When applying for US NSF grants as a PI, does it help my case to discuss how little funding I've had?
To give some background: I am a new-ish faculty member; so far in my career I've received 1/2 of a rather small NSF grant (shared with a co-PI), which didn't even come close to covering the actual cost of a PhD student. On this shoestring budget I've been able to produce a bunch of good work, but in ways that are not sustainable as a long-term funding strategy (getting financial help from senior colleagues, begging my department to let me use startup funds past the original deadline, sending students away for internships so that I don't have to pay for them some semesters, etc.).
Question 1: When applying for new grants, will the NSF panelists consider my productivity relative to my budget? Or do they only care about productivity full stop? If the former, how do I effectively convey this lack of funds in my proposal?
Confounding the situation is that I am at a very highly ranked place in my field. In past talks with programme managers at the NSF, I have heard the message, "we try to spread the funds around and not give it all to people at rich institutions like yours." The problem is that I'm not rich, and if my university has money, I'm certainly not seeing it. Ergo, my impetus to ask this question: how do I convey to the NSF panel that I'm actually pretty "poor"?
Another confounding factor is that students at my institution far more expensive than the national (US) average: I have to ask the NSF for about USD $92k/year for each PhD student I want to fund, whereas I have colleagues at other places who pay about half as much. So even the small amount of money I do get from the NSF doesn't stretch very far. I don't get the sense everyone on the NSF panels realises how big this discrepancy can be: for instance, after receiving the grant above (which covered <1 student) I asked my PM about submitting another proposal; the response was along the lines of, "Why don't you just have fun and enjoy doing research on your current grant?" Which leads to my second question:
Question 2: In my proposals, should I address the fact that PhD students are particularly expensive at my institution? Or will this just turn off panelists who think I am "too expensive?"
To put all of this another way: I once had a vagabond friend who told me, "if you want to beg for money in the rain, you should hide your umbrella." Should I be making it clear that I don't even have an umbrella?