Exponential Growth Revisited

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Exponential Growth Revisited

#1  Postby FACT-MAN-2 » Oct 05, 2013 7:15 pm

This topic has a way of rising out of our economic morass on a persistent basis. Here's the latest:


The Myth of Exponential Growth

Posted: 10/03/2013 4:54 pm
By Dave Pruett
http://www.huffingtonpost.com/dave-prue ... _ref=green

In the last post, I came out of the closet. I'm an Occupier. For most of the past two years of my affiliation with Occupy Harrisonburg (#OHB), I've participated in its small but vibrant Economics Working Group (EWG). I've never before had any interest in economics, nor have I any expertise. So what drew me in?

It's simple, really. For much of my professional life, I've taught introductory calculus to college students, and in Calc I, we learn a basic principle that apparently no politician (OK, Elizabeth Warren excepted) or mainstream economist understands.
One of the first powerful applications of calculus, accessible to every college freshman, is the notion of exponential growth and decay. When politicians or economists chant their mantra -- we must GROW the economy -- they implicitly assume that our economy can growexponentially into perpetuity. So enamored are economists of growth that during recessions they often refer to "negative growth" rather than contraction.

The exponential-growth model fits a host of everyday phenomena: the explosive increase of bacteria that sours milk; the initial growth of unstressed populations, in general; the accumulation of interest on investments compounded continuously. However, in no real-world scenario can exponential growth be sustained indefinitely, because growth implies increased consumption of resources, and resources are always limited. When a biological population has to compete for scarce resources, its growth slows, stops, or reverses. Indeed, the sustained exponential growth of almost anything is pathological.

Sustained growth of a population, for example, is a population explosion, and sustained exponential growth of cells in the body is cancer.

continues ...

Discuss.
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Re: Exponential Growth Revisited

#2  Postby Matthew Shute » Oct 05, 2013 7:24 pm

The last time I checked, the planet wasn't infinite in surface area; neither does it have infinite resources; neither can it support an infinitely increasing population. For all of those reasons, the idea of infinite economic growth seems rather silly... to put it mildly.
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Re: Exponential Growth Revisited

#3  Postby Thommo » Oct 05, 2013 7:33 pm

FACT-MAN-2 wrote:
When politicians or economists chant their mantra -- we must GROW the economy -- they implicitly assume that our economy can growexponentially into perpetuity.


I'm sceptical. A politician that thinks beyond the next election cycle or so is rare, economic forecasts and growth plans seldom extend beyond a decade or so at their most far sighted.

I think we can all duff up this argument that infinite growth is probably not going to work, the only question is whether we cut our knuckles on the straw in the process.

Yet, at this seemingly modest rate, the size of the economy doubles every 22 years, quadrupling in 44 years, and expanding by a factor of 8 in less than three generations. Such growth demands commensurate doubling, quadrupling, and octupling of the energy sources and raw materials that feed the economy.


This one isn't true either.
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Re: Exponential Growth Revisited

#4  Postby VazScep » Oct 05, 2013 7:55 pm

I'd imagine there are subtleties. You could have explosive economic growth in the IT sector and in intellectual property whilst seeing resource usage decline.

That said, I'm not sure why economic growth is a goal. I have a vague intuition that a fiat currency economy is only healthy when it is growing so that it can pay off the interest accumulated when most money circulating is debt.
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Re: Exponential Growth Revisited

#5  Postby FACT-MAN-2 » Oct 05, 2013 10:11 pm

VazScep wrote:I'd imagine there are subtleties. You could have explosive economic growth in the IT sector and in intellectual property whilst seeing resource usage decline.

That said, I'm not sure why economic growth is a goal. I have a vague intuition that a fiat currency economy is only healthy when it is growing so that it can pay off the interest accumulated when most money circulating is debt.

Economic growth is being referred to here as "on the whole."

Constant economic growth is a goal because anything else is stagnation, or recession, or depression, all three of which are anethema to making money and in fact usually bring about losses.
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Re: Exponential Growth Revisited

#6  Postby FACT-MAN-2 » Oct 05, 2013 10:15 pm

Thommo wrote:
FACT-MAN-2 wrote:
When politicians or economists chant their mantra -- we must GROW the economy -- they implicitly assume that our economy can growexponentially into perpetuity.

