# Tax-Free Tax System

If the money paid towards tax are untaxable, then should the system be so for the tax itself? Suppose we want to tax a person with income $A$ and nominal tax rate $R$. The tax amount is then

$RA(1-p)=pA$

Where $p$ is some unknown proportion of $A$ to be paid into taxes this year. Aka effective tax rate.

$R-Rp=p$

$R/(1+R) = p$

A 30% nominal tax rate resolved to effective rate of 23.1% of income in this system.

So to set an effective rate using nominal setting under the system, one would solve for R.

$R = p/(1-p)$

Say some bracket should have effective rate of 30% the rate on taxable income, under this system, would require that nominal tax be set to 42.8%.

However you massage dung, it’s still money you have to pay. But the system should be self consistent. We should not have to pay taxes on money we spent on paying taxes during the year we earn and use that money to pay taxes.