Estimating your DollarShadow    J.L. Henshaw  
ed. 7/05/07 9/28/10 12/3 1/8/11 1/17/14
  08/28/15 08/15/19 8/25 Research notes on How to Understand the True Scale of your Energy Use
note:  These are real numbers but examples only to illustrate scale, and to give you ideas of how to do your own

Understanding the total Economic impacts of what we pay for (hist)(sci)

Example 1: The CO2 caused by the ink, paper & printing for handouts (Ex 2 vii for math)

[CO2/$GDP = ~ 1lb CO2 or .45 kg per $1GDP of average end user consumption]

~$36/ream, CO2 impact on the earth => ~36lb or 16.2 kg CO2

Example 2: Land area of solar farms to supply energy for US GDP (Ex 3 for math)
[PV Farms = 2.9 sq mi/$billionGDP,   US GDP ~$17 trillion/yr]

implied land use impact => ~50,000 sq mi of solar farms today 
then.... w/ normal doubling of the area, and so the energy needed every 35 years
becomes => + 50k, +100k, +200k, +400k... etc.
becoming the total land area of the US (3.806 sq mi) in ~200 years!*

(*if the past pattern of growth continues)


Five True Energy Budget Stories:  Each shows a true calculation of economic energy demands generally ignored...

1) What AVG means 2) Total Energy to Deliver Products   3) Total Land Area Needed for PV
4) Total Demand of a Home 5) Examples for Consumer Products 6) Global PV Land Footprint
7) IEA Data sources 8) World Economic Trend 9) Scientific use of Money as a Proxy


The "big secret" is hidden environmental services all around the world are your largest environmental impact.   What you pay business for gets passed on to pay for widely distributed chains of services as part of what you purchased.   It makes you financially responsible, and moreover directly exposed to, the not so hidden dangers connected to the economic and environmental harms the earth now rapidly emerging, that no seems to realize they are paying for and so responsibility for.

When lacking specific information, a scientific accounting must treat hidden energy uses as "average", using the "null hypothesis" that allows the accounting system to "close".    

It turns out the world community has been making the opposite assumption, only recognizing energy impacts and financial responsibility for them that people have specific information on, a regular practice of ignoring what is hidden, and being directly paid for as we use money.  That's not sustainable!    The practice has been to use the wrong "null hypothesis" for lack of specific information, treating the hidden energy costs of using the economy as "zero".  This has caused all kinds of misunderstanding, treating "sustainability", as meaning "hiding your impacts".

 The world average energy use impact  for any average dollar spent
is the ratio of total purchased energy supply (TPES) to world total end user product (GDP) (7)(sci):

Energy production and use Impacts: ~8000 btu or ~7.6 jules or 2.4kWh  (/$GDP 2006)
CO2 impacts:  ~1lb or .46kg  (/$GDP 2006)
(both declining with regularly improving worls economic efficiency at ~ 1.24%/yr)

that's the "reality math" needed to account for the large hidden energy use behind every product and service,
and to make sustainability accounts "close" by reflecting true shares of the world total
in doing for your Scope 4 Whole Systems Energy Assessment

for example - Volume of CO2 per $ GDP :  0.46 kgCO2/$  *  2.1m3/kgCO2  => 0.97 m3CO2/$ of GDP 2006
so if you make $50,000 a year that's 50,000 cubic meters of CO2 produced for you as a world average, the volume of ~20 three story townhouses...
Pollution is often removed by hiding it, with outsourcing or reducing visible part, quieting the messenger so its silent, but still deadly.


1. What Average means: (& sci notes)

The world average energy use per dollar of GDP is the amount of purchased energy resourced from around the world to deliver an average $'s value of goods or services.   Because it's so much larger than the visible energy uses of commerce it is a much more accurate measure than even very carefully tracing visible energy uses (f).

