David R. Henderson  

Congestion Externality Bleg

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In the cost/benefit analysis course i teach, one of the actual cost/benefit analyses we work our way through--and one that I present as a reasonably good CBA--is a study done by two St. Louis Federal Reserve economists on adding another runway at St. Louis's airport. The authors are Jeffrey P. Cohen and Cletus C. Coughlin.

When I taught it this quarter, I was unable to convince one of the students that congestion is an externality. We had discussed earlier in the course the fact that when you have private property, there is not an externality because the owner takes into account the gains and losses to various people. But I pointed out that the airport is government-owned.

This was not his objection, though. His objection was as follows:

When I show up at the airport, that's a choice on my part. I know that if I show up at a busy time, I will have to wait longer, but I take that into account. So does everyone else who shows up.

My answer was, and is, that, yes, you take into account the amount of time by which you are slowed down, and everyone else takes into account the amount of time by which he or she is slowed down, but no one takes into account the amount of time by which he or she slows others.

That still didn't fly (pun not intended.)

So I gave a numerical example. Let's say there are two people: A and B who arrive at the airport. (It's hard to imagine that two people would create congestion, but if we complicated it with way more people, the essence wouldn't change.) A will lose $10 worth of time by arriving at the airport at a congested time but he values being there at that time, versus the uncongested time, at an additional $15. He also causes B to lose $10 worth of time. Vice versa for B. So A looks at the extra cost he will bear--$10 due to B slowing him down--versus the extra benefit--$15--and decides to arrive at the congested time. B likewise.

Now let's tote up the costs and benefits. The benefits to A and B add up to $30. The costs are $20 each, or $40 total. Why $20 each? Take A. A's cost that he bears is $10--it's imposed on him by B. A's cost that he imposes is $10--it's imposed on B and he doesn't take it into account. They total $20.

This is the first time I've written this down rather than just said it and now I'm feeling implausible. Am I double-counting the $10 that each imposes on the other? I'm getting the uncomfortable feeling that I am. It's funny how writing things down can expose flaws in thinking.

So here's the help I want. First, is my numerical example good or flawed, and why? Second, what's a good way of showing the student that there really is a congestion externality?

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COMMENTS (43 to date)
Nick J writes:

Yes I think you are double-counting. A's total costs (which he takes into account) are $10, B's total costs are $10, so the overall cost is $20, but the overall benefit is $30 if they both go. On the other hand if only one goes, they get $15 worth of benefit, so even though you were double-counting I think it still works in that one person should stay home but both arrive.

Here's my attempt at a simpler example, leaving out the issues of costs (or just packaging them into their net valuation of being in the airport).

A and B value a non-congested airport at $30, and a congested airport at $10. Staying home is worth $0.

Both prefer to go to the airport instead of staying home. But, by going to the airport they make it congested and reduce the other person's worth by $20. So, going to the airport if someone else is going has a externality of $20.

In particular their total value when they both go is $20 and when only one goes it's $30, so A would be willing to pay B up to $20 to just stay home.

Jardinero1 writes:

I go to the store and buy a carton of milk. When I buy the milk, I push the demand curve out and the price of milk rises. Have I imposed an externality on all of the other milk buyers when the price goes up.

I struggle with the concept of externality the same way your student does. I come to the conclusion that externalities were invented to give policymakers an excuse to tax some behavior. The best way to deal with the particular case of airport congestion you highlight is to raise the price of travel when it is most congested.

Kevin L writes:

My first instinct was also that it was double-counting. I think a slightly more complex analysis is that airport - or any other - congestion is an externality if (and maybe only if) there is a price ceiling. Consider that if there were a price ceiling on airline tickets, vacation travelers, who would normally be more cost-conscious than time-conscious, are more likely to fly at the same time as business travelers. Since they're still paying just the artificially low price even though they value their time less than a business traveler, they are imposing an externality on the business traveler.

Numerically, if A is a vacation traveler and B is a business traveler, A might value arriving at a specific time at $10 where as B values it at $100. Since A likely bought his ticket further in advance than B and crowded out B's purchase, A is gaining $10 and B is losing $100.

This doesn't apply to airlines so much because there is price discrimination. I think it does apply to freeways, but I'm not convinced that current congestion-pricing schemes are a solution or just local governments taking advantage of an opportunity for more revenue.

