Actually, People making less than $50,000 pay plenty in social security tax. Aprox 13%. They should be exempt from federal income tax. Otherwise they have little chance of upward mobility. They can’t save and invest.
The goal should be to make poor people middle class,
AND
make middle class upper middle class
AND
make upper middle class richer class.
That way more taxes will come into Treasury, and have a chance to pay the huge national debt.
Households with an adjusted gross income (AGI) less than $50,000 comprised about 80% of all US households in 2012. So, I think your threshold is a little high.
If you were to choose $36,000 as your threshold instead, that was about the median household income in 2012. So, 50% of households had less, 50% of households had more.
If you look at the group with less than $36,000/year, their average individual income tax rate was 3.28% in 2012. So, they were very close to zero. The next 10% (50th to 60th percentile) paid as much income tax as the entire bottom 50%, despite earning only half as much total AGI.