Dynamic Pattern Economic Cybernetics Model (DYPECM) and its Applications

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DYNAMIC PATTERN ECONOMIC CYBERNETICS MODEL (DYPECM) AND ITS APPLICA TIONS H. I lIs l illl l l'

11/

Sys l l'lII.I

c.

Wang

L' lIg i lll'l'ri l,!!;, Sll!I lIgll!li j iOll loll g L'1I i<'l'rsit)', Shollgll!li , I ' N e

Ab!Otract. Dynamic Pattern Economic Cybernetics Model b called" DYFECM " briefly. It is one kind of social economic models developed in China to reflect the dynamic delays or t ime lag!O of social ec~ nomic activities. DYFECM is one of economic cybernetic!O models with discrete state space. It is available for the economic organization !Oystem of macro- r ontrol and micro-activenes!O. DYFECM can be used for macro and/or micro economics. It ha!O been preliminarily and rather effectlvely used for the energy planning of Shanxi Province as well as the macro social economic planning of Xinjiang Autonomous Region in China. Keywords.

Economics; economic cybernetics model; mode ling.

Factors t, ~ El, include accumulative scale, production capacity, products, manpower demand, money and its demand, as well as material s demand, etc. Then , X'j represent s the i-th factor of t he j-th

INTRODUCTION It is necessary for discussing the social economic problems to consider the dynamic delays or time lags of factors, such as investment, fixed capital accumula t ion, depreciation, production capacity accumulation, training of qualified scientists and technicians, man-money-meterials balance, etc. Dynamic Pattern Economic Cybernetics Model, called "DYFECM" briefly, is structured with dynamic pattern for this purpose ( Wang, 1985 ) • This model is distinguished from yet related to other economic models, for example, the Input-Output Tables, Systems Dynamics, Econometrics and the Economic Cybernetics Model with the tradi t ional type ( Chow, 1981; Forrest er, 1968,1973; Klein, 1974; Lange, 1970; Leontief, 1966 ). Hence t he development of DYFECM is meaningful for practice.

pro j ect. In particular, Uj is used t o represen~ the decision variable as a s pecial f a ctor for the J-th project. Here the manpower demand may be divided into several parts, such as medium level and hi gh level. About the money, there are gross output value, net output value, tax-profit, finan ce input-output, fixed capital, depreciation, circulating capital, surplus, etc. The materials may in c lude coal, coke, oil, electric power, iron and steel, cemen t and wood, etc. Elemen tary Type of Dynamic Pattern Equat ions

DYPECM is on ~ of the economic cybernetics models with discrete state space. It is available for economic organization system of macro-control and micro-activeness.

We will write the elementary type . ~f dynamic pattern equations as follows

1./td): Q'j (OJij (t)+ PiJ(t)r{~, {J)!}j(~~,t'ijfi~ { ::c:.j(() = f,j./i) 'l. '1

f,

as

l.:/N)t

.-'

1./ftJtJirIJer

is t he t ransi t ion sta t e ve c tor observed at moment t, t;jc.tlt is "the value of J'j at the moment t " observed at t he moment t, ana .Hjr,f.l )r , 1,2, ••• , (III.j -0, is"the preset value of !'j at the moment t~/.t" observed at the moment t; x ,' , (t)is t he real value of factor t of pro j ect

,,=

,

Here llrojects j, j eJ. include interesting products, or departments, or some key pro ,j ects, such as cotton textile, wool sllinning , sugar, crude salt, leather, raw coal, coke. crude oil, electric power, iron and Rteel, cemen t , etc. The di vision principle fo r uro j ec t s is

n projec t {,

(2)

U)


l./t)~ (~/j)t

Projf!cts

j

r : o'/" ' /T,/

'\ .. (D)=} ,~

s t ructured with the Si ngle Direction ( Wang, 1964 ). DYPECM consists of profactors. We will illustrate them and the of t he model as follows.

nro j ect

I

(I>

,ToI,

where equation (1) i s t he transi t ion equation of sta t e, equation (2) is the read-out equation, and equation (3) is the equa t ion of i n i t ial conditions;

BAS I C FORM OF DYFECM DYFECM is Principle jec t s and structure

t , tU,

T

DYPECM can be used for macro and/or micro economics. It has been preliminarily and rather effectively used for the energy planning of Shanxi Province as well as t he macro social economic planning of Xinj iang Autonomous Region in China.

