Bryan Caplan  

How Rival Is Your Marriage?

Sitting on an Ocean of Alaskan... Market monetarism in 2013...
Two childless singles, each earning $50,000 a year, marry.  Both keep working, living by the old-school principle of "share and share alike."  What happens to their material standard of living?  If all depends on how rivalrous their consumption bundle is.

If all their goods are rival (like food), the answer is "Their standard of living stays the same."  $50,000 times two divided by two equals $50,000.

If all their goods are non-rival (like Internet access), the answer is "Their standard of living doubles."  They pool their money and buy a $100,000 lifestyle for both of them.

In the real world, of course, couples are rarely at either pole  Most goods are in fact semi-rival.  Consider housing.  If you share your home with a spouse, you don't have as much space for yourself as a solitary occupant of the same property.  But both of you probably enjoy the benefits of more than half a house.  If a couple owns one car, similarly, both have more than half a car.  Even food is semi-rival, as the classic "You gonna eat that?" question proves.

Mathematically, married individuals' utility looks something like this:

U=Family Income/2a

a=1 corresponds to pure rivalry: Partners pool their income, buy stuff, then separately consume their half.  a=0 corresponds to pure non-rivalry: Partners pool their income, buy stuff, then jointly consume the whole.

There's little doubt that a<1.  This insight is even built into the official poverty line.  That's why I say that being single is a luxury.  My question: Where does a typically lie in the real world?  Feel free to discuss variation by social class and nationality.  Please show your work.

P.S. If you know of academic references on this exact question, please share.

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COMMENTS (28 to date)
Foobarista writes:

How about specialization? My wife is a far more careful shopper than I am and we spend much less together than I did when I was single (and rather lazy when it came to shopping and finding good deals). OTOH, I'm better at investing than she is, so her portfolio is much better now than it was when she was single.

Sam writes:

I don't have an answer to Bryan's question, but I do have a related question:

If over time, nationwide average household consumption of non-rival goods increases as a percentage of total consumption, could that put downward pressure on inflation even if there's more money floating around?

Does anyone track the portion of GDP that is made up of non-rival goods? No doubt it has grown over time.

ce writes:

Try searching google scholar for Equivalence Scales. There should be loads of academic citations. There is also a New Palgrave entry by Lewbel on this topic.

chris writes:

Maybe i am missing something, but shouldnt be the calculation more like this:

Person 1: U1 = I1 (before marriage)
Person 2: U2 = I2 (before marriage)

After marriage family utility:

U = (I1 + I2)/2^alpha

Change in utilitiy for person1:

dU1 = I1-(I1 + I2)/2^alpha

Change in utilitiy for person2:

dU2 = I2-(I1 + I2)/2^alpha

If those changes in utility are positiv or negativ for an individual person depends on the relation of their individual incomes before marriage.

if someone with an income of 50000 marrys someone with no income he/she is going to loose utility due to the marriage.

Daniel Kuehn writes:

Chen and Woolley (2001), in the Economic Journal write their utility functions in terms of private goods and household goods. So the utility function itself is not some degree of rivalrous as you have it - the goods are. Really that probably makes more sense (otherwise your "a" parameter is going to change depending on what the optimal point is).

If you are talking about shared goods it also seems especially important to consider whether preferences are altruistic/deferential. The benefit of a non-rivalrous good in a marriage is not just that you're going dutch - it's also that you want your wife to have nice meals, a safe home, etc. - and you gain utility from that. If I were single I would not live as well as I do in some ways, not because it's more expensive so much as because it's not something a single guy would do if he didn't have a woman to enjoy enjoying it with him.

The altruistic/deferential preferences are in Chen and Woolley and pretty much all household models.

Daniel Kuehn writes:

There's nothing special about that paper in this regard, btw. I just know it well because I presented it in my gender economics class. Their contribution was not on the utility side, but on modeling how households bargain over budgets.

I'm sure they have the cite to the original versions of the utility functions they use, though.

Thomas Boyle writes:

Don't forget that there are also goods where a>1, representing compromises that reduce (but do not eliminate) the overall gains from 1>a. These could include vacations to places you would have preferred not to go (either at all, or at that price), furniture you would not have paid that much for, house guests you would have preferred not to have, and many of the other suboptimal (and sometimes value-destroying) things you do to "get along".

Daniel Kuehn writes:

"Where does a typically fall in the real world" isn't a particularly meaningful question because it's a monotonic transformation. Again I think the private/household good entering a utility function is the better approach.

So then the question is maybe something like what is the marginal rate of substitution between some representative (or bundle of... but I'd have to think about MRS's of bundles) rivalrous and non-rivalrous goods.

THAT would actually help you get at this, of course.

The MRS of a given non-rivalrous and rivalrous good should be the price ratio of those goods.

Daniel Kuehn writes:

"if someone with an income of 50000 marrys someone with no income he/she is going to loose utility due to the marriage."

