How economically efficient is the grant system?
I know of one such study: Cost of the NSERC Science Grant Peer Review System Exceeds the Cost of Giving Every Qualified Researcher a Baseline Grant.

The authors examine the full costs of the process used by the Natural Sciences and Engineering Research Council of Canada (NSERC) and conclude that it would be more efficient to simply give a base amount to every researcher who meets the requirements to submit a proposal. The costs they consider include the time spent preparing and peer-reviewing grant proposals. In addition, the authors argue that the current system is ineffective, in that it rewards mediocrity and safe bets over curiosity and innovation.

The same journal later published a rebuttal (The Real Cost of the NSERC Peer Review is Less than 5% of a Proposed Baseline Grant) and a reply to the rebuttal (Indeed: Cost of the NSERC Science Grant Peer Review System Exceeds the Cost of Giving Every Qualified Researcher a Baseline Grant).