March 05, 2005

The Trouble with Efficiency

Micah Schwartzman links to a funny article about the limits of Coase's Theorem. I had been thinking of mentioning the theorem (which I first learned of from Jane Galt) in this silly entry. From the article:

The Coase Theorem states that market forces will allocate property rights efficiently, no matter who initially holds those rights, as long as the interested parties can make contracts without additional transaction costs. A corollary, however, is that contracts are almost never made without transaction costs, so legal rules should try to minimize those costs for the parties and for society

and, I might add, to make sure that rights are allocated clearly and unambiguously. The analogy in the previous post would be that argument proceeds efficiently so long as the meanings of terms are stipulated clearly and unambiguously, regardless of what the stipulation is. [NOTE: I don't actually believe that--if you want to be reassured about it, read the rest of the post.]

But there's a point to be made about the article itself.

The situation: Some popular classes at NYU law school are oversubscribed. NYU has an e-mail list "The Coase List," for students who want to trade things--for instance, students who want to switch classes may arrange to meet so that one can add the class as soon as another drops. One student offered to buy spots in some popular classes. The Student Bar Association and administration decided that this was inappropriate, and banned selling class spots.

What interests me is the reasons that were given to defend the ban. Vice Dean Barry Adler said that

legal rules affect not only how resources are allocated, but who winds up spending how much. By barring the sale of classes, the law school aimed to avoid putting pressure on better-off students to buy the classes they wanted, and, even more importantly, pressure on poorer students to sell their valuable seats. "There's nothing inconsistent with Coase's Theorem there," Adler insisted.

Oren Bar-Gill, a behavioral economics professor, argued as follows:

"In a Coasean world, one would think it makes sense to allow trading cash for classes, because both parties are better off," he explained. "But you also have to take into account the ex ante effects of the rule." Specifically, Bar-Gill feared that students would initially bid in the lottery not for the classes they wanted but for the classes most likely to fetch a high price on Coase's List. Then "bright but not so rich students" would avoid N.Y.U., knowing that many spots in the best classes would eventually be sold to their wealthier peers.

Now, I think the simplest account of the problem here can be explained without discussing ex ante effects or any such. (And I think it may be what Adler's getting at.) If you allow unrestricted Coasean bargaining, then you will reach an efficient outcome--in that there will be no persons A and B and goods X and Y such that A has X and B has Y, and B would rather have X than Y, and A would rather have Y than X. But if you want an efficient outcome, and you don't care about the initial allocation of rights, I have a modest proposal: Give me everything. That will lead to an efficient outcome, in which I have everything, and there's no trade that would make both parties better off, because no one else has anything to trade to me.

The point being that efficient outcomes aren't always the best ones. An efficient outcome reached from a certain intial allocation of rights will maximize (roughly, I think) the sum of the following: Each individual's utility multiplied by the amount of resources that person started with. The initial allocation of rights affects each individual's weight in the final allocation, and that can affect how much total utility the society winds up with in the end.

For instance, if I start with everything and you start with nothing, you have a weight of 0, so we can maximize the weighted sum without any regard for your utility. The likely outcome--in which I'm happy and you're miserable--will be worse overall than an outcome in which we started with equal rates, and we both wind up pretty happy in the end. (If everyone has equal weight, the sum you're maximizing is the sum of utility. The more unequal the weights are, the farther away the outcome that maximizes the sum of weighted utilities will be from the outcome the maximizes the sum of actual utilities.)

In this framework, I think it's pretty easy to sum up the problem with selling spots in NYU Law classes. If there is unrestricted Coasean bargaining, spots in classes will tend to get allocated according to who wants the classes most, weighted by how many resources they have. Those resources include intangibles, such as spots in coveted classes, and also money. Money is in much greater supply. So in practice the richest students will get the best spots--and even if this is a Coase-efficient outcome, it may not maximize utility. You can wind up with a rich student getting a spot in a class over a poorer student who wants it more, simply because the rich student can outbid the poorer student.