Mike Davis writes:

I'm sure we both agree that the price of the good includes both the market price and the value of the time spent aquiring the good. I'm sure we both agree that increased demand for a scarce good often results in a higher market price. I'm pretty sure we both agree that when increased demand results in a higher market price we have not witnessed a negative externality. So, if increased demand causes more congestion and hence raises the time cost of aquiring a good, why call that an externality?

The second paragraph of your bleg implies that somehow public ownership is the villian--that if the airport were privatized, the congestion would be priced and efficiency increased. But we see unpriced congestion all over the place in the private sector. It's fun to speculate why congestion goes unpriced (next time you take kids to Six Flags, bring along a colleague) but are we confusing our students when label it as an externality.

Himanshu Sanguri writes:

The loss created by congestion is a collateral loss. I disagree with the numerical illustration provided. Let us take another illustration, where I struggle in heavy traffic between 09:00 to 10:00 hrs on my way to Office. My monthly petrol budget is although varies between 55 to 65 dollars per month. This is because, sometimes I have to burn extra fuel in traffic because of meetings to start at 10:00 hours. In times, when I do not have any booked morning appointments, I take traffic free time to travel and save fuel. But, this does not mean that presence of my car on road is creating a net loss to others. Everyone, is offsetting the upper and lower margins automatically.

John writes:

1) The original claim that private settings result in the decision maker considering everyone's costs is simply false and a very poor approach to explaining externalities. That is the source of your student's "confusion".

I think the attempt to overly simplify the story is also problematic in that it's fails to help shed much light on the problem and obscures aspects as well. For instances, what external effects count as externalities and which do not? Clearly if only A flies, then the airline is not getting the same revenues and needs to adjust it's pricing or losses money (or gets reduced profits). Is that an externality? What about when the airline increases prices and eliminates route? Now A cannot get to where A wanted to go because B isn't flying. Is that an externality B imposed on A?

Nick, when only one goes total value is only 15, not 30 (that's both A and B without congestion) so I don't think there's a trade to eliminate congestion.

I'm pretty sure we both agree that when increased demand results in a higher market price we have not witnessed a negative externality. So, if increased demand causes more congestion and hence raises the time cost of aquiring a good, why call that an externality?

Exactly. I think the problem David is having is with his approach to the problem of congestion; it shouldn't be as an illustration of 'an externality' at all. It's just not a fruitful way to think about congestion.

I had this same discussion with Greg Mankiw several years ago over rush hour traffic congestion. and didn't convince him to abandon a similar line of argument.

Clearly if only A flies, then the airline is not getting the same revenues and needs to adjust it's pricing or losses money (or gets reduced profits).

I agree. In order to price this 'externality' you'd also need to know by how much the presence of the other fliers contributes to lower costs for all fliers. Obviously, if only one person wants to fly the ticket price will be huge, as that one person will have to bear the entire costs of operating the airplane for the flight (as well as amortizing the cost of manufacturing it).

Ken B writes:

Is it "congestion" or A's presence which imposes a cost on B? This is not a trick question, it is possible that under certain conditions A's presence tips the system into a new state. For the first n other drivers say the delay grows linearly, and then suddenly gridlock, or some other strong effect. You see this kind of thing in computer systems as thrashing.

"Congestion" seems like a word to describe the system in one of these pathological states.

Ken B writes:

An example. If I pay a price to hire an unregulated taxi away from you at rush hour the price I must pay incorporates your desire for the taxi. The effect percolates through the market. If I do the same thing with a regulated price taxi then I have imposed a cost on you and no such consideration of your cost occurs. Now consider driving my car. Under periods of low traffic load my use of the road has little effect on your use. So the lack of a price to connect us doesnt much matter. But at rush hour it can be like hiring that regulated taxi; my use of the road directly impairs yours, possibly very greatly, without a commensurate price to me to percolate through the market. That sounds like an externality, when its rush hour.

Nick J writes:

I disagree that there would be difficulties if the pricing was private because the externalities of congestion are completely wrapped up in people's valuation of going to the airport, which is the most they would pay, and a private airport would care about that.

Using the original example, both value it at $15 and by going both impose $10 worth of costs on the other (whether that be congestion or anything else). In the original example, it was better that only one person go than that both go.

Now say you have a profit-maximizing airport which will charge entry fees.

If only one person goes the maximum they can charge is $15 and they make $15.

If two people go then the maximum they can charge is $5 (since each person values the airport net at $5 after accounting for the $10 cost of congestion) and they make $5+$5 = $10.

