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This is a very common argument found in introductory classes and texts. Here's Mankiw's version:

Thinking at the margin works for business decisions as well. Consider an airline deciding how much to charge passengers who fly standby. Suppose that flying a 200-seat plane across the United States costs the airline \$100,000. In this case, the average cost of each seat is \$100,000/200, which is \$500. One might be tempted to conclude that the airline should never sell a ticket for less than \$500. But a rational airline can increase its profits by thinking at the margin. Imagine that a plane is about to take off with 10 empty seats and a standby passenger waiting at the gate is willing to pay $300 for a seat. Should the airline sell the ticket? Of course, it should. If the plane has empty seats, the cost of adding one more passenger is tiny. The average cost of flying a passenger is \$500, but the marginal cost is merely the cost of the bag of peanuts and can of soda that the extra passenger will consume. As long as the standby passenger pays more than the marginal cost, selling the ticket is profitable.

Do airlines actually do anything like the above? I think they don't as I have frequently been on planes with mostly empty seats (even before the current pandemic).

Mankiw says the marginal cost of another passenger is "tiny". Let's say it's \$30. Then if a flight has some empty seats 24 hours before scheduled take-off, why doesn't it offer the seats for say \$50 each and fill them all up? Why is it that, in practice and contrary to the above argument, the airline will usually prefer to leave the seats empty?

What, if anything, is flawed or incomplete about the above argument?

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    $\begingroup$ The argument is more or less correct if the ticket sale is one-shot. But the real world is an iterated game. If an airline sells cheap last-minute tickets once, then people will expect that to happen next time and hold off from buying early. $\endgroup$
    – Nayuki
    Nov 5 '20 at 4:10
  • $\begingroup$ The incremental cost of adding a passenger is substantially more than "merely the cost of the bag of peanuts and can of soda", or even the $30 you use. There's substantial added fuel cost for additional weight carried by the plane. Adding substantial additional weight might also incur other additional costs than just the fuel. The additional cost will, of course, depend on the exact circumstances. This answer on Aviation, for a 737, ballparks $100 as the fuel cost for 170lbs, which is well below the average weight for a passenger + luggage. $\endgroup$
    – Makyen
    Nov 5 '20 at 20:11
  • $\begingroup$ @Makyen - that's a cost for 4 hours of flight. I've never had a 4 hour flight cost anything as low as 500. $\endgroup$
    – Davor
    Nov 5 '20 at 20:31
  • $\begingroup$ @Davor The cost of a flight from Los Angeles to New York, a ~5 hour flight, appears to be in the <$230 range for a lower-end nonstop flight from multiple airlines, or even substantially lower. I'm not trying to say the incremental price is any particular value for any particular flight. I'm just trying to make the point that the incremental cost isn't trivial, and that it is, probably, substantially closer to the cost of a low-end ticket than an assumption of $30 implies (which is assumed for some unspecified flight). $\endgroup$
    – Makyen
    Nov 5 '20 at 20:44
  • $\begingroup$ @Makyen - well, to be honest, I'm European, and my long flights are much more expensive than that. Could be due to them being international, unlike US. Or the prices are currently down because of Covid, dunno. $\endgroup$
    – Davor
    Nov 5 '20 at 21:06
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One possible answer is that Mankiw's argument takes consumer demand for airline tickets as fixed and given. I would speculate that cheap last-minute tickets are a substitute good for regularly priced tickets, and that if enough people came to prefer them, demand for regularly priced tickets would fall and the airlines would lose revenue. In other words, instead of paying full price, too many customers would deliberately hold out for the heavily discounted tickets.

This is the same reason why so many stores destroy their obsolete/stale inventory instead of selling it cheaply or donating it, and is an example of a perverse market incentive, as it leads to unnecessary waste.

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    $\begingroup$ This is a very good answer - it gets right to the point of why most airlines don't do this - but it could use a bit of editing to be less focused on Muflon's previous answer at the start. $\endgroup$
    – Zibbobz
    Nov 4 '20 at 12:36
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    $\begingroup$ Donation is a little different than selling it cheap. Donation recipients are usually controlled and are normally not customers to begin with. However, food donation can have very rigid standards, possibly higher than restaurants, so it's not like you can take your old stale food and donate them because places simply won't accept them. $\endgroup$
    – Nelson
    Nov 5 '20 at 4:06
  • $\begingroup$ @Nelson - Yeah, but poor people still need to eat. If Major Nanso Food Conglomerate destroyed their unsalable food, the poor would have to go out and buy food -- perhaps from the same conglomerate that didn't donate. So the conglomerate gets to have a bit of income, even though Mr. Armand Poor may have to skimp on other needs like rent or medicine. (Which is unfortunate, of course.) $\endgroup$
    – Jennifer
    Nov 6 '20 at 10:56
  • $\begingroup$ @Jennifer But that's what they currently do already. Food donations have a higher standard than salable food, especially cooked food. By the time food is unsalable, you already can't donate it. You can get shut down and get a very heavy fine for doing that. $\endgroup$
    – Nelson
    Nov 6 '20 at 15:23
  • $\begingroup$ @Nelson - Yes, I KNOW that's what they do. The WHY is that they'd be cutting into their own sales if they did -- like I said, it's unfortunate. $\endgroup$
    – Jennifer
    Dec 3 '20 at 6:39
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Do airlines actually do anything like the above?

