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Once artificial intelligence really gets going, how fast can the economy grow? Five per cent a year? Ten per cent? Fifty per cent? Name your number. If you want press coverage, make it a big one.

ARK Invest, an investment manager focused on disruptive innovations, has argued that 7 per cent real GDP growth is plausible. Epoch AI, a think-tank focusing on AI trends, has suggested that growth rates could exceed 20 per cent a year, once certain preconditions are met. Other commentators are vastly more conservative — for example, Nobel laureate economist Daron Acemoglu reckons that over the next few years AI might nudge annual growth rates up by about 0.1 percentage points. That would be nice to have, but not necessarily nice enough to notice.

It’s worth taking a moment to reflect on what such growth rates might mean in practice. At 7 per cent annual growth, an economy would double in size every decade, and, potentially, so might living standards. (Would the proceeds of such growth be widely shared? Another question, for another column.)

In such an economy, people who became parents at the age of 30 could plausibly expect their children to grow up to be eight times richer than them. All but the most profligate governments would see their fiscal problems evaporate, the burden of the national debt vaporised by the white heat of economic growth.

Such numbers are not unprecedented: a few economies, such as those of China, Japan and South Korea, enjoyed long stretches of this sort of growth while playing catch-up with then-richer societies. But to see such growth rates from the world’s richest economies would be something new.

Creating silicon intelligence is not the only problem to solve if we want to see living standards grow

An economy growing at 20 per cent per year is even further removed from our intuitions. At such rates the economy would double in size three times a decade; children would grow up to be about 500 times richer than their parents. Centuries of economic progress would be compressed into decades, and years into months.

Could such growth possibly happen? The theory feels plausible enough. AI becomes sufficiently advanced to help make AI yet more advanced. With ever-better AI helping to develop ever-better AI, the capacity of AI grows at a super-exponential rate, the growth rate increasing each year. These superintelligences help with many other problems — for example, by developing fusion as the near-limitless clean source of energy that would no doubt be needed to fuel all those silicon brains. All the time, the AIs would get better and better — and more and more numerous.

This is all very nice in theory. In practice, the obstacles are clear enough. The most obvious source of doubt: will AIs really become advanced enough to build better AIs? Will AIs be good enough to take over from humans, or multiply the output of humans, not just at abstract processing but making strategic decisions or performing physical and emotional labour too? And is there really enough usable energy to power all this computation?

The history of technology suggests some caution, too. Look back to the 1960s. The world population growth rate was reaching a peak, increasing the number of geniuses who could develop ideas to benefit all humanity. Education was on the rise: more and more people were going to school and on to university, producing a dramatic — and potentially self-reinforcing — increase in trained brainpower. The computer was dramatically lowering the cost of calculation, and computers were being used to help design better computers. The internet was on the horizon, too, and there were countless other potential sources of support: faster, cheaper travel; more sophisticated finance to support new ideas; libraries full of ever more books.

If an economist pointed to all this at the end of the 1960s and argued that the growth rate of leading economies was about to double, would that have seemed so absurd? And yet growth in the US didn’t double. It slumped after 1970 and has been disappointing ever since. Maybe increasing the rate of economic growth isn’t as easy as one might hope.

A recent essay by the economist Luis Garicano points to a couple of reasons why. One is the “O-ring” effect, an idea named after the failure of a simple component that destroyed the Challenger space shuttle, killing all seven crew. In economics, the O-ring represents the idea that sometimes a sophisticated and highly productive system is only as good as its weakest link.

Imagine the robot masseur that only occasionally snaps your neck; the self-driving car that rarely mistakes you for a piece of trash blowing across the road; the generative AI system that can write prose for you, and can go for days, even weeks, before producing a career-threatening error. In some cases it is easy to work around a weakness in the AI system. In other cases those weaknesses, like the brittle O-ring, may be the only thing that really matters.

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A related challenge is the Baumol Effect, named after the economist William Baumol. Baumol and his colleague William Bowen were originally describing the economics of a string quartet, but produced an insight of much broader relevance. Any part of the economy that is valued but cannot easily be made more productive will tend to consume a growing share of spending.

This has happened many times. First, agriculture became vastly more productive. Then steam engines became vastly more productive; then manufacturing; calculation; communication, and so on. Despite these productivity miracles — in fact, because of them — more and more spending is devoted to sectors such as healthcare, education and restaurant meals. If agricultural productivity were to double again tomorrow, that would barely register in the GDP statistics. Computational productivity is doubling all the time, but GDP growth is stubbornly lower than in the 1960s.

There are reasons to speculate that this time is different, but creating silicon intelligence is not the only problem to be solved if we want to see living standards grow at 20 per cent a year. One lesson to take from all this may be this: a growth rate of 1 per cent may be meagre by the standards of the 20th century, but even 1 per cent growth is exponential growth nonetheless — and exponential growth may be harder to sustain than we assume.

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