Thoughts on Teaching the Coase Theorem

Every year I attempt to teach students the Coase theorem, and devise some new question to test their understanding of it. Every year I fail to communicate Coase's ideas. 

Here is this year's Coase question (adapted from one by Jesse Bull):

A rancher and a farmer are located next to each other. Here are the facts of their situation:

• There is no fence between the ranch and the farm
• The cattle enter the farmer’s fields and destroy $300 worth of corn each year.
• The rancher’s business is worth $1000 annually (not taking into account any crop damage).
• The farmer’s business is worth $800 before the cattle trample the corn
• It would cost the rancher $100 to build a fence that would keep the cattle on his property.
• It would cost the farmer $400 to build a fence that would keep the cattle out of her property.

Assume that it costs the rancher and the farmer nothing to negotiate with each other.

1. Suppose the rancher has to compensate the farmer for any crop damage. Will a fence get built? If so, who will build it and who will pay for it? How much better off do you think the farmer will be as the result of the fence? The rancher? Explain your answer.
2. Suppose the farmer has to absorb (pay for) the crop damage herself. Will a fence get built? If so, who will build it and who will pay for it? How much better off do you think the farmer will as the result of the fence? The rancher? Explain your answer.

In The Problem of Social Cost, Ronald Coase argues that  the outcome is "the same whether or not the cattle-raiser is held responsible for the crop damage brought about by his cattle". As long as it is clear who is liable for the crop damage, and there are no costs of negotiating a settlement, "the ultimate result (which maximises the value of production) is independent of the legal position".

In other words, it doesn't matter who is responsible for building the fence, as long as the cost of the fence is less than the cost of the crop damage, the fence will be built - and in the least costly fashion.

Answering part 1 of the above question, the part where the rancher is responsible for damage, is straightforward. The rancher builds the fence, because the cost of the fence ($100) is less than the cost of compensating the farmer for crop damage. Together, the rancher and the farmer are $200 better off ($300 crop damage less $100 fence). The Coase theorem doesn't predict how the gains will be shared - they could be shared equally between farmer and rancher, or the rancher could enjoy the full benefits of not having to pay for crop damage. (When marking this question, I accepted any answer to the "How much better off" question as long as the total added to $200).

The solution in the second situation, when the farmer is responsible for damage, is less obvious. It would cost the farmer $400 to build a fence, and the crop damage is only $300. Perhaps this means the fence doesn't get built? The Coase theorem says that it doesn't matter who is responsible for paying for the damage, the outcome will be the same, and that suggests the fence does get built. But who will build it?

The trick to answering Coase theorem-type question is to think about all of the possibilities. Sure, the farmer could build a fence for $400, but that wouldn't make economic sense. The smart solution is for the farmer to pay the rancher some amount between $100 and $300, say $200, and ask the rancher to build a fence. Since it only costs the rancher $100 to fence in his cattle, surely the rancher would agree to such a proposition. Both would be better off, the fence would be built, and the crops would be saved.

It's not that my students had forgotten, or hadn't studied, the Coase theorem. A number wrote out the Coase theorem correctly - before going on to say the fence would get built if the rancher was liable for damage, but wouldn't if the farmer had to absorb the cost. It's not just this group of students either. The same thing happens every year.

One possibility is that the question itself was not as clear as I imagined it to be. Some seemingly irrelevant detail might have led the students astray. The fact that numbers were included in the question might have led people to think that the numbers held the key to the solution. As always, students were confused by things I hadn't clarified, for example, the fact that the fence is a one time cost, and the crop damage is on-going. A number answered something along the lines of "the farmer would build the fence because it's worth spending $400 once to save $300 on an on-going basis." (This is incorrect: it's still cheaper for the farme to pay the rancher to build the fence.)

The Coase theorem, at least the way that I teach it, involves concepts and ideas that are not given much attention elsewhere in the undergraduate curriculum. It's argued in words, not in diagrams. It talks explicitly about the process and costs of negotiating transactions through the market, which are more often assumed away. I've been trying to teach the Coase theorem without spending much time discussing the processs of negotiation or the nature of transaction costs, and that might be the source of the problem. (Perhaps, also, I need better readings than the Rosen Public Finance textbook).

Maybe if I formalized Coase, and modelled the rancher/farmer problem as a game theoretic problem, it would be clearer:

The Coase theorem can be restated as follows: in a two player game, with full information, unlimited communication and costless enforcement of contracts, players will reach the outcome with the highest net benefits. In this case, the net benefits are highest when the rancher builds the fence and the farmer doesn't. Any agreement will leave each player at least as well off as she would have been in the absence of an agreement, but the division of benefits is not specified by the theorem.

I teach the Coase theorem in the context of a discussion of externalities. Here is a question that applies the Coase theorem to an externalities situation:

Ruth’s demand for piercings (pierced ears, etc) is given by:

P=110-10Q

where Q is the number of piercings. The marginal cost of piercings is $40 per piercing.

1. Calculate the number of piercings Ruth will choose. Illustrate with a picture.
2. Ruth’s father, Phil, intensely dislikes piercings. Ruth’s piercings cause Phil psychological harm of $50 per piercing. Calculate the socially optimal quantity of piercings. Add this information to your diagram from part (a).
3. State and explain the Coase theorem.
4. Individuals under 16 cannot get piercings without the permission of their parents. Individuals 16 and over do not require parental permission. Use the Coase theorem to predict what will happen to (i) the number of piercings Ruth has and (ii) the distribution of resources between Ruth and Phil when Ruth turns 16.

 The students answered, with no difficulty, the first three parts of the question: 

(Notice that the weights of the various parts of the question are not specified, leaving ample room for manipulating the grade distribution ex post by giving more or less weight to the part of the question that all of the students failed to answer correctly).

