A major source of welfare loss, which for some reason economists are only beginning to grapple with, is the uniformity of knowledge goods protection (a term I prefer to intellectual property, the etymology of which is basically that content industries thought, correctly, that calling their work “property” would make lawmakers more willing to increase protection; it is not a neutral term). Acemoglu and Akcigit consider allowing protection to vary depending on how far “ahead” a leader is in a quality ladder sense. They model industries with two firms in Bertrand competition such that the technology leader produces at the cheapest price (and hence sells all of the product), and solve for steady state Markov perfect equilibria (MPE means that collusion is not allowed). Naively, one might assume that less protection should be given to firms with a big lead to incentivize them not to rest on their laurels, and so that the markup can be reduces by a higher frequency of times where both firms have the same technology (hence act as in perfect competition due to the Bertrand assumption). The opposite turns out to be true. More protection the greater the lead incentivizes leaders to invest in R&D to maintain a large lead, and incentivizes followers to invest not only so that they can become the leader, but also because the return to being the leader is now higher. The results hold if compulsory licensing is introduced, and if firms are allowed to choose from “frontier” or “catchup” technology.
I am skeptical of some of the results here; in particular, the numerical results strike me as worthless. For instance, what does it mean to say that growth rises from 1.86 to 2.04 percent under state dependent protection? That is the result of a two firm model, where all innovation is quality ladder innovation, where the only source of protection is patents, where firms compete in Bertrand, and where there is only one country. What would be the result of a shift to state dependent protection in the real world? Who knows, but clearly not .18 percent. For that reason, I don’t understand the point of including such false precision in a theoretical model; the comparative statics are enough. That said, as usual for an Acemoglu model, there is a neat trick here which makes these types of patent problems tractable: assume patents expire with some probability distribution, rather than in T periods. This is not the first paper to use this trick, I believe, but it is a nice one for the toolbox.
A Fine Theorem 