- commit
- 7a6c12d77196964392fd5e8129081ce7ad3f3c49
- parent
- e0c381f950f282144c8b7537211a0b15ee3b38e5
- Author
- Tobias Bengfort <tobias.bengfort@posteo.de>
- Date
- 2025-05-24 18:10
tweak tax curves
Diffstat
M | _content/posts/2025-05-16-tax-curves/index.md | 24 | +++++++++++++++--------- |
1 files changed, 15 insertions, 9 deletions
diff --git a/_content/posts/2025-05-16-tax-curves/index.md b/_content/posts/2025-05-16-tax-curves/index.md
@@ -16,7 +16,10 @@ We will look at functions where $x$ is the income before taxes and $f(x)$ is 16 16 the income after taxes. 17 17 18 18 I am a big fan of folding some form of social security into the tax system, so19 -1 $f(0) = b$ will be the level of basic income everyone should have.-1 19 $f(0) = b$ will be the level of basic income everyone should have. This would -1 20 of course not replace other mechanisms of social redistribution. It would just -1 21 provide a baseline. I find it weird that we use one system above a certain -1 22 income and a completely different one below that. 20 23 21 24 All functions will have a single additional parameter $a$ that can be used to 22 25 adjust the system to the current economic situation, basically raising or @@ -30,6 +33,11 @@ $f(x) = ax+b$ 30 33 31 34  32 35 -1 36 The marginal tax rate is what you have to pay on any additional income you -1 37 make. In mathematical terms, it is $1 - f'(x)$. The average tax rate, on the -1 38 other hand, is the total fraction of your income that you have to pay, i.e. $1 -1 39 - f(x) / x$. -1 40 33 41 With this system, the marginal tax rate is constant, but the average tax rate 34 42 starts out [negative](https://en.wikipedia.org/wiki/Negative_income_tax) and 35 43 then quickly grows towards the marginal tax rate. @@ -37,19 +45,17 @@ then quickly grows towards the marginal tax rate. 37 45 ## Logarithmic 38 46 39 47 Most real-world economies have progressive tax rates. That means: the higher40 -1 your income, the higher your marginal tax rate. The classic mathematical41 -1 function that grows to infinity but slows down while doing so is the logarithm:-1 48 your income, the higher your marginal tax rate. Or: your income after tax still -1 49 grows, but it grows slower. The classic mathematical function that grows to -1 50 infinity but slows down while doing so is the logarithm: 42 51 43 52 $f(x) = a \ln(\frac{x}{a} + 1) + b$ 44 53 45 54  46 5547 -1 Now the marginal tax rate starts at 0% and grows towards 100%.48 -149 -1 The marginal tax rate is what you have to pay on any additional income you50 -1 make. The common believe is that a high marginal tax rate will disincentivize51 -1 people from earning more (= being more productive). That is why I wanted to52 -1 start with 0%.-1 56 Now the marginal tax rate starts at 0% and grows towards 100%. The common -1 57 believe is that a high marginal tax rate will disincentivize people from -1 58 earning more (= being more productive). That is why I wanted to start with 0%. 53 59 54 60 On the other end of the spectrum, I don't see any reason to stop the 55 61 progression at some arbitrary value. If a single person has some astronomical