Human Energy Accounting

by David S. Lawyer mailto:davylawyer1@gmail.com More energy articles by David Lawyer

Aug. 2013 (original March 2007)
In-progress. When trying to estimate the energy it takes to make something (or provide a service), it's not clear how to account for the human labor energy that went into it. This article examines this dilemma and shows that accounting for human energy depends on how it's defined, etc. It develops a "company town analogy" which shows that labor energy for production may be much higher than many think it is. The high energy of "surplus" is explained and illustrated by a feedback model, which reaches similar conclusions.

1. In Progress and Changes; Author's Notes

2. Introduction

3. The Company Town Analogy

4. Mining Town Example (EROEI)

5. Other Examples of Economic Communities

6. A Pair of Company Towns (feedback)

7. Surplus, Feedback, Savings, and Net Production

8. Network of "Economic Communities" (briefly)

9. Embodied Energy in a Fuel

10. The Input-Output (I/O) Model

11. Direct Solution of the Energy to Make a Good

12. Opportunity Cost of Labor Fallacy ?

13. Alive Anyway Fallacy; Job Change

14. What Purposes Does Energy Serve?

15. Appendix: Motivation

16. Appendix: Renewable Energy, Food and Human Energy Examples

17. Appendix: Land, Labor, and Capital

18. Appendix: Embodied Energy

19. Appendix

20. Appendix: Fuel to Make Food

21. Appendix: Number of Service Workers per Production Worker

22. Links, Journal Articles, and Books


1. In Progress and Changes; Author's Notes

1.1 Motivation, Progress, and Changes

While between 2010 and 2013, no progress was made in finishing this article, the author resumed work on it in Apr. 2013 due to a letter received from a reader and also due to finding out that it was cited in the book "Genetics, Biofuels, and Local Farming Systems".

In 2013 I added material on surplus production and realize that surplus production doesn't always go towards the obtaining of surplus type goods. Explicitly included excess leisure time as a good. But work on it ceased in 2014 and I'm now working some on it in 2015.

The "company town analogy" which I thought up in Aug. 2007, was a major breakthrough which brought significant changes. Then in Sept. 2007 I realized the dual nature of output energy from a mine: caloric and embodied and finally think I've got a better understanding of it which I'm in the process of explaining (including formulas for feedback). See Network of Company Towns. I'm also pondering the ultimate purposes of energy. See What are the Ultimate Purposes of Energy?.

In Apr. 2008, I realized that I had failed to show how to account for renewable energy and also failed to emphasize that the required input to a "black box" per unit output is not in terms of embodied energy but in terms of real energy and real commodities. As fossil fuel becomes more and more difficult to extract from the earth, the amount of embodied energy per MJ of fuel will increase. Likewise for the embodied energy in other goods. So more embodied energy to "black boxes" will be required per unit output in the future.

Then in Dec. 2008 I became aware that if one adheres to an input-output model, changes in jobs of existing workers is not permitted. Later on, I began to realized that energy doesn't necessarily have a "purpose" as I had previously assumed. I further realized the the liner I/O models is not realistic except for small scale variations. I'm now adding some of these thoughts to "Author's Notes", and hope to add them to the article.

I'm perhaps 2/3 done writing, researching, revising and proofreading this multifaceted and complex article. I once wrote: In addition to the problems mentioned in the above paragraph, you'll likely find some typos, some lack of continuity, repetition of arguments, poor organization, some lack of clarity, and failure to fully evaluate and compare the various accounting methodologies. You also may find "to-do", "to-finish", "get-ref" or "fix-me" where more work is needed and where there may be a break in continuity. But as of June 2013, it's much improved and not quite as bad as the above implies. Even when it's 100% finished, I hope to continue to come up with some new ideas and clarify old ideas so it will still be sort of a working paper for some time. But if you do find factual errors, let me know.

1.2 Author's Notes re Needed Improvements in this Article

These notes are temporary and will eventually be removed.

What is the energy content of non-surplus?? Math. for the I/O model has been done, but what does it all mean?

Use the name "economic community" instead of "company town" if it isn't similar to a town. Partially done in June 2103.

Flows are really flows of material goods. Energy (real and embodied) are only attributes of the goods. Co. town requirements are in units of physical goods.

Need examples of catastrophic results for failure to count human energy.

There are different ways of defining "embodied energy".:

The same commodity may have widely different amounts of embodied energy (per unit of commodity). For example the embodied energy in oil from a new conventional oil well in a high-yield field is much lower than that of oil from a slow running old well, or from one where high energy intensity is required to extract the oil (such as "secondary recovery") or drill the well (such as fracking or undersea oil). Does this make sense? How is it accounted for? It leads to marginal analysis.

Two town examples: Sustainability (long-run, short-run). Types of infeasibility.

Due to problems of allocating fuel energy between human life for its own sake and the products created by human labor, there is likely no reasonably precise definition of embodied human energy. Does this imply that there is no solution to the question of embodied energy flows and how to allocate human energy between products and life itself? Perhaps there is no conflict here, since while the same energy may have multiple purposes, it doesn't imply that one could save double this energy by eliminating both purposes. In other words, it may be meaningless (in some [or all] situations) to talk about the purposes of energy.

Paradox of self-sufficient Co. town or farm family that accumulates an unbounded amount of embodied energy since there are no sinks for such energy. This is a case of no surplus or luxury goods. Case of negative surplus.

2. Introduction

Today it's very important to estimate the amount of energy it takes to to make a good or service. And part of this energy consists of human labor. It turns out that just asking how much energy it takes to make something is a poorly poised question and thus has no definite answer even if one had full knowledge of the technology of production, etc. A more precise question as to the energy it takes to make something, needs to also specify what other activities are allowed to vary and what is to remain constant. Details and examples will be presented later.

while accounting for human labor is often neglected or significantly underestimated in current energy accounting estimations, it turns out to be quite significant. Human energy accounting is obviously part of energy accounting so much of this article will discuss energy accounting in general with emphasis on the accounting of the human energy component. If you're not already aware of just how significant this problem is, see Appendix: Motivation

The standard economic textbook explanation is that goods and services are the result of 3 basic factors of production but that model is not suitable for energy. See Appendix: Land, Labor, and Capital. But it's obvious that to make a good or create a service (like teaching, retail sales, etc.) requires energy. But how does one calculate that? The energy it took to make a good (such as automobile) must obviously include the energy it took to make each of its components (such as tires, headlights, etc.). And each component has components and so on ad infinitum (as will be shown later on). The infinite number of energy inputs doesn't imply an infinite amount of energy since it amounts to a converging infinite series where the sum is finite. Everything that directly or indirectly went into the making of the good needs to be counted, including human labor. But there are serious problems and dilemmas on just how to account for this human labor.

One way to estimate this is by use of Input-Output Analysis. This (in theory) would show the quantity of components it takes to make each good. For example to make an automobile might require: 4 passenger car tires, 2 quarts of paint, 371 kilowatt hours of electricity, a 1 liter engine, etc., etc. To make the engine might require: 4 spark plugs, 13 pounds of aluminum, 137 pounds of steel, etc. But conventional Input-Output Analysis neglects human labor inputs and thus fails to account for one of the most energy-intensive components of production: human labor.

When someone does a task (such as working at a paid job) it takes energy, but how much? How should the energy content of human labor be defined? It's easy to just calculate how much nutritional energy is expended by calculating the Calories of food energy one burns. But for every Calorie of food one eats it takes roughly 10 or more Calories of fuel energy to make, transport, and cook the food. See Appendix: Fuel to Make Food. But isn't much of what one does when one's not working used to support ones work? For example, for every hour one works, about 1/2 hour of sleep at night is required which also burns Calories. So perhaps all the energy used to keep a worker healthy and happy should be allocated to the energy expended at work. This is not just food energy but includes the energy it takes to build and maintain housing, transportation, and other infrastructure as well as provide services to the worker such as government, medical, financial, repair, and retail trade services. Thus the energy input needed for human labor may be quite high.

In opposition to this view is the argument that a worker is going to be alive and use up energy in living anyway, regardless of where he works, including the case where the worker was or will be unemployed. This will be called the "alive anyway" argument. This point of view, which implies the energy cost of human labor is low, has some merit as well as serious problems with it which will be discussed later. get-ref

Now returning to the high human energy cost point of view. The energy cost of services, of course, includes the energy cost of the human labor that provides these services. Not only that, but both production and service workers themselves require services, etc., etc. Should not some (or all) of this human energy be allocated to the worker who receives such services, thereby enabling him/her to be more productive at work? And again, the energy that these service people expend is not just caloric food energy since they also require shelter, clothing, transportation, information, education, etc., all of which require energy.

Some of this energy to support human life becomes embodied in people (and is one form of "embodied energy"). It's far more than just the caloric value of their physical bodies or the direct chemical energy it takes to create and maintain those bodies (human capital). Even the knowledge people store in their brains took a lot of energy for them to acquire, in addition to the energy it took by society to create and pass on such knowledge. In writings about embodied energy it is usually described as embodied in physical goods or services. But for this article it's also embodied (or embedded) in human beings too. See Appendix: Embodied Energy. However, it turns out that exactly defining embodied energy is partly subjective and it is partly dependent on the problem we are trying to solve.

At first glance it seems that trying to find a reasonable method of estimating the energy content of human labor is an overly complex and subjective task which is difficult to comprehend. But there's a way to frame the problem and to transform the economic geography of the problem so as to be able to better understand that human energy embodies much more than just the energy value of food intake. This method (way) is what I call the "company town analogy" where all the people and capital needed to produce something are concentrated in an isolated "company town". This model will show that the energy cost of human labor is high, thus implying that something must be wrong with the "alive anyway" argument.

3. The Company Town Analogy

3.1 The Model Overview

First we'll make a simple model and later extend it so that it will be both more realistic and cover more situations. This will result in relaxing some of the restrictions imposed by the simple model.

The simple "company town" model is formed by taking a production facility like a factory, farm, or mine and placing it inside an isolated "company town". The town will be solely devoted to the production of just one good from that factory, farm or mine. The sole product made in the company town (such as automobiles, food, or coal) will all be exported out of the town to the rest of the world. The town also houses all the workers needed to make that product including the workers' families and service people needed to provide services to the workers and their families. Note that it is self-supporting and not relying on outside subsidies for its support.

Into the town (from outside) will come all the goods needed to support the town and its one industry. The town will conceptually have a fixed boundary fence and only one gate thru the fence for goods to enter and exit. After the town is populated with people, people do not flow across the town boundaries. To maintain steady population, babies, children and families are raised inside the town. As people retire from work in this company town, they continue to live in the town until they die. It's postulated that the town be in a steady state equilibrium with only enough capital goods flowing into the town to replace worn out capital and with births equalling deaths so as to keep the population constant.

This company town is intended to be a model of production in the real world of today and to use approximately the same amount of energy (as the real world does) to produce the product made in the town. Thus the lifestyles of the people who live in the company town should mirror the lifestyles in real society. For example, the long commutes by auto that take place in the real world will continue to happen in this hypothetical company town (at least on paper) even though they would not otherwise be necessary due to the compactness of most company towns.

A company town could, in some cases represent a vertically integrated industry such as the production of corn-ethanol which requires a town with both farms to grow the corn and an industrial plant to turn the corn into ethanol. In this case the town is large and includes much farmland.

This simple company town model could be extended later on to permit:

But first we'll present the simple model without these extensions.

3.2 Flows Thru the Town Gate

While the model will give the same results if flows in and out of the town were just across its boundary at various locations, a fenced boundary with a gate make it easier to visualize. For the single commodity "company town", there is only one flow out the gate and that's the product made by the town factory, farm, or mine. If such an output flow is an energy good, like ethanol, coal, or crude oil, then the energy content of all the input flows combined should be less than the output flow if the town is to yield a positive "energy return on energy invested" (EROEI or EROI). If it can't yield a positive return but instead yields a negative return, then this town is parasitic on the rest of the world for energy and requires an energy subsidy from the rest of the world but contributes nothing to pay for this subsidy since it only "exports" one commodity to the rest of the world. The "boundary" case where the energy input is exactly equal to the energy output (EROI = 1) will be discussed later. get_ref

The energy flowing into the town includes the energy embodied in the consumer goods for all the people in the town. Also, the supplies, equipment, and energy for the industry in the town flow into it and these all contain embodied energy. The input flow includes goods to maintain and replenish the infrastructure in town including housing, transportation, commercial and public buildings, etc. Utilities like electricity, natural gas, and water flow into the town thru the meters at the town gate and is part of the input flow to the town.

What about the case where the output of the town is not a fuel? It would seem that the energy embodied in the output should be at least equal to the energy embodied in the input, just like the case when the output is an energy good like ethanol or coal. But to establish this we`ll need to wait until later when we attempt to connect up all the inputs and outputs of a number of company towns into a network.

This model makes it clear that to produce the commodity that the town exports, not only must the production workers in the town be supported 24 hours a day, 7 days per week, but all the other people in the town must be supported too: medical workers, utility workers, retail trade workers, financial service workers, government employees, homemakers, children, teachers, retirees, etc. All of the material support for the town comes from outside the town thru the town gate. It represents the input energy cost of obtaining the exported commodity. The part of this material support that supports the lives of the people in the town represents the human labor energy cost of producing the export commodity.

3.3 What Economic Activities Happen in the Company Town?

Since the energy flows into the town from outside become embodied in the output good of the town, the more energy-intensive the lifestyle of the people in the town, the higher the energy cost of producing the output of the town. This is assuming that the higher input energy to the town is less than fully compensated for by higher worker productivity which may not be the case for a town where most workers are living in poverty.

The flow of goods and services into the town also supports some "surplus activates" not essential to the production of the town's product. "Surplus activities" in the town include waste (or all types), criminal activity, harmful drugs, gambling, luxury goods, and the support of parasitic people: non-working owners of assets in the town, people on "welfare", prisoners, people wrongfully receiving disability pensions, the homeless, etc.

One may claim that since these surplus activities don't contribute to the output production of the town, we shouldn't count the energy inputs to support them. But if the town is to mirror the real social structure of society, these surplus activities exist and do accompany production.

It would be of interest to look at two models, one where we have an ideal society with a minimum of wasteful "surplus activities". Human nature being what it is, there will likely always be some waste, cheating, criminality, etc. The other model would mirror the "surplus activities" of the real world for company towns. Note that surplus in the broad sense includes the accumulation of capital goods, works of art, pure science, astronomy, space exploration, etc. all of which represent ultimate consumption which may be represented as sinks for some of the output of company towns.

The support of government, whose services are allocated to the output to the town product, includes both local town government and the town's share of county, state, national, and international government. This obviously includes the military including the support of national troops at home and abroad including support of any military or "peacekeeping" units of the United Nations. The justification for this is that for the town to be safe from possible harm, military protection and law enforcement of international scope is needed. Although such activity actually takes place outside of the town, the model assumes that the town's share of such activities takes place within the town, based on the concept of placing everything needed to support the production of the town within the town. Thus there will be some military, troops, United Nations personnel, etc. living in the town. For the support of such personnel, there will be input flows of goods into the town, including military equipment and supplies. Counterproductive military expenditures (such as possibly the Vietnam and Iraq wars) should be classified as waste under the previously mentioned "surplus activities". Of course non-local governments provide much more than just military services so the town's share of all of these will be located in then town and there will be input flows of goods and energy to support them.

3.4 Human Energy Expenditure for Production

For labor that contributes to production, what is the energy content of it? In the company town, all the inflows of goods, other than those that are direct input to the town's one-product (exported commodity) industry, are for support of the people in the town. The town's population consist of the production workers who make the town's single product and the people dependent on the production workers: service workers, spouses, children, retirees, etc.

Let's define the gross energy per person as the total energy used by society divided by the total population. For the U.S. the energy used per persons is about 120 times food calories. See Food-calories are what percent of fuel energy. In the examples, a figure of 100 times food calories is used. But this figure needs to be increased a few fold to account for the service workers and dependents that are needed by production workers.

The example of a mining town in the next section will present a more concrete example of the energy flows of a company town. This mining example illustrates general principles applicable to the energy flows of all other kinds of goods and services so you don't want to skip it even if you have no interest whatsoever in mining.

4. Mining Town Example (EROEI)

4.1 Introduction

This example is for a hypothetical coal mining operation at a remote location. But it illustrates the general case for a plant or firm that exports its product to the rest of the world outside the company town. It will also look at the question of "energy return on energy invested" = EROEI. Before starting up the coal mining operation, It will be necessary to build a mining town to house the miners and recruit both miners and support personnel to populate the town. The town will produce only coal and export it to the rest of the world.

Normally the criteria on whether or not to go ahead with the project would be profitability. Will the cost exceed the income obtained by selling the coal? For it to be profitable, it would seem that it also must have a positive return on the energy invested in the project (EROEI). So let's examine the EROEI question: Will the coal exported from the mine contain more energy than the energy used to operate the mine and provide for the miners, including energy depreciation of capital investment in the mine, housing, and utilities, etc.?

It will take energy to build a mining town and to provide amenities. The project will require not only miners but service personnel to provide services to the miners: medical workers, food workers, utility workers, repair people, store clerks, government workers, etc. It will also require that a flow of consumer goods (including food), hardware and building materials, transportation vehicles, etc. be sent to the mining town to support both the miners and their service workers. Actually, if it's going to be a sustainable society in the mining town, the miners will need to reproduce and raise children so the town needs to support not only miners and service workers but also their spouses and children. And the retirees from the town need to be supported. The first model to be presented will neglect families and retirees but later models will include them.

4.2 Energy flow diagram (no families or retirees)

This is a model of energy flows for a plant producing a single good. In this case it's a mine producing coal and is shown in Figure 1 below. Flow is the flow of energy per day per miner. It shows energy flows of mostly embodied energy. One unit of flow is the energy needed to maintain one person (about 100 x 2500 kcal/day or about 1.4 GJ/day). See energy per capita. Flow volumes marked with a "*" are flows from world outside of the mining town. The output flow of 4 units of embodied energy is marked with a "+" to remind one that to this embodied energy one may add the caloric value of the coal mined by one miner. The utility of the coal only depends on it's caloric value and not on the embodied energy used to mine it. It's assumed that for each miner, 0.5 of a service worker is required to provide services to the miner. Likewise, each service worker requires the services of 0.5 of a service worker.


                    ____________________     ________________      
                 1  | Production Worker|  2  |   Plant      | Product 4+
               |--->|     (miner)      |---->|   (mine)     |-------->
               |    |__________________|     |______________| (coal) 
       *2      |             /\Services to           /\
------->-------|            1 | Production Worker     | Supplies,
Consumer Goods | 1  __________|________             *2| Parts, Machines
+Housing,      |--->| Service Worker  |-->--|         | Energy, etc.
+Utils, etc.        |   (server)      |     |
                    |_________________|     | 0.5
                                   |  0.5   |   
                                   |---<----|
                    Services of Service Worker to Self

    (note all flows are energy, 1 = gross energy for one person)
           Figure 1: Company Town Energy Flows

4.3 Service Worker

The "Service Worker" shown in Fig. 1 represents the total services provided by a large number of service workers, since only a tiny percentage of an actual service worker's total working time is devoted to the miner. Likewise for the part of the service worker that provides services to the service worker that serves the miner. Since each service worker actually requires some services from a large number of other service workers, each of which require services and so on ad infinitum, it's likely that the "service worker" in the figure represents the amalgamation of services provided by millions of service workers. Many of these services are provided by telecommunication such as financial information, printed and internet information, etc.

Note per Fig. 1 that to support the miner, one service worker (server) is required. But we previously stated that the miner only needs 0.5 servers. There's no conflict here since a server also needs services and the 0.5 of a server who in turn will require 0.25 of a server to support her. Then this 0.25 of a server will require 0.125 of a server, etc., etc. The infinite series sum of all this ( 1/2 + 1/4 + 1/8 + ...) is one server. Thus a whole server is needed even though the miner only uses the services of 1/2 of a server. This is equivalent to the service worker needing to use 1/2 of her service effort to provide services to herself so she is only able to offer the surplus half of her services to the miner. The miner is charged the full energy cost of this server. This is represented by a flow of 1 from the server to the miner. If there wasn't a miner there would be no need for this server.

The loop of value 1/2 in Fig. 1, which flows both from and to the service worker, represents the work that the server does for herself. One might ask why the service energy input to the miner is 1 but the service energy input to the server is only 1/2 (provided by herself).