, a t the moment

t;

is the decision-making vector;

jt ~ .

~(/t)~ [.iij',/(t) J. c),,2 ft) is t he interaction control vec t or;

175

176

H . C. Wang

P.'J. rt)~(f .. (.t) "J,I

The Combination Form of Factors

-'j,,,; (t)]

f." 2r.t)· .. " ..

-'1'

is the explici t pattern matrix; Q'j(t) is the implici t pattern matrix; Wij(t) i s the ratio matrix;

~t ~ [1

D

... 0

With respect to the j-th project we can write the dynamic pattern equations in the combination form as follows

r

l.; (M)' Q"j (0 l.t/O

fij i" the initial condition of !ij ( t) at the moment t= 0 • There are two examples of the dynamic pattern as shown in TABLE 1,where investment pattern is 1',=0.2, ('&= 0.5, ~J= 0.3, production pattern is p,= r2=~' .. 0, 1'~= 0.7, Pr= 0. 2, p,= 0.1 • TABLE 1

where

The Examples of the Dynamic Patterns

Time

0

1

2

3

4

5

6

Inve!ltment (To t al=1. 0)

/

0.2

0.5

0.3

0

0

0

Increments of production (Total=1.0)

/

0

Remark

*

Remark:

{!-rj(f)

0

**

0

0.7

0.2

***

****

(1%)

l..j(t)~ Ct'f lt )

-'J

~./,tH [~~ (t)

~:} (t)

.. '

~;/tH(:X'j(()

JlJj(t)

" ' X;jW]T

W"'j(t)~

i ~.(t) · ..

(w,i (t)

C"'j (t)~ ti..'A.! (

_r,

j ' , (j)

!!;/O

JT

r

WJJ: ft)

£,

:'P

WrJ (,t)]

. ..

-= lTpj>

...

s,'I'trj) J

Wi th respect to all J projects we can write the dynamic pa t tern equations in combination form as follows

* -- make .a decision ** -- the ,first year of inve s tment *** -- the first year of going into

opera·· tion -- the investment and increments of production are all equal to zero when t ~ 7

j-"i (t)

a.. ..j It) ~ J..,'4.! (Q'j (t) Qz j (t) . . ' arj (0] P~j(;f)! dia./(P'j (t) Pzj (() .. ' P%j(()]

0.1

****

:: etj

Pt/()W~/()~/f)+!.j(f) (If)

I-

{

JJftO =arf).!(i)+ P(t)W(I)~ rf) + ~ (I)

( 'J)

~:t'* (t):

(1/1-)

C" .. J- (t)

where

l,rt)t: (1:' d) ~(t)~

Then Wp can write the explicit form of the dynamic pattern equation as follows

[

~;(i)

1""2T(t ) ... 1n (t) JT ~ JT !!z (t) ~ J ct) T

T

T ~(f)~ ( ~ tT, ct) ~*1(t)

!: "'~ (t) ~ [~~ ct) ~;2 Q(t) ~ dr'q.1

fat-, ci)

T

~u (t) (If) ...

JT

3:;J (OJ

G
.,.

Q-I.T(t)j

«,'A.1 U~, CO Pu ({) .. . Pl\'J etl] wet) ~ d,'().! (W1If (t> Wk2 ct) . .. w"J (.t~ en ~ difl,..! (C.~f C. 2 . " C#J J Pet>

and

£

With respect to the additional factors we can get the equation

where

~ (t) ~ ;t.

(t) =

•

and

;: (0 ."

a'i {.

0

0..

/'J''''

(0] r

f

j't

C ~ [c./

If we use the implicit form, there are

-<,p..

