- commit
- e0c381f950f282144c8b7537211a0b15ee3b38e5
- parent
- 1f225ed7e2be6dcf23664e00a0336112ac8daf7b
- Author
- Tobias Bengfort <tobias.bengfort@posteo.de>
- Date
- 2025-05-21 05:35
use latexmath pandoc feature
Diffstat
| M | Makefile | 2 | +- |
| M | _content/posts/2025-05-16-tax-curves/index.md | 75 | ++++++++++--------------------------------------------------- |
2 files changed, 13 insertions, 64 deletions
diff --git a/Makefile b/Makefile
@@ -4,7 +4,7 @@ PAGES_MD := $(shell find _content -name 'index.md' | sed 's/^_content/build/') 4 4 PAGES_FEED := $(shell find _content -name 'index.md' | sed 's/md$$/html/') 5 5 STATIC := $(shell find static -type f | sed 's/^/build\//') 6 6 IMG := $(shell find _content -regex '.*\.\(png\|gif\|jpg\)$$' | sed 's/^_content/build/')7 -1 PANDOC_ARGS = -f markdown-smart --wrap=none --lua-filter filters/*.lua-1 7 PANDOC_ARGS = -f markdown-smart --mathml --wrap=none --lua-filter filters/*.lua 8 8 9 9 .PHONY: all 10 10 all: $(IMG) build/index.html build/projects/index.html $(PAGES) $(PAGES_MD) build/feed.xml build/feed-archive.xml build/feed.json build/feed-archive.json $(STATIC) build/static/style.css
diff --git a/_content/posts/2025-05-16-tax-curves/index.md b/_content/posts/2025-05-16-tax-curves/index.md
@@ -12,30 +12,21 @@ options for tax curves, without any claim to real-world merit. 12 12 13 13 ## Basics 14 1415 -1 We will look at functions where <math><mi>x</mi></math> is the income before16 -1 taxes and <math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is the17 -1 income after taxes.-1 15 We will look at functions where $x$ is the income before taxes and $f(x)$ is -1 16 the income after taxes. 18 17 19 18 I am a big fan of folding some form of social security into the tax system, so20 -1 <math><mi>b</mi></math> will be the level of basic income everyone should have.-1 19 $f(0) = b$ will be the level of basic income everyone should have. 21 2022 -1 All functions will have a single additional parameter <math><mi>a</mi></math>23 -1 that can be used to adjust the system to the current economic situation,24 -1 basically raising or lowering taxes.-1 21 All functions will have a single additional parameter $a$ that can be used to -1 22 adjust the system to the current economic situation, basically raising or -1 23 lowering taxes. 25 24 26 25 ## Linear 27 26 28 27 The simplest model is a flat tax rate with basic income: 29 2830 -1 <math>31 -1 <mi>𝑓</mi><mo>(</mo><mi>𝑥</mi><mo>)</mo>32 -1 <mo>=</mo>33 -1 <mi>𝑎</mi>34 -1 <mo>⁢</mo>35 -1 <mi>𝑥</mi>36 -1 <mo>+</mo>37 -1 <mi>𝑏</mi>38 -1 </math>-1 29 $f(x) = ax+b$ 39 30 40 31  41 32 @@ -49,25 +40,7 @@ Most real-world economies have progressive tax rates. That means: the higher 49 40 your income, the higher your marginal tax rate. The classic mathematical 50 41 function that grows to infinity but slows down while doing so is the logarithm: 51 4252 -1 <math>53 -1 <mi>𝑓</mi><mo>(</mo><mi>𝑥</mi><mo>)</mo>54 -1 <mo>=</mo>55 -1 <mi>𝑎</mi>56 -1 <mo>⁢</mo>57 -1 <mi>ln</mi>58 -1 <mo>(</mo>59 -1 <mrow>60 -1 <mfrac>61 -1 <mi>x</mi>62 -1 <mi>a</mi>63 -1 </mfrac>64 -1 <mo>+</mo>65 -1 <mn>1</mn>66 -1 </mrow>67 -1 <mo>)</mo>68 -1 <mo>+</mo>69 -1 <mi>𝑏</mi>70 -1 </math>-1 43 $f(x) = a \ln(\frac{x}{a} + 1) + b$ 71 44 72 45  73 46 @@ -88,31 +61,7 @@ money than everyone else. 88 61 Another type of functions that go up to infinity but slow down on the way are 89 62 power functions like this one: 90 6391 -1 <math>92 -1 <mi>𝑓</mi><mo>(</mo><mi>𝑥</mi><mo>)</mo>93 -1 <mo>=</mo>94 -1 <msup>95 -1 <mrow>96 -1 <mo>(</mo>97 -1 <mrow>98 -1 <mfrac>99 -1 <mi>x</mi>100 -1 <mrow>101 -1 <mi>a</mi>102 -1 <mo>⁢</mo>103 -1 <mi>b</mi>104 -1 <mrow>105 -1 </mfrac>106 -1 <mo>+</mo>107 -1 <mn>1</mn>108 -1 </mrow>109 -1 <mo>)</mo>110 -1 </mrow>111 -1 <mi>a</mi>112 -1 </msup>113 -1 <mo>⁢</mo>114 -1 <mi>𝑏</mi>115 -1 </math>-1 64 $f(x) = (\frac{x}{ab} + 1)^a b$ 116 65 117 66  118 67 @@ -120,6 +69,6 @@ Like with the logarithm, the marginal tax rate starts at 0% and grows towards 120 69 100%. However, it doesn't grow as quickly, which puts it somewhere in between 121 70 the logarithmic and linear versions. So this feels the most balanced. 122 71123 -1 I also like that <math><mi>a</mi></math> has an intuitive interpretation (how124 -1 curved to curve is). So if I were ever going to be minister of finance, this125 -1 would probably be the version that my advisors would have to talk me out of.-1 72 I also like that $a$ has an intuitive interpretation (how curved the curve is). -1 73 So if I were ever going to be minister of finance, this would probably be the -1 74 version that my advisors would have to talk me out of.