The Labor Cost of Energy

Labor Cost of Energy

Many people talk about the jobs that might be created by switching from fossil fuels to renewable energy sources. However, jobs are not an economic output. Energy is a means to and end and not and end in itself. No one has a flask of gasoline or a charged automobile battery sitting on their coffee table as an art object. Labor dedicated to producing energy cannot be dedicated to producing food, clothing, machinery, etc. If renewable energy sources require more labor per net unit of energy produced relative to fossil fuels, then our overall economic output can be negative effected. Let us examine how large these effects might be.

Suppose all energy currently comes from source 1, but in the near future we will be forced to switch to a more labor intensive source 2. I define the following variables:

f = fraction of labor producing energy from source 1

1-f = fraction of labor engaged in non-energy sectors of the economy

r = L1/L2 ratio of the labor required to produce 1 net unit of energy from source 1 to the labor required to produce 1 net unit of energy from source 2. Obviously r<1 since source 2 requires more labor per unit of net energy extracted.

Suppose that when we shift to the new energy source we make the following changes in our economy. We shift labor from non-energy sectors of the economy to energy producing sectors. We increase the total amount of labor producing energy until the workers left in the non-energy sectors of the economy have the same amount of energy/worker as before (This change may not be possible if r is too small.). We also reduce the energy used for domestic/recreational purposes to maintain a constant ratio with the energy used for manufacturing.

It is clear that with energy source 1 the energy available per worker hour in the manufacturing portions of the economy is proportional to:

[1] f/(1-f)

This proportionality must hold since the net energy produced is proportional to f and the total number of manufacturing workers is proportional to 1-f.

When we switch to the energy source 2 and dedicate a fraction of our labor f’ to energy extraction, then the energy available per worker hour in the manufacturing portions of the economy will be proportional to:

[2] rf’/(1-f’)

The factor of r is required since less net energy is produced per worker hour by precisely this factor. If we equate [1] and [2] an solve for f’ we find:

[3] f’ = f/(f+r-rf)

To give a concrete example suppose f=0.1 and r=0.1. That is we suppose that for the old energy source 10% of our labor is dedicated to extracting energy, and the new energy source requires ten times the amount of labor to extract one net unit of energy. If we plug these number into [3] we find:

f’=.1/(.1+.1-.01)=.1/.19 = 0.526

That is we will now be dedicating 52.6% of our labor effort to extracting energy.

What will have happened to our total economic output of goods and services in the non-energy producing sectors of the economy? Since the energy/worker in these sectors of the economy is the same as it was before, it is reasonable to assume that the output per worker will be the same as before. To find the total productivity of the new economy relative to the old economy we simply have to take the ratio of the number of manufacturing workers between the two cases. In the old economy 90% of our workers were in the manufacturing sectors. in the new economy 100%-52.6%=47.4% of our workers are in the manufacturing sectors. The ratio between the two cases is:

47.4/90 = 52.6%.

That is the new economy will be able to provide nearly 53% of the goods and services provided by the old economy in spite of the fact that ten times the labor effort must expended per net unit of energy produced.

By the way, there is no reason to believe that his response to the higher labor cost of energy is optimal. If a reduction in energy/worker by X% results in a reduction in productivity/worker by less than X% then the above solution is not optimal even in the case of full employment. In the case that our economy contains a significant component of structural unemployment then reintegrating the unemployed workers into the economy would result in further productivity gains. I chose the above option because it fairly obvious how to calculate the relative productivity of the two cases.

If you believe (as I do) that the highly developed nations of the world are already producing and consuming far more economic output per capita than is necessary or desirable then this the prospect of this kind of reduction in economic output is not particularly disturbing. Of course if we woke up tomorrow morning and all energy prices had increased over night by a factor of ten the stock market would come crashing down in ruin. But if we were to abandon the orthodoxy that continuous growth is the raison d’etre of our economic being, we could easily to this ‘disastrous’ transition.

May 17, 2007