This morning I saw an ad for Kinoki foot pads, which allegedly suck toxins out through the soles of your feet while you sleep. Right. But if the description alone wasn’t sufficient to set off your B.S.-detector, this should: they will send you a two-week supply for $19.99, and then if you like it you can get a lifetime supply for free! (Plus shipping & handling.)
That’s the exact opposite of the drug dealers who hand out free samples to new customers, thereby signaling their confidence that you’ll come back for more. With Kinoki foot pads, they charge you for the first shipment and give you the rest free, thereby signaling their expectation that they’ll never see you again.
(Am I misunderstanding the offer? Go to 1:17 in the online video, which is the same ad I saw on television.)
Friday, January 18, 2008
Bad Signaling
Monday, October 22, 2007
Bowling vs. Mini Golf
A recent conversation about dating activities raised the following question: Why is bowling more popular than miniature golf for a date? (I don’t know this is true, but based on the relative number of bowling alleys versus mini golf courses in my region, it seems to be.) The obvious answer? Bowling alleys typically serve booze, while mini golf courses don’t.
But that answer raises a different question: Why don’t mini golf courses serve booze? At first, I figured the answer had something to do with geography. A bowling alley can have one bar convenient to all the alleys, and players can go grab drinks during other players’ turns. But given the circuitous nature of mini golf courses, mini golf players would have to walk long and winding paths to and from a single bar.
Still, it seems like there could be some kind of solution. Have employees wander around with trays of food and drink, like at a baseball stadium. Or place small bars in strategic locations between holes (say, between hole 8 and hole 13, which happen to be contiguous in your mini golf course). If mixed drinks take too long to prepare, serve beer and wine only.
A better explanation, I think, is provided by inter-customer externalities. Drunken players tend to take longer to finish, thereby delaying other customers. In a bowling alley, this effect is very limited – you usually only get ten frames, you only get two shots per frame, and you can only delay people whose games have not yet begun. But in a mini golf course, slow play can affect every player behind you on the course. And while there is allegedly some limitation on the number of swings (6 swings max, I believe), players sometimes flout this rule, and in any case 6 swings can take twice as long as 3 (the usual par).
With most inter-customer externalities, the natural solution is to “tax” the players who create it. This could be accomplished by simply charging more per drink. But if the required tax is especially large – as it might be in this case, given how many other players are affected by any one player’s slowness – then the total price could be higher than most players are willing to pay. And with few enough buyers, it’s just not worthwhile to incur the fixed costs of setting up bars, acquiring liquor licenses, and so on. Boozehounds will just have to wait ’til the nineteenth hole.
Friday, October 19, 2007
Horwitz on Capitalism and the Family
Allow me to recommend "Capitalism and the Family," an essay recently written by Steven Horwitz, Professor of Economics at St. Lawrence University, and published in The Freeman. Steve's thesis, in a nutshell: "Over history measured in centuries, the evolution of the family can be summarized as a movement of work from the household to the market, with the results being the liberation of human beings from unnecessary labor and a shift in the central functions of the family."
In contending that "the market is a key reason why the family has changed the way it has in recent years and that such changes are good," Steve breaks from both the right and the left. Those on the right, while paying lip service to the market, resist the liberating effect it has had on family life. Those on the left, in contrast, celebrate our liberation from household tyranny but fail to give due credit to market forces.
Steve plans, during his present sabbatical, to complete a book expanding on this unique and fruitful approach to family life. Keep your eyes peeled for it. Steve's work has always impressed me as well informed, well reasoned, and well written. About family life, moreover—something we've spent long and pleasant hours discussing—you can count on Steve for sage and fundamentally decent judgment.
Tuesday, September 11, 2007
Toilet Seat Signaling
In Discover Your Inner Economist, Tyler Cowen takes up the issue of toilet seat norms.
One individual wrote an economic or “game-theoretic” analysis of whether to leave the toilet seat open or closed. He used complicated mathematical formulas to conclude that economizing hand motions is the key variable. In his account, we should leave the toilet seat “as is” when done. Why bother switching when the seat might be needed in the same position again, and you’ll just have to switch back?I’d be flattering myself to assume he’s talking about me, since I’m hardly the first to apply math and econ to the toilet seat issue (indeed, my posts were all inspired by others’ analyses). But I have taken the position in question, which Tyler indicts as ignoring the signaling function of the always-down norm:
A more sophisticated approach, based on a longer chat with one’s Inner Economist, would recognize that such matters should be arranged to please one’s wife, and that usually means putting the seat down after use. It is a symbolic recognition of her value.There is something to be said for keeping peace in the household by making small sacrifices. If the women in our lives really think toilet-seat-down is that big a deal, then a wasteful extra hand motion is a small price to pay for domestic tranquility. And if it seems like I think it’s a big deal, that’s only because I get a perverse joy from blogging about the economics of everyday things (in my real life, I generally capitulate to the always-down norm).
The economic idea of “signaling” refers to sending a message by choosing a costly action. I signal when I buy my wife flowers on Valentine’s Day; I am not convinced she needs the blossoms in mid-February. I am sorry to say this to all you cheapskates out there, but the cost of signaling is the entire point. A fancy diamond ring goes further than flowers. ... Such gifts show we value the gift receiver, even if diamonds really are a waste of money.
