A Cybernetic model for analysis and control of Economy

PRAGUE UTIA 1982 2

TECHNICALUNIVERSITY OF BRNO

A CYBERNETIC MODEL

FOR ANALYSIS AND

CONTROL OF ECONOMY

by AEDIL SUAREZ

PRAGUE UTIA 1982 3

TECHNICALUNIVERSITYOF BRNO

FACULTY OF ELECTRONICS

Chair of Theoretical Cybernetics

A CYBERNETIC MODEL

FOR ANALYSIS AND

CONTROL OF ECONOMY

By AEDIL SUAREZ

THESIS SUBMITTED TO THE C.S.A.V. – U.T.I.A

FOR THE Ph. D. DEGREE PRAGUE 1982

CZECHOSLOVAK ACADEMY OF SCIENCES

INSTITUTE OF INFORMATION THEORY AND

AUTOMATION C.S.A.V. – U.T.I.A

A Cybernetic Model for Analysis and Control of Economy Ph.D. Thesis : Aedil Suarez

.

To my wife Cristina and my children

Elio and Angela. They don’t understand

Cybernetics, nothing. But they

are with me… et malgré tout

PRAGUE UTIA 1982 5


ACKNOWLEDGEMENTS

I wish to thank the following people for their scientific advice and

guidance, without whom this thesis could not have been realised.

Eng. Miguel Alonso: Former Chairman of the Mexican Association of

Industrial Engineers AMII - MEXICO.

Eng. František Fuksa: Research Institute of Electrical Engineering

VUSE - PRAGUE.

Dr. Jan Voráček: Chief, Chair of Theoretical Cybernetics, Technical

University of Brno VUT - BRNO.

Dr. Andrew Greenshaw: Department of Psychology, University College

Cardiff.

Also I wish to express my gratitude to my tutor Dr. Václav Kudláček of

the Technical University of Brno, for his kind understanding and support of my

investigation.

Finally I am deeply grateful to Dr. Sc. Jan Bureš of the Czechoslovak

Academy of Sciences for his continuous advice and many stimulating

conversations during the three years of my doctorate.

PRAGUE UTIA 1982 6


CONTENTS

Nomenclature 10

PREFACE 11

CHAPTER I 131. Introduction 131.1 Historical aspects 131.2 The principles of regulation 141.3 Economic regulation 18

CHAPTER II 202. The significance of Neurophysiology for Cybernetics 202.1 Introduction 202.2 Structure of the nervous system in the man 232.3 The brain 262.3.1 Function and processes 282.4 Neural electrical phenomena 292.4.1 The propagating action potential 302.4.2 Synaptic signal transmission 322.4.3 Electric model of a neuron 342.4.4 The neural information system 372.5 The regulatory nervous processes 382.5.1 Homeostasis 382.5.2 The reflexes 392.5.3 Memory and learning 392.6 Diseases of the nervous system 412.6.1 Functional disorders 412.6.2 Diseases affecting the control of movement 422.6.3 Language disturbances 43

3.

CHAPTER III

Economic models as cybernetic systems

45

3.1 Introduction 453.2 Model of prices 483.3 Model of business cycles 513.4 Model of global monetarism 533.5 Model of multibranch 563.6 Model of optimization 573.7 Model of accumulation and reproduction 573.8 Model of shaping the national income 60

CHAPTER IV 614. Neurophysiological arrangement of the economic models 614.1 Basic formulae of economic motivation 624.2 Economic homeostasis 654.2.1 Informatic synapses 69

PRAGUE UTIA 1982 7


4.3 Economic anomalies related to physiological concept 694.3.1 Economic stress 694.3.2 Paralysis in Economics 704.3.3 Schizophrenic behavior of some decisions 714.3.4 Afasia of the model 71

CHAPTER V 735 The model restated in terms of microelectronic circuits 735.1 Introduction 735.2 Electro-analogue methods in Economics 755.3 The Enke’s circuits and its role in the development of

economic cybernetics

76

5.4 Keynes’s circuit 835.5 Market prices circuit 845.6 Global monetarism circuit 845.7 Kalecki's circuit 885.8 Leontief's circuit 895.9 Marx's circuit 895.10 Other circuits 895.11 Logical test of the model 89Concluding remarks 91Bibliography 94

APPENDIX : Computer programs 97A.1 Čapekland. System 1: Learning model for economic policy

decision making

98

A.2 Čapekland System 2: General Software 100A.3 Čapekland System 3: Economic and Complementary

models

101

A.4 Some types of reports 108R.1 Vector of total products per year 108R.2 National income 108R.3 Velocity of circulation of money per year 108R.4 Transactions per year 108

R.5 Prices per year 109R.6 Money demand per year and per branch 109R.7 Level of pollution and penalties 109R.8 Level of employment and new demand of labor

power

110

R.9 Employment policy decisions 111R.10 Inflation policy decisions 112R.11 Production policy decisions 113

ADDENDUM : Materials submitted to the Ph.D. Degree Examination 114

PRAGUE UTIA 1982 8


PREFACE to the first digital edition @ 2006 UTEM Santiago Chile 124

PRAGUE UTIA 1982 9


NOMENCLATURE

Cl chlorine

CNS Central Nervous System

CS Czechoslovakia

dc direct current

E amperage

EDAC error detection and correction

EH economic homeostasis

FET field-effect transistors

f ( ) function of

IC integrated circuit

I2L integrated injection logic

i, j, natural numbers

K potassium

LSI large-scale-integration

MOS metal oxide semiconductor

MSI medium-scale-integration

Na sodium

NEH non-economic homeostasis

NS nervous system

PNS peripheral nervous system

p probability

RC resistor-condenser

RND random

S second

Si silicon

Si 02 silicon dioxide

TTL transistor-transistor-logic

t, e time

U voltage

USA United States of America

VLSI very large-scale-integration

x, y, z, variables

α, β, γ parameters

PRAGUE UTIA 1982 10


PREFACE

The ultimate purpose of this thesis is to design a cybernetic model for

the analysis and control of the economy by means of classical

macroeconomic models restated in terms of micro-electronic,

servomechanisms which interact according to principles related to the

functioning of the human nervous system.

First of all the thesis briefly reviews the most important elements and

methods used for the modeling of economic systems at the level of

theoretical cybernetics, developed by the founder of Cybernetics North-

American mathematician Norbert Wiener (1948), by the founder of Economic

Cybernetics Polish economist Oskar Lange and other prominent authors.

For reasons that will be explained later, neurophysiological aspects

prevail in the first part of the thesis. Concepts which may help to explain

complex phenomena formed by the new relations of the modern Economy,

and which may help to control and regulate these phenomena by. cybernetic

means, may be derived from the analogy between the biological and

technical systems.

Mathematical approaches to economic modeling are briefly presented

at a level permitting the construction of models representing the Economy

both as a whole and as parts of the integrated system in a manner used in

analysis of circuits.

We have considered the concept of the economic model as a system

which abstracts some parts of the real world, economic situation. At present

there are several macroeconomic models and many classifications of them.

For our purpose the most accurate classification of such models was

proposed by Kyn and Pelikán (1965) and includes three groups: (we use, it

with 3 additions: business cycles, monetarism and optimization models).

I. Market models : prices; business cycles; monetarismII. Structural models multibranches; optimizationIII. Aggregate growth accumulation; reproduction; shaping models of

national income

According to previous studies it is possible to represent these models

by means of electrical circuits and mathematical equations (including the

PRAGUE UTIA 1982 11


regulation formula).Now we attempt to relate them to the functions of the

human nervous system according to analogies between the economic model

and some parts of the nervous system.

The proposal that the electrical analogy may also be constructed for

economic models is very well known from the 1950s, however. it was

abandoned because of technological restrictions. Now with the appearance of

integrated circuits (e.g. LSI and VLSI) we have a new possibility to apply the

electric approach to some specific economic problems, particularly the

simulation of production processes.

Of course not only the problem of controlling the rate of production of a

single product can be stated in terms of electronic control systems. It is also

possible to examine control problems in economics dynamics which include a

wide variety of economic variables such as, prices, saving incomes,

consumption, investment, exchange rates employment, and others including

social variables like motivation, level of education, health and culture. All

together representing vital functions of the economy necessary to maintain a

certain level of functioning, similar to homeostasis in the living organism.

It is important to note, that this is not an empirical approach which

tends to convert man into an automaton or any commodity. At the information

theory level, it is the application of the very well know dialectical law of the

transition from quantitative to qualitative change. That in our case, to attempt

to transform the decision making process under incertitude into an economic

game with perfect information.

At the same time, not only a physiological method for analysis and

decision making is presented in this thesis. Also (as by-products) economic

formalization are include concerning some neurophysiologic concepts which,

are very pertinent to economics, like paralysis, stress, schizophrenia,

synapses, homeostasis, learning and others. Wherein fact, some of them

already have an old and popular meaning in economics, but previously no

formal definition.

The thesis conclude with some critical remarks on the power of the

applications of Cybernetics in Economics.

Finally, as an appendix, a simplified computer program for the

simulation of this model is included.

CHAPTER I

1. INTRODUCTI0N

PRAGUE UTIA 1982 12


1.1 Historical aspects

Cybernetics is a word from ancient Greek that always was related with

the notion of control. In this language the term kybernetes (κµβερνητηζ)

which derives from kiberno (κµβερνϖ) means to steer. According to this

definition, we can say that in the ancient Greece the first cybernetician

(κµβερνητικη) was a Greek helmsman.

At 1834 Ampere used the word Cybernetics to define the government

sciences, in French "Science du Gouvernement”. It appears under number 83

in the political sciences part of this book.

But only the year 1948 marks the start of this new specific sciences. by the

simultaneous edition in New York and Paris of Norbert Wiener's important

book “Cybernetics or Control and Communication in the Animal and the

Machine". In choosing this term, Wiener recognized that the first significant

paper on servomechanism was published at 1868 by the well known physicist

J.C. Maxwell under the title “On Governors”, where governor is a Latin

corruption of the Greek kybernetes (κυβερνητηζ) but he does not mention

Ampére's book.

It is important to note that the prologue to Wiener's book was written in

México City, Instituto de Cardiología, and the second edition was dedicated

by Norbert Wiener “To Dr. Arturo Rosenbluet for many years my companion

in science” . Scientific collaboration with this late Mexican physician

considerably influenced the first theoretical studies on Cybernetics,

particularly those concerned with the nervous system and the perception of

forms.

For this reason the ideas of Cybernetics are closely related with the

living organism and are based on analogies between the brain and the digital

computer or between the function of the nervous system and socioeconomic

processes.

Of course, scientists have already worked on problems which we

include today in the cybernetics field before 1948. To name just a few:

J.0.Maxwell (1868) with the theory of servo-mechanism who patented in 1769

the automatic regulator of steam pressure in the steam machine, I.P. Pavlov

with the conditioned reflex theory formulated in the first decade of this century

and published in United States of America in 19271, Kolmogorov (1941) with

PRAGUE UTIA 1982 13


a mathematic theory of information, Shannon's independent contribution to

the same topic, Markov’s mathematic chains as stochastic processes.

Other authors made important contributions to this science

simultaneously with Wiener: John von Neumann who founded the theory of

algorithms as a new branch of mathematics and subsequently Stafford Beer

whose use of mathematic rules in management was represented in a

theoretic form by several papers and books and in a practical form by the

cybernetic system of Stafford Beer for control and decision making processes

in the Chilean industrial sector, unfortunately aborted in 1973 by the Chilean

military Junta.

On the other hand, Wiener continued to drift from mathematical problems

towards biology and especially Neurophysiology even including the problems

where Cybernetics impinges on religion. According. to Wiener these are: the

learning problems, the multiplication of the human species and the relation

between man and machine. In 1964 he was visiting professor in Cybernetics

at the Netherlands Central Institute for Brain Research, Amsterdam this

occasion he was editor of the book "Cybernetics of the Nervous System" in

which he stressed the importance of the investigation of this system, including

the cellular level for a development of the Cybernetics. Unfortunately in March

of this same year he died in Stockholm, Sweden.

