Implications of the Ayres Warr Model of Economic Production: An Introduction

This is a guest post by Ian Schindler, known on The Oil Drum as Schinzy. Ian teaches math at the University of Toulouse in France.

The Ayres Warr Model

Implications of the Ayres Warr Model of Economic Production: An Introduction


Many Oil Drum readers are familiar with the Ayres Warr model of economic production, as discussed in "Accounting for Growth: The Role of Physical Work" by Robert Ayres and Benjamin Warr. As a mathematician, with an interest in economics, I wrote a fairly mathematical paper, extending some of the work done by Ayres and Warr. My paper can be found at this link.

The purpose of this post is to give an overview of the paper I wrote, explained in more elementary terms. Some readers with a more mathematical bent may choose to read my original paper as well. For those readers unfamiliar with the Ayres Warr model, a short introductory piece can be found in point 5 of this post by Gail the Actuary.

Ironically my interest in economics has largely been unmathematical. I have colleagues who are economists with whom I have spoken about both economics and their mathematical models. The models they showed me in general did nothing to improve my intuition of economics. I had always attributed this to a lack of systematic study of economics. Then I learned of the Ayres Warr model of economic production. The more I thought about this model, the more it seemed to make sense to me, and the more of my eclectic knowledge of economics it seemed to explain. I started reading papers of Ayres and Warr, among other papers on economics. The economic analysis I have read most in tune with the Ayres Warr model of economic growth is that written by Gail the Actuary.

The Ayres Warr model of economic production is remarkably simple. In my view, it is like a first simplified model which gives the main story, but which may be modified in the future. In particular, it is missing a stochastic or quasi periodic term with zero average. It says that exergy, or the proportion of energy produced which is available for work, produces most economic output. The rest is essentially produced by capital. Exergy roughly corresponds to efficiency times energy production. Efficiency depends on technology as does energy consumption. A major implication is that peak energy production will roughly coincide with peak economic output. The model is consistent with attributing units of energy to currency.

I made some simplifying assumptions and did some elementary analysis on the Ayres Warr model and came up with an equation from which I arrived at the following conclusions implied by the model:

  1. Price swings of energy produced by changes in energy supply are mitigated by changes in economic output. If production of energy increases, this creates greater economic production which increases the market for energy, thus damping the price decrease. Inversely if production of energy decreases, economic output decreases damping the price increase.
  2. Energy efficiency increases the price per unit of energy. This can be understood in two ways. Increasing efficiency increases exergy, thus increasing economic production which increases the market for energy thus increasing the price. Second: the more work one can do with energy, the more one is willing to pay for energy which increases its worth. So increased energy efficiency is the greatest driver of economic growth, stimulating both the economy and energy producers.
  3. Energy efficiency does not limit production of fossil fuels; it raises prices stimulating production. Therefore many policies people are encouraging to limit global emissions will in fact raise global emissions. If there is a threshold beyond which we cannot burn more fossil fuels, and it is commercially viable to produce beyond this threshold, the only way not to cross it is by sacrificing economic output.
  4. Increasing efficiency ultimately increases energy prices which we need to assure future (renewable) energy production.
  5. The Ayres Warr model is possibly a good tool to detect financial bubbles and troughs (periods in which the market over or undervalues assets) when they are due to over or under estimating economic output. For example increased exergy production during the 1990's implied that the world economy was growing robustly, so that oil was probably under priced in 1998 (at $10 per barrel). On the other hand, flat exergy production since 2005 was a portent of lower economic growth, thus a decrease in demand for oil so that the price of oil in July 2008 was probably too high.
  6. Economic output is largely independent of population. Therefore demographic concerns that there will not be enough future workers to support an aging population are unfounded. Concern should rather be that exergy supplies will be insufficient.
The last item did not come from the equation I came up with, it is a direct consequence of the Ayres Warr model. It can be understood as meaning that population is a possible expression of increased economic output (made possible by increased exergy production), but not a necessary one. In addition to these conclusions, my analysis suggested very simple feedback loops to explain economic growth and contraction.

I have just begun my investigations of the Ayres Warr model of economic production. By talking about it, I'm hoping that others will join me in looking at implications of the model, and integrating the model into simulations to see how well it can predict future economic output and energy prices. Having a reasonable estimate of the future economy has considerable political ramifications. Much policy debate is based on maximizing future economic output. If the Ayres Warr model is a reasonably accurate model for future economic production, much of this debate would be cut short, and we could focus more on how we plan on using the economic production available. We also might question whether maximizing economic output is the best way forward.

Thanks for your work both on the original paper, and on this introduction.

You offer a number of interesting points. You say, "Energy efficiency does not limit production of fossil fuels; it raises prices stimulating production." Do you see climate issues as the major limiting concern for raising efficiency, and since increased efficiency is likely to lead to greater total production? If there were no climate issues, would you see increased efficiency as a reasonable approach to take?

Francois Cellier wrote an interesting post some years ago about computer simulations he had done involving peak oil and climate change. He stated that 8 of 10 scenarios resulted in disaster, that is a world population going from around 7 billion in 2040 to around 1 billion in 2070. He noted that the earlier peak oil hit, the higher the probability of avoiding disaster. Therefore I see peak oil and peak coal as a chance to avoid disaster in spite of ourselves.

We have two dilemmas, one is reducing emissions from fossil fuels, the other is adjusting to a world with less energy available. Efficiency is essential in solving the second problem, it doesn't help with the first. If I were king of the world, I would limit fossil fuel use to preparing for a world without fossil fuels. Increasing efficiency would be the primary tool. This would decrease economic output, and might not be a popular policy, but in the long run it is the policy I think would cause the least suffering.

My first thought when I saw this equation was that post peak oil decline would occur faster than expected because economic production would fall depressing prices which would slow E & P spending on oil. If this is true, it could well be that climate change is not our most pressing problem, but rather economic contraction and lower energy supplies.

If this is true, it could well be that climate change is not our most pressing problem

Based on what? Please be specific and extensive, because you could not possibly be more wrong and I would like to respond in detail.


I haven't done the computations. Monbiot in this post lays out how much CO_2 we can produce. He uses reserve numbers from the World Energy Council and computes that we can burn about 61% of remaining supplies of oil, coal, and gas without catastrophic results. This means that if reserves are over estimated by 100%, we don't have to worry about climate change. Again, I haven't done the calculations, but I wouldn't be surprised if this were not the case.

Whoops, I had to reedit this. I had written 2 other paragraphs, but I was not only off subject, I was contradicting myself. I will just say that there is a very subtle difference between decreasing c(t) and increasing e(t). What I do not have is a good tactic to decrease global warming. Essentially if I don't burn oil which is produced, someone else will, so in order to decrease global emissions I must decrease production.

I am ignoring unconventional sources of fossil fuel, such as tar sands, oil shales, bitumens and methane hydrates, as well as liquid natural gas resources....

Total conventional fossil fuel reserves therefore contain 818 billion tonnes of carbon.

Even ignoring all unconventional sources and all other greenhouse gases and taking the most optimistic of the figures in the two Nature papers, we can afford to burn only 61% of known fossil fuel reserves between now and eternity.

Nevermind. I thought you had something worth responding to.

I'll let the fact that was a thought experiment and, as italicized, not one grounded in reality, speak for itself except to mention there was also ZERO mention of all other positive feebacks, e.g., permafrost, Arctic Amplification. Note the bolded phrase. See, what's likely actually running through your head is, "We can burn 61%" and the EVER part sort of gets set aside by the subconscious.

Monbiot, for all his usual radicalism, is being irresponsible here. I suppose he's trying to make a point that we really CAN'T burn all that carbon, and, look! we haven't even included feedbacks and stuff!, but that's a dangerous, and potentially fatal, game to play. People hear what they want to hear and disregard the rest, at least according to Simon and Garfunkel. Giving them any help in this regard is not smart, imo.

The recent paper from MIT is the one you should be paying attention to, not an op-ed.

I am utterly non-plussed at the willingness of some PO advocates to look for an excuse for AGW to not be a serious problem. It makes no sense.


The MIT article you linked makes no mention of the possible dramatic overestimation of global FF reserves. A more convincing analysis of GW would address this likelihood.

Whether they are aware some think they may be overstated or not, I don't know. I do know it could not possibly be less relevant.

The study also shows that, if all conservatively estimated available fossil fuels were to be burnt, two to three times more CO2 than allowed for the 2°C target would be emitted. This only takes into account the fuels which are already known and which are economically viable to extract. The fossil fuels will therefore not run out before the maximum CO2 emission calculated by scientists is reached.

The above quote means that even if we only have between 1/2 and 1/3 of the FFs generally thought to exist, we still can't burn them all.

There are so many holes in this line of thinking about FFs and climate it's tiresome to have to repeat them to so many posters.

By the way, calling it a likelihood there are far fewer FFs than generally stated because a couple studies posited the thought is a stretch, and certainly not a scientific statement. Given there is far less certainty surrounding coal reserves than oil reserves, and there are large arguments about oil reserves, I'd think you'd be more careful about declaring their "likely" amounts.


Thought lately about coal?

The difference is caused by several factors rather than any single big change. Among these are improved economic modeling and newer economic data showing less chance of low emissions than had been projected in the earlier scenarios.

I wonder what they used here. My optimism came because of my impression that the economy was going to do a lot worse than they are predicting.

You are right about keeping an eye on the issue however.

Increasing efficiency would be the primary tool. This would decrease economic output, and might not be a popular policy, but in the long run it is the policy I think would cause the least suffering.

I partly disagree. In a situation of decreasing energy availability, efficiency that results in energy use below the depletion curve will permit economic growth. Energy Efficiency that matches depletion will show a zero effect, and energy efficiency that exceeds the depletion curve will result in economic contraction.

This comes from my analysis and inversion of Jeavons Paradox.

Jeavons is predicated on a stable and low price of energy and stable and/or increasing amounts of energy availability. If energy becomes increasingly expensive and reduces in quantity, then the only way production can maintain a specific value is with efficiency, and the only way it can increase is through an efficiency that is greater than the depletion rate.

So, if we are experiencing (for example) 3% energy depletion, we need to have 4% increase in efficiency per joule to experience 1% economic growth.

Therefore, I agree efficiency is the best thing we can immediately do.

However, we eventually hit what I call "granularities" in energy requirement which are not negotiable (such as a 1500 - 2500 calorie per capita diet) and when the efficiencies start bumping up against that, then we're on a different (and rather miserable) energetic plane.

Your point 3) "Energy efficiency does not limit production of fossil fuels; it raises prices stimulating production. Therefore many policies people are encouraging to limit global emissions will in fact raise global emissions."

