>Are the rest of us on variable incomes which we can scale up and down at will?

Are you on an income which is, by law, tied to changes in the Consumer Price Index? That's how Social Security works. From the 2016 benefit letters:

"The law does not permit an increase in benefits when there is no increase in the cost of living. So your benefit will stay the same in 2016. There was no increase in the cost of living during the past year based on the Consumer Price Index (CPI) published by the Department of Labor."

So maybe "pegged", as in "pegged to an index", would have been a better idiom, but we're probably stuck with "fixed".