{"id":5176,"date":"2013-01-10T13:34:52","date_gmt":"2013-01-10T11:34:52","guid":{"rendered":"http:\/\/www.randform.org\/blog\/?p=5176"},"modified":"2013-01-10T17:32:08","modified_gmt":"2013-01-10T15:32:08","slug":"german-tax-reloaded","status":"publish","type":"post","link":"https:\/\/www.randform.org\/blog\/?p=5176","title":{"rendered":"German TAX reloaded"},"content":{"rendered":"

Der deutsche Text in diesem Post ist nach dem Link:<\/p>\n

Read the rest of this entry \u00bb<\/p><\/blockquote>\n

<\/span><\/p>\n

As described in the last german TAX post<\/a> I was trying to get information about german income taxes, in particular I wanted to get the concrete formulas. I asked via fragdenstaat.org<\/a> at the Federal Agency for Civic Education<\/a> (Bundeszentrale f\u00fcr politische Bildung: BPB) for that information, since they have a webpage about income taxes. This page however cited only a little phrase, with the names of the different income zones before I wrote the letter, but luckily it got meanwhile at least a little revamped<\/a>. However the page still doesn’t show the formulas, moreover it is not very up-to-date. In addition the BPB was not only not able to help me with my request, but I was told that:<\/p>\n

” In Bezug auf weitere steuerrechtliche Ausk\u00fcnfte bitte ich Sie, von Anfragen bei der bpb Abstand zu nehmen, weil wir definitiv nicht daf\u00fcr zust\u00e4ndig sind.”<\/p><\/blockquote>\n

(translation without guarantee: with regard to further tax law requests I ask you to precind from sending further requests to BPB, because we are definitly not in charge for this.)<\/em><\/p>\n

I should maybe also mention that I asked a representative of the ministry of economics for the formulas, who said I should ask a tax consultant.
\nAs already said in the comment at fragdenstaat.de<\/a> I had then finally found formulas for the taxes 2010-2012 (after a long search). The formulas are on the site of the ministry for finance with the taxcalculator<\/a> and you can get the formulas if you type in any income, and then hit the button “BERECHNEN”. I couldnt however find the formulas for the original draft for the taxes for 2013 from February last year, neither the formulas for the new draft as of december 12 last year for the taxes for 2013. Mr. Liebig, who runs the website www.lohn-info.de<\/a> had however found them and had included the numbers on his site, so I wrote him an email and asked him for the links.
\nI have meanwhile got an answer from Mr. Liebig who had kindly send me the links via email.<\/p>\n

A document<\/a> which describes the taxes for the upcoming year, as of 121212 is at the website of the Bundesrat.<\/a><\/p>\n

A document which was the old draft for the 2013 taxes and which was intended to mitigate the impact of higher taxes due to BRACKET CREEP<\/a> is at
\nhttp:\/\/dip21.bundestag.de\/dip21\/btd\/17\/086\/1708683.pdf<\/a><\/p>\n

I meanwhile included the new numbers into the formulas. Details (in german) and the mathics code can be found after the click.<\/p>\n

The result in short: If I didn’t miscalculate then there are tax reductions of 8-24 Euros\/year for the incomes above 13500 Euros per year. For incomes of <\/span>8100 Euro to 13500 Euros there is a tax increase of about 15 Euros\/per year.<\/span> The procentual bracket creep (not sure wether this is called this way, please look at formulas) is for 6% income increase maximaly about 2.5%, for 2% income increase it is about 0.8%.<\/span><\/p>\n

<\/p>\n

Ich habe jetzt mal die neuen Zahlen angeguckt und eingegeben um u.a. genauer zu sehen wie sehr sich die kalte Progression bemerkbar macht. (Ich hoffe ich habe mich dabei nicht vertippt und habe die Zahlen extra nicht als Variable gesetzt, damit man Tippfehlerschneller sieht)<\/p>\n

Der mathics code ist unten man braucht in nur in die Maus pasten by www.mathics.net einpasten, shift-return dr\u00fccken und bekommt die Ergebnisse.<\/p>\n

Die prozentuale kalte Progression -hoffe das heisst so, was ich meine ist das hier:
\nfProgression[Einkommen_]:=(Steuer2013[Einkommen+Prozent*Einkommen]-Steuer2012[Einkommen])\/Einkommen<\/p>\n

ergibt bei einer Lohnerh\u00f6hung von 2% ungef\u00e4hr<\/em> 8 promille und
\nbei einer Lohnerh\u00f6hung von 6% ungef\u00e4hr 2,5 Prozent des Einkommens. <\/p>\n

