My post on bracket creep brought up some discussion of the idea of a smooth tax curve in place of the piecewise linear one we have now.
I’ve long thought this was a good idea and I have what I think is a neat way to implement it. Instead of providing a table that lets taxpayers calculate their tax payment in one step at present (take the tax payable at the threshold below actual income and apply the marginal rate to income above the threshold), I’d provide a similar mechanism to enable calculation of the average tax rate which would increase linearly between threshold points, just like total tax in the current system. Calculating the tax payable takes one more step – multiplying income by the average tax rate.
The big merit of this it that it focuses attention on the variable relevant to social choices about tax – the average tax rate, rather than on the marginal tax rate, although you can still calculate the latter if you’re so inclined.
John Quiggin 
to answer me no no’s point from below, having a smooth curve doesnt intrinsically adress incentives, this is to do with the shape of the curve (or the shape of the brackets if that makes sense)
i was essentially bringing up two points. however, having a smooth curve does remove some stupid parts of the current tax system. one is that tax rate jumps a lot at certain arbitrary points, one of which is when you go from the dole (negative tax) to being a low income earner with positive tax, for hardly any more money in your pocket, except now you have to wake up at 7 in the morning.
as pointed out by others the jump in tax at this poith is huge. now, you could get rid of this by having lots of brackets all over the place with different rates but why not just be sensible and have a curve.
then at any point on the curve you could easily create upward envy, that is an incentive for people to work as opposed to a disincentive.
(note, this doesnt mean i think everyone should work harder, just that if they choose to do so there are sensible incentives to do so)
quiggins idea is ok, but why have thresholds at all, and then lines between them, instead of a true curve (that is one without cusps)
the gradient of the curve shouldnt jump at certain arbitrary points either.
(apologies if i misunderstood your curve)
But c8to, if we just talked about average tax rates, as Quiggers alludes, then in the current system we know that average rates don’t experience quantum jumps.
The problem at the bottom end wouldn’t be addressed by a curve, as it’s not just the tax rate that’s responsible. Moving from welfare to income and paying tax is a totally a different issue, which requires different solutions.
Surely the most serious challenge is to minimse avoidance – as mentioned previously,no serious attempt to crack down on avoidance has ever been undertaken by any government.
The biggest frustration ( in my view ) for PAYE taxpayers is that they represent the backbone of a program which allows much wealthier individuals to pay little or nothing – whilst availing themselves of the services paid for by the long suffering wage and salary earners.
I’ll vote for anyone determined to tackle this inequity seriously!
For sake of simplicity just have a flat tax but with a threshold to make it progressive and NO deductions.
But c*to you still have to have one cusp – the marginal rate cannot rise indefinitely. and of course if you want a tax free threshold you’ll need a second.
If you want to avoid cusps completely (ie make the marginal rate schedule differentiable) you’ll need a sigmoid curve. Try explaining that in the Tax Pack!
“the variable relevant to social choices about tax – the average tax rate”
Nonsense. For determining economic behavior, the marginal tax rate is what matters. The average rate is completely irrelevant.
Quiggin must have been absent from economics school on the day they taught economics.
George, you must have been absent the day they taught reading, or you would have noticed the word ‘social’ just before ‘choices’.
Under the German system tax owed is worked out, literally, by plugging in income into a quadratic equation (apart from at very high or low incomes). There are therefore hundreds of thousands of different marginal tax rates, one for each DM of income.
This takes the focus right off any discussion of marginal tax rates, and allows, politically, a higher average tax rate than would be allowed if the constant focus of attention was on “you lose half your extra income in tax so there are no incentives to work hard”, as happens here.”
So the economic effects are not relevant for social choices! Why then should we pay any attention to your opinion? I thought your expertise was in economics.
OK, Simon/George, let’s go through it again, really slowly. The main effect of taxes is to transfer resources from one use (private consumption) to another (public expenditure). The amount transferred depends on the average rate of taxation.
The effect of the marginal rate of taxation is, as the name implies, marginal.
As a general point, I try to be polite to commentators. But if someone who has stumbled through undergraduate economics tries to teach me the subject, that person is a fool and can expect to be treated as such.