In Germany, the political party FDP is pushing a new tax scheme now, the so-called „Bierdeckel-Steuer“. The name was coined to indicate that everyone could compute its tax on a beer coaster. I fear that most Germans including those politicians would fail nevertheless.

The idea is to introduce steps with simple percentages. The Heidelberg professor Kirchhof once proposed one single step, later Friedrich Merz took three, and now the FDP wants six. The previous proposals included a radical cut in possible individual tax reductions. But such radical ideas are no longer talked about today, no wonder in the current times. Instead, the proposal talks about lump sums with dubious fairness and results. But that is not my topic here.

The newspapers explain the proposed tax system in the following way: From 8005€ to 12500€ yearly income, you pay 14%, from 12500€ to 35000€ you pay 25%, from 35000€ to 53000€ you pay 35%, from 53000€ to 250000€ you pay 42%, and with even higher income you pay 45%. Some newspapers report this more correctly stating that you have to pay 14% for any income exceeding 8005€, 25% for any income exceeding 12500€ etc. But most describe the system with wrong words, and wrong graphics too. The magazine Focus e.g. speaks of a „Steuersatz“ (tax rate) of 42%, but really means the „Grenzsteuersatz“, which is the derivative of the tax rate. Since the current tax system uses the same 42%, the impression is generated that there is no reduction for high incomes. In fact, the reductions in the lower incomes do also affect the high incomes, albeit not in a progressive way.

You see the comparison between the old and the new system. The reduction is increasing with the income, and reaches about 1600€ at some point, where it stops increasing. Of course, the derivative of these curves look different.

As you see, all they do is to approximate the current smooth derivative with a step function. OK, it is easier. But is it worth the fuzz?

All that remains is that you can now compute more easily how much the tax takes from each additional Euro. But the main problems remain. E.g., it is still unfair to take only a specified rate for incomes of financial investments.

By the way, these computations have been done using my program Euler. See the details on this page (in German).