Could be re-stated to take account of renewable energy as:

Energy efficiency does not limit production of energy; it raises prices stimulating the production of alternative non-FF sources. Therefore many policies people are encouraging to limit energy use will raise the proportion of renewable energy( and possibly lower FF use, but not necessarily).
What do you think?

I think you are absolutely right. I think we should be preparing for a future without fossil fuels, and efficiency should stimulate production of renewable energy.

Therefore many policies people are encouraging to limit energy use will raise the proportion of renewable energy( and possibly lower FF use, but not necessarily).

Necessarily not, in certain circumstances. It depends on the rate of decline of exergy availability and on the rate of exergy payback of the alternative exergy sources.

When the availability of exergy is declining, it would be a brave or tyrannical government that would deprive the rest of its economy of large amounts of it to make investments that will break even in exergy terms only after years.

David, exactly. Given the large amount of upfront energy needed for an investment in wind and solar that would come anywhere near the energy we now consume, it is hard to imagine anything other than a tyrannical government as being able to appropriate that energy. If we were going to replace fossil fuels with alternatives it needed to happen when we had excess. It is not just the energy for the solar panels and windmills but also for the infrastructure to fix the grid and "tank" up electric vehicles. Even investing in more public transport will be a hard sell but I think that would be far more doable than a Manhattan project on solar panels and windmills.

Wind energy returns energy invested in months not years, allowing all energy for 50% growth in new wind to be derived from just those turbines installed 6 months ago. It's happening now, before we have the electric vehicles. Funding in the US budget for grid upgrades.

3) "Energy efficiency does not limit production of fossil fuels; it raises prices stimulating production. Therefore many policies people are encouraging to limit global emissions will in fact raise global emissions.

Could be re-stated to take account of renewable energy as:

Energy efficiency does not limit production of energy; it raises prices stimulating the production of alternative non-FF sources. Therefore many policies people are encouraging to limit energy use will raise the proportion of renewable energy( and possibly lower FF use, but not necessarily). What do you think?

Both of you are making hidden assumptions.

For the author:

  1. "Energy efficiency does not limit FF production; it raises prices, stimulating production."
  2. Assumption: nothing else limits FF production or consumption.
  3. "Therefore many policies people are encouraging to limit global emissions will in fact raise global emissions."

That unstated assumption is necessary for your conclusion, but is known to be false. The simplest example is one of the biggest: personal cars. For most of the industrialized world, fuel costs are only a small part of the cost of an incremental mile driven, with the cost in time usually being the dominant factor and vehicle wear often being the dominant economic factor. If vehicle efficiency doubled, Westerners would not suddenly want to drive twice as many miles.

Fundamentally, it's a mistake to ignore human behaviour when you're trying to model human behaviour.

Neil's response is much better this way, but is still making assumptions:

  1. "Energy efficiency does not limit FF production; it raises prices"
  2. Assumption: raising energy prices stimulates the production of alternative non-FF sources.
  3. Assumption: price rises caused by efficiency will increase the proportion of renewable energy.
  4. "Therefore many policies people are encouraging to limit energy use will raise the proportion of renewable energy"

As with Ian, these assumptions are necessary to your conclusion. These assumptions are much more reasonable - witness the massive surge in interest in renewable energy during the recent FF price rises - although still somewhat questionable (i.e., if the only change is an increase in efficiency, then the relative prices of a kWh of renewable and non-renewable energy will stay the same, which doesn't provide much reason to change their mix).

A much stronger impetus to change the energy mix is likely to come from external factors such as FF scarcity and internal factors such as carbon taxes, as both of these will tend to raise the price of FF energy much more than renewable energy. I expect both of these to have a large effect in the next 50 years.

A second likely factor is changing energy vectors. Electrified rail, for example, is not only 3x more efficient than diesel rail, it's also much more flexible, as it can accept fuel from many sources. A fuel switch from diesel to electricity, then, not only offers the potential for emissions reductions from increased efficiency (as it's improbable that goods transportation would triple due to lower fuel requirements), but also based on fuel type, as the electricity could be derived from lower-emission sources.

I disagree completely. Statement 3) requires no more than the following assumptions:

  1. The Ayres Warr model is a reasonably accurate model of economic production.
  2. The simplifying assumptions I made for my analysis.
  3. Fossil fuel production is a monotone increasing function of price.
you are making hidden assumptions.

I disagree completely. Statement 3) requires no more than the following assumptions:

1. The Ayres Warr model is a reasonably accurate model of economic production.
2. The simplifying assumptions I made for my analysis.
3. Fossil fuel production is a monotone increasing function of price.

And this is better how?

Assumption #3 is known to be wrong; the 90s proved that. Assumption #1 is another way of saying "the future is like the past" and "my model of the past is not too wrong". Assumption #2 is in fact many unseen assumptions; based on the two we've seen, these are unlikely to be fully sound. Accordingly, it is unreasonable to expect to derive strong conclusions from so many questionable and partially-valid assumptions.

Most Westerners would not drive twice as many miles if their cars became twice as fuel-efficient; ergo, it is an invalid conclusion to say that efficiency improvements will lead to increased consumption. If your model says otherwise, your model is wrong.

You're trying to push your model far outside of where it's valid. Fundamentally, it's a mistake to ignore human behaviour when you're trying to model human behaviour, and that's what you're doing.

The 90's did not disprove assumption #3. The 90's proved that oil production is a function of several variables. I guess I should have been more precise. When I say oil production is a monotone function of price, I mean that the partial derivative of oil production with respect to price is positive. It is possible to have increasing price and decreasing production, as well as decreasing price and increasing production. See the oil production model I proposed in my paper for an idea of the kind of function I mean.

In any case, I am not looking for a model that will accurately predict the future, I am looking for a model that will give me an idea of how the variables in the model will effect the future. I think the model is robust enough for that purpose.

Most Westerners would not drive twice as many miles if their cars became twice as fuel-efficient; ergo, it is an invalid conclusion to say that efficiency improvements will lead to increased consumption. If your model says otherwise, your model is wrong.

Not necessarily so. You are also making assumptions, namely that any efficiency improvements in one sector affect that sector only. Energy saved through greater efficiency in transport may be offset by increased consumption of say, manufactured goods. For example, if your car is twice as efficient you may not necessarily drive twice as far but you might use the money you save to purchase another television.

As far as I understand it, the model is designed to look at the economy as a whole, not isolated sectors. You cannot use your example of vehicle miles driven to falsify the model because that's not what it's designed to model. It's 'outside where it's valid'.

What about debt ?

One thing your missing is that debt has built up in the system as it has gone through this cycle your proposing more or less in the past.

Its a ok model for past economic behavior but because your not including the ever increasing debt load explicitly I can't see how its a model for the future.
As long as the debt can be rolled forward you can as you seem to be doing ignore it.

From your paper

Finally we note that similar increases in $ c(t)$ might have different effects on the economy at different times. Gail's post about the amount of debt in the economy suggests that the current economy is fragile, and that small changes in $ c(t)$ might cause large numbers of people to fall out of the middle class.

Where: $ c(t)$ be the proportion of GNP spent on oil.

Intrinsically the problem is how the capitol is partitioned if its primarily earned wealth or savings then I'd argue your on the right track but if its actually primarily a ever larger amount of debt thats being rolled forward then the system is unstable.

I'd argue that to get things to work like your saying then real wealth would have had to accumulate and debt would have slowly declined over time as we passed through these cycles.

It all comes down to the nature of the K(t) or capitol in your paper.

The very first thing that has to happen is this needs to be split out into debt vs saved wealth and then your forced to also deal with inflation and interest.

Obviously my opinion is that if the system is growing its debt load esp as energy declines its toast you don't need to know much more than that :)

My guess is that the world is much poorer than it imagines.

I think that the units of money in the modern world are energy. The reserve banking system creates money out of thin air. I call this artificial money. It is money we use that doesn't really exist until it is paid back. As Gail has pointed out, the system can work if the economy is growing, that is, as long as exergy is growing (according to the model). I don't think this money that has been lent can be paid back, at least not in the same energy units in which it was lent. I think we may be entering time in which long term interest rates are negative, in the sense that if you leave a certain amount of money in the bank, the amount of energy you can purchase with that money in say 15 years will be half of what you can purchase today. So I do not think the current bubble has finished losing air.

The Ayres Warr model is completely independent of debt however. It gives the real size of the economy, and in fact might be a valuable tool for telling us just how big the current bubble is.

In my paper, for simplicity, I assumed that peak oil would not effect capital (the means of producing goods). I do not think this assumption is justified. I think peak oil should increase the depreciation rate of oil dependent capital (non electric transportation producing capital). This should accelerate post peak oil economic decline rates.

I have been advising my mother on her investments for the last 20 years. When the financial crisis hit, she asked me what she should do. I told her to take enough money out of her account to insulate her house, purchase a solar heating system and a rain harvesting system while she could still afford it.

Well I think that debt is the real problem.

Its worse than your suggesting. Debt is incredibly dangerous in a post peak world.

Consider someone that borrows 300k to buy a house in a world of steady debasement of the currency and plenty of energy this person can reasonably expect that inflation will ensure that as the loan ages he has a good chance of finding a buyer that will pay off the loan.

Note I'm not even really talking about bubbles just the steady inflation we have.

However its worse than that capitol has been committed to this loan in the sense that since this loan was made other loans cannot be made. Thus the debt structure is a powerful force for perpetuating the status quo. These loans make the system very inflexible.

You cannot ignore it even in the Ayres Warr equation since it dramatically effects the efficiency of the system for cars its fairly direct the loans make it difficult to alter the fleet.

And next of course a default on a loan taken out for thirty years has to be written off at the time of default i.e the loss cannot be prorated over the thirty year payback time. The fact that it was generally made using fractional reserve lending magnifies the loss.

Thus as debt builds in the system and defaults increase you should see the focus shift to protecting the system of debt at all costs regardless of how the real economy is performing. The collapse of the system of debt is seen at the worst outcome possible.
This effectively means zero capitol will be allocated for efficiency gains. What your equation is looking at becomes almost background noise to the debt elephant.

And of course stabilizing the system of debt is highly inflationary for real assets but the real economy is not benefiting from this as new debt is created to cover debt defaults that are on long term loans. When someone defaults on a 300k mortgage you don't create enough new debt to just cover the 20k or so they pay each year instead you create more than 300k some to cover the defaulted debt and some to recapitolize the system.

Your effectively talking about devaluing of the currency in a few years what would take 30 years to accomplish.

This says that the dollar has devalued by about 5:1 since 1970 thus we should expect as this debt is backstopped and added to the balance sheet of the governments that we will see a similar devaluation in a few years with zero economic gain i.e its all in the banking system.

