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.