Hello!
In my last post I discussed how Malthus correctly predicted the death of hundreds of millions by observing the difference between linear and geometric growth. In this post, I want to expand on this to discuss economic growth.
In a nuclear bomb, a single atom breaks into pieces, and releases energy. Two of the pieces fly off and strike other atoms, causing them to break up. Each of those two atoms relase two more particles, causing a further 4 atoms to fragment. These catalyse the breakup of a further 8, then 16, then 32 atoms. This repeated doubling results in the wave of destruction moving at extraordinary speed, trigering the breakup of millions of billions of atoms in a fraction of a second – a nuclear explosion.
This exponential, doubling pattern of growth always results in an explosion. The mathematics are simple and irrefutable. And this, in ultra slow motion, is the form of growth almost universally recommended for our economy.
When people talk about economic growth, they generally mean a percentage increase in GDP (Gross Domestic Product – a measure of how much is produced). For example an economic target might be a growth in 2% of GDP per year. This
definition of growth has two important features. Firstly, it is growth in activity, or throughput. Secondly, it is geometric, or percentage growth. This contrasts this with a linear growth in stock. Let me explain.
Suppose we invent a machine for knitting thneeds, and we build a new factory. In the first year, we produce 10,000 thneeds. Great!
In the second year, we produce another 10,000 thneeds. Now, a thneed will last for 20 years if properly cared for, so we have just doubled the worlds stock of thneeds. Twice as many people have thneeds as before. Thneeds have halved in
price. Everyone is better off. But the economists will be tutting and shaking their heads. According to them, we have achieved zero economic growth, because the rate at which we produce thneeds has stayed the same, and GDP measures the rate at which thneeds are produced, not how many there are in existence. This is the difference between growth in stock and growth in activity.
In the third year, we produce another 10,000 thneeds, bringing the stock to 30,000 altogether. Great! But now the economists are openly sarcastic. By their definition there has still been zero economic growth. But worse than that, they will say that even by our definition, growth has halved.
What? Surely growth has stayed the same, at 10,000 thneeds a year? Not according to the economists. In the first year the stock grew 100% from 10 to 20 thousand thneeds. But in the second year, stock only grew by 50%, from 20 to 30
thousand thneeds. To satisfy the economists, steady growth of 100% would mean that we have to produce not 10 but 20 thousand thneeds in year 2.
Conventional economic growth does not measure increase in wealth, it measures increase in activity. And for economists, steady growth is not steady growth – it is growth at a steadily increasing rate. This seems an eccentric
definition to most people. And when this definition is used to set targets for “sustainable growth”, it is not just very destructive – it is completely insane.
Linear growth adds the same quantity every year; geometric growth adds the same percentage. Suppose you start with one thousand pounds in a savings account, linear growth of £100 p.a. will result in £1,100 in one year, and £1,200 in two. Geometric (“compounding”) growth at 10% p.a. will result in £1,100 in one year, and 1,210 in two. The extra £10 in year two is the interest on the£100 gained in year one. From this example, it does not seem a very significant difference, but over a longer period the difference is extremely dramatic.
Geometric growth has the property that an initial quantity is doubled in a fixed time period, and ten such doublings in a row will multiply the initial investment by about 1000 (actually 1024). At a growth rate of around 2%, the doubling period is about 20 years. So if you invest £1,000 today at linear growth of £100 p.a., in two hundred years this will have grown to twenty one thousand pounds. But at geometric growth at 2% it will have doubled 10 times over, and have grown to a thousand thousand pounds – you will be a millionaire!
Because ten doublings gives a multiplication factor of 1000, it follows that 20 doublings multiplies by a factor of a million and thirty doublings by a factor of a billion. This leads to some astonishing numbers.
Let us suppose that we are currently using the whole earth’s resources in a sustainable way. At 2% growth in consumption,in just 20 years we will need to either double the productive capacity of the Earth, or find a second planet. That is not long in which to implement a technological revolution! But suppose it can be done.
Two hundred years from now we will consume the resources of 1000 planet earths. Even the most optimistic economists must quail slightly at the prospect of multiplying the productivity of planet earth by a thousand. But in two hundred years – well maybe. Lets just suppose this miracle happens. Just twenty years later, we would need to have doubled consumption again to 2000 planet earths.
In 1000 years time, that is, five factors of a thousand, we will need 1000,000,000,000,000 planet earths to support our extravagant lifestyle. Each one of us would need to continuously consume the productive capacity of 100,000 planets. Twenty such people would consume the estimated resources of all the earth-like planets in the galaxy! When you consider that at even at the speed of light it takes a hundred thousand years just to get from one side of the
galaxy to the other, it is clear that we have gone far beyond the bounds of any sane assessment of reality. This is why all sensible people admit that indefinitely sustained geometric economic growth is an absurd impossibility in any
conceivable universe. In fact the technical term for this kind of growth is “exponential growth” – a phrase that has become synonymous with unsustainability.
Why is it then that there is an unquestioned assumption in all discussion of economics that we need sustainable economic growth of at least 2% a year? It is easy to understand why people should WANT to get better off every year;
and so, it is natural that politicians should promise to deliver it. But why the world’s economists should persist in insisting that we can achieve the manifestly impossible is a mystery. We are currently consuming the worlds resources more quickly that they are being replaced – we are running down the Earths capital. Our food is grown with fossil water, using energy from fossil fuel. Fish stocks are being exhausted, and forests cleared – in other words, even our current rate of consumption is unsustainable. It is just foolish to suggest that we can achieve exponential growth from here.
The bad news is that beyond the very short term, percentage growth in consumption is an impossibility. The good news is that steady growth in wealth is an entirely different matter – and the subject of the next post.