March 12, 2003

Waiting in Line: How Economists Think

What sort of "property" is your position at the head of a line? Is it something that you can sell--or should be able to sell? If it's yours, you should be able to sell it, right? Suppose somebody comes up to the first person in line--you are number five--and offers a fistfull of dollars for his or her place. Do you have a right to object? Does the person "buying" the first place have to also reach an agreement with you?

Lawyers and political scientists think there are interesting and important issues at stake. And perhaps there are. But their discussions are a little bit... unstructured:


The Volokh Conspiracy:
CHRIS BERTRAM ON COMMODIFICATION: Chris writes:

One such question is the following: "Is it morally ok for someone to march to the head of a long queue (for tickets for the theatre or football or whatever) and offer to buy another person's place in that queue?" Since the purchaser buys the place and the person they displace goes away or to the back of the line, the exchange isn't worsening any one's position.

Respondents seem to break down into three categories: people who think it is just obviously ok, people who think it is just obviously wrong, and people who find themselves switching back and forth between perspectives.

Ooooh... I like this one. Many of the standard examples of blocked exchanges or illegitimate commodification in the Michael Walzer/ Margaret Jane Radin school inspire a "so what?" reaction in me. I can't wrap my head around what's so obviously wrong with the sale, and I say that it would be "obviously OK." In this case, I had a strong, immediate "obviously wrong" reaction. There are all sorts of things that get rationed by queue that don't have to be and shouldn't be. (The scalping laws force rationing by queue onto ticket sales, for example.) And I'm sure my economist friends are right to look at rationing by queue and at least often suspect regulatory failure and wrongfully-blocked exchanges.

But queues we will always have with us. Across a wide range of activities (checking out in the grocery store, waiting for admission to a general-seating theater, waiting for a bus or a taxi) it's the natural, socially-evolved norm. And the person walking to the front of the line with a fistful of dollars is accepting that norm for everyone else while seeking to violate it him- or herself.

In Israel, I was once surprised to find, there seems to be no norm of queuing for a bus. When the bus arrives, it's a free-for-all to get on board. Some mild shoving and jostling seems to be permissible. But if I took that approach while waiting for a bus in New York, I'd be getting unfair benefit from my violation of the local norm. Similarly, while one could imagine metro buses that sold seats in advance and were boarded like airplanes, eliminating the need for queuing, the extant norm is not an auction but a queue. Buying one's way to the front seems to me obviously unfair.

And I think this is so even if the good one acquires by queue can then be auctioned off. If I were waiting in line for opening-show tickets to Return of the King, I'd have no objection to the person in front of me buying a ticket and then scalping it on E-Bay. I would object to that person simply selling off his or her place in line.

I'll have to think about this more. I think it makes a very nice, complicated case for Hayekian libertarians in particular: evolved social norms vs. free exchange. One doesn't have to think that the exchange should be blocked by criminal prohibition to think that it's wrong, a violation of rules that shouldn't be violated.


The economist's instinct is different. It is, "Let's build a model of the situation!"

Suppose we have a model, toy economy that works as follows:

There are fifty poor. The poor can either work by waiting in line and selling their places in line to the rich at a market wage w (with the value of w to be determined), or scratch out their living on subsistence farms. Suppose that scratching out your living on the 50th (the worst) subsistence farm earns you $9,000 a year, on the 49th earns you $9,200 a year, on the 48th $9,400 a year, and so on and so forth, with the best farm earning the lucky poor subsistence farmer who owns it $18,800 a year. The poor work too hard and are too tired at the end of the day to think of going to the (publicly provided, free) theater.

There are fifty middle class. Middle class have an income of $20,000 a year, and like to go to the (publicly provided) theater. Theater tickets are free, and the theater is large enough to hold everybody. Unfortunately there is congestion: lines to get your tickets and get into the theater. Congestion is costly: the middle class suffer a reduction in their subjective utility from boredom-in-line that has a monetary value of $20 for each total person who goes to the theater. Thus if all fifty middle class go to the theater, they each suffer a boredom-in-line utility loss of $1000. (Fortunately, each middle class person values going to theater as worth $2,000.

There are ten rich. Rich have an income of $200,000 a year. The most effete, sensitive, and artistic of the rich values going to the (publicly provided) theater as worth $20,000; the second most et cetera values going to the theater as worth $18,000, the third at $16,000, and so on down to the philistine among the rich, who values going to the theater as worth a mere $2,000. Unfortunately for the rich, they are easily bored and value their time highly: the subjective cost to one of the rich of waiting in line is not $20, but $400 for each total person who goes to the theater.

Now let's look at the equilibrium of this toy economy with and without a market in positions waiting in line.

Suppose, first, that the jackbooted thugs of the state prohibit the hiring of others to wait in line for you. If the rich want to go to the theater, dammit, they need to wait in line themselves! What happens?

  • Well, the poor scratch out their living on their subsistence farms, earning incomes that vary from $9,000 to $18,800 a year, depending on whether they are unlucky or lucky in the farm that they own, with an average income of $13,900.
  • The middle class all have incomes $20,000, all go to the theater, all (because all 50 of them are going to the theater) spend so much time in line that they get bored to the tune of $1,000 each, and so each of the middle class winds up with a income-plus-psychic-utility welfare that they value at $21,000.
  • The rich don't go to the theater. The most enthusiastic theater goer among the rich looks at the line, considers the boredom cost of waiting in it--which is $400 x 51 = $20,400--and concludes that it isn't worth it. The rich thus have an lifestyle they value as worth $200,000 a year.

Suppose, second, that a libertarian government comes to power and says, "Why not have a market in waiting-in-line?" What happens?

