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In some recent conversations/speeches (It's voting season), I have noticed many people do not understand how a marginal income tax system works.

Not understanding how they are only taxed at the higher rate, on the income in the higher bracket is one thing.

However for today's question I am looking to address people feel sore that when they work harder (e.g. overtime) they are taxed at a higher rate, so they would like a flat tax rate.

This is true perhaps for those who are the very top income earners. But for everyone below them this is not true. Because they would have had to paid the same, but higher, tax rate on the lower brackets of their income.

So my question is:

Assuming the same dollar amount of income tax for the government* stays the same, what would be the income tax rate be if the marginal tax rates were flatten to a single rate?

Bonus: At what income amount would be the tipping point be, where you would be better or worse off under these different rates.

*I am most interested in what this would be in New Zealand. However I am happy to take answers for any OECD country.


A flat tax rate would almost certainly have some secondary effects. Most likely they would have a negative effect on the total tax taking, and would also likely cause an increased demand on government services; requiring raising of taxes. What and the extent of those secondary effects are warrants a separate question (thesis probably!) So for the sake of simplicity, let's keep them out of scope, for this question.

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  • $\begingroup$ As the question stands it does not have enough info to answer it. It is possible to prove that flat tax is not optimal if income distribution is not approximately log normal (which for most countries is not) or if it does not have other special case parameters (such as 0 income inequality or other cases). However, you don’t provide any parameters from NZ that could be used to calculate tax rate which you ask for in your question and you can’t expect volunteers here to research all necessary parameters. Hence I vote to close as it needs more clarity... $\endgroup$ – 1muflon1 Feb 21 at 7:37
  • $\begingroup$ @1muflon1 I am sure I am not the first person to ponder this question. So I expect someone else with access to more data has probably worked this out. Maybe someone on Economics SE has knowledge of it? Maybe they can answer the question? $\endgroup$ – DarcyThomas Feb 21 at 7:42
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    $\begingroup$ @1muflon1 Although maybe the Optimal-Taxation tag is not the best $\endgroup$ – DarcyThomas Feb 21 at 7:44
  • $\begingroup$ I think the tag is fine. But the way you are asking it, it sounds like you want the answer for NZ now. Unless you are astronomically lucky I doubt there will current research given the current parameters of NZ. Google scholar does not show anything on first few pages. You could definitely make back of the envelope numerical simulation but for that you need to first research or provide assumptions on what for example labor supply elasticity is $\endgroup$ – 1muflon1 Feb 21 at 7:48
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Having worked on these issues myself for quite some time, I am not aware of any study on this for New Zealand. For a back-of-the-envelope calculation of the revenue-neutral flat tax rate, you'd need the following:

  1. The tax base $Y$, i.e. the amount of income subject to income tax. Most probably, the New Zealand Treasury has published statistics on this. Note that total taxable income is different to total earnings which are reported in national accounts.
  2. The number of taxpayers $N$.
  3. You might want to maintain the current exemption $E$ which remains untaxed for each individual.

With current income tax revenue $R$, the revenue neutral flat tax rate $\tau$ can be obtained from:

$ R = \tau * (Y-N*E)$

Note that is the minimal thing to do which abstracts, among other things, from behavioral effects of such a reform.

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  • $\begingroup$ I know you already mention in you answer it does not take into account behavioral effects and so on, but I would like to point out (for the sake of OP) that accounting for labor supply elasticities would change results from this simplified formula a lot $\endgroup$ – 1muflon1 Feb 21 at 19:55
  • $\begingroup$ So I have found the raw data I just need to find some time to crunch the numbers. $\endgroup$ – DarcyThomas Feb 22 at 19:28
  • $\begingroup$ Those are pretty detailed figures. Since you also have the average tax rate, you can work out the income beyond which taxpayers are better off. $\endgroup$ – E. Sommer Feb 22 at 19:40
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All the flat tax proposals that I know of come with an an exemption, so they are really a kinked rather than a flat tax. Income is usually taxed at a 0% rate up to the exemption limit and then flat taxed after that. In the US, abstracting from a lot of complicating factors, the exemption is about 40 percent of mean income.

The paper Flat Tax Reform: A Quantitative Exploration (Gustavo Ventura (1999)), find that the revenue neutral flat tax with a standard deduction of 40 percent of mean income is about 25 percent. The paper has numerous other comparisons of the estimated income, wealth, inequality, taxation and other consequences of this policy change.

Several findings emerge from this study. First, the effects of the flat tax reform on capital accumulation appear to be substantial. Consequently, the effects on the wage and the interest rate are of considerable magnitude. As pointed out in the text, this is a consequence of the replacement of current capital income and income taxes by a consumption based form of taxation. In this regard, this result parallels quantitative findings provided by the vast applied general equilibrium literature that studied the impact of consumption taxes against other forms of taxation.6 Second, the potential impact on labor supply so emphasized by proponents of the flat tax can be divided into two parts. On the one hand, after the tax reform, mean labor hours are relatively constant in the benchmark calculations. On the other hand, significant changes in the distribution of labor hours are observed. Labor hours supplied by agents at the top of the income distribution substantially increase: households in the upper income quintile increase labor hours by no less than 9% in the cases considered. Since these agents are highly productive, this latter effect is the factor behind the overall increase in the value of the aggregate labor input in efficiency units that is observed, which in turn reinforces the effect of higher capital levels on output. Finally, the cross-sectional distributions of earnings, income and in particular wealth become more concentrated in all cases analyzed.

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There is no good answer to this question.

The reality is that not everyone has the same propensity to spend out of income, and it seems reasonable to believe that people with lower incomes spend more. If tax rates were flattened, lower income households would pay more, and this would have a depressing effect on activity. The implication is that we cannot assume that keeping the total tax take unchanged has no effect on the economy.

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