16th June 2020

Gunnar Uldall's 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. Tariff current vs Uldall up 50 kEUR

Now up to 280 kEUR. Tariff current vs Uldall

Julia code is tariff.jl.