Ryan Bourne of the Centre for Policy Studies published a rather nasty little blog the other day under the title 'Rachel Reeves, Jo Swinson and Richard Murphy are wrong on the 50% rate'. The first two were on Question Time last week. I wasn't.

The CPS argument is becasue cutting the 50p tax rate is cheap it should be done.

Then Bourne proceeded to say that I'd wildly overestimated the total tax yield that the 50p tax will generate. I used a figure of about £4.7 billion last week. He said:

The Left's favourite tax expert Richard Murphy appeared across the airwaves yesterday to discuss this issue. Richard has carved a niche for himself as an independent tax accountant who contributes widely to our public discourse.

Unsurprisingly, he was asked to appear on a variety of media outlets yesterday to defend the 50p rate. This in itself is an honourable position. But he repeated claims made in his blog that the 50p rate was actually raising £4.7 billion — far more than the Treasury and HMRC have estimated.

How had he got to this figure?

Well actually, I think you'll now get my best estimate tomorrow Ryan - just wait and see the TUC report on this issue - but he said I'd done it as follows:

I accessed HMRC's income tax liabilities by taxpayer marginal rate table for 2011-12. Sure enough, it says that additional rate taxpayers (the top 1% earning over £150,000) are liable for a total of £47 billion in tax (28% of total income tax revenues). Therefore it seems that Richard has just assumed that lowering the tax rate from 50% to 40% would be equivalent to reducing their tax liability by 10 percentage points, or £4.7 billion.

This is not how our tax system works. In fact, people earning over £150k don't pay 50% of their income in tax. The 50% rate means that any income you earn over £150,000 is taxed at 50% - it's what economists call a marginal rate.

Oh dear Ryan: you clearly got that wrong, didn't you? Actually - you see, if I'd done what he'd suggested I'd have said that the extra tax would be 25% extra on the £47 billion - which is the proportionate increase on the tax yield of £47 billion that would have been due if all the income that had previously been due at the same fixed 40% marginal rate had now been due at 50%. That's because 10% is 25% of 40%. And so the extra tax would have actually been, if I'd committed such an error, a whopping £11.75 billion. In that context it's clear that £4.7 billion more than adequately compensates for the fact that not all the tax on anyone's income is due at the 50% rate. But the CPS, unable to do some simple maths and blinded by some very simple numbers, missed that point. As a result of course they missed the fact in their haste to cast aspersions that I did not make such an error (although I note Tim Worstall has fallen for the same elementary mathematical mistake, amusingly). The 10% extra was on income - not on the tax take, of course. But even then if has to be treated with care.

As you'll see tomorrow my actual estimate of potential tax yield is higher than £4.7 billion - I just used that as a headline last week whilst waiting for my full report to come out. And the CPS will find that if only they'd paid a little more attention to their sums and learning just how to use percentages the real numbers are bigger than those I've trailed. All of which makes keeping the 50p tax rate all the more important.