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10C. SOCIO-ECONOMIC DEVELOPMENT ACCELERATION - FULL
PRIME PUBLICATION -
10
FULL TEXT OF THE THE RESEARCH PAPER GO TO :
CONCEPTS
GEOMETRY
KKK-2 PART#1
PART#2
View in
Social Science Research Net Work (SSRN)
It is less
important to have unanimity than it is making the
right decision and doing the right
thing, even though at the outset it may seem lonesome"
SOCIO-ECONOMIC DEVELOPMENT
ACCELERATION
ACCELERATE YOUR SOCIO-ECONOMIC
DEVELOPMENT
PART - 1 BACKGROUND TO
DESIGN A MODEL
EXECUTIVE SUMMARY Backed by my assignments with international Socio-Economic development institutions, and accredited scholarly associations, I developed a thirst to design a practical model to accelerate the pace of development of the third world nations. The world is divided into many categories, and the prime classification is the "Economic" bracket, as "Developed or Developing or Under developed".In the history, we are yet to see a country in the developing and under-developed category, moving upward into a developed category. This stagnated condition of the world nations was correctly identified and questioned by the Nobel Laureate in Economics (1979), Sir. Arthur Lewis (1915-1991.St.Lucia/UK. Princeton University, Newjersey, USA) as "Is the dependence of the developing country world growth on that of the developed - world inevitable ?". Using this question, as a base, this paper is prepared and presented in two parts. As described by the Nobel Laureate, the constraints on a break-even growth of the developing world are, their rate of population expansion, non-homogeneity of their industrial infra-structure, competition versus their economy of operation, and low demand for raw-materials among themselves. Part-1, is providing adequate background to develop a model towards an "Economic Management" guideline, to make this linkage more eternal than inevitable. This part comprehensively attempts to identify the factors to create a pre-condition to overcome these constraints among the developing world. The starting strategic approach is to "strengthen" the inter- group relationship, through the development of "social infrastructure", in order to utilise their productive capability. Then to "smoothen" the inter-country differences, through appropriate techno-commercial upgrade, in order to improve their linkage, and co-operative efforts. Social infrastructure is developed through an upgrade in tangible "economic satisfaction", and intangible "social comfortability" of individuals, to motivate domestic savings as well as to improve the quality of domestic human potential, which cumulatively contribute towards the national development. The techno-commercial infrastructure upgrade is achieved through methods to promote domestic investments and domestic technology. Both these are maintained and monitored by the optimum infrastructure mix. From a productive angle, Gross National Product is an aggregate of each national sector products, which is the net of their resource productivity and the productivity constraints. Techno - commercial systems assist to reduce the effects of these constraints, develop the technology, and optimises the resource utilisation. These aspects in turn, create cost / wastage reduction, remove excess holding, reinvestment opportunities and motivate domestic innovations and skills.
But, these logical steps are vicious to implement. Hence, it is
necessary to simulate a mathematical model,
solve and interpret the results into implementable decisions.
Through these inferences, this paper provides a "lead" to Part-2, for
designing a mathematical model and its solution.
01. ETERNAL LINKAGE " For the past 100 years, the rate of growth of output in developing world has depended on the rate of growth of the developed world. Is this linkage inevitable ? " This was a question raised and the problems were
tackled through an economic approach by Sir. Arthur Lewis (1915-1991.