If a miner requires one server, why doesn't each server require another service worker? Well, a service worker that only provided services to others would in fact need another server to provide her with surplus services. But in the miner example, just 1/2 of a server provides all her services to the miner so then another 1/2 of a server is needed to provide surplus services to the 1/2 server serving the miner. Another way of stating this is that a server that provides herself with all her needed services doesn't need any other server to provide these service needs for her.

4.4 Recycled energy

The miner has a total input energy flow of 2 while the server has a total input energy flow of 1 1/2. Yet the external input energy flow to support these 2 persons is just 2 (1 per person) as it should be. How can the total input energy flow to these 2 persons be 3 1/2 ( 2 + 1 1/2 )? Because some of the original input energy obtained from outside the mining town is "recycled" within the mining town. All the outside-world energy input to the server gets recycled into the energy input of the miner. Half of the energy input to the server gets recycled to herself (as shown in the loop). This is an example of a general principle for embodied energy: the sum of all the energy inputs to people can be much larger than all the energy produced in society.

This recycling of energy could also be called "pass thru" It's something like recycling paper. The total production of paper can be much larger than the original production of paper from wood pulp, etc. due to recycling. Something like this happens in the natural world of wild animals where the total input calories eaten by animals is greater than that supplied by plants, since some animals eat other animals thus recycling food energy.

4.5 Embodied Energy Intensity (EEI)

Embodied energy itself is not a benefit but a liability since it represents here the fuel energy required to make commodities. The specific embodied energy (per unit of good) is known as the "embodied energy intensity". For example, if a kilogram of flour takes 200 MJ of energy to produce (including human energy) then we say it has an embodied energy intensity of 200 MJ/kilogram. If it takes 10 kcal of fuel to create 1 kcal of food, then the EEI is 10/1 = 10 kcal/kcal or just a factor of 10 (unitless).

Fig. 1 shows a total input of 4 units of embodied energy to the mining town. But this is only true if the input flows of goods to the town have assumed fixed embodied energy intensities. A more precise model would specify the inputs to the town in terms of quantities of real goods and not in terms of embodied energy. Then if we know the embodied energy intensity (EEI) of each such good, we merely multiply each input flow by its corresponding intensity and sum the results to obtain the total input embodied energy. In this case, if the EEI's of the input commodities change then the efficiency of the town's output changes: high input EEI result in a high output EEI and conversely. Before inserting this town into a network of "company towns" with each town supplying goods to other towns, the inputs need to be specified in terms of real values. But even without this, the model is of significant use in illustration the accounting for human labor.

For example for Fig. 1, suppose the 4+ output is 4 units of embodied energy plus 4 units coal fuel energy (caloric). Then the total embodied energy output is 8 but there is only 4 units of useful output flow so the EEI is 8/4 = 2 MJ/MJ. This means that to get 1 MJ of output, it takes 2 MJ of fuel from the earth. This result holds only because the inputs are specified in units of embodied energy. But if instead we specified inputs in terms of real quantities, then the EEI of 2 for the output of the town would vary with the EEI of the inputs to the town. For example if the input to the town was specified as 4 units of real fuel energy, then this could be obtained from the 4 units of fuel energy output from this town. The result would be no net energy output from the town with the EEI of infinity for the zero net output. The meaning of this is that as the net output is reduced by increasing the input requirements to almost 4, the EEI becomes arbitrarily large (approaches infinity).

4.6 Flows of Money, Goods, and Services

This pertains to all energy flow charts like Fig. 1. People and organizations pay for energy flows going to them, so the flow of money is in the opposite direction to energy flow. Thus money flows in the reverse direction of the arrows. The flows of energy may be flows of goods or flows of human mental and/or physical energy. One may take the ratio of the flow of money to the flow of energy and find a "price" for the energy (say in $/MJ). If a certain flow of energy increases due to an increase in the flow of an item (a good or service) the flow of money increase proportionately.

Since a good contains more that just embodied energy, part of the price one pays for a good is to pay for its non-energy content, unless one believes in the "energy theory of value". But there is also an "energy and material theory of value" which would include the value of scarce minerals contained in the good which becomes embodied in the good just like energy does.

Since there is often statistical data available for the flows of money but not for embodied energy, there is a temptation to try to estimate the unknown flow of energy from the known flow of money. To do this one needs is an estimate of the flow ratio of energy to money ("energy price").

In most cases, neither purchasers nor sellers of goods and services try to explicitly evaluate the embodied energy contained in an item. But indirectly, the price of an item reflects (to a certain degree of approximation) the embodied energy. Actually, the %/MJ will vary from item to item but it may not be feasible to estimate this variation. So one can attempt to estimate an average "energy price" and use it to find an estimate for the flows of embodied energy. This is frequently done.

4.7 The Service Economy

The service worker in Fig. 1 actually represents the whole collection of service workers (servers) in the company town and the miner represents all of the miners, including management and office staff. But it's simpler just to make the chart for one miner and one server that would need to be a jill-of-all-trades if there was actually only one server.

But the service economy includes not only the labor of servers but the consumption of material goods needed for services. For example, the provision of medical services includes not only doctors, nurses, and secretaries, but consumes office space, utilities, medical equipment and supplies (including medicines). Where are these shown in Fig. 1? They are part of the consumer goods, etc. input to the miner and service worker. These material goods are part of what is called here energy per capita while the service worker's labor is not part of this per capita energy since it's recycled energy.

Why are services different than goods in this model? It's because services are part of the local company town economy and are not exported to the outside world. It's also possible for a company town to be built around a company that exports services such as providing customer support by telephone or a resort for out-of-town tourists.

The flow chart only shows those services where the server works for pay. Most people provide some of their own unpaid services such as preparing their own food instead of eating out. Do-it-yourselfers also provide their own services for home and auto maintenance and repair, etc.

Dual nature of output energy (brief)

For the mining town, the coal output energy flow has 2 parts to it: The flow of the coal itself which may be represented in energy terms by its caloric value and the virtual flow of embodied energy used to mine the coal (4 units, including 2 units of human energy of the miner). The caloric value of the coal represents it's use value. But the embodied energy to make the coal, represents the energy it took to mine the coal (including human labor). The total embodied energy is the sum of these values and is consumed when the fuel is used. If we look at a fuel (such as coal), caloric energy is generally a benefit while the embodied energy to make it is a cost. This distinction will be dealt with later when a network of company towns is discussed. See Embodied energy in a fuel

4.8 Interpretation of the Company Town (miner) Model

Support for humans goes to mine coal

What this model shows clearly is that all the energy used by both the miner and the service worker must be counted. If the energy supplied to this mining town is not paid back by the coal output, then the mining town must receive an energy subsidy from elsewhere.

For the mining to produce an energy surplus for society there needs to be a a positive energy gain (the ratio of energy returned to energy invested should exceed one). This means the energy flow of coal out should hopefully be significantly larger than 4. But even if it yields a positive return on energy invested, it's not necessarily socially beneficial since burning coal results in pollution (including CO2 which causes global warming) and deprives future generations from using it due to depletion.

4.9 Including Families in the Mining Town

For society to be sustainable it must reproduce itself. This means that both the miner and service worker needs to support a family with children to replace both them and their spouses when they die. While due to the current overpopulation it may be desirable to have less children, eventually generating the replacement amount of children (slightly greater than 2 per woman) will be needed for human life on earth to be sustainable.

So to this mining town we need to add families with children and then estimate the energy inflows from the outside world that it will take to support them. Here's an example based on the addition of families to the previous no-families mining example.


                    ___________________     _______________  Product  ?6
                 2  |Production Worker|  4  |    Plant     |----------->
               |--->|(miner) & Family |---->|    (mine)    | (coal)
               |    |_________________|     |______________| 
       *4      |             /\ Services to Production  /\  
------->-------|            2| Worker's(miner's) Family | Supplies,
Consumer Goods | 2  _________|________                  | Depreciation,
+Housing,      |--->| Service Worker  |-->--|         *2| Energy
+Utils, etc.        | and Family      |     | 1         |
                    |_________________|--<--|             
                                         1  
                    Services of Service Worker to Self

    (note all flows are energy, 1 = flow of energy per capita
      Figure 2: Company Town Energy Flows (includes families
Comparing this with Fig. 1 shows that the flow of input consumer goods, housing, and utilities has doubled from 2 to 4. This has assumed that with families, the mining town's population doubles. If the both the miner and service worker take a spouse and has 2 children then the number of people quadruple. But in reality, adding families may only be equivalent to about doubling the population because:

See Appendix: Number of Service Workers per Production Worker for some mathematical derivations and examples.

In this example, the energy flow to the miner & family due to services has doubled from 1 to 2. The additional person represents a fraction of a (non-employed) spouse plus a fraction of a child. But the provision of services to the miner family is still only 1/2 of a service worker (the same as just for the miner alone). The reason the energy flow doubles is because the miner's family now has to bear the burden of the additional energy to support the service worker's family. The miner's family of 2 persons (including the miner) is assumed to require no more services than the miner alone since the miner's spouse provides some services to the family and herself. Likewise for the service worker family: only 1/2 of a service worker is needed for each such family.. It's doubled in energy value (from 0.5 to 1) since due to the energy cost of supporting a family, the energy cost of a fixed amount service work has doubled.

The services that the newly added spouses provide for their families are not shown in the flow chart but the services that the service worker provides for herself is still shown. The policy for energy flow diagrams here is to only show flows that take place in the marketplace. The service worker serving herself is taking place in the market since the service worker actually represents a composite of a large number of service workers who get paid for their services.

So the result of this example is that the energy flows for support of the town residents has doubled from 2 to 4. Even though the amount of service work provided by paid service workers hasn't changed, the flow of service energy has doubled due to the higher energy cost of labor now that families need to be supported. The amount of labor the miner provides to the mine hasn't changed a bit, but energy cost of his labor has doubled for the same reason. :1

4.10 Including Retirees and the Disabled in the Mining Town

What happens to people that become disabled, perhaps due to a mine accident or retire because they become too old to work effectively? We'll call such people "retirees". Their support is also considered to be the responsibility of the mining town where they worked. Thus more consumer goods from outside the town and services from within the town will be needed to support them. This is also another energy cost of mining. Here's a modified flow chart to include them:


                    ___________________       _______________        
                2  |Production Worker | 5   | Plant (mine)  |Product*7
              |--->|(miner) & Family  |---->|               |---------->
              |    |__________________|     |_______________| (coal)
      *5      |      /\         /\Service to Production  /\  
------>-------|      | 1       2|Worker & Family         | Supplies,
Consumer Goods| 2.5  |   _______|_______________       *2| Depreciation,
+Housing,     |------|-->|  2.5 Service Worker |-->--|   | Energy
+Utils, etc.  |      |   |    & Family         |     | 
              |      |   |_____________________|--<--|1.25 Services to
               |0.5   \              |                     Themselves
               |      1\SS Tax    0.5|Service to Retiree
               |        \____________\/____
               |------->|   1/2 Retiree   |
                 0.5    |_________________|
    (note all flows are energy, 1 = gross energy for one person>
      Figure 3: Company Town Energy Flow: families and retiree
This example assumes that one retiree would need only 1/2 of the services that a miner needs. So the 1/2 retiree only needs 1/8 of a new service worker directly implying 1/4 of a new service worker is required to provide her surplus service to the retiree. This also implies that another 1/4 of spouse/children are added to the service worker family. The result is one more unit of consumer goods energy input flow, split equally between the retiree and the service worker family.

The reason why the retiree needs less services than the miner is because the retiree has time to perform some services for himself. At the same time, a retiree will likely require more medical services.

The energy output of the retiree is labeled "SS Tax" meaning "Social Security Tax" This energy flow goes to the miner who pays a social security tax (flowing in the reverse direction) to support the retiree. It may seem like a fictitious energy flow since the retiree isn't providing any energy or service to the miner, at least not at this time. But in the future when the miner retires, the reverse flow of SS tax that the miner paid should entitle the miner to a forward flow of energy to the retired miner in the form of services and consumer goods. So there is a real energy flow to the miner, but it will be delayed until he retires (or becomes disabled).

5. Other Examples of Economic Communities

5.1 Introduction

The first example presented was a mining town but it's important to look at other examples.

5.2 Factory Town

The company town may be based on a manufacturing factory and all it's employees and servers for the factory workers. In this case one is asking the question: What is the embodied energy content of the production from the factory? All the energy supplied from outside to the factory town is allocated to the product make by the factory. For multiple products, one would need to attempt to allocate the separate inputs required for each product.

Using the example of Fig. 1 for the factory case, the output flow of 4 associated with the product is just the input energy flow to the factory town. To be energy-self-sustaining the output product flow must be sold (exchanged for other goods and energy) that will provide an input energy flow of at least 4 ( = 2 + 2 ). Likewise for Figs. 2 and 3 where the output energy flow contains the embodied energy of the sum of all the input energy flows.

5.3 Farm Town

The same model (Figs. 1 to 3) is applicable to farming with an isolated farming community where the farm town included the surrounding farms All (or almost all) of the farm products are exported to the outside world. All the services to farmers and their families (besides the services provided by their spouses and children) are obtained from service workers that live in the town. And the farm labor is of course provided by people within the farm community.

5.4 Ethanol Production Community

To produce ethanol from corn requires both farms to grow the corn and a plant (factory) to produce the ethanol. So to study the energy flows, lets put all the economic activity to make ethanol (the ethanol economy) in one place and call it the ethanol community. It will consist of a combined farming/ethanol-plant town and include surrounding farms that grow corn. Like the other models, the only export from this community is ethanol and all the material goods sent to support this town are ultimately for the purpose of producing ethanol. This example shows that we can put "vertically integrated" industries into a bounded isolated community for analysis.

Since the solar energy which helped make the ethanol is renewable the total energy of the output may be just the embodied energy it took to make the ethanol. So when the ethanol is burned, all the energy that's consumed is just its embodied energy provided that the ethanol production has not degraded the soil. In reality, the ethanol production process should provide for replenishment of nutrients to the soil (including humus) and prevent topsoil loss. This will make the EEI of ethanol higher. Another issue is the clearing of native vegetation (by burning) to provide farmland for growing ethanol. This will not be accounted for here but the release of carbon dioxide into the atmosphere by such burning is a significant side issue.

5.5 National Park

A National Park has boundaries and exports the service of recreation to the outside world via the visitors who visit it. It's sort of another type of "company town". Not all visitor consume the same energy since ones who camp out in the park use less energy than the ones who stay in lodging, since they are not charged with the energy depreciation on their lodging and don't utilize "hotel services". This is an exception to the simple model since park visitors are allowed to cross the boundaries of the "park resort town".

5.6 Electric Power Plant Town

While the U.S. government classifies electricity as a service, the generation of electricity in a power plant probably should be classified as production of a good. The good is electrons supplied by wires at a substantial voltage between wires. Without a voltage, electrons by themselves are worthless. The electrical workers involved in maintaining the power distribution in "company towns" are service workers. The production workers at the power plant export electricity to the outside world (outside of the "power plant town") while the local electrical workers don't export electricity.

5.7 Freight Railroad Example

A freight railroad provides a transportation service to industry. The transportation is represented by a service input flow to the plants served by rail in various other company towns. This is not the flow of goods that the railroad brings to the company towns but the flow of service that the railroad provides by transporting and delivering the goods.

The "company town" for rail freight consist of a railroad line, including the railroad tracks, yards, stations, and assorted railroad towns strung out along the railroad line to house the railroad workers, and their servers and families. etc.

Freight in railroad cars flows across the boundary of the railroad line at the ends of the line, etc. where the railroad freight cars pass from one railroad line to another line. But this doesn't count as a flow in the flow chart if what enters the railroad also leaves the railroad. What does count are goods like locomotive diesel fuel, replacement rails, repair parts, etc. that enter the railroad but '-t exit it since they are consumed by the railroad. It's assumed that each railroad line does its fair share of maintenance of the railroad cars that travel on more than one rail line.

5.8 Multi-output Economic Community

In order to estimate the energy required to make a single product (or service), one uses the company town model. But if we want to analyze a simple system of a number of company towns which taken together produce many goods and services it will be called an "economic community". It could be a large city that has various industries in it, or even a self-sufficient nation.

5.9 Removing the Isolated Town Condition

In the Company Town Analogy it was implied that the "company town" is supposed to concentrate economic activity from diverse locations into a single town. Thus the "company town" model represents the dispersed economy of the real world associated with the production of the product made by the plant in the company town.

This economy also includes the housing and infrastructure needed for such workers. Then we claim that the models of Figs. 1 to 3 are also applicable to this dispersed "company economy". The reason why the "company town" model looked at an isolated town was so that the energy flows into and out of that town could be easily identified and understood as pertaining to the single commodity produced in the plant (a mine, factory, resort, etc.) in that town. It's easy to visualize the boundary of the model and observe the flows across the boundary. But real commerce is most always more complex.

So let's suppose that we take an isolated company town, remove the fence around it and open it up so that now outsiders can move in. For example, people who work for other industries outside the company town start to move in. Then some of these new entrant workers may start to receive services from the service workers that formerly served the company town plant workers. As this happens some plant workers, still needing the same amount of services, will start to receive them from new service workers brought in to serve the new entrants. This may be thought of as a "service worker swap". It doesn't change the basic model. But now, the service worker boxes in Figs. 1-3 represents the service work from a wide variety of service workers. Since may service workers will now be serving both the original inhabitants and the new entrants, only the portion of their services which (directly or indirectly) provides service to the original town plant workers will be counted. So now the plant economy is only part of the economy of the company town since new economic activity is taking place there. But the model is still valid for the plant economy.

If plant workers and/or their service workers move outside of the factory town, how is this accounted for? One method would be to just expand the boundaries of the company town to encompass this even more dispersed plant economy and consider the people who were already present in the expanded region (and their supporting infrastructure) to be just like the new entrants to the "company town" as explained above. The plant economy still remains intact and is still represented by Figs 1-3. As the plant economy (of this single plant) becomes more dispersed the term "company town" is no longer applicable.

So what we have now is that instead of a plant economy consisting of an isolated company town for which we could draw a circle around on a map we now have a dispersed plant economy which one still might try to represent on a huge map by numerous small circles. But it gets messy since many service workers now only devote a small percentage of their time (directly and indirectly) to the factory workers from a certain plant. Today with the Internet, the geographic range of the dispersed plant economy may include the entire world, since a service worker located on the opposite side of the world may provide services to people in a plant economy. Such a plant economy can be defined conceptually and still represents the isolated company town (with a plant). But to graphically plot all the details of energy flows for each person and items of infrastructure would be an arduous task now that the plant economy of this one plant has become so dispersed.

So now instead of isolated plants in company towns we have numerous "plant economies" each centered around a certain plant but with geographically dispersed workers and service providers. The energy flows within this new "plant economy" are assumed to be as close as feasible to the situation in the company town and conversely.

5.10 Energy per Hour of Labor

In all these company town models, the entire flow of consumer materials and infrastructure input (including depreciation of infrastructure) is ultimately to support the workers of the town plant making the exported product produced by the town such as coal, ethanol, farm produce, products of a factory, etc. So let's estimate just how much more this energy is as compared to the amount of food calories consumed by a production worker. From Human Energy Expenditure for Production the energy to support a worker is about 100 times his food caloric energy (metabolic energy). But since the worker only works about 1/4 of the time, but burns more kcal/hr while working, we must increase the 100-times so that it will only apply to the time spent at work. Assuming that 1/3 of the kcal food intake is consumed on the job, the 100-times becomes 300-times. But then there's about 4 other people (including service workers, spouses, children, and retirees) that must be supported for each worker so the 300-times becomes about 1500 times.

So it seems that for every calorie of food energy burned on the job by a typical production worker, the worker actually requires over 1000 calories of fuel energy (or about 1500 calories as estimated above). For a service worker it's also about 1500 calories also. Why? Just go through the same reasoning as above for the production worker. For every calorie the service worker burns about 100 calories of fuel is used, the service worker also requires the services of other service workers just like the production worker does, etc. So the service worker, like the production worker, consumes (directly and indirectly) about 1500 times the calories burned while at work.

However, since all the energy supplied to support the people in a company town ultimately goes to the production workers. Adding up the total energy attributed to production workers and the total energy attributed to service workers will result in much more energy than is input to the town. Doing this would be double counting since all the energy of the service workers is ultimately passed on to the production workers. One can't just add up the energy supplied to each service worker and come up with a total energy energy supplied to the service workers, since part of each service workers energy input is passed thru to other service workers. Thus there is a lot of recycling of human energy by passing energy from one person to another in the form of services resulting in the total energy input to persons being a few times more than the total energy used by society.

