« "When Politics is Stuck in the Middle" | Main | Assorted links »
Revisiting the Marriage Supermarket
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.
Posted by Alex Tabarrok on February 7, 2010 at 07:41 AM in Books, Economics | Permalink
Comments
Alex, thanks for reminding me why I didn't buy TH's book and why it should not be used to teach economics.
Posted by: E. Barandiaran at Feb 7, 2010 7:50:19 AM
What exactly is the final link supposed to mean? It could be interpreted as saying that lesbianism is an "option". I presume that's not the case.
Posted by: Edward Gaffney at Feb 7, 2010 7:57:07 AM
Well, we should see interesting things in China pretty soon then.
Posted by: Brock at Feb 7, 2010 8:02:33 AM
Of course, this discussion then makes a hash of an earlier link by Tyler about how well college women do in the marriage market. In that article almost all the results are driven by black women. Among whites, the college educated are slightly less likely to marry than those without college. Couple that with the trend whereby more women than before are likely to be unmarried by 40 plus this recent NYT piece on imbalances in college and you see the makings of real trouble in River City.
Posted by: Gorgon at Feb 7, 2010 8:16:49 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...
Posted by: Slocum at Feb 7, 2010 8:20:16 AM
But what happens to that equilibrium when the participants discover that, whatever agreement they might have reached among themselves regarding the division of resources, the store refuses to enforce it?
Posted by: Cyrus at Feb 7, 2010 8:28:22 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.
Posted by: Gary Arndt at Feb 7, 2010 8:46:54 AM
Of course, the woman without a man doesn't get zero. She can raise her utility above zero by borrowing married men. Puts anti-polygamy laws in a new light, huh?
By the way, as a guy in college who should be benefiting from a female heavy population, I have to point out that things are not as glorious as they might seem. 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.
Posted by: GaryM at Feb 7, 2010 9:28:27 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.
Posted by: Andrew at Feb 7, 2010 9:33:09 AM
Except Roissy is actually right on this one and a 50:50 ratio (m:w) ratio is more like a 30:70 ratio in terms of who is actually having relations beneath the surface, for a given month say. So 40:60 on the surface probably brings us to less than 25:75 in bed, which is why the women are complaining.
Posted by: Bock at Feb 7, 2010 10:13:23 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.
Posted by: dearieme at Feb 7, 2010 11:38:38 AM
This assumes that every woman and every man are interchangeable with others of their gender, which is manifestly not the case. Ann might prefer a short wealthy sophisticated stockbroker, while Barb wants a tall honest grass-smoking engineer and Carol wants an outlaw biker.
It also assumes that everyone values a relationship equally, but while Diana may be willing to give 99 to get married, Elizabeth won't go for more than 70 and Francie stops at 35.
So that analysis is basically useless.
Posted by: Laserlight at Feb 7, 2010 11:59:05 AM
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.
Posted by: j at Feb 7, 2010 12:43:48 PM
> The man being rational will accept but this still leaves one women unpaired and she will now counter-offer $70:$30
Wouldn't she be better off switching men and offering $60:$40?
Posted by: Peter de Blanc at Feb 7, 2010 12:47:36 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).
Posted by: knb at Feb 7, 2010 12:52:43 PM
Nothing happened?
http://en.wikipedia.org/wiki/File:Population_growth_rate_world_2005-2010_UN.PNG
That is idle speculation. All I know personally is there are a helluva lot of Chinese dudes in my grad department.
Posted by: Andrew at Feb 7, 2010 1:06:40 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.
Posted by: Helen DeWitt at Feb 7, 2010 1:09:14 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.
Posted by: Helen DeWitt at Feb 7, 2010 1:09:33 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.
Posted by: Helen DeWitt at Feb 7, 2010 1:09:53 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.
One theory claims that the postwar man shortage is the reason why Russian and Eastern European women tend to be so beautiful today. According to the theory, the surviving men were in such a strong bargaining position in the postwar years that only the more attractive women were selected for marriage. In turn, these women passed their beauty to their daughters and granddaughters.
As far as I know the theory has never been proven, and may well be un-proveable. One problem that comes to mind is the fact that Brazil is another country noted for the beauty of its women, yet Brazil hasn't been in any wars for generations.
Posted by: Peter at Feb 7, 2010 2:21:22 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.
Posted by: kevincure at Feb 7, 2010 2:24:46 PM
Well, nice idea, but marriages are not 100 % about money. You don't marry in university, because you could split money. Instead bargaining prices are set, people have mostly unchanagable attributes that you can't undercut (personality, beauty etc.) and thus the market will just leave the worst girl unattended to...
Posted by: Max at Feb 7, 2010 2:47:54 PM
The split would not start at $50 $50.