Die genaue Kurve kann man sich mit dem Befehl<\/p>\n

Clear[Einkommen,Prozent]
\nProzent:=0.06
\nPlot[fProgression[x],{x, 10000, 100000}]<\/p>\n

anzeigen lassen (hier ist z.b. die prozentuale Progression bei einer Gerhaltserh\u00f6hung um 6% in den Grenzen von 10000 Euro Einkommen bis 100000 Euro Einkommen). Leider ist der mathics PLOT Befehl noch etwas kr\u00e4nkelnd.<\/p>\n

Bedenklicher als die kalte Progression fand ich allerdings, dass
\nSteuererh\u00f6hungen in der unteren Progresssionszone stattfanden.<\/p>\n

Das kann man durch den Befehl:<\/p>\n

Simplify[fUntProgZone2013[x]-fUntProgZone2012[x]]
\nSimplify[fUntProgZone2012Entwurf[x]-fUntProgZone2012[x]]
\nSimplify[fObProgZone2013[x]-fObProgZone2012[x]]
\nSimplify[fErstPropZone2013[x]-fErstPropZone2012[x]]<\/p>\n

feststellen. Das Ergebnis ist
\n15.1340205527999 – 0.00579944639999997 \u2062 Floor [ x ] + 2.15299999999999 \u00d7 10 -7 \u2062 Floor [ x ] 2.
\n– 8.86576383720001 – 1.47800000000001 \u00d7 10 -7 \u2062 Floor [ x ] 2. + 0.000104559600000016 \u2062 Floor [ x ]
\n– 24
\n– 24<\/p>\n

Das heisst in der unteren Progressionszone (Einkommen von ca 8100 Euro bis 13500) ergibt sich eine Einkommenssteuer die in 2013 ca. 15-16 Euro pro Jahr h\u00f6her ist als in 2012 f\u00fcr die weiteren Einkommenszonen eine Steuerersparnis von ca. 8 bzw ab einem Einkommen von ca. 54000 eine Ersparnis von 24 Euro<\/p>\n

Ich bitte alle hier die Zahlen und Rechnungen nochmal nachzupr\u00fcfen.<\/p>\n

Der Code ist frei verwendbar und weitergebbar unter Einf\u00fcgung des
\nCopyright Textes<\/p>\n

Die Anfertigung der Anfragen, des Programmierens etc. hat mehrere Tage Zeit in Anspruch genommen.<\/p>\n

————————-COPYRIGHT TEXT——–
\nCopyright (C) <2013 N. Kutz><\/p>\n

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and\/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:<\/p>\n

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.<\/p>\n

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
\n——————————————–<\/p>\n

Der untenstehende Code kann by mathics.net eingepastet
\nwerden:<\/p>\n

Clear[fNullZone2012, fUntProgZone2012, fObProgZone2012, fErstPropZone2012, fZweitPropZone2012,xvar2012,yvar2012,zvar2012]
\nClear[fNullZone2013, fUntProgZone2013, fObProgZone2013, fErstPropZone2013, fZweitPropZone2013,xvar2013,yvar2013,zvar2013, Steuer2012, Steuer2013]<\/p>\n

