"HM Revenue & Customs: The Exchequer effect of the 50 per cent additional rate of income tax"

I've reverse engineered the calculations they made in explaining why cutting the 50p top income tax rate to 45p would probably be revenue-neutral (see their calculations and explanations on page 15 and the chart on page 51) and I've embedded the key part of the spreadsheet below for your entertainment.

Their aim seems to be to set the income tax rate at the revenue-maximising rate, there are a few of problems with this:

1. They accept 12.8% Employer's NIC and 1% Employee's NIC as a given, even though these have both increased by 1% and are just another layer of income tax.

2. They cheerfully admit that they have no idea what the elasticity of supply of labour is (which they refine slightly and refer to as 'Taxable Income Elasticity' or TIE). On pages 18 and 19 they summarise lots of studies from various countries which give figures between 0.2 (people continue working and paying tax, even if wages fall and/or tax rates increase) and 0.8 (people will work less, avoid or evade taxes, move abroad etc if wages fall and/or tax rates increase), ignoring outliers. They can't make up their minds whether to use 0.35, 0.45 or 0.55 (so their chart uses all three).

3. As the calculations show, this is the most important unknown of all; if you assume a low sensitivity of 0.2, then the revenue-maximising income tax rate (i.e. the top of the Laffer curve) is 67%, and if you assume a high sensitivity of 0.8 it's 35%. Of course, different people respond differently; the rate might be different for high earners and low earners; the short term responsiveness might be more or less than long term etc.

4. They say that TIE can be split up into three things: labour supply (people work less or move abroad), tax planning (people work just as much but use legal loopholes) and evasion (people work just as much but do it cash-in-hand), and say the labour supply effect is "between one-third and one-half of the total TIE". This is their roundabout way of admitting that taxes on income have dead weight costs.

5. Those dead weight costs are also an incredibly important consideration. My spreadsheet shows the fall in potential GDP in the last row, i.e. the fall in declared taxable income multiplied by 0.4, which seems to come out at between 10% and 15%. That's a heck of a lot of lost output and unnecessary unemployment, by the way.

The figure for total revenues assumes that GDP starts at 100, with a flat income tax rate of 10% and National Insurance still in place (even these low rates must depress GDP by five per cent or so, let's gloss over that).

6. Another thing they ought to consider is that the cost of welfare is just an upside down Laffer curve; the way to minimise the cost of means-tested benefits is to find out what the revenue-maximising tax rate on lower earners with a small independent income would be and then to use that as the marginal withdrawal rate.

As a matter of fact, marginal withdrawal rates (especially for people who have tax deducted and benefits withdrawn at the same time) are between 70% and 100%, which is way beyond the top of the Laffer curve - in other words, we could reduce the cost of means-tested welfare by reducing income-based means-testing, although that point seems to escape them.