EPA-600/5-73-013
February 1974
THE STATE OF THE SYSTEM
(SOS) MODEL:
Measuring Growth Limitations
Using Ecological Concepts
By
Edward R. Williams
Peter W. House, Ph.D,
Contract No. GS-03S-38351
Order No. P3-01-02023
Program Element 1H1096
Project Officer
Peter W. House, Ph.D.
Director, Environmental Studies Division
Washington Environmental Research Center
Washington, D.C. 20460
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
Tor sale by the Superintendent of Document!, U.S. Government Printing Office, Washington, D.C. 20102
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ABSTRACT
The State of the System (SOS) Model is the result of an
attempt to develop a methodology that relates ecological
concepts including regional carrying capacity to the social
scientists' concepts of regional growth and development,
and quality of life. SOS appears conceptually sound in its
general relationships but it should be considered at this
time as only a conceptual research tool.
The initial operational model, SOS-1, was developed to
investigate details of the results predicted by the theory
and to explore data requirements and needs. Therefore, the
results of the model runs provided are purely illustrative
and should be interpreted using extreme care. Further model
development into a policy analysis technique has been post-
poned pending the outcome of research into improved techniques
for measurement of quality of life. However, in keeping with
the EPA policy of making research results available, this
publication has been prepared.
The SOS Model began as an attempt to provide an example form
of a constrictor model of the Decision Analysis System (DAS)
to be used in conjunction with the General Environmental
Model (GEM). A discussion of the DAS is given in Dr. House's
paper, "Decision Analysis for Environmental Management."
During the design of the constrictor model, SOS took on a
life of its own as a stand-alone model. It is intended that
the later developments of SOS should complete this develop-
ment as a constrictor model within DAS as well as continue
its refinement as a stand-alone analysis tool. The model, as
given in the SOS-1 form, is flexible and new data and algorithms
can be substituted with relative ease. In order to maintain
this ease in later, more complex versions, segmentation of its
procedures into smaller modules would be useful. Such a form
will increase the utility of SOS as an educational and research
tool.
This report was submitted in fulfillment of Task 4.7 of Order
Number P3-01-02023, Contract Number GS-03S-38351 by Chase,
Rosen and Wallace, Inc., under the sponsorship of the Environ-
mental Protection Agency. Work was completed as of September
1973.
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CONTENTS
Page
Abstract ii
List of Figures iiii
Acknowledgments vii
Sections
I Conclusions 1
II Introduction 5
III Environmental Carrying Capacity 11
IV Resources of the Human Ecosystem 27
V Model Overview 40
VI Model Formulation 51
VII The Example Model (SOS-1) 75
VIII Example Data 138
IX Model Test 155
X References 184
XI Appendices 186
111
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FIGURES
Figure
Number Page
1 Ecosystem Energy and Nutrient Conversions 11
2 Population Growth in Finite Systems 16
3 Conceptual Form of the State of the System Model 43
4 Model Procedural Flow 45
5 Elements of the Model 52
6 One Cycle of the Model 54
7 System Adjustment Procedure 72
8 Resource Base Adjustment Procedure 73
9 Example Model System Flow Chart 79
10 Step 1 Flow Chart 81
11 Step 1 Parameters 82
12 Regional Population for a Cycle 86
13 Step 2 General Flow Chart 87
14 Step 2 Parameters 88-90
15 Regional Production Component Data for a Cycle 97
16 Regional Resource Data At a Cycle End 98
17 Step 3 Flow Chart 101
18 Step 3 Parameters 102
19 Demand Measures Value and Resilience 105
20 Time Change Interpolation Function 107
21 Step 4 Flow Chart 108
22 Step 4 Parameters 109
23 Resource Adjustment Formats 113
IV
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FIGURES (CON'T)
Figure
Number Page
24 Step 5 General Flow Chart 115
25 Step 5 Parameters 116-117
26 Short Term Adjustment Formats 121
27 Step 6 General Flow Chart 122
28 Step 6 Parameters 123
29 Long Term Adjustment Formats 128
30 Step 7 General Flow Chart 129
31 Step 7 Parameters 130
32 Demand Measure Threshold Adjustments 132
33 Step 8 General Flow Chart 134
34 Population Data by Age-Year at t=0 140
35 Population Partition Coefficients 142
36 General Data for Resource Categories 145
37 Resource Substitutions 147
38 General Data for Production Components 149
39 Production Formulae for Components Inputs 151
40 Demand Measures Data 152
41 Demand Satisfaction at t=l, 10, and 25, Run 1 157
42 Adjustment Statistics, Run 1 158
43 Resource Status Data, t=l, 15 and 25, Run 1 159
44 Run 1 Summary Data 162
45 Run 1 Population Data 163
46 Pun 1 Public Sector Output Data 164
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FIGURES (CON'T)
Figure
Number
47 Run 1 Private Sector Output Data 165
48 Run 1 Natural Resources Use Data 166
49 Run 1 Energy and Agricultural Products Use Data 167
50 Run 1 Unemployment and QOL Values 168
51 Run 1 Land, Air, and Water Use Data 169
52 Not Used
53 Variation of Initial Data for Runs 1-6 170
54 Comparison of Population Factors, Runs 1-6 171
55 Remaining Stockpiles at t=25, Runs 1-6 173
56 Run 2 Summary Data 174
57 Run 3 Summary Data 175
58 Run 4 Summary Data 176
59 Run 5 Summary Data 177
60 Run 6 Summary Data 178
61 Run 7 Summary Data 180
VI
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ACKNOWLEDGMENTS
The development of the State of the System Model to its
present form of an operational model for testing alter-
native research concepts is the product of a three stage
research effort; this effort has included work by many
other researchers in addition to the principal authors.
As such, the research represents the development of an
operations research product in the classical way of com-
bining the products and talents of a number of profes-
sionals into an integrated final product.
The initial concepts were developed by Dr. House and
were amplified by Sam Ratick, Bob Livingston, John Gerba
and Tom Parry of the Environmental Studies Division.
Their work, later expanded by the authors, is represented
in Sections 2-6 and Appendix 1 of this report.
The design, programming and documentation of the example
model, SOS-1, was produced by a project team of Chase,
Rosen § Wallace (CRW), and included Ernest Heilberg, Roma
Malkani and Penny Colley as well as Mr. Williams.
The model refinement, data collection and model test were
performed by CRW, assisted by members of Dr. House's division
plus Sted Noble of International Research and Technology.
CRW1S'effort is documented primarily in Sections 7-9 and
the other appendixes.
The total effort to bring the original concept to the status
documented in this report was an eight month period. This
development in such a short period reflects well on the
imaginative reasearch and teamwork of all staff members.
Vll
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SECTION I
CONCLUSIONS
Many analyses of regional resource limitations and
environmental damage being caused by population and
industrial growth predict that major, catastrophic pro-
blems will occur. The question arises; is the perceived
level of catastrophy a function of the situation or a func-
tion of the analysis? It appears that a regional model
that includes not only an element that describes a region
but also a systemic element that adjusts consumption pro-
cesses to reduce use of limiting factors might help answer
this question.
The forms and the limits of system adjustment used in
the proposed model require representation of both the
economic levels and the physical levels of resources and
limiting factors that are consumed or modified in the region.
These needs suggested that the concepts applied by ecologists
in the analyses of natural ecosystems might be the appropriate
context for representing the physical aspects of our human
ecosystems while the economic constraints affecting levels
of consumption of the physical limits are best represented
by the traditional laws of supply/demand pricing structures.
These laws should include dynamic unit cost structures so
that resources could not be exhausted no matter what level of
funds existed in the area. Also, the level of unit costs
should control feasible expansion of economically available
reserves and determine when improved utilization of similar
resources can be substituted for critical limiting factors.
A general model formulation, the State of the System
Model, was developed using concepts that represent the
region of interest as an ecosystem dominated by human demands.
Measurement of the ability of the human ecosystem to maintain
growth of man, the dominant species, and growth of his
"nutrient-demands" under a set of limiting factors is the
primary interest in the model design. The basic concepts of
this general formulation appear to reduce some of the limi-
tations of previous regional models.
The general design was followed by development of a
simple operational model (SOS-1) to test the basic proposed
adjustment mechanisms and concepts. To text the model cred-
ibility and sensitivity, a data base generally representative
of values and trends of the United States in 1970 was used.
While much of the data are only rough approximates and the
aggragation of model components is high, a test analysis was
performed that appears quite credible. Specific findings
that were developed include:
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• If specific resource utilization trends are
continued with no adjustment of levels of use
of critical resources, depletion of some natural
ores would depress some production areas by
1977. (Run 13, Appendix 8) *
• Assuming that production adjustments are made using
available technological capabilities, the present
population, and the production growth rates, some
minor problems will occur prior to 1990 but these
fluctuations are only temporary. However, by
1995 the present production patterns would cause
long-term depletion of some nonrenewable natural
ores that in turn would cause shortages in several
major production areas. (It should be kept in
mind that a limited set of adjustment procedures
were represented in the test data base; hence, the
actual system has many more adjustment options.)
(Run 1, Section IX)
• Since the 1970 trends caused major resource deple-
tion and a ragged production pattern, several pro-
cedures to limit these effects were tested including
reduction of annual operating funds and limiting
population expansion. The best single adjustment
factor in the modified data base is limiting pro-
duction operating funds. (Run 2-7, Section IX)
• Under the conditions of the test data base, the
smoothest growth patterns were achieved by setting
annual investment growth of all components to 2
percent. Then resource adjustments were sufficient
to suggest long-term replenishment and adjustment
can be achieved while the population and per capita
demand satisfaction maintain steady, increasing
patterns. Below 2 percent, the trend was smooth
but has diminishing support of population demands.
At 4 percent or higher investment, ragged economic
trends and higher resource depletions occur suggesting
a likelihood of severe short term effects. (Section IX)
• Reduction of population growth from current (1970)
birthrates to ZPG, even when fund growth rates
were set at 2 percent produced a less satisfactory
level of demand satisfaction. Available work units
in the labor force became a significant limiting
factor at ZPG. (Runs 10-12, Appendix 7)
*Later data suggest less critical situation (see page 269)
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t Adjustments that include control or moderation of
per capita demands reduce system stress, increase
system resistance to failure and allow the system
to produce solutions that are marginally better
balanced toward the initial (1970) value system.
(Runs 8-9, Appendix 6)
Thus the set of runs of SOS-1 performed using the initial
abbreviated data base support an analysis that concludes:
The severe resource limitations that occur statically within
7 years are due to lack of adjustments. In fact, at present
funds investment trends and population growth rates, the regional
adjustments will allow a viable society for 25 years. However,
during that' time severe production dislocations and major resource
shortages will cause a quality of life (QOL) pattern that is
ragged. Reduction of investment rates and reallocation of funds
among the production components can produce an regional expan-
sion that will stimulate resource increases and will support
a population at close to the unrestricted growth rate with a
stable QOL. Reduction of operating funds growth to zero and/or
population birth rates to ZPG are overreactions that produce
less stable and productive systems.
Based on these limited, test-bound data, a best growth
solution produced by the model for the region appears to
be a birth rate about one and one-half times the gross death
rate, a funds growth rate about 21 per year allocated to emphasize
areas of least-destructive resource usage, plus maintenance of
per capita expectations at close to the present levels in goods
while allowing moderately increasing expectations for services.
The SOS Model concept appears useful and in its present
form and an improved data base provides a simple, aggregate
analysis capability. It appears that future development
should take two routes:
• Continues development of a simple model form that
uses a small, aggregate data base that is easily
modified for use in quick-reaction general analyses.
• Expansion of the level of model detail and inclusion
of specialized algorithms to allow more detailed
study of specific processes and limiting factors
within a holistic regional analysis context.
For the. aggregate model, the present algorithms with minor
modification appear appropriate after some improvement
in the interpolation calculations. Primary emphasis should
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be in expansion of available substitutions, refinement of
data bases, research into improved population demand measures,
plus modification of the program structure to make it an
easy tool to be applied by users.
The development of a more detailed State of the System
Model requires a several-phase analysis/development plan.
This plan should include a large disaggregation of data base
elements as well as development of improved micro-represen-
tations of production processes, product flow between processes,
and economic and political constraints. Due to the expected
long-term development time for achieving a fully-developed
general model, it is appropriate to perform first an analysis
of the typical problems to which SOS modelling and analysis
can be applied, and then structure a development/applications
plan that will allow early, partial analysis payoff while
research and development continues on an evolutionary schedule.
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SECTION II
INTRODUCTION
PROBLEM BACKGROUND
The "generation gap," so evident in the sixties as the
youth culture gained recognition, grew to such proportions
that many elders shifted from tolerance to counter-rebellion.
Without arguing the pervasiveness of the youth subculture,
it is useful to recognize the underpinnings of the
phenomena. The counter-culture was apparently the inverse
of an existing culture and, at least in its early days, rejected
all of the contemporary American ethos as illegitimate and
useless. This extreme posture attracted sufficient public
attention so that the issues were examined across the resulting
polarity. Those portions of both extreme positions which appear
most useful to society are slowly being melded into a new ethos.
Similar turnabouts can be found throughout sociological
literature as research, action and reaction flow from one period
to the next. One example is of particular interest for this
paper. For years, both public and private planning has
practiced its art assuming a fruitful earth. Problems were
usually couched in terms of improving societal efficiency. For
example, a comprehensive or master plan was normally prepared for
a community to answer questions of its ultimate size and the most
efficient way to spatially distribute the people and their activities
A few of the better plans have included social amenities
or other qualitative goals. Few of the plans questioned the
probability of achieving the goals that were established in
the plans.
On the other hand, an increasing reaction against the
"growth at any cost" school has come from a number of environ-
mentalists. Some have even seriously suggested that all growth
be stopped immediately in some regions. These conflicting
perspectives, like those in the youth vs. establishment conflict,
cannot result in viable goal statements without compromise of
the polar positions. The purpose of this paper is to describe a
model that will analyze the possible ranges of social and economic
growth under conditions of limited available resources and minimal
environmental damage. Thus our model parallels the procedure of
compromise and melding cited earlier.
With the objective above in mind, let us reflect on the goals of
local and regional communities to provide the better things of
life for their citizens. In the past few decades, the unfettered
development of our cities and suburbs, responding primarily to
economic stimuli, has not achieved its purpose of providing
maximum benefit to the majority of the society. Recognition of
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this failure became institutionalized with the widespread
appearance of the planning profession. The nation soon saw the
appearance of the "master" plan and more recently, the compre-
hensive plan. The latter plan was envisioned as the guide of how
a community could (and should) structure its total growth
picture including population, labor, urban form, transpor-
tation, tax laws, and easement and land rights.
At present, many planning efforts to control the develop-
ment of an urban area are based on the thesis that growth and
the preservation of the environment must be symbiotic, not
conflicting, goals. This perspective on environmental quality
challenges the unlimited growth assumptions of the early planners,
invalidating a great number of the early plans. This occurs
because these early plans were seldom subjected to any
credibility test other than to see if the current political
community and the citizenry wanted to aim at the goal-plan.
The plans were seldom subjected to the test of reality in
terms of the communities actually being able to achieve the
prescribed goals within the expected time frames. This lack
of testing is not surprising, since the planners and their
communities both subscribed to the beliefs that this was the nation
of inexhaustible resources and that technological ingenuity that
could solve any problem. Today, we are beginning to question
the possibility of unlimited growth. Thus the comprehensive
plans of localities need to be tested for realism under situations
of limited resources and established required environmental
qualities.
THE REAL WORLD DICTATES
Adjusted for the mandates of the pragmatic world, the
wedding of the diverse goals - growth and environmental
preservation - will only be accomplished through intensive
environmental management. Unfortunately, having named the
required cure, we are not further along in development of a
procedure to implement the cure.
First step toward environment management are along the worn path
of attempting to reduce all of the alternatives to a least
common denominator so that they can be objectively traded off
against each other. Some cost-benefit analyses of this variety
have been attempted. On the assumption that no benefit can be
gained without a corresponding cost, such a methodology attempts
to correlate the costs and benefits. Unfortunately,, the environ-
ment is nothing if it is not comprehensive; it is related to
everyone and every action and they are related to it. The
environmental relationships are difficult to define in general
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and almost impossible to define in detail. The delineation of
environmental-societal relationships is often subjective, and
the perception of the linkages are correspondingly vague. Hence,
this approach has met with limited success.
This paper will deal with a second approach. The
ecologist's rhetoric speaks of a "holistic" representation of
the man-environment relationships. This analysis approach
attempts to reduce the set of possible components to a dominant
group which can be handled conceptually from the vantage
point of the whole system. According to its proponents, this
perspective best assures that all of the various subsectors
of the system will be taken into account and that the chance
for occurrence of totally unexpected events will be mitigated.
Additionally, the holistic school argues that the overview has
to be continued over a period of time, since present-day
actions not only affect all portions of the system, but
continue to do so for long periods of time with decision effects
often occurring after significant delay.
In short, a planning system set up to develop holistic
guidance would display to the decision maker the widest set of
options possible for his decisions. Its dangers include that
the system would also provide him the greatest potential for
confusion due to information overload.
Operationally, such holistic planning systems must
require a change from the planning assumptions of the past.
The extrapolation or trend continuance paradigm must be
•j altered. Planning cannot assume that the future is merely
more of the past and that the public role is to provide
those goods and services necessary to assure a foundation
for the laissez faire growth of the private sector. Peterson(l)*
suggests that there is a rapidly developing counter view that:
• Today's problems are a result of successes as they
were defined in yesterday's terms,
• An extension of the past is not generally the right
prescription for the future,
• The primary planning goals for this nation should
be altered to high quality livability as the major
long-term objective with economic development
shaped to compliment this overriding determinant,
• Science and technology, if oriented toward harmony
with nature, can, within limits, assist in reaching
the highest attainable quality goals, and
*Parenthetic numbers refer to references listed at the end
of the body of this paper.
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• Through social and political action it is possible
to design, modify or block growth and development
trends based on their compatibility with long-
range planning goals that are supported by a
popular consensus.
MODELS OF REALITY
There are several ways of helping the environmental manager
as he begins to make decisions in this new milieu. One of these
methods is application of modelling. The model described
in this report is in an early stage of development; it needs
significantly more design before it can be used for policy
use. This model likely never would have had an audience
in the public sector if it had not been for the current
interest in many U.S. regions in preserving and restoring
an aesthetically pleasing and healthy environment coupled
with the growing uneasiness about the acceptability of
unlimited growth assumptions.
A brief statement should be made as to the utility of
mathematical computer-based models. All decisions are based on
models of one sort or another. Almost no problem is simple enough
to be defined in absolute terms; for decision purposes, it must be
abstracted to the level of its most dominant components. A
computer model merely makes this process explicit. Further,
these explicit statements of assumptions within the model,
coupled with the inherent nature of a computer, allows us to
try to capture a far larger set of variables than is usually
attempted in day-to-day intuitive decision-making. Of course,
the validity and utility of any model is a function of the
accuracy with which the model designers reduced the problem
area to pertinent model variables and relationships; the
same characteristic is true of all problem-solving techniques.
The eventual users of the model described here will be
well advised to take these caveats into consideration. The
developers of this model can not state with absolute certainty
the confidence factor to be attached to the output of such
models. However, like most policy information, the direction
of the predicted effect and the order of magnitude of the
change appear correct. Thus, the State of the System Model
should provide new insight into the real-world situations.
AN INTRODUCTION
The remainder of this paper provides greater detail on
the current concepts and status of the State of the System
(SOS) Model. The discussion is presented in seven sections,
as follows:
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• EnvironmentalCarryingCapacity - The next
section presents some major concepts on which the model
is based. That discussion focuses on environmental
carrying capacity, i*e., the limiting factors of the eco-
system, and the interaction of man with the carrying capacity.
• Resources of the Human Ecosystem - This section
supplements the first by providing adiscourseon problems
related to man's utilization of resources. These concepts
form the backbone of the system adjustment procedures of SOS.
• Model Overview - The next section is a non-
mathematical discussion of" the major features of the model.
It presents the model in diagramatic form and includes dis-
cussion of assumptions, components, and envisioned
application.
• Model Formulation - Presented here are the
major mathematicalrelationships involved in the model,
indicating the types of data required.
• Example Model - This section describes the
initial operational model S6s-l that has been developed to
demonstrate the concepts presented in this paper. This
model is operating; the program is fully documented in
appendixes of this report.
• Example Data - All data used as the normal
data base for SOS-1 is presented as scaled for model use.
This data base for initial conditions is representative
of 1970 U.S. data.
• Model Test - The last section details the input
data used and the results obtained in a test of the
example model. Summary and detailed model outputs are
presented and an initial analysis of some aspects of
model sensitivity are provided.
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SECTION III
ENVIRONMENTAL CARRYING CAPACITY
THE ECOSYSTEM
In developing the concept of the "carrying capacity"
of the environment,* it is necessary to begin with the
ultimate of all physical systems, the ecosystem.
All of our actions affect our physical environment. To
solve environmental and resource allocation problems in
a total context, planners must understand that society
depends on ecosystems for survival. Further, understanding
what ecosystems are and how they work provides insights
into ways to understand and reduce environmental and
resource problems.
In Concepts of Ecology, Kormondy defines an ecosystem
as "the abiotic physico-chemical environment and the biotic
assemblage of plants, animals and microbes."(2) Thus, an
ecosystem is the conglomeration of the living and non-living
entities of a particular locale. Ecosystems are not one size;
the entire Earth is an ecosystem, and alternatively, its
smallest puddle is an ecosystem. Both examples fit the
definition of ecosystem with corresponding components, pro-
cesses and properties.
ECOSYSTEM COMPONENTS
Separation of the biotic (living) and abiotic (non-living)
parts of an ecosystem is difficult. Elements are in a constant
state of flux between various living and non-living states;
very few substances are confined-to a simple state. Perhaps
the easiest way to examine ecosystems is through their
component parts. Odum, in Ecosystem Structure and Function
lists six components that comprise an ecosystem:
• Inorganic substances (carbon, nitrogen, carbon
dioxide, water, etc.) - These substances are
included in material cycles within the eco-
system.
• Organic compounds (proteins, carbohydrates, etc.) -
These compounds link biotic and abiotic substances.
• Climate regime (temperature, rainfall, sunshine
level,etcT)~ The climate'will have a profound
effect on which organisms can prosper in a given
ecosystem.
*Environmental carrying capacity - the level of population
and activity that the environment can maintain, given set
technologies and behavioral practices.
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• Autotrophic organisms (producers) - These components
are largely green plants which are able to manufac-
ture food from simple substances. Autotrophic means
"self-feeding."
• Heterotrophic organisms (comsumers) - These are
largely animals which ingest other organisms. Heter-
otrophic means "other-feeding." There are three
types of heterotrophic organisms:
• herbivore (primary consumer or "plant eaters") -
herbivores get their energy directly from
plants;
• carnivore (secondary consumer or "meat eaters") •
carnivores get their energy from green plants
by consuming herbivores
• tertiary consumers - carnivores that feed on
other carnivores
• Decomposers - Organisms like bacteria and fungi
break down complex substances into more elemental
substances.(3)
A stylized relationship between the components of the ecosystem
is privided in figure 1.
Producers
Herbivores
39
Carnivores
Nutrient Pool
.Decomposers
Energy—
Minerals-
Figure 1. Ecosystem Energy and Nutrient Conversions
11
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The major processes of the ecosystem, as pictured, work
in this well known way: the producers (green plants) get
energy from the sun. In the process of photosynthesis they
use materials from the nutrient pool (in the media of air,
water and soil). The herbivores consume the green plants
absorbing both energy and minerals, and subsequently, the
carnivores, by consuming herbivores, get these products.
When the producers, herbivores and carnivores die, the
decomposers break the organisms down into materials which are
returned to the nutrient pool. Thus, the process is cyclical,
with exogenous periodic input of energy from the sun. When
other aspects of ecosystems are discussed in this paper, the
details and amplifications should be viewed as to how they
would fit in the simple ecosystem diagram of Figure 1. This
central ecosystem and its workings are imbedded within all of
the adaptations of localized phenomena. To reword the process
and its residues:
"There is a progressive diminution of energy in this trophic
or feeding chain, but'the nutrient component is not diminished;
in fact, some [nutrients] may even become concentrated in
certain steps of the chain ... nutrients are not lost in
the manner of energy, for when nutrient-containing protoplasm
is eventually subjected to decomposer activity they (the
nutrients] are potentially available for re-use, for recycling."(4)
Energy diminution and nutrient cycling are at the heart of
ecosystem dynamics.
ECOSYSTEM PROCESSES
There are six processes in ecosystem dynamics: the first
three, which have already been briefly discussed, are:
• Energy flow and diminution
• Nutrient cycles
• Food chains (trophic relationships, i.e., the food
chain in terms of plants, primary consumers,
secondary consumers, and tertiary consumers.)
The other ecosystem processes include:
• Diversity patterns in time and space - Natural
ecosystems over time, expand to larger numbers and
greater varieties in biotic species. Diversity is
directly related to the maturity and stability of
ecosystems.
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• Development and evolution - Ecosystems develop from
initial rapid and successive growth stages to maturity -
a "climax" state. This state is usually an oscillating,
but stable, system. The early successional growth
stage is characterized by a high production/respiration
ratios, high yields, short food chains, low diversity
and small size of organisms, open nutrient cycles and
lack of stability. In contrast, stages of ecosystem
maturity have a high biomass/respiration ratios,
complex food chains, low net production, high
diversity and high stability.
• Cybernetic control - Control in ecosystems is by
sets of feedback mechanisms that regulate growth
and'mix within the components of the ecosystem.(5)
ECOSYSTEM PROPERTIES
There are four essential properties of ecosystems. These
properties form the framework for the actions and interactions
of the components and processes of the ecosystem. Ecosystems
all share:
• Historical continuity - The ecosystem responds to
past and present events (past events through the
succession of previous stages).
• Spatial accessability - The ecosystem responds to
specific events at several different points in
space. Each component is not an independent unit
in itself, it is related to and affected by other
components. The level of the interaction is usually
associated with the proximity of the components.
• Systems control - The ecosystem encompasses many
different component activities governed by complex
feedbacks and interactions.
• Structural inertia - ecosystems and subelements
exhibit characteristics that are defined in
terms of time lags, and minimum and maximum constraint
levels. Thus change and symptoms of interactions
do not appear instantaneously, nor are all changes
smooth and evolutionary.(6)
The systems and structural properties require more discussion
since two.important characteristics of ecosystems, stability and
resilience, are defined within their context.
13
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Ecological systems are not in a state of delicate balance.
They have demonstrated in many instances the capability to
either "bounce-back" or to "adjust" after severe shock. Nor
did man invent severe shocks to ecosystems; long before man
emerged as a dominant factor of regional ecosystems, systems
were subjected to trauma by climatic changes and other geological
processes. The surviving ecosystem forms were those that were
able to adapt or to absorb the effects of the trauma. The
capability of a system to absorb trauma and recover is its
characteristic of stability. The capability of a system to
successfully change to a modified form characterizes its
resilience. Evolving successional ecosystems are characterized
by a high level of resilience, while mature systems usually
include high stability.
While major regional ecosystems have demonstrated consider-
able resilience, we know that their levels of resilience are not
infinite. Examples of forests turning into deserts, or lakes
into the aquatic analogs of deserts, exist. Thus, a key
feature of ecosystems is that, as resilience is lowered by
an incremental series of adaptations or a massive shock,
the level of ecosystem resilience may be exceeded and the
system may show unexpected and dramatic levels of change. (7)
This comes about when the structural thresholds - or the
demands on the system - cannot be met.
Thus, an ecosystem may react in several levels to pertubations:
• A minor change may be noted that is within the
thresholds of the structure; the system will
eventually return to its previous equilibrium
point and meet all processing demands.
• A major change may be noted that exceeds some of
the structural thresholds; the system may
eventually successfully adapt by finding a new
equilibrium point near the original one with a new
set of structural thresholds for this equilibrium
point.
• A major change may cause damage to a degree that
successful adaptation does not occur; the system
reaches equilibrium at much lower levels of component
support and will include a vastly different set
of structural thresholds.
Succession, change, stability and resiliency in ecosystems
are interrelated. "When a large area is stripped of vegetation,
a historical process begins that leads to the evolution of a
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stable ecosystem through a series of successional stages.
Early in this succession, pioneer species occupy the space and
the diversity and complexity of the species and the systems [processes]
are low. The species that can operate under these circumstances
are highly resistant to extreme conditions ... and are highly
productive. Competition is low and a large proportion of the
incident solar energy is converted to the production of biomass
(the standing stock of organic material). As biomass accumulates,
the conditions of the area begin to improve and permit the
appearance of species of plants and animals that otherwise could
not survive. The result is a gradual increase in the variety
of species and in the complexity of their interactions, and
this increase in complexity is accompanied by an increase in the
resilience of the system and a decrease in biomass productivity.
Under stable conditions this successional history can continue
until a stable (climax) ecosystem evolves."(8)
Because an ecosystem is constantly changing, so will its
equilibrium point. Even when a climax ecosystem has been
reached, it is still dynamic, still changing. Ecosystems that
have survived through time are the ones that have been able to
keep their demand thresholds broad enough to absorb unanticipated
shocks and the accumulated consequences of change over time.
ECOLOGICAL CARRYING CAPACITY
Since this approach is concerned with defining and studying
environmental carrying capacity, it is useful to begin with
a description of ecological carrying capacity in the classical
wildlife biologist's terms.
"Carrying capacity is the ability of an ecosystem to
support a given number of consumers and remain healthy and
productive." In examining ecological carrying capacity, we
will consider the ecological laws proposed by Danserau as the
framework in which the species will act:
• Law of Inoptimum - No species encounters in any
given habitat the optimum condition for all its
functions.
• Law of Aphasy - Organic evaluation is slower than
environmental change on the average and hence,
migration occurs.
• Law of Tolerance - A species is confined, ecologically
and geographically, by the extremes of environmental
adversities that it can withstand.
• Law of Persistence - Many species, especially
dominants of a community, are capable of surviving
and maintaining their spatial position after their
habitat and even the climate itself has ceased to
favor full vitality.
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• Law of Factorial Control - Although living beings
react to all factors of the environment, there
frequently occurs a factor which has controlling
power through its excess or deficiency (limiting
factor) .
• Law of Irreversibility - Some components do not
renew themselves, because they were the result of
a process (physical or biological) which has
ceased to function in a particular habitat or
landscape at the present time.(9)
Population Growth of Species
Population dynamics are an integral part of carrying
capacity. The growth of a species population will generally
have the form shown below:
Population
of
One Species
P(t+At)
P(t)
0-
Carrying capacity of the ecosystem
t+At
time
Figure 2. Population Growth in Finite Systems
Under most circumstances a new population grows
entially," i.e., according to the equation:
expon-
* P(t+At) = P(t)exp(rAt)
where P(t) is the population of the species at time t
r is the net growth rate (births minus deaths)
At is a time increment.
This relationship is reflected in the graph by the lower portion
of the solid curve, and its dashed extention. Such an increasing
trend cannot be expected to continue indefinitely in a limited
environment or area.
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"As the limits of the environment are approached, it can
be expected that mortality will increase. Some animals perhaps
will not obtain enough food; others exposed in their search for
food, will fall prey to enemies; others, weakened by food
deficiencies, will die from disease. As the breeding females
fall off in condition, through lack of food or disease, a
decrease in natality will follow. The closer the capacity of
the environment is approached the greater will become the
influence of decimating factors. Consequently, the curve of
population growth will be bent downward again; eventually it
will level off at a point where birth and death rates are in
balance. This point will be the capacity of the habitat to
support animals ."(10)
The reduction in growth rate, as the carrying capacity
of the ecosystem (line L in the graph) is approached, can be
approximated by defining a variable net growth rate using:
r = r'[L-P(t)]/L
where r' is the unconstrained growth rate
L is the carrying capacity.
When P(t) is small relative to L, this relationship results
net growth rate, r, that is approximately equal to r'. On the
other hand, as P(t) approaches L, the net growth rate becomes
smaller and is ultimately zero if P(t) = L.
Each species population in an ecosystem will occupy an
"ecological niche" - a combination of species function and
habitat. "Species occupying closely related niches have
evolved in such a way that conflict between them is ... kept
down to a level where they can all survive ."(11)
A somewhat more complex treatment of population growth
should, however, include consideration of the competition
and demands among the species who share a locale and its
resources. As the carrying capacity of the locale is
approached by any one species the growth rates of all local
species are affected. This can be reflected by further
modifying the net growth rate to:
where i indexes all of the particular species in competition
A(_i,j) is a coefficient of interaction between competing
species i and j
and the summation is performed over all other species
in the locale.
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Communities of Species
Ecosystem carrying capacity depends greatly on how the
community (the collection of all indigenous species) evolves
and changes. As the ecosystem changes over time, so will its
carrying capacity. The intricacies and interrelationships of
species within a community can outlined in terms of the
principles of community evolution:
• All species evolve in communities with interaction
with other species; (and thus the carrying capacity
of the ecosystem to maintain one species of a
community may depend on the population levels of
other species).
• The evolution of a community must entail "parallel"
or coadaptive evolution of the community's species
since the community is an assemblage of interacting
and coevolving species.
• Hence, communities similar in resources and species
change and may diverge in structure and function
from a central community through evolutionary time.
• Through this evolution there will appear adaption
to localized environment for the community as well
as for species. From this adaptation to localized
variety results a mosiac of communities adapted to
the mosaic of the world's environments.(12)
Thus, the carrying capacity of the ecosystem is variable
and responds to changes at both the community and species levels.
When addressing the carrying capacity to support one particular
species, one has to look at the entire ecosystem and the relation-
ship of the population of the particular species to other species
and communities of its locale.
Limiting Factors
The ability to identify the limiting factors of an eco-
system is important in determining its carrying capacity. The
limiting factor is the requirement that is present to the
minimum extent porportion to the needs of a collection of eco-
system components.(13) Factors in an ecosystem that can be
limiting include:
• food
• climate
• ecosystem space (e.g., land)
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• cover and protection
• extent of the niche of species
• amount and distribution of water
• species decimating factors - predation, disease, etc.
• rate of species change or succession.(14)
An important factor to note in determining a carrying
capacity for a population within an ecosystem is that the species
is part of, and subject to, changes in the ecosystem. The
contained species react to changes in the ecosystem and make
adjustments in order to survive; they do not change the ecosystem
to meet their needs. Ultimately, this is the control property
with which we must deal when we look at "environmental carrying
capacity" for man within a system.
EFFECTS OF MAN ON THE ECOSYSTEMS
The evolution of man has introduced into many ecosystems
a species that clearly and increasingly dominates other species.
The characteristics of man that promote him as a dominant species
are:
• Culture* - man can develop culture and apply it;
the application of culture by man plays a major role
in evolving and reshaping the relation of man and
his physical world (ecosystems).
• Mobility - through mobility, man can apply culture
for specialized functions in best production areas.
Transport of products can modify local systems that
do not include the production function.
Hence, a local area may not be a closed ecosystem but
may supply and be affected by factors and events not
developed locally but in distant areas of Earth.
• Social - man has overlaid the natural, symbiotic
relations of organisms with social constraints
and judgments, causing local patterns of adjustment
to depend on both social and ecological processes.
Thus the inclusion of man in regional ecosystems provides
a dominant species that:
*Skills, ideas, arts, etc. of a people at a time.
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• Through culture, modifies natural levels and cycles
of energy and mineral utilization and return to
resource pools.
• Through mobility, augments or withdraws from the
resource pools of a local ecosystem.
• Through social regulation, utilizes resource pools
and changes populations of other species in patterns
not compatible with natural evolutionary and environ-
mental processes.
But man can only modify cycles and pools of non-closed
ecosystems; he is still subject to the extent of the ecosystem
carrying capacities and the mobility of resources that act as
limiting factors. If his modifications and demands are sufficient
to drive the ecosystem past a limiting factor threshold, he will
cause a reduction in the carrying capacity by exceeding the
threshold of an ecosystem limiting factor.
Thus the species man, like other species, is subject to the
ecosystem relations of:
• Physical - man's body is subject to the natural
laws that apply to all abiotic and biotic substances.
• Natural - man is affected by ecosystem factors such
as climate, food, disease and media quality.
He, like all organisms, consumes energy and is part of the
food chain, and through discharge of wastes and death, provides
decomposable matter for renewing the nutrient pool. However,
as a species employing culture and social judgment, man inter-
acts with his environment in a manner of greater complexity
than that of a physical mass and an organism.
It is in the context of the ecosystem and its constraints
on man's needs and wants that the concept of environmental
carrying capacity for man will be defined. However, man's social
and technological abilities to modify ecosystem constraints
need to be specified within this context. They are both power-
ful shapers of man's environment - both in degrading it and in
finding nondestructive ecosystem modifications.
MAN ACTS, THE ECOSYSTEM REACTS
Through the medium of culture man has proceeded through
a series of technological levels to manipulate his environment
over the short run. This mechanism has allowed him to expand
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his ecosystem niche, to regulate the quantities and locations
of all other species in his communities, to modify rate of
production of natural products, and to convert system components
to specialized products that are not normally part of natural
ecosystems. However, application of culture has also fostered
new growth rates in species population and consumption of
non-food specialized functions. The specialized product growth
levels have caused consumption rates of limiting factors in
major regional ecosystems that are far beyond the levels that
are being naturally recycled back into the resource pools.
Even the use of mobility to augment these localized resource
needs is insufficient since world supplies of some limiting
factors are being exhausted.
Thus, it appears useful to trace rapidly the evolution of
man-and his application of culture, and by this means identify
patterns of specialized man-environmental relationships that
need to be included in analyses that expect to predict the likely
outcome of man's impacts on regional ecosystems. Since the
aim here is to model interaction of human population growth
and its demands on environmental carrying capacity, the levels
of impact and primary changes of these demands will be noted.
The Niches of Man
Man, by application of accumulated culture has proceeded
through four major niches or stages within his ecosystems and
appears now to be entering a fifth niche. The four stages have
been within ecosystems that, in most regions, would be defined
as mature, climax ecosystems possessing great stability.
Yet, to pass from each of the first three stages; man, through
application of technology, instituted a new set of limiting
factor thresholds on the ecosystems. Thus man superimposed
within the natural ecosystem constraints, dramatic expansion
of his niche, his population size and his quality of life.
Expansion of any of these caused an increase in demands placed
upon the resources of the ecosystem in which he had influence.
The increased demands, even in the earliest stages, caused
damage in the locale of his habitation. Fortunately, in early
stages the ecological accessibility and the population density
of man was sufficiently low as to provide spatial limitation
of the damage. The niche provided man in the fourth stage
included parallel and rapid worldwide expansion of population,
quality demands, and ecological accessibility. These forced
the present situation in which man cannot simply migrate locally
or apply technology to effectively modify resource utilization.
He must also recognize, the ecosystem limitations for large regions
and recognize that he must adjust his demands when his cultural
adaptations do not sufficiently protect the ecosystem components.
If he does not adjust to the ecosystem requirements, he faces
the very real possibility that the carrying capacity of eco-
system Earth may catastrophically limit population and/or
quality of life.
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Against this background, we will trace species man as
he developed new sets of relationships with his encompassing
ecosystems.
Man, the Natural Species
In man's first ecological stage, his impact on the eco-
system mechanics appears at a level consistent with the other
species of his communities. Prior to development of cultural
techniques that would allow him to systematically locate and
increase control over food production, he occupied a natural
ecological niche. He gathered existent plant supplies, employed
rudimentary tools to kill animals, and extended his range of
habitation to a minor degree by elemental protection devices.
As a natural species augmented by minor tools he was a dominant
species in local ecosystems, but his influence on environmental
carrying capacities were similar to the effects of other species.
His demands were elementary and primarily within the food cycle;
functional specialization was minimal; there were no artificial
demands on usage of ecosystem elements. Population was
controlled by natural processes; dense population centers were
nonexistent. If environmental damage occurred in a locality,
man's inability to modify the damage in the short term caused
him to reduce his effect by immigrating, thus allowing natural
repair to occur.