  • The rich think about hiring someone to wait in line so they can go to the theater. All those for whom the value of going to the theater is worth more than the waiting-in-line market wage w try to hire someone. All those poor whose farms earn them less than the market wage w try to get hired. If demand is greater than supply, w rises. If demand is less than supply, w falls. If w is $10,000, rich #1, #2, #3, #4, and #5 are enthusiastic about hiring someone, and poor #50, #49, #48, #47, and #46 are enthusiastic about being hired. (Rich #6 and poor #45 are indifferent: assume they don't trade in the market). w=$10,000 is thus a market equilibrium price with a quantity of 5: 5 of the poor get hired to wait in line for the 5 rich who are the most enthusiastic theater goers.
    • Rich #1 through #5 gain: their market-plus-psychic incomes are boosted by $10,000 in the case of #1, $8,000 for #2, $6,000 for #3, $4,000 for #4, and $2,000 for #5. The rich as a class gains by $30,000 as a result of the opening up of the market for waiting-in-line.
    • Poor #50 through #46 gain: they are happier waiting in line than scratching on their farm. #50 gains $1,000, #49 gains $800, #48 gains $600, #47 gains $400, and #46 gains $200. The poor as a class gains by $3,000 as a result of the opening up of the market for waiting-in-line.
    • The middle class all still earn $20,000, all go to the theater, but all (because now in addition to all 50 of them waiting in the theater line, there are these 5 hoi polloi holding places for the effete idle rich) spend so much time in line that they get bored to the tune of $1,100 each. Each of the middle class winds up with a income-plus-psychic-utility welfare that they value at $20,900. The middle class as a class loses by $5,000 as the result of the opening up of the market for waiting-in-line.

So how does one evaluate this change?

  • John Rawls might say that it is a good thing. The poorest of the poor gains $1,000. The average of the poor gains by $60. By the difference principle the second society--the one that allows paying for line places--appears better, for it treats its worst-off in a better fashion.
  • Richard Posner certainly would say that the change is a good thing. $30,000 in gains to the rich, $3,000 in gains to the poor, and $5,000 in losses to the middle class--what's not to like? A common-law judge should pretend that there never was any custom, tradition, law, or practice that prohibited paying for line places. If you don't like the distributional implications of judicial decisions, use the legislature to correct them. (But, in this case, the rich and poor together outvote the middle class, and the legislature does nothing.)
  • Vilfredo Pareto would say that you cannot tell whether it is a good thing or not: some win, some lose. However, if you also imposed a tax of $1,000 per head on theater-going by the rich, and used the $5,000 thus gained to compensate the middle class for the extra boredom they suffer from longer lines, then the opening up of the market for waiting-in-line would clearly be a good thing.
  • Michael Walzer might say that this analysis is incomplete. When you open up the market for places in line, the middle class suffer psychic injury not just through extra boredom, but also through having their noses rubbed in the fact that they are second-class citizens in a society structured in dominance by wealth, as they watch the top-hatted silk-scarved rich with their trophy husbands walk up to the front of their line, hand wads of cash to their poor stand-ins, and enter the theater, all the while smirking at the poor middle class who have to wait in the line. The psychic cost to the middle-class of wiating in line rises from $1,000 each to $1,900 each ($100 from extra boredom and $800 from degradation), so the middle class loses $45,000--more than enough to outweigh the $30,000 worth of net extra pleasure received by the rich and the $3,000 of extra income received by the poor.
  • Robert Hall points out that if the middle class weren't envious, they would not be made nearly as unhappy, and that clearly a flat tax on line-standing is also called for in order to reduce congestion and get closer to the first-best.
  • The Referee blows the whistle and rules Hall out-of-order for making an argument forbidden to a card-carrying economist, for whom tastes and technologies are unquestionable primitives.
  • Matthew Rabin says it depends on how the middle class frame the issue. If they frame it as being oppressed by the rich who have made them second-class citizens in a society structured in dominance by wealth, then of course they are unhappy. If they frame it as the poor having greater opportunities for gainful employment and upward mobility, they should be happy to see the poor raised up. In fact, rather than each suffering an $800 psychic injury, they would each receive a $100 psychic benefit from their sense of social solidarity and the pleasure they derive from seeing the poor made better off as being paid for waiting in line allows them to better care for their families. Opening up the market is Pareto optimal, even without compensation to the middle class--if only they would frame the issue properly.
  • Daniel Davies says that in this case, as in so many others, the full armamentarium of economics is pulled out to generate a conclusion that is either trivial or inane or both. Basically, the conclusion is that if the other people in line get really bent and unhappy when a rich guy strolls up to the front and hands the front-liner a fistfull of dollars, then it's a bad thing, and don't. But if the other people in line were to shrug and say "good for him for picking up some extra cash from the toff," then it would be a fine thing, and do.
  • Brad DeLong orders bottles of Napa Valley wine for everybody waiting in line, and charges them to the Hoover Institution endowment.

Any more bids in this card game?

Posted by DeLong at March 12, 2003 05:55 PM | TrackBack

Comments

Bravo! I really, really enjoyed this post.

Posted by: Neel Krishnaswami on March 12, 2003 06:40 PM

I, too, really enjoyed this post. Now allow me to weigh in not as an economist but as a student of religion, trained by crypto-Marxist Unitarians. (That's my way of saying that I have nothing to add to Delong's math, because crypto-Marxist Unitarians don't do math--they organize.)

Nothing has been said about the reason why the fifth person in line would strenuously object to the first person's selling his or her place. I think the reason is as follows: in society in which the gap between rich and poor is extremely wide and the rich have many and varied mechanisms for controlling the access to and distribution of social goods, the queue endures as one of the few truly egalitarian cultural (micro?)institutions. In the world of the queue, all persons are truly equal--the handicapped, women, children, homosexuals, left-handers, African Americans, and all other marginalized and minority groups are on equal footing with the rich, the white, the male, etc. The queue knows only one law, timeliness, and it discriminates only against the tardy. The queue is no respecter of persons: the early shall be first and the late shall be last; end of story.

Hence the egalitarian queue strikes a populist chord deep within the American psyche. To violate the law of the queue by introducing wealth into the equation is an affront to its very makeup and reason for existence. It is the privilege associated with wealth and power that the queue is designed to keep in check.

There's only one way for the rich person to who would buy his or her place in the queue to win: buy off the entire queue. If each member of the queue were paid some negotiated amount to allow the rich person to cut, then this would change the nature of the unwritten contract on which the queue rests. Then, it would be about money for everyone, and the rules would change for everyone. In the scenario as given, though, (i.e. only the person at the head of the line is paid off) the rules would change only for the guy at the head of the line, and hence he'd be operating under a contract that nobody else in line had agreed to.

