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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8 Comments on "Finite Resources and Infinite Growth"

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Resource substitution is likely more important in the long term than incremental productivity improvement. Mineral oil would still displace whale oil even if the whalers would have had access to 21st century ship technology. I expect a similar trend in electricity production in the right geographical locations. PV in sunny areas will eventually displace fossil fuel power even if the fossil fuel plant at some point in the future is 25% more efficient than what it is today, simply because fossil fuels will at some time in the future be 50% more expensive due to increasingly difficult resource extraction, e.g. deeper or more remote coal mines, shale gas instead of conventional gas, etc.

This isn’t likely as clear as it should be in the post – I was trying not to overlap too much with a related post at Macleans (http://www2.macleans.ca/2014/02/01/what-happens-when-we-run-out-of-oil/) where I did a little better job of making clear that alternative energy sources and reducing our economic dependence on energy as well as improving the efficiency with which we extract and use fossil fuels all play a role at some point along that theoretical transition path. It’s certainly not an issue of simply using the same amount of oil or deriving the same amount of useful energy from oil by using it more efficiently. So, in short, you’re right.

I like the graphs for obvious explanation. However, I suspect that last graph to be impossible given the decline of the finite source. Unless overall energy sources are indeed supplanted by better, more powerful sources, it is

impossiblefor efficiency to replace the laws of physics. A continued increase in efficiency can only go so far, especially for powering 10 billion people. It will probably take more energy no matter how close to 100% we can get to overall efficiency.We will slowly run out of fossil fuels but there will be more extraction leaving room for continued efficiency improvements despite “wide spread planetary development”. If the crust had so many ppm of fossil fuels, then it would seem unlimited, but “only everything else” has that seemingly unlimited advantage (rare earths are not rare!). Also, there is the excess CO2 thing to be concerned about.Thus, we must prepare for the obvious: Makeinherently safe, the least expensive most abundant non fossil sources invented in the modern era. Because we can’t conserve till the last drop!Absolutely. It’s not simply a matter of efficiency of energy generation from finite resources. It’s a matter of increased efficiency, decreased reliance on finite resources for energy, and likely increased productivity per unit energy in the economy. Combine those three.

OK, so indefinite growth with finite resources is possible, given exponential growth in productivity. I’ll even grant that sustained exponential growth in resource productivity isn’t as absurd as it might sound, given that recycling of resources can approach 100%. That’s an interesting academic point, but I’m not sure how much relevance it has to the world’s future. The indefinite growth that can be sustained is not exponential; in percentage terms it asymptotically approaches 0% — which rather defeats the usual economic purpose of growth of enabling repayment of debt. For all practical purposes, what you’re looking at is a steady state world.

“The indefinite growth that can be sustained is not exponential; in percentage terms it asymptotically approaches 0%” – why would this be true? For me, it’s much more idfficult to contemplate reaching a point where, no matter what, we can’t find any way to increase per capita consumption with our available energy resources. Whether that growth rate is small or large is one thing, but the idea that, at some point in the future, we’ll reach a point where all the research and development activities cease and we decide that the time as come to ‘mail it in” in live as we are now forever, simply replacing each person with another as they die, seems more far-fetched and “academic” than any dicussion to the contrary.

Leach is absolutely right in his conclusion: supposedly ‘finite’ resources do not limit the potential of economic growth.But his argument emphasizes only part of the reason why, and not the most compelling one at that.Economic growth is measured by the total

value— commonly expressed in monetary terms — of all that is produced and consumed. But economic value is a psychological parameter, not a physical one. Dollars are produced by a melange of human perceptions, desires, and technology. What Leach cites as ‘productivity’ is a manifestation of the ability of human imaginatiion and will to transform inputs of various sorts into objects of desire.Some objects of desire — or more dryly, economic utilities — certainly are rooted in physical necessities: food, water, heat, shelter, and such. But even with population growth, those entities represent an ever diminishing, minor share of overall economic output.Rather, economic progress has been marked by a continuing shift from physical production (mining, agriculture, manufacturing) to a majority of “value-added” from information, knowledge, and similar “intangibles.” In accordance with Moore’s Law and related propositions, the efficiency with which human ingenuity has been able to convert energy and material resources into informational products has been doubling every year or so for decades, and shows no sign of slowing.This epochal shift from the material sectors to the epistemic sectors of the economy is the central focus of George Gilder’s recent book,Knowledge and Power. It was observed years earlier in, among others, Peter Drucker’sThe Post-Capitalist Societyand my book,The Learning Enterprise.We see evidence of this shift in the market valuation of the biggest companies. The value of about 3/4 of these companies, and their businesses, has little connection to physical resources. The market valuation itself is a product of investor psychology rather than physical parameters.Large Cap Company Ticker Market Cap ($in billions)Apple Inc AAPL 439.39Exxon Mobil Corp. XOM 403.32Google Inc GOOG 257.40Berkshire Hathaway Inc. BRK.A 243.60Wal-Mart Stores, Inc. WMT 238.85General Electric Co GE 236.78Microsoft Corporation MSFT 233.53Chevron Corporation CVX 228.01International Business Machines Corp. IBM 226.03Johnson & Johnson JNJ 210.06Procter & Gamble Co. PG 207.55AT&T Inc T 202.21Pfizer Inc PFE 198.72Wells Fargo & Co. WFC 186.93JPMorgan Chase & Co. JPM 186.80Coca-Cola Co (The) KO 168.46Oracle Corp. ORCL 166.22Philip Morris International Inc PM 150.58Bank of America Corp. BAC 131.98Citigroup Inc C 130.06Why would indefinite growth require a growth rate that asymptotically approached 0%? Simple math + physical reality. Any finite, non-zero limit to the growth rate would still be exponential growth; it’s only a question of the value of the doubling time. In a finite universe — or even an infinite one where there is a finite speed of light, indefinite exponential growth is impossible.A friend of mine who was a math instructor at McGill University (and also a social activist and science fiction author — Don Kingsbury) had a nice way of explaining the absurdity of indefinite exponential growth. He was talking specifically about population growth, but similar considerations apply to other types of growth as well. He used the example of something like a sustained 1% growth rate. That would be considered a very modest annual growth rate in most places, but it still results in a doubling every 70 years. It’s a factor of 1000 every 700 years. If the population grew from its present value at 1% per year for a mere 2100 years — an eyeblink in geological time — population would increase by a factor of a billion, and we’d be looking at standing room only on the earth’s surface. A couple more 700 year 1000-fold increases, and the entire mass of the earth would have been converted to human bodies. It would take some unimaginable technology to provide a surface for everyone to stand on, and avoid the thousands of miles of stacked bodies at the upper levels from crushing those below. All still in an eyeblink of geological time.Of course, you were talking about economic growth, not population growth. Which begs the question of just what the hell we actually mean when we talk about economic growth. If it’s simply GDP measured in nominal dollars (whatever

thatis), then we can have indefinite exponential economic growth simply by having simultaneous exponential shrinkage in the “value” of the dollar (again, whateverthatis). All rather far removed from much of anything to do with the real world out there.If all you really wanted to say was that finite resources don’t absolutely necessitate the collapse of civilization and massive die-off, then as it happens, I agree with you. So long as the sun is pouring down as much energy every hour as humans expend in a year, then it’s possible to sustain the current world population in reasonable comfort.Physically possible, that is. Whether that’s what we end up doing is quite a different question.