Man, the Farmer
The development of crop-culture and animal-culture by man
allowed a dramatic change in his relationships within his
ecosystem communities. Selective development of artificially-
maintained species plus improved control over the ecological
niches of competing animal species allowed man to dominate
his communities. Ecosystem disruption was caused by cultivation
using artificial plant patterns that increased the utilization
of local nutrient pools and caused erosion. Introduction of
planned food production - whether crops or domesticated animals
led to increased localized population densities and allowed
the support of a larger human population within a locale than
had been possible. Rudimentary specialization appeared--
huntsmen, farmers, tanners, clan chiefs--allowing improved
utilization of labor resources and technological information.
His ecological niche was significantly enlarged. In
his communities, man became dominant among competing species
and, through technological adaptation, he extended his habitat
significantly. Population, although still limited by many
natural elements, depended less on occurrance of food since
man could both produce and store foodstuffs. His capability
to damage an ecosystem was expanded but, due to his low mobility
and the limited extent of his artificial controls, damage in
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large land areas was minimized. A major new factor, however,
was growth--increased area population and increased demands
per capita. The increases in demand also involved increased
demand of the products of specialized functions, such as pottery,
a dramatic innovation from demand for food and protection.
This last element, in particular, blossomed in the next
stage because this stage, with its rise of per capita
agricultural productivity, released portions of the population
from subsistance employment. Man's unique ability to retain
culture allowed development of, and demand for, "artificial"
products and services not required as part of his natural
functions.
Man, the Specialist
The ability to produce and store food surpluses increased
stresses for man as well as the environment. As he acquired,
stored and consumed larger amounts of possessions, questions
of shelter, trade and defense became more important. Permanent
settlements began to appear, partially because of the realization
that many of his production functions could best be under-
taken collectively or by specialists in the community.
The growth of settlement from centers for the appropriation
and redistribution of food surpluses into more complex cities
was hastened by a growth in social awareness. Permanent
settlements provided an attractive medium for the free exchange
of ideas. In an atmosphere conducive to innovation of products
and division of labor, collaborative efforts extended the zones
of settled life into areas beyond initial centers of agriculture.
As newer farming techniques involving irrigation, plowing and
rotation came into being, previously "marginal" areas for
habitation become more desirable.
Man, in pursuit of a new set of needs, improved his
capability to control the natural conditions of his localities.
He introduced higher productivity capabilities and introduced
new processes well outside the natural food chain processes.
The new specialized functions often improved his natural
defenses against predators and natural cyclical disasters.
While study shows damage to limiting factors of local
ecosystems increasing over previous stages, the development of
mobility and social mechanisms for goods redistribution
expanded the reaches of applicable ecosystems. Hence, these
initial social and economic practices continued to develop
under the assumption that the ecosystem had practically
unlimited resources - system carrying capacity was of no
practical concern. It is interesting to note that this period
also gave orders- o-f magnitude increase to artifacts of
manufacture that were not naturally recycled.
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Man, the Technologist
The development of energy converters together with the
blossoming cultural innovations that initiated the industrial
revolution drove man, as a manipulator of his environment, to
a significantly different niche within continental ecosystems.
The social and economic patterns became increasingly specialized;
urban forms become more dense and more numerous. Productivity
per capita in the highly developed countries drove goods
consumption well above subsistance needs and toward desires
for more and more specialized products. The entreprenurial
spirit and rapidly expanding capital and technological
bases allowed a multiplicative increase in goods availability
and distribution. It also produced the development of a
social structure that would consume the ever increasing
diversity and levels of nonessential goods. Growth became
the keyword to measure the goodness of man's social and
economic systems - growth of population, growth of industrial
output, growth of material consumption.
Unfortunately, growth also occurred in other areas of
human ecosystems. These include intensified population
densities in local areas and in the total system, rapid use of
resources in processes that do not include appropriate
decomposers, and increased byproduct effluents deposited into
the environmental media. Man has achieved such dominance by
his technology that he can modify nearly any ecological process
for short- term gain.
The general laws of ecosystems remain inviolate, however, and
the widespread occurrence of dense populations has forced recon-
sideration of the fact that the ecosystem resources and media
are not unlimited. Many of the limiting factors of the regional
ecosystems appear to have been reached in large localities.
Some of these limiting factors can be adjusted by redistribution,
but many; such as environmental media, elemental energy processes
and land; cannot be relocated. The widespread signals of eco-
system damage under the imposed social value structure of
highly developed nations leads us to reconsider the value of
growth. Man the technologist has driven man the social
organism to high demand levels and provided biological pro-
tection that permits rapid population growth. But he has not
devised a mechanism for guaranteeing continuation of his
regional ecosystems as resilient, stable entities in which
growing human populations can maintain a stable, dominant
niche while increasing their resource usage demands.
Man, the Ecologist
As the ecosystems send out their first powerful signals
of imminent damage to the environment's carrying capacity, the
social structures of man are attempting to determine the levels
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of societal redesign that are needed to balance man's habits
and demands within the regional ecosystem's processes and resources.
A major element for redirection is the redefinition of
acceptable growth patterns under the assumption that the species
size and demands are approaching the ecosystem's renewal limits.
Many new concepts, antithetical to the concepts of the industrial
revolution period, are proposed - zero population growth,
stewardship of goods and resources, alternative lifestyles,
return to simpler forms of society.
But the new awareness and willingness to modify society's
goals are not sufficient; there is a need for development of
mechanisms for evaluating the costs and benefits to the eco-
systems caused by alternate proposed solutions. A major question
for any region is: what new social and economic technologies
are necessary to maintain acceptable qualities of growth within
stable ecosystem carrying capacities? A major corollary to
that question is: for a given pattern of growth, what are
appropriate quality of life demands to maintain man as a
dominant, stablizing element of regional and national ecosystems?
THE LINKS BETWEEN THE HUMAN SYSTEM AND THE ECOSYSTEM
The attributes of the natural ecosystems have been dis-
cussed in detail including the concepts of carrying capacity,
resilience and stability. An essential ingredient in the
vitality of the system is that the limiting factors to growth
within the ecosystem are not overused. If overutilization
occurs, the system suffers stress and undergoes change.
Readjustment of the ecosystem can be accomplished in
several ways. In the simplest case, the stress is only tempo-
rary and a short period of adjustment will return all of the
system characteristics to the previous equilibrium. A more
severe trauma may cause some redesign of the system characteristics
resulting in a new state of equilibrium with some adjustment to
the carrying capacity likely. The trauma can be, and in
historical cases, has been enough to severely damage the
system, causing a sudden degeneration to a very different eco-
system equilibrium that has much lower levels of carrying
capacity--equivalent to the creation of a media-desert.
Man's present relationships to the natural ecosystems
include the capability to completely dominate large regional
systems. In doing this, he determines for at least the short-
term the level of consumption or utilization of the regional
limiting factors. If man demands too high a use of any of
these factors for too long a period, he may produce damage
to the encompassing ecosystem--pollution of media, lower plant
growth due to resource shortages, starvation, too many domesticated
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non-food animals, etc. In each case, man and the other species
of the regional community have passed the natural and technological
capabilities to provide increased quantities of limiting factors
of the human and natural ecosystems of the region.
The limiting factors for human ecosystems are akin to
the resources that technology and agriculture transform into
man's products. They are not limited, however, to the more
classical definitions of resources applied in manufacture but
include all limiting factors of an ecosystem that can be
affected by man. Thus, we must include as generalized resources
the media of the ecosystem--air, water and land—labor, and
capital, as well as crops, ores, and fuels.
Measuring Population Demands
Prior to definition of a tool to study growth within a
large ecosystem, this paper will next describe the forms
and utilization of these generalized resources relative to the
demand of the dominant population.
The demand here is made up of two elements:
• The number of consuming units - a factor related
directly to population size, and
• The size of the demand unit - a factor related to
a per capita demand for level and quality-of-life
style.
The measurement of the per capita demand level is, in the
present state-of-the-art, a rudimentary mechanism. While
research continues for the development of composite indexes
akin to the much less complex set of economic measures used
as diagnostic tools for regional economies, much remains to
be done. In the SOS Model a procedure for utilization of a
family of region-specific demand measures is provided, thus
obviating the need for predicting adjustments using a single
scalar value. However, later refinements of the model may
suggest need for specialized use of such a scalar combinatorial
measure; Appendix 1 of this paper discusses one such procedure.
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SECTION IV
RESOURCES OF THE HUMAN ECOSYSTEM
As suggested in the preceding section, the carrying
capacity of an ecosystem is greatly influenced by the avail-
ability of resources and the manner in which they are utilized,
primarily by man. Thus a key element in the State of the
System (SOS) Model is the treatment of resources availability
and utilization. This section presents the concepts upon
which the model's simulation of resource consumption is based.
To illustrate the danger of prophesizing with absolute
certainty, review this outlandish bad guess of the past:
It will soon be sixty years since Gifford Pinchot
published The Fight for Conservation, as informative
and succinct a guide to the Conservation Movement's
views and judgments as one can hope to find. With
regard to resource adequacy, it presents a generally
somber picture, supported by careful projections based
on the idea that the volume of economic resources in
the United States is defined by their identified
physical occurrence. The lesson that only careful
husbanding can stretch the supply is the logical sequel.
Governor Pinchot summarizes the findings of approaching
resource exhaustion as follows: The five indispensably
essential materials in our civilization are wood, water,
coal, iron, and agricultural products ... We have
timber for less than thirty years at the present rate
of cutting. We have anthracite coal for but fifty
years, and bituminous coal for less then 200. Our
supplies of iron ore, mineral oil, and natural gas
are being rapidly depleted, and many of the great
fields are already exhausted.(16)
Optimistic resource projections normally include a fair
measure of increased technology expectations, a good world-
trade picture and an adaptive organizational structure. Even
the optimistic writers admit of the likelihood of short-term
dislocations and that some of these short-term problems will
cause over-reaction by those affected. Two of the anticipated
contributions of the SOS model are the attempt to develop
changes in availability through substitution of resources using
combinations of similar resource types and by taking into consid-
eration the discovery and delayed development of new areas of
resources based on the existant resource extraction prices. A
third, less positive contribution is the SOS model capability to
over-react, in some cases driving the system to a greater crisis
in other resources.
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The idea of ecological accessability as a limitor has
meaning in developing data to represent the resource constraints.
Because resources are not distributed equally across the
Earth, the insulation of a society or a nation from catastrophe
is a function of its access to scarce resources of production.
The access can be provided by ownership or by trade; the latter
course is less secure over the long run.
In summary, the availability of resources at any particular
time is the result of the interactions among the nature
and size of man's requirements, the physical occurrence
of the resource, and the economic means of extracting or producing
it. Estimates of future availability of resources, therefore,
require the assessment of:
• The particular combination of economic and technological
conditions that determines present production,
• The level of production that would take place under
different economic conditions caused by scarcity,
• The level of production that could take place under
different technological conditions, and
• The nature and quantity of the total physical-existant
stock of both "renewable" and "nonrenewable" resources»
RESOURCE DEFINITIONS
Because the relationships between these physical, human
and economic variables are complex and vary with time and
place, views concerning future supply need to be carefully
expressed and set in a context such as the threefold hierarchy
of total stock, resource, and producible reserve. These
concepts are summarized below from the work of Lovejoy and
Homan (1965), substituting the term total stock for their use
of resource base.
Total stock is the sum of all components of the
environment that would be resources if they could
be extracted from it. Assessment of the total stock
is largely the concern of earth and life scientists,
and the state of knowledge concerning it depends on
the adequacy of prevailing theory, the state of
exploration and survey technology, and the extent of
its application. Applied to what are conventionally
referred to as nonrenewable resources, the total stock
is finite and thus eventually exhaustible. Applied
to renewable resources, the total stock consists of
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highly complex systems in a state of dynamic, delicately
balanced, and only partially understood, equilibrium.
Resources comprise that proportion of the total stock
that man can make available under technological and
economic conditions different from those that prevail.
The assumed state of technology will set the limits within
which different .economic and social variables [will] deter-
mine what proportion of the total stock can become
available. Assessment of a resource [level] involves not only
physical and biological scientists but applied and
social scientists as well. They must make judgments:
about the directions and rate of change of technological
developments (e.g., gradual increase of efficiency of
extraction of a mineral deposit or yield of a crop
as against dramatic, order-of-magniture, break-
through changes); about the impact of changed economic
conditions and new alignments in international relations;
and about public attitudes on such varied matters as
birth and population control, transportation preferences,
and clean air. In essence the question is one of judging
man's potential for creating resources out of the total
stock; of selecting the chief agent of change from among
technological, economic, or other societal forces; and
of determining the relevant time and space dimensions.
Reserve refers to that proportion of a resource that is
known with reasonable certainty to be available under
prevailing technological, economic, and other societal
conditions. This term embraces current extraction rates,
yield, management practices, legal frameworks, and social
attitudes. It is, therefore, the least speculative,
shortest term, most place-specific, and smallest of the
three types of estimates.(17)
These three concepts provide a framework into which each of
the many estimates of resource availability may be fitted
and thue be seen in perspective. By providing a rationale
that accommodates what often appears to be starkly conflicting
professional opinions, these concepts reduce the ground for
misunderstanding, overoptimism, or undue pessimism. Further-
more, they incorporate the notion of resources moving from
one threshold of availability to another in response to
changing values of variables under human control, allow estimates
to be made based on physical or economic assumptions, and yet
permit retention of the essentially "physical world" character
of the materials involved.
GROUPING RESOURCES FOR THE SOS MODEL
The State of the System Model essentially follows the
traditional definitions of resources used in manufacturing and
services. Along with the traditional list of six resource
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groups, the model includes two resource-like groups to permit
consideration of the level of damage caused to the environmental
media of air and water. Thus, the model treats the eight
resource groups:
• Energy sources
• Natural resources (durable ores)
• Agricultural resources (food and fibers)
• Land
• Workers
• Capital (including R § D funds)
• Air
• Water
The eight groups can be divided into the categories
of nonrenewable resources - natural resources and energy
sources - and renewable resources - agricultural goods, land,
workers, capital, air and water. These two general categories
and each of the eight resource groups are discussed separately
be.low.
Non-renewable Resources
The two groups that usually provide their primary reserves
as ores represent a resources category that, when viewed
in the long run and under pessimistic technological projections,
can quickly suggest a dismal future for the regional ecosystem
as these ores are exhausted. However, even if they are non-
renewable- -which for neither ores or energy sources is totally
true-- several hedges exist for prolonging the resource and for
reducing its role as a critical production resource--as an
ecosystem limiting factor.
Non-renewable resources are treated in the SOS Model using
the following viewpoints:
• All resources are measured in terms of the total
stock as defined above. Hence the maximum ore
limit is not a function of economics, but is a
much larger physical value inherent in the eco-
system.
• The total amount of world resources available at
any time (the reserve) is finite and less than the
30
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total stock. The amount is a function of pro-
cessed stock-on-hand supplies plus time delays
for extracting, recycling and distributing the
ores that economically qualify as reserves under
present processing costs.
The total amount of resources available to a
region has an upper bound based on considerations
similar to those above plus the maximum import
potential as reflected in existing ownership and
trade arrangements.
If a resource mixture that can substitute for a
critical resource exists, or if a technological improve-
ment in production reduces the requirement for a
resource, the production sectors undergo significant
time lag and capital expenditures as part of reactive
retooling. Because of the inertia in the processing
changeover, these changes will be made only when a
resource depletion warning is reached. This warning
system of possible resource shortages acts as an
alert to all production components simultaneously.
Energy
Since energy cannot be stockpiled in its processed form,
the amount of energy produced for a given time is a function
of past and projected demand. The selection of the specific sources
of the energy that will be consumed are based on minimization
of cost of an energy unit and the system propensity to
maintain status quo of sources and processes. Therefore,
the mix of energy sources used to meet the demand will
remain relatively fixed unless a shortage in one or more
fuels or conversion methods is imminent. Although,
theoretically, signals for imminent shortages could be based
on stock levels, it is considered that the better
signaling device in energy (and in the other resources) is
the current cost per processed unit. Note that most of the
present energy crisis discussions in the United States have
not been centered on the total stock level but on the facility
construction times and increasing costs of extracting and
distributing the resource fuels using methods that are accept-
able to the population.
When shortages are signalled, the SOS system will
attempt to adapt by substituting one or more energy sources
for the problem one(s). The new mix of energy sources must
satisfy the constraint of lower mean unit cost (equivalent
to improved fuel reserve availability levels) to be an
acceptable substitute. Additionally, the system will check
to determine if the present sales price for the critical
resource ores is sufficient to expand the stocks that can be
classified as reserves.
31
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Substitute energy sources can be of many forms. They can be
of the form of substituting among currently used resources
in new utilization mixes, or the use of a relatively new
source that now becomes an economic alternative. For
example, two of the more popular new sources in today's
discussions are solar and fusion energy. Both are currently
under intensive study and the results, from the experimental
and prototype uses, run the gamut from very hopeful to
hopeless. In the technological areas, changes to the energy
supply picture could come about from several directions:
from new forms of energy conversion; from more efficient
application of today's technology; from new sources or
better extractive methods; and finally, from new types of
applications.
The concepts developed here for increased stock avail-
ability of a particular resource due to changes in the economics
of extraction and of substitutibility of other resources are
relatively unique and,__until further analysis, should be reviewed
with some skepticism. " For example, most of the better-known
estimates of energy ore availability are highly price-related.
This consideration results in different estimates of reserves
based on assumptions of changing demand for goods and services
coupled with assumptions of minor institutional and technological
change. The results of this perspective have been a consistant
under-reporting in absolute amount of resources available as energy
reserves and the concommitant crisis figures often reported
from a mapping of price-related reserves against population
growth.
Similar anomalies are present in the consideration of
substitution among energy sources. It is obvious that price
alone will not determine substitution but that habit, legal
constraints, media pressures and the like might influence the
time of change to be either long before or after the time of
substitution as dictated be economic indicators. Consequently,
a model of the substitution processes will be quite complex
in the final analysis. Of course, surrogates of energy usage in
production processes are available from analysis of fuel changes
in industrial, commercial, and residential uses as extrapolations
over time, but such regressions should be viewed only as stopgap
expedients and fragile in terms of meaningful long run analysis.
Due to the present set of crisis for several fuel types, it is
quite likely that significant departures in mixes of fuel sources
will occur.
This viewpoint becomes even more likely when the side effects
of energy ore mining and energy consumption on the environmental
media are noted. There is a positive correlation between
32
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energy/capita utilization and the level of industrialization;
thus, sincere trepidation of likely effects of energy needs
and of energy consumption rightfully exists. The SOS Model
considers all affected resources and uses a set of adjust-
ment procedures similar to those being affected by the U.S.
planning community.
Natural Resources
Natural resources, like energy, are normally viewed as
a non-renewable reserve category. Like energy, there are
several practical hedges in setting or expanding the actual
stock reserve at any one time. For many resources, as the
unit costs for extraction and distribution of ores increase
significantly, new levels of stocks can be converted from
the resource category to the reserve category--the economically
feasible stockpile. Second, for many of the ores there is
a high level of substitution of other resources in specific
production processes. These substitutions can be caused by
technological improvements or simply a trade-off of one ore
for another similar material. This second process is treated
in the SOS Model by substitution within resource strata, and
the resources within the natural ores category are assumed
to have several strata. Examples of strata include trace
metals, structural metals, non-metallic minerals, etc.
Another conservation device available to natural resources
that was not available to any great degree in the current
primary energy sources is the ability to recycle ore from
debris from processed and consumed industrial goods; a procedure
similar to natural ecosystem decomposition procedures. This
procedure, tempered by the mobility of the various component
products in passing from ore to goods to debris, sets a
natural ore reserve with a size that is once again variable
by cost, here the recycling cost. The comparative levels of
recycling costs to extractive costs will determine the level
of ore salvage from the system debris.
Review: Non-renewable Resources
In the discussion of energy and of natural ores several
caveats must be applied to the definition of non-renewable.
For both energy and natural resources there exist mechanisms
to extend the level of usable reserve beyond the static reserve
levels of the resource. This does not imply that the produc-
tion process allows total recapture of the resource ores after
a time delay, but it does suggest that through mechanisms such
as technological improvement in energy conversion and improved
ore recycling procedures as extraction unit costs increase,
the present resource horizons for non-renewable resources may
be unduly pessimistic. The SOS Example Model will include three
•resource adjustments for ores: substitution, expansion of
economically extracted stocks, and resource recycling.
33
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Renewable Resources
The remaining resource categories have their reserves
limited at any time but are considered renewable because
procedures to recycle the resource presently exist and have
been demonstrated. A major problem for many renewable resources
is the ability to expand the reserve level consistant with
the expansion of demand. Even where expansion is possible,
system inertia often causes a several year delay.
Land
Within a given region the total amount of land does not
significantly change. While it is possible to create some
new acreage from surface water areas or to lose land due to
erosion, the relative change in total land form is judged
insignificant for consideration at the total stock perspective.
However, these special land generation sources, when its specific
utilization or worth characteristics are viewed, may require con-
sideration due to its high intrinsic value to the local population.
The land resource can be subdivided at any point in time
by its expected near-future usage. Six land usage categories
might be considered:
• Residential
• Industrial
• Commercial
• Agricultural (including pastures and non-recreational
forests)
• Recreational
• Other (i.e. not falling into any of the above categories)
The distribution of the total resource reserve among these
use categories can change based on the magnitude and
priority of the demands in the various categories. Additionally,
for at least the first four categories, land utilization can be
intensified by use of other resources in the production process
(e.g. urbanization or greenhouse densities).
In terms of U.S. land use for development (as opposed to
agriculture, recreation or other) the land resource is presently
seen as limited only in ecological distance. Over the whole of the
United States, about three percent of the total land area is
devoted to developed uses; the percentage has not been
increasing extraordinarily rapidly even in the face of
34
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historical major increases of population densities in and around
our urban areas during the past 30 years. The problem of
ecological distance (or accessibility) is handled in the
model by considering the relative utility of the land reservoir
around urban areas in terms of combination of aesthetic,
topographical, and transformation costs. By this procedure,
a capability to increase land availability in each use
category exists and is governed by two factors:
• The total reserve of all usable land
• The present unit costs to transform and maintain
land as compared to the present accepted land
use earnings.
Thus the concept of substitution of similar resources for
scarce materials exists for land--subject to payment of the costs
of transformation are paid and reduction of the reserves of the
land use category from which the substitution is drawn.
Agricultural Resources
If we were to be concerned with the issues identified
by others who have researched in the field of resource
availability, a great emphasis should be placed on the
agricultural portion of the resource base, more specifically,
on its output — food and fibers. Because a nation must
first meet the subsistance requirements of the population,
the first resource of major concern for a region is the
availability of adequate food and shelter.
In America we have land in abundance but it is not
of consistent quality. Differences in soil quality,
climatology, topography, etc. affect the soil's natural
capacity to yield food. These problems have not been critical
since, added to the abundance of arable land in the U.S. there
is a huge scientific and technological superstructure which has
produced startling argicultural increases on marginally arable
land while decreasing inputs of land and labor. However, it is
by no means sure that this fortunate circumstance will continue
as worldwide demands continue to grow and other land-use and
environmental conservation demands are met.
Production of food can be increased in the U.S. and many
other areas by five principal methods:
• New lands
• Enhanced productivity of presently cultivated land
• Prevention of loss (of tithing to rats, fungi,
and insects)
35
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• Innovation, and
• Change in the economic base.
Some projections suggest that the need for both additional
acreage and farm output per acre will occur in the next few
decades, as the per capita food consumption rates continue to
increase or stabilize and as the population grows. Furthermore,
the amount of the limiting total stock base (the land) available for
this use will be a function of relative price among competing
land uses. In fact, some of the most fertile land is
presently under concrete.
There is a growing need for forest products, but conservation
actions of the early twentieth century to assure the supply
of forests has made this demand less critical in the short
term. In essence, the future needs and production of food
and fiber can probably be regulated through the price
mechanism. However, the rapid escalation of today's market-
place food prices suggest that some painful supply dislocations
in this area exist even now due to inertia in changing production
levels.
The possibility of food from the sea has been mentioned
often as a major "agricultural" source in the future. The
limit appears to be much lower than is popularly assumed.
Large tonnages of fish catches or sea-cultured plants and
animals do not appear to be available quickly or inexpensively.
Further, it is not clear what heavy fishing will do to the
carrying capacity of world's fish supply. This very important
source of protein is under study in many nations where
dependence on foods from the sea is greater than it is in the
United States. Although the sea is certain to continue to play an
important role in the world's protein supply; it is clear that, for
the reasonable future, the harvest rates of sea-culture will not
increase significantly.
Hence, the likely procedures for increasing resources now
primarily obtained by agriculgure are:
• Expansion of cultivated arable land
• Intensified yields/acre by increased use of other
resources (use of chemicals with increased toxic runoff
or large-scale greenhouse production of plants)
• Substitution of manufactured structural materials
and fibers for cellular materials and animal fibers.
Thus a new set of mechanisms for increase of the animal pro-
duction of the reserves of foods and fibers exist different than
those noted for ores and energy. In the first two of the three
36
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procedures above the available resource stockpile expands
not by increasing the existant extraction procedures or by
general substitution of one similar resource for another, but
instead demands a change in basic agricultural input/output
procedures. In later sections of this report, appropriate
procedures are defined for SOS as part of the agricultural
production process. However, to obtain this needed model
capability one of the private industrial components that
includes growth must be agriculture. Further discussion of
this consideration is found in Section 7.
Capital
Man-made capital is another resource available to this
culture as an intermediate step between raw materials and
final consumption. As such it is a vital link in the transfer
process and it responds to the same sort of pressures as the
other renewable resources. Capital at any time has a definable
reserve level, its increase has inertial drag that regulates
its rate of expansion. As its value relative to other system
resources increases, funds are expended and the rate of capital
expansion produces a gain in the existant usable and renewable
supply.
Labor
The sixth form of resource used in component production
is labor, measured in work units. This resource is directly
related to specific population age groups and partitions
within the age groups. Like the resources of natural ores,
energy, land, and agricultural output, the labor supply is
considered to be a function of unit cost, in this case average
salaries. Unlike the other four categories the supply does
not simply increase proportionately with the unit cost increases.
Rather, it has an upper limit determined by population size;
the proportion of this maximum stock that becomes the labor
supply is assumed directly affected by the cost in production
(salaries). While a time lag for increase of the reserve
exists, the total stock (the adult population) can be reallocated
more rapidly than most resources into a reserve status. However,
after this reallocation in done, it is assumed that little
additional work unit reserve growth is possible except immigration,
However, immigration regulates work unit increases in direct
proportion to the total population and total goods demands growth;
hence, work unit shortages in periods of high demand can become
a systemic characteristic.
Air and Water Media
As has been evidenced in some areas, urbanization and
industrialization has caused massive increases in waste product
density in the regional ecosystem. A balanced ecosystem will
37
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produce no waste; wastes will be, through natural processes,
converted to the resources of other system processes. The
technologies and densities of human-culture processes can
result in unbalancing the system through overemphasis on
certain processes that include high generation of by-products
or through the development of a set of products that cannot
be naturally absorbed and converted to system resources. When
these imbalances are created, the production system must be
augmented by treatment facilities to reduce the by-products to
useful resources of the regional ecosystem. If this is not done
any of the several forms of pollution will occur. This pollution
of air, water or land may be sufficiently large as to reduce the
carrying capacity of the ecosystem media--thus affecting the
ability of the system to accept growth, and perhaps resulting in
permanent damage to the regional environment and carrying capacity,
Although the ecosystem media of air, surface water and
ground water (and to a more limited extent, land) are not, in
the usual sense, resources absorbed in production processes and
goods; they represent causal resources that can act as eco-
system limiting factors. Our treatment of them will be similar
to that of a capital maintenance function — the SOS model
requires restoration of that part of the media that is not
cleansed by natural ecosystem processes and that is not of a
quality that is demanded by the species of the regional
ecosystem. This funds are allocated prior to use of operating
funds for goods output.
RESOURCE FUNCTIONS
The following general rules can be associated with the
SOS Model simulation of all resources:
• The available resources at any point in time can
be associated with a unit procurement cost. This
cost can be used in a number of model procedures
concerned with the detection and the resolution of
perceived resource crises.
• At any period in time, the stockpile of a given
resource in absolute terms is unknown. However,
the quantities available as resource reserves for
a given unit procurement cost are known and act as
limitors on the regional goods production systems.
• For any resource, the indication of a perceived
resource crisis is associated with preset stock
depletion warning signals. These signals are set
when the present resource stocks no longer can
produce a unit of the resource within the current
unit procurement cost range.
38
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The resources of ores, foods, fibers, energy and land
have resource strata within the general resource
category. Within any strata the mix of associated
resources used to make up a single unit of that
resource strata is maintained without change unless
a stock depletion signal occurs for a resource
in that strata.
If a stock depletion signal for a resource or
a strata occurs, a check of allowable substitutions
is made to determine if another acceptable resource
mix (generally called a substitution) can be made in ,
production processes that generates a lower unit
procurement cost. If this condition is met, the
substitution process is initiated.
For any substitution process, increase in economic
stockpiles, or change in input/output processes,
the full change may require several time periods.
The level of attainment achieved for each subsequent
time period (cycle of model operation) is calculated
and the appropriate level of mixed strategy is used in
production processes for that period.
In addition to the expansion of a critical resource
base by substitution, the availability of resource
total stocks is checked to determine if the current unit
procurement cost will cause a greater stockpile of the
resource to be transferred to the reserve status. Such
increments are carried out using a time delay function
for activating the new reserve sources. Expansion
of the resources of land and labor are subject to
additional constraints in that:
• labor must maintain its total population
partition structure and,
• the total amount of land is constant;
hence expansion of one land or labor strata implies
decreases in other strata.
The natural resources and sub-categories of other
resources can include expansion by recycling
available ores . The rate of recycling is based
on maintaining a minimum unit cost from the
complementary sources of extraction and recycling.
In its present form, the original source of trans-
portable resources (ores, energy, foods and fibers)
is not considered. The selection of stockpile
levels and increments as a function of the price
require calibration to reflect the availability
from sources both internal and external to the
region.
39
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SECTION V
MODEL OVERVIEW
PURPOSE AND APPLICATIONS
The State of the System (SOS) Model is being developed
as a technique to analyze different alternate approaches
for melding the growth desires of a population with the
limitations of the locale in which the populace
exists. To treat this problem, the ecologist's concept
of a ,regional carrying capacity has been used as the basis
in building a mathematical model which will constrain the
demands of the growth desires to remain within the bounds
of the locale's resources. To handle this growth vs. environ-
mental limitations paradigm, the model has been designed to
test various assumptions about the desired growth of an area
under a set of side conditions (boundaries, constraints, or
thresholds) that define the status of the region's limiting
factors. Feasibility is demonstrated if the desired growth
can be achieved without violating these side conditions.
As examples of candidate side conditions, the model would
translate higher level laws and regulations (federal and state,
for example, if the model is of a local government), health
thresholds, natural media limits and the local desires into
quantitative side conditions. For example an analysis could
include values for a minimum level of subsistence per family,
a maximum regional unemployment rate, the various environmental
quality standards, housing and other industrial-commercial
codes, density levels and minimum education levels. From
these boundaries and the resources of the region that can act
as limiting factors, analysis of feasible growth levels
could be made.
Implementation of this model would result in the ability
to test both the present growth trend and apparently desirable
variations. Alternatively the relative impact rates of less
desirable variants could be analyzed.
Such a model could be used to analyze at least three
types of questions. First, it would be able to test the
ability of proposed growth trends to arrive at the goods
of the locale over time as defined by a comprehensive plan.
As a tool within a second analysis form, it could allow the
user to test the probable life of a system operating within the
constraints on growth and discover the most viable and critical
linkages and constraints, given the resources of the locale
and the constraints as set in the initial conditions. Finally,
analyses similar to the two above could be run that use
several different policy alternatives as starting points or
adjustment mechanisms. Such analyses would determine the
relative utility of each alternative.
40
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STkuCTURE
The State of the System Model includes four major ecosystem
structural elements:
(1) Sectors of Growth. This consists of three components:
the population, measured in terms of physical needs
- i.e., as consumer demand levels; the private pro-
duction sector; and the public services sector. The
form of population demands have two elements, population
size and increasing per capita demand levels. The
two latter components are each measured in terms of
annual change in level of expenditures for maintenance
and production (M § P) funds. The private production
sector and the public services sector, each, can
be subdivided into component categories (e.g., heavy
industry production or educational services) with
each category being an independent growth component
of the region. While the population growth is not
divided into components, it is partitioned into
special need groupings in response to the relative
levels of output being produced by the components
of the private and public sectors.*
(2) Production Component Output. This system element
refers to the outputs of regional economic and
government production systems during the period
which are available for regional consumption.
Net export levels are also accounted for within
these outputs as governed by the regional demands
for outputs.
(3) System Limiting Factors. These are of two major
forms;the input limitors are made up of resource
availability and of ecosystem support-media treat-
ment requirements; and the societal constraints
representing present demand levels placed upon
private and public sector output to maintain an
acceptable (or desired) level and quality of life
(QOL) for the present population size.
(4) Long Term Goals of the Society. These provide, at
a minimum, the lowest values of level and quality of
life measures that the society will accept as steady-
state demand levels. From this minimal statement of
society goals, the basic planning mechanism and demands
of the society can be introduced into the model by
having the demand constraints become increasingly
defined and restrictive up to and including exact
and comprehensive regional production plans (the
long-term equivalent of a planned-economy five-year
production plan).
'In the discussion these components are often called production
components where production may be in goods or services. For
SOS, the use of sectors denotes the public and private investment
categories.
41
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The interaction of these four model elements is illustrated
in Figure 3. The state of the system (the regional description)
at any point in time includes the results of the growth pro-
jections and the estimate of output provided by each of the
regional production components. After this description
is provided, an analysis of limiting factors on the production
output is made, determining apparent shortages in resource
availability or deficient quality in ecosystem media. The model
also determines short run failures of the system output in meeting
level and quality of life demands of the system population.
The failures and shortages of the system set into
operation a set of regional subsystem adjustments to achieve
short-term and long-term adjustments within the system. These
adjustments are then compared to the long-term societal goals
to determine if those production and resource availability
adjustments appear sufficient to provide attainment of long-
term goals or, alternatively, to determine the extent to which
the regional population must relax its demand levels. The
forms of adjustments are discussed later in this section.
For those most comfortable with modeling techniques, the
model can be described as one where side conditions are set
by the user or designer and within these bounds the model
is driven by goals of public and private growth. The side
conditions can be visualized as a membrane defined by the
limiting factors set by the ecosystem's ability to support
the needs of the population. In this case, the model groups
the limiting factors as natural resources and demands for
quality of life. If a side condition is not met this will
stretch or rupture the membrane (violate any parameter threshold
in the set of minimum limits). When and if such a stress or
rupture occurs, the model feedback controls attempt to correct
the regional stress in ensuing time periods by introducing
policies which would bring the demand trend back within the
membrane or will relocate the membrane by updating the limiting
factors.
ASSUMPTIONS AND SIMPLIFICATIONS
Since the model is expected to be operated as a regional
model—where the region is national or subnational--the system
does not have a high degree of closure. Hence the model must
account for trade arrangements and other primary exogenous forces.
At this point of the model development these questions are neglected
for the most part. They will be considered in appropriate
detail in the model formulation and data base discussions later
in the paper.
42
-------
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Also, since the model is presently in only a conceptual
formulation, a number of difficulties in measurement of
variables, primarily as to what are the dominant measures of
quality of life, and in selection of surrogate system limiting
factors, are only briefly analyzed. These require in-depth
analyses and are relegated to other research efforts.
The present model also does not treat spatial dimensions.
Rather, it uses the spatial hypotheses of human ecologist
as summarized by Quinn. These have been further reduced to
four general hypotheses:
• Hypothesis of minimum costs. The hypothesis of
minimum costs may be formulated as follows:
Ecological units tend to distribute themselves
throughout an area so that the total costs of
gaining maximum satisfaction in adjusting pop-
ulation to environment (including other men) are
reduced to the minimum. Or, stated in another way,
ecological units tend to distribute themselves
throughout an area so that costs are constant, the
total net satisfactions that result from the
adjustments of the population to environment
(including other men) are raised to the maximum.
• Hypothesis of minimum ecological distance. The
hypothesis of minimum ecological distance is a
corollary of the hypothesis of minimum costs. It
refers only to the costs involved in transporting
men and materials from place to place; and it
assumes that the economic costs of extraction,
manufacture, and selling, as well as social and
cultural influences, are held constant over the
region.
This hypothesis may be stated as follows: If
other factors are constant within an area, ecological
units tend to distribute themselves throughout
.it so that the total ecological distance traversed
in adjusting to limited environmental factors,
including other ecological and social units, is
reduced to the minimum.
• Hypothesis of median location. The hypothesis of
median location refers to the spatial location of an
ecological unit within a functionally organized
area. The hypothesis rests on the logically demon-
strable assertion that less total distance will be
traversed by all units in reaching the median than
44
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would be traveled by them in reaching any other
spatial location in the area. The hypothesis may be
stated tentatively as follows: Within a free com-
petitive system, social and aesthetic factors being
equal, a mobile ecological unit tends to occupy a
median location with respect to: (1) the environ-
mental resources it utilizes, (2) the other units
on which it depends, and (3) the other units that
it serves.
Hypothesis of intensiveness of utilization. Within
an area, various types of ecological units may compete
with one another for a given location. Several eco-
logical units may find their respective medians
located at the same place. Except for competition
with others, each of these units could locate most
advantageously at this median place. Under such
conditions of competition, that ecological unit tends
to occupy the common median which can utilize it
most intensively.
Intensiveness of utilization may depend either on
the direct utilization of resources located at the
site under consideration, or on a special application
of the hypothesis of median location or both.(18)
Quinn recognizes some of the more obvious limitations on
these laws. In general they can be paraphrased as man gen-
erally acts predictably, but in specific places and at certain
unexplained times, violates this pattern. The reasons for
the deviation include tradition, local culture, prejudice,, and
accidents of time.
ALTERNATE SYSTEMIC DESCRIPTORS AND ADJUSTMENT LOOPS
The dynamics of the model structure outlined earlier are
expanded on in Figure 4. That figure emphasizes the cyclic
descriptors of the system which are routinely modified, either
by cyclic growth (if there are no "problems"), or by ecosystem
adjustment reflected in the problem feedback loops.
The descriptive element of each cycle projects the elements
and relationships shown earlier in Figure 3. This step consists
of:
1. Projecting growths of the population size and demands,
and the levels of funds available for operating the
private and public output sectors.
46
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2. Generating the expected levels of goods and services
outputs for each component of the private and public
sectors.
3. Determining status of resource depletion, quality of
ecosystem media, and the level and quality of life
measures.
This procedure describes the system status annually in
terms of the regional carrying capacity--the ability of the
regional output production to meet the demands of a growing
(or stabilized) consumer population under the constraints and
limitations of both resource availability and maintenance of
environmental quality.
If the status of the regional carrying capacity shows one
or more demand measures indicating short-term failures, the
systemic element of the model is entered to determine if the
system adjustment capabilities over the short-term or in the
long-term can relieve the failures; or, alternatively, can
successfully alter the population demands. This portion of the
model can, but need not, be cognizant of regional planning
processes. Hence, the adjustment forms can be of several types
to reflect the intensiveness of regional management.
Thus the model can consider fully planned societies that
attempt to meet detailed preset comprehensive output plans,
or, at the other extreme, laissez faire or natural systems
that require only societal maintenance levels that reflect
minimal regional life-support as growth and demand thresholds.
Two regional processes will be discussed below as examples;
these are the two processes most likely to be considered for
applying SOS to analysis of regions of the United States as
resilient and stable ecosystems.
The Comprehensive Planning Procedure
One useful environmental planning system is an extension
of many past study efforts carried out as municipal and
regional planning studies. This system is characterized by
the specification of a comprehensive plan that reflects
prediction of long-term growth sector demands. From this
an objective function is derived that is expected to be
realizable. Included in the adjustment methods is a procedure
that attempts to perform an overall system-optimization that will
maximize the objective function based on the information gen-
erated in the model operation up to that cycle.