Posted by: Jon Stokes on March 12, 2003 07:06 PM

How long did it take you to build this model and find the equilibrium? Bravo Bravo Bravo. Did you do this by hand? Is the equilibrium you found unique? I would be amazed if this took shorter than a week, but I have a feeling it didn't take DeLong very long. How did you do it?

Posted by: Bobby on March 12, 2003 07:09 PM

How long did it take you to build this model and find the equilibrium? Bravo Bravo Bravo. Did you do this by hand? Is the equilibrium you found unique? I would be amazed if this took shorter than a week, but I have a feeling it didn't take DeLong very long. How did you do it?

Posted by: Bobby on March 12, 2003 07:10 PM

Meanwhile, an entrepreneur who's a fan of Rostow comes alongs, recognises the opportunities and bids for the concession rights for selling ticket seats. They
a) create life-time membership/sponsorship packages for the rich (appeal to art snobs)
b) give charitable poor groups a chance to raffle/auction off tickets to give the impression of high-status value (prize) and free word-of-mouth advertising
c) sell all the rest to deluded middle-class at market prices using artificial queues and last-minute sales to maximise revenue-per-seat
d) uses proceeds to leverage a loan and gain ticket concessions at other theatres recognising the lock-in and convenience factor of a single purchasing channel
e) expands into an international franchise with electronic ticketing for surplus seats to deny competitors pricing/demand information

So therefore market segmentation works, the businessman makes a decent profit (including secondary markets) and everyone is happy
-- except the inland revenue department who's trying to argue that writing off c) at full-prices of a) is not a GoodIdea(TM).

LL

Posted by: LL on March 12, 2003 07:48 PM

Just for giggles, I could throw in Steven Landsburg's argument, as exposited in his Everyday Economics column in Slate, that optimal queueing would require that every new arrival in a queue would go to the HEAD of the line, not the back (or, er, "foot"). I think. I can't recall the logic, but I'll post the link. You can read it for yourselves if you like :)

http://slate.msn.com/id/100332

Posted by: Michael Harris on March 12, 2003 07:57 PM

My feeling is that to the extent that the queue is a group of strangers there's no problem, but that if there's any sort of feeling of friendship or community involved there is a problem. Whoever bought his or her way to the front would be declaring non-membership in (and superiority to the members of) certain kinds of communities. (Some communities might find the behavior non-problematic). This sort of thing is a real factor in the world of today in the marketing of music which is really a commodity, but which is marketed as defining a community.

Within economics its an open and shut case. It's OK.

Posted by: zizka on March 12, 2003 08:04 PM

Given your assumed preferences, I'm not sure about your equilibrium. You assumed that the poor don't go to the theatre because of the hard work they must do. However, those poor who are now place holders in the que for the rich no longer face the hard work and so would want to also go the the theatre. So the benefit from the new job is the wage plus the ability to go the theatre, while the cost to the rich is still just the wage and greater externalities will be faced by the middle class.

While in many ways this is semantic and could be assumed away, it does get more to the idea of a person buying place in a que and the person who sold the place then going to end of the que.

The next question, what if the middle class feel burdened from now having to wait with the poor? Meaning not the psychic utility from being put down upon by the rich or seeing the poor succeed, but the actual uncomfort from having to socialize with the poorest of the poor given the model.

Posted by: Rob on March 12, 2003 09:38 PM

This is probably the funniest thing you've posted. Thanks!

"Just for giggles, I could throw in Steven Landsburg's argument, as exposited in his Everyday Economics column in Slate, that optimal queueing would require that every new arrival in a queue would go to the HEAD of the line, not the back (or, er, "foot"). I think."

Oh my, I'd forgotten about that wretched column:

"(Well, actually they'd leave the line and try to re-enter as newcomers, but let's suppose for the moment that we can effectively prohibit that behavior.)"

Great, thanks a lot Steve. So if we just prohibit something when it's virtually impossible to do so.....

However, why does the line exist anyway; lousy purchasing technology? I'd imagine in a few years that the time cost of buying tickets will be effectively zero; as you walk up to the ticket taker, buy a ticket on your cell phone's web interface.

I actually don't think it's the technology, though, at least for some high-demand low-supply events, such as popular basketball games. I remember reading *somewhere* about how supply-constrainted events keep the price of their event below the first-glance efficient maximum, because they think that the short-run gain in ticket revenue would be offset by the niche, rich-people-only nature that their event would end up acquiring. Basketball that's only watchable in person by businessmen on expense accounts and celebrities would rapidly go down the tubes.

The ticket "underpricing" results in Warsaw Pact-style queueing, ticket scalpers out front, people paid to set in front of a computer hitting refresh on the purchasing page, and so on. The event provider fights this enough to keep a lid on things, but they do a rather crappy job of it.

Now, the above sounds like a broken market, which to me justifies government intervention. Maybe technology will get us a better method of preventing resale?

Posted by: Jason McCullough on March 12, 2003 10:24 PM

Brad, you forgot external characteristics which would mark off the rich from the poor, as well as certain irrational preferences such as racism. Michael Walzer's case is hugely understated if we are talking about some town where for some strange reason, all of the effete rich are white and most of the poor/middle class are black, and the effete rich don't want to get infected by hiring poor blacks to wait for them in line and hand them the tickets, and so hire only poor whites. i.e., the negative externalities in such a market would be huge. Hmm. Maybe the Indian Raj might be a better example.

Also, at some point the political economy dimension needs to be addressed. A market for places in line represents a profit opportunity (i.e., price discrimination) for the theater owners, who are also chummy with politicians and help to finance their campaigns. Pretty soon, the theater owners are hiring underlings to stand in line for the effete rich and giving these underlings only a fraction of the price actually paid for by the rich. And through their political connections, the theater owners get the local police department to beat up any poor hoi polloi who want to do independent work standing in line for someone else. i.e., in any free market, there will always be profit opportunities just waiting to be grabbed up by any firm which becomes profitable enough to affect government policy in its favor, and so libertarian policies go the way of Aristotelian physics.