Eventually this becomes a central bank problem as sovereign debt floods the worlds markets seeking capitol and driving up interest rates.

One can expect private debt offerings to dry up and that articles normally bought using debt instruments that are in surplus to drop dramatically in price as the market demands cash purchases and cash to become increasingly hard to find.

You get massive inflation with massive deflation in the prices of anything purchased with debt. Although not direct one can imagine that anything normally purchased with cash thats in short supply will demand a premium. Its a bit more complex than that because the flow of funds between commodity producers and consumers is important. Commodity producers will demand a higher premium on both their commodities and on recycling the cash to purchase their customers debt. Financing terms get increasingly onerous but whats important is the cash is extracted out of the real economy in the form of rising commodity prices and reinjected into the banking sector via purchase of defaulted debt.

I just don't think you can ignore this cycle it dwarfs and magnifies the underlying structural problems of the "real" economy your modeling.

Its like a 30 pound dog with a 700 pound tick sucking its blood out and your worried if it has enough food. Certainly the supply of food for the dog is the underlying problem but ...

The reserve banking system creates money out of thin air. I call this artificial money. It is money we use that doesn't really exist until it is paid back.

This is a misunderstandings that appears again and again on TOD. Yes, in a fractional reserve system, money is creating through lending. However, depending on how the system is managed, there is no requirement that either the money supply or the debt load expand without limits. There is nothing that precludes the possibility of a "steady-state," with a stable debt load that is continuously being retired and re-issued. As any first year economics textbook will point out, the creation of money by the banking system does not make society wealthier, since each dollar issued is backed by a dollar of debt. The last sentence in the blockquote above is so confused I don't know where to go with it. Do you not understand the concept of the velocity of money?

Don't believe everything you read in a first year textbook-the creation of money/ramping up the money supply definitely causes a wealth effect which eventually reverses (when the growth in the money supply can no longer be maintained)-you should check out Martenson's site for an explaination and education on this one.

Read the qualifiers in my original post. I'm not making any strong claims about the inherent stability of a fractional reserve system. When I read comments like the one above, I doubt the individual in question even knows what "money" is.

So surprising to find a comment on TOD that shows some understanding of money.

take me to school then, what is "money"

I apologize for getting tetchy above. The problem is that money is used in a number of ways here, but when I hear money used in connection with fractional reserve banking, the definition I have in mind is "the usual medium of exchange," or something along those lines, which includes currency in circulation, demand deposits (checking accounts), and possibly some hybrid accounts (savings accounts allowing debit payments).

When I'm reading posts here, it can mean any number of things, including the value of bonds and stocks, annual income, etc. All these things are denominated in dollars, and admittedly the usage here probably matches the colloquial usage ("I put my money in bonds.") rather than the usage when people talk about money creation. Unfortunately, because the usage here is so imprecise, I have trouble understanding the arguments that people are trying to make.

Very interesting article and paper. Thanks Gail and Schnizy!

Money is like art:

When I read comments like the one above, I doubt the individual in question even knows what "money" is.

I can't describe it but I know it when I see it! (Any ten- year- old can do it!)

Actually with the money, a bookkeeping entry is made when money is lent and that entry is removed when the loan is repaid. As for the money itself .... old money never dies, it is inflated into irrelevance.

Anyway the Ayers-Warr approach is useful because it removes the work component from 'Capital', a failing of conventional economics that has gathered the attention of (probably) most ecologically conscious economists. Fuel- derived work does increase GDP. Who'd a thought?

In fact monetary inflation and increases in the money supply also mirror GDP growth, as does increases in the NY Stock Exchange index. Energy use matters but so does speculation.

As to Ayers-Warr's conclusion, I tend to disagree. Efficiency is probably not all it's knocked up to be. From the paper itself:

there is obviously some contribution from `other’ downstream
technical improvements. Evidently growth of GDP in the past quarter century has slightly
outstripped growth of the three main input factors, capital, labor and physical work. Since 1975
or so an additional source of value-added is involved. One possibility is energy conservation and
systems optimization triggered by the energy (exergy) price spike in the 1973-1981 period. The
other obvious candidate for this additional value creation is information and communications
technology (ICT). However, in the spirit of some endogenous growth theories, it would be
possible to interpret this additional productivity to some qualitative improvement in either
capital or labor.

Since GDP is a statistical indicator indexed in currency, accuracy in how the statistics are produced is an issue. There is another:

It does appear that the marginal productivity of physical work is still by far the dominant
driver of past growth and will be for decades to come. This does not mean that human labor or
capital are unimportant. As noted already, the three factors are not really independent of each
other. Increasing exergy conversion efficiency requires investments of capital and labor, while
the creation of capital is highly dependent on the productivity of physical work.
It is tempting to argue that the observed shift starting in the 1970s reflects the influence
of information technology.
Certainly large scale systems optimization depends very strongly on
large data bases and information processing capability. The airline reservation systems now in
use have achieved significant operational economies and productivity gains for airlines by
increasing capacity utilization. Manufacturing firms have achieved comparable gains in machine
utilization and inventory control through computerized integration of different functions.

Efficiency gains are not what they seem. For instance, the airline example does not indicate the overall shrinkage of capacity which is unaffected by what reseration systems are in place. The processing duties have been simply shifted to customers, the tasks themselves have not been eliminated. Reservation making is now an externality to the airlines. From a 'gross efficency' standpoint, jet airplanes are extraordinarily inefficient. For overwater travel, sailboats are most efficent, for overland travel, walking is most efficient as it does not even require a road. Bicycles are efficient but these would need smooth roads. Within the ambit of air travel, expensive airline labor has been replaced by cheaper (free) customer self- help. Simply following the outsourcing approach to its logical end, the greatest efficiency gains would be made by eliminating the pilots and aircrews altogether and letting the passengers fly the aircraft.

They can all fly it collectively; 'Wisdom of the Crowd!'

Only by replacing the airline with some structurally less consumptive method would there be meaningful energy efficiency, that is fuel units consumed per traveler mile. Since the arbitrary 'value' of time 'saved' is higher than fuel use per passenger, the more efficient is at an economic disadvantage. Economic efficiency is not the same as energy efficiency in fact they are opposed.

What is likely most responsible for the change in output post - 1975 has been the transfer of manufacturing processes from the increasingly efficient USA to far less efficient Taiwan and Korea (beginning in the 1970s) and thence to the extremely low efficiency China and India.

The Chinese advantage is cheap human labor, not expensive efficiency. They steal GDP from more efficient producers with low cost inefficiency. Increasing efficiency in developed countries increases labor and capital costs and amplifies the Chinese labor advantage.

For instance, tt is the highly automated European, US and Japanese automakers that are sliding into oblivion, not the Indians or Chinese with their hordes of coolies laboring as slaves in sweatshops ...

... and their burning coal mines, Victorian- era power plants, polluted rivers and desertifying farmland. The more degraded China and India become, the more economic labor and capitals advantage they possess. Likewise, if less fuel becomes available - regardless of price but moreso if it becomes very expensive - the greater economic labor and capital advantage China possesses.

In the inverse or perverse ethical context of industrial production, down is up. Black is white. Progress is degradation; degradation is progress.

The relative inefficiencies of fuel production, distribution and oversimplistic and perverse pricing mechanisms synchronized to the credit cycle ... determine energy prices, not relative efficiencies of the users. Energy users are price takers. This is not so much Jevon's paradox but punitive pricing by cartels and businesses with the occasional power to do so. Price taking removes leverage that would be gained by efficiencies or even alt- energy regimes. What determines prices is the (dis)inclination of producers to cut into each others' market share relative to what the overall market will bear. In the oil busines, perception matters more than reality.

Leaving aside the issue of "what is growth?" there is the issue of what actually is efficiency? Energy efficiency is a chimera. It really cannot exist except in abstract. Why? Because efficiency technology - as with China v. USA - has the efficient and the inefficient coexisting side by side. Since efficiency is relative, the measure of efficiency resides entirely within other levels of efficiency - there is no absolute efficiency. The life cycle of inefficient processes is long - perhaps eternal - and cannot be cut short by the introduction of efficiencies which run parallel. Efficiency advantages tend to be temporary, they only to prolong a resource utilization lifespan. In extremely large scale regimes and long time periods the effect of efficiency is marginal.

What is the long term effect of industrial efficiencies on agriculture, for example? Soil and water depletion? Erosion? Fertilizer and pesticide unoff? Punishingly low crop prices and surrender of economic independence to food packaging companies and distributors?

Efficiency can prolong the lifespan of a basic resource but it cannot conserve it. In other words, a fuel reserve will remain in the ground a bit longer than it would otherwise subject to a less efficient process, provided only there is no other demand on the resource. This is not what the model suggests. Since the efficiency effect stimulates inefficient growth and markeplace demand, the stretching out effect doesn't exist at all. More efficient processes instead accelerate depletion as they are more effective at producing previously hard- to- reach reserves or those too diffuse to obtain by 'inefficient' means.

At the same time, any stretching out the production timeline is economically inefficient as it works against the 'convenience cost' factor which rewards producers for increased material throughput over shorter time frames. The model is satisfied because the producer uses efficiency to increase the rate of extraction at the expense of conservation for future use. More of a resource is produced faster, more efficiently. The logical conclusion of this runs into ccpo's issue of resource 'use' effects on climate. The 'Steve's Economic Model' - efficient or not - requires all resources be used completely regardless of all other conditions. Since utilization confers some actual or perceived advantage - even in terminal decline - all available resources will be exploited as to their greatest possible extent. This the effect of memory and myth. Politicians in the future will evoke the 'Golden Age, when people drove 'Karz' as large as houses just to do so!' In this context there is no energy or effiency constraint to climate disrupting gases. There is, in fact no constraint except for human extinction or some currently unknown 'Gaia Moderating Effect'.

Also, the issue raised by memmel cannot be ignored. Output and production are measured in currencies and those who manage currencies and credit have an interest in cheating. Currencies and credit create their own dynamic cut off from any inputs that do not provoke an immediate return. There is no public interest inherent to economic activity, hands visible or not withstanding. Like most economic models, the Ayers- Warr model suggests an unrealistic ethically neutral public participation event ... this is a model problem, no model has ever predicted an Adolf Hitler, or a Bernie Madoff or a 'Minsky Moment'.!

The matter of 'work' is also qualitatively undefined. A family trip to the beach, a sin- and booze- soaked escape to Las Vegas and a manhole cover made in a foundry are more or less identical from a thermodynamic and even an economic standpoint. Only the manhole cover represents a product that can return some usefulness out of the energy and materials used to make it.