The answer to part 4 of this question is that, according to Coase, Ruth will get the optimal number of piercings, regardless of whether or not she has to get Phil's permission (Becker's Rotten Kid Theorem is basically just an application of the Coase Theorem). If Phil has final say over the number of piercings, he will allow Ruth two piercings, either because he cares about her well-being enough to grant her permission, or because she will persuade him by offering him compensation for the psychological harm the piercings cause "I will study/tidy my room/eat broccoli if you allow me to get my ears pierced." If Ruth has control over her body, Phil has to bribe her not to get piercings: "I will pay for your university tuition as long as you don't get your tongue/eyebrow/belly-button/nose pierced." Who has final say on piercings matters for the distribution of resources between Ruth and Phil, but not for the number of piercings.

Perhaps the reason that my students answered the question incorrectly is that I hadn't shown them how to use formal methods - mathematics, diagrams - to analyze Coase theorem type questions. One way of formalizing the Ruth and Phil problem is shown in the two diagrams below. When Ruth has to get Phil's permission for any piercings, she has to compensate him for damage caused, as shown on the diagram on the left. 

 The amount Ruth is willing to pay Phil for a piercing is 70-10Q, where Q is the number of piercings she has. This is the marginal benefit she gets from a piercing, which we can infer from her demand function, 110-10Q, less the private costs she pays for getting a piercing done, $40. The compensation Phil demands is equal to the psychological harm the piercings cause him, or $50. The number of piercings Ruth gets is the point where these two meet, or 2 piercings. 

When Ruth has the right to get piercings, however, Phil has to compensate her. Her preferred number of piercings is 7, the point where her private costs are equal to her private benefits. Let X equal the number of piercings Ruth doesn't get, defined as X=7-Q, or the number she would like to get less the number she actually gets. Every piercing she refrains from getting has a cost to her of 10X, calculated by substituting X=7-Q into the the net benefits of piercing, 70-10Q, calculated above. However, by paying Ruth $50 not to get a piercing, Phil can persaude her not to get 5 piercings, as shown on the diagram on the right. As before, the number of piercings she gets is 7-5, or 2.

Does formalizing the question like that make things easier? I'm not convinced it does.

When I go over the Ruth and Philip question with the students in class, someone invariably puts up their hand and says "But what if Ruth can't afford to pay Phil $50?" This is a perfectly legitimate point. The Coase theorem assumes away income effects. Many 15-year-olds simply would not have the wherewithal to compensate a parent for the psychological harm caused by a tongue piercing. At 16, they no longer have to.

Students live in a world where income effects matter and negotiations are costly. The Ruth and Phil question asks "Use the Coase theorem to predict...", so the right answer is the outcome predicted by the Coase theorem. However in an exam situation, people often don't take time to read the question carefully. They answer with their intuition, rather than reasoning through the question the way a lawyer would.

Teaching the Coase Theorem is not the real issue. The real challenge is getting people to step back, analyze the underlying structure of costs and benefits, and systematically work through all possible outcomes. That I fail to do.

p.s. Eric Crampton has a number of interesting Coase-related posts on Offsetting Behaviour. The diagrams for the Ruth and Phil question were created by typing, for example, "plot 50+(10^-10)Q, 10Q over Q = 0 to 7" in wolframalpha.com, copying and pasting the image into powerpoint, and then adding labels. The 10^-10 is needed because it can be hard to persuade wolframalpha to plot horizontal lines.

Comments

[Nick Rowe]

Like some of your students, I got distracted by thinking that the fence was a one-time cost, and so started looking for a rate of interest and depreciation rate. Then I realised that the rancher building the fence was cheaper than anything (even more so if it's a one-time cost), so I knew that was the answer. My next thought was: "What was the question again?". Then I got a bit muddled because there are so many other possibilities it was hard to figure out what each person could do unilaterally under each of the two property right regimes. It would take me some thinking to work out the two Nash bargaining "threat points" under each of the two regimes.

A couple of other distractors are: should the farmer/rancher shut down altogether?

[Jeff Graver]

I got distracted by the one-time vs ongoing thing, too, but after reading your explanation, I think you would get better results from your students if you listed cost-free negotiation as one of your bullet-pointed facts rather than as an assumption that appears after the fact-set is delivered. I found that I wanted to jump from the facts to the questions too quickly and skipped over the import of the assumption - which is the key to solving the problem since it draws attention to the possibility of a negotiated solution.

[Nick Rowe]

OK:

1. Rancher builds fence, is $200 better off. Farmer is indifferent.

2. Rancher builds fence, and is paid somewhere between $100 and $300 for building it. Assume it's $200. Both are $100 better off.

I found it a bit hard!

[Frances Woolley]

Nick, true enough. I should have expressed them all as annual costs.

On the shut down distractor - Jesse had the info about the value of each business in his version of the question, but he didn't have the differential fence costs. I wasn't sure whether to keep it in or not. Do you think the question is better without the information about what each business is worth?

People had around 17 minutes to answer the rancher/farmer question, and most people left the exam room early, so I'm sympathetic to "the question was long and wordy", but not *that* sympathetic.

[Mike Sproul]

Here's what I do: The smoke from a steel mill does $5/ton of damage to the laundry next door. The laundry has sued the steel mill. The judge can either make the steel mill liable for the damage or else tell the laundry that the steel mill was there for 100 years before the laundry and so the laundry has no right to complain (This makes the laundry liable.).

