Stephen Hawking's publisher told him that every equation in A Brief History of Time would cost him 10,000 readers.
This column would be lucky to muster that many readers, so I will refrain from putting in an equation, and use words instead. The equation is Hull's Equation for Removing Tax Brackets.
It came about after reading Treasurer Joe Hockey's dismal excuses for relieving the income tax "burden" on the well-off.
Hockey said Australia's top marginal tax rate was too high and cut in too soon ($180,000). Inflation would push more people into this higher bracket and something should be done about it.
He said the same thing about the second-highest bracket which cuts in at $80,000. Inflation would ensure that the incomes of several hundred thousand people would move from below $80,000 to above it, and attract a higher rate.
There is a lot of muddled thinking and politicking here.
Firstly, if politicians were serious about bracket creep, they would index the level of income at which each higher rate kicks in. But no. Instead, they prefer to let inflation silently push income tax up for a few years so they can generously promise "tax cuts" before an election. But they are not real tax cuts, just a reversion to the status quo.
Secondly, the biggest unfairness is not at the higher end. It is at the lower end – particularly the bracket $37,000 to $80,000 where the marginal rate is 32.5 cents. After $80,000, it rises to 37 cents up to $180,000, when it goes to 45 cents.
How can it possibly be fair to tax the 37,001st dollar at 32.5 per cent and tax the 179,999th dollar at 37 per cent, just a trifle higher? Someone on $179,999 is very well off indeed. Someone on $37,001 is really struggling.
Or, how is it fair that the 80,001st dollar is taxed at the same rate as the 179,999th dollar? Someone on $80,001 is probably just getting by, particularly if they have kids and a spouse at home or working only part-time.
The unfairness is that Australia has too few tax brackets.
Thirdly, it is misleading to say that as a multiple of average income, Australia's top rate cuts in at a lower rate than most other developed countries. For a start, "average income" is misleading. High-wealth people in Australia, US and Canada drag up the average in a way does not happen in the more equal nations in Europe.
If you use "median" income – the mid-point at which half of taxpayers are below and half above – you get a different result. Average income in Australia is about $76,000. Median income is about $60,000. Australia's cut-in for the top marginal rate as a multiple of median income moves us more to the middle of the pack.
Further, virtually every Australian on an income above $180,000 pours most or all of the tax-deductible $35,000 into superannuation. In effect, the top marginal rate cuts in at about $35,000 above the apparent rate.
Australia also has other property deductions for high-income earners that are not available in Europe. Some of those convert income into capital gains which are taxed at a lower rate. In short, Hockey should concentrate on tax cuts for people below $60,000 or so.
Further, the availability of the tax-free threshold should be means-tested against spouse's income. That way, spouses of wealthy people cannot get a lazy $18,000 tax free – in effect another tax lurk which again makes Hockey's method of assessing tax levels misleading.
By the by, Hockey wants to pay for the tax cuts for people on higher incomes with cuts in government spending. Given that people on lower incomes benefit more from government spending, Hockey is behaving like a reverse Robin Hood – taking from the poor to give to the rich.
Hockey also said he wanted a simpler and fairer tax system. The trouble is the two do not go hand-in-hand. A nice simple 15 per cent GST would not be fair unless there was concomitant and complex compensation through the welfare and income tax systems.
A complex but fair income tax system would remove the existing four income tax brackets, which are simple but manifestly unfair. They could be replaced with a sliding scale whereby the marginal rate goes up very slightly with each dollar earned.
It is year 12 mathematics. That, of course, means you would be lucky to get three journalists or four politicians in Australia to understand it. But it would be a much fairer system
The dreaded equation in its simplest form has two fixed values. The first is the income at which the marginal rate stops going up (say, $200,000). Let's call that "H". The second is the top marginal rate (say 50 per cent). Let's call that "T".
The marginal rate would rise steadily dollar by dollar from zero at zero income to 50 per cent at $200,000.
To work out the marginal rate ("R") at any given income ("I") you multiply I by T and divide that by H. Thus the marginal rate at $100,000 would be 25 per cent. Unfortunately, this is a bit too simplistic and thus not quite fair or workable.
You have to add two more values: an income level ("L) below which no tax is paid at all – say, $20,000 – and a kick-in rate of tax ("K") for the first dollar above that $20,000 income, say 20 per cent.
Two equations would yield the marginal rate at any given income and the amount of tax payable. The latter is the area under the graph line of the first equation.
I will not risk the loss of 20,000 readers by putting the equations in this column. But they would enable policy makers to tweak the inputs to yield a smoother, fairer progressive income-tax system which would be a big improvement on the present four giant leaps for tax-paying humankind.