Posted by: andres on March 12, 2003 10:37 PM

>>Michael Walzer's case is hugely understated<<

True. But if you can't troll on your own website, where can you troll?

:-)

Posted by: Brad DeLong on March 12, 2003 10:51 PM

People are discussing this as though it's just an abstraction. I think it's useful to qualify one's theorizing with reality. In particular, at Universal Studios (and doubtless other amusement parks), one CAN pay more money to get an express ticket. This gets you to the head of the line, without benefitting anyone else (except Universal Studios) and certainly not the rest of the queue. Nonetheless no-one seems to be bent out of shape that it is un-American, and when I used my express ticket I didn't get any feeling that people were looking at me enviously or angrily. Maybe people just accept inequality, or maybe they unconsciously appreciate the big picture---that the higher price I am paying is subsidizing the lower cost they are paying, and the tradeoff, their time, is one they're willing to make.

Or, to put it differently, is scalping ultimately a non-issue that is only considered a big deal because political types find it useful to bring it out every so often---like so many other non-issues like ethnic conflict where people didn't know they hated their neighbors until they were told they did.

Posted by: Maynard Handley on March 12, 2003 10:56 PM

Nice post Brad. Full disclosure: in my original post I mentioned that the example had come up in conversation at a conference in Brussels. My interlocutor was a card-carrying economist, to whit, Sam Bowles of the Santa Fe Institute, who uses this example among a whole range of others (which I didn't list) to test the intuitions of his students.

Posted by: Chris Bertram on March 13, 2003 03:20 AM

If someone objects to the practice of selling places in a queue, we obviously have some externalities. If we donīt know about the individual preferences, which I think is reasonable to assume, negotiating with all in the line about it isnīt very effective. I think we should ignore this externalities generally.

There are some other issues here though. While the waiting time isnīt affected, the availability of certain tickets will be affected, if not all tickets are equal.

Selling places in a queue can also pose problems with price discrimination and may generate a need for more complex (and time costing) hurdles or make price discrimination impossible. This of course increase social welfare in the Marshallian sense.

Queues at my university are a wonderful way to meet others, so we have a lot of social issues.

Selling theater tickets is different from queues in a supermarket, where not everyone costs the same amount on time, so here the exchange can increase the waiting time of the people in line, which is clearly a externality that should be considered. After all, lines are about waiting time.

I donīt see a good justification for ruling out the possibility to pay someone for waiting in the line. Itīs pretty ad hoc IMO.

I think this case demonstrates mostly how limiting economic models can be.

I hope my thoughts donīt come over as all too confused... ;-)

Posted by: Michael Greinecker on March 13, 2003 04:47 AM

Great! But Daniel Davies would use the word f@ck at least 10 times in his write up

Posted by: jon A on March 13, 2003 04:54 AM

Nice post -- but the values you assign to all the different valued things in the model seem (of course) quite arbitrary. How does fiddling with prices affect the outcome, and is this important?

Posted by: Jeremy Osner on March 13, 2003 06:46 AM

" So if we just prohibit something when it's virtually impossible to do so....."

You mean like laws against scalping, Jason?

These markets are not broken, and they don't need government intervention (part of the problem IS government intervention). The people involved in the markets know exactly what they are doing. E.g., for some events waiting in line is part of the experience, and that experience leads to sales to future events, as well as sales of memorabilia.

Chapter 4 of Stan Liebowitz's "Re-Thinking the Network Economy" has a bit on how "haggling" got replaced by fixed pricing, that is apposite here.

Posted by: Patrick R. Sullivan on March 13, 2003 07:29 AM

>>Nice post -- but the values you assign to all the different valued things in the model seem (of course) quite arbitrary.<<

Yes. The qualitative points are sound: hiring people to wait in line benefits those who get hired and those who hire them. And to the extent it leads to increased congestion, it hurts those others who are in line.

The numbers are, of course, illustrative only...

Posted by: Brad DeLong on March 13, 2003 07:33 AM

How does the 45th poor know that 46 - 50 could make it as line holders? Or the 6th rich know that 1 - 5 didn't have carriage trouble on the way to the theater? There is a real probablility that additional theater goers will show up to capitalize on another's misfortune. Do the rich have to queue for access to the poor? Are there additional opportunities for someone to queue for the rich's access to the poor who will queue for the tickets? I see costs in this system unexpressed in the description. I haven't even touched on the enviornmental costs.

Posted by: LowLife on March 13, 2003 07:53 AM

People who cannot understand how the "middle class" line waiters might get angry have never been in a line behind a busload of homeless people who are given a pittance to get tickets for the brokers. Not only are these "middle class" subjected to the sight of the flagrant exploitation of the poor, but they are also forced to think about the rich people who aren't there but will be getting the good seats anyway.

Now think about the fact that the same thing is happening at every ticket outlet in town. There are no arenas with limitless seating capacity. Some of the "middle class" will not get the tickets they want, though they have waited.

Now add the fact that though all scalping is illegal, well capitalized brokers have evolved a kind of semi-legality that has eluded the entrepreneur scalper. Thus the government is expressing a clear preference for the "rich" class interests over the "middle" class interests.

My conclusion? Do you care about the society where the line exists? Stand in the line. Don't care? Do what thou wilt shall be the whole of the law. Just like the rest of economics.

Posted by: biz on March 13, 2003 08:53 AM

or you could wait till the tickets go on sale, call in (or use tickets.com) and try to purchase at face value (essentially a lottery system) and then decide to sell your ticket (or keep it, depending on the value it has to you) via ebay (anonymous, highest bidder).

if you are poor and have time you could earn considerably more than your normal wages or even the wages that a rich person would pay you to wait in line.

sorry, I used to work in the internet space and sometimes have flashbacks.

Posted by: jjj on March 13, 2003 09:03 AM

The problem with the queue-justice problem is that the good is not "free". It costs time.