Posted by: Doug at Feb 7, 2010 2:47:57 PM
Relax either the full information assumption or the assumption that all pairs earn $100 and the result disappears. Let's see some real econ not shoddy modeling borrowed from a guy who has yet to publish in a worthwhile journal.
Posted by: dmb at Feb 7, 2010 2:57:45 PM
Helen... how are men high maintenance? I've generally only heard that term used to describe women...
Posted by: quadrupole at Feb 7, 2010 3:45:49 PM
Wow... why not just model the problem with spherical cows?
Posted by: Mark at Feb 7, 2010 3:55:27 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.
Posted by: zbicyclist at Feb 7, 2010 4:29:54 PM
People tend to think they are more attractive to the opposite sex than they really are.
Which is often beneficial for men, because women are generally attracted to confidence. If your probability of success is 80% of the probability with which you expect to succeed, you're better off being overconfident than accurate.
Posted by: Brian 2 at Feb 7, 2010 7:25:02 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.
Posted by: Tom Grey at Feb 7, 2010 9:54:50 PM
Looking forward to Alex and Bryan's joint post on the economics of marriage supermarkets during snowstorms.
Posted by: mobile at Feb 7, 2010 10:21:17 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 ]
Posted by: John B. Chilton at Feb 7, 2010 11:27:37 PM
Obviously the model doesn't perfectly describe marriage, but I've thought a similar model pretty much describes oil price spikes and with a little stretch you can see it describing a credit crunch, especially for banks where you can't really substitute payment for higher interest rate loans because it doesn't improve the balance sheet and banks are always insolvent, which is what makes them special.
Posted by: Andrew at Feb 8, 2010 2:33:15 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.
Posted by: memory card at Feb 8, 2010 7:16:16 AM
One theory claims that the postwar man shortage is the reason why Russian and Eastern European women tend to be so beautiful today.
Yes, but they still turn into babushkas after the age of 45 or so. And often cigarette smoking babushkas.
Posted by: anon at Feb 8, 2010 10:33:19 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.
Posted by: hibikir at Feb 8, 2010 10:52:16 AM
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.
Actually, say hello to "courtly love", and chivalry's views towards women. The constant warring in Europe created an imbalance there, just as gang activity (not just the evil prison system) creates one here. Black women near the ghetto haven't managed to pull off the "real men treat their women right" line that so affected Western culture for centuries.
Posted by: Right Wing-nut at Feb 8, 2010 2:43:05 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).
Posted by: Peter at Feb 8, 2010 6:04:12 PM
People tend to think they are more attractive to the opposite sex than they really are.
For what it's worth, I recall a study (can't find a link, sorry) that found that on average, men rated two fifths of women viewed as being less attractive than average, but women rated four fifths of men as being less attractive than average.
Posted by: Jason L. at Feb 9, 2010 6:03:09 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.
Posted by: Joel W at Feb 9, 2010 6:33:38 PM
"If the outside option is worth more then changes in the sex ratio will have smaller effects."
There's your answer. Those extra women should pair off with other women. Besides, everybody knows that the notion that college is for finding a husband is outdated. This is the year 2010 people. College is for experimenting with lesbianism.
Posted by: JR at Feb 9, 2010 11:43:42 PM
"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.
Posted by: Laurents at Feb 10, 2010 2:10:05 AM
Thank you very much for this information.Good post thanks for sharing.
I like this site ;)
-----------
cam balkon cam balkon
/çerçeve çerçeve fizik tedavi fizik tedavitercüme tercüme /otomatik kapı otomatik kapı netlog netlog yemek tarifleri/resim upload/betsson/sohbet
Posted by: seoturk at Feb 10, 2010 3:35:05 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.
Bilgisayar Teknik Servisi Bilgisayar Teknik servisi, gaziantep evden eve taşımacılık Gaziantep evden eve taşımacılık
Posted by: cam balkon at Apr 29, 2010 3:09:51 AM
see and believe now it's never over.
Posted by: kitchen cabinets michigan at May 1, 2010 10:06:15 AM
that was plain and simple! thats what i like i will use it soon
Posted by: kwiaty at May 16, 2010 7:35:08 AM
that was plain and simple! thats what i like i will use it soon
Posted by: Sevgi Büyüsü at May 26, 2010 6:37:51 AM
evden eve nakliyat,nakliye,taşımacılık,evden eve ,ev,www.isikevdenevenakliyat.com,
Posted by: ercan sahin at Jun 7, 2010 6:45:22 AM
that was plain and simple! thats what i like i will use it soon
Posted by: web at Jun 23, 2010 2:24:13 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.
Posted by: health at Jun 23, 2010 2:24:40 PM
paylaşımlarınız için teşekkürler
Posted by: ankara cam balkon at Jul 28, 2010 7:20:26 AM