Yes, in fact now you will see on many airports specialized companies/windows that will offer last-minute flights very cheap. For example, in the past, I used to frequently fly to Vienna Schwechat airport, and there used to be a window where you could get cheap tourist flight but the catch was you could not choose destination - precisely because they would just give you some flight that needed passengers. Of course, this is just anecdotal evidence but you can see hard evidence by just typing cheap last-minute flights into google and see how many offers there are. The Telegraph even has an article comparing prices showing that often last-minute prices are cheaper.

This is also supported by published research as Koenigsberg, Muller, & Vilcassim (2008) claim that:

Many airlines offer last-minute deals, either directly or via resellers. For example, in some European airports, one can buy tickets at greatly reduced prices for same-day flights.

However, at the same time, the same research shows that not all airlines do this. In fact the research above investigates the case of easyJet which is one of the outliers that did not used to offer last-minute deals (although the paper concludes it would be optimal to do so in few instances). Hence, while the above strategy is optimal for many airlines there is more nuance to the situation and some airlines may try and experiment with various different revenue maximizing strategies.

This being said the strategy of offering cheap last-minute ticked does not guarantee filled plane. If plane has 30 empty seats then likelihood that they will all be filled at the last-minute by people suddenly making spot decision to take them, even if price is cheap, is not $100\%$. The point is that it is usually optimal for airlines to do so even if it attracts just few extra passengers and does not completely fill the plane.

In addition Mankiw is also most likely exaggerating when he says that marginal cost of extra passenger is just peanuts. For example, airlines in addition to their own marginal costs (little bit more fuel consumption, more cost on handling the passenger at the gate, baggage handling etc.), will also have to pay per-passenger fees to the airport for the cost of security (e.g. see here) and in many places also various taxes and these are just some examples. These might be small individually but they add up.

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    $\begingroup$ There is also some evidence of such pricing behavior in the cruiseship industry, see Coleman, Meyer & Scheffman. 2003. “Empirical Analyses of Potential Competitive Effects of a Horizontal Merger: The FTC’s Cruise Ships Mergers Investigation.” Rev. Indus. Org. $\endgroup$
    – Bayesian
    Nov 3 '20 at 17:08
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    $\begingroup$ The per-passenger fees are usually due by the passenger though, not the airline. The passenger pays the airline, the airline forwards it to the relevant place. Again, if you've got this set up in a computerized system then the cost per passenger is unmeasurably close to zero. $\endgroup$
    – Graham
    Nov 4 '20 at 9:05
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Pricing of last minute tickets for airlines is a tricky problem.

Yes, discounting fares may attract customers who would not have flown otherwise. But buying a flight is a bit more complex than buying some gadget on discount on Amazon. Few customers can make such last-minute decisions. They usually need that flight, but also a flight back, and the schedules must at least vaguely match their requirements. They also need a place to stay. For some destinations, it might involve paperwork (getting a visa, e-visa, ESTA, ETA or whatever the destination calls it). They may have to get time off from work.

Also remember that leisure passengers who would be willing to book that flight at the last minute prefer things around a week-end, when flights are usually the busiest!

This is a small market which works best through agents who will package the flight with an hotel and possibly other services.

So it's not just because you sell at a discount that you are suddenly going to fill up all those seats.

On the other hand, discounting at the last minute may be counter-productive for airlines. Last-minute bookings are often business travellers that need to travel at a minute's notice. Those can pay more money.

Traditionally, last minute flights are actually more expensive than flights booked in advance. On traditional airlines, you'll see that most discounted fares need to be booked 7 or 14 days in advance, with all sorts of conditions attached to them (no one-way fares, only returns, minimum duration of stay, staying over the week-end...).

Some airlines will try to segregate last-minute discounts (sold as packages through specific channels) from last-minute more expensive bookings (sold with a lot of flexibility). Not all can, especially those who choose to sell only directly.

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One problem with trying to price goods or services at their marginal cost is that customers may hold off on making immediate purchases of goods or services they expect to be available cheaper at a later time. If there aren't enough people who would have any interest in a particular flight to fill it even if tickets were only \$1 each, but the number of people who would be willing pay \$1000/seat if they knew they couldn't get the flight cheaper would be sufficient to make the flight profitable, the airline would need to ensure that the people who would be willing to pay \$1,000 if necessary, actually pay something close to that.

