Growing Problems

‘Ah ha’, I hear people saying; ‘those predictions of economic doom didn’t pan out. The markets are recovering; it was just a correction – and we’re out of the woods now.’


Wrong, I’m afraid.

The problem with predicting economic events is that – well, they’re hard to predict. In general terms, if you were able to predict accurately the day-to-day – or week-to-week – or decade-to-decade fluctuations in the market, you too would be one of the well-upholstered “masters of the universe” to borrow Tom Wolfe’s phrase. A person who always won when you gambled – or at least like the clowns who got us into this mess, if you lost, you could just turn to the government to bale you out – courtesy of the tax-payer.

But the real world is somewhat messier than this. ‘OK’, you say, ‘so we can’t make accurate detailed predictions – but look, these market squalls come around every couple of decades or so. Some people get hosed, for sure – but the FTSE & the DOW always go up in the long-run. Someone’s loss is another man’s opportunity.’

So we generalise: the orthodox view is that economic growth can go on for ever – or the unorthodox view that, at some point, it will end.

So which view is correct?

I am predicting – no, I’m stating – that economic growth must have an end.

In making this claim, am I cheating? Am I just relying upon chance? Is it the case that if given an infinite amount of time, the law of averages dictates that predictions of economic doom would be right eventually?

No. We can state with absolute certainty that growth will have an end – and probably a good deal sooner than we care to imagine.

Don’t believe me?

Let’s take a look at the maths.

And to make it relevant, let’s use an economic sum in today’s news. It’s reported that China “enjoyed” economic growth of a staggering 11.4% last year.

For purposes of illustration, let us assume this figure was repeated annually.

Under these circumstances, how long would it take the size of the Chinese economy to double? And think about that – the entire Chinese economy – doubled. How many more coal-fired power stations and boom-town hi-rise blocks would that be?

Let’s set aside the growth rate in China of 11.4% for the moment, and just look at the basic calculating technique.

It is possible to produce a ready estimate of doubling periods using what is known as the Rule of 70, or the Rule of 72, or the Rule of 76. The best choice of numerator will be determined by the size of percentage growth.

For our purposes, let’s use the Rule of 72, and take an annual percentage growth rate and divide 72 as the numerator into the growth rate sum. For example, say you’re looking at 4% P/A growth. Take 72 and divide it by 4; this gives you an answer of 18. What does this figure mean?

The 18 represents the number of years that it would take your economy to double in size.

So at this 4% steady growth rate, the total size of your economy has to double every 18 years. Can this go on indefinitely? No. Consider an index figure of, say, 20, to represent the starting size of your economy. It doubles – then it’s 40. It doubles again – then it’s 80. It doubles again – then it’s 160.

Thus we see that the quantum of each most recent doubling period is greater than the total of all of the quantum’s which preceded it – combined.

No closed system (like the planet) can sustain such exponential growth indefinitely.

Another interesting thing is the speed at which the boundaries – the limiting factors – of the system are hit. Ecologists use this analogy: imagine you have a large lily pond. It has 1 water lily in it. Overnight, that doubles to 2. Overnight again, that doubles to 4. Again – it doubles to 8. This exponential growth continues until the pond is full after 30 days.

Question: – When was the pond half-full?

Answer: – it was half-full on the 29th day.

Day 29 – and you still have fully one half of your resource, in this case surface area, remaining unused.

And just one day later? That half of your starting resource is also all used up.

So let’s run that Chinese growth rate of 11.4% through our ready-reckoner.

Take 72, divide by 11.4. This gives 6.3157895. I think we can call it 6.32.

So that’s a time period of 6.32 years until the economy has doubled in size if it grows at the, admittedly, extraordinary rate of 11.4%. OK, so such a high growth-rate is an extreme example – but even at this speed, China has still not yet caught up with Western “standards” of “consumption”.

Even setting aside the annihilation of the planet’s biological ‘carrying-capacity’ upon which we all depend (Yep, even Merrill Lynch execs and central bank chairmen) can we even imagine the mineral and energy requirements of such growth?

Well, actually we don’t need to ‘imagine’ it – we just do the maths.

For those possessed of sufficient hubris to imagine that we humans are such a resourceful and brainy bunch that we will techno-fix our way out of such physical constraints, I would strongly recommend the book ‘Collapse’ by Pulitzer-Prize wining science author, Jared Diamond.

The rest of us – if we’re honest – can see that a planet’s worth of SUVs and plasma televisions, holiday flights and luxury homes for all the billions of people in the world just isn’t happening. And as we in the West have had our snouts in the trough for so long, we need to mend our ways. Nothing so condescendingly colonialist as “setting an example” – rather, just facing the truth about the patterns of our society – and maybe recognising that, actually, “consumption” as a mode of living is actually killing us, not making us happy and breaking down the fabric of our society.

Stuart Syvret

This post’s book: The Growth Illusion, by Richard Douthwaite.

This post’s joke: The functions are sitting in a bar, chatting (how fast they go to zero at infinity etc.). Suddenly, one cries “Beware! Derivation is coming!” All immediately hide themselves under the tables, only the exponential sits calmly on the chair.

The derivation comes in, sees a function and says “Hey, you don’t fear me?”
“No, I’m e to x”, says the exponential self-confidently.
“Well” replies the derivation “but who says I differentiate along x?”

(No, I didn’t understand it, either)

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