Curiously, almost at the same time, the founder of the Economic

Cybernetics Oskar Lange died in 1965, also writing (independently on

Wiener) on the importance of the nervous system and on the necessity to

know in detail the function of this sophisticated system.

These are the reasons why aspects of neurophysiology will be given

special emphasis in this thesis.

1.2 The principles of regulation

The first ideas related to Cybernetics were borrowed from Physiology

and from other biologic disciplines, where the principle of organic processes

in the living organisms are maintained in the range which is necessary for

sustaining the vital function. For example in the man, body temperature

should be maintained between 36° C to 37° C, and the level of blood glucose

should be constant at 1 mg/ml. Similarly regulated are the total amount of

water in the body, the amount of energy resources, the osmotic pressure of

body fluids chemical composition of the internal environment (Potassium,

PRAGUE UTIA 1982 14


Calcium, Sodium, and other ions). The regulation of these extremely complex

functions sustained by the nervous system and the hormonal system is

described as homeostasis.

The concept of homeostasis plays a very important role in Cybernetics

and the term is used like a cybernetic word, especially when describing

processes on the basis of body temperature which always serves as an

example of regulation in technical systems. Consider for example a model of

a refrigerator or of a house heating system which maintains the temperature

within certain limits according to the principles of regulation in living

organisms.

A simple representation of a homeostatic mechanism is the thermostat

of the car, as shown in Fig. 1.1 , essentially consisting of an on-off switch

which is connected when the machine temperature rises approximately over

70° C - 80° C, starting the electrical fan, and disconnected when the machine

temperature drops below 70° - 80° C stopping the electrical fan. The aim is to

maintain the machine temperature in this range and to ensure optimal

working conditions of the car.

PRAGUE UTIA 1982 15


Fig-1.1 Functional diagram of the thermostat of the car.

There are many examples of regulation in biological and technical

systems. The principal merit of Wiener was not only the discovery of the

relationships between technological systems and biology but also a

mathematical formulation of a system approach to the control of these

processes. This is illustrated by Fig-1.2, where the input is X, the output in Y,

the motor operator is A, the multiplier operator is λ, and the multiplier operator

produced by the whole feedback mechanism is then A

Aλ+1

.

The output is then and AYXY λ+= and A

XYλ+

=1

or XA

AAY ⋅+

=λ1

which la known as the formula of the regulation.

PRAGUE UTIA 1982 16


Fig-1.2 Wiener’s regulation scheme.

A useful representation of regulation given by Oskar Lange in shown in

Fig-1. 3., where the input is X, t the regulating output is Y, the regulated

system is S, the regulated system is R, and the transmittance ratio in SRS

−1.

Hence we have XSRSY ⋅

−=

1

which is the most simple general formula of regulation, that will be discussed

in detail in section 3.1.

Fig.-1.3 Lange's regulation scheme.

PRAGUE UTIA 1982 17


1.3. Economic regulation

As we known from the preceding section, all regulation problems can

be expressed by mathematical means, especially by the regulation formula,

which finds a very interesting and particular application in Economics. In this

context Oskar Lange pointed out the significance of the Keynesian multiplier

1/( 1- c ), where c is the so called consumption coefficient. which is the ratio

between the net expenditures for consumer goods C, .and the national

income Y. Net expenditures for investments is namely CYA −= or

AYcY =⋅− because by definition YCc = and ( ) AcY =−⋅ 1 .

Hence we obtain Ac

Y ⋅−

=1

1

This is the Keynes’ formula which is a particular case of the basic

regulation formula and is shown in Fig-1.4. In cybernetics terms, the input is

A, the output is Y, the regulated system is 1 the regulating system is c, and

the transmittance ratio is c−1

1, the so called Keynesian multiplier.

Fig-1.4. Regulation diagram of the Keynes’ formula.

We can make many other similar comparisons between Cybernetics

and Economics some of which be explained in section 3.1., but our purpose

is to discover in economic cybernetic models those relations which are

considered important for the understanding and simulation of specific

economic problems, and which on the other hand include human factors. For

example the classical variable used in all national economic models is the

gross product, and the obvious problem is how to obtain its maximization. It is

important and necessary to simulate the functioning of this important

economic variable , but its maximization must be in the best interests of

PRAGUE UTIA 1982 18


society in general, today it is also necessary to include social variables, like

the birth rate or expected life span, which are related to human factors and

offer alternative for the development of the human society. This is one of the

starting points of the line of investigation which we will systematically pursue.

PRAGUE UTIA 1982 19


CHAPTER II

2. THE SIGNIFICANCE OF NEUROPHYSIOLOGY FOR CYBERNETICS.

2.1 Introduction.

At present is very well known that Cybernetics has applied to

Neurophysiology, and of course the opposite is also true. Such links are

fundamental for the design of very sophisticated control systems for research

in control theory, particularly for human communication from

telecommunication and teleprocessing onward to microprocessors networks.

The study of the nervous system was initiated by the ancient Greeks in

the third century B.C., According to Battle's studies, at that time the

relationship between peripheral nerves movement and sensation was known

physicians from the examination of injured patients. But for a long time ideas

on the nervous system were in shadows. From the time of the ancient Greeks

to the nineteenth century, only in the seventeenth century Descartes

contributed to the investigation of nervous functions, when he discovered the

so-called reflex, which explains the reaction of the body through a certain

motor output as a response to some sensory input. The reflex concept formed

the basis for research into the nervous activity in its higher manifestations,

which was initiated by I.P. Pavlov at the beginning of this century.

PRAGUE UTIA 1982 20


He discovered the information of new reflexes in the intact animal, and

the possibility of studying the properties of such responses. called

conditioned reflexes and localized them in the cerebral cortex.

The late nineteenth century was market by the introduction of the

stimulation method as a very important research technique for the

experimental study of the nervous system. First, in 1809 Rolando used with

little success electrical stimulation of the brain in an attempt to find where

movements originated, similarly Flourens in 1850. The connection between

certain areas of the cortex and the contraction of the skeletal muscles was

established in 1850 by Fritsch and Hitzig by means of artificial stimulation of

the cortex. In 1877, Caton's first reports on the fluctuation of electrical

potentials in the brain started another important research method, the

recording of electrical activity.

Toward the end of that century, Waldeyer (1891) argued that the

nervous system in made up of many individual cells called neurons and that

energy is conducted from one to another. This idea was developed by

Sherrington who discovered in 1906 that the most important cellular process

in the nervous system take place at the synapse, that is the junction where

two neurons form a contact (the concept of nervous energy was abandoned

as will be explained in the electrical phenomena section).

PRAGUE UTIA 1982 21


The cybernetic viewpoint can be traced back to an historically important study

on aphasia by Broca (1861) who suggested several possible reasons for the

loss of language ability, which were the starting points for the investigation of

language disorders in man.

Of course there are many predecessors of Pavlov, and the volume of

neuroscience research has been increasing, exponentially in the last fifty

years. The various authors or subjects which are related to Cybernetics

should be mentioned in order to establish functional relationships between

Neurophysiology and Economic Cybernetics:

In this sense the most important topics are: the physiological regulation

processes involved in homeostasis (Cannon 1929, water balance; Ranson

1940, body temperature; Verney 1947, osmoreceptors; Taylor and Farrell

1962, salt balance; P. Milner 1950, Potassium balance; and others), memory

and learning processes (Hebb and Me ton 1961-63, immediate memory;

Warrington and Weiskrantz 1968. amnesia; Bures and Buresova 1963,

consolidation; Cooper and Krass 1963, improved memory; etc ) the

Cybernetics of the nervous system developed by Wiener and Schade in

1964, and new advances in research into signal transmission in the nervous

system (reviewed by Oosting in 1979). This last problem represents the

elementary system of coupled operations which are the key for understanding

the interaction between the parts and the whole in the nervous system,

especially with the help of computers.

PRAGUE UTIA 1982 22


2.2 Structure of the nervous system in the man.

To define the nervous system in living organisms is not an easy task,

because it is the most complicated and sophisticated biological system in

man and other animals, allowing the adaptation of the organism to change in

the internal and external environment. It is important to note that this

coordination in also accomplished through the humoral system, which will be

discussed in relation to the nervous system; especially the importance of the

hypophysis for regulation processes in the brain; and of the thyroid gland for

development of the body and the nervous system.

For our purpose the unicellular organisms and plants are not important

because these have no nervous system. We are interested, however in the

study of the nervous systems of higher organisms piece by piece as par to of

machinery, and particularly in the relationships between neurons as the

building blocks of the nervous system, and in the physiological aspects of the

problem including the nervous diseases.

Anatomically the nervous system of vertebrates is formed by three

main parts shown in Fig-2.1 these are brain and spinal cord which form the

central nervous system (CNS) and the nerves which are referred to as the

peripheral nervous system (PNS).

PRAGUE UTIA 1982 23


Fig-2.1 Structure of the human nervous system.

The motor outflow from the brain to the spinal cord and motor nuclei of the

cranial nerves is mediated by two anatomically defined systems: pyramidal

and extrapyramidal. Physiologically this division is confusing and unfortunate,

because it is difficult to make a clear functional distinction between these two

system which are not anatomically separated. In spite of this the division of

the central system into pyramidal and extrapyramidal systems is useful for

neurology. Lesion of the pyramidal tract from the motor cortex to the synaptic

contacts in the spinal cord cause typical changes of voluntary movements

and muscular tone.

Functions of the extrapyramidal system, that includes the cerebellum

and other centers mediating both voluntary movements and involuntary

movements, are more complex. Some of them can be disclosed by the lesion

PRAGUE UTIA 1982 24


method; thus lesion of the vestibular nuclei reduce spasticity, cerebellar

lesions of the impair equilibrium and cause tremor (ataxia), lesions in globus

pallidus produce tremor and postural rigidity (Parkinsonism) or temporary loss

of strength, lesions of the post central gyrus produce, clumsiness.

The global implication of the above findings are agreement with the ideas of

Lashley (1951) that each movement produces a feedback signal that elicits

the next movement as conditioned reflex. In such a manner each movement

depends only upon the immediately antecedent one, which can be

represented through statistical studies of behavior, by means of Markov’s

chain as follows:

nn PmaP ⋅+=+ 1 (3)

This so called the learning equation and represents the reactions to stimuli as

system of coupled operations are where nP and 1+nP probability of

responses in the time nt and 1+nt respectively. The difference nn tt −+ 1 is

the reflex time or latency of response to stimulus, the parameters a and m are

obtained experimentally.

On the other hand, very important outputs of the central nervous

system, are the parasympathetic and sympathetic nerves, which control the

internal organs.

PRAGUE UTIA 1982 25


2.3 The brain.

The brain is one of the two parts of the central nervous system. It has

the consistency of a raw egg and is and is protected from mechanical

damage by an osseous structure, known as the skull.

The gross anatomy of the brain is show in Fig-2.2, and the functional

aspects are shown in a very simple form in fig-2.3.

The twelve cranial nerves leaving the brain in the skull are: 1. Olfactory, 2.

Optic, 3. Oculomotor, 4. Trochlear, 5. Trigeminal, 6. Abducens, 7. Facial, 8.

Statoacusticus, 9. Glossopharyngeal, 10. Vagus, 11. Accessorius, 12.

Hypoglossal.

Fig-2.2 Anatomical description of the human brain.

PRAGUE UTIA 1982 26


Cranial and spinal nerves mediate the flow of information between the

brain and spinal cord on one side and the sensory and motor organs on the

other side.

Fig-2.3 Functional description of the brain.

Jackson (1870) demonstrated by electrical stimulation that a part of the

cortex controls the motor system.Stimulation of sensory nerves may elicit

reflex behavior. For example Doty and Bosma (1956) showed that the

stimulation of the tongue of a dog produces a swallowing reflex.