To measure individual economic impacts on the earth $1 1 average share of the world economy, its total energy use and all its impacts, since every $ needs the services of the whole economy (i) (ii)... Which turns out to be surprisingly accurate for energy use (f)

World avg. ~= 8000btu/$ GDP (or 2.4kWh/$ GDP) = unit energy demand for average end user products  
(IEA 2006 World TPES/GDP-PPP and 2006$ )

i) Average values are true for individual cases "on average".. and most products require such highly divers energy uses to deliver them it's also rare for the energy required to deliver the $1 of value to be far from average (f).
ii) I finally found people interested and able to study  the sources and equations to confirm these figures from Table 1 below, in a discussion on Azimuth with John Baez.  There was one "small" error found, now corrected, made in revising the whole calculation for this update of the old work.

2.  General scales of visible and hidden energy use:

(rough estimates)

    Energy Use  CO2 pollution
Systems Compared Financial Budget Units Visible Energy in Fuel Use Hidden energy in income uses
2.4 kWh/$GDP
Total Energy Demand The error in counting only visible energy Units Hidden in income uses .45kg/$GDP
a Family in town w/car (iii) House
& Car
mWh house & car
20 + 16
120 156 433% mtonne 22.5
a Family "off grid" w/car (iv) House
& car
mWh house & car
5 + 16
120 141 672% mtonne 22.5
a Family "off grid" walking (v) House
mWh House
120 125 2500% mtonne 22.5
printing paper
200 handouts (vi)
paper, ink &
kWh paper
& elec.
84 169 1690% kg

The reason for the "hidden energy use" is that each dollar spend demands energy services around the world to deliver the product, at a world average rate of 2.4 kWh (or 8000 btu) per $GDP in 2006$.   The rate is slowly declining as world economic efficiency improves as a fairly regular 1.24% per year.

iii) A modest income family, as US national average, maybe a 2000sf house paying $2500 for heat and electric and $1800/yr for gas for a car.
iv)  The same family, generating its own energy by Wind or PV in theory might be able to generate their own heat & electric.
v) The same family, walking to work and store, generating their own energy and just using a taxi now and then.
vi) We print handouts for meetings, hoping the information will have a greater compensating effect on reducing our energy footprint in the end... but it may take a while.  If I spent on anything else, on average it would have a similar scale impact in hidden energy costs throughout the economy.   A 200 page ream of paper on a desktop printer might use up a $25 ink cartridge cost, $.30 electricity and $1 of wear on the printer, and $10 of paper.  The direct energy costs to produce the paper, 8kWh and to run the printer, 1kWh.



 ...Probably the Biggest Surprise...

3. Calculation of PV Land Area Needed 

- using solar radiation availability from map below - 
- the 2008 total area of PV to supply energy to the economy turns out to be ~4 time the size of Colorado,
and - doubling in size every ~35 years to provided for "customary growth"
- and in 200 years a total of 1/4 the landmass of the Earth!

The theory is simple (2019 notes)

Combine values for avg available sunshine (5kwh/m2.dy) with loss factors: avg. PV eff. (19%), land not covered (50%),  and system operation time (83.3%), to estimate the total solar farm size for supplying the world's energy needs. 

I originally did the calculation with 2008 data, though the ceiling for PV efficiency moved up 10%, so I might update that.  The rest of the global data is not much different: global energy demand and growth rate, being the most significant scale factors....   There most clearly is some mistake!!  Can you find it??  What else might I adjust??  I think perhaps everyone else has used finite planning horizons, like local payback, and never bothered to do this calculation.  
What do you think the error is??

