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Embodied energy basis for economic-ecologic systems

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Embodied energy basis for economic-ecologic systems
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Embodied energy basis for economic-ecologic systems
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Costanza, Robert.
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Robert Costanza
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Capital investments ( jstor )
Capital stocks ( jstor )
Economic models ( jstor )
Energy ( jstor )
Financial investments ( jstor )
Gross investment ( jstor )
Input output ( jstor )
Land use ( jstor )
Modeling ( jstor )
Simulations ( jstor )
Miami metropolitan area ( local )

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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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EMBODIED ENERGY BASIS FOR
ECONOMIC-ECOLOGIC SYSTEMS











By


ROBERT COSTANZA


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIRE:-1EIT7 FOR THE
DEGREE CF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1979




































Copyright 1979

by

Robert Costanza













AC YrYO w, P r 17'(;


T am greatly indebted to Dr. FT.T. Odum, my com itte?

chairman, for his knowledge, inspiration, insight, and

encouragement. His all-encompassing world view gave birth

to many of the concepts which led to this study ani quidel

the wore< to fruition. Many special contributions were made

by the other members of my committee: Drs. S.E. Bayley, B.L.

Capehart, W.C, Huber, and C.D. Kylstra.

B. Hannon and 7. Herendeen at the Center for Advanced

Computation, University of Illinois, contributed experienced

help and encouragement with the input-output studies in the

summer o' 1978. 7. Vang and J. Boyles read the manuscript

and provided comments. I would also like to acknowledge tho

valuable interactions with associates and friends,

especially J. Rartholoramel, T. 7ontaine, S. Brown, and D.

Hornbeck.

Work was done at the Center for Wetlands, University of

Florida, and was supported by the Unitad States Department

of Enerqy (Cor tract EY-76-S-05-4398) project entitled

"Energy Analysis of Models of +he United States," n!.T. Odum

principal' investigator.









TABLE OF CONTFN!TS



page

ACKNOHL EDGE ENTS ............ ............................ iii

LIST OF TABLES ........................................ vi

LIST OF FIG""ER.........................................viii

ABSTRACT................................................ xi

TNTPODrUCTION...................... .. ........ ........... 1

Research Plan.... .. ... ............ . ....... 2
Background of Previous Studies...................... 4
Energy ana Society............... ............. 4
Systems Ecology................................. 5
Energy Analysis..***. *................. ..**** .. 6
Embodied Energy................................. 7
Optimization ..... ........... .... .... ....... ... 13
Economic ,odels... .............................. 13
Spatial economicc Moels......................... 17
Simulation Models............................. 19
Description of the South Florida Area............... 20

METHODS.................................*** ...... 23
Description of the Nodeling Language............... 23
Mo.el Development ...............* ............... 25
Dynamic Op inization...... ..................... 25
Simulation Modeling Methos ..................... 26
Molel Parameter Estimation, Validation and
Testing..................,. ..... .... ......... 27
Input-Output Techniques for Calculating Embodied
Energy. S................... ..........*********** ... 28
Double Counting...........,..................... 41
U.S. Economy Data Assembly and Evaluation........... 43
Government and Households as Endogenous
sectors....................................... 44
Environmental Inputs.................. ..... i.. 52
An Endogenous Environment Sector.................. 55
Capital Plows. ............... ...... .......... 57
South Florida Land Use Data........................ 57

RESULTS.............................. ................. 65
The General Conditions for Maximum Power............ 65
Development of a General, Power Maximizing
Simulation Model... .. ........................... 75
Simulations Using Two Components................ 84
Simulations of Spatial Development Using
25 Cells...................................... 91










page


The U.S. Economic-Ecologic System................... 96
Energy Embodied in Goods and Services for 92
U.S. Economy Sectors in 1967................. 96
The Energy to GNP Ratio for the U.S.
From 1920 to 1976................... ..... 114
Total Capital, Investment, and Depreciation
Time Series and a Better Estimate of the
Embodied Energy to Dollar Ratio............... 116
Fourteen Sector Closed System Input-Output
Matrices for 1963 and 1967.................... 126
Five Sector U.S. Economy-Environment
Simulation Mocel.............................. 139
The South Florida System............................ 151
Measured Embodied Energy Paps................... 151
Ninty One Cell South Florida Spatial
Simulation Model.................,....,,..... 163

DISCUSSION ..................... ..... .... .. ... . .... 180
The Case for a Constant Embodied Energy to
Dollar Ratio...................................... 180
Conclusions and Predictions from the Simulation
Models.. ............................ .......... 188
rmbodied Energy Analysis and Economics.........,,.. 190

APPENDIX

I SOUTH FLORPDA LAND USE DATA CO"V'-F"T TO EMBODIED
T 'EPGY U:-.T ... ................................... 193

II ANALOG CCrP"'T-? DIAGRAM POPE "H TWO CO"riNFNT
EXCHA r," rODEL.................................... 203

III FORTRAN LISTING FOP THE 25-CELL SPATIAL IODEL....... 205

IV ENERGY BODIED INII GOODS AT!D SERVICES FOP 92
U.S. ECO:In"Y SECTORS 'Ir 1967..................... 211

V TIME SERIES DATA 7FO THE U.S.
ECONOHIC-ECOLOGIC SY qln.......................... 219

VI FOrTTAT' LISTIFNG FOP THE 5-SECTOR U.S. ECONO1OY-
ENVIPONMETIT SIMULATI"!' MODEL....................... 236

VII FOrTF.T: LISTING FOR THE 91-CELL SO"[! FLORIDA
SI9MULATION M1ODEL AND DATA ......................... 240

LIST OF Tr ?'?rCES .............................. ...... 247

BIOGRAPHICAL SKETCH..................................... 254


I













LTST OF '"ABLEF


Table 1 p ag

1 Characteristics of the input-output and
biosphere embodied energy concepts................ 11

2 Tnput-output transactions matrix in arbitrary
physical units corresponding to the diagram in
figure 7..................................... .... 32

3 rnput-output transactions matrix in embodied
energy units corresponding to the diagram in
Figure ........ ............ ... ......... ..... ..... 36

4 Tnput-output transactions matrix corresponding
to the diagram in Figure 9, using the national
input-output accounting conventions............... 39

5 Relationship of input-output value added
accounts categories....... ............. .... ...... 49

6 estimatedd lan- areas and solar absorption for
major land use types..... ...................... 54

7 Land use subsystem metabolism and structure
estimates in coal equivalents (CE)................ 63

9 Ninty two sector rnmho 'ied energy intensity
statistics............... ,,... ... ............... .103

0 Regression analysis results for total (direct
plus indirect) energy consumption versus total
Dollar output for the four alternative
treatments of labor, government, and solar energy.,113

1I 1197 T.S. business sector capital stock and
investment breakdown (in billions of 1967 dollars).117

11 1967 U.-. government sector capital stock and
investments breakdown (in billions of 1967 dollars).118

12 1?67 U.S. household sector capital stock and
investment breakdown (in billions of 1967 dollars) 119

11 1963 aggregate sector net capital stocks, gross
investment, and depreciation (in billions of
1 6" dollars) ..................................... 134

14 1967 aa ra-re sector net capital stocks, gross
investment, and depreciation (in billions of
1967 dollars)..................................... 136


V1













Table page

15 Sector correspondence............................. 138

16 Initial parameter estimates....................... 149

17 U.S. economy-environment simulation model
performance statistics for the 1929-1969 period... 156

18 South Florida simulation model performance
statistics for 1"53 and 1973.................,,... 178

19 South Tlorida land use data converted to embodied
energy units.............................. ...... 193

2V Pmboiedi energy in goods and services for
12 U.S. economy sectors in 1967.................. 211

21 real GrP, total fossil, hydro, and nuclear energy
consumption, and fossil, hydro, and nuclear
energy to real GNP ratio, 1920-1976............... 219

22 U.7. business sector net capital, investment, and
depreciation time series in constant dollars...... 222

23 TU.. government sector not capital, investment,
and depreciation time series in constant
Dollars ............. .... ........................ 224

24 U.7. household. sector net capital, investment,
and. depreciation time series in constant
Jollars.......... ............................... 226

25 U.S. environment sector, U.S. economy, total
T.S. (Pnvironment plus economy), and rest
of the world net capital stock in
constant dollars.. .................... .. ......... 228

26 Time series or net land stocks in the U.S......... 231

27 mime series of total mineral fuel use and
estimated real dollar value....................,,. 233


--i ;















Figure page

1 Solar energy driving the productive process-s
of the earth.......................... .........., 8

2 Diagram showing the characteristics of the input-
output an" biosphere embodied energy concepts..... 12

3 Diagram showing the standard input-output
accounting setup. ........ ......................... 15

4 Location map of south Plorida..................... 22

5 Energy circuit language symbols used in this study 24

6 Single sector energy balance........... 29

7 Hypothetical three sector economy with all flows
in arbitrary physical units.................,,.... 31

S Hypothetical three sector economy with all flows
in embodied energy units.......................... 35

0 Hypothetical three sector economy cast in the
format of -the national input-output accounting
statistics........................................ 38

10 energy "low diagram of an aggregated 14 sector
U.S. economic-ecologic system..................... 46

11 Diagram showing definitions of national income
variables.......................................... 47

12 Summary of modifications to the input-output
conventions.........,..... ....... ... ............ 53

13 Land use cells for south "'orida.................. 60

it Txample of detailed land use data, showing
cell 45 in Figure 13 for 1973..................... 61

15 Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973................... ... 62

16 Two production systems and their exchange
pathways. ....................................... 72

17 Energy circuit diagram for a two component
power maximizing model of exchange................ 77


L


v, i i


LITT OF rTGUR-ES













Figure page

1R Differential equations for the model in
Figure 17 ......................... .. .... ....... 79

19 Diagram illustrating the partial production
function relations ............. ................ 81

27 Component i difference equation................... 86

21 Two component nodel analog simulation results..... 88

22 Two component mldel analog simulation results..... 92

21 Digital simulation of the power maximizing
model for a spatial grid of 25 components......... 95

21 Diagram showing the system boundaries and flows
included in 4he four alternatives................. 98

25 "r-qu-ncy plots of embodied energy intensities
by sector calculated with and without solar
inputs.... ... ........ ........ .... ..... .. ..... 101

2R 'reguency plots of embodied energy intensities
by sector calculated with and without labor
and government service feedbacks ......,..,..,.. 102

27 Plot of direct plus indirect energy consumption
(calculated excluding solar inputs and labor
and government) versus dollar output for
92 U.S. economy sectors..................,,,..,,, 106

28 Plot of direct plus indirect energy consumption
(calculated including solar inputs but excluding
labor and government) versus dollar output for
92 U.S. economy sectors............................ 108

29 Plot of direct plus indirect energy consumption
(calculated including labor and government but
excluding solar inputs) versus dollar output for
92 U.S. economy sectors........................... 110

3n Plot of direct plus indirect energy consumption
(calculated including solar energy inputs and
labor and government) versus dollar output for
92 U.S. economy sectors....................... 112

31 Fineral, hydro, and nuclear energy consumption
per dollar of real 3NP from 1920 to 1976.......... 115


I













Figure page

32 Time series plot of U.S. business, government,
and household net capital stocks from
1929 to 1969 ...................................... 123

3' Time series plot of 7T.S. environment, U.S.
economy, and total [T.S. net capital stock from
1929 to 1969.............................. ........ 124

34 Time series plot of rest of the world net
capital stocks from 1929 to 1969.................. 125

35 1963 14-sector transactions matrix with all
values converted to millions of 1967 dollars...... 128

36 1967 14-sector transactions matrix with all
values converter to millions of 1967 dollars...... 130

37 Energy flow diagram for a 5-sector U.S.
economy-environment simulation model.............. 141

38 1963 'r-sector transactions matrix with all
values converted to millions of 1967 dollars...... 144

39 1967 5-sector transactions matrix with all
values converted' to millions of 1967 dollars...... 146

tf Simulation results for the 5-sector economy-
environment model from 1929 to 2031............... 153

i1 Simulation results for the 5-sector economy-
environment model from 2031 tO 2131............... 155

42 rbholied energy intensity map for south Florida
for q19C estimated from the 1900 land use map..... 158

43 Embodied energy intensity map for south Fl3rida
for 1913 estimated from the 1953 land use maD..., 160

44 rmhodied energy intensity map for south Florida
for 9"73 estimated from the 1973 land use map..... 162

t5 Simulation results for the 91-cell south "lorida
spatial simulation moel.......... ................ 167

46 Analog computer diagram for the two component
exchange model................. ........... ..... 203













Abstract of Tissertation Presented to the CGraduate Council
of the University of Florida in Partial Fulfillment
of the requirements for the Degree of Doctor of Philosophy


'"POrIFD E'pFRGY BASIS FOR
'CONOMTC-ECOLOGTC SYSTEMS

By

Rober*l Costanza

June, 1979

Chairman: Howard T. Ofum
Major Department: environmentall Fngineering Sciences

The energy basis for economic-ecologic systems was

investigateO using models of th Urnitel Statos and the south

Florifa area. The energy flow necessary (directly and

indirectly) to produce commodities was termed the embodie;1

energy and was studied as a parameter useful for evaluating

systems and their parts. embodiedd energy was calculated

using input-output matrices +o trace the flow of energy

through systems.

The approach was applied to a 92-sector U.S. economy

for 1967. Current accounting conventions for government an!

households were modified to make them endogenous sectors.

Solar energy inputs to the economic-ecologic system were

estimate! and included. These modifications were necessary

to form a closed economic-ecologic system, with only energy

crossing the boundaries. Te changes were made

incrementally so the effects of each could be studied.

Results indicated a very close correlation between embodied

energy and dollar value of output, with the notable


v













exception of the primary energy sectors (P square = .(? when

the primary energy sectors were omitted). The results

implied a relatively constant embodied energy to dollar

ratio with an estimated value of 47000 kcal fossil/1967S.

Additional supporting data on energy/real GNP ratios for

time series of the U.S. economy and international

comparisons of energy/GDP ratios were collected and

presented.

Embodiecd energy was applied as a common measure to

model dynamic exchanges in combined ecologic-economic

systems. This approach internalizes all energy

externalities.

Maximization of power (or embodied energy productivity)

was used as an objective function in developing dynamically

optimizing, nonlinear simulation models. The models adjust

their connectivity structure through time in order to

maximize power and the behavior is therefore discontinuous

in a manner analogous to catastrophe theory. The model was

applied to a 5-sector U.S. economy-environment and a 11-cell

spatial grid of the souhb "lorida region, generating maps of

predict ed development.

The power maximizing model reproduced the behavior of

the U.S. economic-ecologic system over the historical period

from 1929 to 19r9 for which data on net capital stocks have

been estimated. Extrapolated into the future, the model

predicted leveling of the U.S. economy at around the year


vii













20n0 vith a subsequent gradual decline in net capital

stocks.

"The south Florida spatial model employed a sequence of

detailed land use naps based on aerial photographs and soils

information for the years 191V, 1953, and 1973. The model

divided the region into 39 cells with three additional cells

to handle Phe embodied energy changee with the rest of th-

U.S. and the world. the simulation reproduced the essence

of the historical sequence of development using solar energy

as the only exogenous variable and a power maximizing

decision structure. Development of the east coast, Key Test

and Fort Myers was duplicated by the model based on embodied

energy exchanges between these cells and the U.S. economy

cell. The model predicted leveling of the region as a whole

consistent with the U.S. economy-environment model.


__i r 1













I ?I T-0 'C"'TnN


A fundamental -.ssue in ecology is understanding the way

energy and material "lows in ecosystems develop organize'

structures and processes. Mlan's economic systems can be

viewed as subject to many of the same energetic forces as

those shaping ecological systems. Thus, the study of energy

and material flows in combined economic-ecologic systems can

lead to new insights into the way thes? flows develop

organized patterns.

Several important questions can be identified

concerning the role of energy as it affects organization and

succession in combined ecologic-economic systems. How does

energy flow through and organize these systems? What is the

relationship between energy flow and money? How is spatial

development related to sources of energy? Vhat are the

general criteria for natural selection? How can selection

be modeled to predict the dynamic behavior of these systems?

These questions were considered using energy systems

analysis (Olum, 1971). Rodels describing the flow of energy

and materials were developed and evaluated. Specific

emphasis was placed on integrating conventional economic

accounting and analysis techniques into the general energy

systems framework. Input-output techniques and data were

employed to trace energy flows through combined ecologic-

economic systems. ..fforts were made to show relationships












between these different accounting frameworks. Dynamic

simulation models were developed and used to investigate the

temporal and spatial behavior o* complex, self-organizing

systems that can evolve and change their internal structure

and function over time, Lotka's maximum power principle has

been suggested as the fitness criteria for survival of the

system, an.I thus the ultimate goal of evolution (03um 1971).

Can thOse concepts be incorporated in mathematical systems

models? what are the general criteria for survival of

systems? Can optimal control theory be gainfully applied to

this problem? Wha- general characteristics do models of

this type exhibit? -he simulation models developed in this

study were applied to the growth of the U.S. economy-

environment and to the spatially articulated growth of south

Florida in order to predict the general behavior of thes-

systems.





Research Plan



-his dissertation is a study of the way energy affects,

limits, anrd determines the organized nonequillibrium

phenomenon comprising ecological and economic systems. "o

this end conceptual' and mathematical models were davelope.

to indicate the response of these systems to available

energy inputs. T.near input-output models of embodied












energy were developed and evaluated. Ionlinear,

discontinuous optimization models were developed and applied

with Lotka's maximum power principle as the objective

function.

Cross-sectional and time series data were collected for

two related examples. The first was the U.S. economy-

ecology as a whole. Pata for this example include. input-

output transactions at various Ievels of aggregation, time

series of total capital stocks, investment and depreciation,

and time series of energy inputs to the economy and

environment. Most of these data were in dollar terms and a

major part of the study involved integrating them into an

all-encompassing energy flow network that included

environmental systems. The second example was the spatial

evolution of the south Florida region. A series of there%

previously compiled, detailed land use maps of the region

for the years 19n^, 1953, and 1973 (along with supporting

data on the characteristics of the mapped units) ware use?

as the primary data base for this application. The models

were run over the historical period and the results compared

with the collected data. Once a reasonable fit was obtained

the models were run into the future and their predictions

interpreted.













background of Previous Studies


This dissertation includes energy analysis, evaluation,

and simulation of economic-ecologic systems using input-

output, optimization, and spatial models. Some background!

of previous work in theso areas is reviewed.



Trnciv andl Society

The thesis that available energy inputs govern and

limit the structure of human societies is not new.

Boltzmann (1986) pointed out that life is primarily a

struggle for available energy. Soady (1933) state: "If w=

have available energy, we may maintain life and produce

every material requisite necessary. That is why the flow of

energy should be the primary concern of economics" (p. 56).

Lotka (1921) also noted the direct relationship between

energy and economics. Cottrell (1955) provided a detailed

analysis of the ways cultures have historically adapted to

their "surplus energy" supplies. Odum (1971) extended

energy concepts to include all systems, thus providing a

conceptual link between man and nature and many new insights

into the workings of man's economic systems.

Daly (1977) discussed the energy limitations which

ultimately lead to steady state economic systems.

Georarscu-7'oegen (1071) took a more theoretical approach in

his study of the second law of thermodynamics and its












importance in economic systems. Ophuls (1977) reviewed the

political implications of energy and resource limitations.

Cook (1971, 19"6) and Hannon (1973a) have attempted to

quantify the intricate web of energy flows in industrial

societies.



Systems cology

Systems analysis as practiced in ecology is an

integrative approach used to explain the structure,

function, and interrelationship of all systems as the

product of certain general systems principles which

transcpnd thh boundaries of acal--mlc fields. The aim of

general systems theory was formulated by Von Bertalanffy

{1968) as "the formulation and erivation of those

principles, which are valid for 'systems' in general" (p.

32). This paradigm is seen as essential to the

understanding of complex systems with feedback, which has

frustrated the atomisticc" approach of "normal" science.

Odum (1971) produced a unified theory and methodology for

the application oF general systems theory to a broad range

of problems. This is the general approach taken ir this

study.












Zn23rg MI naly!sis

The detailed study of energy flow through systems can

be termed energy analysis. Evaluation of energy flows in

ecosystems has long been an important tool (Juday 1940;

Lineman 1941). Currently in government circles energy

analysis has come to be used more specifically to refer to

the study of energy flows in engineering-economic systems

and the resulting policy implications. This application is

new and the concepts and techniques have not as yet

consolidated into a coherent whole. The house committee

print: "Energy analysis as a policy analysis tool" (Gushen

1976) is a goorl survey of the current literature. The

symposium by GilliTanr (1978) highlights points of

controversy, particularly concerning m?!thods of evaluating

embor"ied energy.

The field includes applications of input-output

analysis (Herendeen and Bullard 1974) and an evaluation of

energy systems diagrams (Gilliland 1975, 1978; Kylstra 1974;

Odum 1968, 1973). -"ho~ applications involve different ways

of accounting for energy flows through systems. This

dissertation develops an input-output technique for energy

accounting similar to the one employed by Hannon (1973b) and

Herendeen and Bullard (1974). Isard (1972) suggested the

application of input-output models to scologic-economic

systems but not in terms of energy accounting. The unigu-

feature of -he input-output energy flow models in this












dissertation is the application to combined economic-

ecologic systems. The relationship between energy analysis

and economic analysis has been the subject of recent debate

and is a major topic or this dissertation. Leach (1975) 3nd

Webb and ?earce (1n75) have challenged the ability of energy

analysis to provide useful information beyond that available

to standard economics. By treating the economic-ecologic

system as a unit and by following energy flows through it,

many of these questions may be clarified.



Fmbodied Enerav

embodied energy is .defined as the total amount of

energy of a single type required directly and indirectly to

produce the substance of interest. For example, Pigure 1

shows solar energy as the primary energy input to the earth.

rMost flows and storage of free energy on the earth can be

thought of as embodied past and present sunlight, since

sunlight has been the most significant source of free energy

for the earth, Tides, nuclear energy, and residual heat

contribute much smaller amounts. "hus the sunlight of past

cons is embodied in the current storage of fossil fuel, raw

materials, soil, etc. that are employed by industrial

society. Tt is convenient to divide the continuum of energy

sources into renewable sources of free energy (embodied

present sunlight) and nonrenewable storage (embodied past

sunlight) on the basis of their relative rates of production





























































Figure 1.


Solar energy driving the productive processes
of the earth.












and consumption. renewablee sources are those whose rate of

production roughly equals their rate of consumption.

Obvious examples are sunlight itself, rain, wine!, and the

shorter time scale products of the interaction of these

inputs, such as forestry, fishery, and agricultural

products. Fonrenewable sources of free energy (embodied

past sunlight) are -hose whose ratl of consumption far

exceeds their ra+e of production. Nonrenewable sources ar?

mine substances, such as the fossil fuels, soil storage,

and mineral -eposits, which are the results of slow

biogeologic production cycles over long time periods.

embodied energy is linked to ability to Fdo work (or

available energy) by the theory that the energy used

(directly and indirectly) to produce a substance shows up as

a proportional increase in the stored order or departure

from equillibrium of the substance, and thus its ability to

do work. 7or example, oil mined and delivered to the point

of use would have more embodied energy (that consumed by the

recovery and transportation process) than oil in the ground.

The delivered oil would also have a larger ability to do

work than the untapped oil, due to its increased proximity

to an oil consuming economic system. A ceremonial mask

would have more embodied energy than the piece of wood from

which it was carved and would also presumably do more work

by performing an important symbolic function in the

ceremonies of the culture of its manufacture.













Several concepts of embodied energy have thus far been

proposed. One employs input-output techniques (Leontief --

1941) to trace input energy flows through the complex webs

of interactions in economic and ecological systems (Hannon

1973b; Tferendeen and ullard 1971) This can be termed the

input-output embodied energy. Tt assumes that embodied

energy is a conservative quantity, or that the sum of the

embodied energy inputs to each sector are emdodied in the

output. When pathways diverge, the total embodied energy is

partitioned among them so that the system of interconnected

flows maintains the conservation constraint. Figure 2a

shows an example of this approach. Another approach reasons

that since all processes are interconnected and in that

sense required for each other's production (either directly

or indirectly), the amount or input necessary to produce any

one product must be taken as the total input (Odum 1978).

This approach assigns equal embodied energy to all by-

products of a process but partitions the embodied energy if

the same commodity is simply divided. The embodied energy

inputs and outputs for each sector do not necessarily

balance. This approach has been applied (Odum 1978) to

estimating the embodied energy in natural energy flows in

the biosphere and can thus be termed the biosphere embodied

energy. Figure 2b shows an example of the concept. Table 1

and figure 2 compare the characteristics of these two

approaches.


I













Table 1.


Characteristics of the input-output an.
biosphere embodied energy concepts,


Characteristic


Tnput-output
embodied energy


Biosphere
embodied energy


Conservation of
embodied energy

All heterogenous
by-products of a
production process
assigned equal.
embodied energy


yes


no


yes
(except for
degraded heat)































(a) INPUT- OUTPUT


Figure 2. Diagram showing the characteristics of the
input-output and biosphere embodied energy
concepts.












The first concept was used in this study, with some

modification and extensions. A complete description of the

technique with examples is given in the methods section.



_Oti mization

Optimization is the search for maxima or minima usually

subject to some constraints. Wilde ani Beightler (1967)

provide a good introduction to the method. Cody (1974)

reviews some of th'e applications of optimization models to

ecological systems. Rapport and Turner (1977) discuss the

underlying similarities of economic and ecologic processes

as an explanation for the success of optimization models in

both fields.

'he maximization of useful energy flow {or maximum

power) was suggest-, as an objective function by Lotka

(1922). olum (1971) has elaborated and generalized on this

theme. Oster and 7ilson (1978) employ what they trm

ergonomic (or work) efficiency as an objective function in

the study of colonial insects. Wang, Odum, and Costanza

(1978) showed an example application of the maximum power

principle to a land and water management problem.



Economic Mofels

current microeconomic theory can all fit under the

umbrella of optimization. In the general optimization

problem there is some objective function to be maximized or


I












minimized usuallyy profit, utility or cost) subject to

constraints dealingg with resource availability, income or

levels of production). -he partial equillibrium theorists

deal with small pieces of the system taken in isolation with

the ubiquitous "all else boing equal" frequently invoked.

Most of the analysis focuses on graphical solutions. Becker

(1971) is a good text along these lines. Tnput-output

analysis and linear programming are important approaches for

determining optimum, equillibrium flows of commodities and

money in an economy. Oorfman, Samuelson, and Solow (1958)

summarize these approaches. Input-output is a general

equillibrium technique developed by Leontief (1911). It is

a tabular accounting system with balance constraints. Tn

the typical application the economy is disaggregated into n

sectors and ;th- production of each sector is expressed as:



Xi = 1ij + Yi (i=1,2,...,n) (1)
j=1

where

7i = total production o' sector i

Xij = production of sector i to be used as input

to sector j

Yi = output of sector i to consumers (final demand)

Figure 3 illustrates this setup.

A set of direct requirements coefficients can be defined as:

A ij = 7ij/ j (2)


or:



















































Xi = EXij Yi


Figure 3.


Diagram showing the standard input-output
accounting setup.












ij = A jXj (3)

substituting (3) in (1) yields:

n

i = ij j + Yi (4
j=1

or in matrix notation for all n sectors:

7 = AX + Y (5)

or solving for the sector outputs in terms of the final

demand (Y) and the direct requirements matrix (A)
-1
X = (T-A) Y (6)

The set of simultaneous linear equations represented by

(6) is useful for tracing interdependencies at a point in

time or for making predictions of the effects of small

departures from equillibrium. Programming models are

similar to input-output models except that more than one

solution to the equations is possible. "he approach

originated as a strategic planning mooei for directing Air

Force activities (Tantzig 1951) The mathematical problem

is finding the best (or optimal) solution from among the set

of feasible solutions. The approach initially was applied

to linear systems (linear programming), and this is still

the major practical application. Gradually, more

mathematically difficult problems were attempted with

current applications to dynamic, nonlinear systems with

stochastic elements. Baumol (1977) reviews these methods,












5Bpatial -cnno-irc models

A good review of models of the spatial distribution of

economic activity can be found in Chorley and Haggett

(196) most of these models can be divided into three main

groups. Central, pace. thlorv is based on the fact that some

goods and services must be produced at "centers" and

transported to users (or the users must be transported to

the center). For a specific mix of goods and services there

is a limited range of distance from the center defining a

market area inside which the marginal revenue exceeds the

marginal cost. In a homogeneous plane with only one type of

qood or service produced, hexagonal market areas are

theorized, since these would represent the closest packing

of the market areas with no overlap. Production of

different types of goods and services leads to hierarchical

arrangements of hexagons, with different levels of central

places producing goods and services with different market

areas. Original works in this area are by Christaller

(1331) and Losch (1941). Berry and ?red (1961) provide a

review. Location theory oostulates that economic activity

will occur at the point of minimum total transport cost.

Transport cost surfaces for each of several inputs and

outputs of a specific economic activity are estimated and

overlaid to find the point of minimum total transport cost

(Weber 1909). The approach is highly amenable to computer

applications as well as to the inclusion of costs other than













those normally taken into consideration. See Smith and Lee

(19'7) for an example. The overlay system used by McHarg

(1960) is essentially a location theory model in which

environmental degradation costs are to be minimizes,

Objective procedures for estimating environmental costs have

limited the application o' this technique. Rent theory is

another extension which attempts to minimize the sum of rent

and transportation costs (vujnovsky 1972).

Previous studies of economic location have concentrated

on static, cost-minimizing models. The spatial simulation

models in this dissertation combine cost and benefit

concepts (in energy terms) in a dynamic framework. The

aE2vitZ morli is so called because its mathematical form is

analogous to the gravity equation in physics. It predicts

that the amount of exchange between two centers will be

proportional to the product of center sizes divil1nl by somn

power of distance between centers.

Or:
a
7ij = KSiSj / ij (7)
where

Yij is some measure of exchange between

centers

Sir,j are some measure of the sizes of centers

,-ij is distance between centers

K,a are parameters of the model












In empirical studies, Yij is often the number of

people-trips between centers and Si and Sj might bo the

populations of the centers. Tsard (1975) reviews these

concepts and applications. The generalized gravity relation

was incorporated in the spatial simulation models developed

in this study.



SimulatI on 1od els

Simulation of dynamic, nonlinear systems of equations

can be accomplished by solving differential or difference

equations using a computer. Examples of simulations of

economic and ecologic systems are those by -orrester (1961,

1969, 1171) and Odum (1971). The approach has been

expanding rapidly in recent years with the decreasing cost

and increasing availability of computers. Hall and Day

(197") provide a compendium of recent ecological simulation

studies. Aifeld anI Graham (1976) is a recent example of

simulation applied to urban systems. In outline, the

techniquee involves deciding on "state variables" or storage

for the system of interest and then writing a differential

or difference equation for the time rate of change of each

of these storage in terms of the other storage and any

external inputs. qiven initial conditions for the storage

and a set of parameter values the computer simulates the

time course of each variable in the system. The solution

can then be compared with reality and adjustments made to

the parameter values.












fi- Sout.h Florida Jrea



Figure ft is a location map of the south Florila area,

The region boundaries were taken as the drainage basin

boundaries of the Kississmee-Fverglades basin. Extensive

background information was developed on the detailed spatial

evolution of land uses in this region as part of a study by

the Center for Wetlands, University of Florida, funded

through the Department of t'e-. Interior and the State

Department of Administration. This dissertation developer

as an attempt to answer some of the questions raised by

these previous studies. The reader is referred to Costanza

(1975) for characteristics of the mapped categories, land

use, energy data, and a detailed description of the mapping

procedure. Prowder, Litttlejohn, and Young (1975) provide

full color land use maps and a general overview of the

application of energy analysis to a region. The technical

report of the south Florida study (Odum and Brown 1975)

provides detailed data encompassing the full range of energy

and environmental problems facing south Florida. Zucchet-t

(1975) provides a retailed systems analysis of the Miami

urban area.













ORLANDO I

82 %OR A E 0t o






$, \ \ 0 to 10 20 0 40 Miles


27--






















261-..


2 l--


- -- --- --- --













ST THODS


--c-r*n-onr of the o'e-li!n LanuaSSess





The energy circuit language developed by H. ". Odum

(1971) was us.l for illustrating the structure of the

models used in this dissertation. The symbols of the

language have associated mathematical functions which allow

the energy circuit molel to be translated directly to

differential or difference equations for computer

simulation. -he symbols used in this thesis are summarized

in Figure r. A complete description of the symbols and

their mathematical connotations can be found in Oun (1971)

and Odue an5 (VIum (1906).

Symbolic modeling languages, such as Otum's (1971)

energy circuit language, Porrester's (1961) industrial

dynamics language, analog computer diagrams, and others are

useful for concise conceptualization and presentation of

complex networks of flows and storage. Diagrammatic

languages allow immediate comprehension (once the language

is understood) of the connectivity structure of the model.

while conveying the same mathematical content as

differential equations which require much closer inspection

before the overall structure is apparent.













0


GROUP SYMBOLS (1) AUTOCATALYTIC SELF-
MAINTENANCE UNITS, (2) PRODUCTION UNITS,
AND (3) GENERAL PURPOSE BOX FOR
MISCELLANEOUS SUBSYSTEMS.


Figure 5.


Energy circuit language symbols used in
this study.


ENERGY SOURCE (FORCING FUNCTION),


HEAT SINK, OUTFLOW OF USED ENERGY.


ENERGY INTERACTION, ONE TYPE OF ENERGY
AMPLIFIES ENERGY OF A DIFFERENT
QUALITY.



ECONOMIC TRANSACTION AND PRICE
FUNCTION.



STORAGE (STATE VARIABLE)




ON-OFF CONTROL WORK (DIGITAL ACTIONS)


- ( 2) (3)












MoI1l D development

A model is an abstract representation of a structure or

process which is constructed to aid understanding.

Development of an appropriate model is guided by the

questions being as!:ed, the general principles which th-

model employs in answering these questions, and the amount

of time and effort which can be devoted to the modeling

effort, including data collection and evaluation. There are

several classes of models but this dissertation focuses on

mathematical models of the dynamic nonlinear type. Several

authors, notably Forrester (161) Nicolis and Prigogine

(1977) and Odum (1971) have argued that questions of time

behavior in living systems can be adequately addressed only

with models of this type.

The topological structure of each model was developed

by deciding on the internal components and external forcing

functions to be considered and then making assumptions about

the interconnections. The models were evaluated with data

from real situations. The simulation results were compared

with observed historical trends to determine the accuracy of

the original assumptions. These were modified as necessary

to improve the 4it.





The general meBhod of Lagrange multipliers was employed

in the development o- the power maximizing simulation













models. Baumol (1977) contains a readable description of

this technique. Tr. essence it allows a static, constrained

optimization problem to be translated into an equivalent

unconstrained problem using the device of the Lagrange

multipliers. This method yielded the general conditions

necessary for optimum (maximum power) behavior of the system

at each point in time. An algorithim, which employed these

conditions in a dynamic simulation framework, was then

developed and teste.



Simulation r'Q l-na "'nho:'

Both analog and digital simulation procedures were

utilized in this study. The main advantage of the analog is

the "hanis on" interaction with the molel that its small

size and continuous operation facilitate. For these reasons

an 717T inic analog computer was used to simulate a

simplified, two component, unscaled version of the model.

This allowed investigation of some theoretical aspects o1

the model and the range of behavior which the model could

produce. An analog diagram of the model is given in

Appendix T7.

Digital simulation requires integration by discrete

approximation and is therefore theoretically less accurate

than the continuous integration possible on an analog

machine. discrete integration quickly approaches the

accuracy of continuous integration as the size of the












integration "nterval is renirc-~ or the order of the

numerical method is increased, however. The main advantage

of the digital machine is its large capacity, allowing th-

simulation of much more complex models than possible on

available analog machines.

An Amrdahal $471 digital. computer was utilized, for

running the large models of the U.S. economy and s-'ith

Florida for which detailed data were available. The no-els

were written in 70??TAN using a rectangular integration

scheme. Listings of the POPTIP76 programs are given in

Appendices T77, VI, and VI7. An Tntecolor microcomputer was

also utilized for testing some mid-sized versions of the

models in BASTC.



flodel Parameter Estimati..on, validation and Testing

Dynamic simulation models of the type used in this

study require a large number of parameters. Frequently,

there are not enough data available to calculate statistical

"best fit" estimates of the parameter values. Therefore,

initial estimates of the parameter values were generated

from the available data and these initial estimates were

adjusted, iteratively until a reasonable fit was obtained

between the model and reality. The adjustment process was

limited to the least well known parameters and required

additional information about the historical behavior of the

system being modeled to compare with the model's output.












This calibration or validation of the model was performed by

manually adjusting the mod,1's parameters. The

discontinuous nature of the simulation models made the use

of nonlinear parameter optimization computer programs for

fitting the model to the historical data impractical. This

was because all of these algorithims (short of brute force)

require a continuous error surface +o operate efficiently.


I rplptIltu Techniqanes for cal.culatijn Tmbod3ied nern-rv

The application or input-output techniques (Laontief

191) to the study of direct plus indirect energy

consumption was developed and documented by the Fn-ray

Research nroup at the Center for Alvanced Computation,

University of Illinois (alrendeen and Bullard 197(t). 7he

technique consists of defining a set of energy balance

equations (one for each sector) and solving the resulting

set of simultaneous linear equations for the energy

intensity coefficients vector e, which is the energy

required directly and indirectly to develop a unit commodity

flow. The underlying assumption of this technique is that

embodied energy is a conservative quantity. Figure 6 shows

the basic "energy balance" for sector j.

wher-

Xij is the transaction from sector i to sector j,

X is the total output of sector j, part of which

may be net change in storage.

ej is the embodied energy intensity per unit of X ,


I
















Ej j e xj





(a)










EXTERNAL
ENERGY
SOURCES .ejxj








(b)


Single sector energy balance.


Figure 6.













for this concept of embodied energy.

7. is the external direct energy input to sector j.

Thus the ernrqy balance for the jth component is:

n

7j = ejxJ nixij (8)

i=1

In matrix notation 'or all components:



= n(X-X) (9)



Here 7 is a vector of direct external energy inputs, X

is a diagonalized matrix of output flows, X is a matrix of

input flows and e is the vector of total (direct plus

indirect) energy embodied in a unit of outflow.

We can solve for e as:







A simple example will clarify the procedure. Consider

a three-sector economy consisting of an agriculture sector,

a manufacturing sector, and a consumers sector as shown in

Figure 7 and Table 2.

The economy is represented both in energy flow diagrams

(Odum '9"1) and corresponding input-output tables with all

the steps Irom physical flow units to embodied energy units

detailed. For simplicity the economy is at steady state




























































Figure 7.


Hypothetical three sector economy with all
flows in arbitrary physical units.














Table 2. Tnput-output transactions table in arbitrary
physical units, corresponding to the diagram in
Figure "









-------------------------------------------------------

'"o ?.gri- Mlanufac- Con- Net m tal
cultr o touring sumers Output Output
From 1 2 3 c

--------------------------------------------------------------------

Agriculture 1 10 5 5 10 30

Manufacturing 2 1n 0 30 10 "00

Consumers 3 .25 .25 1 .5 2

Energy input F 30n 70 -


I












implying no net change in storage over the accounting

period. For systems not in steady state, any change in

storage can be accounted for in the net output column.

In reading the input-output table, the output from a

sector to other sectors is road as a row. In this example

agriculture sectorr 1) delivers 1n units of output to

itself, 5 units to manufacturing (sector 2) 5 units to

consumers (sector 3) and 11 units to depreciation (net

output). Inputs to a sector are read as a column. In this

example consumers (sector 3) receive 5 units of agricultural

products (from sector 1), 31 units of manufactured products

(from sector 2), an, 1 unit from themselves.

To convert to embodied energy units, first calculate

the energy intensity vector e, by applying the equation:
-1
e = E(7-X)



Tn this example:





S 0 2 .25 .25 1



S -5 -5

X) = 5 -3 E = [30 70

.25 -. 25 1













.0618187 ,? 9009 .581P1R2
I1
(X-X) = .0254055 .0272?27 .9454545

.0218182 .no9en090 1.3818182



S= (-X) [31 6.364 21.818 836.364]

To convert the original physical units into embodie!

energy units multiply the energy intensities (e's) by the

appropriate flows. This yields the values shown in Fiqure 8

and Table %.

This embodied energy input-output table exhibits some

of the same characteristics as a dollar value input-output

table. "he total output from any sector equals the total

input to that sector and the total net output, or "final

demand,' in the economic terminology (1000 in this case), is

equal to the total net input, or "value added" (th- E

vector, also 1 in this case). Final demand refers to thp

dollar value of the reat output of the system, while value

addel refers to the dollar payments for the net inputs to

the system. The total final demand or the total value added

is defined in the national income accounts as the gross

National Product (GNP) This would imply a GNP for the

hypothetical economy of 100". However, the conventions used

in the national income accounts are not the same as those

followed! here, 'o demonstrate the relationships, our

example economy's 7-0 fable can be converted into one

consistent with the national accounting conventions.




























































Figure 8.


Hypothetical three sector economy with all
flows in embodied energy units.














Table 3. Input-output transactions matrix in emiboied
energy units, corresponding to the diagram in
Figure 8.








-------------------------------------------------------

"o Agri- ,anufac- Con- Nrt -:)tal
culture during sumers Output Output
From 1 2 3

-------------------------------------------------------

Agriculture 1 313.6 181.q 181.8 363.6 13q0.8

Manufacturing 2 218. 1'0 0.9 654.5 218.2 2181.8

Consumers 3 ?9. 1 2n9.1 836.9 418.2 1672.7

Fnprgy input 3I0 7f) 100"

Total input 1"9r.8 ?181.8 1672.7

-------------------------------------------------------












The major differences concern the treatment of

depreciation, the exogenous energy inputs, and the consumers

sector. In the national input-output accounts, the

depreciation is credited to the value of the output to

consumers. The consumers plus the net output are the final

demand sector. finally, the feedbacks from consumers are

considered to be exogenous and are added to the other

exocenous *nputs. These modifications lead to the flow

diagram anr input-output table given in Figure 9 and Table

4, respectively.

"he "interindustry" flows are not affected, and neither

are the total inputs and outputs from the remaining

endogenous sectors, "he modifications have affected only

the "final demand" and "value added" categories and their

common sum, the 5 72. The GNP is now 1418.1, which is

greater than 4-he previous total of 1000 by 418. 1, the

depreciation o* consumers. The economic accounts aggregate

the consumers sector with final demand and value added.

Tt is interesting to note how the results for the

energy intensities (e's) would differ if the standard, input-

output conventions were followed. Returning to the original

physical flow ratrix (Table 2) and ignoring the input from

consumers yields:



[ [o 13f5
















----- -----------4<----- -_
/
/

\\ 218.2 AG.

\ I-T~AGR.\


Figure 9.


Hypothetical three sector economy cast in
the format of the national input-output
accounting statistics.













Table L.


Tnput-output transaction matrix corresponding to
thp diagram in Fig. 9 using the national input-
outpnt conventi ons.


,o ?gri- Manufac- Consumers + net Total
culture -uring output or output
From 1 2 "final demand"



Agriculture 1 353.6 181.P 545.5 1n9.,8

Manufacturing 2 21q8.2 1fnn.9 872.7 21p1.8

energy input
+ Consumers or
"value added" 509.1 909.1 1481.1

Total input 1^q0. 21q1.8













;-7 = ; = (300 700)



- i.0526316 .005632

.^105263 .0210526


9 = (-X)71 = (23.158 16.316)

This is substantially different from the result with

consumers endogenous.

-'he lower energy intensities that result from an

exogenous consumer sector are due to the fact that the

consumer services (labor) contain embodied energy that is

ignore when this approach is used. An alternative to

having an endogenous consumer sector would be to calculate

independently the consumer services energy intensity, and

use the coefficient to include the energy embodied in

consumer services as an input.

In this example, the intensity of consumer services

(03) was calculated as 836.364 when consumers were

considered to be endogenous, This number can be used to

include the energy contained in consumer services in the

direct energy input vector (the r vector) while leaving

consumers exogenous. "he new r vector is:

S= [300 + .25(836.364) 700 + .25(836.364)]

= rnn,. nnl 90.q9. 91]

Recalculating the energy intensities using this vector

yields:













.0526316 .0052632
-1


.0105263 .0210526
e = [36.3=4 21.818]

These are the original energy intensity figures.

This approach requires an independent calculation of the

energy intensity of consumer services, however.

The approach considering consumers endogenous is more

in keeping with Leontief's original conception of a closed

(except to energy) economic system. It also does not

require the indepen-'ent calculation of the energy intensity

of consumer services. It does, however, require some

manipulations to extract the relevant data from the current

accounting scheme.



Double. Countin

An often raised question concerning any accounting

scheme involves double counting. This is especially true of

input-output schemes tha- display all intermediate flows.

The question becomes clear with reference to the preceding

diagrams and discussion. It is strictly a question of

accurately defining boundaries and making note of those

flows crossing the boundaries (net flows) and those flows

remaining within the boundaries (which when added to net

flows yield gross flows). Double counting problems are

encounter" when the boundary is shifted, but the













redecinitions of gross and net flows (which are defined only

with reference to the boundary) are not made. For example,

consider Figure 9. Here a boundary has been drawn around

the "industrial" sectors of the economy with the consumers

outside the boundary in the manner of conventional

macroeconomics. '"he net output of the industrial sectors

(that which crosses the boundary to consumers) is iefined as

the gross national product (CGNP). The confusion starts with

this misnomer, since the S'P is really a net flow. The

total output or "total transactions" would be a measure of

the true gross product. If the boundary is expanded to

include the consumers, then the GNP is no longer a net

outflow but an internal transaction. The net output with

the expanded bounlarr would be depreciation plus net exports

plus any change in internal storage. Conceptual problems

with double counting arise when this is not realized and th?

now internal transaction from producers to consumers is

still considered to be a ne4 outflow. rAdding the flow from

consumers to producers to the flow from producers to

consumers would obviously be double counting the GP as

previously defined. With the expanded boundary, however,

the GCP is no longer the net output from the system and

shouId be treated like any other internal transaction.













U.7. rconomv Data AssmblZ atn 7valua,-ion


The major data sources for the U.S. economy model wers

the Bureau of economic Analysis' {B'A) input-output tables

(along with their associated amplifying articles) and

Kendrick's (1976) estimates of capital stock and investment

time series. Other statistical sources were consulted as

needed.

'he year 1967 was used as the base year for data

collection since this was the most recent year with measurer

input-output data. Data from the 1963 input-output study

were also used and reference was made to previous input-

output studies back to 191n.

Leontier's (1941) original exposition of input-output

analysis envisione-d a completely closed economic system.

Since then the convention has been to view households and

government as part of "final demand," and to treat them as

exogenously determined. -The original, all-inclusive view of

the economy was deemed necessary in light of the objectives

of this study. Thus, certain modifications to current

accounting conventions were required. The input-output

statistics were modified to achieve a completely "closed"

(in the thermodynamic sense) system. This means that only

energy crosses thm system boundaries. To achieve this goal,

households an' government were brought within the system

boundary (made enrogneous) as were a "U.S. environment"


I












sector and a "res* of the world" sector. The conventional

T-O sectors were aggregated to 10 major groups, making a

total of 1i sectors. Figure 1n is an energy circuit diagram

summarizing the accounting scheme employed in this study.

All flows and storaqges of energy and matter in the world are

included (at least in an aggregated form) in this accounting

framework.



ov2ernment ant Ho7 sl. as ndoSaenous Sectors

Tn orger to make households and government internal

endogenouss) components in the accounting framework, certain

modifications to current accounting conventions and

approximations were necessary. Figure 11 illustrates the

problem. The household sector's inputs from the other

sectors were measured as personal. consumption expenditures

(PC"), which are the dollar payments of individuals for

goods and services from the "producer" sectors. The

exception is the input to households of government services,

which are paid for with federal income taxes, along with

state and local government taxes on households. The outputs

of the household sector to the other sectors are labor

services, which show up in the accounts as the employee

compensation category. Complications arise since the input-

output accounts separate value added (or VA, defined as the

payments to the factors of production) into only three

categories: t() employee compensation, (2) indirect

































L / V, I GOVERNMENT \ GOV.
TOTAL VALUE EXPENDITURES SALARIES
ADDED (VA)
= GNP
PART OF PROPERTY TYPE INCOME (PTI)





Figure 11. Diagram showing definitions of national income variables.












business taxes, and (?) property type income. Table 5

shows the relationship of these categories to the national

income and pronduc accounts categories. The implied wages

of self-employed people or unpaid family workers are not

directly included in the employee compensation category but

show up as a portion of proprietor's income, which is

em',dded in the property-type income category of value

added. Similarly, corporate profits taxes, which are also

embedded in property-type income, should be added to

indirect business taxes to determine the total taxes paid by

business to government.

A detailed examination of questions relevant to the

proper distribution of value added to the economic-ecologi:

sectors was not possible during this study. Certain

approximations were therefore made to derive the estimates.

Value added was distributed by crediting all employee

compensation (rC) plus a fraction of property-type income

(PTT) to householAs and all indirect business taxes (IBT)

plus a fraction of PLm to government. The fractions were

calculated using balance considerations, and the fraction of

PTI remaining after government and household's shares were

remover was considered a net profit attributable to inputs

from the environment (see the following section).

The r-O accounting frameworkk requires that the sum of

the total dollar value of the outputs from a sector equal

the sum of the dollar value of the inputs. This requirement













"able 5.


Relationship of input-output value added
components to the national income and product
accounts categories.


Value ad'ied components Value added components in the
in the input-output national income and product
(1-0) accounts (NIP) accounts

-------------------------------------------------------

Employee compensation -mployee compensation

Indirect business taxes Indirect business taxes

Property type income Proprietor's income

rental income of persons

Corporate profits (before taxes)

Inventory valuation adjustment

Net interest

Business transfer payements

Surplus of government enterprises

Capital consumption allowances













was used to set up accounting identities for the new

household and government sectors, which could be solved for

the percentages of property-type income to be credited to

each sector in order to balance the accounts. This is

admittedly only an approximation which was necessary due to

the lack of data on the allocation of value added in the

input-output accounts. Gross investment and net exports

were assumed to exactly balance against net profits. This

left the following identities. For the government sector:

TB" -+ Xq*(PT) + PT = GP + GS (11)

where

Xg = reactionn of PTI to Government

IBT = directt business taxes

P"T = Property type income

Im = Personal taxes

GP = Government purchases

G! = Government salaries

So the fraction of PTT to government necessary to balance the

sector's accounts is:

Eq = [GP + GS TB" P]l / PTT (12)

For the household sector:

'C + Xh*( TI) +GS = PCE + PT (13)

where

Th = Traction of PTI to households

-C = Fmployee compensation

PTm = Property type income

G7 = Government salaries













PC7 = Personal consumption expenditures

P7 = Personal taxes

So, the percentage of PTT to households necessary

to balance the sector's account is:

Ch = [p + P eC GS! / PTT (14)

The remaining fraction (call it Xe) was considered a net

profit:

XP = 1 xg h 15)

Using data from the statistical abstract of the U.S,

(Unite5 States Department of Commerce 1971) and the bureau

of economic analysis input-output tables (United States

Department of Commerce 1969b, 1974a, 1975) the following

values for 7g and 71 for 1963 and 1967 were estimated.

For 1963: (in millions of dollars)

Xg = [GP + GS TBT PT] / PTT

= [68167 + %553' 5627 61000] / 194248

= ,39n

Xh = rPCE + PT 7C GS] / PTI

= [375540 + 61'r0 341514 55030] / 184248



Xe = 1- Xg 'h = .7551

For 1967: (in millions of dollars )

Vg = [GPr + GS TBT PT] / PCT

= r[9465 + P1659 70239 8300"] / 254060

sh = [PC7 + PT rC GS] / PTT

= [49-qr6" + 83"nn 389136 816541 / 254060

4 17













Xn = I g- Xh = .4944

Figure 12 summarizes the modifications to the T-0

conventions made for this study.



environmental ~ n unDts

Ts with household and government services, there are two

ways of including environmental services. One is to treat

the environment as an exogenous entity and quantify its

inputs to the economy, The second is to treat the

environment as an endogenous sector with flows to and from

the other sectors in an integrated economic-environmental

system. Both of these approaches were utilized in this

study.

An exogenous environment sector was hypothesized for ?2

sector input-output studies of energy flow through the U.S,

economy. thesee studies were carried out in collaboration

with the Energy research Group, University of Illinois at

Champaign. For this analysis the solar energy absorbed by

the p.3, was partitioned to the economic sectors according

to land and water area. Table 6 shows the land and water

use distribution for the U.s and estimates the total solar

absorption (including atmospheric) for the various uses,

The agriculture sector was credited with the solar

absorption over all agricultural land plus 341 of the

absorption over the wetlands, desert, and tundra category,

as agriculture represents 7t, of the remaining land and











































Figure 12.


Summary of modifications to the input-output conventions.













"able m. 4stima-c-d .anE areas and solar absorpTion for
major land use types.



Average solar ,Ttal solar
ArPa(a) absorption (b) absorption
( 6 acres) (E Btu/ac-yr) (E18 Btu/yr)



Total land 2254 28 33.9

Agriculture 1212

Cropland 38-

nrassland pasture 54"

Grazing lan? 288

Forestry 587 '8 16.4

roofland~ pasture 62

Voo dand (not pastured) 50

Forest land 475

Wotlanrs, desertt r, tunrra 272 20 5.

urban F mining 193 20 3.9

Total water 1550 28 43.4

Inland G estuarine 50

Offshore (2?n mile limit) 15F0


Total land plus wa4er 3P14 103.0



a. rrom United states Department of Commerce (1976a).
b. .stimater solar absorption of the earth-atmospharn system
Fru'Iyko o 807, Haar and Suomi loq)).













water use,. his amounted to 35.74 F18 Btu solar/yr. The

forestry an7 fisheries sector was credited with the

absorption over all forested areas plus estuaries and

coastal water to the 200 mile limit plus 60n of the

wetlands, desert, and tundra absorption. This amounted to

63.06 E"8 ntu solar/yr. The remaining 4.20 E18 Btu solar/yr

represents direct utilization by the remaining industrial,

commercial, residential, and governmental sectors of the

economy. "his should be distributed to the remaining

sectors according to their total land areas. Accurate land

use data are not available at this level of disaggregation,

however. As an approximation, the entire 4.20 E18 Btu

solar/yr was credited to the household category since this

category represents about "" of the remaining land area,



Pn -nogonv "nv'-nrnmnrt s- sector

7 more conceptually satisfying method of including

environmental services is to treat the environment as an

endogenous sector, mhis sector contains all the land, air

and water in the U!S. and performs the essential task of

capturing solar energy and converting it into other forms

more usable by the economic sectors. Since the environment

sector is not completely "owned" by economic agents and

competitive markets do not exist for many of its products,

economists have difficulty evaluating many of the flows and

storage in this sector. A broader perpsective based on













energy flows has proved useful (Odum, 1971; Bayley et al.

1975) in conceptualizing this problem.

For the purposes of this study it was assumed that,

where competitive markets exist, market values wer3

proportional to embodied energy content and that both of

these could he considered to be conservative quantities.

Evidence for the validity of this assumption is presented in

the results section. Conservation of dollars and embodied

energy allows many of the flows to and front the environment

sector to be estimate from balance considerations, The

input-output accounts are arranged such that the total

dollar value of all inputs to a sector equals the total

dollar value of all outputs from a sector.

Once the payments to households and government, and

capital flows have been accounted for internally, there

still remains an imbalance between the dollar values of th"

sum oc the inflows to each sector and the dollar value of

the sum of the outflows. There is still a "net input" to

the sector or "profit." This net input was attributed to

services provided by the environment sector. This is

essentially a "pure economic rent" conception of the origin

of profits. Under this view entrepreneurial capacity is a

component of the labor services input necessary to

effectively capture environmental inputs. At steady state

these environmental inputs would just cover the depreciation

of the economic system, "h1 approach can also be viewed as












a form of' "shadow pricing" (Dorfman, Samuelson, and Solow

1958) of environmental services.



Capital Flows

Capital flows are normally not included explicitly in

the input-output tables. Data recently available from the

Bureau of economicc Analysis (SCB Sept. 1975) on

interindustry transactions in new structures and equipment

combined with data from !endrick (1976) on investment and

depreciation of human and government capital allowed the

inclusion oc capital flows in parts of this study.

"Dr the purposes of this study the capital floors were

simply aided to the existing interindustry flows. This

increase' the total input to each sector by the amount of

capital purchased hy that sector during the year and

embedrled th, year's nross Private Fixed Capital Pormation

column in the current transaction's matrix. The capital

purchases by each sector were then added as a "capital

maintenance and growth" column in final demand to balance

the additional input.





South Florida Land Use Data



A time series of three full color land use mans for the

years 19'0, 1953, and 19"3 for the south Florida region wren













produced as part of the study, "Carrying capacity for man

and nature in south Florida", edited by H.T. Odum and M.

Brown (197) The maps are also included in Browder,

Littlejohn and Young (1975) and Costanza (1975) with

supporting data. "he maps were manually digitized using a

cell size of 128 acres for computer manipulation. For this

study, the land use maps were aggregated to 88 larger square

cells, 1( miles on a side, as shown in Figure 13.

For example, Figure 1i is a full size copy of cell 45

in Figure 13 from the 1913 land use map. Figure 15 is a

computer printout of the same data to show how it was

digitized. The correspondence between the symbols on the

printout and the numerical codes for the land use subsystems

listed in Table is given below the printout. Since not

all cells had the same land area, the area include? in each

cell was calculated and recorded. The data in Table 7 (from

Costanza 10"") were employed to perform the aggregation.

The subsystem structure intensities listed in Table 7 were

multiplied by the number of acres of that land use type in

each o* the 8R south Florida cells, and these values wer-

accumulated for each cell to yield estimates of th- total

embodied energy in each of the cells. This was done for

each of the three land use maps. These data are listed in

Appendix I, along with the 'and area, and latitude and

longitude of the centroi-' of each cell,


I




U






60





1 I
0 10 2 0 4

s i 4 I I







4 16 17


I .27
. 27 -
25 26 Z7 287 I9 0 31 32




45 46 47 4? 49 SC 5! 52
71 7--S I







53 5 4 55 56 57 58 593

263 63 5 66 67 G2'

S0 7! 72 7 74
>I 26 7 I 28! i 23032I^31







I34V|S 736 37 8 3 I 1 771 4 43
1--- i i

[1 5 j i
^[ 54 &5J56! 57 5R j5 JSCi





-2S 6! 62 63 64 S





25"

84 LS.JI




e?82 8I 80: 1
--------! ___ _ J ... ______ J __



























































Figure 14.


Example of detailed land use data, showing
cell 45 in Figure 13 for 1973.














































19
20
21
22
23
24
25
26
27-34


Figure 15.


Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973.


+-+-.1- C+ +
-+. : : : ++++ : ++: CC +
::+ : : : +hM 'M M- -4 ++ =+ -- ='I K 4-+++ : :C : :C+ U
:++++: ++-1,~~M + ++ 1++::+i+t+++tCC:+: ::
+++- +:+ ,+MM.M- +++3 1 1 : : :++-1++ C: :C :: :
I-M+ hM++MMMMM: -+++53 11i 1++++- C. ::C
M M++MM+M R++5=1 I +++ : : : :
*MM M.M+I^MM ,MMM:3355=; : 1 1 *^-*-f-^ !<(-C +: : : :+;
S hM'A+ M+ MM : : M+ ---++ C*+ + c C *-+ + x -
55,'- MM M mexiSB s- ::::: ++:: *:::+ i+ C+|
5S ,e5 v. 4 +ig + + + 4c++*CC++*CC+ +
5 ^'^^M + t ++L4AA 4AA ::+++s-*++-+*1CCC+
I M MMM++++ :ex-++ +++++C//+
^ ^MNMA++++: : :++++CC/++
1 ,MM a+++++++++++++-CC.CCCC///
A ^M+ ++++ +++ -=* 't *++C*CC C/
+ MM+++++ ++ +-+ + -** /C/ /UU
M MM-M+++ 1111 1*U=+-'*CUUUUU
M I.M I U++ I 1111 :-: C+- cCUUUU
M M4++++11A : x:: :k*CUUUUU
M IMM4M+: : +11 Ca ::.: : CCIJUUUU
MC+CCC+ +CC ::: : :=CCCCUUUJ
,CCC+C5C'a**: ::CCCC///U
.MMM&CC+CC l.a- : : CCCC/ /
-M'-'CCCC I I s55A4A -CCCCC'
Mi1M5 4-+5555554++. + CC
554++A +++-i5 s ++++ C
e 55+++++ati *xxxC *ZC
PxM+++CC *a**CCa
S3+:5 5*xxx :::++x yCC













Table 7. Land use subsystem metabolism ann structure
estimates in coal equivalents (CE).


--------------------------~-----------------------

Subsystem Su bsyst m
Metabolism Structure
(E1 CE kcal (T'6 CE kcal
Subsystem /ac-yr) /ac)



1. Cleared land 0.5 5.0

2. Lakes an~ reservoirs 0.7 5.5

3. rPcreational space 7.7 24.7

4. Residential (light) 250.0 750.0

5. residential (meF. -aens.e) 520.0 2,250.

