(Now you might be wondering why I’ve ordered the names in the title with Weyl first and Tirole second, instead of alphabetically as is customary in economics. I kid you not, it is done this way in the original paper, with a footnote mentioning that the order is meant to reflect “priority of contribution.” Now, it takes some braggadocio to list yourself before your advisor on a joint paper, particularly so when said advisor is a lock for the Nobel prize, but since Glen’s paper is a good candidate for “Best Job Market Paper of the Year,” we’ll let him off the hook…)
Everybody agrees that, optimally, all goods are priced at marginal cost: this ensures no deadweight loss. When it comes to new goods, however, nearly every country has, for at least the last century, given temporary market power to inventors in order to induce research effort. To the extent that we know a good with social value V greater than cost of research C might exist, it is optimal just to pay a researcher C as a prize, and not give out any patents at all.
The problem is that governments generally do not know C or V. One way around this is to make the prize conditional on demand when the good is sold at marginal cost times some markup. Weyl and Tirole point out that this is not sufficient because it offers no way to distinguish goods with high consumer surplus from those with low consumer surplus. For instance, imagine a drug which is lifesaving for one million people, and cures colds for another million, as well as a second drug which cures colds for two million. Let both drugs have MC of one dollar. At this price, both drugs sell two million, but the consumer surplus of the first drug is much, much higher, so even if cost of development is ten times higher for the first drug, we still want the government to provide incentives for its creation.
In essence, patents and prizes have a tradeoff. Ex-post, or once an invention has been created, prizes avoid all deadweight loss, but are unable to distinguish between high and low value inventions when information about value is asymmetric between inventors and the government. But to the extent that monopoly revenue is strictly increasing in social value created (true for a wide variety of demand functions), patents ensure that high value inventions are created, but at the cost of deadweight loss. If rare “genius” inventions create tons of consumers surplus, but most other inventions create little, then patents are relatively useful, and vice versa. This suggests an optimal mechanism is the solution to a multiattribute screening problem: given private information about cost of development, demand when price equals marginal cost, and optimal monopoly price, the government selects the social welfare-maximizing incentive-compatible price, meaning marginal cost, monopoly price, or something in between; transfers to the inventor ensure that this price suggestion by the government is incentive compatible. By the revelation principle, we need only look at mechanisms where potential inventors truthfully reveal those three attributes.
Though a short argument shows why we can ignore cost of development, we still have a two-attribute screening problem, and these are traditionally a very hairy mathematical challenge. Weyl and Tirole use a technique they call isorewards which is rather technical but which has some nice analogues to classic results in production theory. They show this technique is valid under fairly robust assumptions. The isoreward method gives the following result: if the government has a lot of uncertainty about the social value of “tail” innovations (the “genius” innovations), and if the supply elasticity of innovations is relatively high, then transfers to the inventor will be low and optimal price of the new good is close to the price under patents. If the reverse holds (not exactly, but in some sense), transfers to inventors are high and price is close to marginal cost.
The logic above has applications beyond patent policy. Consider a platform owner, like Apple. When should it enforce a uniform price, paying lump transfers to creators, and when should it let creators choose their own prices? The first is iTunes and the second is the iPhone app store. Weyl and Tirole’s model suggests that in the app store, most apps are written specifically for the store (high supply elasticity) and tail apps unforeseen by Apple are particularly important (how could they have predicted Shazam, for instance); therefore, app creators are allowed wide latitude in pricing. On the other hand, music is created regardless of iTunes policies (low supply elasticity) and it is easy for Apple to know which songs will be popular, as it’s hard to imagine songs that are blockbusters on Apple yet do not sell well in record stores. Therefore, a prize-like system for content creators is best. I find this type of logic quite compelling.
This paper is very long, and quite technical, so clearly I’m leaving out a lot of the details. My only major worry is the modeling assumption that inventions are independent. In particular, it just seems strange to call an invention a “genius” invention if it creates a lot of social value. I would call an invention a “genius” invention if it creates a lot of social value, and if it can only be created by a handful of people (or one person!) in the world. Complementary inventions are equally problematic (and given spillovers plus the “technology ladder”, what isn’t a complementary invention?). There is some brief discussion about how these problems might be dealt with, but surely this problem is the biggest open question remaining.
http://www.people.fas.harvard.edu/~weyl/MGMP_JMP.pdf (Working Paper. Glen’s research website is great, by the way. All of the papers have presentation slides, code, brief notes about the paper, etc. It’s 2010, not 1990: this is what research sites should look like today.)
[…] começo pela metade, discutindo o paper de Wyeil e Tirole (2010) que o A fine Theorem resenhou. Como a resenha tá lá e ele tem mais competência técnica que eu, dê um pulo lá para entender […]