Why Don't The Airlines Just Raise Fares?

[Bob Owens]

How polite of you. When individuals post arguments with which you disagree, and your arguments are exposed as fallible, you tell people to "go away."


You assume that everyone on board HAS to fly at all. What you apparently can't fathom is that flying is discretionary for millions of people. Not everyone HAS to fly. Some choose to fly because of the price. Raise the price on these very price-elastic customers, and they just might stay home.

And the "silly charts"? You keep harranging everyone with your stupid mechanics pay v. CPI graph, yet insult others? You are a piece of work.

[post="235740"][/post]​

Well I've offered to provide all the data and the sources where I got my figures from to anyone who wants them. He comes up with some formula with nothing to back it up. Thats why I said to "go away". My graph on mechanics pay is verifiable. Would you like the data?


Sure they might, but that really depends on how much we raise them and also what happens at the other end . If Hotels and resorts offer reduced rates because the airlines decided to raise fares people may still want to go. You do admit that airline traffic is an intermediate good right? When it costs more to take a cab to the airport than it costs to fly you to yuor destination something is wrong.

 

[Bob Owens]

funguy2,Jan 5 2005, 04:27 PM]Bob:  You are still dancing around the point.

Which is?

I am not arguing your "derived demand" theory. 

Its not my theory, its a theory that some economist used to describe demand in the airline industry..

Most airline passengers do not fly for the shear joy of flight.  However, increasing fares increases the total costs of the trip.  Thus as fares go up, total trip costs go up, and we know that demand decreases as prices increase.  Thus your "derived demand" theory doesn't do much to address the basic supply/demand argument.  Nice try.

Sure it does, you just dont agree. how much has our demand for fuel decrease as the price increased? When they raise the price of electricity how much less do yuo use? So much for your basic theory, obviously it does not apply all the time.

You continue to demonstrate a lack of understanding of how airline pricing and revenue management work. 

The problem is not that I dont understand it, the problem is that the people running the airlines apparently dont understand it. Thats why we are in such a mess. I do my job, you dont see airplanes falling out of the sky.

Delta is "lowering" their fares.  However, I suspect they are trying to increase AVERAGE fares.  How?  Simple, they will offer less cheap seats and more "expensive" seats.  Now, the price range on their one-way transcon fares will probably be $99 to $599 vs. $99 to 2499.  Since $2499 is not a reasonable fare to most folks, they probably sold almost none anyways.  However, by capping fares and reducing the availability of $99 seats, they can "reduce fares" and increase average fares and RASM.  I suspect that is their goal.  AMR failed when they attempted this a decade ago.  America West was successful trying this strategy.  Will DAL be successful?  Who knows.  Yes, there is some hype here, as DAL is just eliminating fares that nobody purchases anyway.  But there could be some underlying value.

I think I already posted something to that effect, albeit in an abbreviated form.

 

[Bob Owens]

Uh huh...as if the legacies offer discounted airfares just so they can beat labor down.

Thats not what I said, although it is a side benifit of a confusing system.

My bet is more of the latter than the former. But, honestly, that's exactly how WN sets their prices. So, does that make it deceptive or not?
I'm going to give the benefit of the doubt that you're not as stupid as your post sounded. I hope I'm right.

Air travel customers tend to be bimodal. Berry, Carnall, and Spiller did a study in 1997 that showed this clearly. The two modes are, basically, business and leisure travelers. (Of course, AA pretty much knew this over two decades before that.) For business travelers, price elasticity is low (i.e., increasing the fare by $10 would make little difference in the number of passengers).

OTOH, price elasticity for leisure travelers is very high. Why? Because they:

are paying out of pocket, and thus feel the price difference viscerally.
can't deduct the cost of the ticket, so they bear the full brunt of the price differential.
have far more substitutes available. Business travelers don't go unless they have to be at the destination. Leisure travelers, by definition, are going because they want to. They can go elsewhere, or not at all.
usually buy several tickets, rather than only one. As a result, each dollar increase is felt multiple times by leisure travelers.

