Welfare is increasingly not a goodwill measure, but a necessity. As time goes on, more and more people will not be able to hold jobs, short of some insane protectionist measures.
I could go on about how automation will eventually pave the way to socialism but that's a long ways off so I won't.
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The GMI would seem like a welfare trap, because you get taxed on the money you'll collect from your job. Unless you get taxed on the GMI anyway, in which case, there is no trap - you'll pay the same tax rate.
Most people will always choose work over a free lunch; many poor people refuse benefits entirely out of principle. The only real issue is where work income is lower than benefits you could get just by being unemployed. A negative income tax solves that issue.
Rather than complicate the system with progressive income taxes, instead, have progressive inheritance taxes. Even so, the allowance can be very generous, allowing quite a bit of money to be amassed over the generations. I could get by on 1,000,000 inherited dollars easily.
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I've proposed an NIT before that gives 10,000 dollars annually per person. 312 million * 10,000 = 3.12 trillion doled out every year. Everything over that is taxed at a flat rate of 20%. So a three-person family brings home 30 K a year, tax free.
The US GDP is 14-16 trillion; let's go with the conservative estimate. 14 - 3 = 11. 11 * 0.20 = 2.2.
2.2 trillion to run the government on. Now, we ran on 3.5 trillion in 2010. Some cuts are necessary, of course. You can play with the rate a bit, though. I do know 25% will squeeze some middle incomes.
Assuming one's single:
Income - Current System - New System
10,000 - 1,075 - 0
20,000 - 2575 - 2000
25,000 - 3325 - 3000
30,000 - 4075 - 4000
35,000 - 4875 - 5000
40,000 - 6125 - 6000
Just about everyone's taxes go down under this system; the only ones who really would lose money are those making ~35K and single. But, rich and poor alike benefit otherwise, and for those in the middle, all they need to do is start a family.