If you have a hammer, everything looks like a nail. If what you have is economics ...
The Price of a Spouse
Men want wives, women want husbands. The price of a wife or a husband is what you have to give up to get her or him. In some societies, but rarely in ours, it takes the form of cash paid as bride price, dowry or dower. While explicit payments of this sort are not a part of our marriage institutions, people who get married do so with some general understanding of the terms they are committing themselves to: how free a hand each will have with the common funds, what duties each is expected to perform, and so on. Think of the terms of this understanding as a price serving the same function as an explicit price in other markets.
Imagine, for example, that a plague kills off many young women of marriageable age. Afterwards, young women find it easy and young men difficult to get married. One result is a change in the price of a spouse. Men are implicitly bidding against each other for wives; their offers include their willingness to accept marriage terms favorable to the bride. This is particularly likely if divorce is easy, as in our society it is; if the man who promised before the wedding to do everything his wife wanted proves less accommodating afterward, some other man will be willing to take his place. The supply of wives has gone down, the price of a wife up. Similarly, with roles reversed, if a war killed off a lot of young man, reducing the supply of husbands — or, if you prefer, the demand for wives. In a barter market, which marriage is, the supply of one good is the demand for the other.
Supply and demand work just as on any other market. The quantity supplied of wives — the number of women willing to marry — will be higher and the quantity demanded lower, the higher the price. The model is symmetrical; we can just as easily speak of the quantity demanded and quantity supplied of husbands. As long as all marriages are monogamous, the number of husbands supplied and the number of wives demanded are the same, since a man seeking to become a husband is a man seeking to obtain a wife, just as, on a barter market, someone who offers to trade wine for beer is both supplying wine and demanding beer.
Omissions
I have so far ignored quality differences in potential husbands and wives, the fact that some people are more desirable marriage partners than others. We could include this in our model by including quality in our definition of the standard contract. A price of zero for marrying an unusually desirable woman means that she receives specially favorable terms to balance the advantage to the husband of such a desirable wife. Perhaps the husband would agree to wash all of the dishes.
Seen from this standpoint, attractiveness is a kind of wealth. A man or a woman with good looks or a pleasant disposition is wealthier, has a greater command over the desirable things of life, than someone who has not, just as someone who has inherited a million dollars is wealthier than someone who has not.
A further complication is that tastes for marriage partners vary. The woman I recognized as a one in ten thousand catch was not even being pursued by anyone else, with the result that I married her on quite reasonable terms; I did not even have to agree to wash all of the dishes. Some of the women that my friends married, on the other hand, were of no interest to me at all. Yet my friends obviously preferred them, not only to remaining bachelors but to trying to lure my intended away from me.
We would observe the same thing in the market for houses or the market for jobs, markets where the problem is not merely the allocation of limited quantities but the proper matching of buyer and bought. While it should be possible to include differing tastes in the analysis, I will for this essay ignore that complication.
The Effect of Legalizing Polygyny or Polyandry
It is possible to analyze the effect of changing the marriage laws to legalize polygyny or polyandry using the same tools used to analyze more conventional markets.
Price is defined relative to a standard contract one of whose features is monogamy, so a man who offers a price of zero for a second wife is offering her terms sufficiently favorable in other ways to balance the cost to her of having to share him, and similarly for any other price. Since a bigamous marriage offer at a price of $1000 is by definition equivalent, from the standpoint of potential wives, to a monogamous offer at the same price, the number of women willing to accept it will be the same. So the legalization of polygyny has no effect on the supply curve for wives, the relation between the price offered and the number who accept it.
Legalizing polygyny is unlikely to make a man who before wanted one wife decide that (at the same price) he now wants none, but it will allow some who before wanted one to marry two instead, even if they must offer terms at which potential wives are willing to accept half a husband apiece. So when polygyny becomes legal, quantity of wives demanded at any price rises; the demand curve shifts out. If the supply curve stays the same while the demand curve shifts out, the price must go up. Since price is defined in such a way that an increased price means a contract more favorable to the wife, this means that women are better off.
What about men? Those who end up with only one wife are worse off, since they must offer her more favorable terms than before. A man who ends up with two (or more) wives may or may not be better off. He prefers, and gets, two wives at the new price instead of one but he might prefer one wife at the old price to two at the new price.