6. Commercial/Industrial 1,600. 11,125.0

7. Transportation 500.0 2,000.0

8. Pownr plants 4,n0o.0 126,e00.0

9. Improved pasture 5.1 24.7

10. Vegetable crops 21.3 294.8

11. "reo crops 9.6 74.9

12. Sugar cane 22.2 313.1

13. Grassy scrub systems 4.0 16.5

14. Pinoeland systems 6.4 80.1

15. Hardwood systems 7.7 235.9

16. Lakes and ponds 1.4 7.4

17. Cypress domes and strands 7,3 214.5

18. ret prairie 5.4 51.6

19. Scrub cypress 5.8 61.3

2M. Freshwater marsh 7.4 228.7













Table 7. fCortinued).




Subsystem Subsystem
Metabolism Structure
(E6 CE kcal (' 6 CE kcal
Subsystem /ac-yr) /ac)

~-------------------------------------------------

21. Sawgrass marsh 8.1 273.7

22. Beach and anne system n.3 u,0

23. Salt flats 0.3 4.

24. Scrub mangroves 1.0 7.2

25. Salt water marsh 5.0 29.5

26. Mangroves 7.3 218.,

Source: Cotanza -------------------------------
Source: Costanza (1T'5)


















PResults include a derivation of the general conditions

for maximum power, developmentt of an algorithim for

approximating the maximum power conditions in a dynamic

simulation model, and applications of the model. Some

features of the model were demonstrated using hypothetical

examples and the model was applied to a 5-sector U.S.

economy-environment and a 91-cell spatial array for south

Florida. The embodied energy intensity of goods and

services was calculated for 92 U.S. economic sectors for

four different alternatives concerning the treatment of

labor and government services and solar energy inputs. Data

ver- assembled on total capital stocks and flows and were

used to determine a better estimate of the mean energy

intensity for goods and services and to create "closed

system" inpnt-output transactions matrices for the U.S.

economy-rnvironment at the 1-sector level.





-e .en1ral Conditionls for Maximum Powser



A major hypothesis of the simulation models in this

study is that complex living systems evolve so as to

maximize their productivity (or power as defined earlier),












There is a large literature on the various aspects of

optimization and specifically dynamic, nonlinear

optimization but these methods are generally not integrated

with simulation studies. Wagner (1975) views simulation as

a last resort to be used only if all else fails. "he

potential benefits of the integration of simulation with

optimal control theories are great, however. In this study

a simple algorithm for achieving this goal is developed.

The objective function is taken as the maximization of total

system power (Lotka's power principle as discussed earlier)

and thz constraints deal with limits on the total amount of

free energy in the system and the exchange of energy between

components of the system. Power is maximized when an

optimal exchange network is used, and this network changes

through time,

The problem can be stated in the mathematical framework

of nonlinear programming for each point in time as follows.

maximize PT = P1 l(QQ2'***,QnT1) +

P2 (Q1 Q2 a* 'n,rE2) + ***

Pn (QI Q2, ***Qn Fn)

subject to Q1 + Q2 +n'+ Qn = Ct

1 = Kit (16)
P2 2t







7n = nt












where

PT = Total power of the system, equal to the sum

of the n individual components

Pl*,P2Fr,** n = Power of the individual components as

functions of the embodied energy storage

in the system (QI1Q2,.. ,Qn) and the dira:t

energy inputs (EI 2,.. ,'n)

The constraints indicate that at any point in time the total

embodied energy in the system is equal to some constant

value Ct, and the direct energy inputs are equal to

constants (Knt ). "he optimization of the system involves

moving the scarce (limited) embodied energy around to elicit

the maximum total system power.

The problem can theoretically be solved using the

method of T.agrange multipliers. Certain additional

conditions must be satisfied to assure the existence of a

solution. Wagner (1975, p. 604) outlines these conditions,

They are divided into two groups, one for the constraints

and one for the objective function. Since the constraints

are all linear in 4the above system, only the objective

function nee" be addressed. The conditions for th?

objective function are:

(i) ny is single valued and finite for each Q and F

satisfying the constraints

(ii) Every partial derivative (DPT/aQi' i) is single

valued, finite, and continuous at each Q and

satisfying the constraints












(iii) PT possesses a finite maximum PT ) over all

values of Q and satisfying the constraints

(iv) PT is concave over all values of Q and I

satisfying the constraints

These conditions guarantee that

(A) There exists at least one feasible solution

(B) Tf PT is strictly concave, then there is a unique

optimal solution

(C) Tf Q, is a constrained stationary point, then

Q, E is a global optimum

Tt will be shown in a later section that the specific

objective function chosen nets the above conditions.

The Lagrange multiplier technique involves creating a

substitute problem tha~ incorporates the constraint

equations into the objective function. This new equation,

called the Lagrangian, can then be maximized (or minimize3)

using standard calculus techniques. The Lagranglan

expression for the above system is:

L = PI(QIQ2,...,Qn' 1) + P2(Q01Q2,*" Qn, 2) + ***

Pn(Q 1Q2'***'Qn,1 n) + 71(Ct- Qi Q2 -** Qn) +

"2ilt- 1) + V3(K2t 2) +' Vn+l(Knt- 7n) (17)
where

V1' 2'" ,* n+1 are unknown Lagrange multipliers

To maximize the original constrained system, one then

maximizes the unconstrained Lagrange expression (L) by

writing the partial derivitives of I. with respect to all the







69





variables including the V's) and setting them all equal to

zero:


aL a P
= ?1
aQ2 a02


a%


aQP
2
2 r


a?1
Pn



aP
n

a2


- v
1



1


(18)


aT.

a5n


San
+

n


aP
n

n


-
1


aL aPl
i" ai1


a2,
-?2


aP2
= 2

2


- 2



3


(19)


* S


Sn
9 9 nn+l
n n


- I1


t


aP1

a"n













c



c
S
-


a


L
= C Q Q -...- Q = 0
S t 1 2 n
1
>L
=7 1 =

2




TL
S- =
nt n


'n+1


Thus there are 3n + 1 equations in 3n + 1 unknowns. Tn

this example the equations in groups (19) and (21) can be

iqnortd since they are simply restatements of the

constraints which specified that for a single small time

intFrval, the direct energy inputs can be considered as

constants. "hus to maximize or minimize the system the

following relations must hold:


P2

Q1

2
+ +,,,+
3aQ2


2 2
+ n+ +
a-Q


an
--n = 1
1

3P
n
n =
-Q1
2


aP
n

-n


3Q1
aPT
a Q

02


1P1

aoQ

aP1

3 2


aPT

n


(21)


P1
3Qn
^n






71





Or,
DPT PT aPT
= =...= r22)
l Q2 an

which says that the marginal total power of all the storage

should be equal in order to optimize the system. 'he

problem is then, how lo living systems go about adjusting

these marginal total power conditions in a fluctuating

dynamic environment? One possibility involves adjusting the

interconnection network of the system by switching selected

pathways on and off, as shown in Figure 16, This does not

violate the condition (ii) that the partial derivatives be

single valued and continuous since at each point in time the

functions are continuous. Mhis approach simply modifies the

problem from one time step to the next.

Consider the potential exchange from component 2 to

component in Figure 16. The diagram indicates that the

pathway is open if:


aPT PT
3 > @ ( 2 3 )
Q1 a802



Tf this condition does not hold then the pathway is switched

off. This would eliminate the term aP1/aQ2 from the

equation for aPT/a2 since Q2 would no longer be a variable

in the equation for Pl" This would lower aPT/aQ2 so that

the condition (23) would hold. By applying this decision



















O PT f PT
on if aQ aQ2


aPT d PT
on if Qz aQ0


EXCHANGE


EXCHANGE


PT = P + P2


Figure 16.


Two production systems and their exchange
pathways.







73




structure to all pathways in a system over time one coulV

prevent it from diverging too far from the optimum. This

may be considered a form of the "feasible directions" method

outlined in vagner (1975).

possibly more accurate but operationally more

difficult approach involves adjusting the model parameters

to achieve the desired partial derivative relations at each

point in time. "'e approach using the switches has an

effect similar to continuous adjustment of the parameters

but is operationally easier and acknowledges the physical

limits to parameter changes.

An alternative derivation of the conditions in (23) can

be formulate, as follows. hhe change in total power caused

by the exchange terms (Y12 and Y21) are composed of direct

and indirect effects. Tn the two component model shown in

Figure 16, the total power is a function of the storage,

direct inputs, and exchange flows.

PT = f(01' O2 9' 2 Y12 Y21) (24)
The rules for total differentiation can be used to determine

dPT/dY12, or the change in total power caused by a change

in the exchange flow Y12"

Using (24) one can write:

PT DPT aT T aPT
P = 3Q + dQ2 + d 1+ RE + dY +
T --- 1 --- 2 --- j 2 ---2I2
QI Q2 ~12 12

aT
--- 21 f)
3Y21


or:





74


e0 9Pp aQ DP (I ap a1L 3p dE aE p
T T TQ1 + T 2 T 1 + T 1 T
= + + + +
Yii2 QI 11]I2 3Q2 dY12 EI1 ~Y12 3'2 1(Y2 ~Y12
aP dY
+ T 21 (26)
Y21 (l12
The third and fourth terms on the right hand side can he

dropped since E1 and "2 are exogenous and.Y12 has no effect

on them, thus:


ds SE
1 2 = (27)
O12 y 12
Since embodied energy units are used throughout, some

additional simplifying relations can be made for this model.

= = 1 (28)
xY 12 Y 21

1 = 1 (29)
12
dQ
S2 = -1 (30)
d 12
Using (29) andf (3C):

dY21 dQ2 2 ()
=- / = -1 31)
12 d 12 (21
then:

dP
T P,T 8P
--- = 1 + 1 (32)
dY 12 Q 1 2Q 2

or:

T T T (33)
Y 12 1 aQ2












whore the firstt term on tho right hand side of (33)

represents the "benefit" and the second term the "cost" of

the transaction Y12. rn a dynamic simulation framework, a

transfer from component ? to 1 (Y12) is seen as beneficial

(leading to increased total power) if:


dP
T
d 1 .1
or (using 33) if:

T T
T >- T ( 3 5 )
aQl 0Q2

which is equivalent to (23). Thus, allowing the pathway

switches in figure 16 to remain open as long as conditions

(35) an (23) ho'li will tend to maximize the total power of

the system.





n-'n l _n4. of a Power MaximiZino Simuowateion oi33el



A specific motel structure and an algorithm for

approximating the maximum power conditions in a dynamic

framework must now be developed for application to real

systems, "he model equations will always represent a

compromise between simplicity (and therefore manageability)

and accuracy. Here the mathematical form of the madel

(inclu-ing the power maximizing algorithm) is laid out,

first for a simple two component case and then for the












general case of n components. It should be noted that this

specific mosel is not the only conceivable way to achieve

the maxi.mum power conditions derived eariler in a dvnamic

system, It is only one of a number of possible approaches,

Figure 17 is an energy circuit diagram of a simple two

component version of the model in Figure 16, showing the

specific production function chosen. The differential

equations for the m'iel are given in Figure 18. The choice

of a production function was difficult, since it involved a

compromise between accuracy and simplicity. The production

funclion chosen was built up from simple, slightly nonlinear

"partial production functions," which exhibit the important

characteristic of diminishing returns.

The algorithm involving the switches on the exchange

pathways in the model is a simplified method for

approximating the maximum power conditions in a complex

dynamic system. The switches are intended to maximize the

total power (PI+P2) in the system by allowing only those

exchanges that lead to a net increase in total power during

a particular small time interval. This function may be

handled in nature by the mechanism of natural selection.

The system of equations is allowed to "evolve" by changing

its connectivity structure as it progresses through time,

The technique is analogous to a "cost-benefit"

calculation for each potential exchange pathway for every

point in time. The "cost" is the loss of productivity due















aP PT aPT
on if 8Q' Q2
aQi a Q2~


a P. a P
on if I> -a
Q2 a QI


PT = P + P2


Figure 17.


Energy circuit diagram for a two component
power-maximizing model of exchange.





















Differential equations for the model in


Figure 17.
where
Ql,' Q2

E1, E2

a1, a2



b12 b21


bl b22

cl, c2

P=P1 +P2
T -1 '2


= embodied energy storage in
components 1 and 2
= direct energy inputs to
components 1 and 2
= direct energy input co-
efficients for components
1 and 2
= transfer coefficients
for exchanges from com-
ponent 2 to component
1 and from 1 to 2
respectively
= internal transfer
coefficients
= depreciation rates for
components 1 and 2
= total embodied energy
productivity (power)
of the system, given
by the first three terms
in the equations


Y12' Y21 = exchange flows from com-
ponent 2 to 1 and 1 to 2
respectively, given by the
third term in the equations


aPT

aQ2


change in total power
_ with respect to the system
storage (Q1 and Q2) all
else being equal


aPT

aQl


I


Figure 18.













2
bll+
+ +


+ a Q1 1 + blaQ


1b2 1 Q2

1 + bl2Q1


aT 3T
if -->
aQI 3Q2


otherwise


9PT
if -
3Q2


QPT
>-Q


otherwise


2
b22Q2


+i +~


1 + b22Q2


?T PT
if --> -
'Ql "Q2


o ther.wse- I


b21Q2Q1

S+ b21
14-b^O,


aPT aPT
if --> -
9Q2 aQ1

otherwise


- c2Q2


(37)


alEl


Q =


1


b21Q2Q1

1 + b21Q2


- clQ


(36)


-2E2 2


1 + a2Q2


b 12QlQ2

1 + b+l2Q












to a decrease in the contributing component's storage, while

the "benefit" is the gain in productivity due to an increase

in the receiving component's storage. Since the model's

production functions are differentiable, single valued,

finite and continuous at each point in time, an optimum

distribution of the storage exists for any point in time,

and the exchange network is adjusted to move the system in

that direction. As already noted, it is necessary to have a

common currency in which P1 and P2 are expressed in order to

perform this calculation, mhis study employs embodied

energy as the common currency.

The equations require some explanation. Sach of the

individual partial production functions (indicated by the

work gate symbols) are given a relatively simple "limiting

factor" form. This is equivalent to saying that there are

infinitesimal storage in the flow (shown by the small tanks

in the diagram), that limit the amount of source material

which can he used. A derivation of the partial production

equation follows. Consider a system given by the energy

circuit diagram in figure 1 and the equations below (Odum

and Odum 1)76).

Q1 lQQT k2Q1 (38)

Q = k3QT k4Q1QT (39)

Now assume that QT is an infinitesimally small storage with:

Q = 0 and k3 = 1 (turnover = 10n%). This yields:

Q = 0 = Q k4QT )

Solving for OT



















































Figure 19.


Diagram illustrating the partial production
function relations.


r












QT = 7/(1 + '4Q1) (41)
Substituting (41) in (38) yields:

Q1 = klQ1/(1 + k4Q1) k2Q1 (42)
A further simplification was that kI = k4 since in

embodied energy terms all of the inflow is embodied in the

input to the tank. The total production function for each

component was created by adding together partial production

functions of the form given above. The power maximizing

logic built into the model was us,"' to decide which partial

production functions were included in the total at any point

in time. Tn differential form the logic is hard to follow,

since it simultaneously uses one decision to make a second!

decision, which is used in making the first decision. The

equations can also be expressed in difference form (which is

necessary for digital computer simulation and is done in a

following section) to clarify the logic. For now one can

imagine? a tiny delay between one recision and the next.

The equation (36) for the rate of change of storage in

component 1 has five terms, mhe first term determines the

rate of capture of direct external energy (7i) as a function

of the amount of stored assets (QI) and the capture

coefficient al., 'he second term determines the amount of

internal interactions within component 1 as a function of Q1

and the coefficient bll. "Te third term determines the

amount of transfer from component 2 to component 1 with a

maximum power constraint. Tf the transfer is deemed to be a












net increase in total power at a particular time, then th2

rate or transfer is the given function of the stored assets

of the two components (Q1 and 02) and the transfer

coefficient b12. "rom ('6) and (37) the following

expressions can be derived for the above partial

derivitives:


3pT ai 2(b111) + (bl111) b 121
= + 4
SQj (^+ l 1 2 11 h~ 1 5 (1b+ 12
--- -------- -i~~le;Z-- r~h207

Q b2ll ( 2Q2
+ (43)
1 + +21Q2
2
T = a2R2 2(b22Q2) + (h22 2) b21Q2



1+ b 1 l --2
1 + bl2Q1

The fourth term in equation (36) is the (potential)

outflow to component 2. It is subject to decisions

analogous to thosp discussed above for the inflow from

component 2 to component 1. The last term in equation (36)

is the depreciation term, which was assumed to be a linear

function of the quantity stored. Thus, cl is the

depreciation rate for component 1's storage.

The morel can he easily expanded to n components.

Figure 21 is a difference -gqation representation for one

component in an n component version of the model, In

applications of the model the components can be sectors in

an economy, areas of land, trophic levels in an ecosystem,












or any other suitable subdivision of the system under stuly.

The difference equation representation makes statement of

the logic sequence easier. In Figure 20 the partial

derivatives are calculated at time t-At for making decisions

at tinm t. The summation signs indicate that there are

potential exchanges with each of the n-1 other components in

the system, at each time step.



Simulations Usinq wo Comoonents

To investigate the range of behavior that a two

component version of the power maximizing simulation moael

can exhibit, some hypothetical situations were set up and

simulated on an EA7 ?iniAc analog computer. An analog

computer diagram of the model is given in Appendix T-. The

simulations also served to test the power maximization

algorithm. This was done by constraining the system to

operate vith the switches either always on (always

exchanging) or always off (never exchanging) and comparing

this with the "unconstrained" situation where the switches

were allowed to perform their normal role. The algorithm

was deemed successful if, for the same coefficient settings

the unconstrained mode consistently led to a higher total

power in the model than a constrained mode. The model was

also run on digital computers as a check.

Four hypothetical cases were investigated with the

model, Tn the figuress the plots labeled "with exchange"





















Figure 20. Component i difference equation
where
Q, = embodied energy storage in
t component i at time t
E. = direct energy input to
L,t component i at time t
a. = direct energy input coefficient
1 for component i
b.. = transfer coefficient for
13 exchange from component j
to component i
c. = depreciation rate for
1 component i

3P T
j= rate if change of total system
\Q i power (P ) with respect to
embodied energy storage in
component i at time t

a T
= rate of change of total system
\3Q ) power (P ) with respect to
embodied energy storage in
component j at time t
















i, t+At i, t


aiEi,tQi,t

1 + aiQi,t
1 1, t


b jtQj ,t

1 + b. .Q





1 +b..Q.
3bjij,tQi,t

1 + bjiQjt


0


if--
Sotet-At

otherwise


if -
j


t-At


otherwise


SiQi,t


n


j=l


t-At


J













indicate the model's behavior with the switches in the

unconstrained mode, while those labeled "without exchange"

indicate the behavior with the switches constrained to the

off position. The time and quantity scales are in arbitrary

units. Tn general this two component version produced

almost identical behavior when the switches were Isft on as

when they were allowed to function normally. This indicated

that with only two possible exchange pathways, it almost

always "pays" in a maximum power sense to exchange, 'his

was not the case for a larger number of components where

more intricate exchange networks were possible.

Case 1: resource consumption. One relevant application

of the mo?!l is to '-he question of resource consumption.

Here one of the components represents a resource pool. A

resource pool can be operationally defined in the context of

this model as a situation where the external energy input

and the depreciation rate are both very low. For example,

the oil deposits of the ?rabian deserts occur in low

productivity areas protected from deterioration by overlying

rock. Tn the language of the model this is a large storage

of structure whose incremental effect on productivity in its

local environment is very small. If another component

capable of utilizing the resource exists in close enough

proximity, the logic of the model would decide to export to

this component in order to maximize power. Figure 21a shows

some simulation results for this situation. Both the


1




Full Text
104
during a year against the total dollar output of the sector.
Btus consumed were derived by multiplying the calculated
energy intensities (in Btu fossil/S) for each of the four
alternatives in Table 20 by the total dollar outputs of the
sectors. Figures are plots of direct plus indirect
energy input versus total dollar output for 1967, for each
of the four alternatives with labor and government services
and solar energy inputs given in Table 20. With the data in
this format, one can ask what percentage of the variation in
dollar output from sector to sector can be explained with
variations in the total (direct plus indirect) energy input.
This question can be answered using a standard linear
regression model, "'he best fit regression line is indicated
on the plots along with its 7 square value, equation, and
the t statistic for the parameters (in parenthesis below the
parameters). The results are summarized in Table 9, both
with and without the energy sectors (sectors 1-7),
The p square value measures the fraction of the total
variation in sector dollar output, which can be explained by
variations in total (direct plus indirect) energy inputs,
The F value is a test statistic. PB>F indicates the
significance level of the test, with lower values of PR>F
indicating a more significant relationship between the
variables.
It is fairly obvious from inspection of Figures 29 and
30 that the energy sectors (sectors 1-7) are outliers and


TOTAL CAPITAL STOCK. xlOlc 1967 dollars
124
YEAR
Time series plot of U.S. environmentU.S.
economy, and total U.S. net capital stock
from 1929 to' 1969.
Figure 33.


31
Figure 7.
Hypothetical three sector economy with all
flows in arbitrary physical units.


Figure 43. Embodied energy intensity map for
south Florida for 1953 estimated
from the 1953 land use map

i o.
no.
3 '),
E 12
LEGEND
----/////\ 1111 + + + + *XXXXX$3$S:S
-===/////! 1 1 1 i+ + + + f XXXXX33333
- = = =yV/// 1*111 + + + + f XXXXX3SS S3
===== /////l 1 1 1 1 + + + ++ XXXXX3SSS3
30. 40. 50. 75. 100. 200.
40. 5 0. 75. 100. 2 00. AMD U"*
CE/123 AC CELL)


Table 13.
(continued)
Aggregate
Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
14. Rest
World
of the
(b)
287984.0
7343.0
4883.0
a. Based on Kendrick's (1976) estimates of Business, Government, and Personal Sector
net capital stocks, gross investment and depreciation (depreciation is gross
investment minus net investment) for 1963 converted to 1967 dollars. The business
sector totals excluding land were distributed to the 10 aggregate business sectors
(2-11) according to data on gross investment by sector in 1963 (United States)
Department of Commerce 1975). The land stock was credited to the environment sector.
b. The rest of the world was assumed to exhibit the same ratios of net capital stock
to gross investment and depreciation as the U.S. The rest of the world net capital
stock for 1963 was estimated at 287084.0 E9 1967$ (see Table 25). Gross investment
was thus 7343 E9 1967$ and depreciation was 4883.0 E9 1967$.
c. See note c to Table 14 and Table 25.
135


page
The U. S, Economic-Ecologic System................... 96
Energy Embodied in Goods and Services for 92
0,S. Economy Sectors in 1967. 96
The Energy to GNP Ratio for the U.S,
From 1920 to 1 976............. 114
Total Capital, Investment, and Depreciation
Time Series and a Better Estimate of the
Embodied Energy to Dollar Ratio. ,116
Fourteen Sector Closed System Input-Output
Matrices for 1963 and 1967,,....,..,,.,,,.,,.. 126
Five Sector U,S. Economy-Environment
Simulation Model,...,.,.,.,........., 139
The South Florida System. 151
Measured Embodied Energy Maps................... 151
Minty One Cell South Florida Spatial
Simulation Model....,.,.,,....,....,....,.,,.. 163
DISCUSSION 180
The Case for a Constant Embodied Energy to
Dollar Ratio...,*.. 180
Conclusions and Predictions from the Simulation
Models............................................ 188
Embodied Energy Analysis and Economics.............. 190
APPENDIX
I SOUTH FLORIDA LAND USE DATA CONVERTED TO EMBODIED
ENERGY UNITS..... 193
II ANALOG COMPUTER DIAGRAM FOE THE TWO COMPONENT
EXCHANGE MODEL 203
III FORTRAN LISTING FOR.THE 25-CELL SPATIAL MODEL....... 205
IV ENERGY EMBODIED IN GOODS AND SERVICES FOR 92
U.S, ECONOMY SECTORS IN 1967.,..,,......,., 211
V TIME SERIES DATA FOR THE U.S.
ECOHOHIC-ECOLOGIC SYSTEM... 219
VI FORTRAN LISTING FOR THE 5-SECTOR U.S. ECONOMY-
ENVIRONMENT SIMULATION MODEL....................... 236
VII FORTRAN LISTING FOR THE 91-CELL SOUTH FLORIDA
SIMULATION MODEL AND DATA. 240
LIST OF REFERENCES,. 247
BIOGRAPHICAL SKETCH 254
v


164
therefore retains all the major features of the u.s. economy
model with the addition of the spatial dimension.
Parameter estimates. For this application even
preliminary estimates of the parameters were not available,
since this would have required detailed transactions data
between all 91 of the models components. To estimate the
8281 intercell transfer coefficients certain simplifying
relationships were therefore assumed. The first was that
the transfer coefficient between any two cells is a function
of the distance between the cells. This is essentially the
"gravity model" approach. There is a fair amount of
empirical evidence supporting this kind of relationship
based on increasing costs of transport with distance. For
exchanges within the region the transfer coefficient was
made proportional to the inverse square of the physical
distance between the cells. For exchanges with the rj.s,
environment, economy, and rest of the world the physical
distance was adjusted with a "coastal modifier" parameter
which made the effective distance from the coastal cells to
areas outside the region lower. This accounted for the
lower transport costs over water. In principle it is the
transport costs which determine effective distance {and thus
the transfer coefficient) and any barriers or corridors in
the spatial field should be accounted for. A detailed
listing of the parameter values used in the final model runs
is included in Appendix FIT.


otherwise
b21Q2Q1
SPT SPT
if
1 + b21Q2
3Q.
5Q
1
otherwise
-C1QX
a2E2^2
b22Q2
+
+
1 + a2Q2 1 + b22Q2
QoQi
3Pt 3Pt
if
1 + k2lQ2
3Q2 3Q-L
otherwise
+
b12QlQ2 9PT
if
3P.
T
1 + b12l
3Q, 3Q.
otherwise
C2^2
(36)
(37)




Table 16
Initial Parameter Estimates
*
Parameter
i = 1
U.S. Environment
i = 2
Business
i = 3
Government
i = 4
Households
i = 5
Rest of the World
a.
X
4.58 E-7
0
0
0
2.31 E-8
b. .
il
3 = 1
4.942 E-7
1.274
E-5
6.753
E-6
5.283
E-6
3.505 E-8
j 2
-
10.252
E-3
9.988
E-5
4.167
E-4
6.516 E-7
3 = 3
-
9.494
E-5
3.644
E-5
2.542
E-5
1.464 E-9
j = 4
-
2.134
E-4
2.289
E-5
1.703
E-5
2.316 E-10
c.
i
j = 5
1.058 E-8
.006
4.378
.086
E-7
r .870
.029
E-8
4.724
.021
E08
5.12 E-7
149


Table '20
(Continued)
Alternative
A
B
Excluding
c
Including
D
Excluding
Labor and
Labor and
Including
Labor and
Government
Government
Labor and
Government
Services
Scrv1 oes
Government
Services
Feedbacks
Feedbacks
Services
Feedbacks
but Includ-
but Exclud-
Feedbacks
and Solar
ing Solar
ing Solar
and Solar
Sector
(numbers in parenthesis are BEA sector equivalents)
Energy Inputs
Energy Inputs
Energy Inputs
Energy Inpub
All values in Btu fossil/?
41.
Primary Iron & Steel Manufacturing (37)
191,670
211,570
517,450
876,150
42.
Primary Nonferrous Metals Manufacturing (38)
61,002
91,975
365,500
712,200
43.
Metal Containers (39)
169,170
196,040
503,020
877,200
44.
Heating, Plumbing & Fabricated Structural Metal Products(40)
75,663
101,485
405,180
774,200
45.
Screw Machine Products, Bolts, Nuts, etc.,S Metal Stampings
(41)
72,656
98,910
404,560
776,950
46.
Other Fabrucated Metal Products (42)
68,788
97,470
391,620
756,450
47.
Engines & Turbines (43)
58,709
75,160
389,760
751,200
48.
Farm Machinery (44)
63,300
84,800
394,780
761,600
43.
Construction, Mining, Oil Field Machiner, Equipment (45)
63,345
81,015
332,830
753,550
50.
Materials Handling Machinery i Equipment (46)
53,108
71,420
387,190
753,900
51.
Metalworking Machinery & Equipment (47)
47,631
62,730
378,670
739,250
52.
Special Industry Machinery & Equipment (46)
50,064
80,210
382,800
760,000
53.
General Industrial Machinery & Equipme-nt (49)
54,403
77,855
385,670
754,350
54.
Machine Shop Products (50)
55,338
69,680
385,170
742,450
214


43
Economy Data Assembly and Evaluation
The major ata sources for the O.S. economy model were
the Bureau of Economic Analysis (BEA) input-output tables
(along with their associated amplifying articles) and
Kendricks (1176) estimates of capital stock and investment
time series. Other statistical sources were consulted as
needed.
The year 1967 was used as the base year for data
collection since this was the most recent year with measured
input-output data. Bata from the 19f>3 input-output study
were also used and reference was made to previous input-
output studies back to 1919.
I.eontiefs (1941) original exposition of input-output
analysis envisioned a completely closed economic system.
Since then the convention has been to view households and
government as part of "final demand, and to treat them as
exogenously determined. The original, all-inclusive view of
the economy was deemed necessary in light of the objectives
of this study. Thus, certain modifications to current
accounting conventions were required. The input-output
statistics were modified to achieve a completely "closed
(in the thermodynamic sense) system. This means that only
energy crosses the system boundaries. To achieve this goal,
households an* government were brought within the system
boundary (made endogneous) as were a "O.S. environment


54
"able 5. Estimate land areas and solar absorption for
major land use types.
Area (a)
(76 acres)
Average solar
absorption (b)
(E9 Btu/ac-yr)
Total solar
absorption
(718 Btu/yr)
Total land
2254
28
33.9
Agriculture
1212
Cropland
38 4
grassland pasture
54 0
Grazing land
288
Forestry
587
28
16.4
Woodland pasture
62
Woodland (not pastured)
5 0
Forest land
475
Wetlands, desert 5 tundra
27 2
20
5.4
urban 8 mining
193
20
3. 9
Total water
1550
28
43. 4
Inland T, estuarine.
50
Offshore (209 mile limit)
1500
Total land plus water
3814
10 3. 0
a. rrom united States Department of Commerce (1976a).
b. Estimated solar absorption of the earth-atmosphere system
(Pu'lyko "978, Haar and Suomi 1969).


61
Figure 14. Example of detailed land use data, showing
cell 45 in Figure 13 for 1973.


121
in Kendricks terms and the value compares well with his
estimate of 122.18 29 5 for 1967. The mean embodied energy
intensity could thus have been calculated as 109.64 215 Btu
fossil/125.61 29 5, or 8.79 25 Btu fossil/f. This is very
close to the mean of the 85 sector embodied energy
intensities (excluding the energy sectors) of 8.5 75 Btu
fossil/$ given in Table 8, alternative D. Kendricks
estimates of gross investment in government and households
can now be included to determine a more accurate value of
the mean energy intensity for the n.S. economy. Tables 11
and 12 give these values as 119.73 e9 $ and 266,94 E9
respectively. adding these to the 122.18 E9 $ gross
investment in business yields 508.85 E9 $. This leads to a
value of 2.15 25 Btu fossil/8 or 5.39 B4 kcal fossil/8.
One additional refinement can be made to the
calculations. The primary input value included an estimate
of the total solar energy absorbed by the U.5. ecologic-
economic system. Tn determining the energy intensities,
only gross investment in the economic sectors was 5.ncluded,
For consistency, one must either reduce the primary input to
include only that portion of the solar input that enters the
economy or include the gross investment in environmental
assets. By assuming that gross investment in land (by
natural processes) was the same percentage of net land
capital stock as in the economy as a whole, an estimate of
gross investment in environmental assets was derived. This


172
++++++++++++++++++++.Y£AP=1950
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
4*
+
+
4
+
+
-i-
+
+
+
+
+
+
+
+
+
+
+ +++ +-
+ 4-4-+ 4
4- 4-4- 4 -4-
+ +4-4- -4
+++++++++++++++++++++++
4-
4-
4-
4-
4-
4-
+
+
+
+
4-
+
- +
4-
+
- +
- 4-
- 4-
- +
- 4-
i- +
+
4
+
4-
4
4-
+
+
4-
4-
+
+
+
+
+
+
+

/////
/ // / /
/ ////
/ ////
xxxxx
xxxxx
xxxxx
xxxxx
+ 4-4-4-4-
+ ++++
+++++
+ ++4- +
+ + + -4+
+ ++ + +
+ ++ + +
+ ++++
+++++
+ 4+++
+ + + ++
+ + + + +
=====XXXXX353S$
===== XXXXXS3 S $3
=====xxxxx s$$ss
=== = XXX XXS S3 $5
::xxxxx+++++
:: xxxxx+++++
::XXXXX+++++
::xxxxx+++++
mu
1 mi
1 mi
i ti 11
+ 4+ 4 +
+++++
4+4+ +
+++++
xxxxx
xxxxx
xxxxx
xxxxx
+++++/////:
+++++/////:
+++++/////:
+++++/////<
//////////
//
+
+
+
4
+
+
+
+
+
+
+
+
+
+
+
+
+
4
+
+
+
+
+
+
+
+
+
+
+
+
+
+ + + + + ++ + + ++ + + + + + + + ++++ + ++ + + ++ ++++44 44+4444444 44 44 444 44
(f)


230
Table 25. (Continued)
Year
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
(Economy)
Net Capital
Stock
Rest of the
World Net
Capital
Stock (c)
1968
13560
5440
19000
282008
1969
13229
5693
18912
290702
(a) Sum of U.S. land stock (Table 26) and estimated value
of mineral reserves. Table 27 gives estimates of
withdrawals of mineral reserve "capital" in direct
energy units and estimated real dollar value.
(b) Sum of U.S. business, government and households' net
capital stock (Tables 22-24)
(c) Estimated as a constant percentage of total U.S. net
capital stock, based on relative land areas.


QUANTITY QUANTITY
92
(a)
(b)
Figure 22. Two component model analog simulation results
(a) Situation when the external energy inputs
to the components are both oscillatory
and out of phase.
(b) Situation when the external inputs are
constant but unequal.


DOUT=DOLLAR VALUE OF TOTAL OUTPUT {xIO9 £/yr)
106


DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xIO9 $/yr)
110


232
Table 26. (Continued)
Year
Land Held by
Business
Land Held by
Government
Land Held by
Households
Total
1951
286.8
54.2
88.9
429.9
1952
288.5
54.6
92.0
435.1
1953
290.2
55.3
95.3
440.8
1954
292.3
55.9
98.6
446.8
1955
294.4
56.5
102.9
453.8
1956
296.5
57.5
107.3
461. 3
1957
299.6
58.7
110.8
469.1
1958
302.7
60.0
114.3
477.0
1959
305.7
61.2
118.1
485.0
1960
310.0
78.6
121.8
510.4
1961
313.3
79.9
125.4
526.9
1962
316.5
81.4
129.0
535.3
1963
319.7
82.8
132.8
535.3
1964
322.9
84.7
136.9
544.4
1965
327.0
86.6
140.8
554.4
1966
331.8
88.5
144.6
564.9
1967
336.1
90.0
148.1
574.2
1968
340.9
91.3
151.8
594.0
1969
344.8
92.5
155.6
592.9
Source: Kendrick (1976) converted to 1967$


249
Georgescu-Eoegen, H. 1971. The entropy law and the economic
process. Harvard University Press. Cambridge,
Hass. 457pp.
Gilliland, FI. W 1975., Energy analysis and public policy,
Science. 189: 1951-1056.
Gilliland, K, w, ed. 1978. Energy analysis: a new public
policy tool. American Association for the Advance
ment of Science, Washington, D. C.
Gushe>e, D.E. '>976. Energy accounting as a policy analysis
tool. The Library of Congress Congressional
Research service, Washington, D.C. 667pp.
Hannon, B 1973a, An energy standard of value, Ann. Am.
Acad. ,Polit. Soc. Scl. 410: 139-153.
Hannon, B. 1973b. The structure of ecosystems, J, "heoret,
Biol. 41: 535-546,
Hannon, B, 1978, An energy theory of value for ecosystems,
Center for Advanced Computation. Hniversitv of
Illinois at Champaign-Hrbana.
Haar, T.H.v,r and 7, E, Suomi, 1969. Satellite observations
of the earths radiation budget. Science. 163:
267-368.
Hall, C.A.S. and J. W. Pay. 1977. Ecosystem modeling in
theory and practice: an introduction with case
histories. John Wiley and Sons. Hew York, 684pp.
Hayes, E.T. 1979. Energy resources available to the
Halted States, 1985 to 2000. Science. 203:
233-239.
Herendeen, E.A., and C. W. Bullard. 1974. Energy costs of
goods and services, 1963 and 1967. CAC Document Ho.
140. center for Advanced Computation. Hniversitv of
Illinois at Champaign-Hrbana. 43pp.
Isard, W. 1972. Ecologic-economic analysis for regional
development. The Tree Press, New York, 270
Isard, W. 1975, introduction to regional science. .
Prentice-Hall, Englewood Cliffs, Hew Jersey, 506pp.
Juday, C,. 1940. The annual energy budget of an inland lake.
Ecology, 21: 438-450,
Kendrick, J. W 1976. The formation and stocks of total
capital. National Bureau of Economic Research.
Hew York, 355pp,


8
Figure 1.
Solar energy driving the productive processes
of the earth.


Table 20
(Continued)
Alterna
tive
A
n
C
D
Excluding
Including
Including
Excluding
Labor and
Labor and
Lalior and
Government
Government
Labor and
Government
Services
Services
Government
Services
Feedbacks
Feedbacks
Services
Feedbacks
but Includ-
but Exclud-
Feedbacks
and Solar
ing Solar
ing Solar
and Solar
Sector
Energy Inputs
Energy Inputs
Energy Inputs
Energy Inputs
(numbers in parenthesis are BEA sector equivalents)
All Values in Bt:u fossil/$
55. Office, Computing & Accounting Machines (51)
28,192
47,655
358,350
722,100
56. Service Industry Machines (52)
50,201
75,140
378,460
745,100
57. Electric Transmission 6 Distribution Equipment & Electrical
Industrial Apparatus (53)
46,727
69,030
375,410
740,400
5B. Household Appliances (54)
54,215
81,855
391,740
750,200
59. Electric Lighting & Wiring Equipment (55)
46,291
66,535
387,030
721,100
60. Radio, Television & Communication Equipment (56)
26,430
50,430
363,060
738,050
61. Electronic Components & Accessories (57)
36., 165
55,895
371,730
742,400
62. Miscellaneous Electrical Machinery, Equipment & Supplies (58)44,233
66,080
374,300
740,900
63. Motor Vehicles & Equipment (59)
54,469
74,160
404,860
785,600
64. Aircraft & Parts (60)
35,540
51,870
380,510
757,600
65. Ocher Transportation Equipment (61)
51,905
190,660
396,120
881,800
66. Professional, Scientific & Controlling Instruments &
740,700
Supplies (62)
37,380
65,610
367,860
67. Optical, Ophthalmic, & Photographic Equipment & Supplies(63)
32,033
50,580
339,640
678,150
215


Figure 37.
Energy flow diagram for a 5-sector U.
environment simulation model
S. economy-


Figure 9.
Hypothetical three sector economy cast in
the format of the national input-output
accounting statistics.
-HP


179-
Coraputerized parameter optimization was out of the question
and manual adjustment of the parameters combined with
judgment gained through experience was necessary. For these
reasons, the results presented here are not necessarily this
models "best fit. Sore time spent adjusting the
parameters could no doubt improve the results but this
effort must be weighed against the increased benefit of a
slightly better fit. The adjustment process was terminated
when the model had demonstrated a "reasonably" good fit
given the added difficulty of this type of modelling over,
say, multiple linear regression models. It must be
remembered that this model receives as input only the
initial conditions and the solar energy input over the
period (considered to be constant) and develops a very
complex pattern of land use which reflects at least the
flavor of reality based on its attempt to maximize power.


tar input
290100





_ ,r
.
4305000
495910(1
'IUTAL mw
39COO
eao'j
MM5
2203
60302
35512
99.110
513209
48)06
435796
. ^08421
2H2793
...mm.
13875068
£LQ32
128


185
rain, winds, and other environmental forces, The period
1920-1945 was one of rapid expansion of agriculture,
forestry and fishery operations which involved capturing
more "natural" energy for the economy. This additional
input required less mineral fuels to be burned to produce a
dollar of GPP, By 1945, the expansion had reached a limit
and the solar energy input to the economy remained nearly
constant over the 1945-1976 period. Any long term trend in
the solar energy input to the rj.S, (as evidenced by the
long term global warming trend over this period) could also
contribute to a declining ratio. A noisy solar energy
contribution to the economy could also explain some of the
noise in the time series.
(3) The quality factors used to convert the different
types of mineral fuels, and the hydro and nuclear power into
equivalent units could be in error. Since the percentage
use of each fuel type has changed dramatically since 1929
this could lead to unwanted trend in the data. For example,
coal was the primary mineral energy source in 1929 (at 787
of the total). mhe data assumed that a kcal of coal is
equivalent (quality factor = 1) to a kcal of oil, but oils
convenience and burnability mean that a larger percentage of
its kcals are actually available for use. Also, less energy
had to be invested in the biogeologic processes of making
coal than oil. Thus coal has less embodied energy than oil
(its quality factor is lower) and more kcal of coal should


REFERENCES
LIST OF
Alfeld, R.I.. and A.K. Graham. 1976. Introduction to urban
dynamics. wright-Allen Press, Cambridge, Nass. 337pp.
American Petroleum Institute. 19^1. Petroleum facts and
figures. Washington, P.C.
Baumol, W. J. 1977. Economic theory and operations
analysis. Fourth Edition, Prentice-Rail, Inc,
Englewood Cliffs, New Jersey, 695pp.
Payley, S., p, Cost.anza, 7. Dolan, R, Gutierrez, and D,
Barile. 1975. A comparison of energetics vs. economic
cost-benefit analysis for the tipper St. Johns river.
Contract report submitted to the D. s. Army Corps of
Engineers, Contract fPACN17-75-c-0D73. Department of
Environmental Engineering Sciences. University of
florida, Gainesville.
Becker, G.S. 1971 Economice theory. Alfred A, Knopf,
New York. 222pp.
Berry, B. and A. Pred. 1961. Central place studies: a
bibliography of theory and applications. Bib
liography series no. 1. Regional Science Research
Institute, University of Pennsylvania. Phila
delphia.
Boltzmann, L. 1886. Der zweite hauptsatz der mechanischan
warme theorie. Gerold, Vienna.
Browder, J., C, Littlejohn and D, Young. 1975, South
Florida: seeking a balance of man and nature.
Bureau of Comprehensive Planning, Division of State
Planning, Florida Dept, of Administration. Tallahassee,
117 pp.
Budvko, FUT. 1978. The heat balance of the earth, Pages
85-113 in J. Gribben, ed. Climatic change, Cam
bridge university Press, Cambridge, England.
Chorley, R.J, and p. Raggett, 1967. Hodels in geography,
Eethuen. London.
Christaller, W. 1Q33, Die zentralen orte in Suddeutschland.
Translated by C,E. Baskin. 1966. as: Central
places in southern Germany. Prentice-Hall, Engle
wood Cliffs. New Jersey.
Codv, H. L, 1974. Optimizat ion in ecology. Sci. 183: 1156-
116 4.
247


122
worked out to bo 74.7 39 S/yr (see Table 14). Adding this
to the gross investment in the economic sectors yielded a
total of 583.4 vg S/yr. Dividing this into the total
primary input yields 1.83 35 Btu fossil/1967$, or 4.212. L
kcaj. fossil/1963$. This value was used to convert from
embodied energy to dollar values in the sections to follow,
Appendix 7 contains time series for the 0s. economic-
ecologic system estimated from Kendricks data and other
sources. Tables 22-24 are time series from 1929 to 1969 of
total net capital stocks, gross investment, and depreciation
for the n8. economy, Kendricks three sector breakdown
consisting of business, government, and household sectors
was expanded to include a .S. environment sector and a rest
of the world sector. Time series for these sectors were
estimated and are included as Table 25, Figures 32-34 are
plots of the net capital stock time series data.
In addition to their interest for general comparison of
capital stock and investment patterns, these data are
necessary for validating the 5-sector D.S. economy-
environment simulation model, which is developed in a
following section. The environment time series was
estimated from Kendricks data for the value of land stocks
and data on the value of mineral reserves (Tables 26 and
27),


PERCENTAGE OF SECTORS IN SPECIFIED RANGE
Alternative C. Including Labor and Government Service Feedbacks
but Excluding Solar Energy Inputs.
2000
3000
Alternative D. Including Labor and Government Service
Feedbacks and Solar Energy Inputs.
750 1000 1500 2000 3000
1967 EMBODIED ENERGY INTENSITY, xIO3 BTU fossil/$
GREATER
THAN 4000
J.
4000
JL
4000
O
O
Figure 26,
Frequency plots of embodied energy intensities by sector calculated
with and without labor and government services feedbacks.


9
and consumption, Penetrable sources ara those whose rate of
production roughly equals their rate of consumption.
Obvious examples are sunlight itself, rain, wind, and the
shorter time scale products of the interaction of these
inputs, such as forestry, fishery, and agricultural
products. Nonrenewable sources of free energy (embodied
past sunlight) are those whose rate of consumption far
exceeds their ra+e of production. Nonrenewable sources are
mined substances, such as the fossil fuels, soil storages,
and mineral deposits, wh5_ch are the results of slow
biogeologic production cycles over long time periods.
Embodied energy is linked to ability to do work (or
available energy) by the theory that the energy used
(directly and indirectly) to produce a substance shows up as
a proportional increase in the stored order or departure
from equillibrium of the substance, and thus its ability to
do work. Nor example, oil mined and delivered to the point
of use would have more embodied energy (that consumed by the
recovery and transportation process) than oil in the ground.
The delivered oil would also have a larger ability to do
work than the untapped oil, due to its increased proximity
to an oil consuming economic system. A ceremonial mask
would have more embodied energy than the piece of wood from
which it was carved and would also presumably do more work
by performing an important symbolic function in the
ceremonies of the culture of its manufacture.


50
was usea to sot up accounting identities for the new
household and government sectors, which could he solved for
the percentages of property-type income to be credited to
each sector in order to balance the accounts. This is
admittedly only an approximation which was necessary due to
the lach of data on the allocation of value added in the
input-output accounts.( Gross investment and net exports
were assumed to exactly balance against net profits. This
left the following identities. For the government sector:
IB" + Xg*(?TT) + PT = GP + GS {11)
where
Xg = fraction of PTI to Government
IB? = Indirect business taxes
PTI = Property type income
PT = Personal taxes
op = Government purchases
GS = Government salaries
So the fraction of PTI to government necessary to balance the
sectors accounts is:
Xg = [GP + GS IB" PT] / PTI (12)
For the household sector:
FC + Xh* (PTI) +GS = PCE + PT (13)
where
Xh = Fraction of PTI to households
FC = Employee compensation
PTI = Property type income
GS = Government salaries


222
Table 22. U.S. business sector net capital, investment, and
depreciation time series in constant dollars
(billions of 1967 dollars (a) ) .
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1929
371.25
43.11
17.67
25.44
1930
378.47
29.93
4.06
25.87
1931
371.94
17.13
- 7.91
25.04
1932
353.41
5.18
-18.37
23.55
1933
331.76
7.85
-14.35
22.20
1934
315.01
12.43
- 8.97
21.40
1935
307.38
23.00
1.70
21.3 0
1936
310.24
30.08
8.16
21.92
1937
318.69
36.30
13.51 '
22.79
1938
320.32
20.56
- 2.45
23.01
1939
318.55
28.87
6.03
22.84
1940
325.63
35.85
12.24
23.61
1941
340.07
42.72
18.12
24.60
1942
347.56
25.57
1.34
24.23
1943
334.21
17.61
- 5.17
22.78
1944
329.58
18.13
- 3.97
22.10
1945
323.72
24.55
2.10
22.45
1946
338.98
59.50
34.90
24.60
1947
369.21
56.98
28.56
28.42
1948
397.81
65.04
33.10
31.94
1949
418.10
49.14
14.50
34.64
1950
439.49
70.68
33.70
36.98


142
models o* the .S. economy depend on exogenously determined
final demand functi.ons. TTsing these models for prediction
thus involves predicting final demand. The final demand
predictions, in turn, are usually extrapolations of past
trends. This makes the models complex rather than simple
extrapolations, a point that is often lost in the
mathematical, rigor of the models. There should be little
trouble predicting solar intensity, however.
(4) The model implicitly contains both supply and
demand considerations based on the marginal embodied energy
productivities of the sectors.
(5) The model is nonlinear with feedback. All sectors
are (potentially) connected to all other sectors.
(6) mho model evolves or changes its structure through
time in an attempt to maintain an optimum pattern. The
fitness criterion for this model is the maximum power"
principle of Lotka (19 22).
Parameter estimates. The data used in estimating the
models parameters (15 in all) and initial conditions (5 in
all) have been presented in a previous section, The
14-sector input-output transactions matrices (Figures 35 and
36) were aggregated to 5 sectors, Essentially, this
involved collapsing sectors 2-11 into one sector. The
aggregated matrices are shown in Figures 38 and 39, As
previously noted,the small number of years of detailed data


ro
o
C
C
c
c
c
SOOTH FLORIDA LAND OSE SIMULATION MODEL
I) AR (91)
10
C
C
C
C
C
241
240
201
200
C
250
C
DIMENSION ED (91,91) ,1(91.91) .0 (91) ,E (91¡
DIMENSION P91) ,D(91).DLAT(9lf,DL0R(91)
DIMENSION F l (91) ,F2 (9 i) ,F3 (91) ,F4(91)
DIMENSION A (91) ,B (9i) ,6 (91) .1(91) ,IA (18,10) ,Z(9)
DIMENSION IS(10),CM(91) ,SS(91)
READ COEFFICIENTS FOR THIS RUN
S'* 1. 4
G=30,0
H=5.0
DO 10 1*1,91
A II) =.05
B(I|*. 002
C JI)=. 02
SS(I) = ,0002
CONTINOE
A (90) *0.
B 89) =5. 3E-8
B 90) *2. 25E-6
B 91)=5. 2E-10
Ss (89) =5E-8
SS|90)*5E-7
SS (91) *10E- 10
READ LATITUDE AND LONGITODE OF CENTROID OF
EACH CELL (IN DEGREEG NORTH AND WEST),
INITIAL STORAGE LEVELS, AND LAND AREAS OF EACH CELL
NRITE ( 6. 241)
FORMAT 1 ,2X,,I*,4Xf*DLATfI) ,4X,DLON(I) ,4X *Q (I) ,
15X,*AR (I) ;5x;*CMr(I) *,5X,*dl*JT)
DO 200 1=1,91
READ (5 ,20 11 DLAT (I) ,DLON(I) ,Q(I) AR (I) ,CM (I)
QIHT=Q?I) /AR (I)
FORMAT(f5 6I16 3)T 'A8(I) 'C" (I) QI NT
FORMAT <5f10.J 3)
CONTINOE
READ(5,250) Z (I) ,1=1,9)
FORMAT (9F6.0)
READ (5,260) (IS (I) ,1 = 1,1 0)


27.82
81.28
10.00
1.0
1.0
27.59
82.32
10.00
1.0
1.0
1.0
27.59
82.06
10.00
1.0
27*§3
81.80
10.00
1.0
1.0
27.59
81.59
10.00
1.0
1.0
27.59
81.28
10.00
1.0
1.0
5.0 10.0 15.0
;-=/i*x$
20.0 25.0
30.0
35.0 40
*
1
O 50.0
209


nSTHODS
Dp script-ion of the Modeling Language
The energy circuit language developed by H. , Odum
(1971) was used for illustrating the structure of the
models used in th5_s dissertation. The symbols of the
language have associated mathematical functions which allow
the energy circuit model to be translated directly to
differential or difference equations for computer
simulation. The symbols used in this thesis are summarized
in figure f. ?. complete description of the symbols and
their mathematical connotations can be found in Odum (1971)
and Odum and Odum (19^6) .
Symbolic modeling languages, such as Odums (1971)
energy circuit language, Forresters (1961) industrial
dynamics language, analog computer diagrams, and others are
useful for concise conceptualization and presentation of
complex networks of flows and storages. Diagrammatic
languages allow immediate comprehension (once the language
is understood) of the connectivity structure of the model
while conveying the same mathematical content as
differential equations which require much closer inspection
before the overall structure is apparent.
23


91
because -external inputs to one component are decreasing and
its structure is becoming relatively underutilized, while at
the same time the other components inputs are increasing,
If the coefficients are such that transport costs of
structure are less than the costs of building new structure
locally, then exchange will be beneficial in that total
power ftp) can be increased by exchange, as shown in Figure
22 a
Case 4: Constant unequal inputs. Che reasons for
business cycles and other internal" oscillations in systems
where the external inputs are constant (or nearly so) have
long been a subject of speculation. Figure 22b shows some-
results of the model applied to this situation. If the
inputs are unequal but constant, the model indicates that
the total power can be increased, under certain conditions,
by setting up internal oscillations where none exist in the
inputs.
some Example Simulations of spatial Development Hsina 25
sills"
The two component exchange model of the previous
examples can be expanded to a large number of cells for more
realistic applications. One possibility that was
investigated was the modeling of spatial development. In
this instance, each component represents an area of land and
the exchange of embodied energy among the cells is
determined by the model in such a way as to maximize the


Table 8.
Ninety-two sector embodied energy intensity statistics
Including energy sectors Excluding energy
Alternative (Sectors 1-7) __ (Sectors 1 -
X s C.V. X s
A
Excluding solar
inputs and labor
and government
(Btu fossil/$)
B
Including solar
inputs but ex
cluding labor and
government
(Btu fossil/$)
C
Including labor
and government
but excluding
solar inputs
(Btu fossil/?)
D
Including solar
inputs and labor
and government
(Btu fossil/?)
1.83 E5 6.28 E5 3.43
5.45 E5 25.10 E5 4.61
5.16 E5 6.19 E5 1.20
12.20 E5
0.69 E5 0.52 E5
1.78 E5 5.00 E5
4.05 E5 0.91 E5
sectors
7)
C.V.
0.78
2.81
0.22
2.44 E5 2.00
8.50 E5
3.49 E5
0.41


APPENDIX I
SOUTH FLORIDA LAND USE DATA
CONVERTED TO EMBODIED ENERGY UNITS


32
Table 2. Input-output, transactions table in arbitrary
physical units, corresponding to the diagram in
Figure i
To
From
.1 gr
cil ture
1
Manufac
turing
2
Con
sumers
3
Met
output
73 tal
Output
hgriculture 1
10
5
5
10
30
Manufacturing 2
10
eg
30
10
100
Consumers 3
.25
. 25
1
.5
2
Energy input E
3 on
700
-


229
Table
Year
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
25. (Continued)
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
Economy)
Net Capital
Stock
Rest of the
World Net
Capital
Stock (c)
18013
2489
20502
304301
17856
2559
20415
303010
17686
2613
20299
301288
17502
2749
. 20251
300576
17319
2866
20185
299596
17130
2992
20122
290661
16948
3112
20060
297741
16748
3237
19985
296628
16537
3375
19912
295544
16328
3506
19834
294387
16122
3628
19750
293140
15905
3759
19664
291863
15697
3897
19594
390824
15468
4040
19508
289548
15230
4191
19421
288257
14981
4361
19342
287084
14723
4543
19266
285956
14454
4744
19198
284947
14169
4973
19142
284115
13872
5208
19080
283224


188
outcome from -both an energetic and an economic point of view
if energy is given its rightful'thermodynamic role as the
ultimate scarce resource. Since all things are forms of
embodied energy, there is no possibility for substitution of
"something else" for this input. An economic system
concernea with the optimum allocation of this all-
encompassing scarce resource will set prices according to
embodied energy cost.
Conclusions and Predictions from the Simulation Models
Both the TT.S. economy-environment and south Florida
simulation models were capable of approximating the
historical behavior of the respective systems based on solar
energy inputs and a power-maximising decision structure.
Due to the inherent difficulty of adjusting the models, no
systematic parameter optimization was attempted, therefore,
the results cannot necessarily be considered as the "best"
approximations of which these models are capable. The
results do indicate the potential and some of the problems
with this type of modeling, however. For example, there are
several models potentially capable of approximating the
historical behavior of the TT.S. economy at the level of
aggregation used in this study. The most popular has been
the simple exponential growth model. Generally, the


30,000-
20,000-
10,000
0
1920
I960
i r
1970 I960
Figure 31. Mineral, hydro, and nuclear energy consumption per dollar of
real GNP from 1920 to 1976.
115


DO 210 1*1,25
E(I)* 1.0*AH II)
DO 211 J*1,25
Y (I,J)*1.
IF (ED (I, J) LE. 0) GO TO
ED (I-JJ*B (I)/ED (I, J)
GO TO 211
ED II, J)*B (I)
CONTINUE
COHTINOE
215
215
211
210
C
C INITIALIZE AND RON
C
100
FT=30.
IPS* 1
DT=1.
pt*o.;
T=0.
GO TO 601
T=T+DT
DO 29 1*1
DO 29 1*1.25
DJI^AJI) *E (I)/ ( {1. A (I) *Q (I))
DO JO J* 1,25
**2)
330
350
30
29
410
430
450
|I=EDJ,lf*Q (J) /CUED (J,I) *Q (J))
IFII.EQ. 0 XI=0
IF (I. EQ. J GO TO 330
So^TO (3§0* *Q iJ) /i0m +ED (I'J> *Q{1)) **2)
d m(*D gf? SP (2*ED (r#J) *Q (I) 1 /(UED (T'J) *Q (I) ) **2
continue'
COHTINOE
DO 40 1=1,25
f 1 ( ti I *Q (I) /{1 + A (I) *Q (I) )
F4 (I) =C(IJ *Q (I)
F2 (ii =0.
DO 42 J=1.25
IF(I.EQ. J)GO TO 430
DI*D (I) 1.1
IF(DI-D(J>) 410,430,430
GIf0 45?)'
YfeJF2)IY,(Q),<'QlJ)/CEDI,J,*Q(T) + M
F
=F2(I) +Y(I
206


248
Cook, E.
1971.
The flow of energy in
an industrial society.
Scientific
liiaerican. 22 4; 134-147.
Cook, E,
1976,
Man, energy, society.
W.H Freeman and
Company. San Francisco. 478pp,
Costanza, R. 1975. ihe spatial distribution of land use
subsystems, incoming energy and energy use in south
Florida from 1999 to 1973. Masters Research Project.
Department of Architecture, University of Florida,
Gainesville. 294pp.
Cottrell, F. 1955. Energy and society. The relation
between energy, social change and economic dev
elopment. McGraw-Hill. N.Y. 339pp,
Court, A. 1914. water balance estimates for the United
States. Heatherwise, 27: 252-255.
Daly, H. id-I. Steady state economics. W.H. Freeman.
San Francisco. 185pp.
Dantzig, G.B, 1951. Maximization of a linear function of
variables subject to linear inequalities. In T.C.
Koopmans, ed. Activity analysis of production and
allocation. John Filey and Sons. Uew York.
Darmstadter, J. 1971, Energy in the world economy. The
John Hopkins press. Baltimore. 876pp.
Darmstadter, J,, J. Dunkerley and J. Alternan. 1977. How
industrial societies use energy; a comparative
analysis, John Hopkins University Press. Baltimore,
282pp.
Darmstadter, J., J.Dunkerley and J. Alterman.: 1978. Inter
national variations in energy use; findings from a
comparative study. Ann. Rev, Energy. 3: 201-224.
Dorfman, R. P.A, Easuelson, and R, M. Solow. 1958. Linear
programming and economic analysis. McGraw-Hill, New
York. BE^pp.
Forrester, J.U. 1961. Industrial dynamics. fl.I.T, Press,
Cambridge, Mass. 464pp.
Forrester, J.W. 1969. Urban dynamics. M, I. T. Press.
Cambridge, Mass. 285pp.
Forrester, J.W. 1971. World dynamics. Wright-Alien Press,
Cambridge, Mass. 142pp.