I dont disagree about the elasticity difference between the two, however I disagree with your figures. The cost of Air Travel is not the inhibiting factor it once was, and it has been steadily getting cheaper to fly since the industry began. I would say that for the leisure traveller $10 would not matter that much, assuming its a long distance flight.

We can go back and forth discussing this theory and that but the fact is that there appears to be demand, as the industry is still running very high load factors, and thats with airlines like AA adding seats which would have the effect of increasing capacity.



So, if your airline manages to capture the entire business market, you can change prices almost with impunity. If, however, you're using the leisure travelers to close the profitability gap, you must price carefully.

Ok, so that does not mean that they cant raise them at all, even they have mostly leisure travelers and how much do they have to raise fares to break even?
QUOTE
Besides your formula has too many assumptions, one of course is that all three/100 consumers can get a seat at $5 less somewhere else.


If you followed the reasoning above thus far, you can look at my post from several months ago about how to properly set a price. It illustrates exactly why those "assumptions" are not really assumptions at all. I'd put a link here, but the search hasn't been re-enabled yet after the move. If you're truly interested, I can rewrite it and put it in this thread, but I'm not going to do it unless you are.

Sure, cut and paste it.

 

[Oneflyer]

Sure it does, you just dont agree. how much has our demand for fuel decrease as the price increased? When they raise the price of electricity how much less do yuo use? So much for your basic theory, obviously it does not apply all the time.

Of course it doesn't apply all the time, its called elasticity of demand. I have to get to work everyday, so i'll by gas no matter what the price is, but I don't have to travel across the country to see my grandmother.

Look Bob, you make some good points, but its nothing that anyone hasn't already thought of already. Your lack of economic understanding is glaring, so just give it up already. You're trying to explain algebra to a calculus class.

 

[mweiss]

The cost of Air Travel is not the inhibiting factor it once was...

In what way? Sure, if you compare today with 1975, you'll find that there are far more leisure passengers. The elasticity, however, remains relatively unchanged at best. It may even be more elastic than it used to be, simply because the customers have more information and have become more savvy purchasers.

I would say that for the leisure traveller $10 would not matter that much, assuming its a long distance flight.

And you would say this because...? Thus far it sounds like a "formula with nothing to back it up."

...the fact is that there appears to be demand, as the industry is still running very high load factors

OK, here's where you're showing your weakness in economic theory. You treat demand in that statement as if it were completely inelastic. It's not.

Ok, so that does not mean that they cant raise them at all, even they have mostly leisure travelers and how much do they have to raise fares to break even?

I think you are missing a couple of words in that sentence, but depending on where they were supposed to be the meaning could be quite different.

In any case, in order to answer your question, I'll have to give you the details I alluded to above. I can't just cut and paste it, because I can't use search on here yet...so I'll have to type it in manually. I'll give the first part tonight, and the rest tomorrow.

In the interest of simplicity, we'll start by assuming that all tickets are sold at a single price. Tiered pricing will come later, so please bear with me.

R = PQ, where R is Revenue, P is Price, and Q is the Quantity sold.

If we assume that there is some elasticity in demand, then Q is a function of P.

Again in the interest of simplicity, we'll assume that demand is linearly elastic. It's not, but we have to start somewhere, and I guarantee you that it also works for non-linear demand functions (if you have taken calculus, this will be much easier to explain).

So, if demand is linearly elastic, then Q = aP, where a is the slope of the demand line. It's always negative, since when the price goes up, the quantity goes down.

This means that R = P (aP).

End of part 1.

 

[Bob Owens]

mweiss,Jan 7 2005, 06:43 AM]
In what way?

In that air travel is far cheaper today than it was in the past.
Sure, if you compare today with 1975, you'll find that there are far more leisure passengers.

Then or now?

The elasticity, however, remains relatively unchanged at best.

Which elasticity?

It may even be more elastic than it used to be, simply because the customers have more information and have become more savvy purchasers.

Define which elasticity you are talking about. Elasticity is a term that can be applied to different things. To say "elasticity remains unchanged" is not specific. As you pointed out, price elasticity for business travellers and leisure travellers is different.

And you would say this because...? Thus far it sounds like a "formula with nothing to back it up."