PRAGUE UTIA 1982 27


2.3.1. Functions and processes.

The electrochemical and biophysical aspects of brain function at a

cellular level, especially the propagating action potential and synaptic

phenomena will be explained in the next section.

Any brain function should be considered at two principal levels, the

single-cell level and at the level of neural networks that include the

relationships between millions of neurons.

Brain function can be illustrated by the example of a voluntary

movement. In the case showed in Fig-2.4 the problem in to jump across an

obstacle. First the association area of cerebral cortex process the general

situation according to the data flow from the sensory and motivational centers

and sets a goal. This information in transmitted to other parts of the brain,

especially to the cerebellum. Which takes into account a large amount of data

from muscles and joints, and processes them like an intelligent computer, in

order to prepare the exact command for the jump, e.g., the correct starting

position, the muscle force, the body position during the jump, etc.

The brain performs all the most sophisticated processes of the higher

nervous activity, such as memory and learning, conditioned reflexes, sexual

behavior, motivation, homeostatic processes, etc. According Pavlov "The

cerebral hemispheres represent the most complicated, the most delicate

structure produced by the creative power of Nature". We can add today that it

is also the most perfect cybernetic system.

PRAGUE UTIA 1982 28


Fig-2.4 Connection between the cerebral cortex and the cerebellum for the

voluntary movement. (adapted from Schmidt, 1975).

2.4. Neural electrical phenomena.

The main purpose of this section is to present the most important

processes in the nervous system at the cellular level which are relevant to

cybernetics economic models.

Two electrical phenomena are basic to the function of the nervous

system: the propagating action potential and synaptic signal transmission.

PRAGUE UTIA 1982 29


2.4.1. The propagating action potential.

The neurons are the integrative units of the nervous system. They are

extremely complex and vary widely one from another, but the general plan is

always as shown in Fig-2.5

Fig-2.5. Schematic diagram of a neuron

The three main parts of the neuron are: the soma or cellular body, the

axon which is a nerve fiber. Whose function is to link the nerve cell with other

cells (nerve cells, muscle cells or glandular cells) and the dendrites which are

outgrowths of the soma extending its receptive function.

Extremely important for our investigation is the knowledge about the

cellular membrane that encloses the cellular fluid, so called cytoplasm, and

separates the intracellular fluid from the extracellular fluid surrounding it.

An unequal distribution of ions (particularly of Potassium and Sodium)

inside and outside the cell is the source of the potential difference between

the intracellular and extracellular fluids, called the membrane potential

(resting membrane potential when the cell is in a resting state). The most

important ions contributing to the membrane potential are K+, Na+, and CL-.

To propagate changes in this membrane potential, and to transmit them to

other cells is the specialized role of the nervous system.

PRAGUE UTIA 1982 30


The activity of a neuron is manifested by a sequential process of

membrane depolarization and repolarization, called the action potential. As

shown in Fig-2.6, the action potential consist of five main phases:

Fig-2.6 Diagram of the time course of a nerve action potential.

(Schmidt, 1975).

1. Threshold potential from which action potential starts.

2. Depolarization that includes the rising phase or upstroke.

3. Overshoot or reversed polarity of the membrane.

4. Repolarization from the peak of the action potential back to the

resting potential.

5. After-potential, which are the potential patterns at the end of

repolarization phase, called repolarization after potential

and hyperpolarization after-potential.

The resting potential, in the first approximation is the potassium

equilibrium potential and the quantitative relationship is expressed by Nernst

equation as a follows:

⋅

⋅⋅=

ionconcentrationicracellularionconcentrationiclarextracellu

FZTRE

__int__ln

In which:

R = gas constant T = the absolute temperature

F = Faraday constant; Z = valance of the ion

For potassium ion (K+) in the mammalian brain this equation reads:

PRAGUE UTIA 1982 31


[ ] [ ]mVKK

mVEo

ki 90log*61 −=

−= +

+

( assuming that 30=

+

+

oKK i

)

It is necessary to note that the ionic permeability of the membrane is called

membrane conductance and for the K+ is expressed by

K

KK EE

IG−

=

In which IK = net potassium flux

E = membrane potential

EK = equilibrium potential for K+

And similarly for Sodium Na

NaNa EE

IG−

=

2.4.2. Synaptical signal transmission.

Another important phenomenon at the neuron level is the synaptic

signal transmission. It occurs at the junction between an axonal ending and a

nerve cell, when the propagated action potential arrives at the synapse.

There are two kinds of synapses: the rather rare electrical synapses,

most frequently encountered in the brains of fishes or lower vertebrates, and

the chemical synapse which is more common.

The electrical synapses. is characterized by tight coupling between two

nerve cells that permits direct electrical transmission of signals. In chemical

synapses the two cells are separated in the region of contact by a gap filled

with extracellular fluid. In this paper we will restrict ourselves to chemical

synapses only.

Fig-2.7.illustrates the main structural elements of the chemical synapse

diagrammatically.

PRAGUE UTIA 1982 32


Fig-2.7. Diagrammatic section through a chemical synapse.

The six important parts are:

1. Axon

2. Presynaptic terminal or axonal ending which contains the synaptic vesicles.

3. Synaptic vesicles which contain the transmitter substance.

4. Synaptic cleft or gap between the presynaptic terminal and the

postsynaptic side.

5. Postsynaptic cell (e.g. a dendrite, neuronal soma, or muscle fiber).

6. Subsynaptic membrane is a parts of the postsynaptic cell forming the

boundary of the synaptic cleft.

The chemical structure of all transmitter substances has not yet been

identified, and the same is true for the enzyme systems inactivating the

transmitter substances.

Chemical synapses can transmit signals in one direction and resemble

thus a diode. Unfortunately we know little about the events occurring between

the arrival of the action potential in the presynaptic terminal and the onset of

the postsynaptic potential. This is an extremely important problem for the

neurophysiology and neuropharmacology, critical for our understanding of

brain plasticity and processes underlying memory and learning; conditioned

reflexes and of course human consciousness language and thought.

According to recent estimates each neurons possess up to 60.000 synapses,

some of them excitatory and some inhibitor.

The spatio-temporal pattern of excitation and inhibition at the multitude

of synapses produces a mosaic of local potential differences. The excitatory

PRAGUE UTIA 1982 33


postsynaptic potential depolarize the membrane and can eventually excite the

neuron. The inhibitory postsynaptic potentials hyperpolarize the membrane

and are thus like the mirror image of the excitatory postsynaptic potentials.

The effect of excitatory synapses can be prevented by simultaneous

activation of an appropriate number of inhibitory synapses.

2.4.3. Electrical model of a neuron.

Some of the properties of the action potential can be modelled when

the axon in represented by a uniform cylindrical cable, shown in Fig-2.8-

Fig-2.8. Schematic drawing of a cable mechanism for the linear membrane

case.

In which:

A = cable radius.

ri = resistance per unit length of the axoplasm.

rm = resistance per unit length of the membrane.,

ro = resistance per unit length of the surrounding medium.

cm = capacitance per unit length.

vm = vi - vm membrane potential.

ii = inside current per unit length in the x direction.

io = outside current per unit length in the x direction.

im = membrane current per unit length in the x direction.

Without current sources or sinks, the potential is described by the

following equations.

iii irxV

⋅=∂

∂ ; oo

o irxV

⋅−=∂

∂; m

oi ixi

xi

−=∂∂

−=∂∂

PRAGUE UTIA 1982 34


ooiioim riirxV

xV

xV

+−=∂

∂=

∂∂

=∂

∂ ;

miooo

i

ii

m irrrxi

xi

rxV

⋅+=∂∂

+∂∂

−=∂

∂)(2

2

or ionmmoi

mm Idvc

rrI

xVi +⋅=

+⋅

∂∂

= 2

2

(6)

The membrane potential consists of two components: capacitive

current potential and ionic current. For current spread and for analysis of the

propagated action potential it is necessary to solve this equation (6), so called

general cable equation.

PRAGUE UTIA 1982 35


An electrical analog model for a neuron assumes that the membrane

behaves like the RC circuit shown in Fig-2.9., and described by formulae (7)

and (8).

Fig-2.9 Electrical analog model for a neuron

The circuit can be presented separately (Fig-2.10)

Fig 2.10 Action potential of a neuron, simulated by means of a RC circuit.

PRAGUE UTIA 1982 36


2.4.4. The neural information system.

The specific role of the nervous system is to generate and transmit

signals in the form of impulses (the propagating action potential).Then in

terms of telecommunication engineering, the encoding process can be

described by converting the nerve impulse to an amount of information.

The relationship between the colloquial term information and its

representation by a numerically measurable quantity was discovered by

Shannon. In the probabilistic model, the elementary data which can be stored

or transmitted are called bits (binary digit 0, 1) and the amount of information

can be expressed by binary numbers, as a combinatory rule

)2,.........2,2( 21 m , where nm =2 is the number of possible combination

or different messages, and ( )nm 2log= bits is called the average

information content, or ( )nI 2log= .

Secondary the foregoing formula must be applied to the nervous

system as follows: ( )1log max2 +⋅= tFm , because here n is equal to the

number of distinguishable states of the discharge response in the afferent

nerve, and which t is equal to observation time, and Fmax is the maximal

discharge frequency in the nerve fiber. With this parametrical formula, we can

obtain a family of curves for the information capacity of a nerve fiber by

means of the time parameter as shown in Fig-2.11.

The quantitative methods for calculating the amount of information in

various regions of the nervous system are very important because they make

it possible to describe the state of this system region by region or as an

integrated entity.

PRAGUE UTIA 1982 37


Fig-2.11. Information capacity of a nerve fiber

2.5. The regulatory nervous processes.

2.5.1. Homeostasis.

In section 1.2. “The principles of regulation" the homeostatic processes were

described as maintaining constant internal conditions of the organism.

Homeostasis in a wider sense also includes defense, consummating and

reproductive behaviors, which are controlled by the hypothalamus in close

collaboration with the hormonal system. A tight correlation between nervous

and humoral controls is essential for the constancy of the internal

environment and normal behavior, itself a manifestation of higher nervous

activity, and a necessary condition for mental function. This is the reason why

hormonal secretion exerts an extremely important influence.

Countless experimental studies indicate that learning depends on the

interaction between sensory system reticular mechanisms and motivational

centers. The failure to demonstrate the isolated localization of memory traces,

suggest that it is a function of all of the brain. In this case special significance

is ascribed to the hippocampus, because hippocampal lesions impair

learning, but leave long-term memory intact in man. The same lesions are

less effective in other animals, perhaps because the role of hippocampus is

different.

Neurophysiologic memory is often compared with the genetic storage,

which can be considered a specific case of memory in the wide sense of this

concept. It must be assumed that the former is the consequence of individual

learning, whereas the latter reflects the evolutionary experience of the specie.

PRAGUE UTIA 1982 38


Recording of the electrical activity of the brain during learning may

reveal the structures involved, and detect changes in the neuronal networks,

which may store the experience of the organism. New or modified

connections in the neural network represent the engrams or memory traces.

This also explains the inseparability of memory and learning.

Each new engram can be easily disrupted by interference with brain

function. With the passage of time, memory becomes more resistant to

disruption, a process called consolidation.

Experimental approaches to the study of the formation on homeostatic

processes and/or intelligent behavior.

Homeostasis is a subset of the regulatory nervous processes in the

living organism, that include in order of increasing complexity: reflexes;

homeostatic processes; memory and learning; and decision making

processes.

2.5.2. The reflexes.

The unconditioned reflexes are stereotyped reaction of the CNS to the

sensory stimuli. The underlying neuronal network extends from the peripheral

receptor through the CNS the peripheral effector. They are called

polysynaptic or monosynaptic reflex arcs (according to the number of

intervening synapses in a complex or a simple reflex, respectively).