If the steel mill is liable, the steel mill faces the following choices:
1) Pay for the smoke (Cost=$5/ton)
2) build a scrubber ($8/ton)
3) Move out of the area ($20/ton)
4) Bribe laundry to move ($10/ton)

If the laundry is held liable, then the laundry faces the following choices:
1) Suffer thru the smoke ($5)
2) Bribe steel mill to build a scrubber ($8)
3) Pay steel mill to move ($20)
4) Laundry moves ($10)

Either way the judge decides, the cheapest solution is for the smoke to persist. The basic idea of the Coase theorem gets through. If the cost of the smoke damage is raised to $12/ton, then the scrubber gets built, regardless of how the judge decides. Coase is proven right again.

Next, suppose that the smoke costs $12, but we find that if the steel mill builds the scrubber it will cost $8, while if the laundry has to bribe the steel mill to build the scrubber, the cost (with lawyer fees, etc.) will be $11. In this case, if the steel mill is held liable, the scrubber is installed at a cost of $8, while if the laundry is held liable, the laundry will move at a cost of $10. The coase theorem is proven "wrong", but what really happens is that the students are introduced to the idea that liability should fall on the least-cost avoider. They learn that a good judge will get the problem solved for $8, while a bad one will get it solved for $10.

Also, there is a diagrammatic way to illustrate the coase theorem. Draw a community production possibilities curve CPPC for two people A and B, and two goods, x and y. Inscribe an Edgeworth box in that diagram so as to show general equilibrium (i.e., the slope of A's PPC=slope of B's PPC, slope of A's indifference curve=slope of B's indifference curve, and slope of each indifference curve=slope of each PPC.) Then transfer some of good x from A to B. The CPPC will not move, thus making Coase's point that reassignment of property rights leaves the community in a state of equilibrium. Now make one more change: All along the contract curve, let MRS be the same (i.e., there are no income effects). In this case, the wealth transfer not only leaves the CPPC unchanged, but also leaves the total amount of goods x and y unchanged.

[Frances Woolley]

Mike - Interesting, it looks like you do that in your ECON 1000 course http://www.csun.edu/~hceco008/tablecontents.htm.

Nick, do our students do Edgeworth boxes in principles?

[Sandwichman]

"Students live in a world where income effects matter and negotiations are costly..."

Yeh, and so does Coase. That's why teaching the "Coase theorem" may be more like indoctrinating students in an unreal and ideological "underlying structure of costs and benefits" than giving them critical thinking skills. Coase's point was that transactions have costs and that Pigouvian taxation implicitly assumed they didn't. But, if one explicitly assumes they don't have costs, then the Pigouvisan tradition offers no advantage over a free negotiation. Steven Medema explains this a lot better than I am explaining it here. Anyway the Coase theorem is NOT Coase's theorem -- it's not the real point that Coase was making in his article.

The real point is that in a world where income effects matter and negotiations are costly, Pigouvian taxation does not solve the problem of social cost any more than negotiation would. The so-called Coase theorem inverts that critique of Pigou into a imaginary solution to the still unsolved problem.

[Nick Rowe]

Compare it to the much simpler question, where the only information is: the fence costs $100 (it's built by a third party fence-contractor, and the only question is: who pays for it); the cattle do $300 damage.

It's not just the shut down and "the fence costs $400 if the farmer builds it" distractors. The big distractor is that the rancher has monopoly power in selling fences, and the farmer has monopsony power in buying fences, so you get bilateral monopoly/monopsony indeterminacy in the second property right regime, but not in the first property right regime.

Actually, this is really making me think about the Coase theorem. How come the distribution of surplus is indeterminate in one regime and determinate in the other???

[Sandwichman]

Thanks for this, Frances. By coincidence, I happen to be lecturing this Thursday on "The problem with 'The Problem of Social Cost'" and it's handy to have a concrete example of how the "Coase Theorem" is taught.

[david]

Teaching the Coase Theorem is not the real issue. The real challenge is getting people to step back, analyze the underlying structure of costs and benefits, and systematically work through all possible outcomes.

Politics makes it hard to think (it literally makes it hard to think: there are some neurological studies to that effect). Students who feel that they are being taught to write something that they feel obliged to object to on partisan grounds will find it unusually difficult to apply it. And talking about tradable pollution rights will trigger that. It may be better to change the example to something completely absent from prevailing policy debates, the more obviously contrived the better. Say, two people arguing over what colour to paint the walls. If the right is tradable, the wall is always coloured the same.

[Min]

One thing that strikes me about your rancher-farmer example is history. Range wars were fought over farmers' fences. Why would we not get this kind of negotiation?

Farmer: Please build a fence to keep your cattle off of my property. I'll pay you $200 to build the fence.

Rancher: Go F- Yourself.

[Frances Woolley]

david:

I challenge you to take that idea of people arguing over what colour to paint the walls and create from it a clear, unambiguous, yet non-trivial question.

Sandwichman - glad to be of service.

Nick: "How come the distribution of surplus is indeterminate in one regime and determinate in the other???" It isn't. Actually the way Jesse had the question set up, he specified that the gains would be shared equally, but any outcome is possible.

In general, the division of surplus is extremely sensitive to the way that the negotiations are set up. For example, who makes the first offer? Is one party able to make the other a take-it-or-leave it offer? Does the other have the right to reply with a counter-offer? How much could each party expect to get if he/she withdrew from the negotiations, that is, what are the outside options? What is each party's discount rate?

The reason you're getting different results in the two scenarios is that in your mind you've imaged different negotiation structures.

[Frank Restly]

Min,

Better:

Farmer: Please build a fence to keep your cattle off of my property.
Rancher: That will cost you $400

The question states that it will cost the farmer $400 to build to the fence. Presumably that cost is immaterial of how the fence gets built - builds it himself, pays farmhands to do it, hires a neighbor to do it.