So the airport has an incentive to reduce congestion.

Philo writes:

A wants to catch a flight at 10 a.m. Because doing so would make that a congested time (B is also going to catch the 10 a.m. flight), A has to come to the airport at 8 a.m. to be on time for his flight. If he caught the 8 a.m. flight instead—a non-congested time—he could arrive on time at 7 a.m.: without congestion, one hour’s advance arrival is sufficient. So the congestion costs him one hour’s time at the airport, during which he can do nothing useful. Dollar value to A of this lost hour: $10. But catching the earlier flight would inconvenience him in the amount of $15. So he takes the later flight and endures the wait; from his point of view that’s better than the second-best alternative, in the amount of $5. Still better—by $10—would be catching the later flight without having to deal with congestion (i.e., with B’s presence).

B’s situation is the same as A’s, *mutatis mutandis*.

Suppose the transaction costs between A and B were negligible. A would offer B as much as $10 not to take the 10 a.m. flight (in which case B would take his second-best alternative: the 8 a.m. flight). Let’s say they settle on $7.50 as the amount of payment. A catches the 10 a.m. flight without congestion (arriving at the airport at 9 a.m.); taking into account the $7.50 payment to B, A is $2.50 better off than if he and B had not transacted. B catches the earlier flight, which is $5 worse than the-later-flight-with-congestion, but because he has been paid $7.50 he is also $2.50 better off than if he and A had not transacted. But now suppose that in reality the transaction costs between A and B would be more than $2.50 apiece; then they cannot achieve this superior result.

(Of course, the perfect symmetry between A and B in this scenario, that makes it indeterminate which one will pay and which will take the earlier flight, would not exist in the real world.)

So this is, indeed, a case in which transaction costs prevent the achievement of a superior outcome; that means it *is* an externality.
Of course, externalities are pervasive: what a wonderful world it would be if transaction costs were always zero!

PrometheeFeu writes:

I don't think there is an externality here. The airlines could just raise the ticket price in order to staff more counters. (perhaps even counters outside the airport) In other words, it is not the number of people which causes "congestion". It is the decision by the airline to offer a slightly inferior product at peak-hours in order to keep prices down. In other words, at peak-hour, the higher demand for labor and space changes the market equilibria to providing an inferior product. (Unless you're willing to pay the higher price by flying first class)

Nick J writes:

Also, Mike Davis, you said as a counter-example to the claim that a private market would eliminate congestion that at amusement parks and stuff there's usually a lot of congestion.

But, the claim isn't that a market in this setting eliminates externalities, but rather that it reduces the harm they cause by incorporating the costs into its pricing.

So I suspect that if Six Flags were lower-priced then congestion would be a lot worse than it currently is, so much worse that it in fact would outweigh the benefits from having more people in the park.

quadrupole writes:

I don't have time right now to think deeply on this now.
But my guy tells me to think about congestion marginally.

I will also comment that, when I was an undergrad
I did some work on the mathematics of traffic, and it turns out that traffic shocks lead to amazingly non-linear results. So I would not at all be surprised to find no linearity here as well.

Further, my gut would be to bring in expectations values.

Peter writes:

In my view, trying to define exactly what is or isn't an externality leads to confusion, and it's better to approach "externalities" as a label for a class of situations where what's good for each turns out not to be good for all. That is, , instead of asking whether there's "really" an externality in some situation, ask under what circumstances individual choice will lead to a suboptimal outcome.

Your example can be framed as a simple game: A and B each have to choose Fly Peak or Fly Off-Peak. If each chooses to Fly Peak, each gains $15 from the timing of the flight but loses $10 from flying congested. That's a net of $5 each. If A chooses Fly Peak and B chooses Fly Off-Peak, then A gets $15 (the value of peak time, with no deduction for congestion) and B gets $0 (the baseline value of flying off-peak, with no deduction for congestion). If B chooses Fly Peak and A chooses Fly Off-Peak, A gets $0 and B gets $15. So if both choose Fly Peak, the sum of benefits ($10) is less than it could be, and there is an inefficiency. One of A or B should pay the other an amount between $5 and $10 to fly at a different time, but transaction costs may prevent that.

Regarding the idea that externalities are all over place, I think the right answer is that indeed they are. There really is an externality every time I buy milk and (slightly) push up the price of milk for other consumers. However, the fact that this negative externality happens through the price system guarantees that it's offset but a positive externality of exactly the same size for milk sellers. Note that if the externality I impose on other milk buyers is longer lines to buy milk (because of a price ceiling, for example), the same reasonaing does not go through; the other buyers are still losing something, but the sellers are not receiving a commensurate gain.