I suppose it is possible to make of efficiency what you will. IMHO, the energy input model has real value but struggles with efficiencies.

Do you not understand the concept of the velocity of money?

I guess not.

There is nothing that precludes the possibility of a "steady-state," with a stable debt load that is continuously being retired and re-issued.

Hmmm. I disagree.

FRB can only be steady state if we are willing to bankrupt approximately 5% (or whatever the going interest rate is) of the population each year, or simply discard the debt (Which I also can't see happening). The principal to be repaid, and the interest on the debt grows every year while the credit does not. This interest is unpayable without invoking credit growth, and it's why we attempt to "grow" our economies every year.

If the interest is paid each year, the principal doesn't grow. If some of the principal is retired (current debtor paying off part of loan), while new debt is issued at the same rate (new borrower), the overall debt load also doesn't increase.

Where does the money to pay the interest come from?

The new debt being created must at least match the retired debt yes, but it must also include the interest on the principal, because that is also new debt continually being created. I don't see how it's possible in that circumstance to be steady state. The new loan has to be bigger.

If you

1: had excess credit or a large enough fraction of circulating cash in the economy to pay the interest


2: treated the interest entirely differently from the principal; no compounding,

then I might be able to see how you could have steady state, but not at the moment.

What do you mean by "money" (see my comment above)? If interest payments are made, the principal doesn't grow. Money changes hands continually. Interest payments come from income and represent a transfer from the borrower to the lender. Provided the size and terms of loans are consummate with the ability of the borrow to repay it, there is no need for either money growth or economic growth to support the continuation of debt.

Jolly -

Sure, all that works just fine as long as the borrower remains capable of servicing the debt (much less retiring it). However, if the debt is not serviced according to a fixed schedule, then the interest owed grows exponentially, and that is where the trouble starts. As it already has ..... in both the US private an public sectors.

As deficits accumulate, a larger and larger fraction of income is needed merely to service the interest on the loan. Once things get past a certain point, it all turns to shite.

The mechanical analogy is an engine that has to expend more and more of its output just to overcome internal friction, to the point where all the machine does is run itself rather than do any useful work.

If people would just write "fractional reserve banking leads to excessive debt" or "the current level of debt can only be serviced if economic growth continues as it did in the past," I'd have no problems. It's the strange claims about "where the money will come from" that bother me. As I've indicated above, perhaps I'm just being pedantic. When posters carry on about "money," I really don't know if they are talking about an income stream, currency, or one of the various monetary aggregates (M1, M2, etc.). And I'm not sure if they know themselves.

What do you mean by "money"

Basically M2.

If interest payments are made, the principal doesn't grow. Money changes hands continually.

Ok, I understand what you mean. You are treating, or attempting to treat the interest payments as distinct from the principal. The problem I have then with steady state FRB is with that "if".

In terms of practicality, I am less than convinced;

  • There is an observation that in reality, banks loan first and look for reserves later.
  • It seems likely that compounding of interest would have to be made illegal (removing the exponential function) to facilitate steady state.
  • There would probably have to be a ready buffer between the interest and the circulating money. The reserve would have to be bigger than the interest.
  • Politicians.

Dear Jolly et al

For anyone who wants a better understanding of money supply, debt and how oil decline will impact the world economy. This is very very good.

There is nothing that precludes the possibility of a "steady-state," with a stable debt load that is continuously being retired and re-issued.

Hmmm. I disagree.

FRB can only be steady state if we are willing to bankrupt approximately 5% (or whatever the going interest rate is) of the population each year, or simply discard the debt

You disagree because you're ignoring several options; in particular, remember that interest doesn't destroy money, it just transfers it. One obvious way that can balance is:

  1. Retirees deposit $100,000 at 2%.
  2. Young couple takes $200,000 mortgage at 2%.

Even if there's no economic growth, we would expect a person's income to be low when they're young, rise as they get more experienced, and then low again after retirement; accordingly, it makes sense to transfer money from one's highest-earning years to one's other years, and that's exactly what the young couple is doing, with the retirees and the bank taking a service charge for helping them do so. (That's also exactly what the retirees have done by saving - they've transferred money from their highest-earning years to their lower-earning years.)

Debt, credit, and interest do not require economic growth.

I do not think that this analysis is correct. Of course retirees are supported by the income (in the sense of the actual physical output of goods and services) by people who are still working in one form or another, as no other physical possibility exists. However, the problem with that income taking the form of interest payments is that the principle does not disappear. If the retirees do not spend down their principle during their lifetime, then their heirs will after they are dead. If interest is not mere inflation and represents an increase in purchasing power above the principle, then real physical wealth corresponding to that increased purchasing power has to be created.

The reserve banking system creates money out of thin air. I call this artificial money.

Yes - but the money created can be used to stimulate real economic activity - building Porsches etc - and has stimulated demand for energy. Fractional banking is in the process of being replaced by governments buying the debt they issue and instinct says this will lead to inflation and irradication of debt - at least that is what is expected in an energy ascending world.

I'm beginning to believe that many of the rules we believe we understood in an energy ascending world may get turned on their head in an energy declining world.

I agree entirely that energy is the real currency - Heinbergs energy slaves. One variable I think is very important is the energy used by the real slaves - 19th century working class in Europe replaced by 21st century workers in Asia. One way of improving energy efficiency is to use real slaves that use little energy.

One variable I think is very important is the energy used by the real slaves - 19th century working class in Europe replaced by 21st century workers in Asia. One way of improving energy efficiency is to use real slaves that use little energy.

I also have been thinking that for a while. Get them to dig coal the old-fashioned way as well?

This is exactly what I not even saw but lived in Asia.

It seems to me your point is moot in the longer term. Let's start with where we must end up: steady state, or something damned close. A steady-state economy would require either a Debt Jubilee, or will come about only after a massive cascade of debt default globally, and at all others. That is, either a managed repudiation of debt or an non-managed one.

If the former, then good. If the latter, we are talking massive, fast collapse, war, famine, etc.

I see no way around these two possibilities. Do you?


Firstly, thanks for this post and for the reference link to Gail's important post from 2007.

The Ayres Warr model went a long way to explaining (to me) the massive gap in 'conventional' economic thinking (and confirming my own 'gut' feelings decades ago when a young adult in England as we emerged from an age of coal and shortages to a world of plastic and motor cars/fast highways, oil refineries and modern mechanized farming). I find valuable also your explanation of efficiency / exergy as the stimulant to 'growth'.

I am interested in feedback loops and energy saving and legacy infrastructure (the latter a form of 'capital'?). We have recently reduced by 50% the use of oil in heating our house and intend to go to zero, using mostly a part reconstruction on 'passiv haus' principles, with the residual need for heat being covered by renewables. We will be consuming our saved 'money' in the next 2 years by amounts very much larger than yearly income. This transfers money (presently invested elsewhere - albeit in our case already as 'cash' mostly in 'renewables' industry) into a legacy structure with a very long life (centuries) and low future maintenance demands. I assume the house will never 'pay for its new self' in our lifetime. I was similarly, at the theoretical level, interested in Dave Rutledge's thought on 'societal' large scale investment in solar glass electricity-producing structures in the desert with a life of perhaps a 100 years. Are we asking for a transfer of consumption away from current 'ephemeral consumption', toward 'capital', 'productive', relatively low-maintenance infrastructure? We get a lower 'ephemeral' return on our investment in the short or medium term, but secure a very large efficiency over the long term? What could this do on the macro scale?

I am continually thinking of these issues as well. What the Ayres Warr model has to offer to this thinking is that efficiency promotes economic growth which benefits society.

In neoclassical economic theory, everyone works for their own benefit, and somehow this benefits society as a whole. My analysis of the Ayres Warr model breaks down what is benefiting society as a whole, and what is only benefiting the individual at the expense of society. In my paper I talk about e(t), which is roughly efficiency and c(t) which is the proportion of the economy devoted to oil. Increasing either e(t) or c(t) produces more profit. When an industry increases its profit by producing more "e(t)", the society as a whole benefits, because exergy is increased which produces economic growth. When an industry manages to increase "c(t)" without increasing exergy (or any other benefit to society), this harms society as a whole because it causes economic contraction (you can look at the Madoff affair in this light).

When you, as an individual invest in efficiency and renewable energy production, you are stimulating economic growth for the rest of society because you are producing exergy. This ought to be included in the cost benefit analysis you make before investing. It seems to me that since all of society benefits, governments should spend money encouraging this type of investment.

Another issue is the total EROI. As you note, your investment will continue to have positive returns long after the end of your life. Currently we tend to look at interest rates and short term returns rather than looking into the long term and computing total EROI over the life of the investment, which could be on the order of several centuries. So you are investing in the well being of future generations. Since government borrowing is borrowing from future generations, this is an investment that could justify taking on government debt.

In more stable times, people routinely invested for the long term, for example in the middle ages, people planted oak trees even though the tree takes several (human) generations of growth before it is ready to be harvested.

This is an excellent concept, and kudos to Schinzy, and also Gail for bringing this to us.

I am thinking along the lines of memmel in that the debt-based financial system will be the over-riding factor in the short term (the next two to ten years) in helping us understand more specifically the economic impacts of peak oil.

I may not have fully grasped the implications of the theory but this statement:
“I think we may be entering time in which long term interest rates are negative, in the sense that if you leave a certain amount of money in the bank, the amount of energy you can purchase with that money in say 15 years will be half of what you can purchase today. So I do not think the current bubble has finished losing air.” implies that (in terms of 2009 US dollars) deflation is essentially impossible. That is the dollar’s purchasing power will be worth less and less over time. With savings being eaten up, the incentive to invest in energy saving efficiencies and alternative energy sources will be difficult. Ironically due to investment disincentives, the price of energy in terms of today’s dollars will have to rise extremely high to encourage investment in energy utilization while world economies continue to deteriorate.

IEA sees 2009 upstream energy investment down 21%
Reuters, Sunday May 24 2009
ROME, May 24 (Reuters) - Investment in oil and gas exploration and production this year is seen falling 21 percent, or almost $100 billion, due to the economic crisis, the International Energy Agency said.

But that’s not the worse we have to look forward to. The world financial system is becoming more unstable over time; possibly leading to a period in the not too distant future where the system will basically ‘break’ and no longer function in the way we currently understand it. The resulting financial disruptions may lead to collapse of the current dollar based world trade system, which could have the unintended effect of further disrupting energy investments despite high energy prices. This may be followed by periods of recovery where the world economy struggles back to potential, but energy reduced, level of economic activity.

Oak can be can be coppiced within 20 years or so. Well within a person's lifetime.