Table 1. 2008 Units
Solar energy available for PV (a)

metric                                           imperial

                          *avg incoming kW     

5 kWh/m^  
1825 kWh/m^ x3.15 579 kbtu/sf.l.yr
High Performance PV loss factors


** reduce for PV efficiency 0.19 19.0%     kbtu/sf.yr
*** reduce for land coverage 0.50 9.5%     kbtu/sf.yr
**** reduce for operation pauses 0.833  7.92%     kbtu/sf.yr
PV farm Energy Conversion rate 144.5 kWh/m^   45.8 kbtu/sf.yr
Ave energy/$GDP ( Fig b or Table 3)          
World GDP (PPP) 2008 63,865 10^9 $GDP      
World energy use 2008 143.1 TkWh x3.41 419 Quad btu's
Long term constant doubling rate 34 yr     34 yr  
Average energy Intensity/$   2.2 kWh/$   6.6 kbtu/$
$'s GDP per unit of area $64.48 $/m^2.yr x10.8 $0.51 $/sf.yr
Area for $1 of avg GDP energy/yr 0.155 m^2.yr   1.98 sf.yr
Area for $40k Income


m^ 10.803 6,701
               $1 million Income


m^   167,533
Area for US $17 trillion GDP 263,646 km^   385,734 sq
Area for World $64.4 trillion 1,291,414 km^   498,665 sq
Share of Earth Landmass 196 M sq mi .0386 of Earth land   .0386 of earth land
Years to cover all land, x2 ea 33yr ~140 Years   ~140 Years
The question of course, how long can we keep doubling our energy use?
    1) Can we even cover whole land masses with solar farms, let alone the entire earth's in 140 years??
    2) The demand for energy doubling every 34 years for a world economy doubling every 22 years is quite clear
    2) After providing 498 sq mi of solar farms for 2008 energy use could we double that in the next 35 years??
    3) There seems no evidence at all of "decoupling" that would allow economic growth with less.
    4) In any case, don't we definitely need to very soon "flatten the curve" to make life sustainable??
sq ft/sq mi = 27,878,000  |  sq ft / m^2 = 10.764  |  m^2 / sq mi = 2,589,900  |  k.btu/kWh = 3.41214

* Avg Incoming solar energy is a mid-latitude average, and not likely the world average, and ignores all other kinds of restrictions such as forbidding terrain and distance from habitation.
**A nominal peak efficiency of 19% is now achievable for solar panels. It might be 50% in the future, but at high cost.
*** A rough estimate that solar panels would cover 50% of the land area in a solar farm
**** The EROI (energy return on energy invested) of 6:1 is a rough estimate using SEA (d)  for the "usual" net energy produced by high performance PV solar farms in the US economy.    It seem likely to be optimal rather than average, but would take study.   The value would be quite sensitive to the costs of the land, operations and equipment, as well as the average radiation from the sun at a particular location.  The value of 6:1 means that 1/6 of the energy gain is lost in the effort to produce energy.

Figure A. Annual average daily solar radiation available in the US overlaid with 1990 US population density (a, e)

One reason to think of our impacts on the earth as proportion to the money we earn and spend is that every dollar is one equal share of the total product of the whole world economy.   All economic impacts are energy impacts, and all the things that cause economic impacts are purchased.  For energy use the "average energy per dollar" also turns out to be a fairly accurate estimate of the real total use of energy and production of CO2 pollution, seemingly +/-15% mostly.    What you can be sure of is it will be fairly close most of the time, and will be a far more truthful measure of the scale of impacts for  any purchase choice than zero.

Why it's fairly accurate most of the time is because energy is the universal resource, and traded around the world at a world price, as discussed a bit further below.   The best present research on this method of analysis is a draft paper Defining a standard measure of energy use for businesses, using a wind farm and its energy return on investment (EROI) as an example.   By switching from adding up the receipts businesses collect from purchasing energy, to treating the prices of things as a receipt for average energy use in all the work that went into what was purchased, four times the energy uses being employed are found.   The main reason is  ... *because we pay for them* ... and the price we pay is an accumulation of all the prices reflecting the work of all the people and machines along the way that brought the product or service to us.   That's the key.   It will change how energy accounting is done entirely when it is appreciated that economic footprints are far easier and more accurately measured with money than trying to follow almost untraceable threads connecting diverse causes and effects, as well as the significance of finding a 500%+/- typical error in our primary measure of sustainability....   9/28/10

