Steve Keen defines a production function based on energy

Professor Steve Keen may be the first mainstream economist to address a fatal flaw in economic theory: omitting or minimizing the role of energy. Keen has developed a production formula incorporating energy, not as one factor of production along with capital and labor, but as the indispensable flow activating both.

“Labor without energy is a corpse” says Keen; “Capital without energy is a sculpture.”

Keen was one of twenty or so economists who made a credible prediction of the 2008-9 crisis, which government economists in the US and abroad declared “unpredictable” – after it blindsided them. His work draws on contemporary economic theory and generates real-world predictions. He’s the sort of economist who financial commentators, investors and even government economists listen to; folks who haven’t heard of Daly’s steady state economy, Odum’s energy flow analysis of the ecosystem-economy, or Hall’s EROI “cheese slicer” model.

Keen’s model implies that economic production is measurable in energy units, as Odum and others argued. Wealth is “nothing but the food, conveniences and pleasures of life,” as the earliest economists recognized. But it results from useful work, which can be measured in kilocalories. (To us weight watchers, just “calories.”) Here is his fundamental equation (the only one here, I promise):

Y(E) = (K.EK.xK.eK)α . (L.EL.xL.eL)1-α

(If that seemed hard to read, try coding it in html.) It’s worthwhile to look at what goes into this equation, the product of a Capital term and a Labor term. Each of these terms is itself a product of energy flow and two small modifiers. To define the terms,

Y is useful work or GDP, a function of energy supply, in kilocalories
K is capital, as the number of machines employed
L is labor, as the number of workers involved
E is a flow of energy to the economy, to workers or to machines, in kilocalories
α is capital’s proportional contribution to production (labor’s contribution is 1-α)
x is Exergy, the proportion of E which is actually usable, always great than zero and less than 1. Per the second law of thermodynamics, some energy is always lost.
e is the efficiency of the process: the proportion which actually goes into production after the costs of maintaining the machine or the worker; always greater than zero and less than 1. Logically this factor should include whole life cycle costs, though I’m not sure if Keen intends this.

To test his model against real data, Keen correlated its results with historical statistics of US GDP, and then compared correlations of GDP with the key terms individually. Over 40-odd years of data, his function correlated 0.79 with US GDP. The correlations with employment (Labor) alone and energy consumption (E) alone were much lower, at 0.60 and 0.59 respectively.

His model might have correlated better if applied to a closed economic system, such as the entire world, or the US prior to 1970, if good data were available. Most of the useful work that supports Americans today is performed in the Far East or in the engines of container ships, and the energy inputs are considerable.

Introducing his test data, Keen remarked that government statistics showing minimal unemployment were “just nonsense”. He presented a measure of employment instead.

“They ask what Trump is complaining about- here’s what he’s complaining about..” (This was back in November.)

A decline of a few percent seems small, but two million fewer Americans in their working years have jobs than before the 2008-9 crisis.

Presenting a chart of industrial energy consumption 1960-present, Keen remarked on the on the long decline since the 1979 peak, his latest values showing consumption comparable to 1967-8. Partly the result of increased efficiency, he said, but also “..becoming intractable because we are moving from highly efficient oil and coal to much less efficient wind and solar.” (Efficiency as energy output per unit of energy input.)

I don’t think I’m overstating to say that Keen’s model marks a breakthrough in mainstream economics, though Keen describes it as merely

“..the beginnings of a decent equation to explain the role of energy in production.”..demonstrating that wealth is “..fundamentally created by the exploitation of free energy, as the Physiocrats argued two centuries ago.”

For those who discount any economic reasoning not expressed in calculus, Keen’s work opens an access to the wisdom of the Physiocrats. Maybe that of Daly, Odum and Hall as well.

Nearly all I’ve said above is taken from Keen’s lecture on You tube, which I highly recommend. There’s a lot more there, including deep historical background and comparisons with contemporary economic theories. If you haven’t listened to a real science lecture since college, it may wake up some brain cells.

Postscript
Having called Keen a “mainstream economist”, I now notice in his blog that he contrasts himself with mainstream economists and complains of a strong institutional bias toward the Neoclassical school. He’s asking for support via Patreon, partly to continue his work on energy-based economic modeling (I signed up.) Still, he’s a lot more mainstream than the environmental scientists I mentioned above.

References
Steve Keen, “The role of Energy In Production”, https://www.youtube.com/watch?v=BAjN6bG7XzM

Charles Hall and Kent Klitgaard, 2012, Energy and the Wealth of Nations: Understanding the Biophysical Economy

Herman Daly and Joshua Farley, 2010, Ecological Economics, Second Edition

Howard Odum, 1971, Environment, Power and Society, also 2007,
Environment, Power and Society for the Twenty-First Century.  The earlier version speaks of energy in familiar, common-sense terms, with all the ambiguity that that implies. The later version introduces the term “emergy” (SIC) and a set of related terms. It’s unambiguous and scientifically correct, but hard to read unless you’ve internalized the emergy terminology.