Negative income tax - some thoughts on a formula.

 The concept of negative income tax is complex to say the least.....

Negative income tax is a taxation system where lower earners are incentivised to earn more, whilst receiving a 'top up' (through negative tax). The core principle of such a system is that people should not be able to earn more by working less - otherwise this would be unfair, however lower earners are given extra support, whilst being incentivised to improve their financial standing.

There is a point at which the earnings cease to be 'topped up', and start getting taxed down, for the purposes of this discussion this arbitrary point will be set at £25,000 (this is a ballpark figure, and is not necessarily accurate).

I have written two formulas (thanks to Rebekka for the help and highly constructive criticisms), one for incomes below £25,000 where incomes will be taxed up. And a second for incomes above £25,000.

For earning below £25,000

Formula: £25,000 - [Earnings](percentage tax rate) 

Example 1

Income = £15,000 (so this person earned £15,000 through their own work)

So post tax income will be (with an example taxation rate of 40%)

£25,000 - £15,000(0.4) = £19,000

So for initial earnings this person will receive and additional £4000 topping their total, post-tax income to £19,000.

Example 2

Income = £14,000 (so this person earned £14,000 through their own work)

So post tax income will be (with an example taxation rate of 45%)

£25,000 - £14,000(0.4) = £18,700

So for initial earnings this person will receive and additional £3700 topping their total, post-tax income to £18,700.

So to summarise: people earning less get a proportionally greater ‘top up’ – but not so much as to be greater than people earning more pre-tax.

This is key as people who earn more must always keep more after tax as if not, there would be no incentive for people to earn more and so the economy would stagnate.

For people earning over £25,000

This is slightly different as the earnings cannot just be plugged into the same formula as those earning less than £25,000 (remembering that this is an arbitrary number).

The formula is therefore:

(Earnings - £25,000) - (Earnings - £25,000)(% tax rate).

Example:

Earnings of £35,000 with a nominal taxation rate of 30%

Final income   =  £35,000 – [(£35,000- £25,000) - (£35,000 - £25,000)(0.3)]

= E - (E - £25,000)(1-% tax rate) = £28,000

so in this situation their income is taxed down, but it can never go below £25,000.

One final caveat

There needs to be some form of support for people who do not earn anything, in order to do this there would need to be some drastic changes to the gradients of the curves on the graphs, alternatively one could give everyone a basic income of, for example, £10,000 which would ensure that no-one starves…

And one final thing to remember: the taxation rates are not fixed and have not been fully costed so are ballpark figures and not necessarily accurate, also the fixed point that separates what is ‘taxed up’ to what is ‘taxed down’ does not have to be £25,000, I merely picked this as it seems a reasonable number.

-       -  Archie