Not every observation has to be backed up by a formula. Its the other way around formulas are created to explain observations.

OK, here's where you're showing your weakness in economic theory. You treat demand in that statement as if it were completely inelastic. It's not.

No that is your interpretation, with quite a bit of stretch I might add. Where do I say anything to support your claim that I'm treating demand as completly inelastic??

My interptetation from what I'm reading is that some are claiming that prices are low decause demand is low, well the figures for load factors do not support that statement. Demand, as measured by load factors, is high. Now at what point demand would drop off if prices were raised depends upon a multitude of factors including but not limited to the amount the ticket is raised, and the overall confidence in the economy, etc. Regardless of whatever formulas you have the fact is that niether you, I or those working for the company can precisely identify that point because it is not stationary.

I think you are missing a couple of words in that sentence, but depending on where they were supposed to be the meaning could be quite different.

I think I brought that same point up about a few words and their placement affecting the meaning of a sentance a few posts back. Glad to see you agree.

In any case, in order to answer your question, I'll have to give you the details I alluded to above. I can't just cut and paste it, because I can't use search on here yet...so I'll have to type it in manually. I'll give the first part tonight, and the rest tomorrow.

In the interest of simplicity, we'll start by assuming that all tickets are sold at a single price.

Problems already. This is a complex situation and we are already allowing you to make assumptions, assumptions that are not factual.

Tiered pricing will come later, so please bear with me.

R = PQ, where R is Revenue, P is Price, and Q is the Quantity sold.

If we assume that there is some elasticity in demand, then Q is a function of P.

Again in the interest of simplicity, we'll assume that demand is linearly elastic. It's not, but we have to start somewhere, and I guarantee you that it also works for non-linear demand functions (if you have taken calculus, this will be much easier to explain).

Actually I aced Calculus, but that was over 20 years ago.

So, if demand is linearly elastic, then Q = aP, where a is the slope of the demand line. It's always negative, since when the price goes up, the quantity goes down.

This means that R = P (aP).

End of part 1.

OK, so far we have made multiple assumptions that we know are inaccurate. With that known there is no way we can come to an accurate conclusion. Sure we can follow through with the formula but right off the bat we know that the assumptions used are wrong so even if we follow through the process correctly the outcome is wrong. Kind of like sending a spacecraft to Mars and having it burn up in the atmosphere because a decimal point was in the wrong place. The calculations were right but the input was wrong.

 

[JS]

Quantity is not just a*P, but k+a*P (otherwise quantity would always be negative). k is the quantity demanded if the product is free.

So, we have R=P*(k+aP)

To maximize R, maximize P*(k+aP)=a*P^2+k*P. The maximum is 2aP+k=0 ==> P=-k/2a.

None of this is very useful for AA, though, because the revenue maximizing price is that charged by a monopoly. AA operates in a competitive environment, so they have to charge the same price as everyone else in order to sell tickets.

 

[JS]

...
My interptetation from what I'm reading is that some are claiming that prices are low decause demand is low, well the figures for load factors do not support that statement. Demand, as measured by load factors, is high. Now at what point demand would drop off if prices were raised depends upon a multitude of factors including but not limited to the amount the ticket is raised, and the overall confidence in the economy, etc. Regardless of whatever formulas you have the fact is that niether you, I or those working for the company can precisely identify that point because it is not stationary.
...

[post="236626"][/post]​

You may have aced calculus, but I can see that you didn't pass economics.

Demand is low means that the quantity demanded at a given price is lower than it used to be. Planes are full because airlines dropped the price to match the lower demand.

You are confusing demand with quantity demanded. They are not the same thing. Quantity demanded is the intersection of the demand curve and the supply curve. If the demand curve shifts to the left (which it most certainly did) and the supply curve also shifts to the left (meaning suppliers are willing to supply the same quantity at a lower price), the intersection of the two moves to the left. The result is the same quantity demanded at a lower price.

 

[Bob Owens]

Quantity is not just a*P, but k+a*P (otherwise quantity would always be negative). k is the quantity demanded if the product is free.

So, we have R=P*(k+aP)

To maximize R, maximize P*(k+aP)=a*P^2+k*P. The maximum is 2aP+k=0 ==> P=-k/2a.

