Economic Development Program
C/58-6
AN ANALOG UDEL FOR STDYING
ECONOMIC DEVELOPMENT PRBLElS
Edward P,, Holland
Center for International Studies
Massachusetts Institute of Technology
Cambridge, Massachusetts
January 1958
2
Abstract
AN ANAWOG
DDE
FOR STUDEIE 'CW01MIC DEVEZOPMENT PEOBEMS
by
Edward Peck Holland
Submitted to the Department of cnomics and Social
Science on January 13, 1958, in partial fulfillment of
the requirements for the degree of Doctor of Philosophy.
This thesis Is the formulation of a dynamic macro-econoic model
which will later be simulated with the electro-nechanical analog at
the Massachusetts Institute of Technology for the putpose of studying
the starting of economic development in underdeveloped countries.
In Part I the economic problem is described, and the applicability of control-system concepts and analysis are discussed. Although
some of the methods of control-system engineers are unsuitable for use
on this problem, the technique of analog simulation promises to be
fruitful. This technique is briefly explained.
In Part II the model is formulated in detail In words and equations and is translated into block diagrams corresponding to the analog
setup. The model represents production and consumption of several kinds
of goods with a flexible price for each, which depends on costs, capacity, and demand. Demands depend on consumers! incomes and preferences.
Capacity in each sector depends on the history of capital creation,
which is motivated partly by profits and partly by government programs.
Exports, imports, and foreign finance also affect the system in ways
that depend on tariff and exchange-rate policies
4
Part III includes a discussion of the procedure of trying out
various development plans repetitively with successive adaptation of
policies for each. Although the projected study will not be quantitatively predictive, it is felt that it will give useful insight into
qualitative modes of behavior of real economic systens and into the
questions of what variables are strategic for control and which are
good indicators of the corrective measures that are needed. It is
concluded that analog simulation of this model is feasible and worth
while, and that the same technique could be used advantageously for
other dynamic economic problems.
Thesis Supervisor:
Max F. Millikan
Professor of Economics
Massachusetts Institute of Technology
3
CONTENTS
PART I:
IETRMUCTION
Chapter
Page
I
PROBLEMS OF DEVELOPMENT POLICY
2
SUITABILITY OF CONTROL-SYSTEM APPROACH
4
13
The Control-System Approach
16
Analog Simulation
21
FORMULATION OF TE MODEL
GENERAL DESCRIPTION OF THE SYSTEM
28
32
Fig. 1 - Supply and Demand Interactions
Fig. 2 - General Outline of Interdependences
33
38
CONSUMERS'
JOINT DEMAND FUCTION
39
General
Choice 1: Food, Other Goods, and Savings
Elasticity Relations
39
41
41
Choice 2: Low-cor, High-cor,
Growth and Developing Tastes
44
45
and Imported Consumer Goods
Fig. 3 - Consumers' Joint Demund Function
AGRICULTURE AND LOW-CAPITAL PRODUCTION
47
53
54
A.
Agriculture (Sector 2)
Short-Run Supply; Capacity Changes
14
B.
Low-cor Consumer Goods (Sector 4)
Short-Run Supply; Changes in Minimum Price;
Capacity Changes; Overhead Costs; Investment
Decisions; Investment Restraint and Augmentation
60
APPENDIX TO CHAPTER 5
6
28
Concepts
The Model
APPENDIX TO CHAPTER 4
5
13
Difficulties of Analysis
PART II:
3
6
70
Fig. 4 - Agriculture (Sector 2)
71
Fig. 5 - Low C.O.R. Consumer Goods (Sector 4)
Fig. 6 - Additions to Sector 4 for Imported Materials
74
75
INDUSTRIAL PRODUCTION AND PUBLIC 09ERHEAD
A.
High-cor Consuror Goods (Sector 1)
Short-Run Supply; External Economies; Profits
and Wages; Profits and Investments; Capital Cost
76
4
B.
C.
D.
Capital Goods
Public Overhead Capital
Government Expenses
APPENDIX TO CHAPTER 6
90
Fig.
Fig.
7 - High C.O.R. Export and Consumer Goods (Sector 1)
8 - Short-Run Supply Price Computer (Sector 1 or 3)
Fig.
9 - Capital Goods (Sector 3)
Fig. 10 - Public Overhead Capital (Sector 5)
7
82
85
89
FOREIGN COMRCE AND PAYMENTS
92
93
96
98
99
Imports
99
Exports
100
Balance of Payments
101
APPENDIX TO CEAPTER 7
1W
Fig. 11 - Foreign Markets
8
INCOMIE, FINANCE,
AND CONTROL
A.
Income
106
B.
Finance and Control of the Investment Pattern
110
APPENDIX TO CHAPTER 8
10
114
Fig. 12 - Income Accounts
116
Fig.
117
13 - Sample Program
Fig. 14 - Price and Inflation Indexes
118
Fig.
119
15 - Investment Controls
PART III:
9
106i
PlANS FOR STUDY
PERIENTAL APPROACH
121
A.
B.
Numerical Data
Development Program Comparianna
121
122
C.
D.
Crises and Readjustments
Nature of Results Sought
12
128
COWLUSIONS AND RECOMMENDATIONS
131
BIBLIOGR/APHY
134
AC~FMLOGMI'3
137
5
PAT
I
INTRODUCTIMo
6
Chapter 1
PRBIEW OF DEVBWPMBNT POLICY
This thesis is the foundation for a larger study, in which
n
electro-mchanical analog will be used to simalate an underdeveloped
In the thesis, the model of the econozy is
economy.
formulated in
economic terms and then translated into a worhing specification of
the analog setup.
Also. the method of investigation by means of
the analog is outlined.
In the larger study, the problem of initiating economic development will be investigated from the dynamic macro-eceonce
point.
The study will have two aims:
stand-
Primarily it will be an at-
tempt to gain significantly better understanding of the dynamic
economic problems involved in starting economic development
Sec-
cndarily, it will be a test of the usefulness of simulation techniques for studying economic dynamics.
This thesis fulfills a pre-
liminary objective by providing a model which is better suited to
the study than any directly soluble model and which can be simulated
with existing equipment.
In the next chapter the technique of analog simulation
ill
be
explained,
wad its suitability for the problem at hand will become
apparent.
First, however, the economic problem is described sad
discussed in the remainder of this chapter*
7
In the kind of country to which the study is relevant, output
per capita is
initially quite low and is mainly agricultural and
handicraft products.
The
cenoW operates by tradition, with no
tendency to develop nw products or more productive techniques.
Food production is
limited by the area of land cleaed, and the
labor force on the farms is much more than is needed for the crop
that is prduced .
what Roatco has
The problem of concern is
hov to bring about
med "the take-off," which he defines as an in-
terval of two or three decades:
a . . during which the rate of investmnt inereases in
such a way that real cutput per capita rises and this
initial increase carries with it radical change in
production techniques and the disposition of income
f los which perpetuate the new scale of investant and
perpetuate thoby the rising trend in
anita cutput.
.
.
.
This, of course, is not a purely economic phenomenon:
a , . The take-off requires . . . a society prepared to
respond actively to new possibilities for productive
enterprise; and it is likely to j4"ire political, social
and institutional clanges. Q
Some theorists maintain that initiation of economie developmt is purely a noneconomie
problem.
is like the growth of a plant.
In this view, economic growth
To encourage it,
one tries to establish
. W. Rostos, "The Take-off into Belf-Sustained Greath,
Reenooic Journal, March 1956, p. 25.
2
lbide
40"NWN..
"The
8
a favorable environment, but does not tamper with the process itself.
Remove joint family obligations, religious prohibition of interest
charges and other commercial practices, and legal obstacles to free
trade between regions and groups, and soanhow modify people's attitudes of disdain for money-makers, and the economy will thrive.
Others have noted, however, cases where the beginnings of economic
progress seem to have induced some of the appropriate changes in
aiistr,
ucture, cultre., and evn
religlis
ds4etrines .
No doubt the truth is that certain noneconomic conditions-as
well as certain economic conditions--have to be established beforo
the process of take-off can fully succeed, but that some of these
conditicns can be established during the take-off, rather than all
having to be accomplished beforehand.
The great importance of non-
economic factors is not denied in this study.
Neither is the in-
portance of establishing economic preconditions, which may take a
long time and without which the take-off may be impossible.
of these aspects, however, is left to others.
Study
This study is direct-
ed solely to the economic dynmics of the take-off.
Any notion
that this aspect of the problem is clear and simple is vigorously
denied.
Apart from this question, however, is the question of laissezfaire versus central planning, or rather of degree in between.
Faith
in the "invisible hand" is not so widespread in advanced countries as
9
it was before the Great Depression, and there probably never was
unch of it
in the underdeveloped countries.
Russia-however mch
we may despise their flouting of personal freedom-has demonstrated
one way of bringing an underdeveloped nation up to advanced industrialism in forty years.
Earlier, Japan had demonstrated another
Iy,with lose central control but with the government actively
manipulating the economic incentives and deterrents.
where economic development is
In countries
a popular objective today, it is taken
for granted that governmnt responsibility extends at least to the
mnipulation of foreign commerce, the tax structure, and the money
system, to the over-all planning of development patterns on a seetoral level, and usually also to the actual building and operation
of public transportation, power, comunication, Irrigation, and
other such system.
There is no real question whether the govern-
ment should exercise controls to try to steer development.
There
are, however, plenty of questions about what kinds of manipulation
will be most conducive to progress .
These are the questions on
which this study is focused.
The problem is to find a combination of programs and policies
which will lead into continuing growth of real disposable income
per person.
What is sought are guides for deciding how much rela-
tive emphasis to give at any time to building up food production,
or consumer-goods industries, or capital-goods industries, or transportation services; whether to combat inflation by encouraging more
10
handicraft production, more industrial manufactures,
or more imports
of consumewr goods; whether to try to balance the foreign account by
protective tariffs, encouragement of export industries, or adjustment of the exchange rate.
The situation presents many dilesms
For example:
An import
surplus is one of the chronic problem of a country trying to start
consumers'
development. An obvious remedy is a high tariff or a quota on/import&.
However, a by-product of such action is
the diversion v2
some of the demand to the doesatic markot, where it
adds to the in-
flationary pressure which is also a normal concomitant of a developmwnt effort.
of payments is
If home prices become inflated, the adverso balance
likely to get worse instead of better.
How can the
proper remedy be chosen in a given case?
Another example:
An antidote to inflation is increased pro-
duction of consumer goods, cometitively priced.
To increase the
capacity of consumr-goods manufaoturing industries requires making
investment expenditures, which increase demd right away, while the
increase in supply will not occur until later.
Hence what may be
deflationary later an has inflationary effects in the short run.
Will the long-run benefits erase the damge that has been done in
the short run?
(The investmnt may very well involve increased
capital-goods imports, which further complicate the problem by disturbing the balance of payments .)
11
Two of the most difficult aspects of the problem
faced by the
makers and executors of development policy are, first, the conflict
between inediate symptoms and ultimate effects of any action and,
second, the sultidimensional nature of both the goals and the effects of various actions.
Whether their decisions are actually
effective toward any particular goals, they cannot tell by watching the imediato conequonces, which often takethe form of crises
in the balance of payments, inflation, anddlstortions in the goods
and factor price patterns.
What to do in such circumstances sust
be decided on the basis of some sort of theory (explicit or Intuitive), for policies based solely on alleviating the short-run difficulties will probably not lead to long-run progress.
The need for a different theoretical technique than those that
are currently conventional in economics arises from the complex
nature of the system and the problem to be dealt with.
The ques-
tiens posed above clearly call for a mltisectoral model, with
flexible prices, capacity limits, capital formation, foreign commerce, and various controls.
Time-delays and time-spreads are
basic to the physical processes of capital-formation and capital
attrition; output in various sectors is limited by past capital
formation; supply prices at capacity are determined differently
than below capacity; and there is contInuous interaction between
production of various sectors, Income, demnd, prices, foreign conmerce, and the balance of payments.
These interactions are too
12
significant to allow reaching valid conclusions from analyzing parts
of the system separately with all else assumed constant; the nonlinearities invalidate linearized analysis; and the time-spreads
and irreversibilities in the system, together with the dynamic
character of the forces applied to it,
little
use.
make comparative statics of
13
Chapter 2
SUITABIITY OF CONTROL-YST3M APPROACH
Difficulties of AnalysiS
Adequate analysis of economic take-off problems, as indicated
in Chapter 1, requires recognition of varios nonlinearities and
tL.-snpread eflct
in a compXa
ot o2 ±nterdependent relation-
The nature of those relatimships has frequent3y been de-
shipa.
soribed and is fairly well agreed upon,
Differences of opinion
center mainly on the question of which ones cam be safely ignored
or grossly simplified beocnse the dynamic behavior of the whole
systen cannot be dealt with by verbal reasoning or direct nathematical solution.
02 acarse, every method of study involves ignoring
or simplifying relationships, but in this problem heretofore it
has
had to be done too drastically.
From a postulated set of relationships to general conclusions
about the system's modes of behavior is basically a matter of deduction:
lead?
given a set of assumptions, to what conclusions do they
Verbal logic9 however, proves inadequate for two reasons.
First, most of the relations are not syllogisms stating that something does or does not happen depending on whether a certain combination of conditions Is
in which the
or is
not met.
Most are magnitude relations,
agnitude of one variable depends on the mgnitude of
14
several others, and moms involve effects distributed through time.
A second reason that verbal logic is inadequate is
system involves many feedback loops.
that the
These are sets of relations
in circular chains such that the dependent variable of a relation
enters other relations fhich in turn affect the independent variables
of the first .
Some feedback loops and mutually determined variables
can be dealt with verbally, but not such a complex network as this
problem involves, especially when the loops also include time-lags,
delays, and nonlinearities.
Verbal analysis can best handle those
chains of emuse and effect that proceed minly in one direction,
where a few premises lead to proof of a first proposition, which is
then caubined with another premise to prove a second proposition,
and so =,
with each stop finished before the next is taken and no
effects coming back "upstream."
As Susanne Langer puts it:
. . . all language has a form which requires us to string
out our ideas even though their objects rest one within
the other; as pieces of clothingthat are actually worn
one over the other have to be strung side by side on the
clothesline. This property of verbal symbolism is known
as discursiveness; by reason of it, only thoughts which
can be arrged in this peculiar order can be spoken at
all.
0 a
Various nathematical techniques also have shortcomings for the
problem at hand.
This is partly because of limitations of the mathe-
smatics and partly because the relative merits of different results
1 Susanne
K. Langer, Philosophy in A NOw Eey, Cambridge:
vard University Press, 1942. Mentor edition, pp. 65-68.
Bar-
15
Cannot be evaluated by a single criterion.
Linear (or even non-
linear) programming is an excellent technique for maximizing or
minimizing a single criterion under conditions of general equilibThe quantities in the general equilibrium may be expanding
rium.
thrcugh time, but the situation is
essentially what Baumol describes
as "statics involving time"1 rather than dynamics.