The degree of complexity can be evaluated from the reflex time (time

between stimulus onset and the reaction of the effector).

A reaction elicited by two simultaneously applied stimuli is either

greater or smaller than the sum of reactions elicited by the individual stimuli.

These phenomena are called facilitation and occlusion, respectively.

2.5.3. Memory and learning.

Despite the progress of neurophysiology in this century, it is impossible

to answer the questions such as “where does the learning process take

place?”, and "where are memory traces (engram) stored in the brain?”.

Answering these two questions will not only expands human know ledge but

may also have far reaching social effects.

PRAGUE UTIA 1982 39


And consolidation of memory traces in animals can be illustrated by the

following example from Bureš (1963) shown in fig-2.12.

Fig-2.12. The apparatus used by Bureš and Burešova for the consolidation

tests.

The experiment consists of three stages, as follows:

On the first day the animal (rat) is placed into the large compartment

and the door between the large and small compartments is open. After three

minutes of exploration the animal is returned into the home cage. The rat

spent 80% of the three minutes of exploration in the small compartment and

only 20% in the large compartment. On the second day the rat is confined in

the small compartment for one minute, and electrical foot shock is applied.

On the third day the situation is the same as on the first day, but now the rat

remains 90% of time in the large compartment and only 10% in the small

compartment. This avoidance of the small compartment indicates that the rat

has learned where the danger is, and remembers it despite the passage of

the time.

PRAGUE UTIA 1982 40


2.6. Diseases of the nervous system.

Nervous diseases can be classified as functional or organic.

Organic disorders are due to some damage of the central or peripheral

nervous system, caused by injury, disease, intoxication, etc. In all case there

is some anatomical defect in the nervous system.

In case of functional disorders, the general architecture of the nervous

system is normal, but its function is abnormal. The malfunction is due to

various factors that may influence the nervous system such as to excessive

fatigue, or exhaustion.

2.6.1. Functional disorders.

Stress: by stress we mean excessive demands on the functions of the

body, by neural stress: demands on the activity of the nervous system. Stress

affects not only the nervous system, but also the endocrine system, and the

general metabolism of the body.

Neural stress prevails in people working in difficult tasks, e.g. a radar

operator, or an executive in a large company. Neural stress may cause some

kinds of neurosis or various somatic symptoms, e.g. high blood pressure,

cardiac infarction, or peptic ulcers.

The most common symptoms of neurosis are anxiety, irritability,

depression, exhaustion.

Although neurosis is typically encountered in adults, it also exist in

children. Symptoms of the neurotic behavior of a child are varied, mostly in

the sphere of social interaction with parents, teachers and other children.

Psychosis: whereas neurosis is a purely functional disorder of the

nervous system, and can be completely cured psychosis may be due to some

metabolic or anatomic irregularity of the brain.

The most typical symptoms are:

- Hallucinations; the patients hears, sees, or smells,

things not existing in reality

- Confabulation: The patients makes complicated stories,

e.g. about other peoples conspiring against him.

PRAGUE UTIA 1982 41


- Catatonic stupor: The patients assume a bizarre posture

and refuse to change it.

- Paranoia: Psychotic state characterized by confabulations

of persecution and delusion of grandeur.

- Manic-depressive: A psychotic state characterized by periods of extreme

activity, social contacts, writing letters, and hard work alternating with periods

of depression when the patient is incommunicative, melancholic, and prone to

commit suicide. The depression is fallowed by a new manic period.

- Schizophrenia: Is a wide-spread mental disease usually appearing in young

patients (about twenty years old), and characterized by the incapability to use

the well-preserved intellectual powers for meaningful goals.

Loss of motivation, inactivity and stupor alternate with agitation and

aggressiveness. Between periods of illness the patients behave normally, but

must be hospitalized during treatment and subject to permanent supervision,

when out of the psychiatric ward.

- Complexes: In Psychiatry a complex is a strong irrational

feeling about something. The guilt complex appears in a person who believes

that he is responsible for a tragic event e.g. f or the death of a child in a car

accident. The inferiority complex is evoked by an inability to cope with the

problems of every day life.

2.6.2. Diseases affecting the control of movement.

Paresis and paralysis: Paresis is weakness in a limb or muscle.

Paralysis is the inability to move some parts of the body. It is a typical

symptom of a cerebral hemorrhage or an occlusion of the vessels which

supply a certain parts of the brain. Damage to the left hemisphere usually

results in a loss of speech. The patient is not able to speak and may not even

understand spoken language. At the same time the right hand and leg are

paralyzed. This state is called hemiparesis or hemiplegia.

The lateralization of the above symptoms indicates that the

hemorrhage in restricted to the left half of the brain which controls muscles of

the right side of the body and receives sensory input from the right hand or

leg.

PRAGUE UTIA 1982 42


The vascular damage is lateralized because left and right carotid

arteries provide blood supply for the left and right half of the brain,

respectively. Small connecting vessels are not strong enough to compensate

from the occlusion of one carotid and the resulting damage is therefore

limited to one half of the brain.

Paraplegia and hemiplegia: Paralysis effecting both sides of the body

(both legs or both arms) is called paraplegia while hemiplegia is limited to one

side. Paraplegia in a typical syndrome of injury of the spinal cord.

When the spinal cord is severed at the level of the chest both legs

become paralysed because the motor control to the legs transmitted through

the spinal cord. The result is permanent paraplegia, which leaves the patient

paralysed for all his life, is common in car accidents or war injuries.

Paraplegia at the level of cervical spinal cord (or neck) may cause

immediate death by arrest of respiration and suffocation due to paralysis of

respiratory muscles.

Epilepsy: is a disease manifested by fits of local or generalized activity

of muscles, which either are rigidly extended or contracted for a few tens of

seconds or are involved in alternating flexion and extension movements, it is

tonic or clonic seizures or convulsions.

Myasthenia gravis: is a muscle disease characterized by muscular

weakness due to the impairment of neuro-muscular transmission.

Ataxia: Lesions of cerebellum cause ataxia manifested by unsteady

gait and impairment of voluntary movement due to incorrect movement

programming.

Parkinsonism: Destruction or degeneration of the subcortical centers of

the extrapyramidal system (basal ganglia) is the basis of the so called

Parkinsonism, which is characterized by two principal symptoms: muscular

rigidity and continuous tremor which disappears only during sleep.

2.6.3. Language disturbances.

Aphasia: Is a loss of language ability. Patients can understand speech

but cannot produce it (expressive aphasia) or they can write, but do not

understand spoken or written words.

Inability to communicate either by speech or writing is called verbal

aphasia, and the inability to read is alexia or dislexia when it is a less severe

disturbance of reading ability.

PRAGUE UTIA 1982 43


Other kinds of language disability are when the patient is unable to

name common objects (nominal aphasia), or responds with unintelligible

statements (jargon aphasia). Patients who can speak accurately enough but

are incapable of making spontaneous statements of more than a few words,

are said to have dynamic aphasia.

PRAGUE UTIA 1982 44


CHAPTER III

3. ECONOMIC MODELS AS CYBERNETIC SYSTEMS

3.1 Introduction

Economics is one of the oldest science, that like other branches of

knowledge studies a specifics subject. But from earliest times economic

schools have been created by different and sometimes antagonistic groups of

society in different countries, and different epochs.

On the other hand, Cybernetics as we have already stressed is one of

the youngest sciences. Curiously, Cybernetics and Economics are very close

because economists are always engaged in problems where Cybernetics

impinges on Economics as in the study of economic regulation processes in

the broadest sense.

In the ancient times the economist sought to formulate the rules of an

incipient market, and later also the laws governing the development of the

economic world, which we define today as an application of Cybernetics in

the investigation of economic processes. Currently this means, first, to know

the functioning of these processes (control), and secondly, to orient this to

specific goals (regulation). Of course we assume as obsolete the premises of

laissez-faire, which were criticized by socialist economist, in the last century

by Marx and later also by capitalist economists like Keynes who saw the

capitalist Economy as a self-regulating system, similar to homeostatic

processes.

After the great crash of 1929 in USA Keynes confirmed the necessity

to introduce into the capitalist Economy, regulatory processes such as state

intervention, planning of public budget, including social and military affairs,

and at present in apparent contradiction with Keynes and other similar

economists like Galbraith (1969 -1975) the strategic planning of the large

transnational companies at a world level, which is one of the most important

results of the application of the Chicago School which Friedman (1977) is

now the world-acknowledged head. Contrary to this, the main technical

purpose of the socialist economies is harmonious regulation of economic

processes by means of centralized economic planning. But in fact, both

PRAGUE UTIA 1982 45


capitalist and socialist economists tries to control the economy by means of

regulatory processes.

In this way the role of Cybernetics is relevant and independent of the

economic schools. Many examples can be given for almost all possibilities

from global monetarism, to planned economies including specific applications

in developing countries.

But, how are we to find the role of Cybernetics in modern economic

though, when clearly at present we have economic system which are

contradictory, antagonistic and irreconcilable?. What groups and classes of

society should we emphasize?. A complete treatment of these questions is

far beyond the scope of this review. Only a partial reply and a brief

presentation of the kind of economic processes that are generally used in

Cybernetics and particularly economic models will be given in this chapter.

In this way, it is important to note, that from ancient times to the

present day there have been many attempts to understand the function of the

economic system, including political or philosophical as well as statistical,

social, psychological and other points of view where Cybernetics is not a

substitute for the above approaches. For that reason the aim of this section is

to present a brief review of the most important mathematical economic

models re-stated in terms of servomechanisms which are useful for model

building in Economic Cybernetics. They represent mathematical systems

which abstract some real-world economic situations so that this set of

assertions or axioms, expressed by means of equation, is not self-

contradictory and that there is a non-empty domain of possible applications to

regulation.

For our purpose the most accurate classification of such models was

proposed by Kyn and Pelikán (1965). We use it with three additions, which

are the follows: the model of business cycles, the model of optimization and

the model of global monetarism. According to these authors, there are three

main groups of these models :

I. Market models - models of prices

- models of business cycles

- models of global monetarism

PRAGUE UTIA 1982 46


II. Structural models - models of multibranches

- models of optimization

III . Aggregate growth models - models of accumulation

- models of reproduction

- models of shaping the

national income

These models will be briefly explained one by one , and at the same time

re-stated in terms of servomechanisms , according to the integrated

circuit technology used in Chapter 5 . , where these models are all joined

together as an integrated system according to principles related to the

functioning of the human nervous system .

It is important to note , that while in some cases we will use the

servomechanism as an electrical analogy of a model ( first case ) , in other

cases only mathematic servomechanism will be used , represented by

means of the regulation formulae ( second case ) . However in all this

cases we attempt to represent the models in a manner commonly used

in electrical circuits at a large or at very large scale of integration ,

particularly bipolar technology ( first case ) and microprocessors ( second

case ) , as will be explained later in Chapter 5.

PRAGUE UTIA 1982 47


3.2 Model of prices

This model abstracts a supply and demand situation in the free market,

assuming market equilibrium when demand D of consumers equals supply S

of goods, and this intersection point C determines the price P of the goods at

time t. Which may be illustrated as in figures 3.1 and 3.2, and represented by

the following equations for a linear case.

1+⋅+= tt PaS α 1+⋅+= tt PbD β

( )ttttt SDPPP −⋅=∆=−+ γ1Where a, b, α, β, γ are parameters determined by econometric

methods.

In every period t an equilibrium point C may be obtain at which stability

depends on the dynamic interaction between the quantity produced QP at the

lowest price PS and the quantity exchange. Qe at the demand price Pd. The

prices are variables which oscillate around the final equilibrium point for each

particular period of time.

A very difficult problem in the formulation and computer programming

of this model as a mathematical servomechanism is the derivation, with

respect to time, of the equations able to describe this oscillatory behavior, in

which the employment of differential equations is necessary.