6. A Pair of Company Towns (feedback)

Before putting company towns into a network, a first step is to show just two company towns connected together. The output flow of each connects to the input flow of the other town. If one of these towns has an input flow of fuel from the earth, it may be considered to be the main town. Its output may be fed to the second town to be transformed into something else which is then input (fed back in altered form) into the main town. Also, there are often output and input flows to/from the rest of the world

6.1 Fuel Flow Components

Fuel contains both caloric energy and embodied energy. To show these flows on a network diagram one needs some well defined variables. There are sometimes simple equations to write down and solve which require such variables, like the MJ/day output of real fuel from a mining town.

But the situation is complex since it takes energy to produce fuel for society and this energy becomes embodied in the fuel. The flow of fuel energy thus has 2 components:
F Fuel flow of caloric energy in the fuel
E Embodied energy flow of embodied energy in the fuel
One may then define 3 additional variables (making 5 variable in all):
T = F + E Total energy flow including embodied energy
e = E/F Specific embodied energy (a ratio)
t = T/F Specific total energy = depletion multiplier

Knowing any two of these 5 variables will determine the remaining 3 variables. t is called the "depletion multiplier since (for example) if t=2 then for every unit of fuel consumed, it's required to take 2 units of fuel out of the ground. In other words, the fuel in the ground depletes at twice the rate as the rate of consumption of that fuel by the consumer.

It's obvious from the above definitions that t = 1 + e. For example, if t=2 (depletion multiplier) then it takes 2 units of depletion of the earth's fossil fuels to obtain one unit of useful fuel. This of course doesn't count the energy losses by converting such "useful" fuel into mechanical energy using motors or into electric energy at power plants.

Thus fuel flow has 2 components to it and just giving one component doesn't adequately describe the flow. Also, while the flow of caloric fuel energy is usually known, the flow of embodied energy often needs to be calculated such as by solving equations using the above defined variables.

It also needs to be specified whether or not the caloric energy of the fuel comes from minerals fuels or "renewable" sources such as solar energy or hydroelectric power. For the case of renewables, the total energy T = E since the caloric energy of the fuel didn't directly come from reserves in the earth. There is still a caloric fuel flow F but it's a different type of F that is not part of T. The embodied energy E is defined to be from fossil fuels. The so called "renewable" energy is not sustainable unless E = 0, If e (= E/F) is less than one, then burning the "renewable" energy consume less of fossil fuels (due to embodied energy) than it would if the fossil fuels were burned directly (and conversely if e is greater than one),

For the flow of non-fuel commodities there are also two components of flow: commodity flow C and embodied energy flow E as defined above. Since most non-fuel commodities do not contain caloric energy, the total energy flow (T) is the same as the embodied energy flow E. e, the specific embodied energy flow will be E/C.

6.2 Feedback of Output Energy with Net Output to the Rest of the World

Simple Model

For a company town that exports fuel energy to the outside world, a simple model is for it obtain all of it's input energy flow for making fuel from its own output by feeding back a fraction p of it's output fuel energy to itself. See Figure 4 below. Note that the input fuel F from the ground is not consumed in the town but is only processed (refined, etc.) to provide its fuel output. This would require that the fuel town only needs its own feedback fuel F1 for input and has means for converting some of this fuel energy to consumer goods (including food) to support the lives of its residents. Thus the fuel town converts some fuel feedback energy to embodied energy in the fuel output. But since the fuel feedback comes from the output, it too contains embodied energy. Let F be both the fuel flow from the ground and the output fuel flow (not including any embodied energy). Then the total output flow is tF where t is the depletion multiplier, and since p of this gets fed back, T=ptF total feedback fuel flow.

But possibly some of this fed back total energy (included embodied) has an ultimate purpose of supporting human life in the fuel town and thus disappears down a "Life Energy Sink". The reason why such a sink is needed is explained in get-ref. Let the c be the fraction of fed back total fuel energy ptF which is allocated to the life energy sink so that the life energy sink flow is thus cptF. c is the sink flow fraction. All this and more is shown in Figure 4 below.


 Fuel From Ground   ______________________ T=cptF Life Energy Sink 
 ------------------>|  Fuel Production   |---->------->
      Fin           |   Company Town     | F=Fin  T=tF       T=(1-p)tF
            |------>|____________________|---->---------|-------------->
            |                                           |     F2=(1-p)F
            |       Feedback Fuel  F1=pF  T=ptF         |  Net fuel out
            |---<-----------------------------<---------| 

      Figure 4: Feedback Flow of Energy from a Fuel Town

Solving for total specific energy t

In Figure 4 we know the values of Fin (fuel in from ground), p (fraction of output energy fed back), and c (fraction of feedback allocated for ultimate use of life support). From these, all the other variables may be found by formula. But first it should be clear that the value of c is subjective. See Value of c, the sink flow fraction

We know F (output) = Fin, which assumes that the fuel mined or pumped out of the earth has about the same caloric energy value when it enters commerce as it did in the earth. So looking at the figure it's clear that if we only knew the value of t, the depletion multiplier, we could readily calculate the other unknowns.

To find t, just equate the total energy inputs and output for the fuel town:
F + ptF = tF + cptF Solving for t gives t = 1/[1 - p(1 - c)]

Value of c, the sink flow fraction

Energy flows of fossil fuels from the earth need to be allocated to various purpose although this is a subjective statement. They flow into the world and only a small part of this flow accumulates in the form of embodied energy in the works of man and in accumulated knowledge. The rest is expended in the lives of people and in wasteful activities. The fuel town can exist OK without a life support sink which is the same as setting c = 0. Then t = 1/(1 - p)

At the opposite extreme, if all the feedback energy is allocated to life support it means that the fuel is produced entirely by human labor since none of the feedback energy is used to support the physical plant used in oil production. In this case c = 1. Since all fuel feedback is allocated to life support, should it also be allocated as embedded energy in the fuel output of the fuel town? See Double Duty

But what difference does it really make? Regardless of how much embodied energy there is in the fuel, the output flow of fuel F from the company town remains the same regardless of the subjective value of c. The monetary cost of the fuel shouldn't depend much (if any) on the value picked for c, unless a higher value of c implies that more luxury goods are being consumed by the town's residents which is made possible by higher wages resulting in a higher price of fuel.

Numerical example: p=0.9, c=0

Figure 5 shows the case for F=1, p=0.9, c=0 (no life support sink). Given these values, it's trivial to calculate all the other ones. By picking p=0.9 it means that 90% of the fuel extracted from the earth must be fed back to the fuel town to provide energy for the extraction of the fuel (including life support energy for the town's residents). If the fuel were petroleum, it would mean that for every gallon of consumption by the rest of the world, 10 gallons of it must be removed from the earth. This means a high amount of embodied energy E in the fuel output of the town, which is 9 times greater than the fuel output (e=9).


 Fuel From Ground  ______________________
 ----------------->|  Fuel Production   | 100% of output  10% of output
      Fin=1        |   Company Town     | F=1 T=10 E=9     Fnet=0.1,
              |--->|____________________|---->----------|------------->
              |                                         |  T=1,E=0.9 
              |      Feedback Fuel  F=0.9  T=9  E=8.1   |
              |---<-----------------------------<-------| 90% of output

      Figure 5: Feedback Flow with p=0.9 c=0 => t=10

The people in the fuel town use the fuel to support their lives and the fact that 90% of fuel output is fed back means that they get a lot of life support from this since they consume much of the feedback energy. The more inefficient the production of energy by the town, the higher the feedback energy is, the more people the town supports, the more rapidly the fuel in the earth is depleted and the more pollution is put into the atmosphere (worse global warming). So what may be a benefit to the town residents is harmful to the rest of the world. Note that the 10% fuel output is actually surplus since the money obtained from selling this fuel does not go towards the support of the town but it may go to the owners of the mineral rights and productive facilities of the town.

As fuel supplies in the earth become more and more depleted and fuel becomes more difficult to extract, then the equivalent of inefficient fuel towns something like figure 5 may become a reality. While it's very bad for the environment, in one way it's seemingly beneficial for the rest of the world. This is because the rest of the world is supplying no energy to the town and yet is getting an output fuel flow of Fnet=0.1. While its embodied energy content is 9 times this (e=9, E=0.9), the energy return on energy invested is seemingly infinite from the viewpoint of the rest of the world (which supplies no energy of any kind into the fuel town).

Sale of the net output Fnet

One thing omitted from this model is what happens to the money obtained from the net output of fuel from this town. The rest of the world is getting fuel from the town but providing nothing in return to the town Since money is presumably being paid for the net fuel output from the town, what does this imply? Normally, one would expect this money to flow into the town which would entitle the town to obtain a flow of goods from the rest of the world along with the embodied energy in these goods. But suppose the money goes to the owners of assets in the town who don't live in the town? One can define the town such that all the people required for the towns existence live in the town which implies that the owners of the assets of the town also live in the town. Even if corporations are present in the town, one can form a model where all the stockholders of the assets of the town live in the town. One exception would be where the government owns the town plant and uses the net output of energy (actually the money obtains from it) to subsidized some other region.

If there is a flow of goods into the town to pay for the oil output, how is the flow diagram (Figure 4 and 5`) modified? The energy associated with this input flow of goods is not needed for the production since the feedback of 90% of the energy production fully supported the town's production. Thus it must be used for surplus goods and capital accumulation. It would be represented by a sink for the ultimate consumption of energy for its ultimate purpose.

Adding a multi-output town in the feedback path

Perhaps a better way to portray the model of Figures 4 and 5 is to not require that the fuel town also be able to convert fuel feedback into goods needed by the town. To achieve this we can envision a "multi-output" company town in the feedback loop. This multi-output town has fuel as a single input and makes all the goods needed by the fuel town, including consumer goods, industrial supplies, etc. This multi-output (one input) town makes all sorts of goods (including food) for both it's residents and the residents of the fuel town. To mirror society, we'll assume that the small-scale production of the town is just as efficient as the large scale production in the real world.

Example with p=0.5

An example of such a "fuel town" with a "multi-output town" is shown in Fig. 6 below where the numbers represent energy flow: E is embodied energy and F is fuel caloric energy (in units of say a TJ/day).


 Fuel From Ground     ______________________
 -------------------->|  Fuel Production   | F=2 E=2      F=1 E=1
      F=2             |   Company Town     |---->----|---------->
              |------>|____________________|         | Net Fuel Output 
   Goods to   |       ______________________         | p=0.5
Support People|  E=2  |    Multi-output    | F=1 E=1 |
  and Plant   |---<---|    Company Town    |----<----| Fuel to Feedback
                      |____________________|
                         (Feedback Town)                                    
      Figure 6: Feedback Flow of Energy from a Fuel Town

It's assumed that all of the energy supplied to the fuel town (except energy from out of the ground) is embodied. It seemingly takes E=2 units of embodied energy input to the fuel town to to extract F=2 units of fuel energy. So it seems like there is no gain in energy. Except that the E=2 embodied energy has a datum of the the earth. (See Energy Datum) but the F=2 excludes any embodied energy and has the fuel town fuel output as a datum. Since these two datums are different, they are not comparable. To correct this error we must use the same datum.

Using the fuel output of the fuel town as a datum, we would have E=0 output from the fuel town (no embodied energy) and thus have only F=1 input to the multi-output town which gets transformed into E=1 output of embodied energy which goes into the fuel town. Thus for E=1 of embodied energy input the fuel town supplies an output of F=2 of fuel so one unit to energy in gets two units out resulting in a gain in energy. Except that there's of course a loss of the two units of energy (F=2) extracted from the earth.

From the point of view of the rest of the world, the town-pair supplies the world with F=1 of energy and requires no input energy from the rest of the world so it's seemingly infinite return on energy invested since no energy is invested. But there is a cost: The F=1 flow to the rest of the world implies a flow of one unit of energy to the rest of the world, but the depletion of energy in the earth is F=2 units along with the pollution resulting from burning these 2 units of energy. Note that like before, this Model neglects sale of net output Fnet

No fuel output to the rest of the world: p=1

When one tries to use the above model where there is no fuel output to the rest of the world, it would seem that the flow of embodied energy becomes infinite. The input flow of energy from the ground continues to be 2 but there is no output flow. This would imply that since energy is not lost (fuel energy burned becomes embodied energy) then huge amounts of energy must be somehow stored in the two towns. But the model has no storage facilities. Where does the energy go to? Well, the fuel supports the lives of the people in the two towns. This life support can be represented by embodied energy flowing out of the towns which disappears into a network sink.


 Fuel From Ground     ______________________   E=1*
 -------------------->|  Fuel Production   |--->Life of residents (sink)
      F=2             |   Company Town     |
              |------>|____________________|---->----| p=1
   Goods to   |       ______________________         | F=2, E=1*, T=3
Support People|  E=2  |    Multi-output    |----<----| Fuel to Feedback
              |---<---|    Company Town    |   E=1*
                      |____________________|--->Life of residents (sink)
                         (Feedback Town)
    Figure 7: Feedback Flow of Energy from a Fuel Town; no Net Output 

An example is shown in Figure 7 above. The two units of embodied energy, E=2, input to the fuel town, does double duty in the fuel town. It supports the lives of the residents which use their lives to create the output of fuel. Thus the E=2 should be counted twice as output: once for supporting the lives of the residents and again for enabling the output of fuel. But that would violate the rule of conservation of energy by having energy output flows exceed the flow of input energy. So in the figure only the input of E=2 is allocated to the outputs and each such output is marked with a * (E=1*) to indicate this. The non-sink output of the fuel town is thus F=2, E=1* (=> T=3). So E=1* is one half of the (double-counted) embodied energy.

This assignment of fuel energy to double-counted embodied energy is in conformance with the "principle" that all fuel energy, even if in embodied form, ultimately goes somewhere and doesn't get multiplied or double counted. However this conservation of fuel energy principle doesn't necessarily imply that if E=2 (embodied energy) is doubled, the result is two of E=1*. It might be E=1.2* and E=0.8* etc. which would also satisfy the conservation of fuel energy since it represents two units of fuel energy. Thus in general, when a unit of embodied energy, E, becomes double-counted, the result is E=x and E=y wheres x and y are non-negative numbers that sum to the embodied energy input, that is: x >= 0, y >= 0, and x + y = embodied energy input.

However one can't arbitrarily assign values to x and y within the constraints. This is because the flow of "embodied fuel energy" to the sinks must be equal to the input flow of fuel energy from the earth. The E=1* satisfies this requirement for the example of Figure 7. But having the life-support sink for the fuel town have flow E=0.8* with E=1.2* for the multi-output town also satisfies this requirement. But it seems reasonable to make each E=1* so that the embodies energy going to each sink due to life support has the same amount of embodied fuel energy.

To-do: Treat non-fuel goods similar to fuel with both a utility component, and an embodied energy component.

7. Surplus, Feedback, Savings, and Net Production

7.1 Introduction

This is about the high energy value of surplus production (net production) which also is a type of savings or a type net production. All this is due to feedback of the outputs of production to the input.

7.2 Simple Examples of Net Production

A overly simplistic example is that of an oil well that requires that some of its production output (oil) be fed back to power the oil well pumping. Then the oil that one gets to consume is the net production. (the oil pumped out of the ground minus the oil needed to operate the pump). Actually, to get the oil out of the ground requires much more energy feedback than this, since oil must be first discovered, the well drilled, the pumping machinery built and installed, etc. But the simple model neglecting these items is easy to understand.

The same concept is illustrated when people save money. In order to save a day's wages, it might be necessary to work for 3 days since the worker must spend part of his wages on living. Thus the worker works 2 days to provide for his food, clothing, shelter, etc. for 3 days, resulting in being able to save his wages for the third day's labor. Thus the net production of 3 days of labor is only 1 day of labor since some of the output of the worker (or the goods the worker receives in exchange for his output via money) is used to maintain the worker, similar to the feedback example for the oil well. This savings is also surplus meaning that it's extra production that the worker doesn't need to live on. This example has a multiplier of 3: one day's net production requires three days of gross production; or it takes 3 hours of labor to get one hour of net output. The term "surplus" will be reserved for use for the case of human beings generating surplus.

7.3 Surplus

The surplus of a workers work is the product that the worker produces above the amount of product needed to sustainably support the worker. Of course a modern-day worker doesn't actually directly consume much of the product that the worker makes. Instead he exchanges what he makes (via means of money) to get products that he needs for living such as food, clothing, shelter, transportation, education, etc.

There are different types of savings. One is surplus savings which may be used for investment (in say stocks, bonds, and/or real estate, or a business), luxury goods, and the like. Another type is savings for buying something that is needed for living such as an automobile or home. These may also count as surplus since they are in a sense investments. However they then need to be depreciated as they are used up so that the worker's cost of living would include depreciation. While in this case the worker needs to put some of his earnings into a deprecation account (of investments) and count it as a living expense, what often actually happens is that one buys a car, home, etc. with borrowed money and then makes payments on the loans. Part of such payments are living expenses and another part is investment (if the loan repayment is higher than the depreciation plus interest).

Thus "surplus" as used in this article is a narrower term than savings or "net production" More about surplus will be presented shortly (after a discussion of "diversion".

7.4 Diversion of Worker's Surplus

A worker who spends all of his income on living and is unable to save may actually be producing surplus since other entities may be getting his surplus (or savings). One example is high land rents for his residence which provides unearned income (surplus) to the landlord. If it were not for this, the worker would be able to save, so the landlord is obtaining the savings (surplus) that would otherwise go to the worker. Partly due to high rents, property prices increase, resulting in land owners and land speculators/investors getting some (or all) of this surplus instead of the landlord. For workers who are homeowners, this diversion of their surplus is due to the high land prices they must pay for the purchase of a home (often paid for in the form of mortgage payments). The cost of the house building (or apartment) itself is part of the legitimate cost of living which is accounted for by depreciation.

But there are other kind of diversions (a Marxist might call this expropriation) of a worker's savings (surplus). One is that portion of taxes that are wasted. Taxes that are reasonable and often benefit the worker are part of the legitimate cost of living. But taxes that are wasted represent a diversion of a worker's saving.

Another diversions is in the profits of the company that the worker works for. While the worker may not be able to save, the company that he works for may be able to save (due to the labor of the worker) and use the savings for dividends or capital investment. However since a company might be considered to be entitled to a nominal interest return on its investment (giving a positive real rate of interest), then only excess profit over this nominal return would represent diversion of surplus. Of course depreciation of plant and equipment is a legitimate expense of production (and isn't surplus) although the "book value" of depreciation per accounting standards is often much in error compared to the actual depreciation. Today in the 2010's, with the real rate of interest negative (interest rates are below the inflation rate) the surplus excess profits in many cases may be small or negative resulting in little (if any) surplus diversion due to profit.

But even if a worker saves money, is it really savings (surplus)? One may argue that the living expenses of a worker should include savings for retirement and emergencies. This tends to reduce the amount of surplus and is a negative diversion. So while savings for retirement is called "savings" is the strict sense (of this article) it may not be surplus.

7.5 Surplus and How It's Spent

The surplus of a workers work is the product that the worker produces above the amount of product needed to sustainably support the worker (and family). Sustainability includes support of a family to provide children to become new workers and savings for retirement and emergencies. But from now on just mentioning the support of the worker will be assumed to imply support of his family, and allow for modest savings as well. For the portion of the surplus that the worker gets (in pay and benefits) the expenditure of it by the worker must be for items not needed for his sustainable support.

This includes luxuries, investments, and leisure time. For the above example of working 2 days to provide living costs for 3 days, the worker could just take the 3rd day off and the surplus would be accounted for by leisure time. However if this time was used for useful personal business (such as education or health endeavors) it might be allocated to the support of the worker and isn't surplus. Thus it might take 3 day's of labor to provide for 3 days of living and thus there would be no surplus. Thus, true surplus only includes excess leisure time not needed for sustaining the worker. As one can see, there is a lot of subjectivity to the estimation of what is or isn't surplus.

Also, since conversation is usually educational and important in human relations, including finding and keeping a spouse for having a family, much of the time spent conversing belongs to the time necessary to sustain the worker. Also, just listening to conversation and watching events, such as in videos and television may be part of this. Although wasting time listening to frivolous conversation or playing video games, may belong mostly surplus.

While surplus provides for frivolous items such as excess leisure time, luxuries, and waste, it also is essential to social progress as it supports the advancement of science (which may help advance technology) and also supports the arts. Surplus also partially supports education to the extent of that portion of education not needed for production or the support of society. In a democracy, voters need to be well educated so as to vote intelligently so that education in the arts, humanities, and social sciences, is often more of a necessity than a luxury. So a majority of educational activities may not be surplus but are likely needed to support human life.

