Week 8: Pay to Skip: Order by Price
Every queue already sorts by willingness to pay — in time. Charging money instead is the most efficient and least popular thing in the course.
26 April 2027
Disney ran FastPass free for two decades. In 2021 it became Genie+ at $15 a day. In October 2022 it gained surge pricing. In July 2024 it became Lightning Lane Multi Pass at $20–$45 a person a day, and that autumn Disney added Premier Pass — every Lightning Lane in the park, once each — at $329 to $449 a person a day at Magic Kingdom, several times the price of getting in.
Hold on to the surge pricing, because it is the tell. The pass costs most on the days the standby line is worst. The thing being sold is the length of somebody else’s queue.
People find this objectionable in a way they do not find the admission charge objectionable. It is worth working out exactly what the objection is, because the obvious version of it does not survive contact with week 4.
The uncomfortable starting point
You already paid to be at the front. You paid in minutes.
Every queue is already sorting by willingness to pay.
A queue is an auction denominated in time. The people who reach the front are the people willing to bid ninety minutes of their life.So what exactly is good about time as the currency?
Not that it is equally distributed — week 4 established that it is not, and that who is standing in the room at 10am on a Tuesday is not a random sample.
And here is the part that should genuinely bother you: the time spent in a queue is burned. When you pay ninety minutes, nobody receives ninety minutes. The value is destroyed. When you pay forty dollars, the park receives forty dollars, and can in principle hire more staff, lower admission, or open another ride.
That is the economist’s case and it is strong. Congestion charging in Singapore, Stockholm and London rests on exactly this argument, and it works: the traffic falls and the revenue funds transit.
Notice what the two currencies have in common and where they part. Both are auctions. Both allocate a scarce thing to whoever bids most. The difference is entirely in what happens to the bid: a queue burns it, a price transfers it. Economists call the burned part deadweight loss, and a queue is one of the purest generators of it in ordinary life — an allocation mechanism whose entire operating cost is destroyed human time.
That is the strongest argument for pricing, and you should be able to state it in one sentence before you attack it: a queue and a price sort the same people in the same order, and only one of them sets the money on fire.
Three objections, hardest last
It sorts by wealth, not valuation. Willingness to pay is willingness and ability. Forty dollars from someone with forty thousand is not the same signal as forty dollars from someone with four hundred, so the auction is not measuring how much people want the ride. It measures what they have. Time, for all its faults, is distributed far more equally than money — everybody gets twenty-four hours, and nobody can buy a twenty-fifth.
That last clause is the strongest version of the argument and it is worth stress-testing, because it is not quite true. People can buy time: childcare, a taxi instead of a bus, somebody else to stand in the line. The correct statement is weaker and still decisive — time is distributed far more equally than money, and converting time into money is far easier in one direction than the other.
It creates a reason not to fix the queue. This is the one that should worry you most. A park’s revenue from priority passes depends on the standard queue being unpleasant. Once a system earns money from congestion it has acquired an interest in preserving it — and this applies to airport security, motorway lanes and customer support alike. Surge pricing on a fast pass is that interest written down as a pricing rule.
It reclassifies the good. Some queues are for things we have decided should not be allocated by price at all: organ transplants, emergency care, a place at a public school. Introducing payment does not just reallocate them, it changes what kind of thing they are. A blood donation system that pays donors is not the same institution as one that does not, even if the litres match. That is week 12.
The measurement everybody skips
Here is the empirical question almost no public argument about fast lanes bothers to ask: what actually happens to the standard queue?
There are two cases and they give opposite answers.
If the paid lane uses spare capacity — a counter that was sitting idle — everyone is better off and the objection is purely symbolic.
If the paid lane uses the same servers, and it usually does, every skip is somebody else’s delay.
Ten per cent buy priority, sharing the same servers. What happens to the population's average wait?
Nothing. Not “almost nothing” — nothing.
Drag the slider below from 0 to 80 per cent and watch the fourth number in the readout. It reads 23.3 minutes at every single setting. That is not the simulation being insensitive; it is a conservation law. Priority is work-conserving: nobody serves faster and nobody goes home, so the mean wait across everybody cannot change. Reordering can only move it between people.
Which means an operator who reports that the fast lane did not raise the average wait is stating a theorem, not presenting evidence. It would have been true before they built it.
Look at the standby group’s ninetieth percentile instead. It goes from 54 minutes to 75 when three in ten buy a pass, and to nearly four hours at eighty per cent. That is where the transfer went, and an average is structurally incapable of showing it to you — the same trap as last week’s classifier, in a park instead of a hospital.