For the above reasons, and in addition to postulate a linear functions

for demand and supply, which is a gross simplification to the properties of the

process of

PRAGUE UTIA 1982 48


Fig- 3.1. Block diagram of the process of shaping prices.

Fig-3.2. Equilibrium point of the final price.

PRAGUE UTIA 1982 49


shaping prices. We prefers re-state this model in electrical terms, according

to an electro-analogue method proposed by Moerhouse, Strotz, and Horwitz

(1950), which use linear and nonlinear circuit systems for simulating of

shaping prices in a dynamic market. In a very short terms we can say that

they propose the following analogies, term by term between these economic

processes and theirs electrical circuits of simulation.

Economic processes Electrical circuits

concepts concepts

- flow of goods - current

- incentives - voltage

- inertias - inductance

- inventory - capacitance

equations

ed QP ⋅−= 11 βα 1111 IRVE ⋅−=

ss QP ⋅+= 22 βα 2222 IRVE ⋅+=

pssd QQPP ⋅+⋅=− 21 λλ221121

••⋅+⋅=− ILILEE

( ) 110

0

1 PdtQQQPPt

tpeed +⋅−⋅+⋅=− ∫γ

λ ( )∫ +⋅−⋅+⋅=−• t

tiEdtII

cILEE

0

2111011

( ) 120

0

1 PdtQQQPPt

tpeps +⋅−⋅+⋅−=− ∫γ

λ ( )∫ +⋅−⋅+⋅−=−• t

tiEdtII

cILEE

0

2122021

Where the dot indicates a derivatives with respect to time.

PRAGUE UTIA 1982 50


On the basis of electrical laws and from the above circuit equations

may be constructed as shown in Fig-3.3, which in chapter 5 will be restated in

bipolar terms of integrated circuit.

Fig-3.3. Electrical circuit of the prices model.

3.3. Model of business cycles.

This so called Kalecki's model in honor of the polish economist Michael

Kalecki (1935) who first postulated a mathematic equation system that takes

into account several macroeconomic dynamic variables, such as

consumption income, investment, depreciation, distribution, production,

increase of capital goods and stock of investment goods.

For similar reasons in section 3.2 and according to an electric

analogue for this economic model described by Smith and Erdley (1952). We

obtain the following 4 main equations as a circuit analogue of the Kalecki's

model:

PRAGUE UTIA 1982 51


( ) ( )etItL −=

( ) dtULKt

⋅−= ∫0

( ) dtLIe

At

⋅−⋅= ∫0

1

( ) kNCAKnBI ⋅−+⋅−

=⋅−⋅=λ

αα1

Where the variables are defined as follows:

K = stock of investment goods, L = production of investment goods, A =

capital goods, B = national income, C = total consumption, I = total net

investment, t and e are time periods, U = depreciation and n, α, γ, are

parameters. (see p.118)

Fig-3.4. Cybernetic diagram of the global monetarism model.

PRAGUE UTIA 1982 52


3.4. Model of global monetarism.

At the present time this is one of the most controversial but also most

powerful models for the analysis and direction of economic phenomena at the

world level. Changes and improvements in the first monetarism approaches,

created very sophisticated mathematical models, that will now be presented

in a simple form, according to the model proposed by Bilson (1979). It is

based on the following set of assumptions: integrated world commodity

markets and exogenously determined domestic price level, exogenous real

national income and interest rate, a stable money-demand function relating

price levels interest rates and real income.

One of the last improvement to the model which was made by

Karacaoglu (1980) demonstrated that the expected sign and magnitude of the

interest rate elasticity of international reserve flows will crucially depend on

money-demand functions across countries. This means that the relationships

between the size of countries and degree of elasticity of money-demand must

be taken into account because the model is inconsistent when the money

demand functions are assumed to be identical across countries.

On the basis of the Bilson's model (1978) Karacaoglu proposed the

following system of dynamic equations for the global monetarism model.

PRAGUE UTIA 1982 53


1uYPM iD ⋅+= − βα

( ) ( ) ( ) ( ) 2uwYwiwPwM D βα +⋅= −

DMM =

( ) ( ) DwMwM =

Where the variables are defined as follows:

M = stock of minimal money balances demanded

P = price level

I = nominal rate of interest

y = level of real income

M = nominal stock of outstanding money balances

S = exchanges rates

W = indicator for the foreign affaires

U = stochastic disturbance terms

α, β = parameters

Future studies on monetarism which reflect the economic world activity

will be followed by new changes in this model which at present do not have

an electro-analogue representation, however, a very good simulation by

means of digital computer it is possible to obtain in developed capitalist

countries. In our case the problem to transform this model to

servomechanism systems is solved as follow:

αβ −⋅+⋅= 1111 1iPUYMD

αβ −⋅+−= 22222 iPUYMD

PRAGUE UTIA 1982 54


1

11

1

MDuY

m Y

⋅=

β111 1uYMDm Y ⋅=⋅ β

( )2

2.2 MD

ipm ip

α−⋅= ( )

α−⋅=⋅ ipMDm ip 22.2

Where by definition:

( ) 1.11 =+ ipY mm

( ) 1.22 =+ ipY mm

11111 ipMDmMD Y ⋅+⋅= ( ) 2.2222 MDmuYMD ip ⋅+⋅= β

111

1 11 ipm

MDY

⋅⋅−

=( )

22.2

2 11 uYm

MDip

⋅⋅−

= β

Considering that:

( ) 12

22

2

22.22 =

⋅+

⋅⋅=

−

MDip

MDuYmm ipY

αβ

We obtain:

( )

22

11

1

2

22

11

1

.2

2

1

111

uYip

mm

uYip

mm

MDMD

Y

Y

Y

ip

⋅⋅

⋅−

=⋅⋅

⋅−

−= ββ

222

11

1

21 1

MDuYip

mmMD

Y

Y ⋅⋅⋅

⋅−

= β

( see figure 3.4 )

which is the relationship between foreign and national stock of minimal

money balances demanded.

PRAGUE UTIA 1982 55


3.5 Model of multibranch

These models represent a very good review of the Economy, branch

by branch particularly in terms of flow between branches, and many other

relationships which make it possible to simulate the behavior of one branch or

of the Economy as a whole. For this reason operational research has a very

good domain of applications here.

In a simple form they are represented by the following linear system of

equations (the nonlinear will be not be discussed in this section)

iiniii YcccX ++++= ...................21

or as input-output matrix

( ) YAIX ⋅−= − 1

Where

A = matrix of input coefficients

I = unit matrix

ija = outlay coefficients of the means of production

iY = final products

ijX = global production by branch

ijc = flow between branch i to branch j

Due to Leontief’s matrix relationships which represent all this model,

we can restate these kind of model in electrical terms or directly with

microprocessor technology such manner to simulate the servomechanism

that we need.

PRAGUE UTIA 1982 56


3.6 Model of optimization

Other simulation models, for example those used by Orrego,

Santamaria, de la Barra, Covarrubias (1979) and Foxley (1975) in the case of

Chile, or other authors that are building economic models for optimization of

the economic function in a specific country, are represented in a matrix

formulation by the following system, of equation.

minimize (or maximize) cXdZ +=

subject to the constraints0≥

≤X

BAX

where X = program vector or decision variables

A = coefficient matrix

B = constraint vector

C = cost vector

d = constant cost vector

As already we have learned, both models, multibranch and

optimization are structural models, for this reason-matrix relationships are

included, and of course the representation of them in electrical terms or

microprocessors is similar. In the second model the principal problem to solve

will be the optimization function or other economic function out of the matrix.

3.7 Model of accumulation and reproduction

These are two models which can be joined into one corresponding to

the Marxist scheme of accumulation and reproduction on an extended scale.

PRAGUE UTIA 1982 57


On the basis of this model we can study the relationships between constant

capital and surplus-value and also between the branches of the Economy,

which permit predictions of the structural development of economic growth,

and of the technological changes represented in production processes,

including the labor variable.

The well known "second illustration" of the schematic presentation of

accumulation and reproduction on an extended scale is given by Marx (1893)

in the second volume of the Capital. It has two basic branches: I, reproduction

of means of production and II, production of articles of consumption, where

the ratio of surplus-value to variable capital s: v = 1 : 12 and the general

average ratio of the variable capital to the constant capital v: c = 1 : 5 (v,

variable capital, c =constant capital, a = surplus-value).

In this historical illustration given for three years we have in the first

year the following equation:

First year

( ) ( ) 500,6083,1147,583000,1417000,5 =+=+++ vcvsvcsc

( ) ( ) 899,1316583,11799,283500,1 =+=+++ vcvsvcsc

399,8=total

PRAGUE UTIA 1982 58


Now we can represent these equation as follows:

iiniii YcccX ++++= ...................21

i

ijij X

ca = nji ,....2,1, =

The first equation represents the inter-branch flows, the second

equation gives the outlay coefficients of the means of production and the

outlay of direct labor is ( )ii sv + :

Where iX = value of total production in branch i

ijc = value of inter branch flow of the means of production

from branch i to branch j

iv = outlays of labor in branch i

is = value of surplus-product in branch i

By inserting the term aii into the first equation, we obtain

iiiniiiiii svXaXaXaX ++⋅++⋅+⋅= ...................21

or in servomechanism form:

( )iiniii

i svaaa

X +⋅+++−

=...................1

1

21

This important equation above permits us to represent these models

by means of integrated circuit technology.

On the other hand, both models have an electro-analogue

representation, according to the mathematical description given by Lange

(1969).

PRAGUE UTIA 1982 59


Such an electric circuit has been constructed by Górecki and Klapkowski,

member of the Chair of Automation at the Academy of Mining and Metallurgy

in Cracow, Poland. At present this electro-analogue model is at the Political

Economy Department of Warsaw University but only for pedagogical

purposes because of technological restrictions in comparison with the modern

digital computer.

3.8 Models of shaping the national income

This model, very well known after the economical crisis of 1929 in the

United States of America was first postulated by Keynes, the elements of

which are explained in section 1.3.

According to Tustin (1957) an electrical generator (dynamo) that is

partly but not wholly self-excitation satisfies relationships identical in form to

those of Keynes's model. Then comparing term by term we have:

Keynes's model electrical analogue

cAI

−⋅=1

1 dynamo

A = investment separate excitationI = income total excitation

C = propensity to consume ratio of transmittance

c−11

Keynesian multiplierfeedback multiplier

However a dynamo is an electromechanical device. Since it is

necessary to establishment the correspondence between a mechanical and

electrical system. An equivalent circuit of a separately excited de machine

proposed by Vowels & Forte (1952) is pertinent for that purpose. But it is

very complicated to transform to integrated circuits, for that reason we prefers

the mathematical servomechanism method, an we will be showed in section

5.7.

PRAGUE UTIA 1982 60


CHAPTER IV

4. NEUROPHYSIOLOGICAL ARRANGEMENT OF THE

ECONOMIC MODELS.

According to section 1.2, the basic formula of regulation SRSY

−=

1

can be divided in two parts, it is, S and SRS

−1 where S is the transmittance

ratio of the regulated system and SR−1

1 is the operation of governor, which

can be written as an infinite geometric series, when the absolute value of SR

is less than 1.We have then:

( ) ( ) nSRSRSRSRS ++++=

−...............1

12

then:

( ) ( )( )XSRXSRXSRXSY n ⋅++⋅+⋅+= .........2

If we take into account the time variable t, and let us assume that 1−tY in the

value- of Y in the previous period t, we have then ( )1−⋅+⋅= ttt YRXSY

Similarly in the Keynes' formula c

Y−

=1

1 also may be represented by

means of the following geometrical series when 1<c and:

mCACACAAY ⋅++⋅+⋅+= ...........2

Let us assume that 1−tY is the value of Y in the previous period t, then:

11 −− ⋅+= ttt YcAY

PRAGUE UTIA 1982 61


In this case the oscillation on the course of time depends on the value of c,

which is the consumption coefficient. It reflects attempts to achieve the

stability of the economic system by the control of consumption. Historically it

is a very unpopular approach producing political problems even in countries

where consumption is maintained at a high level.