If the question is phrased this way:

It would cost the rancher $100 in ranch hand wages to build a fence that would keep the cattle on his property.
It would cost the farmer $400 in farm hand wages to build a fence that would keep the cattle out of her property.

Then it becomes clear how the money is being spent.

[Joseph]

What I have trouble accepting is that the Farmer will have any claim on the rancher, given these values. She may know that she lost $300, but the Rancher will dispute this. Then we will have lawyers involved in the recovery of the $300 (or time in court). These will add friction and costs to the process. Simply refusing to pay damages seems like an even stronger strategy on the part of the Rancher. How likely is the Farmer to be able to do anything about it?

So maybe the intuition is off because we all instinctively grasp that nobody is going to accept these damages, but will dispute, dismiss, use media attention and so forth to set the cost to zero.

[Mike Sproul]

Frances:

"it looks like you do that in your ECON 1000 course"

That's some pretty thorough googling on your part. I teach at USC these days, plus 1 class at UCLA. In both schools, most of us introduce the Edgeworth box in intermediate micro, but not in micro principles.

[Frances Woolley]

Mike: just good searching - it's the second hit (after this page) for mike sproul coase theorem.

Joseph: "So maybe the intuition is off because we all instinctively grasp that nobody is going to accept these damages"

I think part of the issue is that, when the costs of reaching an agreement actually are low, people resolve issues immediately and no negotiation process is observed. In the rancher/farmer example above, no one would actually observe crop damage and negotiations, because the rancher and farmer would take one look at the situation, say 'we can do better than this,' and build a fence. We only observe a negotiation process when negotiations are difficult and costly.

It's like trying to grasp the idea that heavy and light objects fall at the same rate. This is true in a vacuum, but we don't live in a vacuum, so our intuition misleads us.

[Nick Rowe]

Frances: "The reason you're getting different results in the two scenarios is that in your mind you've imaged different negotiation structures."

That would make sense, but I just can't see it. If the rancher pays compensation equal to the damage, the farmer doesn't care what the rancher does, and rancher just builds the fence. I don't see any potential for hold-ups or negotiation. If the fence cost more than the damage, and if the farmer would get over-compensated for the damage, I can see some potentials for trade.

I now think we only get indeterminacy under both regimes if the efficient allocation of resources is different from both of the infinite transactions cost allocations.

(We don't teach the Edgeworth box in ECON 1000. I don't recall seeing it in any intro text.)

[cw]

One teaching strategy that might help with this type of application is to explicitly point out a couple of ideas that students can be on the look out for when thinking about Coase Theorem type situations. For example, you might talk about the idea of 'side payments' or 'bribes' and how those mechanisms can help people realize the gains from trade. By putting a specific name on the general mechanism, you might make it easier for students to identify the solution. Edgeworth boxes might be handy too...but they are pretty abstract. Somehow you want students to recognize that the rancher is both a rancher and a potential seller/producer of fences and that the farmer faces a make vs buy decision. Anyway, sometimes the lingo helps people identify patterns that show up in certain classes situations (or exam questions).

CW

[Donald A. Coffin]

Years ago (1971?) the Hofstra Law Journal published an article on the Coase Theorem (author now unknown to me, as I no longer have a copy of the article). In this article, the author argued that the Coase Theorem ignored one complication, in that it assumed that all parties were constrained by the rule of law. Otherwise,s/he wrote, the cattle rancher and the farmer might circle each other in the corn field, with shotguns, waiting for a clear shot. Obviously, the point remained with me, evenif the article and its author have long vanished from my mind.

[John M]

I heard the Coase theorem discussed in the context of contract breach: there is no need for enforcement of contracts. The argument is made that if a contract is breached, it doesn't matter where the cost of the breach falls -- on the breacher, or on the other innocent party, because they would negotiate the consequences of breach.

If the cost of breaching falls on the breacher, he would decide whether to breach -- damages for breach vs. benefits of breach.

If the cost of breaching falls on the other party, then: If the damages for the breach are less than the benefits for the breaching party, then he suffers the breach.

On the other hand, if the damages for breach are greater than the benefits for the breaching party, he would agree to pay the breaching party those benefits, in exchange for the breaching party not to breach. But then the breaching party breaches that second contract. No problem; there would be negotiations for a contract not to breach in exchange for payment. But then the breaching party breaches that contract. Etc., etc. We get infinite regression without anything being done. The breach occurs, and the innocent party is stuck with the breach even if the cost to the innocent party is greater than the benefit to the breacher.

The Coase Theorem fails completely here.

[William Bruntrager]

I agree with Sandwichman, and would suggest that this question is far more complicated than necessary for understanding the Coase theorem. Here's my question:

Alan and Bob are walking down the street together when they happen to find, on the ground, a ticket to that night's rock concert. There is only one ticket so, to be fair, they decide to flip a coin to determine who gets the ticket. Each of the friends' personal valuations of the ticket are different. For Alan, the ticket is worth $20. For Bob, it is worth $10.

a. Assume Alan and Bob each know how much the other one values the ticket, and neither one is shy about negotiating with the other. If the coin flip determines that the ticket should go to Alan, what happens? What will be different if the coin flip goes to Bob?

b. Now, suppose that the coin dictates that Bob gets the ticket. Alan, as it happens, has just taken an economics class and is convinced that everything he does not like should be deemed an "externality" imposed upon him. How would Coase suggest that Alan deal with the externality being imposed upon him by Bob?

c. How does calling Bob's possession of the ticket an "externality" change the outcome of this scenario?

---end question---

Alright, this question is easy, because "The Coase Theorem" is supposed to be easy to understand. This is why Sandwichman's point about "what was Coase's real goal in writing this article" is important. Coase is saying "We have this whole literature since Pigou about 'externalities,' but I am not sure why it exists. Externalities are what cause market transactions. Always have been."