But for the case of surplus that is diverted from the worker and is spent by others, it may be used for almost any purpose including the necessities of life. For example, diversion of surplus created by workers to wealthy people living off investments not only helps provides the wealthy with the necessities of life but also provides them with many luxuries (such as mansions, luxury travel, vacation homes, yachts, etc.).

7.6 High Energy Value of Surplus

If it takes two days of work to provide for the support of a worker to work a third day to produce a day's worth of surplus, then how many days work (and days energy) did it take to get this one-day's-work surplus? Well, it took only one day to make this surplus but it took two other days of work to save enough to provide for the worker's life for this day. Thus it really took 3 days of work to get this surplus. So does the purchaser of this surplus pay for 3 days of work? No! The purchaser only pays for the one day of work it took to produce a day's product but since this is surplus product (and surplus money) it can't be spent to support the life of the worker.

Then, Who pays for these three days of support of the worker's life? In a monetary economy the worker himself pays for it. The money he earns for the two days pays for these three days of living. You might think that whoever purchases these 2 days of production paid for it, but what happened is that the worker just exchanged (like barter) his product of 2 day's for products that he needed for living, using money as a medium of exchange. One doesn't have to count time in days. For example one may say that for each minute of work on creating surplus, the worker must work two more minutes to obtain life support for himself.

Another example is the case of slaves working on a self-sufficient farming estate. The master may be entitled to the work of the slave, but the master must in turn support the slave. Thus, part of the time the slave must work to support himself and use the rest of his work time to provide goods/services to the master. Using the 3-multiplier example above, to get one day's production out of a slave would require 3 day's of his work (2 days to provide for his support for 3 days). If the slaves are in a modern society and consuming fossil fuels, the energy required for 1 day's work for the master requires the energy consumed for 3 days of living by the slave. To double the amount of work for the master (assuming no limit to the natural resources of the farm including water and land) would require doubling the number of slaves and doubling the amount a energy they use.

In both of these examples we have what might be called a "surplus multiplier" of 3. It's due to the required feedback of the output of production to support the inputs to the living of people (food, clothing, shelter, education, non-wasteful leisure time, etc.)

It's sometimes claimed that when one buys a good, the purchase price includes all the energy it took to make the good. This argument usually implies a moderately high value for the embodied energy in the good. But the above shows that the embodied energy can be even higher due to the surplus multiplier. In an extreme case, the cost of the energy embodied in a surplus good is higher than the cost of the good. This is a difficult concept to grasp and it may seem to be a paradox until one thinks a lot about it.

Not only is the embodied energy in the surplus good high, but the "social cost" of producing it is high. The purchaser only pays the lower cost (without the multiplier) however. Since it is a surplus, the money received for such a good can't be used for support of the worker, but could go into the worker's excess savings or be diverted (Assumes non-excess saving is for the support of the worker --possibly used in his future retirement).

7.7 Very High (or infinite) Surplus Multipliers

As productivity drops (including that due to depletion of natural resources including scarcity of land and water) the surplus multiplier increases. For an extreme case it may take 100 days of work to produce one day's worth of surplus. More extreme is where there is no surplus at all (the multiplier approaches infinity) or the surplus is negative.

If an economic community has a negative surplus, then it is not self-sustaining and is using up stored surplus like capital or worker's health. For example if there is negative non-wasteful leisure time then a worker may be overworked, fail to get sufficient sleep and rest, be subject to excessive stress leading to poor health. The results may include lower productivity making the surplus multiplier even more negative. Negative surplus for an society means that it is in serious decline, is fostering no scientific progress, and may be consuming its own capital investments. In other words it is collapsing (if the negativity is substantial). Of course, only part of a society may have negative surplus, or it may only be a temporary phenomena; or other entities such as nations (or groups of them) may provide aid or loans to prevent (or delay) collapse.

7.8 Accidental Destruction is Surplus

Suppose the one unit of production is accidentally destroyed. How much energy is required to replace it. One way to replace it is to transfer one unit of surplus resulting in less surplus (at the high energy value of surplus). Another way to replace it would be to produce one more item by utilizing non-wasted leisure time. But this time is also surplus and has a high energy content. Thus a product accidentally destroyed has the same energy content as if it were a surplus product. Note that while the surplus production is not likely a surplus type of item (such as a luxury good) what it is exchanged for is a surplus type to item.

7.9 Energy of Non-Surplus Goods Dilemma

If you think that understanding the energy content of surplus goods is complex, the understanding of the energy embodied in non-surplus goods seems to be impossible since its definition is ambiguous. A non-surplus good is an intermediate good used in the production of something else. For example, electricity supplied to a factories is an intermediate good used for production of goods at the factory. Food supplied to workers is an intermediate good enabling the workers to produce products. Note that most intermediate goods can also be used as surplus final consumption. For example, food eaten in excess to make people obese is surplus as is luxury food. So food can either be surplus or an intermediate good (a means to an end).

Now suppose we ask the question of how much energy it takes to produce one more unit of a common food where the food will be fed to workers (and is an intermediate good). But increasing production of an intermediate good will result in an increase in production of some final good(s) (surplus). But which additional final goods will results from the increase in production of an intermediate good? For the case of food, we don't know which workers the food will be fed to and thus don't know which final (surplus) goods will increase. Even if we know that the food will be fed only to workers making a certain product, suppose that product is not the final product. Thus we still don't know what final products will increase in production. The same dilemma faces us in the case of electricity. If we produce more electricity for industry, which industries will get it?

Suppose that in a (futile) attempt to overcome this dilemma, we says that the intermediate good (such as the food or electricity examples above) will not be used, but instead will be put in storage or destroyed. But in such cases the good is a surplus final good and the question asked was about the energy content of intermediate goods and not about final goods. The paradoxical conclusion must be that asking what the energy content is of an intermediate good is not a well poised questions and thus has no answer.

But let us ask a more specific question: How much energy is required to produce an intermediate good A, given that that this intermediate good increase is only going to increase the production of a certain final good B? Using the I/O model it's trivial (using matrix algebra) to find the increased output of the final good B, due to a unit output increase of the intermediate good A (while holding the output of all other final goods constant), as well as determining the energy used. The mathematics of this is similar to Variation of <em/y/ and <em/x/.

This energy is the impact of the unit increase of the intermediate good, but it includes the energy of other intermediate goods needed for the production of B which are not in the supply chain for the intermediate good A. Thus it will require a lot more energy,` and this energy is not what we are seeking. Furthermore, this energy to produce B is normally assigned to good B and not to intermediate good A. So even if one makes the question more specific, there doesn't seem to be any answer. All we can say is that if we increase the output of intermediate good A we can find the energy that is expended in the resulting increase in the output of B, provided that we somehow know that only the final (surplus) output B will increase and the other final outputs will remain the same. This situation seems paradoxical. One can readily think up some examples of this.

7.10 Partial Solution of Non-Surplus Goods Dilemma

One way to attempt to resolve the above paradox is to narrow the scope (boundaries) of the problem and invoke the market. If we have made an intermediate good and don't know what it will be used for, we can sell it in the market (for intermediate goods) where it will be used to make something else, take the money and use it (or part of it) to support the life of the workers who helped make the intermediate good. Making this good isn't surplus, since the sale of it supports the life of the workers. The labor energy, which creates value added to the products the workers make, doesn't get multiplied by any "surplus multiplier" in this case.

In the above, the scope of the economy considered is reduced from the whole economy with an I/O matrix, to just a company town that sells goods to the outside world. Without the I/O matrix (or a network of company towns) one can't find the energy content of a good. But we have implied that there isn't any surplus multiplier acting in this case and thus it seems that intermediate, non-surplus goods do not have a "surplus multiplier" and are thus much lower in energy content than surplus goods.

7.11 Definitions of Surplus

Note that the use of the term "surplus" in this article is not generally the same as it's use elsewhere, especially in accounting. While the term "surplus good" implies that it is a characteristic of a good, it is really a characteristic of the condition of how the good was made. Since the time a worker spends making it doesn't go towards his support, he must work additional time to save for his support while he's working on making surplus. Thus the surplus produced contains more embodied energy than a non-surplus good. But ironically, the purchaser of that good doesn't pay for the extra embodied energy. to-finish

7.12 Mathematical Feedback Model

This model will discuss the quantification of human energy in an economic community using a simple feedback model. The final output will be only surplus goods and services. But first, we'll present the simple incorrect but conventional model where the final output is both consumer goods and surplus. and neglects human energy (no feedback). Later it will be corrected to include human labor, where only the surplus goods and services are the final output.

7.13 Open Loop Model (No Feedback)

This model is presented to show what happens if feedback is ignored (no surplus). The figure below shows an economic community as a black box with an energy input flow F and output flow O. The economy is assumed to be in a steady state condition with no net capital accumulation and no imports or exports. The input flow is the flow of energy from oil wells, coal mines, natural gas wells, etc. The economy (black box) takes this input energy (and other raw materials) and converts them into finished products and services. Also input is solar radiation and falling water used for hydroelectric power but this is not shown in the Fig. 8.

Output energy flow O is the energy content of the final consumer goods and services consumed by people. For example the goods: food, clothing, shelter, recreation, personal autos (and the gasoline to run them), luxury goods, etc.; and the services: medical care, sales clerks, government, etc. All the input energy is allocated to the output consumer goods and services. Most of the output energy is in the form of embodied energy. But some is in the form of actual energy, such as gasoline which in addition to its heat value, contains the embodied energy used to produce it (oil well drilling, refining, transportation, etc.)


                   ______________________
 F (input energy)  |      O = F         | O (output energy)
------------------>| Economic Community |-------------------->
(Energy of fuels)  |____________________| (Energy in consumer goods and 
                                           services)
           Figure 8: Energy Flow in US Without Feedback

The production and consumption of intermediate goods (such as lumber to build houses or glass for automobile windows) all happens within the black box of the U.S. economy. For industrial processes that use energy, much of the input energy becomes waste heat, but all this input energy is allocated to the output goods of the industry. So the energy which was turned into waste heat still winds up as embodied energy in the output. Of course, some of this output is intermediate output which becomes the input of some other industry inside the black box. Thus the input fuel energy F equals the final output energy O. Actually, both the output energy O and the input energy F are energy flows and for the U.S. are roughly 100 exajoules per year. See Total fuel energy We'll often omit the word "flow" when discussing input, output, and feedback energy but it should be understood that it's actually a flow.

Some of the production in the economy goes to making producer goods and also maintaining them: For example, repair (including parts) of factory machinery, office equipment, and buildings. The producer goods and services never leave the "black box". It's assumed that the amount of capital goods remain constant and are maintained in good condition.

While the flows in the above diagram represent energy (mostly embodied) one may think of the flows as being consumer goods, and labor with these flows being measured in terms of energy flow. In other words the amount of each consumer good or unit of labor is measured by the amount of embodied energy it contains. Except that consumer fuels will have both embodied energy plus potential heat energy.

7.14 Closed Loop Model (Labor Feedback)

The model

The next step is to account for human energy which is shown in Figure 9 below. This model quantifies a case of surplus energy discussed above and shows energy flows in a block diagram.

In this section "goods" will often be used to mean both goods and services. "Surplus" goods are output goods and services which are not necessary to support maintain, and reproduce the labor force. Surplus goods consist of luxury goods (such as yachts and second homes, etc.), waste (such as gambling, recreational drugs, and government waste)), and capital accumulation (not counting the requirements of replacement and maintenance of existing capital (or producer) goods).

The method used here is to show the human labor feedback energy flow as being outside the "Production Economy" black box. The final output of consumer goods and services is spilt into two parts: surplus goods (which includes some capital goods) with energy flow S, and the goods necessary to support working people with energy flow L. Since humans must reproduce, educate and raise children to sustain the labor force, all the energy needed for this is included in the human labor energy flow L. The energy embodied in the consumer goods and services, both of which are consumed by workers, is then expended during the labor of the workers and becomes embodied energy in the products they make and the services that they provide. It is thus another energy input to the economy and adds to the fuel energy input F resulting in a total energy input of F + L.

This labor energy L represents positive feedback since it adds to the fuel energy F. Note that like the simple model without feedback, the input energy to the economy is equal to the output energy: F + L = O. But O splits into surplus and necessary energy so O = S + L. Let p be the percentage (or fraction) of the output energy O which supports the workforce. (Note that p is related to the "surplus-multiplier" (s) defined previously: p = (s-l)/s.) So we have L = pO. The rest of O must go for Luxury of S = (1 - p)O. Note that if p is not fixed, this model is invalid. Later on we'll show why it seems reasonable to let p be fixed in value.


                   ______________________
F (fuel)    F + L  |     O = F + L      |    O       S (surplus goods)
-------->|-------->| Production Economy |---->----|---------->
         |         |____________________|         | S = O - C = (1 - p)O
         |         ______________________         |
         |         |   Consumer goods   |         |
         |----<----| sustain labor: L=C |----<----|
         L (labor) |____________________|    C (consumer goods to workers)
                                             C = O - S = pO 
    (note that F, L, O, S and C are all flows of energy, say in J/yr)
      Figure 9: Flows of Energy (mostly embodied) with Labor Feedback

Solving the equations and example

This model is like what one finds in some textbooks on electronic circuits or control theory. It's like an amplifier with a gain of one and with a fraction p of the output fed back to the input as positive feedback. Given an input energy flow F and fraction p, one can readily solve for O, L, C, and S in terms of F and p. First, solve for O: In F + L = O, substitute pO for L (since L = C = pO). This gives: F + pO = O which upon solving for O gives O = F / (1 - p). Now since S = (1 - p)O, substituting for O gives S = F. Since C = pO, we get L = C = Fp / (1 - p) by substituting for O and noting that L = C. This shows the rationale for having p constant. L is directly proportion to F. For example, if fuel flows double so do labor energy flows. The model assumes that the labor to turn energy into consumer goods is directly proportional to the amount of energy. In other words constant productivity of labor. Also implied is that if needed, due to increased energy input, more workers can be obtained from elsewhere, and conversely. Here's the figure again with these results included and an example for the case where p = 0.8 (surplus-multiplier = 5).


                   ______________________ assume p = 0.8
 F (fuel)   F + L  |     O = F + L      | O = F/(1-p) = 5*F
-------->|-------->| Production Economy |---->----|----------> S = F =
         |   5*F   |____________________|         |  O - C = (1 - p)O
         |         ______________________         |  S (surplus goods)
         |         |   Consumer goods   |         |
         |----<----|  become labor: L=C |----<----|
         L (labor) |____________________|  C=4*F (goods to workers)
         L = C = 4*F                     L = C = O - S = pO = Fp/(1-p)
    (note that F, L, O, S and C are all flows of energy, say in GJ/yr)
      Figure 10: Feedback Energy with Equations and Example (p = 0.8)

The results may seem strange at first, but they make sense when one thinks about them. For the example shown in Figure 10 where there isn't much surplus and p = 0.8, then O = F / (1 - p) or O = 5*F. Since L = C = pO then L = C = 4*F. This means the output energy flow O is 5 times the input energy flow F (surplus multiplier of 5) and the feedback labor energy flow L is 4 times F. How can energy flows, all resulting from the input fuel flow, be a few times larger than the energy of that fuel flow?

Interpretation

Labor energy flow is much higher than "total" energy flow due to feedback. It's something like say a circular swimming pool that has circulating water flowing round and round in the pool. The water represents energy. The pool also has an input pipe with water (energy) flowing into the pool and an outlet pipe with water flowing out of the pool with these inlet and outlet flows equal. So the flow within the pool of the water circulating round and round may be much larger than the input or output flows of the pool. In this analogy, the pool includes the feedback loop for labor energy. However, don't carry this analogy too far, since the mathematical flow model used here assumes no storage of energy and the pool and pipes of course store energy (represented by the water). But while this analogy shows that it's feasible to have such high flows of energy, it doesn't explain what it really means.

But note that since S = F (regardless of what p is) the output of surplus energy is equal to the input fuel energy. The final output S is only surplus goods and all the input fuel energy F is allocated to this final output. But since only 20% of consumer output goes for surplus goods, then the energy content per dollar of goods is about 5 times what it would be if human labor were neglected and there was no feedback of consumer goods (which would just flow out of the system). Let's call the embodied energy content per unit of good the "energy intensity" of a good. Using a dollar's worth of goods as a "unit", the energy intensity is in units of embodied energy per dollar (in units of say J/$). Similarly for human labor, let its "energy intensity" be the Joules per dollars worth of labor at prevailing wage rates (J/$).

If the energy intensity of surplus goods is high, so will be the energy intensity of the consumer goods needed to support labor. This is because if we could be more efficient and support labor with less consumer goods (perhaps due to higher quality of the goods), then some of the consumer goods that formerly supported the work force could be diverted from workers to surplus goods. Since these goods are interchangeable with surplus goods, they must have the same high energy content (energy intensity) as surplus goods. Thus the consumer goods to support labor has high energy intensity, just like surplus goods and thus the labor effort made possible by such consumer goods must have high energy intensity. An economist might say that we must account for the "opportunity energy cost" of workers sustenance (consumer goods) since they have an alternate use as surplus goods.

Summarizing: In this model, the energy of human labor, including all the consumer goods and services that support labor (and the reproduction of labor) is an intermediate good. The only final output is surplus goods (including waste and capital accumulation). All the fuel energy input is allocated to the this final output which explains why it has such high energy intensity.

Worker depends on other workers

This model is equivalent to the case of a worker requiring additional workers for his support. If all workers are equally productive and require the same amount of energy to support their living, then the example with p=0.8 is saying that for every person engaged in producing surplus goods 0.8 of a worker is required to produce the necessary consumer goods for him. But that 0.8 of a consumer-goods worker isn't producing anything for his own support so he needs 0.8 x 0.8 of another worker to provide for his support. And so on, ad infinitum. But its easy to show that this geometric series sums to 4 showing that it ultimately takes 4 non-surplus workers (consumer-goods workers) to support one surplus-goods worker.

7.15 Relation to the Company Town Model

It's obvious that the feedback model is something like the model of a large network of company towns. But in many company town models, the surplus goods are consumed right in the company towns, except for capital goods accumulation. On the contrary, the feedback model explicitly shows the flow of surplus goods. The feedback model has service workers within the economy and doesn't show the distinctive role that local service workers play in supporting production workers.

8. Network of "Economic Communities" (briefly)

In order to apply the company town analogy to the world (or to a self-sufficient nation) we need to create a huge number of company towns to make everything used by people and industry. Then all the company towns become nodes in a transportation network where the output of each company town is spit up into a large number of flows of the same good and each such flow flows along a transportation route which connects to the input of other company town or to a "sink" which represents the final consumption of the good. Thus the outputs of company towns become the inputs of other company towns although it's possible that some of the output of a company town might flow to that same town's input. But in order to do this the specific inputs to each town in terms of the amount of input required for unit output needs to be specified for each town.

One major question is: What are the energy sinks for embodied energy? it seems that such sinks are just surplus production (not necessarily of surplus types of goods). See Feedback, Surplus, Savings, and Net Production The answers to this are quite subjective.

The network would contain a great deal of feedback as the output of one community flows to another community, etc. and eventually the some of that energy flow returns to that one community. This is feedback.

9. Embodied Energy in a Fuel

There are two types energy flow out of an economic community when the output good is itself energy. The output of an energy producing economic community (such as a coal mine, oil field town, or ethanol community) is a fuel which has value due to its caloric energy content. But there's also embodied energy that went in to the inputs to the company town that produced the fuel. In non-energy company towns embodied energy is the only energy output. But for a energy company town there is also the caloric energy output based on the caloric value of the output fuel.

These two types of energy output, embodied and caloric represent different things. The caloric value of the coal represents it's use value or utility. But the embodied energy represents the energy cost of making the fuel available. Caloric energy represents a benefit while the embodied energy represents an energy cost it took to get the fuel. Cost and benefits don't usually add. But if you were to burn the fuel, the amount of energy consumed is the sum of the embodied and caloric energy.

A flow of fuel energy needs to have 2 values to the flow: the caloric energy of the fuel and the embodied energy of the fuel. A technological process like using the fuel energy to make something will require a certain amount of caloric energy, regardless of what the embodied energy is. Yet the total energy used up by using the fuel is the sum of the caloric and embodied energy.

In talking about the embodied energy, we must be careful to define what the datum is. If it's fuel in the ground, then the embodied energy in the fuel can be a number larger than the caloric energy of the fuel and the sum of the energy removed from the earth is just the sum of these numbers.

On the other hand, if the datum is fuel ready for use, and if there is to be a positive energy gain, the heat value (caloric) of the fuel (neglecting transportation costs) will have to more than the value of the caloric and embodied energy that went into producing the fuel.