The circuit is
not closed through incomes, consumer preferences, and market prices,
with positive profits affecting investment and with inflation limit-
ing the rate of investment that is tolerable.
Models which are more dynamic have been offered under the general headings of Business Cycle Theory, or Fluctuations and Growth.
Most of the dynamic mechanisms that are significant in business
cycles are also significant in the take-off process, and a really
adequate dynamc model should be suitable for studying both pheAn interesting collection and comparison of models of this
nmena.
type is
presented by R .
. D. Allen.2
Models included are those of
Saselson, Bioks, Goodwin, Kalecki, and Phillips.
cated and elaborate
ies. 3
ne has more recently been forsmlated by Smith-
All of these deal with income and product interchSngeably,
1 W.
J. Baumol, Economic
1-3.
pp.
1951,
Co.,
A more sophisti-
as, New York:
acaillan
Uz
2fR. 0. D. Allen,
athemtical Economdcs, Londcon:
1956, Chapters 7 and 8 and pp. 285-289.
Co.,
Macmillan a
SFor the primary references on all six models, see "Dynamic
Economic Models" in Bibliography.
16
11.e., with fixed prices, or deal solely with incom, disregarding
physical quantities and prices.
None are open to foreign comerce,
or distinguish between different kinds of goods, or have output
limited by capacity (although galecki and Smithies at least go so
far as to make investmnt sensitive to some relation between output
and capacity).
These criticisms are no reflection en the authors;
they reflect, rather, on the limitaticns imposed by mathematical
method
which are chosen to allow solution for general rather than
particular cases.
The article by Smithies in particular offers a
untuber of examles of the disparity between the ele
considers relevant and those to which he is
mtics.
nts the author
limited by the msthe-
For example, after explaining and justifying the assump-
tion that profits have a dominant influence on investment, he finds
it
necessary to assume that profits are a fixed proportion of gross
national product.
Given a technique that permitted it,
Dr. Smithies
surely would have preferred to allow for some of the factors that
ake profits high at some times and nngative at others.
The Control_
stem Aroach
In the search for more effective ways to deal with dynamic
economic systems,
several people have noted the strong similarity
between such system
and feedback control systes in engineering.
The spectacular development of control system engineering since the
beginning of World War IX certainly shculd have produced some tools
17
that could be adapted to similar systems outside of engineering.
One of the keys to this tremendous development was the use of the
laplace transform to study systems in terms of their "frequency
response spect1um" from which their dynamic behavior under any
conditions culd be deduced.
In Tustin's book,
which is a great
pioneering of fort to make the techniques of his field (electrical
engineering) ivailable to economists, this technique is the most
pt
allen also presents it
system
in
his chapter
n closed-loop
J1afortunately, as they both point cut, there are sericus
doubts abirt the usefulness of this analysis to economics, because
it
appli ae only to linear system.
The engineer often takes pains
to deslgn his system to be linear, just so that he can analyse it
betteA, but this choice is not open to the economist.
He knows that
the xconoeg has important nemlinearities, and he cannot change them.
Other parts of Tustin's and Allen's expositions, however, offer
om tools that are more certain to be helpful.
Just the symbolism
of drawing feedback relationships in block-diagram form is a great
help for tracing information from one relation to another and for
seeing which variables are independent relative to the system as a
whole or any part of it .
For the discursive form of language and
Arnold Tustin, The Eschanism of Economic
Harvard University Press, 1953.
t. G. D. Allen,
.
, Chapter 9.
stem,
Cambridge:
18
algebra, it
a nap.
substitutes a pattern of relations that can be se
like
Simply translating an economic model into this form can give
new insight into its character, as shown by Allen's diagrammatic
comparison of the several models mentioned before.I
reains the problem of analyring a complex dynamic
There still
nonlinear system.
All attempts to get direct rathematical solutia
How to break through this nathematical barrier is sug-
seem to fail.
gested by Allen in discussing the advantages of same other engineering approaches to control-system problems:
0 . . the engineer does not often attempt general solutionas; he aims at computing (by numerical or graphical
methods) particular solutions, usually a whole string of
them. . . . As economic models become more complex, and
have a greater empirical content, to make them applicable
to the real world, the answers to general questions become less possible. The economist may need, therefore,
to shift his ground from the general to the particular,
and to 9follw the ethods and the experience of the
engineer .
This means forgetting about formlating the problem so that
a solution is possible in matheasatical symbols, and instead widening the limits of formlation to include whatever can be solved
numerically, graphically, or by any other means, for particular
This approach usually requires a large numbercf solutions
ocases
to survey the effects of chanring various paramters and of apply1
2
,d p. 285.
lbid.
P. 304.
19
ing different disturbances, but if
that can scehos be done, it
can
be very enlighitening.
This approach has been used with rearding results by Phillips,
in his two well-knovn studies of stabilization policy
these he has postulated a simple income-flo
parameters, has subjected it
1
In each of
model with particular
to arbitrary disturbances, and has
tried cut varicus fomalatioms of stabilization policy, to see what
has desirable effects.
Co clusions are based on co mrisoms of
many particular cases.
Incidentally, the results of the second
study strongly bear cut a point that both Tustin and Allen emphasized:
that the form of time lags is very important to the sta-
bility of a feedback system-assuming a discrete delay when the
actual process involves a distributed lag, or vice versa, may lead
to significantly false conclusions.
Application of this approach to a system complex enough for
studying the take-off problem requires co mricon of a very large
number of particular cases, in each of which the computatins
would be extremely cumbersome by numerical methods.
"by hand" would be out of the question.
able:
Calculation
Two alternatives are avail-
digital computation and analog simulation.
Either of these
IA. W. Phillips, "Stabilization Policy in a Closed Econom,"
The Economic Journal, June, 1954, and "Stabilization Policy and the
Ti-For
oM
Reponses
The Econ
Journal, June, 1957.
20
methods oat do the job well; each has oertain advantages that the
other lacks, so that for particular applications one or the other
may ba superior, but for some probless the difference in technical
suitability is
very small.
Digital techniques are being applied to
the econonic dynamics of the firm and industry by a group under
Forrester in the School of Industrial Management at the Msac-bu
&ettz Institute of Technology,a
and to the economic dynamics of tke UoSo
e con o my by another group under Orcutt of Harvard University.
Both are using the IBM 701 machine of the Compton Cosputatice Center at the Masachusetts Institute of Technology.
For this study of the take-off problem, analog similation was
chosen because of its flexibility and convenience for feeling out
unexplored areas and for fitting a progran by cut-snd-try methods
to a set of goals.
The idea of a sinalat or
Is explained by Tustin
as follows:
A siualat or is a physical system, analogous to the
model to be studied, in which there is a more or less
complete part-by-part correspondence, the variables that
are significant in the model appearing as analogous variables-s-mchanioal, electrical or hydraulic or other
quantities-between which corres nding relationships are
set up by suitable construction.
'So Jay W. Forrester, "Systems Technology and Industrial
Dynaics," an article in Adventure in Thougt and Action, School of
Zrcustrial
a
t,
ausett
Institute of Technology, June,
1957' (proceedings of the Fifth Anniversary Convocation). Also published in The Technology Review, June, 1957.
2
Tustin,, M.ct,
p. 137
21
With the simulator that will be used here, the operator sees the
results of each run in the form of graphs, and can make changes for
the succeeding run by turning knobs that directly correspond to
parameters of the program or policy he wishes to alter.
Analog Simlation
The 1957 study by Phillips
has probably been the most fruit-
ful use thus far of analog simulation of an economic system. Earlier
studies siaulated a simple Inventory-fluctuation model,
model,3 and the Ealecki model.4
the Ooodwin
Unlike Phillips' study, these were
primarily experiments in applying the technique to problems for which
solutions had already been found by other means (except the effect of
paramter variations in the Goodwin model).
They were interesting
deastrations of the technique, but did not create awareness of its
potential utility for problem that are otherwise i.tratable. Still
earlier analogs-hydraulic rather than electrical--were invented by
1 Phillip,
"Stabilisation Policy and the Tie-Forms of lagged
Responses, "f Op. cit .
N. F. Morehouse, R. H. Strots, and S. J. Horita, "An ElectroAnalog Method for Investigating Problems in Economic Dynamics: Inventory Oscillations," Ecnoutrica October, 1950, also R. H. Strotz,
J. F. Calvert, and N. F. Morehouse, "Analog Computing T
plied to Economics," Transations of American Institute of Electrical
Engneers, Vol. 70, Part I, 1951.
3R. H. Strots, J. C. McAnlty, and J. B. Haines, "Goodwin's
Non-Linear Theory of the Business Cycle: An Electro-Analog Solution,"
Econometrica, July, 1953.
N. 8. 74.
Reprinted as Cowles Commission Paper,
O. J. Smith and H. F. Erdley, "An Electronic Analogue for an
Economic System," Electrical Engineering, April, 1952.
22
Phillips
and by Abba Lerner.2
These were useful for illustrating
the interdependences in the systems they represented, but not for
investigation beyond the limits of algebraic solution.
Using the
same principles as all of the analogs mentioned above but on a
larger scale and with more diversity, the equipment available at
the Masachusetts Institute of Technology makes it
possible to
simlate a mch more complex model, such as Chapter 1 has indicated
inecessary %ora
tuidy of take-off problems.
The technique of simlation is based on interconnecting various kinds of electronic and electro-mechanical units, each of which
receives and produces signals which can vary continuously through
time.
The signal a unit produces is functionally related to the
signals it
receives from one or more other units.
Different kinds
of units embody different relationships, some depending on the past
history of inputs, some on their derivatives, some just on current
values .
The simplest type of unit receives several varying signals
and produces their sun continuously.
Another type, a "lagT unit,
responds to a single input about the way the speod of an automobile
responds to changes in the accelerator position.
An abrupt change
IA. W. Phillips, "Mechanical Models in Economic
Dynamics,"
Economica, 1950.
2
Abba larner' model, of about 1951, is known to this author
only by hearsay. It was evidently similar to Phillips'.
23
in incoming signal causes the outgoing signal to start immediately
changing toward the level of the incoming signal, but to change
less rapidly as it approaches.
lag.)
(The function is an exponential
Graphically, the response is as follows:
Input
Voltage
Output
Time
-
Other units can select one of two incoming signals depending
on the magnitude of a third, or impose a ceiling on a signal, or
multiply two magnitudes, or integrate a varying signal (so that,
if
the incoming signal repreated a fluctuating rate of flcw of
liquid into a tank, the signal produced would tell the level in
the tank).
These and a number of other kAnds of units can be inter-
ncaoected to simulato auch more complex relationships.
To illustrate the principle, there follows a simple example
translating a dynamic income-mltiplier relationship into a diagram
of analog units and connections:
Example:
Assume that consumption, C, tends toward a con-
stant proportion, a, of income, Y.
In equilibrium, C = cY, but
24
adjustment to changes in Y involves a time-lag of the kind described above.
This my be expressed explaitly in terms of
the rate of change of C as
dt
a
where g is a constant.
g (cY - C)
Combining this with the accounting
identity, Y a C + I, makes a system relating income, Y, dynmsically to investmeut,
1.
The analog of this system uses three units, one to add
C and I, one to multiply Y by the coefficient c, and one to
produce C as a lagging counterpart of OY.
The time constant
of the lag unit is chosen to give a convenient timo-scale in
the analog.
For instance, one second of analog time might
represent one year of real time.
The arrows in the diagram
below show what information comes into sad comes out of eaoh
relationship; in the analog they are actually wires, carrying voltage signals.
25
When this is set up in analog components, the voltage representing I could be varied in any arbitrary way and the corresponding variations in Y recorded.
I,
More important, the incoming signal,
can be produced by other analog units representing an investment
decision function, which in turn responds to market prices, costs,
and financial conditions.
Likewise, the signal produced, Y, can be
connected as one of the inputs to a demand function, and so on.
Thus a large number of separate dynamic relationships can be interconnected so that they interact continuously.
It
is important to an understanding of the more complex dia-
gram in later chapters to visualize the arrows as representing
transmission of information or signals.
They may happen to coin-
cide with flows of goods or payments in sows cases, but in others
the direction may be reversed.
For example, if
business savings,
are determined by some decision function outside of the simple
loop shown above and have to be deducted from income to find disposable incoms, to which the consumption relation applies, the
modification to the diagram is as follows:
I
-A
26
It
is to be noted also that the saw
for any nuber of different purposes.
information can be used
The signal, Y, in the above
diagrams, is represented as going down to the consumption function,
and going also to some unspecified location off to the right, where
it
perhaps might be used with other variables in making Investment
decisicns, and where it
might also enter business saving decisions.
Since the informtion, in the analog, is a voltage signal and not
a current flow, It
is
a simple matter to make mitiple
connections
from one relationship's cutput to the inputs of several others.
After appropriate analog units have been set up and interconnected to correspond to the model, as well as units corresponding
to the programs or disturbances to which it
system is activated and acts out a run.
is to be subjected, the
Voltage signals previously
selected wherever desired In the system are recorded on tima-gphs
by moving pens.
The run is switched off either when it
is consider-
ed to have covered enough time or when some variable has exceeded
its
allowed range.
Voltages to be recorded in this study represent
time histories of such information as output and prices In various
sectors, wages, national incoma, imports, and exports.
27
PART
li
E-2PATION# O? TUi,
EL
28
Chapter 3
GENERAL DESCRIPrION OF THE SYSTEM
This chapter begins the specification of the model which is to
be si.lated.
It discusses concepts and describes the model in out-
line to give the picture of the over-all system and the relatione
between its
l ,diing
d
asc.h of thos
various major parts.
Chapters 4 through 8 fill
each relation specifically, in words and
in the
q
chapters is followed by an sppendix in which the same
sets of relations are presente4 in the form of blocik diagisws, which
are the basis for setting up the analog circuits.
To be useful, of course, the model must have some reasonable
relation to the thousands of different activities that compose the
econories of real countries.
all in detail, but rat
Obviously it
canot represent then
omit meih of what is real, including only
what seems most important.
Wandreds of different kinds of activity
must be lumped together in each of the various aggregate quantities
that are the variables of the model.
How the grouping is done de-
pends on the purposes of the model and on some notion of the charactaristics of particular countries which the model is intended to
resemble
.
The theoretical aspects of grouping production activities into
aggregates are explained by
Leontief
group's study.
athilda Holman in her chapter of the
It
is justifiable to combine goods which
are close substitutes and have similar production functions, and to
combine goods without regard to production function if
plemnts.
discuss it,
they arc com-
Also, althwgh Miss Holzman does not have occasion to
sequential activities may be combinod, as if
the sectov
were a vertically intograted monopoly.
These considerations apply conceptually to this model, although
on a rather loose basis, since the sectors are
ew and very btroad.
Each productica sector is ecaceived of as producing a large variety
of goods which could be groped into sets of complementary goods on
the basis of stability of the ratio in which they are purchased.
Each such set , as a set, has about the same production functico
and the nets are fairly close substitutes .
tains within the seta.
ubstituticn also ob-
Vertical integration is assumed complete
in each sector, except to the extent that som intermediate goods
are imported o
transferecd from one sector to another.