That said, I don’t think Tyler’s signaling theory of toilet-seat norms really works. As Tyler notes, the whole point of signaling is to incur a notable cost. The costly signal helps to distinguish two different groups of people by requiring a sacrifice that only one group will make. Thus, higher education is a signal of high productivity because education is costly enough (in terms of effort) that low-productivity people will find it too costly to acquire. If education is too simple – say, because grade inflation makes it possible for everyone to get a degree – then it fails to perform a separating function. Now, apply this to toilet seat positions. In truth, the act of shifting the seat is very low cost, regardless of who does it. (It’s nevertheless true that change-when-necessary is the efficient norm, because it makes the already-low costs lower still.) It’s hard for me to believe that such a simple activity will really distinguish between caring and uncaring partners, because the signal is too easily faked by the uncaring.
In addition, while signaling games are often inefficient (at least if we ignore the value of the signal), some are more inefficient than others. The best signals are ones that, in addition to conveying information, also provide benefits or services that would otherwise be neglected or underprovided. Take the case of charitable giving. For many donors, charitable giving is about signaling to other people: “I am generous, I am caring, I am trustworthy.” But since the giving usually takes the form of a transfer of wealth, there is little deadweight loss, and value is transferred to people who really need it. A major theme of Tyler’s book is that there are many things we can do to improve the efficacy of our charitable giving. Most of the changes he recommends would produce greater external benefits without substantially reducing the strength of our signals.
Why, then, should we defend a clearly wasteful toilet-seat norm as a means of signaling caring to our partners, especially when less inefficient signals – with greater signal strength – are readily available? As I’ve suggested before, couples could bargain their way to the efficient toilet-seat norm via an agreement by men to give more frequent gifts and foot rubs.
Incidentally, we should note that both parties in a relationship need to send signals to each other. Given that both men and women benefit from having their preferred toilet seat norm, why should this particular signal pass from men to women, instead of the reverse? If we’re going to advocate inefficient norms as signals, why shouldn’t women signal caring to the men in their lives by always putting the seat up? (This would be even more inefficient than always-down; but since p[#1] > p[#2], it would still be appreciated by men.) I’m not actually advocating this, but the possibility should give us pause. Why aren’t women willing to send that signal? Might it have something to do with its inefficiency, especially relative to other ways they show us they care?
Sunday, July 15, 2007
Ladies' Night
Ilya Somin, in two posts, criticizes a class action lawsuit against private night clubs that have ladies’ nights, during which they offer lower drink prices to women. The second post, in the course of explaining why the case shouldn’t be certified for a class-action lawsuit, gets to the economics of the matter:
[M]any of the members of the class in question ("men charged more money or burdened by stricter time restraints than women" at the night clubs in question) actually benefit from these practices. At the risk of belaboring the obvious, a key purpose of ladies nights at night clubs is to benefit (heterosexual) men. Many night clubs and bars become relatively unnappealing [sic] to men because the male-female ratio is too high, reducing male patrons' chances of picking up a date. By attracting more women, ladies' nights improve the dating odds for male patrons. [emphasis added]The blogosphere has visited this territory before. Alex Tabarrok explained the model of inter-customer externalities in a 2005 post and applied the conclusions directly to ladies’ nights. More recently, I applied the model to sex parties. However, on re-reading Alex’s post, I was struck by the following passage:
If men have a higher demand for going to a bar with many women ... than women have of going to a bar with many men ... then in a competitive market the bar must set a higher price for men than for women.Hm. Problem is, while ladies’ nights certainly exist, they are not the norm. They typically occur only one or two nights a week, usually weeknights. One explanation is that men’s and women’s demands for bars don't actually differ that much. Another explanation is that the nightclub scene is not competitive. Based on personal observation, I find both explanations highly implausible. So what gives? Why isn’t every night ladies’ night?
The natural answer is that the male-to-female subsidy happens spontaneously, through the mechanism of men buying women drinks. This norm has the added advantage of making sure the subsidy doesn’t go to all women, but only those who are actually interacting with men at the bar. And the subsidizers aren’t all men, but only those who have the greatest interest in meeting women.
If I’m right, then the problem is turned on its head. The question isn’t why some nights aren’t ladies’ night, but why any nights are. Apparently the spontaneous subsidy must be insufficient on some nights; but why? I’m just guessing here, but I suspect it has something to do with the ladies’ intentions in coming to the bar. If they come to the bar for the opportunity to meet men (but not too many men, as that can be threatening and creepy), then the spontaneous subsidy works well enough. But if women come to the bar primarily for other reasons – e.g., to chat with girlfriends after work – then the spontaneous subsidy is less attractive because a woman must chat with a man to get it. The bar-sponsored subsidy, on the other hand, can attract women even if they are not primarily interested in meeting men. Of course, this explanation implies that the men’s dating odds are lower than they seem. But the men may tolerate this for two reasons – first, because even uninterested women can be pleasant to look at, and second, because men still stand a better chance than if there weren’t as many women present. At least some of the women who come for other reasons may nevertheless be interested if the right (or right enough) guy makes a pass.
Thursday, July 12, 2007
L&S: Tissue Issues
I’m usually very optimistic about new technologies, but I’m not looking forward to this: automatic toilet paper dispensers. Those damnable automatic hand towel dispensers are bad enough. They never dispense enough paper unless you stand there for 5 minutes waving your hand in front of the sensor. But at least wiping my hands on my jeans is a viable substitute for paper towels; the same cannot be said of toilet paper.
Of course, the justification for automatic dispensers is that people overuse paper. And they probably do, given that the marginal cost is zero. (Steve, looking over my shoulder, also observes that risk-averse people are understandably concerned with the risk of having too little paper in one's hand.) But why is that so? Why not charge by the sheet? Presumably because the transaction costs are too high: I don’t want to be depositing nickels in the toilet paper dispenser (and, Steve adds, it’s hard to reach your pocket if your pants are down). Maybe a credit-card swiper (Steve suggests "the sWiper®") would provide a viable alternative. I’d rather run the plastic once than sit there frantically waving my hand in the desperate hope of getting another wad of paper.