Line-jumping seems upsetting because a formerly "equitable" system for the allocation of a free good is being replaced by a market system. But the equitable system is not truly equitable, as it excludes the poor who do not have the time to wait on line. Thus, the system is being altered from one which costs time, the preferred resource of the middle class, to one which costs money, the preferred resource of the rich. Both systems exclude the poor, who don't have any resources.

Having some areas of society immune from domination by the wealthy through the use of queues might be better for social harmony, but in that case perhaps the government should be constructing an allocation system that doesn't exclude the poor as well.

Pointing to the existing social norm for the line doesn't really help either, because that norm has been constructed with a selection bias: only those people who feel the line is a fair way to allocate theater tickets will stand in it.

Posted by: Ethan on March 13, 2003 09:09 AM

Brad correctly anticipates that my position on this question is that if the rich people are OK with the idea of being such dicks, good luck to them and enjoy the show.

But I idly note that this is a partial equilibrium model and does not obviously work in general equilibrium. Five farms are now factors of production which are no longer in use in this economy, seemingly with no effect on the income of anyone ...

Posted by: dsquared on March 13, 2003 09:18 AM

Oh yeh, and the second sentence of the argument Brad attributes to Pareto is actually Hicks & Kaldor, shurely?

And while we're at it ... Veblenians would want to know a lot more about the specific institutions of this market. Brad's assumption appears to be that the rich sign long-term contracts with the poor to employ them to stand in line on a regular basis. Which seems unlikely to me; surely the rich could do better out of something more like the market for scalping that actually exists, whereby the poor put up their own risk capital (in the form of wages foregone) and the rich come along and buy their places in the line if they happen to feel like going to the theatre on that particular night? It strikes me that the unforecastibility of theatre ticket demand, combined with a degree of path-dependence in the labour market, could lead to a number of distinctly suboptimal outcomes for the poor.

For example, people might get attracted away from their farms on the basis of unrealistic expectations of returns from the scalping industry, find themselves unable to return to the farm (because it has become overgrown and they don't have enough capital to clear it) and get stuck in a hand-to-mouth existence on rather worse standards of living in the city. With, of course, large numbers of neoliberal economists on hand to explain that this is just a natural concomitant of the development process, and suggesting that the theatre should be privatised ...

No no no, the more I think about this the more complicated it gets.

Posted by: dsquared on March 13, 2003 09:31 AM

I am not an economist, but I *am* a modeler. I notice a bait and switch:

The original proposition (bait): What if the rich can 'buy' the place at the top of an existing line

The DeLong Libertarian model (switch): The rich add the 5 poor to the top of the Q thereby making the middle class pissed off.

The right model, based on Volokh's proposition is: if the middle class value the theater going proposition at $2000 (less $1000), the equilibrium price is really $1001 - that is the amount that the rich have to bribe the middle class theater goer wannabe's to yield their place in the Q. Why?

From the Middle class perspective, as long as the queue does not lengthen, thereby increasing the wait-in-line cost, the real indifference cost of going to the theater is $1000. Anything over that, they should willingly sell their place in the Q.

Nice model, but solves a different problem than the one originally posed.

Posted by: Suresh Krishnamoorthy on March 13, 2003 09:57 AM

You forgot about Kevin Hassett. He predicts ticket prices will rise dramatically in the next few years, and encourages the middle class to buy and hold ticket futures. No price is too high since tickets will be worth $36,000 in the not too distant future.

Posted by: Boban Kostelic on March 13, 2003 10:33 AM

"... as they watch the top-hatted silk-scarved rich with their trophy husbands walk up to the front of their line ..."

A fashion prediction? Rich, silk-scarved women are going to take to wearing top hats?

Posted by: Jim Glass on March 13, 2003 10:41 AM

Ayn Rand: the middle class would be so grateful to the rich for making it possible for them to appreciate the theater that they would give a silent prayer of thanks as they appreciate the magnificent logic embedded in a story brilliantly told in the theater by beautiful artists who really don't want to be paid but only deeply appreciated by the audience based on shared values.

Posted by: Suresh Krishnamoorthy on March 13, 2003 10:51 AM

>>"... as they watch the top-hatted silk-scarved rich with their trophy husbands walk up to the front of their line ..." A fashion prediction? Rich, silk-scarved women are going to take to wearing top hats?<<

Glad someone caught this. I was beginning to feel unappreciated...

Posted by: Brad DeLong on March 13, 2003 10:52 AM

Basically, there are two separate problems:

1: What is the impact of someone with a fistful of dollars buying the first place in an existing line for a limited number of tickets?

Well, if I am number 2 (or number 20), I should not care. My place is not affected and neither is my wait nor the probability of my getting the good I am waiting for.

If I was number 2 I could offer my place a little cheaper than #1.

A real life example of how this works: the NBA draft. High draft picks are often packaged and traded.


2: What is the impact of someone with a fistful of dollars inserting themselves at the head of an existing line?

This is an entirely different problem and in my analysis, depends on three factors:

a) Is the good limited (tickets) or unlimited (view painting)
b) What is the marginal wait time as people get added in front and the rate of addition?
c) How badly do I want to be in line?

The Libertarian DeLong model addresses the case where a) is unlimited, b) is small and c) is high

A real life example of this is the temple at Tirupathi, India.

The 'good' is the ability to view the deity up close. Obviously unlimited.

The queue is the 'free' queue where the average time from when you enter it to when you are in front of the deity can be about 2 hours.

The fistful of dollars is the ability to enter a 'different' queue that shortens the wait to 10 minutes but you must pay 100 rupees for the privilege. This Q basically inserts itself near the head of the 'long' Q

In the context of this question, the system works since the people in the 'middle class' Q know they can cut their time to 10 mins but are either unable to afford the price or have the time to spare.

Anybody who wishes to have a practical demonstration of this, add Tirupati to your next visit to India!

Posted by: Suresh Krishnamoorthy on March 13, 2003 11:59 AM

Suppose the people putting on the performance want to charge a non-monetary price to attend. This could obviously be time spent waiting in line. They might want to do this, for example, to insure an audience of enthusiasts.

I see no reason why this should not be allowed. It requires help from law enforcement, maybe, but so does punishing people who sneak in without a ticket.