Distinctions between the sectors are on the basis of diff2rent
production functions or different kinds of demand.
Tbus, hndicrafts
1 W.
W. Loontief and others, Studies in the Structure of tho
Amrican_ Econoy, New York: Orford University Presa, 1953; Chapter
0:
§ oblems of Classification and Aggretion" by Mathida HolaN=.
30
and industrially
mafactured
consumer goods are close substitutes,
but differ in capital-output and labor-cutput ratios, while industrially maufactured consumer goods and capital goods have similar
production functions, but one is
amued only by consuers, the
other only by maufacturers, and productive capacity is not convertible from one of these uses to the other .
Goods for export are
combined with industrial casumer goods an the basis that their
production functions are similar and capacitio
between these two outputs.
are transferable
Imports are distinguished by their use
as either consumer goods, Intermadiate goods, or capital goods.
Consumer tastes, including saving habits, are assumed to be
the same for all groups, except that profit-earners tend to save
more.
Their extra savings awe accounted for as if
they were re-
tained in businesses; their consumption preferences otherrise are
like all others.
Consumption and production are assumed equal;
there are no unintended or speculative inventory changes, and the
changes conneoted with expansion are included in capital formtio.
The degree of integration in each sector is presumed to go
from exploitation of natural resources to delivery and servicing
of finished products.
The breadth of each sector is so great that
the high-capital-output-ratio sector, for example, includes all of
the services that distinguish modern urban living from the traditional rural variety.
All of this, of course, goes beyond the rig-
orous limits of mam Holmzan'
prescriptions and leads to serious
questions about product mix and indez number validity.
These will
Either these gross and questicn-
not be discussed further, hwever.
able aggregates must be used, or macro-economica must be abandoned.
The output of each sector is treated in the model as a flew of
a homogenous quantity.
Its flw rate may vary cctinuously.
bikeThis
wise, payments and informtion signals may vary continuously.
formlation is prerred to period analysis partly because it
the way analoeg
work ,
in
It is also a good representatin of processes
that my well Vary from Meek to week When the time span with which
the problem is concerned is twenty to fifty years.
Certainly it
io
superior to analysis by quarters or one-year periods with all delaya
assumed equal to one period-an assumption sometimes made, which is
certain to yield very special results.
Payments are coeived of as flosw of signals which have effects
like ordinary transfers of cash, but include also soae accruals and
putationsa.
For exaMplo
payment because it
sale is construed to include a
a ordit
has the saw effect as a cash sale on the manu-
facturer's production decisions.
under this concept, is
The essential feature of paymnts,
their effect on
produce, to invest, and to consume.
decisin-decisicn
to
Thus the money associated with
a payment my be imaginary or my be newly created in the process
of paymnt.
Rosever, the quantity o2 money in the system is niot an
explicit variable in this analysia and does not have to tie accouted
for.
32
The Model
The model represents an imaginary underdeveloped coutry, whose
rural population is eccessive for its food-producing capacity. Thus
a shortage of people is never a bottleneck in production.
In the
industrial sectors, where relocation and training of people are required, these activities are considered part of the process of capital formation.
C
mers' expenditure flass at ny mont are distriuted be-
tweon four categories of goods, according to disposable income and
the four prices, interacting with a consumrs'
preference function.
Demnd for food is relatively inelastic with respect to both income
and price.
The other three hinds of goods are strong but not per-
feet substitutes for each other.
ThEy are high-eapital-cutput-ratio
mnufactured goods, lsw-capital-output-ratio goods including mmfactures and handicrafts, and cosmers' imports.
To avoid repeti-
tion of the cumbersome descriptions of the first two of these, they
are called high-cor and 1o-cor goods,
respectively.
The price of
each hind of consumer good is determined at any tim by interna&.tia
of the joint demaad function with four supply functions, one for
each of the four categories of ccnsmrs' goods.
actions shown in FIgure 1.)
a ftsd
For
(See the inter-
, there is
world price, subject to a tariff which may be changed by
the governmnt.
The other supply functions are more complex 4
33
Figure 1
SUPPLY ATM DEMATD
(Consumers'
I'JTERACTTONS
and intermediate goods)
)isposable
Income
CI,
SUPPLY
OF IMPORTS
Price
Purchases
34
involving effects of capacity changes and (for all except food) coest
road output i
limited by the area of land that has been cleared
and by the extent of irrigation facilities.
Increases in aggregate
output capacity require large-scale projects which are beyond the
scope of individual proprietors to organise.
Such private projects
as are done are coleentary to govewnment prograns.
ment in deternined by government decisions
Hence, invest-
labor is redundant and
cannot be laid off, but does not receive fixed wages, being largely
made up of proprietors, their dependent relatives, and people who
work for a share of the output
Under these conditions no losses
can be avoided by deciding not to produce, and therefore output
always equals capacity, regardless of price.
The low-cor sector (handicraft and manufactures) has a low
capital-output ratio and static technology, with capacity limited
by the stock of critical tools.
Changes in capacity camn (after a
short wait) from investing in making more tools at a rate above or
below the rate at which they wear out.
In this sector there is a
minimum supply price determined by wages and imported-aterial
prices.
capacity.
Hence, at low levels of demand, output may be less than
High demand raises prices, yields profits, and hence
stimulates private investmant.
are made.
Also, wages tend to rise when profits
Governsment action may add to or limit investmento
35
Industrially manufactured goods (from tho hil
-cor sector) are
sold to both domestic ccnsuers and foreign customers.
any time is
it
Output at
limited by plant capacity--but may be less than capacity
demand is low relative to the supply-price function.
or no capacity.
this sector has little
Initially,
Investments to increase
capacity are motivatod by expected profits, but may be limitod or
augmnted by governmnt action.
Invstment in this sector increasoa
labor productivity as well as expanding capacity.
or laid off to mtch output.
labor is hired
The wage rate index in negotiated up-
ward when business is profitabl,
but nevo
goes do=.
Increases
in capacity, be ides requiring expenditure for elastically-uppied
factors, involve waiting through a significant gestaion time and
purchasing scarce capital goods.
These my be imported (if
echange pormits) or purchased from a doamstic industry (if
foreign
domestic
capacity permits).
The domestic cml.od
sector has character-istics Identical,
except for numerical magnitudes, to the
sector.
anufactured consur-goods~
Its capacity is initially asall or meroe
In addition to
the four doestic sectora described above, there is a gtbgIc cvr~haad
sector, of which the product is not separately identified, being an
internadiate good.
Expansion of this sector reduces costs of pro-
duction in the other sectors.
Investants and current production in the varicus domestic sectors are reflected in the gross national product,
from which tames
36
and business savings are subtracted to ascertain disposable perstmal
income.
This information enters the deM
function to determine
personal savings and the expenditure an each kind of consumer good,
as described initially.
The principal interdependences for the wholt
system are indicated in Figure 2, at the end of this chapter.
Within each domestic sector, and not evident in Figure 2, are
capacity-creatiea processes.
In agriculture and public overhead
those are directly controlled by goverment.
rvev motivated by profit meeking,
they
In the other sectors
Wut entrepreers'
may be modiufieda ,,y governMent controls.
decisions
1The controlls are Introduced
iu the model as direct upper and lower limitations on construction.
Whther they would actually take the form of credit expansien and
restriction, subsidies, license requirements, allocation of scarce
building mterials, or any other form is outside the scope of the
model.
So too are the problem
of manipulating finance.
Taxes
and savings are accunted for, but do not influence the sectoral
investment pattern or, in a direct way, the total ependiture, which
thus my imply deficit iwncing.
The mechanisms of inflation work,
nevertheless, even though budgets are not =do explicit .
The controls on capacity creation will be time-programme
represent development plans.
to
The programmd values my be auto-
watically modified, hewevar, in respnse to inflatien or balanceof-paytents deficits.
Other tools of governnt policy lor which
the model provides are ohangos in interest rates, import tariffs,
?7
and the foreign exchange rate.
Investors'
expectations may later
be associated with government actions or with current economic conditions, but for the present are left as fixed paramters.
Com-
pletely independent or exogencus quantities are the supply prices
of imported goodsat two paramters that define the demand function
for exports, and the time profile of long-term capital inflow from
abroad.
38
Figure 2
GENERAL OITLPTE OF INTERDEPENDENCES
(Not including government controls and policies)
Disposable Income
KEY:
Prices
-
Purchases
Other signals
39
Chapter 4
CONSUMERS
JOINT DEMAND FUNCTION
General
The consmers' demd function is a set of relations allocating disposable incom awong savings and the four kinds of consumer
goods according to their prices,,
Prices,
of course, are determinod
at any timo by the interaction between this function and the four
It
supply functions in a short-run general equilibrium.
is a mat-
ter of convenience, with no restrictive effect, to formulate the
demand function with income and prices as independent and the values
of purchases as dependent variables, end to formulate the supply
functions with purchases independent, prices dependent.
In the
analog the appropriate interactions will occur so that prices and
purchases will be mutually determined.
The consumers' allocation of disposable income nay be thought
of as occurring in two stages.
First, incom
is
divided between
food, all other consimer goods, and voluntary savings.
This divi-
sion depends on disposable income and the price of food, and is independent of other prices and of the interest rate.
Then, the ex-
penditure for "other consumer goods" is allocated amng the three
kinds according to their prices, with a relatively high degree of
substitutibility.
Each of the two allocation functions is a special
40
1
case of a joint demand function developed ar i used by Richard Stone.
This function way be expressed in the following general form for the
expenditure flow on the L-th good in a set on n goods:
D
C.
0
p. Q, + b,
(
YI
2
-
p
0
)
(4.1)
disposable income, megabucks per year.
Where Y
'
C.
4.
$/quant .
price of i -th goodS,
pr
b,
expenditure rate for L-th good, megabucks per year.
Q
a parameter for the L-th good, in mega-quants per year,
w
another parameter for the 1-th good, dimnsionless, and
subject to the condition
b,
I
Summation of these expenditures, with the stipulated condition on
the b constants, confirms that
C,
YD
(.
As Stone points out in his discussion, the relationship is
not meaningful unless
>
Q
40
In the model formulated here, failure to meet this condition will
be equivalent to a state of fanine and hence fai lure of the program
being tried.
1 J.
R. N. Stone, "Linear Expenditure Systems and Demnd Analysis: An Application to the Pattern of British Demand," The Economic Journal, September, 1954
41
Choice 1:
Food,*Other Goods, and Savings
For the set of relations like Equation 4.1, Stone offers the
follaEring common-sense interpretation:
Q> , it entails
Ip '
. . . on the asoumption that
of their inamout
that consumers first use up a certain
ooue. . . . in acquiring the consumption vector [Q ,..., Q%]
at current prices, whatever these may be, and then distribfute
their remaining incoe over the set of available coycdities
.. , b ]
in certain fixed proportions given by [b,
One of the special assumption
in the present model in that only
the demand for food includes the initial inelastic coaponent,
The other two categories,
0
Q
"other goods" and "savings," have Q-w%.
Using the subscript 2 for food and c for other consumer goods, and
with S for savings and a" the warginal propensity to save out of
disposable incom,
the relations are simplified as follows:
C
C
b2
+
2
C2
[Y
b
a
2
SyD
cQ
a,
b2 + be + er=
ElUticit
Qi]
p 2 Qo]
(4.2)
.. Q0
P
Relations
Expressed in quantity rather than money terms, Equation 4.1
becomas:
Q
1
Ibi.,
stone 's is
p. 512.
Ql
+
L
P
(
-D
PQ
)
(4.3)
Notation changed to suit this foranlation.
in vector terms, with different symbols.
42
Differentiating this, the varginal propensity to SpeOd incoMe on a
particular kind of goods is found to be:
a
pt
while the fraction of incone spent thereon is:
-
s
+
-
Q
b.
b.
QQ
- --
The ratio of these two quantities gives the incoe-elasticity of
de for theSi
goa
="
Q
-(4.A)
With the assumptins of Equations 4.2, for food,
0
p
Q
p
2
Gy, < I
for other consumer-goods, or for saving,
p
Q
*
0
PjQj
p2 Q2 >0
Demand for food is relatively income-inelastic, while demand for
43
other goods and savings are relatively income-elastic.
With respect to price, the demand-curve slope to
b.
&QPap2
ji,
P. L
j
and:
00
Q
Q(
-
bo
b.
+
-
p
Q-
Q
The ratio of these quantities gives the price-elasticity of demand:
EpL
1+
(4.5)
bj
00
For positive values of b7 and Q0.
or dond is relatively inelastic.
For
Q
a
0,
Ep;
I,
or dessand is unit-elastic.
goeds as a group.
This is the cane for food deand
This is the case f or other consumr
Mathematically it could be said that this, applies
to savings, but there is little economic
variable price of savings.
ler per'dollar.
.rte;
meaning to the Idea of a
It can generally be taken to be one doi-
(Interest is not the price of money, but its rental
savings are assumed insensitive to interest in this mxel.)
44
Choice 2:
Lw-cor, High-cor, and Iported Consumer Goods
For the first stage of choice, formulated above, these income
and price elasticities are appropriate.
price elasticity is necessary.
For the second stage, higher
In this second stage, the total e-
penditure for nonfood conaumer goods (already determined) is to be
divided among goods from three sources:
production and the import mrket.
sources are not all the saen.
two categories of domestic
The goods produced by these three
Nevertheless enough of them are fully
or nearly equivalent so that strong substitutability exists among
the three groups.
Hence their demnd curves should be relatively
price elastic no that an increased price would reduce the total
expenditure on the corresponding goods.
This elasticity is achieved by using negative values of the
Q parameters in a second demand function of the Stone type.
With
negative values, these paramters can no longer be interpreted in
the common-sense terms of the quotation from Stone's article, given
above.
They reduce to a strategen for obtaining certain desired
mathematical properties.
The demand equation for each good--In
terms of absolute values of Q 's,and with the total nonfood expenditure represented by C -- is:
C.
-
Q0
+ b.
[C
b"
+
1
p
Q|.
The three categories are identified by the following sub-
(NMTE:
1 for high-cor goods,
scripts:
4 for low-cor goods, and 6 for
imports.)
This relation requires restriction, for at some price ratios
In such
it will indicate negative expenditure on one of the goods.
on event this indication must be re-interpreted to mean zero exthe demand functions for the other two gxds must
pdrand
if
the price p 4 Is
For exaMle,
the third were not available.
be chnged to act as if
o high that Equation 4,6 indicates C
(
0,
the following relations are substituted:
Cg = 0
C4
C
W
1b
C6
6% =_6.
1
b6
1
+
b1
(4.7)
I +3
+ P
n(
+
-P
I
m+ob
[Cc + P1. Q,
6
+ P6*
6
If two of the functions indicate negative expenditures, say C4 <
0
and C < 0, the re-interpretation it quite simple:
C
= C4
0
(4.8)
C6
C
Growth ad DvelopingTastes
For two reasons the desad function should not be statico
even if
First,
individual tastes were otatic, the miniuna food requirements,
46
Q
,
should grow proportionally to population growth.