I'm sceptical. A politician that thinks beyond the next election cycle or so is rare, economic forecasts and growth plans seldom extend beyond a decade or so at their most far sighted.

I think we can all duff up this argument that infinite growth is probably not going to work, the only question is whether we cut our knuckles on the straw in the process.

I must say I don't get quite what you're driving at here.

Thommo wrote:[
Yet, at this seemingly modest rate, the size of the economy doubles every 22 years, quadrupling in 44 years, and expanding by a factor of 8 in less than three generations. Such growth demands commensurate doubling, quadrupling, and octupling of the energy sources and raw materials that feed the economy.


This one isn't true either.

How so? Care to explain?
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Re: Exponential Growth Revisited

#7  Postby Thommo » Oct 06, 2013 5:02 am

FACT-MAN-2 wrote:I must say I don't get quite what you're driving at here.


It turns out that the idea that all economists and politicians are so mathematically inept they don't get basic concepts is questionable. Assigning a position to them that they did not say and which there is no evidence to believe is a straw man.

The "no-go" theorem of infinite growth doesn't say anything about whether we can have exponential growth for 200 years and politicians or economists never imply otherwise that I am aware of, it's not representative of what they are saying. Nor does growth for 200 years necessarily imply exponential growth for 200 years either. It's not like economists are puzzled over China's 10% growth compared to the USAs 3%, and indeed make forecasts according to situation, with 8% growth per year for China over the next decade being considered poor in many quarters.

FACT-MAN-2 wrote:
Thommo wrote:
Yet, at this seemingly modest rate, the size of the economy doubles every 22 years, quadrupling in 44 years, and expanding by a factor of 8 in less than three generations. Such growth demands commensurate doubling, quadrupling, and octupling of the energy sources and raw materials that feed the economy.


This one isn't true either.

How so? Care to explain?


It's just not a true statement, doubling of the economy does not demand a doubling in resource consumption. Efficiency changes, recycling, changes in types of consumption from industrial to service etc. can all provide growth at lower rates of increase, or even lower absolute rates of consumption. Simple example - growth in video games during the era of digital distribution.
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Re: Exponential Growth Revisited

#8  Postby Loren Michael » Oct 06, 2013 5:29 am

The premise of this thread is ignorant.

Virtual growth and efficiency-driven growth means that there's lots and lots of room for growth while resource use declines.

Angry Birds only started being a resource hog when they started investing in plushie toy merchandise, and, surprise, that was after they already made $texas.
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Re: Exponential Growth Revisited

#9  Postby GT2211 » Oct 06, 2013 7:21 am

Another example of a writer who starts off by admitting he knows little about what economists actually postulate but then attempts to debunk his (incorrect) interpretation of exponential growth in economics.

So once again I'll post this.

http://noahpinionblog.blogspot.com/2012 ... s-law.html
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Re: Exponential Growth Revisited

#10  Postby Onyx8 » Oct 06, 2013 7:31 am

Back when I was doing protests about this and that it used to be bandied about that economists and accountants couldn't subtract: They knew for instance the value of the trees or coal in an area but they didn't subtract that value when the trees/coal were removed and sold, they just added the value in one column and ignored the fact that there were no more trees/coal to extract.
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Re: Exponential Growth Revisited

#11  Postby iamthereforeithink » Oct 06, 2013 9:16 am

There is some degree of truth in the OP article, but it's obscured by the fallacies that it contains. The fact is that economic growth, like other kinds of non-cancerous exponential growth, is self-limiting by nature. There are both balancing as well as reinforcing feedback loops in operation. And there is a reason why 10% annual growth is expected from China, but not from the US or Western Europe, where 2-3% growth is seen as acceptable. Eventually 2-3% growth will also be acceptable in China.

