It is a little bit worse than this in many cases actually, you pay tax on your earnings AND you have to cover the costs of getting to and from work and things like childcare while you are at work.

That being said, my experience is that among the poor there are very few that are not interested in working but I know of at least one person who did pull out of the workforce after finding that they were further behind with a job. Make of it what you will, I think it is a condemnation of low-skill labor rates, not of the welfare state.

It's not that hard to figure out - you just set a tax-free threshold of at least the amount of the minimum income. Minmimum income is $10k? Then the first $10k of any private income is tax-free.

To entice people to work, you'd probably do it so that it takes a bit more than a dollar of private income to remove one dollar of minimum income, so that you're always better off if you work, and if you properly set up your tax rates, there will never be a point where you are a cent worse off for earning an extra dollar.

This idea that the 'first $x is non-taxable' doesn't generally influence the withholding policies - you can change deductions, etc, but rarely - especially at low-paying jobs - does anyone ever give you actual useful direction on how to manage withholding values. But... telling someone that the first $10k is non-taxable, and they might get a refund 9 months from now - doesn't really help all that much in the day to day world of living expenses.

You still might face very high effective marginal tax rates, though, even if below 100%: instead of an hour of work costing you money, an hour of work might effectively be worth $2.00. Still a huge disincentive.

That's really hard to avoid when you do have conditional benefits that phase out with higher income. To "properly set up your tax rates" amounts to not having conditional benefits, which is a basic income under another name.