4. Suburban Home Example:


Budget for an "average" suburban home with a 1500sf footprint and family income of $80k/yr,


Energy budget


step 1 Energy/GDP => $1 share ≈ 8000btu/$ (or 2.4kWh/$ )  
step 2 Using Solar Panels to produce a $1 share  ≈ .5 sf for a year (table 1).   
step 3 needs 4,000 sf area for PV panels,  
step 4 needing a solar farm ~2.7 times the home's roof area, and growing with income to be truly grid neutral (iv)  

iii) Using Charcoal to Fix the price of carbon emissions assumes no continuing land use cost to protect the buried carbon
iv) "truly grid neutral" and "truly carbon neutral" are a quick way to say that the family provides as much energy and carbon sequestration for the economy as the family's share of the economy as a whole, "on average".  So for the US the energy used to produce our products in China is counted in the US average consumer budget.   "Normal" economic growth of 3.1% per year would increase the PV area and cost of CO2 sequestration ~1.8% per year, slower than the growth rate due to normal efficiency improvement.

5. Consumer product Example:

Money spent on a soda or glass of wine, like a receipt for a share of world energy and carbon costs. As a measure of energy use it's quite accurate, on average, and makes spending or earning a dollar responsible for one equal share of all the impacts of energy use too. You can appreciate the meaning of "average share" using it to measure how much CO2 (your carbon footprint) is created with normal expenses. Try to compare the benefits and the costs with these two examples. (b Table 1)

So... a 16oz soda for $1.50 would put ~24oz of CO2 into the atmosphere, as average spending  from conventional energy sources, and use  the equivalent of 10 oz of oil.   To use solar energy it would take the use of a 100sf of a solar farm for a day to generate the same energy with PV.  

And... a 6oz glass of wine costing $6 would produce ~96oz (6lb) of CO2, 16 times the weight of the drink as average spending for conventional energy sources, using the energy of 39 oz of oil,  or... require the use of a 384sf of a solar farm for the day to get the same energy from PV

6. Global footprint Example:

The global "dollar shadow" for using PV to supply the present world energy demand, estimated in %'s of the World Agricultural Land Area

Table 2 shows the estimate for world energy demand in equivalent land areas of high performance PV, using:

With 1$ of world GDP needing 1.39 sq meters of average sunshine for a day, or .0038 sq meters per yr, to deliver the world average amount of energy to deliver 1$ of end user products.    It's surely a rough estimate, but the intent is to understand the total scale.  It ignores the wide variation in land suited for solar farms, for example, and that the constant coupling of growth and efficiency improvement continues. 

What doesn't change is the coupling of land area and available sunshine. While growth might decline the assumption being tested is that both growth and efficiency continue at the historic coupled rates, as "growth constants" for the whole system's natural rates of sustainable learning and reorganization, as before.    That historic energy use "growth constant" (b)  has been steady for the past 40 years, at 1.89%/yr, and so growing at a rate with a 37 year doubling period.    World GDP $46.9 trillion in 2000(b) that would have cast a dollar shadow of 15,490,000 sq km,  with world agricultural land area 48,033,854 sq km as 40% of the total land mass of the earth, 120,000,000 sq km.

Table 2.

World dollar shadow as a % of present total agricultural land and the world landmass


% of Agricultural Land


as % of Landmass of Earth


% in 37 yr  


% in 37 yr  


% in 74 yr  


% in 74 yr  


% in 111 yr 


% in 111 yr 

.....and continuing to double   ..... ....and continuing to double   .....
would you guess it goes to....   32.5% would you guess it goes to....   12.8%
in another 111 yrs???     in another 111 yr???    


Does anyone see a problem with covering the Earth with PV ?? 
..or with needing to locate the solar farms near the people ??
..or with the cost of renting the land for it,
..or covering the whole earth black
in only a century more??


7. Global Trend Data and Relationships:

 IEA World economic data - Key indicators GDP Energy & CO2
partial 2008 data for Table 3. and Figure 1.,  for 2010 IEA source data see reference (b)

Table 3.








