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Integrating Macroeconomics and Ecology via Energy and the Laws of Thermodynamics

by Steve Keen

One of the glaring weaknesses of economic models of production, from all schools of economic thought, is the absence of any explicit treatment of the role of energy in production. Consequently, economic models fail to conform to the unbreakable Laws of Thermodynamics. Garrett and Keen independently came up with ways to remedy this weakness.

Atmospheric physicist Garrett applied insights from the thermodynamics of clouds to describe human civilization as a heat engine, which functions by isolating energy reserves from the environment, and then exploiting the gradient between these high potential energy (“low entropy”) reserves and the lower potential energy (“high entropy”) environment. This enables human civilization to exist, and develop over time, at a level of energy consumption and organization well above the background level of the environment itself: (Garrett, 2011, Garrett, 2012a, Garrett, 2012b, Garrett, 2014, Garrett, 2015).

Economist Keen applied the insight that “capital without energy is a sculpture, labour without energy is a corpse” to modify existing economic production equations so that energy was shown to have its critical role in enabling useful work to be done—which is otherwise known as GDP (“Gross Domestic Product”): (Keen et al., 2019).

This project enabled these two related but different approaches to making economics consistent with the physical laws of the Universe to be developed further with the assistance of mathematician Matheus Grasselli.

Garrett’s thermodynamically-inspired mathematics postulated a relationship between total accumulated human wealth—the integral of GDP over time—and energy consumption. This is analogous to how a child’s daily energy consumption predominantly maintains its existing body mass, and also allows a small amount of daily growth. This led to “the Garrett Relation” between the integral of GDP over time and energy consumption now, which was empirically confirmed, with a constant 5.9 gigawatts of energy per trillion US$ worth of accumulated wealth closely fitting the last 40 years of economic and energy data—see Figure 1.

The collaboration enabled a significant refinement of Garrett’s mathematics, and also explored whether the relationship could be between the integral of investment over time and energy consumption (“the Grasselli Conjecture”), rather than the integral of GDP over time. This would be much closer to existing economic models, since it implies a constant relationship between Capital (the integral of Investment) and energy consumption, but the empirical relationship was not stable as with the Garrett Relation. We hypothesized, however, that this might be due to deficiencies in the current measurement of capital, a topic we plan to explore in future research.

Keen’s insight had originally been applied to the Neoclassical “Cobb-Douglas production function”, and had not been incorporated in an economic model. The collaborators found that the rival Post Keynesian “Leontief production function”, with a linear relationship between energy and GDP, fitted the economic and energy data far better than the Neoclassical nonlinear relationship even when a much higher coefficient was used for capital (and energy), as recommended by Mankiw (Mankiw et al., 1995).

Figure 2: Change in energy consumption per year and GDP change per year (1970-2017). 0.83 correlation coefficients

We developed two models, one where raw (“fossil fuel”) energy was the input and the outputs were useful energy and waste energy, and another where the inputs were energy and a raw material, and the outputs were a processed material, and both waste energy and waste matter—see Figure 3.

Both models enable an integration of economics with ecology, via the inevitability of the generation of waste matter and energy from production, the impact of the former (both in bio-degradable and non-degradable form) on both the ecology and the productive capacity of the economy, and the depletion of matter and non-renewable forms of energy.

In future research, we plan to extend this model to multiple commodities and energy types, (including renewable energy), and with price, income distribution and private debt dynamics.

This cross-disciplinary collaboration between an economist, a mathematician, and an atmospheric physicist was both highly enjoyable and highly productive, with one published paper already (Garrett et al., 2020) and several others in process.


GARRETT, T. J. 2011. Are there basic physical constraints on future anthropogenic emissions of carbon dioxide? Climatic Change, 104, 437–455.

GARRETT, T. J. 2012a. Modes of growth in dynamic systems. Proceedings Of The Royal Society A: Mathematical, Physical And Engineering Sciences, 468.

GARRETT, T. J. 2012b. No way out? The double-bind in seeking global prosperity alongside mitigated climate change. Earth System Dynamics, 3, 1-17.

GARRETT, T. J. 2014. Long-run evolution of the global economy: 1. Physical basis. Earth’s Future, 2, 127–151.

GARRETT, T. J. 2015. Long-run evolution of the global economy II: Hindcasts of innovation and growth. Earth System Dynamics, 6, 655–698.

GARRETT, T. J., GRASSELLI, M. & KEEN, S. 2020. Past world economic production constrains current energy demands: Persistent scaling with implications for economic growth and climate change mitigation. PLoS ONE, 15, e0237672.

KEEN, S., AYRES, R. U. & STANDISH, R. 2019. A Note on the Role of Energy in Production. Ecological Economics, 157, 40-46.

MANKIW, N. G., PHELPS, E. S. & ROMER, P. M. 1995. The Growth of Nations. Brookings Papers on Economic Activity, 1995: 1, 275-326.

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