EMBODIED ENERGY BASIS FOR
ECONOMIC-ECOLOGIC SYSTEMS
By
ROBERT COSTANZA
A DISSERTATION PRESENTED TO THE GRADUATE CONCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE CE DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1979


Figure 20.
Component i difference equation
where
Q
i,t
= embodied energy storage in
component i at time t
E
if t
a
i
c
i
= direct energy input to
component i at time t
= direct energy input coefficient
for component i
= transfer coefficient for
exchange from component j
to component i
= depreciation rate for
component i
'3P
3Qi/ t
rate if change of total system
power (P ) with respect to
embodied1 energy storage in
component i at time t
'3P
T
k3Q.
= rate of change of total system
power (PT) with respect to
embodied1energy storage in
component j at time t


233
Table 27. Time series of total U.S. mineral fuel use and
estimated real dollar value.
Year
Mineral Fuel Use
(x 101/: kcal/yr)
Dollar Value of Fuel
(x 109 1967 dollars)
(a)
1929
5796
123
1930
5440
116
1931
5481
98
1932
3963
84
1933
4091
87
1934
4356
93
1935
4624
98
1936
5206

111
1937
5527
118
1938
4802
102
1939
5241
112
1940
5817
124
1941
6489
138
1942
6760
144
1943
7361
157
1944
7700
164
1945
7604
162
1946
7349
156
1947
7947
169
1948
8219
175
1949
7600
162
1950
8236
175


221
Table 21. (Continued)
Total Mineral
Fuels, Hydro Energy Consumption
and Nuclear per Dollar
Real GNP Energy Consumed of real GNP
Year (x 10y 1967 $/yr) (x 10-^ kcal/yr) (kcal/1967$)
1962
624.1
12047.9
19304.4
1963
649.0
12543.2
19327.0
1964
684.5
13043.2
19055.1
1965
727.7
13654.2
18763.5
1966
775.2
14453.9
18645.4
1967
795.3
14961.2
18812.0
1968
832.3
15772.2
18890.1
1969
854.7
16675.7
19510.6
1970
851.1
17291.4
20316.5
1971
879.1
17701.9
20136.4
1972
933.5
18522.9
19842.4
1973
988.5
19189.9
19413.2
1974
967.3
18702.4
19334.6
1975
939.6
18240.7
19413.3
1976
934.4
18984.6
19285.5
United States Department of Commerce (1976a)
American Petroleum Institute (1971)
United States Department of Commerce (1971)
Sources:


151
behavior in the model an! in the historical data. The
"goodness of fit" for this run was addressed using linear
regression models with the historical data for the business,
government, and household sectors from 1929 to 1969 as
dependent variables and the models output for this period
as independent variables. This allowed separation of the
models ability to explain the direction of change (given by
the B square values) from the magnitude of change fgiven by
the coefficients of the independent variables) These
statistics are listed in Table 17.
This run of the model projects a leveling of economic
assets at around the year 2000 and a subsequent steady state
with small oscillations. Figure ui shows a continuation of
this run from 2030 to 2130. Over this period, the model
predicts a gradual decline in economic assets due to the low
levels of remainino environmental assets.
^he Fouth Florida Fystem
Measured Fm bodied Fnergy Maps
Figures 42 44 are maps of the estimated embodied
energy intensities (total embodied energy divided by land
area) for south Florida for 1900, 1953, and 1973
respectively. The 1900 map provided initial conditions for
the south Florida simulation model and the 1953 and 1973


24
ENERGY SOURCE (FORCING
FUNCTION),
HEAT SINK, OUTFLOW OF USED ENERGY.
ENERGY INTERACTION, ONE TYPE OF ENERGY
AMPLIFIES ENERGY OF A DIFFERENT
QUALITY.
ECONOMIC TRANSACTION AND PRICE
FUNCTION.
Depreciotion
STORAGE (STATE VARIABLE)
ON-OFF CONTROL WORK (DIGITAL ACTIONS)
GROUP SYMBOLS (I) AUTOCATALYTIC SELF
MAINTENANCE UNITS, (2) PRODUCTION UNITS,
AND (3) GENERAL PURPOSE BOX FOR
MISCELLANEOUS SUBSYSTEMS.
Figure 5.
Energy circuit language symbols used in
this study.


2000 with a subsequent gradual decline in net capital
stochs,
'Ote south Florida spatial model employed a sequence of
detailed land use maps based on aerial photographs and soils
information for the years 1900, 1953, and 1973, The model
divided the region into S3 cells with three additional cells
to handle the embodied energy exchange with the rest of the
U. S. and the world. mhe simulation reproduced the essence
of the historical sequence of development using solar energy
as the only exogenous variable and a power maximizing
decision structure. Development of the east coast. Key west
and Fort nyers was duplicated by the model based on embodied
energy exchanges between these cells and the U. s. economy
cell. The model predicted leveling of the region as a whole
consistent with the TJ. F. economy-environment model.


6
1-SE3I Analysis
The detailed study of energy flow through systems can
he termed energy analysis. Evaluation of energy flows in
ecosystems has long been an important tool (duday *940;
Lindeman 1941). Currently in government circles energy
analysis has come to he used more specifically to refer to
the study of energy flows in engineering-economic systems
and the resulting policy implications. This application is
new and the concepts and techniques have not as yet
consolidated into a coherent whole. The house committee
print: "Energy analysis as a policy analysis tool" (Gushee
1976) is a good survey of the current literature. The
symposium by Gilliland (1978) highlights points of
controversy, particularly concerning methods of evaluating
embodied energy.
The field includes applications of input-output
analysis (Herendeen and Bullard 1974) and an evaluation of
energy systems diagrams {Gilliland 1975, 1978; Kylstra 1974;
Odum 1968, 1973). These applications involve different ways
of accounting for energy flows through systems. This
dissertation develops an input-output, technique for energy
accounting similar to the one employed by Hannon (1973b) and
Herendeen and Bullard (1974), Tsard (1972) suggested the
application of input-output models to ecologic-economic
systems but not in terms of energy accounting. The unique
feature of the input-output energy flow models in this


84
or any other suitable subdivision of the system under study.
The difference equation representation makes statement of
the logic sequence easier. In Figure 20 the partial
derivitives are calculated at time t-At for making decisions
at time t. The summation signs indicate that there are
potential exchanges with each of the n-1 other components in
the system, at each time step.
SB3 Two Components
To investigate the range of behavior that a two
component version of the power maximizing simulation model
can exhibit, some hypothetical situations were set up and
simulated on an EAT Finite analog computer. An analog
computer diagram of the model is given in Appendix II. The
simulations also served to test the power maximization
algorithm. This was done by constraining the system to
operate with the switches either always on (always
exchanging) or always off (never exchanging) and comparing
this with the unconstrained situation where the switches
were allowed to perform their normal role, The algorithm
was deemed successful if, for the same coefficient settings
the unconstrained mode consistently led to a higher total
power in the model than a constrained mode. The model was
also run on digital computers as a check,
Four hypothetical cases were investigated with the
model. In the figures the plots labeled with exchange


76
general case of n components. It should be noted that this
specific model is not the only conceivable way to achieve
the maximum power conditions derived earlier in a dynamic
system. It is only one of a number of possible approaches,
Figure 17 is an energy circuit diagram of a simple two
component version of the model in Figure 16, showing the
specific producti.on function chosen. The differential
eguations for the model are given in Figure 13. The choice
of a production function was difficult, since it involved a
compromise between accuracy and simplicity. The production
function chosen was built up from simple, slightly nonlinear
"partial production functions, which exhibit the important
characteristic of diminishing returns.
The algorithm involving the switches on the exchange
pathways in the model is a simplified method for
approximating the maximum power conditions in a complex
dynamic system. The switches are intended to maximize the
total power fPi+P2) in the system by allowing only those
exchanges that lead to a net increase in total power during
a particular small time interval. This function may be
handled in nature by the mechanism of natural selection.
The system of eguations is allowed to "evolve" by changing
its connoctivity structure as it progresses through time.
The technique is analogous to a "cost-benefit"
calculation for each potential exchange pathway for every
point in time. The "cost" is the loss of productivity due


22
o


211
Table 20
Embodied energy in goods and services for 92 U.S. economy sectors
Sector
(numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C
Excluding Including
Labor and Labor and
Government Government.
Services Services
Feedbacks Feedbacks
but Includ- but Exclud
ing Solar ing Solar
Energy Inputs Energy Inputs
All Values in Btu fossil/S
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
1.
Coal Mining (7)
5,143.600
5,172,000
5,455,600
5,807,500
2.
Crude Petroleum & Natural Gas (8)
2,920,300
2,929,200
3,188,600
3,569,050
3.
Petroleum Refining & Related Products (31.01)
1,422,300
1,432,250
1,748,400
2,085,500
4.
Electric Utilities (68.01)
505,500
513,900
796,220
1,099,950
5.
Gas Utilities (68.02)
809,380
816,400
1,109,700
1,421,000
6.
Other Agricultural Products (2)
81,567
775,090
381,090
1,385,400
7.
Forestry & Fishery Products (3)
62,565
23,297,500
337,420
23,861,500
8.
Livestock & Livestock Products (1)
55,276
340,710
363,800
1,053,500
9.
Agricultural, Forestry & Fishery Services (4)
32,697
202,265
336,640
826,300
10.
Iron S Ferroalloy Ores Mining (5)
65,904
87,840
395,620
755,500
11.
Nonferrous Metal Ores Mining (6)
61,037
99,605
406,060
800,800
12.
Stone £ Clay Mining £ Quarring (9)
97,477
109,420
417,630
760,900
13.
Chemicals & Fertilizer Mineral Mining (10)
59,002
71,645
352,820
667,500
14.
New Construction (11)
54,804
230,245
389,770
913,950


73
structure to all pathways in a system over time one could
prevent it from diverging too far from the optimum. This
may be considered a form of the "feasible directions" method
outlined in Wagner (1975) .
s possibly more accurate but operationally more
difficult approach involves adjusting the model parameters
to achieve the des5.red partial derivative relations at each
point in time. The approach using the switches has an
effect similar to continuous adjustment of the parameters
but is operationally easier and acknowledges the physical
limits to parameter changes.
In alternative derivation of the conditions in (23) can
be formulated as follows. "he change in total power caused
by the exchange terms (Y-^2 an^ ^21^ ars composed of direct
and indirect effects. In the two component model shown in
Figure 16, the total power is a function of the storages,
direct inputs, and exchange flows.
PT = f(Qx, Q2r E1# F2, Y12 Y21 } (24)
The rules for total differentiation can be used to determine
dP /d7^2* or the change in total power caused by a change
in the exchange flow Y ^2.
one can
write;
3Pt
3Pt^ 3Pt 3Pt
9Pt
+ _dQ2 + ^^1 + ^2
+ dYio +
d?12
3QX
9P_
T ,
3Q2 SS-l ?.2
a Yon
9Y21
(25)
or:


18
those normally taken Into consideration. See Smith and Lee
(1970) for an example. The overlay system used by HcHarg
(1959) is essentially a location theory model in which
environmental degradation costs are to be minimized.
Objective procedures for estimating environmental costs have
limited the application of this technique. Rent theory is
another extension which attempts to minimize the sum of rent
and transportation costs (Tujnovsky 1972).
Previous studies of economic location have concentrated
on static, cost-minimizing models. The spatial simulation
models in this dissertation combine cost and benefit
concepts (in energy terms) in a dynamic framework. The
gravity model is so called because Its mathematical form is
analogous to the gravity equation in physics, It predicts
that the amount of exchange between two centers will be
proportional to the product of center sizes divided by some
power of distance between centers.
Or:
where
id
KSiSj
/
d
a
ij
Yj_j Is some measure of exchange between
centers
3,Cj are some measure of the sizes of centers
d is distance between centers
K,a are parameters of the model
7)


Table 10. 1967 U.S. business sector capital stock and investment breakdown.
(All values in billions of .1967 dollars.)
Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
1654.1
921.6
122.18
41.01
81.17
Total Non-Human Tangibles (a)
1331.2
735.7
94.25
29.55
64.70
Structures
695.4
352.4
31.60
10.18
21.42
Equipment
447.9
195.4
54.46
11.18
43.28
Inventories
187.9
187.9
8.19
8.19
-
Total Human Tangibles
-
-
-
-
-
Total Non-Human Tangibles
73.6
45.8
8.13
-8.34
16.47
Basic Research
7.3
. 7.3
0.48
0.48
-
AR & D
66.3
38.5
7.66
-8.82
16.47
Total Human Intangibles
249.2
140.1
19.80
19.80
-
Education and Training
234.3
134.0
17.48
17.48
-
Medical and Health
8.9
4.3
0.60
0.60
-
Mobility
6.1
1.9
1.72
1.72
-
a, excluding land held by businesses
Source: Kendrick, 1976.
117


29
(a)
Figure 6.
Single sector energy balance.


PERCENTAGE OF SECTORS IN SPECIFIED RANGE
Alternative A. Excluding Labor and Government Service
Feedbacks and Solar Energy inputs.
JL
JL
JL
JEL
150
200
JL
250
300
350
GREATER
THAN 400
400
Figure 25. Frequency plots of embodied energy intensities by sector
calculated with and without solar inputs.
101




52
Xe = 1 Xg Xh = 4944
Figure 12 summarizes the modifications to the i-o
conventions made for this study.
FnvIronmental Inputs
?is with household and government services, there are two
ways of including environmental services. One is to treat
the environment as an exogenous entity and guantifv its
inputs to the economy. The second is to treat the
environment as an endogenous sector with flows to and from
the other sectors in an integrated economic-environmental
system. Both of these approaches were utilized in this
study.
In exogenous environment sector was hypothesized for 22
sector input-output studies of energy flow through the B.S,
economy. These studies were carried out in collaboration
with the Bnergy Hesearch Croup, Bniversity of Illinois at
Champaign. For this analysis the solar energy absorbed by
the tt. 3. was partitioned to tie economic sectors according
to land and water area. Table 6 shows the land and water
use distribution for the n. s. and estimates the total solar
absorption {including atmospheric) for the various uses,
The agriculture sector was credited with the solar
absorption over all agricultural land plus 34*5 of the
absorption over the wetlands, desert, and tundra category,
as agriculture represents of the remaining land and


Table 1\9. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(xl012CE)
1973
Embodied
Energy
(xl012CE)
Land
Area
(10 3 128
ac cells)
Latitude
(N)
Longitui
(W)
73
11.20
113.00
264.00
0.89
25.75
80.24
74
0.51
16.50
5.55
0.03
25.75
79.98
75
25.97
25.30
24.90
1.31
25.52
81.02
76
24.10
24.90
24.60
1.28
25.52
80.76
77
10.20
35.30
39.10
1.28
25.52
80.50
78
5.03
11.20
100.00
0.47
25.52
80.24
79
19.01
18.15
17.94
0.88
25.29
81.02
80
20.40
20.40
19.90
1.11
25.29
80.76
81
10.90
9.68
9.66
0.87
25.29
80.50
82
4.99
4.88
58.30
0.24
25.29
80.24
83
5.40
4.16
24.92
0.20
25.06
80.50
84
5.23
6.68
17.85
0.20
24.83
81.02
199


Table 19. South Florida land use data
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(xl012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(xlO3 128
ac cells)
Latitude
(N)
Longitude
(W)
1
12.82
13.10
96.1
0.85
28.51
81.54
2
12.85
33.17
71.83
0.98
28.51
81.28
3
18.30
18.20
17.10
0.97
28.28
81.54
4
22.42
25.52
36.66
1.80
28.28
81.28
5
9.85
14.10
11.40
0.74
28.05
81.54
6
15.06
13.97
13.56
1.68
28.05
81.28
7
9.49
11.60
13.60
0.78
27.82
81.54
8
11.00
12.10
9.97
1.28
27.82
81.28
9
11.30
9.20
10.20
0.92
27.82
81.02
10
4.48
10.10
15.90
0.36
27.59
81.54
11
16.70
20.10
15.00
1.28
27.59
81.28
12
16.70
17.80
11.90
1.26
27.59
81.02


228
Table 25. U.S. environment sector, U.S. economy, total U.S.
(environment plus economy), and rest of the world
net capital stock (in billions of 1967 dollars).
Year
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
Economy)
Net Capital
Stock
Rest of t:
World Net
Capital
Stock (c)
1929
20400
'1671
22071..
327589
1930
20290
1711
22001
326550
1931
20195
1727
21922
325378
1932
20112
1721
21833
324057
1933
20024
1703
21728
322498
1934
19931
1696
21627
320999
1935
19834
1705
21539
319693
1936
19722
1734
21456
318461
1937
19606
1775
21381
317348
1938
19506
1807
21313
316339
1939
19396
1837
21233
315151
1940
19273
1887
21160
314068
1941
19135
1962
21097
313133
1942
18991
2063
21054
312494
1943
18837
2174
21011
311856
1944
18667
2283
20950
310951
1945
18504
2336
30840
309318
1946
18 349
2371
20720
307537
1947
18183
2423
20606
305845


Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the requirements for the Degree of Doctor of Philosophy
EMBODIED EUFRGY BASIS FOR
FCONOHTCFCOLOGXC SYSTEMS
By
Sober4: Costanza
June, 1970
Chairman: Howard T. Odum
Flajor Department: environmental Engineering Sciences
The energy basis for economic-ecologic systems was
investigated using models of the United States and the south
Florida area. The energy flow necessary (directly and
indirectly) to produce commodities was termed the embodied
energy and was studied as a parameter useful for evaluating
systems and their parts. Embodied energy was calculated
using input-output matrices to trace the flow of energy
through systems.
The approach was applied to a 92-sector U. S. economy
for 1967. Current accounting conventions for government and
households were modified to mate them endogenous sectors.
Solar energy inputs to the economic-ecologic system were
estimated and included. These modifications were necessary
to form a closed economic-ecologic system, with only energy
crossing the boundaries. The changes were made
incrementally so the effects of each could be studied,
Pestilts indicated a very close correlation between embodied
energy and dollar value of output, with the notable


i*QCJ)/((1*fED(I,J) *Q (I) ) **2)
330
350
30
29
410
430
450
42
40
C
C
C
QI=ED(I,J)
GO TO 350
jji-CBg (iJ)*Q(i)) J/(1*bd(i#j)^q (i) )*:
CONTINUE
CONTINUE
DO 40 1=1,91
P1 ill = A I)*B ill *Q F4 m=C(I)*Q (I)
F2(I1 = 0
DO 42 0=1,91
IP (I.EQ*J) GO TO 430
DI=DfI)*S
IP^DI-D^J)) 410,430,430
*Q(J)/(ED (I,J)*Q(I) +1. )
CONTINUE
CALCULATE NEW LEVELS
50
C
C
600
C
C
C
601
111
DO 50 1=1,91
SiftiM?+DT*{F1 CHECK TIBE AND PRINT BESOLTS IF NECESSARY
IT=PT*0001
IF (IPR-IT) 601,601,600
PT=PT*DT
GO TO 100
MAPPING ROUTINE
6,111]
WRITE(6,1111
FORMAT (M',2
110
120
C
f {* 11,2X, *1* 5X, *0 (I) ,51, D (II ,5X, #P1(I) 5X,'F
1 %5X *F (I)f,4{,^(,59) f,4i,W(I,§0) ,4X,iY(f ,9
v i*!) 1-1,91
RITE (6,110) I.Q(I) ,D (I) ,
flrt*?'*''*1'
I *P3(I
DO 12
WRITE
II
PORftATlf
CONTINUE
F2
1
,F1 (I) ,F2 (I) ,F3 (I) ,F4 (I) ,


exception of the primary energy sectors (R square = .99 whan
the primary energy sectors were omitted) The results
implied a relatively constant embodied energy to dollar
ratio with an estimated valtie of 47000 kcal fossil/19f57S.
Additional supporting data on energy/raal GNP ratios for
time series of the U.S. economy and international
comparisons of energy/GDP ratios were collected and
presented.
Embodied energy was applied as a common measure to
model dynamic exchanges in combined ecologic-economic
systems. This approach internalizes all energy
externalities.
Maximization of power (or embodied energy productivity)
was used as an objective function in developing dynamically
optimizing, nonlinear simulation models. The models adjust
their connectivity structure through time in order to
maximize power and the behavior is therefore discontinuous
in a manner analogous to catastrophe theory. The model was
applied to a 5-sector 0,5. economy-environment and a 91-cell
spatial grid of the sout-b florida region, generating maps of
predicted development.
The power maximizing model reproduced the behavior of
the it. 5, economic-ecol.ogic system over the historical period
from 1929 to 1959 for which data on net capital stocks have
been estimated, Extrapolated into the future, the model
predicted leveling of the .5, economy at around the year
XJLJL


25
H2£ I2SZSIQ.ESSI1;
A model is an abstract representation of a structure or
process which is constructed to aid understanding.
Development of an appropriate model is guided by the
questions being ashed, the general principles which the
model employs in answering these questions, and the amount
of time and effort which can be devoted to the modeling
effort, including data collection and evaluation. ^here are
several classes of models but this dissertation focuses on
mathematical models of the dynamic nonlinear type. Several
authors, notably Forrester (161) Nicolis and Prigogine
(1971), and Odum (1971) have argued that questions of time
behavior in living systems can be adequately addressed only
with models of this type.
The topological structure of each model was developed
by deciding on the internal components and external forcing
functions to be considered and then making assumptions about
the interconnections, vhe models were evaluated with data
from real situations. The simulation results were compared
with observed historical trends to determine the accuracy of
the original, assumptions. "'hese were modified as necessary
to improve the fit.
Dynamic Optimization
The general method of Lagrange multipliers was employed
in the development o* the power maximizing simulation


TOTAL CAPITAL STOCK, x 10 1967 dollars
125
400 ~'
300-1
200-i
100-i
o ^
1920
1930
1940
1950
YEAR
I
I960
1970
Time series plot of rest of the world net
capital stocks from 1929 to 1969.
Figure 34.


Table 14.
(continued)
Aggregate
Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
14. Rest
World
of the
(b)
253224.0
5660.0
5463.0
a. Based on Kendrick's (1976) estimates of business, government and personal sector net
capital stocks, gross investment and depreciation for 1967. Net capital is accumulat
ed gross investment. Depreciation is gross investment minus net investment. The
business sector total excluding land was-distributed..to the 10 aggregate business sectors
according to data on gross investment in 1967 from BEA (United States Department of
Commerce 1975). The land stock was credited to the environment sector.
b. The rest of the world was assumed to exhibit the same ratios of net capital stock to
gross investment and depreciation as the U.S. The rest of the world net capital
stock for 1967 was estimated as 283224 E9 1967$ (See Table 25). Gross investment
was thus 8860 E9 1967$ and depreciation was 5463 E9 1967$.
c. Aside from the value of land, the net capital stock of the environment sector also
includes mineral reserves. Considering only fuel reserves and using a conservative
figure of 25 E19 Btu fossil, total recoverable reserves at 188 E3 Btu fossil/1967$
gives a total value of $13298 E9. Added to the land stock value, this yields an
(admitted very approximate) estimate of total environmental stock value of $13872 E9.
This value in conjunction with the fuel consumption figures in Table 27 and the land
value figures in Table 26 were used to estimate the environment sector net capital
time series in Table 25.
137


page
Figure
32 Time series plot of .S. business, government,
and household net capital stocks from
1929 to 1 969........ 123
33 Time series plot of n.S. environment, n.S.
economy, and total ti.S. net capital stock from
1929 to 1969. 124
34 Time series plot of rest of the world* net
capital stocks from 1929 to 1969.................. 125
35 1963 14-sector transactions matrix with all
values converted to millions of 1967 dollars...... 128
36 1967 14-sector transactions matrix with all
values converted to millions of 1967 dollars...... 130
37 Energy flow diagram for a 5-sector 0.5.
economy-environment simulation model 141
38 1963 5-sector transactions matrix with all
values converted to millions of 1967 dollars...... 144
39 1967 5-sector transactions matrix with all
values converted to millions of 1967 dollars....., 146
49 simulation results for the 5-sector economy-
environment model from 1929 to 2031............... 153
41 Simulation results for the 5-sector economy-
environment model from 2031 tO 2131 155
42
Embodied energy intensity map for south Florida
for 1900 estimated from the 1900 land use map..... 158
43
Embodied energy intensity map for south Florida
for 1953 estimated from the 1953 land use map..... 160
44
embodied energy intensity map for south Florida
for 1993 estimated from the 1973 land use map..
162
45 Simulation results for the 91-cell south Florida
spatial simulation model.......................... 167
46 Analog computer diagram for the two component
exchange model..,. 203
x


57
a form of "shadow pricing" (Dorfman, Samuelson, and Solow
1958} of environmental services,
£&£i£.i! Flows
Capital flows are normally not included explicitly in
the input-output tables, Data recently available from the
Bureau of economic Analysis (SCB Sept. 1975) on
interindustry transactions in new structures and equipment
combined with data from Kendrick (1976) on investment and
depreciation of human and government capital allowed the
inclusion of capital flows in parts of this study,
^or the purposes of this study the capital flows were
simply added to the existing interindustry flows. This
increased the total input to each sector by the amount of
capital purchased by that sector during the year and
embedded the years Gross Private Fixed Capital Formation
column in the current transactions matrix. The capital
purchases by each sector were then added as a "capital
maintenance and growth" column in final demand to balance
the additional input.
South Florida Land rise Data
A time series of three full color land use maps for th
years 19C0# 1953, and 1973 for the south Florida region wer


EMBODIED ENERGY BASIS FOR
ECONOMIC-ECOLOGIC SYSTEMS
By
ROBERT COSTANZA
A DISSERTATION PRESENTED TO THE GRADUATE CONCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE CE DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1979

Copyright 1979
by
Robert Costanza

ACKNOWLEDGE?!" NTS
T am greatly, indebted to Dr. R.T. Odum, my committee
chairman, for his knowledge, inspiration, insight, and
encouragement. His all-encompassing world view gave birth
to many of the concepts which led to this study and guidei
the work to fruition. Many special contributions were made
by the other members of my committee: Prs. S. E. Bayiey, B.L.
Capehart, W, c. Huber, and C.D. Kylstra.
B. Hannon and p. Herendeen at the Center for Advanced
Computation, University of Illinois, contributed experienced
help and encouragement with the input-output studies in the
summer of 1978. F. Hang and J. Boyles read the manuscript
and provided comments. I would also like to acknowledge the
valuable interactions with associates and friends,
especially J. Bartholomew, T. Fontaine, S. Brown, and D.
Hornbeck.
Fork was done at the Center for Wetlands, University of
Florida, and was supported by the United States Department
of Energy (Contract ET-76-S-05-4398) project entitled
"Energy Analysis of Models of the United States," R.T, Odum
principal investigator.

TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS........................................ iii
LIST OF TABLES......................... vi
LIST OF FIGFF.es,. .viii
ABSTRACT. xi
INTRODUCTION 1
Research Plan.......................... 2
Background of Previous Studies........... 4
Energy and Society............... 4
Systems Ecology.. 5
Energy Analysis................................. 6
Embodied Energy 7
Optimisation.................... 13
Economic Models,,....,...... 13
Spatial Economic Models.,,.,.,.....,.,.,....... 17
Simulation Models............................... 19
Description of the South Florida Area............... 20
METHODS. 23
Description of the Modeling Language................ 23
Model Development,......,.....,....,.,,.......,. 25
Dynamic Optimization................ 25
Simulation Modeling Methods..................... 26
Model Parameter Estimation, Validation and
Testing. 27
Input-Output Techniques for Calculating Embodied
Energy. 28
Double Counting................................. 41
U.S, Economy Data Assembly and Evaluation...., 43
Government and Households as Endogenous
Sectors....................................... 44
Environmental Inputs............................ 52
An Endogenous Environment Sector................ 55
Capital Flows 57
South Florida Land Use Data .57
RESULTS. 65
The General Conditions for Maximum Power..,...,.,... 65
Development of a General, Power Maximizing
Simulation Model...,....,.,...,.....,.,,.. 75
Simulations Using Two Components................ 84
Simulations of Spatial Development Using
25 Cells. 91
iv

page
The U. S, Economic-Ecologic System................... 96
Energy Embodied in Goods and Services for 92
0,S. Economy Sectors in 1967. 96
The Energy to GNP Ratio for the U.S,
From 1920 to 1 976............. 114
Total Capital, Investment, and Depreciation
Time Series and a Better Estimate of the
Embodied Energy to Dollar Ratio. ,116
Fourteen Sector Closed System Input-Output
Matrices for 1963 and 1967,,....,..,,.,,,.,,.. 126
Five Sector U,S. Economy-Environment
Simulation Model,...,.,.,.,........., 139
The South Florida System. 151
Measured Embodied Energy Maps................... 151
Minty One Cell South Florida Spatial
Simulation Model....,.,.,,....,....,....,.,,.. 163
DISCUSSION 180
The Case for a Constant Embodied Energy to
Dollar Ratio...,*.. 180
Conclusions and Predictions from the Simulation
Models............................................ 188
Embodied Energy Analysis and Economics.............. 190
APPENDIX
I SOUTH FLORIDA LAND USE DATA CONVERTED TO EMBODIED
ENERGY UNITS..... 193
II ANALOG COMPUTER DIAGRAM FOE THE TWO COMPONENT
EXCHANGE MODEL 203
III FORTRAN LISTING FOR.THE 25-CELL SPATIAL MODEL....... 205
IV ENERGY EMBODIED IN GOODS AND SERVICES FOR 92
U.S, ECONOMY SECTORS IN 1967.,..,,......,., 211
V TIME SERIES DATA FOR THE U.S.
ECOHOHIC-ECOLOGIC SYSTEM... 219
VI FORTRAN LISTING FOR THE 5-SECTOR U.S. ECONOMY-
ENVIRONMENT SIMULATION MODEL....................... 236
VII FORTRAN LISTING FOR THE 91-CELL SOUTH FLORIDA
SIMULATION MODEL AND DATA. 240
LIST OF REFERENCES,. 247
BIOGRAPHICAL SKETCH 254
v

LIST OF TABLES
Table
pi a?
1 Characteristics of the input-output and
biosphere embodied energy concepts................ 11
?. Input-output transactions matrix in arbitrary
physical units corresponding to the diagram in
figure
32
Input-output transactions matrix in embodied
energy units corresponding to the diagram in
Figure B,................................
Input-output transactions matrix corresponding
to the diagram in Figure 9, using the national
input-output accounting conventions............... 39
Relationship of input-output value added
accounts categories............................... 49
Estimated land areas and solar absorption for
major land use types.............................. 54
Land use subsystem metabolism and structure
estimates in coal equivalents (CF) 63
Kinty two sector embodied energy intensity
statistics.
103
9 Regression analysis results for total (direct
plus indirect) energy consumption versus total
dollar output for the four alternative
treatments of labor, government, and solar energy.,113
m 1957 7,9. business sector capital stock and
investment breakdown (in bi!15_ons of 1967 dollars).117
11 1967 tj.,9. government sector capital stock and
investment breakdown (in billions of 1967 dollars).118
12 1967 n.S. household sector capital stock and
investment breakdown (in billions of 1967 dollars) 119
13 1963 aggregate sector net capital stocks, gross
investment, and depreciation (in billions of
1967 dollars).......,... 134
1U 1967 aggregate sector net capital stocks, gross
investment, and depreciation (in billions of
1 967 dollars)
136

Table page
15 Sector correspondence............... 138
16 Init5.a! parameter estimates. 149
17 U.S, economy-environment simulation model
performance statistics for the 1929-1969 period... 156
18 South Florida simulation model performance
statistics for 1953 and 1 973 178
19 South Florida land use data converted to embodied
energy units.,.,.....*.*..,.,.................,... 193
25Embodied energy in goods and services for
9 2 IT. S, economy sectors in 1967, 211
21 Feal GMP, total fossil, hydro, and nuclear energy
consumption, and fossil, hydro, and nuclear
energy to real GNP ratio, 1920-1976., 219
22 .s. business sector net capital, investment, and
depreciation time series in constant dollars 222
23 !T.S. government sector net capital, investment,
and depreciation time series in constant
dollars, 224
24 n.S. household sector net capital, investment,
and. depreciation time series in constant
dollars.........y............. 226
25 .S. environment sector, n.S. economy, total
H.s. (environment plus economy), and rest
of the world net capital stock in
constant dollars.,.,...,......,....,......,,...... 228
26 Time series of net land stocks in the .S......... 231
27 Time series of total mineral fuel use and
estimated real dollar value.. 233

LIST OF FIGURES
1 Solar energy driving the productive processes
of the earth......*......................*......., 8
2 Diagram showing the characteristics of the input-
output and biosphere embodied energy concepts 12
3 Diagram showing the standard input-output
accounting setup, 15
4 Location map of south Florida......... 22
5 Energy circuit language symbols used in this study 24
6 Single sector energy balance... 29
7 Hypothetical three sector economy with all flows
In arbitrary physical units....................... 31
B Hypothetical three sector economy with all flows
in embodied energy units.......................... 35
9Hypothetical three sector economy cast In the
format of the national input-output accounting
statistics........................................ 38
10 Energy flow diagram of an aggregated 14 sector
IT. S. economic-ecologic system..................... 46
11 Diagram showing definitions of national income
variables 47
12 Summary of modifications to the input-output
conventions. 53
13 Land use cells for south florida.... 60
14 Example of detailed land use data, showing
cell 45 in Figure 13 for 1973.............. 61
15 Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973............. 62
16 Two production systems and their exchange
pathways. 72
17 Energy circut diagram for a two component
power maximizing model of exchange................ 77
vi i

Figure page
18 Differential equations for the model in
Figure 17. 79
19 Diagram illustrating the partial production
function relations.... 81
2D Component i difference equation. 86
21 Two component model analog simulation results..... 88
22 Two component model analog simulation results..... 92
22 Digital simulation of the power maximizing
model for a spatial grid of 25 components......... 95
2U Diagram showing the system boundaries and flows
included in the four alternatives................. 98
25 Frequency plots of embodied energy intensities
by sector calculated with and without solar
inputs. 101
26 frequency plots of embodied energy intensities
by sector calculated with and without labor
and government service feedbacks.... 102
27 Plot of direct plus indirect energy consumption
(calculated excluding solar inputs and labor
and government) versus dollar output for
92 rj.S. economy sectors........................... 106
28 Plot of direct plus indirect energy consumption
(calculated including solar inputs but excluding
labor and government) versus dollar output for
92 U.S, economy sectors........................... 108
29 Plot of direct plus indirect energy consumption
(calculated including labor and government but
excluding solar inputs) versus dollar output for
92 .S. economy sectors........................... 110
3D Plot of direct plus indirect energy consumption
(calculated including solar energy inputs and
labor and government) versus dollar output for
92 TT.5 economy sectors........................... 112
31 Dineral, hydro, and nuclear energy consumption
per dollar of real GFP from 1920 to 1976
115

page
Figure
32 Time series plot of .S. business, government,
and household net capital stocks from
1929 to 1 969........ 123
33 Time series plot of n.S. environment, n.S.
economy, and total ti.S. net capital stock from
1929 to 1969. 124
34 Time series plot of rest of the world* net
capital stocks from 1929 to 1969.................. 125
35 1963 14-sector transactions matrix with all
values converted to millions of 1967 dollars...... 128
36 1967 14-sector transactions matrix with all
values converted to millions of 1967 dollars...... 130
37 Energy flow diagram for a 5-sector 0.5.
economy-environment simulation model 141
38 1963 5-sector transactions matrix with all
values converted to millions of 1967 dollars...... 144
39 1967 5-sector transactions matrix with all
values converted to millions of 1967 dollars....., 146
49 simulation results for the 5-sector economy-
environment model from 1929 to 2031............... 153
41 Simulation results for the 5-sector economy-
environment model from 2031 tO 2131 155
42
Embodied energy intensity map for south Florida
for 1900 estimated from the 1900 land use map..... 158
43
Embodied energy intensity map for south Florida
for 1953 estimated from the 1953 land use map..... 160
44
embodied energy intensity map for south Florida
for 1993 estimated from the 1973 land use map..
162
45 Simulation results for the 91-cell south Florida
spatial simulation model.......................... 167
46 Analog computer diagram for the two component
exchange model..,. 203
x

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment
of the requirements for the Degree of Doctor of Philosophy
EMBODIED EUFRGY BASIS FOR
FCONOHTCFCOLOGXC SYSTEMS
By
Sober4: Costanza
June, 1970
Chairman: Howard T. Odum
Flajor Department: environmental Engineering Sciences
The energy basis for economic-ecologic systems was
investigated using models of the United States and the south
Florida area. The energy flow necessary (directly and
indirectly) to produce commodities was termed the embodied
energy and was studied as a parameter useful for evaluating
systems and their parts. Embodied energy was calculated
using input-output matrices to trace the flow of energy
through systems.
The approach was applied to a 92-sector U. S. economy
for 1967. Current accounting conventions for government and
households were modified to mate them endogenous sectors.
Solar energy inputs to the economic-ecologic system were
estimated and included. These modifications were necessary
to form a closed economic-ecologic system, with only energy
crossing the boundaries. The changes were made
incrementally so the effects of each could be studied,
Pestilts indicated a very close correlation between embodied
energy and dollar value of output, with the notable

exception of the primary energy sectors (R square = .99 whan
the primary energy sectors were omitted) The results
implied a relatively constant embodied energy to dollar
ratio with an estimated valtie of 47000 kcal fossil/19f57S.
Additional supporting data on energy/raal GNP ratios for
time series of the U.S. economy and international
comparisons of energy/GDP ratios were collected and
presented.
Embodied energy was applied as a common measure to
model dynamic exchanges in combined ecologic-economic
systems. This approach internalizes all energy
externalities.
Maximization of power (or embodied energy productivity)
was used as an objective function in developing dynamically
optimizing, nonlinear simulation models. The models adjust
their connectivity structure through time in order to
maximize power and the behavior is therefore discontinuous
in a manner analogous to catastrophe theory. The model was
applied to a 5-sector 0,5. economy-environment and a 91-cell
spatial grid of the sout-b florida region, generating maps of
predicted development.
The power maximizing model reproduced the behavior of
the it. 5, economic-ecol.ogic system over the historical period
from 1929 to 1959 for which data on net capital stocks have
been estimated, Extrapolated into the future, the model
predicted leveling of the .5, economy at around the year
XJLJL

2000 with a subsequent gradual decline in net capital
stochs,
'Ote south Florida spatial model employed a sequence of
detailed land use maps based on aerial photographs and soils
information for the years 1900, 1953, and 1973, The model
divided the region into S3 cells with three additional cells
to handle the embodied energy exchange with the rest of the
U. S. and the world. mhe simulation reproduced the essence
of the historical sequence of development using solar energy
as the only exogenous variable and a power maximizing
decision structure. Development of the east coast. Key west
and Fort nyers was duplicated by the model based on embodied
energy exchanges between these cells and the U. s. economy
cell. The model predicted leveling of the region as a whole
consistent with the TJ. F. economy-environment model.

INTPODCTTOH
A fundamental issue in ecology is understanding the way
energy and material flows in ecosystems develop organized
structures and processes. Mans economic systems can be
viewed as subiect to many of the same energetic forces as
those shaping ecological systems. Thus, the study of energy
and material flows in combined economic-ecologic systems can
lead to new insights into the way these flows develop
organized patterns.
Several important questions can be identified
concerning the role of energy as it affects organization and
succession in combined ecologic-economic systems. Flow does
energy flow through and organize these systems? What is the
relationship between energy flow and money? How is spatial
development related to sources of energy? What are the
general criteria for natural selection? How can selection
be modeled to predict the dynamic behavior of these systems?
These questions were considered using energy systems
analysis (Odum, 1971). Models describing the flow of energy
and materials were developed and evaluated. Specific
emphasis was placed on integrating conventional economic
accounting and analysis techniques into the general energy
systems framework. Input-output techniques and data were
employed to trace energy flows through combined ecologic-
economic systems. Efforts were made to show relationships

2
between these different accounting frameworks. Dynamic
simulation models were developed and used to investigate the
temporal and spatial behavior of complex, self-organising
systems that can evolve and change their internal structure
and function over time, Lotkas maximum power principle has
been suggested as the fitness criteria for survival of the
system, and thus the ultimate goal of evolution {Odum 1971).
Can these concepts be incorporated in mathematical systems
models? 9hat are the general criteria for survival of
systems? Can optimal control theory be gainfully applied to
this problem? Hhat general characteristics do models of
this type exhibit? "he simulation models developed in this
study were applied to the growth of the n.S. economy-
environment and to the spatially articulated growth of south
Florida in order to predict the general behavior of these
systems.
Research Plan
"his dissertation is a study of the way energy affects,
limits, and. determines the organised noneguillibrium
phenomenon comprising ecological and economic systems. ?o
this end conceptual and mathematical models were developed
to indicate the response of these systems to available
energy inputs. Linear input-output models of embodied

3
energy were developed and evaluated. Nonlinear,
discontinuous optimization models were developed and applied
with Lotkas maximum power principle as the objective
function.
Cross-sectional and time series data were collected for
two related examples. The first was the n. s. economy-
ecology as a whole. Data for this example included input-
output transactions at various levels of aggregation, tima
series of total capital stocks, investment and depreciation,
and time series of energy inputs to the economy and
environment. Most of these data were in dollar terms and a
major part of the study involved integrating them into an
all-encompassing energy flow network that included
environmental systems. The second example was the spatial
evolution of the south Florida region. A series of three
previously compiled, detailed land use maps of the region
for the years 190% 1953, and 1973 {along with supporting
data on the characteristics of the mapped units) were used
as the primary data base for this application, The models
were run over the historical period and the results compared
with the collected data. Once a reasonable fit was obtained
the models were run into the future and their predictions
interpreted.

4
3}ackgroun2 of Previous Studies
This di ssertation includes energy analysis, evaluation,
and simulation of economic-ecologic systems using input-
output, optimization, and. spatial models. Some background
of previous work in thes^ areas is reviewed.
Energy and Society
The thesis that available energy inputs govern and
limit the structure of human societies is not new,
Boltzmann (1886) pointed out that life is primarily a
struggle for available energy, Soddy (1933) stated: nif we
have available energy, we may maintain life and produce
every material reguisite necessary. That is why the flow of
energy should be the primary concern of economics (p, 56).
Lotka (1921) also noted the direct relationship behween
energy and economics. Cottrell (1955) provided a detailed
analysis of the ways cultures have historically adapted to
their surplus energy supplies. Odum (1971) extended
energy concepts to include all systems, thus providing a
conceptual link between man and nature and many new insights
into the workings of mans economic systems.
Paly (1977) discussed the energy limitations which
ultimately lead to steady state economic systems.
Georgescu-Eoegen (1971) took a more theoretical approach in
his study of the second law of thermodynamics and its

5
importance in economic systems. Ophuls (1977) reviewed the
political implications of energy and resource limitations,
Cook (1971, 197fs) and Hannon (1973a) have attempted to
quantify the intricate web of energy flows in industrial
societies.
Systems ecology
Systems analysis as practiced in ecology is an
integrative approach used to explain the structure,
function, and interrelationship of all systems as the
product of certain general systems principles which
transcend the boundaries of academic fields. The aim of
general systems theory was formulated by 7on Bertalanffy
(1968) as "the formulation and derivation of those
principles, which are valid, for systems* in general (p.
32). This paradigm is seen as essential to the
understanding of complex systems with feedback, which has
frustrated the "atomistic approach of "normal science.
Odum (1971) produced a unified theory and methodology for
the application of general systems theory to a broad range
of problems. This is the general approach taken in this
study.

6
1-SE3I Analysis
The detailed study of energy flow through systems can
he termed energy analysis. Evaluation of energy flows in
ecosystems has long been an important tool (duday *940;
Lindeman 1941). Currently in government circles energy
analysis has come to he used more specifically to refer to
the study of energy flows in engineering-economic systems
and the resulting policy implications. This application is
new and the concepts and techniques have not as yet
consolidated into a coherent whole. The house committee
print: "Energy analysis as a policy analysis tool" (Gushee
1976) is a good survey of the current literature. The
symposium by Gilliland (1978) highlights points of
controversy, particularly concerning methods of evaluating
embodied energy.
The field includes applications of input-output
analysis (Herendeen and Bullard 1974) and an evaluation of
energy systems diagrams {Gilliland 1975, 1978; Kylstra 1974;
Odum 1968, 1973). These applications involve different ways
of accounting for energy flows through systems. This
dissertation develops an input-output, technique for energy
accounting similar to the one employed by Hannon (1973b) and
Herendeen and Bullard (1974), Tsard (1972) suggested the
application of input-output models to ecologic-economic
systems but not in terms of energy accounting. The unique
feature of the input-output energy flow models in this

7
dissertation is the application to combined economic-
ecologic systems. The relationship between energy analysis
and economic analysis has been the subject of recent debate
and is a major topic of this dissertation. Leach (1975) and
Webb and Pearce (1975) have challenged the ability of energy
analysis to provide useful information beyond that available
to standard economics. By treating the economic-ecologic
system as a unit and by following energy flows through it,
many of these questions may be clarified,
Si.ll£.§.d Energy
Embodied energy is defined as the total amount of
energy of a single type required directly and indirectly to
produce the substance of interest. For example, Figure 1
shows solar energy as the primary energy input to the earth.
Host flows and storages of free energy on the earth can be
thought of as embodied past and present sunlight, since
sunlight has been the most significant source of free energy
for the earth, Tides, nuclear energy, and residual heat
contribute much smaller amounts. mhus the sunlight of past
eons is embodied in the current storages of fossil fuel, raw
materials, soil, etc. that are employed by industrial
society. It is convenient to divide the continuum of energy
sources into renewable sources of free energy (embodied
present sunlight) and nonrenewable storages (embodied past
sunlight) on the basis of their relative rates of production

8
Figure 1.
Solar energy driving the productive processes
of the earth.

9
and consumption, Penetrable sources ara those whose rate of
production roughly equals their rate of consumption.
Obvious examples are sunlight itself, rain, wind, and the
shorter time scale products of the interaction of these
inputs, such as forestry, fishery, and agricultural
products. Nonrenewable sources of free energy (embodied
past sunlight) are those whose rate of consumption far
exceeds their ra+e of production. Nonrenewable sources are
mined substances, such as the fossil fuels, soil storages,
and mineral deposits, wh5_ch are the results of slow
biogeologic production cycles over long time periods.
Embodied energy is linked to ability to do work (or
available energy) by the theory that the energy used
(directly and indirectly) to produce a substance shows up as
a proportional increase in the stored order or departure
from equillibrium of the substance, and thus its ability to
do work. Nor example, oil mined and delivered to the point
of use would have more embodied energy (that consumed by the
recovery and transportation process) than oil in the ground.
The delivered oil would also have a larger ability to do
work than the untapped oil, due to its increased proximity
to an oil consuming economic system. A ceremonial mask
would have more embodied energy than the piece of wood from
which it was carved and would also presumably do more work
by performing an important symbolic function in the
ceremonies of the culture of its manufacture.

Several concepts of embodied energy have thus far been
proposed. One employs input-output techniques (Leontief ^
1041) to trace input energy flows through the complex webs
of interactions in economic and ecological systems {Hannon
1971b; Herendeen and Bullard 1974). This can be termed the
input-output embodied energy. It assumes that embodied
energy is a conservative quantity, or that the sum of the
embodied energy inputs to each sector are emdodied in the
output, llhen pathways diverge, the total embodied energy is
partitioned among them so that the system of interconnected
flows maintains the conservation constraint. Figure 2a
shows an example of this approach, Another approach reasons
that since all processes are interconnected and in that
sense required for each others production (either directly
or indirectly), the amount of input necessary to produce any
one product must be taken as the total input (Odum 1978),
This approach assigns equal embodied energy to all by
products of a process but partitions the embodied energy if
the same commodity is simply divided. The embodied energy
inputs and outputs for each sector do not necessarily
balance. his approach has been applied (Odum 1978) to
estimating the embodied energy in natural energy flows in
the biosphere and can thus be termed the biosphere embodied
energy. Figure 2b shows an example of the concept. Table 1
and Figure 2 compare the characteristics of these two
approaches.

11
Table 1. Characteristics of the input-output an!
biosphere embodied energy concepts.
Characteristic
Input-output
embodied energy
Biosphere
embodied energy
Conservation of
embodied energy
yes
no
All heterogenous
by-products of a
production process
assigned equal
embodied energy
no
yes
(except for
degraded heat)

12
Figure 2. Diagram showing, the characteristics of the
input-output and biosphere embodied energy
concepts.

13
The first ccmcept was use! in this study, with some
modification and extensions, ft complete description of the
technique with examples is given in the methods section.
Optimization
Optimization is the search for maxima or minima usually
subject to some constraints. Wilde and Beightler (1967)
provide a good introduction to the method. Cody (1974)
reviews some of the applications of optimization models to
ecological systems. Rapport and Turner (1977) discuss the
underlying similarities of economic and ecologic processes
as an explanation for the success of optimization models in
both fields.
The maximization of useful energy flow (or maximum
power) was suggested as an objective function by Lotka
(1922). Odum (1971) has elaborated and generalized on this
theme. Oster and Wilson (1978) employ what they term
ergonomic (or work) efficiency as a.n objective function in
the study of colonial insects. Wang, Odum, and Costanza
(1978) showed an example application of the maximum power
principle to a land and water management problem.
Economyc Wodels
current microeconomic theory can all fit under the
umbrella of optimization. In the general optimization
problem there is some objective function to be maximized or

14
minimize! (usually profit, utility or cost) subject to
constraints {Sealing with resource availability, income or
levels of production) mhe partial egu.illibrium theorists
leal with small pieces o4" the system taken in isolation with
the ubiquitous "all else being equal" frequently invoked,
Most of the analysis focuses on graphical solutions. Becker
(1971) is a good text along these lines. Input-output
analysis and linear programming are important approaches for
determining optimum, eguillibrium flows of commodities and
money in an economy. Oorfman, Samuelson, and Solow (1958)
summarize these approaches. Input-output is a general
equillibrium technique developed by Leontief (19H1). It is
a tabular accounting system with balance constraints. In
the typical application the economy is disaggregated into n
sectors and the production of each sector is expressed as:
Xij +
V .
" 1
j=1
(i = 1,2,. . ,n) (1)
where
= total production of sector i
= production of sector i to be used as input
to sector j
= output of sector i to consumers (final demand)
Figure 3 illustrates this setup.
A set of direct requirements coefficients can be defined as:
7! .
- 13
r ./ r .
(2)
or:

15
Xf = Ex¡j Y¡
Figure 3.
Diagram showing the. standard input-output
accounting setup.

16
AjXj
substituting {3} in (1) yields
(3)
n
l
(4)
j=1
or In matrix notation for all n sectors:
7 = AX + Y
(5)
or solving for the sector outputs in terms of the final
demand (T) and the direct requirements matrix (A) :
-1
X = (T-A) Y
(6)
The set of simultaneous linear equations represented by
(6) is useful for tracing Interdependencies at a point in
time or for making predictions of the affects of small
departures from equlllibrium, Programming models are
similar to Input-output models except that more than one
solution to the equations Is possible. The approach
originated as a strategic planning model for directing Air
Force activities (Pantzig 1951). The mathematical problem
is finding the best (or optimal) solution from among the set
of feasible solutions. The approach initially was applied
to linear systems (linear programming), and this is still
the major practical application. Gradually, more
mathematically difficult problems were attempted with
current applications to dynamic, nonlinear systems with
stochastic elements. Ban mol (1977) reviews these methods,

17
economic Hoels
A good review of models of the spatial distribution of
economic activity can be found in Chorley and Baggett
(195"7). Most of these models can be divided into three main
groups, Central place theory is based on the fact that some
goods and services must be produced at "centers" and
transported to users (or the users must be transported to
the center). For a specific mix of goods and services there
is a limited range of distance from the center defining a
market area inside which the marginal revenue exceeds the
marginal cost. In a homogeneous plane with only one type of
qtood or service produced, hexagonal market areas are
theorized, since these would represent the closest packing
of the market areas with no overlap. Production of
different types of goods and services leads to hierarchical
arrangements of hexagons, with different levels of central
places producing goods and services with different market
areas. Original works in this area are by Christaller
(1931) and Losch (1940) Berry and Pred (1961) provide a
review. location theory postulates that economic activity
will occur at the point of minimum total transport cost.
Transport cost surfaces for each of several inputs and
outputs of a specific econom5.c activity are estimated and
overlaid to find the point of minimum total transport cost
(Weber 1909), The approach is highly amenable to computer
applications as well as to the inclusion of costs other than

18
those normally taken Into consideration. See Smith and Lee
(1970) for an example. The overlay system used by HcHarg
(1959) is essentially a location theory model in which
environmental degradation costs are to be minimized.
Objective procedures for estimating environmental costs have
limited the application of this technique. Rent theory is
another extension which attempts to minimize the sum of rent
and transportation costs (Tujnovsky 1972).
Previous studies of economic location have concentrated
on static, cost-minimizing models. The spatial simulation
models in this dissertation combine cost and benefit
concepts (in energy terms) in a dynamic framework. The
gravity model is so called because Its mathematical form is
analogous to the gravity equation in physics, It predicts
that the amount of exchange between two centers will be
proportional to the product of center sizes divided by some
power of distance between centers.
Or:
where
id
KSiSj
/
d
a
ij
Yj_j Is some measure of exchange between
centers
3,Cj are some measure of the sizes of centers
d is distance between centers
K,a are parameters of the model
7)

19
In empirical studies, Yj_j is often the number of
people-trips between centers and S and Sj might be the
populations of the centers. Isard (1975) reviews these
concepts and applications. The generalized gravity relation
was incorporated in the spatial simulation models developed
in this study.
Simulation Models
Simulation of dynamic, nonlinear systems of equations
can be accomplished by solving differential or difference
eguations using a computer. Examples of simulations of
economic and ecologic systems are those by Forrester (1961,
1969, 1971) and Odum (1971). The approach has been
expanding rapidly 5.n recent years with the decreasing cost
and increasing availability of computers. Hall and Day
(19*T_r) provide a compendium of recent, ecological simulation,
studies. Alfeld and Graham (1976) is a recent example of
simulation applied to urban systems. In outline, the
technique involves deciding on state variables or storages
for the system of interest and then writing a differential
or difference equation for the time rate of change of each
of these storages in terms of the other storages and any
external inputs. Given initial conditions for the storages
and a set of parameter values the computer simulates the
time course of each variable in the system. The solution
can then be compared with reality and adjustments made to
the parameter values.

20
ili ilsrli
Figure is a location map of the south Florida area.
The region boundaries were taken as the drainage basin
boundaries of the Kisslssmee-Fverglades basin. Extensive
background information was developed on the detailed spatial
evolution of land uses in this region as part of a study by
the Center for Wetlands, University of Florida, funded
through the Department of the Interior and the State
Department of Administration. This dissertation developed
as an attempt to answer some of the questions raised by
these previous studies. The reader is referred to Costanza
(1975) for characteristics of the mapped categories, land
use, energy data, and a detailed description of the mapping
procedure. Browder, Litttleiohn, and Toung (1975) provide
full color land use maps and a general overview of the
application of energy analysis to a region. The technical
report of the south Florida study (Odum and Brown 1975)
provides detailed data encompassing the full range of energy
and environmental problems facing south Florida, Zucchetho
(1975) provides a detailed systems analysis of the Hiami
urban area


22
o

nSTHODS
Dp script-ion of the Modeling Language
The energy circuit language developed by H. , Odum
(1971) was used for illustrating the structure of the
models used in th5_s dissertation. The symbols of the
language have associated mathematical functions which allow
the energy circuit model to be translated directly to
differential or difference equations for computer
simulation. The symbols used in this thesis are summarized
in figure f. ?. complete description of the symbols and
their mathematical connotations can be found in Odum (1971)
and Odum and Odum (19^6) .
Symbolic modeling languages, such as Odums (1971)
energy circuit language, Forresters (1961) industrial
dynamics language, analog computer diagrams, and others are
useful for concise conceptualization and presentation of
complex networks of flows and storages. Diagrammatic
languages allow immediate comprehension (once the language
is understood) of the connectivity structure of the model
while conveying the same mathematical content as
differential equations which require much closer inspection
before the overall structure is apparent.
23

24
ENERGY SOURCE (FORCING
FUNCTION),
HEAT SINK, OUTFLOW OF USED ENERGY.
ENERGY INTERACTION, ONE TYPE OF ENERGY
AMPLIFIES ENERGY OF A DIFFERENT
QUALITY.
ECONOMIC TRANSACTION AND PRICE
FUNCTION.
Depreciotion
STORAGE (STATE VARIABLE)
ON-OFF CONTROL WORK (DIGITAL ACTIONS)
GROUP SYMBOLS (I) AUTOCATALYTIC SELF
MAINTENANCE UNITS, (2) PRODUCTION UNITS,
AND (3) GENERAL PURPOSE BOX FOR
MISCELLANEOUS SUBSYSTEMS.
Figure 5.
Energy circuit language symbols used in
this study.

25
H2£ I2SZSIQ.ESSI1;
A model is an abstract representation of a structure or
process which is constructed to aid understanding.
Development of an appropriate model is guided by the
questions being ashed, the general principles which the
model employs in answering these questions, and the amount
of time and effort which can be devoted to the modeling
effort, including data collection and evaluation. ^here are
several classes of models but this dissertation focuses on
mathematical models of the dynamic nonlinear type. Several
authors, notably Forrester (161) Nicolis and Prigogine
(1971), and Odum (1971) have argued that questions of time
behavior in living systems can be adequately addressed only
with models of this type.
The topological structure of each model was developed
by deciding on the internal components and external forcing
functions to be considered and then making assumptions about
the interconnections, vhe models were evaluated with data
from real situations. The simulation results were compared
with observed historical trends to determine the accuracy of
the original, assumptions. "'hese were modified as necessary
to improve the fit.
Dynamic Optimization
The general method of Lagrange multipliers was employed
in the development o* the power maximizing simulation

26
models. Baumol (1977) contains a readable description of
this technique, In essence it allows a static, constrained
optimisation problem to be translated into an equivalent
unconstrained problem using the device of the Lagrange
multipliers. This method yielded the general conditions
necessary for optimum (maximum power) behavior of the system
at each point in time. In algorithim, which employed these
conditions in a dynamic simulation framework, was then
developed and tested,
Hp delJ no Hethod s
Both analog and digital simulation procedures were
utilized in this study. The main advantage of the analog is
the "hands on" interaction with the model that its small
size and continuous operation facilitate. For these reasons
an TIT HiniSc analog computer was used to simulate a
simplified, two component, unsealed version of the model.
This allowed investigation of some theoretical aspects of
the model and the range of behavior which the model could
produce. n analog diagram of the model is given in
appendix IT.
Digital simulation requires integration by discrete
approximation and is therefore theoretically lass accurate
than the continuous integration possible on an analog
machine, niscrete integration quickly approaches the
accuracy of continuous integration as the size of the

27
integration interval is reduced or the order of the
numerical method is increased, however, The main advantage
of the digital machine is its large capacity, allowing the
simulation of much more complex models than possible on
available analog machines.
An Amdahal digital computer was utilized for
running the large models of the U.S. economy and south
Florida for which detailed data were available. The models
were written in FOTTRAN using a rectangular integration
scheme. Listings of the FORTRAN programs are given in
Appendices TIT, VI, and VII, An Intecolor microcomputer was
also utilized for testing some mid-sized versions of the
models in BASIC,
node!_ Parameter Estimation, validation and Testing
Dynamic simulation models of the type used in this
study require a large number of parameters. Frequently,
there are not enough data available to calculate statistical
best fit estimates of the parameter values. Therefore,
initial estimates of the parameter values were generated
from the available data and these initial estimates were
adjusted iteratively until a reasonable fit was obtained
between the model and reality. The adjustment process was
limited to the least well known parameters and required
additional information about the historical behavior of the
system being modeled to compare with the model*s output.

28
This calibration or validation of the model was performed by
manually adjusting the model!s parameters. The
discontinuous nature of the simulation models made the use
of nonlinear parameter optimization computer programs for
fitting the model to the historical data impractical. This
was because all of these algorithms (short of brute force)
require a continuous error surface to operate efficiently.
Input-Output Techniques for Calculating Embodied Energy
The application of input-output techniques (Leontief
19ft1) to the study of direct plus indirect energy
consumption was developed and documented by the Energy
Research Group at the Center for Advanced Computation,
University of Illinois (flerendeen and Bullard 197ft).. The
technique consists of defining a set of energy balance
equations (one for each sector) and solving the resulting
set of simultaneous linear equations for the energy
intensity coefficients vector e, which is the energy
required directly and indirectly to develop a unit commodity
flow. The underlying assumption of this technique is that
embodied energy is a conservative quantity. Figure 6 shows
the hasic "energy balance for sector j.
where
X^j is the transaction from sector i to sector j,
Xj is the total output of sector j, part of which
may be net change in storage.
/
ej is the embodied energy intensity per unit of Xj

29
(a)
Figure 6.
Single sector energy balance.

30
for this concept of embodied energy.,
Ej is the external direct energy input to sector j,
Thus the energy balance for the jth component is:
n
-j -j^
13
1 = 1
In matrix notation for all components:
(8)
F = e (X-X)
(8)
Here F is a vector of direct external energy inputs, X
is a diagonalized matrix of output flows, X is a matrix of
input flows and e is the vector of total (direct plus
indirect) energy embodied in a unit of outflow,
He can solve for e as:
e = E(x-x)
(13)
A simple example will clarify the procedure. Consider
a three-sector economy consisting of an agriculture sector,
a manufacturing sector, and a consumers sector as shown in
Figure 7 and Table 2.
The economy is represented both in energy flow diagrams
(Odum 1971) and corresponding input-output tables with all
the steps from physical flow units to embodied, energy units
detailed. For simplicity the economy is at steady state

31
Figure 7.
Hypothetical three sector economy with all
flows in arbitrary physical units.

32
Table 2. Input-output, transactions table in arbitrary
physical units, corresponding to the diagram in
Figure i
To
From
.1 gr
cil ture
1
Manufac
turing
2
Con
sumers
3
Met
output
73 tal
Output
hgriculture 1
10
5
5
10
30
Manufacturing 2
10
eg
30
10
100
Consumers 3
.25
. 25
1
.5
2
Energy input E
3 on
700
-

33
imply5.no no net change in storage over the accounting
period. For systems not in steady state, any change in
storage can he accounted for in the net output column.
In reading the input-output table, the output from a
sector to other sectors is read as a row. In this example
agriculture (sector 1) delivers 10 units of output to
itself, 5 units to manufacturing (sector 2) 5 units to
consumers (sector 3) and 1 units to depreciation (net
output). Inputs to a sector are read as a column. In this
example consumers (sector 3) receive 5 units of agricultural
products (from sector 1), 30 units of manufactured products
(from sector 2) and 1 unit from themselves.
To convert to embodied energy units, first calculate
the energy intensity vector e, by applying the equation:
e = E (X-X) -1
In this example:
30 0
0
10
5
5
X =
0 10 0
n
X =
10
50
30
o n
2
.25
. 25
1
(X-X)
on -q -5
-10 50 -30
[300 ?no 0]
25
25 1

34
(X-X)_1=
.0618137
.0254505
,03131 82
n090n0
.0272737
.0790909
.5818182
.9450545
1.3813182
e = P (Mf1 = [ 36. 364 21,818 836.36Q]
To convert the original physical units into embodied
energy units multiply the energy intensities (e*s) by the
appropriate flows. This yields the values shown in Figure 8
and Table 3.
This embodied energy input-output table exhibits soma
of the same characteristics as a dollar value input-output
table. The total output from any sector equals the total
input to that sector and the total net output, or 'final
demand'* in the economic terminology [1000 in this case), la
equal to the total net input, or "value added" [the F.
vector, also 1090 in this case) Final demand refers to the
dollar value of the net output of the system, while value
added refers to the dollar payments for the net inputs to
the system. "he total final demand or the total value added
is defined In the national income accounts as the Gross
National Product (GNP) This would Imply a GNP for the
hypothetical economy of 1009, However, the conventions used
in the national Income accounts are not the same as those
followed here. To demonstrate the relationships, eur
example economy's X-0 *-able can be converted Into one
consistent with the national accounting conventions.

