[JackdawX]

What you've just calculated there is the cost of giving everyone, including middle class and rich people, a $20k tax break. Obviously this wouldn't work, as the amount of tax in and out of the system needs to be the same. The easiest method or distribution to understand is negative income tax:

https://en.wikipedia.org/wiki/Negative_income_tax

https://www.youtube.com/watch?v=xtpgkX588nM

Would it work in real life? Dunno. Lets see what the outcome of the various tests are. The key question isn't the maths actually, but whether people will choose to work enough to support the system.