In the comments on my previous post contrasting minimum wage and prostitution, Sister Y argues that prostitution in fact has an externality. Some individuals find prostitution morally objectionable, and so they suffer mental costs when someone else hires a prostitute. The idea that we have preferences over each others actions, and that this can lead to conflicts between welfare analysis and various notions of liberty, is a longstanding issue in economics that owes much to Amartya Sen. However, I think the prostitution-as-externality argument is fairly easily resolved and doesn’t generate any conflicts between liberty and welfare analysis.
To illustrate, allow me to use characters from HBO’s Hung, which stars Tom Jane as middle-class, suburbanite, male prostitute Ray Drecker.
Say Ray’s friend Lenore wants to purchase Ray’s prostitution services and she values them at $400. But when Lenore does this it bothers Ray’s other friend Tonya. If the negative utility Tonya experiences is worth more than $400, then the market provides a mechanism for Tonya to satisfy her wants: she can pay Ray $401 not to sleep with Lenore.
You might argue that contracts aren’t complete enough to guarantee that Ray won’t sleep with Lenore anyway the moment Tonya turns her back. But what Tonya can buy from Ray for $401 is only an hour of not sleeping with Lenore, because that is what one hour of his time is worth. If she wants to pay Ray to never sleep with Lenore she has to pay the net present value of all of the future services.
For those who morally object when Ray sells himself to anyone, not just Lenore, this is a moot point because there are other clients anyway, so paying to not sleep with Lenore doesn’t accomplish much less prostitution. The point is that because prostitutes offer a flow of services Tonya has to pay Ray not to sleep with all of his potential clients if she wants him to not be a prostitute. Essentially she has to buy the entire flow of services.
This makes contracting much less simple: if you don’t like prostitution then you can hire the prostitute to do something else. In this way the presence of lots of people who object for any reason, moral or otherwise, to prostitution can drive down the quantity of prostitution services by bidding up their price. What this means is that markets are fully capable of internalizing the mental costs borne by those who dislike prostitution.
People will probably object that this is unbelievable, and that even if it happened once in a while, in the real world this would never be enough objectors to affect the quantity of prostitution. I think this is correct. After all, the objectors would have to value preventing prostitution at more than average rate of $300 an hour in order to outbid the existing buyers. But what this tells you is that the marginal utility gained from prostitution by consumers would vastly exceeds the marginal disutility to objectors.
I think objectors know. After all, market based solutions are possible and yet you never hear objectors push for anything but prohibition. This tells me that their willingness to pay is pretty low, and therefore so is their disutility.

33 comments
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Thursday ~ November 4th, 2010 at 9:39 am
DJAnyReason
The context of Sister Y’s comment was in your defense of anti-littering laws. Your argument here can be applied the same to littering – if society values my not littering more than I value my right to litter, they can pay me not to. So, at this moment, I don’t see why banning prostitution is bad, but prohibiting littering is ok.
Thursday ~ November 4th, 2010 at 11:46 am
imaginary_nums
Yeah, could you respond to DJAnyReason?
If Karl offered you $100 to dump his trash on my lawn, presumably I shouldn’t have to offer $101 to prevent that.
However, I agree that “offending god” or whatever is a ridiculous externality that we shouldn’t legislate on, but Sister Y has a good point that it is hard to define and quantify externalities. Do we just do it on public consensus?
Thursday ~ November 4th, 2010 at 12:01 pm
Johnnie Linn
A public consensus will exist if the act in question is a public bad, or the mitigation of it a public good. The public badness of littering might depend on where it happens: the front yard–yes, the back yard, not so yes.
The problem with prostitution is that an external effect it produces is a public bad, namely envy. If a third party is envious of an act of prostitution taking place–”My morals prohibit my doing such a thing and I am envious of your doing it, and enjoying it, to boot”.–then many third parties may likely be envious. A public bad.
So with any public good/bad, government would have to come in to solve the free-rider/holdout problem.
Thursday ~ November 4th, 2010 at 10:17 am
teageegeepea
I’d like to hear an economist (preferably David Friedman) respond to Nick Szabo’s critique of the Coase theorem.
Thursday ~ November 4th, 2010 at 10:55 am
Johnnie Linn
teageeetc:
Negative sum games will not persist in the competitive equilibrium. Also, the “optimum” amount of force/threat would be determined on the margin and will already have been internalized. There will be professional force-users in the market. See this paper:
http://academics.concord.edu/linnj/PDF%20files/PER2007.pdf
Thursday ~ November 4th, 2010 at 11:58 am
Sister Y
In contract law, “illegal consideration” (as distinct from illegal contracts) is where I offer you $400 not to beat you up. You, of course, gladly accept (trembling in terror before my imposing 120 pounds of fury) – offer, acceptance, consideration, what’s the problem?
My point is that while free exchange is nice, we have to first decide what rights you have – in terms of what you are entitled to without paying for it ,and what you have to pay for. (E.g. Amartya Sen might argue that we are entitled to food and shelter just for being human, whereas a Victorian might tell a seven-year-old to get a job.)