None of this is very useful for AA, though, because the revenue maximizing price is that charged by a monopoly. AA operates in a competitive environment, so they have to charge the same price as everyone else in order to sell tickets.

[post="236629"][/post]​

Ok so not only is the input wrong but the formula is incomplete.

 

[JS]

Ok so not only is the input wrong but the formula is incomplete.

[post="236631"][/post]​

You have to start with a simple example before you can move into more complicated ones. You didn't learn division before you learned 1+1=2, right?

 

[Bob Owens]

You have to start with a simple example before you can move into more complicated ones. You didn't learn division before you learned 1+1=2, right?

[post="236632"][/post]​

Well we can skip all that basic stuff and go right to the point, he said he had some information to support his point that the airlines cant raise fares. I said go ahead and cut and paste it.

I have an understaning of the theories behind supply and demand however I disagree that the price of airline tickets is simply the result of supply and demand, even when you add in competition. There are more factors at work here. Economic theories can not explain all behavior, especially what appears to be irrational behavior.

I dont think that any of us are looking to take an online course in Economics.

 

[mweiss]

Quantity is not just a*P, but k+a*P (otherwise quantity would always be negative). k is the quantity demanded if the product is free.

[post="236629"][/post]​

Point taken. I left it out only because we're going to end up looking at first derivatives, and k will fall out when we do so.

Nonetheless, you are absolutely correct.

 

[mrman]

You guys are making the assumption that if you raise prices that same number of people will fly. If you raise prices you will get less flying and loose revenue. Southwest has always said (I guess before new LCC's came into the market) that their biggest competitor is the auto. If I can fly ISP- Baltimore cheaper than driving, I am going to fly. If I can take the train cheaper than flying I am going to take the train

 

[mweiss]

[The cost of Air Travel is not the inhibiting factor it once was...]In that air travel is far cheaper today than it was in the past.

Not true. The cost is always an inhibiting factor. We've just moved up the demand curve because the leisure fares are cheaper. It's still pretty much the same inhibiting factor.

Sure, if you compare today with 1975, you'll find that there are far more leisure passengers.

Then or now?

Now, of course.

The elasticity, however, remains relatively unchanged at best.

Which elasticity?

Well, both. But in particular I was referring to leisure elasticity.

Not every observation has to be backed up by a formula. Its the other way around formulas are created to explain observations.

Fine. But you're not even explaining observations. You're speculating on what would happen if airfares went up, with not even empirical evidence to back it up.

Where do I say anything to support your claim that I'm treating demand as completly inelastic??

JS answered that one:

You are confusing demand with quantity demanded.

Problems already. This is a complex situation and we are already allowing you to make assumptions, assumptions that are not factual.

Bear with me. I guarantee you that every assumption I make early on will be proven as irrelevant later. Feel free to hang onto all of them and throw 'em at me when I'm done with my explanation of pricing.

Actually I aced Calculus...

Good. So this should be cake for you.

Begin Part 2
R = P(k+aP) [thanks again JS]
which means that R = kP + aP²

If you wish to find the maximum or minimum of a formula, you take the first derivative (in this case with respect to price) and set it equal to zero.

So, maximum revenue would be:
k + 2aP = 0
2aP = -k
P = -(k/2a)

Since you aced calculus, I'm sure you'll recall that this would work for any function Q, linear or not. In the case of airline demand, which is bimodal, you'd end up with two maxima and one minimum. By taking the second derivative, and testing the signs at the three points, you can determine which of the three are maxima and which is the minimum.

Provided that you can accurately discriminate between the two different passenger groups, you can set prices accordingly. If you cannot separate the two groups, then you must test the two price points to determine which produces higher revenue.

Well, that'd all be fine if maximizing revenues were the goal. It's not. Maximizing profit is the goal.

Again, I'll simplify things a bit here, but I'll explain up front why we can do so. The big assumption I will make is that all costs not directly associated with adding an additional person to a flight are "fixed costs." This is true in the sense that once a schedule is set, all of the variable costs associated with schedule changes are no longer variable. And, since we're talking about setting ticket prices for a particular seat on a particular flight, schedule-related costs are now fixed.

