The paper looks at the acceleration of technological progress (the rate at which the speed of progress changes with time), with the basic (and plausible) model given in Eq. 1. Progress is sped by terms that do not depend on the amount of existing technical knowledge (like the existence of grants) and by terms that do (innovation begets more innovation). And progress is slowed by "friction" and "drag" terms (as innovation goes faster, more hurdles will slow it down, perhaps including other patents). The clearest payoff from this model is the observation that "even under a relatively simple model for innovation dynamics, there is no single 'natural' trajectory for innovative progress. Thus, it appears wrong to assume that technological progress naturally proceeds exponentially, linearly, or according to some other simple general form with time." For example, Section IV.B looks at data on the growth of patent counts (which is a problematic measure of innovation, but probably the best available for these purposes). From the log-log plot in Figure 13, Golden concludes that the number of utility patents is "better modeled as having power-law, rather than exponential, time-dependence." While calling this a nice power law would have been a stretch, it is certainly true that it is closer to a power law than an exponential.
What are the implications of this model for patent policy? Golden notes that the relevant measure for patent policy is the ratio of the change between different coefficients in the model, which he calls "dynamic-elasticity" or "double-ratio" tests. He describes the impact of these tests on different industries:
[I]n industries such as the pharmaceutical industry, where regulation and safety concerns help generate large innovative drag that exists independently of the details of patent law, comparatively stronger or broader patent protection might speed progress even if such increased protection imposes substantial costs on follow-on innovators. . . . On the other hand, if a technology (such as software) would be characterized, in the absence of patents, by both strong incentives for innovation and relatively low costs for follow-on innovation, the analysis might be reversed.More generally, he also explains why double-ratio tests help justify both the "abstract ideas" and "natural phenomena" exclusions from patentable subject matter. Some patent theorists might respond, "So what? We knew all that." But even confirming settled patent law understandings in a new way seems valuable, and I can imagine follow-up papers that build on this idea. Besides, I just think it is fun to see a law review article with derivatives (the non-finance kind), exponentials, and power laws. Not many Bluebook rules for those!
*The other physics Ph.D. law professors I know of are Oskar Liivak (Cornell), David Friedman (Santa Clara), and Katherine Strandburg (NYU). Am I missing anyone?