If the net energy gain is small then a lot of fuel is being burned to produce a small amount of net energy gain. This can be a disaster for the environment since it will release much pollution into the environment to obtain just a little net energy. For the case of atomic energy supplying the energy inputs from the external world to the mining town, there may be little or no release of pollution if all goes well, but if it doesn't (an accident for example) it can be very polluting.

9.1 Example of No Energy Gain (no surplus)

Yet even if there is no energy gain, there is still support for the life of the human beings in the fuel company town. Consider the case where the flow of caloric energy of the fuel out of the town is equal to the embodied energy flow into the town from outside (datum is fuel out of the ground) and thus there is no energy gain (zero energy return on energy invested). Yet the output fuel flow could become the input to another company town (with diverse output products) which would convert this input into an output flow of goods suitable to support the fuel town. Thus we have sustainability (until the fuel is depleted) with zero energy gain from the fuel town. But there is no surplus energy flow either. Surplus is needed for capital accumulation and advancement of knowledge, etc.

9.2 Modelling Just the U.S.

If one wanted to consider the United States as an "economic community" one would need to account for imports and exports. To get a network of only two economic communities one could create a special super economic community representing the rest of the world which trades with the U.S. Into it would flow all goods and services to be exported from the U.S. and out of it would flow all goods and services which are imported. For energy independence, one would need to assume that trade is balanced to the extent that the energy content of the imported goods would equal the energy content of the exported goods. Since in reality, the US is running a huge foreign trade deficit this balancing of energy flows of export-import is not valid.

The actual imbalance of trade results in a huge imbalance of energy flow from the rest of the world to the United States. It's like an energy "subsidy" to the U.S. from the rest of the world. But it's not really a subsidy since the U.S. goes into debt to foreign countries (including U.S. equities held by foreigners) to compensate for this imbalance of physical fuel flows. Eventually the situation may reverse where there would be a huge energy subsidy flow from the U.S. to the rest of the world. Except that it's difficult to envision how such a reverse flow will happen and thus the U.S. may eventually just default on it's debt one way or another. But if such a default happens, then the energy subsidy flow is likely to come to a halt.

So the area under study will be called an economic community which is assumed to be the economy of a mostly self-sufficient country as the United States or the Soviet Union were at one time.

9.3 Making the Model Cover Everything

The company towns should be mutually exclusive and exhaustive. This means the following: Exclusive: production firms and people in the economy should be counted only once. Exhaustive: the people in all the company towns should account for all the people in the economy and the outputs should account for all the outputs of material goods and exported services.

to-do

10. The Input-Output (I/O) Model

10.1 Meaning and Limitations

This section assumes you are familiar with Input-Output Analysis or I/O Analysis for short. I/O analysis assumes that for every commodity (including services) of final output, we know how much of all other commodities it directly takes to make it. This is something like the law of definite proportions in chemistry where it takes a fixed number of various types of atoms (elements) to make up a molecule (compound). For example, to make a molecule of water it takes exaction two hydrogen atoms and one oxygen atom. Thus we have direct components of each commodity and we know how much of each such component it takes to make every commodity. See also Input-Output (I/O) and Production Functions.

This is quantified by the A matrix where the column elements represent the amounts of various commodities required to make one unit of the commodity corresponding to the column. For example, the matrix element a[i,j] is the amount of the ith commodity directly required to obtain a unit amount of the jth commodity output. Thus, the vector of final outputs y is y = x - Ax where x is the total production vector. Both the x and y vectors are of the same size (dimension) and represent different values of the same ordered list of commodities. It's simple matrix algebra to solve for x resulting in finding the C matrix so that x = Cy.

It is useful to think of most commodities as components. For example, and automobile consists of various parts such as the engine, transmission, body, etc. and each of these parts is a "component" as well as a commodity. Each components usually consists of still other sub-components (also commodities) on so on. Some components are tangible like the wheels of an automobile. But some are intangible like the energy used to assemble the automobile which is not seen by the eye. Every component consists of other components as shown by the A matrix. When the term "recursively" is used it means counting not only the first order (or direct) components determined by the A matrix but adding on the second order component used to make the first order components, etc. This is shown by the C matrix: each column of C shows how much of each commodity (recursively) it takes to make one unit of the column commodity as a final output.

Expressed mathematically, the production x it takes to make final output y is
x = y + Ay + AAy + AAAy + ..... This is an infinite series that converges. The first term shows that to make y we must run all industries to output at least y. But these industries require input from other industries in the amount Ay and so on, giving the infinite series. Expressing this series as a summation we get
sum [{i=0,infinity}A^i]y where A^0 = I is the identity matrix and A^3 = AAA etc.. One can show that the sum of this infinite series of A^i is just the matrix C which is defined as the inverse matrix of I - A. It's similar to the formula used in high school algebra to find the sum of an infinite series.

What are the problems with this model? A major problem is the lack of accurate data, especially if we wanted to consider the very large number of commodities that exist instead of just commodity classes. For example we would like copper to be a commodity instead of the commodity class of non-ferrous metals. But even with commodity classes where there's better data, there's a problem because due to the large volume of imports in today's world one needs to include the entire world in the model and data collection in other countries may not be easy or accurate and the task is difficult. But there are more major problems. One is that the conventional model doesn't consider human labor at all.

Reviewing the main results: If we pick a production vector x we can find the vector y of final output (using the A matrix and conversely (using the C matrix). So suppose we pick a nice large final output vector y so that people could live in plenty. Then we just need to produce x = Cy to achieve that. But suppose it can't be done due to scarcity of labor, capital, and natural resources. There is nothing in the model to tell us this.

One might argue that while natural resources may be limited, we could increase the birth rate to have more children (people are a renewable resource) and thus in the long run get more labor so as to increase the final consumption y at least in the long run. After all, the model does include depreciation of capital, so it does cover the payback for capital. But with more labor and a larger final output y there are more people to consume this y so on a per capita basis we may be no better off than before. We are actually worse off since with more people, we are depleting natural resources at a faster rate. While the model doesn't include such considerations directly, one can use the model to find the increase in production of x required for a proposed increase in final output of y namely the change in x is just C times the change in y. Then we can separately (not in the model) ask what the environmental impacts will be for the increase in production x.

10.2 Variation of y and x

Lets look at what happens when one element of the final output vector y is increased by one. For example, say we want to see how production of all commodities must increase if we make one more sailboat, then we just use x = Cy and let y = 0 0 0 1 0 ... where the 1 represents the one sailboat. This is correct because the equations are linear. Using the x = Cy equation (and determining C) is one of the main results of the I/O model.

But what happens if we want to find the effect of making one more of a certain commodity (which is an element of x)? Well, just use y = x - Ax to find the resulting final output due to the change in x. But something seems to be wrong here. To determine the resources required we want to know how x changes when one of the elements of x is increased. If one industry increases output then other industries will also need to increase output to supply components (recursively) to that industry so that then all the elements of x should increase. But if we just increase x by say 0 0 0 1 0 ... then the output of other industries hasn't increased like it should. Yet such an increase in just one output, x, doesn't violate the two equations for finding y from x and conversely. Why? It's because that when the production of all other commodities goes up due to the increase of production of the one commodity, the final consumption of the final output of all other commodities goes down which decreases the production x of all such other commodities. Thus we don't increase production of everything else for the simple reason that we have decreased final consumption. That really isn't what we wanted to do if we are thinking about saving energy. One can always decrease energy use by decreasing final output. But before discussing how this "dilemma" should be dealt with lets look at the mathematics of it.

Let's look at y = x - Ax for say x = 0 0 1 0 0 0. Note that all elements of matrix A and vector x are assumed to be non-negative. For the elements of x that are zero, the corresponding values of the elements of y will be non-positive due to the non-negative values in the 3rd column of A and some of them will be negative. Here y represents the change in y. For the element of y corresponding to the 1 of x the change will be positive since to make a unit of this commodity must require an input of less than one unit of the same commodity (as specified in the A matrix).

So how should the dilemma mentioned 2 paragraphs previous be resolved? If the output of a commodity increases (an element of x) it would be nice if we could keep final output y constant and observe how x increases. But linear algebra shows that it's impossible since y = [I - A]x and [I - A] has an inverse so it's so-called "full rank" and maps each x into a unique y. Thus changing x in any way will always change y and this also holds when more than one element of x is varied. So if x changes we must allow for a change in y and can't hold y constant. But suppose that due to an increase in say x[3] we only allow y[3] to change and hold all the other y's fixed. Then looking only at changes, we let x[3] = 1 to see what happens when x is increased by 1. From x = Cy we have y[3] = x[3] / C[3,3] = 1 / C[3,3] since x[3] = 1. Since the other y's haven't changed we make them all zero in x = Cy which results in just dividing the 3rd column of C by C[3,3] to find the values of the change in x.

In general, if there are n industries (both x and y have n elements --the A matrix is of dimensions n x n) then if one knows the values of any n elements, the remaining n elements can be found. For example, if n=5 and we know x2, x5, y1, y4, y5 then we can use liner algebra to find the missing values : x1, x3, x4, y2, y3. Here x2 is shorthand for x[2], etc. The short reason for this is that we essentially have n equations: y = [I - A]x in 2n unknowns: x and y. But if we know the values of n of the unknowns, we have only n unknowns, resulting in n equations in n unknowns which is normally solvable.

One might think there are 2n equations (instead of n) since there are the n equations for x in terms y and conversely. But the second set of n equations are just the first n equations which have been transformed by what amounts to matrix inversion and express the same thing as the first set of n equations, but in a different form. Thus there are only n independent equations.

One possible policy of what to do about final outputs when the production of one industry (or commodity) is increased, is to only allow an increase in the final output of the same industry (or commodity) with all other final outputs remaining fixed (no change). This determines all the other increases in production (n-1 values).

As an example of what goes wrong if we only increase the production of one commodity (or industry) but keep all other productions fixed, let's ask how much energy is required to increase the output of a commodity under this assumption. If x[1] were the production of coal and we increased it by one but kept the other x fixed then we have obviously increased energy consumption. But if we do the same for a non-energy commodity, there is no increase in energy consumption at all. But there is energy consumption when this non-energy commodity is produced since it contains embodied energy. But this is compensated for by reducing the final consumption y of society (excepting the final consumption of the non-energy commodity).

Is there any case where this situation might be a reasonable outcome? Well, suppose that due to lack of resources, skilled labor, or capital we can only increase the output of one industry but no others. Then this model shows that in order to obtain the components needed for the increased production in this one industry we must decrease final consumption.

Whether or not decreasing final consumption is feasible depends on the circumstances. If waste or unneeded luxury goods in the final output can be reduced then it's feasible. But if reducing final output means reducing food supplies consumed by workers that are barely getting an adequate diet, then it's not feasible since it is likely to reduce their productivity. Of course if food for workers is considered an intermediate output, then the above is not valid but we might then consider as "infeasible" the case where we would reduce the production of capital goods needed for economic growth.

So in conclusion, asking the question of what happens when the production of one industry in increased is ambiguous unless n-1 other outputs are specified where such outputs consist of some combination of production outputs x and final outputs y so that their total number is n-1 (or n if the production of the one industry mentioned at the start of this paragraph is included). Simply stated, given n values, we can solve for n more values since we have n independent equations in 2n unknowns x and y. One may also consider the vector of intermediate goods: z=x-y This adds n more equations and n more variables to the problem and since we have then 2n equations, 2n known variables will be needed to solve for the remaining n variables. One can't just pick arbitrarily any 2n variables since, they must satisfy z=x-y.

For the case of a worker changing jobs by changing industries, one industry of the new job would increase production and the other decrease production. But to determine what happens we would need to know the values of n-2 other outputs, similar to the example of the previous paragraph.

11. Direct Solution of the Energy to Make a Good

11.1 Overview

Instead of utilizing the company town model let's attack the problem directly. The problem is to estimate the energy required to produce a good or service which includes all the needed human energy. Consider a closed economy such as the world or a nation which is self-sufficient and in a steady state condition. Also assume that we have all the data on technology and material flows needed to solve the problem.

But what we don't know is exactly what the behavior of people will be. The advent of rapid dissemination of information and misinformation via the media (including the Internet) has resulted in making the reactions of people to the world more difficult to predict. And decisions made by people regarding what and how much to consume, where and how they live, which politicians to elect, and what technology to use has a significant effect on the energy needed to produce something. However one way to resolve this is to assume the average behavior of people for the base case and then examine cases where average behavior changes in certain ways: more altruism, less waste, desire to reduce population, etc.

Suppose we want to make one more unit (or item) of a good (such as an automobile, chair, house, bushel of corn, etc.). In order to make that good it will require energy, both directly in making it and in the embodied energy of the components. Likewise for each component. And the depreciation of the capital goods at each step is also a component of energy as is human energy. By making one more item of a good, it's likely that less of other goods will be made. For example, the additional labor used to make the good may mean less labor to make other goods. To grow more corn, it's likely that less of other crops will be grown due to the scarcity of good farmland.

So making one more of something can have widespread impacts. The overall result might turn out to be less energy consumption if the new good take less energy to make than the goods that are not made due to the impact of making the new item. But what are the other goods that are not made? It depends on who buys the new good and spends money on the new good that otherwise would be spent on these other goods. Since we are thinking about not just one person but about society as a whole the question becomes what expenditure society will forego in order to purchase the new good. It depends on people's preferences, income, tastes, whims, social pressure, advertising, etc. This is not easy to predict and to obtain quantitative answers to this problem doesn't seem feasible.

However, if one ignores the above impacts of making one more of something and assumes that all other final outputs are held constant, one can obtain a solution using Input-Output Analysis. Except that the energy cost of labor is usually neglected in conventional I/O analysis. Of course the production of the components (recursively) required for the one new item increases. In mathematics it's like taking the derivative where the final output of all other goods is kept constant (except for the components recursively of the new good). Note that "recursively" means that we count components of components, and so on ad infinitum.

11.2 Including the Energy Cost of Labor

The energy cost of labor should be included under the same assumptions as above when we ask the question of how much energy it takes to make a new item. Since there is no change in the production of items which are not components (recursively) of the new item, steady state requires that the labor for the non-component goods production remain constant. Also due to steady state, it implies the unemployment rate is constant so we can't draw the new workers needed for the new item (and any of its components recursively) from the unemployed. It turns out that the only way to achieve this is that birth rates must increase to provide new workers. It may take say 20 years or so before the new births become productive worker which as first glance appears to be a major problem. The fallacy of obtaining more labor from other industries (by substituting energy for labor) will be discussed later on. get-ref

But it's not as serious of a problem when one considers a major use of the results, where such results give the total energy, and labor required for each item. For example, we may ask what the energy consumption and labor requirements will be if the production of certain goods increases while the production of other goods decrease. To do this we use the results obtained by solving the conventional I/O model for final demand. Then knowing the energy required for each good we could ask a question as to how energy consumption changes if we substitute one good for another. For example, knowing the energy it takes to make gasoline and ethanol we could ask what is the labor and energy impacts of substituting a gallon of gasoline for an equivalent amount of ethanol (1.48 gallons) which contains the same energy content. Thus for goods that we want more of, more labor will be required and conversely. Thus in such a substitution, the overall change in labor may not be much due to the decreasing labor needed for producing gasoline, but it still may change implying that the birth rates will need to change (decrease or increase) to meet the new conditions.

For the case of a population decrease there are other ways for that to happen besides changes in birth rates. For example, famine (including malnutrition), war, and disease, can decrease the adult population much more rapidly than a decrease in birth rates. Such events are wasteful and tragic, but have historically happened and are to some degree happening today in poorer countries. And the possibility of them becoming significant in richer countries as natural resources become depleted and debt becomes overbearing in some countries (such as the United States), cannot be ruled out.

One might think that if this is a model of a single nation, that the additional labor could come from immigration into that nation from outside but this is a model of a closed system that doesn't allow for this. A self-sufficient nation (as was previously specified) should be able to be self-sufficient in labor as well. Similarly, a decrease in labor requirements can't come from emigration out of the country but must come from within, preferably from decreased birth rates.

So what is the energy cost of labor in this case of creating additional labor by more children (and conversely)? It's about the same as for the company town model. That model included the cost of bringing up children and educating them. This model includes that too, since one has to support the new children (needed for future labor) from birth. This model also includes the energy cost of service workers which support production workers since if we want another worker there will be a need for a few service workers to provide services to that new worker, similar to the company town model. So more future service workers will need to be born.

11.3 Modifying the Input-Output (I/O) Model to Include Labor Energy

How would the conventional input-output model be modified to account for labor? The simplest way is to just add a new "commodity", labor, to the model. One could just aggregate all types of labor into one type of labor-commodity and measure it in units of say dollars at the current competitive wage rates. Then for every commodity there is the amount of labor needed to make one unit of that commodity. For the labor "commodity" there is a list (vector) of the amounts of other commodities needed (food, clothing, shelter, etc.) to produce one unit of labor. Since some services may be included in the model as commodities, then the amounts of these needed to produce one unit of labor would be included in this list (vector). In cases where the service used by the worker is not covered in the model (perhaps housework done by a spouse), then there's an increment to the entry in the list for the amount of labor required to produce one unit of labor.

12. Opportunity Cost of Labor Fallacy ?

12.1 Overview

The concept of opportunity cost has been used to support a high energy cost of human labor. See An Economic Assessment of Solar PV Systems by Jim Airola and David Bergson. See section: 4. Energy Opportunity Costs of Non-Energy Inputs. But while this approach is not valid (except for a special case), it's conclusion about the high energy cost of human labor is valid: Right conclusion by wrong method?

Now to explain opportunity cost. If a worker works at a certain employment, it obviously means that the worker can't spend that time working at a different employment. Thus one way to look at the cost of keeping a worker in a certain job is the value of the loss suffered by not having that worker in a different job where the worker might be of greater value. This is called "opportunity cost" and is a valid concept but does it apply for the case of energy in the input-output model above?

12.2 Substituting Labor for Energy

Considering only energy (including embodied), if a worker could save more energy for another firm by working there, then the energy that could be saved on that other job (but isn't) is an opportunity energy cost of working at his current job. It's assumed that the worker only works on projects to save energy for the other firm since the I/O model requires that output not related to the production of the new item remain fixed. See Direct Solution of the Energy to Make a Good.

A major way to save energy would be to change inputs so that they contain less embodied energy, but this isn't allowed since it would change the outputs of the supplier firms recursively. Thus other internal means would have to be sought for making production more energy-efficient. Nevertheless, for a unit of additional labor, a certain amount of energy may be saved. And this "unit" of labor may be a smaller unit than just one person-day such as a person hour or even as low as a person-minute. In economic jargon, this amount of energy saved is the "marginal rate of technical substitution" of labor for energy from the theory of "production functions".

So in this case we obtain the labor necessary to make the new item in the I/O model is obtained from an industry where the output will be kept constant, even though a unit of labor has been lost. This is possible since additional energy may be substituted for labor. Note that the I/O model also assumes that capital is kept constant.

12.3 Violates Axioms of I/O Model ?

One might think that this would be a valid method of obtaining labor for the production of one more item where the output of all other items (except for the components recursively of the "one more item") is held constant. But it's not. The problem is that the substitution of more energy for less labor violates the assumption of the I/O model that the A matrix of input-output coefficients (the technology matrix) remain constant. The I/O model requires the inputs for making a commodity be in fixed proportion to the output, but the substitution of more energy for less labor (in the firm the employee left) implies that now more energy will be consumed per unit of output. The numbers in the I/O matrix thus change, which is not allowed in the I/O model.

Why would changing the I/O matrix be wrong? Because the I/O matrix represents the technology. By just changing the technology it is often possible to save energy, not just for making the one additional item in the I/O modem but for the current production of making a large number of items. And this is obviously not permitted if we ask the question of how much energy it takes to make one additional item. By changing the technology a little (by changing the I/O matrix) it might be possible to save more energy than it takes to make the additional item, resulting in an erroneous claim that it takes a negative amount of energy to make one more item.

But there is an exception to this. Suppose that the I/O technology matrix A has been optimized with respect to energy, subject to reasonable constraints. The constraints might be that the outputs of all firms remain constant and that the use of non-energy natural resources such as land (and topsoil) be sustainable. This should imply that to first order, a small change in the I/O matrix coefficients (subject to the constraints) makes no change in the amount of energy used by society. The reason for this the that total energy is a function of the constrained values of A and it's like a minimization problem subject to constraints. An optimal solution will result in derivatives of the objective function (minimization of energy) being zero in any allowed direction. As a result substituting labor for energy at the marginal rate of substitution would (neglecting sustainability) would not violate the spirit of the I/O model for very small changes. While in this special case, the opportunity cost model seems to be applicable to human energy accounting, the economies of most all situations are based on maximization of profit and not on minimization of energy consumption so the I/O matrix in reality is almost never 'optimized" to minimize energy consumption.

