progressive tax, by eighths

Great Debates
1

What’s wrong with this tax plan?

  1. Set a standard tax rate, say 12%, for the first X of income, where X is continually adjusted to the mean adult income the previous year.

  2. Set thresholds at powers of 8 times X. Past each threshold, one’s proportion of after-tax take on income over the threshold (“proportion of marginal after-tax income”?) is reduced by 1/8 compared to the “proportion of marginal after-tax income” under the threshold.

So, if the baseline is 12%…
a. Income monies beyond X up to 8X are taxed at an additional 11% for 23% total.

b. Over 8X to 64X, an additional 9.5% for 32.5% total.

c. 64X - 512X, additional 8.5% for 41% total.

etc.

  1. In this vein, the first X/8 of income should probably be tax-free, or at least with a “proportion of marginal after-tax income” 8/7 greater than the baseline (if the baseline is a tax > 12.5%).

  2. Perhaps a negative income tax could obtain for incomes less than X/8.

(I’m sorry if my lack of familiarity with tax law means I missed some clearer normal notation.)

2

How will this plan change the amount of monies taken from various income classes? Will the government get more money or less, total? Why not sevenths or ninths?

3

Maybe before we discuss what’s wrong with it you could posit why it’s better than the current system.

4

I need to do some research on present income distribution. I honestly don’t know if these specific numbers make sense.

It’s better than the current system mainly in that it contains a formula for progressivity to infinitely high income variations & is internally indexed for inflation.

5

I’m checking to see if I understand your numbers. X is $32,000 (this is actually an approximate median income for 2005 not the mean for 2008 but let’s run with it).

So a person with an income between zero and $4000 pays no income tax.

A person who has an income between $4001 and $32000 pays 12% on all income above $4000. So somebody with a $4001 income would pay twelve cents and somebody with a $32000 income would pay $3360.

A person with an income between $32,001 and $256,000 would pay $3360 for the first $32,000 and then 22.5% (it’s 12+10.5 not 12+11) on all income above $32,000. So somebody with a $32,001 income would pay $3360.22 (rounded down) and somebody with a $256,000 income would pay $53,760.

A person with an income between $256,001 and $2,048,000 would pay $53,760 on the first $256,000 and then 31.5% (it’s 22.5+9) on all income above $256,000. So somebody with a $256,001 income would pay $53,760.31 and somebody with a $2,048,000 income would pay $618,240.

A person with an income between $2,048,001 and $16,384,000 would pay $618,240 on the first $2,048,000 and then 39% (31.5+7.5) on all income above $2,048,000. So somebody with a $2,048,001 income would pay $618,240.39 and somebody with a $16,384,000 income would pay $5,659,280.

“etc”

Have I got the concept right?

6

If you’re going to make it formulaic rather than tabulated, why not make it a smooth function without any discrete brackets at all?

7

Yes, Nemo, that’s it.

I haven’t crunched numbers on this kind of formula very much yet. This was very much a back-of-the-envelope idea, & I decided to just throw it out there before spending a lot of thought on it & getting emotionally attached.

Personally, I would love to use a straight mathematical formula instead of brackets, but I have the impression the IRS prefers brackets.

8

I’m not sure what you guys are talking about. Doesn’t the formula produce the tabulated results?

As for avoiding brackets, how would you do that? The only way I see is to have a single percentage for all incomes (essentially one bracket). Or are you saying you don’t like breaking up a person’s income into groups with seperate percentage rates? In other words, saying that people up to X amount of dollars pay Y% on their total income and people above X pay Z% on their income? If so, the problem is that there’s big jumps as you cross those lines. An income increase of one dollar can cause a taxation increase of hundreds of dollars and people can end up losing money because they earn move. For example, say you tax total incomes up to $50,000 at a 25% rate and total incomes above $50,000 at a 26% rate. A person with a $50,000 income would pay $12,500 and a person with a $50,001 income would pay $13,000.26 - they got taxed five hundred dollars for that single dollar of income.

9

Presumably because it’s easier for mathematically challenged individuals to calculate one of a number of formulas of the form y=mx+b.

No, the smooth function he suggested would basically be like the difference between approximating y=x^2 with a series of straight lines (the current function, with discrete brackets), and just using y=x^2. The problem is that a formula which did what the government wants it to would be more complex than that.

10

And I haven’t found a smooth equivalent of this one yet…

11

If I’m understanding you correctly, then a tax rate based on smooth curves rather than “straight lines” would require tax payers to use calculus to determine their tax rate. Propose that and see how popular your plan is.

12

Why would you need calculus? The lawmakers who instituted the plan might need to use calculus to find a formula that does what they want, but the taxpayers would just take that formula and use some simple algebra. Or, more likely, the computer program or accountant the taxpayer uses to figure taxes would use algebra.

13

If we have to go with a progressive tax, I’d rather have it be a smooth curve than the bracket system we have now.

Valete,
Vox Imperatoris

14

It’s regressive.

At least that’s what I get out the OP’s explanation, as opposed to what Little Nemo is getting out of it. Perhaps the OP could flesh this out some more with say 3 different examples, fleshed out into how much income versus how much tax.

15

Urk. I knew I explained it badly, but Little Nemo seems to have understood what I meant.

As for making taxpayers do complex maths, I suppose that would be fair for those on the high end. Surely they can pay someone to do a little math for them. But I’d prefer that Joe Schlemiel be able to do his taxes with a workbook.

16

If Little Nemo has it correct, then it looks like a fairly normal progressive tax. It would be easy to make simple tax tables that accomplish the basic proposal as suggested, so I wouldn’t worry about the complexity. Like others, my question then is, what do you gain, as it doesn’t seem that different than what we currently have?

17

Quadratic equations are not any more “complex” than the myriad tax exemptions and other junk that currently fill the tax code. Of course, politicians would then lose their precious tax exemptions.

Valete,
Vox Imperatoris

18

The smooth function would be of the form (x - d) * (x * q),

where x is income, d is the standard deduction, and q is the progressivity factor.

In other words, as others have said, a quadratic.

Ed

19

If I’m understanding it correctly, what people want is a smooth curve with no straight lines (ie “brackets”). If you were to graph the numbers I wrote in post #5, you’d have a graph of straight lines with the angle of the line increasing at each 8x boundary. All that math you need to do to figure out your exact tax amount is simple addition, subtraction, and multiplication.

But if you have a graph with smooth curves instead of straight lines, you’re not going to have a range of incomes with a constant tax percentage. So you’d need calculus to determine what the exact percentage was at your point of income.

20

Could you plug in some numbers so we can see how it works?