Dangerous exponentials

 “Anyone who believes exponential growth can go on forever in a finite world is either a madman or an economist”. Kenneth Boulding

By Leith van Onselen

Earlier today, The Prince published a thought provoking article questioning the economy’s addiction to population growth.

It’s an issue that I have been pondering since reading the below Strategy Insight from Dr Tim Morgan, Global Head of Research for Tullett Prebon, entitled “Dangerous Exponentials”, as well as reading Chris Martenson’s Crash Course, which explores issues around exponential population growth and resource use (amongst other things) in great detail.

In the Strategy Insight, Dr Morgan presents a series of “dangerous financial and non-financial exponentials” that are not sustainable and ultimately risk destroying the economy, environment, and overall living standards:

We believe that an exponentials analysis can alone explain an impending collision between an economic system which, by its nature, must grow, and a finite resource set which, ultimately cannot grow. When this collision eventuates, it is likely to be one of the most important changes in the lifetime of anyone reading this report.

Key amongst Dr Morgan’s concerns is the world’s population growth, which has grown exponentially to the point that human’s demand for resources is pushing against capacity constraints on what the earth can actually provide:

In fig. 3, we set out the population of the earth from 2000 BC through to projected numbers for 2050. At the beginning of this period, historians estimate the world population at 170 millions, and this number increased only gradually thereafter, reaching 254 millions by 1000AD…

Thereafter, population growth accelerated markedly. Whilst it had taken thousands of years to reach the first billion, the second billion was achieved in the 1920s – that is, adding the second billion took about ninety years. The third billion was added much more quickly – taking about thirty years – whilst the fourth was added in less than twenty years.

From the mid-nineteenth century, the population growth chart turns into a characteristic exponential ‘hockeystick’ shape. The current population total is about 6.7bn, and this is expected to increase to 7.6bn by 2020, and 8.8bn by 2040.

Anyone who is mathematically inclined might point out that any compound progression chart, if projected forward far enough, will take on a hockey-stick shape, and that this doesn’t particularly matter unless the progression begins to hit physical parameters. Moreover, current calculations suggest that population could top out in the middle of the century at somewhere between nine and ten billions, since the global average fertility rate is declining rapidly with improvements in living conditions in the developing world.

But the earth’s resources – such as land, food production capacity, energy and, perhaps most important of all, water – are not infinite, and some specialists believe that the earth’s ‘carrying capacity’ may be limited, with estimates varying between perhaps 8.5bn and 11bn. This range is superimposed on the chart.

If a physical constraint is imposed in this way, the vertical axis becomes referenced, and the hockey-stick trajectory takes on far greater significance. And this observation is by no means confined to the population explosion.

Dr Morgan then turns his sights to the world’s consumption of hydrocarbon energy, which has displayed a similar degree of exponential growth:

From an economic perspective – and beyond intuitive questions about whether the world really can support the projected numbers of people – two things are striking about the population trend.

The first, to which we shall return later, is that the rapid up-tick in the curve began in the mid-nineteenth century. And this, coincidentally – or, in our view, not coincidentally at all – was also when the use of hydrocarbon energy began to expand rapidly.

Chris Martenson contends – and we wholly concur in this belief – that the current population of the earth is sustainable only because of an abundant supply of hydrocarbons, and principally of oil. This is surely obvious enough when we bear in mind the vast scale of hydrocarbon energy inputs employed in modern intensive agriculture…

Agriculture itself was made vastly more efficient, initially through the use of motive power and latterly through the introduction of hydrocarbonbased fertilisers and pesticides. Within a hundred years of the first use of steam-power, the proportion of the populations of most developed countries engaged in farming had fallen to less than ten percent. Specialisation had arrived, courtesy of the harnessing of the energy contained in fossil fuels.

