Most people are aware that the tax system is complicated. The more complicated something is, the more room for mistakes there are. For this reason, I think it ought to be simplified, and believe that it can be done to a great degree.
My ideal tax system would have the following properties:
It appears, to me, that income tax is the most efficient way to implement this: it's a simple and relatively reliable indicator of wealth, it's already implemented at a national level, and it can be quantifiably verified (you can narrow it down to a precise amount, and make sure that's what the income actually is).
After thinking about this a while, I used some very basic differential calculus to derive a function with those properties:
t = -h e ^ ( (s - i) / h ) + bfor i ≥ sand t = 0 for i ≤ s
t = -h e ^ ( (s - i) / h ) + b
for i ≥ s
and t = 0 for i ≤ s
where t is the tax rate (in percentage points), h is the highest rate the tax should go, s is the smallest taxable income, and i is the income (and e is, of course, Euler's number, approximately 2.718281828). In other words, this is a function of t(i), the relation of tax rate to income, and h, s, and e are constants to be set.
This has the advantage of possessing all of the properties I mentioned above; it has a floor, below which you're not taxed, and above which taxes never increase faster than income (to be precise, the slope of the function at i = 0 is 1, and the limit of the slope as i approaches ∞ is 0). This keeps incentive intact, because as you makes more money, you actually receives more and more of it, so returns on job efforts scale up—but at the same time, when you're making more money, you're taxed at an increased rate to reflect that.
This function also allows the tax rate to reflect situational circumstances, by modifying s (or h, but that's a little bit less useful). For example, dependents could affect your tax rate by, say, adding five thousand dollars to s, so if the "base" s is $30,000 (often reported as what one needs to live and have access to modern infrastructure), then with a dependent it would be $35,000.
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