[Aside: This really has nothing to do with the L&S seminar, except for Steve being present to watch as I composed this post.]
Friday, June 22, 2007
Return to Bathroom Arena
I’ve blogged about toilet-seat norms twice before. Now there is another contribution to the debate. However, I don’t think it’s especially helpful. Shorn of all the fancy game-theoretic jargon (like “trembling-hand perfect equilibrium”), the new article shows two things: (1) The change-when-necessary rule is more efficient than the always-down rule. But we already knew that. (2) If the woman can costlessly punish the man for leaving the seat up, then she can enforce the inefficient always-down rule anyway. The punishment in question is referred to as “yelling,” though we might imagine other punishments.
This is really a “duh” proposition. Everyone knows that female disapproval is what preserves the always-down rule in some households. The question, from the inception of the debate, has been whether such disapproval is warranted.
Moreover, the assumption (implicit in the article) of costless punishment is not justified. Yelling involves an expenditure of effort and time. Alternative punishments might involve the woman placing an embargo on certain activities that she, too, finds enjoyable.
The article says that always-down necessarily prevails, but that’s no longer true once punishment is costly. The analytical question is whether the woman can make her threat to punish credible. This can be difficult, since the punishment will always have to be imposed after the seat has been left up. Yelling thus imposes a cost on the woman (as well as the man) without making her life any easier at that moment.
In a one-shot game – say, if the woman is only a one-night visitor – imposing the punishment is simply not rational, because she will impose a cost on herself with no future benefit. So for the threat to be credible, the man must believe the woman is irrational (and not just broadly irrational, but irrational on this particular matter). She must be willing to yell even if it won’t do a bit of good.
In a repeated game, as occurs during long-term cohabitation, the threat can be credible even if the woman is rational. This is where the game theory gets more complicated. But put very simply, future interactions mean that yelling can indeed affect future benefits, thereby justifying the cost. But the logic breaks down if the end of the repeated game is in sight – for instance, in the event of an impending break-up or divorce. In such cases, the credibility of female threats will crumble, so we should expect the change-when-necessary rule to emerge. This is an empirically testable proposition. Any takers?
UPDATE: Hello, Economist readers! Maybe-Megan-McArdle disputes the argument for the efficiency of the change-when-necessary rule. A few responses:
First, MMM emphasizes the costliness of checking the lid’s position. In the daytime, the cost of checking is negligible – it happens instantaneously upon seeing the toilet. So if MMM’s case for always-down rests upon night-blindness and midnight surprises, then she should immediately concede that change-when-necessary is the efficient daytime rule.
Second, about those midnight surprises. Honestly, I’m just incredulous that women are blindly backing up to their toilets without at least sticking out a hand to locate the seat! I would suggest that this is an inherently dangerous activity, irrespective of the rule for seat-position. In any case, the whole problem can be obviated at a low fixed cost ($3.65) and near-zero marginal cost (about 2 cents/year) by installing a nightlight. With low enough wattage, night blindness is not an issue. Plus, a nightlight has ancillary benefits. Walking around in pitch darkness carries many dangers worse than the midnight surprise.
Third, about gender equity. MMM notes that seat-checking costs are borne almost entirely by women. This is true (unless men pony up for the nightlight – which I, for one, would happily do). But under the always-down rule, the seat-adjustment cost is borne entirely by men. So if men’s advocacy of change-when-necessary is tainted by self-interest, so is women’s advocacy of always-down.
More importantly, as I emphasized in a prior post, there is no necessary conflict between efficiency and equity here. If change-when-necessary is indeed the more efficient rule, then side-payments in the form of cash or foot-rubs could be used to compensate women for acquiescing to the socially optimal rule.
P.S. My interest in this issue is purely intellectual, since in my lone-bachelor household the operative rule is always-down. This is an ingrained but inefficient habit, a consequence of having internalized oppressive gender-biased norms. It being too late for me, I speak only for the benefit of future generations.
Tuesday, May 15, 2007
The Tipping Point
Via Julian, I find the Esquire guide for tipping in bars, which says (among other things) that you should tip “at the very least one dollar on a beer or highball and two dollars on a cocktail.” Asks Julian, “I'd been under the impression that $1 [per cocktail] was more or less standard; now I'm wondering whether I've been gradually accumulating the seething hatred of all the booze-slingers at my local bars.”
I share Julian’s impression that $1 is still standard, although I often tip more generously for better service. However, $1/drink seems to have been the norm for a rather long time, without any inflation adjustment. If $1 was the right tip in the year 1998 (and I definitely recall giving $1 tips back then), it should be $1.22 by now, according to the Inflation Calculator. Of course, I’m assuming otherwise constant conditions of supply and demand in the market for bartenders, as well as constant (inflation-adjusted) compensation by the bar owner.
The problem, of course, is that $1.22 is a rather inconvenient amount to tip. The inconvenience is exacerbated by the attitude that leaving change is chintzy (the Esquire guide also advises, “Don't pay or tip with change”). So the $1 tip remains in place.
I propose a simple solution: tip $2 for the first drink and every fifth drink thereafter, and $1 each for the four drinks in between. This will average out to $1.20 per drink. If you think the $1 tip has been stalled since before 1998 (without sufficient adjustment in regular wages), throw in the $2 tip more often. In case you’re wondering, to justify $2 for every drink, we’d need to assume the standard tip has been stalled since about 1983.