[Jacques René Giguère]

A more advanced question,as it includes politics:
In March 2007, a Montreal Hassidic synagogue, fearing that the sight of young women exercising next door would distract their male congregants, paid the YWCA to frost their windows. When this was publicly revealed, public uproar ensued and it was part of the March 2007 elections.
Of course, some women pay to enlist at the women-only Curves chain of gym, in part because they frost their windows, with nobody minding.

Who should pay to frost windows? Should you accept free frosting? Is there a benefit in exercising with non-frosted windows?

[genauer]

LOL, kind of interesting insight in the thinking in your place. Seems to be pretty lawless.

In civilized places the rancher knows that it is socially not acceptable to damage his neighbors, and doesn't need to be asked to built the fence.

He does not even need a government to remind him of this, but this would be the next step, then suing, selling trespassing cows.

[Frances Woolley]

William - part (a) is straightforward enough, but I have no idea what you're looking for in (b) and (c). What does the Coase theorem have to say about this situation other than if Alan gets the ticket, he keeps it, and if Bob gets the ticket, he sells it to Alan for some price between $10 and $20?

Donald, you don't mean Horowitz (1979) "Law and Economics: Science or politics" here? The one that says "I have a strong feeling that the economic analysis of law has "peaked out""? This paper in Yale Law J review the literature, but I can't see a paper with about the right dates.

This is something that any kind of bargaining theory has to deal with - the possibility of using threats or violence to worsen the opponent's fallback position. But the possibility of threats and violence doesn't make it impossible or futile to understand bargaining.

Nick: You're right, because of the way I've set up the question. In the first case, the rancher doesn't need farmer's permission to build fence, so he doesn't have to give the Farmer a share of the proceeds. In the second case, the farmer does need the rancher's permission to get the fence built, because the fence is on the rancher's land. The rancher needs the farmer's permission to build the fence, because the farmer is paying. Because both sides have a say, the outcome is from what it would be when the rancher has both the right to build and the right to pay.

For people who care about these things, the first one is more like an Ultimatum game, the second more like a Rubinstein game. But I could have set it up differently, that is, had a fence that required both parties' permission, but cost the rancher less to build because the rancher had temporary foreign workers on his operation.

[Frances Woolley]

This Stanford Law Review article On Cattle and Coase is kind of fun - it actually goes and studies how Ranchers and Farmers resolve disputes in the real world. From a quick glance, it seems that the author is arguing that Coase is right, but for the wrong reasons - the legal structure has no effect, because people generally ignore the law and work things out with social norms and convention.

[Frances Woolley]

Jacques Rene - lovely suggestion, and I'm looking for questions for my final exam... B.t.w., interesting article in the Guardian on autism today here http://www.guardian.co.uk/lifeandstyle/2012/nov/17/autism-education-saskia-baron-brother

[Min]

genauer: "LOL, kind of interesting insight in the thinking in your place. Seems to be pretty lawless."

Donald A. Coffin: "In a {Hofstra Law Journal} article, the author argued that the Coase Theorem ignored one complication, in that it assumed that all parties were constrained by the rule of law. Otherwise,s/he wrote, the cattle rancher and the farmer might circle each other in the corn field, with shotguns, waiting for a clear shot."

Frances Woolley: "From a quick glance, it seems that the author is arguing that Coase is right, but for the wrong reasons - the legal structure has no effect, because people generally ignore the law and work things out with social norms and convention."

America has a history of feuds, the Hatfields vs. the McCoys perhaps being the most famous. In most of them lawsuits played a role, lawsuits that were supposed to settle matters, but obviously didn't.

[William Bruntrager]

Frances, the idea I was aiming for was that if the situation in part (a) is straightforward, then the Coase theorem says that parts (b) and (c) should be equally straightforward, and if they don't seem that way, then there is something wrong with the way we are thinking about externalities. This is, for me, the point of Coase's article.

To answer my earlier questions, I would expect students to write:

b. Alan is correct to claim that Bob imposes an externality on him by attending the concert. By not giving the ticket to Alan, Bob is causing Alan to lose something that he values at $20, just as surely as a factory belching smoke into my house causes me to lose the value I would have assigned to having clean, breathable air. It is normal to call the smoke case an externality and very abnormal to call this concert-ticket case an externality. That is unimportant. The Coase theorem suggests that where there is a clearly-defined right at issue, that right should be exercised by the person who values it most.

c. It makes no difference whether you call something an "externality." Decisions that have costs and benefits for multiple parties can, in principle, be resolved through bargaining by those same parties.

---end answer---

Sorry to be unclear before, but the point I was trying to make was that the great insight of Coase in this article was not that goods generally end up with the person who values them most. As Coase himself wrote in his FCC article, that was perhaps a novel idea when Adam Smith wrote it. So if there is something uniquely important about externalities, it can't be the fact that some people's decisions are costly to other people. It has to be some aspect of the situation that makes it difficult for those people to bargain.

If Pigovian taxation were easy to implement, it would not be necessary, because people already would have negotiated the efficient arrangement for themselves.

[William Bruntrager]

If I could offer one suggestion for modifying your original question, it would be to make it less complicated by separating out two aspects of the Coase theorem:

1. Initial assignment of property rights are irrelevant.
2. If externalities should be dealt with, they should be dealt with by the person who can do so at the lowest cost.

It might make the problem easier to manage if the question of who builds a fence if there is a fence gets resolved quickly, and the $400 fence can be forgotten as irrelevant. Similarly with the total values of the ranching and farming businesses. There end up being a lot of numbers to keep in mind.

