Economic Growth and Marginal Energy Return Ratios (MERR)

Douglas B. Reynolds
Professor, Oil and Energy Economics
University of Alaska Fairbanks
(Fairbanks, AK)

When considering natural resource economics and economic growth theory, Simon (1983 and 1998) among others believe technology can overcome scarcity to create ever increasing levels of wages and GDP.  Alternatively, Meadows et. al (1972 and 2004) among many look at the real inputs into economic production and proclaim natural resource scarcity as crucial in determining the height of wages and GDP that humans can attain.   On the technology-centric side of the debate, it is assumed that technology creates economic growth through labor and capital productivity enhancements, which can overcome natural resource scarcity.  However on the resource-centric side of the debate it is emphasized that technology is not what makes things move, not what transports people and materials to location and not what drives machinery. Energy does that. Thus, the economy is a physical, engineering, oil consuming machine rather than a pure technology driven machine.  Nevertheless, scientists and economists often talk past each other regarding how economic growth occurs, such that a simplified model, presented here, could enrich the discussion on energy-economy interactions.

While capital, labor, and technology—as opposed to natural resources—tend to be the primary inputs used in economic growth modeling, nevertheless the economy is an engineering system in the tradition of Forrester (1958 and 1961), and as such energy, and especially oil, has a leveraging effect on productivity.  After all, Smil (1991) shows that many of the greatest inventions of the twentieth century were based on liquid fuels from oil such as automobiles, airplanes, and, in general, large autonomous mobile machinery (LAMMs).  Plus, O’Toole (2006), Bogart (1998) and Cervero (1998 and 1996) show that those oil-based technologies had a leveraging effect on other technologies such as allowing economies-of-scale for factories and allowing human-capital mobility in large cities.  So, more oil created more cargo transportation options, which reduced distribution costs, which allowed there to be larger factories further away from expensive city real-estate, which increased the economies of scale of production.  More cars allowed greater labor mobility which enhanced the productivity of labor.  So it should come as no surprise that Hamilton (1983 and 2013) and Cleveland et. al (2000) show a relationship between oil and the economy.

However, Hall et. al. (1986), Hall (2008) and Cleveland et. al. (1984) suggest that one important cost for supplying energy is the energy inputs needed to extract and obtain more energy, which is referred to as the energy return on (energy) investment (EROI), or more generally as Brandt et. al (2013) suggest, energy return ratios (ERR), which can include Hanon’s (1982) and Hagens’ (2010) concept of energy discounting.  ERR is generally defined as the useful energy acquired from a process divided by the necessary energy inputs invested to obtain that useful energy:  

ERR =  (useable energy acquired)/(energy expended to obtain that useable energy)  

The inverse of ERR is a proxy for cost, i.e. the lower the ERR is, the more energy inputs are required for each Btu of energy output, and the higher costs become for supplying energy.  Typically low ERR energy also requires more capital and labor.  Therefore, the cost of a liquid fuel will tend to be low if ERR is high and the cost will tend to be high if ERR is low.  While the economics profession tends not to emphasize ERR as an important concept, since it does not explain all the capital and labor and land costs of attaining energy, nevertheless ERR is helpful in communicating the engineering side of the economic growth debate along the lines of Kümmel (2011), Bardi (2011) and Hall and Klitgaard (2012).

Tar-sand, oil-shale, shale-oil, gas-to-liquids, coal-to-liquids, methanol, ethanol, bio-diesel, and natural gas liquids, such as propane, are all oil alternatives that give a relatively dense liquid fuel that can in many cases be substituted directly for conventional oil.  The problem with many of these oil-substitutes is that they require energy-intensive processes that decrease their ERRs and therefore add to their expense.  Electricity, along with relatively large capital inputs such as power plants, electric grids, dense batteries, and such things as huge electric train track infrastructure can also replace oil but also at a low ERR and a high capital cost.  Conserving oil, such as living closer to a city, can also have a low ERR since there are high capital and energy costs of building new expensive high rise housing.     


Growth Theory and Total Factor Productivity

In order to adjust scientists to the language of economics, consider a simple Cobb-Douglas production function with the inputs of production being capital and labor only, and the output being the production of general goods and services including a small proportion of the output making capital goods used for future goods and services production, here referred to as general GDP.  According to growth theory, technical progress and accumulations of capital account for much of the growth in general GDP as they augment the labor and capital productivity.  Therefore if there is little if any geological constraint on the liquid fuel energy resource, i.e. the oil input cost is very small compared to the total economy, then we can assume capital and labor are the only inputs into general GDP output and we can use a simple Cobb-Douglas equation as follows:

Ya* K b1* L b2                                                                                   (1)

where a is a parameter and b1 and b2 are mathematical powers such that b1 + b2 = 1. 

The equation says people (L) and machines (K) work together in a productive manner to produce general GDP (Y) for society for an entire year.  If we divide all the variables by labor, L, then we get Y/L = y, and K/L = k, and L/L = 1, which makes the equation into an average per capita income estimator.  Thus, we get individual income, also known as general GDP per capita, (y), as a function of capital per person, (k), irrespective of the population, L:

y = f(k) =  a* k b                                                                                  (2)

where a is a parameter, and b is a power less than one.

