What would be the income tax rate be if it were 'flattened'? 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.
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:


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.
The number of taxpayers $N$.
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.