Thursday ~ November 4th, 2010 at 3:18 pm
imaginary_nums
I guess a strict utilitarian would say that those “rights” can only be derived by considering all the problems and required legislation involved with putting the good on the market, and weighing those against the simplified view of just considering it a “right”, and taking the good out of normal markets.
While not rigorous, I think most people would say it’s less costly overall to make “not getting beat up” a right, whereas making “not getting aesthetically/morally (is there a difference?)” offended a right would cause all sorts of problems.
However if everyone agrees on a such an aesthetic/moral issue, it could be easy to make “not getting offended” a right.
Thursday ~ November 4th, 2010 at 3:27 pm
Sister Y
Yup – you illustrate yet another underlying problem, which is how to establish the initial set of rights. Majority rules? Consensus? Unanimity? Can the suffering of some be excused by the happiness of others? (Ah, comparing utility functions . . . )
Thursday ~ November 4th, 2010 at 3:31 pm
imaginary_nums
Are you saying others have utility functions??
Thursday ~ November 4th, 2010 at 6:14 pm
Sister Y
<3 Most of them. Humans who aren't in an irreversible coma, at least. Also probably dolphins and monkeys, though probably not lobsters and crickets. (If lobsters did have a utility function, it would be really cute and simple and piecewise monotonic, I'd bet.)
Thursday ~ November 4th, 2010 at 8:25 pm
Adam Ozimek
Do you really take seriously one individual’s claims over another individuals actions as “rights” when those actions don’t physically affect that first individual or their choice sets? The examples you give are about the right of a person to be free from physical harm. A visceral harm has to be pretty strong in order to be a harm from which one has the presumed “right” to be free from it. This I would say is not in the ballpark of consideration.
Tuesday ~ November 9th, 2010 at 3:39 pm
Sister Y
The nose/fist notion about physical harm being the important thing is widely shared among economists. But (a) it’s a lot more slippery than it sounds, (b) it’s still just based on intuition that is not universally shared, and (c) as a rule/model, it fails to cover all situations.
The nose/fist paradigm tells us little about what constitutes physical harm or how direct the physical harm must be or what level of intention is required. Vibrations, chemicals, sound, light, and smell are all physical interactions. Can I still wear my perfume without permission of others? Can I drive drunk, knowing this entails a greater risk of physical contact?
What argument can we offer to those who don’t buy the nose/fist paradigm, other than . . . that’s what seems right to us?
Cases like vaccination of children and my pet issue, reproduction, are not resolved by a simple nose/fist rule.
Friday ~ November 5th, 2010 at 5:46 pm
imaginary_nums
Really the utility function of a lobster could be quite complicated, as would any organisms’ when outside a very particular context. I mean, what space is the function defined over? Every possible sensory input?
That alone gets mad hectic, you’ll probably have dimensions over which it isn’t meaningful to call things piecewise monotonic.
But don’t get me started on whether utility functions are useful.
Thursday ~ November 4th, 2010 at 12:10 pm
Ted
Even if people were willing to pay enough to prevent prostitution and the courts could actually enforce this contract – it still wouldn’t happen in the real world. The coordination problem is simply too substantial.
Also, a quick note about legalizing prostitution. I’m opposed to it on entirely different moral grounds. In the ideal world I would be fine with consenting adults engaging in this sort of voluntary exchange. What I have a problem with is human trafficking. Ever since prostitution was legalized in the Netherlands back in 2000, human trafficking has skyrocketed there. There are thousands of recognized human trafficking victims in the Netherlands and hundreds more discovered every year – which means, given that most trafficking victims are illegal immigrants and face brutal violence and intimidation, that the number is likely substantially higher. It looks as though this human trafficking was caused by the legalization. Basically everyone in Holland realizes that criminal activity and human trafficking have gotten out of control and now they are considering a bill that imposes substantially more regulations to try and deter the activity. My personal opinion is that I find the act of enslaving women by private parties far more offensive and wrong than the government preventing two people from having sex for money. Since it appears legalization caused the explosion in the Netherlands, I’m very skeptical of whether we should legalize the activity.
There very rarely is a situation where something is entirely just or right – and in the case of prostitution the practical realities of enforcing a “no trafficking” law lead me to believe, morally, prostitution should remain illegal to ensure a more just outcome (i.e. less human trafficking).
Thursday ~ November 4th, 2010 at 4:11 pm
sardonic_sob
Is it possible that more human trafficking is being discovered, not that it has increased, because prostitutes are no longer afraid of the police?
And in any event, the solution is obvious: make pimping a capital crime.
Thursday ~ November 4th, 2010 at 10:51 pm
teageegeepea
One way they might coordinate is with an assurance contract. Bob Murphy is trying to use a web-site which provides that service in order to get Paul Krugman to debate him. I don’t know if I’d choose Murphy for that role, but it could be entertaining.