Or, if you think the whole tipping convention is unnecessary (except maybe for exceptional service), you could continue to insist on dropping $1/drink, and wait for the supply of willing bartenders to shrink enough to force bar owners to pay them more. But while you’re doing that, I’ll be tipping more and getting served before you.
Monday, April 02, 2007
Painting at the Margin
I did a bit of painting, long ago, as an art student. I never got around to working in oils, though. D and the kids remedied that lacuna in 2005, when for Father's Day they signed me up for an oil painting class. I took the class later that summer, completing one painting (which I later pitched) and nearly finishing the work below, "Aloe Study v. 2007.03.29."
Here's the full painting:
Here's a detail:
Why did it take me a year and a half to complete the painting? For a long while, I was content to leave it sitting on an easel in our reading room, squinting at it from time to time and telling anyone who would listen why I remained dissatisfied. Finally, last month, sorely needing a break from my paying gig, I added a few final touches and signed off on the painting.
Properly speaking, I didn't so much finish "Aloe Study v. 2007.03.29" as I gave up. Oils allow you extraordinary leeway to work, rework, and (alas) overwork a painting. That constitutes both the virtue of the medium and its peril. Painting in oils has thus forced me to learn not just how to mix the stuff and apply it to canvas, but also to calculate when the marginal costs of an additional brushstroke outweigh its marginal aesthetic benefits. I can't say that I got it right this last time around, but I don't think I completely botched it, and I enjoyed the exercise.
Friday, March 30, 2007
Anchor Ages
Here’s one of my theories that I really can’t justify. In fact, I’m not sure it’s even mathematically possible. But somehow it just seems true, based on personal observations. (Remember how I promised more half-baked posts? Yeah, this is one of those.)
I believe each individual has an “anchor age” at which his apparent age is the same as his chronological age. Prior to this age, he looks old for his age; afterward, he looks young for his age. I’m not saying that a person always looks like his anchor age, only that his physical age advances more slowly than calendar time, and the anchor age is the crossing point. Take someone whose anchor age is 25. At 22, he looks old for his age – maybe 23. At 28, he looks young for his age – maybe 27. So in a six-year time span (from 22 to 28), his apparent age has increased by only four years (from 23 to 27). Graphically, it looks something like this:
So how does the average 28-year-old look older than this particular 28-year-old? While his anchor age is less than 28, others’ anchor ages are greater. Our idea of what the typical 28-year-old looks like results from averaging both groups.
Put differently, my half-baked theory is that the aging process appears faster when viewed in cross-section (many individuals of different ages at a single point in time) than when viewed in time-series (a single individual viewed over a period of years).
Like I said, I’m not sure this is mathematically possible. The main difficulty is there’s an endpoint problem. On the young end of the age spectrum, most people should not yet have reached their anchor age, so the average-of-apparent-ages should be greater than the chronological age. On the old end of the age spectrum, most people should have surpassed their anchor age, so that the average-of-apparent-ages should less than the chronological age. Both of these are impossible, if our notion of what chronological age X looks like is the average-of-apparent-ages of people at age X.
But maybe my theory can be saved via some kind of misperception (like this one) or non-linearity in the physical aging function. Suggestions welcome.
Sunday, March 18, 2007
Karaoke Queuing
Rationing by price is usually more efficient than rationing by queuing, so there’s always an economic puzzle to be solved when queuing is employed in voluntary markets (as opposed to contexts in which pricing is banned or controlled, such as organ donation or rent-controlled housing). Why, for instance, do nightclubs and restaurants choose to make people wait outside, rather than hiking their cover charges or prices for food and drink?
Economists have proposed a number of answers to the nightclub/restaurant puzzle, but I’ve lately been pondering a different puzzle: karaoke queues. At karaoke venues, the number of people who want to sing is almost invariably larger – sometimes much larger – than the number of singers who can be squeezed into the available time. It would obviously be possible for karaoke hosts to charge a price-per-song large enough to reduce the number of willing singers to the number of available slots. (Indeed, profit maximization might even dictate having fewer singers than available slots.) But karaoke venues almost universally set a price of zero and ration by waiting instead. I’ve only encountered one karaoke venue that had a non-zero price, and even that price was far too low to balance quantity demanded and quantity supplied. What gives?
The obvious answer is that there really are prices; we call them bribes. Anyone who’s done much karaoke knows that most hosts will bump you up the queue if you give them extra-large tips. At some places, your chances of singing if you don’t bribe the host are pretty slim. But why the subterfuge? Why not simply set one price for everyone? The bribery system has a variety of problems, most notably its uncertainty: it’s not always clear whether this particular host takes bribes, how much you need to pay, what you’re really paying for (singing sooner or singing at all?), and so on. I’ve gotten burned by this system myself, when I’ve given “tips” and only found out later that this host sticks to the established queue.
So I have two hypotheses:
1. The absence of prices results from the contract between karaoke host and venue management. The management pays the host a flat fee for the night (this is fact, not speculation) and specifies a price of zero. But why would the management do that? Because the venue makes most of its money from booze, and booze sales are maximized when you have a large number of people waiting around in the hope of getting their chance to sing. I know there are many times when I’ve considered going elsewhere (home or another bar), but I’ve stuck around with the sometimes-mistaken impression that I’ll be singing soon. So the management insists on a zero price to keep as many people hanging around and drinking for as long as possible. This hypothesis is consistent with the common practice of keeping the queue secret instead of letting everyone know where they stand. If the list were public, many people might realize they’re too far down the list and choose to leave.