St.Lucia/UK. Princeton University, Newjersey, USA. Nobel Laureate of 1979)
who was the President of the Caribbean Development Bank, Barbados, WI,
where The possible solutions suggested by the Noble Laureate for an independent rate of growth of the developing world are :
The objective of this paper is to analyse the preconditions necessary to create the surroundings in the developing world to attain a self-sustaining growth, and obviate the limitations. Through this approach, it is also expected to optimise the speed of the engine of growth among developing world, through internal socio-economic development steam generation. 02. STRATEGIC APPROACH A review of the current developing world situations indicate the need to adopt two distinct approaches towards Social and Economic development. In my opinion, the approach to strengthen the social harmony and smoothen the inter-country relationships, may prove to be more strategic and feasible. By this approach, the former could generate a congenial co-existence and the un-quantifiable Intangible social infrastructure T1. The former motivates the local entrepreneurial skills, and the latter could lead to the creation of industries of common economies of scale between groups of nations. These groups could produce and trade, to meet their mutual self-sufficiency, and export the surplus to the developed world. In short, it could generate a pre-condition to the route of demand and supply, between the developing and the developed world, as well as decide and direct the developing national production, on an on-going basis. This constitutes the quantifiable Tangible Economic Infrastructure T2. 02A. INTANGIBLE
INFRASTRUCTURE ( T1 )
T1 in turn is related to the social comfortability of each individual. Social comfortability of an individual S is also a cumulative feelings of their satisfaction as honourable members of the society a, safety and ensured availability of the essential needs of life b, and peace c to reduce psychological tensions and fears of war and destruction. Or
The Intangible infrastructure is derived from the optimum
infrastructure mix of a, b
and c, and contributes to the individual
development through the medium of Social Comfortability.
This tangible infrastructure T2
is closely related to the economic satisfaction E of each
individual, namely the food, shelter, and clothing, and it is the relative
influence of their current needs C, and their future
needs F, with reference to the degree of satisfaction and
psychological
Both the current and future needs are a function of the tangible or quantifiable environmental infrastructure T2 or C = f ( T2 ) and F = f ( T2 ) This is shown in the right half of Link Diagram -1. 02C. OPTIMUM INFRASTRUCTURE MIX The Optimum infrastructure mix for a nation is hence made up of the cumulative effect of the contributory factors of both the Intangible aspect T1, and the Tangible aspect T2. f ( T1 + T2 ) = f { [ X + Y + Z ] + [ L + U + R ] } This is shown at the top of Link Diagram -1. 03. THE OFF-SPRINGS A social group G is made up of individuals. The group development and its productive contribution, is the cumulative outcome of each individual development I, or
The individual development is a combination of their economic satisfaction E and their social comfortability S, among each individual members, or
A set of strong and satisfied social groups with a development value G, within each nation contributes to the prosperity and the Socio-Economic development of the nation D, or
Co-existence, peace and prosperity P among the developing world is the cumulative effect of the socio-economic smoothness between the nations N or
Hence, P the Prosperity as a direct function of G, the Groups in a nation, could be related as
where n is the number of nations and g is the number of groups. The smallest unit in this mathematical relationship is the social group G, and it is easy to strengthen their productive efforts through appropriate Social infrastructure. The bigger unit is the nation N, and it is easy to smoothen their differences through the development of implementable techno-commercial set-up. This is shown at the bottom of Link Diagram -1, along with their upward relationship towards infrastructure mix components. 04. EFFECTS OF INFRASTRUCTURES An optimum intangible infrastructure contributes effectively towards the social comfortability of the individual through the following :-
Similarly an optimum tangible infrastructure could strengthen the domestic resources through economic satisfaction among the local population through :
Thus the first and the prime need for a broad-based socio-economic development is to strengthen the national socio-economic infrastructure. 05. TECHNO-COMMERCIAL SYSTEMS
D = f ( GNP ) The GNP in turn, is the cumulative wealth generation from various sector productivity SP, contributing towards the total productive efforts of the nation, or
The Sector Productivity SP, in a semi-micro level is the net effect of the following :
SP = ( RP - TC ) The common management medium to optimise the sector productivity in a micro-level, is by tuning the Techno-Commercial systems, through the following methodologies :-
The influence of techno-commercial systems on
socio-economic development through sector productivity and GNP
is shown in Link Diagram - 2.
