Economic dynamics - and the real danger

This is a summary paper that I have written to explain the findings from my computer model of an abstract economy's dynamics when it is run mostly on fixed, finite fuel sources such as fossil fuels. This paper is a little more formal than my previous blog on "It's the net energy stupid!" and I will be submitting it for publications at one of the energy-related web sites for wider dissemination. But I thought I'd give my readers a first peek.

The Dynamics of an Abstract Economic System

George Mobus

Associate Professor, Computing & Software Systems, University of Washington Tacoma, Institute of Technology

This is a preview of some of the ideas being developed in a paper by Mobus & Charles Hall being prepared for publication. This version only gives the background and main conclusions to be found in that paper, oriented toward general readers. The author wishes to thank Professor Charles Hall and his students for a very enlightening sabbatical at SUNY-ESF where the ideas for this model effort emerged. Any defects in this version are the fault of the author alone.

The purpose of this contribution is to introduce the concept of an abstract economy in order to explore the general dynamics of economic systems without concern for distracting details that do not alter those dynamics in general, but can cause confusion in trying to understand a more general theory of economics grounded in biophysical science.

An economy is a system that takes energy and raw materials as inputs, involves internal work processes that create and maintain physical structures, and expels degraded materials while losing waste heat to the environmental energy sinks surrounding it. This abstract description needs some more detail but should remain sufficiently general so as to cover a wide range of dynamic systems from living organisms to ecosystems to the societal economies of the world.

The structures that are produced by the work processes include biomass (reproduction and growth) and many kinds of artifacts. Collectively I call these structures — assets — meaning that the structures are considered to be of some kind of worth to the agents participating in the economy. Assets are further divided into long-, intermediate-, and short-term. These temporal categories correspond with examples such as:

• infrastructure, housing, capital buildings and equipment, mass transportation [ten year or greater life spans]
• artifacts such as clothing, personal transportation, furniture, process designs [less than ten years but more than one year]
• food, fuels in stock, supplies [less than one year]

Biomass of humans and pets constitute a separate category of assets. The time scale of human life and reproduction determine the number of individuals within the population (how the biomass is divided into units). As crass as that may sound, the reality is that human beings are generally considered assets by most prevailing value systems. Of course, under the right conditions, all asset types may become liabilities, as when they become obsolete.

Artifact assets also include informational and knowledge recordings such as computer programs used to control work processes (as well as the very real knowledge encoded physically in brains of people). These artifacts are as much physical assets as any other, but they have somewhat unique properties, e.g. being essentially infinitely reproducible at very low energy/material costs. Their value, however, lies in how they affect the movement and interactions of physical structures in the accomplishment of useful work. Notice that missing from this list of assets is the financial instruments typically given asset status in our current economic models. I will address this later after describing debt financing below.

Figure 1, below, shows a diagrammatic representation of an abstract economy with a net accumulation of assets over time as long as there are energy and material inflows. In theory the materials could be recycled if there were enough energy available to recover wastes, refine and reshape them, etc. In practice there is never enough energy available as reflected in the cost limits for recycling operations in the real world. Also, the issue of economic growth (asset accumulation) requires new material resources continually being input into the system.

Figure 1. An abstract economy. Work processes use energy and raw materials to produce assets, some of which are consumed by processes that constitute the major body of the system, some of which will be reinvested in the work processes. Information (thin arrows) flows between the three subsystems.

The dynamics of asset production and decay are governed by the laws of thermodynamics. The general conservation law applies to both matter and energy. But the second law, in particular, has ultimate influence over the efficiency and effectiveness of work processes as well as the entropic decay of all forms of assets. Each asset type can be characterized by its own production and decay constants, but each follows a similar formulation.

A_(t) = A_(t-1) + k_pNE_(t) - k_dA_(t-1)

where:
A is the level of asset accumulation
NE is the net energy available for economic work (e.g. gasoline refined from oil)
k_p is the constant of asset production
k_d is the constant of asset consumption + entropic decay
both constants are << 1.0 and k_p > k_d
and t is the discrete time index

As it happens, since all asset types follow the same dynamics, it is possible to aggregate all assets using a weighting method to aggregate constants so that A_t represents the sum of all assets at time t. Here the dimensions of assets are given in embodied energy units, or emergy. The constant k_d represents both consumption processing and natural decay due to wear and entropy.

