

13 quadrupole February 7, 2010 at 3:45 pm

Helen… how are men high maintenance? I’ve generally only heard that term used to describe women…

14 zbicyclist February 7, 2010 at 4:29 pm

“The ratio of cuties to not-cuties in my current environment is much worse than I’ve experienced in other environments with more even sex-ratios. Quality counts, even for the relatively undiscerning sex.”

There’s fundamental problem. People tend to think they are more attractive to the opposite sex than they really are.

“Why these idle speculations? Why not watch what is happening in the real world? For example: after WWII, there was a general surplus of fertile females in almost all European countries that participated in the fight. What happened for example in Germany in the fifties? In Russia? Apparently nothing, the people adapted to the situation.”

No accident the years after the wars were the golden age of nuns.

“A 2004 survey by Our Sunday Visitor’s Catholic Almanac showed there were approximately 71,486 nuns in the United States, down 50 percent from the 1960s. More alarmingly, from the church’s point of view, is that the average age of nuns is 70 years old.” http://www.msnbc.msn.com/ID/7463291/

It’s possible that we need a different adaptation than the religious life this time around.

15 Tom Grey February 7, 2010 at 9:54 pm

It will be interesting to see if in China or India the cute girls and the parents of the cute girls will be able to change the culture and find marriages so the man comes to live with parents of the girl, rather than girl living with the parents of the man.

And yes, far more made-men going for far younger girls, should also be observed.

16 John B. Chilton February 7, 2010 at 11:27 pm

For those with Harford’s book you can see what he says about polygyny here:

http://www.slate.com/id/2136453/

Some of my favorites bits from that Harford essay [I once interviewed a job candidate who had followed up on whether the women in the Sahel region are better off than counterparts – she found they were measurably better off]:

In the Sahel region of Africa, half of all women live in polygynous households. The other half have a good choice of men and a lot more bargaining power.
. . .
A little over one in 100 American men are in prison – but there are several states where one in five young black men are behind bars. Since most women marry men of similar age, and of the same race and the same state, there are some groups of women who face a dramatic shortfall of marriage partners.

Economist Kerwin Charles has recently studied the plight of these women. Their problem is not merely that some who would want to marry won’t be able to; it’s that the available men suddenly have more bargaining power.
. . .
The women’s response makes sense: girl power. The women affected do everything to make the most of single life, including staying at school for longer and hunting for more paid work. The American prison system hasn’t left them much choice.

[Link to Kerwin Charles: http://tigger.uic.edu/~nba/charles_jail_marriage.pdf ]

17 memory card February 8, 2010 at 7:16 am

Hiring a cleaner is no “get out of jail free† card for a feminist if she or her partner do nothing else to change the power imbalance. But, if she really doesn’t like cleaning, there is nothing stopping her from deciding that she values the person who is doing the cleaning and the work they do, and will pay them an honourable wage regardless of what the patriarchy decreed minimum happens to be. Cleaning as an activity does not make the “underclass of women†; our attitude to women and women’s work makes the underclass.

18 hibikir February 8, 2010 at 10:52 am

And such analysis also misses the point that people’s idea of fair, in many cases overrides their economic interests. We are not homo economicus. Try to run an experiment on such a plan, and see how many men end up unmarried because some women’s concept of fairness will make them refuse the 99:1 split.

Even with homo economicus in play, the model fails utterly the moment the women set up their own side agreement: Agree to pay $2 to the unmarried woman if every woman refuses anything worse than a 50:50 split. If the trust levels are high enough for such an agreement, they end up with a far better deal than they would have otherwise. Hello to organized labor.

19 Peter February 8, 2010 at 6:04 pm

The Marriage Market is the one supermarket I will not shop from. Apparently their product causes financial stomach upset and even financial death in about 45% of the customers:

http://weddedabyss.wordpress.com/

Perhaps one of us should do an Economist’s analysis of “Lifetime Alimony” when we get a chance. You know, how the homemaker spouse can claim equity in a breadwinner spouse’s future (post-divorce) income, but how the breadwinner spouse can’t claim similar equity in the homemaker spouse’s future homemaking services. (i.e. why is alimony a one-way obligation, and not a two-way obligation).

20 Joel W February 9, 2010 at 6:33 pm

Max,

This had nothing to do with money. The money was an example of the surplus supposedly associated with relationships. The money was free because pairing up brings gains.

21 Laurents February 10, 2010 at 2:10 am

“If a university environment favors women (sitting for hours staring doe-eyed at the pinhead at the head of a classroom, or writing long reports dotting every i and crossing every t for example)”

This style was invented and dominated by men for centuries, and now that women have literally outsmarted men at their own game, Andrew goes crying that he never liked the game and wanted to play anyway. Women are catching up in the sciences too and I’d prefer a doctor that crosses those t’s.

22 cam balkon April 29, 2010 at 3:09 am

This had nothing to do with money. The money was an example of the surplus supposedly associated with relationships. The money was free because pairing up brings gains.

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25 health June 23, 2010 at 2:24 pm

This had nothing to do with money. The money was an example of the surplus supposedly associated with relationships. The money was free because pairing up brings gains.

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