The expected Management Controls through the techno-commercial systems are,
Having identified the basic ingredients to develop the intangible social infrastructure and the tangible techno-commercial status, it should be now possible to derive a methodology towards an implementable approach. 06. APPROACH TO OPTIMISATION The above logical steps lead towards a sequence that the social infrastructure could motivate the population towards domestic savings, and that could be utilised for domestic investments. These investments could be productively utilised by appropriate and advanced techno-commercial systems, optimally manned and managed by domestic human potential. But these logical steps are of vicious in dimension, as these involve tangible technical aspects; and intangible social infrastructure development and human skill tuning. Hence, it is necessary to develop a Mathematical model, Simulate the ingredients, Solve their interactive contributions, and Interpret the results into implementable decisions. This is described in Part - 2.
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ACCELERATE YOUR SOCIO-ECONOMIC
DEVELOPMENT
SOCIO-ECONOMIC DEVELOPMENT
ACCELERATION
ACCELERATE YOUR SOCIO-ECONOMIC
DEVELOPMENT PART -2. MODEL DESIGN AND SOLUTION CONTENTS
EXECUTIVE SUMMARY Backed by my assignments with international Socio-Economic development institutions, and accredited scholarly associations, I developed a thirst to design a practical model to accelerate the pace of development of the third world nations. Part-1 provided a " lead" towards creating the pre-conditions to solve the constraints envisaged by the Noble Laureate (1979) Professor Arthur Lewis (1915-1991. St.Lucia/UK. Princeton University, Newjersey, USA) in his Noble prize paper in Economic Science, towards the possible de-link of the growth of developing countries from that of the developed world. The strategic preconditions identified were the infrastructures, made up of intangible "Social Comfortability" and tangible "Economic Satisfaction". Smoothing the inter-country difference is possible through a "Techno-commercial" normalisation, to optimise the resource utilisation, limiting the constraints, and balancing the Sector Productivity in a Micro level. These fine tuning is expected to promote "domestic savings" through group motivation and cost reduction, and pave way for "domestic investment" leading towards productive environments and strengthening of the "domestic technology". These in turn promote local innovations, research and development and domestic skill optimisation. But the implementation of these steps assumes a vicious dimension. Hence a mathematical modelling, simulation of the situations and solution interpretation should be followed. In this part-2, the model is developed in the form of two intersecting circles, one linking the domestic savings with the domestic investments, and the other linking the domestic human potential with the domestic technology. The former representing the external entrepreneurial activity is designated as "Exogenous", and the latter involving internal productive activity is designated as "Endogenous". A geometric approach is used to solve these two intersecting circles, aiming towards the central objectives, namely, integrating the Exogenous and Endogenous aspects, upgrading the socio-economic status, and enlarging the qualitative and quantitative outputs. The inference derived from the geometric solution indicate that, the attempts to accelerate the pace of socio-economic development should be to encourage equal efforts in both the domestic investments through domestic savings, and - utilisation of domestic skills for the domestic technology, updating towards the latest world developments. This will synchronise the Endogenous and Exogenous aspects of Socio- socio-economic development, at any given level. Any attempt to upgrade the existing Endogenous aspect only or Exogenous aspect only, is bound to create an unfavourable disturbance in this synchronisation, and it should be immediately re-synchronised. The qualitative and quantitative dimensions of the economy could be improved by expanding the operating dimensions in the Endogenous and Exogenous aspects, in equal magnitude. The past and current experiences of the developing and the developed world support this model solution. This model development and solution process has attempted to provide enough "reasoning", to the philosophy and methodology to accelerate the rate of Socio-economic development, in line with the remarks by the Greek mathematical philosopher Pytha- goras, whose geometric concepts are used in this paper. Also this is a pioneer attempt to use the Geometrical methodology, which according to the English philosopher Thomas Hobbs, is the only science to please the Gods to bestow the best on mankind, which could be nothing other than an accelerated Socio-economic development. Since the total approach is based on strong foundations and practical experience guidelines, it should be applicable to the development criteria for all the nations in the world, and establish an ever-lasting Peace and Prosperity in the new Millennium. ********************************************************* 07.