…all of the economic ‘exponentials’… are energy-dependent… we are all, as Mr Martenson puts it, “living like kings”, and both the lifestyles of individuals and the specialisations of societies are made possible only by exogenous energy, derived overwhelmingly from fossil fuels…

Dr Morgan also discusses the exponential growth of the money supply and debt, which are equally unsustainable, but those are secondary (in my opinion) to the predicament of exponential population growth / resource use in a finite world.

There is a follow-up Strategy Insight by Dr Morgan, entitled “End-game”, that I will look at tomorrow.

[email protected]

www.twitter.com/Leithvo  Dangerous Exponentials – Tullett Prebon

Unconventional Economist
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  1. darklydrawlMEMBER

    ooooooh… That fossil fuel chart makes me nervous. Mostly as this planet would really suck for most of use without fossil fuels – we know they are not good for us, or going to last forever, but we really don’t seem to have a decent & viable ‘Plan B’ on the horizon.

    I think the really freaky thing is (what someone else mentioned on here in the comments a while back) that we cannot do the industrial revolution again as all the easy, cheap and good stuff is gone.

    The bulk of resources left require high technology and advanced skills to extract.

    All well and good perhaps if we manage to keep the lights on, but if civilisation goes *plurk* for a while, it is going to be awfully tricky to rise up and have a second bite at that cherry…

    • ‘The bulk of resources left require high technology and advanced skills to extract.’

      This is increasingly true and a reason Jeremy Grantham argues that many commodity prices unlikely to return to previous lows.

      The next revolution will be a technological one based on new form of energy. Again the world will recalibrate to the new new, so to speak. One concern on the horizon the the type Peter Theil has recently been discussing – the propensity for modern economies to the ‘horizontal’ (increased regulation, stymied innovation, funds transferred to maintaining ever increasing government expenses (incl modern welfare), propping up of ‘old’ industries etc) rather than toward the ‘vertical’ (greater freedom from regulatory restrictions, promotion of culture of innovation, preparedness for the new, redirection of funds to science/maths/technological development etc).

      I remain cautiously confident!

      • Wow. How you managed conjure up a (Ayn) Randian rant from a discussion about exponential growth, beggars belief.

        Granted, governments certainly get in the way if you want to preserve the status quo — i.e. dig up dirt and flog it to the highest bidder — but if there is to be a technological breakthrough it won’t happen without government funding or government-funded institutions. No-one else can afford the massive investment in basic research with such a high risk-reward ration.

        Fusion is (still) the world’s great energy hope, and last time I looked ITER and the National Ignition Facility weren’t being funded by Big Oil or Big Dirt.

        • darklydrawlMEMBER

          Whilst I wish Fusion was here today, bit really still is a ‘hope’ more than a ‘strategy’.

          Fusion is still fiendishly difficult to do and we are a long way off being anywhere near commercially viable with this technology.

          That is not say I think we should give up on the idea, it is a wonderful dream, but I would also prefer a few more credible and like plan b’s in the pipeline…

          These links were originally posted on this site, worth a revisit if you missed them the first time.




          • That’s why I called it “the world’s great energy hope” not the “world’s energy strategy”. If we have a strategy its “more of the same” which is exactly what the MineBot wants.

          • More of the same for a period is inevitable. When “It” is discovered and perfected we will move on.

            Lorax, especially for you to…mull over…:

            “It gives him great pleasure, makes Rabbit feel rich, to contemplate the world’s wasting, to know the earth is mortal too.”

            Rabbit is Rich, John Updike

          • Base load energy is not the only problem. I believe we can sort base load out pretty quickly and affordably.

            Affordable transport fuels and the dislocation if said fuel becomes unaffordable / unavailable is an issue for mine.

      • 3d1k,

        Your young and enthusiastic and that’s good.

        But let me say I have lived through a couple of commodity spikes; I have seen prices rise and fall almost as fast over not too many a year period.

        There are two things – just cautionary things – that you need to consider.

        The first is that demand for essentials does not by it’s proximity to basics needed mean that they will be satisfied without question no matter the scale.