Stone points out in his discussion, I the Q
Secondly, as
quantities reflect "con-
sumers' notions of their standard of living" which change with experience.
In the first stage of choice, these are crudely accounted
for in the minims food requiremnt by aking Qj increase with time
at an arbitrary rate, higher than the assumed population growth rate:
S
(4.9)
Q+Qt
The savings and total nonfood cocusuption are not modified (xcept
by the food Cross-effect).
In the second-stage choice among dif-
forent nonfood goods, the population effect would make the negative
Q values more negative, wereas the habit effect would work the
other vay.
The not effect is
and is neglected.
Ibid., p. 522.
probably not important to this study,
47
APPENDIX TO CHAPrE
4
In this appendix, the demand function that has been formulated
in Chapter 4 is presented again in terms of block diagram.
This
will be done for each chapter concerned with details of the model.
The language of these diagrams was briefly introduced in the last
section of Chapter 2.
ed .
Additional symbols will be explained as need-
Each block, it will be remembered,
represents an operation per-
formed on the Independent variables (represented by arrows coming
to the block) to determine a single dependent variable (shomn by a
line l.eaving the block, i.c., with
small circle, 0
an arrhead
on the far end).
, is sometimes used to represent summtion of vari-
ables (algebraically, with signs as indicated).
The basic scheme is
like that of Phillips, 1 with some additional symbols.
In the demand function diagrams in this appendix, each block
also corresponds to a specific piece of analog hardware which embodies the relationship, and each line corresponds to a
ire.
In
some diagrams following later chapters, some blocks correspond to
simple combinations of several analog components.
shown in
A
They are not
complete detail because the diagrams would then be too
cluttered to be easily read.
When necessary,
their details are
given separately.
IOp. cit., 1957, or see Allen, op. cit., p. 287.
48
Equation 4.9 calls for a coefficient increasing linearly with
time.
%t
0
Q
%
42
(t
o
-0)
+
0(~
(4.9)
(4 .9
The analog uses a servo-integrator which rotates several shaftmunted potentiometers so that their resistances are proportional
to the independent variable.
For Equation 4.9, this is represented
thus:
EFER.t4CE
//hQ"Qa,
vo1..-rAC e
Also shon here is the multiplication of a signal, p2 , by the variable coefficient, Q0, represented by the potentiometer angle. The
integrator can integrate constant or variable signals.
the constant input, Q
In this case,
is obtained from a reference voltage source
connected through a fixed-coefficient unit which is set to give the
desired value.
(Another similar connection, not shown, Is required
for setting the initial value of Q0.)
The "first stage" of consumers' choice, including the timevarying coefficient, is represented on the next page, first in equations, repeated from Chapter 4, and then in diagram form:
49
C(.
(zf.9)
Q =)
CAL+ ,
b,(y"- pfr
D
(A,2)
beC. (Y P
be.
Q
Ii-b
p.Q
R
(Note:
The other equation,
S
is Implied, but not actually represented.)
The "second stage" of csumers ' choice could be as below,
if there were no
ger of negative C - values:
To eliminate negative values of any one of the C 's a sensing
This includes a two-position switch, which takes one
relay to used.
position if the signal being sensed is positive and the other posiIt is used thus:
tion if it is negative.
C
C
Whicbevor line is left open has zero signl.
signals (if
added to the circuit, with the C
Three such relays are
any) added to C0,
shcwn in the final diagran of the complete system on page 53.
all C values are positive, there are no C
as
When
signals and the system
is exactly equivalent to the simpler cne shown on the previous page.
If
one C signal, say 04, becomes negative, however, the nensing re-
lay aakes the C4 output zero and adds the negative value, C4 ,
algebraically to C .
This transforms the equatios of the system
as follows:
C
=0O
C
=
-P1,Q
|+
b, (C + C4 +-
From this are derived:
4
C-.
(J
piOI+
(1
and
-
p
+
+
~
b4 )
b
-1
+
1
6
(cCbe-
I
10
+
p6 .1
01
52
This corresponds to Rquations 4.7 as desired.
It
can also be shown
that if any two C's are negative, this network will nake then zero
and make the third C a C , as it
should be.
All three C's cannot
be negative unless C < 0, which is prohibited.
C
53
CONSUM&RS'
JOINT DEMAND
FuMNOTioN
FIG.3
54
Chapter 5
AGRICULTURE AND 10W-CAPITAL PRODUCTION
For each of the four kinds of products purchased by consumers,
as well as for certain intermediate and capital goods, there is a
short-run supply function.
At all timms the set of consumer-goods
supply functions is in equilibrium with the joint demand function
the previous chapter.
d4escribed in
Prices and quantitiea
chnmge
with time, however, as income changes and as the short-run supply
curves are shifted by changes in capacity, wages, and costs of intermediate materials .
Each producing sector is
treated so far as
possible as an integrated industry, ranging from the owners of
natural resources to the transporters and retailers of the final
product.
Exceptions to this are necessary for intermediate products
that are imported or transferred between sectors .
Because of signif-
icant differences in assumptions about the different sectors, they
are described individually (not in numerical order)In this chapter
and the next.
A.
AGRICUILURE
(SECTOR 2)
This sector deals primarily with production of food crops, not
including plantation-type production of tea, rubber, etc. or forestry
or mining.
Production from plantations, forests, and mines does not
share some of the distinguishing features of food-crop production and
55
behaves cnsiderably more like industrial production.
Such of this
production as is used for materials at hom is included in the sector that uses it .
significant export products were involved,
It
there should be a special sector for this kind of productim.
ever, for the present it
How-
is asusumed that this kind of production is
negligible in the hypothetical country of this model.
In most underdeveloped countries, a major part of agricultural
production is coased on the farm or in the village without any
ir
11:t t0ransaction.
This rMdl,Ihwever, is1. set up 'S 1if all
of the,
roduct were marketed and som then bcught back for farn consumtion.
The conequences of this assumption are the sam
as if
far-
mers kept part of the crop for home consumption, but only after
coneidering the alternative purchases foregone and choosing the food
as a mtter of preference.
thought to be adequately so.
This is not absolutely realistic, but is
Therefore "agricultural output" always
refaes to the total of the marketed and home-coumed product.
Short-Run Supply
Farm labor is redundant and, being largely made up of proprietors and their dependent relatives, cannot be laid off.
not receive fixed wages, but share the proceeds.
They do
Under these con-
ditions, there are no significant variable costs that could be
avoided by deciding not to produce, and therefore output always
equals capacity, regardless of expected price.
Changes in relattive
56
prices between different crops presumably affect farmers' decisions
of what particular crop to plant next tim, but it
is assumed that
these decisions do not affect the aggregate output; hence they do not
need to be accunted for.
to price changes.
Furthermore there is no inventory reaction
Inventory changes are not explicitly considered
at all and are implied only in the distribution process and in smoothing the crop cycle into a steady flo
to consumers.
Agricultural production capacity is
fixed by the area of lansd
that has been cleared, the extent of irrigation facilities, and the
production technique used.
The physical establishment,
or capital,
is evaluated in terms of Its capacity to produce with a particular
standard technique.
It
does not really require identification sep-
arately from output capacity.
However,
since it
is convenient to
think of a fixed set of land and improvements in slightly different
terms than a potential flor of out put, it
is given a separate sym-
bol, E, and units, "equivalent meg-acres."
With these definitions and assumptions, the short-run supply
characteristics of the agricultural sector can be expressed rather
simply in terms of the following notation (the subscript 2 refers
to the agricultural sector):
Let ~2
=
physical produetion capacity in megatens per year
Q2
=
physical consumption, same units
2
price, dollars per ton
C2 a
omsumption ecpanditures, megabuckw per year,
p 2 Q2
X physical capital, equivalent mg-acres
Then: l
and:
.
w
f2, where
a constant,
1suK2
Q2
with p2 adjusting as necessary to match supply and domand:
p2XK
2
* K~
00'01)
2
Agricultural capital (or capacity) may be incareaed by clearing more land or building irrigation fallities.
Those involve
large-scale projects which are beyond the scope of individual proprietors to organie.
Thus it
is prirarily goverutxmat decisins
that deermine the extent of capacity-creatiUng projects, although
this does not mean that they are all carried out by the governmnt.
Some level of private capital tormtion would be carried out regardless of any goverment actic
nomic variables in the model.
and regardleis
of any of the eco-
In addition, some private capital
formation will be undertaken as a result of government piograms,
which create opportunities to invest in land Improvements, irrigation, and better tools.
The amption made here is that such
private capital formation is in a fixed ratio to gaernment capital
formtion.
SS
From the time a decision is made to start a new capital-gormation project until production from the new capacity can begin, there
is a delay-the gestation period.
ects may have been started.
eanhile, of course, other proj-
In fact there is in general a continu-
cus flow of new projects into the "under construction" category.
This flw , which my vary continuously, is called "the rate of starting new capital formation."
It
is ayabolized:
in equivalent meg-acres per year.
, nd
= is
easuredi
The time-profile of E
ro-
duced after a delay of g 2 years (the gestationM. time), bccaes the
time profile of the flow of newly ocapleted projects into active
production, K -
The total number of equivalent mg-acres of proj-
acts under construction (in gestatica) is designated K-.
It
2
iV,
determined as follors:
t
A capital price index,
K
is defined as the cost per equiva-
lent acre of carrying out a capital project.
In the agriculture
sector such projects involve a mixture of labor and
construction.
The wage
(5.02)
dt
2(two)
2
chnirzed
of rural labor are assumed proportional
to the current price of food; other costs are asumed proportional
to the cost of industrial construction in Sector I (see Capter 6).
Variations in the mixture are not part of this study; it
postulated that capital costs are determined as followas:
K
P2a
k2 3 ~2
+
2
E
1*
i
simply
59
Assuming that the expenditures on each project--measured in
real terms--are uniformly spread over the gestation period, the rate
of expenditure at any time on any particular acre is:
/
dollars per acre per year.
Since this rate is independent of the stage of progress an a particular project, the expenditure rates on all projects in gestaticn
may be sumed to find the total rate of investment at any time in
1
=
(4
(
g)
Attrition of existing physical capital is assumed to take place
unless offset by mintenance and restoration projects.
These are
included with the capacity-expension projects just discussed, and
Thus the investment rate just deter-
are not treated separately.
mined is gross investment, not not.
If gross investaent were en-
tirely stopped, then capital would decay at a rate proportional to
the existing stock.
If
i
is the rate of decay, %
If projects have been started
now being completed at a rate of
g
o
tr2
= 6 %.
years previously and are
at)
2
nr
(t-g)rre
then the current rate of Increase of capItal is:
~dtJ
2
60
and the stock of capital at any time, of course, is the stock at
some earlier time plus the integral of this varying rate over the
time that has since elapsed:
t
K
B.
K
+
+/
LOW-COR CONSMER GOODS
(P
-6)
2
(5.06)
dt
(SBCTOR 4)
This sector embraces both handicrafte and 1o-capital-outputratio shops and factories.
to have lo
Both kinds of production are assumed
capital-output ratio and static technology (constant
capital-output and labor-cutput ratios), with capacity limited by
the stock of critical tools (capital), which, however, are relativoly cheap and readily produced.
Short-Run .Upply
The short-run supply function is characterized by a minimum
supply price, p 4 , which is the same for all firms, and a maJru
production rate, Q4.
These define
GL
an L-shaped supply curve as shcon
in the diagram at the right.
If
demad talis to the left of the corner, (p , Q), then the market price
is
Q <
and some capacity stays idle,
V,
Q.
If demnd is
above the cor-
ner, then Q = Q, and the market
price (pQ in this case) rises as necessary
p
a1
for arket equilibrium:
pa M- 4/
(5.0't)
pia
wher
p4
a
expenditure, negabucks per year
csumpticn
I
C
and
price for capacity output, dollars per quant
Q
M output capacity,
ga
a
per year
Changes in Einianm Price
in this sector o
the model, details of the variable coa- sd
the entrepreneurs' returns that determinethe minim= supply price
are not explicit.
They include, hwoever, a wage coponent, which
may be an actual wage or an opportunity wage of self-employed people.
In one part of the sector, urban small-scale industries, the unorganised workers tend to compete their wage
tence level.
doft nearly to subsis-
Ths the minimum supply price in this part of the
sector reflects change
in the subsistence cost due to changes in
the price of food, p2 .
In the other part of the sector, rural
handicraft occupations, this behavior it not duplicated, but the
same effect of food prices results from the high mobility of people
between farm work and handicrafts.
Other factors which affect the minlmum supply price are the
price of imported raw materials, p6 , and the size of the public
overhead sector, %.
Imported materials are used in a fixed ratio,
q64, to the quantity of output.
is qG
6
Hene their cost per unit output
The concept and operation of the overhead sector are
62
explained in Chapter 6.
Its effects on this sector com abot
through more efficient transportation and marketing of xaterials
and finished goods.
ar
Since distribution and mrketing of the goods
included in the product, the corresponding costs enter into the
price.
When the supply price is in balance with the several omrpennts menticned above, it
is assumed to be a follews (using (F
to symbolize the equilibrium value):
F
(p)*
k
F
p
Adjustment of
p2
+
q1
464 %
to changes in these c
545
o
is not instan-
taneous, but subject to an exponential lag, thus:
FF
dt
S
(k24 P2 +
54646
'54 K5
p4
Capacity Changes
Capacity,
4 ,Qis
determined by the physical stock of tools
and oquipment, or physical capital, %.
Capital is measured in
units of "standard plants," one of which can produce one
of output per year.
Thus, by definition, (Q/C) 4 = 1.
egaquant
now capital
replacement and expansion decisions are made is described below.
As in agriculture, there is a gestation period, g 4 , between the
start of a capital project and its
OPs
4(t)
4(t(g)
readiness for production.
Thus:
(5.09)
63
and capital under construction, as before, is:
4
19.4(tmo) +I4
K9_a
te
- /4t")g
(5.10)
dt
(.0
Investment expenditures, again, are proportioml to the capital
in gestatin multiplied by a price.
In this sector, howerver, a dif-
ferent assumption is made for the price of capital.
The hinds of
tools, simple machines, and equipment that awe used in this sector
are made by the same production factors as make the conumer-good
output of the sector.
Therefore, costs of the two kinds of produc-
tion are closely related
It
is assumed that they are in a fixed
ratio:
4 p4
4
(
acibucw per plant) (5.11)
Hence:
I
F
a(5.12)
As in agriculture, productive capital is subject to attrition.
A different assumption is made, however, for the form of attrition
in this sector.
it
is as if
(It
will apply also in Sectors 1 and 3.)
In effect
each infinitesimal increment of capital (say, each tool)
were fully productive throughout a finite but uncertain lifetime.
An aggregte of such increments of capital, if
they were started
sivultaneously, would yield a time profile of still-productive capital like this:
64
Produc-
tive
Capital
rma
iesa
time
&
No algebraic formnla for this attrition function is
given here,
because what is to be used is a combinaton of electronic circuits
with a combined behavior which is probably best described by the
measured response to an arbitrary input.
The graph above is such
a measured response to a step input.
