I don't work in the industry, so take my words with the appropriate salting.
With that said, typically it's seen as acceptable to ask for *some* work to be done prior to hiring, with the knowledge that it shouldn't be too arduous for the applicant and can't be used by the company as anything other than a test.
I'd guess that 2,000 words could be written in 1-4 hours by most writers. So that isn't *too* involved, although your speed and tolerance for doing this kind of task is something only you know. It might also help to get in writing that this project will only be a sample and can't be used by the company without providing you with compensation. (My guess is that a 2K sample couldn't be used for much, but it might provide some peace of mind.)
As far as rates go, $0.08 is currently the SFWA pro rate. (This would make for an hourly rate of $80/hr if you're writing 1,000 words per hour, which is pretty darned good. Of course, SFWA assumes you're writing and submitting stories to magazines that only pay if they *choose* to accept your stories...and pretty much all magazines have a sub 1% acceptance rate...so your actual $/hr will almost certainly be unlivable if you try to make a living writing short spec fic stories.)
As to what you'll request, I'd argue a lot depends on your own wants/needs. (e.g. if you're just doing this for fun, a low rate per word is probably fine. But if you're hoping to earn a living, you'll need to calculate how much time this will take vs. other things that might keep you afloat, how much it would take to survive, add in payroll taxes, etc.)