        The fact that people die of starvation when their is plenty of food in the world demonstrates that.

        The second thing is that you need to recognize that there is a relationship between the resources consumed in infrastructure and the resources consumed in consumption products.

        That is, it is the demand for consumption products that drives the demand for infrastructure.

        Don’t let me stop you, but keep those two things in mind.

        • Thanks Chester, I am somewhat flattered but I am not as young as you think. I have been in this game (resources) for more than twenty years. I have been involved in a number of different projects in different countries and have certainly seen commodity cycles first hand.

          Much of what has been discussed here is primarily political in nature. Or political and philosophical. I suspect these hurdles far greater than those faced by the sciences.


  2. interested party

    It will take an event to turn peoples perceptions of their reality around, much like the boiled frog model. The smart ones have the plans in place and are now implementing them. Life is certain to change, may even get a bit ugly, so plan well.


  3. Nuclear energy is the only thing that could possibly keep up with such growth, and yet right now governments all around the world are moving away from it.

    But still.. I think the linked article ignores the important factor of WHERE this population growth is occurring. Much of it is in developing countries.

    Why is it the case, where developing countries are growing in population but developed countries are experiencing a decline, or has at least have slowed dramatically enough to cause a significant shift in demographics? Could we see a link between quality of life and birth rates?

    The other thing that this article ignores is the methodology used to recreate population counts in the past. I don’t see anywhere in the document where they talk about how they constructed their historic records OR any estimation of the veracity of such records.

    • Hasn’t there always been a link between quality of life and birth rate?

      The traditional view has been that parents living at a subsistence level in developing countries NEED to have a lot of kids to ensure some of them survive to look after parents in their old age. There’s no social welfare and existence is ‘hand-to-mouth’ so there’s little opportunity to save for the future.

      Developed countries have some form of social safety nets, plus much better medical care (so kids survive), so that having, say two kids, is enough to guarantee there’s someone around when you’re old, plus, even if there isn’t, the state may look after you, or you’ve had enough chance to earn enough to look after yourself.

    • drsmithyMEMBER

      Why is it the case, where developing countries are growing in population but developed countries are experiencing a decline, or has at least have slowed dramatically enough to cause a significant shift in demographics?

      Everything I’ve ever read on the subject eventually brings it down to women’s rights. When women have equal rights, education, and easy/cheap access to contraception and abortion, the birth rate drops dramatically.

      Or, to put it another way, when given the choice most women don’t have more than two children in their lifetime (less than replacement rate) because they, too, want to do more with their lives than raise children.

  4. A better model of population growth was proposed by Verhulst in the 19th century. It’s described by a simple differential equation that takes into account density of population. The solution of this equation is the logistic curve which looks like stretched letter S. The curve is initially quite flat, then steepens and flats out again. Obviously density is one of the many factors that influences the maximum size of the human population and the rate of its growth.

    There are also prey-predator Lotka-Volterra models that can quite well describe dynamics of biological populations. The function of predator can be played by e.g. a contagious disease, one population group exterminating another population group etc.

    The question is whether we let the nature take its course or start planning for the future.

  5. Diogenes the CynicMEMBER

    My view is absent a circuit breaker (cheap fusion energy, mass die off due to virus/disease, aliens landing and helping us out) we are probably going to devolve towards more simpler economic systems, more regional/local/recycling/repair/made to last rather made to be bought repeatedly etc.

    This is the first time in our economic history when we do not have a cheaper/denser source of energy waiting to be used ie 1800s wood to coal, 1900s coal to oil, 2000s oil to ?

  6. no one here gets it,
    or missed the point of
    this post and/or the previous
    one, or the work of CM, Heinberg, Daly etc

    Business as usual – cheap energy fueling economic growth/industrial civilisation is finished. Not to say it is the end
    of development.

    Perhaps we all should look at those
    hockey stick graphs again. CM and his
    ilk having been going on about this stuff for several years now.
    The data has just penetrated msm/macrobusiness.

