When you listen to all the discussion about balancing the budget, about how any increase in spending needs to be matched by an increase in tax, why does no one mention that an increase in spending automatically generates extra tax?
There is no need to raise tax rates!
In fact, unless people choose to save the extra spend then it all comes back to the government as extra tax. In other words the extra spending is self funding.
This seems miraculous. Surely anyone who argues this way must be crazy—a believer in the magic money tree? Actually no, this statement follows from a very solid piece of mathematics that we all learnt at school. Unfortunately most journalists and many politicians were either not very good at maths or prefer not to explain how it really works. As voters, we should demand better.
Before getting to the maths, let’s try to answer a specific question. How much does an extra teacher cost? Or an extra nurse or an extra Doctor?
The naive answer is just to take the teachers salary, but this is wrong because a fraction of this comes back immediately because the teacher pays tax. To work out the net cost we need to discount all the extra tax paid due to the extra worker. In addition to income tax, NI and council tax, the worker also pays VAT, duties on fuel etc. The part that is not immediately repaid in tax creates extra income for others in the economy who consequently pay more tax than they did before. Excluding savings and tax avoidance, and all other things being equal, the maths tells us that the extra cost of the extra worker to current taxpayers is exactly zero!
The piece of maths that proves this is known as arithmetic progression—it says the sum of all the tax paid is equal to the initial spend. Alternatively, if we want to calculate the amount of government spend not returned in tax we can use a geometrical progression which works like this: For simplicity, let’s say that there is a 20 % tax on each exchange whether it is paying wages or VAT. For every £100 the government spends on the extra teacher, then £80 goes to the teacher and £20 goes back to the government. If the £80 is used to buy clothes £64 pounds goes to the shop, and another £16 back to the government. The £64 is mostly spent on wages for the employees, and another £12.80 goes back to the government. The geometrical progression tells us that after 40 such exchanges 99.99% of the money is returned to the government. The extra spend is self funding!
So if money is not the thing, what limits the number of public sector workers? The answer is supply and demand. If we try to create too many posts in public service we may drive up wages and drive down productivity by removing productive workers from other sectors. So the key is to decide if there is a demand, e.g., the economy is less productive than it could be because of crime, bad health or poor education. If the evidence is that we can improve things, then government spending is a simple win-win!
PS. For another take on this see here.