To determine the optimal allocation of funding among investigators in order to maximize "bang for the buck", a funding agency would need to know how the impact of each investigator varies with their funding. Contrary to the authors' assumption, different investigators probably have different impact-funding relationships (e.g., because some are better scientists than others, able to produce more impact for any given funding level). Even if the impact-funding relationship is decelerating for every individual investigator (which it surely is, because as you get more funding other impact-limiting factors kick in), and decelerating overall, it's not necessarily the case that reallocating funding away from more highly-funded investigators towards others would increase overall impact. That might be true, or it might not be--it's an empirical question. Unfortunately, I'm not sure how one would get good data on the shape of the impact-funding curves for individual investigators.

For further discussion of this point, see here: http://dynamicecology.wor...