Overhead costs
Overhead costs are not included in the short-run supply function, but are involved in the investmsnt decisions that shift it.
Overhead is defined to include financing costs, depreciation, and
the miniuam profit necessary to keep entrepreneurs in business at
the current scale of capacity.
While prices and variable costs
(p and p ) are in terms of money per unit of product, overhead is
in terms of aney per year per unit of money invested.
overhead c awssurable with other costs, it
p
(/Q),
To make
must be multiplied by
the cost of plants per unit of output capacity.
units in this sector are defined so that (K/Q)
4
Since
= 1 plant per
ngquant per year, the conversion factor for overhead costs is
e5
I
numerically equal to p , with an appropriate change in units.
Thus
the cost per unit of product, including overhead, is:
F
+
p4
K
hp4
Note that both the overhead rate, h
K
and the capital cost, p , are
,
These are what affect decisions.
current values, not historical ones .
Investment Decisions
Quite different from the assumption for agricultural investment
is the set of assumptions about investment decisions in the low-cor
sector.
(These assumptiows will apply also to the high-cor industrial
sector and to the capital-goods sector.)
The behavior of private investors is closely geared to their
expectations about future profit rates.
The assumption is made here
that such expectations are basod primarily on current profit rata
adjusted by an increment for optimism or pessimism about the future.
The current profit rate per unit of output is:
a
p-p
IT
F
K
- hp
If this is interpreted as the potential profit rate on cutput to bo
produced with now capital (with neutral expectations), then it can
be expressed as a potential rate of return on capital by dividing
by the cost at current prices of the capital required for a unit
of output flow. Since (K/Q) a 1, the divisor, as shown above, is
simply p
.
Thus:
r
Lhp
P L
P-
66
Substituting according to Equation 5.11:
@hF
p - p
-h h
p
y
y
a
Pp p
(1+/A)
F
4
r
k
k F
44 P
44
p
where
M
hk
The expected return, allowing for pessiuism and uncertainty by an
incrernt
6 h4 (negative value for optiism),
p1
-Y
(I
is:
+)
r
-
Ah
(5.13)
k
The aggregate of investmant decisions in this sector depends
partly on this expected return, partly ec financial factors, and
partly an government intervention.
In this formlation, the first
step is to establish what level of capital formtion entrepreneumr
would undertake if credit were unlimited at the current interest
rate and if no special incentives or restraints wore in effect.
This level way then be undertake&A,
or reduced by limited credit or
license requirezents, or increased by governmnt subsidy or direct
investent .
It
is postulated that entrepreneurs plan in terns of
a hypothetical "target" increment of physical capital proportional
to the expected return:
A
This increment is relative to the existing level of capital.
(5.14)
67
Entrepreneurs realise, however, that their decisions will not affect
capital until one gestation period later.
Hnce they adjust this
increment for changes that will take place in the meantime due both
to projects already in gestation and to attrition, arriving at a
"wanted" increment, A K
SE'
measured from the future level:
= AdE + e" -04
=
Where k1
,
rr
+ e
Co..
(.15)
is the quantity of physical capital which inexorably
ill
expire during one gestation period after the current mment, 0g as
before is
capital in gestation, and
m. is a parameter whose devia-
tion from a value of 1.0 Indicates the extent to which individual
entrepreneurs'
allowances for others'
projects add up to more or
less than the actual total of such projects.
Entrepreneurs cannot start all of this increment of capital
simltaneously; they can start now projects only at a finite rate,
e.
If each
ne were trying to hold capital at a constant level,
he would start now projects at exactly the rate (however it
might
fluctuate) that old capital in his firm reached such an age that it
would expire one gestation period later.
This "rate of capital
reaching replacement age" is designated ir.
If these two rates
differ, their difference will be observed one gestation period
later as the rate of change of capital stock:
(t)
(t+g)
\dt
/
(t+g)
68
It
is postulated that the aggregate effect of entrepreneurs'
responses, if they are not interfer ed with by financial or other
restraints, is to adjust K so that the difference (K
K)is
-
proportional to the "wanted increment" of capital,
s
r
+
- ir
+
:
XtKW
A
[
+*x
r
This is of course subject to the restriction is
(5.16)
- ao iK]
.. 0
.
Investment Restraint and Aupanation
The rate of starting new capital projects was explained above
as it would be determined if credit were unlimited at the current
interest rate and if no ceilings, license requireasts, or other
limitations were in effect.
rect.
In sowe conditions this will be cor-
However, a principal part of this study is concerned with
the effects of altering the sectoral pattern and the over-all level
of capital formation by measures which impose ceilings an the investment decisions in some sectors at some times and which augment
them in other sectors or at other times.
The implications regard-
ing means employed are discussed in Chapter 8, Section B.
The pro-
grams and policies which govern the interference with investment
patterns are discussed in Chapter 9, Sections B and C.
Here, it will
suffice to say that policy may dictate both an upper limit, Z!, and
a lower limitr,
this sector.
, on the rate of starting projects at any time in
Ifthe free decisions of entrepreneurs yield a rate
69
between these limits, it
takes effect unaltered.
ever limit is appropriate determines
that time.
t,
Otheiwse, which-
the rate of ne
starts, at
70
APPinDIX TO CAPISER 5
A.
AGRICULTURE
(SECTM 2)
The equations developed in this chapter defining the operation
The
of the agriculture sector are collected on the following page.
equivalent block diagram is also shown.
This includes a delay funo-
tion corresponding to the gestation period.
The distinction should
beo noted between this and the lag function described cn page
and 23.
29
Whereas a lag is defined by the relation:
dt aa
k(x-y),
the delay is defined by:
7
(t)
,(t-g)
The operation of dividing one variable by another uses a
potentiometer driven by a servo-integrator such as is also used
for nultiplying.
Both operations can be done with two potentio-
meters on the same integrator shaft, as indicated.
71
s
Ka
j1 3
-PX
Ca
,
.
F I
-
SECTO R
Z
A G4R IC U LTUR E
~QUFcEIoNS~
t
Ka+
5,0Z
Ka
s6o-5
p K:
L.
4apf<
-
f4
c t)
Kt
506O s~asR=
/
i<*afid-0
-
4za ex
l<!/
R~t~)
K)dt
72
B
W-COR CONSUIER GOWS
(SECTOR 4)
The relations defining this sector are repeated on the next
page and diagrammed on the pages following.
In the first diagram,
EquatonMs 5.08 and 5.16 are each shown in a single block for clarity, although each requires a coubination of several coefficient
and summing units in the analog
E 5 and e
presented by potentiometer positions.
do not have to be re-
Hence the integrations that
produce themae doie purely electrically rather than by servo-
integrato"r,
and a simpler symbol Is used in the diavgo
The
solector for p. is a soning relay like that used in the domand
function (Appendix to Chapter 4).
The block labeled "Limits"
represents a device which imposes the indicated limits,
,
on the signal, K4
and
The life-span function is an electronic
network which responds to a step input as indicated graphically,
The first diagram is simplified by the oission of imported
mterials.
The second showa the additional equipnent required to
account for the
if they are included.
Another piece of equipment,
labeled "Servo" is used here to multiply two variables, neither of
which is generated as an integrator shaft positio.
The servo
positions a potentiometer instantaneously to agree with the input
signal--in this case, C
The potentiometer is used to multiply
(or divide) just liks a potentiometer on an :!ntegrator shaft.
73
EQUA-rOPNS
. 07
seo~
A
FortF SECTOR.
C/a
=
= 44
ctt
K,-,p]
4
0R
OF
5.09
5.IO
4.
K')
(t.--
K'/
F,4
F
Tr
(/~/~q)
11
5.13
V
IY'
5.16
SIt
[r
RS~
'Su3jmc-T
-- )I
T
A14 D
+
K*-oc K'J
ATIOI
L
SPAN
*r
FIN
L
j7-
L~MITL
;LEi
M46+
=
7$
f~t %(,Y
WNHFeN
c
WH"
-4
pto<
-PP
- r
+
r
-
.-
-_I
ADDIT O NS
TO $1c-.ToR L
F
IMPORTE D
MAATER\ ALUS
76
Chapter 6
INDUSTRIAL PRCDUCTIONf AND PUBLIC OVERHEAD
A.
HIGH-M0R CONSU:R GOS (SECTOR 1)
This is a modern capital-intensive industrial sector.
It will
be quite small at the begining of any run but amy grow vory large
the develomnant prcgram is suce'nsul.
The mixture of prohcts
includes conumr goodo for the hove market and goods which my bY?
final or intermodiate for export.
The two categories are combined
because they compete for the use of the same capacity-limiting fac->
tors.
Characteristics of the sector differ In several ways from
those previously described:
1.
Technological progress takes place, in the form of higher
labor-productivity with newer
2.
achines and plants.
Organiazd labor negotiates wage increases and provents
reductions.
3.
Expansion and replacement of capacity require capital goods
from another sector or country; these may be in short apply e
4.
Plants and machinery (i .e., capital) take longer to build
and live longer.
How these characteristics are reflected in the supply function and
the capital-formation process are explained below.
The capital-
77
goods sector is similar, except for details ezplained in Section B,
below.
Short-Run 2upply
A major difference between the high-cor and low-cor sectors is
the effect of technological progress on costs and thereby on the
shape of the short-run mpply curve.
The assumption is that each
new high-cor plant has a slightly more labor-saving production
Thus the labor input par unit of
process than the nex:t older one.
product (man-hours per quant), instead of being uniform, is:
(WQ)
WQ
where
(
is the serial mmber of the plant in question.
put of the sector is leas than
capacity, it is produced by the
more efficient plants.
Thus the
lcser part of the supply curve
(which is cost-determined) has
a positive slope, as shcmn in the
diagram at the right am
below.
-
derived
At Qw0, the cost corres-
ponds to production in the newest
plant, with a serial nube
1
(which is the time-integral of X
in the capital life-cycle).
At any
(6.01)
When out-
78
other value of
Q up to
K, the serial mSer of the marginal
plant is:
N1
c(
-Q)
Substituting this In Equation 6.01 and multiplying by the wage
rate give the labor cost per unit of product of the rarginal plant.
To this is added the cost of imported
aterialn, as in the low-cor
teator, to get the short-run supply price for output below capacity:
FF
FF
-
When demand gets beyond the point (p
capacity"--the pric
goes up very steeply, allowing only a slight further increase in Q.
In the handicraft and low-cor sector, no overhead costs are
ccverod for any plant until the full capacity of the industry Is
used and further dmnd forces the price above the floor0
technologioally progressive sector, on the other hand, L2 r
In this
and
Q
are large eniusgh, profits above overhead are possible for the Most
of ficint
plants, and new investxxt may thereby be induced even
When some older plants are idle.
bt'tewrnal )onomtes
Even more than in the lcwtcor sector, over-all costs in thn
high-cor sector are reduced by development of xablic overhead capi'tal.
Besides the increased efficiency of traasportation, this sector
beinefits fron development of pcmer supplies, coimunication systea,
and ':r1anizaticn.
Thih elfect is accounted for by reducing the labo-
79
input ratio in Equatio 6.02 as the overhead Sector groma, thus:
(W/Q)
(W.
I
K
This revises 3quation 6.02 as follows:
pP
EQ
W
k2'
-k+6
+Q
~(1p1x
61
(6.03)
Alternativelyt this may be expressed:
r
=(W
where (WQ)
pq
F..
i
= in.
Q)
1
0
K
-
Profits ad IGo
With the costs of different firms varying, as assumed above,
two difforent
V
WeasureS of profit are required-evorage and bcat.
average not profit is:
TY ava
where
F
pa,
a
p -pPav.
-
(6.06)
hp
is the supply price at half the current cutput,
the variable cost for the average plant , and
in the overhead per unIt investent cost.
taen
h, au in Sector 4,
Evaluatin of
p
the
cost of capital, is eaplained below.
Tabor in this sector and in the capital-oods sector is union-
imod.
Whenevor average not profit in one of these sectors is poSi-
tive, the unions are able to force wages in tho sector gradually
so
upward:
dw
--
a
a(vT
^
Also0 mobility between these two industrial sectors has a tendency
to equaltec Wages by raising those which are lower:,
- -]L,
\dt
(O
w' -
V
-w 1 )
4w
4{
efects are additive:
These
((1
<
(3
suject to the rostriction, -
1(
0
Wnthe formula above would yield a negative valuo, unions cannot
negotiate rai&4wsn,
Ueica the rettriotion. agzinst negative values,
cut
being
but are asouw1d to be able to prevent wages from
Prcgitn =10 Invent~entc
Averapgo
rofit, as givsn by Equation 46 ( , is th1e masure oA
profit-tax rwrxee,
The average profit rate, however, is not relevant to Invest-1
up 4
rentde
aew
ns0
lantg,
t
ty
and dstermlics wiether wages can be forced
and
What counts there it the potential profit rate on
This is recelad zfroim the going not profit rat,
, an the newest producing plant, adjusted for
ected fu ure change in profits.
rate on the per-mit-product basis is:
'TT V"N
F
p - p min,, .
-lhp
ny uncotain-
Tils best not proft
81
or, per unit of money invented,
F
'IT
P
p PP
where
P
pmia
p
of course, is the value at
Qw 0.
The adjustment for uncertainty and expected change is
treated as a
change in overhoadAh, as before, so that
rX
h
(6.G-3)
P
Investmnt decisions are based on this expected rvetrn, exactly
as explained above for the low-cor sector--1.eo,
a
given by Equsa-
ticn 5.10, awyl are subj&ct, as there, to revision by ceilings or
floors.
KK
The cycale of gestation and attrition of ca4pital In alro lie
that in
the loi-cor nector (Equations 5.09 and 5 .10, end the at-
trition
function shown graphi cal LY) , and investsmnt paments, as
beqfore,
are datermined by the relation:-
P
Capital formatIca In the high-cor sector requires mchinery
ad certain constructionand buliing m
oterials which are manli-
factured by Industries of lmted capacity.
To the =.tent that
82
foreign-ecuchanige policy allows,
the LiiULted domestic supply my be
supplemnted by imports.
The not section of this chapter definas
the joint supply functio
for domestic and imported capital goods,
the price of which is dsignted
p3 .
The quantity of capital
goods required per plant constructed in Sector 1 is designated
k
Capital creation also uses labor of the same degree o2 skill
as those who me the product of Sector 1, paid at the same
rte,
9 v
Thew coefficiet of
labr
inpt
pr
wage
p2ant built is
k
Hence the cost of Capital for Swetor 1, in negabucks per plante is
P
+
1
W
(6410)
"313
%I
r.A C&PITAL GO DS
In the agriculture and tow-cr sectors, replaceent or expans±on of capacity was asumed to be simply a matter of applying
factors of production to appropriate projects for rquired perods
of time.
No limit wan placed on the quantities of the factors
available for this purpoe.
In the high-cor sector, however, ca-
pacity creation required mot only elastica"lly supplied factora but
also mchinery and building mterials produced by Industrial
The sam is
tzue of the two other sectors described in this chapter.
