The exact formula is secret, although if you keep track of what actions you take and how much you are paid then you should be able to figure out what actions are worth the most and taking those kinds of actions even when they might not be necessary. For example sending a PM to someone in relation to a moderation (e.g. being from a moderator as a moderator) likely causes that moderator action to be "worth" more or is separately worth something in itself. One of my alts once had one of it's posts deleted when I replied to a post of Bruno about something that grue claimed was off topic, this was far from a trend and was probably unnecessary to receive a PM about it, however I got a PM around the time the post was deleted saying that my post was deleted because it was a reply to an off topic post.
I would think that the payment is not based on responsibilities, but rather by actions taken. It is just that a higher ranking staff member would have more opportunities to take additional actions, and potentially more valuable actions.
Except it's not really possible as I explained above. I handle too many reports to count and I'm sure I could probably handle much less but still get paid the same seeing as I more or less get the same every month (or didn't get any more after I got promoted so clearly there is a limit or threshold based on staff rank and I'm hitting it). Very active patrollers or mods of local boards like me and Eal got pretty much exactly the same but even after I got made mod of the entire Marketplace and Bitcoin Discussion and my workload must have at least doubled but yet we still get paid pretty much the same.
You could automate the counting of actions taken in a number of ways. That wouldn't be very hard because a good number of moderator functions require you to visit a page within the forum that has a special URL so you could just develop a bot to count each time you visit a webpage that has '?action=deletemsg" in the URL for deleting posts.
It is possible that payment is capped on an action basis. So for example you can only earn a max of "x" for deleting posts, a may of "y" for moving threads, ect. So if you are unable to take additional actions that you were not previously able to do (I don't think going from patroller to moderator of certain sections allows you to take additional actions) then your max payment would remain the same (assuming that payments are in fact capped in some way). I do think that moderators of various sections should probably receive an additional payment for the added responsibility.