16th June 2020, 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 & if x \leq 12000 \\ 0.08 (x - 12000) & if 12001 \leq x \leq 20000 \\ 0.18 (x - 20000) + 640 & if 20001 \leq x \leq 30000 \\ 0.28 (x - 30000) + 2440 & if x \geq 30001 \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 & if x \leq 900 \\ 6 & if 900 < x \leq 1050 \\ 9 & if 1050 < x \leq 1200 \\ 12 & if 1200 < x \leq 1350 \\ 16 & if 1350 < x \leq 1500 \\ 21 & if 1500 < x \leq 1650 \\ 26 & if 1650 < x \leq 1800 \\ 31 & if 1800 < x \leq 2100 \\ 36 & if 2100 < x \leq 2400 \\ 44 & if 2400 < x \leq 2700 \\ 52 & if 2700 < x \leq 3000 \\ 60 & if 3000 < x \leq 3300 \\ 70 & if 3300 < x \leq 3600 \\ 80 & if 3600 < x \leq 3900 \\ 92 & if 3900 < x \leq 4200 \\ 104 & if 4200 < x \leq 4500 \\ 118 & if 4500 < x \leq 5000 \\ 132 & if 5000 < x \leq 5500 \\ 146 & if 5500 < x \leq 6000 \\ 160 & if 6000 < x \leq 6500 \\ 176 & if 6500 < x \leq 7000 \\ 192 & if 7000 < x \leq 7500 \\ 212 & if 7500 < x \leq 8000 \\ 232 & if 8000 < x \leq 8500 \\ 252 & if 8500 < x \leq 9000 \\ 276 & if 9000 < x \leq 9500 \\ 30 ⌊ (x - 10500) / 1000 ⌋ + 330 & if 9500 < x \leq 30500 \\ 80 ⌊ (x - 32000) / 1500 ⌋ + 1040 & if 30500 < x \leq 32000 \\ 80 ⌊ (x - 32000) / 2000 ⌋ + 1040 & if 32000 < x \leq 78000 \\ 100 ⌊ (x - 78000) / 2000 ⌋ + 2900 & if 78000 < x \leq 100000 \\ 0.04 ⌊ x / 5000 ⌋ \cdot 5000 & if x > 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 & if x \leq 9408 \\ (972.87 \frac{⌊ x ⌋ - 9408}{10000} + 1400) \frac{⌊ x ⌋ - 9408}{10000} & if 9409 \leq x \leq 14532 \\ (212.02 \frac{⌊ x ⌋ - 14532}{10000} + 2397) \frac{⌊ x ⌋ - 14532}{10000} + 972.79 & if 14533 \leq x \leq 57051 \\ 0.42 ⌊ x ⌋ - 8963.74 & if 57052 \leq x \leq 270500 \\ 0.45 ⌊ x ⌋ - 17078.74 & if x \geq 270501 \end{cases}

Final tariff is then

Taxes = ⌊ t_{c} (x) ⌋

Add to this 5.5% solidarity extra tariff.

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

Now up to 280 kEUR.

Julia code is tariff.jl.