The demotic zupply of such capital goods is
plant capacity;
at all.
t
strictly limited by
=arly in the developwent proceso
The supply
i my not esist
rom abroad will usually be limited also by
shortage o2 foreign mey.
83
The demand for capital goods is the sua of demands resulting
from capacity creation in three sectors, the high-cor consumergoods sector (Sector 1), the overhead sector (Sector 5, described
later in this chapter), and the capital-goods sector itself (Sector
3).
In each of these it
is assumed that capital goods are needed
in a fixed ratio to gross capacity construction and that these
=mafactured for each project at a uniform rate during
goods are
its
gestation period.
among the sectors.)
(The ratios and the gestation periods differ
Thus each sector requires a flow of capital
goods which at any nmnt is directly proportional to the level of
The total demand is:
capacity under construction,
Q3
M3
K
;
(6.11)
1, 3, 5
This demand is ordinarily affected by the price of capital
goods through the effect of that price on the expected not return
to private investment in the high-cor and capital-goods sectors.
(The investment decision function in the capital-goods sector is
analogous to that in the high-cor and low-cor consumer-goods
sectors; see Equations 5.13 and 5.16.) The effect is not instantaneous, since it acts only on the rate of starting new projects,
is,
which helps determine the rate of change of e
rate of change of capital-goods demand.
and
g
is:
t-
X(12)
and hence the
The relation between K
84
Hence
dQ3
t
where
K
is
1,
;
-
k 3,
3, 5
(6113)
the rate of completing projects and is the "echo" of
of one gestation period earlier.
When the rate of starting projects in Sectors 1 and 3 is de-
termined by floors and/or ceilings overriding private declsions, of
course, the price offect is suppressed.
Capital-creation decisions
in the overhead sector are not directly affected by changes in the
capital-goods price in any case,,
goods,
Thus the total demand for capital
although sometimes affected by price, may at other times be
completely inelastic.
Facing this total demand is a supply made up of both homeproduced and imported capital goods.
The imported goods are elas-
tically supplied at a "tworld price" which is exogenous to the
system, but which may have a tariff added to it.
The domestic
sector is almost identical in form to the high-cor consumer-goods
sector already described.
That is to say, it
has the same kind
of supply function, affected by capital formation, technological
progress,
and wage bargaining; it
has the same kind of investment-
decision function, with possible government intervention; it has
the same kind of capital-goods requirements; and it
kind of capital life cycle.
has the same
85
The combined supply function of domestic and imported capital
goods consists of whatever portion of the domestic supply function
lies below the import price (gross, including tariff), plus a completely elastic supply at that price.
Conceivably, the import price
could be below the whole domestic supply curve, or it
mct the latter at a quantity less than capacity.
could inter-
Under these con-
ditions capital goods might be imported while all or some of domestic
capacity stood idle.
Only when the gross import price Is above the
doaatic price for capacity output will domestic capacity be fully
utilised before imports begin.
In actuality it would be possible
to change this situation by direct control of imports, but -this is
Inconvenient to simulate, and other mons are available to achieve
the same effect.
When policy dictates that domestic capacity should
be used first, a tariff is used, if
necessary, to keep the gro9ss im-
port price above the domestic capacity price.
Separately from this
consideration, the total volume of capital goods demanded and Its
allocation among the three sectors is indirectly controlled by mans
of the ceilings on the rate of starting projects.
C.
PUBLIC OVERWEAD CAPITAL
What is
included in this model under the name " Public Overhead
Capital" is not identical with any of the various concepts of "social
overhead," "public works, " etc. used by other authors.
to one aspect of these others which is
It
is
limited
identified by its effect on
the cost of delivered final produlcts of other sectors.
86
Power plants,
transportation facilities,
water supples, com-
sunication systems, etce are included, but only to the extent that
these exceed a level postulated to be the necessary complement to
the stock of capital in the various producing sectors .
though it
Awkward
may seem at first to visualise, for exaMple, some power
plants as an integral part of an industrial aggregate and others
as supplementary, it
is a convenience to do so for the sake of
separating the affects on capacity fron those on efficiency of
over-all production.
To the greatest possible degree, each of the four sectors
thus far described is conceived as a fully integrated aggregation
of all stages of production and distribution from raw material
extraction to retail sales, including all inputs, transportation
of the products, insurance, the services of various middlemen,
etc.
Each unit of capital created in any sector is a aulti-dimnsional
nixture of additions to capacity in enough of those parts of the
agregate that none become a critical bottleneck.
Thus some
power, transportation, etc. are included there.
Beyond this level, however, increases in the extent of thse
utilities are assumed to have beneficial effects, not on capacity,
but on direct cost of the delivered products.
These effects are
perhaps felt to varying degrees in all sectors, but do not need
to be accounted for in agriculture, with its totally inelastic supply
87
and insensitivity to profits.
They are accounted for in the other
sectors as described below.
Creation of public overhead capital (aside from that implicit
in other capacity creation) is assumed to be programnd and controlled by the governmnt, regardless of whether it
done by government or private concerns.
is actually
As in all other capacity
creation, its rate of starts, i: , is the variable subject to control.
After a di~s~rte 7eatation per.iod this reppemrs
pationsv A'
191o s.Vigicant attrition in
the rete ofc
assumed to occtr
n the
tiAs period of a run on tho simulator (probably 30 to 40 years).
Hence
t
does not have to bo simulated.
Thusa.:
t
%.4)
+-
U
(-
and
t
K5
K$ +f~
,
0dt
(6.15)
The unit cost of capital formation is proportional to that in
Sectors 1 and 3:
K
p5
K
5
P1
Investaint expenditures, as before are:
K
p
1
5
g
(6.17)
88
represented by
The output of the utilities
is
K5
in
the form
For
of intermediate prcducts or services to the producing sectors.
the purposes of this model it does not have to be evaluated.
be considered as part of the final products.
lishing
K
5
is
to relate it
d
In Sectors I and 3 (high-cor
to costs.
capital:
wivthn
in
plained in
1/Q , the
In these sectors, this coefficient is linearly
A (W/Q)
This is
can
The purpose of estab-
and capital goods) there is a function which determines
labor-cutput ratio.
It
-
addition to tb
o S)
k5(a(G
of feet of tochmological progres,
as ex-
Section A above.
In Sector 4, the labor-utput ratio is not explicit; therefore
F
a different approximation is used. The equilibrium value of pV
is affected as follows:
F
(AP4*
h54 AN
k
This affects the actual value of pP4
,
in coibinationl with other
influencea, with an exponential lag, as explained in Chapter 5 amd
Vpecfied
in Equation 5
408c
Tbust
F
dp4
d[
24
2
64
6
-
5
4)
(5.08)
80
D.
GOVE0NMW0
EXPENSEB
The concept of capital formation becomes less well defined in
connection with such undertakings as oducation and public health.
It
can be argued that almost all government expenses are creating
"capital" in the form of a favorable envirmment for economic activity.
still
Here, it
is believed more useful to draw the line (and it
is a vide, fuzzy line) where the effects cannot be trced
ad identified in term of increased capacity or reduced direct
costs of production within a few years of starting an undertakng.
The bureaucracy, military forces, education, health, and welfare
services, etc. are assumed necossary or desirable in themselves, and
their expansion a necessary part of any development program, without consideration of any effects on production of goods
within the
time span being studied.
For lack of a more rational basis, it
ment expenditures,
is assumed that govern-
aside from those for capital, are proportional
to the expenditures on public overhead capital:
O a
k
*
I5
go
APPMDIX TO CHAP15R 6
A.
HIUG-O0R CONSUER GOODS
(SECT(R 1)
Equations and block diagrams for Sector 1 are given on the
following pages,
eaccept that equations for the investment decision
and the capital life cycle, being the same as for Sector 4 (Chapter 5), are omitted.
la
In the first diagram the division,
done by a servo; since only one operation Is involved, the syu-
bol has been condensed .
No now types of relationship or analog
unit are included in these diagrams, and no further explanation
seem necessary
91
FOR
EQUATIONS
6.o5
(V ),.
= (L-/l)
6.06
=
TrA
6.07or
-.
ks, K5
M(L-
=L
pF
-
f
= /0,
-fri
c
oj i
- A
a~Lt
TO
6.o9
6 .09
-K
(6,Io
L,
if
No-r-E :
FoVR
0
-r Ar
-
-
6.04
es
?n,
SL.
, F i c,.
+
4
Ficz. 8
7.-)
+i
K
err->,) ++'4(w
s5
Wll
EC.-r
I
SECTOR
- P-5-J
(cbG4T
ETA
CIA
4
3a/
Lia
os?
r
KO
GH
t
FVG.
031
+
b
+
A2l
7
ODv
~7
-I-
tI
Fxog
RN 'MAIN
NTE .if. PATO M
AGR AM
4',
SHORT- RUN
SUPPLY
PRICE
COMPUTER
MRN
SECTOR
F1G,
I
8
ow-
94
B.
CAPITAL 000S
(SECTOR 3)
Internally, Sector 3 is just like Sector 1.
The circuit which
divides the demand for capital goods between foreign and home supplies, however, needs explaining.
In the diagram of Sector 3 (which can be folded cut and referred to beside this explanatior4 there is a combination of three
senwing relays and an integrator which divide the demandd quantity
fc lgods,
PS ,
the foreign and ha
the two sipply prices are equated when possible,
u
The quantty, Q
is intertaediate goods iMported for use in manufacturing donestic
capital goods, QSH, and is required in fixed proportion to the latter:
q7 3
7N
The quantity, Q7,
2H
is imported finishod capital goods, whjioh are
perfectly equivalent to tho
hce variety.
The two kinds of im-
ports coe Erem the aame market, with the same price index, p ,
and are aggregated into a total quantity of capital-goods imports:
Q,
= ^
The dividing circuit adjusts
total demand, Q., to determine
Q3
+ Q
Q., which is subtracted from the
Q3H, the quantity supplied at homa:
Q3
~ Q7g
95
The relays are shown in the positions they take when sone of
p3 is loser than
both supplies are being used and
In this
p7 .
case a negative signal goes into the integrator to reduce
thereby increasing
Q3H
and raising
p3
pV,the reverse effect would take place.
If
p3
Q
,
were higher than
Under these conditions,
the prices stay nearly equal and the first relay serves no purpose.
This corresponds to the horizontal foreign supply curve intersectquantity which is
ing the home supply curve at soe
(either below or above capacity) and which is
demanded.
If
the hone supply curve drifts upward, with no change in
Q
is increased and
this point the
Q
Q3H
QS3 -sensing relay opens,
the
reduced, until
capital goods are imported.
the latter becomes zero and all
p3
than the quantity
The quantities ere so divided as to equalise the prices,,
foreign supply price,
increase
les
above zero
At
and signals that would
(associated with A p <C 0) cannot pass, even though
may rise far above
p7 .
f
p3
that A p > 0, the signal to reduce
comes down again, however, so
Q
(letting
Q
increase)
Thus
goes through the other branch of the circuit and tales effect.
the cutting off of the balancing circuit is not irrevocable.
Con-
versely, if the home supply curve goes down or demand diminishes to
the point where
Q7
0, the Q7K -sensing relay opens and cuts off
signals that would make Q
become negative.
In either of these
situations, where only one supply is used and the prices are not
equated, the A p-sensing relay selects the appropriate price for use
in investment pricing .
I
SE CT OR.
3.
CAP ~TA L
CooD5
Jlrq
97
C.
PWLIC OVERHEAD
(SECTOR 5)
The equations for
,
and
15
(Equations 6.14 and
6.17) follow the standard pattern and are not repeated here.
Others
are:
6.15
K5
=
+
dt
0
p
6.16
M
1
(WQ)
6.18
-for
Sectors 1 and 3
These relations are diagrammd on the next page.
In those
cotors where Equation 6.18 applies, (I/Q)
Is do-
termined as the output of an integrator, integrating 16.
There-
fore it
is
and add it
convenient to use the derivatIve of the above equation
to the input of the integrator.
as the diagram for Sector I shows.
Thus:
Mwover, the Integrated value
from Equation 6.15 in needed in Equation 5,08 for Sector 4.
98
14
is
TOR
PUBL IC
OV ER HEAD
CAPITAL
.S. ,
FIG,
99
Chapter 7
FOREIGN COMMERCE AND PAYahiElS
From time to time in other chapters imports and exports have been
mentioned.
In this section all import and export functions are speci-
fied and, it necessary, explained.
Some previous statements are repeated,
but in most cases specifications are completed
given o nly in
which were previously
pa-rt.
imports,
Five different domands for imports are developed in
all subject to price effects.
the system,
They are:
1.
for consumer goods, by consumers
2.
for intermediate goods used in Sector 1 (high-cor C-goode)
3.
for intermediate goodE used in
4.
for capital goods used in capacity creation in Sectors 1, 3,
Sector 1 (low-cor C-goods)
and 5 (high-cor, capital goods, and public overhead)
5.
for intermediate goode used in Sector 3 (capital goode)
Supplies of these goods are assued perfectly elastic at two separate
price levels.
V
One price index, p6
,
applies to the first three cate-
gorios--consumer goods and consumer-goods constituents.
p
A second indox,
,;applies to the last two--capital goods and their constituents. These
are "world prices," in terms of foreign money and without tariffs. They
are exogenous,
and ordinarily they will be constant, although a few
100
experiments might be made on the reaction of the system to shocks introducod in them.
The corresponding prices as soon by the various buyers may differ
from the world prices by tariffs, which may be fixed in advance or made
instruments of built-in policy mechanisms .
A tariff on the consumor-
goods price may apply to all of the first three categories of demand
listed above, or only to the first, leaving the second and third free.A different rate may apply to categories 4 and 5.
The whole pattern
may be scaled up or down by a change in exchange rate.
ExpOrts
.
Goods for export, it has been assumed (see page 76), are made with
the same factors as high-cor consumer goods, and hence are supplied by
that sector (Sector 1).
The demand for exports is not perfectly elastic, but has an elasticity greater than one.
Thus an increase in price reduces not only
the quantity but also the value of goods bought.
quantity demanded becomes sero.
I
V
0
xl~~
VP1
or, in terms of quantity:
ube
t
subject to Qlx > Ot or X,2t
At some price, the
Algebraically, the function is:
(7.1)
101
where
4 and v are constants ,
prime on X
The
and p( is in foreign money units
and various letters below indicates values measured in
foreign money units.
The price elasticity of this demand is:
-
Balance of Payments
Collecting the export and import totals from the above relations
gives the balance on current account,
(7.2)
P'/
(Invisibles are included in these totals.)
In addition, there is a
flow of foreign money not accounted for by these transactions, designated
F .
This flow is one of the key erogenous variables whose effects are
to be surveyed.
It
may represent grants or net long-term loans or possi-
bly direct investment--provided that it
is applied to purposes that fit
whatever investment program is being investigated, and assuming that it
does not automatically lead to problems of repayment or capital repatriation.
This does not imply that such problems can be ignored.
It
only assumes that they can be examined separately, and that the whole
situation with regard to foreign money can be summed up in terms of an
effective available money flow varying through time.
