Saturday, March 04, 2017

An Interesting Mistake

I recently gave and graded a midterm exam on the application of economics to law. On one problem a number of students made the same interesting mistake, interesting for two reasons. It illustrates one of the ways in which it is easy to misunderstand economic ideas. And it points to a conceptual mistake this is  common, important and dangerous.

The problem involved the effect of alternative legal rules on the interaction between an airline and three thousand homeowners near the airport. One way of dealing with noise was for the airline to reduce it at a cost of a million dollars. Another was for the homeowners to achieve the same effect by soundproofing their houses at a cost of four hundred dollars each, for a total cost of 1.2 million dollars.

Suppose the legal rule is that the airline has the right to make noise and no  liability for the cost to the homeowners. The obvious outcome is that the homeowners soundproof even though it would cost less for the airline to reduce the noise. That suggests the possibility of bargaining, with the homeowners offering to pay something between a million and 1.2 million in exchange for the airline reducing the noise.

With three thousand homeowners that is unlikely to happen. If the bargain is struck, each homeowner gets the benefit whether or not he contributed to the payment. Thus each will be inclined to try to free ride on the expenditures of the others. They face what economists describe as the public good problem—how to produce something when those who pay for it cannot control who gets it.

Suppose, however, that the three thousand houses belong not to three thousand home owners but to one real estate company that rents them out. Now the public good problem vanishes. The company gets the benefit from sound reduction and will be willing to pay for it.

The mistake was not in predicting what happens but in explaining why. A number of students said something to the effect that combining the houses under one owner "levels the playing field" between home owners and airline. The implication of that way of putting it is that the problem is simply a conflict between two sides. Combining the homeowners into one firm increases their bargaining power and so results in their getting more of what they want, the airline less.

The result of the change is that the homeowners, now combined into a single firm, get more of what they want. But so does the airline. It is being paid at least a million dollars, probably more, to do something that costs it a million dollars. Bargaining over how much it gets is a conflict between the two sides. But the agreement to reduce noise at the expense of the homeowners, which is what combining them made possible, is a win for both. 

The reason the mistake is important to me as a teacher is that it illustrates a common problem in teaching economics and probably other things as well. The student has a pattern of ideas in his head, in this case a simple model of conflict where what helps one side hurts the other. He fits what he hears into that pattern, thinks he understands it, and so never gets the actual idea I am explaining.

But this particular example of that problem is important for a wider reason. A lot of people in a lot of contexts take it for granted that games are zero sum, that what benefits one side must harm the other. That is a very dangerous mistake. Consider some examples.


The term "competitiveness" is routinely used in a way that implies that what matters is how rich or productive the U.S. is relative to other countries, that if China gets richer that makes us worse off. It might be true if we were at war with them, but we are not. In the context of trade, China being richer means that they can buy more stuff from us and sell more stuff to us in our mutual benefit. 

A closely related error is the survival of mercantilist economic theory two hundred years after Ricardo showed why it was wrong, the idea that trade is a war in which each side is trying to sell more than it buys, to get a "favorable" rather than an "unfavorable" balance of payments.


Consider discussions over what has happened to the incomes of rich and poor over the past few decades. As best I can tell—it is not a subject I have looked at very carefully—the answer is that across the income distribution people have gotten at least a little richer but that incomes have increased much more for those at the high end of the distribution. This is often represented as the poor or the middle class losing out, with the implication that the wealth of the rich came at their expense, that there is a single pool from which the rich are getting more and the poor therefor less.

Put that way the claim is obviously false, since average incomes have increased enormously over the past few centuries, both in the U.S. and globally. In any particular situation it might be true, since one way of getting rich is to steal stuff from people, whether legally or illegally. But it cannot be true in general. 


It is tempting to see all political disagreements as conflicts of interest, to assume that it is simply a question of whose side you are on. If you  believe that, there is no point in listening to the other side's arguments. They may say that what they propose is good for everyone, but that is just a trick to blind people to their true motives. It is a very common attitude and a very dangerous one. Carried to its limit, it implies that the other side is your enemy, in which case there is nothing really wrong with lying about them, wiretapping them,  stealing votes. 

All is fair in love and war, and this is war.


Speaking of which, consider the effect on a marriage of assuming that all disagreements are about which partner gets his or her way, which loses out.

I have discussed some of this in at least two previous posts, one on status, one on my disagreements with two other anarchists, one left and one right.


Anonymous said...

