How economically efficient is the grant system? I wonder if someone (or eventually some country, organisation, etc ...) already evaluated the costs of the system of grants. 


It costs at least the salary of the researcher who writes and gets the grant
but also the salary of all the researchers who didn’t get it, and could have done something else than writing a proposal
plus the costs in administration (e.g. the National Contact Point(s) in Europe at several places in each country)
plus the cost of organising the referral (travels, meetings, ...)
plus the cost of the grant itself, of course.


On the positive side, of course the entire society benefits from a completed grant.

So my questions are:


Are there some studies about the economical efficiency of the grant system?
What are their conclusions?
How much does the granting costs?
Are there other system evaluated?


Partially related questions : 


How much time do researchers spend on writing grants?
How to quantify the loss in productivity due to time spent on writing proposals


but this question is really about the economy of research and factual investigations about the system of grants, not about feeling from researchers.
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).