As a further complication, the logic of precisely offsetting externalities when I buy milk also doesn't go through when the market is not perfectly competitive. It's possible for congestion externalities to remain a problem--in the standard economic efficiency sense--if a road is privatized but the owner has monopoly power. But that's just a manifestation of the general fact that forming general rules about what's efficient gets very complicated very quickly once we move away from a perfectly competitive world.

Bill writes:

The 5th paragraph of your post settles it in my mind, in that it emphasizes the DEFINITION of externality.

It's no different, in principle, than my willingness to live down wind from a hog farm. The hog farmer's operation imposes an uncompensated cost on me (an external cost), and my willingness to endure that cost doesn't mean the cost has been internalized by the farmer.

Handle writes:

1. What is "congestion"?

2. Congestion is a sudden, temporary, and sometimes periodic spike in demand for a service the supply of which is highly inelastic.

3. There are several additional features of the goods we call "congested". Most supply-inelasticity occurs is asymmetric and occurs asymptotically to the right at some scarcity threshold. Oil is an example - inelastic upward, elastic downward. Congested services are symmetrically inelastic. If demand is not matched to supply, there is almost always some surplus or shortage. Examples are extremely durable items with low salvage value and lengthy production lag times, like real estate, roads, network bandwidth, and aircraft seats. Utilities would qualify as well, except instead of congestion, they face more traditional shortages.

4. Another feature of congestion items is that they are "public goods" without price, or in some other market without demand-sensitive pricing that can efficiently allocate the scarce resource and deter new consumers via higher prices.

5. Instead of "price" in money, the final property of congestion is that one particular quality of the service declines quickly with increased demand. That quality is a function of "velocity" - the time is takes to provide the service desired. Whether it's "time from A to B" or "time to download a gigabyte".

6. Consumers' utilities of time are vastly different from person to person, and even for the same individual in different circumstances, especially considering his limited alternatives. There is a very wide distribution of consumer surplus.

7. It's perhaps only recently become possible to imagine people being able to make informed decisions on universal demand-sensitive pricing like some cities have done with parking. You could put EZPass sensors on every road and maybe you could make an app that tells give you a list of travel options from A to B and tells you the current prices and the current time estimates.

8. The question of whether a marginal decrease in the velocity of a congested service from the addition of one new consumer is an "externality" seems to depends on how different it is from the marginal increase in price for a similarly supply-inelastic service but one with dynamic pricing. We don't usually call an increase in price an "externality", though it certainly has an impact on everyone else in the market, and even drives out those with a lower consumer surplus. I think your student has a valid point.

9. This leads me to believe that the concept of "externality" is still fraught with ambiguity and too much emotional valence to be useful in most analysis.

Jay writes:

"what's a good way of showing the student that there really is a congestion externality?"

Go with extreme congestion. Two tractor trailers get in an accident on the highway blocking all lanes.

Everyone behind them on the highway has to sit in their vehicles and wait for the authorities to clear the road.

Milton Recht writes:

See GMU's John Nye's article in Summer 2008, issue of Regulation, "The Pigou Problem" at http://www.cato.org/sites/cato.org/files/serials/files/regulation/2008/6/v31n2-5.pdf .

It is a thoughtful discussion of the externality measurement problem.

Carl Chesko writes:

Short answer: Congestion is not an externality at airports. Instead, use highway traffic as an example of congestion as an externality.

Long answer:
I think there are two problems with the congestion example. First, it is a mixed public/private system. The private part of the system sells head-of-the-line privileges (1st class tickets), which partially internalize the cost of congestion for business and wealthy customers. But all customers can adjust their schedule and ticket price preferences. This brings me to my next point.

Second, ticket prices and airline schedules adjust. So if customers truly wish to avoid congestion, they can buy tickets at different times. And if many customers make that choice, then airlines will adjust prices and flight schedules accordingly. So there is no reason to believe that the "cost of congestion" isn't priced into airline tickets already.

