Professor Steve Keen
Distinguished Research Fellow, Institute for Strategy, Resilience & Security (ISRS) at UCL

With the simple insight that “labour without energy is a corpse, and capital without energy is a sculpture”, I realised why economists have failed to properly incorporate the role of energy in production for so long. All previous attempts had treated energy as a third “factor of production”, on an equal footing with Labour and Capital. But that treatment is simply unrealistic.

Adding energy on its own to a production process is like letting off a bomb in a factory: it will produce mayhem, not output. Equally, both Labour and Capital are “sterile”, to use the old Physiocratic term: without energy, they can’t produce anything.

Figure 1: The incorrect way to show energy as a factor of production

The correct way to incorporate energy into economic models of production, therefore, is to see energy as an input to both Labour and Capital (in vastly different forms, of course), which enable them to perform useful work. By the Second Law of Thermodynamics, this useful work necessarily results in disorder (waste energy, mainly in the form of waste matter, including CO2). Also by the Second Law, entropy increases globally, even though it can be reduced locally by the application of energy; so the increase in disorder in the waste from production necessarily exceeds the reduction in disorder manifest in output itself (raw materials turned into finished products).

Figure 2: The correct way: Energy as an input to labour and capital, output as necessarily generating waste

This useful work is what we call GDP, though we currently erroneously measure this as the inflation-adjusted sum of all monetary output—which means we add the cost of traffic accidents to GDP. Instead, the true measure of GDP is the sum of all the useful things we produce and consume: in transportation, that is moving a mass from one location to another in a given time, and traffic accidents (and congestion) subtract from it.

This insight transforms conventional economic models of production into models of the transformation of energy into useful work. When applied to the workhorse “Cobb-Douglas Production Function” used in most Neoclassical macroeconomic models, it increased the significance of energy dramatically. In a three-factor Cobb-Douglas model (Labour, Capital & Energy) following the “cost-share theorem” (where each factor’s share of GDP also indicates its contribution to GDP), an 80% fall in energy input would cause only a 10% fall in output. The energy-based function makes the much more realistic assertion that only a 15% fall in energy inputs would cause a 10% fall in output (Keen, Ayres et al. 2019). The below diagram shows the relationship between GDP and energy input in both of these models.

Figure 3: Energy’s contribution to production is much higher than its share of GDP

“Matter to Gain, Energy to Maintain”

Working directly from thermodynamics, collaborator Tim Garrett realised that the economy could be treated like a growing child: a child needs a large energy input just to maintain bodily circulations within its current size and shape as it has grown from past production of body mass. Child development and growth requires using the energy in food to turn it into added body mass. This production then requires higher amounts of energy consumption.

He found an incredibly tight fixed relationship between GDP and the change in energy consumption each year:  each $1 of global GDP (in year 2005 dollars) between 1970 and 2015 required adding to existing primary energy consumption capacity an additional 7.1 milliwatts (Garrett 2012; Garrett 2014; Garrett 2015).

Figure 4: Garrett’s generalized analogy between thermodynamic and economic systems. This shows economic production as an expansion of an interface between civilization and its accessible energy reserves and a fixed relationship, ? between historically accumulated production, C and current energy consumption, a.

The third collaborator, applied mathematician Matheus Grasselli, is an expert in developing stock-flow consistent financial-economic and ecological models (Grasselli and Costa Lima 2012; Bovari, Giraudet al. 2018)

This project will allow these three researchers from very different fields—economics, atmospheric physics and applied mathematics—to work together to integrate their approaches, and to derive production functions that can be used by economists from all schools of economic thought. They will also extend and explore the implications of these two approaches for economics:

  • Most economic models work with the abstraction of an aggregate good called GDP, but in reality GDP consists of multiple different commodities, each of which has different waste impacts upon the biosphere. We will produce mathematical extensions of our simple aggregate models that acknowledge this;
  • One of the vexed issues in economics is measuring the amount of capital. It’s easy to add units of unskilled labour, since their work is easily measured in terms of hours of labour. But doing the same thing for different machines is problematic, because machines are so different: how do you add together a truck and a blast furnace (Harcourt 1972)? Our work implies one way this can be done, using energy, since all machines use energy to generate useful work; and by focusing on connections that dissipate energy along economic networks.
  • Our approach implies that the GDP could be measured in units of megawatts expressing the rate at which useful work is done. This would include stating human consumption needs in terms of different functions—food, clothing, shelter, transport, entertainment, etc.—and quantifying the amount of energy involved in each at different points in time;
  • Economic models today are generally divorced from the ecological impact of production and consumption. We will produce models in which the economy and the ecology are necessarily integrated via the dependence of the former on energy consumption, and the impact of that consumption on the latter;

Finally, this energy-based model of production has implications for theories of income distribution that relate incomes to the contribution of labour and capital to production—both Marxian and Neoclassical. The Marxian argument that labour is the source of surplus value fails because the energy input of unskilled labour is far below the energy-equivalent of the wage. The Neoclassical argument that the real wage is the marginal products of labour fails for the same reason. Theories based on the relative bargaining power of workers and capitalists are more sustainable.


To read more about this project, click here.

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07 May 2019