It's a wonder anyone marries!

Eelco Hoogendoorn writes:

Clearly, the model is simplified. It assumes that common property leaves us either equally well or better off. Why not make all property communal then?

Perhaps the agency overhead of a single party shopping with a shared wallet is small for a community of two; but anecdote would suggest this is a significant part of the day-to-day equation.

John Palmer writes:

It has been a long time since I looked at the studies, but this issue is closely related to how much compensation a spouse should receive when the other is negligently killed [wrongful death]. My recollection is that many courts (and articles?) concluded that one adult should receive about 70% of the income of the two together to be compensated.

Jason Brennan writes:

I'd guess I spend $3000 a year on stuff that's just for me, and my wife spends $3000 on stuff that's just for her. If we count what goes toward the kids as joint, non-rival expenditures, we're at something close to 98% non-rivalry!

Rob writes:

This one writes utility a little differently, u=c/(1+b), where b reflects the economies of scale in marriage. They say b=0.8. That implies a=0.85 in your utility function.

Hazel Meade writes:

I'm curious about whether there are any utility benefits to having an unemployer stay-at-home spouse.

At what point does the cost of feeding them, clothing them, and paying for their healthcare outweigh the tax advantages and marginal benefits of having someone who does the dishes and miscellaneous housework? Let's leave sex and companionship out of this for now ....

Granite26 writes:

If you think internet access in non-rivalrous, you're doing it wrong.

(i.e. there's only so many video streams a single connection will support)

Joe Smith writes:

False premise.

You assume that for one individual utility is equal to income. It is more likely that realized individual utility goes something like U = k * ln (income).

Consumer surplus will be part of the utility. How does that get factored in?

Being married allows me to consume jointly with my wife things I would not have bought for myself. But the marginal utility of that extra consumption for me must be less than the marginal utility of what I would buy if it was just me.

Yancey Ward writes:

Jeez, this marriage sounds like it is bad for the economy and should be barred.

Thomas Boyle writes:

I nominate Yancey Ward as thread winner.

Andrew_FL writes:

When you say "being single is a luxury" do you really mean being unmarried is a luxury?

Joe Smith writes:

Let's leave sex and companionship out of this for now

But sex and companionship are at the core of most marriages. The economic part is incidental.

JLV writes:

The married couple faces different prices, though, effectively. For perishable goods, they can buy larger quantities without it spoiling, paying a lower cost per unit. This is true even if perishable goods are rival.

Steve S writes:

I don't know of any literature on the subject, but one factor that might affect "a" is whether your income is being spent on goods or services. I can think of counter-examples for each, but it seems that largely, goods skew rivalrous and services skew non-rivalrous.

I would imagine that the lower class would benefit from this the most, as the fixed costs of "keeping a home" (pots/pans, beds, couch) are mostly the same regardless of whether there are 1 or 2 people in a home.

NZ writes:

Why assume both parties keep working? The point of marriage isn't to gain a lifelong boinkable roommate who has legal obstacles to moving out, it's to start a family. And so most couples who get married end up having kids, and usually within a few years of marrying.

I know you were trying to keep the equation simple, but then you asked about how it plays out in the real world. In the real world, the equation doesn't stay that simple.

Daniel Kuehn writes:

It occurs to me that the average person reading this title would have thought it was about either domestic violence or love triangles.

yarbel writes:

I think this model is missing some essential parameters. It would seem to follow from this model that having all of humanity under one roof would be advantageous...

john hare writes:

Two things missing from your equation are risk and govt support. Both were addressed by multiple commentors on your single is luxury post.

Risk of expensive divorce ruining your financial life cannot be ignored in the equation.

Govt support for those below the poverty line cannot be ignored either, for those that would lose redistribution benefits with marriage.

In an ethical world of rational people, your equation would be accurate. Experience suggests we often don't live in that world. By the time you factor in those two rs, marriage looks like a bad idea to a growing percentage of the population.

Also, in answer to Evan in comments on the other post, I have met many women that do view children as an income source.

nl7 writes:

Slightly cramped perspective on marriage and rivalry. I love my partner and when I buy food that she eats, I appreciate that she enjoyed it. So even though that's food I can't enjoy (rival) it is replaced by something I do enjoy (happiness due to my feelings of affection and empathy).

So I am economically consuming a good even when I am not biologically consuming it, if I gain happiness from its use by my partner. Which may in some cases be greater than merely eating it myself - particularly if it's some sort of treat or luxury item.

Henry writes:

Something to consider is that many of these benefits of marriage can be semi-replicated by having roommates. One of the advantages of marriage, then, is having an especially compatible roommate. This reduces the rivalry of a house, since "space for yourself" is somewhat of a nebulous concept - unless you're in a very small house there isn't a lot of physical rivalry, things like privacy and personal space are more important, and those are a lot less concerning with a loving spouse than a pseudo-stranger roommate.

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