12.4 How optimal is the I/O matrix?

This is a big question and it's likely not very optimal. See Input-Output (I/O) and Production Functions Regarding energy and labor, with non-optimal assignments of jobs to workers, there will likely be energy savings by changing job assignments. But that isn't the question we are asking in the I/O model.

12.5 Energy Cost of Labor: Value per Opportunity Cost

So assuming the I/O matrix is optimal with respect to energy in the trade-off between energy and labor, what values may we estimate for the energy cost of labor? Well it's just the marginal rate of substitution of labor for energy (see Substituting Labor for Energy. But what are it's values? A rational firm should be attempting to minimize costs for a given output, so if they can save money by hiring more labor to save energy costs, then they should do so until the marginal savings of energy cost is equal to the cost of the labor needed to effect this savings. So the amount of energy that a worker is worth is just the amount of energy he could buy with his wages provided that he pays the same price for energy it as does the firm he works for.

In the company town model the energy cost of a worker was the energy cost to support that worker (including the energy costs of the service workers recursively needed to support this worker). But the worker's wages should cover all of the expense to obtain this energy. Let's suppose the worker's wages exactly covers the cost of sustainable living which includes the cost of paying for services and raising children. Then the energy cost of labor is the amount of energy (including embodied energy) the worker does buy with his wages. This company-town case is not the same as for the opportunity cost case:

Do these differ? It's obvious that the opportunity cost is at least equal to the company town cost. A worker "could" buy more energy than he "does" buy. This is because some of the living expense of the worker may be spent for basic factors that are neither actual nor embodied energy. That is, unless one subscribes to the energy theory of value. An argument against the energy theory of value it that one might expect that energy (including embodied) is not the only basic thing a worker purchases with his wages. There are also various other minerals besides energy that a worker buys (such as the copper from copper ore) and they become embodied in the goods containing them.

13. Alive Anyway Fallacy; Job Change

13.1 Introduction

The "alive anyway" argument says that if someone takes a new job it may require little or no additional energy to support that person since that person was being supported anyway prior to taking that new job. Thus, even if that person didn't get the new job, they would be still be alive anyway and still consuming the resources needed for their support.

While such reasoning is seemingly valid, it's a moot point because we are not normally asking the question of the energy impacts of a job change (or "employment status change" if the person who gets the job was previously unemployed). Instead, we are asking how much labor energy is required to produce one more unit of a good where the output of all other goods remains fixed, except for the components (recursively) of the unit of the additional good. It turns out that the new labor in this case can't be taken from another job without violating this assumption because it would result in a drop in production in his old workplace so that "the output of all other goods" would not remain fixed. If the labor was previously unemployed, it would result in a decrease in the rate of unemployment which is in violation of the assumption of a steady-state fixed rate of unemployment. It turns out that the new labor has to be obtained by a population increase: be born and added to the population and work force. See Including the Energy Cost of Labor

13.2 Compare to Allocation of Wages to Production

Introduction

One may compare the allocation of human energy to production to the allocation of labor costs to production. When someone works and is paid wages (including benefits) such wages are allocated to the worker's production and are included in the price of the goods produced.

Under capitalism, socialism, and communism

The above is the way it works under both capitalism and socialism. But what about communism? It turns out that countries that the West called "communist" (such as the Soviet Union) had economies that were actually socialist and such countries repeatedly claimed that they were socialist and not communist, even though the political parties prevalent in those countries were named "communist parties". The reason for calling themselves "communist" was that it was claimed that somewhere in the future these countries would make a transition to communism but that they weren't yet ready for it. This entire situation regarding communism is still true for the few "communist" countries remaining but talk about the possibility of a future communist society is very scarce.

But how would labor costs be allocated under true communism?, which supposedly would operate under the motto: "from each according to his ability and to each according to his need". If workers are paid according to their need, there would be widely different labor costs for the same work which would make it difficult to attribute these labor costs to the product produced since it would depend on the particular needs of the workers doing the work. (It's assumed here that communism would operate using money, enabling consumers to choose what they wanted to buy.) One way to resolve this difficulty is to pay workers the same for identical work, but provide them with their needs using taxes and subsidy. Workers that needed more than they earn would receive a subsidy to pay for it, and workers that earned more than they need would be taxed to support the subsidy. This is something like welfare-state capitalism or socialism, which has various benefits to supposedly provide many people with what they need beyond what they can provide from their own resources.

Thus under any of these three economic systems, labor costs are (or could be in the case of communism) allocated to the price of the goods or services produced by such labor.

Wages and Energy

It is generally accepted in economics that labor is a factor of production and that the cost of labor should be included in the price of what the labor produces. Capital also is produced by labor and the cost of such labor should also be included. If labor is a factor of production, then it would seem that the energy to support labor is also a factor of production.

If one were to invoke an "alive anyway" concept, they might erroneously argue that when a worker gets a new job there doesn't need to be any wage paid to the worker to support the worker since the worker was already being supported previous to his getting the new job and thus no additional money to support the new worker is needed. This would also imply that no additional energy needs to be allocated to the new job.

But this would, in general, be unsustainable since people are continuously over time being fired (or laid off) and finding new jobs. Eventually most all workers would be working for free. Who would support them? Well, the employers would need to be heavily taxed to support them, and this tax would be tantamount to paying wages to these workers. To make this tax fair, it should be about equal to the wages that the employer would pay the workers that are working for them for free. It should be clear that a reasonable solution to this hypothetical situation would just be to just pay all new workers wages and not expect them to work for free. And this pay includes the cost of the energy the workers and their families and service workers use.

13.3 Energy Impacts of a Job Change

Of course, one can attempt to ask a different question (which turns out to be ill defined): What are the energy impacts of a change in employment? In this case the alive-anyway argument may be valid although the job change is likely to result in a change in a worker's life-style so that the energy used for living is changed. But the major difficulty here is that a job change will also impact the production of the two firms involved which in turn will impact the supply of inputs to these two firms. Thus there are two different impacts on energy consumption: One is more direct and is due to the change in the life-style of the worker due to the new job. The second is due to the change in production of the two firms involved when the worker leaves firm A and starts work at firm B. These changes in production cause changes in production of most all other firms in the economy due to the changes in the inputs and output of both firms A and B.

13.4 Energy Impacts from Change in Production

It turns out that this problem is ill defined without more information about how final consumption and/or production of other firms will (or should) change as will be explained next.

One way to calculate the energy impacts of a job change is to try to use the Input-Output model where human energy has been included. See Modifying the Input-Output (I/O) Model To do this one can use the value of the amount of labor required per unit of output (an element of the A matrix of this modified I/O model) and then use the inverse of this which is the volume of output per unit of labor input for a certain industry. Thus one can find the increase in production for the worker's new industry and the decrease of production for the worker's previous industry. But the change in energy due to these two changes in production depends on the changes assumed for the final output. See Variation of <em/y/ and <em/x/

In addition to the change in energy consumption due to changes in production there is also the change in energy due to the change in the lifestyle of the worker.

13.5 Energy Impacts if the Unemployed Get Jobs

A significant change in lifestyle energy will happen when an unemployed person gets a new job. An equivalent situation to an unemployed person getting a job can happen if the new job is filled by someone who quits an existing job, and that existing job is filled by someone who quits another job, etc., etc. but ultimately, someone quits a job that get filled by someone who was unemployed.

Unemployed persons will likely have less income and likely live more frugally. Such living uses less energy. For example, the unemployed person may have time to do things to use less energy such as repair broken possessions rather than purchase new, etc. and eat cheaper food (which takes less energy to make). In an extreme case the unemployed person may even be homeless and thus save most of the energy normally used for housing. When the person gets the new job and has more income, the person is likely to live less frugally and thus use more energy. This is an energy cost to hiring an unemployed person.

In most cases, an unemployed persons lives at least partially off the labor of others (a subsidy), such as workers that work for companies which pay unemployment insurance taxes. When the unemployed person gets a job and becomes self supporting, then the subsidy by other workers is reduced and more of the products of their labor are available for consumption by these workers as well as for government, charities, etc. This all takes more energy.

Also, with a new worker, production should increase in that industry resulting in more energy use, as well as the increases in energy of the supplier industries recursively. However, suppose the new job is not to increase production but to increase energy-efficiency of the industry. In this case the result will be a saving in energy. But this is an exceptional case and not typical. If labor is divided into small labor units, an industry would simultaneously hire labor units to increase energy-efficiency and increase production, with most of the labor units going to increasing production with the overall result of more energy use..

13.6 Water Under the Bridge

Another way of showing that that this question of what happens due to a change in jobs is moot (and thus the alive-anyway argument is invalid) is to invoke "water under the bridge" reasoning. When asking the question of how much energy it takes to make something or do something it only depends on the current state of the world and not on the past history of the world. This is the old "water under the bridge" principle. For example, the efficiency of your automobile right now depends only on the current state of the automobile, including the condition of the road and how you are driving it. It doesn't depend on the condition of your previous auto nor on the condition the auto you are driving was in yesterday nor on the condition of the road in the past. It only depends on the conditions that exist right now.

This is not a say that past history is not useful. It is useful in observing cause and effect. And it can also be used to estimate the current state of things. For example, knowing the results of tests done on your automobile yesterday are useful in estimating the current condition of your auto. But once you know the current condition, the past conditions are just water under the bridge.

So the energy used by a person in a new job obviously depends on the worker's lifestyle while working on the new job. But the lifestyle the person led in the past is irrelevant. Whether or not the new worker lived a frugal or extravagant lifestyle and whether he was previously homeless, unemployed, or employed, doesn't change the energy cost of his labor in the present. One might claim that on the contrary, since an extravagant lifestyle in the past may have created a large debt the worker must repay, that the past does matter. However that debt is part of the current state of the word and it's the current debt that counts, not how the debt was created.

But if the question is the energy change resulting from changing jobs, then one can't apply the "water under the bridge" reasoning since we are asking a question of comparing the past to the future which is examining the "water under the bridge".

13.7 Energy Cost of One Job

The question asked previously (see Direct Solution of the Energy to Make a Good) was the energy cost of one more item in the long run, with everything not related to the production of this item remaining fixed. A completely different and ambiguous question is asking what the net energy change for society is if a new job is created and a person starts working. The reason it's an ambiguous and ill defined question is that the result will depend on what is kept constant and what may vary. Also, the boundaries of the problem need to be defined. It also depends on what the new employee was doing previously. See Variation of <em/y/ and <em/x/

One way to look at this is to estimate the energy required to support this person sustainably. The worker receives pay for work and uses it for life support which consumes embodied energy in food, clothing, shelter, health care, etc. and includes the embodied energy in services that the worker needs (or pays for). A diametrically opposite point of view would reason that since the person who gets the job was already being supported and thus consuming energy, little (if any) additional energy life support is required.

Note that this section uses a person-day as a measurement of labor. But strictly speaking, marginal cost should be measured where the change in labor is very small, such as only a second of labor time per day. So when we talk about creating a job, what we actually mean is slightly increasing labor time (say be a second), then estimating the energy cost of this second to find the J/sec of energy cost, and then converting to units of energy per person-day of labor.

13.8 Company Town Case

Introduction

First let's look at what happens if a new production worker is added to a "company town" as previously defined. It assumes that either the company town has full employment or that the unemployment rate is fixed. The additional energy which needs to be supplied to the town is the energy per capita of the new worker plus a few other dependent people: servers, spouses, children, and retirees. Thus it's a few times the energy per capita with a total of approximately 0.1 Gcal/day (giga calorie) or about 300 times the rate of caloric intake per day of the worker's food of about 3Mcal/day (3000 kcal/day). See Calories eaten per day.

When a new worker (actually more person-hours of labor by various types of labor) is added to the workforce, then the output production of the company town increases. This will require not only more labor in the company town but more inputs to the plant from outside the town, all of which contain embodied energy (including embodied labor energy). Thus an equivalent question to ask is what the increase in the energy cost of labor in the company town due to the increased production.

One may object to this by invoking the alive-anyway argument Alive Anyway Fallacy; Job Change and point out that the new worker had to come from somewhere and thus was previously being provided with sustenance. So that while more energy is now being provided to the company town due to the new worker, less energy to sustain the worker is needed elsewhere. The net result: little change in energy support for labor. One thing wrong with this is that the company town model just looks at what happens in one company town. If the new worker is obtained from another company town, then there is a reduction in energy consumed by the town the worker leaves.

But if this were to happen, one could use the normal model (with full costing of labor energy) and ask what would happen if the first company town increased production so as to require a new production worker and the second company town decreased production so as to lose one production worker. The first action increases energy use and the second action decreases it. They don't necessarily exactly cancel out each other so there may be a net gain or loss in energy used. But it does account for the saving in energy due to the departure of the production worker from the 2nd company town.

Where Does the New Employee Come From ?

But if a new job is created in the company town, where does the new worker come from? Since population in the town is constant, people born in the town are just replacements for townspeople who die and don't provide an employee for a new job. So there are two possibilities: the new employee comes from outside the town or the new employee is a extra person born in the town in addition to the births which are replacements for deaths.

Company Town's Population Increases

If the new employee was an additional person born in the town to increase the number of workers, then the town will need more energy input to support this person and also has had additional energy inputs over the past couple of decades to raise and educate the person from birth (actually from about 9 months prior to being born) since the pregnant mother required additional food and health care. But to provide service workers to serve the new employee, it will require that a few additional persons be born into the town. This is just about like the Company Town Case except that there is the additional energy used to rear the new worker which needs to be allocated over the worker's working life. For the steady-state workers already in the town, no such allocation is needed since it is already accounted for by the town supporting the rearing of replacement workers.

New Employee Comes from Outside the Co. Town

The new employee used energy in living when s/he previously worked in some other company town.. This would violate the be Water Under the Bridge reasoning but that's OK since we are asking the question of the energy impacts of one more job. Thus one might try to invoke the alive-anyway argument here and claim that since the new employee was previously consuming resources in the town where he came from, that little or no net additional resources are required. In other words, while more energy and resources are required to support him in the company town he goes to, less energy and resources are required to support workers in the town he came from due to his exit. Note that we are not only examining the company town but since the new employee comes from another company town we are looking at the whole network of company towns.

What's wrong with the above argument is that if we assume that the company towns are in steady state, then we can't take a worker from another company town since that would decrease the output of this town. But due to the required increase in inputs to the company town where the new job was created, increased outputs are required from other towns recursively to supply those increased inputs. Thus the impact of a new production job in a company town is the requirement of energy and resources not only to support that person that got the job, but the required support of people in other company towns that must increase output. On top of that there is the support of the additional service workers, not only in the company town where the new job was created, but the other company towns where production must increase as a result of increased inputs needed by the new-job company town.

13.9 Example of Failure of Alive-Anyway: All Dead Anyway

Here's an extreme example showing that the people one claims will be "alive anyway" may in fact wind up dead if they fail to account correctly for human energy. Suppose we have a closed economy (for example, a small country with no imports or exports). Then suppose we find a way to create energy just by human labor, such as say growing crops and producing biofuels from them. Since only human energy is used in producing such biofuels, one might erroneously argue that since the biofuel workers would be alive anyway, there is no need to make any charge for human energy to the production of biofuels. Thus (if this were true) no energy is used to make biofuels. So it's supposedly a big energy gain even if the productivity of the biofuel workers is low. Most of the biofuels will be exchanged for other goods needed for the life support of the biofuel workers. But suppose that the productivity of the biofuels workers is low: not enough energy is obtained from the biofuels to support the lives of the biofuel workers (who exchange biofuels for the necessities of life, likely using money as a medium of exchange).

The only way to keep the biofuel workers alive (including the people who provide services to the biofuel workers) is to energy-subsidize biofuel workers from the other (non-biofuels) sectors of this closed economy. But suppose that these other sectors are just barely surviving and have no surplus to give as subsidy to the biofuel sector. So in this case the biofuels workers can neither sustain themselves from biofuels nor from a non-existent subsidy. Thus all the biofuel workers die and the assumption that they would be "alive anyway" is false since they are all dead anyway.

There are other extreme cases similar to the above scenario. One would be that the other sectors of the economy are forced to subsidize the biofuel workers, even though they have no surplus to do so. As a result, the workers in these other sectors of the economy die from lack of sustenance due to the subsidy they are forced to provide out of the resources they need for their own sustenance. Then with no workers in the other sectors left to provide subsidy to the biofuel workers, the biofuel workers also die. This is a worse outcome than the case where no subsidy is provided resulting only the biofuel workers dying off.

In reality, it would not likely be this bad. For one, income is not evenly distributed and the rich would likely survive unless there is a violent revolution. Also, some starving people might be able to grow their own food locally. But where is the land for this and can they survive the months needed for the crops to grow to maturity? A more likely outcome would be that there is just enough resources and energy to survive, but at an impoverished standard of living which implies low life-expectancy, poor education, malnutrition, high crime rates, failed government, etc. In other words similar to some of the impoverished countries today.

Note that to support the lives of workers includes supporting the lives of the service people who provide necessary services for them. An equivalent scenario could be done using the company town model with a town devoted to biofuel production.

The above shows that failure to assign a reasonable energy cost to labor using the "alive anyway" argument may result in the "alive anyway" assumption being invalid. These counter-examples further strengthen the case against the "alive anyway" argument.

13.10 Marginal Rate of Substitution fix-me

Another method of estimation is as follows: Let's consider the case of a firm named F that can produce the same output with either: one additional employee or a fixed amount of additional energy input. An economist would call this the "marginal rate of substitution" for the "production function" of this firm where energy is to be substituted for labor. This energy input is assumed to be "pure" energy that contains no embodied energy and thus no human energy. It's like the enterprise is located next to an oil seep in the earth and it can use this oil for energy but nevertheless has to pay for the oil.

It's also postulated that the total output of goods and services remains the same in the short run, otherwise any scheme that reduced such output could save energy. However energy inputs to industries are allowed to vary as an impact of the creation of this new job. We also assume that no additional capital is required to support this new job. Firm F thus has two alternatives: one more employee or a fixed rate of additional energy input (due to not hiring a new employee). In both cases, the output of the firm F is the same. Which alternative for firm F will use less energy? We will examine both the short run impacts and long run population impacts. The short run is perhaps a month or so and the long run is many years.

Three cases will be considered:

fix-me: alternative to employment changing output

13.11 Fixed Rate of Unemployment

If unemployment is at a fixed rate (and population constant) an unemployed person finding a job is accompanied by an employed person losing a job. In this case, in order to maintain constant output, more energy must be used by the firm that loses an employee which isn't replaced. However the hiring firm F reduces their energy consumption by hiring this new employee. In economics one might say that there is an opportunity energy cost to pay since more energy is now required to maintain output by the firm F that lost the employee. Remember that most of the energy saved or lost is in the form of embodied energy of goods.

>The firm that lost the employee will produce less, unless the employee >worked only on energy conservation.

For example, if the new employee redesigns the manufacture of goods so that the goods will last longer, the production of them can be reduced to keep the output constant, resulting in less energy. Note that if a good lasts longer, it's value increases, so to keep the value of output constant, less physical output of goods is needed.

This result using the company town model is similar for a worker switching jobs from one company town to another company town. The worker, along with his dependents and servers just move from the old company town to the new one. Thus there's no change in consumer goods energy input costs for the two company towns as a whole, except that the town where the worker quit now has to import more energy so as to maintain constant output.

So the energy cost of providing this new worker is called the "marginal rate of substitution" of energy for labor in the industry losing the worker. This should be approximately the same as the worker's wage, which covers payment for the support of all the servers and dependents required by the worker. So this is about the same as the huge amount of energy as predicted by the company town model for the case where there one only looks at the company town that took on a new resident worker along with the worker's servers and dependents.

13.12 Company Town; Changes in Unemployment

Suppose someone in a company town is fired from his job thus increasing unemployment, but the input flows of consumer goods don't change so that the fired person is still supported with his previous standard of living. To maintain constant output of the town's industries, a new hire from outside the town, along with his dependents and servers need to enter the town, resulting in a significant increase in energy input with no increase in output. The marginal rate of energy intensity (increase in energy input per unit increase of output) is infinite. In the previous extreme case where the unemployed person gets a job and maintains his standard of living, the marginal rate of energy intensity is zero (more output for the same energy input). So while it's possible to find extreme cases, these are not typical.