[Frances Woolley]

William - thanks for the reply, that makes things much clearer. I am in sympathy with your last point, which applies even more strongly to the supposedly Coasian solutions of tradable permits. To the extent that externalities will be internalized unless there are some kinds of transaction costs, any supposed solution has to work out how to deal with the information, monitoring, and enforcement problems that gave rise to the transaction costs in the first place.

On the answers to the questions - when you say "I would expect students to write" perhaps you mean "I would hope students would write"? I think you'd get quite a few correct answers to (c), because there are only a few possible answers, so some students are bound to stumble on the right one. But I wouldn't want to be the one trying to assess (b).

[Daniel I. Harris]

As a person who's never taken an economics course (though I read many economics blogs), I will tell you my exact thought process in the hope that it will enlighten you a bit about how the question is perceived, especially since, having no knowledge of the Coase Theorem, I got the answer right:

OK, $300 damages, Farmer makes $500, Rancher makes $1000. If the Rancher has to pay for the damages, it's obvious that they would pay the $100 (hmmm, could that also have leisure costs? No, probably not--that would be mentioned if it's relevant, as each person would value their leisure at a different amount. Unless that's the point: we can't know because these variables aren't listed? Perhaps the cost includes the leisure costs, as it doesn't make sense that the actual material would cost the farmer 4x as much). OK, that settles that; the Rancher would build it if the Rancher pays the cost.

If the farmer absorbs the cost... well, it would probably still make sense to build it, as it's a one-time cost... though, hmmm... that would mean the farmer would only have $100 to live off for the year that they build it. Would it be possible that the farmer would not build it because the initial cost is so high that the farmer would not survive the year if they built it? No, that doesn't make sense; the farmer could get a loan. OK, so the farmer would build it and it would pay off over the years (as even assuming they paid it off with a credit card, at 20% interest, they could pay $200 a year and save $100 per year and so come out ahead each year... oh that's right! If the farmer builds the fence before the damage occurs, then they would not incur the damage, and so would have $400 for the year after paying for the fence, not $100. Well, then, the farmer would definitely do it, especially since at credit card interest rates they would still come out ahead in the first year.

Wait... that seemed too easy and straightforward. If everyone gets this wrong, it can't be that easy. There must be something I'm missing. Let me re-read the question. Hmm, I had all the facts right, they can't be changed. Wait, no transaction costs? Oh, what if the farmer paid the rancher? The rancher would be better off, and the farmer would be better off. Is that it? Let me read the answer... I was right!

[Nathan Tankus]

Under the assumptions of this question, it seems to me in the example where the rancher isn't responsible for crop damages the cheapest and most efficient solution for the farmer is to shoot the cows. I'm assuming that the converse is true- the farmer isn't responsible for cattle damages. If one were to respond that it might anger the rancher, the converse would be true for crop damages and would seem to contradict the assumptions of the model such as no negotiation costs.

[Peter T]

If this is set out in an entirely abstract way, preferably not involving people, then it is, to my mind, clear at a glance. If the example involves people with, you know, rights, feelings on property and damage, socially situated, in a world where actual costs and causes are hard to assign exactly, it's much harder to parse the question: you have to exclude all sorts of things that you know would be there. It's not as if it's a question about actual fencing, where most of the factors mentioned would simply be irrelevant (farmer: Your cattle were in my corn again, so I called the warden and he impounded them. If you don't want it to happen again, build a fence. Rancher: [Thinks bitch!] Okay. But it will cost me $100. The law says you have to spring for half....)

[genauer]

Min,

your Frances quote actually came (closely) after me. I knew the similar Harlan, Kentucky Feud from Gladwell: “Outliers”. I looked up now a number of other such feuds. It seems that a lot of Irish are involved (hello Determinant : - ).

For German ears the Coase theorem sounds like: in the end the cheapest solution is done, and the law doesn’t matter. That sounds completely wrong for German ears.
In contrast, we didn’t have any lawless areas here around for many hundreds of years. It is always somebody in control. Revolution means that the worker council is taking over the control, but not that there is a moment without control. Nobody is above the law (some nice story: Legend in http://en.wikipedia.org/wiki/Historic_Mill_of_Sanssouci), it is only the law that counts, and the costs are irrelevant, at first (with a slightly different meaning: iudex non calculat)
Gladwell actually used the Harlan story as a starting point for illustrating that you can trace such behavior over hundreds of years in areas, where that has long ended to be useful or appropriate, like giving right of way in an aisle in a University. And I was reminded of it, with this (francophone) student strike in Quebec this year. That strikers and demonstrators take the right to block streets and ports, like in France, or even take (foreign) managers hostage, is simply incomprehensible here around.

When you look how closely the border of the old Roman Empire resembles, which area went protestant 1500 years later, and how closely it resembles the present day trouble maker states, maybe we just have to forget about any closer union with them. If patience and politeness is just interpreted for weakness, it invites constant conflict.

And, LOL, just to round this off, we have of course laws, which define who has to built the fence, what size, shape, color, make is permitted and needed, and how far I can throw the branches from your tree infringing on my property over the fence : - )

Now, how do you teach a wrong theorem?

[Frances Woolley]

genauer - "the law doesn’t matter"

Not at all. According to Coase, having a functioning legal system, where contracts can be enforced, *does* matter. The farmer couldn't just go out and shoot the cattle without consequences. What *doesn't* matter, Coase figures, is whether this well-functioning legal system makes the rancher or the farmer responsible for crop damage.

Daniel - congratulations, interesting to see your thought processes.

Peter T - I see you read the question carefully enough to notice that the farmer was female!

[Mike Huben]

It strikes me that the misleading aspect of the problem is the unstated possibility that the farmer could pay the rancher to build the fence.