Could be that different varieties grow at different rates, the trees planted for future generations had different uses, or my information was wrong. The beams in our 250 year old house are oak and span 7 meters. Impossible to drive a nail into. I was told that the tree trunks were stored in water for several decades after being cut before being used for construction.

Coppicing I would definitely class as managed wood production, and planting or coppicing oak for 20-30 year harvest makes sense for an individual or family with a long personal horizon, particularly if they are starting with mature trees. Because the mature root structure is already in place, coppiced trees also regrow rapidly, far faster than from seedlings.

I think our current requirement for "growth" makes this method of farming generally uneconomic...

Somehow I doubt that Schinzy's beams were harvested from a coppiced grove.

Increasing efficiency ultimately increases energy prices which we need to assure future (renewable) energy production.

Ian, after 3 years on oil drum, this article is in the top 3. :)

It is clear that electrification of transportation will result in a huge efficiency gain, but since it can be powered with many different types of energy how can the model be expanded to include oil and renewable energy supply?

Since oil will always compete with RE at any price, it seems like we need policy term (P) with exponent gamma that will discourage oil production.

p(t) = C_3 * c(t) * e(t) ^ 7. * E(t) ^ .3 * P(t) ^ gamma

how can the model be expanded to include oil and renewable energy supply?

A good question for future research. I simplified in order to understand.

The only way I see to limit fossil fuel production if this model is valid is to pay fossil fuel producers not to produce.

Good point. Wouldn't cap and dividend do it?

Better yet, subsidies for renewables. If corn ethanol gets $1 /gallon from taxpayers, wind and solar should get an equal subsidy. Perhaps the model could calculate the minimum RE subsidy to tip investors away from fossil fuel.

Glad to see this, I'll read the article shortly.

Meanwhile, for all, I *really* recommend reference [1], i.e., Bob & Benjamin's just-out book The Economic Growth Engine, 2009.
(For some odd reason, they put my blurb first.)

It has a wealth of useful material worth studying, although since it's expensive, you may want to get your library to order it.

Ian - thanks very much for this. I've been saying for a while now that the most energy efficient countries will be able to pay most for energy, the rational being that they manage to produce more per unit of energy used. And the same applies to individuals - one paradox here is that it is often the wealthy who are more efficient.

Therefore many policies people are encouraging to limit global emissions will in fact raise global emissions.

Conversely, certain strategies designed to limit emissions - CCS, H2, C2H5OH - are grossly inefficient and will hobble our economic output.

Energy efficiency is king - but if you go down this route then policies are required to counter Jevons' paradox* - tradable energy quotas and a system of population growth control.


* maybe Jevons needs to be rethought in light of what you say?

I think Jevons is widely over-quoted and over-simplified.

Some of this may come from living in CA, which is serious about energy efficiency, at least in part from Art Rosenfeld.

Let me try some examples, where I don't think the usual simple statement of Jevons works very well.

1) Suppose refrigerator efficiency doubles. Does this mean everyone buys a bigger fridge, or an extra one? Or are some people space-limited, or satisfied with that size, and just happy it costs less to run?

2) Suppose you drive 10,000 miles/year. Your next car gets 2X better gas mileage. Do you drive 20,000 miles/year? Suppose it's 4X? Would you drive 40,000 miles/year, just because it's the same amount of gas? As a farmer, if your next tractor is more efficient, do you take it for joyrides?

Anyway, elasticity curves aren't identical and aren't just linear.

In any case, I don't think this is what we face, which is more expensive energy for quite a while.

2a) You drive 10,000 miles/year. Suppose you think gasoline will cost 2X more, and you are about to buy a new vehicle.

a) You might buy a similar-efficiency vehicle, drive 10,000 miles, because both the vehicle nature and and mileage are inelastic. You'd just have to eat the cost, or pass it along.
Ex: pickup truck used for business.

b) You might buy a similar-efficiency vehicle, but drive it less.
Ex: pickup truck used for a mixture of business and personal transport.
Vehicle nature is inelastic, but some of the usage is elastic.

c) You might buy a 2X more efficient vehicle, and drive it the same 10,000 miles.
Ex: you drive a pickup because you like it, but you hardly ever use it as a truck, but the mileage is inelastic. You buy a more efficient car, and rent a truck a few times/year.

In any case, around here, aggressive businesses are running hard to reduce energy use, in expectation of rising prices, and because it saves them money. They don't leave lights on longer because they've switched to CFLS: they put them in, and take the savings to the bottom line.

Suppose you drive 10,000 miles/year. Your next car gets 2X better gas mileage. Do you drive 20,000 miles/year?

You don't have to drive an extra 20,000 miles/year to encounter Jevon's paradox. You could use the extra money to buy goods from over seas, you could put the money in the bank and it would be lent to someone else who would do the driving. Even if you burned the extra money, someone else will buy the fuel you would have bought (at a lower price) so being more efficient will decrease production marginally at best.

Well, sure. I'm just saying it's more complicated than the usual statements, especially those that conclude:
"Don't bother with efficiency, Jevons says it doesn't help."

Let me try another example.

Suppose people try to make their homes as efficient as possible, for the sake of argument, all the way to net-zero. That reduces the demand for fuel, a little, so other people build even bigger McMansions (say, heated by gas), so total fuel use doesn't go down. Even in the USA, one would expect houses to last 50 years or so.

But what happens when the fuel runs out or gets very expensive?

One group still has livable homes, the second group own expensive stranded assets. What do they do then?

burn wood?
abandon the houses?

Anyway: can you be more explicit about the circumstances in which energy efficiency investments are a good idea or not? (I know what Ayres & Warr think, of course).

I have read John Mashey's reply to your comment on Jevons.
Additionally a thought.
We should perhaps distinguish between 'per capita' energy use and 'thermal efficiency' of production and distribution.
In UK the better-off segment of people, compared with lower income, use more energy per-capita in heating their homes, irrespective of the thermal insulation efficiency. One suspects however in the lower income homes that there could be more utility gain per capita for the lower usage (it maybe unfair, but less comfort is still much better than acute discomfort, although hypothermia in the elderly provides a special case). Something similar might apply in places like Pakistan, where per capita use for example of electricity is low. The efficiency of production also is low, I understand, compared our 'wealthy' UK, but the 'utility' despite intermittent outages and 'brown-outs' that would be unacceptable here, remains nevertheless very high per capita.
A very little goes a long way in a poor country and for poor people. Whether the poor can continue to pay for the little they hath, I would agree is more doubtful.


And the same applies to individuals - one paradox here is that it is often the wealthy who are more efficient.

Energy efficiency is king

These two thoughts taken together are what my mother has done most of her life: it's OK to buy it if it's on sale.

Funny, she still runs up her debts to outlandish levels.

To be clear, being efficient with 26 barrels of oil a year is like like counting the licks it takes to get to the center of a Tootsie Pop: utterly irrelevant. It's the 26 barrels at all that's the problem.

But, then, if one thinks we can't possibly burn enough FFs to wreck our current civilization, well... that would change the picture.


So, America has consumed most of its oil, and spent all its capital on McMansions and foreign wars, all it has left is the coal, and oilshale and natural gas. But still owing China a bundle. Wow!

One of the things that I included in my 2007 post that you linked to is this graph, from one of Ayres and Warr's papers:

Electricity prices and electrical demand, USA 1900 - 1998

In that post I say:

A closely related result from the Ayres and Warr paper is that declining real cost of energy, particularly electricity, and the rising use of the much cheaper electricity, fed economic growth in the 1900 to 1998 period.

What I find disturbing now (that I allude to in the 2007 post) is that we have now passed "trough" electricity price. While electricity price was falling during the 1990 to 1998 period, and fed economic growth, since about 2000 - 2002, it has been rising (in real terms) and holding back growth. Perhaps not by coincidence, the period since 2000-2002 is the period when we have had all kinds of artificial debt financed growth, giving the illusion of growth when it is doubtful if any real growth existed.

Going forward, there are multiple reasons why the average retail electricity price can be expected to increase:

1. Oil scarcity and decreasing EROI are generally pushing the price of fossil fuels upward.

2. Concern about climate change is putting pressure to reduce the amount of coal used for electric generation, removing a lower cost source of electricity-generation.

3. Wind is a higher cost source of generation. Adding wind can be expected to increase the cost of electricity. (Subsidies can make the cost of wind look better, but ultimately the higher cost must be paid by society).

4. To the extent that mandates require building renewable wind capacity where no additional capacity is actually required, the impact is duplication of power-generating facilities, a form of reduced efficiency in electric power generation.

At the same time, electricity demand is being pushed downward, not only by the higher electricity prices, but also by the deflating debt bubble.

All of these factors would point to declining electricity use and declining real GDP.

The Ayres Warr model would suggest some reduction in demand, but I expect the real world reduction will be even greater, because the model does not include things like the recent debt bubble.

Gail -

It sounds to me like in this comment you're implying (but never really coming right out and saying it), that we may really not have to get into things like wind or solar power because we will not need any additional electrical generating capacity due to a depressed demand caused by a shrinking economy. Am I reading you correctly? (Seems to me that our local power company has been saying much the same thing in its effort to scuttle an offshore wind power initiative in Delaware.)

However, in the same breath you've often posted topics dealing with sustainability. Well, correct me if I'm wrong, but continuing to burn coal and natural gas to generate electricity (even at reduced demand) does not strike me as a very sustainable strategy.

So tell me: are you for or against increasing our capacity to generate electricity by means of wind and/or solar power?

I don't make decisions one way or another, until I fully (as possible) understand the situation, and I am still trying to puzzle thing out.

Wind cost now look to me to be far higher than most people think they are, because of the high upfront capital costs, but also because of the need for continual maintenance and repairs. Unless borrowing costs are very low, unsubsidized wind costs are something like double those of coal or natural gas. If we really don't need the wind, it becomes an add-on (rather than substitute for) current electricity production costs, since we will have to pay bond costs on existing power plants, whether or not they are used to capacity. The fuel savings, by itself, isn't very much.

Another option would be to use our unconventional natural gas resources. We seem to have a huge amount of this, especially if we gave this priority. We also have much more natural gas electricity generation capability than we really need already built, and could build more quickly (and cheaply) if we wanted. It seems fairly likely that we could keep natural gas going for as long as we could wind turbines, and we could ramp production up or down as needed. We don't have to make huge decisions on amounts up front, because the cost of the turbines is relatively low relative to the natural gas. Natural gas is relatively low on carbon emissions, but may be unacceptable to some.

Gail -

"The fuel savings aren't very much." ????

