The Exergy-Efficiency Connection

earth view from spaceThe standard neoclassical theory taught in the economic departments of major universities and accepted by most of the economists who advise governments (and business leaders) attributes economic output (GDP) and economic growth to cumulation of only two so-called `factors of production’ namely capital and labor. These two factors are assumed to be freely substitutable for each other but not complementary.

The reasons for this assumption are more historical than logical. Natural resources or `gifts of nature’ were originally attributed to `land’ which later in the 19th century was absorbed into the larger category `capital’. Of course sunlight — needed by plants – can be thought of as proportional to the area of the land on which it falls, hence as a kind of indirect attribute of the land itself. The same can be said of natural rainfall and benign climate.

In any case, standard economic theory, as it evolved in the two centuries up to the first “energy crisis” in 1972, did not treat energy per se as a ‘factor of production’. In standard economic growth theory useful energy was (and still is) treated, instead, as an intermediate product of labor and capital. Somehow, a combination of labor and capital are supposed to produce energy. This makes a certain sense if we think of a coal mine or an oil well as an energy producer. Of course, mines and wells are no such thing. The useable energy was there in the ground – a gift of nature, in fact – and what the capital and input did (does) is merely to extract it. A well is useless junk when the oil is gone, and an exhausted mine is likely to be a blot on the landscape if not actually hazardous.

Useful Energy (Exergy): An essential prerequisite of economic activity

The arguments for and against this awkward formulation are central to the economic paradigm – a sort of mental model — that lies behind the current global situation. The important point is that useful energy (exergy) is not just a product of economic activity, as the standard theory suggests. On the contrary, it is an essential prerequisite of that activity. Machines (including computers) without energy in the form of fuel or electricity to drive them would be inert lumps of metal capable of producing nothing. Similarly with labor: human or animal workers need food  (Calories) just to survive, let alone do any useful work.

Nevertheless standard economic theory glosses – or more accurately smudges – over this point by insisting on energy-as-intermediate product rather than energy as a primary input. Why? The basic reason is historical: once the theory had been built without energy as a factor, it was a going to be a nuisance to change the theory. A lot of textbooks would have to be discarded or rewritten, and a lot of professors would have to go back to school.

Yet the events of the early 1970s – the so-called energy crisis – clearly pointed to the importance of useful energy as a factor of production. The sudden rise in oil prices in 1973-74 and again in 1979-80 led to dramatic downturns in economic activity. That should have been enough of a clue. But the growth theorists had more faith in their theory than in the evidence of a strong connection between the availability of energy as an input and the magnitude of economic output – what we call GDP.

According to another bit of economic theory, all inputs are created equally important, per unit of money. To put it in simple words, the effect of an input limitation on GDP should be exactly proportion to its share of the costs of all factor inputs taken together. Costs are defined as payments to the “factors”. So the cost of labor is the sum of all wages and salaries, the cost of capital is the sum of all dividends, interest charges, rents and royalties. Those payments add up to the total GDP, by definition.

But if energy (exergy) is regarded as a factor of production, how can it be accounted for in terms of cost? [1]The problem is that the exergy itself is a free gift of nature and the only cost to the economy is the cost of capital and labor needed to extract it. In the industrialized countries, until very recently, those costs – being the revenues of the so-called energy industry — amounted to roughly 5 percent of GDP for all the OECD countries.  Economic theory says (or seems the say) that the relative importance of each factor of production[2] must be equal to its cost share, which implies that energy is not important. In fact, it is actually neglected in most models because its cost share is so small..

Thus, if expenditures for energy are only a small fraction – say 5 percent – of the total GDP, it seems to follow from the cost-share theorem that cutting the energy supply, by – say — a factor of two would only reduce the GDP half of 5 percent. Experience with energy price spikes over the past thirty years suggests that the real effect of high energy (oil) prices on GDP growth has been much bigger than it should be according to the cost share theorem.