A key question that needs to be addressed is: given our current heavy reliance on fossil fuels for more than 80% of our energy inputs, what happens in an economy that is growing when the resources are depleting? As most readers of The Oil Drum and other energy related sites are aware, the focus of analysis has been on the dynamics of peak oil, as per M. King Hubbert, and concern has been for the impacts of declining oil supplies after the peak on the economy. The model that I have been working on, and am in the process of refining with Dr. Charles Hall at SUNY-ESF, suggests that this is actually not the relevant focus in terms of economic capacity.

Many people have realized, either intuitively or logically, that what matters insofar as economic activity is concerned is the net energy — the energy available after extraction of the gross energy (in this case crude oil) and refinement or conversion to a form useful in doing work. Energy must be reinvested in energy extraction, transportation, and refinement in order to gain net energy that can be available for asset production (other than assets needed for energy extraction). Thus there is an energy return on energy invested (EROI or EROEI) that must be taken into account in determining if an economy is viable, stable, or growing. Essentially, when the energy costs of extraction and refinement are subtracted from the gross energy extracted, the net is all that society can use for its work processes. Energy costs are similar to monetary costs of doing business. There are actually energy investments, as for example the embodied energy in off-shore drilling rigs, and there are energy operating costs, e.g., pumping oil. In addition there are also on-going maintenance costs to keep the infrastructure in working order.

The "Best-First" principle states that we human agents will always attempt to extract the easiest-to-get resources first. For oil and other fossil fuels this boils down to geophysical facts about the depth and quality, and geographical facts about distribution of field sizes and locations. We have tended to exploit the largest, easiest to get to fields, most of which are now in declining production. What this translates into is increasing amounts of energy must be used to find and extract the oil (read all fossil fuels), hence net energy is less per unit of energy extracted. The increases in energy costs as a result of the Best-First principle are shown in Graph 1, along with gross and net energies. This model is based on an increase in extraction difficulty as a result of depletion. It does not depend on an explicit logistic function and can be seen to not be symmetrical about the peak of gross energy extraction.

Graph 1. The net energy available to the economy is the gross extracted energy less the energy cost of reinvestment in extracting the next units of energy. This graph assumes exponential pressure in the growth of extraction. The reality of a finite resource turns this into a logistic-like curve.

The mathematical basis for this model will be covered in the paper by Mobus and Hall, in development. Sensitivity analysis, using various rate constants, shows that the model has a very stable form in terms of relations between the three curves. Lower rates of cost growth increase the values of net energy, of course, but do not change the overall dynamics of the system.

Of particular note is the fact that the net energy curve peaks before the gross energy curve. In this model the time is about thirty years, but note that energy units and time units are somewhat arbitrary as this is an attempt to ferret out the dynamical behavior of an energy system based on a fixed, finite resource. Why this is important is that for many years now, we have been focusing on peak oil or peak gross production as the most important inflection point. But the economy runs on the net energy. If peak oil has already occurred, then the peak of net energy production has long since passed. I think this is the most cogent point of this exercise.

Secondly, note that the curves for gross and net are not symmetrical about their respective peaks. This is a result of modeling the physics of resource extraction based on the Best-First principle. The pre-peak scenario aligns well with Hubbert’s theory. But the post-peak scenario shows a much faster decline rate. Since this model does not assume anything about peaking behavior and is based entirely on physical relations between extraction work and production rates, it might behoove us to think more carefully about the consequences of post-peak behavior such as this. It is true that under a profit motive for extraction, there would not likely be a continued all-out effort to extract the resources, thus possibly leading to a more extended post-peak scenario. We already appear to be in a bumpy plateau owing to the feedback from an unstable economic system. It is possible that such a plateau and other feedbacks from the financial system might extend the period of post-peak and modify the decline rates as a result. However, this will certainly come with a heavy price in terms of jobs and wealth production as it implies a greatly diminished economy.