47
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The set of adjustments are put into operation primarily
because of the status of resource stockpiles for the particular
cycle. The resources are available at discrete points in
time; thus some shortages may be localized or time dependent,
not necessarily reflecting a permanent resource depletion but,
perhaps, only inertial drag in expanding extraction methods
as reaction to new growth demands. Thus, the management
system can react to warning signals and "brownouts" by
affecting adjustment over the short and/or the long run.
If the projected output of the system is maintained within
the regional carrying capacity by simple adjustment of short
run supply factors, no long-term adjustment of system demand
levels or of sector growth rates need be made. Otherwise, the
projected grwoth rates and/or long-term demand requirements
will be adjusted based on maintenance of minimal degradation
of the objective function. The system description procedures
will then be repeated to determine if the new output projections
are within the carrying capacity limits of the regional
resource allocations and environmental requirements.
An operational model depicting the regional goals as a
comprehensive plan or as the more typical operating system can
be used to analyze the value or practicality of the plan based
on the type analysis that is to be performed.
If the analysis is a capability study of the ecosystem
without regard to a prescribed time limit, then an initial set
of growth rates for the three growth sectors can be set. The
model will then be operated to determine the timing and level
of internal system adjustments that are required to the
individual growth rates in order to maintain the system in a
regenerative form, or alternatively to extend the time frame
of the ecosystem as a viable support system.
Alternatively, for a given time span and as a requirements
study, the levels of the output required at that ending time can
provide trend lines to indicate intermediate values to
which the outputs generated each time period can be compared.
This annual comparison determines what and how much demand levels
and growth rates must be adjusted in order to maintain the trend
line. The model adjustment loops will attempt to recover to
the trend lines as soon as possible or, if recovery is not
feasible, to make the minimum degradation of trends goals.
The Operational System
A second representation of the regional system is closer
to the ecological and economic management patterns observed
in most U.S. regions today. This procedure suggests that,
48
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while there are many system thresholds that must be met, many
of the growth and output adjustment choices are not developed
in an "optimal" fashion, but reflect existant "policy" and
other regional desires and initiatives after satisfying the
natural system thresholds. The model then must first determine
the area of acceptability of demands and output by interpreting
a set of side conditions - resource constraints, demand thres-
holds, ecosystem minimums, output increase maximums, etc.
Given that the outputs for a time frame occur within the area
of acceptability meet all demand thresholds, no further
adjustment of outputs toward an optimal or growth-maximizing
result is made, but, rather, output and export patterns of
the past periods are maintained.
This model description and adjustment form remains within
our earlier definition of carrying capacity where the area of
acceptability is equivalent to the range in which the ecosystem
"remains healthy and productive." It also provides a definition
of the level to which local desires and mores can prevail - any
area-specific pattern is allowed as long as the end result is expected
to be within the area of healthy productivity of the ecosystem.
If at anytime, the projections for the ecosystem
suggest that the full set of population demands are not met,
then the ecosystem resilience is lost and adjustments must be
made using the feedback adjustment schemes. These adjustments
combine several of the items that are characteristic of the
existing regional adjustment mechanisms:
• No overall optimization of the individual component
production processes to meet total society goals
under normal (healthy) conditions.
• A capability in crisis situations to intensify and
unify planning within the public-private processes
to meet minimum demand standards.
• Each component of growth and of output individually
attempts to adjust productivity to not only meet
minimum standards (the society thresholds) but also
to increase the resiliency and the stability of system
by suboptimization of components in the total system.
It is worth noting that this second management process
can be made to approach the first, the regional Comprehensive
plan process, by raising society minimum demand thresholds
toward the realizable goals of the exacting comprehensive
production plan.
49
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SUMMARY
In general terms the State of the System Model, described
in its simplest form, will allow the user to iterate through
time until it is projected that one or another of the system
resources will be exhausted or costs of media treatment will become
prohibitive. This means that the system can be conceived of as
having several independent limits or thresholds any of which will
modify its further growth. As one, or all, of the system resources
begin to be scarce and relatively expensive, there is a tendency
first to skimp on maintenance to a given level and then to curtail
affected growth. The indicators of public-private output levels
compared to system demands begin to decline consistently and across
the board. Unless drastic steps are taken to circumvent the serious-
ness of the shortage(s), the system may be in terminal decline.
A model of only,this descriptive form, however, is of limited
use to the policy maker who must make day to day decisions based
on little information. Consequently, the State of the System
Model is seen to have a number of adjustment loops representing
local and partial system reactions, permitting it to serve as
a local policy device. In particular a large set of resource
adjustment capabilities exist provide a reasonably representation
of resource constraints by using economic substitution to
effect adjustments.
One application of a model of this type is to test the
operating or comprehensive plan of a specific region. The
test is of the type which makes the assumption that either plan
has represented the appropriate set of recommended changes within
the data base, and that the region will make whatever adjustments
are necessary to implement the plan. With this design in mind,
the model iterates through time constrained by the desired end
goals of the local inhabitants. Whenever a specific value (or
series of values) is out of phase with the desired plan, the
model will adjust itself to refocus the subsequent iterations
toward the end goal.
The questions addressed by the model then are whether
the region has the capability of arriving at the desired
goals of the population given the existing resource problems
and the area-specific adjustment processes to manage the
region's resources.
50
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SECTION VI
MODEL FORMULATION
GENERAL
This section provides an examination of the principal
variables and functional relationships of the State of the
System Model. These present the general model structure,
the type data required for model operation, and will serve
as basis for subsequent research efforts. The relationships
are presented in four groups paralleling the four model
elements discussed in the Overview (See Figure 5). The
groupings are:
• System Inputs - These relationships are associated
with the sectors of growth, specifying the total
sector change. 'The inputs include total regional
funds and allocation of expenditures to the private
and public sector, plus the population size, age
distribution and quality of life demands.
• System Outputs - These relationships translate the
inputs to an overall demographic and economic
description of the region for the year considered.
• State of the System - These relationships are
associated with the system limiting factors or demand
constraints. They define resource utilization, the
quality of the environment and the satisfaction of
quality of life demands within the system.
• System Adjustments - The last group of relation-
ships are associated with the long term goals. They
provide the necessary adjustments and feedbacks when
the state of the system is found to be incompatible
with the ultimate goals.
CYCLE CALCULATIONS.AND ADJUSTMENTS
In essence, the workings of the SOS Model can be visualized
as follows: (See Figure 6)
The particular system under study can be expected (pn
the basis of known patterns) to grow at a given rate.
This growth includes changes in population and goods demands
levels plus the funds used by the public and private sectors.
During a. cycle the desired growth rates would project a pro-
duction output level. From this set of output levels a set
of factors can be checked against the carrying capacity of
the system. This carrying capacity can be seen to have two
types of limits — those set by the desires of its local in-
habitants for output (Quality of Life) and those set by the
51
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r
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ecosystem. The human desires tend to be of a short run
nature and are changeable through time but not at an instant
in time. The ecosystem limiting factor constraints are, of
course, more enduring and consist of the availability of
natural resources--energy, food, and the like--but include
environmental quality.
The model is so conceived that the amounts of resource
reserves are set for discrete points in time (normally a yearly
increment). Shortages can be due to circumstances which
are localized and time dependent, but that do not necessarily
reflect a permanent depletion of a resource. On the other
hand, because the system reacts to shortages and "brownouts,"
such occurrences will be handled as system warnings which may
produce both short and long run adjustments of resource supply,
resource utilization and resource demands.
If the projected output of the system during a particular
time period is within the limits set by its carrying capacity
and meets the population demands then the model will continue
to the next cycle. If the output demands are beyond the system
capacity, the projected growth rates will be adjusted and the
adjustment cycle repeated until the projected output is within
system limits. Throughout this process, the growth of the
study system is compared against the stated goals of the
inhabitants--the quality of life demand-measures.
The model can also respond to the whim of potential pressure
and public fancy. In addition to the "rational" feedbacks of
the model itself, it responds to exogenous perturbations. This
extra-regional procedure lists the areas of public expenditure,
(education, transportation, etc.) and checks to see whether each
public area has (1) recently had an infusion of public funds, and
(2) is an area where more funds would have a noticeable
effect on the Quality of Life. The resultant output from
the algorithm is a vector of weights for each public services
component as an index of popularity.
SYSTEM INPUTS
Total Production Growth
The model takes its impetus for iteration from yearly
growth and development rates. These rates are determined by
forces endogenous and exogenous to the system. The closer
the regional system is to closure, i.e., the more it represents
a worldwide system rather than regional growth expectations,
the more the rate of change is endogenously determined. The
efficacy with which the growth rates are changed by the feed-
back loops is the key to the success of the adjustment portions
53
-------
I/) T3 !H
U 4-> 3 0 |3
0 3 13 -H O
•T-l P, O rC (fl
O +-> f-i U
-------
of the model. However, while the growth rates can change,
the total input to the regional system cannot. The input to
growth sectors other than population is in terms of funds
available for conversion to real goods production plus the
maintenance of the physical (developed and undeveloped)
elements of the system. The total amount of funds available
for a cycle includes two sources - the endogenous funds generated
based on consumption of the past period production, and exogenous
funds allocated on a non-historical trend, popularity basis.
The exogenous funds could represent national to regional
transfers and can be negative. The total funds for a region
for any time are:
TFUND(t) = PRIVFD(t) + PUBLFD(t) + EXOGFD(t)
where TFUND(t) is the total funds avialable for use by all
production components in the public and
private sectors for year t,
PRIVFD(t)are funds generated endogenously by the private
sector activities for time t
PUBLFD(t)are the funds generated endogenously for the
public sector, and
EXOGFD(t)are the funds transferred to the region from
outside sources through importation, subsidies,
net taxation transfers, etc., plus the contri-
bution through the popularity vector.
For either the private sector or the public sector, the basic
funds for the cycle are equal to the funds generated by each
component for the cycle based on its rate of growth. For
example the private sector:
PRIVFD(t) = Y M$PFD(c,t-l)*(l+RG(c,t-l))
c in private
where M6jPFD(c,t-l) is the level of funds used by component c
in the component's operation last cycle.
RG(c,t-l) is the rate of funds growth provided component
c in the last cycle. This rate of growth is a complex
function described later in this section and that can
undergo further modification in system adjustment
processes.
The exogenous funds are made up of two elements, the
net exports balance and a cash transfer capability that is
not wholly a function of the previous period. This second
factor is set to vary based on a probabilistic range about
55
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an expected transfer value that is region-specific. For
example, for the United States, the value could represent the
outflow of aid to other nations funds with a range of
variability consistant with the past trends of Congressional
appropriations. As a second case, for a region of the United
States receiving significant assistance within one of the public
component areas, a mean transfer level modified by an annual
stochastic variance might be applied.
EXOGFD(t) =2_NEXP(c,t-l) + f(RN,t)*TRNFD(t)*(1+RGT)
c
where NEXP(c,t-l) = (EXP(c,t-l)-IMP(c,t-l))*(l+RG(c,t-l))
EXP(c,t-l) is the funds received for exports for
component c in the last cycle
IMP(c,t-l) is the funds paid out for imports of component
c in the last cycle,
f(RN,t) is a weighted random function distribution of
transfer fund variability.
TRNFD(c,t-l) is the level of funds transferred into the
region last cycle, and
RGT(t-l) is the mean rate of funds growth expected over
the long term
This level of total available regional funds sets an
upper constraint on inputs to the production sectors and com-
ponents for the current cycle. The process of allocating
funds' to production components is done subject to the
condition: the funds available to the components must equal
to the total regional funds.
The allocation process has two major steps. First,
an expected (or median) allocation of funds is provided
assuming that the relative growth rates set and adjusted for
each component in the past cycle are maintained. Additional
increases or reductions of growth rates are introduced as
functions of net exogenous-funds-available and the population
preference for types of goods or services this cycle. Thus, the
general form of the growth of funds for a sector or a component
can be represented as:
RG(c,t) = M$PFD(c,t-l)*(l+RG(c,t-l))+EXOGFD(t)*f(CONPRF(c,t))
where RG(c,t) is the normalized funds growth rate for component
c and time t
and f(CONPRF(c,t)) is a function of the regional preference
to add or delete funds from component c to adjust
to exogenous funding levels in all components.
The function is subject to the property that
f(CONPRFCc,t) = 1
56
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and includes components of
f(CONPRF(c,t))= f(Maintenance of capital and media, and
exogenous or endogenous preference to invest
in component c for this t)
Thus
CONPRF(c,t)) = GROWTH(MAINT(c,t) + QOL(c,t) + RESDEP(c,t)
+ PREF(c,t)).
a level of additional directed growth for a combination of factors
including capital maintenance (MAINT), environmental mainten-
ance and human desires (QOL), resource depletion (RESDEP),
and/or subjective preference of the funds supplier or the
ultimate consumer (PREF).
The fund allocation produced by the process above is
described below, using the newly generated rates of fund
growth for production components, RG(c,t). First, however,
a static representation of the production sectors appears
useful.
The Production Sectors
The sectors of regional growth, other than regional
population and demands, are the production and services
components of the private sector and the public sector.
The dimension of growth for both sectors, and hence their
input to the system, is the level of funds used annually to
procure and transform resources into capital and ecosystem
maintenance* and sector production outputs (M § P funds).
Due to the need to partition the sectors into more
meaningful elements, both the private sector and the public
sector are decomposed into components that represent natural
regional subdivisions. For the private sector, production com-
ponents are established; e.g., heavy pollution industry, light
polluting industry, commercial goods and services, agriculture,
and household-related industries. In the public sector and
a national region, typical service components could be education,
welfare, safety, defense and administrative services, health,
and transportation/communication. In SOS each of these com-
ponents has related with it a rate of yearly M§P funds growth as
defined above.
For static representation of the production elements of
the system, the funds .expended are:
TFUND(t) = TEXPN(t) - EXPPUB(t) + EXPPRI(t)
*Capital maintenance here is expansion and maintenance of the
facility and equipment of the production element.
57
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All funds available to the region will be expended since
over-production is transformed into exports and increased
stimuli of population demand.
EXPPUB(t), expenditures in the components of the public
sector, and
EXPPRI(t), expenditures in the components of the private
sector.
Further decomposition of the expenditures yield that
EXPPUB(t) = y~EXPCOM(c,t)
T~ in public
and EXPPRI(t) = >EXPCOM(c,t)
c in private
where EXPCOM(c,t) is the expenditures of component c for M § P.
Thus, for any time peri'od, the funds available to the region
are balanced by the production expenditures of the region
TFUND(t) = 2_EXPCOM(c,t)
Expanding the consideration to annual increase or reduction
of M § P funds available to the components; for any component,
the funds can be calculated from:
M§PFD(c,t) = M$PFD(c,t-l)*(H-RG(c,t))
where RG(c,t) is defined earlier and represents the component
investment growth of new regional funds that
come into (or out of) the area due to exogenous
effects, and due to growth in regional components.
These rates are constructed such that:
TFUND(t) = 2^M$PFD(c,t) =£_M$PFD(c,t-l)*(l+RG(c,t))
c c
and also that the funds of a sector equal the funds of
its components .
As implied in the above formulation, the model is vis-
ualized as being responsive to changes in many parameters of
the public and private sectors. The model takes direct note of
endogenous "rational" changes through the adjustment feedback
mechanism discussed later in this section. In addition, the model
can also reflect exogenous and endogenous economic and political
58
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pressures and public fancy to produce growth in the various
components. Generally the latter will be reflected through
the preference function within the growth rates.
The Population Sector
Population has been called a passive factor in change
by Quinn.(19) He discusses it as being a regional change
factor which has great potential, but without corresponding
organizational shifts the potential probably will never be
realized. Further, population growth as such is not seen as
significant in the sense of regional limits until it is
related to territory - the larger the physical space in which
the population is housed, the less pressure is exerted on
the group in the sense of food and living space demands -
other things being equal. In fact, the limiting factor of
population growth often is not land, food, organization or
transportation as described in the society's own domain but
may be caused when its growth intrudes on the domain of
another society.
For SOS, we shall assume that the necessary organizational
structure required to support any level of population will
exist when it is required. This means that the expected growth
rate of the population of the system will be largely determined
from exogenous forces and the regional attainment of societal
desires. Changes in population birth and death rates are
outside our perview except when the level of satisfaction of
demands in a region reaches catastrophically low bounds. The
model causes most variation in population growth to occur due
to changing area attractiveness; this primary rate-change
mechanism is reflected through the net migration rate.
Total Population
Demographers have noted that the changes in population
levels, and the composition of the population in terms of its
basic characteristics do not change drastically in the short
run. The growth of the population each year can best be
described by the reasonably constant relationship between the
birth and death rates plus the changes in the net migration rates.
The migration is postulated to change in accordance with the
basic desirability of a specific area. For SOS the basic desirability
is a function of employment opportunities and the prevailing
level of attainment of the population demands.
The size of the regional population for any year, t,
can be calculated by:
TPOP(t) = TPOP(t-l)*[l+BRTH(t)+AT(t)*NTMG-DETH(t)]
59
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where TPOP(t) is the total population of the region for year t
BRTH(t) is the birth rate for year t
DETH(t) is the death rate for year t
NTMG is the normal net immigration rate for the region
AT(t) is the region attractiveness function for
migration during year t, reflecting current
system conditions.
Population Characteristics
The demographic structure of the population is of interest
in SOS for two reasons. First, the population is grouped into
ages. These age groups allow a representation of the resource
of labor in terms of level and ability of the regional population
to rapidly expand the work-unit supply as a function of produc-
tion sector demands for the labor resource. Secondly, the
population age groups are partitioned to determine the expected
consumption rates of the population for types of output; the
level of specific demands are affected by the size of the
various partitions. Included in this partitioning process
are a number of factors that can be correlated to the regional
outputs and represent the present socio-economic level of
the society. Typical partition characteristics include:
• length of immaturity/educational time
• mean rates of short-term and long-term infirmity
• ratio of educational units to work units in each
age grouping
• death rates by age grouping
• size of worker force, further partitioned as:
• employed, paid workers
• unemployed, paid workers
• workers not in paid status (housewives, volunteers)
The population characteristics are assumed to change
directly with the production and services output levels of
the private and public sectors. These changes are shifts
of population elements from one partition to another,
e.g., from unemployed to employed. This is reflected by:
RPOP
Cj,t) = £a(j,c)*UTOTO(c,t-l)
where RPOP(j,t) is the "relative" population of
partition j in year t
60
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UTOTO(c,t-l) is the total output of production
component c in year t-1 in real goods
a(j,c) is the factor relating production output to
population partitioning.
To obtain actual population values, rather than relative
values, the current total population must be applied.
Thus:
POP(j,t) = TPOP(t)*RPOP(j,t)/£ RPOP(j,t)
]
where POP(j,t) is the size of population
partition j in year t.
SYSTEM OUTPUTS
The major inputs used for setting system output are
the expenditures by the various production components to
produce the output. The input, i.e., th
investments dis-
cussed earlier, include not only production funds but also
maintenance funds. Thus:
M$PFD(c,t) = TOTO(c,t)+MAIN(c,t)
where TOTO(c,t) are the funds devoted to production output
in year t
MAIN(c,t) are the funds devoted to maintenance in
year t
This yields:
TOTO(c,t) = M$PFD(c,t) - MAIN(c,t)
Maintenance is considered here as having three major
elements and, thus, differs from the usual maintenance
expressions that consider only offsetting plant and equipment
depreciation. In addition to the capital depreciation offset,
the model considers the ecosystem equivalent, the expenditure
to restore the environmental media (water and air) to a "clean"
state; i.e., the costs of effluent treatment; these ecomedia
treatment costs are related to the component output level.
The third maintenance element represents the annual expenditure
of capital investment to increase the production facilities
of the component. Thus:
MAIN(c,t)=TOTO(c,t)+*(MNDEP(c,t)+MNEFF(c,t))
+(TOTO(c,t)-TOTO(c,t-l))*MNCAP(c,t)
61
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where MNDEP(c,t)= depreciation cost per unit of output
MNEFF(c,t)= effluent treatment cost per unit of output
MNCAP(c,t)= capital cost to expand output facilities
(allocated over ten years subsequent to the
expansion year)
Substituting this into the expression for TOTO(c,t)
above yields with simplification:
fc t1= MSPFDCc,t)H-[TOTCc,t-l)*MNCAP(c.t)1
(.c , t j i+MNDEP (c , t) +MNEFF (c , t) +MNCAP (c , t)
It will be noted in the above expressions that the
maintenance components are not constant over time. The
depreciation offset costs may vary with time since these
costs can be deferred for future times to allow a short-term
increase in production funds. Expansion of facilities can change
cost over time due to change level of expansion and in construction
resource costs. The effluent treatment costs vary over time
based on the variation of overall media pollution quantities
compared to the system's natural regeneration.
Specifically, for this last consideration:
MNEFF(c,t) = 2_ KMNEFF(c,m)*f(m,t)
m
where m is an index over the media types (e.g., air and water)
KMNEFF(c,m,) is the cost of totally treating the
effluent of one output unit released into
media m.
f(m,t) is the fraction of the effluent to media m that
must be treated in year t.
The fraction to be treated is determined by first calculating:
f'(m,t) =(POLL(m,t)-CLEAN(m))/POLL(m,t)
where POLL(m,t)= is the overall pollution level expected if there
were no treatment
CLEAN(m) is the level of pollution cleanable by natural
processes.
Then: , 1
f (m,t) = Max [0,f' (m,t)J
STATE OF THE SYSTEM
The major measures to describe the state of the system
are the levels of available resources and the level and
quality of life. Only resource levels will be discussed in
-------
detail here. Development of appropriate formulations for
quality of life measures is a major part of the future effort
for the model. The example model described in the next section
illustrates one approach to QOL treatment as non-scalar system
demand measures.
Resource Utilization
In addition to the utilization of capital funds and
volumes of eco-media within the maintenance element of the
expenditures, the outputs of the various growth components use
resources in a production-transfer system that is postulated
in the model as being directly related to the units of real
goods output. Thus for any component, there is operating at
any time one or more input/output functions which relate
consumption of a combination of resource units to the production
of one output unit for the component. For any of the production
components, this resource utilization vector has as its
components:
V
RU(r,c,t) = ^_RSIN(r,n,c)*RFTH(n,c,t)
n
where RU(r,c,t) is the number of units of resource r used
in year t to produce one output unit by
component c
n is an index over a series of possible resource
mixes (input/output functions) that can be used
by production component c
RSIN(jr,n,c) is the number of units of resource r used to
produce one output unit by component c, if the
nth resource mix is employed
FRTH(n,c,t) is the fraction of component c that mix n
in year t.
The use coefficients, RSIN, could also be treated as functions
of time. This would allow consideration of the effects of
technological developments and their staged implementation on
resource usage levels.
The cost for production of a unit of a production component
can be developed as:
UCSTCc,t) = ^_RCST(r,t)*RU(r,c,t)
r
where RCST(r,t) is the cost to purchase one unit of resource r.
63
-------
Knowing the output of a component in terms of expenditures
(TOTO(c,t)) and the unit production cost, the output of a
component in real goods is:
UTOTO(c,t) = TOTO(c,t)/UCST(c,t)
The total usage of each resource can now be obtained from:
TRU(r,t) = ^UTOTO(c,t)*RU(r,c,t)
c
Effect of Technology on Resource Utilization
A major consideration for this more general form is the
determination of when, and at what cost, technology changes are
allowed. The model as conceived admits as future facts that
institutional and technological change occurs. To provide for
"idea(s) whose time(s) have come" requires an appropriate-
treatment of the timing and impetus for change.
The procedures provided in the model for incorporation of
technological change is driven by the cumulative expenditure
of capital toward research and development. The model assumes
that R ^ D expenditures for technological improvements in
utilization of natural resources, energy resources, agricultural
resources and land density are made at a rate relative to the
level a component expends to procure the resource. These R§D
investments are cumulated for each resource category and as
the threshold of cumulated capital is passed that would cause
a technological improvement, the production processes for
all components are then adjusted to reflect the input/output
transfer improvement due to technology.
Effect of Consumer Preference on Resource Utilization
A second reason for changes in the input/output transfer
function is represented by a more gradual trend over the time
limits of the model and represents the shift in production
output mix demanded by the population to maintain a production
level that is considered constant over time. Unlike the
change due to technological improvement, this change in
consumer education and preference for materials, and its resultant
change in types of resources utilized, is considered to be continuous
and reasonably linear over a model run of one or two gener-
ations. For longer periods of analysis more complex functional
forms may be required.
Resource Availability
In general new resource levels are determined by subtracting
the total annual usage (TRU) from reserves remaining from the
previous year and then adding on the level of replenishment for
64
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renewable resources. A key feature of the model's consideration
of such resources is that the "available" reserve level is the
amount that can be extracted (or otherwise obtained) at a
relatively fixed unit cost (see the earlier discussion of
resources). Thus resource reserve levels can be increased by
improved processing techniques or by accepting a higher unit
cost, thus making more ores economically accessible. The latter
process is discussed under System Adjustment that follows.
Determination of resource availability levels for fixed unit
costs are discussed below for each of the various resource
categories.
Energy
At any time the total energy stock available to a region
is the sum of the amounts of the various energy sources. At
the present level of the model no energy utilization types
(for example, stationary consumption vis-a-vis moving energy
consumers) are made. However, by properly defining levels
of substitution of fuel types in the data base, cognisance of
consumer types can be made.
The total level is determined as:
TSTKE(t) = £STKEl(e,t) + 7 STKE2 (f,t) +HISTKE - NEXPE(t)
e F
where RSTKECt) is the total energy resource for the region in
year t.
STKEl(e,t) is the amount of energy that is available for
the region by the fuel type e from regional sources,
where the fuel source is a non-renewable ore, e.g., a
fossil fuel.
STKE2Cf,t) is the amount of energy that is available for
the region by the energy type of that is renewable but
limited in terms of recovery rate from regional sources.
These energy types include hydroelectric power, geothermal
wells, nuclear fission power plants, solar conversion, etc.
NEXPE(t) is the net export level of energy sources (pro-
cessed or unprocessed) from the region.
HISTKE is additional energy avialable through a technological
breakthrough, e.g., new energy source that requires minor
depletion of other regional resources or eco-support media,
e.g., magnetic power sources; etc.
Natural Resources
Natural resources, like energy, is normally viewed as a
nonrenewable category. However, there are two important
hedges in considering the actual stock reserve at any one
65
-------
time. First, for many of the ores, a high level of substitution
of other resources within production processes is possible.
These substitutions can be caused by technological improve-
ment or simply a trade-off of one element for another, like
material. This process in defined here to be substitution
within resource strata, and the resources within the natural
ores category are assumed to have several strata. Example of
strata include trace metals, structural metals, nonmetallic
minerals, etc.
A second hedge available to natural resources, but not
available to any great degree in the most often used energy
sources, is the ability to recycle debris from processed and
consumed goods to regain natural ore in the form of salvage.
This procedure, tempered by the mobility of the various com-
ponent products in passing from the system statuses of ore to
goods to debris, sets a resource reserve that is once again
variable by cost, i.e., the recycling costs that will determine
the level of ore salvage from the system debris.
The following equation is used to set the stock levels of
each strata:
TSTKN(s,t) = V (EXTR(n,t)+RECY(n,t) - NEXPN(n,t))
nes
where TSTKN(s,t) is the level of natural resources in strata
s for year t.
EXTR(n,t) is the amount of natural resource of type n
extracted in the region
RECY(ji,t) is the amount of natural resource n salvaged
in the region through recycling.
NEXPN(t) is the net export of natural resource n from
the region and the summation is over all
resources in strata s .
The mix of extraction to recycling is a function of the
relative costs associated with preparation and distribution of
each mode. This adjustment is assumed in the example SOS Model
to be a continuous process of cost minimization.
Land
Within a given region the total amount of land does not
significantly change. While it is possible to create some new
acreage from surface water areas or to lose minor amounts of
land due to erosion, the relative change in total land form
is judged insignificant for consideration at the total stock
perspective.
66
-------
The major considerations with respect to land availability
is availability by land use type, and the potential conversion
costs between land use types. Thus:
TSTKL(t) = ^_DRTL(u)*STKL(u,t)+RCLM(t)
u
where TSTKL(t) is the total available stock of land.
STKLCu,t) is the stock of type u (e.g. residential,
industrial, commercial, agricultural
recreational and undeveloped)
DRTLCu) is the expected depreciation rate of land use
type u
RCLM(t) is the land under reclamation.
Methods for expanding reserves of a land use category are
developed similar to other resource categories. The maximum
potential for transformation at various cost levels is defined.
If the potential land that can be transformed is added to the
existent stock of land, the sum represents the total stock level
for a given land use in a region at a given land cost. From these
data a resource reserve generation procedure, as used in non-renewable
resources, is possible. In this procedure land use succession adjust-
ments is activated for a given land use type as the unused land use
reserve reaches a stock depletion warning level. At that time
additional reserves for that land use are generated by a minimum
cost algorithm. The major difference in the land category
procedure from that of ores is that generation of new reserves in
one land use category requires their removal from others.
To generate new land of a specific category requires developing
a minimum cost transformation from all other land categories. Thus
the cost to produce one unit of land stock u is:
CSTL(U) = fCTCP,STKL(U'))
where T is a matrix of transformation by land use
C is a matrix of indices representing the amount of
STKL(u') that is aesthetically acceptable as STKL(u)
P is a matrix of indices representing the amount of
STKLCu1) that is topographically consistant with
STKLCu) .
Application of this expression in a cost minimization routine
will generate the amount and sources of new land of type u for a
given cost.
The matrix of transformation costs (T) is simply a table of
coefficients which relates, in the form of a square matrix, an
index of the relative costs for transforming a unit of land to
any of the defined land uses form any other. In general form, the
67
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coefficients employed on these cells can be subject to price and
technological change. Taken in conjunction with the topographical
and aesthetic matrices which modify availability to reflect
physical, legal and cultural constraints, the cost matrix defines
the potential maximum for any particular land use in an area at a
point in time for a given cost.
Agricultural Resources (Foods and Fibers)
Based on research in the field of resource availability
and national needs, specific emphasis should be placed on the
agricultural portion of the resource base. Availability of
agricultural products to the regional system is given by:
TSTKACt) = F(DRTL(u)*STKL(u,t))+IMPTA(t)+SEA(t)
where TSTKA(t) is the total available agricultural resource
u is the land use index representing agricultural use.
IMPTA(t) is the net import level for agricultural
products.
F( ) is an agricultural production function related
to resource costs per agricultural land unit.
SEACt) is the amount of the resource obtained from
the sea.
Capital^
Capital is also an important renewable resource used as
an intermediate step between raw materials and final consumption
This resource is measured by:
TSTKKCt) - £ STKK(k,t-l)*(l+MNTK(k,t) - DRTK(k))
+£(RDK(c,t) + INVK(c,t)>
c
where TSTKK(t) is the total capital stock in year t
STKK(k,t-l) is the stock of capital type k for the
previous year
DRTK(k) is the decay rate of capital type k
MNTK0c,t) is the maintenance rate of capital type k to
offset decay
RDK(c,t) is the capital investment in R§D by production
component c
INVKCc,t) is the investment in capital goods by
production component c
Labor
Labor as a resource is measured in work units. The
population partition representing paid workers provides at
any time the instantaneous maximum labor supply level (the
68
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labor reserve). The labor cost unit is a function of the rate
at which this level is utilized at that time--the full labor
force employment rate. Additional labor units can be generated
as a function of this rate by transferring, in later time periods,
work units from the population partitions of-in training or in-
unpaid-work-activities.
This resource is measured using:
TSTKW(t) = g(POP(j,t-l), EMPR(t-l))
where TSTKW(t) is the total labor resource for year t
j is the population partition representing paid workers
EMPR(t-l) is the previous year employment rate
gC ) is a function which adjusts work force size based on
an employment rate reference point.
Air
Unlike with other resources, the model is not concerned
with the quantity of the air media. Rather, it is the
pollution in the air which is of concern. This is determined
from:
POLL(a,t) = POLL(a,t-l)*
. c
TOTO(c,t)
TOTO(c,t-l)
- Ba*KLNA
where POLL(a,t) is the air pollution level
KLNA is the percent of total expenditures devoted to
perfect air cleanup.
B is a pollution coefficient indicating the efficiency
of cleanup.
This value is used in the ecosystem maintenance function
discussed earlier under system outputs.
Water
Water, like air is measured in terms of pollution generated.
This level is expressed similar to the air formulation:
POLLCw,t) = POLL(w,t-l)*
ZTOTOCc,t)
TOTO(c,t-
L C
1)
- Bw*KLNW
where the parameters are defined similar to their air pollution
analogs.
Level and Quality of Life
The major elements of the state of the system are measured
in terms of societal perceptions - a set of judgments dealing
with various components of material output and quality of life.
69
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Our particular system must be area-specific, plus represent the
planning system that would accomplish the adjustments of growth
and output to achieve an acceptable quality of life. Hence, only
a general formulation of the quality of life measures can be
provided here. First, consider each of the two planning systems
discussed earlier as they relate to selection of these state
of the system indicators.
In the first alternative - achievement of the comprehensive
plan goals - the procedure is reasonably straight forward.
Each production goal by itself is a specific threshold to be
realized. The relative importance assigned the production goals
in the plan provides a set of weighting coefficients to determine
priorities in establishing excess production tradeoffs, given
that total achievement of goals cannot be accomplished. Thus
the only requirement in setting of goals is to restate the
production component output goals in terms of parameters as expressed
in the model algorithms that measure population demands. These
parameters will be primarily measures of real growth; e.g.,
production component outputs as related to total system popul-
ation demands, indicators in the form of per capita outputs,
the rate of total population growth, and size of specific
population partitions.
The second alternative is the system that requires achieve-
ment of certain minimum values giving a marginally acceptable life
state. It involves supplementary measures relating to the
resiliency of the production system in remaining above these per
capita demand minimums. Each of the collection of demand
measures a dissatisfaction threshold. The resiliency of the
system provides an ecosystem adjustment capability measured in terms
of the relative demand level above the threshold for that demand.
Unlike the first system, where the measures are generated
directly from the comprehensive goals, a set of measures must
be selected in terms of the area-specific needs and desires
of the society in the region. The general forms of these measures
will be similar to those of the plan above with the exception
that a minimum acceptable demand value rather than maximum
achievement goal is set.
Of greater difficulty for both systems is the setting of
relative weights to combine the composite set of measures.
However, this need not be accomplished as part of the SOS Model.
Instead an iterative process can be carried out, which measures the
state of the system as a set of criteria and then adjusts M§P fund
levels among the production components until all thresholds are met
or a suboptimized minimum miss-distance is projected.
70
-------
An extension of the procedure of setting thresholds of
minimum acceptable values is to have the threshold values
change based on population expectations. If for any period
of time a value of a demand measure remains high as compared to
its threshold, experience suggests that the consumer changes
his level of want to a level of need. This is equivalent to
increasing the threshold to a new set of demand thresholds
representing society desires rather than a more basic set of sub-
sistance needs. In a similar vein, if for a period of time, a pop-
ulation must go without a level of goods or services that it desires, a
reduction of the consumer preference is likely. To account
for this phenomenon, the thresholds of each measure can be auto-
matically set in the SOS Model as a function of simulated historic
output trends .
TMEAS(n,t) = f (MEASii^) ; 7-1,2 ,.. .t-1)
where TMEAS(n,t) is the threshold value of QOL measure n
at t and ,
MEASn(7") is the achieved value of the measure at a
previous time T
-------
Is Realized
SOS Greater Than
Desired SOS?
No
Make
Short Term
Adjustments
Is
Adjustment
Satisfactory?
Make
Long Term
Adjustments
No
V
/"" Ls ^\
f Adjustment ]_
V Satisfactory?/"
No
V
Adjust
Goals or
Thresholds
Yes
Yes
FIGURE 7
SYSTEM ADJUSTMENT PROCEDURE
72
-------
(c) rescheduling the annual transfer of funds from one
sector to the other where deficiencies exist and
then repeating procedure (b). This, of course,
is used only if all components of one sector are
not deliquent and hence can give up growth funds.
(d) adjusting the rates and direction of net migration
to reduce per capita consumption needs if significant
unemployment exists in the region.
If none of the long term adjustments produce a satisfactory
correction of the projected state of the system, one final form
of adjustment is made to permit the simulation to continue.
In this situation the system goals (for the comprehensive
plan analysis simulation) or the level of dissatisfaction
thresholds (for the operating system alternative) are modified
to lower levels. This will allow a possibility of maintaining
the regional growth projections as a stable situation at the cost
of a less acceptable level and quality of life.
Figure 7 illustrates the adjustment procedure.
Resource Base Adjustments
Finally, the resource base adjustments are melded into
the general carrying capacity model. The following diagram
of the adjustment algorithm is illustrative:
Resource
Demand
V
A
Resource
Supply
A
Reduce
Supply To
Demand
Short-
Run Ad-
justment
FIGURE 8
Resource Base Adjustment Process
73
-------
The system reaching a natural limit to its carrying
capacity may merely suggest a short run imbalance of the
demand and supply of a specific resource. This imbalance
can be corrected by changing the rate of extraction and
distribution of the resource in question. If, on the
other hand, the reaching of a depletion symptom at a par-
ticular point in time heralds the beginning of a serious
shortage of a particular resource, there are several
possible responses:
• The rate of extraction could be increased, because
increasing costs increase economically available
reserves.
• More supplies could be demanded from other regional
systems at higher costs.
• Adjustments may be lower resource use by substituting
a more available and lower cost resource mix.
74
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SECTION VII
THE EXAMPLE MODEL (SOS-1)
The State of the System Model provides a new capability
to examine a region of national or subnational areas for large
countries as a human ecosystem. To represent an ecosystem, the
model has a rather complete description of the present state
of the regional carrying capacity plus feedback procedures
for adjusting growth as a function of the physical needs
of the population, technocratic improvement of resource and
eco-media utilizaiton, and area-specific societal value
judgments and demands. Additionally, it allows for a stable
adjustment of processes within the region to account for
limitations of resources while maintaining viable historical
trends.
MODEL CHARACTERISTICS
As a first step in determining the utility of the SOS
Model, an example formulation of the model, SOS-1, has been
developed and programmed that has the following major
characteristics:
• Three growth sectors are represented: the
population of the region with its growth in terms
of both size and per capita demands, five pro-
duction components of the private sector, and
five services components of the public sector.
• Up to 15 level and quality of life demand
measures can be set. They must be of the form
of satisfaction as based on output production
per capita for various combinations of output
components.
• Up to 20 resources can serve as surrogates for
representing the caracteristics of the six
resource categories and the two ecosystem media.
It is not required that all categories be
represented nor need any specific resource be
included.
• Any number of substitution formulations for any
resource can be set. These substitutions can
include up to five resources. Since the resource
for which the substitution is to be carried out can be
included in the substitution, partial substitution
is possible. The substitution algorithm includes
the setting of a time length (in years) to fully
perform an activated substitution, thus allowing
build-up of impact and a capability of overreaction
of adjustments.
75
-------
• At least one, and in most cases, more than one input/
output function to represent the mix of resources
consumed in the production of each component output
can be set. One of these for each component is
marked as active at the initiation of the simula-
tion. Also, each production function has an
associated time that is required to retool for full
application of the function.
• The resource assumptions are as given in the dis-
cussion of resources earlier, except no R§D break-
through or time-dependency for improved resource
utilization within an input/output function is
considered in the example model. These assumptions
are listed at the end of Section 4.
• The methods for measuring the state of the system
and for adjusting operating funds levels between
production components, substitution of resource
allocation and utilization functions, and modifica-
tion of society demands, are modeled on the second
system form (laissaz-faire suboptimization) discussed
earlier. This will include consideration of eco-
system concepts that include society demand thresholds
and system resiliency plus historical trend main-
tenance of the division of M^P funds among components
given that the minimum demand thresholds are met.