THE DESIGN LEAD This approach in a summary, started with the question raised by the Noble Laureate in Economic Science (1979), Sir Arthur.W.Lewis (1915-1991. St.Lucia/UK. Princeton University, Newjersey, USA) on the existence of an inevitable linkage of the developing world growth rate, to that of the developed ones, the possible solutions and their constraints. In order to create a pre-condition to overcome the problems existing within the developing countries, the strategic approach should be to strengthen the inter-group relationship within a nation through social infrastructure development, to utilise their productive capacity, and smoothen the inter-country differences through techno-commercial upgrade. Social infrastructure development is a function of intangible social comfortability and the tangible economic satisfaction. Techno-commercial systems approach upgrades the technology, reduces the influence of constraints, and optimises the resource utilisation. Both these result in the development of four basic ingredients namely, the domestic savings through group motivation and cost reduction; the domestic investments through productive orientation, the domestic technology through local innovation, research / development; and domestic skills through improved productivity, modern management methods, and operations research techniques. But, the implementation of these logical steps assume a vicious dimension. Hence, it is necessary to simulate a mathematical model, solve, and interpret the results into implementable decisions. 08. THE BI-CIRCULAR MODEL. In line with the lead
provided in Part-1, and the recommended approach by the Noble Laureate
Sir. Arthur Lewis (1915-1991. St.Lucia/UK. Princeton University, Newjersey,
USA. Nobel Laureate of 1979), an econometric discussion is used in
this part, to select an appropriate model. According to the Nobel
Laureate, "If a sufficient number of developing countries reach self
sustaining growth, then we are in a new world. It will be the growth of
the developing country production that determines the developing country
trade, and internal forces that will determine the rate of growth of
production".
DEVELOPMENT CIRCLES
In line with these thoughts, the intangible domestic infrastructure should be the support for domestic investments by the domestic savings. The tangible infrastructure is to develop domestic technology and synchronise the domestic skills for its optimum utilisation. These are represented by four points on space, and a circle is drawn to link domestic savings to domestic investments, and another circle is drawn to link the domestic technology with domestic skills. The domestic technology and human potential development are intangible know-how development within a nation, and the circle connecting these are designated as Endogenous in line with their internal orientation. The domestic savings and domestic investments are tangible wealth development through surplus potential creation in a nation, and the circle connecting these are designated as Exogenous, in line with their external surplus generation orientation. If the Exogenous and Endogenous circles stand apart, then the financial aspects of the former could not meet the know-how potential of the latter, and there could not be any productive results.
DEVELOPMENT CIRCLES
DEVELOPMENT CIRCLES
Hence, for any development orientation in a nation, it is assumed that the two circles should cut each other to result in two distinct points of intersection. One point of tangible inter-section is the Capital formation, representing an offspring of the domestic savings approaching to meet the needs of domestic investments. The other point of intangible inter-section is the Goods and Services output, as a result of the utilisation of the national technology by the domestic human potential.
GEOMETRIC CONSTRUCTIONS ON CUTTING
DEVELOPMENT CIRCLES
The area of the arc in the right side of the Y - Axis represents the quantum of Entrepreneurial background support provided by the Exogenous circle. The area of the arc in the left side of the Y - Axis represents the equivalent Technical Infrastructure generation by the Endogenous circle Using this model, a geometric solution is attempted to optimise the Socio-Economic Development. 09. DEVELOPMENT OPTIMISATION The mathematical optimisation is carried out in a three dimensional process through : - A)
Perfect synchronisation of Endogenous and
Endogenous 09A. SYNCHRONISATION OF CIRCLES The synchronisation of Endogenous and Exogenous circle is an attempt to integrate and normalise the technical infrastructure represented by the former, with the entrepreneurial background provided by the latter. In order to aid this
solution, the lines CG, DH in the
Endogenous Circle, and EI, FJ in the
Exogenous Circle, are drawn parallel to the Y axis, meeting the X axis at
G, H, I and J respectively. The complete
geometric solution is presented in Geometric Model Solution. The
interpretation of the solutions are : -
DEVELOPMENT CIRCLES WITH
COMMON ORIGIN
DEVELOPMENT CIRCLES
09B. DEVELOPMENT UPGRADE Once the Endogenous and
Exogenous circles are synchronised within a nation, then the next attempt
should be to upgrade the degree of socio-economic development. To initiate
this dimension, an external Y-axis PY1 representing the
Socio-Economic Development status is drawn on the left side of the
circles, parallel to the axis YY' ( See Geometric
Model ).