Is the change a net improvement or a worsening, judged by the criterion of economic efficiency, the summed effect on all affected, discussed in an earlier post? It is an improvement. To see this, imagine that we make it in two steps. The first consists of changing to the new price while keeping the allocation of husbands and wives (to each other) fixed. That is a pure transfer; wives gain what husbands lose. The next step is to allow husbands and wives to adjust to the new price. Men who do not change the number of wives they have are unaffected; men who reduce the number of wives they have from one to zero in response to the higher price or increase the number above one to take advantage of the legalization of polygyny, and women who at the old price did not choose to marry but at the new price do, are better off. A pure transfer plus an improvement adds up to an improvement.
The analysis of the effects of legalizing polyandry would be identical, with the roles of women and men reversed. Since some women now buy two (or more) husbands, the demand curve for husbands shifts out. At the old price for husbands, quantity demanded is greater than quantity supplied, so the price rises. Women marrying only one husband must compete against the polyandrous women to get him, hence must offer better terms than before. Men are better off, monogamous women are worse off, and polyandrous women may be better or worse off. The net effect is an improvement.
To many readers, the conclusion may seem extraordinary—how can women possibly be made better off by polygyny and men by polyandry? That reaction reflects what I sometimes describe as naive price theory: the theory that prices do not change. If polygyny were introduced and nothing else changed, women would be worse off—except for those who prefer to share the burden of a husband. But when polygyny is introduced, something does change; the demand curve for wives shifts up, and so does the price implicit in the marriage contract. Wives who end up with one husband get him on more favorable terms since he must bid more for a wife because of the competition of his polygynous rivals. Those women who accept polygynous marriages do so because the price they are offered is sufficient to at least balance, for them, the disadvantage of sharing a husband.
All of this assumes that, as in our society, potential marriage partners belong to themselves, pay or collect the implicit price. In a society where the price is paid to the bride’s parents, bride price (but not payments which go to the bride such as dower or ketubah), legalizing polygyny makes parents of daughters better off but not necessarily their daughters.
The result would seem less paradoxical if we substituted cars and car buyers for wives and husbands (or husbands and wives). Suppose there were a law forbidding anyone to own more than one car. The abolition of that law would increase the demand for cars. Sellers of cars would be better off. Buyers who did not take advantage of the new opportunity would be worse off, since they would have to pay a higher price. Buyers who bought more than one car would be better off than if they bought only one car at the new price (otherwise that is what they would have done) but not necessarily better off than if they bought one car at the old price, an option no longer open to them.
One thing you may find confusing in all this is the time sequence. Am I describing a situation in which, after polygyny becomes legal, some men divorce one wife to marry two others, and some women insist on renegotiating their marriage contracts? No. What I am doing is comparing two alternative futures, one with polygyny (or polyandry) and one without. The man who would have married one wife if polygyny had remained illegal either marries one wife on different terms if polygyny is legal, marries two (or more) wives, or is priced out of the market and remains a bachelor.
Attitudes to Other People’s Sexual Tastes
Viewed in terms of the class interest of heterosexual men, one would expect approval of male homosexuality, disapproval of female. Every mm couple means two fewer men competing for wives, every ff couple two fewer women to be competed for. By the same argument, one would expect the opposite attitude by heterosexual women.
It is not what we observe. Heterosexual men tend, by casual observation, to have a more positive attitude to female homosexuality than to male, perhaps because finding women sexually attractive seems natural to them, finding men sexually attractive unnatural. I am told that gay pornography is mostly written by women, suggesting a similar pattern, perhaps the same explanation, with sexes reversed.
Individual behavior and attitudes are shaped by individual interests and preferences, not group loyalty. As I once wrote in a different context:
The manufacturer of widgets may spend his evenings on his knees praying for the price of widgets to go up, but he spends his days behind a desk making it go down.
[I discuss the marriage market in more detail, and with more mathematics, in Chapter 21 of my Price Theory].
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Why we are failing to solve matching problem? Dating/matching apps are massive multi billion dollars industries. So there is plenty of demand
I think you must be wrong about a bigamous offer for $X being equivalent to a monogamous offer for $X. The sole wife gets all of whatever time and effort her husband is prepared to spend on emotionally supportive labor within the marriage; but it's not likely that a man with two wives will spend twice the time and effort that he would on one wife (since a second wife typically provided less marginal utility than a first). The second wife must anticipate that she will get an inferior service; on the other hand, the first wife may well fear that she will see what she gets diminished to the benefit of the second wife. I don't think you can say ceteris paribus about the tradeoff outside of money and material assets.