Let us then see what the model predicts about wealth or asset production. Graph 2 shows a basic scenario for the production and accumulation of assets (in emergy units) given the above energetics.

Graph 2. Assets are produced as a function of net energy according to the equation above. This graph is for the aggregate of all asset types as described above. Assets decay or are consumed at a rate less than production as long as net energy is in its pre-peak phase. Assets continue to accumulate and the peak of asset accumulation comes after net and gross have both peaked.

The three colored regions between net energy and assets represent three distinct phases in economic activities. The green region, labeled ‘debt payback feasible’ represents a phase in which net energy is growing faster than production can add to the asset base by the above equation. During this time it is easy to imagine how expectations that future periods will always have a capacity for growth in asset production arise and lead to the institutionalization of debt financing. From the perspective of agents making decisions about how and when to create new asset wealth, the fact that there will be more such wealth in the future can be taken for granted. Debts can presumably be paid back with interest. The form of modern capitalism relies on such an assumption.

Though money is not explicitly modeled it can be thought of as convenient tokenization of energy units that facilitates trade and represents a claim on future work. In that sense, debt instruments can be denominated in such tokens in order to represent future amounts of work that will be done to service the debt and pay some presumed future profit in the form of interest on the loan. Money is the main form of information flows (thin arrows) shown in Fig. 1. It circulates between the processes and the asset stores to regulate what gets built and when. Financial instruments such as bonds, stocks, and other forms of future obligations are superimposed on this information stream as a way to push promises of future work further out in time. So far as agents creating these instruments without foreknowledge of the limits to growth, this seemed perfectly reasonable in the green region.

The yellow region represents a phase in which net energy is decelerating and converging with still growing asset accumulation. This convergence and ultimate cross-over is a period in which the potential to pay back loans, based on future work, is coming to an end. Once net energy is no longer in exponential growth, the expansion of assets also goes into deceleration. Agents within this phase may or may not recognize the problems associated with decelerating work capacity. One might speculate that such agents, having been so successful at using debt-based financing for wealth production in the past (green phase) would be tempted to elaborate more abstract debt instruments in an attempt to continue at least the appearance of wealth production growth. Various forms of financial bubbles might appear followed by collapse since it would become progressively harder to create real physical wealth (assets) due to decreasing available net energy. For agents that sensed a change in the general milieu there was incentive to change the organization of work processes in order to reduce costs — ultimately energy costs of production — such as moving manufacturing to regions of cheaper labor. The yellow region represents a period of adaptation, where possible, to decelerating net energy flow.

Eventually, however, once net energy production falls below the asset accumulation curve, the capacity for paying back debt-based obligations is no longer. Indeed, in the red region it is not even possible to create legitimate debt instruments since all net energy production should be now going strictly to maintenance work. No new assets can be created without ignoring the maintenance of current assets (and the concentration of wealth in the hands of the most powerful agents) and all work is geared toward fighting entropy and struggles to supply consumption processes (one imagines this to be chiefly oriented toward maintaining food production).

The vertical line marked ‘today’ is an arbitrarily placed marker for peak oil, presumed to have already happened (reports on various energy web sites strongly suggest this). If this is the case, then we are already into the red region where it is impossible to create debt-based financing (legitimately) since there is absolutely no possibility of paying off that debt with future work resulting in greater asset accumulation. Is it possible that this is exactly the problem we are seeing in our heavily debt reliant economy today? Our financial systems have clearly gotten out of sync with our real asset producing economy. We are in the throes of debt-unwind and very possibly massive defaults as nations, corporations, and individuals (who have no jobs) are incapable of promising to work more in the future to pay back their obligations. Those who would loan money (claims on assets) to those who propose to create new wealth would do well to reconsider since the model suggests that it will be impossible to even get back the principal, let alone the interest.