DEVELOPMENT UPGRADE (PUSH
UP)
The locus of the origin O ( 0,0 ) along the X Axis, upward or downward with reference to PY1 represents the development status of any nation on a relative scale. Movement of X axis with reference to PY1 will proportionately disturb the synchronisation pattern of Endogenous and Exogenous circles. 1. A movement
of the X - Axis upward, or attempts to improve a) Increase
in the distances DH and EI, representing
a need for
LOWERING THE DEVELOPMENT
2. On the other
hand, a movement of the X - Axis downward, or
09C. DIMENSIONAL IMPROVEMENT Besides a vertical socio-economic development shift, it should also be possible for a nation to moderate the qualitative and quantitative aspects of the economy along an external X axis PX1, drawn parallel to the axis XX' ( See Geometric Model ). The dimensional improvement
is measured on a 10 point scale, marked on either side, with zero aligned
to the origin O of the Endogenous and Exogenous circles.
QUALITATIVE IMPROVEMENT IN DEVELOPEMNT
1. The qualitative
improvement is exhibited by increasing the
It implies that the
qualitative potentials of both the domestic skills and domestic technology
should be simultaneously synchronised, when the diameter CD
of the Endogenous circle is increased. Hence, any upgrade in technology,
should be equally linked to the human potential infrastructure
development.
QUANTITATIVE IMPROVEMENT IN DEVELOPEMNT
d) The degree of synchronisation of domestic investment with
10. MODEL DIRECTIVES. To reach a status that the internal forces among lesser developed nations will determine their own rate of growth, Sir Arthur Lewis (1915-1991. St.Lucia/UK. Princeton University, Newjersey, USA. Nobel Laureate of 1979) in his Nobel prize paper said that "For those who talk the language of centre and periphery, this means that, a number of countries leave the periphery and join the centre. Or, if they are specially linked to each other by preferential trade and currency arrangement, one may even speak of creation of a new centre, consisting of former peripheral nations that have built a new engine of growth together". The eccentric bi-circular model developed and solved in this paper, is an approach to move the centre of the socio-economic development of nations upward, with the synchronisation of its peripheral components, on the qualitative and quantitative axes of the wheels of engines of growth. Either internally or with
foreign assistance to start with, every nation should attempt within a
possibly minimum period, towards domestic investment supported by domestic
savings. This is an Exogenous factor. The methodology to generate such
internal surplus is the development of indigenous technology to suit the
domestic environments, its productive utilisation and updating through
domestic skills. This is an Endogenous factor. There should be equal
efforts towards internal investments as well as the technology utilisation,
as productive results are possible only when they intersect and
co-ordinate together. The Endogenous and Exogenous environment
synchronisation could lead a nation towards optimum socio-economic
development orientation.
