Abstract
The first step in understanding the economic metabolism is to account for the flow of materials through the economy and the exchange of materials with the biosphere. In this chapter, we develop a framework for accounting material flows and accumulation within economies. We begin by considering accounting in everyday life and continue with concepts from thermodynamics, such as system boundaries, control volumes, and the First Law of Thermodynamics, to develop a rigorous accounting framework. The framework is applied first to a one-sector then two-sector model of the economy as we construct a general framework for material accounting. We then apply the framework to the real-world example of the US auto industry.
Well, I have my rights, sir, and I’m telling you I intend to go on doing just what I do! And, for your information, you Lorax, I’m figgering on biggering and BIGGERING and BIGGERING and BIGGERING … [1]
—The Once-ler
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- 1.
The logic of the treadmill is:
-
a
Capital (production equipment) is accumulating in Western economies as labor is replaced by technologies;
-
b
These technologies require far more materials and/or energy than the previous, labor-intensive processes;
-
c
Moreover, unlike labor, the new technologies represent forms of sunk capital;
-
d
Because the remaining labor inputs can more readily be cut back (as opposed to sunk capital, see Sect. 1.3.3) labor is further reduced to sustain production at higher levels;
-
e
More capital is added to replace further reduced levels of labor \cite[p. 296]{bib8}.
-
a
- 2.
For the sake of absolute rigor, we must point out that, in actuality, iron is created within the core of silicon-burning stars. Mass and energy may also be converted in such processes, such that only mass–energy is conserved. However, for the purposes of terrestrial processes, the total mass (in kg) of atomic iron (Fe) is constant. There are, additionally, some economic processes, within nuclear reactors, that change the atomic structure of elements and thus violate the accounting law presented here. Because the mass flows involved with these nuclear plants is negligible compared with total materials flows, we shall assume that the mass of elements are conserved for this book.
- 3.
- 4.
Double subscripts on quantities (e.g., \(\dot{R}_{ij}\)) indicate a flow from sector i to sector j. The first index always indicates the sector from which a quantity flows, and the second index indicates the sector to which a quantity flows. Single subscripts on quantities such as K can mean one of two things: \(\dot{K}_{j}\) (with a dot to indicate a flow) refers to the outflow of capital within the product outflow from sector j, whereas \(K_{j}\) (without the dot) denotes the capital stock of sector j.
- 5.
See Footnote 8 in this chapter for more discussion on the inclusion of human beings as societal capital stock.
- 6.
While this inequality may be true in theory, it may be that in practice, the large amount of material, e.g., water or oxygen, that passes straight through the economy “unaffected,” i.e., without being embodied in products, is very large compared to the additional flow of short-lived goods produced within the economy, i.e. \(\dot{S}_{11} << \dot{S}_{01}\). This is a matter for empirical investigation.
- 7.
There is an open question as to what sort of stuff should be included within the capital that accumulates in society. Should the material constituting literal human capital—human bodies—be included? If humans are to be included within \(K_{1}\), some resource flow (\(\dot{R}_{i1}\)) must be converted into human capital flow (\(\dot{K}_{11}\)) which then adds to the stock of human capital (\(K_{1}\)) within society. This resource flow is food. Food itself represents a large “resource” flow and has a large associated energy content. Additionally, within industrial economies, a large amount of energy resources are channeled toward the production of food, meaning that the embodied energy of food may actually be several times larger than the direct energy content of the food itself.
Further questions arise. What is the “product” of society? A materialistic view might hold that the product of society is human bodies and the labor they can accomplish. If so, should the agriculture industry be accounted as part of the energy sector because its aim is to provide an energy service (labor)? For nonindustrial, agrarian societies, the proportion of total energy flow comprised by manual (or draft) energy may be large. In industrialized societies, it may be negligible, however, the energy flows necessary to support agriculture may be many times larger than the food energy (and certainly many times larger than the labor energy) delivered. Agrarian societies are necessarily constrained by the fact that the energy content of the food delivered must be greater than the labor (and draft animal) energy required to produce it.
Another view is that societal capital (\(K_{1}\)) includes only human-made capital, i.e., items manufactured by humans, but not humans themselves. For the purposes of the framework outlined in this book, we favored the latter view. Other researchers favor the opposing view bib11. However, the framework presented in this book is general enough to encompass either point of view.
- 8.
As such, we can deduce that the economy must always be a (wholly-owned!) subsidiary of the biosphere open to flows of materials both from (resources) and to (wastes) the biosphere. This fact has direct implications for dematerialization of our economies, which is discussed in reference to our framework in Sect. 8.4. There are fundamental limits to the amount of material that must be directed to desired end services. For example, automobiles must have a minimum level of embodied materials. Note that this minimum is likely many times lower than the mass of current automobiles, which are driven largely by preference. The Rocky Mountain Institute has done some work on the ultralight, “hypercar” concept bib14. Despite the drive to dematerialization and the apparent “unhooking” of the material and energy intensity of GDP, much of the dematerialization of “developed” nations has occurred by exporting manufacturing to other countries bib15. The material footprint of OECD nations, when weighted by consumption, has increased significantly since 1990 bib16.
- 9.
Note that such flows violate the “one sector-one product” assumption of the Leontief inversion method which we will use in Chap. 7. Other methods based on make-use tables, as developed by von Neumann bib17 and Sraffa bib18 are able to account for multiple products from each sector.
- 10.
\(\gamma_{K_{1}}\) has units of inverse time, e.g., 1/year, and is inversely proportional to the average lifespan of human-made capital.
- 11.
This depreciation term will be discussed in more depth in Sects. 5.2.3 and 8.2.2.2.
- 12.
In actuality, both \(\dot{R}_{11}\) and \(\dot{K}_{11}\) are zero, as will be discussed shortly.
- 13.
We assume that flow (\(\dot{S}_{12}\)) is the adenosine triphosphate (ATP), used as an energy carrier within the cells of organisms, which is consumed during activity (labor).
- 14.
A counter-example to this assumption is the production of food outside of the agricultural industry, i.e., by households, which may be large in agrarian economies.
- 15.
If we were assuming that the human population was accounted within \(\dot{K}_{1}\), then the “product” of Final Consumption (1) would be human beings (and the labor they provide), resource flow \(\dot{R}_{11}\) would be material resources provided to human reproduction and “capital goods” flow \(\dot{K}_{11}\) would be material added to the human population stock. Again, this issue is discussed in greater detail in Footnote of this chapter.
- 16.
There may be some exceptions to this, as in the case of energy from industrial waste streams.
- 17.
It is worth remembering here that \(\dot{R}_{01} = 0\;\text{and}\;\dot{R}_{21} = 0\), because Final Consumption (1) takes resources (in the form of food) from goods and services (3) only and that \(R_{32} = 0\) because the goods and services sector (3) does not provide resources to the energy sector (2).
- 18.
The issue of lack of physical flow data is discussed in several places in this book, especially in Chap. 9.
- 19.
In 2006, prior to the Great Recession, the automobile industry purchased 40 trillion kJ (\(4.0 \times 10^{13}\) kJ) of total energy and produced 4.4 million cars.
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Heun, M., Dale, M., Haney, B. (2015). Stocks and Flows of Materials. In: Beyond GDP. Lecture Notes in Energy, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-12820-7_3
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