From a9ff49aae998171eb79750a086dcc7c70870e72f Mon Sep 17 00:00:00 2001 From: Lars Bogner Date: Sat, 27 Mar 2021 14:03:37 +0100 Subject: [PATCH] Added Lorenz-Curve and Gini coefficient to Wirtschaft --- Wirtschaft/Wirtschaft.md | 8 ++++++++ Wirtschaft/Wirtschaft.pdf | Bin 2602627 -> 3128297 bytes .../500px-Gini-Coefficient-pure.svg.png | Bin 0 -> 15204 bytes Wirtschaft/assets/lorenzkurve.jpg | Bin 0 -> 505287 bytes 4 files changed, 8 insertions(+) create mode 100644 Wirtschaft/assets/500px-Gini-Coefficient-pure.svg.png create mode 100644 Wirtschaft/assets/lorenzkurve.jpg diff --git a/Wirtschaft/Wirtschaft.md b/Wirtschaft/Wirtschaft.md index ff63332..5d8aab7 100644 --- a/Wirtschaft/Wirtschaft.md +++ b/Wirtschaft/Wirtschaft.md @@ -318,8 +318,16 @@ siehe Abbildungen *Bruttoinlandsprodukt der letzten Jahre* und *Prognose des BIP ![Prognose des BIP](assets/wirtschaftliche-entwicklung/statistic_id5848_prognose-zur-entwicklung-des-bruttoinlandsprodukts-in-deutschland-bis-2022.png) +\newpage + ## Gerechtigkeit im Staat ### Verteilungsgerechtigkeit +Die Verteilung des Vermögens in einem Staat --- auch die Schere zwischen Arm und Reich genannt --- spielt vor allem in einer sozialen Marktwirtschaft eine große Rolle, da sie ein großer Faktor in der sozialen Ungerechtigkeit spielt. +Eine mögliche Form, wie diese Ungerechtigkeit gemessen werden kann ist der sogenannte Gini-Koeffizient. Für diesen wird die Lorenzkurve (vgl. Abbildung *Lorenzkurve*) eines bestimmten Wirtschaftsraums betrachtet. Die Lorenz-Kurve ist die aufsteigende kumulierte Funktion der Einkommen der Einzelpersonen in einem Wirtschaftsraum. Somit lässt sich beispielsweise ablesen, wie viel Prozent des Einkommens die untersten $x$ Prozent der Bevölkerung verdienen. Somit lässt sich leicht die Ungleichverteilung erkennen, denn ein perfekt gleichverteilter Wirtschaftsraum hätte eine Gerade als Lorenzkurve. Diese Eigenschaft macht sich auch der Gini-Koeffizient zu nutze, welcher das Verhältnis zwischen der Fläche zwischen realer Lorenzkurve und gleichverteilter Lorenzkurve zu Fläche unter der gleichverteilten Lorenzkurve ist (vgl. Abbildung *Gini-Koeffizient*). Als Gleichung dargestellt ergibt sich: $$GUK = \frac{A_{gl} - A_{real}}{A_{gl}}$$ + +![Lorenzkurve](assets/lorenzkurve.jpg){ width=250px } + +![Gini-Koeffizient](assets/500px-Gini-Coefficient-pure.svg.png){ width=250px } ### Wohlstand im Staat diff --git a/Wirtschaft/Wirtschaft.pdf b/Wirtschaft/Wirtschaft.pdf index 367c12d5eafd09a4773c00e63e7bbf2ed439d839..5122cc5d94a40f4bd27756e085a17c64ffc7ca37 100644 GIT binary patch delta 636790 zcmb5UcRZV4{QrGL%!oZ2MFmk?gO;S!E(vPSqV{Ty2sK)j*egb26H0AbHH*?V_NLWk zmkK)2qNO@-pYQK?|Ngk|fA0I_dOptk@y&rlj-HSa`O2AG8G zFxKkc`FNJ%Jxhx&p3oks>QlhPm!!8pyLLtC+7sDvfX2v2Wy6Q$tCob8K)O&47l$5aWg~r-JCux3!05 z)_wN~C>EJ$Bku=_4I8x23YbW(g!i%L6;l@Bxsjd^QTGeKaRnK*@5fg&P3(Jf_lsK2 z^F{OVxb53Lh+1qG(A(g-*n0>bJZ8JSz-pbz=LZ=DURHAlUQt9`*zp%Kc((rJk9gKC zhGa{#TT^-Yzng@0i9%W&=V*%$T+@>@g02ht5@v0VIexK|vKGE-Dnt}WDE3^9*zb{F zs)@UCtt5@(#Y9b;_T@puD00z-Dy`;iHCC&S@V=E0`}Mb}W!!t7@<^xg-pwoeTkMCf zBMD!tnJ(oDF4+fFu1xvrWNIg(p2gml7%L38C0I*%pd!AuBC*r?Ukobdnb~ 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