Gunnar Uldall's Tax Tariff

This post was automatically copied from Gunnar Uldall's Tax Tariff on eklausmeier.goip.de.

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. $$ t_m(x) = \begin{cases} 0 & \mbox{if } x\leq900 \\ 6 & \mbox{if } 900100000 \\ \end{cases} $$ 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.

Now up to 280 kEUR.

Julia code is tariff.jl.