In fact, this is allowed, and enforced, in some cases. What is acceptance at a university but an admission ticket? We do not allow these tickets to be resold.

So maybe the answer lies in the wishes of those issuing the tickets. If they say, "you must wait in line," then no selling of spots. If they don't care, then OK.

Posted by: Bernard Yomtov on March 13, 2003 12:07 PM

Suresh appears to be on the right track that the equilibrium price is really $1001.
Now all ten rich go to the theatre and gain $99,990.
40 middle class go to the theatre and gain $10 assuming they are not allowed to re-enter the line. If they can re-enter the line and we re-apply their boredom costs, then: all 50 middle class go to the theatre and gain $10,010
The 50 poor stay home and talk about how life sucks.

Posted by: Dan on March 13, 2003 12:22 PM

"' So if we just prohibit something when it's virtually impossible to do so.....'

You mean like laws against scalping, Jason?"

Good point. The laws against scalping are rather ineffective, though. Maybe technology will fix both?

Posted by: Jason McCullough on March 13, 2003 12:44 PM

My attempt to think like an economist:
Brad's model treats all places in the line as equal. That's a useful oversimplification, but I think there's a real-life moral hazard problem. (If I have the right term.)

Suppose it's well established that you can sell your place in line. I have a book to read, and it doesn't matter to me where I spend the three hours reading it. So I arrive at the line three hours before the show starts, hoping someone will buy my spot. If no one does, I will leave the line. The line becomes crowded with lots of people who have little interest in the show, but who hope to sell their spots. This seems like a bad outcome, somehow.

In effect, the presence of freelance place-holders who don't want to see the show would reduce Suresh's problem 1 to problem 2--someone who buys a place-holder's ticket is effectively pushing everyone else back a spot.

With premium lines, as Maynard and Suresh describe, there's no incentive to stand in lines for things you don't want, as I describe.

Posted by: Matt Weiner on March 13, 2003 12:51 PM

Such a post.
A wonder.
My my.

I'm puttin on my top hat, brushin off my tails. Tap, tap tap....

Posted by: anne on March 13, 2003 01:55 PM

Your model is too weird for me. Everyone who shows up gets into the event, so standing in line has no benefits, only costs. It's more like a traffic jam than a ticket sale. And if rich people pay poor people to make deliveries during rush hour, then middle-class commuters are worse off. Like, duh!

For what it's worth, it would not bother me to have somebody in the front of a line scalp their ticket.

Posted by: Arnold Kling on March 13, 2003 02:51 PM

I can't help but think of responses to traffic congestion-Something I learned a lot about in a recent trip to the bay area. With a few small changes the same things would probably be said about how to alleviate road congestion. But no one would find it nearly as funny. By using lines, rather than roads, you end up seeing how really absurd sopme positions would be.
I would add:
Lawrence Kudrow- "And thus once again supply creates its own demand." (But he isn't really an economist.

Posted by: Lawrence on March 13, 2003 04:18 PM

I thought this was a really,really funny post. Then it occurred to me there is a real issue like this-traffic jams and road congestion-and many of the responses would have been identical to those listed. Yet no one finds humor in those commentaries. So by putting this into lines rather than roads one can see how absurd some real issue type commentary is.
I would add a few:
Gary Becker: "Thus labor market efficiency is improved, those with low value time preferences stand in line for those with high value time preferences."
Lawrence Kudrow: "Once again we see the relevence of the observation that supply creates its own demand."
Doug North: "Clearly difined property rights on the line leads to the market..."

Posted by: Lawrence on March 13, 2003 04:24 PM

Try putting in a comment from Nassau Senior on wages. The description is incomplete because, while it shows what the poor would otherwise do to LIVE, it says nothing about other food production and availability in the economy. It is quite plausible that being paid to queue wouldn't help the poor enough, as their food prices could rise. Certainly it is possible that increases in queuing for a living could decrease food supplies; whether it would happen or not depends on whether the price signals drove people back into subsistence living. Certainly the money income stated for the subsistence farmers is no measure of their wellbeing - it is net after subsistence. (That is the fallacy in many interpretations of Dollar & Kraay's work, since describing increases in cash incomes in developing countries omits non-cash parts, whether it is good enough description of the real value of the nominal cash they get or not.) With market imperfections, or distortions like privatising the subsistence resources and so achieving a hidden wealth transfer, there could easily be apparent but fictitious improvements as people were separately forced into cash dependency - that has happened in a number of times and places before.

Posted by: P.M.Lawrence on March 13, 2003 04:27 PM

As Chris B's original post pointed out, intuitions on this case can get distorted by the influence of other intuitions about the justice of the distribution which serves as the background for the offer.

If you think that the prevailing distribution is in some important way unjust, you may think that the rich person making the offer is exploiting their (unjustly) favoured position. That's compatible with saying if the background distributive scheme were just, there'd be nothing wrong with the offer. I think I want to say both these things.

In unequal societies, a practice like queueing preserves a space in which some kind of norm of equality gets asserted. And I'm going to say that anything that places the more affluent in situations in which their wealth does not grant them non-coercive but unjust power over their fellow human beings is a good thing.

Objection: Even if the distribution is unjust, it's still the case that in the here and now, some people in the line will prefer the money to their place. Is it OK for a passing tycoon to make one of them the offer? Perhaps, if there's some kind of broader movement towards a distribution which is closer to being just.

In the real world, there's no such movement, and we need to hang on to possibly symbolic practices that remind us, intermittently, of the fundamental moral equality of human beings. Count me as voting for the 'non-obviously wrong' party.

Posted by: Tom Runnacles on March 13, 2003 06:06 PM

As Chris B's original post pointed out, intuitions on this case can get distorted by the influence of other intuitions about the justice of the distribution which serves as the background for the offer.

If you think that the prevailing distribution is in some important way unjust, you may think that the rich person making the offer is exploiting their (unjustly) favoured position. That's compatible with saying if the background distributive scheme were just, there'd be nothing wrong with the offer. I think I want to say both these things.

In unequal societies, a practice like queueing preserves a space in which some kind of norm of equality gets asserted. And I'm going to say that anything that places the more affluent in situations in which their wealth does not grant them non-coercive but unjust power over their fellow human beings is a good thing.