    • interested party

      Bingo Arne, as I commented above, it will take some event to change peoples perceptions. I for one “get it” and am well advanced in my preparations.
      I am not pessimistic on the future but realistically wary and concerned.

      CM has nailed it and the more people that recognize this, the better.

    • It says in that link that a “lifter” may not reach commercial stage for another 20 years, something I believe they said about the whole process 20 years ago. Sort of sounds a lot like fusion – always the energy of the future…meanwhile peak oil looms over the horizon. Nature is poised, ready to solve our population and sustainability conundrum, but not in a way we may like.

  7. Problem with posting?

    I’ve posted twice and not made it up while other posts have popped up in the interim.

  8. Exponential popn growth? I’m not worried. We can always count on the military industrial complex to start WW3 somewhere down the line.

  9. systems_and_limits

    Good job.

    Macrobusiness has had occasionally a habit of focusing more on dollars (abstract things than can be created and destroyed) than on resources, which are finite and cannot be created.

    Another criticism of mine has been that economists often treat the environment as being a subset of the economic system, rather than realising that the economy is a fully owned subsidiary of the environment.

    So, this post on hard limits to the things that the economy must consume in order to exist is most timely. You are also starting to venture in the direction of Energy Bulletin and Oil Drum, although Oil Drum tends to be energy focused and Energy Bulletin tends to focus more on responses to resource limits and climate change.

    Be aware that when introduced to the unaware, these kinds of issues tend to scare the crap out of people – they tend to either turn around and accuse you of being a doomer, or fight like hell to deny reality. It’s very hard to have a productive dialogue with such people – best to point things out and then leave them to work things out themselves.

    There are also lots of people out there who genuinely get it, and for these people talking about how to respond is most productive.

    Again, good job.

    • Good grief. A waste if MB goes down that route – there are ample peak oil peak, energy sites out there.

      What can an economics/finance blog focussing on a small open resource rich economy hope to achieve? Apart from a xxxxload of frenzied and fearful comments. 🙂

      • I agree, ironically the web has reached ‘peak’ Malthusian catastrophe sites already.

        And it will just be too hard to generate additional Malthusain catastrophe content without bidding up the price of such content to infinity.

        • So are you betting against Malthus? I pose a challenge. Lock yourself in a small room, without any food or water for 6 months and see if your human ingenuity can get you out of your predicament.

          Unlike ours and all other species living on a finite planet with limited resources, you as an individual, can always choose to leave the room and head to the nearest fully-stocked, climate-controlled supermarket.

          • Gee, there’s a false analogy if ever I’ve seen one.

            In my lifetime, yes I am betting against him.

            Do you have any idea the amount of energy the sun sends earthward every minute, let alone harnessing power of gravity or nuclear technologies.

    • Be aware that when introduced to the unaware, these kinds of issues tend to scare the crap out of people – they tend to either turn around and accuse you of being a doomer, or fight like hell to deny reality. It’s very hard to have a productive dialogue with such people – best to point things out and then leave them to work things out themselves.

      Too true, now I am going to watch a news segment about a bunch of people in Holland who want to communicate with angels on their mobile phones.

  10. All this speaks to “what is the market for”?

    Consider the market is poised to allocate up to say $100 billion for Facebook. Now facebook with all due respect does not solve any human ‘problem’, they don’t need any money from the markets. What are they going to do with the capital other than park it in Treasuries?

    I think most people agree that oil will eventually run out, the question is are we funding sufficient R&D to have the next technologies, i.e. latest nuclear design, thorium reactors, and eventually Fusion ready to go.
    ‘The market’ allocates very little capital to these activities as compared to what is allocated to a whole bunch of nonsense.

    • Fantastic fairy-tale stuff!

      More people, consuming more than ever before, with more people in abject poverty than ever before, low mortality rates (i.e. more young people waiting to enter the reproductive stage) and no indication where all the energy and resources are going to come from to keep this Orwellian juggernaut rolling along.

