Waiting in line and location values.

There are of course lots of interesting theories about queueing, and I am sure there are a few basic generic types of queue (the British English word for "line").

- a physical queue for tickets to a one-off event like Wimbledon or a status product like a new Apple iPad or iPhone.
- a physical queue for a regularly repeating event like a bus or train.
- a normal queue in a shop, train station or post office;
- a non-physical queue, like the waiting list for social housing or for a new car in the old Soviet bloc.

We know that there are some people pay other people to queue for them (like sending a servant or assistant to the shops) or adopt other queue-jumping measures, like taking a disabled person with them Disneyland.

If you have been in queue for a while, you don't want to "lose your place" by leaving the queue, and the nearer you are to the front, the less willing you are to lose your place, because you have "invested" your own time in standing there (or registering for the social housing and simply waiting for the letter to arrive).

So your place in the queue clearly has value - that value is a function of various things:

Let's illustrate this using a basic example: you are in a normal queue at the post office which seems to have ten people in it all day long, one person joins the queue every two minutes and it takes two minutes for each person to buy his stamps. After you have been there ten minutes, you are up to fifth place and there are five people behind you.

i) How much longer you have to wait.

Clearly, your time has value, even if that is only a ten pence a minute. So the second place in the queue is worth £1.80 more than the last place (the "marginal" place). So this depends on how many people are in front of you, if you are in fifth place and somebody in front of you leaves the queue, you have made a windfall gain of 20p.

ii) How many people are behind you.

You might imagine that this time value of £1.80 from (i) is a function of how long you have already been waiting ("time invested"), which is mathematically true, but that is actually a sunk cost and irrelevant.

Let's say, you suddenly realise you forgot to bring your money with you and have to leave the queue, go home, come back and start again, you will have to "invest" another ten minutes getting back to where you were.

What matters here is the number of people behind you. It's started raining and nobody has joined the queue for a while, so after ten minutes there are only four people in the queue when you come back - you have lost nothing by starting again. Or perhaps the five people behind you get bored and all go home. You are now last in the queue and your place is worthless, you don't care if you lose it. The value of your place falls from 90p to zero as a result of the people behind you walking off.

iii) How likely it is that the product will run out before you get served.

This is unlikely to happen in the post office, but what about limited products, like a new iPad or iPhone, or bread during wartime or in a socialist country? If people know that only five hundred products are to be sold, one per person, then the value of a place starts falling sharply from 400, onwards - fewer products might be delivered, some might be snaffled and auctioned off by staff, some people in front of you might manage to buy two.

Places down to 600 or so still have some small value - people in front might not have the money, might change their minds, might be queueing for something else entirely, more of the product might arrive. But from place 600 onwards, the place in the queue has no value.

So nobody would pay a servant or assistant to go and stand in 600th place, it is just not worth it.

iv) How highly you value the product/what the personal benefit is to you.

Private businesses try and set their prices to maximise their profits by trading off price and volume. But there is always a consumer surplus, which is different for different people.

One person might desperately need a stamp to send off a job application that day - he will line up patiently, even if there are, unusually, twenty people in the queue. Somebody else who just wants to buy a few stamps in case he needs to post a letter in the next few weeks will turn round and leave the post office if there are more then three or four people in the queue because he'd rather be doing something else.

There is also non-price rationing - there is huge demand for social housing in the UK, and to a large extent it is rationed by waiting list.

That "consumer surplus" is much higher for things like social housing, that is a straight freebie, so if the net present value of the cash saving you can make by moving out of expensive private rented housing into social housing is £100,000 over your lifetime, places near the front of the queue are worth nearly £100,000. Of course you cannot monetise your place directly by selling it, it's take it or leave it, but you could be sneaky and when you finally get your social housing allocated, simply sub-let it for a market rent and collect the £100,000 over your lifetime.

v) With some things, there is a bizarre sort of status to being in the first few places.

Think about a queue for Wimbledon tickets, the Harrod's sale, the new iPhone. You are there with like-minded people with similar interests, you all now that you will get what you want and the media send photographers and journalists round to interview you.

So big tennis or Apple fans actually enjoy queueing, they will turn up two or three days before the product goes on sale and are happy to waste two or three days out on the pavement just to show how dedicated they are to their own peer group.

vi) And finally, one thing which I have not mentioned yet...

... as it is implicit in the whole concept of queueing, is that nobody will queue jump and push in ahead of you. If people are allowed to push to the front no matter what, we observe a different phenomenon - people will pack more densely at the front, it is a trade off between being up close the action and having a bit of space to yourself.
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I hope that this all fairly clear and uncontentious so far, and regular readers will have guessed what I am leading up to.

The rules which dictate the value of a place in a queue are almost exactly the same as those which dictate the location value of land! The plots near the 'centre' (be that the motorway junction, train station, park, a good state school, a hospital, the park, the beach) are worth a lot more than those further away in exactly the same way as the places in front of the queue are worth more than those further away.

For example, Rule (i) is simply that the value of a place/a plot depends on how long it will take you to get to the front; so a house or a hotel one minute's walk from the beach is worth more than one ten or twenty minutes' walk away, the difference in value is the time saving you can make by being in the former not the latter.

I won't bore you by going through the other Rules, you can do that for yourselves, see also Fraggle's post of a couple of years ago. But what it boils down is that the person doing the queuing can do absolutely nothing to change the value of his place, he did not create it, if he weren't there in sixth place then somebody else would be in sixth place, and the value of that sixth place would be the same.

And the big difference between the value of a place in a queue and the location value of land is that the former is ephemeral - if you go to the trouble of being first in the queue, you have the longest wait, the value of your place expires when you have been served, it extinguishes.

With the location value of land, the owner is permanently ahead of everybody 'further out', he has a five minutes shorter walk to the shops, station, ten minute shorter commute time effectively for ever, and he in turn is pushing up the value of the plots which are even nearer the shops, station etc. They are like allowing a German tourist to be the first to put his towel down on the first day the hotel opens and him having dibs on that sun-lounger for ever, even to the extent of being able to rent his sun-lounger to the hotel's paying guests.