- W with a pass
- —
- W standby
- —
- W₉₀ standby
- —
- W everyone
- —
- W₉₀ standby, no passes
- —
The conservation law is worth one more sentence, because it is the single most transferable fact in Act II. Any work-conserving reordering of a queue leaves the mean wait exactly where it was. Week 6’s shortest-job-first appears to break this and does not — it lowers the mean per customer only because it front-loads the short jobs, and the total person-minutes of waiting is what falls. Priority by payment does not even do that: rich and poor jobs are the same length. It is a pure transfer, and the fact that it is pure is precisely why no efficiency argument can defend it once the lane shares the servers.
Where this has actually been done, and what happened
Theme parks are the easy case because nobody has to ride. Roads are the hard case, and the record is better than most people assume.
Singapore, 1975. The Area Licensing Scheme: a paper licence to enter the central district in the morning peak, checked by people standing at the roadside. Electronic Road Pricing replaced it in 1998, with gantries and variable rates by time of day and level of congestion. Fifty years of continuous operation, which makes it the longest-running natural experiment available.
London, February 2003. A flat daily charge to drive into the centre. Politically survivable because the traffic effect was immediate and visible, and because the revenue was hypothecated to buses.
Stockholm, 2006. The most instructive of the three, because of the order events happened in. A trial ran from January to July. A referendum followed in September. The charge was made permanent the year after — and the reason it passed is that support for it was substantially higher after people had lived with it than before. Asked in the abstract, a charge to drive is a tax. Asked after a summer of measurably shorter journeys, it is a different question.
New York, January 2025. The first such scheme in the United States, after roughly two decades of proposals.
Two lessons come out of that list, and neither is “pricing works”.
What makes a price acceptable is not the price. It is where the money goes.
Singapore, London and Stockholm all recycled the money visibly into the alternative to driving. The schemes that fail are the ones where the revenue disappears into a general fund.And the second: experience moves opinion in one direction. The abstract version of a fast lane is universally disliked; the lived version is frequently tolerated. That is an uncomfortable fact for anyone designing one, because it means the honest way to find out is to run it, and running it is the part you cannot take back.
The decay nobody advertises
Push the slider past 50%.
The advantage of the fast lane collapses, because the fast lane is now a queue. At 80% uptake a pass buys you a 5.6 minute wait instead of a 3.0 minute one, and it costs the same. At high uptake you have a pure transfer from customers to operator with almost no change in service — everybody has paid, and nobody is faster.
This has a name in the wild — priority inflation — and once you look for it you will find it everywhere that a fast lane has been a commercial success. Airport expedited screening works beautifully until enough people enrol. Priority boarding is a queue of its own on most flights now. A support tier labelled “premium” stops meaning anything the moment it is the majority tier.
The value of a fast lane is not a property of the lane. It is a property of how few people are in it — which means an operator selling access to it has an incentive that is in direct conflict with the product they are selling, and the conflict only resolves in one direction.
Find that point for a system you use. It is the number the operator most wants to know and least wants published, and finding it is a legitimate basis for your simulation report.
A checklist for the next one you meet
You will be in the room for one of these arguments within five years of leaving here. Four questions, in order, and they are the entire lecture.
1. Is the fast lane using spare capacity or shared capacity? If spare, most objections evaporate. If shared, every skip is somebody’s delay and you should say so out loud.
2. Who is in the slow lane? Week 4’s question. If the standard queue is disproportionately people who could not have paid, the scheme is a transfer from them, and the fact that they “chose” the free option is not a defence.
3. Where does the revenue go? Into capacity that shortens the queue for everybody, or into margin that depends on the queue staying long? This is the single best predictor of whether a scheme survives contact with the public.
4. What is the uptake at which it stops working, and who is watching it?
A hospital proposes paid priority for elective surgery, using the same operating theatres. Run the checklist.
It fails at question one and never recovers.
Shared capacity, so every private slot is an NHS slot that did not happen, and the mean wait across everybody is fixed by the conservation law — the total is untouched and the distribution moves toward whoever paid.
Question two makes it worse: the people in the slow lane are, by construction, the ones who could not pay. Question three is where it becomes interesting rather than simply objectionable — a scheme whose revenue demonstrably funds additional theatre capacity is a different proposal, and worth arguing about on its merits.
And question four is the one that gets skipped: at what uptake does the paid list become its own waiting list? Nobody proposing these publishes that number, because nobody has computed it.
Notice that you did not need an opinion about healthcare to get this far. You needed four questions and a conservation law.Where this goes
Next week: the alternative nobody in this argument ever mentions, which is not having the queue at all.
Teaching team
- Adaeze Nkemelu — convenor