• Model operating characteristics for the test simula-
tion are SOS operation for 25 annual cycles using data
for a region similar to the United States with
the beginning situation data similar to 1970
statistics.
• Since the model is expected to be operated as a
regional model - where the region is national or
subnational - the region does not have a high degree
of closure. Elements that may be candidates for
crossing system boundaries are resource imports,
finished goods exports and imports, population
migrants, and flow of investment funds. The model
must account for each of these and must scale the
level of the exogenous activity using model data.
Thus the algorithms and data base can be varied to
represent trade agreements, the state of the system
in other regions, other region resource shortages,
import and immigration quotas, etc.
• The present model structure is not at a detailed level
but represents its various elements at aggregate
levels. Additionally many of the detailed inter-
actions of the components are not simulated or are
76
-------
represented in a much simplified form; e.g., the
procedure by which the manufacturing component outputs
affect volume of commercial outputs. Many of the
elements such as population demands and resource
types are depicted by the use of indicators and
surrogates. It is anticipated that later model
versions will include critical elements and relation-
ships as determined from empirical analysis of
early model results.
• A major assumption in the model is the representation
of many functions, such as the output coefficients
that produce changes in consumer-need partitions,
as linear or constant when even the most cursory
analysis refutes this assumption when the entire
range of possible data values is considered. In this
experimental model, general trends in expected
ranges of data are to be explored and in these ranges,
small compared to the total possible ranges, much of
the empirical data suggests that the assigned forms
of fit are reasonable. A corollary to these assumptions
is the set of assumptions that suggests constancy of
many of the relationships over time. Once again the
range of the practical analysis is severely limited
by this assumption but in the first applications of
the model, using total simulation periods of about
25 years, the assumption provides an appropriate level
of structural detail.
MODEL STRUCTURE
The model describes the state of the regional system and
processes required system adjustments on an annual basis. The
general procedure is to operate on the existent data base and
the state of the system descriptors as given for the last cycle
in order to, first, describe the system for the current cycle
and, second, to affect needed short-term (this cycle) and long-
term (affecting future cycles only) system adjustments. The
general steps required in an SOS cycle are:
DESCRIPTIVE MODULE
• Describe the population,
• Describe the availability of maintenance and
operating funds, resource utilization and output
levels of the production components,
• Describe the state of the system, in terms of:
77
-------
resource depletion levels,
quality of ecosystem media,
attainment of social demand goals (measures of level
and quality of life),
SYSTEMIC MODULE
• Adjust critical resource usage by substitution of
lower cost replacement resource mixes and, if
appropriate, expansion of ore extraction and/or
recycling facilities in subsequent cycles,
• Adjust short term procurement for additional goods
using maintenance or export funds,
• Adjust long-term M§P funds growth trends to meet pro-
jected demands for increased output of components and
sectors,
• Adjust demand thresholds in future cycles to realizable
levels,
• Reset the data base for the next cycle.
The logical flow through these eight steps is provided in
Figure 9. Each step of the example model, SOS-1, is dis-
cussed in turn below. Additionally, Appendix 2 provides
detailed narrative flow charts of the steps of the model, and
Appendix 3, the detailed program listings.
THE DESCRIPTIVE MODULE OF A CYCLE
A full description of the regional human ecosystem for
a year is developed by the first three steps of the model
simulation. The data, base used in development of this des-
cription is loaded initial information. After the
first cycle, nearly all data are modified as part of the last
step of the last cycle operation to reset for the next cycle.
The description of the system includes:
Population Growth
• Total population
• Total net immigration effect
• Population in each age cohort (4)
• Annual death rate by age cohort
• Cohort populations, each partitioned into
six consumption groups
78
-------
0) ^
rf3 QO
4-) \
"4-1
XI O
•H a
M 0) 0)
U -P -P
in rt t/)
^ \ (f>
1 /
1
stitute
Economic
Feasible
3 M-i PI
C/D -H rt
CD
xpand
Deserves if
conomic and
easible
M-l K W MH
A
0)
0)
o
o
IX)
PI
•H
4->
rt
3-H
^ 0)
ft
PI CO O
O -P
H rt rH
P u rt
U O £
O 10
H t3
3T3rH
•r-» o cs bo PS
t3 M 0 H
en
O
O
w
nj
a,
w
79
-------
Public and Private Sector Components
• Expenditure of funds for generalized mainten-
ance and production processes for each production
component
• Output units produced in the region
• Unsatisfied regional demand for output units
• Unit production costs
State of the System
• Attainment of demand satisfaction
• Resilience level above threshold levels of demands
• Unsatisfied demand levels
• Resources in a reserve depletion warning status
• Treatment level required for ecosystem media
The detailed procedures for calculating each of these
values and other parameters are discussed in the descriptions
of Model Steps 1-3.
Step 1: Describe the Population
This first step of an SOS cycle provides the full descrip-
tion of the human population of the region for the year of
interest (t). The general system flowchart for Step 1 is
provided as Figure 10. All data requirements and their sources
are listed in Figure 11.
Assumptions
The primary assumptions for developing the demographic
data are: '
The migrants into (or out of) the region have the same
demographic characteristics as the nonmigrating population.
Hence, at least as a net effect, the long-standing pattern
evidenced in U.S. immigration patterns of early arrival of
workers' of a family later augmented by the full family is not
considered here. However, under the assumption that the time
delay in such a process is short and that the population growth
rate due to immigration is not large compared to the total
population base, this assumption is justified.
80
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Begin
Calculate
Total
Population
W
/For Each\
I Age Cohort/
c
\t
]?or Each Age
And Partition
e
y\t
\
For
A p1 o
f
Each^
I/ear y -*
Calculate
Deaths for
Age
Calculate
Population
of Age
For Each Partition
Ste
ition V
\t
> 2
Calculate
Total Deaths
-5*
Calculate
Relative
Population
Calculate
Partition
Population
Calculate
Total
Population
Calculate
Population
FIGURE 10
STEP 1 FLOWCHART
81
-------
FIGURE 11
STEP 1 PARAMETERS
Name
TPOP(t)
BRTH(t)
DETH(t)
NTMG(t)
POP(y,t)
POP(y,-t-l)
DTHPT(y,t)
GPOP(y,t)
PDTH(y)
GDTH(y,t)
RPOP(y,k,t)
a(j,k,y)
OUTPT(j ,t-l)
POP(y,k,t)
POP(y,k,t-l)
POP(k,t)
Definition
Total population at time t
Birth rate at t
Death rate at t
>let immigration rate at t
Population in region of age y at t
Last year population of y
Deaths of y at t
Population of age group y at t;
y, * y * y2
Fraction of deaths occurring in age .
y population
Deaths in y at t
Change in population of kth partition
of y at t
Coefficient of output j contribution
to change in kth partition size for
y age grouping
Units of production of component j
last year
Total population of y in k at t
Total population of y in k last year
Total population in k at t
Source
Calculated
Step 8 (t-1)
Step 8 (t-1)
Step 8 (t-1)
Calculated
Step 1 (t-1)
Calculated
Calculated
Constant
Calculated
Calculated
Constant(10,6,'
Matrix
Step 2 (t-1)
Calculated
Step 1 (t-1)
Calculated
82
-------
The distribution of death rates among age cohort is
assumed to be proportional to the relative population of the
group. Hence, throughout the period of simulation a constant
death rate for an age cohort can be set.
Change in the size of the six consumption partitions of
each age cohorts has been related directly to only the annual
output levels of private and public components. While this
indicates no explicit direct tie to the quality of life
measures of the system capability to meet population demands,
defined in Step 3. following, these are also related to the same
component outputs, usually on a per capita basis. Thus, the
reaction of population partition sizes do reflect the system
reaction to level of attainment of quality of life demand
thresholds since the reactions have the same independent
variables.
Algorithms
The total population within the system for the current
year, t, is last year's population plus its increases due to
the birthrate and net migration rate minus the loss due to
the annual death rate.
(1) TPOP(t)=TPOP(t-l)*[l+BRTH(t)+NTMG(t)-DETH(t)]
All rates can be adjusted due to the present capability of the
system outputs to meet the population demands; these adjustments
are performed in Step 8 of the previous cycle.
The next calculations develop for each age-year of the
population, the total deaths and the age-year populations.
An age-year represents for i=l,2,...,64 all population at
an age in the range (i-l,i) and for i=65 (i-1, greatest age).
The death population is':
(2) DTHPT(y,t)=POP(y-1,t-1)*DETH(t)*PDTH(y)
for y=l,2 , ... ,64
DTHPT(<64,t)=[POP(64,t-l)+POP(<64,t-l)]*DETH(t)*PDTH(^64)
The living age-year population at t is:
(3) POP(0,t)=TPOP(t-l)[l+NTMG(t)]*BRTH(t)
POP(y,t)=POP(y-l,t-l)*[l+NTMG(t)]-DTHPT(y,tr
for y=l,2,3,...,64
83
-------
64,t) = [POP(<64,t-l)+POP(64,t-l)]*[l+NTMG(t)]
-DTHPT(<64,t)
For the model use in other procedures, most population
data is in terms of four age-groups. The age groups, y, used
in the SOS-1 Model are:
Z. age-years
1 1-17
2 18-24
3 25-64
4 64
The cohort annual death rates and living cohort populations
are simply summations over the included age years.
y2
(4) GDTH(y,t)=£ DTHPT(y,t)
n
where y=[ylf y2]
?2
(5) GPOP(y,t) =£ POP(y,t)
Yl
As a final set of calculations of Step 1 the cohort popula-
tions, GPOP(y,t) are divided into 6 partitions. These
partitions serve two roles in other Steps of the model.
First the resource of work units of paid workers and the
potential to expand the work unit size is represented by
setting the numbers of population in each cohort that are
workers in training, paid workers and unpaid workers. Second,
the six partitions can be used to represent differing demand
levels for the public and private sector output units.
The changes in distribution of cohort population among the
partitions are based on weighted linear combinations of the
production component outputs of the past period. The relative
(or unnormalized) distribution within cohort among the
partitions are:
(6) RPOP(y,k,t) = y a(j,k,y)*OUTPT(j,t-l)
(_>
j
where k is the partition index k-l,2,...,6 and j is the
production component index
The actual population of a partition in cohort is-:
84
-------
(7) POP(y,k,t)=POP(y,t)*[RPOP(y,k,t)/ RPOP(y ,k,t) ]
k
Finally the total population within a partition is the sum
of the partition population over all cohorts.
(8) POP(k,t) =
y
Population Description Outputs
The output of each annual cycle of Steps 1, 2 and 3 can be
suppressed at the submission of a computer run by setting the
program print option parameter, NPRNT1=2.0 (see Appendix 4).
If the data output is not suppressed, for each cycle the
demographic output table as formatted in Figure 12 will be
printed.
Additionally, at the end of the simulation, population
summary data appears in two table/graph sets. In the Summary
Set, a ratio of the system's total population, normalized
to the initial total population (TPOP(O)), is provided as one
of the nine summary statistics as a yearly tabulation. In
the second set, Population, is provided for each year, the total
population, and the age-group population as a ratio of TPOP(O).
Step 2 : Describe the Production Components
Based on the projected level of funds available for the
maintenance and production functions of the components each
year and the present procurement costs associated with resources,
determine :
• Maintenance costs for each component
• Total resource and labor unit costs for each component
• Units of output for each component
• Present (beginning and ending) reserve levels and
unit costs associated with the system resources
• Resource recycling levels, and
• Occurrance of stock depletion warning levels.
The general system flowchart for the Step is given in
Figure 13 and all data required by the Step are in Figure 14.
85
-------
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87
-------
Name
M§PFD(j,t)
M§PFD(j ,t-l)
RGROW(j,t)
RMNFACCJ ,t)
RMNNOR(j)
DEFMN(j,t-l)
RMNECO(j,t)
REXCAP(j,t)
REMAIN (j,t)
MNFD(j ,t)
PRDFD(j ,t)
RUCST(r,t)
RUCST(r,t-l)
RUCST(r,t-2)
FIGURE 14
STEP 2 PARAMETERS
Definition
Funds available to component j
at t
Funds available to last year
Rate of funds growth for j at t
Rate of funds used to maintain
facilities offsetting depreciation
at t
Normal rate used to maintain
facilities of j
Amount of facility maintenance of j
deferred last year
Rate of funds used to maintain
ecosystem media prorated for j at t
Rate of funds used to increase
facilities at t based on past j
output
Rate of funds used for maintenance
of j at t
Total funds to be used for mainten-
ance of j in all categories at t
Funds to be used for production of
j at t
Mean resource unit cost for r at t
Mean resource unit cost for r last
year
Mean resource unit cost for r in
year t-2
Source
Calculated
Step 2, t-1
Step 6, pre-
vious t
Calculated
Constant
Step 5, t-1
Step 8, t-1
Step 8, t-1
Calculated
Calculated
Calculated
Calculated
Step 2, t-1
Step 2, t-2
88
-------
Name
UTIL(r,j,t)
UOCST(j,t)
KFACT(j)
OSCT(j,t)
ROUTPT(j,t)
OUTPT(j,t-l)
RESOUR(r,j,t)
RESOR(r,t)
STKDEP(r,t)
ESTCK(k,r,t)
REREC(r,t)
PILE(r,t)
STKEX(r,t)
STKRE(r,t)
MRCST(r,t)
MRCST(r,t-l)
FIGURE 14 (CONT)
STEP 2 PARAMETERS
Definition
Required amount of resources to
output one unit of j using current
production formula(s) mix
Unnormalized unit cost to produce
output of j at t
Unit cost normalizing factor for j
Unit cost to produce output of
component j at t (normalized)
Rate of increased output over past
cycle at t
Number of units produced by j, last
year
Units of resource r used by j at t
Units of resource r used all j at t
Fraction of resource r reserves
expended at start of cycle t
Fraction of resource r reserve
expended at end of t
Ratio of resource recycled to
extracted at t
Amount of total reserve available
at unit cost for t prior to depletion
Amount of resource extracted at t
Amount of resource recycled at t
Maximum unit cost of resource at t
Maximum unit cost of resource, last
year
Source
Step 8, t-1
Calculated
Step 2, Cycle 1
Calculated
Calculated
Step 2§5, t-1
Calculated
Calculated
Step 8, t-1
Calculated
Calculated
Step 8, pre-
vious t
Calculated
Calculated
Calculated
Calculated
89
-------
Name
ECST(r,t)
MECSTR(r,t)
ECSTR(r,t)
COMEXP(j,t)
FLAG(r,t)
VFLG(k,r)
MOUTPT(j ,t)
FCOUTU,(j,t)
FIGURE 14 (CONT)
STEP 2 PARAMETERS
Definition
Mean unit cost of r at t
Maximum unit procurement cost of
r at t
Mean unit procurement cost of
r at t
Cost of facilities expansion in t
for component j
Existance of depletion warning this
year for resource r
Depletion levels of existant stock-
pile on which warnings are set
Maximum output level of j prior to t
Fraction of existant facilities of
j in production at t
Source
Calculated
Calculated
Calculated
Calculated
Calculated
Constant
Step 2, pre
vious t
Calculated
90
-------
Assumptions
The general resource functions listed at the end of the
fourth section of this paper are applied here in the development
of data and cost functions for the eight resource categories.
Maintenance to offset depreciation of facilities and the
ecosystem are assumed to be linear functions of the operating
levels of the various components as produced in the last cycle.
Capital expansion costs are set based on whether the
output level of a component is greater than the output of any
previous cycle. If so, an expansion cost as a linear function
of the difference in outputs is set and spread evenly over
ten years of annual payment. This cost is included in the
maintenance portion of M§P funds.
Many of the data approximations are performed here as
simple interpolations, reducing computer running time. When
more exacting algorithms and data are introduced, refinement
of estimating procedures with SOS using iterative procedures
should be included.
Algorithms
Many of the calculations of this step are performed
multiply. For example a component calculation must be repeated
for all ten components; a resource calculation for each of the
20 resources. Throughout this and subsequent steps the index
j will be used for the 10 components of the production sectors
and index r for resources.
The first calculations of Step 2 generate the new level
of M§P funds available in time period t, and then determine
the level spent on the maintenance component with the residue
available as the production funds. Note that the main-
tenance is the generalized form discussed in the general
model formulation (Section 6), and includes capital expansion
funds; capital maintenance, current and deferred; and ecosystem
effluent treatment costs.
Available operating funds for component j are:
(9) M§PFD(j,t)=MSPFD(j,t-l)*[l+RGROW(j)]; j=l,2,...,10
The funds used for maintenance of existing facilities,
as a fraction of total available funds are the sum of this
years value and funds needed due to deferred maintenance last
year.
91
-------
(10) RMNFAC(j,t)=RMNNOR(j)+[DEFMN(j, t-1)/M§PFD(j,t)]
The total funds for all forms of ecosystem maintenance, as
a fraction of M§P funds are the sum of fractions needed for
maintenance, ecomedia treatment, and facility expansion.
(11) RMAIN(j,t)=RMNFAC(j,t)+RMNECO(j,t)+REXCAP(j,t)
(12) MNFD(j,t)=M§PFD(j,t)*RMAIN(j,t); j = l,2,...,10
The funds available for production costs are the total funds
reduced by the maintenance funds.
(13) PRDFD(j,t)=MSPFD(j,t)/(l+RMAIN(j,t)) j=l,2,...,10
The second major set of calculations of Step 2 provides
the setting of an estimated unit cost for producing one
output unit of component j and then schedules the total level
of output units that will be produced by the system. Prior
to these calculations'the estimated mean procurement cost to
components for each of the 20 resources must be made. The
estimate is based on the assumption that the cost per resource
unit will maintain the same rate of increase noted in the
previous year.
(14) RUCST(r,t)=2*RUCST(r,t-l)-RUCST(r,t-2)
for all r.
For each component there is a current mix of resources
that are required to produce one unit of output, the set
{UTIL(r,j,t)]. An unnormallized unit cost to produce one
level of output can be produced by:
UOCST(j,t)=£uTIL(r,j,t)*RUCST(r,t)
This volume is then normalized (or scaled) using a normalizing
factor developed by SOS-1 in Step 2 of the first cycle of each
simulation. In order to be able to compare growth among the
several components that produce diverse goods and services, a
common form of output is required that gives relative output
volume rather than a strict listing of products. For this
reason the normallizing procedure is based on the model scaling
of all output levels of the first cycle to be 1,000 units (see
the data discussion of the next section). Under that con-
dition the normalizing factor, KFACT(j), is developed as:
KFACT(j)=PRDFD(j,1)/1000.*UOCST(j,1)
92
-------
Then the normalized output unit cost, OCST(j,t), of any cycle is:
(15) OCST(j,t)=KFACT(j)*UOCST(j ,t) j=l,2,...,10
This use of a normalizing cost factor deserves further
explanation in order to explicitly state its assumptions. The
production formula for component j, [UTIL(r,j,r)] includes only
20 surrogates of resources. It is decidedly easier to calculate
present day resource costs in terms of the known present day
costs of the resource surrogates than to determine in detail
all resources and their costs for, say the commercial component
and then assign each resource to a surrogate category that
has a single mean cost set. Therefore, under the assumption
that the set of resource surrogates are appropriate and the
second assumption that the mix of surrogates in the production
equation is generally balanced, the alternate procedure of
developing an unnormalized cost is used. This cost, if the
resources are properly balanced, should have its component
costs in approximately the ratios that are observed in the
base year data. Then the normalization maintains this ratio
and allows the scaling of the diverse set of component outputs
to an output volume that is easy to interpret as trends in
later cycles.
The output scheduled for each component, scaled to the
original value of 1,000, is:
(16) OUTPT(j ,t)=PRDFD(j , t)/OCST(j , t)
Based on the scheduled output levels it is now possible
to calculate the resources utilization requirements of the
system, including the labor force, land use, and media treat-
ment requirements. First the resource requirements for each
production component are calculated and then these are summed
to give the system's total requirements.
For each (j,r) combination; j = l,2 ,. . . ,10 ; r=l,2 ,3,...,20 ;
(17) RESOR(r,j,t)=OUTPT(j,t)*UTIL(r,j,t)
and for each resource r;
(18) RESOR(r,t)= £_RESOR(r,j ,t) .
j
The status of resource data at the end of the cycle, and
for mean values, can be calculated. Data of interest are
unit procurement costs, end of period stock status, stocks
extracted, stocks obtained by recycling, and cost to extract
93
-------
a unit plus recycle the associated ratio of stocks from pro-
duction debris. All of these calculations are based on the
assumptions used in determining stock levels and costs pro-
vided at the end of Section 4 plus the simplifying assumption
on calculations that simple interpolation procedures can
be used, rather than iterating for more exact solutions. Each
of the following calculations are done for each resource. The
information produced does not affect the scheduled production
levels that are set above but are used for display of
resources availability and costs for the year and in
the resource adjustment calculations that appear in Step 4.
The end of cycle stock depletion level is the fraction
of the total stockpile that was originally available to the
system at the present unit extraction cost. This is not
necessarily the stockpile available at t=0. It is the fraction
that was depleted at the beginning of the cycle (and end of
last cycle) plus the fraction of stock that is extracted and
used during the present cycle.
(19) ESTCK(r,t)=STKDEP(r,t)+RESOR(r,t)/[PILE(r,t)*
[l+REREC(r,t-l)]]
The actual quantities of stock that are extracted and
are recycled are calculated as:
(20) STKEX(r,t)=PILE(r,t)*[ESTCK(r,t)-STKDEP(r,t)]
(21) STKRE=RESOR(r,t)-STKEX(r,t)
The recycling rate associated with the end of cycle
stock depletion levels for this cycle, and used in the next
cycle calculations is a function of the ESTCK value since
the unit costs are directly associated with ESTCK.
(22) REREC(r,t)=K4(r)+K5(r)*ESTCK(r,t)2
where K4(r) and K5(r) are constants defined in the next section.
The maximum unit extraction costs are also a function of
the value of ESTCK. In order that the system not consume
resource stocks that are not available, the regulatory mechanism
is set within this function by causing rapidly escalating
costs as the depletion of the existant stockpile is approached.
Two escalating factors are included: one is a permanent unit
cost increase while the second, used only if overusage of
resources appears imminent, produces a temporary severe escalation
of the unit costs. The general unit costs equation to represent
the end of cycle or maximum unit costs is:
94
-------
(23) MRCST(r,t)=[Kl(r)+[K2(r)*ESTCK(r,t)K3(r)]]*TEMP(r,t)
where TEMP(r,t), the temporary escalatory factor is
(24) TEMP(r,t)=Max[1.0,[[l.+K6(r)]/[l.-ESTCK(r,t)]]K7(r)]
In the experimental model data base K6(r) = .90 except for
labor where K6(r) = .92, and K7(r) = 3 for nonrenewable resources,
K7(r) = 1 for renewable resources and K7(r) = 2 for labor.
The mean unit extraction cost is interpolated between.
the maximum values for last cycle and this cycle.
(25) ECST(r,t)= . 5[MRCST(r,t)+MRCST(r,t-1)]
Since it is assumed that the extraction unit costs include
the cost for producing the associated recycled ores, the unit
procurement costs are set as:
(26) MECSTR(r,t)= MRCST (r,t)/[l+REREC(r,t)]
(27) ECSTR(r,t)=ECST(r,t)/[l+REREC(r,t)]
The final calculation that is general to all resource data
is determination as to whether the stock depletion level has
reached a point where it is considered critical. Four critical
points can be set for a test of the present range of depletion
for each resource; if the value was passed during the current
cycle, a critical depletion flag is set to signal the need
in Step 4 to consider available, economic adjustments of stock
availability and utilization. The form of the test is:
(28) If ESTCK(r,t-l)
-------
For agricultural levels it is assumed that the initial
output levels of 1,000 produces an annual 1001 replacement of
initial food stocks and an annual 5% replacement of fiber
stocks. Thus, for all cycles a third term is subtracted from
equation (19) for these two resources equal to:
K8(r)*OUTPT(j,t)
where r is food or fiber
and j is the agricultural production component
For all renewable resources (e.g. land, labor, electricity)
after the stock depletion tests are made as shown in equation
(28), the stockpile size is returned to its original value as
of the start of the cycle.
The usage of existant production facilities and the need
to expand these facilities is the last set of calculation in
Step 2. Throughout the simulation, for each production com-
ponent, the maximum output in any previous cycle is maintained
(MOUTPT(j,t)). The first calculation provides a test of the
amount of facilities that are used in this cycle:
(29) FCOUTU(j,t)=OUTPT(j,t)/MOUTPT(j,t)
If FCOUTU(j,t) is greater than 1.0 the facilities must
be expanded to account for the excess. The cost of expansion
is:
(30) COMEXP(j ,t)=OUTPT(j,t)*[FCOUTU(j,t)-1]*EXCST(j,t)
where EXCST(j,t) is the expansion cost for production of one
unit of component output.
These costs are spread over a 10 year period and are added
to other costs assigned these years from past expansion. Hence
for all t'=t + i; i-i,2 ,2,...,10
(31) REXCAP(j,t')=REXCAP(j,t')+0.1*COMEXP(j,t)
Production Component Description Outputs
If the cyclic data output for Steps 1, 2, and 3 are not
suppressed, component data and resource data are printed as
formatted in Figures 15 and 16. In the tabulation a Com-
ponent or a resource number is associated with the element's
name; in later tables or diagnostic messages only the number
is printed. For resources having no name, no data is being
processed; these numbers are available for later expansion of
SOS-1 data bases, e.g. addition of a fourth energy resource
category. Units for all data entries are discussed in the next
section. These values normally follow the following scaling rules
96
-------
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98
-------
Funds and unit costs are in million dollar units.
Production units are scaled so that t=l production
is 1000.
Resource stockpile units are scaled so that t=l reserve
stock is 10,000 units, except for labor.
Additionally, at the end of the simulation, component
inputs and outputs are presented in three table/graph sets,
while resource usage appears in five table/graph sets. In all
cases the data is presented as a ratio to the t=l values,
thus allowing simpler comparisions between the diverse categories.
In the Summary Set, columns three and four provide the
annual expenditure of M§P funds for public components and pri-
vate industry components, respectively. The actual statistic
is:
where j ranges from 1-5 for public and 6-10 for private components
Note that these values do not measure real output of goods
but represent the relative level of funds committed to the
components. Columns 6-10 provide similar composite measures
of resource usage; in each case the statistic is analogous
to the form above except actual units of usage are considered.
• Column six is average relative use of the 6 natural ores
• Column seven is average relative use of the 3 energy
types
• Column eight is average relative use of the 2 agri-
cultural resources plus the 3 land use categories
• Column nine is relative use of worker units
• Column ten is average use of treated effluent units
of water and air media.
In the supporting table/graph sets these data are dis-
played in greater detail. In each case there is a column or
symbol that provides the relative annual values for each com-
ponent or each resource.
• Table Number Two provides the public sector output
units.
• Table Number Three provides the private sector output
units.
99
-------
0 Table Number Four provides the natural resource
usage data.
• Table Number Five provides the energy and agricultural
usage data.
• Table Number Six provides the work unit unemployment
rate.
• Table Number Seven provides the land use and media
treatment.
Step 5: Describe the State of the System
From Steps 1 and 2, much of the regional description is
provided in terms of population and production growth, plus
usage and present stock and unit cost levels for system resources.
Step 3 completes the evaluation by comparing the current demand
levels for goods and services to the annual output of the produc-
tion components. The form to express population demand is
development of a set of area specific measures giving per capita
usage for combinations of outputs. The users (the per capita
size) are expressed as total population or as one or more
partitions of the population (see Step 1 for partition defini-
tions). For each of these measures, a threshold, or minimum
acceptable per capita output level, is set initially and adjusted
as appropriate by the model operation. Comparison of the actual
annual values for the measures with the thresholds allows
expression of the region in terms of an ecosystem. Data
provided can show:
• System resilience for each measure
« System processes acting as limiting factors
• The severity of the limiting processes
• Insight for adjustment of relative levels of the
system processes.
The general flowchart of the Step calculations and examples
is provided as Figure 17. Figure 18 gives data requirements
ans sources.
Assumptions
It is assumed that all demands of the population can be
translated into a series of demand levels for production goods
and services. Hence, all measures can be set up as linear
combinations of output levels divided by the consuming popu-
lation size.
100
-------
Begin
FIGURE 17
STEP 3 FLOWCHART
For Each
Measure
Done
(
Done
V
Step 4
Calculate
Value
Calculate
Resiliency,
Delinquency
Level
Assign Level
Of Delinquency
To Components
>y
f
For Each "\ ^
Component^/ ^
'
\
Determine
Maximum
Delinquency
Level
Develop
Cumulative
Delinquency
Levels
101
-------
Name
MEAS(n,t)
Cnj
OUTPT(j,t)
POP(n,k,t)
TMEAS(n)
RESIL(n,t)
DOUTPT(n,j,t)
CFAIL(n,j,t)
COUNT(n,t)
FIGURE 18
STEP 3 PARAMETERS
Definition
The value of the nth measure at
time t
Coefficient relating output of j to
measure n
Output units of j at t
Total population in partition k at t
used in measure n
Established threshold (minimum) value
for n
Relative level of measure n over
threshold at t
Required additional output of j to
meet threshold in year t
Cumulative deficient output since
threshold was missed for n at t
Years of consecutive misses of thres-
hold for n at t
Source
Calculated
Constant
Step 2
Step 1*
Step 7, pre
vious t
Calculated
Calculated
Calculated
Calculated
*POP(7,t) = TPOP(t)
POP(8,t) = TPOP(0 ),t=year preceding first year in analysis.
102
-------
The form of the population demand thresholds are assumed
to represent perceived needs; the level of need that is perceived
is assumed to be a function of the past satisfaction of the
demand. Therefore, if oversatisfaction has been maintained for
a period of time (in SOS-1 set as two years) the threshold level
will be increased to that past value. Similarily, if all adjust-
ments of resources and funds distribution cannot produce a system
that appears to regain resiliency, the levels of thresholds
may be lowered until an absolute threshold level is reached.
It should be noted that the description of the State
of the System does not require a arbitrary combination of
the several measures into a single value. On the contrary,
each measure allows measurement of a selected area of quality
of life as described in demand satisfaciton terms. Since
later Steps include adjustments within and between component
outputs based on the relative resiliency shown for each measure
value, it is appropriate to use a large set of measures, each
measuring a discrete and narrow segment of demand satisfaction.
Thus, although the set of measures will include demand for all
component outputs, each measure should show demands for only
one to three component outputs in order that the later adjust-
ment processes can diagnose the problems as they exist in
specific components.
While the set of measures must cover the spectrum of
interests, it is not necessary that the measures be independent
of each other. In fact, since the measures are not combined
into a single scalar value, if one measure was the exact
duplicate of another, no added weight is produced for this
measure in the later Steps adjustment processes.
Algorithms
The first procedure of Step 3 calculates the present value
assigned to each of the active measures for this time, t. All
measures are of the form:
(32) MEAS(n,t)= [Cnj*OUTPT(j , t) ] /POP(n,k,t)
j
where POP(n,k,t) is the assigned partition of population for
measure n,
and n= 1,2, 3,. ..,15.
To determine how well the value of the measure satisfies
the population demands a test is made of the form:
(33) kn=MEAS(n,t)-TMEAS(n)
103
-------
If k is greater than or equal to zero all required demand
is satisfied and the system resiliency for measure n is set
equal to the excess in output available to required output;
this is computed as:
(34) RESIL(n,t)=MaxfO,kn/TMEAS(n)]
If kn is less than zero the production system was unable
satisfy all required demands associated with measure n. For the
unsatisfied values a set of calculations are carried out to
be used in later Step adjustment procedures. First for each
component having a non-zero value for Cnj, there is assigned
a pro rata delinquency of output:
(35) DOUTPT(n,j)=[kn*POP(k,n,t)]/Cnj if Cnj*0
=0 if Cnj=0
The cumulative delinquency and time since the last year when
MEAS(n,t) was resilient is calculated:
(36) CFAIL(n,t)=CFAIL(n,t-l)+DOUTPT(n,j)
(37) COUNT{n,t)=COUNT(n,t-l)+l
For all measures where kn=0 the values of DOUTPT(n,t),
CFAIL(n,t) and COUNT(n,t) are set to zero.
After all calculations associated with the individual
measures are complete, a set of calculations to determine the
maximum unsatisfied demand for output of each production
component is carried out. For each component j, a test is made
to determine the largest value of delinquency in output and
the value of n associated with that value
(38) N(j)=n[Max[DOUTPT(n,j,t)]]
n
Then for that value of n, the period and cumulated
amount and years of delinquency are calculated:
(39) DOUTPT(j ,t)=DOUTPT(N(j) , j ,t)
(40) CFAIL(j,t)=CFAIL(N(j),j,t)
(41) COUNT(j,t)=CQUNT(N(j),j,t)
It should be noted that if no level of delinquency was
noted for j in any measures, then (39), (40) and (41) all
yield zero.
104
-------
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105
-------
With the conclusion of Step 3 for a given year all elements
of the regional system are described; thus the descriptive
module of the SOS-1 system is completed.
State Description Outputs
If the cyclic output of Steps 1, 2 and 3 are not suppressed
a tabulation of the values of each measure and the level of
resilience or delinquency is produced as shown in Figure 19.
Note that a negative value for resilience is equivalent to the
level of delinquency.
THE SYSTEMIC MODULE OF A CYCLE
General Procedure
Within the first three steps of a cycle a number of
elements may have been described as unsatisfactory when
the system values were compared to its goals or thresholds.
The next four steps provide a set of mechanisms for adjusting
these components of our human ecosystem in order to adjust
values this cycle or to reorient the system processes for subsequent
cycle adjustments. Of these four steps, the next step, adjust-
ment of the resource base, operates independently of the
other adjustments. It is driven by its own special set of
diagnostic signals, the resource stock depletion warnings,
as developed in Step 2, equation (28).
The Steps 5, 6 and 7 are processed in a hirerarchical
order to reduce the level of dissatisfaction of population
demands within the human ecosystem. The hierarchy represented
to meet these unsatisfied demands are:
• Generate short term remedies by purchase of imports
and delay of certain maintenance expenditures.
• Generate long term solutions by modifying production
processes to use more economical production functions
and by redistribution of M$P funds among sectors
and among components.
• Lower the per capita demands of the consumers to
reflect recognition that specific demands cannot be
met at future times by the production sectors, and
hence perceived needs will deminish if they are
above the subsistance level.
If a previous step is forecast to reduce the problem area
to an acceptable level, then the adjustments within the subsequent
steps are not processed. If, however, the previous step does
106
-------
not appear to sufficiently reduce the level of unsatisfied
demand, then the step is processed and the attempt to reduce stress
levels is done independently of forecast adjustments of the
previous steps, thus allowing the incidence of over-reaction.
Simulation of Long-Term Adjustment Timing
The procedures common to Step 4 and Step 6 include intro-
duction of changes that do not occur at once but begin in the
next cycle and undergo cumulative change to a maximum value
over several annual cycles. The rate of introduction of these
changes (or changeovers) is represented by a normalized cumulative
normal distribution using the range (-20", 2cr) . The present time
is equated to t=M-2CTwhile the final time, t+^t=M+2 . The
amount of change for any t
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108
-------
FIGURE 22
STEP 4 PARAMETERS
Nam_e_
T(t')
FLAG(r,t)
SUBFOR(n)
SBCST(r,n,t)
C(r')
MRCST(r',t)
SB5CST(n,r,t)
CPILE(r,t)
Definition
Degree (fractional) of process trans-
formation at time t'
Condition of stock level signal of r
at t
nth substitution formula available
Unit cost of nth substitution at t
Units of resource r' in substitution
for one unit of r
Maximum unit cost of r' at t
Five year estimated cumulated unit
cost for affecting substitution r at t
Level of expansion of resource reserve
stock given that expansion in feasible
at t.
Source
Calculated
Step 2,t
Constant
Calculated
Constant (in
SUBFOR(n))
Step 2,t
Calculated
Constant
109
-------
• Conversion from one production process to a lower
cost process.
Elements of adjustment that do not require significant
time delays (occur at least by next cycle) are:
• Deferral of capital maintenance for expansion of
production funds.
• Increasing importation of component output.
• Transfer and reallocation of rates of M§P funds
growth.
• Increase or reduction of demand measures.
Step 4: Adjust Resource Reserves and Utilization Factors
The fourth step of the cycle is processed only for those
resources for which a critical stock depletion signal was set
in Step 2 (i.e. FLAG(r)=l.0). For each such resource, the
feasibility and economic utility of substitution, in whole or
in part, and expansion of the reserve stockpile in reaction
to increased unit extraction prices is simulated.
There exists a third adjustment of resource availability
for durable resources not considered in this Step but automatically
introduced in Step 2 calculations. The level of recycling of
durable ores from production debris is increased from cycle to
cycle as a function of change in unit procurement costs of the
resource (see equations 21-22).
Figure 21 provides the general flowchart of Step 4 while
Figure 22 lists the parameters of the algorithms and their sources.
Assumptions
Within any resource projection, the adjustment procedure
will forecast data based on the maximum values at time t, rather
than attempting to make non-linear projections of future values.
If a substitution for a resource by a mix of resources
occurs in this step it affects the original utilization in all
production components equally.
Once a substitution is initiated, the procedure will
continue until it is completed. However, other substitutions
can be initiated involving this resource and total change will
be constructed across the hierarchy of initiated substitution
changes.
110
-------
A substitution need not completely replace the use of a
resource; in fact, it generally does not. Typically a substitution
includes the resource in its formulation but at a lower level
than the amount for which the substitution is made.
If two substitutions are available and economically
feasible, only one is initiated in a given cycle. The choice
is based on selection of a minimum mean-unit-cost for an
arbitrary period of time. In SOS-1 the time period is set as
5 years.
Algorithms
For each resource a test is made to determine if it has
a critical stock depletion warning. For those resources in
this condition the other algorithms of Step 4 are processed;
for other resources no further action is taken in this Step.
For each resource r the test is made:
(42) FLAG(r,t)=1.0?
if yes, continue Step 4 for r;
otherwise process next r.
For each resource for which the test is positive, deter-
mine which, if any, of these substitution equations apply.
For each applicable formula, check to make sure the substitution
process is not presently underway. Additionally, for some
resources the substitution can be done one time only. For
those meeting the feasibility criteria calculate the present
costs to substitute the new mix for a unit of resource and
the projected five year resource unit costs for time-phased
conversion. This procedure is stated below:
(43) Is substitution SUBFOR(n) for r? n=l,2,...,m
if yes, continue process
if not, do test for the next n
(44) Is SUBFOR(n) not in process?
if yes, continue process
if not, do test above for the next n
Calculate the two costs cited above.
(45) SBCST(r,n,t)=Z C(r') *MRCST(r' ,t)
r'5
(46) SB5CST(r,n,t)= £ [MRCST(r,t)*(l-f(n,u))
U=l
+SBCST(r,n,t)*T(n,u)]
111
-------
After all substitutions are tested and the successful ones
have values for equations (45) and (46) developed, the appropriate
substitution is selected or all are judged unacceptable. The
acceptability is set by cost comparison to the resource pro-
curement costs; the specific substitution selected is the
minimum of the (5 years) cost alternatives.
For the test to be an economical substitution candidate:
(47) Is SBCST(r,n,t)0
if yes, continue
no, return to the initial action of Step 4 (test (42))
and the next r.
Store in the Future Actions File for all times
-------
ADJUSTMENTS**
RESOURCE SUBS. STOCKPILE YEAR
NUMBER NUMBER INCREASE COMPLETED
A A 0.0 7
5 5 0.0 7
4 0.0 2500. 7
5 0.0 1000. 7
FIGURE 23
RESOURCE ADJUSTMENT FORMATS
NOTE: Figure 16 keys resource
numbers to resource names.
113
-------
If Step 4 output is not suppressed, a table of all resource
adjustments for the cycle is printed as shown in the example
in Figure 23. For each adjustment there is a line entry;
therefore, for any resource up to two lines may be printed.
No adjustment procedures are shown explicitly in the
table/graph sets at the end of the simulation.
Step 5: Perform Short Term Output Adjustments
After calculating the level of goods to be exported for
each component in this cycle, a check is made to determine if
the output levels of any component produced unsatisfied demand.