% change


Mt CO2 Sectoral method




















TPES   (QuadBtu)










TPES  (QuadkWh)










GDP   (billion 2000 US$)










GDP PPP   (billion 2000 US$)




























































Population   (millions)










kg CO2 / GDP 2000 US$










kg CO2 / GDP PPP  2000 US$)










Ton CO2 per capita)










Mton CO2/QBtu











^ 2007 IEA data, rounded for use in generic footprint calculations in brackets [##], for 2014 est ~ 3.6% lower, for regular historic rate of the economy's improving energy efficiency. 
x - original data converted to Btu & kWh units
* energy/$ values (economic intensity) declining over time at 1.3%, ~25% in 30 years
** ratios of GDP adjusted and unadjusted for "purchasing power parity" PPP to remove monetary exchange rate discrepancies, for the US unadjusted GDP$ is only ~5% higher than its PPP adjusted value. 
*** For climate change the key observation is that steadily improving producer efficiency completely overcomes consumer efficiency, to continually multiply energy use, it also does NOT change the share of fossil fuel used to produce energy at all, as reflected in the near constant CO2/Btu ratio... Info on CO2 from Wikipedia

8. Historical Coupling Constants for Growth -    We see here the surprisingly regular progressively changing rates of world economic growth (+3.1%/yr), the energy use required (+1.9%/yr), CO2 produced (+1.9%/yr), and our rate of improving energy efficiency, at (+1.2%/yr).   

It's very odd, that these curves clearly show the world economy having a highly regular behavior as a whole, and so also indicate the world economic system having a stable "design", in how the parts are organized and working together.   It's both odd that the world economy has such remarkably consistent behavior, and also that it is very generally not discussed, particularly in relation to our world preoccupation with changing the linkage of these very same behaviors of the world economy, for "sustainability".    

That we don't seem to study the design of the system we're trying to change, is a problem.    The regularity of the curves shows a highly regular behavior.   Plans for an opposite behavior would need to take into account, like the staple designs for "sustainable development", for having efforts to increase efficiency and producing alternative energy to result in decreased energy use and CO2 (respectively) the reverse of their historic whole system behavior of accelerating increase with improving efficiency.

                              Figure B (f, h)

9. The scientific basis for measuring impacts with money:

It sounds crazy at first, and so most people then never ask "What about the averages".   That's the secret, being cautious about your snap judgments, when the whole problem seems to be "How would anyone know?".    Here's the answer to how anyone can know.   

In paying for the economy to deliver goods and services, nearly all our uses of money are passed on to such a wide variety of people, who all spend the money they receive on such a wide variety of different kinds of consumption, the sum total of the hidden energy uses involved ends up being similar to paying for anything else, i.e. "about average'.   It's not that further studies aren't needed, of course.  It's that based on that distribution, and your initial lack of better information:

  1. "average" is probably a reasonable estimate for scale, and certainly far more truthful and accurate than 'zero', and

  2. for those studies to find where it varies, "average" is the only scientifically legitimate place to start, necessary to "close the accounts" by having the totals of impacts equal the total of responsibilities assigned for them.

The more technical ways to reach the same conclusion involve modeling how money travels in the economy.    My way of doing it starts with setting proper bounds.  It's clear that you want to only count energy uses once, and for the total to equal the economy's total.   That is not assured using the method mentioned in the original paper "Systems Energy Assessment" of tracing a typical pattern of money being passed to multiple contributors to the service provided.   Like the reasoning in #1 above, finding that in three month's time parts of any dollar used would end up in the accounts of every person on earth, demonstrates a wide distribution, and "startling likelihood", but there is no "end point" for that distribution.   