[ ", (j)

(f)

~
The dynamics of the dynamic pa ttern equations ( 8 ) and (9) corresponds to the dynamics of the following equation

>( ..

4J

7:.

et) . ..

Xr

(of)

J

T

et) ~z

(16) ...

C.J

J

The Interaction of Factors The dynam i c processes are reflected by the dynamic pattern equations. Then the interaction of factors can be represented as follows

where

l (t)

is the corresponding exogenous vector,

F(t) is the interaction matrix. The interaction diagraph is shown in Fig. 1 • The Basic Model Combining the equations (13) and (17), we can get the basic model of nYFECM ,

1 (ttl) =A(t)1 (l) B(t) ~ (I) -tl (,t) of

('I)

177

Dynamic Pattern Economic Cybernetics Model where

Art) = Q(t).,. Frt) B(t)::; Pff)

((9)

W(t)

where ~op(t) is the optimization-constraints matrix. The optimization goal function can be structured with the Possible-Satisfiability Method (PS method) (Wang, 1982,1984), i.e.

(20)

PS _

Thus we obtain the typical form of state space in the control theory for the social economic model.

1?1a.%

01)

!:!op (t)

s:t.

t;op

?5(t) ~

50p et)

where PS is the value of Possible-satisfiability as the functi on of lct) , ~(t),

The Dynamic Equations for Coefficients There are many coefficients in the matrices r(t) , Q.(t), W(t}, f:ct) and others. Some of these coefficient" are stationary, and some of them are timevarying coefficients are affected by the technical advance, inherpnt or connotative expanded reproduction, price change as well as the economic system reform.

(J2)

This function is nonlinear generally. In special cases, it may be of quadratic form. SIMULATION AND SOME RESULTS

The dynamic process of a time-varying coefficient ~(t) can be represented as follows

'/"ci) :: H (l(t), ~(t), ... )

(24)

The equation can b'· ')btained with the techniques of Identification and forecasting. In the case of the linear equation of one order,

(2) , and ~ ar" t r e parameters. The corresponding proceSB is

I..(t) :: j3t~(O)

t-{

-r lol

-A

~

on

or

(25) When

l.ft I

< 1, t hen we can get

/..(t):

P~(Jd()- ~(rJO))

For discussion on the economic benefit and the growth rate, the concept of "economic surplus" is adopted. For instance, with respect to the energy, including crude oil, raw coal, coke, hydroelectric power and thermal power, the economic surplus curves are given as shown in Fig. 3, where surplus 1 is the tax and return minus investment of fixed capital, and surplus 2 -- the tax and return plus depreciation minus investment of fixed and circulating capital. For discussion on the benefit and effectiveness, some economic surpluses per capital investment for 12 products are given as shown in Fig. 4.

ti{()4)

:: ,:tl.(o) - (1-;t)t..(IXJ)

For discussion on the materials balance, there are the surplus curves as shown in Fig. 5.

where

Deci~ion-making

There are three decision-making blocks in the DYPECM, i.e. ~cenario-decision-making. balancedeci~ion-making and optimization-decision-making. If tre basic model (18) is operated with t hese de"icion-making blocks, then the Ovarall Model of DYPECM is structured as shown in Fig. 2 • Here the decision-making vector !:! (:t) can be divided into three pArts,

where

The DYPECM has been used for the macro social economic planning of Xinjiang Autonomous Region in China. For this task, the program DYPECM-02 is given and the simulation is taken for A.D. 1980-2000 year. By the simulation we have forecasted the economic development of the 24 factors for dividual and total re 'mlts of 12 projects. From these basic forecasted results, a lot of analyses of economic problems and a series of derived data and results can be obtaine~. For example:

~sc(t) is the scenario-decision-making vector,

.!!os C.t) is the balance-decision-it>..... ing vector, ~o~ct) i~

the optimization-decision-making vector. They can operate independently or simultaneously. The decision-maker must consider the balance-constraints ~8(t) ,

G-S(t) is the balance-constraints matrix. The deci~ion-maker must also consider the optimization-constraints ~.p(t) and the optimization goal.