For each component that had a delinquent output level a short
term adjustment by deferring maintenance and using the funds
for importing output is performed. For those components still
delinquent, additional goods are purchased up to the available
export balance level. If some components remain delinquent
after these actions, jStep 6 is processed; otherwise, the
systemic module is complete and Step 7 is initiated to upgrade
measure thresholds only.
Figure 24 depicts the general flowchart of Step 5 while
Figure 25 includes all parameters used in the.Step.
Assumptions:
For all components having resiliency, the export/internal
consumption ratio will be maintained at the historical levels.
Thus, system resiliency does'not lead only to increased con-
sumption over ecosystem thresholds, but also may be converted
to cash flow within the export funds.
Imports of component output supplement internal production
only up to threshold needs. Additional cash flow due to exports
is accumulated for use as needed in later cycles.
Deferred maintenance can be accomplished only on that
element of maintenance associated with plant and equipment
depreciation; facility expansion and ecosystem maintenance
costs cannot be deferred.
No resilient components will defer maintenance to generate
funds for importation of needed goods for other components.
Goods imported are imported at a cost to the maximum
production costs if the goods were produced internally. Thus,
no price break occurs by importation except that internal
resource reserves are not depleted.
114
-------
FIGURE 24
STEP 5 GENERAL FLOW CHART
Begin
/'
y
Each
Component
Done
Calculate
Exports
1
Cumulate Funds
Balance Values
/Each Delinquent^
\Cpmp ohent _J*
Done
Defer
Maintenance
Adjust
Component
Output Data
V
/Each Private
I Sector Delin-
\quent Component,
Done
| X
Import Goods
Jsing Export
Balance
Adjust
Component
Output
Rat;e
Yes
Each Delinquent
Public Sector
No
Import
Goods
Adjust
Output
Rate
Yes
"^ Step 7
Upgrade Only
115
-------
Name
EXPORT(j,t)
OUTPT(j,t)
OUTPT(j,t-l)
RESIL(n,j,t)
RESIL(n,j,t-l)
EXPORT(j,t-l)
EXFUND(j,t)
RUCST(j,t)
MARKUP(j)
EXFUND(t)
CEXFD(t)
CEXFD(t-l)
MOCST(j,t)
UTIL(r,j,t)
MRCST(r,t)
INCST(j,t)
DOUTPT(j,t)
DEFMN(j,t)
M$PFD(j,t)
RMNNOR(j)
CFAIL(j,t)
CEAIL(j,t-l)
FIGURE 25
STEP 5 PARAMETERS
Definition
Units of component j exported at t
Units of component j produced at t
Units of component j produced at t-1
Resiliency of j in measure n at t
Resiliency of j in measure 'n at t-1
Units of component j exported at t-1
Funds produced by component j exports
at t
Mean unit cost of j output at t
Markup on component j goods sold as
export
Total funds from exports at t
Cumulative total funds from exports
at t
Cumulative total funds from exports
at t-1
Maximum output unit cost for j at t
Units of r used in one unit of j at t
Maximum unit cost of resource r at t
Cost to import needed goods of j at t
Required additional goods of j at t
Maintenance funds deferred of j at t
Total funds available to j at t
Normal maintenance level for offset
depreciation for j
Cumulative output failure level to
date at t for j
Cumulative output failure level
last year
Source
Calculated
Step 2,t
Step 2,t-1
Step 3,t
Step 3,t-1
Step 5,t-1
Calculated
Step 2,t
Constant
Calculated
Calculated
Step 5,t-1
Calculated
Step 2,t
Step 2,t
Calculated
Calculated
Calculated
Step 2,t
Calculated
Calculated
Step 5,t-1
116
-------
FIGURE 25 (CONT)
STEP 5 PARAMETERS
Name Definition Source
MDEFMN(j,t) Maximum maintenance funds of j that Calculated
can be deferred at t
SINCST(s,t) Cost to import all needed sector Calculated
goods at t
KFACT(j) Normalizer of unit costs for component Step 2, Cycle 1
j
117
-------
If importation occurs using the export balance, first all
private production demands are fully met; then the residual
funds are used to augment public output as needed.
Algorithms
The first calculations of Step 5 develop the levels of
exportation of goods for the cycle based on the past trends
and the current required use of a components output to meet
system demands. After the export levels are set, the generated
funds and the current export funds balance is calculated.
First the calculation for amount of exports is:
(52) EXPORT(j,t) = OUTPTM.t) *Min[RESIL fn. j . t) ] *EvpORT(1 t
J J OUTPT(j,t-l)*Min[RESIL(n,j,t-l)] EAruK1 U »*
Generated funds by exports of each component are:
(53) EXFUND(j,t)=RUCST(j,t)*MARKUP(j)*EXPORT(j,t)
Funds cumulated over all components and added to the
past balance are:
(54) CEXFD(t)=CEXFD(t-l)+ £EXFUND(j,t)
j
After the export calculations are complete, the first
set of short term adjustments for delinquent production com-
ponents, (DOUTPT(j, t)>0), is begun. If no components are
delinquent then Step 7 is initiated at this point, bypassing
both the short-term and long-term component adjustments.
The first short-term adjustments are performed within the
delinquent components only. Up to the level of required funds
or the level of M§P funds used to offset plant depreciation,
the maintenance funds are deferred and the funds are used to
purchase needed imports for that component.
To determine the maximum funds needed for the component,
first a maximum unit cost for the cycle is calculated:
(55) MRCST(j,t)=KFACT(j)*£]uTIL(r,j,t)*MRCST(r,t)
r
Then the total funds required by the component to supple-
ment its production in the system is:
(56) INCST(j,t)=DOUTPT(j,t) *MRCST(j,t)
The maximum funds available by deferring maintenance is:
118
-------
(57) MDEFMN(j,t)=M$PFD(j,t)*RMNNOR(j)
If sufficient funds exist for the total adjustment,
sufficient deferral is made to produce the necessary adjustment;
otherwise all deferrable funds are deferred and the funds are
used to reduce unit demands prior to entering the next set of
adjustments.
(58) If MDEFMN(j,t)^INCST(j,t) then the deferred funds are:
(59) DEFMN(j,t) = INCST(j ,t)
and the residues for further need are:
(60) DOUTPT(j,t)=0
(61) INCST(j,t) = 0
(62) CFAILCj,t)=0
Otherwise if INCST(j ,t)>MDEFMN(j ,t) the values are:
(59) DEFMN(j,t)=MDEFMN(j,t)
Residual needed output for j is:
(60) DOUTPT(j,t)=DOUTPT(j,t)*[l-[DEFMN(j,t)/INCST(j,t)]]
and residual funds needed are:
(61) INCST(j ,t) = INCST(j ,t) -DEFMN(j ,t)
The remaining cumulative failure rate is recalculated as:
(62) CFAIL(j ,t)=CFAIL(j ,t-1)+DOUTPT(j ,t)
If at the end of the deferral process above, no com-
ponents continue delinquent, Step 7 is initiated. Otherwise,
the second process of short term adjustment is initiated,
as described below.
If any funds are available in the export funds balance,
this fund can be used to augment imports as needed and as
available. The process is performed first for components in
the private sector.
Needed funds for private sector components are:
(63) SINCST(priv,t)= £ INCST(j,t)
119
-------
If SINCST is zero, proceed to the calculations for the public
sector components. Otherwise, calculate
(64) k=Min[l,CEXFD(t)/SINCST(priv,t)]
The funds used for the private components will leave a
residue of:
(65) CEXFD(t)=CEXFD(t)*[l-k]
Remaining residues for the delinquent components of the
private stor are:
(66) DOUTPT(j,t)=[l-k]*DOUTPT(j,t)
(67) INCST(j,t)=[l-k]*INCST(j,t)
After these calculations are completed for all private
sector components, a test is made of k. If it is equal to 1,
sufficient export funds remain to determine if the public
sector needs may be met. Otherwise, the simulation exits
to Step 6, for long term adjustments.
If k=l, the total funds needed for the public sector
components to meet needs are calculated:
5
(68) SINCST(publ,t)= V" INCST(j,t)
If SINCST is greater than zero, equations (64) through
(67) are processed for public components. Then if k is not
equal to one, Step 6 is initiated. If SINCST is zero or if k
equals one, then Step 6 is bypassed since short-term adjustments
are sufficient, and Step 7 is initiated only to upgrade thresholds
Short-Term Funds Adjustment Outputs
If the output for each cycle of Step 5 is not suppressed,
then a tabulation for each affected component of deferred
maintenance funds and/or export funds expended for imports
is printed. An example of the table is shown in Figure 26.
Additionally, the level of the export funds not expended at
the end of Step 5 is printed as shown in Figure 26.
Step 6: Perform Long Term Component Output Adjustments
If some components, after Step 5 short-term adjustments
are performed, remain delinquent (DOUTPT(j,t) 0 at the end of
Step 5), there is no further adjustment in this cycle that
120
-------
SHORT TERM FUNDS ADJUSTMENTS
COPCNENT MAINT.A^'T UNITS FRCK
NUMBER DEFERRED EXPORT EAL.
2 1510.30 O.C
8 2960.22 2.66
0 18R8.76 2.C8
10 2055S.95 O.C
CUMULATIVE EXPORT BALANCE IS 0.0
FIGURE 26
SHORT TERM ADJUSTMENT FORMATS
NOTE: Figure 15 keys component
numbers to component names.
121
-------
FIGURE 27
STEP 6 GENERAL FLOW CHART
Begin
V ,
' Delinquent^
^Components/
Done
/ Each
V Sector
Done
'Carry out
Needed
(Feasible
,Funds Transfer
..
''Each
\Component
[Determine
Economically
^Feasible
Process
Substitutions'
(Determine
Five Year
[Minimum Cost
Substitutes
Schedule
Process
Changeover
Determine
Ability to
Transfer
Funds
JDetermine
_\|Needs for i
"
Adjust Funds
Rate of Growth!
To Adjust
Delinquency
[Rates
No
Step 7
Upgrade
Only
Yes
Step 7
122
-------
FIGURE 28
STEP 6 PARAMETERS
Name
SBCST(n,j,t)
[AUTIL(n,j,r)
MRCST(r,t)
MOCST(j,t)
RT5CST
(n,n' ,j,t)
Y(n,t)
M§PFD(j,t)
RGROW(j)
M$PND(j,t+l)
DOUTPT(j,t)
TPOP(t)
TPOP(t-l)
SCND(s,t+l)
Definition
Unit cost of substitute process n at t
] Alternate resource use functions for j
Maximum unit cost of r at t
Maximum unit output costs of j at t
Five year cumulated mean unit cost
beginning at t
Change over time lag function
Total funds used by j at t
Current funds growth rate for j
Needed funds for j at t+1
Additional output needed after short
term adjustments of Step 5
Total population at t
Total population at t-1
TRNFDCs,t)
SUMND(j,s,t+l)
KFUND(s)
NEEDFD(j ,t+l)
SCNEED(s,t+l)
SCFUND(s,t+l)
Additional funds needed by sector s
components
Set level of funds transfer to s
Funds available from healthy com-
ponents of s
Pro rata adjustment of fund levels
of components in s
Funds needed above available levels
for j at t+1
Total NEEDFD in s for delinquent j
at t+1
Total funds available in s for
resilient j at t+1
Source
Calculated
Constant
Step 2,t
Calculated
Calculated
Calculated
Step 2,t
Step 7, pre-
vious t
Calculated
Step 5,t
Step l,t
Step l,t-l
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
Calculated
123
-------
can be performed in order to meet the population demands.
However, several adjustments can be made over the long-term
(succeeding periods) that are, over time, expected to reduce
the level of delinquency. Three types of adjustment are
possible:
• Reduction of production costs by introduction of
new production formulas
• Reallocation of M§P funds within sectors
• Transfer of M§P funds between sectors.
Figure 27 provides the general flowchart and Figure 28
defines the parameters in Step 6 .
Assumptions
All adjustments or transfer of funds. are performed in the
smallest neighborhood possible - within the component (Step 5) ,
within the sector, and then between sectors. Within each
neighborhood the adjustments are performed without regard to
other neighborhood adjustments.
In the present form of SOS-1, available funds are generated
based on the prevailing rates of growth and fund levels for each
component. Reallocation of funds determine the total funds
available for the next cycle and then change the rates of growth
of components appropriately so that the total funds growth from
t to t+1 is constant.
Algorithms
The long-term adjustments are performed in the order
of adjustment of input/output formulas and then funds
reallocation.
If any component which remains delinquent after Step 5,
each of the available production formula alternatives are checked
to determine if it is projected to lower unit production costs
for any component. If a lower cost alternative exists, then a
substitution process as detailed in Step 4 is affected.
First, calculating the substitution cost and the 5 year
conversion costs for alternative production formulas:
(69) SBCST(n,j ,t)= AUTIL(n,j ,r) *MRCST(r , t)
if n is a substitution feasible for component j
124
-------
(70) RT5CST(n,n' ,j,t)=
[SBCST(n,j,t)*[l-T(n,u)]
n=l
MOCST(j,t)*T(n,u)]
(71) I£ SBCST(n,j ,t)
-------
If both SCND are positive, sufficient funds exist in each
sector to perform needed adjustments. If both SCND are negative,
neither sector has sufficient funds for its own needs and hence
cannot transfer funds to the other sector. In either of these
cases, funds are not transferred and the process will skip to
equation (80) for intra-sector adjustments. For the case
where one SCND is positive and the other negative, inter-sector
funds transfer is done. The level of funds transferred is the
minimum value of the needed funds and the excess funds.
(77) TRNFD(s,t+l)=Min[SCND(s,t-H)-SCND(s' ,t+l)]
where s is the receiving sector.
The funds are allocated to components in sector s on a
pro rata basis using M§PFD(j ,t+l) as the base.
For all j in s;
(78) M§PFD(j,t+l)-M$PFD(j,t+l)* l
jes
The withdrawal of funds from sector s1 are assigned on a
similar pro rata basis:
For all j in s ' ;
(79) M§PFD(j,t+l)=M§PFD(j,
jes '
After these intersector transfers are completed, equation
(75) is repeated for all j and then the process for intrasector
transfers below is done.
Two totals are first calculated; the total funds required
as an addition to delinquent components:
(80) SCNEED(s,t+l)= V Max[0,NEEDFD(j,t+l)]
jes
and the total of funds available as an addition to delinquent
component funds:
126
-------
(81) SCFUND(s,t+l)= _ -Min[0,NEEDFD(j ,
jes
Within a sector there are sufficient funds for all
adjustments if:
(82) SCFUND(s,t+l)>SCNEED(s,t+l)
if so then
m_ SCNEED(s,t+l) and n=l
SCFUND(s,t+l)
otherwise
m=l and n= SCFUND(s ,t+l)
m L and n SCNEED(s,t+l)
For components receiving additional funds:
(83) M§PFD(j ,t+l)=M$PFD(j , t+1) +NEEDFD(j ,t+l)*n
and for components transfering funds:
(84) M$PFD(j,t + l)=M§PFD(j,t + l)+NEEDFD(j,t-f-l)*nt
For all components the new rate of growth, as a fraction, is:
(85) RGROW(j,t+l)=
After this calculation is complete for all components a
test as to whether all components received adequate funds is made,
If not, some measure thresholds in Step 7 may be lowered.
Otherwise, only increasing thresholds are allowed in Step 7.
This test completes all Step 6 actions.
Long- Term System Adjustment Outputs
If Step 6 cycle outputs are not suppressed, then two types
of output may be produced (Figure 29). First, for changes in
production processes, during the year in which the adjustment
is made a printout giving component number, substitution process
number and year of changeover completion is produced. Second,
if any component has its rate of funds growth change, the
new growth rate (in %) is printed for all components.
Step 7: Adjust Long Term Population Demands
The existing thresholds for a demand measure may be
changed for either of two reasons. First, as a continuation
of the system adjustment processes begun in Step 5, if the adjust-
ments in neither Step 5 nor Step 6 can be projected to meet the
127
-------
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128
-------
FIGURE 30
STEP 7 GENERAL FLOWCHART
Begin
\
\Each
^— -,
A s
Component^ ^
I
Estimate
t+1
Production
Data
fione
Each
Measure
Calculate
Projected
t+1
Compare
v/To Measure
X''
Threshold
1
one
V
/
\
X
X
f
V.
Value
Lower
Measure
Threshold
Upgrade
inresnoiu
To t-2
Value
',
1
_, L-w— .
N/
/^
Yes XThresl
^ \Great
l
Yes XUpg'
No
Step 8
129
-------
FIGURE 31
STEP 7 PARAMETERS
Name
OUTPT(j.t)
MEAS(n,t+l)
Cnj
POP(k,n,t)
TMEAS(n)
Definition
Units of output for component j
imported and produced at t
Value of measure n at t+1
Coefficient of output j in measure
n
Size of the kth population at t used
in n
Threshold of measure n
Source
Steps 2§5
Calculated
Constant
Step l,t
Step 7, pre
vious t
130
-------
amount of a specific measure, its threshold may be reduced in
Step 7 to reduce stress on the system. Secondly, however, if
a measure has been above its threshold for a period of time,
SOS-1 adjusts the threshold higher to reflect perceived needs
and their increase due to availability of outputs above the
threshold. The general flowchart and the included parameters
are displayed in Figures 30 and 31.
Assumptions
Although Step 6 may have adjusted data for long-term change,
Step 7 considers the data base as it exists at the end of the
short-term adjustments (at the end of Step 5). Hence, a Step 7
degradation adjustment, with or without a Step 6 adjustment,
should normally overcompensate for the past delinquency, causing
a chance for the ecosystem to become resilient again.
The simulation of changing perceived needs are simulated
in SOS-1 by increasing thresholds based on the arbitrary rule:
If the measure has been above threshold for the last two cycles
and has not decreased in that time, the new threshold is set
to the measure value of two cycles ago. No decrease in thresholds
is made until the adjustment procedures of Steps 5, 6 and 7 force
the decrease.
Algorithms
If Step 7 is entered from Step 6 the following equations
are processed in order for each measure. If another route of
entry was followed, Step 7 will skip to action (89) for each
measure in turn.
The first action is to estimate the value of the measure
anticipated for next year. This is done using the same procedure
as in Step 3 but the output level now includes the outputs imported
as well as those produced internally. Secondly, a more severe
requirement is set by assuming that the consuming population
will grow by ten percent in the next year.
(86) MEAS(n,t + l)= cnj *OUTPT M , t)
l.l*POP(n,k,t)
A test of the acceptability of the measure threshold is
made nejct using the following test:
(87) Is MEAS(n,t+l)
-------
DEPAND THRESHOLD ADJUSTMENTS
MEASURE
MMBER
1
2
3
4
5
6
7
3
9
10
II
Nfcl*
UPGRADE
0.0
0.760S
0.0
1.038E
7.7738
0.0
0.0
0.0
0.0
0.0
0.0
VALUE
DEGRADE
2.273A
0.0
0.4035
0.0
0.0
0.5184
0.9893
0.3624
0.0602
0.1149
0.0588
FIGURE 32
DEMAND MEASURE THRESHOLD ADJUSTMENTS
NOTE: See Figure 40 for data used in
construction of each measure.
132
-------
Degrade the threshold of the measure n to:
(88) TMEAS(n)=Max[0.05,MEAS(n,t+l)]
(For the purposes of the initial tests of SOS-1, for
every measure, the threshold of subsistance is arbitrarily
set to 0.05.)
At this point the next measure is processed without
doing action (89).
A two-level test is done to determine if the measure
threshold should be increased:
(89) Is MEAS(n,t-l)>MEAS(n,t-2) and
is MEAS(n,t-2)>TMEAS(n)
if so, then
(90) TMEAS(n)=MEAS(n,t-2)
otherwise, TMEAS(n) remains the same.
After all measures are processed, Step 7 is complete and
Step 8 is initiated.
Demand Threshold Outputs
If Step 7 output is not suppressed, any measure that has
its threshold upgraded or degraded is tabulated with the new
value placed under the appropriate type of action (see Figure 32)
CYCLE BOOKKEEPING
After Step 7 is completed, the systemic module of the cycle
is complete. Step 8 is performed each cycle to perform required
bookkeeping to properly set the data base for the next cycle.
Since the initial data base is designed for immediate use
in Step 1 for t=l, the initializing of the data base for a
cycle can be performed as the last cycle action, rather than
as the initial cycle action. The general flowchart is given
in Figure 33.
Step 8: Reset the Data Base For Next Cycle
Step 8 is entered after the completion of Step 7; it
includes a number of bookkeeping chores as well as performing
time-dependent data updates. These actions include:
133
-------
FIGURE 33
STEP 8 GENERAL FLOWCHART
Begin
Calculate
QOL
Set Birth,
Death, Migration
Modifiers
V
j
For Each
Active
Resource
Substitute
Set Substitute
Level for t+1
Done
^
For
Active
Resource
Expansion
Set Expansion
Level for t+1
Done
V
For Each
Production
Process Change-
over
Set Degree
Of Changeover
At t+1
Done
Complete Cycle
Bookkeeping
No
Output
134
-------
• Calculating modifiers of the birth, death and
migration rates
• Adjustment of the work force distribution among
paid and unpaid workers
• Performing time-delayed adjustments of substitutions
and stockpile expansions.
Additionally, Step 8 includes preparation of the output table/
graph sets that are printed at the end of the run.
As part of the calculations for the birth, death and
immigration rates, a linear combination of the demand measures
into a quality of life scalar is used in SOS-1. The value is
used only for this set of calculations, and then comes into
play only when the values of the measures approach or pass below
the subsistance thresholds.
Algorithms
The first set of calculations develop modifiers to the
normal population rates based on the QOL scalar value, and
for immigration, on the level of employment. These modifiers
are applied as multipliers to the normal rates as defined as
constants in the data base (see the next section).
The QOL scalar is a linear combination of the ratio of the
individual measure values to their original thresholds.
(91) VALLQL(t)= ^,*{MEAS(n,t)/TMEAS(0)]
The birthrate modifier is:
(92) FBR =1.0 if VALLQL>k/2
=0.0 if VALLQLk/2
=1.0+ k/4 if VALLQL
-------
(94) FMG = 1.0*k i£ VALLQL>3k/4
=0.0 if VALLQL
-------
RUN OUTPUTS
While examples of each type of cycle outputs have been pro-
vided at the end of each subroutine description, a set of
outputs that summarize possible cycle and run outputs may
be helpful at this point. Appendix 9 provides a complete
listing of all outputs for one test case that is discussed
in the later section, Model Text. In particular, the
cycle output for year 22 provides a list of all but one
possible cycle outputs. The missing output, a resource
substitution, is given in year 2 output. The final 16
pages provide a full set of run summary outputs.
137
-------
SECTION VIII
EXAMPLE DATA
The initial operation of the model to test its adjustment
characteristics draws upon a data base that is primarily
United States data available for 1970. This section of
the report discusses each data element as used in the basic
case for the test of the SOS-1 Model. The data are organ-
ized as:
« population data
• resource data
• production component data
• demand measures data.
In each of these four elements the data are organized in the
order in which the data are first used in the equations as
processed in SOS-1.
POPULATION DATA
The population data allows development of the total population,
the population first by age-year, and then grouped into four
age-cohorts, and finally major consumer/work-unit partitions
within the age cohorts.
Total Population
The total population for the year 0, the initial conditions,
is set as 203,210 thousand people. The normal birthrate (BR)
and normal deathrate (DT) are set as .0182 and .0094. The
normal net migration rate for an unemployment rate of 51 is
set as .0021. These and the later population data represent
U.S. Census figures for April 1, 1970, as taken from the 1972
Statistical Abstracts of the U.S. The projection series is E,
equivalent to a total reproduction index per mature female of
2.11.
These normal growth rates are subject to multiplicative modi-
fication as a function of the combined QOL demand value (VALLQL)
of the past cycle (see equations (91)-(94) Section 7). Addi-
tionally, the net migration rate has a second multiplier based
on the past cycle employment level. These functions are:
Birthrate
FBR =1.0 if VALLQL > TQOL/2
=0.0 if VALLQL < TQOL/4
= 1-[(TQOL/2-VALLQL)/TQOL/4] otherwise
when TQOL is the initial combined measure threshold value.
138
-------
Deathrate
FDT =1.0 if VALLQL > TQOL/2
= 1.0 + C if VALLQL 3TQOL/4
- 0 if VALLQL < TQOL/2
= l-[(3TQOL/4-VALLQL)/TQOL/4] otherwise
F2MG = (20*EMPR-18)
where EMPR is the fractional employment rate for paid workers.
Age-Year Data
Additional data required to develop population by age-year
and age-cohorts are the ranges of the age cohorts, the initial
population and the normal deathrate for each age-year. The
age cohorts are:
1-17 (immature, non-workers)
18-24 (young adults, normally in education or work units)
25-64 (working adults)
£ 65 (retired adults)
Figure 34 provides a list of these data.
Population Partitions
Within each of the four age cohorts, the resident population
is subdivided into six mutually-exclusive partitions:
in education
in institutions
in non-working status
in training or welfare (unemployed)
in paid work status
in unpaid work status
(The partition selection is performed from the top;
i.e., if the person qualifies in education he is
considered for no other partition)
The development of partition size requires a coefficient
matrix, the elements of which are multiplied by the output
of goods by the appropriate component last cycle, to provide
139
-------
Population of
Age-Year for
Age
Year
1
2-5
6
7-14
15
16-18
19-21
22-25
26-35
36-45
46-55
56-64
65
>65
Previous Year
(thousands)
(calculated)
3430.8
3430.8
4581.3
3959.8
3959.8
3505.7
3545.0
2390.7
2308.8
2322.0
1859.0
1859.0]
20066. OJ
Age -Year Death
Rate per 100
.0204
.0008
.0004
.0004
.0004
.0013
.0013
.0013
.0016
.0031
.0072
.01660
.05775
FIGURE 34
POPULATION DATA BY AGE-YEAR
140
-------
the partition population. These data are given in Figure 35.
The values are equal to the 1970 data (scaled as thousands
of people) for each partition and output component. As an
example value: in age cohort 1, for each of the education
units produced there are associated a population of 45,863.
Since 1,000 output units are produced in 1970, the unnor-
malized education population size (equation (6) of the pre-
vious section) is 45.863 million school children less than
18 years old in publically operated schools.
RESOURCE DATA
For the initial operation of the model, 17 of the maximum
of 20 entries for resources were used. While these resources
represent surrogates in many cases, the range of character-
istics in this set is considered reasonably comprehensive
for the test of the example model. The simplified description
of the categories, keyed to the SOS-1 resource index, r-1,2,
...,20 are:
1. Structural metals (iron, aluminum), in good supply at
present unit costs
2. Copper, in fair supply at present unit costs
3. Lead and zinc, in good supply at present unit costs
4. Mercury, in poor supply at present unit costs but
substitutes and presently non-economic reserves exist
5. Silver, in poor supply at present unit costs, little
substitution available, fair non-economic reserves
exist
6. Trace minerals and metals, in good supply and the
most likely partial substitutes for mercury and
silver
7. Coal, in good supply but not a preferred energy source
8. Oil, in poor supply, little substitution possible, but
good non-economic reserves exist at present
9. Electricity, supply level is static but annually
renewable, substitution is conversion of plants to
consume coal (represents 1970 stock of electricity
producing sources)
10. Not used
11. Fibers (lumber is surrogate) in fair supply, renewable
over a long period
141
-------
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142
-------
12. Food, in good supply, renewable annually, surplus
level is fixed as a function of agriculture pro-
duction levels.
13. Not used
14. Urban land, in good supply, easily increased by sub-
stitution
15. Suburban land, in good supply, easily increased by
substitution
16. Arable land, in good supply, level is fixed or
decreasing only, in 1970 one-third is held as soil
bank
17. Not used
18. Paid worker units, function of population character-
istics, initial unemployment level is moderate
19. Treated air, static quantity, in good supply as a
renewable value
20. Treated water, static quantity, in good supply as a
renewable value.
Resource Supply and Cost Data
Associated with each resource at any time is the initial
economically available resource level (the reserve stockpile
for a given unit cost), the level of the resource used to
date prior to cycle 1 of SOS-1, the level of recycling
accomplished, set by the prevailing unit prices, the mean
and maximum unit prices and the present annual use rate.
Several of these values are composites of more detailed
data. Each statistic is defined to its detailed elements
and the data elements are listed in Figure 36.
Initial resource levels for all resources except paid-work-
units are set arbitrarily as 10,000 units. For example, if
iron is a surrogate for structural metals, all reserves of
all materials of the category are totalled and then are
assumed to equal 10,000 times the level of stocks that have
not been depleted. For iron this is 10,000 times .99 or
9,900 units available in the reserve stockpile.
143
-------
For paid workers, the reserve level is the paid worker parti-
tion size, in thousands.
The stock level used to date is the fraction of the 10,000
units that have been consumed and are non-renewable at
the present time. For annually renewable resources this
value is zero since each of these is assumed annually
renewable in its entirety.
Present unit cost for a resource is set by first determining
the maximum unit price at the projected level of use for the
cycle, and then developing a mean unit price from this
maximum value and the previous year's maximum value. The
level of usage for any cycle can be calculated from the
projected levels of production output for the cycle (see the
production data discussion). From this the used stockpile
at the end of the cycle (ESTCK(R)) can be obtained. The
maximum unit price is:
MRUCST(R) = (Kl(R) + (K2(R)*ESTCK(R)) K3 ^*ESCAL*.00001
when ESCAL is set by equation (24) of Section 7.
and K1(R), K2(R) and K3(R) are given in Figure 36.
The values for K1(R) and K2(R), as well as the initial stock
level were selected primarily to produce changes in costs
during the first few cycles that appear to be appropriate for
the surrogates in the next few real-time years. Thus for
silver the initial cost when the stockpile is 5000 units is
(0 + .948*.5}2; after another 1000 units are used then the cost
is (.948*.6)2 ; an increase of 44%. Additionally, the initial
values were scaled so that the costs in production for a
given resource type would be typical of its share in the
present production-costs structure in the component outlays,
using data from the U.S. Statistical Abstract.
•
The recycling rate for a non-renewable ore represents that
fraction of the ore that can be obtained from recycling
debris from earlier production processes (output no longer
in use). The rate used at any time is obtained from:
REREC(R)=K4(R)+(K5(R)*ESTCK(R))2
For all of the resources used in the initial tests K4(R) was
set equal to 0.0 (negligible recycling). The values for
K5(R) are given in Figure 36 and represent conservative
estimates of recycling capabilities with today's technology.
144
-------
INITIAL USED LEVEL
PRIOR TO t=l
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
.01
.25
.20
.50
.50
.01
.05
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
7
2
16
26
1
1
1
5
0
0
Kl
.9
.0
.8
.079
.33
.00
.7
.4
.0
.0
.0
.00
K2
4.9
32.0
5.2
.132
.948
.158
320.8
58.7
11.19
16.7
26.4
1.0
1.0
1.0
5.9
0
0
K3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
K5
0.0
0.75
0.8
1.0
0.6
0
0
0
0
.45
0
0
0
0
0
0
0
1
.3
.3
.3
.6
.6
.3
.3
.3
.6
.6
.9
.8
.8
.8
.9
--
FLGDAT(RJ
2 3
.6
.6
.6
.75
.75
.6
.6
.6
.75
.75
.87
.87
.87
.87
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.92
.95
4
.95
.95
.95
.95
.95
.95
.95
.95
.95
.95
.95
.95
.95
.95
.98
CPILE
5000.
5000.
5000.
2500.
1000.
10000.
5000.
5000.
0
0
0
0
0
0
0
0
FIGURE 36
GENERAL DATA FOR RESOURCE CATEGORIES
145
-------
Note that no recycling is considered for renewable resources
for the test case; in the general case this restriction can
be lifted without altering the model algorithms.
The present annual use rate for resources is a function of
the production processes. The determination of the level
of resources that are withdrawn from the existing reserve
stockpile vis-a-vis produced by the recycling process from
production debris is obtained from the values of the initial
stockpile for the cycle, the associated recycling ratio and
the projected level of use of ores during the cycle.
Resource Usage Adjustment Date
As resources are used, thus depleting the available stock-
pile, a set of tests are made to determine if the level of
resources have reached a depletion level that is critical
enough to project a expansion of the available stockpile;
(i.e., extraction of neglected ores now become economic due
to a rise in unit sales prices) or to have all production
processes substitute, partially or completely, for a resource
in short supply.
To select the times when a resource is considered to be in
short supply, four points of stockpile depletion are set for
each nonrenewable and renewable resource. In any cycle where
one of these points (VFLG(L)) is past or if the stock deple-
tion is greater than .985, the search for economic adjustments
is initiated. The four values used for the test case are
given in Figure 36.
If a stock depletion point is past, two contingencies are
checked. One of the resource checks determines whether the
existing stockpile reserve can be increased. This can occur
if the incremental size of the stockpile is greater than zero
and if an increase is not presently underway. The increase
of stocks to the new level is assumed to take five years.
The incremental stockpile size (CPILE) assumed for the test
cases is shown in Figure 36.
The second resource check determines if there are one or more
substitutions available to reduce the usage of the resource.
If any exist, the least costly for the next five years is
selected. In the test case, once a substitution for a non-
renewable resource is done, it cannot be made again. Each
substitution that is activated is initiated during the next
cycle and takes several years to be fully implemented. Figure
37 provides the initial set of substitutions and the associated
time factor. As an example, substitution 9 allows a change
in use of urban land by any production process that uses urban
146
-------
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147
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land. The substitution is, for every unit of urban land (as
existant in 1970) that is used formerly, .9 units of urban
plus .3 units of suburban (1970 census) can be used. Note
that the unit sizes are not equal.
COMPONENT PRODUCTION DATA
The resource utilization and the production of outputs for
regional consumption and for export requires data including:
• annual funds projected for maintenance and
production
• maintenance rates for capital expansion, capital
maintenance and environmental maintenance
• historical export fraction
6 resource utilization formulae for production of
one unit of output (both active and alternative
formulae)
Funds Data
The initial level of production and maintenance funds and
the initial annual rate of funds growth are input for each
production component. These values are shown in Figure 38.
M§P funds are in millions of dollars; rate of growth as a
percentage. Data are taken from official U.S. figures;
1970 for the level; the 1950-1970 data for the real dollar
funds growth rates.
Maintenance Data
The cost to create a new plant complex that is sufficient to
produce one unit of output on a scale where the output for
a component is 1000 units annually, (CAPVL), is given in
Figure 38 in millions of dollars. Hence an investment of
this amount will increase the production component capital
0.1%.
The normal annual cost to maintain the existing plant and
capital complex for production of output is given as a per-
centage of the M^P funds; this is given in Figure 34 as
MNRNOR.
The cost to maintain environmental media quality assumes
that 1000 units of each media are naturally cleaned during
any year. All other media units that are polluted by the
production processes must be treated at a unit cost that
148
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149
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is set as a fraction of the operating expenses to produce
one unit of treated, clean media (QOLT). Hence, if agri-
culture causes one unit of polluted water for each produc-
tion unit, 5% of its operating funds may be used for water
treatment. Figure 38 provides these values as used in SOS-1.
Export Data
Since the level of exports depends in part on the historical
export levels, a percentage of goods produced that were
exported in the cycle must be initially entered. These are
labelled EJOT in Figure 38 and reflect data trends from
1960-1970.
Resource Utilization Data
For each production component a present production formula--
usage of each resource type to produce one unit of output --
plus alternative production formulae are entered. Each entry
consists of the number of units of each resource to be used
for one unit of output (scaled by 1000) , an indication as to
whether the formula is initially in use, and a time in years
required to fully implement a change to a nonactive formula.
Figure 38 provides these data.
Looking at column 3 of Figure 35, the production component
(2) is transportation, the use of resource 1 (iron) to
produce one unit of output is 20 (scaled to .02 for one unit).
Thus in 1970 when transportation output is 1000 units, the
use of iron is 20 units of the present stockpile, which
earlier was set at 9,900 units of ores. If resource row one
(iron ore) is added across for active formulas the total
annual usage is 200. Hence the predicted (statically)
annual depletion is about 1/50 of the reserve, and trans-
portation will use about one tenth of that.
DEMAND MEASURES DATA
The calculation of the 11 demand measures used in the
initial SOS-1 runs require development of the coefficients
associated with production output, an initial threshold
value for the measure (TMEAS), and selection of the popu-
lation base (DN) to be used in selecting the per capita
size. When the set of measures are combined into a scalar
to set the birth, death and immigration modifiers a weighting
factor (VN) is required. All data are given in Figure 40.
The values of Cnj are scaled by (10$).
As examples of the measure constructions, measures 1 and 2
reflect education satisfaction. For measure 1 the population
considered (DN) is school attendence, while 2 relates the
150
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152
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measure to a total population per capita measure. The relative
contributions of the 10 production components are 80.6% from
government operated education, 19.4% from private schools
(assigned to the commercial sector) and none from other com-
ponents. In 1970 when all component output was 1000 units
and total population is about 200 million, the measure 2
value is:
CLOOOC.806) +1000C.194))xl05 - .50
200,000,000
Since the threshold is .35, education is exceeding its lowest
required value; here, by a resilience level of (.50-.35)/.35 =
.42.
These measures provide a major driving force for adjustments
of funds and resource usage in SOS-1. Because of this, in a
policy analysis, considerable care is needed in setting each
measure to reflect a discrete population goal or interest that
is representative of the region under analysis. In measure
development the following guidelines should be observed:
• Each of the measures should represent a discrete area
of the production processes. If a measure is set up
that includes all or many component outputs as contri-
butors and, for a run, it becomes delinquent, this
forces each of the included components to attempt
to expand output. Thus, a general measure can cause
attempts that overcompensate and that signal that the
majority of the output areas are in trouble when the
actual cause is much more localized.
• Not all components need to be included in the set of
measures; however, if a component measure is not included
in at least one measure, then there is no driving force
to make it boost funds for output as resource costs grow.
On the other hand, even if it is not included it does
contribute to adjustments in terms of adjusting output
formulas or resource substitutions. Thus it acts as
a component having a set pattern of growth that is not
changed by population preferences but that does act as
a user of resources and a recipient of technological
change.
• Each measure has equal weight in the adjustment process
and is independent of all other measures; hence, each
measure can be constructed without regard to other
measures as long as the set of measures includes a
non-zero coefficient for each output component that
should be sensitive to regional desires.
153
-------
• Initial threshold values for measures should be
set relative to the known initial measure values
to represent the level of initial relative stress
patterns. For example, if all output areas other
than education are considered adequate, the example
data thresholds might have been set so that the
resilience of measures 1 and 2 were -.10 and all
others were .15. This would have caused in cycle
1 immediate pressure to boost educational and
commerical (private school) output.
For the test data, the set of measures were derived for
two purposes; to provide typical measures for a national region
and to provide a full set of construction types. The set can
be interpreted as:
1. Education output per full time student - a measure of
educational quality change for students.
2. Education output per capita - a measure of educational
availability and quality for full time and part time
students.
3. Transportation output per capita - a>measure of trans-
portation improvement as a per capita value.
4. Health output per capita - a measure of health services
per capita for the total population.
5. Welfare output per welfare recipient - a measure of
welfare services per recipient.
6. Manufacturing output per capita - a measure of goods
supply per individual.
7. Manufacturing output per worker - a measure of goods
production compared to personal income level.
8. Commercial output per capita - a measure of availability
of services per capita.
9. Agricultural output per capita - a measure of food
availability compared to consuming population.
10. Agricultural output per worker - a measure of food
and fiber compared to personal income level.
11. Household and recreational output per capita - a measure
of supply of shelter and recreation per capita.
154
-------
SECTION IX
MODEL TEST
The example model, SOS-1, has been operated over a
set of closely allied data bases that have, as initial
data, values that are generally representative of
the United States in 1970. The use of data bases with
small variations has allowed analysis:
• to verify that the simulation reacts credibly,
• to develop insights as to model sensitivity to
data variation, and
•• to determine the most useful avenues for further
model"development and application.
