It's a simple enough mistake. Australians on the top tax rate do indeed pay 45 cents in the dollar. The rate cuts in at $180,000. They also pay the temporary deficit reduction levy (another 2 per cent), the Medicare levy (yet another 2 per cent) and the Medicare surcharge where applicable (a further 1.5 per cent). The total comes to 50.5 cents in the dollar. But the amount of tax actually collected from those Australians is nothing like that much, as a quick workout of the Australian Tax Office calculator makes clear. An Australian earning $200,000 pays around 36 cents in the dollar including the Medicare levy and the deficit surcharge, far short of the claimed 50. Even an exceptionally high earner on $500,000 pays no more than 44 cents in the dollar. Typical high earners pay much less. An Australian on $80,000 pays $19,147. An Australian on $120,000 pays $34,747. The difference between the quoted rates and the actual rates comes about because all Australians - even the highest earners - enjoy a tax free threshold. They pay no income tax on their first $18,200 of income no matter how much they earn. And they pay just 19 cents in the dollar for the part between $18,200 and $37,000 and 32.5 cents for the slice between $37,000 and $80,000.

Only the part of their income in excess of $80,000 gets taxed at their marginal rate (for really high earners $180,000). Most high earners don't take home that many dollars above the threshold. Bemused number crunchers on Twitter have been trying to calculate how much someone would need to earn to actually pay half of it in personal tax. One came up with $6 million, another with $3 million. Whatever the figure, it's beyond the reach of most high earners. The Treasurer was making a broader point, that it is "wrong" to say low-income households are the biggest losers from the budget. "That story is wrong because it fails to take into account a range of things, like the fact that higher-income households pay half their income in tax, low-income households pay virtually no tax," he said. But those two things aren't in conflict. It would be quite possible for low-income households to be the biggest losers from the budget and for them to pay less tax than high earners.

Calculations of winners and losers - the sort carried out by the Treasury and included in every budget since 2005 until this one - are a measure of who is made better or worse off than they were, not of how well or badly off they are in absolute terms. Mr Hockey says high-income Australians pay tax in order to support low-income Australians. This is indeed a feature of the tax system. But it is not relevant to a calculation of the change in circumstances that will result from the budget. Separate calculations released under the Freedom of Information Act show the Treasury believes the change will be negative for lower-income households, less negative for higher-income ones. The Treasurer's deeper point is that if you wind back benefits you'll necessarily take some away from people who would have got them. He is right. With the outrageous exceptions of the superannuation tax concessions and the negative gearing tax arrangements, high earners don't get anything like as much government support as low earners. That's the way the system is designed. Cutting into welfare has to mean cutting into benefits. Unless you cut into high-income welfare, which the budget didn't do. Peter Martin is economics editor of The Age.

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