Real Hard Numbers: Grantham’s Story Problem on Economic Growth

Between increasingly tedious irrigation sessions, I’ve found little time to read and less time to write, but I’ve made time to copy this paragraph from one of Jeremy Grantham’s quarterly newsletters.

Four years ago I was talking to a group of super quants, mostly PhDs in mathematics, about finance and the environment. I used the growth rate of the global economy back then – 4.5% for two years, back to back – and I argued that it was the growth rate to which we now aspired. To point to the ludicrous unsustainability of this compound growth I suggested that we imagine the Ancient Egyptians (an example I had offered in my July 2008 Letter) whose gods, pharaohs, language, and general culture lasted for well over 3,000 years. Starting with only a cubic meter of physical possessions (to make calculations easy), I asked how much physical wealth they would have had 3,000 years later at 4.5% compounded growth. Now, these were trained mathematicians, so I teased them: “Come on, make a guess. Internalize the general idea. You know it’s a very big number.” And the answers came back: “Miles deep around the planet,” “No, it’s much bigger than that, from here to the moon.” Big quantities to be sure, but no one came close. In fact, not one of these potential experts came within one billionth of 1% of the actual number, which is approximately 1057, a number so vast that it could not be squeezed into a billion of our Solar Systems. Go on, check it. If trained mathematicians get it so wrong, how can an ordinary specimen of Homo Sapiens have a clue? Well, he doesn’t. So, I then went on. “Let’s try 1% compound growth in either their wealth or their population,” (for comparison, 1% since Malthus’ time is less than the population growth in England). In 3,000 years the original population of Egypt – let’s say 3 million – would have been multiplied 9 trillion times! There would be nowhere to park the people, let alone the wealth. Even at a lowly 0.1% compound growth, their population or wealth would have multiplied by 20 times, or about 10 times more than actually happened. And this 0.1% rate is probably the highest compound growth that could be maintained for a few thousand years, and even that rate would sometimes break the system. The bottom line really, though, is that no compound growth can be sustainable. Yet, how far this reality is from the way we live today, with our unrealistic levels of expectations and, above all, the optimistic outcomes that are simply assumed by our leaders.

Incidentally, Grantham, along with Warren Buffett, says, “Tax the Rich!” Don’t know how rich Grantham is, but he’s rich enough to have given several million to a university, and his GMO partnership is managing over $106 billion dollars. The entry level investment for his clients is several million dollars, so GMO isn’t a name that’s all that well known among the peasants.

In any event, Grantham’s newsletters are available on the website.

Back to the fossil-fuel based yellow irrigation tubing.



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