Today the Telegraph had an article claiming that “the top one per cent of British earners are now paying almost 30 per cent of all income tax.” It’s then painted as a bad, unexpected revelation. But I’m not sure that should be the case. In one of my mini-Ben Goldacre moments, I think it’s one of those areas where your intuition and the numbers don’t necessarily align.

This post isn’t about politics or fairness or even, really, taxes. Instead it’s about maths, because what the story fails to say is that you would absolutely expect a small number of high earners to foot most of the bill.

Let’s make some silly assumptions and see how the numbers work out:

• Everyone pays the same 20% tax rate. We’re ignoring the tax-free component so that should work out to be considerably less than the rich pay but more than almost everyone else
• We’ll say that 90% of people earn £20000. The national average is higher than that, but there are a lot of people who work part time and pay no income tax at all
• And we’ll say the last 10% earn £60000. I don’t know how realistic that is as an average, but it’s nearer high-rate tax band cut-over than it is the millions that some CEOs and bankers get and it’s still a long way from the 50p tax rate

How do the numbers work?

The people on the lower income each pay £4000 in tax and the more comfortable pay £12000. But there are nine of the average people for every one of the rich, making the total take £4000 * 9 + £12000 * 1, or £48000.

So the high earner pays £12000 of the complete tax take of £48000, which is 25%.

(If you increase the tax rate on our hypothetical higher earner to 30% he ends up paying a third of all income tax.)

As I say, I don’t want to get into the fairness of it all, but a little maths, some wild assumptions and no research shows that, actually, the rich probably should be paying a reasonable percentage of the total income tax bill.