Objection: Even if the distribution is unjust, it's still the case that in the here and now, some people in the line will prefer the money to their place. Is it OK for a passing tycoon to make one of them the offer? Perhaps, if there's some kind of broader movement towards a distribution which is closer to being just.

In the real world, there's no such movement, and we need to hang on to possibly symbolic practices that remind us, intermittently, of the fundamental moral equality of human beings. Count me as voting for the 'non-obviously wrong' party.

Posted by: Tom Runnacles on March 13, 2003 06:08 PM

As Chris B's original post pointed out, intuitions on this case can get distorted by the influence of other intuitions about the justice of the distribution which serves as the background for the offer.

If you think that the prevailing distribution is in some important way unjust, you may think that the rich person making the offer is exploiting their (unjustly) favoured position. That's compatible with saying if the background distributive scheme were just, there'd be nothing wrong with the offer. I think I want to say both these things.

In unequal societies, a practice like queueing preserves a space in which some kind of norm of equality gets asserted. And I reckon that anything that places the more affluent in situations in which their wealth does not grant them non-coercive but unjust power over their fellow human beings is a good thing.

Objection: Even if the distribution is unjust, it's still the case that in the here and now, some people in the line will prefer the money to their place. Is it OK for a passing tycoon to make one of them the offer? Perhaps, if there's some kind of broader movement towards a distribution which is closer to being just.

In the real world, there's no such movement, and we need to hang on to possibly symbolic practices that remind us, intermittently, of the fundamental moral equality of human beings. Count me as voting for the 'non-obviously wrong' party.

Posted by: Tom Runnacles on March 13, 2003 06:09 PM

"I can't help but think of responses to traffic congestion"

Ah, but the alternative to not driving your car is to take the bus, not to forego the trip entirely.

Posted by: Jason McCullough on March 14, 2003 01:32 AM

Continuing the traffic analogy by Arnold and Lawrence, the destination is irrelevant (since it is a free good in limitless supply) and only the bottleneck through which the line must pass matters. We could be talking about queues at theater gates, or interchanges at rush hour. In that context, Suresh's premium line is the toll lane that runs down the middle of the free higway. Those who have more money than time will pay more to arrive faster.

Posted by: Ethan on March 14, 2003 06:40 AM

Thanks to Brad DeLong for a stimulating and humorous article. To me, the example model and discussion suggest that using artificially imposed inconvenience as a mechanism for allocating resources is foolish. People in queues suffer "pain" from boredom and also forfeit substantial opportunity costs. There should be a better way to allocate resources while avoiding these spurious costs. The notion of creating a market in queue positions hints at a better solution. For concreteness, let us consider ticket sales. The direct dispersal of tickets by event organizers using electronic auctions/lotteries is a superior mechanism I think. Extensive participation in these auctions/lotteries is now realizable because of ready internet access via personal computers, library terminals, and kiosks.

Revenue goes primarily to the event organizer who can use it to pay for performers, venue, and ancillary services. Scalpers, line-standers, middle-men and other mediators are displaced. If auctions are used then the wealthy can metaphorically purchase positions at the "front of the line" using money. This would be undesirable from the moral standpoint of some egalitarians and equalitarians. However, if lotteries are used then any candidate attendee able to pay the face-value of a ticket would have an equal chance. The wealth advantage would be neutralized in the initial dispersal of tickets. Yet, a secondary market in tickets would reintroduce a wealth advantage. To prevent this a linkage between the identity of the lottery winner and the actual event attendee could be enforced. Participants in lotteries could provide an electronic credential and event attendees could then establish a connection with the credential at the venue entrance. (Note, airlines demand display of a drivers license or passport now to crudely check identity.) To help preserve privacy it would be possible to use a "blinded" credential but that is beyond the scope of this comment.

It is time to stop the needless suffering imposed upon mankind by the antiquated and overused mechanism of queuing.

Posted by: Garson Poole on March 14, 2003 06:56 AM

If the poor really are subsistence farmers, then pulling them out of production won't affect the agricultural products in the market too much, as their meager overproduction in a good year is sold below market price for shoes, schoolbooks for the kids, or maybe a bit of coffee or refined sugar.

I assume these poor farmers are renters or sharecroppers, and the land is owned by the rich. If #50-46 pull out, then I assume that the rich will either persuade poor #1-5 to increase their share, put that land to mechanized agribusiness, or perhaps subdivide it and develop it as suburban homes for the middle class, who will flee from the new influx of urban poor.

However, I think that the real problem is a likely oversupply of speculative queue-standers. Imagine 150 people queued for 50 seats, of whom 110 are speculators. If 5 wealthy late-arrivers show, you could wind up with a $1001 place in line for the cost of a cup of coffee, and five empty seats in the theater for a heckuva good show.

Meanwhile, I'm going to hang out outside the theater, where I imagine that Anne looks remarkably like a young Marlene Dietrich.

Posted by: Hard Pressed on March 14, 2003 10:58 AM

Hard Pressed

Oh, yes. Looking....

Posted by: anne on March 14, 2003 01:17 PM

"If the poor really are subsistence farmers, then pulling them out of production won't affect the agricultural products in the market too much, as their meager overproduction in a good year is sold below market price for shoes, schoolbooks for the kids, or maybe a bit of coffee or refined sugar."

Right now small farming women in southern Africa are in terrible terrible trouble. Women do most of the small farming in southern Africa. As illness strikes a family member, and AIDS is ever so fiercely prevalent, the production of women farmers suffers. Whether there is a national food surplus is almost incidental, for the farm family begins to lose what viability they had. Unless there is an inflow of food stuffs or other farm products, the conditions of families in agricultural communities slowly but fearfully deteriorate.

I can not stress how important this problem is and will continue to be in light of the AIDS epidemic. Perhaps, we can write to this issue as well.

Posted by: anne on March 14, 2003 01:30 PM

Kofi Annan

"The devastating impact of AIDS on food production - with seven million African farmers already dead - is only too obvious. Infection rates are rising among African women - who account for 8 out of 10 of Africa's small farmers, and who traditionally provide the vital coping skills needed in times of food crisis. The latest figures show that women now make up 58 per cent of Africans already infected.