W,",,'re

Uo)

For discussion on the balance of productions of departments, the elasticity c o~f ficients relating to total production for 1980-2000 year are obtained on the basis of the basic forecasted results as follows: oil -- 0.64, raw coal -- 0.60, coke -- 0.51, electrioity -- 0.92, steel -- 1.57, cement -- 2.1, wood -- 1.57, labour force -- 0.7, qualified personnel -- 1.0, etc. REMARKS

1. Generally, the coefficients in economic cybernetics model can not have the physical meaning directly, but there are clear economic and physical illustration of all these coefficients in DYPECM. 2. DYPECM can consider the dynamic delays or time lags of all those inputs and outputs simUltaneously, such as investment, production and others. 3. DYPECM can be used not only as a strategy model, but also as the working model for determining the 5-year planning.

178

H . C. Wanf;!; Capacity

Product 1

Product 2

-;rp2~

C_. ~ross

Net

x,ztt)~r~(f) XJ(,f)

Energy "X1;-(t"J

X,6 (t">

:r'7 d) XI'

7(21

(It>

(.:t)

An Exam .).le of Interact ion Dia .o~raph

Di sturbance s Jf (:t)

r - - j - - - -,

rI

I

Information

I

Decision ~(tJI

I

De cision(making ) block

PSI

...."'"x

50f{!>

c;n;;tr~i~t; l ~ ft) -

Fig. 2

I

...J

System Diagram of DYFECM

D~sturbances

JI". t)

s ta te

-I-'

:/(i} _

f(.t")

,t)

:!',.

Dynamic Pattern Economic Cybernetics iVloclel

179

economic surplus unit

100 t otal production 2

o

unit

raw coal

year surplus 2

1990

1980

surplus

Fig.

!lurplus 1

I

The Eco nomic Surplus

~

vestment scheme A •

10

C

0

')

-1 "

o >< ~ -')

C 0

~

v.

.-<

+-' 0

("

()

Fig. 4

c

:-

':>8-"

~

.-<

-;>

~

CJ

C C

v.

rro.iect

,-<

tu: ..... ..,'" .....c

rl

I'll ~

Q)

+' CJ 'r< ~

.c

..,'" Q;

I'll

~ i': ,..." " 'to

()

o'

0 CJ

:>

!-,

""'"

Cl

"

'"

~.-<

0

rl

Q)

:> 0 E -.:; "'-'" » ..c: +'

-.:;

~()

Q;

0

~

.c

Q)

I'll

''"," -.:; C I'll

c 0

.....~

..,

coke

cQ)

'"

Q) ()

Fig. ')

The Materials Surplus

Economic Surplus per Cari tal .:nvestmen t

REFERENCES Chow, G. C. (1981). Econometric Analysis by Control Methods, John Wiley & Sons. Forrester, J. W. (1968). Principles of Systems. MIT Press. Forrester, J. W. (1973). World Dynamics. Second edition. Wright-Allen Press. Klein, L. R. (1974). A Textbook of Econometrics. Prentice-Hall. Lange, O. (1970). Introduction to Economic Cybernetics. Polish Scientific Publishers. Leontief, W. (1966). Input-Output Economics. New York Oxford University Press.

Wang, H. c. (1964). Automatic Control Theory. Xian Jiaotong University Press. Wang, H. C. (1982). Multi-Objective Decision Mothod with the Concept of Possibility and Satisfaction. Systems Engineering -- Theor & Practice. 1982, No. 1~ pp.14-22. Wang, H.C. (1984), Xu, X. Y. Typical Combination Rules for Multi-objective Decision-making. Journal of Systems Engineering. (Sample Ed.), pp.33-41. Wang, H.C. (1985). Priciples of Dynamic Pattern Economic Cybernetics Model (DYFECM). Systems Engineering. 1985, No. 1, pp.1-11.