xvar2012[x_] := Floor[x]
\nyvar2012[x_] := 0.0001*(Floor[x]-8004)
\nzvar2012[x_] := 0.0001*(Floor[x]-13469)
\nfNullZone2012[x_] := 0
\nfUntProgZone2012[x_] := (912.17 * yvar2012[x] + 1400) * yvar2012[x]
\nfObProgZone2012[x_] := (228.74 * zvar2012[x] + 2397) * zvar2012[x] + 1038
\nfErstPropZone2012[x_] := 0.42 * xvar2012[x] – 8172
\nfZweitPropZone2012[x_] := 0.45 * xvar2012[x] – 15694
\nSteuer2012[x_]:= If[x<8005,fNullZone2012[x],If[x<13470,fUntProgZone2012[x], If[x<52882,fObProgZone2012[x], If[x<250731,fErstPropZone2012[x],\nfZweitPropZone2012[x]]]]]\n\nxvar2012E[x_] := Floor[x]\nyvar2012E[x_] := 0.0001*(Floor[x]-8130)\nzvar2012E[x_] := 0.0001*(Floor[x]-13685)\nfNullZone2012Entwurf[x_] := 0\nfUntProgZone2012Entwurf[x_] := (897.39 * yvar2012E[x] + 1400) * yvar2012E[x]\nfObProgZone2012Entwurf[x_] := (225.14 * zvar2012E[x] + 2397) * zvar2012E[x] + 1055\nfErstPropZone2012Entwurf[x_] := 0.42 * xvar2012E[x] - 8303\nfZweitPropZone2012Entwurf[x_] := 0.45 * xvar2013[x] - 15803\nSteuer2012Entwurf[x_]:=If[x<8131,fNullZone2012Entwurf[x],If[x<13686,fUntProgZone2012Entwurf[x], If[x<53728,fObProgZone2012Entwurf[x], If[x<250000,fErstPropZone2012Entwurf[x],\nfZweitPropZone2012Entwurf[x]]]]]\n\n\nxvar2013[x_] := Floor[x]\nyvar2013[x_] := 0.0001*(Floor[x]-8130)\nzvar2013[x_] := 0.0001*(Floor[x]-13469)\nfNullZone2013[x_] := 0\nfUntProgZone2013[x_] := (933.70 * yvar2013[x] + 1400) * yvar2013[x]\nfObProgZone2013[x_] := (228.74 * zvar2013[x] + 2397) * zvar2013[x] + 1014\nfErstPropZone2013[x_] := 0.42 * xvar2013[x] - 8196\nfZweitPropZone2013[x_] := 0.45 * xvar2013[x] - 15718\nSteuer2013[x_]:=If[x<8131,fNullZone2013[x],If[x<13470,fUntProgZone2013[x], If[x<52882,fObProgZone2013[x], If[x<250731,fErstPropZone2013[x],\nfZweitPropZone2013[x]]]]]\n\n\nDann passiert erstmal nichts, denn das Programm hat erstmal die Daten bekommen. \n\nAb hier kommen die Befehle mit denen man sich verschiedene Sachen angucken kann.\n\n--------------------------\nEin Graph der jeweiligen Steuern (hier zwischen 0 und 100000 Euro)\n\nPlot[Steuer2012[x],{x, 0, 100000}]\nPlot[Steuer2013[x],{x, 0, 100000}]\nPlot[{Steuer2012[x], Steuer2013[x]},{x, 0, 20000}]\nPlot[{Steuer2012[x], Steuer2012Entwurf[x]},{x, 0, 20000}]\n\n\n---------------------------\nHier werden die verschiedenen Einkommenszonen von einander abgezogen:\n\nSimplify[fUntProgZone2013[x]-fUntProgZone2012[x]]\nSimplify[fUntProgZone2012Entwurf[x]-fUntProgZone2012[x]]\nSimplify[fObProgZone2013[x]-fObProgZone2012[x]]\nSimplify[fErstPropZone2013[x]-fErstPropZone2012[x]]\n\n\n----------------------------\nHier sind Berechnungen zur kalten Progression (Prozent ist hierbei der Prozentsatz einer Einkomenserh\u00f6hung):\n\nClear[fProgression, Einkommen, Prozent]\nfProgression[Einkommen_]:=(Steuer2013[Einkommen+Prozent*Einkommen]-Steuer2012[Einkommen])\/Einkommen\nEinkommen := 100000\nProzent:=0.02\nSteuer2012Entwurf[Einkommen+Prozent*Einkommen]-Steuer2012[Einkommen]\nSteuer2013[Einkommen+Prozent*Einkommen]-Steuer2012[Einkommen]\nfProgression[Einkommen]\n\n\n-----------------\nUnd hier nochmal ein Graph zur kalten Progression:\n\n\nClear[Einkommen,Prozent]\nProzent:=0.06\nPlot[fProgression[x],{x, 10000, 100000}]\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"

Der deutsche Text in diesem Post ist nach dem Link: Read the rest of this entry \u00bb As described in the last german TAX post I was trying to get information about german income taxes, in particular I wanted to get the concrete formulas. I asked via fragdenstaat.org at the Federal Agency for Civic Education […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[13,15,33,26,2,31],"tags":[],"_links":{"self":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5176"}],"collection":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5176"}],"version-history":[{"count":18,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5176\/revisions"}],"predecessor-version":[{"id":5194,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=\/wp\/v2\/posts\/5176\/revisions\/5194"}],"wp:attachment":[{"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5176"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5176"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.randform.org\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5176"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}