The primary fallacy is to club all industry categories under "economy" and talk about their growth as a singular whole. The "economy" includes industries that experienced rapid exponential growth in an earlier era, but are now stable/ stagnant or declining. It also includes other industries that are now experiencing exponential growth but will eventually stagnate or decline. The nature of exponential economic growth is encapsulated by variations of the "diffusion of innovations" bell curve:

Image

If you look at the growth of the global steel industry, for example, you will find it grew exponentially in the early part of the 20th century in most of the western world (incl. US, Germany and Japan), reached maturity and stagnation in the 70s, and is currently not growing at all. In China and India on the other hand, exponential growth in the steel industry took off on the 70s/ 80s, and will eventually see a similar maturity and stagnation. A similar story is seen for the auto industry, with a slightly shifted timeline. The smartphone industry (for example) on the other hand, is currently witnessing exponential growth in the western world but will see a similar maturity at some point in the future.

Another fallacy is conflating different kinds of growth. Most industries that are currently experiencing exponential growth are service industries, whose growth depends much more on the growth of intellectual capital, than on the increasing exploitation of natural resources. There are also constraints and negative/ balancing feedback loops applicable to this kind of growth, but they are not necessarily related to the finite nature of natural resources. I could go on for several pages, but in summary, the real story is a lot more complex than is encapsulated by the OP article.
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Re: Exponential Growth Revisited

#12  Postby FACT-MAN-2 » Oct 06, 2013 6:28 pm

iamthereforeithink wrote:There is some degree of truth in the OP article, but it's obscured by the fallacies that it contains. The fact is that economic growth, like other kinds of non-cancerous exponential growth, is self-limiting by nature. There are both balancing as well as reinforcing feedback loops in operation. And there is a reason why 10% annual growth is expected from China, but not from the US or Western Europe, where 2-3% growth is seen as acceptable. Eventually 2-3% growth will also be acceptable in China.

The primary fallacy is to club all industry categories under "economy" and talk about their growth as a singular whole. The "economy" includes industries that experienced rapid exponential growth in an earlier era, but are now stable/ stagnant or declining. It also includes other industries that are now experiencing exponential growth but will eventually stagnate or decline. The nature of exponential economic growth is encapsulated by variations of the "diffusion of innovations" bell curve:

Image

If you look at the growth of the global steel industry, for example, you will find it grew exponentially in the early part of the 20th century in most of the western world (incl. US, Germany and Japan), reached maturity and stagnation in the 70s, and is currently not growing at all. In China and India on the other hand, exponential growth in the steel industry took off on the 70s/ 80s, and will eventually see a similar maturity and stagnation. A similar story is seen for the auto industry, with a slightly shifted timeline. The smartphone industry (for example) on the other hand, is currently witnessing exponential growth in the western world but will see a similar maturity at some point in the future.

Another fallacy is conflating different kinds of growth. Most industries that are currently experiencing exponential growth are service industries, whose growth depends much more on the growth of intellectual capital, than on the increasing exploitation of natural resources. There are also constraints and negative/ balancing feedback loops applicable to this kind of growth, but they are not necessarily related to the finite nature of natural resources. I could go on for several pages, but in summary, the real story is a lot more complex than is encapsulated by the OP article.

Well, it actually isn't.

Economists refer to growth on the whole, or as the net average of all the different rates of growth you mention. It doesn't matter if one industry or economic sector is growing at 10 per cent and another is growing at three per cent, what matters is the net effect on the whole of an economy. And that's what the article was referring to.

There can be all sorts of diffeing growth dynamics going on within an economy, but it's the whole that economists and policymakers are concerned with and what they mostly talk about. To go inside the net overall effect sidetracks the discussion; because it doesn't matter how much differentiation in growth rates among various sectors or industries goes on, they still net out to an overall average for an economy, and it's that overall average that economists use to measure or describe economic health. They can and do break it down to what's going on in various industries or sectors as they attempt to explain the overall average, but it's the net effect on the average with which they are concerned, and the level at which the OP addressed the question.
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Re: Exponential Growth Revisited