The administration might well like to have spots in classes allocated according to who wants them most. That would mean it would be OK to have bargaining with spot-switching, because everyone starts off with more or less the same initial allotment (I assume you're all allowed to sign up for a certain number of classes); but bringing money in would not lead to a desirable outcome, and it would be banned.

And I'm a little distressed that a ton of people studying law and economics don't immediately say something like this: "The problem is that unrestricted bargaining, though it leads to an efficient outcome, won't necessarily lead to the best outcome. In the presence of inequality, creating an unrestricted market will mean that the rich will be able to crowd the poor out of desirable positions. And that's not necessarily the most desirable outcome."

If you want to bring it back to the philosophical point (which doesn't follow from the case, it's just analogous): Efficiency in argument isn't the be-all and end-all. Making the right stipulation actually matters. Sometimes you have to allow some argument over the initial stipulations rather than just declaring a technical use of a term and going on ahead.

(I have now linked all but one of the Crooked Timber posters, not counting the dead guy! Yay!)

Posted by Matt Weiner at March 5, 2005 03:57 PM

In fact, if we are in the mythical world of the Coase Theorem, it doesn't matter whether classes are allocated by the market (i.e., by prices) or by a central planner (i.e., administratively). The outcome would be optimally efficient either way because information would be completely and costless obtained. This is a point Steven Chueng made to Coase, and Coase accepted as true.

Importantly, the first person to point out the limits of the "Coase theorem" was Coase, who (a) denied that the properties of such a world would not be worth exploring mainly because they could not possibly exist and (b) deplored being shackled (by Stigler) with the label, "The Coase theorem."

Posted by: Dan Cole at March 6, 2005 08:59 AM

Thanks for these points, Dan! I'm a bit unclear about the first one--does this mean that it doesn't matter if classes are initially allocated by the market or the central planner, so long as people are allowed to trade? The "allowed to trade" part seems like it must be the crucial point here. If the classes were allocated by the central planner, and people weren't allowed to trade, it wouldn't matter if they could obtain information costlessly.

The point I was trying to make rests more on the idea that saying that the outcome would be optimally efficient doesn't mean that the outcome would be optimal--because efficiency doesn't maximize total utility. And changing the initial allocation will change the total utility of the optimally efficient outcome you wind up with.

I'm not an economist, as you can probably tell, so apologies if I've misunderstood you. I wouldn't go on so confidently about the weighted sum if Brad DeLong weren't always talking about it--he seems like an authority. :-)

Posted by: Matt Weiner at March 6, 2005 10:28 AM

Given a world in which some people have more cash than others - the point you're making about initial conditions - it is acceptable for some things to be convertible into currency, but it's unacceptable for others to be. Where this line gets drawn (or even if a sharp line can be drawn) depends on the ideology of the drawers. For example, almost everyone, perhaps excepting the most rigid libertarians, objects to the sale of human organs, whether from live or dead donors. On the other hand, few of us consider it a pressing moral dilemma that the rich have larger TVs than the poor.

As you say, one would like to see members of a university administration, law and economics faculty come out and "We don't give a crap about living up to the theory of Coase's Theorem. We're banning this because spots in classes shouldn't be bought and sold. It's immoral and promotes inequality. We have rules against buying term papers, too."

But you aren't going to see them say this. The reason is that it strikes too close to the economics of the modern university. At any university, but especially a law school, or especially an expensive private university such as NYU, spots are already allocated partially on the basis of the ability to pay. They just do it at matriculation time. There isn't enough financial aid in the country to change that fact. Fortunately, university admissions are not a fully unrestricted market - yet. But being able to afford Kaplan test prep or better sure helps.


Posted by: Martin Marprelate at March 6, 2005 12:48 PM

Isn't there an assumption in the discussion that there is one "best" that everyone wants?

Also: I have two kidneys, but there are rules against my selling one of them to someone who wants it. And some people have more children than they want, but there are rules (laws) against their selling any.

Posted by: Matt's mom at March 8, 2005 10:49 AM