Thus the "balance
102
of-payments surplus" is:
P' aF'
+
P'
c.a.
=
F
+
X
-
(7.3)
N'
It may be noted that the structure of the model has not yet
provided for extracting oil or minerals or growing rubber, bannas,
etc. for export.
Although these activities in some countries take
forms that are outside of the scope of this model, there is one extreme form that they often approach which can be easily accounted for.
That form is what might be called the "foreign
eclave
4"
Such a
sector is developed by foreigners with foreign money, forei
goods, and foreign technical. and managerial staffs.
expotted.
capital
The product is
Profits are either used for expansion--with foreign capital
goods--or spent abroad.
The only connections with the national economy
are through taxes or royalties, wages paid to local labor , and sometimes
purchases of some intermediate goods and services.
The appropriate way to deal with a sector approaching this extreme is
to treat it
as a foreign country.
The intermediate products
sold to it are considered as exports, wages to local labor are added to
personal incomes as transfers, and royalties or tax receipts are an inflow of foreign capital to the govermrentr.
In the present model,
even
these effects are not represented in any explicit function which would
tie them to some measure of size of the sector.
Nevertheless, part of
the exogenous flow of foreign money may be conceived of as a first
approxi
mation to the effect of a foreign enclave which uses negligiblo nounts
of local labor or intermediate goods.
103
APPENDIX TO CHAPTER 7
The diagram titled "Foreign Markots" is a collection of several
circuits that are essentially separate.
In the upper left corner is
the demand for exports, according to Equation 7.1:
X
In
-
(7.1)
vp
terms of homo-mney units (with x the exchange rate)
P
~P X and X,
At the right is a pair of coefficients which, if desired, can be
made to change in steps representing tariff rate increases whenever
the balance of payments is in deficit.
This applies to intermediate
and finished consumer goods (or can be wired to the latter alone).
The world price, assumed constant, is translated into a home-money
price including tariff thus:
P6
W
P6 (1 + t6)
The gross expenditure in this category is put in fozreign money, not of
tariff, thus:
M6
(M
=61
+ M
64
+ C
C6
( 1 + to6
In the lower left part of the diagram, a similar arrangement provides for adjusting a tariff on capital goods if it is desired to keep
104
their gross price above that for capacity output of the home capitalgoods industry.
The relays shown are additional poles on sensing
relays used for other purposes in
Sector 3.
If
capital goods are be-
ing imported while there is idle capacity at home, both relays close
and the tariff rises either until all home capacity is in use
(Q 3
=Q
3
) or until imports are stopped (Q7 M 0).
The block directly above those relays indicates a setup which
can be made to switch the exchange rate to a new value in all six
places where it is used.
This can be set to switch either at a par-
ticular time, chosen from results of a previous run, or in response
to a feedback such as a particular level of deficit of the balance of
payments.
A servo-integrator is substituted when a continuously vari-
able exchange rate is desired.
The diagram also includes an integrator to time-program the foreign
long-term capital inflow and a summer to compute the balance of payments
position.
x1
#L
a
C"6
JV-+
ago%
N'D
TAIC I F F
2
Iw
-
PAVAEW
F.
t4P(WW4
V-
S
*N;
CAP i TAL-
My-CHAtA r E:
RATS C-ANra
p
0100
I
N
4,
4.
Tc~ ~~4'JE. STME~T
TAR I FrFC7
JCLOSE IF
>0
Itos 4F~S
QiK
LFI~.
II
FOREI~GN
MIAR KET5
106
Chapter 8
INCOME,
A.
FINANCE, AND CONTROL
INCOME
"Income" is a term used with so many different meanings that It
is necessary to define which one is intended here .
One of the sources
of confusion has been the assumption, in many analyses, of conWtant
pricoe,
making It
possible to &'lpback and forth betwon real prcducts
and money flows without always making it
clear wkich is whIcht. nh
model a basic distinction is carefully maintained between money and
products, with flexible relations between the two.
crucial.
This is considered
If the "real" part of the economy--production and distribu-
tion of goods and services--be thought of as analogous to a physicalchemical process, then mouey flows are like signals in a control system
which opens and close* valves, and regulates pumps,
and nature of the process.
affecting the rate
The flows of electric current in the control
system are not uniquely related to what 18 happening in the physicalchemical process and are not reliable indicators of its state, even
though they play an essential role in controlling it.
The primary purposo of measuring income in this model is
tain what coumrers spend.
This does not require deflating it
to asceror im-
puting corrections for capital consumption, use of self-owned durablca,
107
etc.
(It
does involve imputations for home-consumed products,
plained in Chapter 5.)
as ex-
Gross national income is the total rate at
which people are earning money to save or spend on consumer goods.
Not all that is earned is available for these purposes, some being retained in businesses to cover capital replacement and expansion costs
and some being taken in
taxes.
The individual inuoms which add up
to gross national income are earned directly or indirectly in producing
consumer goods and export goods,
operations.
in capital creation, and in government
Expansion of capacity in any sector implies expansion of
working inventories--that inventory level that might be considored
"normal."
Goods which go into such inventory ension
are part of the
physical capital or capacity expansion.
Inventory levels in reality change also because of speculation by
producers and because of errors by producers in Judging consumers'
demands.
These changes are usually also counted as investent--some-
times "unintended investment"--but they have no relation to expansion
of productive capacity.
A more complex model might include a separate
mechanism for simulating unintended inventory fluctuations, but for thia
model this was felt to involve too much complication to be justified.
Rather than assume that unintended and speculative inventory changes
are of the same nature as capital formation, they have been assumed to
be negligible for the problems on which this study is focused.
In the production of goods for consumption and export the incomes
earned are equal to the market value of the goods sold (there being no
108
inventory change) less the expenditures for imported materials. Incomes
earned in capital formation are equal to the total outlay for investment less the expenditure for imported capital goods.
(Note that the
value of capital goods produced is included in investment outlays .)
In addition, services to the government earn incomes equal to government expondituro.
ment investment in
already counted .
Y
This last ita
c of course, does not include govern-
capital formation, which is
part of total inveatment
Thus gross national income t
(C;
-
a
) +
+ Zi
-& 7
(8.1)
which reduces to
Y
C -zM
+ X+
I + 0
(8.2)
Since C is the total expenditure of consumers and I the total outlay
of investors, the value of imports subtracted to get the corresponding
home incomes must include any tariff that applies.
This is not the
same as the value of imports used in finding the balance of foreign
payments, since the tariff does not go abroad.
How much of gross income is available for consumption depends on
its
division between profits and wages.
The assumption is that profits
are more susceptible than rages to taxation as well as to savin; (both
through retention in business and through a higher propensity to save
on the part of ontropreneurs).
In those sectors whaere diroct costs are
109
so identified (Sectors 1, 3, and 4), the gross difference between sales
It includes fixed
revenue and direct costs is called gross profits.
cost and not profits.
The fixed costs include depreciation reserves,
intorest and "normal" divideuds, and the minimum satisfactory return
to entrepreneurs.
Of these, the first are saved (whether invested or
not); the others are paid out as disposable income, but are subject to
a higher-than-normal rate of saving,.
The not profits are partly re-
tained for business use, partly taxed (in
addition to the ordinary
income taz), and partly paid out as disposable inoone, but are porhaps
also subject to a higher rate of saving than wage incomes.
The com-
bination of all these effects is approximated by assuming that some
constant fraction of gross profit is withheld from consumption, in
addition to taxes and savings that are based, respectively, on total
income and the joint demand function.
not necessary to know how much is
It
is also assumed that it is
in taxes and how much in savings.
(Seo the discussion of finance in the next section.)
The quantity, then, that goes into the consumers' demand function
is actually disposable income less savings above the ordinary rate by
profit earners.
However, it is labeled simply "disposable income."
Its formula is:
D Y - t
Where t
Y -
T(.)
is the normal income tax rate,
is
the
t"o, aum
Of the
110
profit tax and the excess saving rate, and
or
T
Qj p-
1)
Q
Lo wL
T
is gross profit:
-
(LbpL)
(8.4)
(8.5)
B. FIANCE AND CONTROL OF THE INVESTNMT PATTERN
The problem of domestic finance is avoided here except to the
extent that it
is implied in the formulation Just given for total
disposable income.
Actually a very important aspect of the problen
of starting a development process is the problem of savings and taxes
and where in the sectoral structure they occur.
This problem is set
aside for the present solely on the grounds that within certain limits
it can be analysed separately, and that investigation and understandIng of the allocation problem will be more feasible with this simplification.
It
is necessary, of course, to recognise the assumptions
implicit in this simplification and to be aware of the conditions
under which they may be unrealistic.
Government investment allocation policy is expressed in the model
by ceilings on capital formation in some sectors, floors in others, and
specific magnitudes in others .
it
When a coiling is operative in practice
may be effected by taxation, by tight credit, by requiring licensing
of construction, or by controlling the supply of critical capital goods
to the sector involved.
Which of these means in used is not explicit
in the simulated system; it
is only assumed that the method usad is
111
effective.
Such investment as takes place either up against a ceiling
or with no restraints operating may be financed from retained profits
or by loans from credit institutions, or partly from each source.
separato accounting is made .
No
When a minimum level of investment is
called for and maintained above the level that private entrepreneurs
would undertake even with easy money, it
is
implied that the government
is either constructing plants of its own or subsidizing (not merely
financing) their cons truction by private operators.
Again, the dis-
tinction Is not accounted for.
In two sectors, public overhead and agriculture, the magnitude
of investment is directly determined by the government, which prosumably--but not necessarily--finances all of it in public overhead
and a fixed major proportion of it in agriculture.
Private investment
in agriculture is induced by the government activities and is selffinanced by directly connected acts of saving.
It is assumed that the
ratio of private investment to government investment is fixed.
Hence,
the private investment is carried implicitly in the "effective capitaloutput ratio"--tho ratio of government investment to total
4.ncrease
in
output.
The omission of oxplicit accounting for taxes and for the sectoral
pattern of business savings means that patterns of investment are decided on independently of the sources of funds .
It violates the ofton-
observed tendency for profits to be plowed back more freely than outride
money would be invested.
Thus it
is
implied in some circumstances that
112
profits from one sector are diverted to investment in another, either
voluntarily through the capital market, or involuntarily through taxa-
tion and governmsnt loans or subsidies.
Under some conditions such
transfers may be very difficult to accomplish,
another problem--important,
but that is considered
but not to be dealt with hore,
Another implication under some circuxstances is
is being created for deficit financing.
flationary.
that new money
This may or may not be in-
The problem of balancing over-all government plus pri-
vate investment by sufficient taxes and savings (and not imports) to
avoid excessive inflation is not treated explicitly, but is handled
on the basis of using a price index as a signal to tell the government when investments need to be slowed dcn.
The variables in the model which can be time-programmed or
manipulated to represent actions of the government are as follows:
;
Direct control of investment projects:
Uppor limits on investment projects:
r
;
Lower limits on investment projects:
Interest rate and tax disincentives,
included in
which affects Sectors 1, 3, and 4
Ah
Tariff, either on consumer goods alone
or on those and intermediate goods
for Sectors 1 and 4:
t
Another tariff, either on finished
capital-goods alone or on finished and intermediate capital goods:
tK
;
113
Exchange rate, domestic for foreign
moneY:
x
In addition, to represent aid or investment from abroad, there
is a time--program of foreign capital inflor:
F
Any of these variables can be set to a fixed value or set to
follow an arbitrary time profile during a run.
Also, varicus ones
an be made to zhange in response to conditions as they develop.
For example, a tariff can be sot to Jump to a higher level whenover
a balance-of-payments deficit exceeds some arbitrary level; or the
cailing on investment in one or more sectors can be made to move
down when a certain rate of inflation is exceeded.
Thus not caly
preplanned programs but also revisions and readjustments can be
simulated, as discussed in Section C of the following chapter.
114
APPNDIX TO CAP=R 8
A.
INCOMXE
The first of the diagrams in this appendix represents simply
the arithmstic of the follouing equations:
6.19
G
0
I5
(Ci-
Y
)
M6
+
X
+0I
- -M
+
t
.,3
Y
(Equation 8.5,
to which it
B.
TT
Y (1-ty)
m
(Alp
%;3TF
-
AV
is included in each nector
applies.)
CONTROLS
rigure 13 showrs how a set of capital-projoct ceilings, floors,
and direct program sight be st
up for tho five sectors.
Notes
indicate 'policies which might modify these programs in caee of a
forcign exchange crisis or excessive
inflation.
The imicatica of
a foreign exchange crisis is the balance-of-paymenta deficit from
the circuits of the Chapter 7 appndix
indicator is needed.
For inflation, another
This is provided by the circuit of Figure 14,
which first constructs a coasumr price inde= and thn compares it
with a 'normal" level of the index, baed c
its pst
history.
The
115
"normal price,"
p
,
is a weighted average of the continuum of past
prices, with the highest weight for the most recent
weight diminished exponentially with age.
nd with the
(The formula is cc the
diagram.)
The last figure shows the circuits by which various progrens
like the sample will be set up.
The integWator at the lower left
acts as a timer, driving a set of potenticeters, some of which
are ronUner
Programs like those shov
4 and 5 zr-equirc :r
priAnl2eC are
in
prtsL thant ore shova in
agr
oification
the sample for Sectors
the diagram, b'
the
in reasne 'to forein
exAhange unbalnce and inflation are mde through the three otr
integrators, for Sectors 1, 3, and 5, in accordance with the notes
cn the sample program*
FIG, I2Z
INCOM E
ACCOU NTS
(c + r)
ca
Y
S7T
Ti;
4
Id
Ml
+ .x),
.L.3
11'1
time
R5
IMPOSSE
CTOR
IN
NO
CASE.
OF
2.A
SE
cTo
it.
CELT-RNG/
SECTOR
R s
--
REDucE.. \N F.K
CRISIS
I
oR
NFLAT 10 t-A
5E CTO R
5
SAMPL E
time
-
FROGRAM
F i G- 13
t pf
CON SUM ER
PR Ic E
Pa
+
-NORMAL.
INFLATIOAN
PRICE"
IND.X
FIGF
PRICE
AND
INFLATI ON
INDEXE5
e~
I
NFLAT
INDEX
t
PR ~
R
S
NVE S TMENT
CON TPO LS
(ONE
AL~r~ERF4AThiVE
FIG. L5
120
PART
III
PIANSFOR STUDY
121
Chapter 9
EXPERIMENTAL APPROACH
A. NUMERICAL DATA
Part II of this exposition defines the model in complete detail-verbally, algebraically, and in the symbolism of block diagrams.
sufficiently defines
This
hat array of analog units will be required and
how they will be interconnected.
However, it still does not toll what
ratio to use between economic units and electrical voltage for each
variable, what coefficients to set in various relationr, or what Initial value to set up for each variable.
Since the analog is a concrete
and particular model--even though almost infinitely adjustable--every
variable and parameter must have a definite value at any time.
Rela-
tions between economic variables and the voltages which represent them
must be so chosen that the voltages will be neither too high nor too
low during the oxperiments.