2. The bribery system facilitates a clever system of price discrimination. Lots of people want to sing, but only a fraction want it enough to pay a bribe. Say you have 50 available slots and 100 people who want to sing. A price of $2/song might reduce the number of willing singers to 50, yielding $100 of revenue. But if you keep the queue in place, the 10 or 20 most motivated singers (who would only have paid $2 like everyone else) will cough up $10 each, yielding revenues at least as high and probably higher than under the pricing scheme. But why not charge everyone $2 each and charge the most motivated singers more? Because then the motivated singers would only be paying for the privilege of singing sooner, rather than singing at all, and they won’t pay as much for that. The bribery system does a better job of sorting the motivated from the unmotivated singers.
These two explanations are not mutually exclusive, but there is a tension between them. If the management is trying to maximize the number of drinking patrons by keeping the price per song at zero, bribery partially thwarts the goal. Motivated singers who pay to sing might leave shortly thereafter, and if other patrons realize they’re being pushed down the list by bribery, they might opt out as well. There may be a kind of principal-agent problem at work: the karaoke host (agent) has incentives that run counter to those of the management (principal), and bribery is a form of shirking. The need to conceal the shirking helps explain why karaoke hosts choose to keep bribery on the down-low while maintaining a secret queue. Still, given that most karaoke patrons know that bribery goes on, it’s hard to believe the management is oblivious. It’s more likely, I think, that the management considers the bribery a portion of the host’s compensation, provided the practice is not so obvious that it drives customers away. This enables the management to pay a smaller flat fee to the host, in essence taking a cut of the bribe revenue. Thus, the current arrangement might in fact constitute an optimal contract between management and karaoke host.
Thursday, March 08, 2007
What's Comb Over You?
Here is the paradox of the comb-over: Men with comb-overs are presumably more image-conscious than most men, because the whole purpose of the comb-over is to hide baldness. Yet those who wear comb-overs almost always look worse than those who bare their bald skulls with pride.
Given the near-universal scorn for comb-overs, how do some men end up with them, and why do they keep them? It seems obvious there must be some degree of self-deception going on. They must believe that others don’t notice, or that the comb-over still looks better than the bald spot. But how did they get there? What psychological mechanism facilitates this level of delusion?
Naturally, I have a theory. I surmise that comb-overs don’t happen all at once, but by degrees. More importantly, in the early stages the comb-over actually works. Imagine a man whose hair is just starting to get a little thin on top. By moving his part just a tiny fraction of an inch toward his temple, he will increase the apparent thickness on the top of his head, while leaving his part in the acceptable range. He will actually look better! But as the thinning advances, the head-owner gradually moves his part farther and farther down the side of his head, until eventually he winds up with a full-blown comb-over.
This process would fail, however, if there were a clear line between moving-the-part and combing-over. Imagine if our heads were shaped like blocks, with actual corners left and right. As soon as you started to comb your hair from the flat side over the corner onto the flat top, the comb-over would be instantly obvious. But our actual heads, being more oval in shape, don’t permit such a bright-line distinction.
I conclude that comb-over-ers have fallen victim to a version of the sorites paradox, also known as the paradox of the heap. This paradox shows that when a concept has vague or fuzzy boundaries, it’s possible to move, by a series of individually logical or sensible steps, to an outcome that is thoroughly untenable. For instance, if you start with a heap of sand, you can always remove one grain of sand and still have a heap. But apply that premise repeatedly, and you’ll eventually conclude that a single grain of sand constitutes a heap. That is the position of the late-stage comb-over victim, who has concluded those last few pathetic combed-over strands constitute a full head of hair.
Tuesday, February 27, 2007
Evidence
A few months ago, when I posted my ugly furniture theory, commenter Kevin requested photographic evidence of the ugliness in question. I didn't have a digital camera then, but I do now. 
I rest my case.
Monday, February 26, 2007
Pricing a Swingers' Party
Neal sent me the link to this post about a swingers’ party. Examining the pricing structure, the author observes, perhaps not surprisingly, that women can get in more cheaply than men. Specifically:
(a) unattached men are not allowed in for any posted price;
(b) the implicit price of admission for a man, when calculated as the price for a hetero couple minus the price of an unattached woman, is higher than the price for an unattached woman; and
(c) the implicit price for a man, when calculated as the price of an MMF trio minus the price for a couple, is again higher than the price for an unattached woman.
The author then speculates on the causes:
So, is this wholly a matter of supply and demand? Or are swingers parties focused on protecting women from men, or are they protecting men from each other? Perhaps the overarching message is that men’s sexuality is still deemed dangerous, problematic, and uncontrollable.There is, of course, the simple fact that men are more willing to attend a sex party than women, so if this market is less than fully competitive, price discrimination could allow the organizers to charge men a higher price. But the more important fact is that men’s greater willingness to attend creates substantial inter-customer externalities. Every added woman who attends makes it easier (that is, less costly) to provide value to the other attendees at the party. Added women thus create a positive externality, so it makes sense for the organizers to subsidize their attendance. In a 2005 blog post, Alex Tabarrok discussed how the same story explains why it’s less expensive to rent a U-Haul van for a one-way trip from Las Vegas to L.A. than the reverse:
At the end of the day, UHaul would like the same number of trucks at each of its locations. But this is possible only if departures equal arrivals and to help achieve that balance UHaul lowers the price on the low demand Vegas to LA trip and raises it on the high demand [LA to Vegas] trip. (It’s more complicated than this because there are many more than bi-directional considerations but you get the idea.)And as Alex observes, the same analysis also explains why bars will subsidize women’s drinks on “ladies’ night.” The only difference in the case of a swingers’ party is that sex is more explicitly on the table.