Wind doesn't use ANY fuel (aside from a very small amount related to construction and routine maintenance). So I don't understand what you mean by that. Look, this is largely a matter of choosing between high initial capital cost/low operating cost (e.g., wind) and low initial capital cost/high operating cost (gas turbines). Recent history has also shown that fossil fuel prices are rather chaotic and difficult to predict.

As far as carbon emissions go, please keep in mind that natural gas is 75% by weight carbon, whereas most bituminous coals are roughly 78 to 81% carbon. On a carbon-per-BTU basis coal is a little worse than gas, but I think it is a common misunderstanding that natural gas is 'carbon friendly' while coal is not. From a broad perspective there really isn't all that much difference. So, carbon emissions is largely a weak issue in choosing between the two. (Ash handling problems and pollutants are a whole other story, of course.)

Anyway, I get the distinct impression that you more or less agree with the party line of the US public utility industry: stay the course and don't change anything until you are absolutely forced to.

Perhaps this an unfair hunch on my part, and if so please set me straight.

Hello Joule & Gail,

Joule's Quote: "Recent history has also shown that fossil fuel prices are rather chaotic and difficult to predict."

If advances in climate and more time-immediate weather modeling continue to move ahead in improvement, so that you could statistically predict windflows over many WTs' blades more accurately than flucuating FFs prices and flowrates, then the buildout of large WT networks would be the way to go postPeak [along with solar, of course].

How ironic would that be if the weather's gusty pulses becomes more predictable than irrational [totally unpredictable?] human economic-impulse? LOL!

Bob Shaw in Phx,Az Are Humans Smarter than Yeast?

totoneila -

Good observation! One would probably have better luck predicting the high and low temperature for May 25, 2029 than what the price of natural gas will be on that same date.

The other thing that bothers me is that I think it is a mistake to increase the amount of natural gas used for power generation because before too long that gas is going to be far more valuable for the production of ammonia fertilizer (as well as for various petrochemicals).

Batteries and gravity storage also automatically damp out fluctuations, so hopefully we can even filter out the minor fluctuations.

People might want to read 9-page talk by Peter Darbee at the UN, on energy efficiency, renewables, etc. I've heard him talk - he's very articulate, and he does run a utility that serves 15M people.

Peter is CEO of our local utility PG&E, which is seriously fanatic about energy efficiency.

We don't do a lot of wind here in CA (nowhere near as good as in US Midwest) but there are plenty of ways to use intermittent sources sensibly, without requiring complete duplication.

I think, in practice, if one could actually lower demand, it means taking older coal plants out of service, and running gas peaker plants less. After all, once one has built solar or wind, they use ~zero fuel, so the running cost/MWh is lower than burning fossil fuel.

In any case, I repeat my comment on the Ayres+Warr book:

`Would you want your great-children in 2100AD to have a 22nd-century industrial economy? If so, read this book to grasp how strongly wealth depends on energy and its efficient use. Start treating fossil energy, not as continuing income, but as one-time energy capital to spend on efficiency and long-term sustainable energy production. Otherwise, your descendants will inherit a broken 20th-century economy that only worked with cheap fossil fuels. They will not be rich and they will wonder what their ancestors were thinking.'

Some of that was inspired by Charlie Hall's "cheese slicer:.

Wind is a higher cost source of generation. Adding wind can be expected to increase the cost of electricity. (Subsidies can make the cost of wind look better, but ultimately the higher cost must be paid by society).

Actually the opposite is true. Wind Power actually subsidises all electricity users such that the savings which customers receive are greater than the value of the wind power 'subsidies'. There has been quite a bit of research into this and Jerome a Paris posted a good article on wind power in the Oil Drum Europe a couple of weeks ago.

I don't agree. Jerome showed that in certain circumstances the pricing or electricity is lower, but he didn't show that the pricing is sufficient to cover the costs of wind production. This is the big problem--without a (high) feed in tariff, one cannot generate enough funds to cover the cost of production.

Every study that has been done shows that a subsidy is needed for wind to be viable.

We have evidence of that in the US. Every time the Production Tax Credit reaches expiration and is not renewed, the number of new wind turbines drops to zero. Once it is renewed, the number of turbines goes way up. The value of the Production Tax Credits is more than the wind itself, according to this analysis.

This presentation from 2008 in Denmark talks about the need for subsidies for Danish wind. When Denmark cut its subsidies, it had exactly the same experience as the US: virtually no new wind turbines.

Also notice Why Europe's Renewables Roadshow Is Rolling Stateside:

Well it seems that the days of the great European socialist ´blank check´ for green energy programs is over. Having seed-funded the first generation of renewables, especially numerous wind turbines, the blatantly poor investment-to-energy return ratio has consistently kept private investors away. What the economic crisis has done is to hasten the day when even ideological-driven European leaders must demand a better return from an industry still commercially unproven. EU strategy has been to throw money into an ´unfocused´ green energy pot that requires diverse energy protagonists to scrap for every penny. . . When it comes to funds all manner of energy projects vie for a steadily dwindling pot, as governments are forced to cut back on their financial commitments. Burgeoning planning problems in the face of increasing public (even environmental) opposition has meant that competing for European green energy funding has turned into a business nightmare. Enter Obama´s $80 billion ´windfall´ funds specifically for renewables projects. Coupled with a presidential commitment to easing planning regulations, and a whole new, potentially more ´lawless´, green energy frontier beckons.

I wonder how much of this is due to short term economics. When we evaluate an investment, what people look at first is the percentage return on investment, rather than the total return on investment. For example, which investment is better: an investment that returns 10% for 14 years (you recover your money in 7 years, you double your money in 14 then you figure out what to do with your money), or an investment that pays 2% for 105 years (you recover your money in 35 years, you triple your money in 105 years)? The first investment pays faster, but the second investment has a greater total return.

Pre-peak oil, the first investment is much better, post-peak oil, I wouldn't be surprised if the second investment turned out to be much better because investments with positive returns might become scarce.

It seems to me that EROI should be related to total return on investment. EROI for wind is, if memory serves me correctly, between 5 and 35 depending on technology and location, with most new installations doing about 25. EROI for oil is around 30, not much better. Nate Hagens has said that EROI for new oil fields is much lower.

The EROI of wind is one of the things we are puzzling about among Oil Drum staff members right now. It doesn't make sense that wind has a high EROI, yet seems to always need a substantial subsidy to "work". Something is missing somewhere in the calculation.

One difference between wind and other types of production is the huge-up front investment required. The upfront cost is probably equivalent to nuclear, and something like ten times that of natural gas, relative to the amount of electricity that can be produced in a year from each source. Somehow, this huge up-front wind investment also has to be financed as well, further adding to the cost. EROI does not deal well with the time value of money and availability of credit.

I agree about the puzzles - will we regret a major decision if we deliberately favor wind? Could we have put the investment to better use elsewhere? I think though one of Jerome's points is that a lot of the upfront cost is in paying for the risk (greater risk arising from not definitely being able to quantify a return) inherent in any longer term investment? If, though, some longer term return is guaranteed then that should make it more of an engineering decision?
I posted last year a link to a detailed EROEI study of wind turbines that elicited a careful worked response from kiashu. It looks pretty conclusive to me. A few months perhaps to a few years at most for energy payback.

The EROEI payback is probably better now for 2-3MW turbines than that quoted for 600kW turbines. New turbines are probably going to last longer than 20 years further increasing EROEI, but if the payback is only a few months, it doesn't really matter if the EROEI is 50:1 or 100:1, it means that very little energy will be needed for very fast growth, other things will be limiting, not energy.

Perhaps TOD's EROI calculation for wind isn't using the right value for wind's income?? This topic is of great interest to me also - understanding intermittant power providers' EROI and EROEI is important. Finding proper rate info for grid connected wind power is typically not easy; but, for example, BPA's rate info -

"2009 Wind Integration - Within-Hour Balancing Service rate is $0.68 per kilowatt per month applied to installed wind capacity;" - pages 11 and 33, "2009 WIND INTEGRATION RATE CASE FINAL PROPOSAL FINAL RECORD OF DECISION",

Pretty low rate for installed capacity. Compare wind and ground solar to workers who show up to work at random times to workers (like dispatchable power sources) who actually work an assigned shift. Imagine both work 40 hours a week on average, but which would you rather employ?
That is why power companies are not eager to use wind or ground solar and why the low rate for installed capacity.

Every study that has been done shows that a subsidy is needed for wind to be viable.

Here in NZ we have no subsidies whatsoever for wind power, and it's certainly viable and competative. Power is also significantly cheaper here than in Europe. Wind is set to become more valuble in the future as our largest gas field, Maui, goes into decline in 2011, leaving NZ dependent on LNG imports if we want to continue to run the gas power stations (currently about 25% of total electricity). That would require ongoing buying of the fuel and building the LNG terminal facilities leaving us at price risk of the gas besides the huge cost of the infrastructure.

A better long term solution to me is replacing the gas fired capacity with wind. I guess it really depends on what you think the future price of gas is and I think that it's going to get a lot more expensive. Current planning indicates this. While there is some talk of a peaking gas plant near Auckland, the vast majority of new planned capacity is unsubsidized wind.

3. Wind is a higher cost source of generation. Adding wind can be expected to increase the cost of electricity. (Subsidies can make the cost of wind look better, but ultimately the higher cost must be paid by society).

Air pollution from power plants causes about 30,000 deaths per year in the US, which has purely economic costs in terms of medical costs and lost work. 25,000 deaths - roughly coal's share - at an actuarial cost of $6M each is $150B; if we figure $0.10/kWh for coal (final retail) and $0.20/kWh for wind/hydro, preventing those 25,000 deaths would economically compensate for switching 1,500B kWh from coal to wind/hydro. There are about 2,000B kWh generated from coal in the USA; accordingly, it is not at all clear that coal-fired electricity is cheaper for society than wind+pumped hydro electricity.

If you're going to consider the cost of construction subsidies for wind (which you should), then you should also consider the cost of medical subsidies for coal. Additional externalities - reduced work or increased expenses due to non-fatal ailments, lost environmental services from pollution damage (acid rain, mercury, etc.), lost environmental services from mining damage, mining ailments and deaths, etc. - are likely to make the cost that society pays for coal-fired electricity significantly above the $0.18/kWh that I've calculated here.

Indeed, based on this quick calculation it seems likely that the USA would see a net reduction in overall cost with the addition wind backed by pumped storage (with unbacked wind being clearly beneficial, as it's cheaper than backed wind).

I agree, I do. But when you go from direct accounting to indirect costs supported by models that don't have direct measurements, the politics get sticky. Especially when the biggest swing states are all dependant on coal. What you often end up with is talk about IGCC and carbon capture that quickly gets forgotten after the election cycle.