To most non-economists it is not surprising that energy is an important factor of production. In fact, every price spike since the 1970s has been followed by a recession. This implies a strong link. But the cost-share theorem stands in the way and some growth theorists have been ready with other explanations of the observations.

However, if (useful) energy is really an important factor of production, despite its small cost share, then much of past economic growth must have been attributable to the declining cost and increasing consumption of useful energy from sources other than food or animal feed. Whereas the standard theory attributes most economic growth to technological ‘progress’ (undefined), it turns out that past growth of the US and several other countries can be explained remarkably well by including useful energy – converted to useful work – as a third factor of production together with capital and labor. In other words, it is not necessary to explain past growth in terms of an undefined exogenous variable called ‘technological progress’.

We argue, to the contrary, that while `raw’ energy (exergy) inputs (as raw materials and sunlight) do not explain economic output over a long period, energy converted into `useful work’ in the physical sense, does have a lot of explanatory power. Useful work can be thought of as the product of raw energy (exergy) inputs, such as biomass and fossil fuels, multiplied by the efficiency of conversion into useful forms, such as mechanical work (lifting, pushing, pulling) electric power and useful heat.

The qualitative argument for introducing useful work as a factor is that economic growth has always been a positive feedback cycle, in which lower costs lead to lower prices (of goods and services) which generates increased demand and – through economies of scale, R&D and learning from experience, lower costs again. Evidently the costs of useful work as produced by so-called `prime movers’ – such as the steam engine – has fallen by orders of magnitude since the industrial revolution began. These declining costs have caused lower costs of iron and steel, engineering products, structures, and so on.

Unfortunately, none of these arguments have been convincing to the mainstream economic growth theorists, apart from a small group that has focused on the phenomenon called   “the rebound effect”. The argument is that efforts to cut energy consumption by increasing energy efficiency generally yield less than proponents hope. Why?  Because greater efficiency cuts energy costs to the user and thus encourages greater use. Thus, if air-conditioning costs less to use, people will use it more. In extreme cases, the rebound effect may “backfire” resulting in an actual increase in energy use, rather than a reduction  {Brookes, 1990 #988;Brookes, 1992 #989}; {Saunders, 1992 #4457}  {Brookes,  1993 #990;Brookes, 2000 #7058} {Saunders, 2000 #7061} {Sorrell, 2004 #6609} {Herring, 2009 #6241}.

However in the last few years a new argument has emerged which should change the situation. In brief, it can be proved mathematically that the ‘cost share theorem’ for a three-factor model is only valid in a simple situation where the three factors are independent and unconstrained. The theorem is more complicated if there are physical relationships (constraints) among the factors. The existence of complementarity between any two factors is such a constraint. (There are other constraints as well). A German physicist, Reiner Kuemmel, has proved that, when such constraints exist, the cost share theorem must be modified to take into account shadow prices associated with the constraints. The implication is that the supposed equality between cost share and output elasticity is no longer valid. In short, the output elasticity can be much larger (or smaller) than the cost share.

The simple implication of this important result is that useful work has a much larger output elasticity than its cost share. (The reason, in simple terms, is simply that the exergy content of all primary sources, including fossil fuels, is really a free gift of nature. It has consequently been under-priced.) That sounds very theoretical, but it really means that useful work is a much more important contribution to output, and hence to growth, than its small cost-share implies.

Economic growth since the industrial revolution has been driven, in large part, by declining cost of fossil energy (exergy) and of energy services (“useful work”). At first it was coal that fueled the industrial revolution. Later came petroleum and natural gas. However, since about 1980 discoveries of oil have consistently lagged behind consumption and, for that reason alone, oil prices will have to go up in the future and other fossil fuel prices will follow e.g.{Benes, 2012 #7399}. A number of analysts now expect “peak oil” within the next decade or two e.g. (Strahan 2007), although with prices around $100 per barrel it appears that reserves are larger than previously assumed{Witze, 2007 #7410}. ‘Peak gas” is expected to follow by three or four decades.

