21 May 2013

Climb every mountain...

This outing is to explain a type of chart I’m thinking of using in later posts.  It’s intended as something I can link back to as background material if and when I do.  Pending inspiration for a better name, I call it a hill-climb or effort chart.  I’ve not seen one used before, but given I’ve never had an original thought in my life I suspect I must have come across something like it in the distant past.

The idea for it came to me when I was driving on a freeway/highway/motorway and came to an exit-ramp.  It was one of those that goes up and then over the main road.  My little car struggled a bit because the exit was quite steep and I found myself imagining walking instead.  I idly pondered the fact that if I stepped out 500 paces along the main road I would have travelled further horizontally than if I did 500 paces on the exit-ramp.  That’s because on the exit ramp some of my paces would have gone into getting me higher off the ground.  Alternatively, to travel a distance equivalent to 500 paces horizontally while also going up the ramp would require a lot more effort than on flat ground.

Not exactly mind-boggling stuff, but it was a long, boring drive and any mental diversion was welcome.  Anyway, I then started to wonder if I could use the analogy of climbing up a hill, where some horizontal travel is replaced with vertical, to represent the “journey” someone faced when trying to increase their disposable income.   I could show the gain in disposable income as the horizontal journey, and the amount paid in tax or “lost” in reduced transfer payments as the hill.  If the hill was very steep, then for a given $ increase in gross income the person would not move far horizontally (ie, little gain in disposable income) but move quite a distance vertically (ie, significant increase in tax paid or transfers lost).

At this point a picture might help and I’ll start with one showing how the income tax scale looks when portrayed using this idea.  The current basic scale is as per this table:

Table 1

Taxable income

Tax payable

% rate on excess

















So, if we run our picture out to a taxable income of $200,000 we will pick up all four points at which the rate changes.  Here it is:

Chart 1

We can see that if the objective is to increase disposable income by $10,000 (measured from the starting point of zero) the terrain ahead is flat – all we have to do is earn $10,000.   In contrast, if we already had a disposable income of $20,000, getting an extra $10,000 is a bit harder.  We have to go up a bit of an incline, requiring us to take a longer “journey” overall.  In fact we’d have to earn an extra $12,346 to get to our chosen point.  The inclines become steeper as we progressively cross over the thresholds from Table 1.

(Note too that although I said this was a picture of incomes out to $200,000 it seems to end well before that, at a little under $137,000.  That’s because the horizontal axis is disposable income.  If you add the disposable income at the end point to the tax paid you’ll get the full $200,000.)

At this point you might be saying “so what”.  After all, there are easier ways to establish how much has to be earned to get a given disposable income – a simple disposable income chart would be better for that purpose.  But this chart is not really intended for analysis of that kind.  It’s just trying to give a visual representation of how easy/difficult it is to increase disposable income.  This becomes more apparent when you add in the effect of other tax-transfer system elements.

Chart 2 has the same basic concept of plotting the “lie of the land” for a journey to increase disposable income by $60,000, and for reference retains the basic tax line from Chart 1.  In addition it has traces for a few household types which include a larger range of tax-transfer elements.

Chart 2

Here it becomes apparent that the journey toward higher disposable incomes is rather more difficult that the earlier basic tax line would suggest.  In fact, for the single income couple, parts of the journey look very difficult indeed.   If the couple wants to get past a gain of roughly $14,000 in disposable income they need to climb a vertical cliff face that’s about $5,000 high.  In other words, increasing income by $5,000 at that point gives the couple nothing – they don’t move horizontally toward their higher income destination at all.  (Actually, they do gain a tiny bit as the cliff isn’t quite vertical – they’d get about $50).

In some spots the lie of the land exhibits something akin to a rocky overhang – the most visible being the one for the single Newstart (NSA) trace at a disposable income of about $50,000.   That particular one is caused by the imposition of the medicare levy surcharge – the unpleasantness of the climb at that point being a deliberate imposition to encourage the take-up of private health cover (none of our intrepid climbers have it, by the way).

Other overhangs are due to the “sudden death” style withdrawal of some payments (eg, schoolkids bonus in the single parent case).  The small one for the couple at around the $10,000 disposable income point is due to the loss of an income support bonus and a design flaw in the sequential income test.

Also apparent is the somewhat gentler slope experienced by the single parent on NSA compared to the other two NSA examples.  This reflects the 40% taper in the NSA income test for this group, compared to the 50/60% faced by the others.

So there we have it.  A chart that tries to show the effort needed to increase disposable income, by portraying it as a hill-climb or mountaineering expedition.  I intend to use it, along with some more conventional EMTR material, in future posts.


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