"Because of AIDS, skills and knowledge are dying out rather than being passed from one generation to the next. Both at the household level and the government level, resources are being diverted from food production to health care. In turn, food shortages fuel the disease, through malnutrition, poverty and inequality."

Posted by: anne on March 14, 2003 01:34 PM

Remember too, AIDS is a young person's disease. Young women or men are stricken and weaken, and who is there to care for the children? Southern Africa is witnessing grandparents increasingly having to care for their children's children. Again, farming is a fairly young person's activity on small African farms and grandparents have only so much energy.

Posted by: anne on March 14, 2003 01:49 PM

"If the poor really are subsistence farmers, then pulling them out of production won't affect the agricultural products in the market too much, as their meager overproduction in a good year is sold below market price for shoes, schoolbooks for the kids, or maybe a bit of coffee or refined sugar."

Surely in light of the African AIDS epidemic this sentence is haunting on moral and socio-economic levels.

Guess how much the new AIDS drug by Roche is being sold for in Europe. Guess. 22,000 dollars a year. In Europe. This sort of cost has important implications for America as well as Europe. China? India? Brazil?

What of the use of such a drug in Africa? I am at a loss to understand, and wish discussion now and again.

Posted by: anne on March 14, 2003 02:07 PM

I forgot to mention this but you can actually purchase an exemption from traffic regulations in Moscow. You get a little red light for the top of your car and you get to run red lights, speed, and presumably other things-(I don't know if they have dui regs in Russia-I suspect not). What do you think would happen here in the US if this was tried-? ;>)

Posted by: Lawrence on March 14, 2003 02:12 PM

This reminds me of my time on Capitol Hill, when bike messengers were often found at the head of the line for admission into important hearings that had small public seating capacities. Sometimes you would got the hill at the crack of dawn to be able to be there for an event that didn't start until the afternoon. I've heard of capitol hill police enforcing the line, not allowing the lobbyist who showed up ten minutes before to take the place of the paid sitter. In situations like this, particularly when you are unsure of how many seats will be allowed, anyone leaving the lne for any reason also has to be worried about maintaining their place.

Posted by: edmuir on March 14, 2003 02:24 PM

There is no externality on the middle class in this model. Allowing the rich to pay the poor to stand in line for them simply increases demand for theatre tickets, so price (in terms of cost of waiting in line) goes up. Therefore the only effect on the middle class is through the price mechanism, i.e. it is not an externality.
If I start drinking a whole lot of coffee, so the price of coffee goes up, my action has an effect on all other coffee drinkers, but that does not oblige me to compensate them for their loss of purchasing power.

Posted by: Joannes Jacobsen on March 15, 2003 02:30 PM

>>>>Suppose the people putting on the performance want to charge a non-monetary price to attend. This could obviously be time spent waiting in line. They might want to do this, for example, to insure an audience of enthusiasts.

Surely this only ensures an audience that isn't time-poor. E.g. the face ticket price is Ģ50. Distributed by scalping, all tickets are worth Ģ250. Distributed by queueing, tickets take 5 hours to acquire.

I.e. enthusiast A is a madly keen student, who has 20 hours spare to queue, but "only" Ģ200 to buy a ticket, gets to go to the show at any queue length up to 20 hours, but wouldn't at any scalped price of over Ģ200. Enthusiast B is ana accountant has 2 hours but Ģ500 spare. Casual viewer C has 5 hours to find some entertainment, or Ģ100.

If you distribute tickets by queueing, the student and the casual viewer go. If you distribute by scalping, only the accountant can go. Neither solution, in this not unreasonable case, will see an enthusiast only audience.


The numbers above (except the price paid, which is more than I can reach for) are fairly close to the prices involved in acquiring tickets for rugby internationals in England. However, the distribution mechanism is rather more sophisticated than the queue.

To apply for tickets for big games, you must be a member of a rugby club. These are allocated tickets based on their requests (never receiving enough for big games), and then their members ballot or otherwise receive them. Tthere are also corporate entertainment options, which we shall ignore. The time-rich can get access through a serious commitment to a club (being president, treasurer, or coaching kids), as they'll get them periodically a rewards. The money-rich can pay to join multiple clubs and take their chances in the ballots. The casusal viewer is excluded from access to tickets to popular games.

Posted by: The Philosophical Cowboy on March 16, 2003 02:32 AM

What Anne said about "If the poor really are subsistence farmers, then pulling them out of production won't affect the agricultural products in the market too much, as their meager overproduction in a good year is sold below market price for shoes, schoolbooks for the kids, or maybe a bit of coffee or refined sugar.", plus:-

- The people who REALLY get hurt in transitions like these are the "broken men", newly landless, who have to find cash work paying enough cash to live off, while competing with cash work being done by people who still have a subsistence toehold; these are the ones selling below price, only it is their surplus labour not their direct agricultural surplus they sell. For them, the market price of food, measured in wages available, DOES go up above what they need for survival. It's not the presence of food in the market that matters but its effective availability - the market determines WHO will starve. Think Amartya Sen on the Bengal famines.

- People like that aren't subsistence farmers but nearer the Kulak level. What SUBSISTENCE farmers try and get from any surplus is cruder clothing than bought shoes, any taxes and rents they are forced to pay in cash, and any essentials of a subsistence lifestyle that are only needed intermittently. Text books and luxury consumables like coffee and sugar are NOT among these.

The bottom is a REALLY long way down, and people on the brink can be tipped over by even tiny declines.

Posted by: P.M.Lawrence on March 16, 2003 02:09 PM

I was just alerted to this post by a friend. Well done. I enjoyed it immensely, especially given my recent experience with line sitters (see http://dclawstudent.blogspot.com/2003_05_01_dclawstudent_archive.html#94736192)!

Posted by: Scott on May 28, 2003 06:48 AM

Would you say that when you wait in a long line for a long time to mail a package at the post office, is this a negatice externality?

Posted by: Mary on October 26, 2003 02:15 AM
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