"consider the effect on a marriage of assuming that all disagreements are about which partner gets his or her way, which loses out."

In my case, it ended in divorce. My ex-wife could never view disagreements as anything other than zero-sum games. It's hard to play a positive-sum game when the other person is stuck in the zero-sum mindset.

Anonymous said...

The pervasiveness of these mistakes over time is interesting. I wonder if the misunderstandings of "competition" and pre-Ricardo mercantilism are so widespread because (a) we somehow struggle as a species to cognitively understand it, or (b) these are mistakes which continue to be kept alive by demagogues with political incentives for re-enforcing those same ideas. I suspect it must be a decent measure of both.

ErolB1 said...

A belief in "economic coercion" as a real thing in the same moral category as physical coercion and fraud seems to be very common.

The old joke with the punchline "Now we're just negotiating over price" gets its punch from denying the concept, from denying the moral/economic intuition of most people that an offer of one million dollars is qualitatively different from the offer of one dollar. That the guy making an offer of one million dollars to sleep with him is making "an offer you can't refuse." That offering the woman in the joke one million dollars is more like pulling a knife on her than it is like offering her one dollar.

Xerographica said...

From my perspective, the best way to teach the students is to simply replace voting with spending (coasianism). Ie... should class be inside or outside? Each student writes down three things...

1. name
2. preference
3. WTP

Once they all turn in their valuations, you write them on the board. Whichever side was willing to pay the most gets the right of away. They turn in their money. The side that doesn't get the right of way doesn't have to pay anything. Instead, they proportionally get all the money that was paid. It's a win-win situation.

It's a rather involved process for determining whether to have class inside or outside... but the point is really for the students to appreciate that spending uses a lot more brainpower than voting. As a result, the outcome is far more rational/intelligent.

Unknown said...

'Put that way the claim is obviously false, since average incomes have increased enormously over the past few centuries'

Do you mean median? The average increasing is consistent with the top percent getting gains and everyone else staying the same.

Anonymous said...

The situation where this logic is commonly applied that comes to mind for me is employment. That an employer is always in a position of power over its employees, because there is one big firm employing many comparatively small individuals, is often taken as so obvious as not to be worth stating, much less defending.

David Friedman said...


The problem with your suggestion is that getting the class where you want it (inside or outside) is a public good. If I offer two dollars instead of one, that has a small chance of flipping the outcome, a large chance of costing me money. It it flips the outcome it flips it for everyone, including the others who voted my way, but I don't get their benefit.

You could make it work with preference revealing voting, but that, although an elegant solution, gets a little complicated for your purposes. The amount you actually pay in that system is the amount of your offer that was needed to switch the outcome your way, given what everyone else offered. If you are not familiar with the idea, you may want to work out the logic for yourself. As long as everyone makes his offer independently, it is in the interest of each to tell the truth about the value of the outcome to him.

Xerographica said...

David Friedman, let's say that you prefer having class inside. Of course you want to pay the least amount of money possible to get your way. Except, what if your side loses? Then your compensation is going to be a lot less than your harm of not getting your way.

Let's say that enough people want to have prohibition again. I'd for sure oppose it... and of course I'd prefer to pay the least amount of money possible to get my way. Except, what if my side loses? Then my compensation would be a lot less than the harm of not getting my way.

Hmmmm... how much benefit do I derive from a year's worth of drinking? Let's say $250. If this is my WTP and my side wins, then this is how much I'd have to pay. I'd be paying $250 dollars for an equivalent benefit. Maybe not the best deal. But what if my side loses? Then I wouldn't have to pay anything and my compensation would be greater than $250 dollars.

Just to be clear, all valuations are determined independently and privately. They are only publicly revealed after everybody has submitted their valuations. Also, the compensation is proportional. If the compensation was equally divided among the "losers" then there would be a free-rider problem. People would have suboptimal incentives to report their true valuations (preference intensity).

My strategy would simply be for my WTP to equal my true valuation. I'd rather not waste my time trying to predict the outcome...

"It is impossible for anyone, even if he be a statesman of genius, to weigh the whole community's utility and sacrifice against each other." - Knut Wicksell, A New Principle of Just Taxation

Here's the most relevant passage from Smith's book...

"The people feeling, during the continuance of the war, the complete burden of it, would soon grow weary of it, and government, in order to humour them, would not be under the necessity of carrying it on longer than it was necessary to do so. The foresight of the heavy and unavoidable burdens of war would hinder the people from wantonly calling for it when there was no real or solid interest to fight for." - Adam Smith, Wealth of Nations

I think this is the most relevant passage from your book...