Of course, the real global economy is not 100% reliant on fossil fuels; though the mix of other sources makes it difficult to incorporate into this model except possibly by actual data (e.g. nuclear power production started after the mid fifties and has not grown, globally, in proportion to fossil fuel use). Conceivably, where the real economy is hobbling along and not seeming to crash as expected from this model, it is due to more stable energy production from, for example, hydroelectric, sources. Also much growth, especially in electricity generation, has been due to coal rather than oil. But a necessary caveat here is that the extraction of coal is fully dependent on the availability of diesel fuel for transportation and excavation (as in mountain top removal). So I would expect the peak of net energy from oil is already having a deceleration pressure on net energy from coal. It may be too early to say what the dynamics will look like if natural gas proves to be a viable alternative to either coal (electricity) or oil (transportation and heating). If the current claims about recoverable resources (at least in the US) pan out, it could both extend the energy curves and delay the overall aggregate fossil fuel peaks for some time. Nevertheless, the basic shape of these curves will be the same. If we do end up buying more time with natural gas we would do well to use it wisely.

It takes energy to do work. And work, constructing real assets (vs. paper assets), is necessary to create real wealth in order to retire debt obligations. If this model of an abstract economy, fueled as in this case by a fixed, finite supply of energy, truly captures the essence of the dynamics of a real economy then we should consider carefully the meaning of the earlier peaking of net energy flow as well as the potentially dangerous rapid decline in post-peak production. And we should certainly consider the implications of the three phases of economic growth, deceleration, and final decline as shown in this model. Peak oil may only signal that we are already past the point at which our economic systems can function as wealth accumulators instead of signaling that the trouble is about to start.

Comments

[Rajiv]

George,

It would be interesting to see your models hooked up with Steve Keen's See Circuit Theory and the state of Post Keynesian Economics.
http://www.debtdeflation.com/blogs/2009/12/16/circuit-theory-and-the-state-of-post-keynesian-economics/

and also some of Frank Rotering's work at http://www.needsandlimits.org

[Rajiv]

Also I wondered if you were familiar with the real-world economics review and the post-autistic economics network http://www.paecon.net/

[George Mobus]

Hi Rajiv.

Thanks for the links. I will take a look sometime this week. With the holiday bearing down on me, I might not have time to do a thorough review until next week though.

The term post-autistic economics is most intriguing!

George

[George Mobus]

Rajiv,

Thanks again for the links. I've had a bit of time to follow up.

The post-autistic economics stuff is fascinating. I had run into heterodox economics because of my delving into ecological economics. Also, biophysical econ would fit into the category of "not neoclassical econ".

As for circuit theory I watched some of the video on his web site. My impression (would take much closer attention to details to come to any conclusion) is that he is talking about money creation in a closed-loop system but without reference to external inputs (e.g. work creating real assets). This sounds a lot like the closed system approach of neoclassical econ where there are just firms and households (his includes bankers) that transact without concern for limits from nature.

But interesting to see alternative ideas being explored within 'not neoclassical' econ.

George

[Rajiv]

George,

Keen's analysis depends on a study of credit flows, following Minsky's work. Neo classical economics depends upon equilibrium analysis as opposed to the dynamic study of the flows. In my view his models add much -- however, as you point out they are missing much of the real world material constraints. My thought was that both your models might serve to enhance when taken together. many of his lectures are avaiable on his website - http://www.debtdeflation.com/blogs/lectures/

And of course, there are other ways to look at the world -- than the view that sees profit maximization as the ultimate goal of human society

[George Mobus]

Rajiv,

I will be taking more looks at Keen and the whole post-autistic economy stuff some more.

Couldn't agree more with your last sentence!

George

[sgouris]

George, this is interesting work. You may be interested in taking a look at this paper: http://doi:10.1016/j.enpol.2009.11.049
on using energy as a parallel currency.It certainly seems to complement your work in some ways and would be interesting to explore how an energy currency would evolve as EROEI worsens.

Sincerely
Sgouris

[George Mobus]

Sgouris,

Thanks. The link doesn't seem to work for me.

I will mention that there have been a number of proposals to link monetary currency and energy flow. Howard Odum, the Technocrats, even my own poor efforts (see: http://questioneverything.typepad.com/question_everything/2008/03/what-is-money-r.html )

My later proposal is that the money supply should be based on the total exergy (net energy available to do useful work) which would shrink as our energy supplies shrink, a la this post. That is, of course, a hard pill to swallow!

George

[Belstaff Abbigliamento UOMO]

So cute! I already like you on FB and also get your posts on Google Reader. :)