IDEAL SYNCHRONISATION OF DEVELOPMENT
The synchronised national environment should be upgraded to lift the economy towards medium and full development form under and developing status. This shift will disturb the achieved synchronisation between the Endogenous and Exogenous aspects of the economy. Then the immediate attempt should be made to re-stabilise the degree of synchronisation, and renew the efforts for upgrade. In a parallel process, the qualitative and quantitative aspects of the economy should be improved by expanding the operating diameters of the Endogenous and Exogenous environments respectively. It implies that investments through indigenous sources should be expanded in equal dimension with technological advancement, utilising the domestic skills. The socio-economic superiority of the developed nations are due to the application of the directives generated by this geometric model. Non-attempt towards these directives explain the socio-economic stagnation, deterioration, and increased dependence of under developed and developing nations on assistances from the developed world. The ideal situation in a Concentric Solution shown in the Geometric Model above . 11. MODEL AND THE WORLD The applicability of this Model directives could be evaluated from the situations in both in the Under-developed / Developing and the Developed nations. 11A. UNDER-DEVELOPED / DEVELOPING NATIONS
11B. DEVELOPED NATIONS
12. CONCLUSION Pythagoras, the Greek philosopher and mathematician, who lived between 582 and 500 B.C, in his "Diogenes Laertius" said that "The soul of man is divided into three parts, as Intelligence, Reason and Passion. Intelligence and passion are possessed by other animals, but Reason by man alone..... Reason is immortal, all else is mortal." Using his geometric foundations, this paper has attempted to provide enough "reason" for the philosophy and methodology to upgrade the status, and create a self-sufficient existence for the developing world. Thomas Hobbs, the English philosopher, who lived between 1558 and 1679 A.D said in his "Leviathan" that "Geometry which is the only science that it hath pleased God to bestow on the mankind". This bi-circular model and its geometric solution is expected to please the Godly aspects of socio-economic development, and bestow its immortal-scientific effects on the mankind of the world. This should be the Model
guideline for all nations in the New Millennium 2000. |
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GEOMETRY OF THE MODEL
THIS-BOOK

GEOMETRIC MODEL SOLUTION
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GEOMETRIC FORMATION / CONSTRUCTION & SOLUTION A. POSITION. The X-axis XX' is selected to pass through the
centres of the two circles, and the Y-axis YY' through their points of
intersection. With reference to these axes, the centre of Exogenous circle
O1 is at
( a,0 ), with radius
R1. The centre of Endogenous
circle O2 is at (
b,0 ),
with radius R2. Their points
of inter-section are A (0,Y01), and B (O,Y02).
The origin is B1. ENDOGENOUS CIRCLE.
Points C ( X11,Y11 ) and D ( X12,Y12 ) are on Endogenous circle, with centre ( a,0 ) and radius R1. By using the theorem of squares by Pythagoras, ( X11 + a ) **2 + ( Y11 ) **2 = ( R1 ) **2 Or ( X11 ) **2 + ( a ) **2 + 2X11a + ( Y11 )** 2 = ( R1 )** 2 ----( 01 ) ( X12 - a )** 2 + ( Y12 )** 2 = ( R1 )** 2 Or ( X12 )** 2 + ( a )** 2 - 2X12a + ( Y12 )** 2 = ( R1 )** 2 -----( 02 ) Subtracting ( 02 ) from ( 01 ) [ (
X11 )**
2 - (
X12 )**
2 ]
- 2
a
( X12 - X11 ) + [ ( Y11
) **2
- 2
a
( X12 - X11 )
= [ ( X11 )**
2 - (
X12 )**
2 ] + [ (
Y11 )**
2 - a
= [ ( X11 )**
2 - (
X12 )**
2 ] + [ (
Y11 )**
2 - (
Y12 )**
2 ]
/ B2. EXOGENOUS CIRCLE.