Put differently, a customer who travels from Las Vegas to LA reduces the cost to UHaul of running its network because it lets UHaul sell an LA to Las Vegas trip. The direct costs may be similar but the indirect costs related to running the network are very different. UHaul's pricing strategy reflects both the direct and indirect costs.
There may also be another externality at work here – the negative externality that I first discussed here in the context of bars and clubs. Although straight men and women both want to convene in the same place, men are willing to tolerate a higher male-to-female ratio than are women. When the male-to-female ratio rises above women’s tolerance level, women start to leave, thereby pushing the ratio higher, inducing yet more women to leave, pushing the ratio yet even higher… with the resulting unraveling effect known affectionately as a sausage fest. Of course, if men foresee this outcome, they won’t bother to come either. Obviously, it’s in the financial interest of the party organizers to prevent this result, whether or not they have any concern with protecting women or controlling men’s sexuality. They can do so in two different ways: One, they can keep men out (via a velvet rope or, in this case, a ban on unattached men). Two, they can employ a price differential to internalize the negative externality (via higher priced drink prices at a bar or, in this case, a higher entrance fee).
Thursday, January 18, 2007
Doing Lines, Part 2
A couple of weeks ago, I promised a couple of new ideas for increasing the blog’s level of activity. Here is one of them: more half-baked posts! This post’s topic is one I’ve been wrestling with for a couple of days, and it’s turned out to be surprisingly difficult to wrap my head around. I’m not sure at all I’ve reached the right conclusion, but I’m posting it anyway to see if my readers (especially the mathematically and economically inclined) can confirm or correct my thinking.
As I stood in line to buy popcorn at the movie theater on Saturday, I noticed that the young couple in front of me had split between two lines: the girl stood in my line, the boy in the next line over. When it became clear that the boy’s line was moving faster, she joined him. This is a strategy that I often use myself when I have a companion. I have a vague impression, however, that there’s a mild social stigma against it. No one will actually call you out for it, but they might give you the stink-eye. When I do it, I generally try to be subtle – no words, just gestures.
But as I stood in line Saturday, I began to think the stigma is unjustified. The line-splitting strategy does not just help those who employ it; it also performs a useful social service. The line-splitters improve the efficiency of the system by allocating more customers to the faster checkers, thereby lowering the average waiting time. They also tend to equalize the waiting time across lines, much as they would if they knew in advance which checker was fastest and simply chose that line – yet the effect occurs without their actually possessing such knowledge.
Or at least, that was my logic while standing in line. I later formalized my logic like so. Suppose there is one fast lane and one slow lane. The lines are currently equal in length because customers don’t know which lane is faster. Just arriving at the lines is one couple (C), followed by two singles (S1 and S2). Assume the singles will not switch lines after joining, perhaps because new customers fill in behind them. Are S1 and S2 better off when splitting is allowed or banned? The key insight is that regardless of the policy, someone, either S1 or S2, will have to wait behind C to get served. If the policy allows splitting, C will always end up getting served in the fast lane, so either S1 or S2 (whoever joined the fast lane) will have to wait through one more fast transaction. If the policy bans splitting, then about half the time C will choose the fast lane by pure luck, and the result be just as if they had split between lines. But the rest of the time C will unluckily choose the slow lane, and that means either S1 or S2 (whoever joined the slow lane) will have to wait through one more slow transaction.
More simply: Someone has to wait for the couple to get served. But how much time it takes for them to get served depends on where they get served, and splitting assures that they get served in the fast lane. Therefore the expected waiting time for whoever’s behind them goes down.
Now, however, I think this logic is incomplete. Why? Because it doesn’t extend easily to the case in which lots more customers fill in the lines behind C, S1, and S2. If the new arrivals simply filled in the lines in equal numbers, then the analysis would clearly apply. In fact, it would be strengthened, because more people would share in the benefit of assuring the couple gets served in the faster lane. But if one lane is faster than the other, then it will get shorter more quickly, and thus more new arrivals will join that lane (without even knowing that it’s faster). That means a larger number of people will end up waiting behind the couple in the fast lane, while a smaller number will benefit from not having to wait behind the couple in the slow lane. It turns out that this effect cancels out the efficiency gain I showed above. For instance, if the fast line is twice as fast, it will serve twice as many customers. Moving a couple from the slow lane to the fast lane will save each slow-lane customer twice as much time as each fast-lane customer loses (this is why it appeared, in the two-singles case above, that switching allowed an overall gain in efficiency). But twice as many fast-lane customers suffer the loss, so the scale balances.
And now I may have an explanation for the taboo. Line-splitting, while having no efficiency effect, does have a distributional impact. The couple assures itself of getting served in the fast lane. As the single customers fill in the lines behind, they will be just slightly more likely to end up in the slow lane than they would have otherwise, because that’s necessary to balance the ratios. So the couple’s gain comes at the singles’ expense, although on average waiting time does not change.
Then again... Well, let me stop here. I think there’s still a flaw in my analysis, but I can’t quite put a finger on it, so I’ll leave that part to you. Bonus points if you see the analogy with insider trading.
