The demise of the 50p top tax rate was the big headline from the budget.

Labour leader Ed Miliband, called it “a millionaire’s budget”. But the chancellor, George Osborne, claimed “we’ll be getting five times more money each and every year from the wealthiest in our society” as a result of the measures unveiled.

FactCheck tries to cut through the rhetoric.

Who are the winners and losers?

This table from the main budget document has been seized on by Conservative bloggers that Mr Osborne really is hitting the rich hardest. It shows that people in the top ten per cent income bracket are paying more than anyone else as a result of today’s announcements.

And broadly speaking, the lower your income, the less you lose out.

But this is in cash terms, and of course a cash cut of, say, £200 a year means something entirely different to a millionaire than it does to someone on the poverty line.

The next table helpfully puts things in terms of cuts as a percentage of people’s expenditure, reflecting the real impact on living standards. And that changes things. The top decile are still the hardest hit, but next worst off are the very poorest.

Will the wealthiest pay more or less?

The cut of the top income tax rate from 50 to 45 per cent for those who earn more than £150,000 means critics of the government are inevitably focusing on the “millionaire’s tax cut”, as Mr Miliband called it.

But the chancellor insisted counter-measures will mean five times more money will be squeezed out of the super-rich than handed back.

On the face of it, he’s right. Or to put it another way, that’s a fair representation of government projections.

This table from the independent Office for Budget Responsibility’s (OBR) budget overview sums up the expected position, with the cost to the treasury from lowering the top rate (3) outweighed by other measures that will hit the highest earners (4,5 and 6) by more than five to one every year.

Of course, these are all just projections. If the cap on tax relief and the “mansion tax” don’t rake in as much, Mr Osborne’s boast will proved wrong. But for now the independent watchdog backs him on the “five times more money” line.

How did they get it so wrong on the 50p top tax rate?

What happened to those millions we were expecting to get from Labour’s decision to increase the higher tax rate from 40 to 50 per cent in 2010?

The move was expected to net £2.6bn in 2012/13, but the government now puts the real expected haul at just £0.6bn. It’s such a huge shortfall that both sides have only just stopped short of accusing each other of cooking the books.

When the Treasury produced their original estimates in March 2010, they tried to take into account the changes in behaviour that tax hikes inevitably inspire.

Change the rules and people – particularly the richest people – will do all they can to move their money around, work less, or look for tax avoidance wheezes.

Tax boffins try to allow for this behaviour by calling it taxable income elasticity (TIE) and assigning it a number. The higher the number, the better you are at dodging tax.

When the Treasury did their estimates for the effects of 50p in 2010 they used a TIE of 0.35, which is at the lowest end of the scale approved by most independent academics.

Studies on tax behaviour from the US put the TIE of top earners much higher, and the most relevant British study, carried out by researchers from the Institute of Fiscal Studies (IFS) came up with a TIE of 0.46.

All academics stress that these numbers are vague and forecasts can easily be wrong, but the numbers the government preferred to use in 2010 appeared to be as low as it was possible to go while staying within a range approved by academics, thus inflating the revenue projections.

Shadow chancellor Ed Balls has criticised the HMRC study, saying: “It is a political report. It is not an independent report.”

But as far as we can see, all the report does is set out the academic case. It concludes, not unreasonably: “It is difficult to construct a plausible scenario that would result in a yield estimate that is in line with those original forecasts.”

Mr Balls also called for the OBR to look at the issue. Well, it has, and it agrees with HMRC (here, p109), backing the current government’s use of a higher TIE of 0.45.

We ought to say that the very low numbers being claimed for 50p by George Osborne are still provisional, so this isn’t the final word on whether the Labour move was a success or a failure.

But it’s fair to say that say that the OBR and the IFS – both independent – say the Labour government’s original forecasts back in 2010 were skewed towards a big overestimate from the outset.

By Patrick Worrall