35
Figure 8.
Hypothetical three sector economy with all
flows in embodied energy units.

36
Table 3, Inpat-output transactions matrix in embodied
energy units, corresponding to the diagram in
Figure 8,
"o
From
Agri
culture
1
Hannfac
turing
A
Con
sumers
3
Net
Output
Total
output
Agriculture 1
363.6
181.0
181.8
363.6
1090.8
Kanufacturing 2
210. 2
1090. 9
654,5
218.2
2181.8
Consumers 3
209. 1
836.9
418.2
1672.7
Energy input F
onn
700
toon
Total input
1090.0
2181.0
1672.7

37
The major differences concern the treatment of
depreciation, the exogenous energy inputs, and the consumers
sector. In the national input-output accounts, the
depreciation is credited to the value of the output to
consumers. The consumers plus the net output are the final
demand sector. finally, the feedbacks from consumers are
considered to be exogenous and are added to the other
exoaenous Inputs. These modifications lead to the flow
diagram and input-output table given in Figure 9 and Table
4, respectively.
"he interindustry" flows are not affected, and neither
are the total inputs and outputs from the remaining
endogenous sectors. The modifications have affected only
the "final demand" and "value added" categories and their
common sum, the G9?. The GHP is now 1418.1, which is
greater than the previous total of 1000 by 418.1, the
depreciation of consumers. "'he economic accounts aggregate
the consumers sector with final demand and value added.
It is interesting to note how the results for the
energy intensities (es) would differ if the standard input-
output conventions were followed. Returning to the original
physical flow matrix (Table 2) and ignoring the input from
consumers yields:
30 0
1C
5"
T =
0 100
10
50


Figure 9.
Hypothetical three sector economy cast in
the format of the national input-output
accounting statistics.
-HP

39
Table o. Input-output transaction matrix corresponding to
the diagram in Pig, 9 using the national input-
output conventions,
Prom
To
Agri
culture
1
Manufac
turing
2
Consumers + net
output or
"final demand"
Total
output
Agriculture
1
353,6
181,0
545. 5
1099,8
Manufacturing
2
210. 2
ioon,9
872.7
2181,8
Energy input
+ Consumers or
"value added"
509, 1
909.1
198 1. 1
Total input
1090, 9
2181.8

40
X-X =
_5
1f?
50
(300 700)
tX-X)
.0526316
.0105263
005632
0210526
9= o (7-7) 1 = {23,153 16.316)
This is substantially different from the result with
consumers endogenous.
The lower energy intensities that result from an
exogenous consumer sector are due to the fact that the
consumer services (labor) contain embodied energy that is
ignored when this approach is used. An alternative to
having an endogenous consumer sector would, be to calculate
independently the consumer services energy intensity, and.
use the coefficient to include the energy embodied in
consumer services as an input.
In this example, the intensity of consumer services
(e3) was calculated as 836. 36 when consumers were
considered to be endogenous, This number can be used to
include the energy contained in consumer services in the
direct energy input vector (the 5 vector) while leaving
consumers exogenous. The new F vector is:
V; = [30 0 + 25 (836. 36) 700 + .25 (836. 364) ]
= 6509.0^1 909.091]
Recalculating the energy intensities using this 3 vector
yields:

41
- -1
e = T, fl-X)
[ 599.091 909.091]
.0526316 .0052632
.0105263 .0210526
_
e = [35.364 21.818]
These are the original energy intensity figures.
This approach requires an independent calculation of the
energy intensity of consumer services, however.
The approach considering consumers endogenous is more
in keeping with Leontief*s original conception of a closed
(except to energy) economic system, It also does not
reguire the independent calculation of the energy intensity
of consumer services. It does, however, require some
manipulations to extract the relevant data from the current
accounting scheme.
Double Counting
hn often raised question concerning any accounting
scheme involves double counting. This is especially true of
input-output schemes that display all intermediate flows.
The question becomes clear with reference to the preceding
diagrams and. discussion. It is strictly a question of
accurately defining boundaries and making note of those
flows crossing the boundaries (net flows) and those flows
remaining within the boundaries (which when added to net
flows yield gross flows). Double counting problems are
encountered when the boundary is shifted, but the

42
redefinitions of gross and net flows (which are defined only
with reference to the boundary) are not made. For example,
consider Figure 9 Here a boundary has been drawn around
the "industrial' sectors of the economy with the consumers
outside the boundary in the manner of conventional
macroeconomics. The net output of the industrial sectors
(that which crosses the boundary to consumers) is defined as
the gross national product (GNP), The confusion starts with
this misnomer, since the GPP is really a net flow. The
total output or "total transactions" would be a measure of
the true gross product. If the boundary is expanded to
include the consumers, then the GPP is no longer a net
outflow but an internal transaction. The net output with
the expanded boundary would be depreciation plus net exports
plus any change in internal storage. Conceptual problems
with double counting arise when this is not realized and the
now internal transaction from producers to consumers is
still considered to be.a net outflow,, tiding the flow from
consumers to producers to the flow from producers to
consumers would obviously be double counting the GNP as
previously defined, With the expanded boundary, however,
the GPP is no longer the net output from the system and
should be treated like any other internal transaction.

43
Economy Data Assembly and Evaluation
The major ata sources for the O.S. economy model were
the Bureau of Economic Analysis (BEA) input-output tables
(along with their associated amplifying articles) and
Kendricks (1176) estimates of capital stock and investment
time series. Other statistical sources were consulted as
needed.
The year 1967 was used as the base year for data
collection since this was the most recent year with measured
input-output data. Bata from the 19f>3 input-output study
were also used and reference was made to previous input-
output studies back to 1919.
I.eontiefs (1941) original exposition of input-output
analysis envisioned a completely closed economic system.
Since then the convention has been to view households and
government as part of "final demand, and to treat them as
exogenously determined. The original, all-inclusive view of
the economy was deemed necessary in light of the objectives
of this study. Thus, certain modifications to current
accounting conventions were required. The input-output
statistics were modified to achieve a completely "closed
(in the thermodynamic sense) system. This means that only
energy crosses the system boundaries. To achieve this goal,
households an* government were brought within the system
boundary (made endogneous) as were a "O.S. environment

44
sector and a rest, of the world sector. The conventional
X-0 sectors were aggregated to 10 major groups, making a
total of sectors. Figure 10 is an energy circuit diagram
summarizing the accounting scheme employed in this study,
All flows and storages of energy and matter in the world are
included {at least in an aggregated form) in this accounting
f ramework.
Government and Households as Endogenous Sectors
In order to make households and government internal
(endogenous) components in the accounting framework, certain
modifications to current accounting conventions and
approximations were necessary. Figure 11 illustrates the
problem. The household sectors inputs from the other
sectors were measured as personal consumption expenditures
(PCF) which are the dollar payments of individuals for
goods and services from the producer sectors, The
exception is the input to households of government services,
which are paid for with federal income taxes, along with
state and local government taxes on households. The outputs
of the household sector to the other sectors are labor
services, which show up in the accounts as the employee
compensation category. Complications arise since the input -
output accounts separate value added (or VA, defined as the
payments to the factors of production) into only three
categories: (1) employee compensation, (2) indirect



Figure 11. Diagram showing definitions of national income variables.
-j

48
business taxes, and (3) property type income. Table 5
shows the relationship of these categories to the national
income and produc4- accounts categories. The implied wages
of self-employed people or unpaid family workers are not
directly included in the employee compensation category but
show up as a portion of proprietors income, which is
embedded in the property-type income category of value
added. Similarly, corporate profits taxes, which are also
embedded in property-type income, should be added to
indirect business taxes to determine the total taxes paid by
business to government.
a detailed examination of questions relevant to the
proper distribution of value added to the economic-ecologio
sectors was not possible during this study. Certain
approximations were therefore made to derive the estimates.
Value added was distributed by crediting all employee
compensation (EC) plus a fraction of property-type income
(PTT) to households and all indirect business taxes (IBT)
plus a fraction of PTT to government. The fractions were
calculated using balance considerations, and the fraction of
PTI remaining after government and household's shares were
removed was considered a net profit attributable to inputs
from the environment (see the following section).
The X-0 accounting framework requires that the sum of
the total dollar value of the outputs from a sector equal
the sum of the dollar value of the inputs. This requirement

49
Table 5, Relationship of input-output value added
components to the national Income and product
accounts categories.
Value added components
in the Input-output.
(1-0) accounts
Value added components in the
national income and product
(NIP) accounts
Employee compensation Employee compensation
Indirect business taxes Indirect business taxes
Property type income Proprietors income
Rental income of persons
corporate profits (before taxes)
Inventory valuation adjustment
Pet interest
Business transfer payements
Surplus of government enterprises
Capital consumption allowances

50
was usea to sot up accounting identities for the new
household and government sectors, which could he solved for
the percentages of property-type income to be credited to
each sector in order to balance the accounts. This is
admittedly only an approximation which was necessary due to
the lach of data on the allocation of value added in the
input-output accounts.( Gross investment and net exports
were assumed to exactly balance against net profits. This
left the following identities. For the government sector:
IB" + Xg*(?TT) + PT = GP + GS {11)
where
Xg = fraction of PTI to Government
IB? = Indirect business taxes
PTI = Property type income
PT = Personal taxes
op = Government purchases
GS = Government salaries
So the fraction of PTI to government necessary to balance the
sectors accounts is:
Xg = [GP + GS IB" PT] / PTI (12)
For the household sector:
FC + Xh* (PTI) +GS = PCE + PT (13)
where
Xh = Fraction of PTI to households
FC = Employee compensation
PTI = Property type income
GS = Government salaries

51
PCS = Personal consumption expenditures
PS = Personal taxes
So, the percentage of PTI to households necessary
to balance the sector's account is:
Xh = [PCF. + PC EC GST / PTI (14)
Che remaining fraction (call it Xe) was considered a net
profit:
Xe = 1 Xg Xh (15)
Using data from the statistical abstract of the U,S,
(United States Department of Commerce 1971) and the bureau
of economic analysis input-output tables (United States
Department of Commerce 1969b, 1974a, 1975) the following
values for Xg and Xh for 1963 and 1967 were estimated.
Por 1963: (in millions of dollars)
Xg = [GP + GS 1BC PC] / PTI
= [6B167 + 55 93 54627 61099 ] / 194243
= 9 399
Xh = [PCE + PC EC GS] / PCI
= [ 375549 + 61^0 341514 55030 ] / 184248
= 29 59
Xe = 1 Xg Xh = .7551
Por 1967; (in millions of dollars)
rg = [GP + GS TEC PC] / PCI
= [ 'T465 + 31654 79239 83009] / 254969
Xh = [PCB + PC BC GS] / PCI
= [499669 83999 339436 81654] / 254969
49 37

52
Xe = 1 Xg Xh = 4944
Figure 12 summarizes the modifications to the i-o
conventions made for this study.
FnvIronmental Inputs
?is with household and government services, there are two
ways of including environmental services. One is to treat
the environment as an exogenous entity and guantifv its
inputs to the economy. The second is to treat the
environment as an endogenous sector with flows to and from
the other sectors in an integrated economic-environmental
system. Both of these approaches were utilized in this
study.
In exogenous environment sector was hypothesized for 22
sector input-output studies of energy flow through the B.S,
economy. These studies were carried out in collaboration
with the Bnergy Hesearch Croup, Bniversity of Illinois at
Champaign. For this analysis the solar energy absorbed by
the tt. 3. was partitioned to tie economic sectors according
to land and water area. Table 6 shows the land and water
use distribution for the n. s. and estimates the total solar
absorption {including atmospheric) for the various uses,
The agriculture sector was credited with the solar
absorption over all agricultural land plus 34*5 of the
absorption over the wetlands, desert, and tundra category,
as agriculture represents of the remaining land and

NET INPUT
Capital Consulption Allov/onccs and
Payments to Land and ResourcessXo*PH
TOTAL INPUT
Figure 12.
Summary of modifications to the input-output conventions.
tn
u>

54
"able 5. Estimate land areas and solar absorption for
major land use types.
Area (a)
(76 acres)
Average solar
absorption (b)
(E9 Btu/ac-yr)
Total solar
absorption
(718 Btu/yr)
Total land
2254
28
33.9
Agriculture
1212
Cropland
38 4
grassland pasture
54 0
Grazing land
288
Forestry
587
28
16.4
Woodland pasture
62
Woodland (not pastured)
5 0
Forest land
475
Wetlands, desert 5 tundra
27 2
20
5.4
urban 8 mining
193
20
3. 9
Total water
1550
28
43. 4
Inland T, estuarine.
50
Offshore (209 mile limit)
1500
Total land plus water
3814
10 3. 0
a. rrom united States Department of Commerce (1976a).
b. Estimated solar absorption of the earth-atmosphere system
(Pu'lyko "978, Haar and Suomi 1969).

55
water use. This amounted to 35.74 E18 Btu solar/yr. The
forestry and fisheries sector was credited with the
absorption over all forested areas plus estuaries and
coastal water to the 300 mile limit plus 605 of the
wetlands, desert, and tundra absorption. This amounted to
63.06 E^B Btu solar/yr. The remaining 4.20 E18 Rtu solar/yr
represents direct utilisation by the remaining industrial,
commercial, residential, and governmental sectors of the
economy. This should be distributed to the remaining
sectors according to their total land areas. Accurate land
use data are not available at this level of disaggregation,
however. As an approximation, the entire 4.20 E18 Btu
solar/yr was credited to the household category since this
category represents about 755 of the remaining land area,
An Endogenous Environment Sector
A more conceptually satisfying method of including
environmental services is to treat the environment as an
endogenous sector. This sector contains all the land, air
and water in the n.S. and performs the essential task of
capturing solar energy and converting it into other forms
more usable by the economic sectors. Since the environment
sector is not completely "owned bv economic agents and
competitive markets do not exist for many of its products,
economists have difficulty evaluating many of the flows and
storages in this sector, A broader perpsective based on
A

56
energy flows has proved useful (Odum, 1971; Bayiey et al,
19 75) in conceptualising this problem.
For the purposes of this study it was assumed that,
where competitive markets exist, market values were
proportional to embodied energy content and that both of
these could be considered to be conservative guantities.
Evidence for the validity of this assumption is presented in
the results section. Conservation of dollars and embodied
energy allows many of the flows to and from the environment
sector to be estimatd from balance considerations. The
input-output accounts are arranged such that the total
dollar value of all inputs to a sector equals the total
dollar value of all outputs from a sector.
Once the payments to households and government, and
capital flows have been accounted for internally, there
still remains an imbalance between the dollar values of the
sum of the inflows to each sector and the dollar value of
the sum of the outflows. There is still a "net input to
the sector or profit. 'his net input was attributed to
services provided by the environment sector. This is
essentially a pure economic rent conception of the origin
of profits. Tinder this view entrepreneurial capacity is a
component of the labor services input necessary to
effectively capture environmental inputs. At steady state
these environmental inputs would just cover the depreciation
of the economic system. The approach can also be viewed as

57
a form of "shadow pricing" (Dorfman, Samuelson, and Solow
1958} of environmental services,
£&£i£.i! Flows
Capital flows are normally not included explicitly in
the input-output tables, Data recently available from the
Bureau of economic Analysis (SCB Sept. 1975) on
interindustry transactions in new structures and equipment
combined with data from Kendrick (1976) on investment and
depreciation of human and government capital allowed the
inclusion of capital flows in parts of this study,
^or the purposes of this study the capital flows were
simply added to the existing interindustry flows. This
increased the total input to each sector by the amount of
capital purchased by that sector during the year and
embedded the years Gross Private Fixed Capital Formation
column in the current transactions matrix. The capital
purchases by each sector were then added as a "capital
maintenance and growth" column in final demand to balance
the additional input.
South Florida Land rise Data
A time series of three full color land use maps for th
years 19C0# 1953, and 1973 for the south Florida region wer

58
produced as part of the study, "Carrying capacity for man
and nature in south Florida", edited by H.7. Odum and H.
Brown (1075), The maps are also included in Browder,
Littlejohn and Young (1975) and Costanza (1975) with
supporting data. mhe maps were manually digitized using a
cell size of 128 acres for computer manipulation. For this
study, the land use maps were aggregated to 88 larger square
cells, 15 miles on a side, as shown in Figure 13.
For example, Figure 14 is a full size copy of cell 45
in Figure 13 from the 1973 land use map. Figure 15 is a
computer printout of the same data to show how it was
digitized. '"'he correspondence between the symbols on the
printout and the numerical codes for the land use subsystems
listed in Table is given below the printout. Since not
all cells had the same land area, the area include? in each
cell was calculated and recorded. The data in Table 7 (from
Costanza 1975) were employed to perform the aggregation.
The subsystem structure intensities listed in Table 7 were
multiplied by the number of acres of that land use type in
each of the 88 south Florida cells, and these values were
accumulated for each cell to yield estimates of the total
embodied energy in each of the cells. This was done for
each of the three land use maps. These data are listed in
Appendix I, along with the ".and area, and latitude and
longitude of the centroid of each cell.


60

61
Figure 14. Example of detailed land use data, showing
cell 45 in Figure 13 for 1973.

62
Figure 15.
4+-*: : : *+-*i>* v.+* *+++++: : **;* ** + : u: cc ++ +u"
: : +: ; : :+mmm*m444++ :=+*:=+++++ : : : c :: C+ :¡J
;: + + + + : *+-.im*** + + +1 1 1++:: + + i i+++c:c:+: ::
+++M +: ++MMMM* +++3 uik:: +++++C:: c :: ::
>m+ M++ + WMMWM :+++53iiii + -*-++***c:: : c:: : : ::
MMMM MM + + MMM+M 3 + + o 1 1 i** = *.*+++ **4 : i .
M.M + MMM MM M 335 5 3 : 1 1 =** + < *;+** *C* + Z : I '.+
MM3B-5=45: : .* + -M-C + -*++*c ?=** + + *-*
'33*544: : :: *++*:: **:: : +*-*c+
f.|,M jt *5*44i.tt4*'t-* + + + **C++,!1CC + i
fJIMiM
M M MMMMM
S5M MM M
55
1
!.!.(iM+ + +4444*< I + +-J- *++*Â¥CCC>
M MMM++++ :4-**H+**+++++C//+
MMM4+ + ++ : :ai**e***t + + tCC/-H-
MM M 4+ +++++++ + +**CCCCCC///
.M MM++++ + +++ *** **t+C*CCC///
M M MM + + + +++*+++**++***/c / / U
M MM+ff+I lili *U* = ;* + *:*CUUUUU
m mm i u++11111 ***:: +**ccuuuu
m mm + +++11114:**::**cuuuuu
m MMM+:: + n C4 ^ccuuuuu
Mc+ccc++cc4i:::::-ccccuuu
, CCC+-C 5C4a***::: cccc///u
mmm&cc+cc 144.44.344: : * MMMCCCC l 1 45554444.a ?¡CCCCC **
MMM 5 54++ 5555554 5 54 +++-*-5* *5 ++ ++ * * * C
?jc 55++.4t.+ aa:4cj!at>*j 5t M +++ c C * * * * C C =4 C * C C
g si: -4+- 4-f. + 36 56 56 J- I ; -ir 56 *C W W 36 Tp 3! C £
*3**+5 5*****>4: ::++****CC
r:5t55T5c; ; 56 36 35** .T£'4>6 5:3C CC
M>5'5XC56 5656 5R5;'^5e565Cw:* ; *C5s(^ CC
1 = 1
2=2
3 = 3
4 = 4
5=5
6 = 6
7 = 7
8 = 8
9 = -
10
=

19
=
(
11
=

20
=
U
12
=
&
21
=
w
13
+
22
=
B
14
=
*
23
ss
9
15
=
H
24
=
N
16
=
25
=
S
17
=
C
26
=
M
18
=:
/
27-34
=
Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973.

63
Table 7 Lane! use subsystem metabolism and structure
estimates in coal equivalents (CE).
Subsystem
Subsystem
Metabolism
: (E6 CE kcal
/ac-yr)
Subsystem
Structure
(E6 CE kcal
/ac)
1.Cleared land
0.7
5.0
5. 5
2. Lakes and reservoirs
3. Pscreational space
4. Pesiflential (light)
5. Eesidential (med. -dense)
6. Commercial/Tndustria1
7. Transportation
8. Power plants
9. Improved pasture
10. .Vegetable crops
11. Tree crops
12. Sugar cane
13. Grassy scrub systems
14. Pineland systems
15. Hardwood systems
16. Lakes and ponds
17. Cypress domes and strands
18. Pet praire
19. Scrub cypress
20. Freshwater marsh
7.7
24. 7
250.0
750.0
520. 0
2,250.0
1, 600.0
11,125.0
500. 0
2,000.0
4,000.0
126,000.0
5.1
24. 7
21.3
294. 8
9.6
74, 9
22.2
313. 1
4, 0
16, 5
6.4
80.1
7.7
235. 9
1. 4
7. 4
7.3
214.5
5.4
51. 6
5. 8
61.3
7.4
228. 7

64
Table 7, (Continued) .
Subsystem
Subsystem
Metabolism
(E6 CE kcal
/ac-yr)
Subsystem
Structure
(06 CE kcal
/ac)
21. Sawgrass marsh
8. 1
273. 7
22. Beach and dune system
0.3
4. 0
23. Salt flats
0.3
4. 0
2$. Scrub mangroves
1.0
7.2
25. Salt water marsh
5.0
29. 5
26. Mangroves
7.3
218. 4
Source: Costanza {1975).

RESULTS
Results include a derivation of the general conditions
for maximum power, development of an algorithim for
approximating the maximum power conditions in a dynamic
simulation model, and applications of the model. Some
features of the model were demonstrated using hypothetical
examples and the model was applied to a f-sector .S.
economy-environment and, a 91-cell spatial array for south
Florida. The embodied, energy intensity of goods and
services was calculated for 92 O.S. economic sectors for
four different alternatives concerning the treatment of
labor and government services and solar energy inputs. Data
were assembled on total capital stocks and flows and were
used to determine a better estimate of the mean energy
intensity for goods and services and to create "closed
system" input-output transactions matrices for the .S,
economy-environment at the 15-sector level.
"he General Conditions for Maximum Power

K major hypothesis of the simulation models in this
study is that complex living systems evolve so as to
maximize their productivity (or power as defined earlier).
65

66
here is a large literature on the various aspects of
optimization and specifically dynamic, nonlinear
optimization but these methods are generally not integrate!
with simulation studies, Wagner (1975) views simulation as
a last resort to be used only if all else fails. The
potential benefits of the integration of simulation with
optimal control theories are great, however. In this study
a simple algorithm for achieving this goal is developed.
The objective function is taken as the maximization of total
system power (Lotkas power principle as discussed earlier)
and the constraints deal with limits on the total amount of
free energy in the system and the exchange of energy between
components of the system. Power is maximized when an
optimal exchange network is used, and this network changes
through time,
The problem can be stated in the mathematical framework
of nonlinear programming for each point, in time as follows,
maximize PT = Px CQ1,Q2* * Qn/%) +
?2CQi#Q2'***'Qn'E2^ + ** +
Pn 1* C2f * Qn#
subject to Q-l + Q2 +...+ Qn = Ct
- Kit nfi>
1 *2 = K2t
= K
nt

67
where
PT = Total power of the system, equal to the sum
of the n individual components
= Powec lb individual components as
functions of the embodied energy storages
in the system (Qp, Q2 ,. Qn) and the direst
energy inputs E2* ** En)
The constraints indicate that at any point in time the total
embodied energy in the system is equal to some constant
value Ct, and the direct energy inputs are equal to
constants (Knt ). The optimization of the system involves
moving the scarce (limited) embodied energy around to elicit
the maximum total system power.
The problem can theoretically be solved using the
method of Lagrange multipliers. Certain additional
conditions must be satisfied to assure the existence of a
solution. Wagner (1975, p. 604) outlines these conditions.
They are divided into two groups, one for the constraints
and one for the objective 'function. Since the constraints
are all linear in the above system, only the objective
function need be addressed. The conditions for the
objective function are:
(1) Up is single valued and finite for each Q and E
satisfying the constraints
(ii) Every partial derivative (3PT/3Q^, is singla
valued, finite, and continuous at each 3 and "
satisfying the constraints

68
(iii) ?T possesses a finite maximum fPT) over all
values of Q and B satisfying the constraints
(iv) PT is concave over all values of Q and E
satisfying the constraints
These conditions guarantee that
(1) There exists at least one feasible solution
(B) If PT is strictly concave, then there is a unique
optimal solution
(C) If Q, is a constrained stationary point, than
Q, B is a global optimum
It will be shown in a later section that the specific
objective function chosen meets the above conditions.
The Lagrange multiplier technique involves craating a
substitute problem that incorporates the constraint
equations into the objective function. This new equation,
called the Lagrangian, can then be maximized (or minimized)
using standard calculus techniques. The Lagrangian
expression for the above system is:
L = P]_ (Q]_fQ2'# ** Qn'El> + p2^1'Q2'* Qn'E2> + * +
^2' ^l^t ~ Q l ~ Q 2 ~ Qn) +
V2^1t~ "l> + V3{K2t- ... Vn+1(Knt- En) (17)
where
vl,72# * ,7n+l are unknown Lagrange multipliers
To maximize the original constrained system, one then
maxIm5..zos the unconstrained Lagrange expression (L) by
writing the partial derivitives of L with respect to all the

69
variables (including the v*s) an setting them all equal to
zero:
91
3pi
9P2
9Pn
=
+
+ +
- ?
= o
3Ql
3Q^
3Q¡"
?Q-
1
31.
dV
3P?
9P
=r
X
+
z
+ +
n
v
= n
q2
q2"
io2-
'l


9
-




9




*




91.
3P,
3P2
9P
=:
X
+
z
n
- V
= o
9pn"
Hq~
n
3Q~
n
1
3L
9P
=
X _
V, = n
9i¡
2
91,
9P
z _
^2
V = 0
3


*

9
* m


* 9
3T,
9P
n
ap
t*
n+1
O La
n
n

70
3L
3?
r o
t ul
Q ry * ** Q
2 n
= n
3L
3~
It
= n
(29)
3l
37
= Kr,4- Kr,
nt n
= 0
n+l
Thus there are 3n + 1 equations in 3n + 1 unknowns* In
this example the equations In groups (19) and (20) can be
Ignore! since they are simply restatements of the
constraints which specified that for a single small time
interval, the direct, energy Inputs can be considered as
constants. Thus to maximize or minimize the system the
following relations must hold:
8Pt
3?1
3P2
3P.

3Q
?o~
SQ*
3Q
3Pt =
3Pl
3r2
3P.
+ * +
9Q¡



9Q
9
*
9Pt =
a
3 Pi
a
3P2
9
3 P
]
4-
+ +
3*0
~]
= V,
= 7.
= V,
(21)

which says that the marginal total power of all the storages
should be equal in order to optimize the system. he
problem is then, how do living systems go about adjusting
these marginal total power conditions in a fluctuating
dynamic environment? One possibility involves adjusting the
interconnection network of the system by switching selected
pathways on and off, as shown in Figure 16. This does not
violate the condition (ii) that the partial derivatives be
single valued and continuous since at each point ia time the
functions are continuous. This approach simply modifies the
problem from one time step to the next.
Consider the potential exchange from component 2 to
component in Figure 16. The diagram indicates that the
pathway is open if:
9?t 9 Pm
> (23)
9Qq_ 9 Q2
If this condition does not hold then the pathway is switched
off. This would eliminate the term 9p1/3q2 from the
equation for 3PT/3Q2 since Q2 would no longer be a variable
in the equation for p^. his would lower 9pt/3q2 so that
the condition (23) would hold. By applying this decision

72
Two production systems and their exchange
pathways.
Figure 16,

73
structure to all pathways in a system over time one could
prevent it from diverging too far from the optimum. This
may be considered a form of the "feasible directions" method
outlined in Wagner (1975) .
s possibly more accurate but operationally more
difficult approach involves adjusting the model parameters
to achieve the des5.red partial derivative relations at each
point in time. The approach using the switches has an
effect similar to continuous adjustment of the parameters
but is operationally easier and acknowledges the physical
limits to parameter changes.
In alternative derivation of the conditions in (23) can
be formulated as follows. "he change in total power caused
by the exchange terms (Y-^2 an^ ^21^ ars composed of direct
and indirect effects. In the two component model shown in
Figure 16, the total power is a function of the storages,
direct inputs, and exchange flows.
PT = f(Qx, Q2r E1# F2, Y12 Y21 } (24)
The rules for total differentiation can be used to determine
dP /d7^2* or the change in total power caused by a change
in the exchange flow Y ^2.
one can
write;
3Pt
3Pt^ 3Pt 3Pt
9Pt
+ _dQ2 + ^^1 + ^2
+ dYio +
d?12
3QX
9P_
T ,
3Q2 SS-l ?.2
a Yon
9Y21
(25)
or:

74
SPT 3PT 351 3PT a02 3PT SE1 3PT 3PT
5L IQi ^12 "^2 3*12 3S], dY^ **12 12
3P ai
T
21
9Y2iaY12
(26)
The third and fourth terras on the right hand side can be
dropped since Eand E2 are exogenous and.Y12 has no effect
on them, thus:
dT
dE
(27)
12 1*12
Since embodied energy units are used throughout, some
additional simplifying relations can be made for this model.
9Pt
9Pt
si
9Y21
ao1
1
ii"i2
dQ2 _
-1
di12
= 1
(28)
(29)
Dsing (29) and (30)
dl2i _
dQ2
ao
/
dY 12
3Y 12
di
2
21
-1
(31)
then:
or:
dP T
1 +
9 P,T
9Pt
dY 12
"9Q~
flPT =
9Pt
. 9Pt
di-i2
9 Q
3 Q 2
- 1
(32)
(33)

75
whore the eirst term on the right hand side of (33)
represents the "benefit and the second term the "cost" of
the transaction Y12 In a dynamic simulation framework, a
transfer from component 2 to 1 (?12) is seen as beneficial
(leading to increased total power) if?
aPm
>0 (34)
dYi2
or (using 33) if:
3Fm 9Pm
os)
SQi 9Q2
which is equivalent to (23), Thus, allowing the pathway
switches in figure 16 to remain open as long as conditions
(35) and (23) hold will tend to maximize the total power of
the system, .
P^yejopmont of a Power Maximizing Hi mula tign Model
A specific model structure and an algorithm for
approximating the maximum power conditions in a dynamic
framework must now be developed, for application to real
systems. The model equations will always represent a
compromise between simplicity (and therefore manageability)
and accuracy. Here the mathematical form of the model
(including the power maximizing algorithm) is laid out,
first for a simple two component case and then for the

76
general case of n components. It should be noted that this
specific model is not the only conceivable way to achieve
the maximum power conditions derived earlier in a dynamic
system. It is only one of a number of possible approaches,
Figure 17 is an energy circuit diagram of a simple two
component version of the model in Figure 16, showing the
specific producti.on function chosen. The differential
eguations for the model are given in Figure 13. The choice
of a production function was difficult, since it involved a
compromise between accuracy and simplicity. The production
function chosen was built up from simple, slightly nonlinear
"partial production functions, which exhibit the important
characteristic of diminishing returns.
The algorithm involving the switches on the exchange
pathways in the model is a simplified method for
approximating the maximum power conditions in a complex
dynamic system. The switches are intended to maximize the
total power fPi+P2) in the system by allowing only those
exchanges that lead to a net increase in total power during
a particular small time interval. This function may be
handled in nature by the mechanism of natural selection.
The system of eguations is allowed to "evolve" by changing
its connoctivity structure as it progresses through time.
The technique is analogous to a "cost-benefit"
calculation for each potential exchange pathway for every
point in time. The "cost" is the loss of productivity due

on if
on if
£Pt > ££t
dQ¡ dQ2
d P-, d P-r
<3Q2 3Q|
PT = P, + P2
Figure 17.
Energy circuit diagram for a two component
power-maximizing model of exchange.

Figure 18.
Differential equations for the model in
Figure 17.
where
Ch C>2 = embodied energy storages in
components 1 and 2
E^, E2 = direct energy inputs to
components 1 and 2
a1, a_ = direct energy input co
efficients for components
1 and 2
1*12' = transfer coefficients
for exchanges from com
ponent 2 to component
1 and from 1 to 2
respectively
b,. b99 -- internal transfer
coefficients
c., depreciation rates for
components 1 and 2
total embodied energy
productivity (power)
of the system, given
by the first three terms
in the equations
Y.0, Y?1 = exchange flows from com-
^ ponent 2 to 1 and 1 to 2
respectively, given by the
third term in the equations
change in total power
with respect to the system
storages (Q. and Q^) all
else being 1equal
t
3 Qx 3Q2
p =p +p =
a 1 2

otherwise
b21Q2Q1
SPT SPT
if
1 + b21Q2
3Q.
5Q
1
otherwise
-C1QX
a2E2^2
b22Q2
+
+
1 + a2Q2 1 + b22Q2
QoQi
3Pt 3Pt
if
1 + k2lQ2
3Q2 3Q-L
otherwise
+
b12QlQ2 9PT
if
3P.
T
1 + b12l
3Q, 3Q.
otherwise
C2^2
(36)
(37)

80
to a decrease In the contributing components storage, while
the "benefit Is the gain in productivity Sue to an increase
in the receiving components storage. since the models
production functions are differentiable, single valued,
finite and continuous at each point in time, an optimum
distribution of the storages exists for any point in time,
and the exchange network is adjusted to move the system in
that direction. as already noted, it is necessary to have a
common currency in which and ?2 are expressed in order to
perforin this calculation, This study employs embodied
energy as the common currency.
The equations require some explanation. Each of the
individual partial production functions (indicated by the
work gate symbols) are given a relatively simple "limiting
factor" form, This is equivalent to saying that there are
Infinitesimal storages In the flow (shown by the small tanks
in the diagram), that limit the amount of source material
which can be used. & derivation of the partial production
equation follows. Consider a system given by the anergv
circuit diagram in Figure 1q and the equations below (Odum
and Odum lO^S) .
(38)
(39)
Row assume that QT is an infinitesimally small storage wihh:
Qt = 0 and k^ = 1 (turnover = 1 COT,). This yields;
rC)
Solving for 0T

81
Figure 19.
Diagram illustrating the partial production
function relations.

82
Qt = 8/(1 + R4Q-L) {41}
Substituting (41) in (3 8) yields:
Qg = kjSQ-j/O + k^Qj) \2Qi (42)
<\ further simplification was that since in
embodied energy terms all of the inflow is embodied in the
input to the tank. The total production function for each
component was created by adding together partial production
functions of the form given above. The power maximizing
logic built into the model was used to decide which partial
production functions were included in the total at any point
in time. In differential form the logic is hard to follow,
since it simultaneously uses one decision to make a second
decision, which is used in making the first decision. The
equations can also be expressed in difference form (which is
necessary for digital computer simulation and is done in a
following section) to clarify the logic. For now one can
imagine a tiny delay between one decision and the next.
The equation (38) for the rate of change of storage in
component 1 has five terms. The first term determines the
rate of captmre of direct external energy (Tj) as a function
of the amount of stored assets (Q-jJ and the capture
coefficient a^ The second term determines the amount of
internal interactions within component 1 as a function of Qj
and the coefficient b^. Tie third term determines the
amount of transfer from component 2 to component 1 with a
maximum power constraint. If the transfer is deemed to be a

83
net Increase in total power at a particular time, then the
rate of transfer is the given function of the stored assets
of the two components (Q^ and Q2) ani^- transfer
coefficient h12* from (36) and (37) the following
expressions can he derived for the above partial
derivatives:
9 V.
T al^l ^ll0!1 + fbllQl}
b122l
9% (1+a1Q1)2
(1 + bllQl)
(1 + bl2QlP
9Pt =
b21 ~2
^ + b21^2
a2K2
3Q2 Tl+i2Q2}2
b12 1
2^b22^2^ + -h22Q2^
^"+b222^
1 + b12Ql
(U3)
b21Q2
lT7b"Q¡) 2
(hQ)
The fourth term in equation (36) is the (potential)
outflow to component 2. It is subject to decisions
analogous to those discussed above for the inflow from
component 2 to component 1 The last term in equation (36)
is the depreciation term, which was assumed to be a linear
function of the quantity stored* Thus, c^ is the
depreciation rate for component Vs storage.
The model can be easily expanded to n components.
Figure 22 is a difference equation representation for one
component in an n component version of the model. In
applications of the model the components can be sectors in
an economy, areas of land, trophic levels in an ecosystem,

84
or any other suitable subdivision of the system under study.
The difference equation representation makes statement of
the logic sequence easier. In Figure 20 the partial
derivitives are calculated at time t-At for making decisions
at time t. The summation signs indicate that there are
potential exchanges with each of the n-1 other components in
the system, at each time step.
SB3 Two Components
To investigate the range of behavior that a two
component version of the power maximizing simulation model
can exhibit, some hypothetical situations were set up and
simulated on an EAT Finite analog computer. An analog
computer diagram of the model is given in Appendix II. The
simulations also served to test the power maximization
algorithm. This was done by constraining the system to
operate with the switches either always on (always
exchanging) or always off (never exchanging) and comparing
this with the unconstrained situation where the switches
were allowed to perform their normal role, The algorithm
was deemed successful if, for the same coefficient settings
the unconstrained mode consistently led to a higher total
power in the model than a constrained mode. The model was
also run on digital computers as a check,
Four hypothetical cases were investigated with the
model. In the figures the plots labeled with exchange

Figure 20.
Component i difference equation
where
Q
i,t
= embodied energy storage in
component i at time t
E
if t
a
i
c
i
= direct energy input to
component i at time t
= direct energy input coefficient
for component i
= transfer coefficient for
exchange from component j
to component i
= depreciation rate for
component i
'3P
3Qi/ t
rate if change of total system
power (P ) with respect to
embodied1 energy storage in
component i at time t
'3P
T
k3Q.
= rate of change of total system
power (PT) with respect to
embodied1energy storage in
component j at time t

86
, t+At t +
n
j=l
a E . Q .
i l, t i, t
1 + a Q ,
i i,t
bijQi,tQj,t
1 + b 0
3-3 i/t
t-At
otherwise
j/ t-At
n
3=^
bjiQj,tQi,t
1 + bjiQj.t
t-At
otherwise
t-At
c Q .
i l,t

87
indicate the models behavior with the switches in the
unconstrained mode, while those labeled without exchange
indicate the behavior with the switches constrained to the
off position. The time and quantity scales are in arbitrary-
units, In general this two component version produced
almost identical behavior when the switches were left on as
when they were allowed to function normally. This indicated
that with only two possible exchange pathways, it almost
always pays in a maximum power sense to exchange, ^his
was not the case for a larger number of components where
more intricate exchange networks were possible,
Case 1; "Resource consumption. One relevant application
of the model is to the question of resource consumption.
Here one of the components represents a resource pool, A
resource pool can be operationally defined in the context of
this model as a situation where the external energy input
and the depreciation rate are both very low. For example,
the oil deposits of the Arabian deserts occur in low
productivity areas protected from deterioration by overlying
rock. In the language of the model this is a large storage
of structure whose incremental effect on productivity in its
local environment is very small. If another component
capable of utilizing the resource exists in close enough
proximity, the logic of the model would decide to export ho
this component in order to maximize power. Figure 21a shows
some simulation results for this situation. Both the

QUANTITY
88
(a)
(b)
Figure 21. Two component model analog simulation results.
(a) Situation when one component (Q^ in
this case) represents a resource pool.
(b) Situation when one component (Q2 in this
case) has no external energy source and
survives only on exchange with a
production unit (Q^ in this case).

89
external energy inflow and the depreciation of component 1
have been set very low, making it the resource pool in this
run. ^he plots labeled Tp are the accumulated power of the
two components used as an index of the success of the power
maximization routine {Tp = / (Py +1*2 ) dt),
mowing exchange in this case greatly increases the
total accumulated power of the system. Also, when exchange
is allowed, the standard curves (Odum 1971) for the
depletion of a large energy storage by an autocatalytic
consumer result. The difference between this model and most
other models of this relationship is that the resource tank
is not a completely passive system, but a dynamic system in
another area. To make the example more concrete, suppose
the resource area were Arabia and the consumption area were
the tt.S, Without trade, the resource (oil .in this case)
still has some productive value in its local environment
(e.g. in geologic processes or as a minor input to the local
economy) but this value is low compared with its value to an
industrialized economy. The model determines that exchange
will increase the total power; therefore oil is transported
from Arabia to the TJ.S. After a short time, however, a
backflow of tt.S. structure (goods and services) develops
since the model determines that they can be effectively
interacted with the remaining Arabian resources in Arabia,
This backflow tends to attenuate the rate of decline of the
resource as compared with its treatment as a passive storage
and is a more accurate picture of the real system.

90
Case 2: Production consumption pair. Another situation
to which the model may be applied is that of production and
consumption. In this situation one of the cells receives no
external energy of its own and survives strictly on exchange
with the producer component. The energetic rationale for
having a consumer population is that if the producers have
accumulated more structure than they can effectively use
{3Tp/3Q]_ is low), then the total power can be increased by
exporting some of the underutilised structure to a consumer
population, which utilizes it as its main energy source
f9Tp/9Q2 is high}., Figure 21b shows simulation results for
a producer population with an oscillating input approximated
by a sine wave.
The upper curve for Qx is the result when the switches
are constrained to the off position (without exchange) while
the lower curve is the result of unconstrained operation of
the switches. In this case, total power is increased by
developing a consumer population.
Case 2; Out of phase inputs. Another situation
producing the potential for exchange is the case of out of
phase inputs, Figure 22a shows some simulation results for
two systems with oscillating external energy inputs that are
90 degrees out of phase. mhis might correspond to two
systems in two different climatic regimes that are
relatively close together, such as might occur on a mountain
slope, exchange can increase total power in this situation

91
because -external inputs to one component are decreasing and
its structure is becoming relatively underutilized, while at
the same time the other components inputs are increasing,
If the coefficients are such that transport costs of
structure are less than the costs of building new structure
locally, then exchange will be beneficial in that total
power ftp) can be increased by exchange, as shown in Figure
22 a
Case 4: Constant unequal inputs. Che reasons for
business cycles and other internal" oscillations in systems
where the external inputs are constant (or nearly so) have
long been a subject of speculation. Figure 22b shows some-
results of the model applied to this situation. If the
inputs are unequal but constant, the model indicates that
the total power can be increased, under certain conditions,
by setting up internal oscillations where none exist in the
inputs.
some Example Simulations of spatial Development Hsina 25
sills"
The two component exchange model of the previous
examples can be expanded to a large number of cells for more
realistic applications. One possibility that was
investigated was the modeling of spatial development. In
this instance, each component represents an area of land and
the exchange of embodied energy among the cells is
determined by the model in such a way as to maximize the

QUANTITY QUANTITY
92
(a)
(b)
Figure 22. Two component model analog simulation results
(a) Situation when the external energy inputs
to the components are both oscillatory
and out of phase.
(b) Situation when the external inputs are
constant but unequal.

93
total power of the system In a dynamic process, Using
digital simulation techniques and a matrix to represent the
arrangement of the cells on the landscape, some hypothetical
results were obtained, A FORTRAN coding for the model is
given in Appendix ITT, The equations used are those given
in Figure 20 with n = 25. For this application, an
effective distance parameter was employed as a prime
determinen!, of the transfer coefficients. The transfer
coefficients were made proportional to the inverse square of
the distance between components. Figure 23 shows the
results of one simulation intended to isolate the effects of
relative position on spatial development from the more
direct effects of unequal external energy inputs and unequal
initial conditions. The external energy inputs and. initial
conditions of all the cells in the matrix were set at the
same values. The transfer coefficients were a direct
function of the distance between components.
Figure 23 shows that under these conditions, the model
produces a concentration of structure in the center of the
matrix due to the locational advantage (smaller average
distance) of the center component. This is consistent with
what would, be expected from central place theory, and the
equations used for the transfer flows in the model are
essentially those of the gravity model. Thus, the model can
be viewed as an extension of central place theory and
transportation theory to include energy principles, The

yig'are:23* Digital simulation of the pover maximising
aoaal for. a spatial grid of 25 components.
04
D
.
WWWVlOp
wvivn'jinfc
A'JWVJM i
*?viv}y>

MKKMCO
MHtttn
KMKK
KK
+ + + 4-
4 + + + ir,o
+ + 4- +
4 ^
r-f-fr'OUTi
VA\
\\\\vno
W I! || l¡ I!
W H l! |i i( om
pq It !| II (I INOI
M II II II II
ii ii li !;
mm **
Ilii mo
III! -(N
I 1 t t
MM *
> *4 M * R
*r?!Lg
tM>t>
(MUI n
t* * f -
4 £ 4 4
. r *tf;o
* s 4 r-
4 4*
>
OLO

< 4 #
G£=
/////1 L l U/////
///// U l i t /////
///// UUi ////A
/////I till/////
Ulli.+<+ + - III It
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l 1111++ ++ 4-1111 l
1 lit l++{-+-¡-l ill, l
/////mu/////
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SI
SEIS
-*> ..
* *3 -O
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V-" z*
ft tr
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4
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S6

96
important provision for including spatial differences in
inputs and initial conditions and time variability of inputs
may allow dynamic simulations that can generate practical
predict ions.
^he TT.O. Economic-Geologic System
Gmbodied Energy in Goods and Services for 91 0,S, Economy
Sectors in 1967
The embodied energy intensities (in Btu fossil/S of
output) for 92 .S, economy sectors were calculated both
including and excluding labor and government service
feedbacks and solar energy inputs. The detailed results are
given in appendix TV, Table 20. Figure 24 illustrates the
four alternative treatments and a fifth possibility. These
results were obtained in collaboration with the Energy
Research Group, TJniversity of Illinois at Champaign. Sector
correspondences for comparison with the Bureau of Economic
Analysis (BGA) sector designations are indicated in
parentheses following the sector names in Table 20 All
values are converted to fossil fuel equivalents using the
conversion factor of 2000 Btu solar/Btu fossil (Odum et al
1977), none of these calculations considered depreciation
or net growth of household and government assets as a net
output from the system. The numerical values of the energy

gure 24. Diagram showing the system boundaries
and flows included in the four
alternatives
(a) Excluding labor and government
services feedbacks and solar
energy inputs
(b) Including solar inputs but excluding
labor and government services
(c) Including labor and government
services feedbacks but excluding
solar inputs
(d) Including labor and government
services and solar energy inputs
(e) Same as (d) but also including
depreciation and net growth of
households and government as a
net output

98
NET EXPORTS
/LABOR AND
/ GOVERNMENT
SERVICES IGNORED
SYSTEM BOUNDARY
^^
t X \
1/
"industrial'
SECTORS
GNP
NET EXPORTS
HOUSEHOLDS
3
GOVERNMENT
NET EXPORTS
'X. LABOR AND
GOVERNMENT
SERVICES
NET EXPORTS
LABOR AND
GOVERNMENT
SERVICES
NET EXPORTS

99
intensities in Table 2f> are therefore high. Inclusion of
these flows anti their effects on the results will be
addressed in a following section.
Column ?. of Table 20 lists the energy intensities (in
Btu fossil/) excluding government and labor services
feedbacks and solar energy inputs. This is the previous
approach of the Energy Besearch Group (Herendean and Bullard
1974). The results presented here differ from that study in
one respect. Dollar flows were used throughout in the
present study whereas, in the previous study, direct energy
flows were used to measure the distribution of fossil fuels,
hydro, and nuclear energy from the energy sectors to the
remaining sectors.
The use of direct energy flows is preferable if the
output from the energy sector is physically homogeneous
(which is a fair approximation for the fossil fuel producing
sectors). Including solar energy inputs to the economy
requires, however, that one create energy sectors whose
output is physically very nonhomogeneous (such as
agricultural products) and for which dollar flows are the
best weighted aggregate available. In order to maintain
consistency, dollar flows were used throughout..
is in the previous study, the embodied energy
represents the total fossil fuel Btus (plus the total solar
Btus converted to fossil fuel equivalents for columns B and
T> of "able 29) required to produce a dollars worth of

100
output, but it is not simply the sum of the individual
energy sectors contributions. This is necessary to avoid
double counting, since refined is produced from crude, some
electricity is produced from coal and crude, etc. In this
study the total primary fossil fuel energy intensity was
calculated using the formula:
e (Primary) = s (Coal) + e (Crude + Gas) +
.61652 e (Electricity) +
.nnpg e (Solar)
where the factor .61652 accounts for the fraction of
electricity produced from hydro and nuclear sources
(Herendeen and Bullard 1974) and the .000 5 factor accounts
for the conversion ^rom solar to fossil fuel quality (Odum
et al. 1977).
Column B of Table 20 lists the embodied energy
intensities (in Btu fossil/T) calculated excluding labor and
government services feedbacks but including solar energy
inputs. Column C lists the embodied energy intensities
including labor and government services but excluding solar
energy inputs. Column T) lists the embodied energy
intensities inducing both labor and government services and
solar energy inputs. Figures 25 and 26 show frequency plots
of the four alternatives. able 8 gives summary statistics
for the embod5.ed energy distributions.
Another way of looking at these statistics is to plot
the total direct plus indirect Btus consumed by each sector

PERCENTAGE OF SECTORS IN SPECIFIED RANGE
Alternative A. Excluding Labor and Government Service
Feedbacks and Solar Energy inputs.
JL
JL
JL
JEL
150
200
JL
250
300
350
GREATER
THAN 400
400
Figure 25. Frequency plots of embodied energy intensities by sector
calculated with and without solar inputs.
101

PERCENTAGE OF SECTORS IN SPECIFIED RANGE
Alternative C. Including Labor and Government Service Feedbacks
but Excluding Solar Energy Inputs.
2000
3000
Alternative D. Including Labor and Government Service
Feedbacks and Solar Energy Inputs.
750 1000 1500 2000 3000
1967 EMBODIED ENERGY INTENSITY, xIO3 BTU fossil/$
GREATER
THAN 4000
J.
4000
JL
4000
O
O
Figure 26,
Frequency plots of embodied energy intensities by sector calculated
with and without labor and government services feedbacks.

Table 8.
Ninety-two sector embodied energy intensity statistics
Including energy sectors Excluding energy
Alternative (Sectors 1-7) __ (Sectors 1 -
X s C.V. X s
A
Excluding solar
inputs and labor
and government
(Btu fossil/$)
B
Including solar
inputs but ex
cluding labor and
government
(Btu fossil/$)
C
Including labor
and government
but excluding
solar inputs
(Btu fossil/?)
D
Including solar
inputs and labor
and government
(Btu fossil/?)
1.83 E5 6.28 E5 3.43
5.45 E5 25.10 E5 4.61
5.16 E5 6.19 E5 1.20
12.20 E5
0.69 E5 0.52 E5
1.78 E5 5.00 E5
4.05 E5 0.91 E5
sectors
7)
C.V.
0.78
2.81
0.22
2.44 E5 2.00
8.50 E5
3.49 E5
0.41

104
during a year against the total dollar output of the sector.
Btus consumed were derived by multiplying the calculated
energy intensities (in Btu fossil/S) for each of the four
alternatives in Table 20 by the total dollar outputs of the
sectors. Figures are plots of direct plus indirect
energy input versus total dollar output for 1967, for each
of the four alternatives with labor and government services
and solar energy inputs given in Table 20. With the data in
this format, one can ask what percentage of the variation in
dollar output from sector to sector can be explained with
variations in the total (direct plus indirect) energy input.
This question can be answered using a standard linear
regression model, "'he best fit regression line is indicated
on the plots along with its 7 square value, equation, and
the t statistic for the parameters (in parenthesis below the
parameters). The results are summarized in Table 9, both
with and without the energy sectors (sectors 1-7),
The p square value measures the fraction of the total
variation in sector dollar output, which can be explained by
variations in total (direct plus indirect) energy inputs,
The F value is a test statistic. PB>F indicates the
significance level of the test, with lower values of PR>F
indicating a more significant relationship between the
variables.
It is fairly obvious from inspection of Figures 29 and
30 that the energy sectors (sectors 1-7) are outliers and

Figure 27.
Plot of direct plus indirect energy consumption
(calculated excluding solar inputs and labor and
government) versus dollar output for 92 U.S.
economy sectors

DOUT=DOLLAR VALUE OF TOTAL OUTPUT {xIO9 £/yr)
106

Figure 28.
Plot of direct plus indirect energy consumption
(calculated including solar inputs but excluding
labor and government) versus dollar output for
92 U.S. economy sectors

DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xl09§/yr)
176 -
160
144-
128-
T
5G000
108

Figure 29.
Plot of direct plus indirect energy consumption
(calculated including labor and government but
excluding solar inputs) versus dollar output for
92 U.S. economy sectors

DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xIO9 $/yr)
110

Plot of direct plus indirect energy consumption
(calculated including solar energy inputs and
labor and government) versus dollar output for
92 U.S. economy sectors
Figure 30.

DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xl09§/yr)
112

Table 9.
Regression analysis results for total (direct plus indirect) energy
consumption versus total dollar output for four alternative treatments
of labor, government and solar energy inputs
Alternative
Including energy
(Sectors 1 -
sectors
7)
Excluding energy
(Sectors 1 -
sectors
7)
R2
F
PR> F
R2
F
PR>F
A
Excluding labor
government and
solar energy
.0210
1.89
0.1729
.5539
100.57
0.0001
B
Including solar
energy but excluding
labor and government
.0629
5.90
0.1710
.2042
20.78
0.0001
C
Including labor
and government
but excluding
solar energy
.7809
313.73
0.0001
. 9907
8633.95
0.0001
D
Including labor,
government and
solar energy
.8535
512.74
0.0001
.9454
1401.31
0.0001
113

114
their omission from the data greatly improves the R square
values. Some possible reasons for this will be discussed.
Table 9 also indicates that inclusion of labor and
government service feedbacks leads to a highly significant
relationship between total {direct plus indirect) energy
input and dollar output for economic sectors, especially if
the energy sectors are omitted from the data. Inclusion of
solar energy inputs does not seem to help {or hurt) the ^it
very much, but this is no doubt due to the rather crude
method used for approximating the points of entry of solar
energy to the economy used in this study.
tg GMP P at to for the n.P. from 1920 to 1976
In addition to the cross-sectional analysis of the
previous section, one might look at the time series of
various indicators of energy consumption and economic
activity. Table 21 in Appendix 7 lists real G!!P fin 1967
dollars), total mineral fuel, hydro, and nuclear energy
consumption and the ratio of these two quantities for the
same period. Figure 31 is a plot of the mineral, hydro and
nuclear energy consumption per dollar of real GPP for the
years 1929 to 1976

30,000-
20,000-
10,000
0
1920
I960
i r
1970 I960
Figure 31. Mineral, hydro, and nuclear energy consumption per dollar of
real GNP from 1920 to 1976.
115

116
otSl £SEa!r Investment, and Depreciation Time Series a ni
a Better Estimate of the Embodied Is§i92 2 EsiiiE Batlo
The numerical values of the mean embodied energy
intensities in Table B are misleading because of omissions
of one sort or another as shown in Figure 24, To be
complete, household and government depreciation and net
growth (as shown in Figure 24e) should be included, This
requires a more all-inclusive treatment of capital and
capital flows, This kind of treatment has recently been
attempted by Kendrick (1976) for a three sector n.s.
economy. He has taken a view that is consistent with the
closed system approach to economic accounting in developing
estimates of what he terms total capital stocks for the
0, S, economy. His capital stock estimates are based on
investment and depreciation time series, not only in the
traditional categories of structures, equipment, and
inventories, but. also in human capital, including such
intangible but nonetheless real categories as education and
training, medical and health investments, and. mobility. He
notes that: "while economists have been increasingly
treating the various forms of intangible outlays enhancing
tangible factor productivity as investments, estimates of
resulting capital stocks are a unique feature of the present
study (p. 9),
tables 19-12 are examples of the results of Kendricks
analysis for the business, government, and household sectors
of the u.S. economy for 1967. Kendrick's land category was

Table 10. 1967 U.S. business sector capital stock and investment breakdown.
(All values in billions of .1967 dollars.)
Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
1654.1
921.6
122.18
41.01
81.17
Total Non-Human Tangibles (a)
1331.2
735.7
94.25
29.55
64.70
Structures
695.4
352.4
31.60
10.18
21.42
Equipment
447.9
195.4
54.46
11.18
43.28
Inventories
187.9
187.9
8.19
8.19
-
Total Human Tangibles
-
-
-
-
-
Total Non-Human Tangibles
73.6
45.8
8.13
-8.34
16.47
Basic Research
7.3
. 7.3
0.48
0.48
-
AR & D
66.3
38.5
7.66
-8.82
16.47
Total Human Intangibles
249.2
140.1
19.80
19.80
-
Education and Training
234.3
134.0
17.48
17.48
-
Medical and Health
8.9
4.3
0.60
0.60
-
Mobility
6.1
1.9
1.72
1.72
-
a, excluding land held by businesses
Source: Kendrick, 1976.
117

Table 11. 1967 U.S. household sector capital stock and investment breakdown.
(All values in billions of 1967 dollars.)

Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
4882.8
3049.1
366.94
87.92
179.02
Total Non-Human Tangibles (a)
1451.8
781.0
96.93
22.58
74.35
Structures
801.2
422.2
22.24
7.84
14.40
Equipment
546.4
234.7
73.88
13.93
59.95
Inventories
104.2
104.2
0.81
0.81
-
Total Human Tangibles
1442.3
992.9
56.44
38.10
18.34
Total Non-Human Tangibles
10.3
9.0
0.95
0.95
-
Basic Research
7.4
7.4
0.66
0.66
-
AR & D
2.9
1.6
0.28
0.28
-
Total Human Intangibles
1978.3
1266.2
112.62
26.29
86.33
Education and Training
1635.6
' 1092.1
81.49
24.37
57*. 12
Medical and Health
271.6
142.6
15.58
1.08
14.50
Mobility
71.1
31.4
15.55
0.84
14.71
a. excluding land held by households.
Source: Kendrick, 1976.
118

Table 12. 1967 U.S. government sector capital stock and investment breakdown.
(All values in billions of 1967 dollars.)
Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
1980.4
1237.5
119.73
86.46
33.26
Total Non-Human Tangibles (a)
895.9
486.5
48.83
15.57
33.26
Structures
612.8
358.2
26.24
11.37
14.87
Equipment
248.3
93.4
21.74
3.35
18.39
Inventories
34.8
34.8
0.85
0.85
-
Total Human Tangibles
-
-
-
-
-
Total Non-Human Intangibles
149.4
100.6
14.56
14.46
-
Basic Research
24.1
24.1
2.22
2.22
-
AR & D
125.3
76.5
12.34
12.34
-
Total Human Intangibles
935.2
650.4
56.33
56.33
-
Education and Training
839.2
599.7
49.72
49.72
-
Medical and Health
91.8
49.0
6.00
6.00
-
Mobility
4.2
1.7
0.62
0.62
-
a. excluding land held by government
Source: Kendrick, 1976.
119

120
subtracter! an! included in a separate environment sector for
this study, Cross investment is the total dollar value of
investments in capital stock, where capital stock includes
human capital. Net growth is gross investment minus
depreciation. Gross capital stock is accumulated gross
investment minus retirements, while net capital stock
subtracts double declining balance depreciation estimates,
For most purposes in this study, net capital stock is the
more appropriate measure.
Kendricks estimates of gross investment in the
household and government sectors allowed a more accurate
calculation of the numerical, value of the mean embodied
energy intensity for the U.S. economy. The values in Table
8, alternative D, were calculated using a total primary
input value of 1C9.64 E15 Btu fossil/yr. This was composed
of S'?. 52 El5 Etu fossil/yr of mineral, hydro, and nuclear
fuels consumption and 104.4 E18 Btu solar/yr, which when
converted to fossil fuel gnality using a conversion factor
of 2000 Btu solar/Btu fossil (Odum et al. 1977) yields 52, 20-
El S Btu fossil/yr. The total primary input divided by the
net output from the system yields an estimate of the mean
value of the embodied energy intensities. For alternative D
in Table 8, the net output was assumed to be gross private
fixed capital formation plus net exports plus net inventory
change {see Figure 12). This was 125,61 E9 $ in 1967. The
sum of these three categories are gross business investment

121
in Kendricks terms and the value compares well with his
estimate of 122.18 29 5 for 1967. The mean embodied energy
intensity could thus have been calculated as 109.64 215 Btu
fossil/125.61 29 5, or 8.79 25 Btu fossil/f. This is very
close to the mean of the 85 sector embodied energy
intensities (excluding the energy sectors) of 8.5 75 Btu
fossil/$ given in Table 8, alternative D. Kendricks
estimates of gross investment in government and households
can now be included to determine a more accurate value of
the mean energy intensity for the n.S. economy. Tables 11
and 12 give these values as 119.73 e9 $ and 266,94 E9
respectively. adding these to the 122.18 E9 $ gross
investment in business yields 508.85 E9 $. This leads to a
value of 2.15 25 Btu fossil/8 or 5.39 B4 kcal fossil/8.
One additional refinement can be made to the
calculations. The primary input value included an estimate
of the total solar energy absorbed by the U.5. ecologic-
economic system. Tn determining the energy intensities,
only gross investment in the economic sectors was 5.ncluded,
For consistency, one must either reduce the primary input to
include only that portion of the solar input that enters the
economy or include the gross investment in environmental
assets. By assuming that gross investment in land (by
natural processes) was the same percentage of net land
capital stock as in the economy as a whole, an estimate of
gross investment in environmental assets was derived. This

122
worked out to bo 74.7 39 S/yr (see Table 14). Adding this
to the gross investment in the economic sectors yielded a
total of 583.4 vg S/yr. Dividing this into the total
primary input yields 1.83 35 Btu fossil/1967$, or 4.212. L
kcaj. fossil/1963$. This value was used to convert from
embodied energy to dollar values in the sections to follow,
Appendix 7 contains time series for the 0s. economic-
ecologic system estimated from Kendricks data and other
sources. Tables 22-24 are time series from 1929 to 1969 of
total net capital stocks, gross investment, and depreciation
for the n8. economy, Kendricks three sector breakdown
consisting of business, government, and household sectors
was expanded to include a .S. environment sector and a rest
of the world sector. Time series for these sectors were
estimated and are included as Table 25, Figures 32-34 are
plots of the net capital stock time series data.
In addition to their interest for general comparison of
capital stock and investment patterns, these data are
necessary for validating the 5-sector D.S. economy-
environment simulation model, which is developed in a
following section. The environment time series was
estimated from Kendricks data for the value of land stocks
and data on the value of mineral reserves (Tables 26 and
27),

TOTAL CAPITAL STOCK (x IO,c 1967 dollars
123
YEAR
Time series plot of U.S. business, government,
and household net capital stocks from 1929
to 1969.
Figure 32.