4.1. Basic formulae of economic motivation

Another types of political decisions, which are more intelligent than that

mentioned above, tries to control the Economy by means of incentives, where

the individual members and groups of society are converted into the players

of a big game controlled by the government or by a similar institution. At

present the digital computer has been playing an important role in this

context, because of the possibility to simulate economic political decisions

before they are applied to the Economy.

In section 2.2. “The structure of the human nervous-system”, we have

shown that the learning equation is as follows:

1−⋅+= nn pmap

When ∞→n ppp nn ˆ1 == +

Hence pmap ˆˆ ⋅+=

Or m

ap−

=1

ˆ and ( )bam +−= 1 where a and b are negative and positive

stimuli. respectively, and 10 <+< ba is the intensity of incentives. Then

we can write:

baap+

=ˆ or

1ˆ

+=

ba

ba

p

PRAGUE UTIA 1982 62


but ba is the structure of motivation. For instance, if 3=b

a it means that

the positive incentives are 3 times greater than the negative incentives and

75,0ˆ =p .

In the economical case, positive incentives are profits and negatives

incentives are losses. Of course both concepts of profit and loss are

understood in a wider socioeconomic sense.

On the other hand, as we have learned, in neurophysiology exist the

physiological cycle: memory-learning-motivation will be represented in a first

approach as the economic processes: accumulation-reproduction-economic

politics, respectively. Of course it is in the interest of the society that,

reproduction increases with minimum oscillations, which is very close with an

appropriate economic politics.

If in time 1+= ntt the magnitude of deviations (oscillations) from the

optimal trend p̂ is ppp nn ˆ11 −= ++ we obtain the following equation:

baapp nn +

+= ++ 11

By substituting in the equation of learning, we obtain the following

expression:

nn pmaba

ap ⋅+=+

++ 1 or ba

apmap nn +−⋅+=+ 1

But bam −−= 1 ; ppp nn ˆ+= ; ba

ap+

=ˆ

Then we obtain

( ) ( )ba

aba

abapbaap nn +−

+⋅−−+⋅−−+=+ 111

PRAGUE UTIA 1982 63


Or ( ) nn pbap ⋅−−=+ 11

If in time t = to, po is the probability with which the players react to

given set of incentives before the new economics politics starts, we obtain by

means of the recurrent methods, the following equation:

( ) 01

1 (1 pbap nn ⋅+−= +

+ ; 10 <+< ba

In this equation, the speed of convergence or decreasing of oscillation

with tendency to an optimal value, which means economic stability, is when

the value of the intensity of incentives, represented by the sum of negative

and positive economic incentives is increasing with a continuous

development. It is in economics, to increase the sum of profit and losses, but

in the wider sense of this concepts. Similar to physiology, ba representing a

very simple mathematical form, the structure of economic motivation.

It is important to note, that the concept of players is according to the

game theory (von Neumann 1948) and their degrees of freedom, depend

upon the structure and particularly the diversity of economical incentives.

Which is very closed with the possibilities to obtain a stable economy, and

with the reflections on the ways of the society. It is also very good reason

why many substantial sections of this thesis were devoted to studies on

neurophysiology and particular to the regulatory processes in the nervous

system.

PRAGUE UTIA 1982 64


4.2 Economic homeostasis

Economists define a stable economy on the basis of several

economics indicators, which are necessary to maintain in a certain range.

By analogy with physiology, we define economic homeostasis as a

process that permit to maintain the most important economic variables in a

certain level of functioning. Which in according to optimal functioning of

economy as an interacting whole.

For an ideal economy this set of variables that defines the economic

homeostasis and theirs ranges of functioning is as follows:

- with some differences according countries-economic

- growth : 6 - 8%- annual

- inflation : 0 - 3% annual

-employment : 96- 98% labor--power

-consumption: 50-60% National Income

-investment : 25-30% National Income

-Scientific

research : 2 - 3 % National Income

-health : 70-75 years of expected life

-level of

education : 12-14 years an minimum

-tax : f (income)

-profit f :(production, quality...)

Many other variables must be include in this set, like level of public

debt, military budget, foreign loan conditions, income per capita, insurance of

unemployment, etc. Which are represented in the optimal point as a number

or as a function of other economic variables.

PRAGUE UTIA 1982 65


Optimization models used in operational research are similar in

functioning to this process, when the values-of variables for a specific set of

optimal points are given as data input to this model of optimization. In this

case. the optimization function is known and evaluated in the set of optimal

points, and is necessary to know some un known elements of matrix of

technical coefficients and vector of resources. Normally, these models work

in an inverse form, it is searching the set of optimal points according some

resources, and restrictions and technical coefficients. In all cases, these kind

of models are consistently used in economic research.

As a manner to satisfy the above requirement, stressed in first three

sections of this chapter, and according to Chapter 3 "Economic models as

cybernetic systems", we propose to organize these mentioned economic

models as a hierarchical structure similar to human nervous system.

That is the principal reason why these economic models and other

accessory models necessary for analysis and direction of the economy are

arranged according to the principles of the human nervous system as shown

in Fig-4.1 Physiological arrangement of economic models. Which in fact

represent the block schemata of the cybernetic economic model proposed by

us.

PRAGUE UTIA 1982 66


Fig- 4.1 Physiological arrangement of economic models.

PRAGUE UTIA 1982 67


Allocation and linking between these models are made by analogy between

properties of each model and their similarity with properties of the human

nervous system. In that way, the model of market prices is at sense organs

level or nerves, because it is a typical model of interaction directly with the

economic environment. Model of multibranch is at spinal cord level, because

it is like a communication network between environment and economic

decision centre. Accumulation and reproduction as we have learned in

section 4.1 "Basic formulae of economic motivation” require memory and

learning.

Other economic models are included by similar analogies. But it is

important to note, that many times a specific model has a part in one level

and other parts or links in another level. We considered three level:1 brain,

2.opinal cord, 3. sense organs or nerves.

Complementary models like employment, pollution and particularly

experiential model, are extremely important for regulatory and decision

making processes.

This late process is based in the experiential proc cases simulated by

an economic learning model (see section 2.1), which produces suggestions

for economic makers decision or in some cases, the model makes decision

automatically.

For instance, if a specific economy represented by this model has a

free change of money, then, the market prices of foreign currencies, will be

the same as that proposed by this model. In opposite case, financial

government restrictions must be introduced.

Other very controversial case is the pollution problem. By means of

analog signals it is easy to detect air pollution, water pollution and other

kinds of pollution, dangerous for the vital environment, and at the same time

to transmit it to the decision center of the model. At high level of pollution the

center must suggest to close some sources of pollution, represented by

industrial companies or other causes.

Great economic problems arising where health considerations impinge

on profit, which do not permit an automatic decision . In such case, it is that

the model decision can be vetoed by the decision maker.

PRAGUE UTIA 1982 68


4.2.1. Informatic synapses

From the point of view of informatics, we can define synaptic function

as the junction process between the elements of an information system which

improve the organization level of this system.

For our, purpose synaptic function will be defined as a process in

which an economic element intrinsic to the model makes junctions with other

economic elements. In this way, the synapses are good in economic

modeling, where there are many junctions and they are operative at all levels

of a specific model, particularly at the decision level. This may have positive

effects on-the perspective of the mankind only when the model perm its free

decision making. The benefit of society.

Consequently, the major effort must be devoted to development and

implementation of a wide spectrum of coupled systems within the model, in

order to obtain a maximum of relationships between these elementary blocks,

represented by the commodities or goods which are flowing in every

economic system.

For that reasons, the vectors of the commodities and goods

determined of their properties, are considered as nerve cells of the model.

Pollution, .accidents, calamities and everything adversely affecting

individual and social benefit, will be represented an negative commodities or

goods.

4.3. Economic anomalies related to physiological concept

4.3.1 Economic stress

An we have learned, simple equations presents large sociopolitical

projection when they are applied to economic field. One of them is the

learning equation which relates the structure of motivation and the probability

of react ion to these specific stimuli.

According to Lange (1965), a stable economic growth is possible-

beside other reasons-when the economical structure of motivation is strong

and in continuous development. It means a permanent creation of negative

and positive stimuli, with clear prevalence of the latter. However it in not a

problem of elimination of negative stimuli by means of insurance against risks

and positive stimuli that permit maximization of profits. It in related to the

alternatives ways offers by the economical incentives which must to permit

maintain the individual and group economic in a continuous development (or

PRAGUE UTIA 1982 69


at least in this manner to appear) to players of this game represented by a

specific Economy.

Absence of economical motivation or existence of a feeble structure of

economical motivation, retard the development of countries and consequently

high social tension and tendency to emigration to countries with a better level

of development.

On the other hand, the application of an economical structure of

motivation which does not take into account characteristics of religion,

customs or historical reasons, may provoke violent social reactions. Also

countries with relative high level of development, may arrive to an exhaustion

state of the economic system, manifested by delay or disappearance of the

reactions to economic incentives. Such state generator abnormal phenomena

in the individual and social behavior, normally impossible to predict but

leading surely to socioeconomic violence. In neurophysiologic terms we may

speak about economical stress induced by unfortunate economical policy.

4.3.2 Paralysis in Economics

Paralysis in a well known pathophysiologic term applied in Economics to

represent a critical economic phenomena. A situation of paralysis arises

when activity in a specific economy as a whole or in a branch or sector of

economy decreases to zero. Productivity reactions to economic stimuli are

decreasing and disappearing. The first case in tendency to paralysis, the

second case is a state of paralysis.

Big worker strikes for economic demands produce a momentary state

of paralysis of some economic sector, but commonly without serious

consequences for the future of economy.

Also, a new technology or world market changes produce tendency to

paralysis of some economic activity, sometimes leading to disappearance of

an economic branch.

Of course an unfortunate economic policy is the most usual cause of

rapidly developing how to achieve economic paralysis with a social cost at

large scale.

PRAGUE UTIA 1982 70


4.3.3 Schizophrenic behavior of some decisions

Traditionally, a very high level of concentration in the decision-making

processes, produce a phenomena known as bureaucracy or government of

"bureau”. In this case officials are decision makers obliged to make a very

large amount of simple and complex decisions. But normally the decisions

are not always according to rules or laws accepted by the contributors or by

users.

Also, if we considered that in this process exist only one decision

center, it is that always to make any decision conduces to this same center

without alternatives ways. Then, it means that contributors and users are

obliged to attempt to make a relationships with a schizophrenic subject.

For our purpose, schizophrenic behavior of bureaucracy and also of

our model, is when in some case at the same conditions we have a different

reactions to stimuli. However in a majority of cases, we have with a high

probability of success a normal and predictable behavior. But in all cases,

never at 100 % level. Here, by probability we understand a mind state, not

only as a specific number between zero and one. For instance, if for a user

of bureaucracy, the probability of success for to make come official, contract

is 99.90 %, it means for him a very good business. But, if this same user have

an official problem, which has the same probability of no success, it is, 0.1 %,

then for him, bureaucracy is surely a not good business.

4.3.4 Afasia of the model

Afasia of the model is when there are communication problems

between the economic model and environment.

In that case, the decision making process intrinsic to the model is not

in accordance with the interest of economic decision makers. Consequently,

suggestions given by the model are not applied to real-life economic situation

because of political problems to implementation, or misinformation problems

produced by the model.

One of the most important problems of economic model is to feed the

model with data, which are necessary to maintain it in continuous flow.

When sometimes data are not good reflection of real-life situation, then

also we have. a problem of afasia in the model. Similar situation arises when

data are good, but interpretation by the model is wrong.

