Since the UK general election in May there has been a lot of discussion about tax credits and whether the proposed cuts would make the poorest worse off. On one side the government says that the increase in minimum wage to the living wage as well as an increase in the tax free allowance would make low earners better off, whereas the critics point to the fact that a £4.4 billion cut has to have a detrimental effect. The proposed cuts were passed in the conservative lead house of commons, but was blocked by the house of lords, where the government does not hold a majority. As a result the Chancellor of the Exchequer, George Osbourne, announced in the Spending Review that the proposed cuts would not go ahead.
At the time there were a lot of figures being thrown around about who would be better and worse off, but mainly used by people with an allegiance to a particular group or political party. As I wasn't sure who to trust I decided to take a look at the numbers myself as a non-partisan observer, with no preferred political party, who currently doesn't even live in the UK.
The first part is the simple bit; looking at the current tax and national insurance rates. The tax brackets are fairly well known with only a few simple rules:
Tax free allowance - £10,600
Basic rate 20% - £0 to £31,785
Higher rate 40% - £31,786 to £150,000
Additional rate 45% - Over £150,000
The tax free allowance goes down £1 for every £2 above £100,000.
Note that these are the basic rules for taxable income, there are other forms of tax relief from charitable donations, pension contributions etc. I am just interested in the simplest case.
There are also rules for national insurance contributions (NIC)
NIC threshold - £8,060
NIC at 12% for earnings between £8,060 and £42,385
NIC at 2% for earnings above £42,385.
This again is the basic Class 1, category A case (other cases here).
These rules were written as a function in Julia and run for a range of yearly wages.
The tax and NIC lines (red and black respectively) show various bumps where the different rules kick in. Also plotted is the percent of salary after tax (green), this is perhaps the more interesting graph as the various rules are more distinct. First the region with no tax or NIC, then NIC starts being paid before the different tax bands are applied. I find the most striking region to be between £100k and £120k where the tax free allowance is removed linearly.
The obvious question is whether this is the best way to tax people. It seems like the tax band structure creates a very artificial form to the percentage of salary graph. Perhaps a smooth function with the same 45% asymptote and tax free personal allowance would be fairer. But also what is fair in tax is not trivial and best left to another day.
At the time there were a lot of figures being thrown around about who would be better and worse off, but mainly used by people with an allegiance to a particular group or political party. As I wasn't sure who to trust I decided to take a look at the numbers myself as a non-partisan observer, with no preferred political party, who currently doesn't even live in the UK.
The first part is the simple bit; looking at the current tax and national insurance rates. The tax brackets are fairly well known with only a few simple rules:
Tax free allowance - £10,600
Basic rate 20% - £0 to £31,785
Higher rate 40% - £31,786 to £150,000
Additional rate 45% - Over £150,000
The tax free allowance goes down £1 for every £2 above £100,000.
Note that these are the basic rules for taxable income, there are other forms of tax relief from charitable donations, pension contributions etc. I am just interested in the simplest case.
There are also rules for national insurance contributions (NIC)
NIC threshold - £8,060
NIC at 12% for earnings between £8,060 and £42,385
NIC at 2% for earnings above £42,385.
This again is the basic Class 1, category A case (other cases here).
These rules were written as a function in Julia and run for a range of yearly wages.
The obvious question is whether this is the best way to tax people. It seems like the tax band structure creates a very artificial form to the percentage of salary graph. Perhaps a smooth function with the same 45% asymptote and tax free personal allowance would be fairer. But also what is fair in tax is not trivial and best left to another day.
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