I like the Ayres Warr model, though I'm not convinced that I'll be using the phrase "exergy" in my day to day conversations anytime soon. The production function is amiable to neoclassical analysis, and I gather from the parts of their papers that I've read that they do so. Marginal productivity analysis yields demand functions in a straight-forward manner with the same general functional form as those in Schinzy's paper (i.e. pS=cY). With Cobb-Douglas, the income share of any factor is constant, with the share equaling the coefficient on the factor. All the usual intuitions then apply: reduce the supply of energy and it's price increases, while output, the wage and the "rental rate of capital" all fall.

I feel I must ask all here. Have you read and do you understand the implications of Taleb’s: “The Black Swan: The Impact of the Highly Improbable”? “Fooled by Randomness” by the same author is also in the same vein.

If so, why does any rational person attempt to apply a mathematical model or considered response to anything in the real world when there are an almost infinite number of variables?

When you get the model’s prediction (or response) perfected, ask yourself if congress could possibly screw it up. Or ask yourself, what if a methane tipping point is reached, how now?

A Zen master and student came to a stream where a young lady could not cross because of her beautiful long dress. The Zen master picked her up and carried her across the stream. Further down the way the student asked, “Master, we are not supposed to be involved with women, yet you carried her.” The master answered, “I put her down on the other side of the stream. Why are you still carrying her?”

Answer: You were taught to apply mathematics and you can’t put it down. It won’t work and you will have to apologize in a little while but you just can’t put it down. Further, any graph that extends beyond ‘now’ is in error … some “Close but no cigar” and some really gross.

Be honest, last year at this time did your model show $147 high and $30 low? If not, why not? And even today, is it supply or speculation or demand or the wind of a butterfly’s wings that is setting the price?

I dreamed I was a butterfly who was dreaming he was a man. I wondered, “Am I a man or a butterfly?” When I first awoke, I flew away laughing on rising currents and the second time I awoke I was sitting at my computer about to type something. I still wonder …

I've read Taleb's books. I agree we can't predict the specifics of our future, however we do know that every outcome must conform with the laws of physics and biology.

So I don't know what will happen to me tomorrow but I do know that I will be a day closer to death. And I don't know what will be the outcome of PO but I do know it will involve less energy. Knowing there will be less energy eliminates a whole bunch of possible outcomes so I believe it is possible to predict general outcomes (like lower complexity) but it is impossible to predict specifics like peace or war getting there.

Please: The outcome of peak oil might be the invention of antigravity and practical cold fusion and more energy than ever. Why can't people just say, "I don't know". Because they are human and think they know a lot but they continue to screw up time after time.

A simple real world model any fool can figure. Car 'A' leaves Tucson for Phoenix 100 miles away at a constant speed of 40 MPH. A car 'B' leaves Phoenix for Tucson at 60 MPH. Where will they pass?

A: 40 miles out of Tucson
B: 40 miles out of Phoenix
C: half way in between
D: I don't know!

Now in the real world if you can't model this ... how in hell do you expect to model oil depletion or the results thereof?

The answer is "I don't know!". Car 'A' crashed 10 miles out (or maybe not). Car 'B' had a flat tire and the spare was flat too (or maybe not). No one can model the real world if you really understood Taleb.

This is quite a common strawman. But playing along, what you do is add a stochastic element and figure out the likely outcomes. So if you want, you can put in the probabilities of accidents or flats according to NHTSA statistics.

This is approximately what you end up doing for resource depletion model. Nothing actually follows a deterministic path, but the stochastic arc has a relentless consistency.

Taleb does have a point but you have to analyze the right measure. The Phoenix/Tucson example is well-behaved and so won't blow up with insane results considering the significance of the outcome. In the post above Schinzy admits that the stochastic element is missing and there might be some lurking Black Swan or "fat tail" behavior. I just find it sad that we would ever want to give up trying to figure this stuff out. It is human nature to try to understand our condition.

Plus, as Justin Fox wrote in the current edition of Time: "But there's a thriving line of academic research showing that including divergent opinions and models of how the world works makes groups better at solving problems"

Web, Tnx for the Reply:

It is late here and I am off to bed. Unfortunately or fortunately I live most of the time in the here and now in my woodworking shop or with a new garden. It took hours to rabbit-proof the garden area but a squirrel or a coon climbed the fence and got into my carrots.

I have a problem with mathematical models forecasting real world events. The problem is they are often given as gospel while knowing full well reality is a WAG. The dishonesty portrayed is my problem I guess.

The problem is they are often given as gospel while knowing full well reality is a WAG. The dishonesty portrayed is my problem I guess.

And, really, that was Taleb's critique: the presentation of uncertainty as fact. In the case of Wall Street, this meant claiming they had conquered risk. (Although I read somewhere or other the bright fellow who created the model they all used to pretend there was no risk claims those who implemented it didn't understand it and used it incorrectly. Gee, imagine that...)

I doubt if you asked him directly Taleb would say that all analysis of future probabilities is useless. Rather, he would caution to actually include all possibilities - and the worst thing you can imagine possibly happening, even outside the scope of the models - in making your decisions.

We can't pretend there is no future, Lynford.



1) Suppose you have an honest coin, and you flip it 1000 times.
Can you predict the sequence of heads and tails?
Can you predict the trajectory of (#Heads - #Tails)?
Can you predict the likely distribution of (#Heads - #Tails) after 1000 flips?
Sure: binomial calculator, set n=1000.

2) This is like climate models, which do *not*
- predict global average temperature 2 years' away
- even try to predict when a Pinatubo-like volcano might happen

but model multi-decadal bulk effects.

3) There's a lot of economics whose math I just don't yet understand, an whose formalisms I sometimes wonder about... but Ayres originally trained as a physicist, and Ayres&Warr's models seem (to me) much more grounded in reality, and much more geared to modeling long-term properties than short-term gyrations.

4) I've read both of Taleb's books and liked them in general, but sometimes he writes with total confidence about processes and people he does not understand, so be careful.

Hi John:

You and the binary calculator make the same mistake. A mathematical solution is not correct for a flipped coin.

I used to program slot machines. I have "flipped" a virtual coin many millions of times with a Nevada certified random number generator and the longest string of heads or tails I got was 24. YMMV I retired right after Y2K. If you set 2 billion flips, you might very well be plus or minus 24 (or more or less) from 1 billion heads total count.

As soon as you throw congress into the mix, we could all freeze by 2020. They have the power and the stupidity to put up an opaque sun screen between the sun and us.

There is lots of economic math that is really bad because economists (and physicists) can't say, "I don't know". My WAG is this or that is OK but human nature will not permit that if you are to be king of knowledge in any field. To pretend to 'know' is a certain way to a latter apology.

If they are grounded in reality, I wonder how much money they made last year to $147 thence to $35?

Of course Taleb writes with confidence ... he is a Lebanese man. Have you ever known a middle-east man who said, “I’ll check with my wife to see what she thinks about it.” :-)

I don't understand how I'm wrong on the coin flips. I didn't say that that I expected 500 heads, I said:

"Can you predict the likely distribution of (#Heads - #Tails) after 1000 flips?"

The calculator thinks that with 1000 flips, the chances of getting #H-#T >= 24 is ~20%.

Goerge Box sayeth:

"All models are wrong. Some are useful."

I make no claims that most math in economics is right, I certainly don't know. I reviewed a draft of their book, and it made more sense to me that some other math economics I'd seen. It makes sense to me that wealth relates to energy, and their book has a lot of data to back up the relationships they posit.

How about looking at what they write before saying they don't know anything?

Unfortunately there is a huge logical flaw or conundrum to any argument that involves Las Vegas.
Consider that the owners of a gambling establishment would never invest in such an enterprise unless they were assured of the outcome in a probabilistic sense. As you suggest, they could have empirically derived the probability of a long string of heads leading to some huge jackpot and payout liability. So the conundrum is that what happens if they did not know what these possibilities were? But of course they know! That's why they continue to make money, as they keep the game artificially constrained. And that is why they do not allow card-counters, which adds a hugely deterministic outcome.

Unfortunately for the insurance bets and the defaults that the financial system occurred during 2008, no one actually knew the constraints of the problem, and it ran open loop. There is a class of problems called martingales where you end up losing every time. A double or nothing bet on a coin flip is such an outcome. Given the finite nature of money, you will end up losing everything.

So I guess the point is that we might want to do these models to provide a sanity checks on outcomes. Even though for certain problems you may not the exact outcome, you can predict that the ultimate outcome likely won't be a positive one :)

Hello WHT & others on this gambling mini-thread,

I enjoyed reading this discussion. It is amazing to me the number of people that become addicted to slots & other forms of casino odds-favored gambling. Surely they must eventually realize the odds are purposely stacked against them as they become the obvious suckers who have to pay for the expensive equipment, labor, lavish buildings, and profits. I wonder how slot-addicts graded out in high school math? My guess is pretty badly.

This huge, innumerate-human aggregate attempt to defy math probabilities is tantamount to many millions of molecules of water suddenly defying the Laws of Physics, then flowing uphill to jump onto a scorching hotplate.

We should be very thankful that water droplet behavior is more predictable than many individual humans.

Alcoholics and drug addicts realize on a conscious level that the usage is destroying their lives-this conscious realization does not prompt change-addicted gamblers are the same. Check out the James Caan film THE GAMBLER for an excellent and entertaining insight into this phenomenom.

Similarly, knowing that 25,000 people die each day from malnutrition doesn't stop the rest of us enjoying our food.

I agree that Taleb has an attitude that approaches arrogance. he may be well researched and brilliant but he is also fallible.

All mathematical models are false, but some are useful.

Mathematical models serve the following purposes:

  • They clarify. Mathematics is very precise. If you can express your intuition using mathematics, you have to know what you mean.
  • They simplify. As you point out, the world is too complex to comprehend at a single glance. Mathematics allows you to break a problem down into understandable bits. For example to understand the flight of a baseball, you start with Newtonian mechanics, neglect the atmosphere, assume gravity is a constant, assume the ball and the earth are just point masses. When you understand that, you add the atmosphere but neglect the spin of the ball, etc. By simplifying the problem, you are able grasp what's going on and improve your intuition.
  • They can be analyzed. Mathematics has a rich array of transformations, operations, and tools which can give you consequences of your intuition that you hadn't imagined. Analysis also improves your intuition about things.
  • Be honest, last year at this time did your model show $147 high and $30 low?

    I certainly hope not. As I stated above, the model is missing a term with zero average. In the best case, the model will give a value which will be approximately the moving average price (say the average price for the year). This would tell me if the market is over or under valuing oil.