A series of seven simulation runs were made for use in the
example analysis of model output included in this section;
additional simulation runs were made to support the supple-
mentary analyses of appendixes 6-8. All runs used the
algorithms-and data base of SOS-1 and the previous section
except for exceptions as noted in the discussion of each
run. Since the output of a single run of 25 years is at
least 66 pages, only one full set is reproduced in this
report. This run, the Base Case, uses the documented data
base and algorithms exactly and is reproduced as Appendix 9.
THE TEST CASES
For the purposes of model testing and use in example
analyses, several sets of parametric variation of a single
statistic or algorithm were made. In the body of this
report, the analysis is confined to detailed discussion
of the output of the Base Case Run plus comparison of the
output of seven runs in which the only data variation is
the rate of annual growth in funds used for operating and
maintaining the production components.
Other areas of variation from the Base Case Run are
briefly discussed in appendixes. These are:
• Appendix 6 - maintaining learned gratification levels
(thresholds of quality of life measures) at initial
values to increase later year adjustment flexibility.
• Appendix 7 - setting the gross population birth
and death rates equal (ZPG for non-migrant
population).
155
-------
• Appendix 8 - removal of systemic adjustment algo-
rithms, thus reducing the Base Case to a rigid
consumption system that allows no change of usage
levels or rates except resource procurement costs.
THE BASE CASE
Run 1, using the example data of the previous section,
represents a severe case for the testing of adjustment
procedures of the model. This high stress level is caused
by three primary factors:
• The trends of investment growth as projected
using the period 1950-1970 are maintained, thus
allowing a regional capability of rapid expansion
(an annual rate of 4.9 percent) of operating funds.
This trend should cause rapid depletion of scarce
resources and perpetuation of relative growth
patterns among production components.
• The birthrate is maintained throughout the twenty-
five year period at about twice the death rate.
Over 25 years the unconstrained population growth
rate would be 32.4%, to 269 million, causing the
demand for production output to increase at least
at this rate. (This growth rate is equivalent to
U.S. Census Series E growth projections.)
• The per capita demand rates have required grat-
ification levels that automatically increase if
the appropriate production 'components have supplied
goods above the threshold rates. Thus, not only
is the demand increased due to a larger consumer
population but may also because of increased satis-
faction of previous per capita demands.
During the 25-year base case simulation, the model made numerous
adjustments and significant short-term trauma occurred. Yet,
even the rather rudimentary set of adjustments of this data
base allowed support of the population growing at a rate
close to the projected unconstrained level, and provided
goods to meet levels of demand well above the initial
annual values. The total population change over the 25
years was 31.4%, or 971 of the level projected for popula-
tion growth that is unconstrained by productivity.
In the gross analysis of demand satisfaction, after
25 years, the annual investment growth rate of nearly 5%
has increased the composite demand satisfaction to
156
-------
1.8 times the original value. However, this value is a
combination of 11 submeasures that have not increased in
a smooth pattern. Figure 41 provides the value of the
individual measures for years 1, 10, and 25.
t=10
t=25
1EASURE
NUMBER
I
2
3
4
5
6
7
8
S
10
11
12
PRESENT
VALUE
1.6899
0.4866
0.4668
0.4668
4.8139
0.4868
1.2491
0.4668
0.4863
1.2491
0.4868
0.0
PRESENT
RESILIENCE
0.3412
0.3908
0.2170
0.217C
0.3754
0.0813
0.0409
0.3908
0.6227
0.6655
0.3908
0.0
PRESENT
VALUE
2.2150
0.5742
0.4114
0.7148
5.9868
0.4786
1.2328
C.3142
0.3780
0.9737
0.5S44
0.0
PRESENT
RESILIENCE
0.1107
O.C598
-0.1549
0.1815
0.1C88
-0.0168
0.0274
-0.2312
-0.0603
-0.0484
0.1140
0.0
PRESENT
VALUE
4.7121
1.3596
0.47S7
2.0432
18.0411
0.6634
1.5814
0.4C56
0.2945
0.7C19
0.5S32
0.0
PRESENT
RESILIENCE
Q.2C79
0.2203
-0.0145
0.1840
0.5002
0.0645
0.0520
-0.1669
-0.2680
-0.3140
-0.1558
0.0
FIGURE 41
DEMAND SATISFACTION AT t-1, 10, AND 25
Comparing t-10 to t=l, six of the eleven measures have de-
creased. By t=25, the number of reduced measures is to
four. Greatest increases are in measures 1, 2, 4, and 5.
These reflect increased output per capita in the areas of
education, health and welfare (see Figure 40) while output/
capita in the other seven production areas have fallen or
remained about the same. These three very healthy areas
reflect areas that have a high annual investment growth
rate «8%) and low use of natural and land resources.
Comparing t=2S to t=l, the values reflect that the produc-
tion components of transportation, commercial, agriculture,
and household have maintained output growth rates lower
than the population growth rate. Thus, while the gross
measure of satisfaction has shown an increase, many of the
individual measures indicate areas of regional production
weakness. Additionally even the combined measure has shown a
157
-------
rate of growth that is much less than the growth in funds
during the period.
Figure 42 provides a comparison of remaining resource stock-
piles and resource unit procurement costs for years t=l,
t=15, and t=25. In several resource categories the available
resource stockpiles have increased over the 25 year period;
e.g. lead, zinc. In this case, the penalty for having
increased resources is an escalating unit cost, up 24 percent
at t=15 and 64 percent at t=25. The resources with the most
dramatic cost increases are silver (essentially a depleted
resource by t=25) , food, coal, oil, and work unit costs. Each
of these resources contributed to major fluctuation or depres-
sion of production output during the run. With the exception
of silver, all stocks are acceptable at t=25 but this has
been achieved for eight resource categories by increased unit
costs in excess of 301 over the initial costs.
In Appendix 9, a complete listing of all simulation outputs
plus the summary statistics for the Base Case Run is given.
Review of those outputs shows that the region made the follow-
ing number of system adjustments.
Adjustment Type Number
Increase of stockpile 19
Substitution for resources 9
Importing of scarce goods 19
Change of production formula 3
Redistribute investment funds growth 2
Demand Threshold:
Upgrade 78
Downgrade 0
Salary increase 3
FIGURE 43
ADJUSTMENT STATISTICS, RUN 1
In Run 1 a volatile situation occurred, yet at the end of
25 years a reasonably healthy econony existed, population
growth was maintained and only one resource was effectively
depleted. In order to provide an appreciation as to the
methods of adjustments and the immediate outcomes, the
following narrative of Run 1 major events is provided:
In year 2, the smooth expansion of the economy to date
caused the threshold values of 8 to 11 measures to increase.
However, two major problem areas also surfaced. A depletion
158
-------
LU
_J
U
9"
O
co
co
f-< O> O 4- ^
o en
o o
O
a
LO
ra
II
^-OOOOOCMUOOOOOOOOOOOOOO
r- a
LO
iH
II
-M
r\)
O O
O O
l»- O
O >O O Q
OMOWOOOOOUOOOOOOOOOOOO
xz»»*»»»»»»»»»»*»»»»»«
K-3OOOOOOOOOOOOUOOOOOOO
LO
(SI
LO
CM
LU 1
C£. '
LU
_l I
u
>•
o
O<_JU-**T -OrO
0
l~1OUO<->*«*OOO*-*O!i3OO
^O «O (\J
>r ^ Vn£_i_i_jv
OUJZOE:UJ<<»-
-------
warning for both mercury and silver caused an expansion of
the economically available stockpiles for both plus the
initiation of partial substitute resource usage formula for
both. Also in this year, the low unemployment rate caused
a work unit cost increase of 201.
In year 3 the effects of higher work unit costs and the
increase in demand thresholds caused a temporary strain on
output needs. The salary change caused output to be depressed
about 25%, causing in turn seven demand thresholds to be
missed. This deficiency was fully met in year 3 by seven
production components deferring capital maintenance and by
importation of some goods in two component areas. Full long-
term adjustment of funds to counter the depressed output
took several more years.
Also in year 3, a stock depletion warning for copper caused
a small stockpile increase plus a substitution adjustment.
This substitution with the two previous resource substitu-
tions caused a higher use of iron and zinc, lead, and a much
higher use of trace minerals.
ii year 4, although the thresholds of 5 measures were missed,
the thresholds of 2 other measures were upgraded.
In year 7, low unemployment again escalated work unit costs,
this time an additional 15%. Two production components defer-
red maintenance while 4 demand thresholds were upgraded. The
first energy shortage, oil, was signalled causing higher usage
of coal as a substitute.
From year 9 to year 15, depletion warnings and adjustments
occurred for iron, copper, mercury, zinc-lead, silver, trace
minerals, land and electricity. In each case the warning was
early enough and adjustment procedures flexible enough to
alleviate the situation by a short term adjustment.
From year 19 to year 22, silver underwent large unit cost
increases. These costs depressed the output levels of two
components 40% by year 22. Also from 19 to 22 food costs
increased 50%. The effects of the silver and food unit costs
of year 22 caused the following problems:
• five outputs depressed
• eight demand thresholds missed
• the export fund balance exhausted without meeting
all import needs
160
-------
• three production components adjusted component
production formulas
• annual investment growth funds were redistributed
to attempt long-term balancing of problems.
Since the silver shortage did not affect all production outputs;
two demand thresholds were upgraded even in this year of
general economic stress.
By year 25 the large set of adjustments to the silver and the
food shortage were sufficient so that only one production
component required use of export funds.
The narrative above indicates that SOS-1 does include cap-
abilities to adjust to needs; the primary deficiencies of
the model output appear to be that the escalating prices
require better interpolation procedures. The primary data
deficiencies of the small adjustment data base for this test
are the number of available substitutions and the need to
introduce improved non-linear stockpile data.
The summary data for the Base Case, in which the efforts of
the problem areas of the narrative above can be noted, follow
(Figures 44-51). These figures are also used in the para-
metric analysis that follows this Base Case analysis.
Findings that appear appropriate for the Base Case--and its
associated data base assumptions--are:
• The region is able to maintain an adequate base
to support the population and its demands for
the 25 year time period.
• While certain problems near the end of the run
period suggest that a longer simulation period
may see significant regional degradtion, the
data deficiencies may overly accent these. Speci-
fically, an expanded set of substitutes might
reduce the need for silver ore and an agricultural
rate of growth greater than .3% might allow for
improved food output.
161
-------
SUMMARY TABLE - STATE OF TI-E SYSTEM
(SCALED TO ORIGINAL VALUE)
YEAR
1.
2.
3.
4.
5.
6.
7.
a.
9.
10.
1L.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
POPULATION
IP)
1.0109
1.0211
1.032?
1.0342
1.0442
1.0544
1.0663
1.0794
1.0824
1. 0-345
1.1071
1.1215
1.1257
1.1403
1.1550
1.1700
1.1651
1.2005
1.2161
1.2318
1.2478
1.2639
1,2803
1.2969
1.3137
PUBLIC
FUNDS
(G)
1.0000
1.0848
1.1612
1.2302
1.3402
1.4769
1.5851
1.7094
1.8195
2.0174
2.1841
2.3592
2.5277
2.8152
3.0372
3.2941
3.5823
3.8883
4.2057
4.5535
4.9514
5.3795
5.8179
6.2952
6.6859
PRIVATE
FUNDS
(I)
l.CCCO
1.C371
1.0670
1.C684
1.1261
1.1657
1.2056
1.2631
1.2906
1.3363
1.3831
1.4:il
1.4934
1.5470
1.6C48
1.6£t7
1.7427
1.8C80
1.8125
1.5405
2.0116
2.CS49
2.1535
2.2467
2.3369
giAHTY
LEVEL
1C)
l.CCCO
1.0310
C.82S6
C.9636
0.9918
1.C26S
1.0548
0.8748
1.0143
1.0528
1.0878
C.9C61
1.0600
1.1055
1.1451
1.1959
1.2467
1.3013
1.3559
1.1136
1.4583
1.3034
1.5168
1.7338
1.C2C5
NATURAL
ORE LSAGE
(N)
l.CCOO
1.0478
C.83C2
C.95CO
1.0090
1.C5C3
1.C92C
0.9098
1.C586
1.1262
1.1777
C.SS70
1.1673
1.2628
1.3614
1.5018
1.6394
1.7S50
1.9441
2.C912
2.2280
1.5? 14
2.4748
2.6421
2.8169
ENERGY FARM ANC
USAGE LAND USAGE
(E) IF)
l.CGCO 1.0000
1.0450 1.0270
0.8321 0.9469
0.9645 1.01C9
1.0161 1.0369
1.0670 1.0641
1.1113 1.0900
0.89C1 1.0289
C.9992 1.0935
1.0580 1.1239
1.1097
C.93S5
1.1358
1.2662
1.4158
1.6099
1.E443
2.0512
2.2446
2.4518
2.61C8
.1537
.0972
.1716
.20J5
.2459
.2863
.3264
.3689
.4099
.4549
.4181
2.2721 1.2165
2.9227 1.2063
3.515S 1.2961
3.639C 1.3468
EMPLOYED
WORKERS
(U)
1.0000
1.0504
0.7976
0.9.506
1.0031
1.0636
1.1138
0.8773
1.0495
1.1172
1.1801
O.S384
1.1284
1.2096
1.2789
1.3578
1.4416
1.5319
1.6239
1.7229
1.8309
1.8499
2.0652
2.1966
2.3210
TREATED
ECO-MEOIA
IK)
1.0000
1.0308
0.8631
0.9599
O.t917
1.0245
1.0543
O.S160
I.C174
1.0512
1.C834
0.9499
1.0593
1.C951
1.1332
1.1844
1.2225
1.2666
1.31C4
1.3549
1.3635
1.1559
1.3253
1.3961
1.4545
3.6
3.2
2.3
STATE OF THE SYSTEM
« YEARS
2.4
2.0
1.6
1.2
c.a
G I I
w i i P w
M M P F M M
F M
M
G
I
M
G
G
G
G
I
I I
I
F W
P M M M
F M
M
M
I I
P W
F M
N
M
E
N
N
E I
N I
E I
N H
I I H
I E N H
I M
N W F Q
E F F Q M
H F Q M W
M W P M P P P
P C M P
P
E I
M
I 1
M
N
a
a
N
Q M
M
Q P F F
F F
f
C.4
-0.0
1.0
3.5
6.0
8.5
11.0
YE«RS
13.5
16.0
FIGURE 44
RUN 1 SUMMARY DATA
162
18.5
G
21.0
G G G
23.5
G G
26.0
-------
2.0
TABLE NUMBER CNE - FCPILATION
(SCALEC TO OPIGIML VALUE)
... ~T.Sc, ,"Ss SjB Hi5' "°Hr
n S4I1 C.L237 0.4435 C.1019
O'.ioo] O:l258 0.4*98 0.1048
;i iiss sss r-is Sias tss
I 1 I II 1 I
I 1 I I 1 1
1 I I I II 1
POPLLATION
, . i i • YEARS • '
4.0
3.6
3.2
2.8
P P P
1.2 P P P P P
P P P P P P
P P P P P P P
P F P P
O.B
333
3333333
33333333
C.4 3333333
llllllll 11111111111
111111
4444
i t
1.0 3.5
44444'
i i
6.0 8.5
444
i
11.0
4 4
YEtRS
13.:
444
•
16.0
4 4
i
18.5
444
•
21.0
444
i
23.5
26.0
FIGURE 45
RUN 1 POPULATION DATA
163
-------
TA8LF MNBFR TWO - PUBLIC SECTOR ('I IT PUT UMTS
(SCALED TO ORIGINAL VALUCI
YE'AR
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
EDUCATION
(E)
1.0000
1.0819
0.8308
1.0294
1.1146
1.2245
1.3089
1.0417
1.2768
1.3841
1. 5167
1.2167
1.4933
1.6485
1.7770
1.9202
2.0804
2.2519
2.4292
2.6208
2.8337
3.0668
3.3602
3.7345
4.2434
TRANSPCRTATION
(T)
1.0000
1.0328
0.7644
0.8803
0.9102
0.9411
0.9725
0.7438
0.8846
0.9150
0.9459
0.7305
0.8662
0.8956
0.9256
0.9572
0.9893
1.0226
1.0575
1.0921
1.1274
1.1640
1.2017
1.2407
1.2807
HEALTH
1.0000
1.0906
0.8580
1.0657
1.2039
1.2963
1.38S2
1.1412
1.4066
1.58S8
1.7046
1.4119
1.7571
1.9858
2.1573
2.3750
2.6183
2.8B10
3.1468
3.4425
3. 7936
2.3828
4.4899
4.9665
5.4544
PEFfNSF
AND TTHFB
(P)
1.0000
1.0500
0.7785
0.<;b60
1.0042
1.0546
1.1047
0.8479
1.0235
1.0800
1.1329
0.8808
1.0699
1.1227
1.1788
1.2331
1.2900
1.3544
1.416?
1.4815
1.5500
1.6245
1 .6996
1.7789
1.8621
(W)
1.0000
1.0880
O.P323
1.0313
1.123?
1.2503
1.3411
1.C668
1.3073
1.4629
1.57<.?
1.7700
1.5601
1.7466
1.88(14
2.0507
2.2355
2.4312
2.634?
2.8559
3.1090
3.3811
3.8465
5.8451
6.1298
0.4
PUBLIC
YFAPS
3.6
3.2
2.8
2.0
1.6
1.2
H
H
H H =
H Vi Vt
H M E
W H
W
H E
M
H F
M
F
H H W
E
Vi M
E r
H
D
W D
0 D D
0.8
-0.0
1.0
3.5
6.0
8.5
11.0
YFAPS
13.5
16.0
FIGURE 46
RUN 1 PUBLIC SECTOR OUTPUT DATA
164
18.5
21.0
23.5
H W
26.0
-------
TABIE NUMBER THPFE - PRIVATE SECTPP riJTPUT UNITS
(SCALED. TO CRIGINAL VALUE!
YEAR
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
1*.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24,
25.
HEAVY POLL.
MANUFACTURE
(H)
1.0000
1.0398
0.8039
0.9403
0.9B72
1.0352
1.0752
0.8796
1.0230
1.0689
1.1104
0.9119
1.0658
1.1103
1.1591
1.2339
1.2802
1.3405
1.3952
1.4524
1.5111
1.0064
1.6765
1.7400
1.8318
LICI-T POLL.
MANUFACTURE
(L)
1.0000
1.0454
0.8118
O.S378
0.9814
1.0267
1.C658
0.8810
1.0123
1.0602
1.1042
0.9146
1.0538
1.10?2
1.1520
1.2426
1 . 2 8 74
1.3452
1.4007
1.4578
1.5168
1.5818
1.56d3
1.6719
1.7103
(C)
1.0000
1.0208
0.7486
0.8581
0.8771
0.8964
0.9132
0.6939
0.8143
0.8324
0.8492
0.6504
0.7636
0.7809
0. 7986
0.8169
0.8369
U.8559
0.8753
0.8956
0.9153
0.8996
0.9840
1.0342
1.0827
AGRICULTURE
(F)
1.0000
1.0005
0.8443
0.9202
0.9229
0.9256
0.9263
0.7850
0.8379
0.6407
0.8424
0.7095
0.7740
0.7767
0.7790
C.7614
0.7836
0.7862
0.7886
0.7907
C.7709
0.6989
0.7102
0.7538
0.7861
HPUSEHCLD £
RECREAT inn
(R)
1.0000
1 .0358
1.0639
1 .0989
1 .1323
1.1676
1.2027
1.2400
1.2811
1.3221
1.3635
1.4093
1.4640
1.5160
1.5720
1.6321
1.6922
1.7539
1. 8?1 0
1.8879
1.8096
1.4671
1.4043
1.5241
1.5835
PRIVATE SECTnp
4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
R R
R R
L R R L
R L L L
F F F F L
FCC H F
C F
C
L L L
L
F - F
0.4
-0.0
1.0
3.5
6.0
8.5
11.0
YEARS
13.5
16.0
18.5
FIGURE 47
RUN 1 PRIVATE SECTOR OUTPUT DATA
165
21.0
73.5
26.0
-------
TABLE MJMBER FOUR - NATURAL RESOURCES LSAGE
(SCALED TO ORIGINAL VALUEI
YEAR
1.
2.
3.
4.
5.
6.
7.
a.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
1RCN
(I)
l.JOOO
1.0358
C.8048
0.9685
1.2883
1.4J72
1.2086
1.3984
1.4570
1.5105
1.2386
1.4413
1.4985
1.5604
1.6558
1.7146
1.7901
1.8596
1.9319
2.0039
1.4746
2.1375
2.2779
2.3878
COPPER
(C)
l.OCOC
1.0404
C.8C47
O.S036
C.7249
0.7600
0.6862
0.5279
0.6132
C.64C8
0.6659
0.5473
0.6302
0.6399
0.6399
0.6410
0.6149
0.5912
0.5688
0.5568
0.5543
0.3830
0.5S<6
C.6239
0.6551
LEAC
AND ZINC
(L)
1.0000
1.C419
0.8077
0.9462
C.9958
1.0420
1.CB35
C.6797
1.0285
1.C830
1.1262
0.9207
1.C942
1.1712
1.2580
1.2832
1.5021
1.6364
1.7671
1.8909
2.0081
1.J227
2.2344
2.3582
2.4944
MERCURY SILVER
m (s>
1.0000 1.0000
1.0514 1.0633
0.8267 0.7614
0.6065 0.4671
C.6465 C.5093
0.5165 0.3197
C.4713 0.2432
C.4084 C.1984
0.4676 0.2388
C.5005 0.2611
0.5245 0.2763
0.4567 0.2272
C.5285 C.2762
0.5676 0.3030
C.6007 0.3244
C.6449 C.3526
0.6663 0.3810
C.1323 0.4125
0.7785 0.4438
O.E286 0.4784
C.8131 C.5186
0.6383 0.3368
C.9392 0.6026
1.021S C.6564
1.C973 0.7130
TRACE
ORES
IT)
1.0000
1.0541
0.9759
1.8C61
1.9434
2.3754
2.6308
2.2361
2.6054
2.8148
2.9607
2.5317
3.0362
3.3963
3.7849
4.3331
4.9378
5.6055
6.2467
6.8604
1.4078
5.2290
8.2855
8.9141
9.5540
4.0
3.6
3.2
2.S
NATURAL RESOURCES
• YEARS
2.4
2.0
I '
L
1.6
1.2
0.8
0.4
C C
M
S M
S
I I
I
i I
I I
C C MM
C C M M C
C M M C M
S S S
S S S S
S S S
-0.0
< • • ' • YEARS '
1.0 3.5 6.0 8.5 11.0 13.5 16.0
T T
FIGURE 48
RUN 1 NATURAL RESOURCES USE DATA
18.5
T T
21.0
T T T
23.5
T T
26.0
166
-------
TA8LE NUMBER FIVE - ENERGY £ AGRICULTURAL USAGE
(SCALEC TO ORIGINAL VALUE)
Y64R
1.
2.
3.
4.
5.
b.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
CCAL
(C)
1.0000
1.0*25
0.8306
C.9592
1.0082
1.0562
1.0981
1.0019
1.259C
1.3249
1.3838
1.2264
1.5955
1.9540
2.4383
3.0770
3.9128
4.5929
5.207C
5.U625
6.3031
5.4605
7.0740
8.5725
S.3719
CIL
(0)
l.CCCC
i.ojea
C.8315
C.9517
O.SS4S
1.C370
1.0744
0.713-)
0.6148
0.6452
0.6725
C.5623
0.6508
0.6E67
0.7188
0.7604
C.7S79
0.83S5
C.8815
C.9262
C.S651
O.S57C
1.C2S3
1.1051
1.1864
ELECTRICITY
IE)
l.COOO
1.0539
C.8341
C.S826
1.C452
1.1C79
1.1616
C.S545
1.1238
1.2040
1.2728
1.C2S8
1.1610
1.1579
1.0902
0.9924
C.8222
0.7211
C.64S4
C.5666
0.5641
C.4989
0.6647
O.E661
C.S5S8
TIMBER
IT)
l.CCOO
1.0372
C.SS68
1.C265
I.C6L5
1.CS82
1.1327
1.0777
l.l!38
1.1946
1.2343
1.1850
1.2709
1.3183
1.3687
1.4337
1.4692
1.5415
1.6003
1.6597
1.6323
1.4448
1.4135
1.5264
1.5846
FOOC
IF)
l.COOO
1.0287
1.0200
1.0631
1.0904
1.1192
1.1475
1.1490
1.1925
1.2259
1.2S93
1.2693
1.3260
1.3631
1.4134
1.4620
1.5105
1.5604
1.6145
1.6685
1.6019
1.3135
1.2655
1.3700
1.4240
4.0
3.6
3.2
2.8
2.4
2.0
ENERGY C AGRICULTURES)
' YEARS
1.6
1.2
C.8
E
f
F
T
E
F
T
0
F F
F F C T
CO C
E
C
F
C
C
F F
T
F
T
E
F
T
E
F
T
E
0.4
-0.0
1 • • ' • YE»RS
1.0 3.5 6.0 8.5 11.0 13.5
FIGURE 49
16.0
1S.9
C C
21.0
C C C
2J.9
C C
26.0
RUN 1 ENERGY AND AGRICULTURAL PRODUCTS USE DATA
167
-------
TABLE NUMBER SIX
UNEMFL3YMENT AND COL VALUES
YEAR UNEMPLOYMENT CUALUY
(Ul IQ)
1. O.OC81 1.3487
2. 0.0355 1.3905
3. C.27B9 1.1189
4. C.0800 1.2497
5. 0.0768 1.3377
6. 0.0415 1.3877
7. 0.0169 1.4227
8. 0.2427 1.17S8
9. 0.0431 1.3680
10. C.0348 1.4199
11. C.0010 1.4671
12. 0.2207 1.2222
13. 0.0010 1.4296
14. C.0010 1.4910
15. 0.0010 1.J445
16. 0.0010 1.6129
17. 0.0010 1.6815
18. 0.0010 1.1551
19. 0.0010 1.8268
20. 0.0010 1.S066
21. 0.0010 1.S668
22. 0.0010 1.1580
23. 0.0010 2.0458
24. 0.0010 2.33E5
25. 0.0010 2.4555
4.0
EMPLOYMENT, COL
• YEARS
3.6
3.2
2.8
2.4
2.0
1.6
1,2
C.8
0.4
-C.O
3.5
u u u
I
6.0
U
I
8.5
u -u
I
11.0
UU
YEARS
u
I
16.0
13.5
FIGURE SO
RUN 1 UNEMPLOYMENT AND QOL VALUES
16S
u.s
U U U
•
21.0
lt.0
-------
TABLE NUMBER SEVEN - LAND, AIR AND WATER USAGE
(SCALEC TO ORIGINAL VALUE)
YEAR
1.
2.
3.
4.
5.
6.
7.
a.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Id.
19.
20.
21.
22.
23.
24.
25.
URBAN
(U)
1.0000
1.0335
C.9623
1.0236
1.0546
1.0871
1.1194
1.0690
1.1411
1.1/72
1.2135
1.0567
1.1280
1.1668
1.2082
1.1272
1.1&72
1.2082
1.1272
1.1670
1.1363
C.9744
0.-J569
1.0255
1.0648
SLBURBAN
(S)
1.0000
1.0354
O.S512
1.0210
1.0550
1.0905
1.1243
1.0638
1.1421
1.18C9
1.2191
1.2654
1.3591
1.407S
1.460C
1.6274
1.6657
1.7479
1.9190
1.S8E6
1.9492
1.6511
1.6856
1.8C48
1.8746
ARABLE
(F)
1.0000
1.COC5
0.8443
0.9202
C.9229
0.9256
C.?2<3
C.7850
0.6379
C.84C7
0.6424
0.7095
C.7740
0.7767
C.7790
0.7814
C.7836
0.7862
0.7866
C.79C7
C.77C9
0.6999
C.7102
0.7538
0.7861
TREATED UMTS OF MEDIA
(Al IM)
l.COOO
1.0453
0.8001
C.9350
C.S813
1.0300
1.C746
0.8717
1.0241
1.C725
1.1190
C.9235
1.C820
1.1319
1.1854
1.2536
1.3078
1.37CO
1.4316
1.4942
1.5217
1.2020
1.5402
1.6214
1.7021
1.0000
1.0313
0.8576
0.9647
C.9974
1.0313
1.0611
0.9182
1.0193
1.0556
1.C895
C.9512
1.0662
1.1057
1.1475
1.2074
1.2465
1.2965
1.3444
1.3931
1.3870
1.1877
1.2732
1.3740
1.4340
4.0
3.6
3.2
2.8
2.4
LAN013), AIR ANC WATER
YEARS
1.6
1.2
C.8
A
M
U H
S A
M
S S
M M
F F
S
M
F
S
W
A
f
S
M
f
S
M
F
S
M
F
S
S
U
U M
W
F
S
A
M
F
U
M
F
M
U
F
A
M
U
F
A
M
U
F
A
M
U
F
M W
U U
F F
A
M
U
0.4
-0.0
i t • • • YEARS •
1.0 3.5 6.0 8.5 11.0 13.5 16.0
FIGURE 51
RUN 1 LAND, AIR AND WATER USE DATA
169
13.5
21.0
23.5
26.0
-------
• Useful data base variants to be checked parametrically
include:
• reduction of initial economic output by
reducing availability of input funds
• reduction of demand levels - both total
consumer levels and per capita thresholds.
The first variation is analyzed next, the second is considered
in appendixes of this report.
PARAMETRIC VARIATION OF INVESTMENT GROWTH RATES
In order to reduce stress on the region, several data
changes could be made. For the next analysis, the growth
of production was reduced by altering the annual growth
rate of funds available for maintenance and production.
As a first analysis, five runs in addition to the Base
Case were done with identical data except the funds growth
rates. Figure 53 lists the level of funds used for each
variation.
Annual Fund Growth Rate (in %)
Component/Run 12345 6
Education 8.2 5.0 4.0 2.0 0.0 -2.0
Transportation 3.4 3.4 4.0 2.0 0.0 -2.0
Health 9.9 5.0 4.0 2.0 0.0 -2.0
Defense § Other 5.0 5.0 4.0 2.0 0.0 -2.0
Welfare 8.8 5.0 4.0 2.0 0.0 -2.0
Hvy. Polluting Ind. 4.7 4.7 4.0 2.0 0.0 -2.0
Lgt. Polluting Ind. 4.6 4.6 4.0 2.0 0.0 -2.0
Commercial 2.2 2.2 4.0 2.0 0.0 -2.0
Agricultural 0.3 0.3 4.0 2.0 0.0 -2.0
Household § Rec. 3.8 3.8 4.0 2.0 0.0 -2.0
FIGURE 53
VARIATION OF INITIAL DATA FOR RUNS 1-6
170
-------
Thus, Run 2 varied from Run 1, the Base Case, only by reducing
the rapid growth of education, health and welfare funds
of the past twenty years to a level still in excess of any
level noted in components of the private sector. Runs 3
through 6 provide growth rates for all components that are
constant within each run; as such, in Run 3, the components
of the private sector actually have more funds growth than
in Run 1 while all other sectors for all other runs have
reduced funds, thus predicting reduced rates of resource
usage.
The question arises; what statistics from a run of the model
provide an appropriate comparative measure of regional quality
over the 25 years? For this analysis the effectiveness measure
was taken as having three elements:
• no resource should be depleted, or have an appearance
of imminent, long-term depletion
• satisfaction of demands and levels of production
should be reasonably smooth over the entire run
• population growth and demand satisfaction for all
11 measures should be maximized and growing with
relative consistancy.
Figure,- 54 addresses the third of these factors by listing
the final values of population size, the final year value of
the combined QOL demand satisfaction measure, plus the number
of measures that were not satisfied in year 25 or whose thres-
holds were lowered during the run. Also listed is the need
for long term funds redistribution during the run.
Population Size 1.314 1.295 1.297 1.279 1.143 .998
Combined QOL 1.820 .977 1.096 1.110 .865 -601
Deficient Measures 5 4 7 2 4 11
Reset Funds Y N N N N N
FIGURE 54
COMPARISON OF POPULATION FACTORS, RUNS 1-6
171
-------
As an initial analysis, the following elements are noted.
Run 1 does support the greatest population with the highest
combined QOL level of all of the runs; however, as was noted
in the analysis above for the run the QOL values do not have
an internally consistant trend and major resource deficiencies
exist.
The comparative values of the QOL measures in Runs 1 and 2
had a different cause; in Run 1 it had been noted that the
growth in values was quite divergent among the measures due
to the level of funds available to the components of HEW.
When the growth of HEW were effectively reduced 40% for
Run 2, the combined QOL value was significantly reduced,
never growing above 1.10 of the original value. Hence,
Run 2 must be rated as inferior to Run 1 and highlights the
primary problems of Run 1, imbalance of the measures plus
significant depletion of scarce resources (food, silver,
fuels) .
Runs 3 and 4 appear the smoothest in terms of population
and QOL growth plus maintenance of demand thresholds with-
out a major funds adjustment. Run 4 supported a population
smaller than Run 3 by 1.5% at a 2.01 higher QOL and at a
much lower funds growth level (2% vis-a-vis 4%) and while
maintaining high, consistant satisfaction of per capita
demands (9 satisfied compared to 4).
The output of Run 5 (0.0 funds growth) and Run 6 (reduction
of funds) clearly indicate that stagnation in economic growth
while allowing population growth to continue provides a much
reduced QOL satisfaction level and, for SOS-1, resulted in
high unemployment and out-migration.
A second analysis of these six runs concerns the avialability
of resources. This comparison is not quite the straight-
forward trend that might be expected. Increased resource
usage in some cases caused a price rise, thus stimulating
in SOS-1 adjustments expanded economically available stock-
piles. Figure 55 provides the remaining stockpiles for year
25 for the eight nonrenewable resources.
172
-------
Iron
Copper
Lead, Zinc
Mercury
Silver
Trace Metal
Coal
Oil
12900. 6700. 7300. 12100.
17100. 17900. 17000. 16900.
13600. 3800. 8900. 4200.
1400. 4900. 4900. 5100.
0. 800. 1200. 1000.
12600. 20400. 21000. 18742.
5800. 7400. 7700. 7600.
4800. 5000. 9800. 4900.
FIGURE 55
14000. 13200.
14100. 14600.
20100. 20200.
4200. 5300.
1000. 900.
13700. 15300.
8600. 7200.
6200. 17900.
REMAINING STOCKPILES AT t=25, RUNS 1-6
The unit cost mechanism for expanding stockpiles and perserving
stocks of critical resources by substitution 'appears quite
effective except for Run 1, silver and mercury. To choose a
best usage run among Runs 3-6 is hazardous. Run 2 appears
consistantly lower in reserves than the other 4 runs but has
no emergency situation in the durable ores. Hence, based
on this statistic any run among 2-6 appears quite acceptable.
In the other resources, Runs 1 and 2 as discussed earlier had
a severe shortage in food. Both also had high salary rate
growth and extended work weeks in year 25. Run 3 had a salary
increase over 25 years of 50% while Run 4 experienced a 10%
increase. In terms of steady low unemployment Run 4 is the
smoothest; Run 3 in five years had unemployment over 10%
while Runs 5 and 6 have steadily increasing unemployment to
high values as production dropped. For Run 4 the employment
spread is 4.5%-9.0% except for two years.
Based on the resource utilization and availability statistics
Run 4 is appears best followed by Run 3. Run 1 is unacceptable
and Run 2 suggests growing problem areas.
The final criterion of goodness is smoothness of trends. Figure
44 is the summary data for Run 1; Figures 56-60 provide the
same for the other runs. Runs 1-3 provide rather ragged
173
-------
SUMMARY TA8LF - STATE OF THE SYSTEM
(SCALED TO ORIGINAL VALUE)
YEAR
I.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
POPULATION
tP)
1.0109
1.0211
1.0324
1.0376
1.0478
1.0582
1.06?7
1.0817
1.0917
1.1048
1. 1084
1.1155
1.1305
1.1436
1.1576
1.1678
1.1830
1.1 E67
1.2011
1.2151
1.2308
1.2468
1.2629
1.2786
1.2952
PUBLIC
FUNDS
(G)
1.0000
1.0491
1.0915
1.1162
1.1715
1.2356
1.3073
1.3619
1.4306
1.4935
1.5299
1.6074
1.7372
1.8110
1.8938
1.9841
2.0958
2.1613
2.2762
2.4419
2.5626
2.6780
2.8002
2.9415
3.0834
PRIVATE
FUNDS
(I)
i.oooo
1.0371
1.0670
1.0884
1.1258
1.1792
1.2126
1.2533
1.2974
1.3365
1.3736
1.4185
1.4977
1.5468
1.6033
1.6453
1.7368
1.7895
1.8513
1.9269
2.0268
2.0830
2.1702
2.2612
2.3554
QUALITY
LEVEL
(0)
1.0000
1.0187
0.9015
0.9777
0.9947
1.0235
1.0374
1.0041
1.0556
0.8908
1.0015
1.0179
1.0593
1.0740
1.0067
1.0794
0.8908
1.0276
1.0471
1.0799
1.0837
1.0420
1.0488
1.0518
0.9771
NATURAL
ORE USAGE
(N)
1.0000
1.0373
0.9157
0.9852
1.0278
1.0R25
1.1033
.0826
.1635
.9759
.1063
.1574
.2596
.3270
1.2984
1.4600
1.2573
1.5048
1.6079
1.7109
1.8081
1.8399
1.9167
1.9880
2.0159
ENERGY
USAGE
(E)
1.0000
1.0346
0.9164
0.9992
1.0369
1.0893
1.1170
1.0568
1.0906
0.9172
1.0345
1.072?
1.1365
1.1686
1.1190
1.2429
1.0703
1.3055
1.4498
1.6431
1.7723
1.8351
1.9406
2.0177
1.9087
FARM AND
LAND USAGE
(F)
1.0000
1.0270
0.9892
1.0364
1.0629
1.0940
1.1190
1.1239
1. 1634
1.1077
1.1729
1.2053
1.2484
1.2802
1.2766
1.3339
1.2764
1.3617
1.4033
1.4502
1.3945
1.2114
1.2369
1.1840
0.8581
EMPLOYED
WORKERS
(U)
1.0000
1.0381
0.8959
0.9921
1.0315
1.0769
1.1158
1.0815
1.1632
0.9445
1.0878
1.1316
1.1960
1.2363
1.1462
1.2585
0.9786
1.1639
1.2144
1.2773
1.3334
1.3801
1.4349
1.4940
1.5431
TREATED
ECO-MEDIA
(M)
1.0000
1.0308
0.9417
1.0086
1.0418
1.0869
1.1127
1.0984
1.1586
1.0257
r. 1250
1.1591
1.2162
1.2502
1.2026
1.2774
1.1170
1.2504
1.2933
1.343-0-
1.3573
1.2980
1.3381
1.3440
1.2215
4.0
3.6
3.2
2.8
STATC OF THE SYSTEM
YEARS
1.6
1.2
0.8
G
M
I
F
M
I
f
I
M
W
G
I
V
C
G
I
M
0
G
I
F
M
Q
r,
i
M
E
a
i
F
M
W
G
I
M
W
E
I
F
M
E
0
I
H
M
0
I
F
M
E
0
G
H
M
W
E
0
G
I
N
f
M
P
0
I
F
P
M
K
Q
I
N
F
E
M
W
0
I
N
E
f
M
W
Q
1
N
E
F
M
W
0
I
E
F
f
P
Q
E
W
M
F
Q
E
N
M
M
F
0
E
N
M
M
P
F
0
N
f
W
P
M
Q
F
0.4
-0.0
r.o
T.5
6.0
8.5
11.0
YEARS
13.5
FIGURE S6
16.0
RUN 2 SUMMARY &ATA
174
18.5
21.0
-------
SUMMARY TABLE - STATE Of THE SYSTEM
{SCALED TQ CRIGINUL VALUE)
YEAR POPULATION
1.
2.
3.
4.
5.
6.
7.
3.
g.
U.
11.
12.
13.
14.
15.
16.
17.
18.
1-3.
20.
21.
22.
23.
24.
25.