TOTAL CAPITAL STOCK. xlOlc 1967 dollars
124
YEAR
Time series plot of U.S. environmentU.S.
economy, and total U.S. net capital stock
from 1929 to' 1969.
Figure 33.

TOTAL CAPITAL STOCK, x 10 1967 dollars
125
400 ~'
300-1
200-i
100-i
o ^
1920
1930
1940
1950
YEAR
I
I960
1970
Time series plot of rest of the world net
capital stocks from 1929 to 1969.
Figure 34.

126
Fourteen sector Close! System Input-Output Ha trices for 12.5.1
an!~2252
Figures 35 an! 36 are 14 sector input-output
transactions matrices for the U.S. economy-environment for
the years *96 3 an! 1967 with all values converted to their
equivalent in 1967 dollars. As previously noted, the system
is considered to he thermodynamically closed with only
energy crossing the system boundaries. Under this setup,
the energy input to the U.S. economic system derives from
three possible sources. Che first is the net input row of
the matrix, which is the dollar value (arrived at through
balance considerations) of the years input of solar energy.
The n.s. environment sector and the rest of the world sector
(which contains its own environment component) are the only
sectors receiving this input directly and are, therefore,
the only sectors with an entry in the net input row. This
is equivalent to saying that all solar energy is first
absorbed and transformed by the environment, before entering
the economic sectors. The current years sunlight enters
the economic system as "renewable products of the
environment such as rain, winds, and biomass.
Some of the sunlight absorbed by the earth ov=r past
eons has been stored in the environment sector in the form?;
of mineral and soil deposits and landforms. Depletion of
this "environmental capital" is the second path for energy
entering the U.S. economy. Industrial societies* use of
fossil fuels is the foremost example of the consumption of

Figure 35
1963 14-sector transactions matrix with all values
converted to millions of 1967 dollars

tar input
290100





_ ,r
.
4305000
495910(1
'IUTAL mw
39COO
eao'j
MM5
2203
60302
35512
99.110
513209
48)06
435796
. ^08421
2H2793
...mm.
13875068
£LQ32
128

Figure 36.
1967 14-sector transactions matrix with all values
converted to millions of 1967 dollars

IJ-.T IKPOT
290100



__.
, ,
__
X305000
'lOl'\L Ttlpur
097110
74 K
-1B3-10
2280
65784
41122
.107156
627237
00566
-2222M
51Q3j
-Jaisi
-232210-
1214087'
UOMJi
130

131
the embodied sunlight, of past eons. In the matrix this
depletion of environmental assets shows up as a net decrease
in the capital stock of the environment sector over the year
(the change in storage portion of the net output column).
A third pathway for energy input is through imports
from the rest of the world sector, which is transferred to
the .S. economy and shows up as a net import from the rest
of the world sector. Input-output tables in dollar terms
have total inputs balanced by total outputs for each sector.
This constraint was utilized in determining many of the
quantities in the tables that were not measured directly,
The inclusion of the environment, households, and government
as endogenous sectors required the copious use of this
identity In deriving estimates. Some of the conceptual and
quantitative approximations necessary to complete the tables
follow.
The n.S, environment sector contains all land, air,
water, and raw materials in the .S. Its inputs from the
other O.S. economy sectors consist of "waste products,"
which wore assumed to have a zero value. Actually, some
portion of the depreciation of the contributing sector
should be counted as an input to the environment, as shown
in Figure 10 Lacking any guantative way of making this
distinction, all the depreciation was considered to be a net
output. The depreciation estimates (from Kendrick 1976) are
summarized in Tables 13 and 14, The environment sector and

132
the rent of the world sector, which implicitly contains its
own environment sector, are the only sectors receiving a
direct input {in the form of sunlight) under this sectoring
scheme. The dollar value of the direct solar input in hoth
1963 and 196* was estimated as 299, 1 E9 S, from balance
considerations. The self-sales category was assumed to be
the same percentage of total output as in the economic
sectors. This was 16. Uf, in 1963 and 14.215 in 1967, and thus
the "self-sales' value for the environment sector was
imputed as 195.9 T9 $ in 1963 and 98.1 29 $ in 1967.
The gross investment and depreciation numbers for the
environment sector are critical and largely unknown. An
estimate was made by assuming that the mineral reserve
portion of the environment stock had no investment or
depreciation and that the land portion had investment and
depreciation at the same rate as the economic sectors
expressed as a percentage of net stock (see Tables 13 and
14), The output of the environment sector to the economic
sectors was measured as a residual. The additional value
needed to balance the total output of each sector with the
value of all its purchased inputs (including labor and.
crovernment services) was credited to inputs from the
environment.
The 1963 and 1967 tt. s. economy input-output data from
BEh were used to generate the bulk of the U.s. economy
section of the table (United States Department of Commerce

133
1969b, 1974a, 1979}, These were supplemented by Sata from
Kendrick (1976) on hats an and government, capital flows. The
sector correspondence used in aggregating the data are given
in Table 15. Iks noted earlier, the government and household
sectors are endogenous with inputs from the other sectors
measured as government purchases and personal consumption
expenditures, respectively, and outputs estimated as the
percentage of value added attributable to government and
households. The gross investment of the economy sectors was
partitioned (using estimates from Kendrick 1976) into
investment to cover depreciation and net change in stock.
The depreciation and change in storage together make up the
total net output.
The rest of the world sector receives the exports and
supplies the imports to the u.S. economy, It is considered
to be an aggregate of all the economies and environments
other than the U.S. Tables 13 and 1 are estimates of the
net capital stock, gross investment and depreciation for the
14 sector breakdown for the years 1963 and 1967. The data
on gross investment and depreciation were incorporated into
the transactions matrix. Table 15 lists the sector
correspondences between the 14 aggregate sectors and other
breakdowns

Table 13.
1963 aggregate sector net capital stocks, gross investment and depreciation(a)
(in billions of 1967 dollars).
Aggregate Sector
Net
Capitol
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction
Total U.S
Depre
ciation
1.
Environment
14981.0 (c)
.7746
80.67
.1631
80.67
.2452
2.
Raw Materials
3.9
.0002
0.48
.0010
0.33
.0010
3.
Fuel Industry
34.1
.0018
4.17
.0084
2.85
.0087
4.
Forestry and
Fisheries
0.4
-
0.05
.0001
0.03
.0001
5.
Agriculture
46.8
.0024
5.72
.0116
3.91
.0119
6.
Power Plants
40.7
.0021
4.98
.0101
3.40
.0103
7.
Construction
26.1
.0013
3.19
.0064
2.18
.0066
8.
Manufacturing
106.7
.0055
13.05
.0264
8.91
.0271
9.
Transportation 33.5
.0017
4.10
.0083
2.80
.0085
10.
Services
411.8
.0213
50.38
.1018
34.40
.1046
11.
Communications 39.9
.0021
4.89
.0099
3.34
.0102
12.
Government
1048.7
.0542
101.76
.2057
32.39
.0984
13.
Households
2567.97
.1328
221.3
.4473
153.80
.4675
TOTAL U.S.
19341.5
1.0000
494.73
1.0000
329.0
1.0000
134

Table 13.
(continued)
Aggregate
Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
14. Rest
World
of the
(b)
287984.0
7343.0
4883.0
a. Based on Kendrick's (1976) estimates of Business, Government, and Personal Sector
net capital stocks, gross investment and depreciation (depreciation is gross
investment minus net investment) for 1963 converted to 1967 dollars. The business
sector totals excluding land were distributed to the 10 aggregate business sectors
(2-11) according to data on gross investment by sector in 1963 (United States)
Department of Commerce 1975). The land stock was credited to the environment sector.
b. The rest of the world was assumed to exhibit the same ratios of net capital stock
to gross investment and depreciation as the U.S. The rest of the world net capital
stock for 1963 was estimated at 287084.0 E9 1967$ (see Table 25). Gross investment
was thus 7343 E9 1967$ and depreciation was 4883.0 E9 1967$.
c. See note c to Table 14 and Table 25.
135

Table 14
1967 aggregate sector net capital stocks, gross investment and depreciation(a)
(in billions of 1967 dollars.)
Aggregate Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
1.
Environment
13872.0(e)
.7270
74.7
.1280
74.7
.2030
2.
Raw Materials
6.2
.0003
0.8
.0014
0.5
.0014
3.
Fuel Industry
36.7
.0019
4.9
.0084
3.2
.0087
4.
Forestry and
Fisheries
0.8
-
.1
.0002
.1
.0003
5.
Agriculture
49.1
.0026
6.4
.0110
4.2
.0114
6.
Power Plants
63.2
.0033
8.4
.0144
5.6
.0152
7.
Construction
32.3
.0017
4.3
.0074
2.8
.0076
8.
Manufacturing
174.3
.0091
23.1
.0396
15.3
.0416
9.
Transportation 64.2
.0034
8.5
#
.0146
5.7
.0155
10.
Services
441.3
.0231
85.5
.1003
38.9
.1057
11.
Communications 53.3
.0028
7.1
.0122
4.7
.0128
12.
Government
1237.5
.0649
119.73
.2052
33.3
.0905
13.
Households
3049.1
.1598
266.9
.4575
179.0
.4864
TOTAL U.S.
19080.2
1.0000
583.4
1.0000
368.0
1.0000
136

Table 14.
(continued)
Aggregate
Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
14. Rest
World
of the
(b)
253224.0
5660.0
5463.0
a. Based on Kendrick's (1976) estimates of business, government and personal sector net
capital stocks, gross investment and depreciation for 1967. Net capital is accumulat
ed gross investment. Depreciation is gross investment minus net investment. The
business sector total excluding land was-distributed..to the 10 aggregate business sectors
according to data on gross investment in 1967 from BEA (United States Department of
Commerce 1975). The land stock was credited to the environment sector.
b. The rest of the world was assumed to exhibit the same ratios of net capital stock to
gross investment and depreciation as the U.S. The rest of the world net capital
stock for 1967 was estimated as 283224 E9 1967$ (See Table 25). Gross investment
was thus 8860 E9 1967$ and depreciation was 5463 E9 1967$.
c. Aside from the value of land, the net capital stock of the environment sector also
includes mineral reserves. Considering only fuel reserves and using a conservative
figure of 25 E19 Btu fossil, total recoverable reserves at 188 E3 Btu fossil/1967$
gives a total value of $13298 E9. Added to the land stock value, this yields an
(admitted very approximate) estimate of total environmental stock value of $13872 E9.
This value in conjunction with the fuel consumption figures in Table 27 and the land
value figures in Table 26 were used to estimate the environment sector net capital
time series in Table 25.
137

Table 15. Sector correspondence.
Aggregate sector
ERG 90 order
sectors
BEA 357 order
sectors
Leontief (1953)
96 order sectors
2.
Raw Materials
10-13
5,6,9,10
22,39,43
3.
Fuel Industry
1-3
7,8,31.01
45.50
4.
Forestry and Fisheries
7
3
9,54
5.
Agriculture
6,8
1,2
1-8
6.
Power Plants
4,5
68.01,68.02
52
7.
Construction
14,15
11,12
68,69
9.
Manufacturing
16-28,30-68,78
87-90
13-25,27-30,31.02,
31.03,32-64,68.03
78-79,81-83
10-21,23-38,40-42
53,55,56,58-67
9.
Transportation
69-75
65
70-73
10.
Services
9,79-86
4,69-77
74-91
11.
Communications
29,76,77
26,66,67
51,57
12.
Government
92
13.
Households
94
138

139
Five Sector F.S. Sconomv Simulation Molel
Figure 37 is an energy flow diagram for a 5-sector 0.5,
economy-onviromnen+'-vorld simulation model. The model
breaks the economy into three major components: a business
sector consisting of all the conventional 'industrial"
sectors, (sectors 2 11 in Tables 13 and 14) a government
sector, and a household sector. These are linked to a 0.5.
environment sector and a "rest of the world" sector. "he
difference equations used to simulate the model are those
given in Figure 2", with n = 5. 1 FORTRAN listing of the
model is given in Appendix VI,
The salient features of this model can be summarized as
follows:
(1) The model is a thermodynamically closed system.
Only energy fin the form of radiation) enters or leaves the
system.
(?) "he model is holistic in the sense that the entire
world is included in the model (in a very aggregated way).
(3) The model has only one exogenously determined
variable solar radiation. Models which are intended to
be used for predict i.ve purposes must keep exogenous
variables to a minimum since the model behavior is a direct
function of these variables, It does no good to have a
model that makes accurate predictions based on a large
number of exogenous variables unless those variables can be
predicted accurately. For example, many of the econometric

Figure 37.
Energy flow diagram for a 5-sector U.
environment simulation model
S. economy-

141

142
models o* the .S. economy depend on exogenously determined
final demand functi.ons. TTsing these models for prediction
thus involves predicting final demand. The final demand
predictions, in turn, are usually extrapolations of past
trends. This makes the models complex rather than simple
extrapolations, a point that is often lost in the
mathematical, rigor of the models. There should be little
trouble predicting solar intensity, however.
(4) The model implicitly contains both supply and
demand considerations based on the marginal embodied energy
productivities of the sectors.
(5) The model is nonlinear with feedback. All sectors
are (potentially) connected to all other sectors.
(6) mho model evolves or changes its structure through
time in an attempt to maintain an optimum pattern. The
fitness criterion for this model is the maximum power"
principle of Lotka (19 22).
Parameter estimates. The data used in estimating the
models parameters (15 in all) and initial conditions (5 in
all) have been presented in a previous section, The
14-sector input-output transactions matrices (Figures 35 and
36) were aggregated to 5 sectors, Essentially, this
involved collapsing sectors 2-11 into one sector. The
aggregated matrices are shown in Figures 38 and 39, As
previously noted,the small number of years of detailed data

Figure 38.
1963 5-sector transactions matrix with all values
converted to millions of 1967 dollars

From Sector
RWIRONMENT 1
105900
163972
102023
158994
32708
BUSINESS 2
675358
73859
411337
29068
GOVERNMENT 3
70290
42052
68590
101
HOUSEHOLDS 4
362459
61877
116354
36
REST OF WORLD 5

20369
2982
6751
39508082
-31673C
149060
4067
62150
6937C
32390
67500
153800
-1562448
5899332
396000
1292448
282793
762026
43875068
NET INPUT
290100



4305000
4595100
TOTAL INPUT
396000
1292448
282448
762026
43875068
.
46608335

Figure 39.
1967 5-sector transactions matrix with all values
converted to millions of 1967 dollars

NET INPUT
290100

.

4305000
4595100
TOTAL INPUT
397136
1544900
349455
972946
42140377
45405844
146

147
available made a regression fit of the parameters
impossible. The parameters were estimated by taking the
average values generated from the two years of 1-0 data as
initial estimates and then "fine tuning the least well
known parameters by fitting the simulation results to known
time series data. This was done using a manual directed
search technique (known in the vernacular as trial and
error). Sensitivity of the model to certain parameters was
also noted. Table 16 lists the initial estimates of the
model parameters (a^, b^j and c j) Estimating the a^
required information on the solar energy input to the U.s,
environment and the rest of the world (E ^ and Eg, Ewsre
assumed equal to 9), These values were estimated as 44,3
and 657.7 (E1B kcal/yr, respectively) based on data from
Budyko (19TB) and relative area figures.
"he dollar value of the direct inputs were estimated as
299 and 43"5 (E9 1967 5, respectively). The a were
estimated from the model relation:
7 i = a^E^Q^/1 + a^ where 7 ^ = value of the
direct input (in billions of 1967 $/yr)
E^ = energy of direct input (in E15 teal solar/yr)
solving for a^ yields:
ai = ~lT i / Qi(7j_ E). Eimilarily, the b^j parameters
were estimated from the 1963 and 1967 intersector flow data,
from the model relations:

148
Yij = ^ij Qi Oj / 1 f ^ij^i where Yj_j = value of flow
from sector j to sector I (in billions of 1967 $/yr)
= net capital stock of sector i (in billions of 1967
9} solving for the b.¡_j yields:
bj_j = *7j_j / Q-¡_ (Y^j Qj). The c^ were estimated from
the model relations:
H = Ci Qi where: = net outflow for sector i (in
billions of 1967 9/yr)
= net capital stock of sector i (in billions of
1967 9} solving for yields:
c. = IT. / Q.
l l 7 l
The initial estimates of the parameters (using the
above relations and the average of values obtained from the
1963 and 1967 input-output data in rigures 38 and 39) are
given in Table 16. In the section to follow on simulation
results, the parameter values actually used in each run are
given along with the plots. The sensitivity of the model to
changing selected parameters are discussed.
Simulation results. Figure 49 is a plot of the models
output over the period from 1929 to 2030. This run employed
the coefficients given in the accompanying figure legend.
To fit the model to the historical data as closely as
possible, the least wall known of the coefficients were
varied from the initial estimates. These were the
coefficients governing inputs from the environment sector to

Table 16
Initial Parameter Estimates
*
Parameter
i = 1
U.S. Environment
i = 2
Business
i = 3
Government
i = 4
Households
i = 5
Rest of the World
a.
X
4.58 E-7
0
0
0
2.31 E-8
b. .
il
3 = 1
4.942 E-7
1.274
E-5
6.753
E-6
5.283
E-6
3.505 E-8
j 2
-
10.252
E-3
9.988
E-5
4.167
E-4
6.516 E-7
3 = 3
-
9.494
E-5
3.644
E-5
2.542
E-5
1.464 E-9
j = 4
-
2.134
E-4
2.289
E-5
1.703
E-5
2.316 E-10
c.
i
j = 5
1.058 E-8
.006
4.378
.086
E-7
r .870
.029
E-8
4.724
.021
E08
5.12 E-7
149

150
the economic sectors, lb21* ^31' ^41^ internal transactions
within the sectors (h^j), flows from business to government
(b23, b32) an! depreciation rates. It also became
necessary for stability reasons to multiply one of the
partial derlvitares in the decision structure by a small
factor. This factor is labeled s and is listed with the
other parameters. The model was very difficult to adjust
due to its nonlinear equations and the discontinuous nature
of its time behavior. These features made computerized
parameter optimization techniques relatively useless and
necessitated many hours of manual adjustment. It also
produced an exceedingly "rich model, or one capable of
exhibiting many distinct types of behavior, depending on the
values of the coefficients. Only a very limited set of
coefficients produced results that coincided with the
historical behavior of the system, however.
Comparison of the models output (Figure 40 ) with the
historical behavior of the system from 1929 to 1969 (Figures
32-34 replotted on Figure 4r) shows that the model
reproduces the general behavior of the real system over this
period. The flat response of the business sector during the
depression and World War II (1929-1945) followed by the
postwar boom Is accurately reflected in the model. The
rapid increase In government assets during the war and post
war leveling are a^so indicated. Households, environment,
and the rest of the world all exhibit the same smooth

151
behavior in the model an! in the historical data. The
"goodness of fit" for this run was addressed using linear
regression models with the historical data for the business,
government, and household sectors from 1929 to 1969 as
dependent variables and the models output for this period
as independent variables. This allowed separation of the
models ability to explain the direction of change (given by
the B square values) from the magnitude of change fgiven by
the coefficients of the independent variables) These
statistics are listed in Table 17.
This run of the model projects a leveling of economic
assets at around the year 2000 and a subsequent steady state
with small oscillations. Figure ui shows a continuation of
this run from 2030 to 2130. Over this period, the model
predicts a gradual decline in economic assets due to the low
levels of remainino environmental assets.
^he Fouth Florida Fystem
Measured Fm bodied Fnergy Maps
Figures 42 44 are maps of the estimated embodied
energy intensities (total embodied energy divided by land
area) for south Florida for 1900, 1953, and 1973
respectively. The 1900 map provided initial conditions for
the south Florida simulation model and the 1953 and 1973

Figure 40. Simulation results fop the 5-sector o.s.
economy-environment simulation model. This run
used tne following coefficients
CT
0.458E-06 0.Q00E 00 O.OOOE 00 0.000E 00
0.494E-06 0. 150E-05 0.400E-05 0.200E-05
0.652E-05 0.500E-04 0.150E-03 0.417E-03
0.206E-05 0.800B-04 0.100E-01 0.254E-04
0.437E-05 0.213E-03 0.229E-04 0.100E 00
0. 105E-07 0.438E-06 0.487E-07 0.472E-07
0.015 0.030 0.030 0.030
1. 200
0.231E-07
0.351E-07
0.652E-06
0.146E-08
0.232E-09
0.512E-06
0.021

\ ENVIRONMENT (MODEL)
153

Figure 41.
Continuation of the simulation run in Figure 40
to the year 2131

155

Table 17.
U.S. economy-environment simulation model
performance statistics for the 1929-1969
period.
Sector
R square
PR>F
Regression
Coefficient
2 Business
.981
. 0001
.410
3 Government
.959
.0001
.614
4 Households
.939
.0001
.836
Average
.960
.0001
.620

Figure 42. Embodied energy intensity map for
south Florida for 1900 estimated
from the 1900 land use map
it
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from the 1953 land use map

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LEGEND
----/////\ 1111 + + + + *XXXXX$3$S:S
-===/////! 1 1 1 i+ + + + f XXXXX33333
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30. 40. 50. 75. 100. 200.
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091

Figure 44. Embodied energy intensity map for
south Florida for 1973 estimated
from the 1973 land use map
LEGEND
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* : : : : : ===.- = /////11 1114-++-M- xxxxxsss
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Oi W ifi

I I T T 1 X' X X X' X
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291

163
maps ware used to validate the model. The maps indicate
t
that in 1901 the everglades area south of Lake Okeechobee
represented the highest embodied energy intensities, while
coastal areas had relatively low values. Urbanization in
the region has concentrated in the east and (to a lesser
extent) west coastal areas and also at Key west and Orlando,
leading to higher embodied energy values in those areas in
1953 and 1973. These data represented the primary input to
the 91-cell south Florida simulation model.
Ninety One Cell Couth Florida Spatial Simulation H22.E
The changing patterns of land use in south Florida have
been extensively documented. A detailed historical sequence
of land use maps and supporting material have been prepared,
It therefore represented a logical choice for a spatial
simulation study, is previously noted, the region was
broken into 88, 16 by 16 mile cells for the simulation.
Three additional cells, one representing the U, S
environment, one for the n.S. economy, and one for the rest
of the world were also included. The model used in this
study was the general, power maximizing model outlined
earlier. The difference equations used to simulate the
model are those in Figure 20 with n = 91. A FORTRAN listing
of the model is given in Appendix VII.
'"his application can be viewed as merely a different
way of grouping the u. S. economy-environment model, It

164
therefore retains all the major features of the u.s. economy
model with the addition of the spatial dimension.
Parameter estimates. For this application even
preliminary estimates of the parameters were not available,
since this would have required detailed transactions data
between all 91 of the models components. To estimate the
8281 intercell transfer coefficients certain simplifying
relationships were therefore assumed. The first was that
the transfer coefficient between any two cells is a function
of the distance between the cells. This is essentially the
"gravity model" approach. There is a fair amount of
empirical evidence supporting this kind of relationship
based on increasing costs of transport with distance. For
exchanges within the region the transfer coefficient was
made proportional to the inverse square of the physical
distance between the cells. For exchanges with the rj.s,
environment, economy, and rest of the world the physical
distance was adjusted with a "coastal modifier" parameter
which made the effective distance from the coastal cells to
areas outside the region lower. This accounted for the
lower transport costs over water. In principle it is the
transport costs which determine effective distance {and thus
the transfer coefficient) and any barriers or corridors in
the spatial field should be accounted for. A detailed
listing of the parameter values used in the final model runs
is included in Appendix FIT.

165
Simulation results. Figure 45, a-k shows maps of the
mofle!s output over the period from 1900 to 2000. These may
be compares with the measured embodied energy intensity maps
for 1053 (Figure 43) and 1973 (Figure 44), The model does a
fairly good job of duplicating the historical time sequence
given only the initial (1990) conditions and the solar
energy input to the system. Other environmental energy
inputs to the region (such as rain, wind, and tides) are
considered to be the result of exchanges between the local
cells and the .S, and rest of the world environment cells
and are calculated internally in the model. The rapid
growth on the east coast and, to a lesser extent, on the
west coast and at Key West was a result in the model of
exchanges of these cells with the 0.5, economy cell, which
of course was growing exponentially over this period.
As with the 0.5. economy simulation, linear regression
models were used to address the goodness of fit of the
south Florida model. Here the 88 land use cells for 1953
and 1973 were used as observations (rather than time series)
with the measured data as the dependent variable and the
models output as the independent variable. These
statistics are listed in Table 18.
Owing to the nonlinear, discontinuous nature of the
model, the lack of good initial estimates on the parameter
values, and the large number of state variables, this model
was very difficult to fit to the historical data.


in o
Figure 45. Simulation results for the 91-cell
south Florida spatial model
(a) Initial conditions (1900)
(b) 1910
(c) 1920
(d) 1930
(e) 1940
(f) 1950
(g) 1960
(h) 1970
(i) 1980
(j) 1990
(k) 2000
LEGEND
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. 10. no. 30. 40. 50. 75. 100. 20
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LLT

178
Table 18. South Florida simulation model performance
statistics for 1953 and 1973.
Year
R square
PR>F
Regression
Coefficient
1953
.677
.0001
.522
1973
.717
.0001
.411
Average
.697
.0001
.467

179-
Coraputerized parameter optimization was out of the question
and manual adjustment of the parameters combined with
judgment gained through experience was necessary. For these
reasons, the results presented here are not necessarily this
models "best fit. Sore time spent adjusting the
parameters could no doubt improve the results but this
effort must be weighed against the increased benefit of a
slightly better fit. The adjustment process was terminated
when the model had demonstrated a "reasonably" good fit
given the added difficulty of this type of modelling over,
say, multiple linear regression models. It must be
remembered that this model receives as input only the
initial conditions and the solar energy input over the
period (considered to be constant) and develops a very
complex pattern of land use which reflects at least the
flavor of reality based on its attempt to maximize power.

DISCUSSION
^he Case for a Constar!. Embodied SELS.E2.Z. .2 Dollar Patio
The results of this study generally support the
hypothesis that there exists a constant ratio of total
embodied energy (as defined here) to economic value as
astermine3 in a competitive market, both cross-sectionally
and intertemporally. There are three main lines of evidence
supporting the hypothesis. The first involves studies of
the detailed input-output structure of the economy at a
specific time.
The input-output technique is useful in assessing the
total direct and indirect energy necessary to produce goods
and services in an economy. This dissertation contains
results of modifications to the input-output method for
obtaining energy intensities (Herendeen and Bullard 1974).
The modifications were aimed at achieving consistency with
the boundary definitions of the economy. The results (Table
29 and the summary statistics in Tables 9 and 9) indicate
that inclusion of labor and government services feedbacks
significantly reduce the variation in energy intensities and
increase their average magnitude, while inclusion of solar
energy inputs increase both the variation and magnitudes.
Table 8 allows comparison of the statistics of calculated
180

181
energy intensities for four alternatives concerning the
treatment of labor an! government services an! solar energy
inputs. Comparison of the two alternatives without solar
energy inputs shows a reduction in the coefficient of
variation from 3.43 to 1.2 with the Inclusion of labor an!
government services feedbacks, and a corresponding increase
from 1,35 ^5 to 5.16 55 Btu fossil/* in the mean energy
intensity. similarly, the two alternatives with solar
energy show a reduction in the coefficient of variation from
4,61 to 2.2 with the Inclusion of labor and government
services feedbacks, and a corresponding increase from 5.45
E5 to 12.20 05 Btu fossil/* in the mean energy intensity,
Comparison of the two alternatives without labor and
government services feedbacks shows an increase in the
coefficient of variation from 3.43 to 4.61 with the
inclusion of solar energy Inputs and a corresponding
Increase from 1.85 E5 to 5.45 E5 Btu fossil/S in the mean
energy intensity. Similarly, the two alternatives with
labor and government, services feedbacks show an increase in
the coefficient of variation from 1.2 to 2.0 with the
inclusion of solar energy Inputs and a corresponding
increase from 5.16 E5 to 12.20 B5 Btu fossil/* in the mean
energy Intensity.
hs noted earlier, the distribution of solar energy
inputs to the economic sectors is imperfectly known and only
a crude, approximation was used in this study. Since the

182
total magnitude of solar energy absorbed by the .s. in 1967
was fairly well known, the inclusion of solar energy in the
manner adopted in this study may have distorted the
distribution but not the total magnitude of embodied solar
energy due to imperfect knowledge of the input distribution.
For example, the total primary energy intensity of forestry
and fisheries products (sector 7) is an extreme outlier at
238.61 F5 Btu fossil/S compared to a mean of 12.2 F5 Btu
fossil/$ in Table 29, alternative D. This is probably due
to an overestimate of the solar energy input to this sector
relative to other sectors.
The statistics on the total primary energy intensities
are somewhat misleading due to their non-normal
distribution. Figures 25 and 26 are frequency plots of the
total primary energy intensities given in cable 2B, which
demonstrate clearly that the numbers are much more clustered
than the statistics indicate. If the outliers are
eliminated by excluding the primary energy sectors (sectors
1-7) from the statistics, then the means, standard
deviations, and coefficients of variation for the total
primary energy intensities in Table 8 drop significantly.
For example, alternative D*s mean drops to 8.5 E5 Btu
fossil/T with a standard deviation of 3.49 F5 and a
coefficient of variation of 9.41.
Translating the data into a regression format
highlights more clearly the nature of the relationships.

183
Figures 27-30 show the relationships between the total
energy (direct plus indirect) input to the sectors and the
total dollar output tor each of the four alternatives on
labor, government, and solar energy. Table 9 summarizes the
regression statistics. it is clear from these results that
if labor and government services are included in the
calculations, the total (direct plus indirect) energy input
explains a significant percentage of the variation in sector
dollar output. For the best case (excluding the energy
sectors) over 99") of the variation in sector dollar output
could be explained with variation in total embodied energy
input, his is the same as saying that the ratio of
embodied energy to dollars is nearly constant.
The primary energy sectors (sectors 1-7) are outliers.
Primary energy inputs can thus be said to be underpriced
in that their dollar costs do not reflect their embodied
energy costs or their competitive market value.
Many conceptual and empirical refinements to the
technique remain to be made. There are still problems with
capital flows, incomplete coverage, joint products, and
transfers, and there is the need for much better data on the
distribution of renewable energy inputs. Better data on the
allocat.ion of value added to labor and government are also
needed. it this point, however, the following conclusions
can be drawn from the input-output study of total energy
costs:

184
(1) Fhen all energy inputs and feedbacks are accounted
for, there is a very close cross-sectional relationship
between total (direct plus indirect) energy cost and
competitive market value. This is the same as saying that
the ratio of embodied energy to dollars, for competitive
sectors, is nearly constant.
(2) The outputs of the primary energy sectors are
underpriced in terms of both their embodied energy cost
and their free market value.
The second line of evidence for a constant embodied
energy to dollar ratio deals with time series of this ratio
in real dollar terms for the aggregate 0.S. economy. Table
21 and Figure 31 are examples of this time series for the
years 1920 to 1976. The relative constancy of the ratio is
striking, at least for the 1940 to 1976 period. There are
several possible explanations for the apparently declining
ratio during the 1920 to 1940 period.
(1) There are problems with converting to constant
(equivalent purchasing power) dollars with the older data
due to changes in the product mix and quality and changes in
accounting conventions.
(2) An embodied energy theory of economic value requires
the total energy to real GHP ratio remain constant. Figure
31 gives only the mineral fuels, hydro and nuclear energy
inputs to the economy while ignoring energy inputs from
direct capture of solar energy and embodied solar energy in

185
rain, winds, and other environmental forces, The period
1920-1945 was one of rapid expansion of agriculture,
forestry and fishery operations which involved capturing
more "natural" energy for the economy. This additional
input required less mineral fuels to be burned to produce a
dollar of GPP, By 1945, the expansion had reached a limit
and the solar energy input to the economy remained nearly
constant over the 1945-1976 period. Any long term trend in
the solar energy input to the rj.S, (as evidenced by the
long term global warming trend over this period) could also
contribute to a declining ratio. A noisy solar energy
contribution to the economy could also explain some of the
noise in the time series.
(3) The quality factors used to convert the different
types of mineral fuels, and the hydro and nuclear power into
equivalent units could be in error. Since the percentage
use of each fuel type has changed dramatically since 1929
this could lead to unwanted trend in the data. For example,
coal was the primary mineral energy source in 1929 (at 787
of the total). mhe data assumed that a kcal of coal is
equivalent (quality factor = 1) to a kcal of oil, but oils
convenience and burnability mean that a larger percentage of
its kcals are actually available for use. Also, less energy
had to be invested in the biogeologic processes of making
coal than oil. Thus coal has less embodied energy than oil
(its quality factor is lower) and more kcal of coal should

186
have to be burned to produce a dollar of real GNP than kcal
of oil. This could show up in the data as an apparent
increase in energy use efficiency. Failure to properly take
into account the quality factors of the various forms of
energy, combined with a pronounced trend in the percentages
of each form used, can lead to a trend in the energy to GNP
ratio, along these same lines, the depletion of virgin
forests and mineral and soil deposits are energy inputs to
the economy whose omission could lead to trend in the energy
to GNP ratio.
1 third line of evidence for a constant embodied energy
to GNP ratio deals with international comparisons of data on
GNP and energy consumption. Darmstadter has taken the lead
in these studies (Darmstadter 1971, Darmstadter, Dunkerly
and Alt.ermann 1977, and Darmstadter, Dunkerly and s.ltermann
1978) In the latter paper data on the fossil energy to
gross domestic product (GDP) are presented for 9
industrialized countries for 1972. The authors conclude
that there are major differences in the energy/GDP ratios
for the countries and trace the cause to differences in
energy prices. 'hey also note a close inverse correlation
between their energy/GDP ratio and the import dependence of
the country. Countries like Canada (a net exporter) and the
U.S. (12T imports in 197 2) with low import dependence had
high energy/GDP ratios. Countries which import most of
their fossil fuel (Japan, France, Italy) had low energy/GDP

187
ratios, an alternative explanation for this relationship
can be formulated in terms of embodied energy. Imported oil
has more energy {the energy reguired for transportation)
embodied in it than domestic oil, Thus if one calculated
the embodied energy/GDP ratios for the nine countries, they
would find more nearly constant values. The postulated
equivalence between embodied energy and dollar cost
manifests itself in the fact that energy prices are higher
in the countries with a larger percentage of their fossil
energy coming from imports {which have higher embodied
energy costs).
Darmstadter, Dunkerly and Alterman {1977) also
presented a 34 country survey of energy consumption versus
GDP. They found a high {R square = 0.85) correlation
between GD? and fossil and hydro energy consumption (or a
relatively constant energy/GDP ratio). Their survey covers
only the more industrialized nations so their inclusion of
only fossil and hydro energy was an adequate approximation
of total energy consumption, They also presented time
series data on the energy/GDP ratio for 5 of the countries
from 1961 to 1974 which show the relative constancy of the
ratio through time.
^aken together, the preceding data and arguments
provide significant evidence for a very close relationship
between total embodied energy and economic market value both
cross-sect!onally and intertemporally. This is a reasonable

188
outcome from -both an energetic and an economic point of view
if energy is given its rightful'thermodynamic role as the
ultimate scarce resource. Since all things are forms of
embodied energy, there is no possibility for substitution of
"something else" for this input. An economic system
concernea with the optimum allocation of this all-
encompassing scarce resource will set prices according to
embodied energy cost.
Conclusions and Predictions from the Simulation Models
Both the TT.S. economy-environment and south Florida
simulation models were capable of approximating the
historical behavior of the respective systems based on solar
energy inputs and a power-maximising decision structure.
Due to the inherent difficulty of adjusting the models, no
systematic parameter optimization was attempted, therefore,
the results cannot necessarily be considered as the "best"
approximations of which these models are capable. The
results do indicate the potential and some of the problems
with this type of modeling, however. For example, there are
several models potentially capable of approximating the
historical behavior of the TT.S. economy at the level of
aggregation used in this study. The most popular has been
the simple exponential growth model. Generally, the

189
simplest model capable of reproducing the systems behavior
is considered to be the best. This is not necessarily
true, however, if the criterion is a general understanding
of the system and thus predictive ability. For example,
Newtonian physics is simpler than relativistic physics but
not as general. A more complete understanding of the system
is possible with relativity. Newtonian mechanics represents
a special, case which is nonetheless very useful.
The exponential growth model can be viewed as a special
case of the more general biological growth models applicable
only during a limited phase of the growth cycle. In the
same sense, the power-maximizing models developed in this
study can be viewed as more general statements of biological
growth models, intended to take into account evolutionary
changes in the internal connectivity structure of the
system.
It is clear that predictive models must limit their
exogenous variables to those which can be predicted. In the
simulation models presented here, solar energy, input (which
can be assumed to be constant with a high degree of
confidence) and the initial conditions are the only
exogenous variables. The.models predict behavior which is
consistent with the ultimate thermodynamic limits faced by
all systems.
The major problems with the models involved the lack of
systematic methods of fitting them to historical data, and

190
the resultant time intensity and uncertainty concerning
their use. In this study approximately 1000 man-hours were
spent developing and adjusting the models, and it is certain
that another 1000 could have led to better results. This
time intensity of even moderately sized nonlinear simulation
models has been a major stumbling block for many studies.
It is also apparen* that linearization or other
simplifications to sidestep the problems are not adequate,
This represents a major area where mathematical and computer
science research could prove fruitful.
Embodied Energy analysis and Economics
The results of this study indicate an intimate
connection between the input-output, embodied energy concept
and the behavior of economic systems. The importance of
energy flow in biological systems is well known and there is
no reason to suspect that humanity and its habitat are
immune to thermodynamic lim5.tations. The constant embodied
energy to dollar ratio (when embodied energy is calculated
using the input-output approach) may indicate that the
market and price mechanism have evolved as a relatively
inexpensive way for humans to quantify the total
thermodynamic cost of alternative actions, and to act
accordingly. Thus energy flow is the primary concern of
economic systems.

191
Some potential times of the embodied energy concept in
dealing tilth combined economic-ecologic systems were
presented. The range of possibilities is enormous, however,
and there is already a large literature of applications
using similar ideas. As our economic systems approach the
limits of the stored environmental assets, explicit
consideration of energy flows can only become more
important.

APPENDIX I
SOUTH FLORIDA LAND USE DATA
CONVERTED TO EMBODIED ENERGY UNITS

Table 19. South Florida land use data
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(xl012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(xlO3 128
ac cells)
Latitude
(N)
Longitude
(W)
1
12.82
13.10
96.1
0.85
28.51
81.54
2
12.85
33.17
71.83
0.98
28.51
81.28
3
18.30
18.20
17.10
0.97
28.28
81.54
4
22.42
25.52
36.66
1.80
28.28
81.28
5
9.85
14.10
11.40
0.74
28.05
81.54
6
15.06
13.97
13.56
1.68
28.05
81.28
7
9.49
11.60
13.60
0.78
27.82
81.54
8
11.00
12.10
9.97
1.28
27.82
81.28
9
11.30
9.20
10.20
0.92
27.82
81.02
10
4.48
10.10
15.90
0.36
27.59
81.54
11
16.70
20.10
15.00
1.28
27.59
81.28
12
16.70
17.80
11.90
1.26
27.59
81.02

Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longituc
(W)
13
4.48
4.82
2.96
0.50
27.36
81.54
14
16.70
13.90
12.60
1.28
27.36
81.28
15
16.70
16.00
9.82
1.28
27.36
81.02
16
15.95
14.87
17.50
1.39
27.36
80.76
17
19.62
17.54
10.47
1.46
27.36
80.50
18
12.33
6.66
3 8.50
0.90
27.36
80.24
19
4.34
4.10
3.51
0.50
27.13
81.54
20
13.10
13.40
10.40
1.28
27.13
81.28
21
12.10
13.10
10.80
1.28
27.13
81.02
22
6.15
4.81
5.97
1.28
27.13
80.76
23
19.10
13.60
12.20
1.28
27.13
80.50
24
19.19
13.00
47.56
1.43
27.13
80.24
194

Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitu<
(W)
25
7.27
8.69
6.95
0.57
26.90
82.06
26
14.20
9.35
15.20
1.10
26.90
81.80
27
13.60
10.80
17.60
1.24
26.90
81.54
28
12.20
12.10
9.38
1.28
26.90
81.28
29
19.00
20.50
27.30
1.28
26.90
81.02
30
3.48
3.72
6.12
1.28
26.90
80.76
31
32.70
33.50
33.00
1.28
26.90
80.50
32
21.10
19.00
12.60
1.28
26.90
80.24
33
7.13
15.20
59.00
0.53
26.90
79.98
34
0.49
1.78
0.40
0.05
26.67
82.32
35
10.80
12.50
15.40
0.79
26.67
82.06
36
15.00
55.60
83.60
1.18
26.67
81.80
195

Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitu<
(W)
37
15.80
11.80
20.10
1.28
26.67
81.54
38
19.50
19.10
16.00
1.28
26.67
81.28
39
21.80
22.20
12.10
1.28
26.67
81.02
40
40.40
45.50
50.30
1.28
26.67
80.76
41
44.80
45.90
52.60
1.28
26.67
81.50
42
29.90
32.10
31.10
1.28
26.67
80.24
43
6.35
44.40
113.00
0.59
26.67
79.98
44
2.25
3.99
8.39
0.16
26.44
82.06
45
14.10
14.60
27.50
0.96

26.44
81.80
46
16.20
17.30
30.30
1.28
26.44
81.54
47
14.80
16.00
20.30
1.28
26.44
81.28
48
17.30
18.00
15.50
1.28
26.44
81.02
196

Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE
49
42.80
41.80
43.80
50
44.30
44.90
46.20
51
31.60
40.30
41.10
52
4.40
21.60
62.10
53
9.72
12.60
73.70
54
27.20
27.00
28.00
55
22.00
23.20
29.30
56
16.00
16.40
16.70
57
34.20
27.40
34.10
58
44.00
41.90
43.80
59
30.20
41.70
107.00
60
3.58
25.00
107.00
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitude
(W)
1.28
26.44
80.76
1.28
26.44
80.50
1.28
26.44
80.24
0.48
26.44
79.98
0.67
26.21
81.80
1.28
26.21
81.54
1.28
26.21
81.28
1.28
26.21
81.02
1.28
26.21
81.76
1.28
26.21
80.50
1.28
26.21
80.24
0.31
26.21
79.98
197

Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitui
(W)
61
4.52
3.81
4.72
0.22
25.98
81.80
62
19.60
18.50
19.90
0.94
25.98
81.54
63
18.30
19.60
19.00
1.25
25.98
81.28
64
11.10
11.30
11.50
1.28
25.98
81.02
65
26.90
28.50
32.00
1.28
25.98
80.76
66
42.80
42.90
41.60
1.28
25.98
80.50
67
22.40
84.00
257.00
1.26
25.98
80.24
68
2.38
36.00
49.30
0.16
25.98
79.98
69
16.55
16.11
15.98
0.69
25.75
81.28
70
14.00
13.50
13.20
1.27
25.75
81.02
71
20.40
20.30
25.70
1.28
25.75
80.76
72
31.90
36.80
51.80
1.28
25.75
80.50
198

Table 1\9. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(xl012CE)
1973
Embodied
Energy
(xl012CE)
Land
Area
(10 3 128
ac cells)
Latitude
(N)
Longitui
(W)
73
11.20
113.00
264.00
0.89
25.75
80.24
74
0.51
16.50
5.55
0.03
25.75
79.98
75
25.97
25.30
24.90
1.31
25.52
81.02
76
24.10
24.90
24.60
1.28
25.52
80.76
77
10.20
35.30
39.10
1.28
25.52
80.50
78
5.03
11.20
100.00
0.47
25.52
80.24
79
19.01
18.15
17.94
0.88
25.29
81.02
80
20.40
20.40
19.90
1.11
25.29
80.76
81
10.90
9.68
9.66
0.87
25.29
80.50
82
4.99
4.88
58.30
0.24
25.29
80.24
83
5.40
4.16
24.92
0.20
25.06
80.50
84
5.23
6.68
17.85
0.20
24.83
81.02
199

Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitude
(W)
85
1.00
0.83
2.47
0.03
24.83
80.76
86
2.51
16.54
29.66
0.07
24.60
81.80
87
3.83
3.62
8.07
0.14
24.60
81.54
88
1.01
0.96
1.58
0.04
24.60
81.28
200

APPENDIX II
ANALOG COMPUTER DIAGRAM FOR THE
TWO COMPONENT EXCHANGE MODEL


£03

APPENDIX III
FORTRAN LISTING FOR THE
25-CELL SPATIAL MODEL

c
c
c
c
c
10
c
c
c
c
c
241
25 CELL SPATIAL SI ISOLATION MODEL
DIBENSIOS ED(25,25
DIMENSION P *
(25)
D/25,25) ,Y(25.25),Q(25),Ejr25) AR
I25);dC2§);DIT(25) #DLbfjf25)
DIMENSION Fl|25f ,F2j25,F3 (25) .F4 (25)
DIMENSION A (25) § (25) .fc (25) X (5) ,'lA (5, 5) ,Z (9)
DISENSION IS (10) ,CM (25)
ASSUME CONSTANT COEFFICIENTS FOR THIS RON
DO 10 1=1,25
A II) =.94
B (I) =. 3
C (I) =. 03
CONTINUE
READ LATITUDE AND LONGITUDE OF CENTROID OF
EACH CELL (IN DBGREEG NORTH AND NEST),
INITIAL STORAGE LEVELS, AND LAND AREAS OF EACH CELL
HRITE (6. 241)
FORMAT (M ,2X,I,4X.*DLAT(I) .4X,DLON (I) ,4X,Q(I) ,
15X,*AR (I) *^5X**CM(I) *,5X,*QINT^)
DO 200 I=l!25
READ(5,2pi[DLAT(I) ,DLOH(I) ,Q(I) ,AR(I) ,CM(I)
QIHT-QJ(I) /AR (I)
HHITE3d.5tgi. bLAT (I) DLON (I) Q (I) AR (I) CM (I) QINT
FORMAT (I5.6E 10. 3)
FORHATJ5F10.3)
CONTINUE
READ (5,250) (2(1) ,1=1,9)
FORMAT (9F6.0)
240
201
200
C
250
C
READ (5,26 0) (IS (I) ,1=1,10)
260 FORMAT (10 A1)
C CALCULATE IHTERCELL DISTANCES
C
DO 202 1=1,25
DO 203 J= 1, 25
^ED|IgJ^=( j[DLAT(I)-DLAT(J) ) *69.5256) **2* ( (DLON (I)-DLON (J))
203 CONTINUE*
202 CONTINUE
C C
C ASSUME CONSTANT EXTERNAL INPUTS FOR EACH CELL

DO 210 1*1,25
E(I)* 1.0*AH II)
DO 211 J*1,25
Y (I,J)*1.
IF (ED (I, J) LE. 0) GO TO
ED (I-JJ*B (I)/ED (I, J)
GO TO 211
ED II, J)*B (I)
CONTINUE
COHTINOE
215
215
211
210
C
C INITIALIZE AND RON
C
100
FT=30.
IPS* 1
DT=1.
pt*o.;
T=0.
GO TO 601
T=T+DT
DO 29 1*1
DO 29 1*1.25
DJI^AJI) *E (I)/ ( {1. A (I) *Q (I))
DO JO J* 1,25
**2)
330
350
30
29
410
430
450
|I=EDJ,lf*Q (J) /CUED (J,I) *Q (J))
IFII.EQ. 0 XI=0
IF (I. EQ. J GO TO 330
So^TO (3§0* *Q iJ) /i0m +ED (I'J> *Q{1)) **2)
d m(*D gf? SP (2*ED (r#J) *Q (I) 1 /(UED (T'J) *Q (I) ) **2
continue'
COHTINOE
DO 40 1=1,25
f 1 ( ti I *Q (I) /{1 + A (I) *Q (I) )
F4 (I) =C(IJ *Q (I)
F2 (ii =0.
DO 42 J=1.25
IF(I.EQ. J)GO TO 430
DI*D (I) 1.1
IF(DI-D(J>) 410,430,430
GIf0 45?)'
YfeJF2)IY,(Q),<'QlJ)/CEDI,J,*Q(T) + M
F
=F2(I) +Y(I
206

F3(31=F3(J) *1(1,3)
CONTINUE
CONTINUE
CALCULATE HE LEVEIS
DO 50 1=1-25
[iljgjl) +DT* (F1 (I) *F2 (IJ-F3 (I)-F4 (I))
CHECK TIHE AND PHINT HESDLTS IF NECESSARY
IT=PT*.0001
IF (IPR-IT) 60 1,60 1,600
600 PT=PT*DT
GO TO 100
C
C HAPPIHG HOOTIHE
C
601
111
42
40
C
C
C
50
C
C
110
120
C
180
146
145
WRITE (6,1111
IkliKfetf' ',im 'f2(i) r3m *m(i> *d(i
CONTINUE
150
DO 145 K=1,5
DO 146 1*1,5
IA CONTINUE
COHTIHOE
DO 150 1*1,25
K=5. 0 1 ( (DLAT (I) -
L=5. 01-i (DLON (I j -
ri)/ABI) .it*
IJ/AR I .GE.
I)/AH I .GE.
Q I)/AR I)
I /AR(I
I /AR I
I /AR I
[I /AR I
I)/AH I
!5kMW
GE.
.GE.
.GE.
.GE.
.GE.
.GE.
.GE.
27.59
81.28
2H
2
3
4
(5
6
7
8
2(9
l) /.23)
/.26
IA (K,L
IA K,L
IA K,L
IA iK,L
IA K,L.
IA ¡ K,L
IA K,L
IA K,L
IA K,L
IA K,L
=IS
= IS
=IS
=IS
=IS
= IS
=IS
=IS
=IS
= IS
(1
k
5
6
7
8
9
1
D)
207

WHITE f 6. 1 60) TX
160 FORMAT (M',16X,
DO 156 K=1, 5
DO 158 1=1.4
TIME =* ,F3.0)
170
158
156
C
C PHIHT LEGEND
C
FORMAT (10 X,25A1)
CONTINUE
CONTINOE
75
171
76
77
78
1000
WRITE 6.7 5)
FORHATjO *^30X, LEGEND8)
RsMJU/1 Is<1) 'IS(I' ,IS,I> IS,I)
CONTINUE
WRITE (6, 77) (2111-1*1-9)
FORMAT 12X. 8 0*,2x, 9F§. 0)
WRITE (6.78) (Z ill ,f=1.9)
FORMAT {10X,9F5.6,1X.*AND
IF (T.GE. FTGO T0#1000
PT=DT
DP*)
GO TO
STOP
END
100
28 51
82.32
10.00
1.0
1.0
28.51
82 .06
10.00
1.0
1.0
28.51
81.80
10.00
1.0
1.0
28.51
81.54
10.00
1.0
1.0
28.51
81.28
10.00
1.0
1.0
28.28
82.32
10.00
1.0
1.0
28.28
82.06
10.00
1.0
1.0
28.28
81.80
10.00
1.0
1.0
28.28
81.54
10.00
1.0
1.0
28.28
81.28
10.00
1.0
1.0
28.05
82.32
10.00
1.0
1.0
28.05
82.06
10.00
1.0
1.0
28.05
81.80
10.00
1.0
1.0
28.05
81.54
10.00
1.0
1.0
28.05
81.28
10.00
1.0
1.0
27.82
82.32
10.00
1.0
1.0
27.82
82.06
10.00
1.0
1.0
27.82
81.80
10.00
1.0
1.0
27.82
81.54
10.00
1.0
1.0
208

27.82
81.28
10.00
1.0
1.0
27.59
82.32
10.00
1.0
1.0
1.0
27.59
82.06
10.00
1.0
27*§3
81.80
10.00
1.0
1.0
27.59
81.59
10.00
1.0
1.0
27.59
81.28
10.00
1.0
1.0
5.0 10.0 15.0
;-=/i*x$
20.0 25.0
30.0
35.0 40
*
1
O 50.0
209

APPENDIX IV
EMBODIED ENERGY IN GOODS AND SERVICES
FOR 92 U.S. ECONOMY SECTORS IN 1967

211
Table 20
Embodied energy in goods and services for 92 U.S. economy sectors
Sector
(numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C
Excluding Including
Labor and Labor and
Government Government.
Services Services
Feedbacks Feedbacks
but Includ- but Exclud
ing Solar ing Solar
Energy Inputs Energy Inputs
All Values in Btu fossil/S
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
1.
Coal Mining (7)
5,143.600
5,172,000
5,455,600
5,807,500
2.
Crude Petroleum & Natural Gas (8)
2,920,300
2,929,200
3,188,600
3,569,050
3.
Petroleum Refining & Related Products (31.01)
1,422,300
1,432,250
1,748,400
2,085,500
4.
Electric Utilities (68.01)
505,500
513,900
796,220
1,099,950
5.
Gas Utilities (68.02)
809,380
816,400
1,109,700
1,421,000
6.
Other Agricultural Products (2)
81,567
775,090
381,090
1,385,400
7.
Forestry & Fishery Products (3)
62,565
23,297,500
337,420
23,861,500
8.
Livestock & Livestock Products (1)
55,276
340,710
363,800
1,053,500
9.
Agricultural, Forestry & Fishery Services (4)
32,697
202,265
336,640
826,300
10.
Iron S Ferroalloy Ores Mining (5)
65,904
87,840
395,620
755,500
11.
Nonferrous Metal Ores Mining (6)
61,037
99,605
406,060
800,800
12.
Stone £ Clay Mining £ Quarring (9)
97,477
109,420
417,630
760,900
13.
Chemicals & Fertilizer Mineral Mining (10)
59,002
71,645
352,820
667,500
14.
New Construction (11)
54,804
230,245
389,770
913,950

Table '20
(Continued)
Alternative!
Sector
(numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
B
Excluding
Labor and
Government
Services
Feedbacks
but Includ
ing Solar
Energy Inputs
All Values
C
Including
Labor and
Government
Services
Feedbacks
but Exclud
ing Solar
Energy Inputs
in Btu fossil/S
C
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
15.
Maintaince and Repair Construction (12)
42,803
102,060
384,660
801,350
16.
Ordnance & Accessories (13)
41,768
78,285
381,130
772,600
17.
Pood & Kindred Products (14)
62,872
346,845
390,760
1,054,700
18.
Tabacco Manufactures (15)
30,009
197,715
469,000
1,068,550
19.
Broad & Fabrics, Yarn & Thread Mills (16)
68,156
167,815
392,370
830,400
20.
Miscellaneous Textile Goods & Floor Coverings (17)
67,389
125,200
384,490
775,450
21.
Apparel (18)
.38,845
295,135
371,107
974,600
22.
Miscellaneous Fabricated Textile Products (19)
50,462
117,365
376,750
784,250
23
Lumber & Wood Products, Except Containers (20)
54,159
2,829,200
372,490
3,478,850
24.
Wooden Containers (21)
39,681
1,102,550
365,030
1,766,750
25.
Household Furniture (22)
42,521
448,550
371,210
1,119,850
26.
Other Furniture & Fixtures (23)
50,180
248,375
373,900
919,850
27.
Paper & Allied Products Except Containers & Boxes (24)
88,279
366,800
405,650
1,013,750

Table 20
(Continued)
Sector
(numbers in parenthesis are DEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C
Excluding Including
Labor and Labor and
Government Government
Services Services
Feedbacks Feedbacks
but Includ- but F.xclud-
ing Solar ing Solar
Energy Inputs Energy Input3
All Values in Btu fossil/$
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputo
28.
Paperboard Containers & Boxes (25)
64,123
0
36,051
191625
393,530
863,800
29.
Printing & Publishing (26)
93,360 .
365,790
766,700
30.
Chemicals 6 Selected Chemical Products (27)
218,430
262,410
528,740
893,050
31.
Plastics & Synthetic Materials (28)
141,730
179,180
463,370
834,300
32.
Drugs, Cleaning & Toilet Preparations (29)
58,672
54,725
372,110
733,650
33.
Paints s Allied Products (30)
107,100
160,680
425,290
809,300
34.
Paving Mixtures & Blocks (31.02)
361,470
377,745
1,003,400
1,676,300
35.
Asphalt Felts & Coatings (31.03)
246,420
295,110
639,540
1,082,750
36.
Rubber 8, Miscellaneous Plastics Products (32)
95,144
128,870
432,050
814,050
37.
Leather Tanning & Industrial Leather Products (33)
133,600
146,235
369,910
627,950
38.
Footwear & Other Leather Products (34)
51,714
105,720
367,620
751,400
39.
Glass & Glass Products (35)
56,916
105,600
379,200
763,400
40.
Stone & Clay Products (36)
97,629
124,345
423,790
789,300
213

Table '20
(Continued)
Alternative
A
B
Excluding
c
Including
D
Excluding
Labor and
Labor and
Including
Labor and
Government
Government
Labor and
Government
Services
Scrv1 oes
Government
Services
Feedbacks
Feedbacks
Services
Feedbacks
but Includ-
but Exclud-
Feedbacks
and Solar
ing Solar
ing Solar
and Solar
Sector
(numbers in parenthesis are BEA sector equivalents)
Energy Inputs
Energy Inputs
Energy Inputs
Energy Inpub
All values in Btu fossil/?
41.
Primary Iron & Steel Manufacturing (37)
191,670
211,570
517,450
876,150
42.
Primary Nonferrous Metals Manufacturing (38)
61,002
91,975
365,500
712,200
43.
Metal Containers (39)
169,170
196,040
503,020
877,200
44.
Heating, Plumbing & Fabricated Structural Metal Products(40)
75,663
101,485
405,180
774,200
45.
Screw Machine Products, Bolts, Nuts, etc.,S Metal Stampings
(41)
72,656
98,910
404,560
776,950
46.
Other Fabrucated Metal Products (42)
68,788
97,470
391,620
756,450
47.
Engines & Turbines (43)
58,709
75,160
389,760
751,200
48.
Farm Machinery (44)
63,300
84,800
394,780
761,600
43.
Construction, Mining, Oil Field Machiner, Equipment (45)
63,345
81,015
332,830
753,550
50.
Materials Handling Machinery i Equipment (46)
53,108
71,420
387,190
753,900
51.
Metalworking Machinery & Equipment (47)
47,631
62,730
378,670
739,250
52.
Special Industry Machinery & Equipment (46)
50,064
80,210
382,800
760,000
53.
General Industrial Machinery & Equipme-nt (49)
54,403
77,855
385,670
754,350
54.
Machine Shop Products (50)
55,338
69,680
385,170
742,450
214

Table 20
(Continued)
Alterna
tive
A
n
C
D
Excluding
Including
Including
Excluding
Labor and
Labor and
Lalior and
Government
Government
Labor and
Government
Services
Services
Government
Services
Feedbacks
Feedbacks
Services
Feedbacks
but Includ-
but Exclud-
Feedbacks
and Solar
ing Solar
ing Solar
and Solar
Sector
Energy Inputs
Energy Inputs
Energy Inputs
Energy Inputs
(numbers in parenthesis are BEA sector equivalents)
All Values in Bt:u fossil/$
55. Office, Computing & Accounting Machines (51)
28,192
47,655
358,350
722,100
56. Service Industry Machines (52)
50,201
75,140
378,460
745,100
57. Electric Transmission 6 Distribution Equipment & Electrical
Industrial Apparatus (53)
46,727
69,030
375,410
740,400
5B. Household Appliances (54)
54,215
81,855
391,740
750,200
59. Electric Lighting & Wiring Equipment (55)
46,291
66,535
387,030
721,100
60. Radio, Television & Communication Equipment (56)
26,430
50,430
363,060
738,050
61. Electronic Components & Accessories (57)
36., 165
55,895
371,730
742,400
62. Miscellaneous Electrical Machinery, Equipment & Supplies (58)44,233
66,080
374,300
740,900
63. Motor Vehicles & Equipment (59)
54,469
74,160
404,860
785,600
64. Aircraft & Parts (60)
35,540
51,870
380,510
757,600
65. Ocher Transportation Equipment (61)
51,905
190,660
396,120
881,800
66. Professional, Scientific & Controlling Instruments &
740,700
Supplies (62)
37,380
65,610
367,860
67. Optical, Ophthalmic, & Photographic Equipment & Supplies(63)
32,033
50,580
339,640
678,150
215

Table 20. (Continued)
Sector
(Numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B
Excluding
Labor and
Government
Services
Feedbacks
C
Including
Labor and
Government
Services
Feedbacks
but Includ- but Exclud
ing Solar ing Solar
Energy Inputs Energy Inputs
All Values in Btu fossil/$
68. Miscellaneous Manufacturing (64)
45,403
130,965
366,890
69 Railroads & Related Services (65.01)
60,218
72,575
399,140
70. Local, Suburban & InterurbanHighway Passenger Transportation
(65.02)
56,240
61,570
348,]20
71. Motor Freight Transportation & Warehousing (65.03)
80,561
89,095
422, 150
72. Water Transportation (65.04)
85,647
105,430
484,970
73. Air Transportation (65.05)
122,630
143,910
452,230
74. Pipe Line Transportation (65.06)
132,980
143,285
468,340
75. Transportation Services (65.07)
5,672
11,615
346,970
76. Communications Except Radio & Television Broadcasting (66)
13,571
19,640
359,400
77. Radio & TV Broadcasting (67)
20,722
40,165
354,050
78. Water & Sanatary Services (68.03)
68,101
86,080
425,490
79. Wholesale S Retail Trade (69)
29,302
43,265
411,490
80. Finance & Insurance (70)
17,472
30,195
364,840
81 Real Estate & Rental (71)
26,362
45,465
357,320
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inpute
787.350
762.500
655.700
784,600
918.650
814.700
825.700
706,750
716.650
718.500
812,300
814.350
737.350
707,250
216

Table 20
(Continued)
Sector
(numbers in Parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C D
Excluding Including
Labor and Labor and Including
Government Government Labor and
Services Services Government
Feedbacks Feedbacks Services
but Includ- but Exclud- Feedbacks
ing Solar ing Solar and Solar
Energy INputs Energy Inputs Energy Inpujs
All Values in Btu fossil/S
82.
Hotels & Lodging Places; Personal & Repair Services,
Except Automobile Repair (72)
41,839
58,875
359,550
705,900
83.
Business Services (73)
23,146
43,995
339,610
689,250
84.
Automobile Repair & Services (75)
41,209
51,365
359,280
698,200
85.
Amusements (76)
22,217
55,395
376,110
771,500
86.
Medical, Educational Services Nonprofit Organization
(77) 32,253
46,590
354,370
704,950
87.
Federal Government Enterprises (78)
27,503
32,695
362,330
720,750
88.
State & Local Government Enterprises (79)
61,893
82,185
441,310
855,800
89
Business Travel, Entertainment and Gifts (81)
69,697
282,015
401,410
962,150
90
Office Supplies (82)
49,223
152,390
373,710
814,700
91.
Government


717,160
1,393,050
92.
Households


358,350
738,050
to
M

APPENDIX V
TIME SERIES DATA FOR THE U.S.
ECONOMIC-ECOLOGIC SYSTEM

Table 21
Real GNP, total fossil, hydro, and nuclear energy
consumption and fossil, hydro, and nuclear energy
to real GNP ratio, 1920-1976.
Yea
Total Mineral
Fuels, Hydro Energy Consumption
and Nuclear per Dollar
Real GNP Energy Consumed of real GNP
(x 109 1967 $/yr) (xlO1^ kcal/yr) (kcal/1967$)
1920
168.5
5004.9
29702.7
1921
164.6
4151.8
25227.6
1922
174.3
4355.4
24988.0
1923
197.2
5486.3
27821.0
1924
203.2
5174.6
25465.6
1225
208.0
5237.5
25420.7
1926
221.6
5691.3
25682.8
1927
223.7
5522.5
24687.1
1923
226.4
5662.4
25010.6
1929
240.0
6010.3
25042.9
1930
217.2
5638.9
25961.8
1931
202.0
4756.1
23545.0
1932
171.8
4147.2
24139.7
1933
167.1
4275.7
25537.7
1934
182.9
4538.1
24811.9
1935
201.9
4834.1
23943.0
1936
228.8
5418.8
23682.6
1937
242.3
5756.0
23755.7
1938
231.2
5029.6
21754.3
1939
249.9
5462.0
21856.7
219

220
Table 21. (Continued)
Year
Real GNP .
(x 109 1967 $/yr)
Total Mineral
Fuels, Hydro
and Nuclear
Energy Consumed
(x 1012 kcal/yr)
Energy Consumption
per Dollar
of real GNP
(kcal/1967$)
1940
271.7
6048.7
22262.4
1941
314.4
6736.1
21425.3
1942
352.4
7057.9
20028.1
1943
391.7
7701.8
19662.5
1944
419.7
8050.7
19182.0
1945
414.0
7979.9
19275.1
1946
373.0
7715.0
20683.6
1947
372.7
8316.1 -
22313.1
1948
387.0
8600.5
22223.5
1949
386.5
7995.8
20687.7
1950
420.0
8640.7
20673.1
1951
451. 3
9339.0
20693.1
1952
465.4
9253.7
19883.3
1953
486.2
9537.3
19616.0
1954
479.4'
9199.1
19133.3
1955
515.9
10103.9
19594.7
1956
525.9
10627.3
20224.2
1957
533.0
10605.8
19898.3
1958 .
526.9
10497.7
19923.5
1959
560.6
1107.3'
19634.9
1960
574.5
11338.4
19736.1
1961
585.7
11530.0
19685.8

221
Table 21. (Continued)
Total Mineral
Fuels, Hydro Energy Consumption
and Nuclear per Dollar
Real GNP Energy Consumed of real GNP
Year (x 10y 1967 $/yr) (x 10-^ kcal/yr) (kcal/1967$)
1962
624.1
12047.9
19304.4
1963
649.0
12543.2
19327.0
1964
684.5
13043.2
19055.1
1965
727.7
13654.2
18763.5
1966
775.2
14453.9
18645.4
1967
795.3
14961.2
18812.0
1968
832.3
15772.2
18890.1
1969
854.7
16675.7
19510.6
1970
851.1
17291.4
20316.5
1971
879.1
17701.9
20136.4
1972
933.5
18522.9
19842.4
1973
988.5
19189.9
19413.2
1974
967.3
18702.4
19334.6
1975
939.6
18240.7
19413.3
1976
934.4
18984.6
19285.5
United States Department of Commerce (1976a)
American Petroleum Institute (1971)
United States Department of Commerce (1971)
Sources:

222
Table 22. U.S. business sector net capital, investment, and
depreciation time series in constant dollars
(billions of 1967 dollars (a) ) .
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1929
371.25
43.11
17.67
25.44
1930
378.47
29.93
4.06
25.87
1931
371.94
17.13
- 7.91
25.04
1932
353.41
5.18
-18.37
23.55
1933
331.76
7.85
-14.35
22.20
1934
315.01
12.43
- 8.97
21.40
1935
307.38
23.00
1.70
21.3 0
1936
310.24
30.08
8.16
21.92
1937
318.69
36.30
13.51 '
22.79
1938
320.32
20.56
- 2.45
23.01
1939
318.55
28.87
6.03
22.84
1940
325.63
35.85
12.24
23.61
1941
340.07
42.72
18.12
24.60
1942
347.56
25.57
1.34
24.23
1943
334.21
17.61
- 5.17
22.78
1944
329.58
18.13
- 3.97
22.10
1945
323.72
24.55
2.10
22.45
1946
338.98
59.50
34.90
24.60
1947
369.21
56.98
28.56
28.42
1948
397.81
65.04
33.10
31.94
1949
418.10
49.14
14.50
34.64
1950
439.49
70.68
33.70
36.98

223
Table 22. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
473.94
76.04
36.88
39.16
1952
503.09
66.26
25.61
40.65
1953
524.61
67.16
25.05
42.11
1954
540.95
59.79
16.13
43.66
1955
562.33
77.24
31.49
45.75
1956
592.84
79.44
31.31
48.13
1957
618.44
75.24
24.94
50.30
1958
633.42
63.65
12.02
51.63
1959
648.95
78.05
25.08
52.97
1960
672.10
80.05
24.81
55.24
13 61
692.39
76.19
19.00
57.19
1962
715.14
87.66
28.32
59.34
1963
743.87
91.00
38.87
62.13
1964
776.01
99.25
33.81
65.44
1965
817.69
115.71
45.97
69.74
1966
870.94
130.36
54.35
76.01
1967
921.60
122.18
41.01
81.17
1968
964.36
126.47
41.65
84.82
1969
1009.72
135,54
46.90
88.64
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.