In cases where a flight is sometimes full and sometimes not, customers may be willing to pay more for a guaranteed seat than for a standby seat. If a flight is almost never full, however, some customers whose travel plans are uncertain might be willing to pay more to buy a ticket right before a flight (once they know that outside factors won't prevent the trip) than they'd be willing to pay for a non-refundable ticket a week in advance (running the risk that outside factors might prevent the trip and cause them to forfeit the ticket price).

If airlines could practically run smaller planes for flights they expect to be less full, they could almost certainly benefit from doing so. Unfortunately, airplanes are a sufficient capital expense, as is the training necessary to let crews fly a variety of different ones. Thus, it's often necessary for airlines to fly larger planes than would be ideal for some flights, in order to ensure that they have adequate capacity for others.

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I think the other answers covered well why airlines don't usually do quite what Mankiw described. But everything I have read about airline pricing says they are acutely aware of marginal costs. Even if the discounted seats are sold well before the flight, it can be seen as charging less than otherwise desired to avoid ending up with an empty seat.

The practice of overbooking and then giving vouchers to volunteer to fly later can be seen in a similar light. Because of no-shows, there will likely be empty seats. But, instead of trying to sell them at the last minute, they sell them in advance and risk having to pay someone off to fly later.

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One theoretical flaw I don't think have been mentioned yet: The market clearing price is not the same as the revenue-maximizing price, if there is low competition. Suppose there are no other flights from A to B left at the last minute. Customers X, Y, Z are willing to pay \$500, \$200, \$100. Then the revenue-maximizing choice is to price the three seats at \$500 and only sell one, even if the marginal cost is zero.

This is separate from other issues raised, like customers waiting until later if they know the price is going to drop. It also ignores dynamic price-changing options, e.g the price gradually drops and people claim seats when their surplus balances the risk of the supply running out.

A note: I think you know this, but just to emphasize, this argument says prices can reasonably be low, but it doesn't say they should be low. It just puts a floor on the reasonable price, but the actual price depends on other factors.

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For airlines that operate on a traditional model (as opposed to low-cost carriers,) the biggest factor here is probably last-minute business travelers. In non-pandemic times, these represent an enormously outsized percentage of airline revenue. For example, this Investopedia article says that business travelers tend to account for about 12% of airline passengers (in normal years,) but can account for as much as 75% of the revenue for the flight. It's usually actually the tickets being sold far in advance that are well below the average cost per seat, as they're being sold primarily to leisure travelers planning vacations many weeks or months in advance.

The primary reason that airlines frequently have some seats left near the time of the flight in the first place is that they intentionally plan to do so. They want to have those seats open to sell to business travelers scheduling meetings near the last minute who are willing to shell out 3x to as much as 10x what the average leisure flyer is paying for the equivalent seat right beside them booked months in advance.


Regarding the argument of it being better to sell the ticket for \$50 to someone flying standby rather than letting in fly empty: That's technically true if there's someone waiting to fly standby and that person isn't willing to pay a higher price and the seat would definitely otherwise go empty. In reality, the people who are only willing to pay \$50 for a flight are very rarely flying standby, with the possible exception of airline employees and their friends/family.

Low-revenue leisure travelers normally need to schedule their trips weeks or months in advance. Most of them don't want to spend their days off from work hanging around an airport all day waiting for a cheap empty seat to open up at the last second and taking the risk that they won't get to their destination at all (at which they likely have accommodations booked which are too close-in to cancel for a refund) all to save maybe \$50-\$100 vs. booking early.

On the contrary, the revenue passengers waiting for a standby seat are often actually business travelers willing to pay hefty sums for a seat on a flight where the airline didn't end up holding enough seats for late bookings. It's comparatively much more rare to have leisure travelers only willing to pay very low prices hanging around the airport waiting for an open last-minute cheap seat.

As someone who is usually traveling on leisure myself, I know I don't want to do that. I want to know that when I show up at the airport, there's a seat on my booked flight waiting for me. I want to spend my vacation at my booked destination, not waiting around an airport hoping for a cheap seat to become available.

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It's a useful theoretical example illustrating the difference between fixed and marginal costs. And airlines totally do things like that--think of all the last minute 'discount' tickets sales. Airline tickets 'spoil' like fruit--after the flight date, they are useless. So an airline has every incentive to sell a ticket for every seat they can, regardless of the price.

But it misses the point that it's the average cost that determines the feasibility of the route. Selling half the tickets for seven hundred and half the tickets for three hundred still manages the average. So does selling one ticket for $100k and the rest for a penny.

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