Thus it
is necessary to estimate in ad-
vance a range of values for every economic variable, and to choose for
each parameter a range of values through which it may be adjusted for
different runs.
Although many runs will be improvised according to
the results of other runs, nevertheless it
is necessary to lay out in
advance a program of surveys of parameters and initial values of variables to be sure that some areas are not forgotten.
Choice of these many numerical values is not part of this thesis.
It is
the step to be done next.
While it involves a good deal of work,
122
there is nothing about it
bility of the study.
that is crucial to the question of feasi-
Where possible, statistics from underdeveloped
countries will be the basis of the necessary estimate.
Of course,
statistics are not available on some of the parameters and are not
very well known on others, so that some guessing will be involved.
The it
will not be posslble to consider the simulation as a quantiof any particular country.
tative reresettion
Fortunately,
it
is
of ten possible to learn much that is
usoful
from simulation of a system even when some paraneter values are not
known.
When information is lacking or uncertain, some of the explorav-
tions are repeated several times with different assumed values.
In
this way it is sometimes possible to find generalizations that do not
depend sensitivoly on the unknown value ,
On the other hand, some
parameters may be found critical to the behavior of the system.
This
may show the need for more accurate data on particular parameters, or
suggest alteration of some policy in a way that leads to more reliable
results.
B.
DgVLPENT-PROGRAM COMPARISONS
After ranges of parameters and variables have been estimated,
and workable scale factors have been chosen relating economic units
to voltages and dial settings, the actual analog components will be
put into place and interconnected according to the diagrams in the
appendixes to Chapters 4 through 8.
(Actually, further detail will
123
have to he added to the diagrams first,
the whole analog setup.)
graphical recorders.
but schematically they specify
Selected variables will be connected to
Next, operation of various parts of the system
will be checked against some hand-computed solutions, faulty components
Then the investigation
will be replaced, and wiring errors corrected.
will begin.
Several different kinds of questions will be investigated by making
comparative runs with many variations.
One of the basic comparisono, to
be made under various boundary conditions, will be between investment
plans with emphasis on different sectors or with different sequences of
shifting emphasis among sectors.
For example,
one plan will be to en-
courage heavy investment in capacity to produce capital goods, prohibiting
consumer-goods imports to conserve foreign exchange, and at the same time
expanding agriculture and handicrafts, somewhat,
to meet increased demand,
Under this policy, investment in the high-cor consumer-goods industries
will be held to a very low level at first.
Later on, it may be allowed
to expand.
A contrary approach will be to concentrate on expanding the highcor consumer-goods industries (and to some extent agriculture) first
while holding down the capital-goods industries, at least until consumergoods capacity has expanded a great deal.
Still another plan will develop
the public overhead sector rapidly, and agriculture enough to meet population growth, while letting investment in other sectors be determined
by private decisions.
124
In terms of the model as formulated, what are to be explortd are
various sets of time profiles of limits on capital-formation projects-floors, ceilings, and direct specifications of is in different auctors.
What happens under the various programs will be evaluated from timo
graphs of such variables as:
National income, gross and disposable
Production from each of four hnom
sectors
Price of each of four home goods
Consumers'
price index
Wage rates in two industrial sectors
Imports
Exports
To aid in understanding the behavior of these criterion variables, still
others will be recorded, such as:
Tariff rates
Profits in three sectors
Rate of starting construction in three sectors
Price of capital construction in three sectors
In cases of peculiar results that call for more detailed investigation,
runs can be repeated to record any other desired variables.
Comparing the different types of development programs is not simply
a matter of running each one with everything else equal.
For one thing,
the appropriate scale of each program is not known in advance. If the
125
exogenous flow of foreign money be taken as given (for the time being),
repeating a particular program at different scales will preusimably give
different rates of inflation.
Perhaps an arbitrary value can be set
for the highest perlssible rate,
Or perhaps the effects on the balance
of trade will show where a limit is needed.
But that may depend on
tariff policy, which will also have to be explored.
For other invest-
ment plans, such explorations have to be repeated, for what is optimum
tariff
policy wit
one pattern may be entirely wrong- rith
coumrse, variatAons i
another .
Of
the soctoral structure and time phasing of each
type of investmut plan must also be tried, for the decision to emphasiz.
one sector does not determine what the relative weightz of the other four
should be.
When all of these variations have been worked out in several combinations, there is no asourance that the relative merits of the different
allocation policies will be the same at different levels of feig-ney
flow, for nonlinear offects are certainly to be expected.
Indeed, the
supporting policies that have been matched to a particular type of inves*wmont program may even need revision when the flow of foreign money changeo.
It
is not at all unilkely, for example,
that a high tariff policy could
prove beneficial with low flows but harmful with high flows.
Therefore,
explorations will be made with different foreign money inflows.
C.
CRISES AND READJUSTNTMI
Comparison of investment programs has been discussed above almost
126
as if
there were a clear-cut procedure for choosing their time profiles
in advance, after which it
would be only a question of a few experiments
to find the right over-all scale and appropriate supporting policies for
each.
This is a gross oversimplification.
One of the most versatile
and many-sided sets of variables in the whole problem is
profiles of the control variables.
the set of time
The process under study i
one in
which conditions at any time are determined by the system's history, and
effects of a small deviation early in the program can accumulate to significant size in the 20, 30, or 40 years that are covered in a typical
run. Clearly, then, it will make a difference whether a high rate of
project starts is undertaken for a few years in some sector, or a lower
rate over a longer time, and whether expansion is started simultaneously
in two sectors or one is phased later than the other, etc.
If a representative set of variations of time-profile combinations
were surveyed on an area coverage basis, and if
optimized for each by trial and error, and if
supporting policies were
the whole survey were then
repeated for several different combinations of magnitude and time profile
of foreign money flow, it would require thousands of runs.
Many of theca
runs could be rejected as impractical or unsuccessful on first inspection
of the results.
Fortunately, there are ways of avoiding much of the lost
motion in this process.
What happens in reality when a five-year plan
proves unworkable is that it is either stretched out over a longer time
or thoroughly revised.
One might think of watching the development
127
process as the simulator generates it,v and making adjustments if at
some time the balance of payments seems to be getting out of hand, or
inflation seems to call for some corrective action.
Our brains, how-
ever--even our reflexes--would probably not do a very good job of this
with the simulator grinding out two years of history every second.
(This is not the only possible time scale, but the order of magnitudo
could not be
uc=h dif forent )
'Thw other methods are feasible
the occasion.
-and both will be used as suit
In one method, the investigator studies the time his-
tories of variables fron a run and decides, perhaps, that they are
satisfactory up to a given tims, but that a change in program Irom
that time on would improvo resulto.
This may
n a speed-tup or a
vlow-dovn, and may affct one or several programmed variables.
chnnges the program accordingly and repeats the run.
otitions may converge on ta
results ho esos .
e~nticip'ate what kinds of trouble m4ght aric,
He
Succssive rep-
The other method is to
decide on the corrective
action that would be thaen, and buld into the analog autotatic devies
to take the action whenever the warning symptoms appar
up, the atomatic response can be %djustedin
uccesasive
With this satruns if
its
effects are either too strong or too zl4.
Two automatic corrective devices of this kind wore Amentioned at
the end of the previous chapter,,
One is a circuit which senses an
128
indication of consumer--goods price change and can be made to lower the
investment ceiling in any desired sector or ombination of sectors i
the rate of inflation threatens to exceed a value chosen in advance
as tolerable,
In the kind of real situation this simulates, a plan in
followed at firsts thon inflation becomes serious, and changes are made
in the plan in an effort to stabilize prices.. Fron then on, readjustments may be made wore or less continuously, if necessary, with au
ye
on the price Ind~ez.
The other autematic device is
policy is
the tarIff raiser.
When a protectli
to be simulated, this device can be set to raiso the consumer-
goods tariff by a step whenever the balanco of payments is in deficit
(or, it
can be based on the balance of trade, if
desired)
Either of
those circuits cavn be adjustad to various threhld3s and strengths of
response, or can be made inactive.
D.
NATURE OF RESULTh SUGHT
Obviously, a study like this one is not going to yield a Oet of
numerical values defining the optiunin development progran for any real
country .
Neither will it yield a quantitative forecast of the outcome
of any particular program.
Such results, if
not ruled out by the approx.-
imatious of the model formulation, would at least depend on accurate
values of many parameters, some of which are not ordinarily
ubjects of
statistical studies, and some of which may aot be very directly merable..
Nevorthelss, as stated earlier, it
should be possible to learn
129
some useful things about the behavior of this kind of system in general,
without having detailed numerical data.
It
should be possible, for example, to conclude that a development
plan with emphasis on some particular sector is most likely to be effective if
combined with some particular foreign trade policy.
other sectoral emphasis,
better.
For some
the opposite foreign trade policy may work
Those conclusions may or may not depend sensitively on some
other conditions--either parameters of the system or other policies.
Knowledge of such sensitivity or insensitivity is also a significant
result.
Dynamic interactions between sectors--o .g., between investment
in the high-cor and low-cor consumer goods sectors, with incentives
coupled through the joint demand function--ay exhibit modes of behavior
that are significant at a purely qualitative level, showing the mechanisms whereby one sector's growth may induce either growth or decay of
another, or whereby oscillations may develop.
Most likely such a result
will depend on parameters of the sectors and perhaps of the rest of the
economy.
The precise values of the parameters will, of course, not be
directly relevant to real economies,
but what will be important is to
know what modes of interaction are possible and which parameters ma e a
difference.
Most significant for planners and policy-makors, of course, will
be indications of the indirect effects of programs aimed at definite
direct goals and the long-run effects of short-run policy measures.
130
With the unusually large number of interacting dynamic relationships
in this model, it
may turn out that some of the effects usually neg-
lected are actually very important in some circumstances.
So another
kind of result sought is more complete information on the kinds of
effects produced by different control actions.
Possibly even more important is to find variables which make good
indicators of the need for various kinds of program adjustment or other
remedial action.
Te timing of corrective action is extremely important
in any system,1 and good timing of course depends on recognizing incipient trouble early.
Good feedback signals, properly used, will also
compensate for much of the uncertainty of long-range planning.
Such
indicators may not be obvious and will be found only by trial and error.
Any of these several kinds of results will help clarify the problems of economic development.
It is hoped that experimentation with
the analog will lead to more effective strategies for dealing with them.
As shown by Phillips, in his 1957 article,
pcit
131
Chapter 10
CONCLUSIES AND RECOM!)ATIONB
This thesis is not a report on experiments done, nor is it an
analysis giving answers to a definite economic problem,
Nevertheless
there are conclusions to be drawn.
First:
Althout hit
sas not actually been set up aS yet
the
economic Mndel that i& fcrCamulated vorihally and algebraically in
Chap--
tars 3 through 8 has been translated, in the appendixes to those chapters, Into a detailed specification of the aalog compononts ad interconnections that wifl be required to aot up the simulation,
In comparison with other oca-omic systems that havo been &±imulatod,
this one involves many mor
parts, but both the parts and the circuit
using them are like those previously used.
All of the components in-
dicated are available in the laboratory here at the Masachusetts Institute of Tecbnology and the ways in which they are combined and
interconnected are straightforward.
It
is
concluded, therefore, that
it will be feasible to sot up the simlation and carry out the propozed
study.
Second:
In comparison with other macrc-economic models that have
boon explicitly solved either algebraically or nunerically in connection
with economic development problems, this Zormulation is
to lead to false conclunios through oversimplification.
far less likely
Its greater
132
complexity allows flexible prices, capital accumulation,
sumers'
income, con-
preferences, and foreign trade to have their complex interacting
effects, with proper regard for the gestation time and life span of
physical capital.
It is concluded,
therefore,
that the planned study
can contribute significant new insight into the problems of starting
oconomic development.
ThirdS
It
is noteworthy that models very similar to this one,
~uit ed to studyingarous, other dynnic sconomic probleme by
techniquos!
Probles o- the ftr
Imiltar
or Industry as well as national and
international a.ggregativo problems would be amenable to this treatment.
It
would be a particularly fruitful approach to studying business cycles.
The third und final conclusion, therefore, is
that the technique of
simulation, whose application to the development problem has been worked
out here, has a far wider application with potentially very fruitful
results in many aspects of economics.
Other work that could well be recommended along lines similar to
those pursued in this thesis includos simulation studies of the followiug situations:
Underdeveloped countries with different sectoral structures, e .g.,
an export economy and an economy with bottlenecks in production of
intermodiate goods,
An underdeveloped country without diguised unemploymont.
Interplay of two or more countries in international commerco and
finnce .
133
Detal
study.
of the financial problems not covered in the present
Business cycles in advanced economies.
The dynamics of the wage-price spiral.
The effects of major technical change,
of automation on a large scale.
such as the introduction
All of these situations are too dynamic and complex to be adequately
handled with current methods and would be worth studying by simulaTion,
Howaver, before formulating a great variety of models, the most worth
whilo undortaking in this field right now is to use the foundation
horeby laid and proceed to simulate and experiment with the model
specified in this thesis.
It
is intended that this be done.
134
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Sym bolsm
Langer, Susanne K,
Phi
Qo
University Pressq 1942.
hn
a Now K!e
Cambridge,;
Harvard
137
The development of the ideas in this thesis was possible only
with help and encouragement from both economists and engineers.
Professor Ibx y. Millikan, director of the Canter for International
Studies at the
thesi
assaohucetts Institute of Technology, who was ao
advisor, w
largely responsible for steering me into the
field of economics and for giving me ample opportunity to develop
my ideas as well as helpful guidance in the conception and formulation of the model.
Encouragemnt and constructive criticism were
given alao by W. W. Rosto,
R. S.
Eckaus, R. M. SolsW, F. N. Bator,
and by the other two mesiers of or thesis committee, Professors
C. P. Kindleberger and P. A. Samelson.
For keeping alive the idea of using an engineering approach
to dynamic economic problems, and for making the analog equipment
available for preliminary experiments,
I thank Professor W. W.
Seifert, assistant director of what was formerly the Dynamics
Analysis and Control Laboratory at the Massachusetts Institute of
Technology.
His help, and that of C. W. Steeg and C. 0. Blanyer,
his assistants, was indispensible in teaching me what can be done
with analog simulation equipment and how to do it.
The seed of the idea that engineering thought patterns might
be useful in economics was probably planted by an article by Arnold
138
Tustin in the Scientific American of September 1962, before I had
any thought of becoming an economist .
Growth of the idea was great-
ly stimulated by his book, The Mechanism of Economic 8a
, after
I had started my transition into this field.
For financial support, thanks are offered to the Center for
International Studies and to the Sloan Research Fund of the School
of Industrial Maanemet
at the Massachusette Institute of Tech-
naolo~y
Thanks also to Mr. Benjamin Tencer for his able assistance in
working out arrangeMents and details of block diagras,, to Mise
ledvig Pocius and Mrs. Marelle Jones for capably handling the
difficult typing job, and to Mrs. Jean P. S. Clark for her help
with many details of production.
Edward Peck Holland
Cambridge, Massachusetts
January 1958