(P)
1.010S
1.0211
1.0324
1.0334
1.0475
1.058C
1.0692
1.0816
1.0876
I.C99C
1.1106
1.1240
1.1332
1.1472
1.1541
1.1678
1.1830
1.1881
1.2027
1.2112
1.2330
1.2490
1.2651
1.2615
1.2S70
PUBLIC
FUNDS
(G)
1,0000
1.0400
1.0742
1.0885
1.1323
1.1779
1.229S
1.2747
1.3136
1.3730
1.4336
1.4834
1.5398
1.6111
1.6603
1.7447
1.8148
1.8782
1.9541
2.0387
2.1334
2.2182
2.2981
2.4245
2.5025
PRIVATE
FLNDS
(I)
l.OCCO
1.C400
1.0721
1.C943
1.1369
1.1567
1.2352
1.2726
1.3037
1.37CC
1.4165
1.4675
1.5280
1. 5((5
1.6289
1.7185
1.7624
1.8396
1.S336
2.CC60
2.C£68
2.1651
2.2451
2.3384
2.4171
CUALITY
LEVEL
(C)
i.ccco
1.0259
0.9C77
C.99C9
1.0189
1.0436
1.C790
C.9669
i.csts
1.C923
1.1253
1.C595
1.1357
1.0228
1.1227
1.1703
C.S954
1.13C9
1.16C5
1.1934
1.2365
1.2649
1.28<1
1.0355
I.CS64
HATUKAL
CRE LSAGE
IN)
i.coco
1.0345
O.S057
C.S732
1.0140
1. 0444
1.CS57
0.9743
1. C672
1.1242
1. 1681
1.1C94
1.2259
1. 1201
1.2731
1.4033
1.2175
1.4286
l.53«3
1.6249
1.7012
1.7637
1.8C28
1. 1819
1.4654
ENERGY
USAGE
HI
1.0000
1.C370
0.9142
C.S996
1.0415
1.C8C5
1.C97I
0.9460
1.C347
1.C875
1.1356
1.0717
1.1590
1.04C7
1.1420
1.2133
1.C364
1.21C9
1.3227
1.4547
1.6534
1.6058
1.9346
1.57S5
1.6422
FARM AND EMPLOYED
LAND USAGE WORKERS
(F) (Ul
1.0000 1.0000
1.0379 1.0388
1.0040 0.8899
1.06CC 0.9880
1.1021 1.0291
1.1379 1.0687
1.1815 1.1179
1.1545 0.9761
1.2185 1.0851
1.2679 1.1349
1.3147 1.1923
1.3C98 1.1069
1.3813 1.2080
1.3569
1.4368
1.5090
1.4454
1.5470
1.6163
1.6753
1.7486
1.8083
1.8399
.C497
.1727
.2436
.0056
.1619
.2114
.2609
.3324
.3835
.4297
1.0437 1.3053
1.3303 1.4164
TREATED
ECO-MEDIA
(W)
i.ccco
1.0363
0.9468
1.C18T
1.0615
1.CS88
1.1477
1.C675
1.1486
1.2071
1.2558
1.2129
1.3058
1.2051
1.3012
1.3799
1.2256
1.3521
1.4207
1.4749
1.5447
1.5993
1.6352
1.0184
1.2632
4.0
3.6
3.2
2.8
STATE OF THE SYSTEV
• YEARS
2.4
2.0
1.6
1.2
0.8
0.4
I
f
M
I
I F H
F M M M
M W
I
F
p*
W
E
I
F
M
M
E
I
M
W
E
I
F
M
M
P
I
F
M
P
M
G I
I I
f F
M F M
M M N
E N M
W
Q
I
G
I I F
I F
F F E
F N M N
F F H
C N M W
M fc W
M M E M K 0 0
o P M Q a
M
E
F
W
Q
P
-0.0
< ' • • • YEARS
1.0 3.5 6.0 8.5 11.0 13.5
FIGURE 57
RUN 3 SUMMARY DATA
175
16.0
13.5
21.0
23.5
26.0
-------
SUMMARY TABLE - STATE OF THE SYSTEM
[SCALED TO CRIGIML VALUE)
YEAR POPULATION
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
(Fl
i.oios
1.0211
1.0317
1.0423
1.0531
1.0(40
1.0748
l.C£56
I.OS64
1.1072
1.1181
1.1290
1.1401
1.1511
1.1638
1.1764
1.1895
1.1942
1.2050
1.2155
1.2267
1.2387
1.2515
1.2647
1.2785
PUBLIC
FUNDS
(G)
1.0000
1.0200
1.0368
1.0547
1.0724
1.0909
1.1095
1.1287
1.1482
1.1682
1.1886
1.2094
1.2341
1.2580
1.2832
1.3082
1.3342
1.3294
1.3599
1.3910
1.4268
1.4573
1.4896
1.5194
1.5756
PRIVATE
FUNDS
(I)
l.CCCO
1.02CO
1.0360
1.0536
1.C702
1.C853
1.1034
1.1215
1.1399
1.1568
1.1763
i.isei
1.2217
1.2440
1.2(63
1.2924
1.3166
1.331C
1.357S
1.3850
1.4127
1.4605
1.4846
1.5139
1.M24
CUALITY
LEVEL
1C)
l.CCCO
i.ccti
1.0083
1.C145
i.ciae
1.0199
1.0261
1.0324
1.0390
1.0456
1.0514
1.C575
1.C669
1.0741
1.C624
1.C899
0.9420
1.C287
1.0412
1.0545
1.C7C8
1.0865
1.CS66
1.1062
1.1179
NATURAL
CRE LSAGE
IN)
1.0000
1.0146
1.0210
1.02QI
1.0353
1.0424
1.C549
1.0713
1.0615
1.1030
1.1190
1.1449
1.1629
1.2313
1.2951
1.3661
1.2215
1.3748
1.4336
1.4666
1.5364
1.5970
l.«238
1.6539
1.6824
ENERGY
USAGE
(6)
l.COCO
1.C170
1.C3CO
I.C461
1.C643
1.C7S5
1.C6Q2
1.C4C1
1.054S
1.C732
1.09CO
1.1C70
1.127C
1.1454
1.1657
1.2028
1.C632
1.2C80
1.3055
1.4187
1.5423
1.7016
1.7842
1.8499
1.S032
FARM AND EMPLOYED
LAND USACE WORKERS
(F) (Ul
1.0000 1.0000
1.0179 1.0189
1.0321 1.0343
1.0498 1.0521
1.0662 1.0694
1.0765 1.C859
1.0968 1.1042
.1147
.1331
.1513
.1700
.1890
.2C89
1.22S7
1.2524
1.2751
1.2131
1.2712
1.3018
1.3271
1.3510
1.3325
1.4082
1.4356
1.4623
.1230
.1420
.1611
.1805
.2003
.2235
.2453
.2684
.2918
.0711
.1847
.2120
.2395
.2693
.3006
.3278
.3540
.3859
TREATED
ECO- MEDIA
(M)
l.OOCO
.C169
.0300
.C462
.0653
.C793
.C976
.1159
1.1344
1.1523
1.1708
1.1894
1.2114
1.2315
1.2534
1.2751
1.1391
1.2199
1.2478
1.2733
1.3003
1.3412
1.3642
1.3904
1.4156
3.6
3.2
2.8
2.4
2.0
1.6
1.2
C.8
C.4
STATE OF THE SYSTEM
• YEARS
M
N
M
N
M
Q
M
G
V|
M
C
M
E
Q
M
E
M
E
W
M
E
M
E
a
M
E
G
N
M
E
Q
N
M
M
P
C
I
F
M
M
N
I
M
W
Q
N
F
M
0
N
E
f
M
0
E
I
M
M
Q
N
I
F
M
P
C
I
M
k
P
C
I
M
H
P
Q
I
T
M
P
Q
-0.0
i i • i i YEARS •
1.0 3.5 . 6.0 8.5 11.0 13.5 16.0
FIGURE 58
RUN 4 SUMMARY DATA
176
18.5
21.0
23.5
26.0
-------
SUMMARY TABLE - STATE Pf THF SYSTEM
(SCALED TO ORIGIKAL VALUE)
YEAR POPULATION
IP)
1. 1.0109
7. 1.0711
3. 1.0309
4. 1.0401
5.
6.
7.
8.
9.
10.
a.
12.
13.
14.
15.
16.
17.
1»,
IS.
70.
21.
22,
23.
24.
25.
.0436
.0564
,0639
,07C«
.0771
.0032
.0888
.0939
.0987
.1033
.1075
.1116
.1155
.1193
.1230
.1265
.1299
.1332
.136*
.1395
.1425
PUBLIC
FUNDS
(G>
1.0000
1.0000
1.0000
0.9954
0.995*
0.9954
0,995*
0.995*
1.0000
1.0000
1.0000
1.0000
1.9000
0.9954
0.9954
0.995*
0.995*
0.995*
C.9954
0.995*
0,9954
0.9954
0.995*
0.995*
0.9954
PRIVATE
FUNDS
(I)
1.0000
1.0000
1.0000
0.9979
0.9840
0.9840
0.9840
0.9840
0.9861
0.9861
0.9861
C.9861
0.9861
0.9840
0.9840
0.9840
0.9840
0.984Q
0.9840
0.98*0
0.98*0
0.9840
0.98*0
O.S840
0.9840
QUALITY
LEVEL
(Q)
1.0000
0.9864
0.974*
0.9595
0.9*75
0.9*05
0.9328
0.9263
0.9281
0.9231
0.9175
0.9128
0.9085
0.8982
0.8950
0.8913
0.8879
0.8846
0.8812
0.8784
0.8757
0.8728
0.8701
0.8674
0.8649
NATURAL
ORE USAGE
IN)
1.0000
0.99*7
0.986*
0.9688
0.9532
0.9*67
0. 9428
0.9419
C.9440
0.94*1
0.9432
0.94?*
0.9497
0.9634
0.9871
1.0192
1.0575
1.0950
1.1250
1.1504
1.1660
1.1730
1.1720
1.1709
1.1692
ENERGY
USAGE
IE)
1.0000
0.9971
0.9945
0.9894
0.9803
0.9808
0.9800
0.9464
0.9207
0.9210
0.9206
0.9202
0.9198
0.0133
0.9128
0.9119
0.9112
0.9103
0.9089
0.9091
0.9089
0.9084
0.9078
0.9072
0.9064
FARM AND
LAND USAGE
IF)
1.0000
0.9979
0.9967
0.9953
0.9918
0.9918
0.9911
0.9907
0.9937
0.9940
0.9939
0.9937
0.9936
0.9912
0.9909
0.9903
0.9899
0.9895
0.9890
0.9886
0.9884
0.9880
0.9876
0.9872
0.9868
EMPLOYED
WORKERS
(U)
1.0000
0.9989
0.9980
0.9901
0.9877
0.9878
0.9873
0.9870
0.9959
0.9962
0.9960
0.9959
0.9958
0.9872
0.9869
0.9864
0.9861
0.9857
0.98S1
0.9850
0.9848
0.9845
0.9842
0.9838
0.9834
TREATED
ECO-MEDIA
(M)
i.oooo
0.9970
0.9941
0.9950
0.9836
0.9841
0.9832
0.9825
0.9834
0.9837
0,9832
0.9827
0.9822
0.9818
0.9813
0.9803
0.9796
0.9787
0.9773
0.9772
0.9771
0.9765
0.9759
0.9752
0.9743
4.0
3.6
3.2
2.8
2.4
2.0
1.6
STATE Qt- THE SYSTEM
1 YEASS
1.2
0.8
0.4
-0.0
lilt" YEARS '
1.0 3,5 6.0 8.5 11.0 13.5 16.0
FIGURE 59
RUN S SUMMARY DATA
177
18.5
21.0
23.5
26.0
-------
SUMMARY TABIE - STATE OF THE SYSTEM
(SCALED TO ORIGINAL VALUE I
YEAR
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
POPULATION
-------
growth patterns while the data points for Runs 4-6 are nearly
always fully consistant with the trend lines. However, both
Run 5 and 6 show that the region's trend is for an increasingly
inferior set of standards. On the other hand Run 4 is a slow,
generally increasing set of trends indicating growth within
the region's carrying capacity limits.
Review of the comparative analysis above indicates that
Run 4 is consistantly the best run while Run 3 is normally
the second choice. Hence, based on these data and varying
only the funds parameter, the best solution appears to lie
between 2-4 percent annual growth, and probably is closer to
9 9-
L •& .
To verify this finding, a seventh run was made to compare
to Run 3 and 4 output. The funds levels were set at 3% for
components of the government sector and 2% for private com-
ponents. The results are reasonably consistant with the
findings above. Population size approaches Run 4 but QOL is
below Run 4. Missed measure thresholds for year 25 are con-
sistant and no long term adjustments were necessary. The
remaining nonrenewable resource stockpiles are better than
either Run 3 or 4. Unemployment is better than Run 3 but
worse than Run 4. Run 7 trends (see Figure 61) are decidedly
rougher than Run.4 but not rougher than Run 3.
Additionally, the following trends are noted in Run 7
as compared to Run 4. While productivity in the government
sector is slightly higher in the Run 7 data, the productivity
of Run 4 in the private sector is clearly higher; ranges are
1.10-1.53 for Run 7 and 1.35-1.49 for Run 4. Thus, for less
funds (Run 4) higher overall production was made due to
differentials in resource unit costs at year 25. These
differences were stimulated by the higher public sector invest-
ments. On the other hand, growth in effluent treatment costs
over the 25 years is 33% for Run 7 and 51% for Run 4; if it is
assumed that effluent treatment is less than 100% effective, the
higher level of environmental degradation occurs in Run 4.
Based on this last analysis it appears that the best funds
rate is very close to 2.1% if a standard rate is applied
to all components and if no variation on levels of population
or demand gratification are introduced to the SOS-1 model
inputs. Additional discussion in Appendixes 6 and 7 provide
consideration of ZPG and Zero Output Demand Growth. The
primary findings of these appendixes are that:
179
-------
SUMMARY TABLE - STATE OF THF SYSTEM
I^CALFD TO ORIGINAL VALUE)
YFfG POPULATION
1.
2.
3.
4.
5 .
6.
7.
8.
9.
10.
11.
12.
n.
14.
15.
Ifl.
17.
IP.
l<3.
20.
?1.
22.
73.
24.
2^.
IP )
1.0109
1.0211
1.0119
1.0431
1 .0546
1. 05P9
1.06 SO
1.0767
1.0859
1.0954
1.105R
1. 1164
1.1275
l.l'<>4
1. 1521
1.1654
1. 1730
1.1856
1.1982
1.2119
1.2266
1. 2331
1.2468
1.2A03
1.2748
PUBLIC
FUNDS
(G)
1.0000
1 .0300
1 .0554
1.082*
1.1104
1.1144
1. 14*2
1.1811
\.2.1 90
1.2651
1.2970
1.3323
1.372P
1.4126
1.4788
1.5152
1.5218
1.5687
1.6211
1.6778
1.7623
1.7740
1.8337
1.8956
1.9979
PP 1VATE
FUNDS
(I)
1.0000
1.0200
1.0360
1.0537
1.0703
1.0726
1.0924
1.1127
1.1332
1. 1531
1.1735
1. 1938
1.2171
1.2389
1.2629
1.2860
1.3163
1.3383
1.3638
1.3892
1.4144
1 .4501
1.4792
1 .5094
1.5394
QUALITY NATURAL
LFVFl 0"E USAGE
1.
1.
1.
1.
0.
0.
0.
0.
0.
1.
1.
1.
1.
1.
1.
0.
1.
1.
1.
1.
0.
I.
1.
1.
1.
(0)
0000
0100
0147
0234
IN)
.0000
.0173
1.0253
.0261
8910 0.8897
9611 0.9525
9699 0.9698
9835 0.9908
9982 1.0139
0192
0260 ]
0366
0501
0610
0696
9667
0365
0449
C61R
0752
9386
0315
0444
0601
0837
.0413
.0558
.0838
.1231
..1710
.2261
. 1480
.2872
.3493
.4094
.4514
.2669
.4071
.4367
.4747
.5192
ENERGY
USAGE
IE)
1.0000
1.0208
1.0367
1.0582
0.9182
0.9913
1.0136
1.0022
0.9910
1.0219
1.0393
1.0604
1.0B46
1.1068
1.1253
.0174
.0970
.1207
.1517
.1783
.0-401
.1792
.2632
1.3721
1 .5095
FARM AND
LAND USAGE
(F)
1.0000
1.0185
1.0333
1.0516
1.0017
1.0399
1.0582
1.0773
1.0976
1.1202
1.1387
1.1583
1.1790
1.2004
1.2203
1.1847
1.2351
1.2580
1.2.859
1.3072
1.2489
1.3127
1.3445
1.3721
1.4042
EMPLOYED
WORKERS
1
I
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
I
1
1
1
1
I
1
(U)
.0000
,0258
.0473
.0718
.9029
.9936
.0200
.0474
.0762
.1165
.1408
.1683
.1998
.2300
.2584
.1134
.2117
.2433
.2874
.3239
.1174
.2485
.2864
.3256
.3832
TREATED
ECO-MED1A
(M)
1.0000
1.0189
1.0338
1.0540
0.9475
1.0044
1.0245
1.0454
1.0681
1.0994
1.1186
1.1392
1.1635
1.1859
1.2042
1.1180
1.1876
1.2101
1.2475
1.2717
1.1421
1.2340
1.2636
1.2926
1.3348
3.6
2.ft
2.4
2.0
1.6
1.2
O.P
STATE OF THF SYSTEM
YEARS
M
N
I
F
I
V
G
F
f*
G
M
F
G
I
M
E
G
F
M
E
G
W
f
E
G
G
I
M P
E E
Q
G G
G
I
W M
M F F
E Q M
E
G
N
M
M
E
0
G 1
N I I N E
N ! I N N f W
N W M F M M M
MMMFMMPP
E E E M E
0 0 Q W Q Q fi
g
-0.0
' ' • • ' YEARS
1.0 3.5 6.0 8.5 11.0 13.5
FIGURE 61
RUN 7 SUMMARY DATA
180
16.0
18.5
21.0
23.5
26.0
-------
Limiting population but not growth of demand to original
limits produces little differences; the lower population
raises demand to stress the production system quite similar
to the runs discussed above. In a set of comparison runs
(Appendix 7) the ZPG case normally fared worse than the standard
case.
Limiting demand thresholds to the original values produce
a more balanced set of trends plus greater fund reserves for
needed long term adjustment. In a set of comparative runs
(Appendix 6) this flexibility had little long term impact.
181
-------
FINDINGS AND RECOMMENDATIONS
The model results generally appear credible; anticipated
major trends occur and differences between runs appear to be
appropriate.
All forms of the system adjustments appear to function
properly and to produce changes in resource utilization data
that extend the region's capability to sustain the attempted
growth and reduce the impact of degradation of the system
when the growth pattern cannot be sustained.
While the model results are considered credible because expected
adjustment patterns exist, the results are not fully predictable
from static analysis nor are the details of the results at all
predictable. The model algorithms and adjustment produce detailed
results that gave unexpected answers and insights to which
problems may occur and the methods used by the system for
adjustment.
The major set of problems with the model at this time is a need
to refine certain averaging procedures and a mechanical change
to extend the sets of options of adjustments. The linear inter-
polation procedures used in many calculations of Step 2 and the
linear extrapolations as applied in Step 7 should be replaced with
more exacting calculations in later versions of SOS, as the data
base is improved. Additionally, the sets of adjustments, partic-
ularly in the resource substitution mixes and the production
resource utilization formulas, should be extended to include
more choices and more mixed strategies as end points.
The question arises; should the total data base be expanded
for SOS applications? Our answer is yes and no; there appear
a set of analyses that can be analyzed efficiently and
rapidly using SOS at approximately its present level of detail.
The results of these rough-grain analyses will produce some
results that require more detailed study. These results can be
usefully addressed by a form of SOS that included much greater
detail in data and specialized algorithms. Suggested develop-
ment plans for both SOS forms; the quick reaction, aggregate
tool (SOS-Q) and the larger, more detailed system (SOS-D) follow.
For SOS-Q, there appears to be little need in expanding the
number of demand measures, resources or production components,
that are discretely considered. As noted earlier, the primary
expansion needed in the data base is expansion of the number
of adjustments options allowed. The question of introduction
182
-------
of some new elements into the data set is straight-forward.
For resources and for demand measures additional space exists
to introduce 3-4 elements while retaining the present elements.
Additionally, any of these which appear dominated by other
elements can be replaced; this modification requires primarily
a change in data and in output print formats.
Primary development should be to improve the current inter
polations noted above. Then the model can be used to test
out new adjustment or allocation techniques with minor modifi-
cation of procedures; the modular design of the program will
allow ease in such changes. Initial candidates for insertion
are elements of the model formulation that were not included
in this example model. These include:
• Treatment of exogenous additions to operating funds
• Technological impact on production formulas as R§D
expenditures cumulate
• Consideration of maximum demand thresholds as well
as minimum thresholds.
Even without the additional procedural changes, SOS-Q appears
ready to be of some assistance as a rough analysis tool,
after the initial adjustments are performed (interpolations,
data expansions, improvement of data).
The development plan for SOS-D appears to be a long-term
venture. As such, it appears appropriate that the process
begin with an applications analysis to determine what class
of problems are likely to be addressed by SOS-D. From this should
be produced a useful, evolving development/applications plan so
that partial use of the SOS model is available early in the
development and then both activities (use/refinement) can continue.
While the initial steps to changing the model to a more detailed
form are straight-forward, considerable planning should be
introduced to lessen the burden of data collection and output
data reduction on the later users; therefore, the application
study should be followed by a development of general (but specific)
model design effort that sets context and goals for the follow-on
detailed designs of the individual model elements. As development
and use of SOS-D suggest changes, periodic updates to the general
design should be done.
183
-------
SECTION X
REFERENCES
Peterson, E.K., "Limitations in Classical Planning,"
in Alternative Futures and Environmental Quality,
page 101, Environmental Studies Division, Washington
Environmental Research Center, U.S. Environmental
Protection Agency, Washington, D.C., 1973.
2. Kormondy, Edward, Concepts of Ecology, Prentice Hall,
Inc., Englewood Cliffs, New Jersey, 1969.
3. Odum, Eugene, "Ecosystem Theory in Relation to Man,"
in Ecosystem Structure and Function, Proceedings of
the Thirty-First Annual Biology Colloquim, Edited by
John Wiens, pages 15-16, Oregon State University
Press, Corvallis, Oregon, 1972.
4. Op. cit. Kormondy, page 3.
5. Op. cit. Odum, page 16.
6. Rolling, C.S., and Goldberg, M.A., "The Nature and
Behavior of Ecological Systems," in An Anthology of
Selected Readings for the National Conference on
Managing the Environment, page 1-21, International
City Management Association, Washington, B.C., May
1973.
7. Ibid., page 1-20.
8. Ibid., page 1-23.
9. Dansereau, P., Biogiography, An Ecological Perspective,
pages, 54, 122, 203-204, 257, and 293, The Ronald Press,
New York, 1957.
10. Dasmann, R.F., Wildlife Biology, page 154, John Wiley
§ Sons, Inc., London, 1964.
11. Turk, Turk and Wittes, Ecology, Pollution, Environment,
page 15, W.B. Saunders Co., Philadelphia, 1972.
12. Whittaker, R.H., "Evolution of Natural Communities,"
in Ecosystem Structure and Function, page 138, Oregon
State University Press, Corvallis, Oregon, 1972.
184
-------
13. Op. cit. Dasmann, page 75.
14. Ibid, page 154.
15. Quinn, James A., Human Ecology, page 23, Anchor Books
Hamden, Connecticut, 1971.
16. Landberg, Hans H., The U.S. Resource Outlook: Quantity
and Quality, Johns Hopkins Press, Baltimore, 1972.
17. Lovejoy, W.F., and Homan, P.T., Methods of Estimating
Reserves of Crude Oil, Natural Gas, and Natural Gas
Liquids, Johns Hopkins Press, Baltimore, 1965.
18. Op. cit. Quinn, pages 282-289.
19. Ibid.
Other
Alternative Futures and Environmental Quality, Environ-
mental Studies Division, Washington Environmental Research
Center, Washington, B.C., 1973.
IBM System/360, FORTRAN IV Language, GC28-6515-7.
International Business Machines, Inc., Systems Reference
Library, Poughkeepsie, N.Y., October 1968.
IBM System/360 Operating System, FORTRAN IV (G and H)
Programmers Guide, GC28-6817-0, IBM Systems Reference Library,
Poughkeepsie, N.Y., November 1968.
IBM System/360 Operating System, Job Control Language
Reference, GC28-6704-1, IBM Systems Reference Library,
Poughkeepsie, N.Y., June 1971.
Meadows, D.H., Meadows, D.L., Randers, Jr., and Behrens,
W.W. III. The Limits to Growth, Potomac Associates, Signet
Book, New York, 1972.
Meadows, D.L., and Meadows, D.H., Toward Global Equilibrium:
Collected Papers, Wright-Allen Press, Inc., Cambridge, Mass-
achusetts, 1973.
The Quality of Life Concept, U.S. Environmental Protection
Agency, Washington Environmental Research Center, Washington,
1973.
Quality of Life Indicators, U.S. Environmental Protection
Agency, Environmental Studies Division, 1972.
185
-------
SECTION XI
APPENDICES
APPENDIX TITLE PAGE
1 Measuring Quality of Life 187
2 SOS-1 General Flowcharts 194
3 SOS-1 Model Program Listings 204
for OSI/EPA Computer Using
WYLBUR/FORTRAN-IV G
4 Users Guide for Operating SOS 253
Model Using WYLBUR on the OSI
Computer
5 Procedure for Code Modifications 260
and Editing a Data Set Using
WYLBUR
6 Maintaining the Initial Satis- 265
faction Thresholds
7 Setting Population Growth to ZPG 267
8 Reduction of Systemic Adjustments 269
of SOS-1
9 Listing of All Output for the 279
Base Case
186
-------
APPENDIX 1
MEASURING QUALITY OP LIFE
A measure of the Quality of Life can be generated in a
number of ways. It can be a series of measures which attempt
to encompass all of the relevant parameters; or it can involve
an additional step and turn the series of indices into
a single index. There is much to be said for both attempts.
Since the set of indices are components of the latter,
we shall only investigate the process of developing the
single index here. This index for Quality of Life is to consist
of three parts — a Preference Function, Indicators of Status,
and Resource Costs. A combination of these three parts could be
used to yield an expression used as a measure of the Quality
of Life.
The Preference Function is a construct, highly theoretical
in nature, used to represent a numerical measure of that illusive
thing the sociologists call culture. If culture as a learned and
inculcated feature of human existence has any meaning, and if
the psychologists' premise, that deeply held beliefs control
both our individual and group actions, has validity, then this
Preference Function should be able to be approximated. One
possible way of operationalizing this is to give the random
group of people a finite number of points to distribute among
the selected factors. The average of these weightings would yield
a distribution which should be a useful approximation of the
Preference Function of the society represented by the group and,
as such, should provide a guide to the society's long-run actions.
187
-------
As this paper is not meant to be an exhaustive treatment of
any of these concepts, we shall settle for an overall explanation
of them and a general discussion of their properties. Consequently,
the Preference Function can be viewed as a measure of the relative
importance of selected features of a region and its society to the
members of that society. The approach is simplicity itself in that
it consists of a relative ranking of the factors which make up the
Quality of Life by a randomly chosen sample of the people in the
particular society. As theory, it suggests that given a series
of items [a, b, c, d, e] a randomly selected group of the society
can rank them in order of importance, such that they reflect the
preferences of the people for the chosen items. The same measure
could be used for sub-sectors of the society.* A sample of this
is presented as Figure 1-1.
Without delving into setting the Preference Function further
at this point, let us consider the Indicators of Status.
Assuming that we have agreed upon a set of measures which define
the Quality of Life and have weighted these among themselves, then
it is necessary to actually quantify the state of the society in
terms of these same factors. In other words, where is the system
in relation to where it wishes to be? Such measures could be
constructed as a series of indices and each of these indicators
can be looked upon as a satisfaction index which relates an element
of the desired and observed state of the system at a particular
point in time.
See Mann and Hobson (1) for operational use of a similar concept,
188
-------
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189
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There are obviously many ways of constructing such an index;
the following is one of the simplest but is illustrative of the
methodology. Suppose, regardless of the factor under consideration,
we plan to record both an empirically measurable reflection of its
status and a measure which reflects the level desired by the group
for the same phenomena. The observed measure can either be directly
obtained from monitoring data of one sort of another or can be
obtained from a suitable surrogate whose movement correlates highly
with the parameter under consideration. The desired measure can
be obtained by interview or from goals statements. The observed
measure is then converted to a scale of 0 to 10, with 10 being a
perfect score. The ratio of the observed score to the desired score
will then yield a measure of the short-run status of the system.
This measure leads us directly to an analysis of the last
function, the Resource Costs of the system. The resources under
consideration consist not only of money but of time, power and
other factors used by the system. In short, it is a function
which measures the relative cost to either maintain the system at
levels which it considers adequate or expenditures which it.proposes
to make to redress imbalances. The resource cost is measured so
that it can be seen in terms of raising the level of a factor by
one unit.
2
It is assumed that the ratio is always
190
-------
The combination of these three functions in a single
expression gives us a rather interesting trade-off probability
curve. Consider the Indicators of Status for three factors, where
each index individually has a maximum of 100. Then the general
form of the Quality of Life Index would become:
n.
IXi'e. -loo
Therefore, the closer the system is to satisfying its desires,
the higher will be its Quality of Life. Additionally the closer
the measure value will be to 100. The measure also allows us to
predict which factors in the equation will likely be the greatest
increase in expenditures in a given year if the planner attempts
to maximize Quality of Life. They are those items which are (1)
very important to the system as meausred by its Preference Function
value (which, remember, is the long-run indicator of system
performance) (2) low in terms of its observed Indicator of Status
and (3) most cost effective to redress (eg. cost is low to
performance increase) will receive the most attention, at least
until the item in question is no longer out of balance and there-
fore has a decreasing marginal toward increasing the Quality of
Life.
This paradigm of a society allows us not only to explain a
number of events which have occurred throughout history, but, if
measurement could be implemented, it could give us a powerful tool
for forecasing future events. For example, theoretical structure
behind the Preference Function suggests that the society's intrisic
values structure is quite rigid and the society will go to some
191
-------
lengths to maintain it. Elements within the structure, of course,
are subject to change over time, but many take relatively long
periods to change in order to readjust the societal equilibrium.
On the other hand, it is possible to influence this Function
in the short run, say through the media. A concerted effort on
the part of the public or private sector to emphasize one or more
segments or factors can temporarily change weights in the
Preference Function and cause the society to allocate resources
in a fashion that it ordinarily would not have without media
influence. To the extent that this preference change becomes
imbedded in the society, the Preference Function is actually
changed and is no longer temporary. If it is not, then the
influence is of the nature of a fad and the Function swings back
to an equilibrium position close to the original values. The
current interest in the environment is a case in point. It is
obvious that the environment and its problems did not suddenly
come into being, but that the interest evidenced in it recently
has come about because of a concerted effort on the part of many
groups to make us more aware of the dangers and needs of our
physical support system. To the extent that those who are most
concerned succeed in implanting an "environmental ethic," then
the Preference Function will be permanently readjusted to reflect
this change in the ethos of society. The extent to which they
fail provides the degree by which the present trend is a fad.
Let us look at the other parts of our equation. Possibly the
most controversial portion of this construct is the ability to get
192
-------
measingful desired and observed values of measures described as
making up the Quality of Life. As noted earlier, much effort
has gone into the construction of indicators and yet the effort
never seems to climb out of the infancy stage. Work needs to be
done to determine both the procedures to measure the factors selected
and whether the factors and indicators chosen are useful indicators
of the value that are to be measured.
Finally, the concept of resource cost and effectiveness is
hard to get at. The idea of the "biggest bang for the buck" is
intuitively easy to grasp and is often difficult enough to derive
when just economic factors are considered. When other, non-
monetary, resources are added in, the data problem is magnified
several times.
REFERENCES
(1) Mann, S. H. and R. Hobson, "Toward the Development of a
Quality of Life Index," Division of Man-Environment Relations,
Pennsylvania State University, Unpublished paper, 1972.
(2) U. S. Environmental Protection Agency, Environmental Studies
Division, Office of Research and Monitoring, The "Quality of
Life" Concept; A Potential New Tool for Decision-Makers,
Office of Research and Monitoring, Working Papers in the
Environment, 1973.
193
-------
APPENDIX 2
PROGRAM FLOWCHARTS
194
-------
FLOWCHART 2-1
THE SOS-1 EXECUTIVE PROGRAM, MAIN
^f ^w / OUTPUT \
I
3 .S \ RESULTS /
1
^
/ STEP 1 \ / STEP 2 \ / STEP 3 \
(POPULATION \ b/ PRODUCTION \ fJ DEMAND \
NDESCRIPTION/ \§ RESOURCES/ SATISFACTION/
v
r
(STEP 4 \
ADJUST \
RESOURCE /
VAILABILITV
J
/ STE1
/ EXPOI
\ SHORT
\ADJUSr
V
r
3 5 \ ^\
?TS ^ \ b^*^58~0 O^^s^-SL
TERM / '^ST >^~"~
rMENTS/ ^^/^
Yes]
>
SET / STEP 6 \
PSUM1. A , / LONG-TERM M-
PSUM2 VVDJUSTMENTS/
FOR STEP 7 \ /
_5
t
/ STEP 7 \
< MODIFY }
\ DEMANDS /
^
/STE1
\BOOKK]
7
rr\
:LE >
EEPING/
T
195
-------
FLOWCHART 2-2
STEP 1: DESCRIBE THE POPULATION
CALCULATE
TOTAL
POPULATION
(TOPT1
/FOR
' AGE
V j=i
D^H.
/FOR
AGE
V I=
CW*.
\
LjL
EACH\
YF_T\P i „ o
,65 /
L
EACH \
nponp \ „ it
1,4 ~J
CALCULATE
DEATHS
(DTPHT(J) )
CALCULATE
(AGEPT(J))
ACCUMULATE
(AGRIT(I))
-4
"FOR EACH "\
AGE GROUP I \ ..
IN PARTITION K/ v
1=1,4; K=1,6X I
£W
_^
/FOR
PARTI
VK=
Done
\
ACCUMULATE
POPULATION
POPKT(I.K))
=1,4; K=l,6
• +
EACH\
i.e^/
ACCUMULATE
POPULATION
POP(K)
F
ACCUMULATE
N DEATHS THIS
9 YEAR
(DTHPTA(I))
T
£
CL
g
[STEP 2
196
-------
FLOWCHART 2-3
STEP 2: DESCRIBE THE PRODUCTION COMPONENTS
v
;FOR EACH \
COMPONENT
J-1,10 )
Dune.
/
f
V
V
X
CALCULATE
AMOUNT OF
INVESTMENT
AVAILABLE
THIS CYCLE (INVST)
STORE PUBLIC
PRODUCTION
SUMMARY TABLE
(°UBDIV]
ESTIMATE UNIT
x
•r
SET THE STOCK
PILE (WORK UNITS)
POPULATION
OF PAID WORKERS
ie SET PILEC18)
STORE PRIVATE
PRODUCTION
GROWTH IN
SUMMARY TABLE
fPRIDIV)
ACCUMULATE THE
DEFERRED CAPITAI
^MAINTAINENCE (*)
> OF THIS CYCLE
AND LAST CYCLE
J (MNNORMCJ")")
SET FUNDS
f, FOR COMPONENT
x PRODUCTION
(INVOUT(J))
CALCULATE THE
CALCULATE THE
s.
SET MAINTENANCE
RATE TO REPAIR
ENVIRONMENTAL
MEDIA (MAINR(J))
\
SET T
MAINTENA
MAINT(J)
+MAINR+C
EXPANSIC
r
OTAL
NCE ie
MNNORM
APITAL
N COSTS
FOR EACH
COMPONENT
J=l,10
r
^
y
f
STORE THE
RESOURCE
REQUIREMENTS
IN THE ARRAY
fSUMMATCNCYUE.JV
ESTIMATE UNIT
COSTS OF
PRODUCTION FOR
THIS CYCLE
fRUCSTfim
•s
CALCULATE THE
ESTIMATED COST
FOR ONE UNIT
OF OUTPUT
(OCST(Jl)
SCHEDULED
OUTPUT UNITS
FOR EACH COMPONEN1
JOTCS1
CALCULATE THE
RESOURCE REQUIR-
EMENTS FOR EACF g-
RES. FOR CYCLE
fRESOR(R))
T
FOR EACH
RESOURCE
R=l,20
I
THE STOCK
DEPLETION
LEVELS FOR
EACH RES.fSTDEPfRl
ARE
TOCK LEVEL
RITICAL?
TURN ON THE
STOCK DEPLETION
FLAG
(FLAGR(R))
CALCULATE
CAPITAL EXPANSION
COSTS § ALLOCATE
COSTS OVER NEXT
10 YEARSfMNCAPCK.TI
CALCULATE
THE RES.UNIT
COST MEAN VALUE
(ECST(R))
SET AS FUNCTION
OF STOCK USED
THE RATIO OF
UNITS RECYCLED
TO UNITS MINED
CRECREC(R;n
CALCULATE
RESOURCE
UNIT COSTS
TO "MINE
UNIT MAX. VALUE
(MECSTRW)
CALCULATE
RESOURCE
UNIT COSTS
TO "MINE" COST
UNIT MAX. VALUE1
(ECSTR(R))
CALCULATE THE
RESOURCE UNIT
COST MAX. VALUE
(MECST(R))
197
-------
FLOWCHART 2-4
STEP 3: DESCRIBE THE STATE OF THE SYSTEM
(STE
i
;CAL . M
VAL
FOR EA
MEASURE
N=l
\
(FOR
COMPO
J=l
P 3 )
\f
-------
FLOWCHART 2-5
STEP 4: ADJUST RESOURCE RESERVES § UTILIZATION FACTORS
FOR EACH
RESOURCE
R=l,20
IS STOCK
EPLETION FLA
ON?
•D«
SEARCH FOR
SUBSTITUTION
VECTORS.MARK(K
STORES INDEX
FOR ALL SUBS-
TITUTIONS WHICH
PASS THE FLAG
TEST CALCULATE
CUMULATED COST
OF UP TO 5 SUBS
fSCSTfLL))
IS THERE
SUBSTITUTION FO
RESOURCE R?
PUT MARK(K)
INTEST
VECTOR=TO IV
OSITION § NUMBER
CHECK FOR FLAGS
TURNED ON IN
THE SUBSTITUTING
RES. OF SUBSTITUTION
VECTORS(FLAGR(Ri;)
S SUB
OST RES.COST?
SCST(LL)^
MECSTRfR
STORE 5 YEAR
COST OF SUBS.
FOR ALL VECTORS
STILL ACTIVE(ORES;
T
is
RESOURCE'S. hlo ^XkESOURCgX^ M
IR OR WATER, i>>—^$ARM GOODS, ie
IS R=19,20J
s
ESOURC
WORKERS, ie
IS R=18?
FOR EACH
RESOURCE
R=l,20
RESOURC
ANNUALLY
NEWABLE2
IS
AMOUNT 0
EXPANSION, ie
PILE(R)>0'
IS
N INCREAS
BEING DONE, ie
ORK(R)>0?
DEVELOP TIME
PHASED INCREASE
FOR 5 YEARS
(SUBPIL(JCTR))
199
-------
FLOWCHART 2-6
STEP S: PERFORM SHORT TERM OUTPUT ADJUSTMENTS
T
( STEP 5 J
\
f FOR
t
C A PU
v
COMPONENT (J) \ Xl>V CAL • LEVEL OF J
DETERMINE IF \ -/OUTPUTS. .. MAINT THAT CAN
MORE OUTPUT 1— >«f DELINQUENT ;>J2A_^ BE DEFERRED
IS DEMANDED / \MDEL (JJ/ (DEFMN)
fl=l 101 CMnFTCTII/ >v- \S 1 - '
Dor7<.
