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A single benefit usually has an appropriate incentive structure, but a lot of people get multiple benefits -- even from different levels of government (local, state, federal) -- and adding up phase-outs in different systems can result in marginal phase-outs rates above 100%. It's hard to avoid that entirely given that we want to have a lot of transfers to the bottom of the income distribution while phasing those out by roughly the median. It would be easier to avoid phase-outs above (say) 80% of marginal income is we only had federal and state aid as predictable money transfers, but for various reasons we provide a lot of transfers in-kind or with limited authorized uses. Those limitations aren't necessarily wrong, but they do mean that transfers aren't fungible, so there's an incentive to provide transfers for other "good" uses, and that diversity is what makes it hard to bound the marginal phase-outs for everyone.
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This does happen in Finnish tax system. Your tax rate (percent with one decimal) is calculated based on your annual gross income. Rates are supposed to be calculated smoothly, and they are certainly calculated for each individual separately.

In reality they are step functions. It is surprisingly common to have people refuse promotions because if would put them above an income tax threshold, bump up their rate, and end up with less money after taxes in the end.

The UK tax system is far from fair but at least it has clear brackets: income above threshold X is taxed at rate Y.

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Are you talking about this tax system? <https://nordisketax.net/pages/en-GB/taxation/?country=finlan...>

Because that is a marginal system, (and unless they've messed up the calculations, which they haven't in this case) you should never end up with less from earning more. Can you give an example of two income amounts where the lower income ends up with more money after-taxes than the higher income?

Or is it the additional municipal, church, or health levies mentioned on that page which have the discontinuities?

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The UK system doesn't either though. The rate for 100-125k is higher than for 125k+ due to the phasing out of the personal allowance. It gets worse if you have kids and can even result in a >100% marginal rate.
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I agree, but almost everyone today can use a computer or smartphone. They can type in their income, and the computer can calculate it, providing them an average number of what their percentage of actual taxable income was- I think Turbo Tax and other software might do something like this.

They don't have to understand how it works to do their own taxes.

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They may not trust it if they can't understand it.
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You might just be taking people too literally.

I've heard the same thing -- if they take a job they will lose money. What they really mean is that if they take a job (trade time for money), they will lose some of the pension they have already earned. This is a real economic loss (even if they might have a few more bucks at the end of the week) to say nothing of their lost time.

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