Highway traffic (excluding toll roads) is a better example because there is no public / private confusion and there are no adjusting prices. So in this example, you can point out that the "market value" of highway access changes at different times of day. Ex./ It's not about congestion, it's about time of day. Truckers, UPS drivers, and business owners often have no choice about what time of day they drive. They would pay for access to the roads at specific times. You, on the other hand, can go visit grandma at any time. By charging $5 for rush hour access to the highway, we force each driver to think about the cost of congestion. You must chose between visiting grandma now for $5, or visiting at an off peak time for free. (Then you could lead into a discussion about public vs. private management. Profit maximization is one way to ensure that tolls are set efficiently. Ex./ $50 tolls would lead to empty freeways, $0.25 tolls would have no effect on congestion.)

Bill writes:

Frank Knight's 1924 QJE article, "Some Fallacies in the Interpretation of Social Cost " uses Pigou's road congestion example to evaluate some differences between private and public ownership of facilities subject to crowding externalities.


Dan writes:
I'm pretty sure we both agree that when increased demand results in a higher market price we have not witnessed a negative externality. So, if increased demand causes more congestion and hence raises the time cost of aquiring a good, why call that an externality?

There is an externality. This results from the producer's inability to perfectly price discriminate. In other cases there may be positive network externalities whereby your demand may reduce overall prices all which you don't capture. In most markets some set of customers subsidize others. Nothing wrong with calling it externalities as long as you actions do indeed affect others without compensation.

Bill writes:

There is a distinction between technological externalities and pecuniary externalities. The former are modeled as entering either a production function or utility function of a third party. Pecuniary externalities exist when a purchasing activity of Agent A affects market prices faced by other agents. Pecuniary externalities are the market's way of signaling changes in scarcity in the market.

Philo writes:

@ Milton Recht:

Thanks for the citation to Nye's article; it is very insightful. I wonder what is the response of, e.g., Mankiw.

Steven H. Noble writes:

Certainly your math is wrong. You do not count expected costs as realized costs.

I think I would respond to your student slightly differently. If a cost isn't an eternality if it is expected then what externalities are left? Where can't you make this argument?

If the answer is this doesn't apply to the externality of an upstream village dumping waste into the river then the issue is one of symmetry. Simply change your example so that the cost of congestion is 0 for only one of the passengers.

If this argument applies even to the upstream village (eg "the downstream village expected that there would eventually be waste in their water when they built a town there") then the whole concept of externalities is at question.

To this you must show that the externalities definition is useful. Show numerically how an externalities tax affects behaviour in the same way in all of these cases. And that is why they are all given the same name.

BC writes:

There is a congestion externality here, and here is how to see it. If only A or B, but not both, arrive at the preferred time, then one will get $15 of value, while the other will get $0. Total welfare will be $15. However, if both arrive at the preferred time, then each will get a net benefit of only $5, and total welfare will be only $10. Thus, there will be a loss of $5 in total welfare if we do not impose a price for arriving at the popular time. From A's perspective, B will be imposing a $10 externality on A while only receiving a net benefit of $5. (Hence, the $5 loss in total welfare.) Vice-versa from B's perspective. I don't know how one resolves who is imposing an externality on whom.

On the other hand, if we auction the right to arrive at the preferred time, limit that right to 1 person, and use the auction proceeds to provide a discount/rebate to the one that agrees to arrive at the less preferred time, then either A or B will win the auction with a bid of $7.50, and we will get the full $15 of value from the airport. (The one arriving at the preferred time will get a net benefit of $15-$7.50, while the one arriving at the less preferred time will get a net benefit of $0+$7.50.)

Thus, I think the issue of whether the airport is privately or publicly owned is a red herring. The issue is whether congestion pricing, charging more to arrive at the airport at the popular time, is allowed. It may be more difficult to charge people for arriving at the popular time if the airport is publicly owned due to objections based on "fairness", but public ownership is not the problem per se. If, however, one is unwilling to allow congestion pricing, then both A and B will arrive at the popular time, reducing total welfare by $5.

One can say that public ownership of *the right to arrive when one wants* is the cause of the externality. The auction effectively privatizes the *right to arrive at the popular time*, and that privitization eliminates the externality.

The point is that arriving at popular times does impose an external cost on others and the way to get people to consider those costs is through congestion pricing.

Mark P writes:

I think it can be stated much more clearly. Assume A has committed to going to the airport. If B decides to go, A bears an additional $10 cost; that is the externality, A bearing a cost due to B's action. Total costs & benefits are irrelevant.

