Assume utility is logarithmic in income, and the goal is to set the experienced tax burden to be constant.
Then, we have the formula that the average tax rate, where a is a parameter controlling the experienced tax burden and z is the break-even point, is as follows:
f(x)=1−(xz)a−1
x is the input income, and f(x) is the average tax rate.
Pseudo-flat tax formula:
Assume utility is logarithmic in income, and the goal is to set the experienced tax burden to be constant.
Then, we have the formula that the average tax rate, where a is a parameter controlling the experienced tax burden and z is the break-even point, is as follows:
f(x)=1−(xz)a−1x is the input income, and f(x) is the average tax rate.
Fans of math exercises related to toy models of taxation might enjoy this old post of mine.
What is x and why isn’t it cancelling?
x is the initial income, and I forgot to cancel it. Good point.
Turns out, it’s far simpler than I had it as.
Can a eat that −1?
It could do, but a represents the amount of utility remaining.
Maybe the more natural thing would be to have a be the effective tax rate, and have it be (z/x)^a.