224
Table 23. U.S. government sector net capital, investment/
and depreciation time series in constant dollars
(billions of 1967 dollars (a)).
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1929
247.05
18.64
13.65
4.99
1930
258.21
20.98
16.03
4.95
1931
270.57
22.43
17.39
5.04
1932
282.40
20.92
15.75
5.17
1933
292.10
18.93
13.56
5.37
1934
302.07
22.23
16.81
5.42
1935
313.36
21.85
16.26
5.59
1936
327.71
29.54
23.90
5.64
1937
344.19
26.18
19.91
6.27
1938
360.80
29.57
23.02
6.55
1939
378.61
30.82
23.81
7.01
1940
397.48
32.94
25.45
7.49
1941
423.53
46.96
38.08
8.88
1942
482.80
103.13
91.30
11.83
1943
578.48
133.04
111.01
22.03
1944
663.00
137.43
76.44
60.99
1945
695.16
97.08
5.92
91.16
1946
672.57
23.98
-20.41
44.39
1947
641.34
24.72
-12.42
37.14
1948
622.47
30.17
- 0.74
30.91
1949
615.16
36.59
10.35
26.24
1950
615.43
37.68
14.39
23.29

225
Table 23. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
623.14
47.77
25.61
22.16
1952
652.24
76.15
56.54
19.61
1953
695.43
78.93
55.17
23.76
1954
733.17
74.31
47.07
27.24
1955
763.34
70.82
41.99
28.83
1956
791.11
93.92
44.91
29.01
1957
821.54
79.25
49.88
29.37
1958
857.16
87.87
57.52
30.35
1959
897.03
90.91
59.98
30.93
1960
926.80
85.43
53.49
31.94
1961
964.27
93.40
61.83
31.57
1962
1005.07
96.72
64.67
32.05
1963
1048.66
101.76
69.37
32.39
1964
1092.78
102.83
69.62
33.21
1965
1135.31
102.45
68.95
33.50
1966
1182.08
112.01
79.11
32.90
1967
1237.50
119.73
86.46
33.27
1968
1296.24
123.40
88.92
34.48
1969
1351.79
123.38
87.79
35.59
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.

226
Table 24. U.S. household sector net capital, investment,
and depreciation time series in constant dollars
(billions of 1967 dollars (a)).
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1329
1052.21
77.02
19.42
57.60
1930
1073.79
63.96
5.65
58.31
1931
1084.33
58.93
- 0.19
59.12
1932
1085.31
46.64
-11.54
58.18
1933
1080.29
45.05
-12.10
57.15
1934
1079.18
51.76
- 5.11
56.87
1935
1084.58
56.87
- 0.41
* 57.28
1936
1095.98
65.11
5.40
59.71
1937
1112.04
68.34
7.66
60.68
1938
1125.77
62.93
0.75
62.18
1939
1140.12
70.77
8.89
61.88
1940
1164.15
79.92
18.86
60.96
1941
1198.23
93.50
27.90
65.60
1942
1232.44
84.23
15.79
68.44
1943
1261.25
83.47
13.36
70.11
1944
1288.72
81.42
9.87
71.55
1945
1317.28
87.59
11. 69
75.90
1946
1359.22
109.61
30.03
79.57
1947
1412.43
113.99
34.14
79.85
1948
1468.58
121.19
38.06
83.13
1949
1525.71
123.88
36.07
87.81
1950
1588.00
141.03
47.83
93.20

227
Table 24. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
1651.88
137.45
38.75
98.70
1952
1710.73
139.25
35.61
103.64
1953
1772.28
149.34
41.88
107.46
1954
1837.99
153.59
42.07
111.52
1955
1911.56
173.64
57.61
116.03
1956
1990.76
173.83
49.83
124.00
1957
2066.16
175.50
45.87
129.63
1958
2137.03
173.44
40.62
132.82
1959
2212.68
190.74
54.35
136.39
1960
2298.50
192.49
52.59
139.90
1961
2383.10
193.81
50.32
143.49
1962
2470.27
210.14
61.89
148.25
1963
2567.87
221.29
67.49
153.80
1964
2673.92
236.86
75.87
160.99
1965
2791.01
255.12
85.64
169.48
1966
2920.49
269.36
97.26
172.10
1967
3049.10
266.94
87.92
179.02
1968
3179.43
292.50
104.38
188.12
1969
3321.65
305.30
105.12
199.74
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.

228
Table 25. U.S. environment sector, U.S. economy, total U.S.
(environment plus economy), and rest of the world
net capital stock (in billions of 1967 dollars).
Year
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
Economy)
Net Capital
Stock
Rest of t:
World Net
Capital
Stock (c)
1929
20400
'1671
22071..
327589
1930
20290
1711
22001
326550
1931
20195
1727
21922
325378
1932
20112
1721
21833
324057
1933
20024
1703
21728
322498
1934
19931
1696
21627
320999
1935
19834
1705
21539
319693
1936
19722
1734
21456
318461
1937
19606
1775
21381
317348
1938
19506
1807
21313
316339
1939
19396
1837
21233
315151
1940
19273
1887
21160
314068
1941
19135
1962
21097
313133
1942
18991
2063
21054
312494
1943
18837
2174
21011
311856
1944
18667
2283
20950
310951
1945
18504
2336
30840
309318
1946
18 349
2371
20720
307537
1947
18183
2423
20606
305845

229
Table
Year
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
25. (Continued)
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
Economy)
Net Capital
Stock
Rest of the
World Net
Capital
Stock (c)
18013
2489
20502
304301
17856
2559
20415
303010
17686
2613
20299
301288
17502
2749
. 20251
300576
17319
2866
20185
299596
17130
2992
20122
290661
16948
3112
20060
297741
16748
3237
19985
296628
16537
3375
19912
295544
16328
3506
19834
294387
16122
3628
19750
293140
15905
3759
19664
291863
15697
3897
19594
390824
15468
4040
19508
289548
15230
4191
19421
288257
14981
4361
19342
287084
14723
4543
19266
285956
14454
4744
19198
284947
14169
4973
19142
284115
13872
5208
19080
283224

230
Table 25. (Continued)
Year
U.S. Envir
onment Net
Capital
Stock
(a)
U.S. Econ
omy Net
Capital
Stock (b)
Total U.S.
(Environ
ment plus
(Economy)
Net Capital
Stock
Rest of the
World Net
Capital
Stock (c)
1968
13560
5440
19000
282008
1969
13229
5693
18912
290702
(a) Sum of U.S. land stock (Table 26) and estimated value
of mineral reserves. Table 27 gives estimates of
withdrawals of mineral reserve "capital" in direct
energy units and estimated real dollar value.
(b) Sum of U.S. business, government and households' net
capital stock (Tables 22-24)
(c) Estimated as a constant percentage of total U.S. net
capital stock, based on relative land areas.

Table 26
231
Time series of net land stocks in the U.S.
(in billions of 1967 dollars).
Year
Land Eeld by
Business
Land Held by
Government
Land Held by
Households
Total
1929
288.9
51.0
53.3
393.2
1930
293. 9
50.9
54.2
399.0
1931
296.6
51.0
54.8
402.4
1932
296.7
51.0
55.4
403.1
1933
295.9
51.0
55.5
402.4
1934
395.9
51.2
55.5
402.6
1935
295.9
51.3
55.5
402.7
1936
295.4
51.7
55.4
402.5
1937
297.0
51.7
55.2
403.9
1938
299.6
51.3
55.2
406.1
1939
301.0
51.4
55.5
407.9
1940
300.8
51.7
56.4
408.9
1941
298.4
51.7
59.3
409.4
1942
294.4
51.8
62.7
408.9
1943
294.4
52.0
65.6
412.0
19 4 4
295.4
52.1
68.4
405.9
19 4 5
281.3
52.2
71.2
404.7
194 6
280.0
52.5
73.8
406.3
1947
280.2
52.8
76.6
409.6
1948
281.3
52.9
79.5
413.7
1949
293.2
53.3
82.4
418.9
1950
294.8
53.7
85.4
423.9

232
Table 26. (Continued)
Year
Land Held by
Business
Land Held by
Government
Land Held by
Households
Total
1951
286.8
54.2
88.9
429.9
1952
288.5
54.6
92.0
435.1
1953
290.2
55.3
95.3
440.8
1954
292.3
55.9
98.6
446.8
1955
294.4
56.5
102.9
453.8
1956
296.5
57.5
107.3
461. 3
1957
299.6
58.7
110.8
469.1
1958
302.7
60.0
114.3
477.0
1959
305.7
61.2
118.1
485.0
1960
310.0
78.6
121.8
510.4
1961
313.3
79.9
125.4
526.9
1962
316.5
81.4
129.0
535.3
1963
319.7
82.8
132.8
535.3
1964
322.9
84.7
136.9
544.4
1965
327.0
86.6
140.8
554.4
1966
331.8
88.5
144.6
564.9
1967
336.1
90.0
148.1
574.2
1968
340.9
91.3
151.8
594.0
1969
344.8
92.5
155.6
592.9
Source: Kendrick (1976) converted to 1967$

233
Table 27. Time series of total U.S. mineral fuel use and
estimated real dollar value.
Year
Mineral Fuel Use
(x 101/: kcal/yr)
Dollar Value of Fuel
(x 109 1967 dollars)
(a)
1929
5796
123
1930
5440
116
1931
5481
98
1932
3963
84
1933
4091
87
1934
4356
93
1935
4624
98
1936
5206

111
1937
5527
118
1938
4802
102
1939
5241
112
1940
5817
124
1941
6489
138
1942
6760
144
1943
7361
157
1944
7700
164
1945
7604
162
1946
7349
156
1947
7947
169
1948
8219
175
1949
7600
162
1950
8236
175

234
Table 27. (Continued)
Year
Mineral Fuel Use
(x 1012 kcal/yr)
Dollar
(x 109
Value of Fuel
1967 dollars)
(a)
1951
8936
190
1952
8845
188
1953
9145
195
1954
8825
188
1955
9730
207
1956
10223
218
1957
10209
217
1958
10058
214
1959
10578
225
1960
10926
233
1961
11114
237
1962
11529
247
1963
12095
257
1964
12561
267
1965
13124
279
19 6 6
13919
295
1957
14360
306
1968
15118
322
1969
15694
340
Source:
American Petroleum Institute
(1971).
(a) based on a conversion ratio if 47000 kcal fossil/1967 $

APPENDIX VI
FORTRAN LISTING FOR THE 5-SECTOR
.S. ECONOMY-ENVIRONMENT SIMULATION MODEL

NJ
U>
tTi
c
c
c
9
11
10
13
12
700
701
DISENSION
DISENSION
DISENSION
DISENSION
(5) ,F4 (5)
f?Qsa:
X{5) ,IP (45) IS (6)
READ INITIAL CONDITIONS AND COEFFICIENTS
5
A (I) C (I) E (I)
A'(i),C(f),E(I)
DO 10 1=1
READ 15
WRITE (
FORHAT,
FORSATJ4F15.3)
CONTINUE
DO 12 J=1,5
READI5.13) (B (I.J) 1=1. 5)
WRITE (6,1JV (B (I/O) ,I=* 5
FORHAT(bE10.3}
CONTINOE
READJ5#700^ (^HAX(I) ,1=1 ,5)
5)
20
C
C
C
{5,70 11
ATJ6A1
0 1=1,5
J=1,5
= 1.
OE
291
292
293
294
295
296
290
FORHAT (5F1
READ
FOBS
DO 20
DO 20
y(!.J
INITIALIZE AND RON
WHITE(6,291
RITE i 6,292
RITE 6,293
RITE 6,294
WRITEJ6.295
FORHAT {* 1 .
FORHAT 71, B =
FORMAT 7X,*G =
FORHAT 7X H =
FORHAT 7X,W =
(IS (I) ,1 = 1,6)
,QHAX 1
,QBAX 2
,QSAX 3
,QMAX (4
, QHAX
SHITE(6,296)
FORHAT (24X, QOANTITT*)
WRITE(6.290)
FORHAT(21,YEAR*,1X,*0
1 MAX)
FT=200.
IPR=2
V
2
3
4
51
E = E7RbNHENTAL ASSETS',OX ,A1, MAX = *,F7.0)
BOSINESS ASSETS',13X.A1,* MAX = ',F7.0)
GOVERNMENT ASSETS*.11X.A 1. MAX = ,F7.0)
HOOSEHOLD ASSETS' ,i2X,A1.' MAX = '.F7.0)
REST OF THE WORLD ASSETS' 4X PA 1 MAX = ',F7.0)

too
DT*1./24.
PT=0.
TP=Os
TPH=0.,
T=0.
GO TO 601
T=T*DT
DO 29 1=1-5
*e (i) /(c 1.n (i) *q (i)) **2)
DO *30 0=1-5
330
350
30
29
IF (I. EQ. JIGO TO 330
QI*B <1,01*Q (J)/ < <1. tB (1,0) *Q (I) ) **2)
GO TO 350
*(2*B(X,J)*Q(I)))/(1+B(I,J)*Q(I))**2
COHTINOE
40 1=1,5
iUc lifts
w
F4, ,
F2 (it =0.
DO 42 J=15
IF(I.EQ.O)GO TO 430
DI=D <11*1.2
CCCCCCCCCCCCCCCCC
IF IDI-D1J)) 410,430,430
410
430
450
WiS &
42
40
C
C
C
TI.J) =B (I, J1*Q F2 III =F2(lf i fl, J
F3joi=F3(J)+I *Q COHTINOE
COHTIHOE
CM.CUL&TE NEB LEVELS
DO 50 1=1 ,5
50
? Jii?2 ,i,'p3 -m(i)
:>)
COHTIHOE
TP=TP+P(1)+P (2) *P (3) +P (4)
TP8=TPH+P (1) +P (2) 4P <3) +P (4) *P (5)
J
237

c
c
600
CHECK TIRE AND PRINT RESULTS
IT=PT*.0001
IP (IPR-IT) 60 1*60 1*600
PT=PT+DT
GO TO 100
C
C PLOTTING ROOTINE
C
601 DO 110 1=1.5
110
270
260
111
200
150
750
W
770
TX=T*1929.
DO 270 1=1-45
IP 01*15(6)
CONTINUE
DO 150 1=1,5
DO 200 J=1 45
IP (IQ (I) EQ.J)GO TO 111
IP (IP {if. HE. IS (6) ) GO TO
IP (J) = IS 16)
GO TO 200
IPJJ) =IS (I)
CONTINOE
CONTINOE
200
RTE (6,750) TX, (IP (J) -J=1 *45)
FOHHATJlX,F6.0* *1* 45a1 * I*)
TO
1&00
I? (T.GE.FT)GO
PT=DT
GO TO 100
RITE(6,760) TP
FORflATfM '.BX,'TOTAL O.S.
HRITE(6.770)TPH
FORHAT (7X,*TOTAL WORLD
STOP
END
PRODUCTIVITY =*,E15.6)
PRODUCTIVITY = K1 5. 6)
4.580E-007 .015
321. 0. .03
247. 0. .03
1052. 0. .03
302834. 2.310E-008 .021
4.942E-0070.150E-0050
0.652E-0G50.500E-0040
44300.
0.
0.
0.
657700.
400E-0050.200E-0053. 505E-008
150E-0030.417E-0036.516E-007
0.206E-0050.800E-0040.100E-0012.542E-0051.464E-009
4.375E-0062.134E-0042.289E-005100.0E-0032.316E-010
238

APPENDIX VII
FORTRAN LISTING FOR THE 91-CELL
SOUTH FLORIDA SIMULATION MODEL AND DATA

ro
o
C
C
c
c
c
SOOTH FLORIDA LAND OSE SIMULATION MODEL
I) AR (91)
10
C
C
C
C
C
241
240
201
200
C
250
C
DIMENSION ED (91,91) ,1(91.91) .0 (91) ,E (91¡
DIMENSION P91) ,D(91).DLAT(9lf,DL0R(91)
DIMENSION F l (91) ,F2 (9 i) ,F3 (91) ,F4(91)
DIMENSION A (91) ,B (9i) ,6 (91) .1(91) ,IA (18,10) ,Z(9)
DIMENSION IS(10),CM(91) ,SS(91)
READ COEFFICIENTS FOR THIS RUN
S'* 1. 4
G=30,0
H=5.0
DO 10 1*1,91
A II) =.05
B(I|*. 002
C JI)=. 02
SS(I) = ,0002
CONTINOE
A (90) *0.
B 89) =5. 3E-8
B 90) *2. 25E-6
B 91)=5. 2E-10
Ss (89) =5E-8
SS|90)*5E-7
SS (91) *10E- 10
READ LATITUDE AND LONGITODE OF CENTROID OF
EACH CELL (IN DEGREEG NORTH AND WEST),
INITIAL STORAGE LEVELS, AND LAND AREAS OF EACH CELL
NRITE ( 6. 241)
FORMAT 1 ,2X,,I*,4Xf*DLATfI) ,4X,DLON(I) ,4X *Q (I) ,
15X,*AR (I) ;5x;*CMr(I) *,5X,*dl*JT)
DO 200 1=1,91
READ (5 ,20 11 DLAT (I) ,DLON(I) ,Q(I) AR (I) ,CM (I)
QIHT=Q?I) /AR (I)
FORMAT(f5 6I16 3)T 'A8(I) 'C" (I) QI NT
FORMAT <5f10.J 3)
CONTINOE
READ(5,250) Z (I) ,1=1,9)
FORMAT (9F6.0)
READ (5,260) (IS (I) ,1 = 1,1 0)

260 FGEBAT (10 A1)
C
C CAI.C0Lfi.1K XBTERCELL DISTANCES
t'*
DO 202 1=1,91
DO 203 3= 1,9 1
^ED|Xf(J&IAT (I) -DLAT (J)) *69,5256) **2* ( (DLON (I) -DLON (J) )
203 CONTINUE^
202 CONTINUE
0 205 1=1,88
DO 205 3=90,91
IFfCHm.LE. 1.16OTO205
pMmti*'*'''''
CONTINUE
205
C C
C ASSUME CONSTANT EXTERNAL INPUTS FOR EACH CELL
C
DO 210 1=1.91
| (I)
D
Y ij = ^
IF(D (I,J) .LE.O) GO TO 215
ED(I,j[=B (I)/ED(I,J)
SO TO 211
ED
CO
CONTINUE
215
211
210
C
C
C
ju Z IU - 1,^1
5 fII =1.0*AR (I)
Ljli = A (I) /AR jl)
>0 211 3= 1,91
¡MSS(I*
INITIALIZE AND RUN
FT=150.
IPR=10
DT=1. ,
PT=0.
T=0
GO T 601
100 T=T*DT
DO 29 1=1.91
DJI)=A (I) *E (I)/ { (1. *A(I) *Q (I)) **2)
F3(I> =0.
DO 30 3=1,91
XI=ED(J,lf*Q (J) / (1*ED (3,1) *Q (3))
IF (I. EQ. J) XI=0
241

i*QCJ)/((1*fED(I,J) *Q (I) ) **2)
330
350
30
29
410
430
450
42
40
C
C
C
QI=ED(I,J)
GO TO 350
jji-CBg (iJ)*Q(i)) J/(1*bd(i#j)^q (i) )*:
CONTINUE
CONTINUE
DO 40 1=1,91
P1 ill = A I)*B ill *Q F4 m=C(I)*Q (I)
F2(I1 = 0
DO 42 0=1,91
IP (I.EQ*J) GO TO 430
DI=DfI)*S
IP^DI-D^J)) 410,430,430
*Q(J)/(ED (I,J)*Q(I) +1. )
CONTINUE
CALCULATE NEW LEVELS
50
C
C
600
C
C
C
601
111
DO 50 1=1,91
SiftiM?+DT*{F1 CHECK TIBE AND PRINT BESOLTS IF NECESSARY
IT=PT*0001
IF (IPR-IT) 601,601,600
PT=PT*DT
GO TO 100
MAPPING ROUTINE
6,111]
WRITE(6,1111
FORMAT (M',2
110
120
C
f {* 11,2X, *1* 5X, *0 (I) ,51, D (II ,5X, #P1(I) 5X,'F
1 %5X *F (I)f,4{,^(,59) f,4i,W(I,§0) ,4X,iY(f ,9
v i*!) 1-1,91
RITE (6,110) I.Q(I) ,D (I) ,
flrt*?'*''*1'
I *P3(I
DO 12
WRITE
II
PORftATlf
CONTINUE
F2
1
,F1 (I) ,F2 (I) ,F3 (I) ,F4 (I) ,

TX=1900.*T
160
C
C
C
75
10X,EMBODIED ENERGY INTENSITY MAP'/r10X
IDA*/,10X,* FOR THE YEAR ,P10.0)
PRINT LEGEND
174
76
77
78
79
180
146
145
150
171
170
158
WBITEJ6.75)
FORMAT (*0 30X, LEGEND )
DO 76 3=1-5
WRITE (6,174) IIS (I) ,IS (I)
FOHHATJMOX, 50A1)
CONTINUE
WHITE (6,77) (Z (I),1=1,9)
FOBHAT 112 X, 0 *, 2X, 9P5. 0)
WRITE J6,78) (Z (if ,1=1.9)
FOBHAT(10X-9F5.0,IX,*AND
WRITE (6,79)
FORMAT (25X,M E12
DO 145 K=1,18
DO 146 L=1,10
IA
CO
COHTINOE
DO 150 1=1,88
K= 18. 0 1- ( (DLAT (I)-24.6)_/.23^
IS (I) ,IS(I) ,IS(I) ,1=1, 10)
UP*)
CE/12B AC CELL) ')
L=10 0 1-JfDLON (I
Xl^AR
/IB I
I)/AS
/AR
/AR
/AS I
NOE
/AR
/AR
/AR
I,
I
I
LT.Z
.GB.Z
. GE.Z
I .GE.Z
I .GB.Z
.GE.Z
. GE* Z
.GE.Z/7
GE.Z(8
GE.Z (9
7i)?iV
1
2
3
4
1
IA
IA
IA
IA
IA
IA
IA
A2
(K, L =IS
*K,L =IS
K, L =IS
K,L =IS
K,L =IS
K,L
K,L
K,L
IA k;l
IA(K,L
= IS
= IS
=IS 8
= IS (9
=IS
10)
FORMA1!^ 1%>V//#1 OX, *YEAR= VF5. 0,
1 *+ + + + *+*)
DO 156 K=1, 18
DO 158 1=1,4
U U IJU JL ml
WRITEJ6, 170) (IA (K,L),IA(K,L) ,IA(K,L)
FOBHAT 1101, * iX,50A1 ,iX, *< *)
,IA (K,L) ,IA (K,L) ,L=
CONTINdE
1,10)
243

o
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REFERENCES
LIST OF
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other urban areas. PhD Dissertation. University of
Florida, Gainesville. 298pp.

BIOGRAPHICAL SKETCH
Robert. Costanza was born in Pittsburgh, Pennsylvania,
on September 14, 1950, in 1957 his family moved to
Hollywood, Florida, where he attended and graduated from
Chaminade High School. In September of 1968 he entered
Purdue University as a student in Aerospace Engineering.
After three semesters, he transferred to the University of
Florida where he earned a Bachelor of Design degree in 1973
and a Master of Arts in Architecture degree in 1975. After
working for six months as a Research Associate at the Center
for Wetlands, University of Florida, he enrolled in the
doctoral program in Environmental Engineering Sciences,
Systems Ecology program. Ffe was graduated with a Doctor of
Philosophy degree from the University of Florida in 1979
254

I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
'T/L^
Howard T. Odum, Chairman
Graduate Research Professor of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
'Suzahne E. Bayley
Assistant Professor "of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully sdequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
B ar ney^L?^ Capeh
Associate Professor of
Industrial and Systems
Engineering
ihajf
iesso:

I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy
Wayne C. Huber
Associate Professor of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy
Chester D. Kylstfh
Associate Professor of
Nuclear Engineering Sciences
This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council, and
was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy
June 1979
Dean, College of Engineering
Dean, Graduate School

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7
dissertation is the application to combined economic-
ecologic systems. The relationship between energy analysis
and economic analysis has been the subject of recent debate
and is a major topic of this dissertation. Leach (1975) and
Webb and Pearce (1975) have challenged the ability of energy
analysis to provide useful information beyond that available
to standard economics. By treating the economic-ecologic
system as a unit and by following energy flows through it,
many of these questions may be clarified,
Si.ll£.§.d Energy
Embodied energy is defined as the total amount of
energy of a single type required directly and indirectly to
produce the substance of interest. For example, Figure 1
shows solar energy as the primary energy input to the earth.
Host flows and storages of free energy on the earth can be
thought of as embodied past and present sunlight, since
sunlight has been the most significant source of free energy
for the earth, Tides, nuclear energy, and residual heat
contribute much smaller amounts. mhus the sunlight of past
eons is embodied in the current storages of fossil fuel, raw
materials, soil, etc. that are employed by industrial
society. It is convenient to divide the continuum of energy
sources into renewable sources of free energy (embodied
present sunlight) and nonrenewable storages (embodied past
sunlight) on the basis of their relative rates of production


APPENDIX IV
EMBODIED ENERGY IN GOODS AND SERVICES
FOR 92 U.S. ECONOMY SECTORS IN 1967


60


12
Figure 2. Diagram showing, the characteristics of the
input-output and biosphere embodied energy
concepts.


253
Von Bertalanffy, L. 1 968. General system theory. George
Braziller, New York. 289pp.
Wagner, H.H. 1975. Principles of operations research.
Second S3 it. ion. Prentice-Hall. Englewood
Cliffs, Hew Jersey..1939pp.
Walderhaug, A.. J. 1973. The composition of value added in
the 1963 input-output study. April survey of current
business. Bureau of Economic Analysis. Washington,
9. C.
Wang, F.C., H.7. Odum and p. Costanza. 1978. Concepts for
the assessment of the energy related impacts of water.
American Society of Civil Engineers Spring Convention.
Eeprint no. 3246. Pittsburgh, Pa.
Webb, H., and 9. Pearce, 1975. The economics of energy
analysis, Energy Policy. 3: 318-331.
Weber, A. 1990. TJbecden standort der industrien. Trans
lated by c.J, Friedrick as: Alfred Webers theory of
location of industries. University of Chicago Press,
Chicago.
Wilde, 9. J, and C. S, /Height ler. 1967. Foundations of
optimization, Prentice-Hall. Englewood Cliffs,
New Jersey.
Yugnovsky, 0. 1972. Problems of developing holistic models
of urban growth: review and conclusions for Latin
American plann-ing research. Public policy and urban
ization in the Dominican Pepublic and Costa Rica:
agenda and perspectives for future research. Ed.
Gustavo A. Antonn!. Center for Latin American
Studies. University of Florida, Gainesville.
Zucchetto, J. J, 1975. Energy basis for Miami, Florida, and
other urban areas. PhD Dissertation. University of
Florida, Gainesville. 298pp.


27
integration interval is reduced or the order of the
numerical method is increased, however, The main advantage
of the digital machine is its large capacity, allowing the
simulation of much more complex models than possible on
available analog machines.
An Amdahal digital computer was utilized for
running the large models of the U.S. economy and south
Florida for which detailed data were available. The models
were written in FOTTRAN using a rectangular integration
scheme. Listings of the FORTRAN programs are given in
Appendices TIT, VI, and VII, An Intecolor microcomputer was
also utilized for testing some mid-sized versions of the
models in BASIC,
node!_ Parameter Estimation, validation and Testing
Dynamic simulation models of the type used in this
study require a large number of parameters. Frequently,
there are not enough data available to calculate statistical
best fit estimates of the parameter values. Therefore,
initial estimates of the parameter values were generated
from the available data and these initial estimates were
adjusted iteratively until a reasonable fit was obtained
between the model and reality. The adjustment process was
limited to the least well known parameters and required
additional information about the historical behavior of the
system being modeled to compare with the model*s output.


58
produced as part of the study, "Carrying capacity for man
and nature in south Florida", edited by H.7. Odum and H.
Brown (1075), The maps are also included in Browder,
Littlejohn and Young (1975) and Costanza (1975) with
supporting data. mhe maps were manually digitized using a
cell size of 128 acres for computer manipulation. For this
study, the land use maps were aggregated to 88 larger square
cells, 15 miles on a side, as shown in Figure 13.
For example, Figure 14 is a full size copy of cell 45
in Figure 13 from the 1973 land use map. Figure 15 is a
computer printout of the same data to show how it was
digitized. '"'he correspondence between the symbols on the
printout and the numerical codes for the land use subsystems
listed in Table is given below the printout. Since not
all cells had the same land area, the area include? in each
cell was calculated and recorded. The data in Table 7 (from
Costanza 1975) were employed to perform the aggregation.
The subsystem structure intensities listed in Table 7 were
multiplied by the number of acres of that land use type in
each of the 88 south Florida cells, and these values were
accumulated for each cell to yield estimates of the total
embodied energy in each of the cells. This was done for
each of the three land use maps. These data are listed in
Appendix I, along with the ".and area, and latitude and
longitude of the centroid of each cell.




167
>-
,u
Â¥
h
+
+
+
h
+ :: :: : === =
+ :::::::::::::::
+ :::::::::::::::
+ :::::::::::::::
+
f + -- + + ++ + + +++ 4- + + + +<-+++++ +4- + ++-*-++-}-+ hr
--f-4-4-
+
+
4-
h
+
+
+
f
+
4--r -+-*+ 4- -h
(a)
+ + + + + + + ++ ++ + + + + + +


Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE
49
42.80
41.80
43.80
50
44.30
44.90
46.20
51
31.60
40.30
41.10
52
4.40
21.60
62.10
53
9.72
12.60
73.70
54
27.20
27.00
28.00
55
22.00
23.20
29.30
56
16.00
16.40
16.70
57
34.20
27.40
34.10
58
44.00
41.90
43.80
59
30.20
41.70
107.00
60
3.58
25.00
107.00
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitude
(W)
1.28
26.44
80.76
1.28
26.44
80.50
1.28
26.44
80.24
0.48
26.44
79.98
0.67
26.21
81.80
1.28
26.21
81.54
1.28
26.21
81.28
1.28
26.21
81.02
1.28
26.21
81.76
1.28
26.21
80.50
1.28
26.21
80.24
0.31
26.21
79.98
197


147
available made a regression fit of the parameters
impossible. The parameters were estimated by taking the
average values generated from the two years of 1-0 data as
initial estimates and then "fine tuning the least well
known parameters by fitting the simulation results to known
time series data. This was done using a manual directed
search technique (known in the vernacular as trial and
error). Sensitivity of the model to certain parameters was
also noted. Table 16 lists the initial estimates of the
model parameters (a^, b^j and c j) Estimating the a^
required information on the solar energy input to the U.s,
environment and the rest of the world (E ^ and Eg, Ewsre
assumed equal to 9), These values were estimated as 44,3
and 657.7 (E1B kcal/yr, respectively) based on data from
Budyko (19TB) and relative area figures.
"he dollar value of the direct inputs were estimated as
299 and 43"5 (E9 1967 5, respectively). The a were
estimated from the model relation:
7 i = a^E^Q^/1 + a^ where 7 ^ = value of the
direct input (in billions of 1967 $/yr)
E^ = energy of direct input (in E15 teal solar/yr)
solving for a^ yields:
ai = ~lT i / Qi(7j_ E). Eimilarily, the b^j parameters
were estimated from the 1963 and 1967 intersector flow data,
from the model relations:


42
redefinitions of gross and net flows (which are defined only
with reference to the boundary) are not made. For example,
consider Figure 9 Here a boundary has been drawn around
the "industrial' sectors of the economy with the consumers
outside the boundary in the manner of conventional
macroeconomics. The net output of the industrial sectors
(that which crosses the boundary to consumers) is defined as
the gross national product (GNP), The confusion starts with
this misnomer, since the GPP is really a net flow. The
total output or "total transactions" would be a measure of
the true gross product. If the boundary is expanded to
include the consumers, then the GPP is no longer a net
outflow but an internal transaction. The net output with
the expanded boundary would be depreciation plus net exports
plus any change in internal storage. Conceptual problems
with double counting arise when this is not realized and the
now internal transaction from producers to consumers is
still considered to be.a net outflow,, tiding the flow from
consumers to producers to the flow from producers to
consumers would obviously be double counting the GNP as
previously defined, With the expanded boundary, however,
the GPP is no longer the net output from the system and
should be treated like any other internal transaction.


234
Table 27. (Continued)
Year
Mineral Fuel Use
(x 1012 kcal/yr)
Dollar
(x 109
Value of Fuel
1967 dollars)
(a)
1951
8936
190
1952
8845
188
1953
9145
195
1954
8825
188
1955
9730
207
1956
10223
218
1957
10209
217
1958
10058
214
1959
10578
225
1960
10926
233
1961
11114
237
1962
11529
247
1963
12095
257
1964
12561
267
1965
13124
279
19 6 6
13919
295
1957
14360
306
1968
15118
322
1969
15694
340
Source:
American Petroleum Institute
(1971).
(a) based on a conversion ratio if 47000 kcal fossil/1967 $


33
imply5.no no net change in storage over the accounting
period. For systems not in steady state, any change in
storage can he accounted for in the net output column.
In reading the input-output table, the output from a
sector to other sectors is read as a row. In this example
agriculture (sector 1) delivers 10 units of output to
itself, 5 units to manufacturing (sector 2) 5 units to
consumers (sector 3) and 1 units to depreciation (net
output). Inputs to a sector are read as a column. In this
example consumers (sector 3) receive 5 units of agricultural
products (from sector 1), 30 units of manufactured products
(from sector 2) and 1 unit from themselves.
To convert to embodied energy units, first calculate
the energy intensity vector e, by applying the equation:
e = E (X-X) -1
In this example:
30 0
0
10
5
5
X =
0 10 0
n
X =
10
50
30
o n
2
.25
. 25
1
(X-X)
on -q -5
-10 50 -30
[300 ?no 0]
25
25 1


From Sector
RWIRONMENT 1
105900
163972
102023
158994
32708
BUSINESS 2
675358
73859
411337
29068
GOVERNMENT 3
70290
42052
68590
101
HOUSEHOLDS 4
362459
61877
116354
36
REST OF WORLD 5

20369
2982
6751
39508082
-31673C
149060
4067
62150
6937C
32390
67500
153800
-1562448
5899332
396000
1292448
282793
762026
43875068
NET INPUT
290100



4305000
4595100
TOTAL INPUT
396000
1292448
282448
762026
43875068
.
46608335


36
Table 3, Inpat-output transactions matrix in embodied
energy units, corresponding to the diagram in
Figure 8,
"o
From
Agri
culture
1
Hannfac
turing
A
Con
sumers
3
Net
Output
Total
output
Agriculture 1
363.6
181.0
181.8
363.6
1090.8
Kanufacturing 2
210. 2
1090. 9
654,5
218.2
2181.8
Consumers 3
209. 1
836.9
418.2
1672.7
Energy input F
onn
700
toon
Total input
1090.0
2181.0
1672.7


252
Smith, D. n. .and T. H. Lee, 1970. A programmed model for
industrial location analysis. Discussion papers, 1.
Dept, of Geography, Southern Illinois University.
Carbondale.
Soddy, E, 1933. Wealth, vixtual wealth and debt: the
solution of the economic paradox, D.P. Dutton and
Co, New York. 329pp.
United States Department of Commerce. 1969a. Input-output-
structure of the U.S. economy: 1963, Volume 1
Transactions data for detailed industries. Washing
ton, D.C. 195pp.
United States Department of Commerce, 1969b, Input-output
structure of the u.S. economy: 1963. November survey
of current business, Bureau of Economic Analysis,
Washington, D.C.
United States Department of Commerce. 1971. The statistical
abstract of the U.S. Bureau of the census. Cresset
and Dunlap, Inc., New York,
United States Department of Commerce. 1974a. Input-output
structure of the U.S. economy: 1967. February survey
of current business. Bureau of Economic Analysis,
Washington, D,C,
United States Department, of Commerce. 1974b. Input-output
structure of the U.S. economy: 1967 Volume 1
transactions data for detailed industries. Wash
ington, D.C. 195pp,
United states Department of Commerce. 1974c. Definitions
and conventions of the 1967 input-output study.
Social and economic Statistics Administration.
Bureau of Economic Analysis Interindustry Economics
Division. Washington, D.C,
United states Department of Commerce. 1975. Interindustry
transactions in new structures and equipment, 1967.
September survey of current business. Bureau of
economic Analysis,. Washington, D.C.
United States Department of Commerce. 1976a. Historical
statistics of the United states. Colonial times to
1971, Bureau of the Census, U.S. Government Print
ing Office. Washington, D.C.
United States Department of Commerce. 1976b. The national
income and product accounts of the United States, 1929-
197 4. U.S. Bureau Economic Analysis. U.S.
Government Printing office. Washington, D.C,


26
models. Baumol (1977) contains a readable description of
this technique, In essence it allows a static, constrained
optimisation problem to be translated into an equivalent
unconstrained problem using the device of the Lagrange
multipliers. This method yielded the general conditions
necessary for optimum (maximum power) behavior of the system
at each point in time. In algorithim, which employed these
conditions in a dynamic simulation framework, was then
developed and tested,
Hp delJ no Hethod s
Both analog and digital simulation procedures were
utilized in this study. The main advantage of the analog is
the "hands on" interaction with the model that its small
size and continuous operation facilitate. For these reasons
an TIT HiniSc analog computer was used to simulate a
simplified, two component, unsealed version of the model.
This allowed investigation of some theoretical aspects of
the model and the range of behavior which the model could
produce. n analog diagram of the model is given in
appendix IT.
Digital simulation requires integration by discrete
approximation and is therefore theoretically lass accurate
than the continuous integration possible on an analog
machine, niscrete integration quickly approaches the
accuracy of continuous integration as the size of the


133
1969b, 1974a, 1979}, These were supplemented by Sata from
Kendrick (1976) on hats an and government, capital flows. The
sector correspondence used in aggregating the data are given
in Table 15. Iks noted earlier, the government and household
sectors are endogenous with inputs from the other sectors
measured as government purchases and personal consumption
expenditures, respectively, and outputs estimated as the
percentage of value added attributable to government and
households. The gross investment of the economy sectors was
partitioned (using estimates from Kendrick 1976) into
investment to cover depreciation and net change in stock.
The depreciation and change in storage together make up the
total net output.
The rest of the world sector receives the exports and
supplies the imports to the u.S. economy, It is considered
to be an aggregate of all the economies and environments
other than the U.S. Tables 13 and 1 are estimates of the
net capital stock, gross investment and depreciation for the
14 sector breakdown for the years 1963 and 1967. The data
on gross investment and depreciation were incorporated into
the transactions matrix. Table 15 lists the sector
correspondences between the 14 aggregate sectors and other
breakdowns


Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longituc
(W)
13
4.48
4.82
2.96
0.50
27.36
81.54
14
16.70
13.90
12.60
1.28
27.36
81.28
15
16.70
16.00
9.82
1.28
27.36
81.02
16
15.95
14.87
17.50
1.39
27.36
80.76
17
19.62
17.54
10.47
1.46
27.36
80.50
18
12.33
6.66
3 8.50
0.90
27.36
80.24
19
4.34
4.10
3.51
0.50
27.13
81.54
20
13.10
13.40
10.40
1.28
27.13
81.28
21
12.10
13.10
10.80
1.28
27.13
81.02
22
6.15
4.81
5.97
1.28
27.13
80.76
23
19.10
13.60
12.20
1.28
27.13
80.50
24
19.19
13.00
47.56
1.43
27.13
80.24
194


90
Case 2: Production consumption pair. Another situation
to which the model may be applied is that of production and
consumption. In this situation one of the cells receives no
external energy of its own and survives strictly on exchange
with the producer component. The energetic rationale for
having a consumer population is that if the producers have
accumulated more structure than they can effectively use
{3Tp/3Q]_ is low), then the total power can be increased by
exporting some of the underutilised structure to a consumer
population, which utilizes it as its main energy source
f9Tp/9Q2 is high}., Figure 21b shows simulation results for
a producer population with an oscillating input approximated
by a sine wave.
The upper curve for Qx is the result when the switches
are constrained to the off position (without exchange) while
the lower curve is the result of unconstrained operation of
the switches. In this case, total power is increased by
developing a consumer population.
Case 2; Out of phase inputs. Another situation
producing the potential for exchange is the case of out of
phase inputs, Figure 22a shows some simulation results for
two systems with oscillating external energy inputs that are
90 degrees out of phase. mhis might correspond to two
systems in two different climatic regimes that are
relatively close together, such as might occur on a mountain
slope, exchange can increase total power in this situation


189
simplest model capable of reproducing the systems behavior
is considered to be the best. This is not necessarily
true, however, if the criterion is a general understanding
of the system and thus predictive ability. For example,
Newtonian physics is simpler than relativistic physics but
not as general. A more complete understanding of the system
is possible with relativity. Newtonian mechanics represents
a special, case which is nonetheless very useful.
The exponential growth model can be viewed as a special
case of the more general biological growth models applicable
only during a limited phase of the growth cycle. In the
same sense, the power-maximizing models developed in this
study can be viewed as more general statements of biological
growth models, intended to take into account evolutionary
changes in the internal connectivity structure of the
system.
It is clear that predictive models must limit their
exogenous variables to those which can be predicted. In the
simulation models presented here, solar energy, input (which
can be assumed to be constant with a high degree of
confidence) and the initial conditions are the only
exogenous variables. The.models predict behavior which is
consistent with the ultimate thermodynamic limits faced by
all systems.
The major problems with the models involved the lack of
systematic methods of fitting them to historical data, and


Table 20
(Continued)
Sector
(numbers in parenthesis are DEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C
Excluding Including
Labor and Labor and
Government Government
Services Services
Feedbacks Feedbacks
but Includ- but F.xclud-
ing Solar ing Solar
Energy Inputs Energy Input3
All Values in Btu fossil/$
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputo
28.
Paperboard Containers & Boxes (25)
64,123
0
36,051
191625
393,530
863,800
29.
Printing & Publishing (26)
93,360 .
365,790
766,700
30.
Chemicals 6 Selected Chemical Products (27)
218,430
262,410
528,740
893,050
31.
Plastics & Synthetic Materials (28)
141,730
179,180
463,370
834,300
32.
Drugs, Cleaning & Toilet Preparations (29)
58,672
54,725
372,110
733,650
33.
Paints s Allied Products (30)
107,100
160,680
425,290
809,300
34.
Paving Mixtures & Blocks (31.02)
361,470
377,745
1,003,400
1,676,300
35.
Asphalt Felts & Coatings (31.03)
246,420
295,110
639,540
1,082,750
36.
Rubber 8, Miscellaneous Plastics Products (32)
95,144
128,870
432,050
814,050
37.
Leather Tanning & Industrial Leather Products (33)
133,600
146,235
369,910
627,950
38.
Footwear & Other Leather Products (34)
51,714
105,720
367,620
751,400
39.
Glass & Glass Products (35)
56,916
105,600
379,200
763,400
40.
Stone & Clay Products (36)
97,629
124,345
423,790
789,300
213


Figure 41.
Continuation of the simulation run in Figure 40
to the year 2131


(3)
44444444444444444444444444444444+ 444444444 4 44 4 4 44 + + + + +
+ : ::: :=====///// +
+ :::::=====///// +
+ :::::=====///// +
+ :::::=====///// 4
+ ========== +
4 ========== 4
4 ========== 4
4 = = = = = = = = == 4
+ ///// 4
4 ///// 4
4 ///// 4
4 ///// 4
4
4
4
4
4
4
4
4
4
4
4
4
4-
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
.
*
4
4
*r
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4 444 44 4 4 444444444444444 0 6SI


25.060
24.830
24.030
24.600
24.600
24.600
35.00 80
35.000
20.00 -90.00
5.0 10.0 20.0
80.500 5.400 0.200 1.
81.020 5.230 0.200 1.
80.760 1.000 0.030 1.
81.800 2.510 0.090 2.
81.540 3.830 0.140 1.
81.280 1.010 0.040 1,
10 1004463. 28210. 1.0
80.000 56870.000 1507.800 1,
16200000. 954900. 1.00
30.0 40. 0 50.0 75.0 100,
010
010
010
500
010
000
000
O 200.0


81
Figure 19.
Diagram illustrating the partial production
function relations.


2
between these different accounting frameworks. Dynamic
simulation models were developed and used to investigate the
temporal and spatial behavior of complex, self-organising
systems that can evolve and change their internal structure
and function over time, Lotkas maximum power principle has
been suggested as the fitness criteria for survival of the
system, and thus the ultimate goal of evolution {Odum 1971).
Can these concepts be incorporated in mathematical systems
models? 9hat are the general criteria for survival of
systems? Can optimal control theory be gainfully applied to
this problem? Hhat general characteristics do models of
this type exhibit? "he simulation models developed in this
study were applied to the growth of the n.S. economy-
environment and to the spatially articulated growth of south
Florida in order to predict the general behavior of these
systems.
Research Plan
"his dissertation is a study of the way energy affects,
limits, and. determines the organised noneguillibrium
phenomenon comprising ecological and economic systems. ?o
this end conceptual and mathematical models were developed
to indicate the response of these systems to available
energy inputs. Linear input-output models of embodied


83
net Increase in total power at a particular time, then the
rate of transfer is the given function of the stored assets
of the two components (Q^ and Q2) ani^- transfer
coefficient h12* from (36) and (37) the following
expressions can he derived for the above partial
derivatives:
9 V.
T al^l ^ll0!1 + fbllQl}
b122l
9% (1+a1Q1)2
(1 + bllQl)
(1 + bl2QlP
9Pt =
b21 ~2
^ + b21^2
a2K2
3Q2 Tl+i2Q2}2
b12 1
2^b22^2^ + -h22Q2^
^"+b222^
1 + b12Ql
(U3)
b21Q2
lT7b"Q¡) 2
(hQ)
The fourth term in equation (36) is the (potential)
outflow to component 2. It is subject to decisions
analogous to those discussed above for the inflow from
component 2 to component 1 The last term in equation (36)
is the depreciation term, which was assumed to be a linear
function of the quantity stored* Thus, c^ is the
depreciation rate for component Vs storage.
The model can be easily expanded to n components.
Figure 22 is a difference equation representation for one
component in an n component version of the model. In
applications of the model the components can be sectors in
an economy, areas of land, trophic levels in an ecosystem,


APPENDIX VII
FORTRAN LISTING FOR THE 91-CELL
SOUTH FLORIDA SIMULATION MODEL AND DATA


RESULTS
Results include a derivation of the general conditions
for maximum power, development of an algorithim for
approximating the maximum power conditions in a dynamic
simulation model, and applications of the model. Some
features of the model were demonstrated using hypothetical
examples and the model was applied to a f-sector .S.
economy-environment and, a 91-cell spatial array for south
Florida. The embodied, energy intensity of goods and
services was calculated for 92 O.S. economic sectors for
four different alternatives concerning the treatment of
labor and government services and solar energy inputs. Data
were assembled on total capital stocks and flows and were
used to determine a better estimate of the mean energy
intensity for goods and services and to create "closed
system" input-output transactions matrices for the .S,
economy-environment at the 15-sector level.
"he General Conditions for Maximum Power

K major hypothesis of the simulation models in this
study is that complex living systems evolve so as to
maximize their productivity (or power as defined earlier).
65


30
for this concept of embodied energy.,
Ej is the external direct energy input to sector j,
Thus the energy balance for the jth component is:
n
-j -j^
13
1 = 1
In matrix notation for all components:
(8)
F = e (X-X)
(8)
Here F is a vector of direct external energy inputs, X
is a diagonalized matrix of output flows, X is a matrix of
input flows and e is the vector of total (direct plus
indirect) energy embodied in a unit of outflow,
He can solve for e as:
e = E(x-x)
(13)
A simple example will clarify the procedure. Consider
a three-sector economy consisting of an agriculture sector,
a manufacturing sector, and a consumers sector as shown in
Figure 7 and Table 2.
The economy is represented both in energy flow diagrams
(Odum 1971) and corresponding input-output tables with all
the steps from physical flow units to embodied, energy units
detailed. For simplicity the economy is at steady state


Figure 40. Simulation results fop the 5-sector o.s.
economy-environment simulation model. This run
used tne following coefficients
CT
0.458E-06 0.Q00E 00 O.OOOE 00 0.000E 00
0.494E-06 0. 150E-05 0.400E-05 0.200E-05
0.652E-05 0.500E-04 0.150E-03 0.417E-03
0.206E-05 0.800B-04 0.100E-01 0.254E-04
0.437E-05 0.213E-03 0.229E-04 0.100E 00
0. 105E-07 0.438E-06 0.487E-07 0.472E-07
0.015 0.030 0.030 0.030
1. 200
0.231E-07
0.351E-07
0.652E-06
0.146E-08
0.232E-09
0.512E-06
0.021


87
indicate the models behavior with the switches in the
unconstrained mode, while those labeled without exchange
indicate the behavior with the switches constrained to the
off position. The time and quantity scales are in arbitrary-
units, In general this two component version produced
almost identical behavior when the switches were left on as
when they were allowed to function normally. This indicated
that with only two possible exchange pathways, it almost
always pays in a maximum power sense to exchange, ^his
was not the case for a larger number of components where
more intricate exchange networks were possible,
Case 1; "Resource consumption. One relevant application
of the model is to the question of resource consumption.
Here one of the components represents a resource pool, A
resource pool can be operationally defined in the context of
this model as a situation where the external energy input
and the depreciation rate are both very low. For example,
the oil deposits of the Arabian deserts occur in low
productivity areas protected from deterioration by overlying
rock. In the language of the model this is a large storage
of structure whose incremental effect on productivity in its
local environment is very small. If another component
capable of utilizing the resource exists in close enough
proximity, the logic of the model would decide to export ho
this component in order to maximize power. Figure 21a shows
some simulation results for this situation. Both the


44
sector and a rest, of the world sector. The conventional
X-0 sectors were aggregated to 10 major groups, making a
total of sectors. Figure 10 is an energy circuit diagram
summarizing the accounting scheme employed in this study,
All flows and storages of energy and matter in the world are
included {at least in an aggregated form) in this accounting
f ramework.
Government and Households as Endogenous Sectors
In order to make households and government internal
(endogenous) components in the accounting framework, certain
modifications to current accounting conventions and
approximations were necessary. Figure 11 illustrates the
problem. The household sectors inputs from the other
sectors were measured as personal consumption expenditures
(PCF) which are the dollar payments of individuals for
goods and services from the producer sectors, The
exception is the input to households of government services,
which are paid for with federal income taxes, along with
state and local government taxes on households. The outputs
of the household sector to the other sectors are labor
services, which show up in the accounts as the employee
compensation category. Complications arise since the input -
output accounts separate value added (or VA, defined as the
payments to the factors of production) into only three
categories: (1) employee compensation, (2) indirect


171
+ + +++4-4- + 4-4-4-4-4- + 4-4-4-4-4-4-Y!EA??=l 940. + 4- + 4-4-4-4-4-4-4-4-4- +4-+++++++ 4-
+
+
+
+ : : : ::
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
4"
4-
+
4-
+
+
+
+
+
4-
4-
+
+
4-
4-
+
4-
4-
4-
4-
4-
4-
4-
4-
4- 4- 4- 4- + 4-4
: l
: l
: 1
: 1
: 1
11
11
11
11
i l
nil
u
un
11
11
11
11
11
11
11
4-4-4--
1
1
1
1
+ +
111
111
1 i l
111
44-4-
4-
4-
4-
4-
+
4-
4-
4-
4-
+
4-
+
4-
4-
4-
4-
+
+
4-
4-
+
4-
4-
+
4-
4-
+
+
4-
4-
+
4-
4-
4-
4-
4-
4-
4-
+
t
+
4-
4-
+
+
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
+ 4- 4- 4- 4- 4- 4-4-4- 4- 4- 4-4- 4- 4- 4- 4- 4- 4- 4-4- 4-+ + + 4- 4- + 4- 4- 4- 4- + + 4-4-4-4-
1 1
1 1
nil
mn
11111
mn
inn
inn
=====i 1111 $$$$$
===== 1 1 l 1 1 533 5*5
=====1111133335
=====11 1 1135555
4- 4-4-4-4- 11111
+++++1 1 1
4-4-4-4-4- 111
4- 4-4-4-4- 1 1 1 l 1
/////
/////
/////
/////
11111
1 11 11
1 1 11 1
1 mi
mu
mn
11 n i
11111
11
11
i/////:::
i/////: ::
i/////:::
1/////:::
//////////
//////////
//////////
(e)
+ + + ++ + + + + + + --+ + 4-+ +