Barry writes:


See Frank Knight's "Some Fallacies of Social Costs" in QJE, 1924 on congestion costs. The relevant point I see is that congestion from additional travelers raises the costs of all travelers, thereby creating the deviation between increasing marginal and average cost. Since travelers consider only per unit congestion costs and Knight's roads and your terminals do not use marginal cost pricing, there is too much congestion.

Capt. J Parker writes:

Dr. Henderson's problem is definitional. He says "My answer was, and is, that, yes, you take into account the amount of time by which you are slowed down, and everyone else takes into account the amount of time by which he or she is slowed down, but no one takes into account the amount of time by which he or she slows others." This statement contains a logical fallacy. Someone does in fact take into account the amount of time by which I slow down others. That someone is all the others I am slowing down. In fact, the people I am slowing down are the only ones capable of accounting for the congestion costs imposed on them by me. There is no way for me to account for the non-monetary congestion costs I impose on them. Only they can determine what those costs are and those non-monetary costs are unique to each individual. If all users of the airport account for the congestion costs imposed only on them then all congestion costs at the airport are accounted for and congestion at the airport is not external to the economic activity of taking a plane trip using that airport. This means Dr. Henderson's student is correct, congestion at the airport is not an externality and that Dr Henderson's example double counts congestion costs.

I think this logical fallacy in Dr. Henderson's "answer" arises from the desire to define an externality as a cost you impose on others for which you do not account. But, it isn't important that the economic actor imposing a cost account for the cost. What matters is whether the cost influences the activity from which it arises or does is get dumped on someone outside of the economic activity and therefore doesn't play a role in decision making or resource allocation within the economic activity. I would define an externality as a cost arising from an economic activity that does not influence any of the willing participants in the economic activity from which the cost arises. Since extra congestion at the airport caused by a new runway is very likely to influence the users of the airport, congestion at the airport is not an externality to the economic activity of using the airport. Congestion on the highway leading to the airport that imposes costs on people who have no desire to use the airport is an externality as far as airport use is concerned.

I don't think the issue of private vs. government ownership has a lot to do with determining what is an externality. Government may make rules that a private owner cannot and thereby change the very nature of an economic activity but, a private owner does not "take into account the gains and losses to various people." She can't. She doesn't know what the gains and losses are. She might be more willing and able than government to react to a decline in business or to complaints but that's all. There's no economic law that says government couldn't do the same. (But, there's plenty of real world reasons why government seldom acts this way) And, a private airport next to my house is as capable as a government airport of imposing the externality of noise costs on me.

Martin writes:


The Numerical Example:

The costs and benefits to A in the congested equilibrium are 15 - 10. The costs and benefits to B in equilibrium are 15 - 10. The total costs and benefits are therefore 30 - 20.

Congestion Externality:

This is a problem with multiple equilibria. Both players, A and B, can choose to wait at home and arrive at the uncongested time or to go the airport and arrive at the congested time.

We can write down the pay-offs as followed, where we assume that Y is the time/cost they have to wait at the airport behind each other with probability of one half, and where X is the time/cost they would have to wait at home:

1. (Go,Go) = (0.5*Y ; 0.5*Y)

2. (Go,Wait) = (0 ; X)

3. (Wait, Go) = (X ; 0)

4. (Wait,Wait) = (X+0.5*Y ; X+0.5*Y)

Now if I would try to solve this game rigorously, then I would have solve for the time each would have to wait at home, and for the probability that each would choose Go over Wait.

It is however enough to point out that both parties could gain by coordinating on #3 or #4.

Surely, it would be better if they could communicate and contract so that one stays comfortably at home (X would be a benefit), and arrives at an uncongested time, and another one would go to the airport earlier and would also arrive at an uncongested time.

Bill writes:

Another issue that should demand attention is whether a particular (level of) externality is worth addressing with corrective intervention. That is, would the potential benefits of removal/reduction of the externality exceed the costs, or in the Buchanan/Stubblebine framework, "Is the externality 'Pareto Relevant' ?"

James M. Buchanan and Wm. Craig Stubblebine, “Externality,” Economica 29 (November 1962): 371–84.

Nick J writes:

I was thinking this morning about how to convince people that it is an externality, since 'other people are taking it into account' is a intuitively convincing argument.

Maybe a good way is to ask them to pretend that when you go to the airport all of the congestion that other people experience as a result is magically transferred to you. If it's really true that it's enough that other people take the congestion you cause into account then no-one's behavior should change.

