Disclaimer: I'm on this forum because I was doing research for a class I am teaching on CG lighting and ran across this topic. I am not a cinematographer. Before I started teaching, I worked as a CG lighter, VFX artist, and art director. The question is generic for professional freelancers though and I have plenty of experience doing that and in hiring for freelance and permanent positions.
My favorite way of dealing with this question is to ask for a "fair rate relative to the project" with the proviso that if I later decide it wasn't fair, then I'll be busy the next time I'm called by that client. If the "fair rate" requires mortgaging my house to survive while I do the job (because it takes six months, I have to bring my own gear, etc), then it is not acceptable regardless if it is fair. Bottom line is that the career is more important than the money on any one job. If you are working, you (potentially) have something to add to your reel and credits and you'll get something to tide you over while you wait for the bigger jobs you really want to do. An honest producer will give a fair rate proportionate to the means of the project. A dishonest producer won't, but hopefully you can spot these guys a mile away and refuse to work for them. I knew a writer who wasted five years of career time involved in a lawsuit over payment. He won the lawsuit and got the money he would have earned during that period if he had been working, but because of the lawsuit he wasn't working. This means that for five years of painful effort, he got five years' wages (minus legal fees), a lot of heartburn, and nothing for his resume. For people starting out, low rates are less a concern than the importance of working. After you get more established, the rates become more important. Even then, they should never become the only reason for saying yes to a job. I know one guy who was offered $50k or 5% of a project. He took the $50k and regretted it because the 5% turned out to be worth millions (which was paid to others who agreed to that payment formulation).
I've been stiffed on fees before, but it is very rare, and I've done free work that got me other jobs. I've taken low rates and very high rates. Overall, I have always been most satisfied with the jobs where I was not the highest paid guy in the room, but not the lowest either.
FWIW,
AP