Typically by adding more capital per person to the economy, the economy is able to increase its per capita output.  For example in developing countries workers may use cheap shovels to build a road, but in developed countries, they use expensive backhoes, which increases a worker’s productivity and therefore, indirectly, his wage.  However, due to the law of diminishing returns, you get a curved, log-linear relationship, of equation 2, as shown in Figure 1.  So, adding capital does not have a one-to-one relationship with higher wages. 


Figure 1.

The Law of Diminishing Returns to Capital. 

This shows the curve that represents the Cobb-Douglas production function, which closely models many real world economies.  When more capital is used per person as an input into production, income and general GDP per person goes up but at a decreasing rate. 

Economic growth can occur by moving up the curve and using more capital, or it can occur independently with better technology.  Technological progress is where Figure 1 shifts upward while becoming more elongated with the base attached to zero.  This is often referred to as a Solow (1956), or Swan (1956), increase in total factor productivity, where both labor and capital become more productive.  Many theories about how economic growth occurs can be seen in Acemoglu (2009) and Aghion and Howitt (2009).  However, instead of theorizing about how growth can occur with more capital and better technology, what we want to do is to theorize how decline can occur with less oil. 


Capital and Output Space with Changes in Marginal ERR

In order to understand a decline in general GDP in relation to oil, consider using the marginal ERR concept.  Reynolds (2014) identifies what can be called an equilibrium marginal energy return to investment (MEROI) or more simply an equilibrium marginal energy return ratio (MERR), which interacts on an ERR market.  When the market clearing MERR is high, oil is less scarce and less expensive.  When the market clearing MERR is low, then oil is scarcer and more expensive and energy availability becomes a limiting factor of general GDP output.  Assume, in an exaggerated fashion, that the equilibrium MERR starts high, at say 100, but then declines substantially, to say 5, such that oil scarcity affects general GDP output.  The decline in MERR not only makes oil more costly, but also means the economy needs to use more capital to conserve oil.  We can map the change in capital on the GDP-capital space of Figure 1.

Consider Figure 2.  We start at k’, which is the amount of capital per person that produces general GDP per capita at y1 and at point 1.  Technology is assumed constant.  The equilibrium MERR for oil is 100 at point 1, so the oil supply is abundant with a low price. Essentially, oil is a rabbit in elephant stew as Hogan and Manne (1977) put it, and oil production requires very little of the economy’s capital.  Next, there is a shock to the economy and the MERR for oil declines to 5—like for example if conventional oil attains Hubbert’s (1956) peak, similar to Benes et. al (2012), and the economy is forced to use tar-sands bitumen (oil) with a 20 fold increase in the capital and labor inputs at the margin.  In order to overcome the shock, the economy needs to rearrange capital and labor inputs to alleviate the detrimental effects of high cost oil.  Nevertheless, the oil substitution and conservation strategies remove capital available for general GDP output and add capital to oil production or conservation, such as using more electric trains instead of trucks.

We can track the change on the capital-output space of Figure 2.  Because the MERR declines, the economy uses more capital for tar-sands production or other substitution strategies.  Capital is therefore taken away from general GDP and put into oil.  In the per-capita, capital and output space, we start with a capital per person of k’ but move to k” as we divert capital away from general GDP to oil substitution and conservation.  The capital available for general GDP is reduced from k’ to k”, and general GDP is reduced from point 1 to point 3 on Figure 2. 



Figure 2. 

Capital and output space with a change in MERR.


When MERR declines, more capital is needed to produce the oil substitute or to conserve oil.  Then there is less capital available for general GDP.

On Figure 2, point 1 has an output function, f1(k), and a capital input of k’ and an oil usage rate at that capital level of O1.  The MERR at point 1 is high at 100.  Suddenly, the MERR declines to 5, i.e. the MERR supply curve of Reynolds shifts inward.  The economy can no longer produce general GDP at point 1 with capital k’, but produces general GDP at point 3 with capital k’’.  The rest of the capital, k’ – k’’, is used to produce the oil alternative or to run the oil conservation strategy.  The general GDP declines to y2.  However, at point 3 and y2, we still have k’ capital available, it is just that not all of that k’ capital is available for general GDP, as k’ – k’’ is used for alternative energy.  The oil used to run the economy is reduced, O1 > O2.  We can map point 3 into point 4 where general GDP is now located on the lower function, f2(k).   The entire capital stock, k’, is being used:  k” for general GDP, and k’ – k’’ for oil alternatives, and the general GDP curve has now shifted down to f2(k). 

Thus, baring a prodigious technological revolution, oil scarcity can cause economic decline.  Clearly, though, past examples of prodigious technological revolutions occurred when economies switched to high grade energy with high MERRs, not when switching to low grade energy with low MERRs as Reynolds (1994 and 2011) shows.




Dr. Reynolds heats with coal, bike rides to work and has consulted on many energy projects at the University of Alaska Faribanks.  He has lived and worked in Kazakstan, Mexico, Norway, Russia, Turkey, France and Poland.


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