/
r
V Ho
DETERMINE
MINIMUM
>—.,._. ^ RbblLlbNCi
;OR JCRESMN;
^ CALCULATE ^ :ALCULATE FU>
' CUMULATED FUNDS v" WAILABLE TH]
(CFUNDT) -YCLE (EFUNDT
IDS
S
')
— $
X.
>
S
DETERMINE
COST TO
IMPORT GOODS
•TO MEET DEMANI
(MOCST(J))
CALCULATE OUTPUT
UNITS TO EXPORT
(1) (EJOT(J))
\
f
1
CALCULATE FUNDS
GENERATED BY
EXPORT (EFUND(J))
S*^ /^v
DETERMINE
» OF DEM
BY MAIN
DEFERRAL
FRACTION
AND MET
TENANCE
(CMIN)
DETERMINE THE
RESIDUE OF
OUTPUT DEMAND
(MDEL(J))
^
^
DETERMINE
NEW OUTPUT
UNITS BASED
ON CMIN § MDEL(J]
(JOT(J))
DETERMINE
IF IMPORTS
|STILL NEEDED
(SINCST(I))
(1=1.2)
ARE
?RIVATE SI
IMPORTS NEEDED^/
.(SINCSTm
ARE
UBLIC SECTOR
IMPORTS NEEDEI
IS
CFUNDT
"SUFFICIENT FOR'
PUBLIC SECTOR
EMANDS?^
'FUNDS TO
fOTALLY MEET PRIt
EEDS? CFUNDT
INCST(1)J
OF
SECTOR DEMAND1
THAT CAN BE
MET USING ALL
.CFUNDT (PSEC)
CAL. AMOUNT OF
GOODS IMPORTED
USING CFUNDT
CASH(XINJO(J))
*
o
V
CAL. AMOUNT OF
GOODS IMPORTED
USING
CASH
//»
CFUNDT
XINJO(J)
>.
^
LOWER
EXPORT
FUND
LEVEL
rcnwriT
|
ALL CUMULATED
FUNDS (CFUNDT)
EXHAUSTED
SET 58=1.0
ALL CUMULATED
FUNDS NOT
EXHAUSTED
USING CFUNDT
CASH. SET
58 = 0.0
200
-------
FLOWCHART 2-7
STEP 6: PERFORM LONG TERM COMPONENi UUTPUT ADJUSTMENTS
IS
THE PRESENT
ROCESS COST LES
THAN ALTERNATE
PROCESS COST?.
STORE I/O
SUBSTITUTION
DATA IN SUBIOP
MATRIX
FIND MINIMUM
SUBSTITUTE
WITH MINIMUM
(MINfYOCST))
SECTOR NEEDS,
SUBSTITUTION
EXTRAPOLATE
FUNDS NEEDED
OR EACH OUTP
(INEED2)
SECTOR FUNDS,
FUNDS EXPECTED
OVER NEEDED
TRANSFER FUNDS
TO ADJUST RATES
OF GROWTH FOR
EACH COMPONENT
(J=1.10)
EXTRAPOLATE
FUNDS EXPECTED
FOR EACH OUTPU'.
(INVST2)
IS
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FULLY MET?
DIFFS(K)
RANS(K)
INTERSECTOR
FUNDS TRANSFER
S=l,2
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PARAMETERS TO
SEE IF THRESHOLD
OF STATEMENTS
NEED TO BE
LOWERED
(PSUM1),(PSUM2^
RECALCULATE
THE SECTOR
FUNDS, POSITIVE
IOVBR2riNUP21
ALL
OMPONENT
OF SECTO
DON
BE MET CAL.
AMOUNT OF
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NEEDS,NEGATIVE
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ONLY PARTIAL
MEETING OF
DEMAND POSSIBl:
CALCULATE
FRACTION
POSSIBLE(K31
201
-------
I STEP 5
j(PSUMl=1.0
iPSUM2=0.0)
FLOWCHART 2-8
STEP 7: ADJUST LONG TERM POPULATION DEMANDS
STEP 6 |
PSUM1,PSUM2)I
INITIALIZATION.
OF MEASURES
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TMEAS)?
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N.I,12 >
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o MAXfOiOS,
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IS
EASB2
-------
FLOWCHART 2-9
STEP 8: RESET DATA BASE FOR NEXT CYCLE
\
/
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AND SCALE
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-------
APPENDIX 3
SOS-1 MODEL PROGRAM LISTINGS FOR OSI/EPA
COMPUTER USING WYLBUR/FORTRAN-IVG
The program for the example State of the System Model (SOSMDL)
is listed on the following pages of Appendix 3. Of particular
interest to the user are the numbers listed in sequence as a
right-most column; these are the WYLBUR line references and
are cited in Appendix 4 within the procedures required to make
data base changes.
The specific elements of SOSMDL are:
MAIN, the executive routine
BLK DATA, the existant data base that is used for a run
if no modifications are introduced
SUBROUTINE STEP 1
SUBROUTINE STEP 2
SUBROUTINE MATMPY, a utility routine to perform matrix
multiplication
SUBROUTINE STEP 3
SUBROUTINE STEP 4
SUBROUTINE NORMAL, the routine that sets up the level of
process and resource changeover accomplished in each of the
subsequent simulation years
SUBROUTINE STEP 5
SUBROUTINE STEP 6
SUBROUTINE STEP 7
SUBROUTINE STEP 8
SUBROUTINE PLOT, a modified utility program to plot
various statistics (up to nine) on a yearly basis
SUBROUTINE OUTPUT, the program that outputs the table/
graph sets that summarize a run result as 8 tables with
associated graphs.
204
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251
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APPENDIX 4
USERS GUIDE FOR OPERATING SOS MODEL USING
WYLBUR ON THE OSI COMPUTER
Sign-On Procedure
The procedure described below is for operating the SOSMDL
Program, using WYLBUR with an Acoustic Coupler.
1. For a 10-15 cps terminal, check to see that the DUPLEX switch,
located on the back of the coupler, is in the FULL position
and that the ACST-TEL.TERM. switch, also on the back of the
coupler, is set to ACST. In the case of the 30 cps terminal
the duplex switch located on the front of the coupler, should
be in HALF position.
2. Turn the terminal on.
3. Dial the number of the computer (OSI 652-9028 for 30 cps,
and 654-1370 for 10-15 cps) on your telephone. When the
computer answers with its high-pitched tone, place the
hand set in the cradle of the coupler, with the cord
coming out the front.
4. Turn on the coupler. The light underneath the ON-OFF
switch will come on and remain on as long as the terminal
is connected to the computer.
5. Press the RETURN key on the terminal. If the terminal
has a Correspondence Keyboard, then type COR followed
by a carriage return. If it is a 30 cps terminal, then
the system will ask the user to supply the model number.
252
-------
The user should type in the number 33, followed by a carriage
return (CR) as follows:
MODEL? 33 (CR)
The system will respond by first typing the name of the instal-
lation followed by the telephone line number, date and time.
OSI/WYLBUR XX MM/DD/YY HH:MM:SS P.M.
This signifies that the terminal is ready to receive
information.
The system will follow this with another line giving
the message of the day which includes any special information
of which the user should be aware.
In these examples, for the sake of clarity, the system
response is always in upper case letters whereas what the user
should type is in lower case letters.
Now the system will type the prompt, "INITIALS?". The
user should answer by typing his registered initials and a
carriage return (CR).
INITIALS? rpm (CR)
Next the user is asked to identify himself by giving his
account number.
ACCOUNT? a053 (CR)
Then the user is asked to supply a keyword
253
-------
KEYWORD? rpm (CR)
Provided that the correct response is made, the user
is asked to supply the number of the terminal which he is using.
TERMINAL? t70 (CR)
COMMAND?
The system has now completed the sign-on procedure and
the terminal is now ready to accept WYLBUR commands. The
system response "COMMAND?" can be answered as follows:
COMMAND? set terse (CR)
The SET TERSE command causes the WYLBUR command prompt
to be shortened from "COMMAND?" to "?."
The user may now type in the SET VOL command. This command
sets for the user a default volume. Since the data set SOSMDL
is stored on the TS0002 volume, the user may now type the
following command in response to "?."
? set vol = tso002 (CR)
In order to bring back a copy of the data set SOSMDL,
the user should issue a USE command
? use SOSMDL (CR)
254
-------
After receiving this information, WYLBUR will locate
the data set and make a copy of it available for use as the
working data set.
USE OF THE PRINT OPTIONS PROVIDED IN SOSMDL
The print switches provided are:
APPROXIMATE
OF SWITCH DEFAULT VALUE DESCRIPTION LINES OF OUTPUT*
NPRNT1 1.0 Print-out for STEP1, 1860
STEP2 and STEP3 of SOSMDL
NPRNT2 1.0 Print-out for STEP4 , STEPS, 900
STEP6, STEP? and STEPS of
SOSMDL
PPLOT 1.0 Print-out for all the graphs 480
of SOSMDL
*Assumes a 25 year simulation output history
If no print-out from STEP1 , STEP2 and STEP3 is desired
then the user must use the following procedure:
? mod 65
65. DATA NPRNT1/1.0/, NPRNT2/1.O/
ALTERS? r2 (CR)
65. DATA NPRNT1/2.0/, NPRNT2/1.0/
ALTERS? (CR)
255
-------
If no print out from STEP3, STEP4, STEPS, STEP6, STEP7
and STEPS is desired then the user must use the following
procedure:
? mod 65 (CR)
65. DATA NPRNT1/1.0/, NPRNT2/1.0/
ALTERS? r2 (CR)
65. DATA NPRNT1/1.0/, NPRNT2/2.0/
ALTERS? (CR)
?
If no graphs of the SOSMDL are desired then the user
must use the following procedure:
? mod 244 (CR)
244. DATA PLTMAT/250*0.0/, PPLOT/1.0/
ALTERS? rO (CR)
244. DATA PLTMAT/250*0.O/, PPLOT/0.0/
ALTERS? (CR)
?
If data modifications are to be made then use APPENDIX 3
for WYLBUR line number reference. As an example, if rate
of growth data needs to be changed then use the following
procedure:
? mod 105(CR)
105. DATA RGJ/8.2,3.4,9.9,5.0,8.8,4.7,4.6,2.2,0.3,3.8/,
256
-------
ALTERS? r4.6 (CR)
105. DATA RGJ/8.2,4.6,9.9,5.0,8.8,4.7,4.6,2.2,0.3,3.8/,
ALTERS? (CR)
9
After all required modifications have been made, the user
must submit the job through WYLBUR to be processed by the
computer
? run (CR)
266 IS YOUR JOB NUMBER
9
The RUN command directs WYLBUR to put the user's working
data set into the input stream. The output of this run will
be printed at the OSI Central Computer Facility, Bethesda.
Users who have available a high speed remote station
can have their output diverted to it. They indicate in the
command the remote station number they want their output on.
? run remote = xx (CR)
After a job has been submitted through WYLBUR the user
may wish to find out what (if any) processing has been done
to it. The LOCATE command can be used to do this
? loc 266 (CR)
WYLBUR will respond with one of several messages indicating
the state the job is in:
257
-------
1. AWAITING EXECUTION - the job is waiting to be run.
2. IN HOLD STATUS - the operator must take some action
before the job is run.
3. BEING EXECUTED - the job is running.
4. AWAITING PRINT - the job had run and the output is
awaiting to be printed.
5. BEING PRINTED - the output is being printed
6. NOT LOCATABLE - the job has been completed and has
left the system.
Sign-Off Procedure
To end a WYLBUR session the LOGOFF command is used. The
CLEAR option should be typed to indicate -if it is O.K. to
clear the working data set. WYLBUR will reply with various
statistics on the session and disconnect the telephone line.
? LOGOFF CLR (CR)
EDITING TIME =9.80 SECONDS
WYLBUR EXCPS = 1287
MILTEN EXCPS = 922
RESOURCE TIME = 80.19 SECONDS
ELAPSED TIME = 00:04:32
END OF SESSION.
258
-------
APPENDIX 5
PROCEDURE FOR CODE MODIFICATIONS
AND EDITING A DATA SET USING WYLBUR
I. To list lines the user may use the LIST command, e.g.
COMMAND? list 7/9 (CR)
This will list WYLBUR line numbers 7 through 9
COMMAND? list 7,9 (CR)
This will list WYLBUR line number 7 and 9
COMMAND? list 7 (CR)
This will list WYLBUR line number 7
II. The user may delete (erase) a series of lines by giving
the DELETE command and the numbers of the first and last
lines of the range he wants erased.
COMMAND? del 7/9 (CR)
A single line can be erased as follows:
COMMAND? del 7 (CR)
III. The INSERT command is used to insert one or more lines.
COMMAND? ins 12.02 (CR)
12.02? (User supplied text) (CR)
COMMAND?
259
-------
COMMAND? ins 12.02, 12.03 (CR)
12.02? (User supplied text) (CR)
12.03? (User supplied text) (CR)
COMMAND?
IV. The MODIFY command makes it possible to alter a line
without retyping the whole line, e.g.
COMMAND? mod 1795 (CR)
1795. IF (R.EQ.18) GO TO 370
ALTERS?
Several types of alternatives may now be made to the
line of text. After an alteration is made, WYLBUR will
type a copy of the altered line and then prompt for
further alterations.
In the following example the use of
delete used by the letter d
insert used by the letter i
replace used by the letter r
will be demonstrated.
COMMAND? mod 1795 (CR)
1795. IF (R.EQ.18) GO TO 370
ALTERS? d (CR)
1795. IF (R.EQ.18) .GO TO 70
260
-------
ALTERS? d d(CR)
1795. IF (R.EQ.18) GO 70
ALTERS? i TO (CR)
1795. IF (R.EQ.18) GO TO 70
ALTERS? i.OR.R.EQ.12 (CR)
1795. IF (R.EQ.18.0R.R.EQ.12) GO TO 70
ALTERS? r7(CR)
1795. IF (R.EQ.17.0R.R.EQ.12) GO TO 70
ALTERS? rGT(CR)
1795. IF (R.GT.17.0R.R.EQ.12) GO TO 70
ALTERS? (CR)
?
The user signals that he has made all alterations to the
line by typing nothing into the ALTERS? line but a
carriage return.
Note: Using (ATTN) instead of (CR) will cause WYLBUR
to revert to the original version of the line.
V. To save the modifications just made to the working
data set, the user must use the SAVE command as follows:
COMMAND? save smodel (CR)
VOLUME? tso002 (CR)
"SMODEL" SAVED ON TS0002
COMMAND?
261
-------
As a result of this the working data set has been
saved under the name SMODEL.
If the user wants to replace the original data set SOSMDL
i.e., the SOSMDL should include the present alterations
that have been made then do as follows:
COMMAND? save sosmdl rep (CR)
VOLUME? tso002 (CR)
"SOSMDL" REPLACED ON TS0002
COMMAND?
VI. In order to get a listing of the program the following
steps need to be done.
COMMAND? mod 2
2. //SOI EXEC FORTGCLG,FARM.FORT-fNOSOURCE,NOUST,NOMAP',
ALTERS? d d (CR
2. //SOI EXEC FORTGCLG,
ALTERS (CR)
COMMAND?
VII. The user may ask WYLBUR to show the names of all data sets
he has saved on any given volume.
COMMAND? show dsn on tso002 (CR)
TS0002
DEVEP
DEVEP1
SOSMDL
COMMAND?
262
-------
VIII. The SCRATCH options allows a user to delet those data
sets he ho longer needs.
COMMAND? scratch devep2 (CR)
"DEVEP2" SCRATCHED ON TS0002
COMMAND?
263
-------
APPENDIX - 6
MAINTAINING THE INITIAL SATISFACTION THRESHOLDS
In order to measure the effect in SOS-1 of raising the demand
measure thresholds if the demand per capita is more than satis-
fied during the past two years--simulation of learned gratifica-
tion levels--two additional runs of the model were made where
the initial thresholds were maintained even if output surpassed
required levels. These runs are:
RUN 8: comparable to RUN 1 (the base case)
RUN 9: comparable to RUN 4 (fund growth limited to 2.01)
COMPARISON OF RUNS 1 AND 8
Run 1 is discussed in detail within the Model Test Section
of this report. The major characteristics of that run to be
considered within this analysis are:
Thresholds of measures were upgraded 79 times and reduced
0 times.
The price of silver became prohibitive in year 22 causing
significant long term adjustment redistribution of investment
funds.
The increased cost of suburban land contributed to the region's
problems in year 23.
By year 25 the population Had increased to 1.314 times the
original and the combined QOL measure was 1.82.
In Run 8, the following results were noted:
Similar results to Run 1 are noted in that food and silver
again depressed productivity.
As in Run 1, silver became a problem in year 22. However,
even with the secondary food problem of cost increases by
year 23 to 1.6 times the original level, short term adjust-
ments continued to supplement production adequately for the
region.
Run 8 never required lowering of QOL thresholds through year
25; however, it appeared adjustments to lower levels were
imminent when the run was ended.
264
-------
In summary, while differences occurred between Run 1 and
Run 8, and the expected greater flexibility of adjustments
did appear in Run 8; no major differences existed to select
one set of output over the other if the simulation were
continued past year 25.
COMPARISON OF RUNS 4 AND 9
The next two runs used investment funds set to an annual
growth level of 2.0%. Neither run produced a major adjust-
ment problem during the 25 year run. Comparison of population
levels and individual measures of demand satisfaction at year
25 shows only minor variations. Comparison of unit costs for
resources suggests that there is little difference again
although Run 4 would be favored. Although the flexibility
for adjustments appear higher for Run 9, this is not tested
in the 25 year run and hence the relative merit is not
measured.
FINDING
Although some short term merit is noted in the flexibility of
adjustments introduced by maintaining per capita demand at
constant threshold levels, the differences produced appear
to be small for long term adjustments under heavy stress. If
a system is well balanced to carrying capacity of a region
this aspect may become important but no demonstration of this
has been produced in SOS-1 runs to date.
265
-------
APPENDIX - 7
SETTING POPULATION GROWTH TO ZPG
A set of analyses were performed setting the gross birth rate
and death rate equal, thus causing all population change to
be set by net immigration rates. The set of runs considered
in the analysis of this appendix are:
RUN 10: all data same as RUN 1 except the birthrate
RUN 11: all data same as RUN 4 (2% funds growth)
except the birthrate
RUN 12: all data same as RUN 5 (0% funds growth)
except the birthrate.
COMPARATIVE DEMAND SATISFACTION
In the comparisons, the need to produce output was forced
by the increasing demand thresholds even though the popula-
tion sizes for the ZPG cases are much smaller than for the
original cases. Figure 7-1 lists the population levels
and demand satisfaction levels for each run at t=25. Then
the product of these two statistics is provided.
RUN
Population
QOL Level
Product
12
.924
.865 1.104
.99 1.02
1 10 4 11 5
1.314 1.056 1.279 1.028 1.143
1.820 2.160 1.110 1.370
2.39 2.28 1.43 1.41
FIGURE 7-1
COMPARATIVE DEMAND SATISFACTION LEVELS
In the third comparison (5 and 12) the combined satis-
faction levels are similar; in both of these cases high
unemployment has caused similar salary levels. In the
other two comparisons a significant production drop has
occurred due to the relative shortage of work units in
the ZPG cases (10 and 11).
266
-------
The question exists, however, which is preferable; a high
QOL or a larger population? For the 0.0 funds growth
case a significant drop in population has occurred from the
initial situation suggesting that the ZPG alternative may
have hidden detrimental effects. However, for the 2.0% funds
comparison either run has output results that appear appropriate
Since the Run 4 case was selected the best parametric case
in the analysis of the main report, an alternate population
growth case may be appropriate as a "best" demand satisfaction
case with the birth rate about 50% greater than the death
rate--a case midway between Run 4 and Run 11.
While Run 10 has comparative data that suggests it has
merit it caused the same problems that are discussed for
Run 1 in the body of the report. Two major resource depletions
have been caused by year 25, suggesting that the regional
carrying capacity is significantly affected. Hence, it is
not a viable alternative to Runs 4 or 11.
Case 11 was run again with the demand thresholds held
constant to the initial run values. As has been noted in
the cases discussed in Appendix 6, this apparent increase in
adjustment flexibility produced no significant improvement
over the Run 11 values.
FINDINGS
In the comparisons of present day population growth to
ZPG under different fund levels, the general finding of the
comparative analysis of the report body was maintained--best
investment funds growth is about 2.01. Also, the ZPG rate
did not improve QOL as much as population size was lowered.
Hence, while a lower birth rate may produce a better outcome,
the rate is not as low as a ZPG rate.
267
-------
APPENDIX - 8
REDUCTION OF SYSTEMIC ADJUSTMENTS OF SOS-1
The data base used for the Base Case of the model test
incorporates a number of resource categories that, if
no adjustments were allowed, would rapidly be critically
depleted. These levels for the initial reserve stockpile of
nonrenewable resources are based on the generally accepted
static stockpile sizes that are documented in several sources
Figure 8-1 provides a list of the expected length of avail-
ability at the initial usage rates.
Iron
Copper
Zinc/Lead
Mercury
50 yrs
30 yrs
25 yrs
8 yrs
Silver
Trace Metals
Coal
Oil
FIGURE 8-1
5 yrs *
100 yrs
250 yrs
20 yrs
Expected Life of Static Resource Levels
The SOS-1 model includes the capability to adjust stock-
pile reserves as a function of unit costs, and to increase
procurement funds available for resource purchases. A fully
operating version of this is Run 1; the Base Case, 25 year
output is completely reproduced as Appendix 9.
During its run, adjustments were made as follows:
Stockpile increases -19
Resource substitutions -9
Years in which imports were made -19
Years in which funds were adjusted -3.
To determine if the model would react similar to other
models that do not include these adjustment mechanisms and
to determine the selective effects of elimination of some
adjustments, a set of SOS-1 runs were made in which major
portions of the model were systematically removed. This
appendix documents the effects of three such runs; all exactly
comparable to the Base Case run.
RUN 13 removed all adjustments
RUN 14 allowed only long term funds reallocation
*Later data suggest 11 years.
268
-------
RUN 15 allowed long term and resource adjustment
but no short term adjustments.
RUN 13: THE RIGID DESCRIPTIVE SYSTEM
Within Run 13 the only adjustments in the use of data
are the changes in unit costs for resources as the available
stocks are consumed. Thus it can be anticipated that com-
ponents that use critical resources will use somewhat less
amounts each year until the stock is depleted; then the pro-
duction of that component will be reduced to a negligible
level. Since the two resources in shortest supply are silver
(statically 5 years) and mercury (8 years), the using components-
health, heavy polluting manufacture and commercial for silver;
health, both manufacturing components, agriculture and house-
hold and recreation for mercury--should fail inside the first
decade. Figures 8-2 and 8-3 provide the output histories for
all ten components.
In year 2, the first major effect on production was
an increase in salaries per work unit, causing most output
levels to drop to 75-85 percent of the first year levels
in year 3. By year 5 nearly full recovery had been made.
In year 6, the stocks of silver were 98% depleted and for
mercury were 931 depleted. In year 7, the components
of health and heavy polluting industries dropped to one-
fifth the initial production level. By year 8, three compon-
ents that require silver ceased production. In year 9,
escalating unit costs for mercury reduced outputs for light
polluting manufacture, agriculture and household to negligible
levels.
Thus the model reacted as anticipated under the no adjust-
ment case. If a rigid, no adjustment system is used,
the model reacts as predicted.
RUN 14: FUNDS REALLOCATION ONLY
Run 14 differed from Run 13 only in the area of allowing
long term allocations to occur as soon as an economic justi-
fication was provided. Thus the expected reaction to a resource
shortage would be shifting of funds to the components affected
by the shortage, thus allowing them to pay higher unit costs.
The result should be a system collapse that occurs somewhat
faster than in Run 13.
This was realized; by year 6 silver costs escalated
putting the outputs of the affected components at negligible
levels in year 7. The heavy shifting of funds to compensate
269
-------
TABLE MMPER TWO - PUBLIC SFfTOF OUTPUT UNITS
(SCALFQ TO PPICINAL VALUF)
YEAR
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19,
20.
21.
?2.
23.
24.
25.
EDUCATION TRANSPORTATION
(Fl (T)
1.0000
1.0819
0.8308
1.0479
1.1346
1.2219
1.1085
1.4091
1.5154
1.6311
1.7565
1.8919
2.0473
2.2047
2.3761
2.5669
2.7759
3.0006
2.9857
3.3870
2.2382
3.0215
3.28S5
3.5797
3.8770
1.0000
1.0328
0.7644
O.S207
0.9520
O.Q843
1.0171
1.0501
1.0840
1.1186
1.1547
1.1916
1.2314
1.2707
1.3112
1.3530
1.3961
1.4406
1.3687
1.4749
0.9358
1.2001
1.2420
1.2849
1.3291
HEALTH
(HI
1.0000
1.0906
0.0573
1.0869
1.1954
1.2752
0.2315
0.0000
0.0000
a. oooo
0.0000
o.cooo
0.0000
0.0000
o.oooo
0.0000
0.0000
O.COOO
0.0000
o.oooo
o.oooo
o.oooo
0.0000
0.13000
0.0300
AMD CTHFR
in)
1.0000
1.0500
0.7785
0.9560
1.0042
1 .0545
1.1045
1.1530
1.2038
1.2573
1.3135
1.3725
1.4411
1.5053
1.S739
1.6458
1.7219
l.!)076
1.7410
1.9170
1.21t5
1 ,6096
1.6922
1.7849
1.RRL6
WELFARE
(W)
1.0000
1.0RHO
O.H323
1.0586
1.1529
1.2457
1.3415
1.4501
1.5665
1.6136
1.B370
1.9P.26
2.1585
2.3353
2.5297
2.7497
2.9909
3.2523
3.2'tf?
3.7?04
2. 4430
3.3391
3.6645
4. 0203
4.3756
PUBLIC SFCTPh
4.0
3.6
3.2
YEASS
2.8
2.0
1.6
1.2
T T
T T
0.8
0.4
-0.0
HI-HHHHHHHHHH
t i i « • YFARS ,1
1.0 3.5 6.0 8.5 11. 0 13.5 16.0 18.5
FIGURE 8-2
RUN 13 PUBLIC SECTOR OUTPUT DATA
270
HHHH
21.0
23.5 26.0
-------
TAflE NUPEER THREE - PRIVATE SEfTCF PUTPLT l.NITS
(SCALFD'TQ CRIMINAL VALUE)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
HEAVY POLL.
MANUFACTURE
(H)
1.0000
1.0398
0.8034
0.9615
1.0035
1.0401
0.2260
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
LIGHT POLL.
MANUFACTURE
(L)
1
0000
1.0454
0.8118
0.9720
1.0166
1.0622
1.0971
1.1172
0.0063
0.0017
0.0012
0.0008
0.0006
0.0005
0.0004
0.0003
0.0003
0,0003
0.0002
0,0002
0.0002
0.0002
0.0002
0.0001
0.0001
COMMERCIAL
(C)
1.0000
1.0208
0.7485
0.0900
0.9096
0.92P9
0.7436
0.0000
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
O.OC01
0.0001
0.0001
0. 0001
O.C001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
AGRICULTURE
in
1 .0000
1.0005
0.8443
0.9202
0.9229
0.9255
0.9258
0.9251
0.0116
0.0082
0.0058
0.0037
0.0027
0.0020
0.0016
0.0013
0 .00 1 1
0.0009
0.0008
0.0006
0.0006
0.0005
0.0004
0.0004
0.0003
HCUSEHCLD £
RECRE/IT ION
1.0000
1.0358
1.C639
1.0989
1.1323
1.1671
1.2023
1.2366
0.0365
0.0098
0.0072
0.0047
0.0036
0.0028
0.0023
0.0019
0.0017
0.0014
0.0013
0.0011
0.0010
0.000°
0.0008
0.0008
0.0007
PRIVATE SrCTPF
4.0
3.6
3.2
2.8
2.4
2.0
1.6
YEAPS
1.2
O.B
P R
R
L L L
F F F
C
0.4
-p.o
CRR.PRPPRPRRR
• i • i i YEAPS ' '
1.0 3.5 6.0 8.5 11.0 13.5 16.0 18.5
FIGURE 8-3
RUN 13 PRIVATE SECTOR OUTPUT DATA
21.0
23.5
26.0
271
-------
this shortfall reduced the pressure on mercury usage so
that its affected components did not collapse until year 10.
However, by year 10, shifting of funds and resource outages
reduced 7 of the production output components to negligible
output levels as predicted.
RUN 15: NO SHORT TERM SMOOTHING ADJUSTMENTS
Run 15 allowed all types of resource adjustments and long
term production and funds adjustments but did not allow
short term marginal compensations for minor, local deficiencies
As such its output should be similar to Run 1 in that all
components should continue reasonable production, but different
in that very ragged production trends should be produced due
to overreaction to local problems.
This did occur; as early as year 1 major changes were
introduced that did not occur in Run 1 until year 22.
The set of long-term adjustments in Run 1 occur only
after all short-term adjustment mechanisms have been exhausted;
hence all changes in component input-output functions are
conservative and all funds rates of growth changes occur only
after more local changes have been found deficient. Thus in
Run 1 (see Appendix 9) only four components adjusted the input-
output formulas, each once and all in year 22. Also, in years
22, 23, and 24, redistribution of funds growth rates occurred.
The removal of short-term adjustments in Run 15 produced
many long term changes beginning with both funds changes and
input-output changes in year 1. Six components changed input-
output formulas; three of them twice; two of which were
reversals to the original formulas. Long term funds realloca-
tion occurred 11 times in Run 14.
Figures 8-4 through 8-7 provide data for runs 1 and 15
on public and private output patterns. The effect of lack
of short term adjustments for Run 15 are quite apparent; the
patterns are much more ragged than in Run 1.
FINDINGS
The model components are causing results as anticipated
in the design of SOS-1:
• Removal of resource adjustments causes the regional
production systems to rapidly collapse due to rapid
depletion of scarce natural resources.
272
-------
TABLE NUMBER TWO - PUBLIC SECTOR CUTPLT UNITS
(SCALEC TO ORIGINAL VALUE)
YEAR
1.
2.
3.
4.
5.
6.
7.
6.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
EDUCATION
(E)
1.0000
1.0819
0.8308
1.0294
1.1146
1.2245
1.3089
1.0417
1.2768
.3841
.5167
.2167
.4933
.6435
.7770
1.9202
2.0804
2.2519
2.4292
2.6208
2.8337
3.0668
3.3602
3.7345
4.2434
TRANSPJRT.ATIO
(T)
l.OOOC
1.0328
0.7644
C.8803
0.9102
0.9411
C.9725
0.7438
0.8846
0.9150
0.9459
0.73C5
0.8662
0.8956
0.9256
0.9512
0.98S3
.0226
.0575
.0921
.1214
.1640
.2017
.2407
.2807
HEALTH
IH)
i.coco
1.0906
0.8530
1.0657
1.2039
1.2943
1.3892
1.1412
1.4066
1.58S8
1.7046
1.A119
1.7571
1.S858
2.1573
2.3750
2. (183
2.8810
3.1468
3.4425
3.7936
2.3828
4.4899
4.S6E5
5.4544
DEFENSE
AND CTHER
(C)
l.CCCO
1.C500
0.7785
C.S560
1.0042
1.C546
1.1047
0.6479
1.0285
1.C800
1.1329
C.88C8
1.0699
1.1227
1.1788
1.2331
1.2900
1.3544
1.4U2
1.4815
1.5500
1.6245
1.6996
1.7789
1.8621
WELFARE
(Ml
1.0000
1.0880
0.8323
1.0313
1.1232
1.2503
1.3411
1.0668
1.3073
1.4629
1.5792
1.2700
1.5601
1.7466
1.8884
2.0507
2.2355
2.4312
2.6343
2.8559
3.1090
3.3811
3.8465
5.8451
6.1298
4.0
3.6
3.2
PUBLIC SECTOR
YEARS
M E
•M E
2.8
M E
2.4
2.0
1.6
1.2
0.8
H E
H E
E
T T
T T
T T
0.4
-0.0
• • • • • YEARS •
1.0 3.5 6.0 8.5 U.O 13.5 16.0
FIGURE 8-4
RUN 1 PUBLIC SECTOR OUTPUT DATA
18.5
21.0
23.5
H H
26.0
273
-------
TABLE MJMBCft THREE - PRIVATE SECTOR OUTPUT UMTS
(SCALEC TO ORIGINAL VALUE)
YEAR
1.
2.
3.
4.
5.
«.
7.
a.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
11.
20.
21.
22.
23.
24.
29.
HEAVY POLL.
MANUFACTURE
(HI
1.0000
1.0398
C.8039
C.9403
C.9874
1.0352
1.0752
0.3796
1.0230
1.0689
1.110*
C.9119
1.0653
1.1103
1.1591
1.21)9
1.2302
1.3*05
1.3952
1.4524
1.5111
1.0064
1.6765
1.7400
1.8318
LIGHT PCLL.
MANUFACTURE
(L>
1.0000
i.o*;*
c.ane
0.9378
C.9814
1.0267
1.0656
C.8B1C
1.0123
1.C602
1.1042
O.S146
1.0528
1.1022
l.i:20
1.2426
1.2(14
1.34!J
1.4CCJ
1.4578
1.5168
1.5818
l.S6(3
1.6T1S
1.7103
CCMMERCIAL
1C)
1.0000
1.0208
0,7486
0.6581
C.1771
0.8S6*
0.9132
C.6939
0.8143
C.6324
C.E492
0.650*
0.1636
C.7BC9
0.7986
C.1169
0.6369
C.C559
C.67!3
0.8S58
C.S153
0.89«6
C.S840
I.C342
1.0827
HOUSEHOLD G
AGRICULTURE RECREATION
(ft (R)
1.0000
1.CG05
C.8443
0.9202
0.9229
0.9256
6.9263
C.7850
O.G379
C.6407
C.8424
0.7095
0.1140
0.7767
0.7790
0.7814
0.7836
C.7C62
C.7886
0.7S07
C.77C9
0.6589
0.7192
C.7*38
.0000
.0358
.C639
.0989
.1323
.1676
.2027
.2400
.2811
.3221
.3635
.4093
.4640
.5160
.5720
.6321
.6922
.7539
.8210
.8879
.8096
.4671
.4043
.5241
0.7861 1.5835
PRIVATE SECTOR
4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
YEARS
L L ft R
L L R
R R
L R R L
R R L L
O.B
FCC
C
C C C C
F f f f f F
C.4
-0.0
i • i i • YEARS < •
1.0 3.5 6.0 8.9 11.0 13.5 16.0 18.5
FIGURE 8-5
RUN 1 PRIVATE SECTOR OUTPUT DATA
274
21.0
23.5
26.0
-------
TABLE NUMBER TWO - PUBLIC SECTOR OUTPUT UNITS
(SCALED TO ORIGINAL VALUE)
YEAR
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
EDUCATION
IE)
1.0000
1.0985
0. 8685
1.1505
1.3275
1.5132
1.7626
1.9834
2.2909
2.6790
2.9453
3.1874
2.4948
3.1834
3.4729
3.0578
3.7020
15.7182
47.6771
14.1677
8.8037
5.7611
4.0363
2.9890
1.8847
TRANSPORTATION
IT)
1.0000
1.0328
0.7653
0.9213
0.9527
0.9850
1.0182
1.0516
1.0863
1.1217
1.1573
1.1953
0.8532
1.0471
1.0789
0.8927
1.0260
1.0607
0.0946
0.3692
0.6364
1.0956
1.8652
3.1598
5.3490
HEALTH
(H)
1.0000
1.0906
0.8570
1.C9?4
1.1930
1.2333
1.3345
1.3886
1.5400
1.7503
1.8961
2.0800
1.6606
2.1479
2.3621
2.1127
2.5872
2.8383
3.0965
3.0676
3.1439
3.1776
3.2308
3.2524
3.2959
DEFtNSE
AND CTHER
(D)
1.0000
1.0500
0.7792
0.9565
1.0038
1 .0490
2.563B
2.20S8
2.3562
2.5314
2.6930
2.8312
2.0983
2.6196
2.7598
2.3434
2.7494
3.2165
1. 70 ! 3
1 .7302
1.7401
1 .7637
1.7948
1.8127
1.S328
WELFARF
(W)
1.0000
1.1407
1.2143
1.5258
1.9182
2.1352
4.0087
3.6700
4.0748
4.5848
4.8941
5.3129
4.2624
4.4412
2.3776
2.1394
2.1598
2.3R46
5.0356
5.0903
5.2333
5.3222
5.4528
5.47°1
5.5337
4.0
PUBLIC SFCTCP
VFARS
3.2
H H
T
2.8
2.4
2.0
1.6
E 0
D
D H
ODD
1.2
0.8
V
D
W T
EH
H D
0 T T
D T
T T T
0.4
-0.0
• i i i i YEARS '
1.0 3.5 6.0 8.5 11.0 13.5 16.0
w w w w w
FIGURE 8-6
RUN IS PUBLIC SECTOR OUTPUT DATA
275
18.5
21.0
23.5
26.0
EWWWWWWW
-------
TABLE NUMBER THREE - PRIVATE SECTOR TUTPUT UMTS
(SCALED1 TO ORIGINAL VALUE)
YEAR
I.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
HEAVY POLL.
MANUFACTURE
(H)
i.oooo
1.0417
0.8136
0.<38"33
1.0478
1.0798
1.1253
1.1497
1.2059
1.2713
1.3251
1.3871
1.0700
1.3313
1.3760
1.1958
1.4039
1.4679
0.4047
0.7432
0.8824
1.0416
1.2208
1.4103
1.6309
LTCHT POLL.
MANUFACTURE
(L)
1.0000
1.0443
0.8103
0.9791
1.0300
1.0637
1. 1118
1.1384
1.2057
1.2952
1.3555
1.4252
1 .0978
1.3500
1.4140
1.2242
1.4253
1.5082
0.4126
0. 7448
0.8851
1 .0446
1.2273
1.4303
1.6639
COMMERCIAL
(C)
1.0000
1.0205
0.7485
0. 8858
0.8992
0.9038
0.9164
0.9211
0.9405
0.9704
0.9886
1.0079
0. 7250
0.8737
0. 8908
0.7313
0.8320
2.2213
0.5861
0.8983
0. 8559
0.8119
0.7756
0.7501
0.7341
AGRICULTURE
(H
1.0000
1.0084
0.8560
0.9411
C.9508
0.9556
0.9646
0.9686
0.9818
1.0009
1.0128
1.0234
0.8440
0.9425
0.9522
0.8443
0.9116
0.7658
0.6192
0.3810
0.7334
0.6021
0.5051
0.4352
0.3im
HOUSEHOLD 6
RECREATION
1 .0000
1.0350
1.0622
1.0848
1.1070
1.1263
1.1501
1.1698
1.1976
1.2288
1.2546
1.2fl54
1.3239
1.3562
1.3896
1.4236
1.4577
2.0782
0.8750
1.1795
1.1871
1.1981
1.2129
1.2311
I.ZW8
PRIVATE SECTTP
4.0
3.6
3.2
2.8
2.4
2.0
1.6
1.2
0.8
0.4
L
L L P R
L » R
L
R
R
F
C
R
L
F
R
L
F
f R R R
L L
f f f f \
F C C C
L
• f
F
C
R
F
C
0.0
1.0
3.5
6.0
8.5
11.0
YEARS
13.5
16.0
18.5
FIGURE 8-7
RUN 15 PRIVATE SECTOR OUTPUT DATA
276
21.0
23.5
26.0
-------
Provision of long term funds redistribution without
resource availability adjustments hastened the rate
of collapse since funds were shifted to purchase
scarce goods driving their unit costs still higher.
Inclusion of the resource adjustments and long term
adjustments without short term adjustments to smooth
reactions caused a system that remained reasonably
viable for the run history but included ragged output
trends, over-reaction to symptoms and much increased
use of funds redistributions that led to introduction
of new problems.
277
-------
APPENDIX 9
LISTING OF ALL OUTPUT
FOR THE BASE CASE
(RUN 1)
278
-------
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