#13  Postby iamthereforeithink » Oct 06, 2013 7:10 pm

Its fine to refer to overall growth of the economy for accounting or calculation purposes, but not when you are trying to build a theory about exponential growth and making claims about its nature. Then you have to account for all of its internal dynamics in detail. Otherwise all you get is fallacious conclusions borne of ignorant premises, such as in the OP. It's meaningless to make a claim about the growth dynamics of the overall economy, when you don't independently account for all the different sub-dynamics that constitute it. There is no "net effect" you can talk about coherently when trying to determine the limits to growth, without reference to the constituent parts. Its poor and unscientific methodology, but I'll grant you that it makes for good copy. People tend to prefer simplistic, sweeping generalizations over complex and detailed analyses.
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Re: Exponential Growth Revisited

#14  Postby FACT-MAN-2 » Oct 07, 2013 9:42 pm

iamthereforeithink wrote:Its fine to refer to overall growth of the economy for accounting or calculation purposes, but not when you are trying to build a theory about exponential growth and making claims about its nature. Then you have to account for all of its internal dynamics in detail. Otherwise all you get is fallacious conclusions borne of ignorant premises, such as in the OP. It's meaningless to make a claim about the growth dynamics of the overall economy, when you don't independently account for all the different sub-dynamics that constitute it. There is no "net effect" you can talk about coherently when trying to determine the limits to growth, without reference to the constituent parts. Its poor and unscientific methodology, but I'll grant you that it makes for good copy. People tend to prefer simplistic, sweeping generalizations over complex and detailed analyses.

Complex detailed analyses aren't suited to a blog piece, which by its nature has to be generalized.

Nevertheless, the point made in the OP still stands. If the US economy, for example, were to grow at a net three per cent per annum that could not be sustained over any extended period. The global economy is almost five times the size it was a century ago and if it keeps growing at the rate it has, it'll be 80 times bigger come the year 2100. That's just not sustainable, and in fact the slowdown in growth we've seen in the more developed parts of the world in recent years reflects the difficulty of keeping growth goiing at the rate it grew in the post war era.

This is not a theory, it's a practical conclusion. The OP was not trying to "build a theory" about exponential growth, the writer was merely reporting on observations made regarding economic performance. The economy has and continues to grow, to become ever bigger, and his idea is that this can't go on ad infinitum.

It's really quite a simple proposition, and as much as you'd like to decouple the resource base from growth, that can't be done because (growing) populations will always be consuming resources, building more and more homes and cars and refrigerators and TVs and factories, and consuming ever larger quantities of food. IP may drive growth in some sectors, but it won't ever become the exclusive driver or even the principle driver.

The issue has driven many researchers to begin examining no-growth economic systems, such as John Daly at the University of Maryland and the economist Tim Jackson in the UK. They are envisioning "steady-state" structures that does not require growth to sustain themselves.

We canb't hope to sustain a consumer-driven economy ad infinitum. Somewhere along the line we'll have to chage up the way we do eonomics and get ourselves on a sustainable footing.
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Re: Exponential Growth Revisited

#15  Postby GT2211 » Oct 07, 2013 10:19 pm

I want to point out the neo-classical growth model* is a steady state growth model.
http://en.wikipedia.org/wiki/Neoclassical_growth_model

*growth in the model is dependent on exogenous factors such as rates of technological advance. Which is where other endogenous models have been created such as Romer's.
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Re: Exponential Growth Revisited

#16  Postby Thommo » Oct 08, 2013 9:06 am

FACT-MAN-2 wrote:It's really quite a simple proposition, and as much as you'd like to decouple the resource base from growth, that can't be done because (growing) populations will always be consuming resources, building more and more homes and cars and refrigerators and TVs and factories, and consuming ever larger quantities of food. IP may drive growth in some sectors, but it won't ever become the exclusive driver or even the principle driver.


Economic and population growth are totally separate issues, you can't just equivocate between them.
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Re: Exponential Growth Revisited

#17  Postby Thommo » Oct 08, 2013 9:26 am

FACT-MAN-2 wrote:Nevertheless, the point made in the OP still stands. If the US economy, for example, were to grow at a net three per cent per annum that could not be sustained over any extended period. The global economy is almost five times the size it was a century ago and if it keeps growing at the rate it has, it'll be 80 times bigger come the year 2100. That's just not sustainable, and in fact the slowdown in growth we've seen in the more developed parts of the world in recent years reflects the difficulty of keeping growth goiing at the rate it grew in the post war era.


