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.
- 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.
- 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:
where Q is the number of piercings. The marginal cost of piercings is $40 per piercing.
- Calculate the number of piercings Ruth will choose. Illustrate with a picture.
- 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).
- State and explain the Coase theorem.
- 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.