13.13 Long Run Population Change

Since energy and global warming are long run issues, we are especially concerned with long run effects. For a developed country, More jobs available will likely increase birth rates to provide workers to fill those jobs, and conversely. Economic conditions do influence birth rates in modern countries such as the low birth rates in the United States during the great depression and in Russia in recent times due to the depression in Russia. Thus in the long run, creating a job may mean that there will be a few more people to provide energy for and conversely. The company town model itself doesn't address the issue of long run population change.

13.14 Animals and Slaves

Let's look at the case of domestic work animals such as horses. If one maintains a work horse using feed produced using fossil fuels, then that energy obviously is assigned to the useful work done by the horse. Also, the non-feed energy needed for maintaining the horse counts also. If we don't need the horse anymore, then we can sell the horse to someone who does and will pay for the cost of sustaining the horse. If there are excess horses and little demand for them, then we can breed less horses and thus save the energy required to maintain the horse. The surplus horses could be put out to pasture until they dies of old age, or we could even kill the horses for horse meat. Thus for a horse, in contrast to humans, the long run impact would be saving of the total energy used to maintain the horse.

The situation for slaves is intermediate between the case for horses and non-slave humans. If slavery were legal today, the slave owners might be able to control the reproduction of slaves. Thus if one less slave is needed, there would be a lower birthrate for slaves and conversely. Thus all the energy required to maintain and reproduce a slave would be charged to the services and goods produced by the slave.

Even in the case of free people (non-slaves) the government may have a population control policy (such a China). If less (or more) labor will be needed in the future the government can modify its population policy to try to decrease (or increase) the birthrate. Even with no population policy (such as the United State) a lack of jobs signals a need for less workers and people tend to have less children in hard times. See Long Run Population Change

14. What Purposes Does Energy Serve?

14.1 Introduction

Asking "What is the purpose of energy?" is something akin to asking the metaphysical question: "What is the purpose of life?". But while energy itself may not have a purpose since it's not alive and doesn't think, there's another concept of "purpose". Energy is in fact used for various specific purposes (such as transportation, residential heating) and for more general purposes such as the support of human life.

One might think that energy could be assigned to various purposes in a way that all energy was assigned (and not double counted). But this is not correct since the same energy can be used for multiple purposes due to the recycling of it. A common example is the energy (much of it embodied) that is used to support the lives of workers also becomes embodied in what they produce (including services). Thus the energy that flows into the workers flow out of them into the products they produce and this is like recycling.

One might think that such energy could be uniquely allocated by say allocating half of the energy to support the workers' lives with the other half going into the goods they make. But this isn't so. All the energy must go to support the workers lives, since if they were not living, none of this energy would be used. All of it also becomes embedded in the products they produce, since if the products weren't made the consumers of the products would not buy them and provide the workers with money to purchase the goods and services needed for living (all of which contain embodied energy).

The above statements may be oversimplified since surplus provided to the worker is neglected. For example, if luxury goods which the worker doesn't really need are deemed to "support the lives of workers" then the consumption of such goods represents a sink in the flow chart which absorbs the energy which doesn't make it into the products made by the workers. But one may argue that such luxury goods don't support the lives of workers and thus the above paragraph is correct.

An obviously major problem in energy analysis is estimating what is surplus and what are intermediate goods. This separation is required to use the Input-Output model. And such a determination depends on purposes such as "Is the purpose of this product the support of lives of workers?"

Intermediate production assigns the energy it uses into the embodied energy of the intermediate goods and services. But the ultimate purposes are like sinks in energy flow. The energy used by them disappears and is lost forever. Well not always since the sinks in the energy flow may be works of art that will survive for many centuries, or knowledge that will be of use in the future. But by assigning all the energy to the ultimate purposes, these purposes become very energy intensive and great energy savings can be achieved by reducing these ultimate surplus outputs.

Still, a great deal of understanding may be obtained without examining the question of ultimate purposes. Take, for example, the economic community model. More energy flowing into it than out means it is being heavily subsidized by the rest of the world. Unless of course it is producing surplus goods such as great works of art or accumulating significant amounts of capital or knowledge that will be of value to society at large (beyond the economic community).

Modern society produces energy and it would be nice to be able to account for it in terms of the ultimate purposes for which it is used. For example, one might say that an ultimate use of energy is to provide automobile transportation. But if the automobile is used by a firm to produce a good or service, should not that transportation energy be assigned to that good or service produced? And if that good or service is not a final output (i.e. an ultimate purpose of energy) then one needs to look for ultimate purposes further along in the embodied energy flow chain.

14.2 Economies Without People

A very simple energy economy is one without human beings and even more elementary is an energy economy with only plants (and perhaps some bacteria to help decompose dead plants). In this case the sunlight energy provided to the plants is just to grow the plants. Insofar as some of the plant material becomes trapped in the earth, it is converted to fossil fuels, one could claim that one result (purpose ?) is to create fossil fuels and another result (purpose ?) is to generate oxygen from carbon dioxide, thus creating a planetary atmosphere more suitable for future animal life. Since animal life evolved from plant life, one could claim that an ultimate results (purpose ?) is to prepare the way for evolution into animals and ultimately human beings.

If we add animals to this world of plants, and if some animals are carnivores and eat other animals, then what is the result of the solar energy that provides energy to the plants and ultimately to the animals? Since the animals depend on the plants for their survival, one result of the solar energy is to support animals. But what about the result of supporting plants? The animals don't eat all the plants so part of the result of the solar energy used must be to support plants. So the ultimate result (purpose ?) is to support both plants and animals.

14.3 Primitive Economies with People

After some of the animals evolve into people, then the ultimate result of the solar energy would seem to be the support of plants, animals, and people. Some might claim that the main result is to support people and that the population of humans could become so large that there is no place left for wild animals and plants. But don't people have a lot to learn from observing the life of wild animals and plants? And isn't there also a recreational aspect? Does wild nature have an inherent right to exist even if it were of little or no benefit to humans? Thus, how to allocate the solar energy depends in part on ones philosophy of the relation of humans to the natural world.

14.4 Mineral Fuel Economies with People

The extraction and use of mineral fuels such as coal, petroleum, natural gas, and uranium is done by human beings and not by wild animals or plants. Thus it would seem that the purpose of this energy is to support human life. A simple allocation model would be to allocate all of this mineral fuel energy to the consumer goods used by people which are made possible by the consumption of these fuels. In other words the ultimate use of the energy would be to support human life with food, clothing, shelter, etc.

A complementary point of view is that much of the support of human life is merely a means to an end. Humans use a significant part of their lives to work and help produce goods and services. They are thus something like machines (or work animals or slaves). You provide them with food, clothing and shelter and they produce surplus goods: luxury goods for the rich (and sometimes not-so-rich); capital goods for industrial capital accumulation; works of art, music, science, literature; recreational goods; etc. Then the ultimate use of energy is to supply surplus goods to society. In this scenario, the energy is allocated to a much smaller subset of goods than the allocation in the above paragraph which includes food, clothing and shelter as final output. Thus the embodied energy intensity (EEI) of the surplus goods is very high.

14.5 The Fuel Company Town

How does this apply to a company town which produces fuel for it's output? While the fuel itself is not the ultimate use of that fuel energy, from the viewpoint of the world at large the fuel town gets energy input from the embodied energy of the consumer goods flowing into the town plus industrial goods and energy flowing into the town, and outputs only fuel. The human labor and support of all the people in the town is just part of the production process and is an energy cost input for the obtaining of the exported fuel output.

But let's look at this from the point of view of the residents of the fuel town. Their livelihood comes from the extraction of fuel, they exchange the fuel they produce for consumer goods. For them, the ultimate use of the fuel they extract is to support their lives in the town. In a sense, the embodied energy supplied in consumer goods to the town is used twice: once to provide fuel output due to the labor of the people and again to support their lives. Work has a dual purpose: It both produces output and provides a livelihood for the workers. Can a unit of embodied input energy both flow into an ultimate purpose sink of supporting human life and also be converted into fuel due to the labor of the workers. Mostly no, but possibly yes for the case where there is no surplus.

In economics there is something called joint products, like the mutton and wool from sheep. But what we are talking about concerning the fuel town is something quite different. Some of the food the sheep ate went into growing wool and other elements of the sheep's food went into growing meat. In the fuel town, the same elements of consumer goods both supported the workers lives and went into the production of the exported fuel. In other words the same fuel input accomplishes two different purposes at the same time.

14.6 What are luxury goods and waste?

It should be obvious that there will be differences of opinion as to whether or not specific goods or services should be included in the surplus good category (luxury/waste items) or whether they are necessary goods for workers. For example, what types of vacation travel are luxury and what types are needed to maintain the physical health, morale, and education of workers?

Here are some wasteful economic activities: commercial gambling (including lotteries), civilian government waste (including unjustified subsidies), military spending wrongfully used (example: Vietnam, Iraq), most recreational drugs, waste by monopolies such as overpaid top management and railroad train operators, etc.

15. Appendix: Motivation

Both the problems of global warming and the depletion of fossil fuels has heightened the public awareness of the need for energy conservation. Conserving fossil fuels puts less carbon dioxide into the air and helps reduce the acceleration of global warming. It also conserves the fuels for use by future generations but unfortunately the future use of this saved fuel in the future could exacerbate global warming.

Thus it's important to be able to get good estimates on the energy it takes to produce various goods and services since people and governments often favor the goods and services that allegedly have the least energy content. For example: Does it take more fossil fuel energy to make ethanol than the energy contained in the ethanol? But a major problem in energy accounting is how to estimate the human energy it takes to make goods (such as ethanol).

As a digression: Favoring low-energy-content goods by subsidizing them is (in the authors opinion) bad policy. Using fuel energy does harm to the environment and the future. Just like smoking cigarettes is harmful, subsidizing goods that use less energy and are thus the less harmful is like subsidizing cigarette brands which are the less harmful because they contain lower levels of tar and nicotine. Such subsidy is not fair to those that don't use the product at all.

For example, someone who travels little and doesn't own an automobile is likely saving more energy than someone who drives a fuel-efficient automobile. Thus if there's subsidy for energy-efficient autos, there should be even more subsidy to people who don't even use an auto, but there isn't. Thus if government operated more rationally and didn't subsidize goods that are supposedly energy-efficient, knowing the energy content of goods would not be as important.

Many studies of energy flows in the economy simply (and erroneously) neglect the human energy factor. An example is the book: Environmental Life Cycle Assessment of Goods and Services, An Input-Output Approach by Chris T. Hendrickson, Lester B. Lave, and H. Scott Matthews. RFF Press, April 2006 (260 pages).

16. Appendix: Renewable Energy, Food and Human Energy Examples

What is often called renewable energy isn't really renewable at all, since to produce "renewable energy" often requires a lot of embodied energy (including human energy) to produce.

When human beings work, play, or rest they use energy and put carbon dioxide into the air by breathing. But this carbon dioxide by itself doesn't directly contribute to global warming since the food was created by the sun shining on plants and the plants removed carbon dioxide from the air in order to get the carbon used to form the food. For the case of meat, the animals that grew to create the meat ate food generated by the sun. Thus it might seem that food is a renewable resources created by solar energy and eating it doesn't increase the carbon dioxide content of the atmosphere. But this is an illusion because to produce food the modern way requires machinery, fertilizer, transportation, and human labor that use a lot of fossil fuel energy and thus heavily contribute to global warming.

The energy content of food (measured in Calorie=kilocalorie=kcal) is food energy consumed by humans; and the carbon dioxide we breathe out is a result of the digestion of this food. But for every kcal of food consumed, it roughly takes about 10 kcal of fossil fuels burned to produce it and transport it to the consumer. See Appendix: Fuel to Make Food All this also contributes to global warming. But the impact of using human energy doesn't end there. Humans, in addition to food, require clothing and shelter. Without these, they would die (at least in cold climates) and thus not be able to exert any physical or mental energy. So clothing and shelter are necessary prerequisites for human energy to be available. Note that human energy output is not just muscle power but also includes the mental energy used by people at work, study, recreation, etc. To further explain this requires explaining the concept of Embodied Energy.

So most all of both food energy and human energy is derived from fossil fuels and is thus not renewable.

17. Appendix: Land, Labor, and Capital

The standard economics textbook explanation is that goods and services are the result of 3 basic factors of production: land, labor, and capital. The use of minerals and fossil fuels would be included under "land". But fossil fuel energy becomes embodied in labor and capital, making it infeasible to utilize this textbook model. What is needed is a new model incorporating the renewable and non-renewable uses of land. Growing crops sustainably where all the waste products resulting from the crops (including human excrement) is returned to the soil is a renewable use of land. Extraction of fossil fuels from land and burning them is a non-renewable use. This article will not attempt to reformulate the conventional model but it will not use it.

18. Appendix: Embodied Energy

18.1 Introduction

Most studies either ignore human labor energy or grossly underestimate it. See Company Town Analogy which explains why human labor energy is very large.

The energy expended to make a product (such as an automobile) or a service (medical care), or an adult person is called the embodied energy of the item and is depreciated as the product, service ,or person is utilized. Just like an automobile depreciates in value as it is used and ages, so does the embodied energy in the automobile or person depreciate. The embodied energy of an automobile is not just the direct energy it took to assembly the automobile but includes the sum of the embodied energy of all the components that went into the automobile: light bulbs, the battery, tires, windows, human labor, etc.

Of course, each component itself is a product and contains the embodied energy of its components. And so on ad infinitum. It's really infinite because each chain of components eventually begins to loop.

But the adding up of an infinite number of values doesn't result in an infinite sum because the complicated series of numbers we add converges. For a very simple example, if we add up the series: 1 + 1/2 + 1/4 + 1/8 + ... we get 2 although there are an infinite number of terms.

Synonyms for "embodied energy" include: "embedded energy", "indirect energy", and possibly "emergy".

18.2 Iron and Coal Loop Example

A simple example (neglecting human labor) of a loop with 2 components is iron and coal. It requires coal to make iron since the carbon in coal combines with the oxygen in iron ore to create carbon dioxide gas, thereby removing the oxygen from the iron oxide ore and leaving just iron. But it requires iron (actually steel) to mine coal since coal mines use steel (mostly iron) to hold up the roofs of the mines, etc. Suppose that to make x tons of iron requires ax tons of coal and to make x tons of coal requires bx tons of iron So to make a ton of iron requires this many tons of coal from this 2-item loop process: a + aba + ababa + .... This is just an infinite geometric series which sums to a/(1-ab).

Another way to find this result without using an infinite series is by simple algebra. Let the total amount of coal required to make x tons of iron be cx. Let's find the value of c in terms of a and b. We have cx = ax (direct amt. of coal) + c(bax). The first term, ax is the amount of coal needed to make the iron. But using up this ax amount of coal will engender some more use of iron which is the second term c(bax). Since we need bax more iron to make ax amount of coal, this will result in c(bax) more iron needed. Solving results in c = a/(1-ab), the same as obtained using the formula for the sum of an infinite series. Actually, much more coal than this is required to make a ton of iron since there are many other loops and chains involved. For example, the steel mill that makes iron uses electricity that may have been generated by coal.

18.3 Automobile Embodied Energy Example

Returning to the automobile example, as the auto is driven, ages, and wears this embodied energy is consumed and charged to using the auto. In other words, we deprecate the embodied energy just like we would depreciate the monetary value of the auto as it ages and as it's driven. Thus in addition to burning gasoline as we drive, we also "burn" some of the embodied energy of the auto. Where does this burned energy go to? If the automobile transportation has a purpose, then the energy may be assigned to this purpose. For example, if the auto transports a worker to his workplace, then one could allocate the fuel and embodied energy "burned" by the auto to the products or services produced by that worker.

18.4 Human Energy Compared to Automobile Energy, Etc.

Trying to calculate the embodied energy in a product such as an automobile, isn't simple. But it gets much more complicated when we try to account for the human energy expended in making something. At first glance, one might think that human energy is small compared to other types of energy, such as the energy used to fuel automobiles and keep them in motion. After all, a human being doing heavy work only exerts about 1/5 of a horsepower while an auto uses perhaps a hundred times more horsepower when it's moving fast. Note that in cruising on level ground at moderate speed, only a small fraction of the horsepower of an automotive engine is actually utilized. The above example is for an auto which uses only 20 horsepower for driving along a level highway.

But if we fully count human energy, then it becomes very significant. As mentioned previously, providing humans with food, clothing, and shelter requires many times more energy than just the calorie value of the food we eat. One reason is that for every calorie of food we eat, the takes over 10 calories of fuel to create it (see Eric Hirst's Study, 1974 and David Pimentel's Study) Also, due to the inefficiency of the human body in turning food energy into muscle work, the energy requirements of human beings are even higher. Furthermore, a productive society requires a certain amount of government, transportation, buildings, and other infrastructure. And a person with a desk job needs additional exercise to stay healthy. All of these things and more are necessary to maintain a worker and require energy, mostly by using up the embodied energy in consumer goods and services provided to people.

Let's compare a human being to an automobile in terms of the energy used. An active adult needs only about 2,500 kilo-calories a day (=2,500 Calories with a capital C in the U.S.) of food. See Calories eaten per day. This is equivalent in heat value to only .08 gallons of gasoline. But when one realizes that it took the equivalent of about .8 gallons of gasoline energy to create this food it becomes more significant. Now each adult over 14 in the U.S. uses about 1.5 gallons of gasoline per day Gasoline Consumption per Adult for transportation. This is almost double the energy used to produce ones food. But when all the other energy required for living is included, then human energy consumption becomes much higher than the energy in automotive gasoline consumption. It's thus of great significance and something that should never be neglected or underestimated in energy accounting although unfortunately, it often is.

As I'll explain later, human energy flows are actually much higher than implied above, due to "positive feedback" which I'll also define and explain. get-ref

18.5 Input-Output (I/O) Analysis

Introduction

Input-output analysis is a linear model of energy flows using vectors and matrices. It only works for a closed/self-sufficient economy, but since today the U.S. is no longer very self sufficient, one needs to use the entire world. Unfortunately, good data just isn't available.

The model presented here is the conventional model which ignores the energy cost of labor. Thus the output of consumer goods that support labor is considered to be a final output (which is likely a wrong assumption). See Modifying the Input-Output (I/O) Model for how to fix this.

Here's how you do input-output analysis: You partition all industries of the world into a large number of sectors so that all economic activity is covered. For every sector of the economy you define what one unit of output is. For example, for the steel industry sector the output could be defined in dollars or in tons of steel. Whatever units are chosen for output of a sector the same unit of measure must be used for the input of it to other sectors. But units may be mixed: one sector may measure output in dollars, another in tons, and another just in number of units (such as the number of compact automobiles). The units of output must be defined for all sectors. Money, such as dollars, is the simplest unit but not necessarily the best.

Then for a sector (say it's steel) you find say how many tons of coal it directly took to make a ton of steel. Then you ask how much electricity it directly took to make a ton of steel, etc. So now for steel you have a list of numbers showing how many units of the output of various other economic sectors it took to make one unit output of steel. In this case the output of one industry (say electricity) becomes the input to another industry (and often some of the output of an industry becomes the input to the same industry. Thus the name "Input/Output model" or just I/O model for short. This list of what inputs it takes to make one unit of output is in a sense a list (or vector) of the factors of production (where the number of factors is much more than just land, labor and capital). They are called input-output coefficients (or technological coefficients). The components of such a vector often have low values of less than one (but not always).

Of course, you don't stop with steel but determine these coefficients (vectors) for all sectors of the economy that you've defined. Then using these coefficients, you write a set of equations to find the inputs needed from each sector, given a vector which represents the outputs of all sectors. The equation are simple linear equations and can be written in matrix form. Each such vector of technological coefficients becomes a column in matrix A (the technology (Leontief ?) matrix).

The "outputs" mentioned above are the gross outputs. Part of the output of each sector is used for inputs to other sectors and the rest of the output is consumed as final output. For example, part of the electricity we generate goes to factories, offices, stores, etc. to help provide for the creation of goods and services and the rest of the electricity goes to residences for final output to the public. It's not quite this simple since if you earn money while at home, then part of the home electricity is for production of goods and/or services. Note that if the conventional I/O model included labor energy (but it doesn't), then most home electricity would go to support that labor instead of being a final output.

Input-Output Mathematics

In mathematical terms, Let y be the final output vector of goods and services available for human consumption (net output) and x be be vector of gross outputs. A portion of each such output (intermediate output) is used as the input to another sector. The rest of such output is consumed directly by people (final output).