The other reason for higher energy prices is, of course, the need to cut carbon dioxide emissions to the atmosphere to stabilize the climate before it passes the “tipping point”(Hanson 2006). While there are significant opportunities to cut emissions by increasing efficiency – even with negative costs – it is a major concern that the powerful energy industry has adopted a strategy to convince governments and the public that this can be done by a “techno-fix” called carbon capture and storage or CCS. Without going into details, however, this involves separating the carbon dioxide from the nitrogen in the flue gas (which takes a lot of exergy) and then compressing and liquefying it (which takes even more exergy) and pumping it down through a pipe to a “safe” rock formation several kilometers deep in the earth. Apparently 25% – 40% of the electric power output of a 500MW coal-fired power plant will be needed to accomplish this. It means that from one to two thirds more such power plants will be needed to produce the same net amount of electric power for the rest of the economy. It means that the cost of electricity will have to rise by up to 70 percent. In the case of a cement plant, I have an authoritative estimate that CCS will add $50 per ton to a product that now costs $70 per ton (Meric 2010).

The forthcoming advent of “peak oil”, whether it has already happened or whether it occurs ten or twenty years in the future, must also have – other factors remaining equal – a significant negative impact on future global economic growth. The reason is that energy in general, and liquid fuels from oil in particular, are essential to virtually all economic activity. There have been many observations of growth slowdowns following energy price spikes (Hamilton 1983; Hamilton 2003, 2005). Yet, mainstream economists have long assumed that the output elasticity of energy inputs – a measure of economic importance – should be equal to the “cost share” of those inputs in the national accounts.

There was a debate in the economics literature back in the early 1980s on this issue, because modelers like Dale Jorgenson had concluded that the large oil price increases in 1973-74 and again in 1979-80 had had a major negative impact on economic growth. However the “Dean” of growth accounting, Edward Denison of Brookings Institute said this was impossible because energy only accounted for around 5% of the US economy, and therefore could not have a significant impact on GDP (Denison 1984). Since then mainstream economists have assumed that energy (exergy) is not a significant “factor of growth”. However, it has recently been proved mathematically that in a three factor model, where the factors are interdependent (or constrained) the output elasticity (importance)  of energy – and energy services like “useful work” – are not equal to, and may be much greater than, their cost share (Kuemmel, Ayres, and Lindenberger 2010).

In fact, there is econometric evidence that the output elasticity of useful energy (or useful work) – tends to be much larger than its cost-share, whereas the output elasticity of labor in the industrialized countries tends to be much smaller than its cost share. This discrepancy can be interpreted in a more down-to-earth way. It can be argued that raw (unskilled) labor is over-priced in modern economies whereas flows of energy, especially petroleum, have been relatively under-priced up to now. The econometric evidence for this would take me far afield. But the simple observation that most firms are able to increase profits by reducing employment seems to suggest that employment is being kept artificially high, partly for social and political reasons and partly as a way of supporting consumption. Meanwhile, the price of useful energy has been much too low for much too long. (I think the Resource Panel agrees with this.)

Growth of the US and EU economies since the 1970s has increasingly been (partly) consumption driven where the consumption was greater than current income allowed and hence was paid for by borrowing from the (fewer and fewer) countries with large favorable trade  balances, especially Japan, China, and the OPEC countries . But now the size of the debt mountain of the US and European countries (except Germany and Scandinavia) is such that more and more countries  are in the process of “socializing” private debt. Some countries are reaching borrowing limits and there is a growing fear of defaults. The standard response of the IMF is to require draconian cuts in government spending that will cut demand further and trigger a downward economic spiral – with corresponding social distress – unless the few countries with large export surpluses and financial reserves are willing to see much of those reserves wiped out. I think that is highly unlikely.

Efficiency as the driver{Laitner, 2013 #7411}

To summarize: accumulation of capital stock and labor cannot explain economic growth, as Solow showed back in 1956-57. Solow had to introduce an exogenous driver called “technical progress” (also “a measure of our ignorance”) to explain most (87%) of the US growth from 1909 through 1949. Since Solow’s time, “technical progress” has never been adequately explained by any of the mainstream modelers, (including “endogenous growth” theorists who want to explain it in terms of “human capital”.)