A good way to define an end point is a new way of using the same device that economists use for measuring the total product of the economy, GDP, as the sum of the "end user" purchases in a given year.   That defines an end point if the chains of production of the economy.   The other "end" of the economy is the accumulation of services paid for to deliver the end products.    So you have a 1-1 mapping of the economy, from "end users" (as the people consuming the products) to the "end producers" (as the people paid for their services in producing it, who use what they are paid for their own end consumption)

So the economy can be mapped as an accountable exchange between end users and end producers.    Money that is paid for any end use is granted "free and clear" of obligations (except those paid for) to the service provider, and then at first largely "passed along", from one business to the next to the next, with some at each stage being paid to people also "free and clear" as "end producers", for them to use for their end uses.   So the money being paid for all the multiple branching services in the product and service chain that are needed to deliver any product, has no destination other than some person, mostly hidden from view way down the chain somewhere, being reimbursed for contributing their end services, free and clear.

The visible services used in delivering a purchase to the end user

The chains leading to mostly hidden services from the end producers needed

Figure C.

 (table 4 shows that most of the end producer services needed are in the "fat tail" of the chain)

What a mathematical model seems to show is that the hidden part of the distribution is much larger than the visible part.  The distribution has what is called a 'fat tail' in the sense that most of the end producer consumption is far down the line, and so also more likely to be "average".   Statistics won't help much, but network science could somewhat, if only to help further clarify how reliable the scale estimate of "average" is, and why it will be economically infeasible to use any other estimate except for large impacts for which information is readily available.  

If you assume that economic supply and service chains have a "normal" branching pattern, you can examine the shape of the distribution.   You might guess that spending on end products normally goes to a mix of smaller and larger businesses.   To study that you start with a simpler model, and see if it's possible to model more realistic assumptions.  What is fairly easy to explore is a rule that the largest part of the economy is made of businesses with 40 employees and 50 business service providers paying about 20% of their revenue in salaries.  That might vary widely in reality, of course.   The Wind Farm we modeled for SEA (see p 17) seemed it would have only about 2% of its revenue in salaries, while employing lots of business services from companies with a more normal ratio.

So taking the simpler case, you get a polynomial expansion, with each step

  1. removing 20% from the money chain,

  2. multiplying the number of employees by a factor of 40 and

  3. multiplying the number of businesses by a factor of 50.  

We'll try to trace where the money goes for a single $100 purchase from a business, in turn paying 40 employees of all kinds and purchasing producer services from 50 businesses, which each also have 40 employees and buy services from 50 businesses.   After just 4 steps, one purchase is shown having paid for the services of a highly diverse group of over five million people running and operating over 120 thousand businesses, with only 50% of the end production services paid for.

Numbers of people & businesses paid for services
along a business production chain

Table 4.

Starting from the consumer purchase - steps along the chain







$ to businesses






$ to people






(share remaining)












# of people pd






Tot people pd












# of businesses pd






Tot businesses pd













Network analysis could be done on the data for international trade, such as is compiled and used for EF, Ecological Footprinting, for example.  That or similar studies might shed some light on what kinds of spending or what kinds of producers deliver lower than average impact products and services.   They won't erase the problem that most "end producers" will remain hidden from view, lost in the fat tail of the distribution, just because the information gathering task is too difficult.    As competing designs for lowering the economy's impacts are studied and tested, more exceptions may appear, but using this kind of complete accounting approach won't cause all the prior hidden impacts to re-disappear or things like that.  

jlh 2/20/14


a -  National Renewable Energy Laboratory,  Historical average solar radiation at the ground: (picking a "typical" average mid latitude location)
b -
 IEA World Highlights:  & 2010 historical data: 
c -  Agricultural land use figures
d -  Method for measuring whole system energy use and EROI: System Energy Assessment (SEA)

e - ThoughtForm pop. map
f -  see System Energy Assessment (SEA) for Whole Business Systems, Henshaw et all, 2011 extending a 2009 talk
h - Understanding why the economy behaves as a whole The curious use of Stimulus for Constraint, Henshaw 2011
i -  an archive copy of this page from 2009 with possibly useful early thinking on the issue


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