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Sunday, April 22, 2012

Doing The Math for "Physicist versus Economist", for Earth Day 

From "Do The Math"...
Physicist: [I]f you plot the U.S. energy consumption in all forms from 1650 until now, you see a phenomenally faithful exponential at about 3% per year over that whole span. The situation for the whole world is similar. So how long do you think we might be able to continue this trend?
Physicist: ... First, I’ll just mention that energy growth has far outstripped population growth, so that per-capita energy use has surged dramatically over time—our energy lives today are far richer than those of our great-great-grandparents a century ago. So even if population stabilizes, we are accustomed to per-capita energy growth: total energy would have to continue growing to maintain such a trend.
The statements above are seriously erroneous. See below.
Second, thermodynamic limits impose a cap to energy growth lest we cook ourselves. I’m not talking about global warming, CO2 build-up, etc. I’m talking about radiating the spent energy into space... Alright, the Earth has only one mechanism for releasing heat to space, and that’s via (infrared) radiation. We understand the phenomenon perfectly well, and can predict the surface temperature of the planet as a function of how much energy the human race produces.
The upshot is that at a 2.3% growth rate (conveniently chosen to represent a 10× increase every century), we would reach boiling temperature in about 400 years. [Pained expression from economist.] And this statement is independent of technology. Even if we don’t have a name for the energy source yet, as long as it obeys thermodynamics, we cook ourselves with perpetual energy increase.
It's difficult to "plot U.S. energy consumption in all forms from 1650 until now", being that the US did not exist before 1789. But we can plot both energy consumption and population growth since 1790. From the US Census we get population, and via EIA.gov we get energy consumption...

populationenergy*E per capita**
17903.9 mil35691.3
2010308.7 mil98,000317.5
growth79.15x275.28x3.48x
ave rate2.01%2.59%0.58%
* trillion btus


** million btus


Contrary to the claim "energy growth has far outstripped population growth" we see the exact opposite is the truth – over US history population growth has outstripped energy growth per capita by more than 3 to 1. But a much greater misrepresentation is this ...
"So even if population stabilizes, we are accustomed to per-capita energy growth: total energy would have to continue growing to maintain such a trend"
... ignoring the reality that in the USA energy consumption is declining per capita right now, and has been for the past 30 years -- as GDP of course continued to grow.

USA from 1979 to 2009...

[] Real GDP per capita: +58.8%
[] Energy consumption per capita: -14%
[] Cost of energy as % of GDP: -35%
[] Energy consumption per real dollar of GDP: -47%  [EIA.gov]

In a moment we will accept the invitation to "do the math" in determining a realistic projection of future world energy consumption. But first, a word of what is going on in the above numbers, as wealth and income grow while energy consumption declines.

Advanced economies grow by increasing productivity – that is, by producing more of value from less. Energy and material inputs are a cost – economies advance by producing more value while reducing these costs. That's how we all get richer.

Thus, two pounds of a rotary dial single-line telephone becomes the few ounces of a smart phone that can connect by sound or image to near all the information in the world ... deca-tons of steam engine pulling deca-tons of railroad cars along kilo-tons of steel rails become a hollow aluminum tube that flies through the air at ten times the speed ... drinks once distributed in steel cans (opened with "church keys") came to be distributed in tin cans, light aluminum, lighter plastic ... and so on, with endless examples.

If you are either a consumer or a business, you know you get more value from products built more smartly, more lightly, with less material and energy input, and thus less cost. So advanced market economies drive relentlessly in this direction. Material inputs are cut much faster than energy inputs – as US GDP per capita has increase 125% over 40 years, mineral consumption declined 40%.

OK, back to doing the math. World energy consumption per capita has grown at a 0.79% annual rate, 1971-2009. But this is far from a uniform rate around the world. Consumption growth is much smaller or negative in advanced economies, larger in poor but rapidly growing economies.

In advanced economies energy consumption per capita has flattened or is falling. This is true across the world, not just in the US. In the European Union, advanced economies with somewhat lower per capita GDPs than the USA, energy consumption today basically is flat overall, and turning negative in the more advanced nations. For instance, during 1997 to 2007, total primary energy consumption in the UK declined 3% while real GDP grew 33%, while in Germany energy consumption declined 1.7% while GDP rose 18%.

In the poor but rapidly developing economies energy consumption is growing much faster. But even these economies are growing far more energy efficiently than did the US and other "first mover" economies, because they can copy and use from the start energy-efficient technologies that the first movers had to invent as they went along.

For instance, compared to the USA at the same level of per capita GDP, India today uses only one-fifth as much energy per capita as the USA did, and China uses less than half as much energy. We see again how the relation between economic growth and energy consumption is far from uniform -- the later in time, the less energy is used at a given level of national income.

Now to "do the math" for a simple projection of future energy consumption we need only two more items. First is an estimate of future world population. We can use the United Nations middle projection, which estimates population rising from today's 7 billion to 10.1 billion in 2100, remaining stable thereafter. Second is an estimate of future growth of world GDP per capita. The actual growth rate of world GDP per capita has been 1.8%, 1980-2010, and we'll project this going forward.

Our simple projection of future energy consumption multiplies per capita energy consumption each year by world population. It calculates annual increase in world energy use per capita from today's level starting with the recent 0.79% annual rate. But as we know this rate declines with increasing GDP, we must reduce it going forward as world GDP rises.

Thus the rate is reduced proportionately as world GDP per capita rises at the 1.8% annual rate from the recent $9,892 (in 2005 dollars) to approach $26,000 (2005 dollars) – the level at which energy use began declining per capita in the USA (and other advanced economies). When world GDP per capita goes above $26,000, energy use per capita is projected to decline each year by 0.35% - 10% over 30 years – somewhat less than the actual 14% decline in the USA, 1979-2009. (This is a very conservative projection as it credits zero increase in energy efficiency in the future).

Applying the resulting annual rate of energy growth per capita to the annual increase in future population, given in the UN middle estimate, gives the increase in energy consumption compared to today's base period. When graphed the result is, of course, a curve...



Total energy consumption peaks 50 years in the future, at a level 62.5% above today's. It thereafter begins a mild but steady decline, as population grows for another 38 years before stabilizing at just above 10 trillion.

Now, this is a simple model, with no doubt a large margin of error.  But it based on actual empirical data and economic principles proven in the data -- it is realistic, which cannot be said about simpleminded "exponential consumption growth" projections that have no support in either empirical data or economic logic, and which in fact are refuted by both.  There is nothing "exponential" about consumption related to economic growth.  It is entirely finite within very limited bounds.

And you can make the margin of error around it as large as you want -- that 62.5% maximum increase in energy consumption before a subsequent decline is a long, long, long way from "boiling the earth".