But of course if all the congestion you cause is transferred to you then while everyone else is still happy to go to the airport, your costs will rise, and it's not hard to imagine that that might induce you to not travel.

Philo writes:

So, David, what's the upshot? Were any of the comments helpful? Can you now convince your student . . . or will you withdraw your claim and endorse his view?

John writes:

To directly answer David's first question, it is double counting to say that total costs in the example he gives are $40. Total costs are just $20 ($10 suffered by A imposed by B presence, $10 suffered by B for A presence). However, the principle of the example is not invalid.

Social surplus in the congested airport is (15+15-10-10) = 10. Social surplus in the non-congested airport is (15+0) = 15. Yet for either A or B the private benefit for attending the congested airport is a net +5. So for me, if you work through the example correctly, it does still provide a textbook example of an externality.

The economic problem from the example is that it appears that no one owns the right to enter the airport. If this right is made private to either A, B or some third party (such as the airport authority), then if transaction costs are zero there is a surplus enhancing transaction possible.

To illustrate the externality concept, my preferred example is a smoker sitting beside a non smoker (I visualise it at a bar). When lighting up, the smoker considers the cost of the cigarettes, the impact on his own health, etc. However, he doesn't consider the costs borne by the non-smoker sitting next to him (discomfort, health, etc).

[This is a different "John" from the one who commented previously in this thread. I suggest that one or the other of you might want to take on a more identifying nick, such as a last initial or some other more identifying info when you post comments. Just a suggestion, lest readers confuse your comments.--Econlib Ed.]

Arthur writes:

You are double counting. And the problem is that just because people are considering the cost it doesn't mean it isn't an externality.

The problem is not that some costs are not accounted when there are externalities. The problem is that people who account the costs are not the same people who produce the costs.

Let me try a prisoner's dilemma example:

There are two ways to get to the airport, by bus and by car. People prefer to go by car, but that imposes externalities on others.

The payoffs for two agents A and B are:

Bus/Bus: {2,2}
Car/Bus: {3,-1}
Bus/Car: {-1,3}
Car/Car: {0,0}

When changing from Bus to Car an agent imposes a cost of 3 on the other agent. To internalize this externality we could tax this choice by 3, and give 3 to the other agent. The payoffs then become:

Bus/Bus: {2,2}
Car/Bus: {0,2}
Bus/Car: {2,0}
Car/Car: {0,0}

And people start riding the bus.

J Scheppers writes:

Mike Davis (with Patrick Sullivan's concurance) along with Capt. Parker have great responses.

Let's say for example you had a pigouvian fairy that took $10 from passenger A and gave it to passenger B for the costs imposed. Wouldn't the fairy need to do the same in the reverse direction. Not meaning A did not impose a cost on B, but to a reasonable degree the costs are internalized.

Let Say Sam the regulatory correctly calculates the average $10 value of time and imposes a $10 tax. The likely outcome is fewer people would make the trip, but even though Sam the regulatory accepted full payment for the externality, it is highly likely that the A and B still on many occasions cause each other congestion, because they don't know if the other will show. This leading to a reduction in welfare.

Congestion in the sense of your example is fully internalized. Variation in valuation of time would induce an externality by a user, and arbitrage opportunities should exist to reduce the congestion.

I thank you Dr. Henderson. I have asked the question your student has asked to many economists. You laid out the question beautifully and elicited many great response, that will cause a significant externality as continue to question many more economists.

An externality must have a frame of reference to know external to what.

Jason writes:

I say airports, or maybe just smart corporations, often practice congestion pricing.

In St. Louis, parking is always available in the garages next to the Terminal. I think it's $23/day. The off-site parking can be maybe $5-$7/day with a 5 min shuttle ride.

The real economic story is what the cost/benefit analysis shows in hindsight. For St. Louis, the expansion was likely a rent-seeking exercise for TWA (Who?) started 20+ years ago. When StL was a TWA hub, there was a reasonable bit of traffic. But the futurists who could predict the growth of congestion failed to see the purchase TWA by American, who had more efficient hubs elsewhere and basically left town while the expanded runway was being constructed. There were traveler tax increases, eminent domain hearings, native american burial ground relocation, noise abatement procedures; just a political power smorgasbord.

Save weather events, today there is little actual flight congestion at Lambert Airport. I think they work really hard to put some use to the new runway.

There are slowdowns in the TSA lines at times, probably because staffing is right-sized due to so little flight congestion.

But I can even bypass most of the congestion there by paying Southwest Airlines for the "Fly-By" line.

