There is idea behind that, but continuous is not enough.
The variable is all transfers, taxes and benefits T = [all taxes - all benefits] as function of income per person (including children). T starts negative (benefits are negative taxes).
Goal: monotonously increasing effective marginal T rate.
This. No need for continuity in the derivative - the marginal tax rate should be fine to jump around - but should start low (I'm fine with negative) and increase as you earn more. Like US federal tax brackets, but with benefits also considered.
Continuously differentiable is fine with jumps in that derivative.
I agree in principle. And I also suggest that we should probably only have one bureaucracy that does means testing that can then administer both taxes and benefits. No need to duplicate the effort.
However most benefits and taxes aren't just means tested against income, but a myriad of other conditions. So net transfers aren't just a function of income.
The variable is all transfers, taxes and benefits T = [all taxes - all benefits] as function of income per person (including children). T starts negative (benefits are negative taxes).
Goal: monotonously increasing effective marginal T rate.