, 2 min read

Gunnar Uldall's Tax Tariff

Original post is here eklausmeier.goip.de/blog/2020/06-16-gunnar-uldalls-tax-tariff.


Gunnar Uldall wrote a a book with title "Die Steuerwende" in 1996.

1. Proposal. In this book he proposed the following tariff, $x$ is in DEM.

$$ t_u(x) = \begin{cases} 0 & \mbox{if } x\le12000 \\ 0.08\left(x-12000\right) & \mbox{if } 12001\le x\le20000 \\ 0.18\left(x-20000\right)+640 & \mbox{if } 20001\le x\le30000 \\ 0.28\left(x-30000\right)+2440 & \mbox{if } x\ge30001 \end{cases} $$

Of course, Gunnar Uldall opposed to add any solidary extra tax. Unfortunately, his proposal did not make it into law, although his proposal was well received in the public.

Gunnar Uldall makes a short historic reference to von Miquel's tariff. The tariff from 1891 with $x$ is in Goldmark is given below.

$$ t_m(x) = \begin{cases} 0 & \mbox{if } x\leq900 \\ 6 & \mbox{if } 900\lt x\leq1050 \\ 9 & \mbox{if } 1050\lt x\leq1200 \\ 12 & \mbox{if } 1200\lt x\leq1350 \\ 16 & \mbox{if } 1350\lt x\leq1500 \\ 21 & \mbox{if } 1500\lt x\leq1650 \\ 26 & \mbox{if } 1650\lt x\leq1800 \\ 31 & \mbox{if } 1800\lt x\leq2100 \\ 36 & \mbox{if } 2100\lt x\leq2400 \\ 44 & \mbox{if } 2400\lt x\leq2700 \\ 52 & \mbox{if } 2700\lt x\leq3000 \\ 60 & \mbox{if } 3000\lt x\leq3300 \\ 70 & \mbox{if } 3300\lt x\leq3600 \\ 80 & \mbox{if } 3600\lt x\leq3900 \\ 92 & \mbox{if } 3900\lt x\leq4200 \\ 104 & \mbox{if } 4200\lt x\leq4500 \\ 118 & \mbox{if } 4500\lt x\leq5000 \\ 132 & \mbox{if } 5000\lt x\leq5500 \\ 146 & \mbox{if } 5500\lt x\leq6000 \\ 160 & \mbox{if } 6000\lt x\leq6500 \\ 176 & \mbox{if } 6500\lt x\leq7000 \\ 192 & \mbox{if } 7000\lt x\leq7500 \\ 212 & \mbox{if } 7500\lt x\leq8000 \\ 232 & \mbox{if } 8000\lt x\leq8500 \\ 252 & \mbox{if } 8500\lt x\leq9000 \\ 276 & \mbox{if } 9000\lt x\leq9500 \\ 30\lfloor (x-10500)/1000\rfloor + 330 & \mbox{if } 9500\lt x\leq30500 \\ 80\lfloor (x-32000)/1500\rfloor + 1040 & \mbox{if } 30500\lt x\leq32000 \\ 80\lfloor (x-32000)/2000\rfloor + 1040 & \mbox{if } 32000\lt x\leq78000 \\ 100\lfloor (x-78000)/2000\rfloor + 2900 & \mbox{if } 78000\lt x\leq100000 \\ 0.04\lfloor x/5000\rfloor\cdot5000 & \mbox{if } x\gt 100000 \\ \end{cases} $$

By design this tariff has discontinuities. The first fixed values cannot easily be fitted with a linear, quadratic or cubic polynomial.

As can be seen by this tariff, it starts with a rate of less than one promille. Then slowly increases to at most four percent.

2. Current situation. The current tax tariff for $x$ in EUR as of 2020 is

$$ t_c(x) = \begin{cases} 0 & \mbox{if } x\le 9408 \\ \left(972.87{\lfloor x\rfloor-9408\over10000} + 1400\right){\lfloor x\rfloor-9408\over10000} & \mbox{if } 9409\le x\le 14532 \\ \left(212.02{\lfloor x\rfloor-14532\over10000} + 2397\right){\lfloor x\rfloor-14532\over10000} + 972.79 & \mbox{if } 14533\le x\le 57051 \\ 0.42\lfloor x\rfloor - 8963.74 & \mbox{if } 57052\le x\le270500 \\ 0.45\lfloor x\rfloor - 17078.74 & \mbox{if } x\ge270501 \end{cases} $$

Final tariff is then

$$ \mbox{Taxes} = \lfloor t_c(x)\rfloor $$

Add to this 5.5% solidarity extra tariff.

Graphical comparison of the two tariffs. First for amounts up to 50 kEUR. Photo

Now up to 280 kEUR. Photo

Julia code is tariff.jl.