David O. Cushman writes:

The situation can be interpreted as a Cournot problem, but duopsony rather than duopoly. (1) Assume two buyers, A and B, who recognized their mutual dependence. (2) Keep it simple: assume no marginal cost to "buy" (use) the airport (or whatever) service. (3) Assume linear demands and, to continue keeping it (relatively) simple, some concrete numbers: In the absence of the other person, assume each would use the airport 10 times per "month" (Q demanded at zero marginal cost), while a marginal cost (or price) of $10 would generate 0 uses by a given person. Assume that for each time per month B uses the airport, A reduces trips by 1/2 a trip in response to congestion, and B responds the same to A. (That is, each person's marginal congestion cost is $0.50 for each trip by the other.)

Now, if only A uses the airport, A's consumer surplus is $50 and B's is 0. Meanwhile, in the Nash equilibrium A and B each use the airport 6.67 times and the marginal congestion cost is $3.33. Each earns a consumer surplus of $22.22 for a total of $44.44, less than $50.

If each can be induced to use the airport only 5 times, marginal congestion cost for each is $2.50 and each receives a surplus of $25.00; total surplus is back to $50. If a congestion tax is used to accomplish this (a tax of $2.50 per trip works), then the govt. gets some of the surplus.

Note that this story would be a lot easier to explain if graphs could be used to illustrate. And it might not be considered that simple by some if you've also got to show how to solve the two reaction functions to get the Cournot equilibrium.

Bill writes:

The existence of external cost does not necessarily lead to a reduction in combined consumer surplus compared to what would occur if only the first user were present. That is, the gain in consumer surplus enjoyed by the second user may be greater than the reduction in consumer surplus suffered by the first user (due to the externality.)

David O. Cushman writes:

I'm not sure whether Bill just above was questioning my conclusion or making a general conjecture, but I think I should clarify my model a bit. My computations of total consumer surplus do take account of the losses by the first person, say, A, being offset to some extent or other by the gains of the second person, say, B, and follow from my assumption of constant marginal cost of congestion. Let me elaborate on this assumption.

Suppose there are 10 days in a "month." Focus on person A. Suppose A does not know for sure in advance whether B will be there. Suppose that if A goes to the airport and encounters the congestion that occurs when B is also there, A suffers a cost of $5 (not $0.50 as I somehow mistakenly wrote above). Suppose A expects B to go 10 times, or every day on average, to the airport. Then A will likely see B on any trip A makes, that is, the expected number of encounters with B is 1 on any given trip, and thus A faces an expected additional or marginal cost of $5 for each additional trip. This MC crosses A's demand curve, which is also A's marginal benefit curve, at a value of 5 trips for A. So that is one point on A's reaction function.

Suppose A expects B to go only 5 times. Then on any given trip there is an expected cost of 5/10 times $5, or $2.50. With this expectation the MC of congestion is thus a constant $2.50, as I wrote above, and A would like to go to the airport 7.5 times, which is where MC now crosses the demand or marginal benefit curve.

Finally, suppose A expects B to go 6.67 times. Person A expects to see B 2/3 of the time and the expected marginal cost to A of any trip is thus 2/3 times $5 or $3.33. The MC of $3.33 crosses A's demand/marginal benefit curve at Q=6.67. This is, as I indicated above, the Nash equilibrium, because if both A and B expect the other to go 6.67 times, each also chooses to go 6.67 times and expectations are confirmed.

So, with the various MC curves and the demand curves I have assumed, one can tote up the areas of the various relevant triangles and rectangles, and one will see, I think, that my consumer surplus computations are correct.

Of course the discussion depends on the relatively unsophisticated structure of the Cournot model, but I think it is one way to approach Prof. Henderson's query and shows one way in which congestion can reduce total consumer surplus. Finally, it is worth saying that if the cost to A or B of encountering the other is something less than $5, then the congestion costs may not be enough to reduce total consumer surplus compared to the no-B-present case, and commenter Bill's conjecture is realized.

Bill writes:

My point was, indeed, a "general conjecture," viz, in the presence of congestion, the arrival of the second user may or may not represent a potential Pareto improvement as reflected in the change in magnitude of total consumer surplus.

Daublin writes:

The example can be clarified to make it definitely an externality. Instead of viewing the airport is the product, say that the airport is the place. Have person A fly on Delta, and person B eating lunch at the airport's food court.

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