Where's this figure come from? If you fit a single exponential growth curve to this data then if one century gives growth from z to 5z, then two centuries gives growth from z to 25z, since if we have e1 as the size of the economy after a period of time t has elapsed and e2 as the size of the economy after a period of time 2t has elapsed then we get:-

e1=e0at , and
e2=e0a2t

Thus
ln(e1)=ln(e0at) and therefore ln(e1)=ln(e0) + t.ln(a) , and
ln(e2)=ln(e0a2t) and therefore ln(e2)=ln(e0) + 2t.ln(a)

Hence
2ln(e1) - ln(e0)=ln(e0) + 2t.ln(a)=ln(e2) , giving ln(e12/e0.)=ln(e0) + 2t.ln(a)=ln(e2)

And finally
e12=e0.e2
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Re: Exponential Growth Revisited

#18  Postby 4 Hours » Nov 07, 2013 6:27 am

VazScep wrote:I'd imagine there are subtleties. You could have explosive economic growth in the IT sector and in intellectual property whilst seeing resource usage decline.


Believe it or not, it takes a lot of resources to make and run computers.

Loren Michael wrote:Virtual growth and efficiency-driven growth means that there's lots and lots of room for growth while resource use declines.


There are, ultimately, thermodynamic limits to efficiency gains. As for "virtual growth", see above, and remind me when it becomes possible to start eating silicon wafers.

GT2211 wrote:Another example of a writer who starts off by admitting he knows little about what economists actually postulate but then attempts to debunk his (incorrect) interpretation of exponential growth in economics.

So once again I'll post this.

http://noahpinionblog.blogspot.com/2012 ... s-law.html


Even as an ardent transhumanist, I think Singularitarianism is a pretty far-fetched scenario conceived of by a futurist (Ray Kurzweil) who has already gotten a crapload of predictions wrong. Also, I would like all of you who think that the "virtual" / "service" economy has some sort of ghostly disembodied existence that doesn't depend on physical inputs (including heavy industry goods) to take a good long look at how strongly real GDP and energy use are correlated in a number countries well into the present time, along with other facts:

http://ourfiniteworld.com/2011/11/15/is ... gy-growth/

Gail Tverberg writes:

Why does world energy intensity remain flat, while energy intensity for many individual countries has been decreasing?

We are dealing with a large number of countries with very different energy intensities. The big issue would seem to be outsourcing of heavy manufacturing. This makes the energy intensity of the country losing the manufacturing look better. Outsourcing transfers manufacturing to a country with a much higher energy intensity, so even with the new manufacturing, its ratio can still look better (lower). It is hard to measure the overall impact of outsourcing, except by looking at world total energy intensities rather than individual country amounts.


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Re: Exponential Growth Revisited

#19  Postby stevecook172001 » Nov 12, 2013 11:02 pm

VazScep wrote:I'd imagine there are subtleties. You could have explosive economic growth in the IT sector and in intellectual property whilst seeing resource usage decline.

That said, I'm not sure why economic growth is a goal. I have a vague intuition that a fiat currency economy is only healthy when it is growing so that it can pay off the interest accumulated when most money circulating is debt.
Economic growth is an intrinsic goal of our economic systems because of the way un-backed FIAT debt/credit (othwerwise known as "money") is lent into existence at interest.
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Re: Exponential Growth Revisited

#20  Postby stevecook172001 » Nov 12, 2013 11:04 pm

Thommo wrote:
FACT-MAN-2 wrote:It's really quite a simple proposition, and as much as you'd like to decouple the resource base from growth, that can't be done because (growing) populations will always be consuming resources, building more and more homes and cars and refrigerators and TVs and factories, and consuming ever larger quantities of food. IP may drive growth in some sectors, but it won't ever become the exclusive driver or even the principle driver.


Economic and population growth are totally separate issues, you can't just equivocate between them.
Economics and population growth are utterly connected.
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