Saturday, December 16, 2006
Macking on Models
I’ve been trying to wrap my brain around Julian’s model of macking behavior (“macking” being Julian’s preferred term for flirting or hitting on people). Julian is reacting to Heather’s observation that men in D.C. are “vanilla pansies that are scared to approach a woman in a bar,” despite D.C. women being (in her opinion) relatively attractive on average. Julian suggests that greater hotness of women could lead to a reduced level of overall macking. Here’s his model:
Assume there are diminishing returns to hotness. Which is to say, there's some threshold of physical attraction below which things probably aren't going to get off the ground whatever other good traits someone has. And there's a range within which improvements along this dimension will get significant weight. But between potential partners sufficiently high on that dimension – say ranging from "very attractive" to "stunning" – those other traits (smart, witty, kind, fun, whatever) become relatively more important.I think Julian might be onto something, but I keep foundering on uncertainty about the parameters of the model. What is the relevant alternative to hitting on an attractive woman? Is it not talking to anyone at all, talking only to your wingman, talking to some woman you already know, ditching the place in favor of a reliable booty call, or making a cold approach on a different woman in the bar?
Now, someone considering a cold approach in a bar really only has one dimension to go on: Hotness, which differs from the others in being pretty readily apparent in a noisy, crowded room. Even for someone unfazed by the risk of rejection, the cold approach carries some probability of ending up in a tedious conversation with an otherwise unappealing person. So other things equal, the expected value of a cold approach will depend on the relative salience, given your prospective partner pool, of the hotness dimension. If, to put it bluntly, you live among trolls, that will tend to be a high-salience dimension, making a cold approach to one of the rare attractive people you encounter more appealing. But if median attractiveness is high, then hotness is cheap: The expected returns to striking up a conversation with someone about whom you know only that they're hot are far lower. Ergo: More hotness, less macking.
Let’s take the last option. If it’s simply a choice about whom to mack upon, then Julian’s conclusion (more hotness, less macking) does not follow. If you don’t hit on one woman, you hit another, so the total amount of macking is unaffected by the median hotness of the crowd.
But if your outside option is any of the others I listed, then the outcome depends crucially on the quality of that option. For now, take the utility of your outside option as fixed. A hotter potential target automatically means a greater expected gain relative to the quality of your outside option. (Unless hotness is negatively correlated with the other qualities you want. Let’s assume that’s not the case, although that could be the subject of a future post...). A higher return compared to a fixed cost – the risk of getting trapped in a tedious conversation – should result in more macking, not less. So again, Julian’s conclusion does not follow.
To justify Julian’s conclusion, I think we have to say something about how the quality of outside options is affected by the overall hotness of the population. Say there’s a woman you already know that you could chat with. If she’s relatively low quality, it will seem more worth your while to do a cold approach on someone else. But as her quality rises, diminishing returns to hotness – again weighed against the fixed risk of an annoying conversation – mean that it will seem less and less worthwhile to bother macking on anyone else. Thus, if a hotter female population means that guys typically have higher-quality outside options, then greater hotness could indeed lead to less macking.
Some alternative assumptions might justify the same conclusion. For instance, the likelihood of success could have an effect. If success (defined as initiating contact with a desirable person and getting a positive reaction) becomes more likely, more guys will be willing to take a chance. However, they will also remain out of the macking pool for longer, given that success presumably means either longer conversations or shorter ones followed by a hasty exit. So there could be offsetting effects here. But this post is already too long, so I will leave that question for another time.
Monday, December 04, 2006
Inframarginal Football Fans
In response to last week’s post on the death of the TV theme song, Trent McBride forwarded me another example of how satisfying marginal customers can reduce the utility of inframarginal customers: sportscasting for non-fans.
[Why I like] Marv [Albert] and Boomer [Esiason]: Let's just say that they're more up my alley than their TV counterparts on Monday night. And why? Because they concentrate solely on telling us what's happening and why. They avoid anecdotes and insta-puff pieces and don't worry about appealing to non-football fans with those compact, adorable, 45-second yarns about how some player made it to the NFL even though he was raised by jackals, or some player is playing again even though he donated a kidney to a Somalian refugee he met at a Costco over Thanksgiving, that kind of stuff. (Maybe I'm heartless, but I just don't care. I want to watch football.) Marv and Boomer aren't name-dropping coordinators and deluging us with information and anecdotes that we don't need to hear. They aren't awkwardly setting each other up for jokes and they aren't pushing the game aside for celebrity guests.Trent adds, “I know a lot of football fans who would agree with this, and very few who would not.” The devoted sports fans are the inframarginal customers in this scenario; the unreliable watchers, who might not even care much for sports to begin with, are the marginal customers. The latter group’s preferences are those that affect the producers' selection of sportscasters, because the fans will watch anyway. The problem could potentially be reduced via the deployment of selective muting technology (you can mute the color commentator while keeping the play-by-play), or technology that gives viewers multiple sportscaster options for the same game on the same channel, much as DVDs include multiple language tracks. The question is why producers would bother providing the additional tracks for viewers who will tune in regardless.
Wednesday, September 13, 2006
Ugly Furniture Theory
Sometime last year, they renovated the faculty lounge at my college. The lounge is much more pleasant than it used to be, with sturdy and surprisingly comfortable new furniture. There's just one problem: the furniture is all ugly as sin. Burnt oranges and olive greens fused in hideous herringbone patterns. Really, truly awful.
Does the person who made the purchases have really lousy taste? Maybe. But thinking back, I realize that I've hardly ever seen attractive furniture in faculty lounges, dormitories, and other institutional settings. This is a general phenomenon. And I don't think it's just cost-cutting, because as I said, the furniture in question is sturdy and comfortable.
So why is institutional furniture ugly? Here's my hypothesis: Theft deterrence. Furniture in these semi-public areas can be easily stolen. But the offensive color patterns assure that the furniture will match hardly anyone's home decor. This is much cheaper than chaining the furniture to the ground, posting guards, or ordering new furniture any time something gets stolen.