PRAGUE UTIA 1982 71


Other problems of afasia is when the output of information is

unintelligible because of hardware or software problems. This in extremely

important, because a correct functioning of the model require continuous high

level man-computer interaction. Without this interaction the model is isolated

from the decision maker.

PRAGUE UTIA 1982 72


CHAPTER V

5. THE MODEL RESTATED IN TERMS OF MICROELECTRONIC CIRCUITS

5.1 Introduction

Over the last two decades, the electronic industry has been involved in

an ongoing revolution in digital and analogue large-scale-integration (LSI) of

electrical circuits.

Today microelectronics is causing a revolution in all established fields

of electronics, as well as in other areas, including economics. According to

some authors, microelectronics is the continuation of the industrial revolution

(von Vessen 1979).

At present microelectronics world market is approximately 10 % of the

world economy (Heikee 1981).

Furthermore, this percentage in destined to increase with time,

particularly over the next two decades.

Basically North American and Japanese companies have domestic

markets which are almost by an order of magnitude larger than markets of

any individual European country.

Microelectronic market or integrated circuit market, is also, known as the

Silica business because it is based on Silicon (Si), which is used in

transistors, rectifiers and electronic devices particularly in integrated circuits.

As a semiconductor substrate, it in superior to Germanium or other elements.

But of course advances in microelectronics are not confined to the silicon

chip. The silicon dioxide Si 02 in the most common of the all materials. It is

estimated to form 60 % of the earth's crust (Clason 1971).

It is important to note that today there are three basic technologies for

integrated circuit chip fabrication: Bipolar or TTL which produces gates

composed of bipolar transistors; metal oxide semiconductor, MOS which

produces gates composed of field effect transistor and integrated injection

logic, I2L, which combines the packing density of MOS with the high speed of

TTL processing.

Curiously one of the fundamental problems with these LSI circuits,

which largely improve the operation speed and decrease the equipment cost,

is that, the technique is difficult to apply to small quantity custom

requirements. This is not the case in economics, where it is necessary to

PRAGUE UTIA 1982 73


satisfy a very large quantity custom requirements, i.e. to manipulate

sophisticated input-output data systems, large data banks and complicated

data processing systems.

For instance, a small chip Intel 8080 microprocessor is capable of

executing between 110,000 and 500,000 instructions per second and the new

Intel 8080-2 has a throughput equivalent to twelve microprocessors working

in parallel. Despite this advanced technology contemporary large scale

computer for large economical models need much time for executing

instructions using hardware that requires a large numbers of high-speed

standard integrated circuits.

On the other hand, also in economical data processing there are many

problems in detection and correction of errors. In all cases accelerated

testing methods and additional sources of errors in very large scale integrated

VLSI circuits are discussed, and the use of error detection and correction

(EDAC) will become more widespread in the next two decades.

In this context, it is important to note, that the tendency in

microelectronics is digitalization of the integrated circuits including the use of

optoelectronics and integrated optics for transformation of analogue signals

into digital ones. Next decade forecasting predicts one hundred thousand

digital circuits per chip. Improvement in analogue circuits will also be

considerable. Approximately one hundred operational amplifiers will be

packaged in one small chip.

Despite this tendency, it is not so clear only digitalization for

economical modeling, because should be a strong simplification to represents

an economy, by means of combination of two signal, only. Particularly due

to non linear and stochastic behavior of social economical variables and the

necessity of continuous functioning of these models as an integral system or

as an interacting whole.

PRAGUE UTIA 1982 74


In this chapter, we attempt to implement the cybernetic economic model give

in section 4 . 3 , with a hybrid computers i. e. a computer for economic data

processing using both analogue representation and digital representation of

data. The computer includes, an obligatory hybrid interface of connections

between digital and analogue systems.

In this chapter abbreviations are used extensively to save space. Their

meaning is given in Nomenclature .

5.2. Electro-analogue methods in Economics

The literature about analogies that exist between economic processes

and physical systems, was abundant during the 1950s. With appearance of

operational research as a mathematical tool for planning and decision making

in management and economics, electrical analogies for economic modeling

were abandoned because of their technical restrictions. Today, with

appearance of integrated circuits this attitude is changing, as will be

explained later.

Curiously, the first authors in this field of research (Moorhouse 1950,

Enke 1951, Smith and Erdley 1952, Tustin 1953) were electrical engineers

and not economists. For that reason their work represent a very good

approach to economic problems from the point of view of the theory of control

systems in electrical engineering, which is now at a very high level of

development. It is extremely important for analysis of the economic regulation

processes for the prevention of unwanted oscillations, and high probability

anticipation whether the development of an economic system will be stable,

with irrelevant oscillations around the optimal economic trend.

In this context the paper by Smith and Erdley (1950) is pertinent which

described an investigation of the behavior of Kalecki's model of business

cycles using an electronic analogy. Another important study is by Tustin

(1953) who describes an electrical system on the basis of a dynamo and

other electrical devices, which has the same functional structure of

dependence as Keynes model discussed in sections 1.3 and 3.1.

There are two tendencies in the application of control system theory in

economics: one applies the mathematical concepts describing electrical

oscillations, to time series analysis of the behavior of economic variables. The

other attempts to represent the elements and interactions of an economic

PRAGUE UTIA 1982 75


system by means of equipment and devices which are electrical parts of the

circuit that has the same scheme of dependence as this economic system.

5.3. The Enke´s circuits and its role in the development of economic

cybernetics.

The end of the 1940s marked the start of the transcendental epoch of

transistor and of the electro-analogue models for investigating problems in

economics. Stephen Enke of the University of California developed one of

these models, which was published in Econometrica in 1951.

It is a simple electrical circuit shown in Fig-5.1.a.

It is consists of batteries, resistors, rectifiers, etc. Which can simulate

and determine the prices and flows of commodities between spatially

separated markets.

This specific case represents four markets and a homogeneous good,

but is possible to obtain the solution of multiple-market by the same

analogue, where for n markets are necessary n(n-1) rectifiers.

The circuit behaves according to electrical laws, particularly Ohm's and

Kirchhoff's. Transportation costs are represented by negative voltages.

The electrical conventions are as follows:

U.S. $ 1 cent = 1 volt

1,000 bushels = 1 ampere

When these and other electrical and economical considerations, are

taken into account the voltmeter indicates prices in cents, and the volume and

direction of the flow of commodity can be read from an ammeter.

This electrical circuit have many advantages because it is very simple

and cheap and well suited to simulation of many problems.

At that time two main limitations prevented wide application of this

model and other similar models: first, the integrated circuits technology was

still unknown, and second, the operational research applied in management

and economics started only after the Second World War. This latter approach

is based on mathematical modeling which can be implemented by means of

digital computers.

Now with the integrated circuit technology and particularly with

microprocessors, the situation changes.

PRAGUE UTIA 1982 76


On the basis of unipolar FET and bipolar TT1 there appeared in 1960s the

MSI circuits in 1970s the LSI circuits and now the VLSI circuits, which

reduced the circuit in size and cost and increased its speed of operation.

For instance Enke´s circuit can be reduced by means of the bipolar

technology (TTL) to four integrated circuits as shown in Fig-5.1(b) and (c).It

means that many economic models, represented by complicated mathematic

apparatus with a software which is difficult to operate, may be changed to

small inexpensive circuits, which are easy to operate and produce high

quality economic information.

In our case Enke´s circuits was reduced by means of bipolar TTL

technology because this permits a very high speed of working functions,

although in bipolar circuits energy consumption is higher than in unipolar

circuits. Combination of unipolar with bipolar circuits produces the best

microelectronic systems.

Unfortunately the situation is not the came with the electrical models

for neurons, because they have many internal functions in a very small space

and are connected with ten thousands of nerve cells, particularly in the

learning process or in simple reflex activities that activate relatively small

groups of neurons (Bures, Tuma 1964).

As we have shown in section 2.4 Neural electrical phenomena, the

neurons have some properties of a condenser, which complicates their

modeling by LSI or VLSI integrated circuits.

PRAGUE UTIA 1982 77


Fig. 5. 1. The Enke´s circuit: (a) adapted from original form, (b) and (c) IC

version

This is one of the reason why it is still difficult to establish connections

between cellular neurophysiology and economic cybernetics. Such

connections are required if the informatic synapses are to be used in the

cybernetic economic models. The human needs and the technological

changes are interconnected as a system of coupled operations, where

PRAGUE UTIA 1982 78


technological advances satisfy the needs of the society, but where many

needs are at the same time created by the new technology.

For our purpose, IC technology available on the micro electronic

market will be used for restating the economic models in terms of

microelectronic circuits.

5.4.Keynes's circuit

According to section 3.8 Models of shaping of national income:

cAI

−⋅=1

1 or

cAI

−=

11

This equation can be simulated by means of an operational amplifiers.

Because this model is equivalent to non inverting amplifier, which is

represented by:

1

21

1

2

RRR

UU +

=

Or 1

2112 R

RRUU +⋅= when

1

21

11

RRR

c+

=−

and 21

2

RRRc+

= since

10 << c .

Term by term comparison reveals the following analogy:

PRAGUE UTIA 1982 79


Mathematical model Electro - analogue model

cAI

−⋅=1

1

1

2112 R

RRUU +⋅=

c−11

1

21

RRR +

10 << c 1021

2 <+

<RR

R

I 2UA 1U

Comparison between the mathematical model version and electro-

analogue model version of Keynes's economic model is shown in the next

figures, Fig-5.2 a and Fig-5.2 b.

Type of operational amplifier recommended to use in this

microelectronic version of the Keynes economic models is Fairchild MA 709

or Tesla MAA 741.

If we will use the last mentioned IC, the situation will be us shown in

figures Fig-5.2c and Fig-5.2d. The connections of the 8 pins of the MA 741

IC are as follows:

Pin connection

1 compensation

2 inverting input

3 non-inverting input

4 Ucc battery

5 compensation

6 output

PRAGUE UTIA 1982 80


Fig-5.2a Cybernetic diagram of the Keynes´s model

Fig-5.2b Microelectronic diagram of the Keynes´s model

PRAGUE UTIA 1982 81


Fig-5.2c Base connection diagram of the MAA 741

Fig. 5.2d Base connection diagram of the Keynes´s model

7 Ucc battery

8 not connected.

Notice, that in this linear integrated circuit we don't need pins 1 and 5,

serving for electrical compensation on in the range of 2 mv to 5 mv of input

potential, which is irrelevant in electro-analogue economic models. Pin 6 is

the output of this IC, which serves for display of information and also as an

input to Kalecki's model, linked to the Keynes' model according to Fig-4 Block

schema of t he cybernetic economic model.

PRAGUE UTIA 1982 82


5.5 Market prices circuit.

According to section 3.2 Model of price, there are five equations

representing this model, which was proposed by Morehouse, Strotz and

Horwitz in 1950 for shaping of market prices by means of electrical circuit.

Today is possible to represent these equations one by one by means

of linear integrated circuits, particularly with differential amplifiers and

additional non-inverting amplifiers. But we prefer to implement this system of

electrical equations with an analog computer as shown in Fig-5.3 Analogue

computer for model shaping of the market price.

Operating of this analogue computer requires the following

parameters: ( system of equations is given on section 3.2 )

PRAGUE UTIA 1982 83


Fig-5.3 Analogue computer for model of shaping the market prices

5.6 Global monetarism circuit

Since at present there is not electrical version of this model, we prefer

to represent it by several servomechanism equations which can be solved by

means of operational amplifiers as shown in Fig-5.4 Microelectronic version

of global monetarism model.

Multiplication of variables is not an easy task in analog computers. IC

technology offers new possibilities in this respect. We employed a special

analog integrated circuit B-B 4213 BM Burr-Brown USA, which is used also in

linearization, algebraic computation and many other such as division,

squaring, etc (Burr-Brown 1970).

PRAGUE UTIA 1982 84


It is important to note that the diameter of this integrated circuit is only

10mm and the height 5mm. Other elements are normally available

operational amplifiers.

