The Parliamentary Budget Office has very clearly shown the government’s sales pitch for the income tax cuts to be false. Had you gone by the marketing you would be believing the government was giving those on median income or “middle Australia” the biggest help. But the PBO has shown that the tax cuts are overwhelmingly targeted towards giving the wealthiest the biggest cut.

The overriding reason given by then prime minister and treasurer Malcolm Turnbull and Scott Morrison for their income tax cut policy was that we needed to help “aspirational” workers and that bracket creep was doing them damage.

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The argument on bracket creep was always pretty disingenuous given Turnbull at the time suggested it was all about people turning down a higher paying job.

In June he rather oddly asked “how many times have we heard over the years – people say bracket creep is a real disincentive for people getting ahead? For getting another job, for taking a promotion, for working overtime?”

Suddenly it seemed we lived in a world where someone on $50,000 was turning down the offer of a job on $90,000 because $3,000 of that new salary would be taxed at 37% rather than 32.5%. It was a pretty disappointing approach from a man who certainly knows how the tax system works.

The overriding problem with Turnbull and Morrison’s arguments was that bracket creep is actually an issue, and last week the PBO revealed just how poorly it is addressed by the government’s income tax policy.

Each year the PBO releases its medium-term budget projections. These, as with all PBO work, is done independently of treasury and finance but does rely on the assumptions within the budget such as “above trend economic growth for much of the period and a return to close to trend wages growth by the end of the forward estimates period”.

The PBO estimates that the budget should be back in surplus by 2019-20. It is also worth noting that while government spending is expected to fall as a percentage of GDP at no point in the next 10 years is it expected to reach a level that would have seen a budget surplus in any of the years from 2008-09 to 2016-17.

As I noted after the May budget, budget surpluses occur due to increased revenue, not reduced spending:

And that increase in revenue is mostly coming from increases in income tax.

The PBO projects that by 2028-29 the level of personal income tax will have risen from 11.5% of GDP this year to 12.5% – the highest since the introduction of the GST. At the same time the level of company tax revenue is expected to fall to 4.3% of GDP from its current level of 4.7%:

This might seem surprising given most of us are getting a tax cut. Indeed the PBO confirms that under the government’s tax plan the average tax rate for everyone earning over $36,000 will fall:

But as I noted at the time the benefits were greatly skewed in favour of the wealthy. The PBO confirms this by finding that the cut in the average tax rate increases from 0.62% pts for those earning $86,000 to 3.63% pts for those on $199,000:

The change in the average tax rate however does not detail the increased amount individuals will pay in income tax due to bracket creep.

Bracket creep involves you paying a higher average rate of tax because of increases in your wage – not due to your taking a new job, but because of a pay rise.

Income tax is paid on nominal income, so even if your wage goes up only in line with inflation and thus in real terms you are no better off, the level of your average tax rate will have increased.

It is always a bigger issue for those earning lower amounts. When you look at the graph of the average tax rates, it is clear why this is the case – the more you earn the flatter the average tax rate becomes.

Consider that even under the new income tax plan, going from $45,000 to $55,000 involves your average tax rate going from 13.3% to 16.8%, an increase of 3.5% pts, even though they remain in the same marginal tax bracket. By contrast someone going from $125,000 to $135,000 sees their average tax rate go from 25.6% to 26.1% - an increase of just 0.5% pts – ie barely noticeable and absolutely no real disincentive to work at all.

So any policy to combat bracket creep must therefore be overwhelmingly targeted towards lower to middle incomes, and yet the government’s plan does not.

The PBO highlights this by looking at the changes in the average tax rate not by income but by income quintiles.

The PBO estimates that those on the lowest income quintile (ie the poorest 20% of the population) will not see much of a rise in their tax rate. This is not surprising given most of these people earn less or just over the tax free threshold.

But for those in the second bottom and middle income quintile the impact of bracket creep is substantial – causing their average tax rate to rise by 5.4% pts compared to just 2.9% pts for the richest 20%.

Now that again is not surprising given the median taxable income is around $55,000, so those earning around that or just below it are going to see big increases in their average tax rate should their wage go up by $5,000 to $10,000 over the next 6 years compared to someone in the top 20%.

But the problem is that while the tax cuts will remove three quarters of the bracket creep for the richest 20%, it will only account for 15% of the bracket creep for the median income earners:

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As a result those in the second and third income quintiles will see their average tax rates go up by 4.5% pts and 4.6% pts even after the tax cuts, while the top 20% will see their average tax rate rise by just 0.8% pts – the same amount as for those in the lowest income quintile.

The government’s income tax policy was always pitched as being for average Australians, for “middle Australia”. That was always a fib, and the PBO has very loudly made this clear.

It is an income tax policy designed to benefit those who need tax relief the least. A policy designed to deliver large tax cuts to the wealthy under the guise of helping those on median incomes. Don’t believe the marketing, believe the facts.

• Greg Jericho is a Guardian Australia columnist