Sunday, July 23, 2006
Adverse Selection in the College Cafeteria
This week I’m serving as a faculty member at the Institute for Humane Studies’ Liberty & Current Issues Seminar, hosted by the Catholic University of America in Washington, D.C. As usual, both faculty and students are housed in the dorms and treated to college cafeteria food. These conditions are made tolerable by the great company and intellectual stimulation. (Seriously. I do at least one of these events every summer, and it’s always one of the highlights of my year.)
I bring up the cafeteria food not to complain, but because I realized today at lunch (while discussing the food with two student participants) that it could be a nice example of adverse selection.
Have you ever wondered why college meal plans are so expensive relative to the quality of fare? Most college meal plans are all-you-can-eat propositions. With extra servings free at the point of service, students tend to consume more food until the marginal benefit is zero (contributing to the well-known phenomenon of the freshman fifteen). The excess consumption explains part of the price; it’s crappy food, but you’re paying for quantity, not quality.
But there’s more to the story. Some students naturally eat more than others. Yet most college cafeterias set a uniform price for all students, and that price must cover at least the average cost per student in order for the cafeteria to break even. Then each student (and their parents) must decide whether to enroll in the meal plan at that price, and this is where the adverse selection sets in: Those who eat more than average are getting a good deal, so naturally they enroll. Those who eat less, however, are more inclined to drop the plan and get their food elsewhere. As a result, the meal plan disproportionately attracts the heavy eaters, so the average cost per enrolled student must rise… and the cafeteria has to hike its price accordingly. The higher price leads yet more of light-eaters to drop the plan, and so on.
There are ways of controlling the problem. One way is to offer different meal plans that limit the number of meals per week. These plans deal adequately with the difference between students who eat many meals and those who eat few, but not the difference between those who eat a lot per meal and those who eat a little. Another possible solution is to offer meal plans with different restrictions on the food quantities and types; this approach is akin to health insurance companies’ practice of offering a menu of differing insurance policies to their customers, so that consumers’ choices effectively sort them into differing groups. Yet another solution, adopted by some colleges, is simply to require enrollment in the meal plan by all students or, as is more typically the case, all freshmen. This approach holds down prices by preventing the defection of light eaters, but it also effects a cross-subsidy from the light eaters to the heavy eaters. In addition, this grants greater monopoly power to the cafeteria, which can push prices back up (unless the prices are regulated by the provider’s contract with the university) or quality down.
Saturday, February 18, 2006
Coase's Toilet
About a year ago, I linked Gil Milbauer’s analysis of toilet seat norms. Specifically, Gil addresses the eternal question of who should raise or lower the toilet seat and when. As I said then, Gil’s logic is absolutely correct and strongly supports the CWN (“Change When Needed”) rule over the AD (“Always Down”) rule. Why? Gil presents the math, but really the names say it all. The AD rule requires toilet-seat adjustments in some cases where they are unnecessary (between two consecutive male urinations). The CWN avoids such unnecessary adjustments, thereby minimizing the total seat-adjustment burden.
Now I find – via Marginal Revolution – another mathematical analysis of toilet-seat norms. The calculations are similar, and author Richard Harter agrees with Gil about how to minimize the burden: “It is readily seen that ... the joint total cost is optimized by strategy J” (strategy J is equivalent to Gil’s CWN). But, Richard says, this strategy is “suspect” because men have a selfish interest in advancing it. The CWN rule involves more seat-adjustment by women, whether compared to the AD rule (which puts all the burden on men) or living alone (where there is no such burden). Women will therefore strongly resist the CWN rule.
Richard’s conclusion is that “there is an inherent conflict of interest which can be resolved by [an] equity solution.” His proposed solution involves dividing the increased seat-adjustment burden (which results from choosing to cohabit) between the man and woman. But this equitable arrangement is inefficient, at least until the disutility of relationship discord is taken into account.
While Richard’s analysis is correct as far as it goes, it suffers from a shortage of imagination. The seat-adjustment issue is a kind of externality problem, and like many such problems, it is susceptible to a Coasean solution. As Ronald Coase observed, we can reach efficient outcomes through voluntary transactions so long as the parties are free to bargain. In this case, let’s suppose Richard’s equitable solution defines the initial allocation of duties. Then both parties can be made better off if they switch to the CWN rule and the man gives the woman some form of compensation – perhaps more frequent gifts, extra foot rubs, or straight-up cash payments.
So why doesn’t this actually happen? Well, maybe it does with some couples. But one condition of the Coase Theorem is that initial property rights must be well defined, or else bargains will be difficult to reach. In the seat-adjustment problem, men and women are still fighting about the initial rights allocation. Thus, Richard’s analysis could still be useful, not for establishing the correct final seat-adjustment rule, but for establishing a viable initial rule as the baseline for bargaining.
[An addendum: Some women seem to think the AD rule is better simply because it avoids the “Midnight Surprise” problem of sitting down and plopping one’s rear in the water. I find this unconvincing. Are women blindly backing up to the toilet before sitting? All it takes is a quick glance. Men, too, are potentially subject to the Midnight Surprise when doing operation #2, but I’ve never heard a man complain about it. That’s because men don’t assume the seat will be down. After becoming accustomed to the CWN rule, women wouldn’t assume that either. In any case, the MS doesn’t vitiate the Coasean argument. Start with Richard’s equity solution, which involves seat-down in the evening already, and then let the negotiations begin. If the disutility of a potential MS is large enough to make CWN inefficient, then the bargain won’t occur.]