Recently taxation of the rich has been in the news. Mathematician Bernoulli came up with an equation that shows the rich should pay a higher tax rate. Here's some info, my question is at the end.
An article was found in the 4-volume set of books The World of Mathematics, circa 1956. The following is from Volume 2, from the article "The Application of Probability to Conduct" by John Maynard Keynes.
There are several interesting passages in the article, but I'll use one found on page 1369: " . . . no one but a miser regards the desirability of different sums of money as directly proportional to their amount; . . . . Daniel Bernoulli deduced a formula from the assumption that the importance of an increment is inversely proportional to the size of the fortune to which it is added."
Let's call m the moral fortune, and p the physical fortune. There is some value at which the physical and moral fortunes are equal; this can be any amount, which can be thought of as the income at which $1 equals $1 to the owner. These lead to an equation involving a natural logarithm which shows that the tax rate should increase as the income increases.
I want to reevaluate the constants in this equation. The Federal poverty level for a family of 4 is $23000. But what is the income at which moral and physical income is the same--where does an actual dollar equal a dollar of worth? $60000???
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