Points E ( X21,Y21 ) and F ( X22,Y22 ) are on Exogenous circle, with centre ( b,0 ) and radius R2. By using the theorem of squares by Pythagoras, ( X21 - b )** 2 + ( X22 )** 2 = ( R2 )** 2 Or ( X21 )** 2 + ( b )** 2 - 2X21b + ( Y21 )** 2 = ( R2 )** 2 ------( 04 ) ( X22 + b )** 2 + ( Y22 )** 2 = ( R2 )** 2 ( X22 )** 2 + ( b )** 2 + 2X22 b + ( Y22 )** 2 = ( R2 )** 2-----( 05 ) Subtracting ( 05 ) from ( 04 ) [ (
X21 )**
2 - (
X22 )**
2 ] - 2
b (
X21 - X22 ) + [ ( Y21
)** 2
- 2
b
( X21 - X22 ) = [ (
X21 )**
2 - (
X22 )**
2 ] + [ (
Y21 )**
2 - b
= [ (
X21 )**
2 - (
X22 )**
2 ] + [ (
Y21 )**
2 - (
Y22 )**
2 ] / 2 B3. CONSTRUCTION Draw CG, DH, EI and FJ parallel to Y Axis, meeting X Axis at G, H, I, and J respectively. Then
OG = X11, OH = X12,
OI = X21, OJ
= X22, CG = Y11,
C. CONDITION # 1. ORIGIN TO BE THE
COMMON If the Endogenous circle should have origin O (
0,0 ) as its centre, then the value a
should become zero. Hence from [ (
X11
)**2
- (
X12 )**2
] + [ (
Y11
)**2
- (
Y12 )**2
] / ( X11 )**2 - ( X12 )**2 + ( Y11 )**2 - ( Y12 )**2 = 0 Or ( X11 )**2 + ( Y11 )**2 = ( X12 )**2 + ( Y12 )**2 Substituting the values of X and Y Co-ordinates from the Construction, we get (
OG
)**2
+ (
CG )**2
= ( OH
)**2
+ (
DH )**2
Or ( OC
)**2
= Or OC = OD -----------( 11 ) If the Exogenous circle should have origin
O ( 0,0 ) as its centre, , then the value
b
should become zero. Hence from [ ( X21 )**2 - ( X22 )**2 ] + [ ( Y21 ) **2 - ( Y22 )**2 ] / 2 ( X21 - X22 ) = 0 Or ( X21 )**2 - ( X22 )**2 + ( Y21 )**2 - ( Y22 )**2 = 0 Or ( X21 )**2 + ( Y21 )**2 = ( X22 )**2 + ( Y22 )**2 Substituting the values of X and Y Co-ordinates from the Construction, we get (
OI
)**2
+ ( EI )**2
= ( OJ
)**2
+ ( FJ )**2
Or (
OE
)**2
= Or OE = OF ---------( 12 ) INFERENCE - 1 : If both circles should have origin as their centre, then any two points on both circles should be equally distributed with reference to the junction of the lines connecting their centres and their points of inter-section. D. CONDITION # 2. BOTH CIRCLES TO HAVE If both circle should have equal radii then the condition is
[ (
X11 )**2
- ( X12 )**2
] + [ ( Y11 )**2
- ( Y12 )**2
] / [ (
X21 )**2
- ( X22 )**2
] + [ ( Y21 )**2
- ( Y22 )**2
] / Multiplying both sides by 2, and Substituting the values of X and Y Co-ordinates from the Construction, we get [ ( OG )**2 - ( OH )**2 ] + [ ( CG )**2 - ( DH )**2 ] / ( OH - OG ) = [ (OI )**2 - ( OJ )**2 ] + [ ( EI )**2 + ( FJ )**2 ] / ( O I - OJ ) Or [ ( OG )**2 + ( CG )**2 ] - [ ( OH )**2 + ( DH )**2 ] / ( OH - OG ) = [ ( OI )**2 + ( EI )**2 ] - [ ( OJ )**2 + ( FJ )**2 ] / ( O I - OJ ) Applying the concept of direction,
If both circles to have a common centre as per (
11 ) and Then OC = R1, OD = R1, the Radius of the Endogenous Circle, and OE = R2, OF = R2, the Radius of the Exogenous Circle. Hence, [ ( R1 )**2 + ( R1 )**2 ) ] / GH = [ ( R2 )**2 + ( R2 )**2 ) / IJ If both circles should have the same radius, then
2 ( R )**2 / GH = 2 ( R )**2 / IJ Or GH = IJ INFERENCE - 2 : If both circles should have equal radii and common centres, then the sum length of the components of any two points on both the circles, along the line joining their centres should be equal. ************************************** Nobel Laureate in Economic Science Sir.
W.Arthur Lewis (1915-1991) Nobel
Laureate of 1979 in Economic Science Selected Economic Writings of Sir.W.Arthur Lewis.
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