Note that x and y are the same type of vector with the same components but x and y have different values. For example both x[27] and y[27] might be electricity but the numerical values differ. Then let A (previously defined) be the Leontief matrix and write: y = x - Ax which says that whats left over for human consumption y is the gross output x minus the portion Ax of the gross output required to create that output. This Ax is also the input vector which is required as input to get gross output x.

Now what we would like to know is: how much production x will be needed for any given final consumption output y. To do this we just solve the above matrix equation y = x - Ax for x. The result is: x = Inverse[I - A]y where I is the identity matrix and Inverse[I - A] is just the inverse matrix of matrix I - A (which we define as matrix C). Thus x = Cy is the solution for x in terms of y.

From the above solution, it's trivial to find the energy required to increase the output of the i th final output good y[i] by one unit. To find this, just let y = (0 0 0 0 0 1 0 0 0 ...) where the 1 is in the i th position of column vector y. This represents an economy that produces only one unit of the i th good (as final output). Then substitute this y in x = Cy to find the vector x of production to get 1 unit of final output good y[i]. This is also the additional production x due to consuming one more unit of the i th good due to the distributive property of matrix multiplication: if a and b are vectors then Aa + Ab = A(a + b). Let a = y + (0 0 0 0 0 1 0 0 0 ...) and b = -y.

Then find the primary energy taken from the earth to get this value of x and you have found the energy required per unit of the i th good (of final output).

Since y = (0 0 0 0 0 1 0 0 0 ...), x = Cy is just the i th column of matrix C since the 1 of y is in the i th position. Let this i th column vector be c[i]. Let e[i] be the primary energy used per unit of production of the x[i] good, with e being the vector of all the e[i]. Then the primary energy used for a production vector x is just the inner product of x and e or for the case of the i th good, the inner product of c[i] and e. This the energy from the earth required for creation of the i th good (as a final output) or the "embodied energy intensity" of the i th good. Thus the vector of embodied energy intensities is just eC where e is a row vector.

In finding the e[i] values, take care not to double-count. For example, there's a primary energy value associated with extracting crude oil from the earth. But if you also count the energy of crude oil used as input to an oil refinery, you are double counting since you already counted it when it was pumped from the earth. Similarly for coal burned to generate electricity. If you count it's energy content when its mined, you can't count it again when you burn it to generate electricity even though coal is an input to the electric power industry.

While the above is a somewhat brief explanation, you may find more detailed explanations on the Internet, but the ones I found were not well explained. See Leontief-Matrix (DOC) and Input-output model

The above matrix method of input-output analysis accounts for both direct and indirect input from all sectors of the economy. Thus it also accounts for embodied energy. A very serious defect is that the conventional model ignores the energy supplied by labor. But it's obviously better than just estimating the direct energy inputs or using only the first level of indirect energy inputs by including the (direct) energy inputs to the first-level direct energy inputs. The matrix method is equivalent to summing an infinite number of components (where the sums converge, of course, to a finite value). Eric Hirst's Study, 1974 discusses the practical limitations of this method, and why it's not possible to "properly formulate", although he ignores human energy input.

One can modify the standard input-output analysis method described above to include human energy. See Modifying the Input-Output (I/O) Model for a brief proposal.

18.6 Input-Output (I/O) and Production Functions

A production function is a function which, given the inputs to a firm (or production process) finds the output of the one good made by that firm, assuming that the all the given inputs are efficiently used to produce the output good. For example, Numbering goods (and services) 1 thru 5 and designating Xij to be the flow of the i th good to jth firm (for making the j th good), then the production function for the 3 rd good is em/F3(X13, X23, X33, X43, X53)/ which is the output of the 3rd good. For example, function F3 could return a certain number of tons of steel, a certain number of compact automobiles, etc. One way such a production function (like F3) may be used is to keep production of say the j th good fixed: Fj(...) stays constant and then find the combination of inputs: X1j, X2j, X3j, etc. so as to minimize cost. This is what firms are supposed to do to maximize profit: select inputs so that costs are minimum for a fixed output. If cost includes social cost (such as a tax on fossil fuels to compensate for their future depletion and contribution to global warming, then one might say that the inputs have been optimized for a given output.

Note that in both I/O and production function models the X and F variables for production quantities are actually flows such as the amount produced per year, month, day, etc.

How do production function models relate to I/O models? The production function tells one what output would be obtained for a set of given inputs. But the I/O model places a constraint on inputs: they must be in definite proportions for each good as specified by the A matrix (I/O matrix). Let Aij be the elements of the A matrix where Aij is the element in at i th row and j th column. For one unit of good 3 it requires an input of A13 units of good 1, A23 units of good 2, etc. And since output varies linearly with input in the I/O modem, to make X3 units of good 3 it would take X3 x A13 units of good 1, X3 x A23 units of good 2, etc. In terms of the flows from the i th firm (which makes the i th good) to the j th firm:
Xij = Xj x Aij which is just statement of the previous sentence but generalized to i's and j's.

Now for an output Xj of the jth firm the production function model can (in theory) find the optimal values of the ingredients of Xj: X1j, X2j, etc. This is done by holding Xj = Fj(...) fixed and varying the Xij's (j fixed) to find the lowest cost ingredients, possibly including social costs. From the previous paragraph for the j th good, solving for Aij give
em/Aij = Xij/Xj/. But the production function model has found the Xij's for assumed Xj's so it has thus determined all the Aij's of the A matrix.

It must be assumed that there are no economies of scale, or at least that they are not too pronounced. Otherwise the Xij's found for the jth good would not vary linearly with the production of that good as assumed by the I/O model.

The I/O model has a production function of sorts since for every firm there is a list of inputs needed to make one unit of output and output is directly proportional to input (linear). But a realistic production function is in general not linear and the inputs may be arbitrarily selected. No so for the I/O model where the inputs must be in definite proportions. Thus most arbitrary inputs for an I/O model would not be in the definite proportions specified by the column of the A matrix for the firm in question. Thus these inputs would not be feasible. Since the inputs must be in definite proportions, knowing just one input value will allow us to find all the others using the appropriate column of the A matrix. Thus a production function maps n input values into one output value and the function is usually non-linear. The I/O model maps just one input value linearly into one output value, with a constraint that all the other input values must be in definite proportions as specified by the appropriate column of the A matrix. Mathematically, since we previously showed that Xij = Xj x Aij solving for Xj results in Xj = Xij/Aij so we have found the output of the j th firm is just its i th input (Xij) times a constant (1/Aij). This results in constraining all the other inputs to the j th firm, Xkj, k != i, to be Xkj = XjAkj = XijAkj/Aij.

Thus while the I/O model is not much of a production function, the standard production function enables one to find (in theory) an optimal A matrix for the I/O model. However, to actually do this requires a great deal of disaggregation for the I/O data and detailed analysis of specific production processes. There is also the problem of judgements about the future and social costs when making decisions about the technologies which will determine the optimal A matrix. A more practical approach is to disregard optimality and just use statistical data to estimate the A matrix. Each firm should know what their inputs were and what their output was and this determines a column of the A matrix. Of course there's the problem of joint products if the firm is considered to have more than one output. And inputs should include depreciation of capital (and human labor per this article).

18.7 Energy Datum

There's an old saying that "a bird in the hand is worth two in the bush". Likewise for energy, a barrel of oil above ground is worth more than a barrel of oil in the earth. The barrel above ground contains the embodied energy that was needed to extract it (and perhaps refine it) while the barrel in the ground does not. When most people say that they burned a calorie of energy, they mean the energy content of the fuel (or food) and exclude the embodied energy contained in that fuel or food, etc. Furthermore, someone may calculate how much fuel it takes to make food and assume that the fuel contains no embodied energy. The fuel energy it took to make food becomes embodied in the food. But since there are two different ways of calculating the fuel energy in the food, either including the embodied energy in the fuel (the energy it took to extract and process the fuel from the ground) or excluding this embodied energy, then there will be two different values for the embodied energy of the food. In one case we start with fuel in the ground which contains zero embodied energy so one would say that this larger value of embodied energy of the food has a "datum" of the earth. For the other case where the fuel is assumed (perhaps incorrectly) to have zero embodied energy the "datum" might be the fuel at the point of sale. Wherever the datum is, at that location the embodied energy of a commodity (such as fuel or food) is assumed to be zero.

In energy accounting, it's often necessary to add up the embodied energy of the components of a good to obtain the total embodied energy in a good. In this case, the embodied energies all should have the same datum. If they don't, it's like adding apples and oranges and the results are erroneous.

An example of the importance to the "datum" is as follows: Suppose we say that to produce a barrel of oil it consumes two barrels of oil to extract the third barrel. What does this mean? Well, if it takes two barrels of oil taken from the output of a refinery to create a barrel of oil at the refinery output, it's obviously a losing process and infeasible. The datum for this comparison is refinery output.

But suppose that the "two barrels of oil" needed represents two barrels of oil in the ground (datum is in the ground). Now we are saying that it takes two barrels of oil in the ground to extract one barrel from the ground. In contrast to the other interpretation, this is perfectly feasible. We use the net energy obtained from extracting 2 barrels from the ground to obtain a third barrel. Three barrels in the ground are removed resulting in only one barrel net of oil output from the refinery. Actually, all three barrels may be output from the refinery but two of those barrels (or the equivalent) are required to extract and refine the single net barrel of oil. The energy required to obtain the oil includes the support of the workers involved and energy depreciation of the plant.

19. Appendix

19.1 Gasoline Consumption per Adult

Transportation Energy Data Book (Oak Ridge National Lab., U.S. Dept of Energy) Table 2.9 "Highway Usage of Gasoline ..." shows about 133 billion gallons of gasoline consumed in 2003. See Chapter 2 Energy - Transportation Energy Data Book

CIA - The World Factbook -- United States showed under "People in the United States" about 237 million people of age 15 or over in 2006. Dividing gallons by this number and then dividing by 365 days (in a year) results in 1.54 (about 1 1/2) gallons of gasoline per adult per day used mostly for automobiles (including SUVs and personal trucks). The figure also includes some commercial gasoline trucks which helps compensate for the omission of diesel automobiles.

20. Appendix: Fuel to Make Food

20.1 Introduction

It's often claimed that for every Calorie of food one eats, it took (on average) about 10 Calories of fuel energy to grow, harvest, process, transport, and cook that food. The source of this 10 ratio is often not cited. Is it really 10? A couple of sources for it seem to be based on research in the 1970s by Eric Hirst and later on by David Pimentel. After some preliminaries we'll look at these studies.

Note that the food calories also includes an appropriate amount of vitamin, minerals, proteins, and fiber, etc. Thus a calorie of food is more than just energy which is one of the reasons that it takes such a large amount of calories of fuel to produce nourishing food that contains more than just calories.

20.2 Preliminaries: Food Calories, 1970 and 2000

What data do we need?

Some studies will claim that a certain percentage (e.g. 12%) of total energy consumption (of mostly fossil fuel) in the U.S is used to produce food. But we would like to use this 12% figure to find out how many Calories of fuel it takes to make a Calorie of food. To do this we need to estimate how many food Calories are consumed in the U.S. each year and divide this by fossil fuel Calories consumed to obtain the amount of food Calories eaten as a percentage of the total energy consumed. For example, if food Calories are 2% of fossil fuel Calories, then if 12% of our fossil fuel is used to produce food, it means that it took 6 ( 12%/2% ) Calories of fuel to produce each Calorie of food

Total fuel energy

We'll estimate these values for both 1970 and 2000. Let's start with looking up total energy consumed in those years. Per Minerals Yearbook (U.S. Bureau of Mines), 1971, p. 23, table 8: "Gross consumption of energy resources ..." we find 67.2 quadrillion BTU (aka a "quad") of energy consumed in 1970. Per Energy Consumption by Sector: Energy Consumption Estimates by Sector 1949-... from "Annual Energy Review" of the Energy Information Administration (U.S.), it was 98.98 quads in 2000 (67.84 quads in 1970 but we'll use the 67.2 quads per above). Since a BTU is 1055 Joules, we get 104.4 exajoules for 2000 (104.4 x 10^18 Joules) or 514 GJ/capita. For 1970 it was 70.4 exajoules or 347 GJ/capita.

Calories eaten per day

Now, to find food Calories. Per Statistical Abstract of the U.S., 1970 population was 203 million in 1970. The amount of Calories eaten per day was estimated by surveys reported in: Centers for Disease Control and Prevention (CDC): (Feb. 6, 2004) "Trends in Intake of Energy and Macronutrients -- United States, 1971-2000." MMRW Weekly 53(04):80-82. Available at CDC and at http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5304a3.htm

For 1971 for people between the ages of 20 and 74, average daily consumption was: men 2450 Calories (same as kcal), women 1542 Calories. These average to about 2000 Calories/day (=8.4 MJ/day). For the year 2000 the average was about 2250 (people are eating more). But since the population figure includes children and very old people (outside of the 20-74 age range) who eat less food than average, the 2000 Calories/day figure has been reduced by me to 1800 Calories/day. This was done by assuming that 80 % of the population consumes 2000 Calories/day with 20% (mostly children and very old people) consuming on average 1000 Calories/day.

Food-calories are what percent of fuel energy

Using the 1800 Calories/day estimate, the food energy eaten in 1970 was: 203 million-persons x 1800 Calories/person-day x 365 days/year x 3.968 Calories/BTU = 0.47 quadrillion-BTU/year of food. In 2000 it's 281 million-persons x 2025 Calories/person-day x 365 days/year x 3.968 Calories/BTU = 0.82 quadrillion-BTU/year.

The 0.47 quadrillion BTU for 1970 is only 0.70% of the 67.2 quadrillion BTUs consumed in 1970. For the year 2000, the 0.82 quads is 0.83% of the 99.0 quads consumed in 2000. So for 2000, total energy consumption was about 120 times as much as food calorie consumption. Thus food Calories are well under 1% of our energy consumption:


Food Calories as a Percent of Total Energy Consumption [Total Energy
over Food Calories] 
1970:  0.70%  [145]        2000: 0.83%  [120]

20.3 Eric Hirst's Study, 1974

"Food Related Energy Requirements" by Eric Hirst in Science, 12 April 1974 (vol. 184 No. 4133) pp. 134-138. See abstract at Food-Related Energy Requirements by Eric Hirst, 1974.

Hirst claims that about 12% of total energy consumed by the U.S. is used to create food (including it's distribution and preparation). But we found in Preliminaries: Food Calories, 1970 and 2000 (last paragraph) that in 1970 food Calories consumed represented only 0.70% of the total energy used in the U.S. Thus for every Calorie of food eaten, it took 17 Calories of energy to created it (12/0.7 = 17). This is significantly higher than the figure of 10 commonly given.

Why is this so high? For one, Hirst used input-output analysis using Leontief matrices. I can find no satisfactory explanation of the Leontief matrix on the Internet but see Leontief-Matrix (DOC) and Simple Leontief Model. This method accounts for both direct and indirect input from all sectors of the economy to the food industries. If properly formulated, it accounts for all embodied energy, except for human labor energy. It is equivalent to summing an infinite number of components (where the sums converge, of course, to a finite value). Hirst discusses the practical limitations of this method, and why it's not possible to "properly formulate" it as mentioned above.

Later investigations didn't use the sophisticated input-output analysis used by Hirst and thus may have missed a lot of components needed to produce food. Thus the low ?? value of 10 Calories-fuel per Calorie of food. To resolve this issue (Is 10 a good estimate or should it be higher?) requires redoing input-output analysis and including human labor energy. But it's not easy to do due to the huge amount of imported goods into the United States for which we don't have much data on the energy it took to produce them, etc.

20.4 David Pimentel's Study

See the book: "Food, Energy and Society" by David Pimentel and Marcia Pimentel (editors). University of Colorado Press. 1996. (Third edition to be published in late 2007 by CRC Press).

On p. 8 and again on p. 290 it's claimed that about 17% of fossil fuel energy used in the US goes into food production. But since about 0.75% of such fossil fuel energy is represented by food Calories, there is thus about 23 Calories of fuels consumed to create each Calorie of food eaten. 0.75% represents a compromise between the 0.70% figure for 1970 and the 0.83% figure for 2000. See Preliminaries: Food Calories, 1970 and 2000 (last paragraph).

This value of 23 Calories-fuel per Calorie-food is even higher than the 17 obtained by Hirst. A possible reason for it being higher than Hirst's is that Pimentel counts some of the energy in human labor, although Hirst doesn't say if he counted it.

There's another statement by Pimentel et. al. that the figure is "over 10". See (url url="http://dieoff.org/page69.htm" name="The Tightening Conflict: Population, Energy Use, and the Ecology of Agriculture"> in the section "Fossil energy and the food system".

21. Appendix: Number of Service Workers per Production Worker

This is a simple mathematical model and derivation to find the number of service workers S required given P production workers: S = f(P). To determine the function f(.), the population will be divided into 3 classes of people: Production Workers (P), Service Workers (S), and Dependents (D). People who fall into more than one class are pro-rated to those classes. For example, a spouse who works half-time would become 1/2 of a dependent and 1/2 of a worker. The total population is P + S + D. Dependents include retirees, children, and non-employed spouses. Dependents don't have any dependents themselves but do need service workers. Let (on average):

In the equation for S we may substitute the equation for D and then solve for S resulting in S as a function of P, s, and d:
S = [ s (1 + d) P ] / [ 1 -s (1+ d) ]
This formula is of course valid if d = 0 so then
S = sP / (1 -s)
Note that if s = 1 then S becomes infinite (division by zero) and it's not feasible. It's easy to understand why. Start with yourself and take on a service worker for you (since s = 1. Then that service worker must have another service worker to serve him, etc., etc. The resulting number of service workers required is:
1 + 1 + 1 + 1 + 1 ... which is infinite. So it's required that s < 1. Similar reasoning shows that for the case of dependents s (1 + d) < 1 which .

It's also of interest to know how many persons are needed as servers and dependents (S + D) per production worker. Since D = d(P + S) using the above formula for S we obtain after some cancellation:
S + D = P[ s + sd + d ] / [ 1 -s (1+ d) ]
Note that the denominator is identical to the solution for S so the above inequality constraints hold true.

An example where s = 1/2 and d = 1/2 results in S = 3P and S + D = 5P. In other words, if each worker requires the services of 1/2 of a service worker and has 1/2 of a dependent, then each production worker needs 3 service workers plus 2 dependents. The production of the production worker supports not only the 1/2 dependent of that production worker, but the 1 1/2 dependents of the 3 service workers.

An unfeasible example is where s = 1/2 and d = 1. One might question if society (with s = 1/2) can reproduce itself and provide for retirees if d must be less than one. Well, d can be kept low by late retirement and working spouses. Also, s can be lowered if non-employed spouses and retirees do some of their own service work (such as repairing their own residence, car, etc.).

Rich people can of course have higher d's and s's but to compensate for them it's necessary for others to have lower values of d and s. This model doesn't reflect this aspect since it assumes that all people have the same values of d's and s's.

The boundary equation for feasibility is s (1 +d ) = 1. This is a hyperbola which intersects the s axis (d=0) at s=1. s > 1 is not feasible. But d can be arbitrarily large if s is small enough. Of course, a large d would not be feasible either due to the excessive amount of resources required to support an excessive number of dependents per worker. But this equation only shows infeasibility due to an excessive number of service workers and doesn't include other practical constraints on the values of the variables and parameters.

22. Links, Journal Articles, and Books

Net energy analysis in Encyclopedia of Earth; see section on "Human Labor". Journal Article: Energy Accounting: Some New Proposals, by Albert Punti, in Human ecology v. 16, no. 1 (March 1988), pp. 79-86. The first 2/3 of this article is about "Human Energy Accounting". On p. 80 it lists a few authors in the 1980's who proposed using "the whole energetic cost of all goods and services consumed by workers". It also lists other authors (a majority) who did not. A "new proposal" made by Punti is to include the energy use for "reproduction of the labor force" (a quote from the book Capital by Karl Marx) in the energy cost of labor. No numerical examples are given for the use of full energy accounting nor is any argument for its validity given, such as the company town model of this article.

Books:
"Environmental Accounting, Emergy and Decision Making" by Howard T. Odum, 1996. This book is not very good and hardly mentions the human energy accounting problem, but it does have a sentence or two about it. To-do.

"Genetics, Biofuels, and Local Farming Systems" Section: "Human Labor and Green Manure, Two Overlooked Factors for Energy Analysis" by J.Y. Wu, M. Martinov, Vitro I. Sardo. pp. 215+. See abstract and references Publisher: Springer, 2011 (Cites this article by Lawyer.)