Thursday, November 22, 2012

Economics as a Unifier of Law: A True Story

I have just finished teaching a course on intellectual property theory. The main text was a book of readings on the subject compiled by two prominent IP scholars. One of the reading was an article that Lou Kaplow, a prominent (and very able) law and economics scholar at Harvard, published in 1984 ["The Patent—Antitrust Intersection: A Reappraisal, 97 Harv. L. Rev. 1913 (1984)]. What most interested me about the article was that I wrote it. In 1981.

Neither Lou nor I engaged in plagiarism, with or without the aid of a time machine. I first saw his article only a month or so ago; he had never seen my article when he wrote his and may not have seen it yet. The two articles were on entirely different topics, his on patent law, mine on criminal law. Yet they were, in their essence, the same article. Each of them hinged on a single simple idea—simple enough so that I can explain it in a blog post, as I am about to demonstrate. And it was the same idea in both articles.

The conventional view of patent law is that it rewards inventors with a temporary monopoly in order to give them an incentive to make and reveal inventions. Lou was looking at the question of how long the term of the monopoly should be and what the inventor should be permitted to do with it. Part of that was the question of how large the reward for making an invention should be.

There is an obvious answer to that question, obvious at least to an economist. Set the reward equal to the social value of the invention. That way it will be in the interest of inventors to make any invention that costs less than it is worth. Applying that rule in practice faces a host of difficulties, but the theoretical answer seems straightforward.

It is also, as Lou pointed out, wrong. The reason it is wrong is that giving the reward is costly. For reasons familiar in economic theory, the benefit a monopoly provides to the monopolist is less than the cost it imposes on his customers, the difference being what economists refer to as "deadweight cost."

To see the relevance of that, imagine that there is an invention whose social value we can somehow measure as ten million dollars. Further imagine that we have calculated that ten years of monopoly will give the inventor a reward of exactly that sum. Should we give it to him?

No. Suppose we reduce the term of patent protection from ten years to nine and that doing so reduces his reward from ten million dollars to nine million. If the cost of making the invention is less than nine million dollars, he will still make it, we will still get the benefit—and we will have a year less of deadweight cost. That is a net benefit. If it happens that the cost is between nine million and ten million the invention won't get made. That is a cost, but it is a cost, on net, of less than a million dollars, since we (consumers and inventor together) will lose a ten million dollar benefit but save a cost of between nine and ten million. To figure out what the optimal length of protection is we would need more information—a probability distribution for the cost, telling us how likely it is that any reduction in the reward will result in the invention being made, and a way of calculating how large the deadweight cost is for any length of protection. 

But it is easy to see that the optimal term of protection can be less than ten years and only a little harder to see that it almost has to be [readers uncomfortable with mathematics are advised to skip the rest of this paragraph]—because if the term of protection is 10 years - X, both the chance that the shorter term will result in not getting the invention and the cost of doing so are proportional to X, making the combined effect proportional to X squared—what an older generation of scientists referred to as of the second order of smalls. The savings in deadweight loss is proportional to X, since that is much less time we bear it. So if X is small enough, the gain has to be larger than the loss.

Lou's conclusion was that the conventional answer, optimal reward equal to value of invention, was wrong. As long as giving a reward costs something, the optimal reward is instead at the point where any further extension of term costs as much in increased deadweight loss as it gains in increased chance of invention. That was the central point of Lou's article, and it was correct—obviously correct, once stated.

My article ["Reflections on Optimal Punishment or Should the Rich Pay Higher Fines?," Research in Law and Economics, (1981)] was on how to calculate the optimal penalty for any criminal offense. In that case too, there was an obvious answer, obvious at least to any economist, and the logic of the answer was the same. Set the penalty (more precisely, the combination of penalty if convicted and chance of conviction) equal to the damage done by the offense. That way the only offenses it is worth committing are those where the gain to the offender is greater than the loss to the victim, in which case deterring the offense would make us, on net, worse off.

That obvious answer is also wrong, and for precisely the same reason. Catching and punishing criminals, like rewarding inventors, is costly. If an offense costs the victim $100 and benefits the criminal by $99, it imposes a net cost of $1. But if raising the punishment by enough to deter that offense costs $10 in extra enforcement and punishment costs, costs of paying cops and running prisons, we are better off not doing it. The level of punishment that minimizes net costs is the level at which any further increase would cost as much in extra enforcement and punishment costs as it would gain in deterring offenses that do net damage.

There are differences in detail between my case and his, in particular the fact that the cost of deterrence is sometimes negative—if you deter an offense you don't have to punish it. Anyone sufficiently interested can find the details in the relevant chapter of my Law's Order and, in a more mathematical form, in a virtual footnote to that chapter. But the logic of the two articles is identical, as is the logic of the two errors, one in patent theory and one in criminal theory, that they critique.

Which is evidence of how economics unifies the law, makes the same analysis, the same ideas, the same logic apply across a wide range of apparently unrelated legal fields.