So, with an established schedule, the marginal profit associated with a passenger can be expressed as
marginal profit = P-c,
where P is the price paid, and c is the marginal cost of carrying the additional passenger. That marginal cost includes several factors, such as the additional fuel burn caused by the additional weight, wear and tear on the aircraft interior, the marginal costs of selling the ticket and addressing any customer service issues (e.g., calls to res to change the seat), etc., etc....the list is long.

The total profit for a particular flight, assuming a single price for every ticket, can be expressed as:
profit = Q(P-c)
Now, if you had different prices, you'd have to express it more like this:
profit = Q1(P1-c) + Q2(P2-c) + Q3(P3-c)......
It makes the math more complicated, so this exercise is left up to the reader if you wish to test it out for yourself. And, yes, you could even break down different marginal costs for different passengers if you have more time on your hands.

Anyway, we'll go back to the simpler single-price model. Recall that Q=k+aP. Substitute it into the single-price profit model and you get
profit = (k+aP)(P-c) = kP-kc+aP²-acP

Take the first derivative to find the maximum, and you'll get
k-ac+2aP=0
2aP=ac-k
P=(ac-k)/2a

Again, if the demand function isn't linear, you still can do exactly the same thing.

Incidentally, a, the slope of the demand curve, represents the degree of elasticity. If a=0, demand is perfectly inelastic (i.e., quantity demanded would remain unchanged regardless of price). If a=∞ (that's infinity, in case your computer doesn't display it properly), demand is perfectly elastic (i.e., a tiny change in price would have an infinite impact in quantity demanded).

Anyway, as before, if you have a more complex polynomial expression for the demand curve, you can find the local maxima and minima by taking the first derivative and setting it equal to zero, and you can determine if they're minima or maxima by taking the second derivative at those points and checking their signs.

Now for the next level of complexity. This is more advanced pricing.

If you want to truly maximize profits, you'd charge exactly the maximum that each person is willing to pay. This would allow you to get much more profit than with a single-price model. Your total profit function would be
profit = §(P-c)Q
where § represents the integral (it's the closest symbol I could find). Since we've already discussed Q as a function of P, I'm not going to go back into the substitution...just understand that we're integrating with respect to P, and Q is a function of P.

When setting your lower bound for the integration, you must set it to the higher of these two values:
1) Available capacity
2) The marginal cost c
in order to maximize profit. In other words, you want to either sell out a flight or be unable to sell any tickets for more than it costs you to serve that one additional passenger. The upper bound could be set to infinity, but realistically it makes no sense to set it any higher than the highest price anyone is willing to pay for the ticket.

To the degree that you approach the integration model (i.e., adding additional fares), your profits should rise.

Of course, with all that I've discussed here, the biggest assumption is that we know what the demand function looks like. At best, we have a visceral sense of what it looks like. One of the jobs of Yield Management is to ascertain as clearly as possible exactly what the demand function's shape is. If they know the shape, they can determine exactly what pricing to set.

YM has one other big job. As I said above, if you want to truly maximize profits, you'd charge exactly the maximum that each person is willing to pay. In order to do that, you have to figure out what differentiates one customer from another, so as to be able to price accurately. YM gets to figure that stuff out, too. That's how the rules for each fare code are determined.

One final note. The profit maximizing functions mentioned above are simplified to the case where the airline has a monopoly on the route. Naturally, for most routes, that is not the case. However, you can adjust your demand function accordingly by applying the reasonable assumption that if your competitors charge a lower price for the same fare rules, they will get those customers before you do. If you all charge the same price for the same rules, you can apply varying levels of sophistication to determine the market share breakdowns.

OK. If you managed to follow all of that, you should be able to understand why increasing prices will not necessarily translate into increasing profits, or even increasing revenues.

 

[Wretched Wrench]

.

OK. If you managed to follow all of that, you should be able to understand why increasing prices will not necessarily translate into increasing profits, or even increasing revenues.

OK, so we can't raise fares. So, what can be done?


BTW, DiffyQ was my all-time hardest course. All you guys who aced calculus have my admiration.