Who will pay for the rise in VAT? It's such a simple question. Unfortunately, the facts leave plenty of room for politicians - and others - to disagree.

You would think it was all pretty easy. The government is raising an extra £12.1bn in 2011-12 from increasing VAT to 20%. There are 26 million households. So, you would think, the average household will pay an extra £465 per year.

Except, you'd be wrong. Because it turns out, only around two-thirds of VAT is paid directly by households. As Bill Dodwell, Deloitte's head of tax policy, reminded me, the rest is paid by property companies, government departments, charities, and other businesses who for one reason or another can't claim back their VAT. (Of course, all taxes are paid by households, eventually - either as consumers, or shareholders, or employees - but I'm talking here about the direct hit from raising VAT).

So there's maybe an extra £8bn being raised directly from households with this increase (two-thirds of £12.1bn). If you divide that by 26 million, you get an average loss of around £307 per year.

But of course, a lot gets lost in an average. Mr Dodwell and his colleagues at Deloitte have taken the trouble to look at what families in different parts of the income distribution actually spend on VAT-able items, as revealed by the ONS Family Spending survey [1.52MB PDF] . On that basis, they were able to tell me what the impact would be on different families' weekly expenditure, if they tried to buy the same goods as they were before.

On average, Deloitte calculates that as a result of the VAT rise:

Households in the middle of the distribution (the fifth and sixth decile, by spending) will have to pay an extra £3.96 per week, or £206 per year.

Those in the top 10% of households will pay an extra £10 per week - or £520 per year.

And those in the bottom 10%, by expenditure, will pay an extra £1.30 a week, or £68 a year.

As a share of expenditure, the Deloitte figures show the poorest losing 0.8%, the middle losing 0.96%, and the richest just over 1%. In that sense, these figures back up the point made by the government, that the VAT rise is not regressive if you look at the impact on households, relative to their expenditure.

Back in the summer, the IFS made this point in their response to the June Budget [488KB PDF] . It came up with roughly similar percentages to Deloitte.

And yet, the traditional definition of a regressive, or progressive tax is relative to income. In those terms, the VAT rise is clearly regressive (as you can see on page 9 of that presentation from the IFS) The hit to the poorest 10th represents about 2.5% of their income, versus a roughly 1% hit for the those at the top. In that old-fashioned sense, the tax change is regressive.

The same point emerges, more strongly, when you consider the combined impact of all of the tax and benefit changes due to come into force over the next two years. As the IFS has said for some time, these are clearly regressive across the bottom 9/10ths of the income distribution. The poorest 10th stand to lose 3.4% of their income, by January 2013, which is more than any other group except the top 10th, which lose 4.1%. Again, the picture looks fairer if you measure the losses relative to expenditure. By that measure, the poorest lose 1.9% and the richest lose 6.2%.

Looking beyond today's news, to the freeze in child benefit, the removal of family tax credit from many families, the real terms cut in the higher rate threshold, and all the rest, James Browne at the IFS tells me that households in the middle of the income distribution (the fifth and sixth deciles) will have lost about £10.60 a week - or more than £550 a year - by January 2013. So VAT going up to 20% is, quite literally, not the half of it.