Friday ~ November 5th, 2010 at 10:10 am
Michael Price
I find this hard to believe. So a bunch of women claimed to have been enslaved because really they weren’t just illegally working voluntarily. Correct me if I’m wrong but pimping is still illegal right? So setting up a voluntary consensual business is made harder. Meanwhile the government does such a bad job protecting rights (according to you) that it’s cheaper to enslave people than hire them. Sounds like it’s not prostitution that’s the problem. There are a lot of activists out there trying to claim trafficing is a big problem so they can get government money to fight it. If it was then why aren’t the free prostitutes (and there must be some) the ones exposing it to get rid of the competition?
Thursday ~ November 4th, 2010 at 3:24 pm
imaginary_nums
Also, speaking of prostitution and sexytimes in general, how many people have seen the full picture used as a header for this blog?
http://www.its.caltech.edu/~weissman/modeled.jpg
Thursday ~ November 4th, 2010 at 5:40 pm
Johnnie Linn
I have always wondered what topic the lady was writing about. With the new pic we can see more of the blackboard but for some reason it’s hard to get a good focus on the writing.
Thursday ~ November 4th, 2010 at 8:58 pm
My name here
The topic seems to be particle physics, but either the specifics are over my head, or its a jumble of not quite right stuff meant to look impressive. I lean the second but its been a while since I’ve done any particle physics. There is a higher resolution version of the photo available here:
http://www.wallpaper-place.com/images/wallpapers/sexy_teacher_hd_widescreen_wallpapers_1920x1200.jpeg
Friday ~ November 5th, 2010 at 10:17 am
Johnnie Linn
The equations seem to be about the radial distribution function of ammonia, i.e., the probability that particular atoms in the molecule are at particular places. Also, someone with poor motor skills seemed to have scrawled something on the board perhaps to copy something already there.
I’m glad we have this cleared up.
Friday ~ November 5th, 2010 at 12:42 pm
imaginary_nums
Yes but it is not so simple.
You’ll notice that there are strange looking scrawls at the top of the board. Those look so unnatural because of the obvious photoshop job (hereafter referred to as “shooping”)
You can see that the center of the board is composed of pieces of the left side, copied and enlarged.
You can tell by the pixels.
Thursday ~ November 4th, 2010 at 3:31 pm
Yglesias » Prostitution Externalities
[...] think Adam Ozimek’s post on “The Visceral Externality of Prostitution” nicely illustrates why nobody likes economists: Say Ray’s friend Lenore wants to purchase Ray’s [...]
Thursday ~ November 4th, 2010 at 4:38 pm
Yglesias» Prostitution Externalities « Politics
[...] think Adam Ozimek’s post on“The Visceral Externality of Prostitution”nicely illustrates why nobody likes economists: Say Ray’s friend Lenore wants to purchase Ray’s [...]
Friday ~ November 5th, 2010 at 11:09 am
Overcoming Bias : Disapproving Via Bans
[...] Say Ray’s friend Lenore wants to purchase Ray’s prostitution services and she values them at $400. But when Lenore does this it bothers Ray’s other friend Tonya. … The marginal utility gained from prostitution by consumers would vastly exceed the marginal disutility to objectors. (more) [...]
Friday ~ November 5th, 2010 at 11:30 am
MrTimbo
It seems to me that one important issue is that paying to prevent the action simply won’t produce the satisfaction the prohibitionists are seeking, not because prohibition has no value to them but because the method by which the desired thing is achieved affects how much they desire the thing.
Friday ~ November 5th, 2010 at 12:42 pm
kharris
Um, actually, there is a bigger problem than finding enough people who are willing and able to pay for the time of all current prostitutes, and not to have sex with them. This slice of the labor market is not so different from all the others. When there is demand for services, the ranks of the unemployed can be drawn on to supply those services. There may not be a limitless supply of men willing to be paid to have sex, but the limit is not binding in any world we know of. All the money in the world would not be enough to prevent (male) prostitution. Pay today’s prostitutes to go sit the bench (by the pool) and a bunch of rookies will offer to take their place at bat.
Friday ~ November 5th, 2010 at 10:44 pm
Noumenon
I still haven’t seen a response to DJAnyReason. Also, could you give any real-world example where this phenomenon occurs:
if you don’t like prostitution then you can hire the prostitute to do something else… What this means is that markets are fully capable of internalizing the mental costs borne by those who dislike prostitution.
Is there any case where real live people have, say, hired abortionists as gynecologists to get them out of the clinic? I’d say that’s an illustration of how powerless the markets are in these kinds of cases, if that’s the only solution.
Tuesday ~ November 9th, 2010 at 11:58 am
Sister Y
This isn’t exactly the same thing, but I believe the Quakers used to buy slaves and free them, and I think American churches even up to the present day have engaged in this practice. Of course, it creates a market for slaves . . .
Friday ~ November 12th, 2010 at 10:12 am
An Economic Analysis of Prostitution | John Goodman's Health Policy Blog | NCPA.org
[...] whole post is actually quite funny. Matt Yglesias weighs in [...]
Sunday ~ January 30th, 2011 at 9:02 pm
More against the stationary bandit overlord « Entitled to an Opinion
[...] usage of the Coase Theorem. His primary target, David Friedman, has not responded but Johnnie Lin did with a paper of his own. LikeBe the first to like this [...]
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