However, economic growth from 1900 through 2000 has now been explained quite well by putting energy services (useful work) back into a 2-parameter production function (Ayres and Warr 2005, 2009). This works, as mentioned above, because it is no longer necessary (or realistic) to assume that output elasticities must be equal to cost shares, or that they must be constant over long periods of time. More recent results (unpublished) allow for the impact of information technology (IT) and non-energy related innovation.

The non-equality of output elasticities and cost shares has important consequences for the standard theory of economic growth. The first implication is that the Cobb-Douglas production function must be discarded, because the C-D function assumes that output elasticities are equal to cost shares and that the latter are constant. Dropping this assumption implies that the output elasticities of factor inputs must be functions (such as ratios) of all the input variables, namely capital, labor and energy or energy services. Kuemmel et al. have shown that the simplest functional form for a production function that allows for non-constant output elasticities, takes into account the energy flows in a physically plausible way, and permits an explicit parametric formulation of the constraints, is the so-called LINEX production function (Kuemmel, Henn, and Lindenberger 2002; Lindenberger et al. 2008; Ayres and Warr 2005, 2009). Its mathematical characteristics have been discussed elsewhere and need not be recapitulated here.

In several quarters there is a suggestion that CCS might be justified on the basis of “impact decoupling” if not “resource decoupling”. I understand the argument – that reducing the GHG buildup in the atmosphere is desirable, ceteris paribus – but other things are not equal. There is an unstated implication that some authoritative body has looked at all the other ways of abating the problem and concluded that CCS is the least bad. I don’t agree with that implication at all. CCS is the brainchild of the energy industry that sees it as a way of continuing with business as usual – in fact more so – without the need to do anything serious about developing alternative technologies.  On the contrary, wide deployment of CCS (as assumed by the IEA) would be a growth stopper.

There are strong empirical arguments for the so-called `Hubbert thesis’, namely that global petroleum output is now approaching its peak. Recent (2004-2005) sharp increases in oil prices, which show no signs of being a temporary `spike’, make the Hubbert theory increasingly plausible. This event would have obvious implications for prices and economic activities directly dependent on oil products, especially petrochemicals and transportation.

While the Hubbert arguments are not (yet) universally accepted by oil geologists or by the oil industry – at least in public – they cannot be dismissed lightly. One reason, among several, is that economic incentives facing powerful economic interests strongly favor continuing indefinitely on the `business as usual path’. For instance, the stock market valuations of major oil companies, such as Shell, BP and Exxon are directly dependent on proven reserves. This fact, alone, makes the public pronouncements of the established petroleum interests suspect. Another reason for skepticism is the obvious competition for influence among members of the OPEC cartel.

Finally, among the economic incentives for refusing to acknowledge the reality – perhaps the only one that restrains the largest producers, and the OPEC cartel from price gouging – is the fear that, if oil prices were to rise too high (and remain high), the industrial countries might get serious about reducing consumption through taxation or regulation such as extended CAFÉ standards. An even scarier scenario for the oil exporters is the prospect – however dim – of rapid development of viable technological energy alternatives.

1 The technical measure of importance is called output elasticity. It is defined as the percentage increase (or decrease) in output resulting from the same percentage increase (or decrease in the input factor. 

2.The technical term for useful energy – the part that can be converted into work – is exergy. See any thermodynamics textbook for details.

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About the author:

ayres bw smallRobert Ayres’s career has focused on the application of physical ideas, especially the laws of thermodynamics, to economics; a long-standing pioneering interest in material flows and transformations (Industrial Ecology or Industrial Metabolism); and most recently to challenging held ideas on the economic theory of growth.

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2 thoughts on “The Exergy-Efficiency Connection

  1. Pingback: What is Exernomics? | Exernomics (under construction)

  2. Pingback: What is Exernomics? | Network Dispatches

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