If I was to teach the Coase Theorem, I would emphasize that the assumption of no negotiating costs means that ANYONE could use the lowest price that anyone else has BECAUSE they could simply hire the person with the lowest price. I would teach students to identify the lowest prices, and then see how each player could achieve that lowest price. Isn't that all that people who "understand" the Coase Theorem are doing? But because it is a two-step procedure, it is not a pattern that all students perceive quickly.

There is a huge amount concealed in the assumptions of "no negotiating costs" and "economic rationality".

[Livio Di Matteo]

The answer to the question is simple and can be found in the musical Oklahoma. The farmer and the cowboy should be friends.:)

[bakho]

Maybe it would sink in better if you set up a financial game that students played every day in class?. You could set up an externality that would force students to respond. They could play the game and discover which policy was optimal empirically. Then when you present Coase, it might be more internalized.

[John]

The reason why the Coase Theorem is hard for students is that the theory is wrong.

Negotiation is not based on the assumptions on which the Theorem is based.

Negotiation is based on deception, which is why I cannot buy a Twinkie at the 7-11 this morning.

[GeorgeK]

Fascinating discussion for non-economist: however I deal with real world Ag issues such as trespass.
http://tilth.org/news/organic-farm-prevails-against-pesticide-spraying

[dilbert dogbert]

Coase is much much much above my pay grade. My resolution would be for the farmer to round up the cattle and sell them. Rancher would build the fence pronto. Damn cattle brands would be a handicap for that solution. A nasty person would put some contaminated cattle feed out, say with some urea in it and see what happens. Another approach would be to plant a band of poisonous to cattle plants on the common border. Star Thistle is poisonous to horses but not cattle, but there must be some plant that would do the cattle in.
My recollection is in law, in the old west, it is the farmers responsibility to protect his property.

[genauer]

I read the original Coase text in the meanwhile, in apparent contrast to most commenters here. The original text is clear and in agreement with the common understanding of the law of most people, at least here around.

I takes written general law, clear and enforcable as the starting point, and that means of course that the rancher is fully liable for any damage.

Only based on that, it points out, that in some cases this might spring private contracts to optimize trade offs. It also states, that often there is no situation of clearly measurable effects and that transaction costs are high.

The whole problem comes from people interpreting different things into the various cases and making "pseudo simplifying" miss statements of the situations, which then cause of course deviating interpretations.

The lesson from this is: read the originals.

90 % of the discussion here circles around issues which are simply not in the original text.

[Donald A. Coffin]

Yep, it was the Horowitz aricle. I did not remember accurately how long ago I read the thing...

[Sandwichman]

"90 % of the discussion here circles around issues which are simply not in the original text."

Yes, yes, yes, yes, yes! And which brings the matter back to the point that the "Coase Theorem" is by no means Coase's theorem. Coase's critique of the "Pigouvian tradition" was trenchant. What has replaced Pigou, though, is a "Coasean tradition" that is as wide of the mark as the tradition that Coase critiqued. What a round about way of getting back to where we started except with the omniscient market replacing the omniscient state.

But Coase also only analyzed the kind of social cost in which the problem is really a reciprocal one -- that is one in which remedying the harm done to a third party imposes costs on the party who is responsible for that harm. But what about externalities that don't have such a tidily reciprocal form? I would submit that the most important social cost or externality conditions are precisely those that do not conform to that reciprocal straitjacket. Thus the Coasean analysis is a distraction that draws attention to a trivial sub-class of externalities that cannot serve as a model for how to deal with the more prevalent conditions. And this is before the questions of transaction costs and clearly-defined property rights.

[genauer]

Just to illustrate that a litte more,
I just flew over the Coase paper and the relating wiki pages.

If somebody would have asked me, to summarize the rancher/farmer case in a very few sentences, I would probably have left out the fence, and just focused on the non-linear cost-benefit function, the element which creates the existence of a trade-off optimum, but which is missing in Frances version.

And the coarseness of the solution, 3 steers, and not 2.5 : - )

The other cases:
- that typically the law does not honor to be there first, but that smoke, noise has to be within general limits (We have an interesting case of a Xian church vs muslim newcomers here, and dont get me started on beergardens : - )

- that one of the reasons for the existence of a (large) company is exactly the high transaction costs in adressing "externalities" -> Coase 1937, "the nature of the firm" and coase 1960 as a kind of summary of practical examples of the original arguments.

[Frances Woolley]

genauer, thanks for bringing the discussion back on topic.

The Ruth/Phil example (that no one has discussed yet) generates a unique solution with non-linear cost-benefits (Phil's total costs are $50*number of piercings, Ruth's total benefit function is quadratic, given by the integral of 110-10Q).

[genauer]

Good point, that nobody touches the piercing example. Why ?

So I try it for me. I find piercings gross, underclass. To bargain over that in a family is even more crass. The whole setting detracts (at least me) completely from finding "optimum solutions". I think I stopped reading at "psychological harm", after all I dont have to earn grades from you : - ) And we didnt talk openely about the weighing discretion, at my time : - )

The impression of a rotten child does not change any more substantially with more than 1 piercing.

The rodden kid theorem, I looked up for my answer to you, I find even more weird. Do you know people who think like that ?

In short, the "practical example" introduces more distraction than applicability, at least for some old conservative hack like me.

[Min]

genauer: "The lesson from this is: read the originals."

:)

[J.V. Dubois]

Am I the only person who has more trouble with the second question? My general objection is in terms of what david wrote "Students who feel that they are being taught to write something that they feel obliged to object to on partisan grounds will find it unusually difficult to apply it.". Only I would add "common sense" instead of "partisan grounds".