Xerographica said...

The law enforcement part sounds so complicated. Taxpayers should just pay to enforce the laws that they want enforced. If I want drugs to be illegal...then I'd go to the DEA website and submit a tax payment.

How much revenue would the DEA receive? If drugs are illegal, but nobody is willing to pay to enforce the law, then does the law matter?

Am I missing something? Is there a situation when people shouldn't have to put their money where their mouths are?

David Friedman said...

"Am I missing something?"

Yes. You are confusing two quite different questions:

1. What institutions are most likely to produce the right answer to a legal question


2. What is the right answer to that legal question?

For an analogy ... . Suppose we were discussing how to best increase the fuel efficiency of an automobile. It might be true that we will get the best automobiles if they are produced on the free market. But that fact doesn't tell us what they will, or should, be like--that's an engineering question.

Similarly here. The question I was asking in my article was how you would in principle calculate the punishment for any offense, if your objective was what economists call economic efficiency—loosely speaking, maximizing the size of the pie, the net benefit to all affected. I have written elsewhere about what institutions would tend to generate efficient law—my solution is a good deal more radical than yours—but that wasn't the topic of the paper of mine I described in the post.

Anonymous said...

I've occasionally gotten bills in the mail for extremely small amounts (less than a dollar) and wondered whether it was costing the company more money to print and mail the bill, cash my check, and (with small probability) chase me down for failure to pay, than the amount I was supposed to pay them.

Would there be negative consequences, perhaps involving customer expectations, to a company that routinely didn't bill for amounts less than a dollar?

Anonymous said...

Xerographica: your proposal has a problem well-known to economists.

The amount of enforcement of a given law is unlikely to be a simple linear function of the available funding; more likely, up to a certain point it won't be enforced at all. Which leads to a "freeloader's paradox".

If the law is not currently enforced due to insufficient funds, the amount I can afford to chip in to enforce it is unlikely to push it over the threshold, so I'm unlikely to get any benefit at all for my payment, so I'm unlikely to donate. OTOH, if it is being enforced, then my payment won't make it any more enforced, so again I'm unlikely to donate.

The only kind of person likely to donate for enforcement of a particular law is somebody wealthy enough to afford the full cost of that enforcement. As a result, laws of interest to rich people (say, theft) would be enforced disproportionately relative to laws of interest to all people (say, murder) or laws of interest to poor people (say, worker safety). And if I can afford to enforce the law myself, I might skip the government entirely and just hire my own enforcers. Which may be the sort of world some would prefer to live in, but consider carefully before going that direction.

Xerographica said...

David Friedman, it's a problem, a significant problem, to consider "engineering" solutions out of context. Sure...there was an engineering solution to building the pyramids...but what about the opportunity cost? Same thing with the extermination of Jews during WWII and the war on terror.

Whether the solutions to "problems" are efficient or not has absolutely no real value or meaning out of context.

When we put criminal behavior in context then it's not just a simple matter of deterring becomes a complex issue of a stitch in time saving nine.

Your solution is a good deal more radical than mine...this is true. Unfortunately, its efficacy is limited by how radical it is. Plus...if your solution truly maximizes the size of the pie...then why wouldn't my solution put us on the path to your solution?

"It is, of course, not desirable that anything should be done by funds derived from compulsory taxation, which is already sufficiently well done by individual liberality." - J.S. Mill

Why would taxpayers pay public organizations to do anything that is already sufficiently well done by private organizations?

Xerographica said...

hudebnik, if you use the term "freeloader" to refer to people who pay taxes...then what term would you use to refer to people who do not pay taxes?

You're technically critiquing anarcho-capitalism...but what you're actually trying to critique is a taxpayer division of labor. But why would it be effective/efficient for every single taxpayer to evaluate every single possible solution to every single problem?

Command economies (ie our public sector) fail because they fail to incorporate even the smallest fraction of the massive amount of information/values that are incorporated by market economies...

"It must be remembered, besides, that even if a government were superior in intelligence and knowledge to any single individual in the nation, it must be inferior to all the individuals of the nation taken together. It can neither possess in itself, nor enlist in its service, more than a portion of the acquirements and capacities which the country contains, applicable to any given purpose." - J.S. Mill

Individual agency...what each and every one of us chooses to spend our own time/money on...incorporates the information/values that economies need in order for the output to actually be relevant. Individual valuation is the essential and accurate feedback mechanism. It is the fail safe device that prevents massive amounts of limited resources from being wasted on tilting at windmills. For example, I'd be willing to bet $900 that if I asked you to paypal me $1000 that your willingness to do so would depend on my explanation.

If we create a market for public goods then taxpayers would have the freedom to shop for themselves in the public sector. Congress would still be there nothing would stop you from giving all your taxes to personal shoppers.

And if you didn't approve of how Jeff Bezos was spending his taxes...then foregoing the convenience of shopping on would certainly be an option for you and everybody else.