5.7 Kalecki's circuit

In a manner similar to the model of prices, this Kalecki's model can be

restated in terms of analog computation by a circuit described by Smith and

Erdley in 1952. (see section 3.3 Model of business cycles).

On the basis of the above electric system, we designed the analogue

computer shown in Fig-5.5 Analogue computer for the Kalecki's economic

model, and Fig-5.5a Analogue computer for the time-delay system of the

Kalecki's economic model. The necessary components easy available on the

IC market.

Parameters necessary to calculate are the follows:

PRAGUE UTIA 1982 85


Fig- 5.4 Microelectronic version of the global monetarism model

PRAGUE UTIA 1982 86


Fig- 5.5 Analogue computer for the Kalecki´s economic model

PRAGUE UTIA 1982 87


Parameters of Kalecki´s circuit

Coefficients Parameters2111 ==⋅ mYka 6,0=θ year

95,0=m

zm bTYkaka

⋅=⋅=⋅

13322

2

zT=θ

12=n110 =s year

θm

bNNkaI

I ⋅⋅

=⋅ 44 LI NN =1=b addressees

4,01 =a (250)

nbN

NkaI

I ⋅⋅

=⋅ 55

1667,02 =a (230)

uI

u

Nun

bNN

ka ⋅⋅⋅

=⋅ 661667,03 =a (167)

sN are Standard and sK scales 158,04 =a (220)

α=a β=b 12,05 =a (147)Inputs are given by Keynes ‘s circuit

and interface 1ua .12,06 = mod

018,015,012,0 =⋅=

5.8 Leontief´s circuit

At present there is no available analogue IC technology for matrix

operations. Matrix functions for shaping pictures on television screen or

similar display equipment are exceptional cases, without important

mathematic applications.

Digital technology for matrix operations started simultaneous by in

England and USA, during and after the Second World War and developed

rapidly, because of war requirements. It created a new branch of the

management sciences so called operational research (operations research in

USA), which today has extended software for manipulating of complicated

models using mathematic programming. Particularly optimization models

stored in digital computers can be easily obtained on the computer market.

For that reasons we proposed to use microprocessor technology for

simulating of the model of multibranch, and of the models of optimization (see

section 3.5. section 3.6, and appendix).

PRAGUE UTIA 1982 88


5.9 Marx's circuit

According to section 3.7. Model of accumulation and reproduction, we

can represent this model in terms of microelectronic circuits as shown Fig-

5.6.

Fig-5.6. Microelectronic version of the Marx's model.

When 1

12

3

34

1

3

1111

1212

2

1

)(1 RRR

RRR

UU

aa

XX +

⋅+

==+−

+=

αα

5.10. Other circuits

Complementary models like pollution, employment and learning model

for economic policy decision making are not restated in terms of

microelectronic circuit. But they are represented by means of digital programs

in Appendix: computer programs.

5.11. Logic test of the model

According to Chapter III "Economic model as cybernetic system”, and

Chapter IV “Neurophysiologic arrangement of the economic models"

particularly Fig-4.1, which in fact represents the block schema of our model.

We made a digital simulation model named CAPEKLAND (in honor to Karel

Capek ) that include three main systems:

System 1: Learning model for economic policy decision making, see

Appendix: A 1

PRAGUE UTIA 1982 89


System 2: General software see Appendix: A 2

System 3: Economic and complementary models, see Appendix: A 3

For effect of simplification, we assume that economy have four

branches: agriculture, industry, services, and foreign commerce. Data are

fictions.

Several logic verifications of Capekland were tested in a digital

computer TEKTRONIX 4051 and in a computer Hewlett Packard 9825T with

a very good performances in terms of accuracy, speed and man-computer

interaction, as we showed by means of some types of reports, see Appendix:

A 4 .

PRAGUE UTIA 1982 90


CONCLUDING REMARKS

One of the most useful features of Cybernetics is the significance

ascribed to the analogy between biological and technical systems.

Particularly important for us, were analogies between economic system,

neurophysiologic phenomena and properties of microelectronic circuits.

At present, the Cybernetics approach to economic systems is in its

infancy but in accelerated development. The importance of theory of control

system in economics is twofold. First, it provides a theoretic method for

analysis and forecasting the dynamic processes in the Economy, particularly

in connection with the oscillation and stability problem. Second it permits to

represent the economic systems by means of electric elements as electronic

circuits. Introducing non-linear effects into electronic circuits permits a

continuous study of non-linear problems which are tedious and extensive to

solve by digital computer.

In this way our cybernetic model should be uses in an indefinite

number of ways to simulate socioeconomic real-life situations, in order to

predict what would happen if a set of economic decisions is made. If

necessary the model can incorporate step by step a series of influences, and

can this be flexibly applied in economic research.

Also, this model is well compatible with other complementary model,

because of maximum possibilities of coupling given by the model, which

improve the function of informatic synapses.

Disadvantages of this model are obvious, one is large storage space

required, however using the teleinformatic service of a normal economic data

bank is sufficient; other that it is very expensive and suitable only to

economics.

That is true but profits should be very high for society, because it is an

important improvement to decision-making in all key problems in economic

politics.

On the other hand by means of cybernetics approach we have

stressed many valid analogies between certain neurophysiologic phenomena

and the processes studiedly economics. It is homeostasis, reflexes, memory

and learning, decision making and hierarchical structure in the human

nervous system, also including nervous disease and the very important

PRAGUE UTIA 1982 91


analogies between neural functioning at the cellular level and the economic

functioning at the level of elemental parts or "cells" of economic system.

Combination of these elements will make it possible in the near future

to construct economic models on the basis of interaction of these "economic

cells" an systems of coupled operations. Such models will share the

intelligence and perfection of the human nervous system with the rapidity and

infallibility of the electronic control systems based on the integrated circuits at

the very large scale of integration. They will represent a jump from the

quantitative to qualitative approach in the analysis and control of the

economic processes.

This was the ultimate purpose of our research the theoretic elements

of which were presented in this thesis.

Finally, I would like to make this last comment: Prague is a good place

for thinking about artificial beings. It is not only due to modern literature about

cybernetics and science fiction, but because of old Czech legends, fictions,

theatre plays and films about "Golem”, an artificial human being created by

Jehuda Liva Ben Becalel, world known at the scholar and pedagogue Rabbi

Löw ( Rabbin lion of Prague). He died in 1609 and is buried in The Old

Jewish Cemetery of Prague. This tombstone with the figure of a lion is always

covered with very small pebbles left by visitors. According to legends a small

stone in the front of Golem gives him a full knowledge of everything. Of

course, our model does not strive for a similar effect in economics when

implemented with computer. A completely automated system for decision-

making on economic policy in all affairs including domestic and individual

affairs should be the best instrument for a corporate society. In this way the

man-machine interaction will produce new "amphibian” similar to that created

by Karel Capek in his prophetic book "The war of salamanders”: Let us point

out, how ever that, the starting point of our model goes back to the same

ingenious Karel Capek, to his visions of future mentioned above and

particularly to his book R.U.R. (Rosum's Universal Robot) which marks the

starting point of the robot concept.

Robot is a Czech word that according to Czech means work of

servitude in benefits of man. In general cybernetics applied to economics is a

powerful tool of visualization and control of the economic functions. But first of

all, it is a way of thinking in economics, with alternatives not always serving

the mankind. Our model understands cybernetics as serving to man in his

PRAGUE UTIA 1982 92


economic differences and interests, but never acting against man. Which is

according to "The three laws of robotics" mentioned by Asimov (1 970).That is

the reason why our model is named Capekland.

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PRAGUE UTIA 1982 96


APPENDIX : COMPUTER PROGRAMS

Appendix: Computer programsA.1 Čapekland. System 1: Learning model for economic policy

decision makingA.2 Čapekland System 2: General SoftwareA.3 Čapekland System 3: Economic and Complementary

modelsA.4 Some types of reports

R.1 Vector of total products per yearR.2 National incomeR.3 Velocity of circulation of money per yearR.4 Transactions per yearR.5 Prices per yearR.6 Money demand per year and per branchR.7 Level of pollution and penaltiesR.8 Level of employment and new demand of labor

powerR.9 Employment policy decisionsR.10 Inflation policy decisionsR.11 Production policy decisions

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A1 .Čapekland. System 1: Learning model for economic policy decision making

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A.2 Capekland System 2: General Software

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A.3 Capekland System 3: Economic and Complementary models



A.4 Some Types of Reports



ADDENDUM : MATERIALS SUBMITTED TO Ph.D. Degree Examination

AD.1 Capekland model : example 1 English version

AD.2 Capekland model : example 1 Spanish version

AD.3 NAZEV DIZERTACNI PRACE Czech version of Capekland AD.4 RESUME Russian version of Capekland *

* Capekland : A Cybernetic Model for Analysis and Control of Economy



AD.1 Capekland model : example 1 English version



PRAGUE UTIA 1982

AD.2 Capekland Model example 1. Spanish Version

116


AD.3 NAZEV DIZERTACNI PRACE : Czech Version of Capekland



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120


AD. 4 RESUME : RUSSIAN VERSION of CAPEKLAND

PRAGUE UTIA 1982

123


Preface to the first digital editionAcknowledgements

In memoriam to my Tutor Vaclac Kudlacek

Almost a quarter of century has passed since this Ph.D. thesis was published by UTIA Prague on November 1982 . Its continued success has called for a further digital edition in The Economist System by means of academic software applied to CyberEconomics and now around the planet with the wide world web page

technologies ,including the university venture neural network .

The most important acknowledgment is to my tutor during my Ph.D. training program at Technical University of Brno: Vaclav Kudlacek .

Second , I thank Dr. Josef Kolar for first software edition available on PC platforms named The Economist System version 1.0 and 2.0 ( MEXICO-1989) and TES on

Line ( PRAGUE 2001) . I thank to Dr. Hector Medellin and many graduate students at Tecnológicos Regionales de México for carefully reviewing the discussion of The

Economist System and for making a preliminary versions of real application handbooks ( UTEM CHILE 2005).

I am deeply grateful to Dr. Klas Ernald Borges at Lund University for his continuous advice ( SWEDEN 2001 , CHILE 2003 and 2005) and for induce me to

put on line my original Ph.D. thesis .Of course as always ,my acknowledgements to Dr. Dietrich Fischer at Pace

University of New York for guidance since 1976 and for include me in the Board members of ECAAR or EPS : Economist for Peace and Security . Finally I thank

them and the others who have contributed to the development of this thesis :

PROGRAMMERS

Eng. Vladimir Korenc : Capekland Systems 1 & 2. VUSE Prague

Eng. Milan Mayor : Capekland System 3 . VUSE Prague

DESIGNER

Eng. Arq. Rolando Carrasco CVUT-PRAGUE



TUTORS : POST DOCTORATEVisitor Professors at UTEM CHILE

Dr. Dietrich Fischer PACE Univ. New York

Dr. Josef Kolar CVUT-PRAGUE

Dr. Klas Ernald Borges Agreement : LUND - UTEM SWEDEN-CHILE

Dr. Hector Medellin Agreement : ITZ - UTEM MEXICO CHILE

DIGITAL DESIGNERS First Digital Edition @2006 Santiago Chile

Daniel Lopez Becker UTEM

Ariel González UTEM

Miguel Melo UTEM

WEB DIGITAL COMPOSER

Marcos Rivas UNIVERSITAS

LINES of RESEARCHS on this Ph.D. Thesis

1. The State of the Arts on artificial neural network applied in Economics

since 1982 until today 2006

2. Memory and learning for social and economic effects by means of the

Apparatus used by Bures and Buresova on consolidation test.

3. Capekland systems in terms of computer programs and Internet

technologies .

4. M. Sc. & Ph.D. Training programs on Economic Systems .

UTEM The State Technological University of Chile Santiago 2006


A Cybernetic model for analysis and control of Economy

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