    I haven't read The Black Swan, but I enjoy reading Taleb. He's a good mathematician.

6. Economic output is largely independent of population. Therefore demographic concerns that there will not be enough future workers to support an aging population are unfounded. Concern should rather be that exergy supplies will be insufficient.

Looking at the equation, this pops out as rather obvious. It looks like L=Labor adds a 0.02 exponent or a 1/50 root to the result. So if we had labor that increased by 100x, it would only add about 10% to the output. I would suggest seriously that you remove Labor completely from the equation.

This will make Robert Solow cry, but then he is an economist and should realize that sunk costs are no excuse for getting at the truth. The reality demonstrates that Net Energy should wholly replace Labor and substitute at least partially for Capital in our empirical understanding.

As far as first principles are concerned, I don't understand how the exponents are generated except that they produce a diminishing marginal return to either of the factors. So if this is the case it is really a heuristic in its fundamental formulation.

Another question is why they call it Exergy whereas wouldn't Net Energy or something more naturally evocative be used in the model? It seems that inventing new words leads people to believe it is some sort of quackery. For that reason calling it Energy Humours is definitely out :)

They call it exergy because it's the standard term.

Google: exergy yields 200K+ hits.

According to Encyclopeida of the Earth,the term was coined in 1953 by Zoran Rant.

The Wikipedia entry is not bad.

Thanks, I just never recalled seeing that term in school. I guess entropy and enthalpy sound strange too on first hearing :)

Yes, for sure, each discipline has its precise terms, and I'm just as glad if they make up new words for precision, rather than reusing common words in some domain-specific way.

But,it could be worse- one might guess energy, exergy, emergy and the other e*y words might have some relationship.

On the other hand, consider subnuclear physics, whose whimsy-level is interesting,
with gluons and 6 flavors of quarks:

up down charm strange top bottom

I would suggest seriously that you remove Labor completely from the equation.

I made the same remark in my paper (it's not my equation).

Correct conclusion :)

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In your article your article you point out that the 7x efficiency gains from 1900 to 2000 cannot be repeated because e(t) cannnot exceed 1.

As an illustration, [Ayers and Warr] estimate e(1900) = .03, e(2000) = .2

However, this assumes that energy is coming from fossil fuel, if we calculate the e_sun(t) for the US, then we must consider all of the solar energy incident on the land area of the US (10m sq km) at 41 MW per km2 = 410,000 GW of US potential solar energy . As of 2008, installed PV was 8.8 GW and wind was 25 GW totaling 34 GW. This means e_solar(2009) = 0.00008. Clearly, we have a long way to go. We could also calculate e_moon(t) based on tidal energy but I think you get the point.

Good point. I hadn't thought of that. I don't know how Ayres and Warr computed efficiency, I didn't read that paper. I suspect that the model should be modified depending on the source of energy.

I'm wondering how much critical scrutiny the Ayers Warr model has gotten. There seems to be good agreement with US GDP and a least squares analysis that contains an (efficiency*energy) term (eE). But how much does this "prove" that eE is a driver of economic growth? (And what about other countries?)

Couldn't the eE term just be a "passive" factor that accounts for the availability of cheap energy (a neccessary but not sufficient factor for growth)? For instance, economic growth has dropped in the last year. This is probably not because efficiencies or available energy has dropped. Nevertheless energy use has fallen. It has followed but not driven GDP.(Obviously, Ayers Warr would be more convincing if it could model the oscillatory GDP flucuations we are possibly witnessing!) In other words, there must be other "active" factors at work. Are we dealing with causation or just correlation?

It could be that Ayers and Warr deal with this question in their book. (I was happy to see the first 60 pages or so in the link that Ian provides). But I think it's important to understand more fully how factors like government intervention and investment can stimulate economic growth. And how we can take a more active role in planning for our future, rather than leaving things to a neoliberal market to govern us.

1) Well, theirs seems to be a minority opinion in economics. Many economists appear to think energy isn't very relevant to economics, or don't care about it, which I don't understand. I've raised the issue on a bunch of blogs, and mostly get "interesting question" in reply, at best.

My concern has been especially that models that combine climate and economics seem to think that GDP growth continues at the same rate as last century's, indefinitely, an hence, either:
a) The world will have 6-15X higher GDP in 2100, and hence any climate problems canbe deferred for those who will be richer.
b) Working on climate mitigation simply slows down growth, but not too much.

2) However, *read the book*, but in advance of that, you might try:

LECTURE 5: ECONOMIC GROWTH (AND CHEAP OIL). Look especially at the *last* page, which describes the US economy under various efficiency conditions in the face of Peak Oil.

and This talk, PPT.

3) Other countries:
The book does US & Japan, as does the first tpaper above. The PPT has some charts on UK and Austria as well.

4) See p.19 of the Accounting for Growth paper, in which they conjecture about recent gains from computing.

5) As to predicting short-term oscillations, these models don't do that or expect to do that.

As I mentioned earlier, this is like climate modeling compared to weather modeling. The former are *boundary value* problems rather than *initial value* problems like predicting the weather for the next few days or the stock market.

Put another way, in a long-time-frame view, short-term jiggles are just noise. Of course, in many uses, the noise is more immediately interesting.

6) As to causation, that's always hard to prove, but they motivate it strongly, and it certainly makes sens, at least in comparison to terms like:

Solow Residual
Technology progress
Total Factor Productivity

It also makes sense in the simplest domain example: farming.

a) A farmer who has no electricity, tractors, or even draft animals is not wealthy. Most subsistence farmers are poor, because they are limited to their own and family's physical labor, usually on a few acres.

b) Old Amish don't use tractors or electricity, but do have teams of horses, are superb farmers, and can handle more land (say 40-160 acres), and can have reasonable lives, although stopping formal education ~8th grade and averaging ~7 children/family is not for everybody.

c) A Kansas farmer with electricity, tractors, and a 300HP combine, can, with a little seasonal help, handle 100s of acres of crops, and maybe even afford vacations in nice places, if they're lucky. See Kansas farms, whose average size is 700 acres.

7) Anyway, I seriously recommend studying Ayres & Warr's work, even if it takes some effort to plow through the math and econ-speak.

John, I'm absolutely with you on using Ayers-Warr to critique the infinite growth paradigm. (I hope you can do a TOD post on this.) I'd certainly like to see us move towards a steady-state economy before too long. But I'm also drawn to progressive economists like Dean Baker and James Galbraith who think economic (namely, productivity) growth is compatible with a healthy environment, indeed necessary to ward off collapse of the dollar.

Thanks for the links. Will definately read more of Ayers. But I don't see global GDP tackled. As far as I know, global GDP dropped after the 1970's as the economies shifted from Keynesianism to neoliberalism. I still tend to see "energy efficiencies" as "passive" followers or enablers of economic growth. The "active" factors or levers that we can influence I tend to see as government policies.

Look at the phenomenal growth of China compared to its neighbors who followed the "Washington Consensus". (Note: the last thing I want is an authoritarian government that spies on its citizens... Well I suppose we do have the spying thing going on in the US, surrepticiously at least!) How could the Ayers-Warr model account for different socio-political organization of the economy? (I still like it. I just thing its usefulness as a predictive tool will be limited.)

As you imply, agricultural producivity will become more and more difficult to increase as global warming ravages a petroleum-scarce planet. (I was glad to see National Geographic tackle the issue in its latest issue.) Here's hoping Ayers-Warr can help bring the attention of mainstream economists and policy-makers to these matters.

I think we should clarify some things. I haven't waded through all of the comments, so please forgive me if someone else has mentioned what I'm going to say.

First, Ayres is looking at long-term correlations. He doesn't show that changes in either net primary energy production (exergy) or physical work ("exergy services") cause changes in economic output. Given that we know that changes in vehicle miles travelled, and freight miles are caused by changes in economic output, a strong argument can be made for causation in the other direction.

2nd, Ayres works backwards: he calculates physical work by looking at various forms of work in the economy, and then looks at the correlation between energy and work, and between work and GDP.

3rd, He finds that the correlation between net primary energy and work is very poor: only 14% of GDP is "explained" by energy production/consumption.

4th, the intermediate factor of "efficiency" can be considered a fudge factor. It's a ratio of work to primary energy inputs, and the fact that it's changing is a measure of the lack of relationship between energy consumption and work.

5th, energy was never in short supply until the 70's, and so the predictive power of this analysis for an era of limits to oil production is questionable.

6th, work and GDP were found to be closely correlated but, as you'd expect from point #5, that relationship started to break down in the 70's. We see this breakdown especially clearly lately: from 2004 to 2008 world GDP grew about 20%, while crude oil production was essentially flat.

I have first hand experience with the concepts Ayres-Warr discuss in their papers, namely, the reduction in energy intensity of industrial processes. This is what many engineers who work in heavy industry, particularly like steel, chemicals and pulp and paper, are trained and paid to do, and they would instinctively recognize that continuously lowering the inputs to production (like energy) by improving processes (or methods) is as important as labor and capital.

In one of the papers I read, Ayres-Warr used electricity as the example for calculating thermodynamic efficiency, and I have no issues with their method. Electricity is essentially work because it is convertible to work at high efficiency. Also, excellent data on heat rates exist. Of course, no analogy is perfect; for example, hydro power is not really a heat engine for which thermodynamics was developed. Nevertheless, we can calculate a first law efficiency (conservation of energy) for hydro, which is convertible to electricity at nearly 90%. We would further have to know the energy used to develop the hydro project and it’s useful life to calculate the life cycle efficiency.

Obviously a model consisting of components for thermally generated electricity, labor and capital does not completely describe an economy. In industry we analyze manufacturing systems using fishbone (Ishikawa) diagrams with components that were typically grouped as money/machines (capital), manpower, materials and methods/processes and lately environment has been added to the analysis.

While something like processes may mean an entire way of making something, for example chemical X, there may be several ways of making X using different feedstocks with different processes requiring different amounts of energy. However, if we use the example of an assembly line, we could construct the line differently and use more or less manpower or capital without significantly affecting energy use. This is only discussing the production side of the economy while ignoring services, which is the largest component.

I believe that the economic model could be further improved by adding the materials function, which could show the effect of lower resource quality. Also, the manpower component could be used to reflect the age structure of the population and the worker to dependent ratio.

While I believe it is a coincidence that the Ayres-Warr model has a decent fit with performance of the economy, it seems that the trend in thermodynamic efficiency is representative of the improvement of the various fishbone type factors that make up our economy.

I think Ayres-War’s papers are very interesting and show some fascinating data on the historical role of energy in the economy. This type of work is a must read for anyone calling themselves an economist or for anyone interested in the role of energy in the past, present or future.