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Majority of countries (if not all) use tax brackets to define how much tax should the earning workforce pay. So we could have something like this.

Pay | Tax
0 - 10,000 | 10%
10,001 - 20,000 | 20%
20,001 - 30,000 | 30%
etc.

The breakpoints are what I am going to ask about. It has been proven in other schemes, such as the UK's Stamp Duty Land Tax that separating tax into categories like this leads to clusters on the lower bound of the breakpoints. My understanding is that this is not a desired effect and the distribution on the scale should be more fluid.

I come more from the software engineering side as opposed to the economic side, so I assume that in the past it was easier to calculate tax using this system and that's why it was chosen. Humans would not be able or willing to do complex tax calculations had we used rules that can be charted for example as S curves.

However, I wonder if we could have a better system today? (Assuming the current system is not sufficient.) Are there any proposals or significant movements that are not satisfied with the current tax system?

Note: I am not making assumptions about how the collected money is being spent, or how much is being collected. This is purely about the curves behind the tax brackets and clustering.

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    $\begingroup$ The income tax bracket is base on assumption that subsequent bracket reaping/exploits more resources from the society. However, there is tax brakes/incentive to reduce reaching the bracket or reduce amount to be paid. $\endgroup$ – mootmoot Jul 10 '17 at 8:24
  • $\begingroup$ The way the question is currently formulated it is asking for opinion on a hypothetical tax system. Unfortunately we do not deal in opinion-based answers. $\endgroup$ – Giskard Jul 10 '17 at 15:01
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    $\begingroup$ Part of the reason for using brackets is to make planning easier. If I know which bracket I fall into I can figure out about how much tax I own with a pencil and paper. If the marginal rate changed for each dollar I earn, it turns into a complex problem. It is much easier to plan when i can make a rough but good enough guess at my tax liability. And ability to plan is a huge deal in economic endeavors. $\endgroup$ – zeta-band Jul 25 '17 at 19:46
  • $\begingroup$ @zeta-band I understand your idea about easier planning for those who pay taxes. But on the other hand: I do not see what the problem would be if there was a formula-based (steady) curve to link income with tax rates (instead of stepped brackets). The tax payer could anyway make a "rough but good enough guess" (as you said) on his tax liability. Or it would even allow for a better guess, because a steady curve by definition does not have steps (like if you earn 99,999 vs 100,000 and you fall into a completely different bracket just because of the difference of 1 [currency unit]). $\endgroup$ – Christian Geiselmann Nov 3 '17 at 12:19
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I think you've misunderstood how the (UK) income tax brackets work. They work differently to how stamp duty used to work.

Stamp duty brackets used to be absolute rates: so when the purchase price crossed over the bracket threshold by £1, the marginal rate would be huge, as the whole purchase price was taxed in the higher rate. Hence the clustering.

That's not what happens with income tax. (and it's no longer what happens with stamp duty, either)

With income tax, only the amount of income that's above the threshold, gets taxed at the higher rate. So, the marginal rate is always equal to the band rate. i.e. if the rates are as in your example, and your income rises from 10,000 to 10,001 then you would pay 10% on the first 10,000 and 20% on the extra 1. You would not pay 20% on all 10,001.

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  • $\begingroup$ Hey, you're right, I actually wasn't aware this was how the rate is calculated. I didn't get to see Christian's original reply below, but I assume he had the same misunderstanding. Thanks for this! $\endgroup$ – lmenus Nov 5 '17 at 23:15
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The way tax brackets currently work is a fixed marginal rate that increments at set intervals. Solving the amount of tax to be paid can be done with a pocket calculator and basic algebra. Using a curve implies a constant change to the marginal rate implying every dollar earned will have a slighly different tax rate and you need to use calculus to figure out how much to pay.

At the end of the day, the people running the tax office are not going to care about having a beautiful curve for tax rates as they are dealing with all of us incompetent tax payers paying the wrong amount of taxes. As well, complicated tax calculations hurt small business owners and the self-employed, who can't be expected to be using calculus just to pay their taxes.

Politicians are smart enough to realize just because it's pretty that doesn't mean it's practical. You've got to consider the audience of people actually implementing the rules.

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  • $\begingroup$ Hey, yes, all valid points and it's indeed something I considered. I keep thinking that we're technologically progressing at such pace that in the future it won't matter how complicated the graph is or whether you can calculate your amount due in your head. As such, my original question assumes software would be used to perform these calculations and there would be no-to-low human intervention. E.g. software like FreshBooks would automatically do all of this for you, so as a business owner you don't care about the complexity behind the tax formulae. $\endgroup$ – lmenus Nov 5 '17 at 23:21
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I have been asking myself this question for a long time.

Indeed using a steady curve (instead of brackets) for linking income to tax rates would be simpler and clearer.

Everybody could easily calculate their tax rates at a given income. Or if he or she is traumatised by maths in school: government could publish look-up tables anyway.

So why don't states do this?

The only explanation I can imagine is that

a) politicians are often maths- and formula-averse, or

b) they are not but they feel that a majority of population is formula-averse and that they would not meet the necesssary level of understanding in the electorate, so it is unattractive for them to propagate such an improved system, or

c) bureaucrats in financial authorities are change-averse and do not suggest that solution to politicians.

All of these are weak reasons. But still I do not see better ones.

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    $\begingroup$ "you fall into a different bracket, and your taxes eat up your entire pay raise and more" That is not how tax brackets work. $\endgroup$ – Giskard Nov 3 '17 at 13:46
  • $\begingroup$ Okay. Thanks. I removed the respective section as it was indeed inadequate. - Still the main question remains: why not use a steady curve? $\endgroup$ – Christian Geiselmann Nov 3 '17 at 15:21

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