"But market demands are in dollars, not votes. The legality of heroin will be determined, not by how many are for or against but by how high a cost each side is willing to bear in order to get its way. People who want to control other people's lives are rarely eager to pay for the privilege; they usually expect to be paid for the 'services' they provide for their victims. And those on the receiving end— whether of laws against drugs, laws against pornography, or laws against sex—get a lot more pain out of the oppression than their oppressors get pleasure. They are willing to pay a much higher price to be left alone than anyone is willing to pay to push them around."

I didn't pay for either book. I didn't figure out and report my true valuation of either book. This is a problem because the optimal supply of things depends on people figuring out and reporting their true valuations. This is true for everything from economics books to group decisions.

From my perspective, what I just shared is a coherent economic story. As far as I can tell it's the only coherent economic story. Every other economic story is contradictory. Unfortunately, I suck at telling stories. You're a lot better at telling stories.

Philo said...

A more realistic problem would assign different costs of soundproofing and different degrees of eagerness for reduced noise to the various homeowners. A still more realistic problem would note that no one in the scenario knows what all of these costs and degrees of desire are. Even if all the houses are owned by a single landlord: while he can be presumed to know cost of soundproofing, he would not be sure about the intensity of desire for quiet of his tenants and of those who are potentially his tenants in the near future.

Even in your simpler version, if someone did know all the information you give the cost of bringing about a successful negotiation, even one involving 3,000 homeowners, might well be less than the $200,000 gap between the two methods of noise abatement: the airline would get somewhat more than $1 million (> $334 from each homeowner) and undertake the necessary measures itself, even though there was not just a single landlord. Lack of information is a major part of the problem.

But yes, zero-sum thinking and mercantilism are pervasive.

Unknown said...

The situation between the homeowners and the airline you describe however doesn't feel like any kind of healthy marriage and sounds more like a potential negative sum game than a true positive sum game.

View it with a cynical eye: The airline wants to maximize profits, if the homeowners in their negotiation try to get the airline to accept, say, 1,100,000 then there's an additional option open to the airline: be even more noisy to pressure the homeowners. They have the option to turn a debatably positive sum game into an entirely negative sum game. Why settle for 1,100,000 when you can push for 1,190,000 + the threat of months or years of negative utility for the homeowners before they can all get their homes sound proofed?

One side has no power to put any pressure on the other in any way while the other does have power to make the lives of the first group worse. Why shouldn't they absorb almost all the gains to be had in negotiations?

Plus if it's real humans doing the negotiating there's going to be a certain "being a dick" and "being pissed off at someone being a dick" set of factors which diverges from perfect rationality.

Joshua Kronengold said...

In the real world, what would likely happen is a class action lawsuit from homeowners demanding that the airlines deal with the noise or pay out enough to each homeowner for them to do the noise abatement themselves. But that doesn't make as clean an educational case, since it would be the airline deciding whether it's worth putting 1.2 mil in escrow (with the assurance that much of it isn't going to get paid out) or spending 1 mil out of pocket to fix their noise problem.

I think the central point is solid -- although it skips over the point that sometimes a power imbalance -can- result in problems -- people being fantastically rich isn't a problem per se -- but when it results in them having more voting power than others, this can result in them controlling government against the interests of a majority.

Walter Clark said...

A person steeped into the usefulness of the State will right away observe that solution that gets an A from the professor, must have rules and courts which are associated with government. But those are just used only in the finding of a solution not in being the solution. It is assumed that government does not have the ability to enforce its ruling (like trying to force polite treatment of black restaurant customers or preventing the consuming of dope) and must appeal to a solution where both want it to happen.
Since this is straight out of Arnold Coase we have to recall that he said that there are some occurrences where the government solution is the only one available or cheaper or something... I forget.

Maxmaz said...

The Coasian perspective in real estate has been best analyzed by Spencer McCallum since the ´60s starting with his "The art of community". In doing so, Spencer also gave us a framework of how could a quasi-anarchist world work in practice, for example overcoming the tough problems of production of law, military defense, and even eliminating the apparent (for many) problems of a policentric security system. It always puzzled me that you did not discuss Spencer's ideas in the otherwise excellent The machinery of freedom (my preferred gift and tool when I find somebody interested in anarchism). Regards.