      Green technology, elimination of poverty and global governance. Does that resemble in any way the world we are currently living in? If anything, we are running completely in the other direction and at staggering speed.

      The cliff edge looms just ahead for modern man I’m afraid, because the world is full of such muddleheaded thinking. And why not? If it panders to the beliefs and prejudices of ignorant and fearful people everywhere, who are not prepared to abandon unsustainable lifestyles, as nature will surely compel them to do, but not in any sentimental way.

  11. Gee, there’s a false analogy if ever I’ve seen one. In my lifetime, yes I am betting against him. Do you have any idea the amount of energy the sun sends earthward every minute, let alone harnessing power of gravity or nuclear technologies.

    Why is it a false analogy? Are you afraid that if you ran the experiment, you may fail and concede that Malthus was correct?

    About you’re second point. Yes a staggering amount. We already commandeer nearly 40% of it for human use alone. Is it any wonder species extinction is accelerating and that the oceans will be nearly dead by 2050?

    Now, imagine if economic growth was able to just keep going and going. We might double the amount of sunlight commandeered for our exclusive use again to 80%, but not a third time. The end result, a dead pill of a planet.

    • Earth receives ~90PW of energy from the Sun.
      I seriously doubt primary energy consumption of the earth is 40% of that number.

      And that doesn’t even include energy generation potential from tidal or other nuclear technologies.

        • I just hate seeing good websites taken over by an invasion of Malthusian doomers.
          Once they invade, you will notice a tendancy of all comments to head toward Malthusian catastrophe. Sort of like a new Godwins law.

          • Don’t worry V, cornucopian thinking like yours has long carried the day, so what is there to worry about from the taunts of a long dead economist? Unless of course you secretly fear he may ultimately be correct. Care to carry out that closed room, no food or water experiment and find out?

      • Perhaps I should have been more precise as to say; The human appropriation of the products of photosynthesis is running at around 40% and climbing. Is it any wonder the environment and climate are knackered in the way that they are?

        • Assertion without evidence doesn’t amount to anything, mercury4. If there is evidence for your assertion, tell us what it is.

      • Where is the evidence that those technologies are supplanting fossil fuel use? Or that their existence at the same or similar levels of current fossil fuel energy use wouldn’t be as destructive on the environment, or climate? Assuming the resources and energy to build this phenomenal amount of infrastructure were available?

        • As ever it will be a question of price and the capital spent on genuine scientific R&D, which is pretty poor at the moment. Paradoxically the best thing for genuine scientific endeavour will be higher oil prices in real terms (we must take into account Bernankes proclivity to print)

          I think getting off fossil fuels would be a good thing, but not so much for the ‘climate’ or ‘we are running out’ type issues. But more due to issues of particulates, radiation emissions, health/loss of life issues etc from blindly burning and mining the stuff.

          And I’m not necessarily saying we will maintain our current stds of living or propensity to consume. Indeed ‘consumption’ per-se may prove to be a quaint 20th century cultural notion.
          After all the world has always seen, war, famine, plagues etc.

          • Oh, hoo, hoo! That is rich, price and capital will wean us off fossil fuels, when all 10 years of rising oil prices have done is generate more extraction of dirtier and less energy dense fossil fuel compounds, like tar sand and oil shale.

        • Well it may be a cornucopian view. But there really isn’t any other viable choice is there?

          I haven’t heard any Malthusians with any sort of solution, other than ones that require either a totalitarian solution, or some quaint notion of people going back to raise their own chickens. One solution being dangerous to human freedom and endeavour, and the other just not going to happen.

          Yes the cornucopian view is uncertain, but isn’t life itself? There are far larger forces at play in the universe. (Ask the dinosaurs, they were living a reasonably sustainable lifestyle after all)

    • Geez. Oh well, at least some claim the Stoneage Diet is healthy – we will all live longer. In our caves.