Table 14
1967 aggregate sector net capital stocks, gross investment and depreciation(a)
(in billions of 1967 dollars.)
Aggregate Sector
Net
Capital
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction of
Total U.S.
Depre
ciation
1.
Environment
13872.0(e)
.7270
74.7
.1280
74.7
.2030
2.
Raw Materials
6.2
.0003
0.8
.0014
0.5
.0014
3.
Fuel Industry
36.7
.0019
4.9
.0084
3.2
.0087
4.
Forestry and
Fisheries
0.8
-
.1
.0002
.1
.0003
5.
Agriculture
49.1
.0026
6.4
.0110
4.2
.0114
6.
Power Plants
63.2
.0033
8.4
.0144
5.6
.0152
7.
Construction
32.3
.0017
4.3
.0074
2.8
.0076
8.
Manufacturing
174.3
.0091
23.1
.0396
15.3
.0416
9.
Transportation 64.2
.0034
8.5
#
.0146
5.7
.0155
10.
Services
441.3
.0231
85.5
.1003
38.9
.1057
11.
Communications 53.3
.0028
7.1
.0122
4.7
.0128
12.
Government
1237.5
.0649
119.73
.2052
33.3
.0905
13.
Households
3049.1
.1598
266.9
.4575
179.0
.4864
TOTAL U.S.
19080.2
1.0000
583.4
1.0000
368.0
1.0000
136


NET INPUT
Capital Consulption Allov/onccs and
Payments to Land and ResourcessXo*PH
TOTAL INPUT
Figure 12.
Summary of modifications to the input-output conventions.
tn
u>


Table 20. (Continued)
Sector
(Numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B
Excluding
Labor and
Government
Services
Feedbacks
C
Including
Labor and
Government
Services
Feedbacks
but Includ- but Exclud
ing Solar ing Solar
Energy Inputs Energy Inputs
All Values in Btu fossil/$
68. Miscellaneous Manufacturing (64)
45,403
130,965
366,890
69 Railroads & Related Services (65.01)
60,218
72,575
399,140
70. Local, Suburban & InterurbanHighway Passenger Transportation
(65.02)
56,240
61,570
348,]20
71. Motor Freight Transportation & Warehousing (65.03)
80,561
89,095
422, 150
72. Water Transportation (65.04)
85,647
105,430
484,970
73. Air Transportation (65.05)
122,630
143,910
452,230
74. Pipe Line Transportation (65.06)
132,980
143,285
468,340
75. Transportation Services (65.07)
5,672
11,615
346,970
76. Communications Except Radio & Television Broadcasting (66)
13,571
19,640
359,400
77. Radio & TV Broadcasting (67)
20,722
40,165
354,050
78. Water & Sanatary Services (68.03)
68,101
86,080
425,490
79. Wholesale S Retail Trade (69)
29,302
43,265
411,490
80. Finance & Insurance (70)
17,472
30,195
364,840
81 Real Estate & Rental (71)
26,362
45,465
357,320
D
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inpute
787.350
762.500
655.700
784,600
918.650
814.700
825.700
706,750
716.650
718.500
812,300
814.350
737.350
707,250
216


Table '20
(Continued)
Alternative!
Sector
(numbers in parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
B
Excluding
Labor and
Government
Services
Feedbacks
but Includ
ing Solar
Energy Inputs
All Values
C
Including
Labor and
Government
Services
Feedbacks
but Exclud
ing Solar
Energy Inputs
in Btu fossil/S
C
Including
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
15.
Maintaince and Repair Construction (12)
42,803
102,060
384,660
801,350
16.
Ordnance & Accessories (13)
41,768
78,285
381,130
772,600
17.
Pood & Kindred Products (14)
62,872
346,845
390,760
1,054,700
18.
Tabacco Manufactures (15)
30,009
197,715
469,000
1,068,550
19.
Broad & Fabrics, Yarn & Thread Mills (16)
68,156
167,815
392,370
830,400
20.
Miscellaneous Textile Goods & Floor Coverings (17)
67,389
125,200
384,490
775,450
21.
Apparel (18)
.38,845
295,135
371,107
974,600
22.
Miscellaneous Fabricated Textile Products (19)
50,462
117,365
376,750
784,250
23
Lumber & Wood Products, Except Containers (20)
54,159
2,829,200
372,490
3,478,850
24.
Wooden Containers (21)
39,681
1,102,550
365,030
1,766,750
25.
Household Furniture (22)
42,521
448,550
371,210
1,119,850
26.
Other Furniture & Fixtures (23)
50,180
248,375
373,900
919,850
27.
Paper & Allied Products Except Containers & Boxes (24)
88,279
366,800
405,650
1,013,750


80
to a decrease In the contributing components storage, while
the "benefit Is the gain in productivity Sue to an increase
in the receiving components storage. since the models
production functions are differentiable, single valued,
finite and continuous at each point in time, an optimum
distribution of the storages exists for any point in time,
and the exchange network is adjusted to move the system in
that direction. as already noted, it is necessary to have a
common currency in which and ?2 are expressed in order to
perforin this calculation, This study employs embodied
energy as the common currency.
The equations require some explanation. Each of the
individual partial production functions (indicated by the
work gate symbols) are given a relatively simple "limiting
factor" form, This is equivalent to saying that there are
Infinitesimal storages In the flow (shown by the small tanks
in the diagram), that limit the amount of source material
which can be used. & derivation of the partial production
equation follows. Consider a system given by the anergv
circuit diagram in Figure 1q and the equations below (Odum
and Odum lO^S) .
(38)
(39)
Row assume that QT is an infinitesimally small storage wihh:
Qt = 0 and k^ = 1 (turnover = 1 COT,). This yields;
rC)
Solving for 0T


13
The first ccmcept was use! in this study, with some
modification and extensions, ft complete description of the
technique with examples is given in the methods section.
Optimization
Optimization is the search for maxima or minima usually
subject to some constraints. Wilde and Beightler (1967)
provide a good introduction to the method. Cody (1974)
reviews some of the applications of optimization models to
ecological systems. Rapport and Turner (1977) discuss the
underlying similarities of economic and ecologic processes
as an explanation for the success of optimization models in
both fields.
The maximization of useful energy flow (or maximum
power) was suggested as an objective function by Lotka
(1922). Odum (1971) has elaborated and generalized on this
theme. Oster and Wilson (1978) employ what they term
ergonomic (or work) efficiency as a.n objective function in
the study of colonial insects. Wang, Odum, and Costanza
(1978) showed an example application of the maximum power
principle to a land and water management problem.
Economyc Wodels
current microeconomic theory can all fit under the
umbrella of optimization. In the general optimization
problem there is some objective function to be maximized or


gure 24. Diagram showing the system boundaries
and flows included in the four
alternatives
(a) Excluding labor and government
services feedbacks and solar
energy inputs
(b) Including solar inputs but excluding
labor and government services
(c) Including labor and government
services feedbacks but excluding
solar inputs
(d) Including labor and government
services and solar energy inputs
(e) Same as (d) but also including
depreciation and net growth of
households and government as a
net output


66
here is a large literature on the various aspects of
optimization and specifically dynamic, nonlinear
optimization but these methods are generally not integrate!
with simulation studies, Wagner (1975) views simulation as
a last resort to be used only if all else fails. The
potential benefits of the integration of simulation with
optimal control theories are great, however. In this study
a simple algorithm for achieving this goal is developed.
The objective function is taken as the maximization of total
system power (Lotkas power principle as discussed earlier)
and the constraints deal with limits on the total amount of
free energy in the system and the exchange of energy between
components of the system. Power is maximized when an
optimal exchange network is used, and this network changes
through time,
The problem can be stated in the mathematical framework
of nonlinear programming for each point, in time as follows,
maximize PT = Px CQ1,Q2* * Qn/%) +
?2CQi#Q2'***'Qn'E2^ + ** +
Pn 1* C2f * Qn#
subject to Q-l + Q2 +...+ Qn = Ct
- Kit nfi>
1 *2 = K2t
= K
nt


39
Table o. Input-output transaction matrix corresponding to
the diagram in Pig, 9 using the national input-
output conventions,
Prom
To
Agri
culture
1
Manufac
turing
2
Consumers + net
output or
"final demand"
Total
output
Agriculture
1
353,6
181,0
545. 5
1099,8
Manufacturing
2
210. 2
ioon,9
872.7
2181,8
Energy input
+ Consumers or
"value added"
509, 1
909.1
198 1. 1
Total input
1090, 9
2181.8


15
Xf = Ex¡j Y¡
Figure 3.
Diagram showing the. standard input-output
accounting setup.


48
business taxes, and (3) property type income. Table 5
shows the relationship of these categories to the national
income and produc4- accounts categories. The implied wages
of self-employed people or unpaid family workers are not
directly included in the employee compensation category but
show up as a portion of proprietors income, which is
embedded in the property-type income category of value
added. Similarly, corporate profits taxes, which are also
embedded in property-type income, should be added to
indirect business taxes to determine the total taxes paid by
business to government.
a detailed examination of questions relevant to the
proper distribution of value added to the economic-ecologio
sectors was not possible during this study. Certain
approximations were therefore made to derive the estimates.
Value added was distributed by crediting all employee
compensation (EC) plus a fraction of property-type income
(PTT) to households and all indirect business taxes (IBT)
plus a fraction of PTT to government. The fractions were
calculated using balance considerations, and the fraction of
PTI remaining after government and household's shares were
removed was considered a net profit attributable to inputs
from the environment (see the following section).
The X-0 accounting framework requires that the sum of
the total dollar value of the outputs from a sector equal
the sum of the dollar value of the inputs. This requirement


56
energy flows has proved useful (Odum, 1971; Bayiey et al,
19 75) in conceptualising this problem.
For the purposes of this study it was assumed that,
where competitive markets exist, market values were
proportional to embodied energy content and that both of
these could be considered to be conservative guantities.
Evidence for the validity of this assumption is presented in
the results section. Conservation of dollars and embodied
energy allows many of the flows to and from the environment
sector to be estimatd from balance considerations. The
input-output accounts are arranged such that the total
dollar value of all inputs to a sector equals the total
dollar value of all outputs from a sector.
Once the payments to households and government, and
capital flows have been accounted for internally, there
still remains an imbalance between the dollar values of the
sum of the inflows to each sector and the dollar value of
the sum of the outflows. There is still a "net input to
the sector or profit. 'his net input was attributed to
services provided by the environment sector. This is
essentially a pure economic rent conception of the origin
of profits. Tinder this view entrepreneurial capacity is a
component of the labor services input necessary to
effectively capture environmental inputs. At steady state
these environmental inputs would just cover the depreciation
of the economic system. The approach can also be viewed as


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4 4
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4
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4
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4
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4
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4
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4
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4
4
4
4
4
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4
4
4
4
4
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4
4
4
+
4
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frZ. I


Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitude
(W)
85
1.00
0.83
2.47
0.03
24.83
80.76
86
2.51
16.54
29.66
0.07
24.60
81.80
87
3.83
3.62
8.07
0.14
24.60
81.54
88
1.01
0.96
1.58
0.04
24.60
81.28
200


Figure 28.
Plot of direct plus indirect energy consumption
(calculated including solar inputs but excluding
labor and government) versus dollar output for
92 U.S. economy sectors


DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xl09§/yr)
176 -
160
144-
128-
T
5G000
108


250
Kylstra, C. .1974..- Energy analysis as a common basis for
optimally combining man's activities and nature. The
National Symposium on Corporate Social Policy.
Chicago, Ill.
Leach, G. 1975, Net energy analysisis it any use? Energy
Policy. 3: 332-344.
Leontisf, W. w, 1941. The structure of american economy.
1919, 1979: an empirical application of eguillibrium
analysis. Harvard University Press, Cambridge, lass,
Lindeman, E. L 1991. Seasonal food-cycle dynamics in a
senescent lake. ft mer. Midi. Na t. 26: 636-673,
Losch, ft. 1940. nie raumliche ordnung der wirschaft.
translated by W.H. Noglom. 1954. as: The
economics of location. Yale University Press, New
Haven, Conn.
Lotka, A.J. 1921. Note on the economic conversion factors
of energy. Proc. Nat. ftcad. Sci. 7: 192-197.
I.otha, ft. J. 1922. Contribution to the energetics of evo
lution. Proc. Nat. ftcad. Sci, 8: 147-150.
Lotka, ft. J. 1956. Elements of mathematical biology. Dover.
New York. 456pp,
McHarg, T.T.. 1969, Design with natura. Doubleday. Garden
City, New Jersey. 197pp.
Nicolis, G. and I. Prigogine. 1977. Self organization in
noneguillibrium systems: from dissipative structures
to order through fluctuations. John Wiley and Sons.
New York, 491pp.
Odum, H.T.
rophic structure and productivity of
Sil ver Springs, Florida. Fcol. Monogr., 27: 55-112.
Odum, H.c, 1968. Work circuits and systems stress. Pages
81-138 in H.E. Young ed, Symposium on primary pro
ductivity and mineral cycling in natural ecosystems.
University of Maine Press, Orono.
Odum, H.T. 1971 Environment, power and
society. Wiley Interscience. New York. 331pp,
Odum, H.T. 1973, Energy, ecology and economics, ftmbio,
2: 220-227.


155


which says that the marginal total power of all the storages
should be equal in order to optimize the system. he
problem is then, how do living systems go about adjusting
these marginal total power conditions in a fluctuating
dynamic environment? One possibility involves adjusting the
interconnection network of the system by switching selected
pathways on and off, as shown in Figure 16. This does not
violate the condition (ii) that the partial derivatives be
single valued and continuous since at each point ia time the
functions are continuous. This approach simply modifies the
problem from one time step to the next.
Consider the potential exchange from component 2 to
component in Figure 16. The diagram indicates that the
pathway is open if:
9?t 9 Pm
> (23)
9Qq_ 9 Q2
If this condition does not hold then the pathway is switched
off. This would eliminate the term 9p1/3q2 from the
equation for 3PT/3Q2 since Q2 would no longer be a variable
in the equation for p^. his would lower 9pt/3q2 so that
the condition (23) would hold. By applying this decision


Table 17.
U.S. economy-environment simulation model
performance statistics for the 1929-1969
period.
Sector
R square
PR>F
Regression
Coefficient
2 Business
.981
. 0001
.410
3 Government
.959
.0001
.614
4 Households
.939
.0001
.836
Average
.960
.0001
.620


182
total magnitude of solar energy absorbed by the .s. in 1967
was fairly well known, the inclusion of solar energy in the
manner adopted in this study may have distorted the
distribution but not the total magnitude of embodied solar
energy due to imperfect knowledge of the input distribution.
For example, the total primary energy intensity of forestry
and fisheries products (sector 7) is an extreme outlier at
238.61 F5 Btu fossil/S compared to a mean of 12.2 F5 Btu
fossil/$ in Table 29, alternative D. This is probably due
to an overestimate of the solar energy input to this sector
relative to other sectors.
The statistics on the total primary energy intensities
are somewhat misleading due to their non-normal
distribution. Figures 25 and 26 are frequency plots of the
total primary energy intensities given in cable 2B, which
demonstrate clearly that the numbers are much more clustered
than the statistics indicate. If the outliers are
eliminated by excluding the primary energy sectors (sectors
1-7) from the statistics, then the means, standard
deviations, and coefficients of variation for the total
primary energy intensities in Table 8 drop significantly.
For example, alternative D*s mean drops to 8.5 E5 Btu
fossil/T with a standard deviation of 3.49 F5 and a
coefficient of variation of 9.41.
Translating the data into a regression format
highlights more clearly the nature of the relationships.


227
Table 24. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
1651.88
137.45
38.75
98.70
1952
1710.73
139.25
35.61
103.64
1953
1772.28
149.34
41.88
107.46
1954
1837.99
153.59
42.07
111.52
1955
1911.56
173.64
57.61
116.03
1956
1990.76
173.83
49.83
124.00
1957
2066.16
175.50
45.87
129.63
1958
2137.03
173.44
40.62
132.82
1959
2212.68
190.74
54.35
136.39
1960
2298.50
192.49
52.59
139.90
1961
2383.10
193.81
50.32
143.49
1962
2470.27
210.14
61.89
148.25
1963
2567.87
221.29
67.49
153.80
1964
2673.92
236.86
75.87
160.99
1965
2791.01
255.12
85.64
169.48
1966
2920.49
269.36
97.26
172.10
1967
3049.10
266.94
87.92
179.02
1968
3179.43
292.50
104.38
188.12
1969
3321.65
305.30
105.12
199.74
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.


186
have to be burned to produce a dollar of real GNP than kcal
of oil. This could show up in the data as an apparent
increase in energy use efficiency. Failure to properly take
into account the quality factors of the various forms of
energy, combined with a pronounced trend in the percentages
of each form used, can lead to a trend in the energy to GNP
ratio, along these same lines, the depletion of virgin
forests and mineral and soil deposits are energy inputs to
the economy whose omission could lead to trend in the energy
to GNP ratio.
1 third line of evidence for a constant embodied energy
to GNP ratio deals with international comparisons of data on
GNP and energy consumption. Darmstadter has taken the lead
in these studies (Darmstadter 1971, Darmstadter, Dunkerly
and Alt.ermann 1977, and Darmstadter, Dunkerly and s.ltermann
1978) In the latter paper data on the fossil energy to
gross domestic product (GDP) are presented for 9
industrialized countries for 1972. The authors conclude
that there are major differences in the energy/GDP ratios
for the countries and trace the cause to differences in
energy prices. 'hey also note a close inverse correlation
between their energy/GDP ratio and the import dependence of
the country. Countries like Canada (a net exporter) and the
U.S. (12T imports in 197 2) with low import dependence had
high energy/GDP ratios. Countries which import most of
their fossil fuel (Japan, France, Italy) had low energy/GDP


QUANTITY
88
(a)
(b)
Figure 21. Two component model analog simulation results.
(a) Situation when one component (Q^ in
this case) represents a resource pool.
(b) Situation when one component (Q2 in this
case) has no external energy source and
survives only on exchange with a
production unit (Q^ in this case).


ACKNOWLEDGE?!" NTS
T am greatly, indebted to Dr. R.T. Odum, my committee
chairman, for his knowledge, inspiration, insight, and
encouragement. His all-encompassing world view gave birth
to many of the concepts which led to this study and guidei
the work to fruition. Many special contributions were made
by the other members of my committee: Prs. S. E. Bayiey, B.L.
Capehart, W, c. Huber, and C.D. Kylstra.
B. Hannon and p. Herendeen at the Center for Advanced
Computation, University of Illinois, contributed experienced
help and encouragement with the input-output studies in the
summer of 1978. F. Hang and J. Boyles read the manuscript
and provided comments. I would also like to acknowledge the
valuable interactions with associates and friends,
especially J. Bartholomew, T. Fontaine, S. Brown, and D.
Hornbeck.
Fork was done at the Center for Wetlands, University of
Florida, and was supported by the United States Department
of Energy (Contract ET-76-S-05-4398) project entitled
"Energy Analysis of Models of the United States," R.T, Odum
principal investigator.


Table 11. 1967 U.S. household sector capital stock and investment breakdown.
(All values in billions of 1967 dollars.)

Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
4882.8
3049.1
366.94
87.92
179.02
Total Non-Human Tangibles (a)
1451.8
781.0
96.93
22.58
74.35
Structures
801.2
422.2
22.24
7.84
14.40
Equipment
546.4
234.7
73.88
13.93
59.95
Inventories
104.2
104.2
0.81
0.81
-
Total Human Tangibles
1442.3
992.9
56.44
38.10
18.34
Total Non-Human Tangibles
10.3
9.0
0.95
0.95
-
Basic Research
7.4
7.4
0.66
0.66
-
AR & D
2.9
1.6
0.28
0.28
-
Total Human Intangibles
1978.3
1266.2
112.62
26.29
86.33
Education and Training
1635.6
' 1092.1
81.49
24.37
57*. 12
Medical and Health
271.6
142.6
15.58
1.08
14.50
Mobility
71.1
31.4
15.55
0.84
14.71
a. excluding land held by households.
Source: Kendrick, 1976.
118


132
the rent of the world sector, which implicitly contains its
own environment sector, are the only sectors receiving a
direct input {in the form of sunlight) under this sectoring
scheme. The dollar value of the direct solar input in hoth
1963 and 196* was estimated as 299, 1 E9 S, from balance
considerations. The self-sales category was assumed to be
the same percentage of total output as in the economic
sectors. This was 16. Uf, in 1963 and 14.215 in 1967, and thus
the "self-sales' value for the environment sector was
imputed as 195.9 T9 $ in 1963 and 98.1 29 $ in 1967.
The gross investment and depreciation numbers for the
environment sector are critical and largely unknown. An
estimate was made by assuming that the mineral reserve
portion of the environment stock had no investment or
depreciation and that the land portion had investment and
depreciation at the same rate as the economic sectors
expressed as a percentage of net stock (see Tables 13 and
14), The output of the environment sector to the economic
sectors was measured as a residual. The additional value
needed to balance the total output of each sector with the
value of all its purchased inputs (including labor and.
crovernment services) was credited to inputs from the
environment.
The 1963 and 1967 tt. s. economy input-output data from
BEh were used to generate the bulk of the U.s. economy
section of the table (United States Department of Commerce


Figure 27.
Plot of direct plus indirect energy consumption
(calculated excluding solar inputs and labor and
government) versus dollar output for 92 U.S.
economy sectors


I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy
Wayne C. Huber
Associate Professor of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy
Chester D. Kylstfh
Associate Professor of
Nuclear Engineering Sciences
This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council, and
was accepted as partial fulfillment of the requirements
for the degree of Doctor of Philosophy
June 1979
Dean, College of Engineering
Dean, Graduate School


Figure 18.
Differential equations for the model in
Figure 17.
where
Ch C>2 = embodied energy storages in
components 1 and 2
E^, E2 = direct energy inputs to
components 1 and 2
a1, a_ = direct energy input co
efficients for components
1 and 2
1*12' = transfer coefficients
for exchanges from com
ponent 2 to component
1 and from 1 to 2
respectively
b,. b99 -- internal transfer
coefficients
c., depreciation rates for
components 1 and 2
total embodied energy
productivity (power)
of the system, given
by the first three terms
in the equations
Y.0, Y?1 = exchange flows from com-
^ ponent 2 to 1 and 1 to 2
respectively, given by the
third term in the equations
change in total power
with respect to the system
storages (Q. and Q^) all
else being 1equal
t
3 Qx 3Q2
p =p +p =
a 1 2


181
energy intensities for four alternatives concerning the
treatment of labor an! government services an! solar energy
inputs. Comparison of the two alternatives without solar
energy inputs shows a reduction in the coefficient of
variation from 3.43 to 1.2 with the Inclusion of labor an!
government services feedbacks, and a corresponding increase
from 1,35 ^5 to 5.16 55 Btu fossil/* in the mean energy
intensity. similarly, the two alternatives with solar
energy show a reduction in the coefficient of variation from
4,61 to 2.2 with the Inclusion of labor and government
services feedbacks, and a corresponding increase from 5.45
E5 to 12.20 05 Btu fossil/* in the mean energy intensity,
Comparison of the two alternatives without labor and
government services feedbacks shows an increase in the
coefficient of variation from 3.43 to 4.61 with the
inclusion of solar energy Inputs and a corresponding
Increase from 1.85 E5 to 5.45 E5 Btu fossil/S in the mean
energy intensity. Similarly, the two alternatives with
labor and government, services feedbacks show an increase in
the coefficient of variation from 1.2 to 2.0 with the
inclusion of solar energy Inputs and a corresponding
increase from 5.16 E5 to 12.20 B5 Btu fossil/* in the mean
energy Intensity.
hs noted earlier, the distribution of solar energy
inputs to the economic sectors is imperfectly known and only
a crude, approximation was used in this study. Since the


NET INPUT
290100

.

4305000
4595100
TOTAL INPUT
397136
1544900
349455
972946
42140377
45405844
146


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Table 15. Sector correspondence.
Aggregate sector
ERG 90 order
sectors
BEA 357 order
sectors
Leontief (1953)
96 order sectors
2.
Raw Materials
10-13
5,6,9,10
22,39,43
3.
Fuel Industry
1-3
7,8,31.01
45.50
4.
Forestry and Fisheries
7
3
9,54
5.
Agriculture
6,8
1,2
1-8
6.
Power Plants
4,5
68.01,68.02
52
7.
Construction
14,15
11,12
68,69
9.
Manufacturing
16-28,30-68,78
87-90
13-25,27-30,31.02,
31.03,32-64,68.03
78-79,81-83
10-21,23-38,40-42
53,55,56,58-67
9.
Transportation
69-75
65
70-73
10.
Services
9,79-86
4,69-77
74-91
11.
Communications
29,76,77
26,66,67
51,57
12.
Government
92
13.
Households
94
138


BIOGRAPHICAL SKETCH
Robert. Costanza was born in Pittsburgh, Pennsylvania,
on September 14, 1950, in 1957 his family moved to
Hollywood, Florida, where he attended and graduated from
Chaminade High School. In September of 1968 he entered
Purdue University as a student in Aerospace Engineering.
After three semesters, he transferred to the University of
Florida where he earned a Bachelor of Design degree in 1973
and a Master of Arts in Architecture degree in 1975. After
working for six months as a Research Associate at the Center
for Wetlands, University of Florida, he enrolled in the
doctoral program in Environmental Engineering Sciences,
Systems Ecology program. Ffe was graduated with a Doctor of
Philosophy degree from the University of Florida in 1979
254


116
otSl £SEa!r Investment, and Depreciation Time Series a ni
a Better Estimate of the Embodied Is§i92 2 EsiiiE Batlo
The numerical values of the mean embodied energy
intensities in Table B are misleading because of omissions
of one sort or another as shown in Figure 24, To be
complete, household and government depreciation and net
growth (as shown in Figure 24e) should be included, This
requires a more all-inclusive treatment of capital and
capital flows, This kind of treatment has recently been
attempted by Kendrick (1976) for a three sector n.s.
economy. He has taken a view that is consistent with the
closed system approach to economic accounting in developing
estimates of what he terms total capital stocks for the
0, S, economy. His capital stock estimates are based on
investment and depreciation time series, not only in the
traditional categories of structures, equipment, and
inventories, but. also in human capital, including such
intangible but nonetheless real categories as education and
training, medical and health investments, and. mobility. He
notes that: "while economists have been increasingly
treating the various forms of intangible outlays enhancing
tangible factor productivity as investments, estimates of
resulting capital stocks are a unique feature of the present
study (p. 9),
tables 19-12 are examples of the results of Kendricks
analysis for the business, government, and household sectors
of the u.S. economy for 1967. Kendrick's land category was


55
water use. This amounted to 35.74 E18 Btu solar/yr. The
forestry and fisheries sector was credited with the
absorption over all forested areas plus estuaries and
coastal water to the 300 mile limit plus 605 of the
wetlands, desert, and tundra absorption. This amounted to
63.06 E^B Btu solar/yr. The remaining 4.20 E18 Rtu solar/yr
represents direct utilisation by the remaining industrial,
commercial, residential, and governmental sectors of the
economy. This should be distributed to the remaining
sectors according to their total land areas. Accurate land
use data are not available at this level of disaggregation,
however. As an approximation, the entire 4.20 E18 Btu
solar/yr was credited to the household category since this
category represents about 755 of the remaining land area,
An Endogenous Environment Sector
A more conceptually satisfying method of including
environmental services is to treat the environment as an
endogenous sector. This sector contains all the land, air
and water in the n.S. and performs the essential task of
capturing solar energy and converting it into other forms
more usable by the economic sectors. Since the environment
sector is not completely "owned bv economic agents and
competitive markets do not exist for many of its products,
economists have difficulty evaluating many of the flows and
storages in this sector, A broader perpsective based on
A


150
the economic sectors, lb21* ^31' ^41^ internal transactions
within the sectors (h^j), flows from business to government
(b23, b32) an! depreciation rates. It also became
necessary for stability reasons to multiply one of the
partial derlvitares in the decision structure by a small
factor. This factor is labeled s and is listed with the
other parameters. The model was very difficult to adjust
due to its nonlinear equations and the discontinuous nature
of its time behavior. These features made computerized
parameter optimization techniques relatively useless and
necessitated many hours of manual adjustment. It also
produced an exceedingly "rich model, or one capable of
exhibiting many distinct types of behavior, depending on the
values of the coefficients. Only a very limited set of
coefficients produced results that coincided with the
historical behavior of the system, however.
Comparison of the models output (Figure 40 ) with the
historical behavior of the system from 1929 to 1969 (Figures
32-34 replotted on Figure 4r) shows that the model
reproduces the general behavior of the real system over this
period. The flat response of the business sector during the
depression and World War II (1929-1945) followed by the
postwar boom Is accurately reflected in the model. The
rapid increase In government assets during the war and post
war leveling are a^so indicated. Households, environment,
and the rest of the world all exhibit the same smooth


34
(X-X)_1=
.0618137
.0254505
,03131 82
n090n0
.0272737
.0790909
.5818182
.9450545
1.3813182
e = P (Mf1 = [ 36. 364 21,818 836.36Q]
To convert the original physical units into embodied
energy units multiply the energy intensities (e*s) by the
appropriate flows. This yields the values shown in Figure 8
and Table 3.
This embodied energy input-output table exhibits soma
of the same characteristics as a dollar value input-output
table. The total output from any sector equals the total
input to that sector and the total net output, or 'final
demand'* in the economic terminology [1000 in this case), la
equal to the total net input, or "value added" [the F.
vector, also 1090 in this case) Final demand refers to the
dollar value of the net output of the system, while value
added refers to the dollar payments for the net inputs to
the system. "he total final demand or the total value added
is defined In the national income accounts as the Gross
National Product (GNP) This would Imply a GNP for the
hypothetical economy of 1009, However, the conventions used
in the national Income accounts are not the same as those
followed here. To demonstrate the relationships, eur
example economy's X-0 *-able can be converted Into one
consistent with the national accounting conventions.


Copyright 1979
by
Robert Costanza


Table page
15 Sector correspondence............... 138
16 Init5.a! parameter estimates. 149
17 U.S, economy-environment simulation model
performance statistics for the 1929-1969 period... 156
18 South Florida simulation model performance
statistics for 1953 and 1 973 178
19 South Florida land use data converted to embodied
energy units.,.,.....*.*..,.,.................,... 193
25Embodied energy in goods and services for
9 2 IT. S, economy sectors in 1967, 211
21 Feal GMP, total fossil, hydro, and nuclear energy
consumption, and fossil, hydro, and nuclear
energy to real GNP ratio, 1920-1976., 219
22 .s. business sector net capital, investment, and
depreciation time series in constant dollars 222
23 !T.S. government sector net capital, investment,
and depreciation time series in constant
dollars, 224
24 n.S. household sector net capital, investment,
and. depreciation time series in constant
dollars.........y............. 226
25 .S. environment sector, n.S. economy, total
H.s. (environment plus economy), and rest
of the world net capital stock in
constant dollars.,.,...,......,....,......,,...... 228
26 Time series of net land stocks in the .S......... 231
27 Time series of total mineral fuel use and
estimated real dollar value.. 233


< 4 #
G£=
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100
output, but it is not simply the sum of the individual
energy sectors contributions. This is necessary to avoid
double counting, since refined is produced from crude, some
electricity is produced from coal and crude, etc. In this
study the total primary fossil fuel energy intensity was
calculated using the formula:
e (Primary) = s (Coal) + e (Crude + Gas) +
.61652 e (Electricity) +
.nnpg e (Solar)
where the factor .61652 accounts for the fraction of
electricity produced from hydro and nuclear sources
(Herendeen and Bullard 1974) and the .000 5 factor accounts
for the conversion ^rom solar to fossil fuel quality (Odum
et al. 1977).
Column B of Table 20 lists the embodied energy
intensities (in Btu fossil/T) calculated excluding labor and
government services feedbacks but including solar energy
inputs. Column C lists the embodied energy intensities
including labor and government services but excluding solar
energy inputs. Column T) lists the embodied energy
intensities inducing both labor and government services and
solar energy inputs. Figures 25 and 26 show frequency plots
of the four alternatives. able 8 gives summary statistics
for the embod5.ed energy distributions.
Another way of looking at these statistics is to plot
the total direct plus indirect Btus consumed by each sector


Table 21
Real GNP, total fossil, hydro, and nuclear energy
consumption and fossil, hydro, and nuclear energy
to real GNP ratio, 1920-1976.
Yea
Total Mineral
Fuels, Hydro Energy Consumption
and Nuclear per Dollar
Real GNP Energy Consumed of real GNP
(x 109 1967 $/yr) (xlO1^ kcal/yr) (kcal/1967$)
1920
168.5
5004.9
29702.7
1921
164.6
4151.8
25227.6
1922
174.3
4355.4
24988.0
1923
197.2
5486.3
27821.0
1924
203.2
5174.6
25465.6
1225
208.0
5237.5
25420.7
1926
221.6
5691.3
25682.8
1927
223.7
5522.5
24687.1
1923
226.4
5662.4
25010.6
1929
240.0
6010.3
25042.9
1930
217.2
5638.9
25961.8
1931
202.0
4756.1
23545.0
1932
171.8
4147.2
24139.7
1933
167.1
4275.7
25537.7
1934
182.9
4538.1
24811.9
1935
201.9
4834.1
23943.0
1936
228.8
5418.8
23682.6
1937
242.3
5756.0
23755.7
1938
231.2
5029.6
21754.3
1939
249.9
5462.0
21856.7
219


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IJ-.T IKPOT
290100



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X305000
'lOl'\L Ttlpur
097110
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130


67
where
PT = Total power of the system, equal to the sum
of the n individual components
= Powec lb individual components as
functions of the embodied energy storages
in the system (Qp, Q2 ,. Qn) and the direst
energy inputs E2* ** En)
The constraints indicate that at any point in time the total
embodied energy in the system is equal to some constant
value Ct, and the direct energy inputs are equal to
constants (Knt ). The optimization of the system involves
moving the scarce (limited) embodied energy around to elicit
the maximum total system power.
The problem can theoretically be solved using the
method of Lagrange multipliers. Certain additional
conditions must be satisfied to assure the existence of a
solution. Wagner (1975, p. 604) outlines these conditions.
They are divided into two groups, one for the constraints
and one for the objective 'function. Since the constraints
are all linear in the above system, only the objective
function need be addressed. The conditions for the
objective function are:
(1) Up is single valued and finite for each Q and E
satisfying the constraints
(ii) Every partial derivative (3PT/3Q^, is singla
valued, finite, and continuous at each 3 and "
satisfying the constraints


yig'are:23* Digital simulation of the pover maximising
aoaal for. a spatial grid of 25 components.
04
D
.
WWWVlOp
wvivn'jinfc
A'JWVJM i
*?viv}y>

MKKMCO
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141


Several concepts of embodied energy have thus far been
proposed. One employs input-output techniques (Leontief ^
1041) to trace input energy flows through the complex webs
of interactions in economic and ecological systems {Hannon
1971b; Herendeen and Bullard 1974). This can be termed the
input-output embodied energy. It assumes that embodied
energy is a conservative quantity, or that the sum of the
embodied energy inputs to each sector are emdodied in the
output, llhen pathways diverge, the total embodied energy is
partitioned among them so that the system of interconnected
flows maintains the conservation constraint. Figure 2a
shows an example of this approach, Another approach reasons
that since all processes are interconnected and in that
sense required for each others production (either directly
or indirectly), the amount of input necessary to produce any
one product must be taken as the total input (Odum 1978),
This approach assigns equal embodied energy to all by
products of a process but partitions the embodied energy if
the same commodity is simply divided. The embodied energy
inputs and outputs for each sector do not necessarily
balance. his approach has been applied (Odum 1978) to
estimating the embodied energy in natural energy flows in
the biosphere and can thus be termed the biosphere embodied
energy. Figure 2b shows an example of the concept. Table 1
and Figure 2 compare the characteristics of these two
approaches.


£03


89
external energy inflow and the depreciation of component 1
have been set very low, making it the resource pool in this
run. ^he plots labeled Tp are the accumulated power of the
two components used as an index of the success of the power
maximization routine {Tp = / (Py +1*2 ) dt),
mowing exchange in this case greatly increases the
total accumulated power of the system. Also, when exchange
is allowed, the standard curves (Odum 1971) for the
depletion of a large energy storage by an autocatalytic
consumer result. The difference between this model and most
other models of this relationship is that the resource tank
is not a completely passive system, but a dynamic system in
another area. To make the example more concrete, suppose
the resource area were Arabia and the consumption area were
the tt.S, Without trade, the resource (oil .in this case)
still has some productive value in its local environment
(e.g. in geologic processes or as a minor input to the local
economy) but this value is low compared with its value to an
industrialized economy. The model determines that exchange
will increase the total power; therefore oil is transported
from Arabia to the TJ.S. After a short time, however, a
backflow of tt.S. structure (goods and services) develops
since the model determines that they can be effectively
interacted with the remaining Arabian resources in Arabia,
This backflow tends to attenuate the rate of decline of the
resource as compared with its treatment as a passive storage
and is a more accurate picture of the real system.


62
Figure 15.
4+-*: : : *+-*i>* v.+* *+++++: : **;* ** + : u: cc ++ +u"
: : +: ; : :+mmm*m444++ :=+*:=+++++ : : : c :: C+ :¡J
;: + + + + : *+-.im*** + + +1 1 1++:: + + i i+++c:c:+: ::
+++M +: ++MMMM* +++3 uik:: +++++C:: c :: ::
>m+ M++ + WMMWM :+++53iiii + -*-++***c:: : c:: : : ::
MMMM MM + + MMM+M 3 + + o 1 1 i** = *.*+++ **4 : i .
M.M + MMM MM M 335 5 3 : 1 1 =** + < *;+** *C* + Z : I '.+
MM3B-5=45: : .* + -M-C + -*++*c ?=** + + *-*
'33*544: : :: *++*:: **:: : +*-*c+
f.|,M jt *5*44i.tt4*'t-* + + + **C++,!1CC + i
fJIMiM
M M MMMMM
S5M MM M
55
1
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M MMM++++ :4-**H+**+++++C//+
MMM4+ + ++ : :ai**e***t + + tCC/-H-
MM M 4+ +++++++ + +**CCCCCC///
.M MM++++ + +++ *** **t+C*CCC///
M M MM + + + +++*+++**++***/c / / U
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m mm + +++11114:**::**cuuuuu
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g si: -4+- 4-f. + 36 56 56 J- I ; -ir 56 *C W W 36 Tp 3! C £
*3**+5 5*****>4: ::++****CC
r:5t55T5c; ; 56 36 35** .T£'4>6 5:3C CC
M>5'5XC56 5656 5R5;'^5e565Cw:* ; *C5s(^ CC
1 = 1
2=2
3 = 3
4 = 4
5=5
6 = 6
7 = 7
8 = 8
9 = -
10
=

19
=
(
11
=

20
=
U
12
=
&
21
=
w
13
+
22
=
B
14
=
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23
ss
9
15
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24
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16
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17
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26
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18
=:
/
27-34
=
Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973.


51
PCS = Personal consumption expenditures
PS = Personal taxes
So, the percentage of PTI to households necessary
to balance the sector's account is:
Xh = [PCF. + PC EC GST / PTI (14)
Che remaining fraction (call it Xe) was considered a net
profit:
Xe = 1 Xg Xh (15)
Using data from the statistical abstract of the U,S,
(United States Department of Commerce 1971) and the bureau
of economic analysis input-output tables (United States
Department of Commerce 1969b, 1974a, 1975) the following
values for Xg and Xh for 1963 and 1967 were estimated.
Por 1963: (in millions of dollars)
Xg = [GP + GS 1BC PC] / PTI
= [6B167 + 55 93 54627 61099 ] / 194243
= 9 399
Xh = [PCE + PC EC GS] / PCI
= [ 375549 + 61^0 341514 55030 ] / 184248
= 29 59
Xe = 1 Xg Xh = .7551
Por 1967; (in millions of dollars)
rg = [GP + GS TEC PC] / PCI
= [ 'T465 + 31654 79239 83009] / 254969
Xh = [PCB + PC BC GS] / PCI
= [499669 83999 339436 81654] / 254969
49 37


190
the resultant time intensity and uncertainty concerning
their use. In this study approximately 1000 man-hours were
spent developing and adjusting the models, and it is certain
that another 1000 could have led to better results. This
time intensity of even moderately sized nonlinear simulation
models has been a major stumbling block for many studies.
It is also apparen* that linearization or other
simplifications to sidestep the problems are not adequate,
This represents a major area where mathematical and computer
science research could prove fruitful.
Embodied Energy analysis and Economics
The results of this study indicate an intimate
connection between the input-output, embodied energy concept
and the behavior of economic systems. The importance of
energy flow in biological systems is well known and there is
no reason to suspect that humanity and its habitat are
immune to thermodynamic lim5.tations. The constant embodied
energy to dollar ratio (when embodied energy is calculated
using the input-output approach) may indicate that the
market and price mechanism have evolved as a relatively
inexpensive way for humans to quantify the total
thermodynamic cost of alternative actions, and to act
accordingly. Thus energy flow is the primary concern of
economic systems.


Table 13.
1963 aggregate sector net capital stocks, gross investment and depreciation(a)
(in billions of 1967 dollars).
Aggregate Sector
Net
Capitol
Stock
Fraction of
Total U.S.
Net Capital
Stock
Gross
Invest
ment
Fraction of
Total U.S.
Gross
Investment
Depre
ciation
Fraction
Total U.S
Depre
ciation
1.
Environment
14981.0 (c)
.7746
80.67
.1631
80.67
.2452
2.
Raw Materials
3.9
.0002
0.48
.0010
0.33
.0010
3.
Fuel Industry
34.1
.0018
4.17
.0084
2.85
.0087
4.
Forestry and
Fisheries
0.4
-
0.05
.0001
0.03
.0001
5.
Agriculture
46.8
.0024
5.72
.0116
3.91
.0119
6.
Power Plants
40.7
.0021
4.98
.0101
3.40
.0103
7.
Construction
26.1
.0013
3.19
.0064
2.18
.0066
8.
Manufacturing
106.7
.0055
13.05
.0264
8.91
.0271
9.
Transportation 33.5
.0017
4.10
.0083
2.80
.0085
10.
Services
411.8
.0213
50.38
.1018
34.40
.1046
11.
Communications 39.9
.0021
4.89
.0099
3.34
.0102
12.
Government
1048.7
.0542
101.76
.2057
32.39
.0984
13.
Households
2567.97
.1328
221.3
.4473
153.80
.4675
TOTAL U.S.
19341.5
1.0000
494.73
1.0000
329.0
1.0000
134


183
Figures 27-30 show the relationships between the total
energy (direct plus indirect) input to the sectors and the
total dollar output tor each of the four alternatives on
labor, government, and solar energy. Table 9 summarizes the
regression statistics. it is clear from these results that
if labor and government services are included in the
calculations, the total (direct plus indirect) energy input
explains a significant percentage of the variation in sector
dollar output. For the best case (excluding the energy
sectors) over 99") of the variation in sector dollar output
could be explained with variation in total embodied energy
input, his is the same as saying that the ratio of
embodied energy to dollars is nearly constant.
The primary energy sectors (sectors 1-7) are outliers.
Primary energy inputs can thus be said to be underpriced
in that their dollar costs do not reflect their embodied
energy costs or their competitive market value.
Many conceptual and empirical refinements to the
technique remain to be made. There are still problems with
capital flows, incomplete coverage, joint products, and
transfers, and there is the need for much better data on the
distribution of renewable energy inputs. Better data on the
allocat.ion of value added to labor and government are also
needed. it this point, however, the following conclusions
can be drawn from the input-output study of total energy
costs:


WHITE f 6. 1 60) TX
160 FORMAT (M',16X,
DO 156 K=1, 5
DO 158 1=1.4
TIME =* ,F3.0)
170
158
156
C
C PHIHT LEGEND
C
FORMAT (10 X,25A1)
CONTINUE
CONTINOE
75
171
76
77
78
1000
WRITE 6.7 5)
FORHATjO *^30X, LEGEND8)
RsMJU/1 Is<1) 'IS(I' ,IS,I> IS,I)
CONTINUE
WRITE (6, 77) (2111-1*1-9)
FORMAT 12X. 8 0*,2x, 9F§. 0)
WRITE (6.78) (Z ill ,f=1.9)
FORMAT {10X,9F5.6,1X.*AND
IF (T.GE. FTGO T0#1000
PT=DT
DP*)
GO TO
STOP
END
100
28 51
82.32
10.00
1.0
1.0
28.51
82 .06
10.00
1.0
1.0
28.51
81.80
10.00
1.0
1.0
28.51
81.54
10.00
1.0
1.0
28.51
81.28
10.00
1.0
1.0
28.28
82.32
10.00
1.0
1.0
28.28
82.06
10.00
1.0
1.0
28.28
81.80
10.00
1.0
1.0
28.28
81.54
10.00
1.0
1.0
28.28
81.28
10.00
1.0
1.0
28.05
82.32
10.00
1.0
1.0
28.05
82.06
10.00
1.0
1.0
28.05
81.80
10.00
1.0
1.0
28.05
81.54
10.00
1.0
1.0
28.05
81.28
10.00
1.0
1.0
27.82
82.32
10.00
1.0
1.0
27.82
82.06
10.00
1.0
1.0
27.82
81.80
10.00
1.0
1.0
27.82
81.54
10.00
1.0
1.0
208


226
Table 24. U.S. household sector net capital, investment,
and depreciation time series in constant dollars
(billions of 1967 dollars (a)).
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1329
1052.21
77.02
19.42
57.60
1930
1073.79
63.96
5.65
58.31
1931
1084.33
58.93
- 0.19
59.12
1932
1085.31
46.64
-11.54
58.18
1933
1080.29
45.05
-12.10
57.15
1934
1079.18
51.76
- 5.11
56.87
1935
1084.58
56.87
- 0.41
* 57.28
1936
1095.98
65.11
5.40
59.71
1937
1112.04
68.34
7.66
60.68
1938
1125.77
62.93
0.75
62.18
1939
1140.12
70.77
8.89
61.88
1940
1164.15
79.92
18.86
60.96
1941
1198.23
93.50
27.90
65.60
1942
1232.44
84.23
15.79
68.44
1943
1261.25
83.47
13.36
70.11
1944
1288.72
81.42
9.87
71.55
1945
1317.28
87.59
11. 69
75.90
1946
1359.22
109.61
30.03
79.57
1947
1412.43
113.99
34.14
79.85
1948
1468.58
121.19
38.06
83.13
1949
1525.71
123.88
36.07
87.81
1950
1588.00
141.03
47.83
93.20


96
important provision for including spatial differences in
inputs and initial conditions and time variability of inputs
may allow dynamic simulations that can generate practical
predict ions.
^he TT.O. Economic-Geologic System
Gmbodied Energy in Goods and Services for 91 0,S, Economy
Sectors in 1967
The embodied energy intensities (in Btu fossil/S of
output) for 92 .S, economy sectors were calculated both
including and excluding labor and government service
feedbacks and solar energy inputs. The detailed results are
given in appendix TV, Table 20. Figure 24 illustrates the
four alternative treatments and a fifth possibility. These
results were obtained in collaboration with the Energy
Research Group, TJniversity of Illinois at Champaign. Sector
correspondences for comparison with the Bureau of Economic
Analysis (BGA) sector designations are indicated in
parentheses following the sector names in Table 20 All
values are converted to fossil fuel equivalents using the
conversion factor of 2000 Btu solar/Btu fossil (Odum et al
1977), none of these calculations considered depreciation
or net growth of household and government assets as a net
output from the system. The numerical values of the energy


TX=1900.*T
160
C
C
C
75
10X,EMBODIED ENERGY INTENSITY MAP'/r10X
IDA*/,10X,* FOR THE YEAR ,P10.0)
PRINT LEGEND
174
76
77
78
79
180
146
145
150
171
170
158
WBITEJ6.75)
FORMAT (*0 30X, LEGEND )
DO 76 3=1-5
WRITE (6,174) IIS (I) ,IS (I)
FOHHATJMOX, 50A1)
CONTINUE
WHITE (6,77) (Z (I),1=1,9)
FOBHAT 112 X, 0 *, 2X, 9P5. 0)
WRITE J6,78) (Z (if ,1=1.9)
FOBHAT(10X-9F5.0,IX,*AND
WRITE (6,79)
FORMAT (25X,M E12
DO 145 K=1,18
DO 146 L=1,10
IA
CO
COHTINOE
DO 150 1=1,88
K= 18. 0 1- ( (DLAT (I)-24.6)_/.23^
IS (I) ,IS(I) ,IS(I) ,1=1, 10)
UP*)
CE/12B AC CELL) ')
L=10 0 1-JfDLON (I
Xl^AR
/IB I
I)/AS
/AR
/AR
/AS I
NOE
/AR
/AR
/AR
I,
I
I
LT.Z
.GB.Z
. GE.Z
I .GE.Z
I .GB.Z
.GE.Z
. GE* Z
.GE.Z/7
GE.Z(8
GE.Z (9
7i)?iV
1
2
3
4
1
IA
IA
IA
IA
IA
IA
IA
A2
(K, L =IS
*K,L =IS
K, L =IS
K,L =IS
K,L =IS
K,L
K,L
K,L
IA k;l
IA(K,L
= IS
= IS
=IS 8
= IS (9
=IS
10)
FORMA1!^ 1%>V//#1 OX, *YEAR= VF5. 0,
1 *+ + + + *+*)
DO 156 K=1, 18
DO 158 1=1,4
U U IJU JL ml
WRITEJ6, 170) (IA (K,L),IA(K,L) ,IA(K,L)
FOBHAT 1101, * iX,50A1 ,iX, *< *)
,IA (K,L) ,IA (K,L) ,L=
CONTINdE
1,10)
243


Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitu<
(W)
25
7.27
8.69
6.95
0.57
26.90
82.06
26
14.20
9.35
15.20
1.10
26.90
81.80
27
13.60
10.80
17.60
1.24
26.90
81.54
28
12.20
12.10
9.38
1.28
26.90
81.28
29
19.00
20.50
27.30
1.28
26.90
81.02
30
3.48
3.72
6.12
1.28
26.90
80.76
31
32.70
33.50
33.00
1.28
26.90
80.50
32
21.10
19.00
12.60
1.28
26.90
80.24
33
7.13
15.20
59.00
0.53
26.90
79.98
34
0.49
1.78
0.40
0.05
26.67
82.32
35
10.80
12.50
15.40
0.79
26.67
82.06
36
15.00
55.60
83.60
1.18
26.67
81.80
195


126
Fourteen sector Close! System Input-Output Ha trices for 12.5.1
an!~2252
Figures 35 an! 36 are 14 sector input-output
transactions matrices for the U.S. economy-environment for
the years *96 3 an! 1967 with all values converted to their
equivalent in 1967 dollars. As previously noted, the system
is considered to he thermodynamically closed with only
energy crossing the system boundaries. Under this setup,
the energy input to the U.S. economic system derives from
three possible sources. Che first is the net input row of
the matrix, which is the dollar value (arrived at through
balance considerations) of the years input of solar energy.
The n.s. environment sector and the rest of the world sector
(which contains its own environment component) are the only
sectors receiving this input directly and are, therefore,
the only sectors with an entry in the net input row. This
is equivalent to saying that all solar energy is first
absorbed and transformed by the environment, before entering
the economic sectors. The current years sunlight enters
the economic system as "renewable products of the
environment such as rain, winds, and biomass.
Some of the sunlight absorbed by the earth ov=r past
eons has been stored in the environment sector in the form?;
of mineral and soil deposits and landforms. Depletion of
this "environmental capital" is the second path for energy
entering the U.S. economy. Industrial societies* use of
fossil fuels is the foremost example of the consumption of


191
Some potential times of the embodied energy concept in
dealing tilth combined economic-ecologic systems were
presented. The range of possibilities is enormous, however,
and there is already a large literature of applications
using similar ideas. As our economic systems approach the
limits of the stored environmental assets, explicit
consideration of energy flows can only become more
important.


APPENDIX III
FORTRAN LISTING FOR THE
25-CELL SPATIAL MODEL


163
maps ware used to validate the model. The maps indicate
t
that in 1901 the everglades area south of Lake Okeechobee
represented the highest embodied energy intensities, while
coastal areas had relatively low values. Urbanization in
the region has concentrated in the east and (to a lesser
extent) west coastal areas and also at Key west and Orlando,
leading to higher embodied energy values in those areas in
1953 and 1973. These data represented the primary input to
the 91-cell south Florida simulation model.
Ninety One Cell Couth Florida Spatial Simulation H22.E
The changing patterns of land use in south Florida have
been extensively documented. A detailed historical sequence
of land use maps and supporting material have been prepared,
It therefore represented a logical choice for a spatial
simulation study, is previously noted, the region was
broken into 88, 16 by 16 mile cells for the simulation.
Three additional cells, one representing the U, S
environment, one for the n.S. economy, and one for the rest
of the world were also included. The model used in this
study was the general, power maximizing model outlined
earlier. The difference equations used to simulate the
model are those in Figure 20 with n = 91. A FORTRAN listing
of the model is given in Appendix VII.
'"his application can be viewed as merely a different
way of grouping the u. S. economy-environment model, It


Table 9.
Regression analysis results for total (direct plus indirect) energy
consumption versus total dollar output for four alternative treatments
of labor, government and solar energy inputs
Alternative
Including energy
(Sectors 1 -
sectors
7)
Excluding energy
(Sectors 1 -
sectors
7)
R2
F
PR> F
R2
F
PR>F
A
Excluding labor
government and
solar energy
.0210
1.89
0.1729
.5539
100.57
0.0001
B
Including solar
energy but excluding
labor and government
.0629
5.90
0.1710
.2042
20.78
0.0001
C
Including labor
and government
but excluding
solar energy
.7809
313.73
0.0001
. 9907
8633.95
0.0001
D
Including labor,
government and
solar energy
.8535
512.74
0.0001
.9454
1401.31
0.0001
113


184
(1) Fhen all energy inputs and feedbacks are accounted
for, there is a very close cross-sectional relationship
between total (direct plus indirect) energy cost and
competitive market value. This is the same as saying that
the ratio of embodied energy to dollars, for competitive
sectors, is nearly constant.
(2) The outputs of the primary energy sectors are
underpriced in terms of both their embodied energy cost
and their free market value.
The second line of evidence for a constant embodied
energy to dollar ratio deals with time series of this ratio
in real dollar terms for the aggregate 0.S. economy. Table
21 and Figure 31 are examples of this time series for the
years 1920 to 1976. The relative constancy of the ratio is
striking, at least for the 1940 to 1976 period. There are
several possible explanations for the apparently declining
ratio during the 1920 to 1940 period.
(1) There are problems with converting to constant
(equivalent purchasing power) dollars with the older data
due to changes in the product mix and quality and changes in
accounting conventions.
(2) An embodied energy theory of economic value requires
the total energy to real GHP ratio remain constant. Figure
31 gives only the mineral fuels, hydro and nuclear energy
inputs to the economy while ignoring energy inputs from
direct capture of solar energy and embodied solar energy in


224
Table 23. U.S. government sector net capital, investment/
and depreciation time series in constant dollars
(billions of 1967 dollars (a)).
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1929
247.05
18.64
13.65
4.99
1930
258.21
20.98
16.03
4.95
1931
270.57
22.43
17.39
5.04
1932
282.40
20.92
15.75
5.17
1933
292.10
18.93
13.56
5.37
1934
302.07
22.23
16.81
5.42
1935
313.36
21.85
16.26
5.59
1936
327.71
29.54
23.90
5.64
1937
344.19
26.18
19.91
6.27
1938
360.80
29.57
23.02
6.55
1939
378.61
30.82
23.81
7.01
1940
397.48
32.94
25.45
7.49
1941
423.53
46.96
38.08
8.88
1942
482.80
103.13
91.30
11.83
1943
578.48
133.04
111.01
22.03
1944
663.00
137.43
76.44
60.99
1945
695.16
97.08
5.92
91.16
1946
672.57
23.98
-20.41
44.39
1947
641.34
24.72
-12.42
37.14
1948
622.47
30.17
- 0.74
30.91
1949
615.16
36.59
10.35
26.24
1950
615.43
37.68
14.39
23.29


86
, t+At t +
n
j=l
a E . Q .
i l, t i, t
1 + a Q ,
i i,t
bijQi,tQj,t
1 + b 0
3-3 i/t
t-At
otherwise
j/ t-At
n
3=^
bjiQj,tQi,t
1 + bjiQj.t
t-At
otherwise
t-At
c Q .
i l,t


165
Simulation results. Figure 45, a-k shows maps of the
mofle!s output over the period from 1900 to 2000. These may
be compares with the measured embodied energy intensity maps
for 1053 (Figure 43) and 1973 (Figure 44), The model does a
fairly good job of duplicating the historical time sequence
given only the initial (1990) conditions and the solar
energy input to the system. Other environmental energy
inputs to the region (such as rain, wind, and tides) are
considered to be the result of exchanges between the local
cells and the .S, and rest of the world environment cells
and are calculated internally in the model. The rapid
growth on the east coast and, to a lesser extent, on the
west coast and at Key West was a result in the model of
exchanges of these cells with the 0.5, economy cell, which
of course was growing exponentially over this period.
As with the 0.5. economy simulation, linear regression
models were used to address the goodness of fit of the
south Florida model. Here the 88 land use cells for 1953
and 1973 were used as observations (rather than time series)
with the measured data as the dependent variable and the
models output as the independent variable. These
statistics are listed in Table 18.
Owing to the nonlinear, discontinuous nature of the
model, the lack of good initial estimates on the parameter
values, and the large number of state variables, this model
was very difficult to fit to the historical data.



