Your first $40k may be taxed at 10% and your next $20k may be taxed at 15% or whatever, but you are not "in a tax bracket".
The idea of being "in" a tax bracket gave rise to the dumb idea that making more money can net you less after taxes, which is virtually never the case.
Your welfare example has nothing to do with taxes. Welfare benefits are set by gross income level with some COL and other local adjustments. Your tax status is irrelevant.
People in the USA forget that we have TWO tax systems.
One is the regular tax system that everyone knows and loves to hate.
The other is the closest thing we have to a "flat tax" and it's called AMT. It has different rules and different rates.
When you do taxes, you compute your tax liability using BOTH systems and you pay the HIGHER amount. That's how it works.
I pay AMT and it sucks.
The IRS even reduces your taxes if you lose money in the stock market, if your business property depreciates, and so forth. I like to refer to those cases as "the government paying you to be a loser." Just another case where doing better means you do worse.
Let's not even try to pretend this is a fair or well-designed system. Even Warren Buffet, surely one of the greatest beneficiaries of the system, has spoken out against it.
"So now you owe an extra 10% on your $40K salary which is $4K. And you also owe 35% on that $50k which is around $18K."
Based on the numbers, this is clearly a misunderstanding of how tax brackets work, and not anything to do with the AMT.