In this post, I exhibit the progressive income tax visualisation tool I’ve published as a Shiny App.
Just Show the Thing
Without ado, here it is:
Waxing Poetic
I still remember the aha-moment when I finally took the time to understand progressive tax schemes. My prior assumption, like many others’, was that a single tax rate was applied to the total income, depending on which bracket contained the total income. This assumption leads to incorrect inferences about disincentivisation of hard work and striving for higher income.
If a promotion were to bump someone’s income up into the next bracket, would they end up taking home less income due to the higher tax rate? No! That would be ridiculous, and if true, would lead me to believe my government was incompetent.
In fact, progressive income tax is quite a reasonable solution to the trade-offs between different framings of fairness in taxation. It seems to me that its main weakness lies in its bracketed (discontinuous) nature, which makes it more difficult both to understand and compute than a continuous taxation function.
Continuous Progressive Taxation
Proponents of bracketed progressive taxation point to its ease of calculation. Simply apply the relevant percentage to the relevant income bracket, sum everything up, and hey presto! Total liability! So easy it can be done by hand (ideally with a calculator).
It seems just as easy and even more simple to do this with a continuous tax rate function. Simply apply the function to the total income and hey presto! Total liability! So easy it can be done by hand (ideally with a calculator).
A simple quadratic function would do the job, and be much more easily interpreted.
\[y = ax^2 + bx + c\]The intercept \(c\) is the minimum tax liability (this can be negative!), with one coefficient \(b\) for the “flat” tax rate, and one coefficient \(a\) for the smooth increase of tax rate as income increases.
Recognising that a “simplifying” change to tax codes is not at all likely to come about via random blog posts by average Joes, I won’t expound further. If you’d like me to, have any clarifying questions, or want to have a riveting chat about tax formulations, just send me a message!