Figure 29.
Plot of direct plus indirect energy consumption
(calculated including labor and government but
excluding solar inputs) versus dollar output for
92 U.S. economy sectors


82
Qt = 8/(1 + R4Q-L) {41}
Substituting (41) in (3 8) yields:
Qg = kjSQ-j/O + k^Qj) \2Qi (42)
<\ further simplification was that since in
embodied energy terms all of the inflow is embodied in the
input to the tank. The total production function for each
component was created by adding together partial production
functions of the form given above. The power maximizing
logic built into the model was used to decide which partial
production functions were included in the total at any point
in time. In differential form the logic is hard to follow,
since it simultaneously uses one decision to make a second
decision, which is used in making the first decision. The
equations can also be expressed in difference form (which is
necessary for digital computer simulation and is done in a
following section) to clarify the logic. For now one can
imagine a tiny delay between one decision and the next.
The equation (38) for the rate of change of storage in
component 1 has five terms. The first term determines the
rate of captmre of direct external energy (Tj) as a function
of the amount of stored assets (Q-jJ and the capture
coefficient a^ The second term determines the amount of
internal interactions within component 1 as a function of Qj
and the coefficient b^. Tie third term determines the
amount of transfer from component 2 to component 1 with a
maximum power constraint. If the transfer is deemed to be a


187
ratios, an alternative explanation for this relationship
can be formulated in terms of embodied energy. Imported oil
has more energy {the energy reguired for transportation)
embodied in it than domestic oil, Thus if one calculated
the embodied energy/GDP ratios for the nine countries, they
would find more nearly constant values. The postulated
equivalence between embodied energy and dollar cost
manifests itself in the fact that energy prices are higher
in the countries with a larger percentage of their fossil
energy coming from imports {which have higher embodied
energy costs).
Darmstadter, Dunkerly and Alterman {1977) also
presented a 34 country survey of energy consumption versus
GDP. They found a high {R square = 0.85) correlation
between GD? and fossil and hydro energy consumption (or a
relatively constant energy/GDP ratio). Their survey covers
only the more industrialized nations so their inclusion of
only fossil and hydro energy was an adequate approximation
of total energy consumption, They also presented time
series data on the energy/GDP ratio for 5 of the countries
from 1961 to 1974 which show the relative constancy of the
ratio through time.
^aken together, the preceding data and arguments
provide significant evidence for a very close relationship
between total embodied energy and economic market value both
cross-sect!onally and intertemporally. This is a reasonable


14
minimize! (usually profit, utility or cost) subject to
constraints {Sealing with resource availability, income or
levels of production) mhe partial egu.illibrium theorists
leal with small pieces o4" the system taken in isolation with
the ubiquitous "all else being equal" frequently invoked,
Most of the analysis focuses on graphical solutions. Becker
(1971) is a good text along these lines. Input-output
analysis and linear programming are important approaches for
determining optimum, eguillibrium flows of commodities and
money in an economy. Oorfman, Samuelson, and Solow (1958)
summarize these approaches. Input-output is a general
equillibrium technique developed by Leontief (19H1). It is
a tabular accounting system with balance constraints. In
the typical application the economy is disaggregated into n
sectors and the production of each sector is expressed as:
Xij +
V .
" 1
j=1
(i = 1,2,. . ,n) (1)
where
= total production of sector i
= production of sector i to be used as input
to sector j
= output of sector i to consumers (final demand)
Figure 3 illustrates this setup.
A set of direct requirements coefficients can be defined as:
7! .
- 13
r ./ r .
(2)
or:


APPENDIX II
ANALOG COMPUTER DIAGRAM FOR THE
TWO COMPONENT EXCHANGE MODEL


APPENDIX VI
FORTRAN LISTING FOR THE 5-SECTOR
.S. ECONOMY-ENVIRONMENT SIMULATION MODEL


40
X-X =
_5
1f?
50
(300 700)
tX-X)
.0526316
.0105263
005632
0210526
9= o (7-7) 1 = {23,153 16.316)
This is substantially different from the result with
consumers endogenous.
The lower energy intensities that result from an
exogenous consumer sector are due to the fact that the
consumer services (labor) contain embodied energy that is
ignored when this approach is used. An alternative to
having an endogenous consumer sector would, be to calculate
independently the consumer services energy intensity, and.
use the coefficient to include the energy embodied in
consumer services as an input.
In this example, the intensity of consumer services
(e3) was calculated as 836. 36 when consumers were
considered to be endogenous, This number can be used to
include the energy contained in consumer services in the
direct energy input vector (the 5 vector) while leaving
consumers exogenous. The new F vector is:
V; = [30 0 + 25 (836. 36) 700 + .25 (836. 364) ]
= 6509.0^1 909.091]
Recalculating the energy intensities using this 3 vector
yields:


NJ
U>
tTi
c
c
c
9
11
10
13
12
700
701
DISENSION
DISENSION
DISENSION
DISENSION
(5) ,F4 (5)
f?Qsa:
X{5) ,IP (45) IS (6)
READ INITIAL CONDITIONS AND COEFFICIENTS
5
A (I) C (I) E (I)
A'(i),C(f),E(I)
DO 10 1=1
READ 15
WRITE (
FORHAT,
FORSATJ4F15.3)
CONTINUE
DO 12 J=1,5
READI5.13) (B (I.J) 1=1. 5)
WRITE (6,1JV (B (I/O) ,I=* 5
FORHAT(bE10.3}
CONTINOE
READJ5#700^ (^HAX(I) ,1=1 ,5)
5)
20
C
C
C
{5,70 11
ATJ6A1
0 1=1,5
J=1,5
= 1.
OE
291
292
293
294
295
296
290
FORHAT (5F1
READ
FOBS
DO 20
DO 20
y(!.J
INITIALIZE AND RON
WHITE(6,291
RITE i 6,292
RITE 6,293
RITE 6,294
WRITEJ6.295
FORHAT {* 1 .
FORHAT 71, B =
FORMAT 7X,*G =
FORHAT 7X H =
FORHAT 7X,W =
(IS (I) ,1 = 1,6)
,QHAX 1
,QBAX 2
,QSAX 3
,QMAX (4
, QHAX
SHITE(6,296)
FORHAT (24X, QOANTITT*)
WRITE(6.290)
FORHAT(21,YEAR*,1X,*0
1 MAX)
FT=200.
IPR=2
V
2
3
4
51
E = E7RbNHENTAL ASSETS',OX ,A1, MAX = *,F7.0)
BOSINESS ASSETS',13X.A1,* MAX = ',F7.0)
GOVERNMENT ASSETS*.11X.A 1. MAX = ,F7.0)
HOOSEHOLD ASSETS' ,i2X,A1.' MAX = '.F7.0)
REST OF THE WORLD ASSETS' 4X PA 1 MAX = ',F7.0)


72
Two production systems and their exchange
pathways.
Figure 16,


139
Five Sector F.S. Sconomv Simulation Molel
Figure 37 is an energy flow diagram for a 5-sector 0.5,
economy-onviromnen+'-vorld simulation model. The model
breaks the economy into three major components: a business
sector consisting of all the conventional 'industrial"
sectors, (sectors 2 11 in Tables 13 and 14) a government
sector, and a household sector. These are linked to a 0.5.
environment sector and a "rest of the world" sector. "he
difference equations used to simulate the model are those
given in Figure 2", with n = 5. 1 FORTRAN listing of the
model is given in Appendix VI,
The salient features of this model can be summarized as
follows:
(1) The model is a thermodynamically closed system.
Only energy fin the form of radiation) enters or leaves the
system.
(?) "he model is holistic in the sense that the entire
world is included in the model (in a very aggregated way).
(3) The model has only one exogenously determined
variable solar radiation. Models which are intended to
be used for predict i.ve purposes must keep exogenous
variables to a minimum since the model behavior is a direct
function of these variables, It does no good to have a
model that makes accurate predictions based on a large
number of exogenous variables unless those variables can be
predicted accurately. For example, many of the econometric


11
Table 1. Characteristics of the input-output an!
biosphere embodied energy concepts.
Characteristic
Input-output
embodied energy
Biosphere
embodied energy
Conservation of
embodied energy
yes
no
All heterogenous
by-products of a
production process
assigned equal
embodied energy
no
yes
(except for
degraded heat)


28
This calibration or validation of the model was performed by
manually adjusting the model!s parameters. The
discontinuous nature of the simulation models made the use
of nonlinear parameter optimization computer programs for
fitting the model to the historical data impractical. This
was because all of these algorithms (short of brute force)
require a continuous error surface to operate efficiently.
Input-Output Techniques for Calculating Embodied Energy
The application of input-output techniques (Leontief
19ft1) to the study of direct plus indirect energy
consumption was developed and documented by the Energy
Research Group at the Center for Advanced Computation,
University of Illinois (flerendeen and Bullard 197ft).. The
technique consists of defining a set of energy balance
equations (one for each sector) and solving the resulting
set of simultaneous linear equations for the energy
intensity coefficients vector e, which is the energy
required directly and indirectly to develop a unit commodity
flow. The underlying assumption of this technique is that
embodied energy is a conservative quantity. Figure 6 shows
the hasic "energy balance for sector j.
where
X^j is the transaction from sector i to sector j,
Xj is the total output of sector j, part of which
may be net change in storage.
/
ej is the embodied energy intensity per unit of Xj


225
Table 23. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
623.14
47.77
25.61
22.16
1952
652.24
76.15
56.54
19.61
1953
695.43
78.93
55.17
23.76
1954
733.17
74.31
47.07
27.24
1955
763.34
70.82
41.99
28.83
1956
791.11
93.92
44.91
29.01
1957
821.54
79.25
49.88
29.37
1958
857.16
87.87
57.52
30.35
1959
897.03
90.91
59.98
30.93
1960
926.80
85.43
53.49
31.94
1961
964.27
93.40
61.83
31.57
1962
1005.07
96.72
64.67
32.05
1963
1048.66
101.76
69.37
32.39
1964
1092.78
102.83
69.62
33.21
1965
1135.31
102.45
68.95
33.50
1966
1182.08
112.01
79.11
32.90
1967
1237.50
119.73
86.46
33.27
1968
1296.24
123.40
88.92
34.48
1969
1351.79
123.38
87.79
35.59
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.


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6/10/08 8:45 AM




98
NET EXPORTS
/LABOR AND
/ GOVERNMENT
SERVICES IGNORED
SYSTEM BOUNDARY
^^
t X \
1/
"industrial'
SECTORS
GNP
NET EXPORTS
HOUSEHOLDS
3
GOVERNMENT
NET EXPORTS
'X. LABOR AND
GOVERNMENT
SERVICES
NET EXPORTS
LABOR AND
GOVERNMENT
SERVICES
NET EXPORTS


70
3L
3?
r o
t ul
Q ry * ** Q
2 n
= n
3L
3~
It
= n
(29)
3l
37
= Kr,4- Kr,
nt n
= 0
n+l
Thus there are 3n + 1 equations in 3n + 1 unknowns* In
this example the equations In groups (19) and (20) can be
Ignore! since they are simply restatements of the
constraints which specified that for a single small time
interval, the direct, energy Inputs can be considered as
constants. Thus to maximize or minimize the system the
following relations must hold:
8Pt
3?1
3P2
3P.

3Q
?o~
SQ*
3Q
3Pt =
3Pl
3r2
3P.
+ * +
9Q¡



9Q
9
*
9Pt =
a
3 Pi
a
3P2
9
3 P
]
4-
+ +
3*0
~]
= V,
= 7.
= V,
(21)




INTPODCTTOH
A fundamental issue in ecology is understanding the way
energy and material flows in ecosystems develop organized
structures and processes. Mans economic systems can be
viewed as subiect to many of the same energetic forces as
those shaping ecological systems. Thus, the study of energy
and material flows in combined economic-ecologic systems can
lead to new insights into the way these flows develop
organized patterns.
Several important questions can be identified
concerning the role of energy as it affects organization and
succession in combined ecologic-economic systems. Flow does
energy flow through and organize these systems? What is the
relationship between energy flow and money? How is spatial
development related to sources of energy? What are the
general criteria for natural selection? How can selection
be modeled to predict the dynamic behavior of these systems?
These questions were considered using energy systems
analysis (Odum, 1971). Models describing the flow of energy
and materials were developed and evaluated. Specific
emphasis was placed on integrating conventional economic
accounting and analysis techniques into the general energy
systems framework. Input-output techniques and data were
employed to trace energy flows through combined ecologic-
economic systems. Efforts were made to show relationships


17
economic Hoels
A good review of models of the spatial distribution of
economic activity can be found in Chorley and Baggett
(195"7). Most of these models can be divided into three main
groups, Central place theory is based on the fact that some
goods and services must be produced at "centers" and
transported to users (or the users must be transported to
the center). For a specific mix of goods and services there
is a limited range of distance from the center defining a
market area inside which the marginal revenue exceeds the
marginal cost. In a homogeneous plane with only one type of
qtood or service produced, hexagonal market areas are
theorized, since these would represent the closest packing
of the market areas with no overlap. Production of
different types of goods and services leads to hierarchical
arrangements of hexagons, with different levels of central
places producing goods and services with different market
areas. Original works in this area are by Christaller
(1931) and Losch (1940) Berry and Pred (1961) provide a
review. location theory postulates that economic activity
will occur at the point of minimum total transport cost.
Transport cost surfaces for each of several inputs and
outputs of a specific econom5.c activity are estimated and
overlaid to find the point of minimum total transport cost
(Weber 1909), The approach is highly amenable to computer
applications as well as to the inclusion of costs other than


Table 20
(Continued)
Sector
(numbers in Parenthesis are BEA sector equivalents)
A
Excluding
Labor and
Government
Services
Feedbacks
and Solar
Energy Inputs
Alternative
B C D
Excluding Including
Labor and Labor and Including
Government Government Labor and
Services Services Government
Feedbacks Feedbacks Services
but Includ- but Exclud- Feedbacks
ing Solar ing Solar and Solar
Energy INputs Energy Inputs Energy Inpujs
All Values in Btu fossil/S
82.
Hotels & Lodging Places; Personal & Repair Services,
Except Automobile Repair (72)
41,839
58,875
359,550
705,900
83.
Business Services (73)
23,146
43,995
339,610
689,250
84.
Automobile Repair & Services (75)
41,209
51,365
359,280
698,200
85.
Amusements (76)
22,217
55,395
376,110
771,500
86.
Medical, Educational Services Nonprofit Organization
(77) 32,253
46,590
354,370
704,950
87.
Federal Government Enterprises (78)
27,503
32,695
362,330
720,750
88.
State & Local Government Enterprises (79)
61,893
82,185
441,310
855,800
89
Business Travel, Entertainment and Gifts (81)
69,697
282,015
401,410
962,150
90
Office Supplies (82)
49,223
152,390
373,710
814,700
91.
Government


717,160
1,393,050
92.
Households


358,350
738,050
to
M


16
AjXj
substituting {3} in (1) yields
(3)
n
l
(4)
j=1
or In matrix notation for all n sectors:
7 = AX + Y
(5)
or solving for the sector outputs in terms of the final
demand (T) and the direct requirements matrix (A) :
-1
X = (T-A) Y
(6)
The set of simultaneous linear equations represented by
(6) is useful for tracing Interdependencies at a point in
time or for making predictions of the affects of small
departures from equlllibrium, Programming models are
similar to Input-output models except that more than one
solution to the equations Is possible. The approach
originated as a strategic planning model for directing Air
Force activities (Pantzig 1951). The mathematical problem
is finding the best (or optimal) solution from among the set
of feasible solutions. The approach initially was applied
to linear systems (linear programming), and this is still
the major practical application. Gradually, more
mathematically difficult problems were attempted with
current applications to dynamic, nonlinear systems with
stochastic elements. Ban mol (1977) reviews these methods,


TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS........................................ iii
LIST OF TABLES......................... vi
LIST OF FIGFF.es,. .viii
ABSTRACT. xi
INTRODUCTION 1
Research Plan.......................... 2
Background of Previous Studies........... 4
Energy and Society............... 4
Systems Ecology.. 5
Energy Analysis................................. 6
Embodied Energy 7
Optimisation.................... 13
Economic Models,,....,...... 13
Spatial Economic Models.,,.,.,.....,.,.,....... 17
Simulation Models............................... 19
Description of the South Florida Area............... 20
METHODS. 23
Description of the Modeling Language................ 23
Model Development,......,.....,....,.,,.......,. 25
Dynamic Optimization................ 25
Simulation Modeling Methods..................... 26
Model Parameter Estimation, Validation and
Testing. 27
Input-Output Techniques for Calculating Embodied
Energy. 28
Double Counting................................. 41
U.S, Economy Data Assembly and Evaluation...., 43
Government and Households as Endogenous
Sectors....................................... 44
Environmental Inputs............................ 52
An Endogenous Environment Sector................ 55
Capital Flows 57
South Florida Land Use Data .57
RESULTS. 65
The General Conditions for Maximum Power..,...,.,... 65
Development of a General, Power Maximizing
Simulation Model...,....,.,...,.....,.,,.. 75
Simulations Using Two Components................ 84
Simulations of Spatial Development Using
25 Cells. 91
iv


223
Table 22. (Continued)
Year
Net Capital
Stock (b)
Gross
Investment
Net
Investment
Depre
ciation
1951
473.94
76.04
36.88
39.16
1952
503.09
66.26
25.61
40.65
1953
524.61
67.16
25.05
42.11
1954
540.95
59.79
16.13
43.66
1955
562.33
77.24
31.49
45.75
1956
592.84
79.44
31.31
48.13
1957
618.44
75.24
24.94
50.30
1958
633.42
63.65
12.02
51.63
1959
648.95
78.05
25.08
52.97
1960
672.10
80.05
24.81
55.24
13 61
692.39
76.19
19.00
57.19
1962
715.14
87.66
28.32
59.34
1963
743.87
91.00
38.87
62.13
1964
776.01
99.25
33.81
65.44
1965
817.69
115.71
45.97
69.74
1966
870.94
130.36
54.35
76.01
1967
921.60
122.18
41.01
81.17
1968
964.36
126.47
41.65
84.82
1969
1009.72
135,54
46.90
88.64
(a) Based on estimates in Kendrick (1976) converted into
constant 1967 dollars for ease of comparison with the
1-0 data for this year.
(b) Excluding land, which was credited to the environment
sector.


5
importance in economic systems. Ophuls (1977) reviewed the
political implications of energy and resource limitations,
Cook (1971, 197fs) and Hannon (1973a) have attempted to
quantify the intricate web of energy flows in industrial
societies.
Systems ecology
Systems analysis as practiced in ecology is an
integrative approach used to explain the structure,
function, and interrelationship of all systems as the
product of certain general systems principles which
transcend the boundaries of academic fields. The aim of
general systems theory was formulated by 7on Bertalanffy
(1968) as "the formulation and derivation of those
principles, which are valid, for systems* in general (p.
32). This paradigm is seen as essential to the
understanding of complex systems with feedback, which has
frustrated the "atomistic approach of "normal science.
Odum (1971) produced a unified theory and methodology for
the application of general systems theory to a broad range
of problems. This is the general approach taken in this
study.


LIST OF TABLES
Table
pi a?
1 Characteristics of the input-output and
biosphere embodied energy concepts................ 11
?. Input-output transactions matrix in arbitrary
physical units corresponding to the diagram in
figure
32
Input-output transactions matrix in embodied
energy units corresponding to the diagram in
Figure B,................................
Input-output transactions matrix corresponding
to the diagram in Figure 9, using the national
input-output accounting conventions............... 39
Relationship of input-output value added
accounts categories............................... 49
Estimated land areas and solar absorption for
major land use types.............................. 54
Land use subsystem metabolism and structure
estimates in coal equivalents (CF) 63
Kinty two sector embodied energy intensity
statistics.
103
9 Regression analysis results for total (direct
plus indirect) energy consumption versus total
dollar output for the four alternative
treatments of labor, government, and solar energy.,113
m 1957 7,9. business sector capital stock and
investment breakdown (in bi!15_ons of 1967 dollars).117
11 1967 tj.,9. government sector capital stock and
investment breakdown (in billions of 1967 dollars).118
12 1967 n.S. household sector capital stock and
investment breakdown (in billions of 1967 dollars) 119
13 1963 aggregate sector net capital stocks, gross
investment, and depreciation (in billions of
1967 dollars).......,... 134
1U 1967 aggregate sector net capital stocks, gross
investment, and depreciation (in billions of
1 967 dollars)
136


41
- -1
e = T, fl-X)
[ 599.091 909.091]
.0526316 .0052632
.0105263 .0210526
_
e = [35.364 21.818]
These are the original energy intensity figures.
This approach requires an independent calculation of the
energy intensity of consumer services, however.
The approach considering consumers endogenous is more
in keeping with Leontief*s original conception of a closed
(except to energy) economic system, It also does not
reguire the independent calculation of the energy intensity
of consumer services. It does, however, require some
manipulations to extract the relevant data from the current
accounting scheme.
Double Counting
hn often raised question concerning any accounting
scheme involves double counting. This is especially true of
input-output schemes that display all intermediate flows.
The question becomes clear with reference to the preceding
diagrams and. discussion. It is strictly a question of
accurately defining boundaries and making note of those
flows crossing the boundaries (net flows) and those flows
remaining within the boundaries (which when added to net
flows yield gross flows). Double counting problems are
encountered when the boundary is shifted, but the


Figure page
18 Differential equations for the model in
Figure 17. 79
19 Diagram illustrating the partial production
function relations.... 81
2D Component i difference equation. 86
21 Two component model analog simulation results..... 88
22 Two component model analog simulation results..... 92
22 Digital simulation of the power maximizing
model for a spatial grid of 25 components......... 95
2U Diagram showing the system boundaries and flows
included in the four alternatives................. 98
25 Frequency plots of embodied energy intensities
by sector calculated with and without solar
inputs. 101
26 frequency plots of embodied energy intensities
by sector calculated with and without labor
and government service feedbacks.... 102
27 Plot of direct plus indirect energy consumption
(calculated excluding solar inputs and labor
and government) versus dollar output for
92 rj.S. economy sectors........................... 106
28 Plot of direct plus indirect energy consumption
(calculated including solar inputs but excluding
labor and government) versus dollar output for
92 U.S, economy sectors........................... 108
29 Plot of direct plus indirect energy consumption
(calculated including labor and government but
excluding solar inputs) versus dollar output for
92 .S. economy sectors........................... 110
3D Plot of direct plus indirect energy consumption
(calculated including solar energy inputs and
labor and government) versus dollar output for
92 TT.5 economy sectors........................... 112
31 Dineral, hydro, and nuclear energy consumption
per dollar of real GFP from 1920 to 1976
115


I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
'T/L^
Howard T. Odum, Chairman
Graduate Research Professor of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
'Suzahne E. Bayley
Assistant Professor "of
Environmental Engineering
Sciences
I certify that I have read this study and that in
my opinion it conforms to acceptable standards of scholarly
presentation and is fully sdequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
B ar ney^L?^ Capeh
Associate Professor of
Industrial and Systems
Engineering
ihajf
iesso:


c
c
600
CHECK TIRE AND PRINT RESULTS
IT=PT*.0001
IP (IPR-IT) 60 1*60 1*600
PT=PT+DT
GO TO 100
C
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601 DO 110 1=1.5
110
270
260
111
200
150
750
W
770
TX=T*1929.
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IP (IQ (I) EQ.J)GO TO 111
IP (IP {if. HE. IS (6) ) GO TO
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GO TO 200
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STOP
END
PRODUCTIVITY =*,E15.6)
PRODUCTIVITY = K1 5. 6)
4.580E-007 .015
321. 0. .03
247. 0. .03
1052. 0. .03
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44300.
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657700.
400E-0050.200E-0053. 505E-008
150E-0030.417E-0036.516E-007
0.206E-0050.800E-0040.100E-0012.542E-0051.464E-009
4.375E-0062.134E-0042.289E-005100.0E-0032.316E-010
238


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o o o


F3(31=F3(J) *1(1,3)
CONTINUE
CONTINUE
CALCULATE HE LEVEIS
DO 50 1=1-25
[iljgjl) +DT* (F1 (I) *F2 (IJ-F3 (I)-F4 (I))
CHECK TIHE AND PHINT HESDLTS IF NECESSARY
IT=PT*.0001
IF (IPR-IT) 60 1,60 1,600
600 PT=PT*DT
GO TO 100
C
C HAPPIHG HOOTIHE
C
601
111
42
40
C
C
C
50
C
C
110
120
C
180
146
145
WRITE (6,1111
IkliKfetf' ',im 'f2(i) r3m *m(i> *d(i
CONTINUE
150
DO 145 K=1,5
DO 146 1*1,5
IA CONTINUE
COHTIHOE
DO 150 1*1,25
K=5. 0 1 ( (DLAT (I) -
L=5. 01-i (DLON (I j -
ri)/ABI) .it*
IJ/AR I .GE.
I)/AH I .GE.
Q I)/AR I)
I /AR(I
I /AR I
I /AR I
[I /AR I
I)/AH I
!5kMW
GE.
.GE.
.GE.
.GE.
.GE.
.GE.
.GE.
27.59
81.28
2H
2
3
4
(5
6
7
8
2(9
l) /.23)
/.26
IA (K,L
IA K,L
IA K,L
IA iK,L
IA K,L.
IA ¡ K,L
IA K,L
IA K,L
IA K,L
IA K,L
=IS
= IS
=IS
=IS
=IS
= IS
=IS
=IS
=IS
= IS
(1
k
5
6
7
8
9
1
D)
207


Figure 38.
1963 5-sector transactions matrix with all values
converted to millions of 1967 dollars


Figure 36.
1967 14-sector transactions matrix with all values
converted to millions of 1967 dollars


on if
on if
£Pt > ££t
dQ¡ dQ2
d P-, d P-r
<3Q2 3Q|
PT = P, + P2
Figure 17.
Energy circuit diagram for a two component
power-maximizing model of exchange.


3
energy were developed and evaluated. Nonlinear,
discontinuous optimization models were developed and applied
with Lotkas maximum power principle as the objective
function.
Cross-sectional and time series data were collected for
two related examples. The first was the n. s. economy-
ecology as a whole. Data for this example included input-
output transactions at various levels of aggregation, tima
series of total capital stocks, investment and depreciation,
and time series of energy inputs to the economy and
environment. Most of these data were in dollar terms and a
major part of the study involved integrating them into an
all-encompassing energy flow network that included
environmental systems. The second example was the spatial
evolution of the south Florida region. A series of three
previously compiled, detailed land use maps of the region
for the years 190% 1953, and 1973 {along with supporting
data on the characteristics of the mapped units) were used
as the primary data base for this application, The models
were run over the historical period and the results compared
with the collected data. Once a reasonable fit was obtained
the models were run into the future and their predictions
interpreted.


APPENDIX V
TIME SERIES DATA FOR THE U.S.
ECONOMIC-ECOLOGIC SYSTEM


Table 12. 1967 U.S. government sector capital stock and investment breakdown.
(All values in billions of 1967 dollars.)
Gross
Capital
Stock
Net
Capital
Stock
Gross
Invest
ment
Net
Invest
ment
Depre
ciation
Grand Total
1980.4
1237.5
119.73
86.46
33.26
Total Non-Human Tangibles (a)
895.9
486.5
48.83
15.57
33.26
Structures
612.8
358.2
26.24
11.37
14.87
Equipment
248.3
93.4
21.74
3.35
18.39
Inventories
34.8
34.8
0.85
0.85
-
Total Human Tangibles
-
-
-
-
-
Total Non-Human Intangibles
149.4
100.6
14.56
14.46
-
Basic Research
24.1
24.1
2.22
2.22
-
AR & D
125.3
76.5
12.34
12.34
-
Total Human Intangibles
935.2
650.4
56.33
56.33
-
Education and Training
839.2
599.7
49.72
49.72
-
Medical and Health
91.8
49.0
6.00
6.00
-
Mobility
4.2
1.7
0.62
0.62
-
a. excluding land held by government
Source: Kendrick, 1976.
119


DISCUSSION
^he Case for a Constar!. Embodied SELS.E2.Z. .2 Dollar Patio
The results of this study generally support the
hypothesis that there exists a constant ratio of total
embodied energy (as defined here) to economic value as
astermine3 in a competitive market, both cross-sectionally
and intertemporally. There are three main lines of evidence
supporting the hypothesis. The first involves studies of
the detailed input-output structure of the economy at a
specific time.
The input-output technique is useful in assessing the
total direct and indirect energy necessary to produce goods
and services in an economy. This dissertation contains
results of modifications to the input-output method for
obtaining energy intensities (Herendeen and Bullard 1974).
The modifications were aimed at achieving consistency with
the boundary definitions of the economy. The results (Table
29 and the summary statistics in Tables 9 and 9) indicate
that inclusion of labor and government services feedbacks
significantly reduce the variation in energy intensities and
increase their average magnitude, while inclusion of solar
energy inputs increase both the variation and magnitudes.
Table 8 allows comparison of the statistics of calculated
180


68
(iii) ?T possesses a finite maximum fPT) over all
values of Q and B satisfying the constraints
(iv) PT is concave over all values of Q and E
satisfying the constraints
These conditions guarantee that
(1) There exists at least one feasible solution
(B) If PT is strictly concave, then there is a unique
optimal solution
(C) If Q, is a constrained stationary point, than
Q, B is a global optimum
It will be shown in a later section that the specific
objective function chosen meets the above conditions.
The Lagrange multiplier technique involves craating a
substitute problem that incorporates the constraint
equations into the objective function. This new equation,
called the Lagrangian, can then be maximized (or minimized)
using standard calculus techniques. The Lagrangian
expression for the above system is:
L = P]_ (Q]_fQ2'# ** Qn'El> + p2^1'Q2'* Qn'E2> + * +
^2' ^l^t ~ Q l ~ Q 2 ~ Qn) +
V2^1t~ "l> + V3{K2t- ... Vn+1(Knt- En) (17)
where
vl,72# * ,7n+l are unknown Lagrange multipliers
To maximize the original constrained system, one then
maxIm5..zos the unconstrained Lagrange expression (L) by
writing the partial derivitives of L with respect to all the


35
Figure 8.
Hypothetical three sector economy with all
flows in embodied energy units.


Figure 44. Embodied energy intensity map for
south Florida for 1973 estimated
from the 1973 land use map
LEGEND
* * - *-- / / / / / \ 1 1 1 1 f ++ 4i+- XXXXX$5$
* : : : : : ===.- = /////11 1114-++-M- xxxxxsss
: :: : : =====///// 11 111 t+-i-++xxxxx3S
.. .. : : :: : =====/////i i 111 + + 4-++ xxxxxsssss
5. 10. .70. 30. 40. 50. 75. 1 00. 20 0.
10. 20. 30. 40. 50. 75. 100. 200. AND UP
( El 2 05/123 AC CELL)
Oi W ifi


I I T T 1 X' X X X' X
II 1 T T X X >' X X
I I I 11XX/XX
IT I T T X X X X X
291


(?)
4
+
4
+
4
4
4
4
4
+
+
+
4
4
4
-<
4
+
4
4
4
4
4
4
4
4
4
+
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
I T TI ITIT II
I T I I T I I I IT
TITITTITTI
I I I I I I l T T I
-4H
n i ns$$$s
I I I I I S £ $5 $
II 1 l !£££$$
II I TUiSiS
££$£$
$$$$$
£$$$$
££$$$
£$£££
£££££
£££££
£$£££
S S£
££££ £
£$£££
£££££
££££££££$$--
££££££$$$£
£££>£££££££
£.£$£££$£$£
££££££££££
££$£££££££
£££££££££$
££££$
£££££
£££££
££ ££$
££££ $
££ £££
£££££
£££££
£££££
$£$$$
SSSS
£££££
£££$$
£££££
££££$
I I 1 I 1
I I 11 I
I I 11 X
I 1 11 I
i it i r
TTI.IT
T IT I I
T II I I
-£ £££ £
-££$££
-£££$£
ii
///.//
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
*0661=oV3A'
9£T


in o
Figure 45. Simulation results for the 91-cell
south Florida spatial model
(a) Initial conditions (1900)
(b) 1910
(c) 1920
(d) 1930
(e) 1940
(f) 1950
(g) 1960
(h) 1970
(i) 1980
(j) 1990
(k) 2000
LEGEND
:: : : :=== = = /////! i j. 11 f++++xxxxx$$
:: :==== = /////i i 111 + ++++ xxxxxrsss
::: : :=====///// 11 111 f++++xxxxxss$
: ::::=====/////! i 11t f+f+fxxxxxsss
. 10. no. 30. 40. 50. 75. 100. 20
. 23. 33. 40. 50. 75. 100. 200. AN
( E12 CE/128 AC CELL)
\
OOl) yi ir th


Figure 35
1963 14-sector transactions matrix with all values
converted to millions of 1967 dollars


Figure 42. Embodied energy intensity map for
south Florida for 1900 estimated
from the 1900 land use map
it
m *
5. 10.
10. 20.
1.
20 .
30.
E 12
.EGO MO
--- = // //i i 111 *4 +
---///// \ 1111 -*+*- + /.XXX'XSSS
=/////! 1111 H-+t+XXXXX31S-,3
= ==/////] l 11 1 :-- + 4(;XXXXiS2-3i
30. 40. SO. 75. 100. 200.
40. 50. 75. 100. 200. AMO U
CF/120 AC CELL)


37
The major differences concern the treatment of
depreciation, the exogenous energy inputs, and the consumers
sector. In the national input-output accounts, the
depreciation is credited to the value of the output to
consumers. The consumers plus the net output are the final
demand sector. finally, the feedbacks from consumers are
considered to be exogenous and are added to the other
exoaenous Inputs. These modifications lead to the flow
diagram and input-output table given in Figure 9 and Table
4, respectively.
"he interindustry" flows are not affected, and neither
are the total inputs and outputs from the remaining
endogenous sectors. The modifications have affected only
the "final demand" and "value added" categories and their
common sum, the G9?. The GHP is now 1418.1, which is
greater than the previous total of 1000 by 418.1, the
depreciation of consumers. "'he economic accounts aggregate
the consumers sector with final demand and value added.
It is interesting to note how the results for the
energy intensities (es) would differ if the standard input-
output conventions were followed. Returning to the original
physical flow matrix (Table 2) and ignoring the input from
consumers yields:
30 0
1C
5"
T =
0 100
10
50



148
Yij = ^ij Qi Oj / 1 f ^ij^i where Yj_j = value of flow
from sector j to sector I (in billions of 1967 $/yr)
= net capital stock of sector i (in billions of 1967
9} solving for the b.¡_j yields:
bj_j = *7j_j / Q-¡_ (Y^j Qj). The c^ were estimated from
the model relations:
H = Ci Qi where: = net outflow for sector i (in
billions of 1967 9/yr)
= net capital stock of sector i (in billions of
1967 9} solving for yields:
c. = IT. / Q.
l l 7 l
The initial estimates of the parameters (using the
above relations and the average of values obtained from the
1963 and 1967 input-output data in rigures 38 and 39) are
given in Table 16. In the section to follow on simulation
results, the parameter values actually used in each run are
given along with the plots. The sensitivity of the model to
changing selected parameters are discussed.
Simulation results. Figure 49 is a plot of the models
output over the period from 1929 to 2030. This run employed
the coefficients given in the accompanying figure legend.
To fit the model to the historical data as closely as
possible, the least wall known of the coefficients were
varied from the initial estimates. These were the
coefficients governing inputs from the environment sector to


tt)
+++++++4+++ +++++++++ + 4 44 4 4-4 + +++ + + + + + 4+ ++ ++ + 4+ 4-4 44 4 4 4+ 4
4
+
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
:::::nni$£$
4
4
:::::imi$$
4
+
: : :: : U T I !£££$$
4
4
::::: T T i i !£$£$ $
4
+
nintim
4
4
iinmui
4
+
nimn u
4
4-
IIllllTtU
4
4
£££$£
4
4
£££££
4
£$$£$
4
4
£££$$
4
4
^<4 *
#97 t ^
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
SSS$£
tSSSS
T <£ £ XX XXX --
xxxxx
XXXXX
XXXXX
$$££$$$$&$*
S5S5$$£SS$
£S££SSS£$$* *
$$$SS$$S$$** *
?£££$$$£$$
£S£S$$$$$$* *
S£$S$S5S$J
£i$££SS$$£* 1 *
SSS
£££$$
SS£S$
S5SS2
S£££ $
£££££
&£$$$
£££££
££$££ ; ;;
£££$£ :::
£££££ :::
££££$ :::
£££££ : ::
££$$£ I I I
££SS£ :::
££$££ :::
i i TT x
nm
tint
1 T 11 i
I TI I I
I U *1 T
1 nn
mu
£££$£ /////
S £££ s /////
$££!-£ /////
£££££ /////
4
4
4
4
4
4
4
4
+
4
4
4
4-
4
4
4
4
4
4
4
4
4
4
4
-i
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
+ +4 4-4 4-+++ + + + + +4 4+44 + + + + *C 00 Z~ + 4+4 +4 4 4+ 44 + 4+4 4+ + + +
LLT


75
whore the eirst term on the right hand side of (33)
represents the "benefit and the second term the "cost" of
the transaction Y12 In a dynamic simulation framework, a
transfer from component 2 to 1 (?12) is seen as beneficial
(leading to increased total power) if?
aPm
>0 (34)
dYi2
or (using 33) if:
3Fm 9Pm
os)
SQi 9Q2
which is equivalent to (23), Thus, allowing the pathway
switches in figure 16 to remain open as long as conditions
(35) and (23) hold will tend to maximize the total power of
the system, .
P^yejopmont of a Power Maximizing Hi mula tign Model
A specific model structure and an algorithm for
approximating the maximum power conditions in a dynamic
framework must now be developed, for application to real
systems. The model equations will always represent a
compromise between simplicity (and therefore manageability)
and accuracy. Here the mathematical form of the model
(including the power maximizing algorithm) is laid out,
first for a simple two component case and then for the


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Table 26
231
Time series of net land stocks in the U.S.
(in billions of 1967 dollars).
Year
Land Eeld by
Business
Land Held by
Government
Land Held by
Households
Total
1929
288.9
51.0
53.3
393.2
1930
293. 9
50.9
54.2
399.0
1931
296.6
51.0
54.8
402.4
1932
296.7
51.0
55.4
403.1
1933
295.9
51.0
55.5
402.4
1934
395.9
51.2
55.5
402.6
1935
295.9
51.3
55.5
402.7
1936
295.4
51.7
55.4
402.5
1937
297.0
51.7
55.2
403.9
1938
299.6
51.3
55.2
406.1
1939
301.0
51.4
55.5
407.9
1940
300.8
51.7
56.4
408.9
1941
298.4
51.7
59.3
409.4
1942
294.4
51.8
62.7
408.9
1943
294.4
52.0
65.6
412.0
19 4 4
295.4
52.1
68.4
405.9
19 4 5
281.3
52.2
71.2
404.7
194 6
280.0
52.5
73.8
406.3
1947
280.2
52.8
76.6
409.6
1948
281.3
52.9
79.5
413.7
1949
293.2
53.3
82.4
418.9
1950
294.8
53.7
85.4
423.9


220
Table 21. (Continued)
Year
Real GNP .
(x 109 1967 $/yr)
Total Mineral
Fuels, Hydro
and Nuclear
Energy Consumed
(x 1012 kcal/yr)
Energy Consumption
per Dollar
of real GNP
(kcal/1967$)
1940
271.7
6048.7
22262.4
1941
314.4
6736.1
21425.3
1942
352.4
7057.9
20028.1
1943
391.7
7701.8
19662.5
1944
419.7
8050.7
19182.0
1945
414.0
7979.9
19275.1
1946
373.0
7715.0
20683.6
1947
372.7
8316.1 -
22313.1
1948
387.0
8600.5
22223.5
1949
386.5
7995.8
20687.7
1950
420.0
8640.7
20673.1
1951
451. 3
9339.0
20693.1
1952
465.4
9253.7
19883.3
1953
486.2
9537.3
19616.0
1954
479.4'
9199.1
19133.3
1955
515.9
10103.9
19594.7
1956
525.9
10627.3
20224.2
1957
533.0
10605.8
19898.3
1958 .
526.9
10497.7
19923.5
1959
560.6
1107.3'
19634.9
1960
574.5
11338.4
19736.1
1961
585.7
11530.0
19685.8


Figure 39.
1967 5-sector transactions matrix with all values
converted to millions of 1967 dollars


114
their omission from the data greatly improves the R square
values. Some possible reasons for this will be discussed.
Table 9 also indicates that inclusion of labor and
government service feedbacks leads to a highly significant
relationship between total {direct plus indirect) energy
input and dollar output for economic sectors, especially if
the energy sectors are omitted from the data. Inclusion of
solar energy inputs does not seem to help {or hurt) the ^it
very much, but this is no doubt due to the rather crude
method used for approximating the points of entry of solar
energy to the economy used in this study.
tg GMP P at to for the n.P. from 1920 to 1976
In addition to the cross-sectional analysis of the
previous section, one might look at the time series of
various indicators of energy consumption and economic
activity. Table 21 in Appendix 7 lists real G!!P fin 1967
dollars), total mineral fuel, hydro, and nuclear energy
consumption and the ratio of these two quantities for the
same period. Figure 31 is a plot of the mineral, hydro and
nuclear energy consumption per dollar of real GPP for the
years 1929 to 1976


251
Odum, H, 0* 1077 "nergy, value and money. In C.A.S, Hall
and J.H. Day, eds. Ecosystem modeling in theory and
practice, John Wiley and Sons, Hew York, 684pp,.
Odum, H.T. 1078. Energy analysis, energy quality and
environment. In H.F. Gilliland ed. Energy analysis:
a new public policy tool. ARPS Selected Symposium
9, Westview Press, Dew York,
Odum, n.T, and J, Alexander, eds. 1977. Energy analysis of
models of the united states. Annual report to DOE,
Contract #EY-76-5-05-4398. Systems Ecology and Energy
Analysis Group. Dept, of Environmental Engineering
Sciences. university of Florida, Gainesville,
Odum, -H.T. and H.T. Brown, eds. 1975. Carrying capacity
for man and nature in south Florida. Final report
on contract CX090110057 to National Park Service, tj. S,
Pspt. of Interior and the Florida Division of State
Planning, center for Wetlands, University of
Florida, Gainesville. 885pp.
Odum, H^, H. Brown and R, Costanza. 1976. Developing a
state for man and land: energy procedures for regions
planning. In Science for Better Environment. Proceed
ings of the International Congress on the Human
Environment (RISC), Pages 343-361. Published by the
Asahi Evening T'ews. C.P.O. Box 555, Tokyo, Japan.
Odum, H.T. and E.C, Odum. 1976, Energy basis for man and
nature. HcGraw-Rill, New York. 297pp.
Odum, H.T., F, C, Wang, J. Alexander, and H. Gilliland, 1978.
Fnergy analysis of environmental values: a manual for
estimating environmental and societal values
according to embodied energies, Report to the Nuclear
Regulatory Commission. Contract #NRC-04-77-123.
Center for Wetlands. University of Florida.
Gainesville, 172pp.
Ophuls, W. 1977, Ecology and the politics of scarcity.
W.H Freeman and Company. San Francisco. 303pp.
Oster, G.F. and E.0,.Wilson, 1978. Caste and ecology in the
social insects. Honographs in Population Biology no. 12,
Princeton University Press. Princeton, R.J. 352pp,
Rapport, D.J. and J.E. Turner, 1977, Economic models in
ecology. Sci. 195:


175
+ 4-4-4-4- -M- 4-4- +4-4-4- + +++* + + YEAR = 1 980
4-
+
+
4*
4-
4-
4-
4-
+
4-
4-
4-
4-
+
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
+
+
4-
4-
4-
4-
4-
4-
I-
4-
4-
4-
4-
4-
4-
4-
4-
+
4-
4-
4-
4-
4-
4-
+
4-
4-
4-
4-
4-
4-
4*
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4- 4-
5 33 S 3
S3 '3 $
SSSS
S$$3$
11111
11111
1 1*11 1
11111
1 11 l 1
11111
l 11 1 1
11111
+ 4- 4- 4- 4-4- 4- 4- 4- 4- 4* 4- 4- 4- 4- 4- 4- 4- 4- 4- 4*4-4-
4-
4-
+
4-
4-
4-
4-
4-
4-
+
4*
4-
4-
4-
+
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
3 3 5 35
SS3$5
3 33 3$
$ .3 3 S S
33SS-3
S33S3
3 3$ 33
33SSS
3$33$
3 33 3 S
3SSSS
: :3.333s
::$333$
::$3333
: s$$ s$
3SS3S
sssss
$3333
S3S3S
$3333
£3333
SS333
$ 3333
33 3 33
3 S3 33
3 3 3 3 3
$33 33
33333
$$$53
$33 33
$ 3 3 3 $
$33 33
SSS5S
3 3 3 3 3
3 33 33
3 3 3 3 $
$333$
33333
S 3 3 $ 3
$$$$$
33333
$ 3 3 3 3
3 3$ 3$
$ 333311 1 11
$33331 lili
£533311111
3333311111
4-4- 4- 4-4- 4- 4- 4-4- 4- 4- 4-4- 4- 4-4- 4- 4-4-4-
11
11
I L
II
1 1
1 1
1 i
1 1
lilil
lilil
lilil
lilil
4-
4-
4-
1-
4-
4-
4-
4-
4-
4-
4-
4-
+
4-
4-
4-
4-
4-
-t-
4-
4-
4*
4-
4-
4-
4-
4- + 4- 4- 4- 4-4- 4- 4- 4- + 4-4- 4- 4- 4-4- 4- 4- 4- 4- 4-4- 4-4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4- + + 4- 4-4-4-
(i)


091


131
the embodied sunlight, of past eons. In the matrix this
depletion of environmental assets shows up as a net decrease
in the capital stock of the environment sector over the year
(the change in storage portion of the net output column).
A third pathway for energy input is through imports
from the rest of the world sector, which is transferred to
the .S. economy and shows up as a net import from the rest
of the world sector. Input-output tables in dollar terms
have total inputs balanced by total outputs for each sector.
This constraint was utilized in determining many of the
quantities in the tables that were not measured directly,
The inclusion of the environment, households, and government
as endogenous sectors required the copious use of this
identity In deriving estimates. Some of the conceptual and
quantitative approximations necessary to complete the tables
follow.
The n.S, environment sector contains all land, air,
water, and raw materials in the .S. Its inputs from the
other O.S. economy sectors consist of "waste products,"
which wore assumed to have a zero value. Actually, some
portion of the depreciation of the contributing sector
should be counted as an input to the environment, as shown
in Figure 10 Lacking any guantative way of making this
distinction, all the depreciation was considered to be a net
output. The depreciation estimates (from Kendrick 1976) are
summarized in Tables 13 and 14, The environment sector and


64
Table 7, (Continued) .
Subsystem
Subsystem
Metabolism
(E6 CE kcal
/ac-yr)
Subsystem
Structure
(06 CE kcal
/ac)
21. Sawgrass marsh
8. 1
273. 7
22. Beach and dune system
0.3
4. 0
23. Salt flats
0.3
4. 0
2$. Scrub mangroves
1.0
7.2
25. Salt water marsh
5.0
29. 5
26. Mangroves
7.3
218. 4
Source: Costanza {1975).




Table 19. (continued)
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitui
(W)
61
4.52
3.81
4.72
0.22
25.98
81.80
62
19.60
18.50
19.90
0.94
25.98
81.54
63
18.30
19.60
19.00
1.25
25.98
81.28
64
11.10
11.30
11.50
1.28
25.98
81.02
65
26.90
28.50
32.00
1.28
25.98
80.76
66
42.80
42.90
41.60
1.28
25.98
80.50
67
22.40
84.00
257.00
1.26
25.98
80.24
68
2.38
36.00
49.30
0.16
25.98
79.98
69
16.55
16.11
15.98
0.69
25.75
81.28
70
14.00
13.50
13.20
1.27
25.75
81.02
71
20.40
20.30
25.70
1.28
25.75
80.76
72
31.90
36.80
51.80
1.28
25.75
80.50
198


120
subtracter! an! included in a separate environment sector for
this study, Cross investment is the total dollar value of
investments in capital stock, where capital stock includes
human capital. Net growth is gross investment minus
depreciation. Gross capital stock is accumulated gross
investment minus retirements, while net capital stock
subtracts double declining balance depreciation estimates,
For most purposes in this study, net capital stock is the
more appropriate measure.
Kendricks estimates of gross investment in the
household and government sectors allowed a more accurate
calculation of the numerical, value of the mean embodied
energy intensity for the U.S. economy. The values in Table
8, alternative D, were calculated using a total primary
input value of 1C9.64 E15 Btu fossil/yr. This was composed
of S'?. 52 El5 Etu fossil/yr of mineral, hydro, and nuclear
fuels consumption and 104.4 E18 Btu solar/yr, which when
converted to fossil fuel gnality using a conversion factor
of 2000 Btu solar/Btu fossil (Odum et al. 1977) yields 52, 20-
El S Btu fossil/yr. The total primary input divided by the
net output from the system yields an estimate of the mean
value of the embodied energy intensities. For alternative D
in Table 8, the net output was assumed to be gross private
fixed capital formation plus net exports plus net inventory
change {see Figure 12). This was 125,61 E9 $ in 1967. The
sum of these three categories are gross business investment


c
c
c
c
c
10
c
c
c
c
c
241
25 CELL SPATIAL SI ISOLATION MODEL
DIBENSIOS ED(25,25
DIMENSION P *
(25)
D/25,25) ,Y(25.25),Q(25),Ejr25) AR
I25);dC2§);DIT(25) #DLbfjf25)
DIMENSION Fl|25f ,F2j25,F3 (25) .F4 (25)
DIMENSION A (25) § (25) .fc (25) X (5) ,'lA (5, 5) ,Z (9)
DISENSION IS (10) ,CM (25)
ASSUME CONSTANT COEFFICIENTS FOR THIS RON
DO 10 1=1,25
A II) =.94
B (I) =. 3
C (I) =. 03
CONTINUE
READ LATITUDE AND LONGITUDE OF CENTROID OF
EACH CELL (IN DBGREEG NORTH AND NEST),
INITIAL STORAGE LEVELS, AND LAND AREAS OF EACH CELL
HRITE (6. 241)
FORMAT (M ,2X,I,4X.*DLAT(I) .4X,DLON (I) ,4X,Q(I) ,
15X,*AR (I) *^5X**CM(I) *,5X,*QINT^)
DO 200 I=l!25
READ(5,2pi[DLAT(I) ,DLOH(I) ,Q(I) ,AR(I) ,CM(I)
QIHT-QJ(I) /AR (I)
HHITE3d.5tgi. bLAT (I) DLON (I) Q (I) AR (I) CM (I) QINT
FORMAT (I5.6E 10. 3)
FORHATJ5F10.3)
CONTINUE
READ (5,250) (2(1) ,1=1,9)
FORMAT (9F6.0)
240
201
200
C
250
C
READ (5,26 0) (IS (I) ,1=1,10)
260 FORMAT (10 A1)
C CALCULATE IHTERCELL DISTANCES
C
DO 202 1=1,25
DO 203 J= 1, 25
^ED|IgJ^=( j[DLAT(I)-DLAT(J) ) *69.5256) **2* ( (DLON (I)-DLON (J))
203 CONTINUE*
202 CONTINUE
C C
C ASSUME CONSTANT EXTERNAL INPUTS FOR EACH CELL


4
3}ackgroun2 of Previous Studies
This di ssertation includes energy analysis, evaluation,
and simulation of economic-ecologic systems using input-
output, optimization, and. spatial models. Some background
of previous work in thes^ areas is reviewed.
Energy and Society
The thesis that available energy inputs govern and
limit the structure of human societies is not new,
Boltzmann (1886) pointed out that life is primarily a
struggle for available energy, Soddy (1933) stated: nif we
have available energy, we may maintain life and produce
every material reguisite necessary. That is why the flow of
energy should be the primary concern of economics (p, 56).
Lotka (1921) also noted the direct relationship behween
energy and economics. Cottrell (1955) provided a detailed
analysis of the ways cultures have historically adapted to
their surplus energy supplies. Odum (1971) extended
energy concepts to include all systems, thus providing a
conceptual link between man and nature and many new insights
into the workings of mans economic systems.
Paly (1977) discussed the energy limitations which
ultimately lead to steady state economic systems.
Georgescu-Eoegen (1971) took a more theoretical approach in
his study of the second law of thermodynamics and its


Table 19. (continued).
Cell
No.
1900
Embodied
Energy
(x1012CE)
1953
Embodied
Energy
(x1012CE)
1973
Embodied
Energy
(x1012CE)
Land
Area
(103 128
ac cells)
Latitude
(N)
Longitu<
(W)
37
15.80
11.80
20.10
1.28
26.67
81.54
38
19.50
19.10
16.00
1.28
26.67
81.28
39
21.80
22.20
12.10
1.28
26.67
81.02
40
40.40
45.50
50.30
1.28
26.67
80.76
41
44.80
45.90
52.60
1.28
26.67
81.50
42
29.90
32.10
31.10
1.28
26.67
80.24
43
6.35
44.40
113.00
0.59
26.67
79.98
44
2.25
3.99
8.39
0.16
26.44
82.06
45
14.10
14.60
27.50
0.96

26.44
81.80
46
16.20
17.30
30.30
1.28
26.44
81.54
47
14.80
16.00
20.30
1.28
26.44
81.28
48
17.30
18.00
15.50
1.28
26.44
81.02
196


49
Table 5, Relationship of input-output value added
components to the national Income and product
accounts categories.
Value added components
in the Input-output.
(1-0) accounts
Value added components in the
national income and product
(NIP) accounts
Employee compensation Employee compensation
Indirect business taxes Indirect business taxes
Property type income Proprietors income
Rental income of persons
corporate profits (before taxes)
Inventory valuation adjustment
Pet interest
Business transfer payements
Surplus of government enterprises
Capital consumption allowances


Plot of direct plus indirect energy consumption
(calculated including solar energy inputs and
labor and government) versus dollar output for
92 U.S. economy sectors
Figure 30.


too
DT*1./24.
PT=0.
TP=Os
TPH=0.,
T=0.
GO TO 601
T=T*DT
DO 29 1=1-5
*e (i) /(c 1.n (i) *q (i)) **2)
DO *30 0=1-5
330
350
30
29
IF (I. EQ. JIGO TO 330
QI*B <1,01*Q (J)/ < <1. tB (1,0) *Q (I) ) **2)
GO TO 350
*(2*B(X,J)*Q(I)))/(1+B(I,J)*Q(I))**2
COHTINOE
40 1=1,5
iUc lifts
w
F4, ,
F2 (it =0.
DO 42 J=15
IF(I.EQ.O)GO TO 430
DI=D <11*1.2
CCCCCCCCCCCCCCCCC
IF IDI-D1J)) 410,430,430
410
430
450
WiS &
42
40
C
C
C
TI.J) =B (I, J1*Q F2 III =F2(lf i fl, J
F3joi=F3(J)+I *Q COHTINOE
COHTIHOE
CM.CUL&TE NEB LEVELS
DO 50 1=1 ,5
50
? Jii?2 ,i,'p3 -m(i)
:>)
COHTIHOE
TP=TP+P(1)+P (2) *P (3) +P (4)
TP8=TPH+P (1) +P (2) 4P <3) +P (4) *P (5)
J
237


Figure 11. Diagram showing definitions of national income variables.
-j


74
SPT 3PT 351 3PT a02 3PT SE1 3PT 3PT
5L IQi ^12 "^2 3*12 3S], dY^ **12 12
3P ai
T
21
9Y2iaY12
(26)
The third and fourth terras on the right hand side can be
dropped since Eand E2 are exogenous and.Y12 has no effect
on them, thus:
dT
dE
(27)
12 1*12
Since embodied energy units are used throughout, some
additional simplifying relations can be made for this model.
9Pt
9Pt
si
9Y21
ao1
1
ii"i2
dQ2 _
-1
di12
= 1
(28)
(29)
Dsing (29) and (30)
dl2i _
dQ2
ao
/
dY 12
3Y 12
di
2
21
-1
(31)
then:
or:
dP T
1 +
9 P,T
9Pt
dY 12
"9Q~
flPT =
9Pt
. 9Pt
di-i2
9 Q
3 Q 2
- 1
(32)
(33)


20
ili ilsrli
Figure is a location map of the south Florida area.
The region boundaries were taken as the drainage basin
boundaries of the Kisslssmee-Fverglades basin. Extensive
background information was developed on the detailed spatial
evolution of land uses in this region as part of a study by
the Center for Wetlands, University of Florida, funded
through the Department of the Interior and the State
Department of Administration. This dissertation developed
as an attempt to answer some of the questions raised by
these previous studies. The reader is referred to Costanza
(1975) for characteristics of the mapped categories, land
use, energy data, and a detailed description of the mapping
procedure. Browder, Litttleiohn, and Toung (1975) provide
full color land use maps and a general overview of the
application of energy analysis to a region. The technical
report of the south Florida study (Odum and Brown 1975)
provides detailed data encompassing the full range of energy
and environmental problems facing south Florida, Zucchetho
(1975) provides a detailed systems analysis of the Hiami
urban area


178
Table 18. South Florida simulation model performance
statistics for 1953 and 1973.
Year
R square
PR>F
Regression
Coefficient
1953
.677
.0001
.522
1973
.717
.0001
.411
Average
.697
.0001
.467


69
variables (including the v*s) an setting them all equal to
zero:
91
3pi
9P2
9Pn
=
+
+ +
- ?
= o
3Ql
3Q^
3Q¡"
?Q-
1
31.
dV
3P?
9P
=r
X
+
z
+ +
n
v
= n
q2
q2"
io2-
'l


9
-




9




*




91.
3P,
3P2
9P
=:
X
+
z
n
- V
= o
9pn"
Hq~
n
3Q~
n
1
3L
9P
=
X _
V, = n
9i¡
2
91,
9P
z _
^2
V = 0
3


*

9
* m


* 9
3T,
9P
n
ap
t*
n+1
O La
n
n


99
intensities in Table 2f> are therefore high. Inclusion of
these flows anti their effects on the results will be
addressed in a following section.
Column ?. of Table 20 lists the energy intensities (in
Btu fossil/) excluding government and labor services
feedbacks and solar energy inputs. This is the previous
approach of the Energy Besearch Group (Herendean and Bullard
1974). The results presented here differ from that study in
one respect. Dollar flows were used throughout in the
present study whereas, in the previous study, direct energy
flows were used to measure the distribution of fossil fuels,
hydro, and nuclear energy from the energy sectors to the
remaining sectors.
The use of direct energy flows is preferable if the
output from the energy sector is physically homogeneous
(which is a fair approximation for the fossil fuel producing
sectors). Including solar energy inputs to the economy
requires, however, that one create energy sectors whose
output is physically very nonhomogeneous (such as
agricultural products) and for which dollar flows are the
best weighted aggregate available. In order to maintain
consistency, dollar flows were used throughout..
is in the previous study, the embodied energy
represents the total fossil fuel Btus (plus the total solar
Btus converted to fossil fuel equivalents for columns B and
T> of "able 29) required to produce a dollars worth of


LIST OF FIGURES
1 Solar energy driving the productive processes
of the earth......*......................*......., 8
2 Diagram showing the characteristics of the input-
output and biosphere embodied energy concepts 12
3 Diagram showing the standard input-output
accounting setup, 15
4 Location map of south Florida......... 22
5 Energy circuit language symbols used in this study 24
6 Single sector energy balance... 29
7 Hypothetical three sector economy with all flows
In arbitrary physical units....................... 31
B Hypothetical three sector economy with all flows
in embodied energy units.......................... 35
9Hypothetical three sector economy cast In the
format of the national input-output accounting
statistics........................................ 38
10 Energy flow diagram of an aggregated 14 sector
IT. S. economic-ecologic system..................... 46
11 Diagram showing definitions of national income
variables 47
12 Summary of modifications to the input-output
conventions. 53
13 Land use cells for south florida.... 60
14 Example of detailed land use data, showing
cell 45 in Figure 13 for 1973.............. 61
15 Example of detailed land use data, showing
computer coding for cell 45 in Figure 13
for 1973............. 62
16 Two production systems and their exchange
pathways. 72
17 Energy circut diagram for a two component
power maximizing model of exchange................ 77
vi i


DOUT = DOLLAR VALUE OF TOTAL OUTPUT (xl09§/yr)
112


\ ENVIRONMENT (MODEL)
153


260 FGEBAT (10 A1)
C
C CAI.C0Lfi.1K XBTERCELL DISTANCES
t'*
DO 202 1=1,91
DO 203 3= 1,9 1
^ED|Xf(J&IAT (I) -DLAT (J)) *69,5256) **2* ( (DLON (I) -DLON (J) )
203 CONTINUE^
202 CONTINUE
0 205 1=1,88
DO 205 3=90,91
IFfCHm.LE. 1.16OTO205
pMmti*'*'''''
CONTINUE
205
C C
C ASSUME CONSTANT EXTERNAL INPUTS FOR EACH CELL
C
DO 210 1=1.91
| (I)
D
Y ij = ^
IF(D (I,J) .LE.O) GO TO 215
ED(I,j[=B (I)/ED(I,J)
SO TO 211
ED
CO
CONTINUE
215
211
210
C
C
C
ju Z IU - 1,^1
5 fII =1.0*AR (I)
Ljli = A (I) /AR jl)
>0 211 3= 1,91
¡MSS(I*
INITIALIZE AND RUN
FT=150.
IPR=10
DT=1. ,
PT=0.
T=0
GO T 601
100 T=T*DT
DO 29 1=1.91
DJI)=A (I) *E (I)/ { (1. *A(I) *Q (I)) **2)
F3(I> =0.
DO 30 3=1,91
XI=ED(J,lf*Q (J) / (1*ED (3,1) *Q (3))
IF (I. EQ. J) XI=0
241


93
total power of the system In a dynamic process, Using
digital simulation techniques and a matrix to represent the
arrangement of the cells on the landscape, some hypothetical
results were obtained, A FORTRAN coding for the model is
given in Appendix ITT, The equations used are those given
in Figure 20 with n = 25. For this application, an
effective distance parameter was employed as a prime
determinen!, of the transfer coefficients. The transfer
coefficients were made proportional to the inverse square of
the distance between components. Figure 23 shows the
results of one simulation intended to isolate the effects of
relative position on spatial development from the more
direct effects of unequal external energy inputs and unequal
initial conditions. The external energy inputs and. initial
conditions of all the cells in the matrix were set at the
same values. The transfer coefficients were a direct
function of the distance between components.
Figure 23 shows that under these conditions, the model
produces a concentration of structure in the center of the
matrix due to the locational advantage (smaller average
distance) of the center component. This is consistent with
what would, be expected from central place theory, and the
equations used for the transfer flows in the model are
essentially those of the gravity model. Thus, the model can
be viewed as an extension of central place theory and
transportation theory to include energy principles, The


63
Table 7 Lane! use subsystem metabolism and structure
estimates in coal equivalents (CE).
Subsystem
Subsystem
Metabolism
: (E6 CE kcal
/ac-yr)
Subsystem
Structure
(E6 CE kcal
/ac)
1.Cleared land
0.7
5.0
5. 5
2. Lakes and reservoirs
3. Pscreational space
4. Pesiflential (light)
5. Eesidential (med. -dense)
6. Commercial/Tndustria1
7. Transportation
8. Power plants
9. Improved pasture
10. .Vegetable crops
11. Tree crops
12. Sugar cane
13. Grassy scrub systems
14. Pineland systems
15. Hardwood systems
16. Lakes and ponds
17. Cypress domes and strands
18. Pet praire
19. Scrub cypress
20. Freshwater marsh
7.7
24. 7
250.0
750.0
520. 0
2,250.0
1, 600.0
11,125.0
500. 0
2,000.0
4,000.0
126,000.0
5.1
24. 7
21.3
294. 8
9.6
74, 9
22.2
313. 1
4, 0
16, 5
6.4
80.1
7.7
235. 9
1. 4
7. 4
7.3
214.5
5.4
51. 6
5. 8
61.3
7.4
228. 7


(6)
4 4 44 4 4 44444444444 44444444444
+
4
4
+
4
4
+
+
4
4
4
+
4
4
+
4
4
4
4
4
4
+
4
4
4
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19
In empirical studies, Yj_j is often the number of
people-trips between centers and S and Sj might be the
populations of the centers. Isard (1975) reviews these
concepts and applications. The generalized gravity relation
was incorporated in the spatial simulation models developed
in this study.
Simulation Models
Simulation of dynamic, nonlinear systems of equations
can be accomplished by solving differential or difference
eguations using a computer. Examples of simulations of
economic and ecologic systems are those by Forrester (1961,
1969, 1971) and Odum (1971). The approach has been
expanding rapidly 5.n recent years with the decreasing cost
and increasing availability of computers. Hall and Day
(19*T_r) provide a compendium of recent, ecological simulation,
studies. Alfeld and Graham (1976) is a recent example of
simulation applied to urban systems. In outline, the
technique involves deciding on state variables or storages
for the system of interest and then writing a differential
or difference equation for the time rate of change of each
of these storages in terms of the other storages and any
external inputs. Given initial conditions for the storages
and a set of parameter values the computer simulates the
time course of each variable in the system. The solution
can then be compared with reality and adjustments made to
the parameter values.


TOTAL CAPITAL STOCK (x IO,c 1967 dollars
123
YEAR
Time series plot of U.S. business, government,
and household net capital stocks from 1929
to 1969.
Figure 32.


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