I mean how real is an example where father/daughter conversation ends up as money haggling where daughter bribes the father? Especially if you assume that daughter can enforce the deal by not being such a good daughter or something? In what way exactly should this "example" make it easier for students to grasp the theorem? One possible answer for question 4 would be: "Father would not permit any piercing for Ruth hoping that by the time she turns 16 she will come to her senses and won't need any piercing at all"

This is really bad example as people tend not to think in market terms when dealing with family crises. The Mike's example is much better as it really shows how this can be applied to the real world unlike poor Ruth and Phil.

[Frances Woolley]

J.V. "This is really bad example as people tend not to think in market terms when dealing with family crises.'

Guess what, people tend not to think in market terms when dealing with environmental damage either.

Education is about expanding people's horizons, getting people to think about things in new ways.

Interestingly, these economics of the family type questions end up being cultural specific. People with more individualistic cultural orientations e.g. of Northern European + North American background, don't do as well as students from places where the family is relatively more important as a social/economic/organizational unit.

[J.V. Dubois]

Frances: I get it, maybe I did not explain my objection correctly. So let's sum it up

1. First, you frame a decision to get piercing as something where the cost of getting one is something important.
2. Then you frame parenting in an economic way as if parents evaluate how much various decisions of their children impact THEM.

This for me as a student would be a signal to switch-off my "creative" thinking and just change "Ruth", "Daddy" and "Piercing" for "Person A", "Person B" and "Good" so that I don't get distracted. And then if as a response to this totally unrealistic scenario some student would ask "What if daughter does not have money to bribe her father?" there are several possible answers to that question:

a) Technocratic answer. It is clearly assumed that "Person A" has enough money to buy her preferred quantity of goods (7 x $40 = $280) - at least you wrote it as part of answer for question 1. Why change this assumption for question 4? It would be silly to think about this example if Person A had no means to make her purchase.

b) What I would think as a student hearing somebody asking it: Really? Is this the only thing that you found wrong with the example? Oh, wait. You just want to seem active and thoughtful before our prof. Disgusting.

[Neil]

I was somewhat distracted by the idea that there may be a wealth transfer at work - I read that by destroying crops, the cattle were eating them, and thus saving the rancher some money if crop damage remained the farmer's responsibility.

Coase's theorem is like a lot of abstract economics. It's difficult to grasp because its assumptions (free negotiations, free contract enforcement) eliminates any relationship with the real world. You then provide a pseudo-real world example and expect people to remain focused on applying a purely theoretical rule. Creating a more abstract problem might help.

[kevin quinn]

Frances: For the Ruth and Phil case, you don't really need the 2nd diagram. For the second case, the "what Phil must be paid" schedule becomes the "foregone marginal payment from Phil" schedule. This is a now a marginal cost to Ruth of a piercing, so she choose the number of piercings where marginal net benefit equals marginal foregone payment from Phil: 2 piercings.

One of the things that bothers me about the textbook expositions of Coase is that they all concern external effects that are confined to a single agent. Once the Marginal external effect is spread out among many people - surely the more typical case - the Coasian solution requires that we solve a collective action problem. Getting the problem fixed is then a public good, subject to free-riding. And then we can see how the scorned Pigouvian tax/subsidy is precisely a solution to such a collective action problem.

[Frances Woolley]

Kevin: "One of the things that bothers me about the textbook expositions of Coase is that they all concern external effects that are confined to a single agent."

Absolutely, because with multiple agents, the assumption of zero transaction costs isn't particularly appealing. But as you say, the externalities that exist - which exist precisely because they can't easily be internalized through negotiation - tend to be ones affecting multiple actors.

Neil "Creating a more abstract problem might help" It might help students answer the question correctly, but would it help them apply Coase to real world situations.

J.V., sorry, my reaction was unnecessarily snappy.

[Mike]

I agree with Mike Huben. When I was presented with these problems during my undergrad, I had trouble grasping that you could pay someone to take advantage of their lower costs (or higher benefits). Your game example illustrates it perfectly because the student thinks the farmer only has one decision to make with two possibilities, i.e. to build their own fence or not. They don't fully get that you can negotiate to make one of those outcomes more or less likely to happen.

[Greg Ransom]

Bizarre that you think the only costs which matter to choice are "given" money costs.

Countless additional subjective costs of various kinds can be imaged for the actors in this situations.

The stipulated "givens" of any whiteboard people falsify the nature of choice -- as Coase repeatedly attempted to get economists to think about .... but failed.

[Frances Woolley]

Greg: "Bizarre that you think the only costs which matter to choice are "given" money costs."

I'm not sure who "you" refers to here. People make decisions. The basic premise of economics is that those decisions are made on the basis of costs and benefits. Those costs and benefits may be either monetary or non-monetary. In fact, they almost always are both monetary and non-monetary.

In order to make a decision, however, people have to say either "the costs are greater than the benefits" or "the benefits are greater than the costs." Implicitly, this requires aggregating benefits and costs in some way. Expressing things in dollar terms is nothing other than a convenient way of aggregating costs and benefits.

Aggregating in dollar terms, rather than say utiles, implicitly assumes that it is possible to compare, e.g., Phil's psychological harm and Ruth's psychological benefits. Yet people do make such trade-offs. There was a fascinating paper published, I think in the Feminist Economics volume on Amartya Sen, that looked at situations where people had made explicit trade-offs between, say, freedom and security (freed slaves petitioning to be re-enslaved in order to be with family and receive care in old age, for example).

People make choices. People have alternatives. Recognizing that is the basic value of economics.

[Sandwichman]

"Rancher" number two now appears and offers to build a $100 fence to contain his prospective cattle if the farmer pays him $200. He builds the fence, pockets his $100 profit and sells the fenced property. Rancher number three now appears...