Globe and Mail featured a column by Gary Mason on a world without oil. ”If you believe that the economy is structured in such a way that it needs to grow continually in order to survive,” it states, “then it will take an endless supply of energy to feed it. ” The article then raises the question, ”How does an economy grow exponentially forever if the one element it needs more than anything to flourish is contracting with time?” This is a common refrain from environmentalists such as David Suzuki (here, here, here and likely a thousand other places): “it’s absurd to rely on economies based on constant growth on a finite planet.” But, is it? I’ll have more on this at Macleans in a couple of days, but this will serve as a technical primer.

Intuitively, it sounds simple – if I use up a certain amount of a finite quantity each year, it will eventually run out. But that tells you that you can’t have constant or increasing resource extraction from a finite resource, it doesn’t tell you anything about what you do with the resources you extract, how productive they are, or whether or not they enable continued economic growth. It’s certainly possible to sustain *exponential* growth infinitely with finite resources, as long as productivity improves.

Let me take you through an example (this is a really basic model, but I’ve fit it with some reasonable numbers so its intuitive). Suppose that gross world product (real, including all environmental costs) is given by 1450*R*X, where R is resource productivity and X is extraction. If you use oil extraction as a proxy for resources, and we extract about 31.4 billion barrels of oil per year, and let R equal 1, you’ll get a gross world product of $45,515 billion, about the same as the CIA World Factbook estimate of 2012 gross world product. Let’s also suppose, for the sake of this argument, that the 1.8 trillion barrels of oil in current global reserves represents the sum total of all the oil which will ever be extracted – a finite resource.

With those numbers, the myopic approach to maintaining constant growth with no change in productivity would lead to all oil resources being exhausted in 55 years, and then instant economic collapse.

Of course, this would not actually happen, since prices would adjust even if there were no productivity changes. To understand what would happen, go to the last period before the collapse – a period in which the world extracts 35 billion barrels of oil out of a remaining stock of about 40 billion barrels. Knowing what was going to happen if you stuck with that plan, you’d likely decide that it makes sense to carry some extra oil through to the following year, to stave off collapse and/or to profit from absurdly high prices. In doing so, you’d raise prices in that year. Of course, people would have seen this coming too, leading to conservation of oil from previous years as well. This is a clumsy explanation of what Harold Hotelling wrote down almost 100 years ago – that since oil is like a capital asset, owners will act to maximize returns and this will smooth price and extraction decisions over time. If you imposed a Hotelling solution – one which maximized the value of oil over time, you’d end up with something which looks something like this:

However, Hotelling doesn’t get you to economic growth with finite resources – production is still decreasing over time, and tends asymptotically to zero – it’s just that there is no collapse and oil is distributed over time such that there are no gains in net present value to be achieved by shifting production forward or back in time. (In the graph above, I approximated a 400 year solution – I didn’t solve the full optimal control problem).

If you want to get to increasing economic growth with a finite resource, you need an increase in productivity. Suppose that you still have the same finite resource stock, but that you become 3% more productive each year in your use of resources – you generate 3% more total product from each unit of resource extraction. The growth in productivity allows you to use fewer resources each year, while still increasing production. Resource stocks still decline, and approach zero asymptotically, but it’s like going half the distance to the goal line in football – you’ll get closer every time but you’ll never score.

So, how do you increase productivity? Energy is used in our economy as a complement to labour and capital, so if you want to increase the productivity of your finite resource then increase energy efficiency, decrease the resource-intensity of energy, increase labour productivity, or increase the quality of your human and physical capital. This is what Queen’s University economist John Hartwick had in mind when he wrote down the Hartwick rule – the mathematical proof of what I’ve just tried to do in words: as long as you invest sufficiently in improvements in productivity, and manage resources optimally, its possible to sustain infinite growth from a finite resource. Of course, the Hartwick rule is not a law – it doesn’t guarantee that this will always be achieved, and it certainly doesn’t say that it can be accomplished with any level of investment – it just tells you that its mathematically possible.

Saying that it’s impossible to achieve *exponential *growth infinitely with finite resources does nothing to advance our discussions of resource management and ignores plenty of evidence to the contrary in the economics literature. What we should be discussing instead is how to make sure we follow Hartwick’s rule, but that’s another story for another day.

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