XL = 459.51

.X = 1681.922

x =axi f iJ 3

P, = x, - ix Xij

i=l(j = 1,2,3)

?'I

\

iW"apl.

I

II

111

_----

l&&u1

i&hJn

57.44 280.88 12.12 350.41

114.83 560.08 48.46 723.4:

80.41 233.70 121.15 435.2t

-_------------

252.73 1074.66 181.73

206.78 607.26 424.00

459.51 1681.92 605.73 I

C I G

80 0 30

iO0 200 160

150 0 30

- - - - -

110 460.44

960 1683.42

180 615.26

- -

tiDP

1250

_---

Using Intermediate Use (hods) TOTAL

\ OUTPUT

'reducing ( 1') (21 *-- tn) (ntl) (Xi)

(11 X X . . . x X‘1 XII L" Lt"+L1 L

(2) X X . . . x X11 X=? In OClT+ll 2

I . . . . . . . ..I......................... i

(nl X X . . . x X X"l na nn "‘"+Ll n

(ntl) X X . . . x X Xtn+,, , ‘"+L,* cn+t>n tn+L~cn+L> "+t

rOTAL INPUTS x X . . . xL X1 n n+ L

(x41

TOTAL OUTPUT (xi) = Intermediate Use (Goods)

TOTAL INPUTS (x,1 X X . . . x XI a n "+L

ntl

x = xx. (i=1,2,...,n,q+t)i r,

j=l

ntl

x = Px. (j=1,2,...,n,n+l)3 11 3

i=l

X = X t&j i = j (total autput = total inputs)i f

= a xLL 1 + a.‘ZX, + . . . t arnxn +a Lc”+llx”+,L

X = a x2 1‘ L + aIaXz t . . . + aznx, + a Itn+*lXn+L

. . . . . . . . . . . . . . . ..ll.........................................

Cl-a lx - a ,ax, - .a; - a ,“x, - a I<,+L,x”+,= 0LL t

-a x + Cl-a2,1xZ - . . . - a x - a = 0II L I” n r‘“+LrXn+l

.,......,..*......,.,..,......,.......................~............

,

-a x - a x - . . . t Cl-a lx - a X = 0“l L “Z ? nn n ntn+L> n+,

- a X - atn+,,, L ,,+,,ax2 - ‘.’ - a cn+,,nXn + C1-ac”+*,cn+L,‘xn+L = O

(1): Cl-a I = - C- a - a3, - .** - an, - aCn+,,,lLL a,

* ’ aunwrduii (homdgeneous e q u a t i o n s ) ix&Tnaha 1 #UWiT9 am775

kkhwwwm4 ( c o n s t a n t term) 1 3 UGpfi

Cl-a 1 =1,

xiJ

t a =-iJ x,

XL

X

X K X11 "1 ‘"+L)L- + . . . t - tX

x,X

L t

a a, + .” + ani + a‘n+,,L

= - C - aaL - a3, -:.s - anL - a<“+,,,1

1 = 0‘“+‘I L

= 1 - Ca LL t azr t l a* + an, t a,,,,,,]

X X X X‘L a, n‘ ‘n+L>L

= 1 - [- t-t ..* t - t 1X X X X

L L L L

X LL + xPL + *** + X"& + xc"+L,l= 1 - c 1

xI

XL

=I--

x,

=1-l

= 0

= thnnl~a

- C l - a I- a‘ L - . . . -12 a -‘” a ,C”+L,

- a II t Cl-alp1 - .., - a - aan a<“+,,. . . . . . . . . . . . . . . . . . . ..~............................

-a -“ , a -.., tCl-a l-“2 ann “<“+I,

--a -atn+*,, - a<n+L>2 “’ cn+,,n + rl-a<“+Ll<“+L,’

r

Cl-Alx = 0 : 0 = La”lm&l~I

5 . 2 n75mwaLiaafl:

X = CI-Al-‘0

=O

s o l u t i o n ) tillh:,UURO:

IC I-Al31

x = 8 j=t,Z,...,n,(n+l)3I I-AI

ICI-AIJI

x =3I I-Al

(M?ci?liln”: undefined)

W?;i Wiifl

\ I 11 111 WFJ

iW"aol. KWJ"

I 0 1 3 4

I I 3 0 1 4

III 2 1 0 3

il&&un 5 2 4 “11

x, = x +x +xL‘ ‘2 ‘3

x1 = x t xz2 + xz3a,

x = x tx tx1 3, 32 33

x ‘1 = a l xif 3 Ci,j = 1,2,3)

X =ax+aL + aLI L ‘ZXZ L9x3X =axta1 2, 1 aaX, + a23x3X =ax+a3 3, L anXa + a 3xX3

(1-a )x - aLL L Lax2 a iSX3 = 0

-a,lXI + (l-aga)x - a aaX = 02‘-a x -91 ‘ a 9zxz + (l-a33)xl = 0

1 3X - -x - -x

L 22 43= 0

3 1- - x + x - - x =o5' 2 43

2 1- -x --x t ,x = 05' 2' =

. . . . ..(l)

.... ..(2 1

.... ..(3 1

‘IslEl%%lhUd4 (elimination-of-variables method)!

3m4vUUaam74 4 . 7 :

X X

idh ( 1)/x L tia:z

1 - f(- )I 3

- 3(-) = 0 . . . ...(4)2 x 4 xL L

X

uaa C(z)-(3)7/xL Zia: - i2

t 3(- )x1

- 5(-) = 0 ' . . . ...(5)2 x 41 *I

1 xz 3 x3- -(-) - -(- 1 = - 12 x 4L XI

X

5? X3

-) - I(- =1

)2 x 4 XL JL

X .Xa

3(-I

) - L-14 x El xI L

iJEll

iiui%l

14 x3-1

-2 x L

X 3

X ‘

X 3

3 x2- -(-) - ;+

4 x 1

X 2

X 1

.*.... (8)

1

lo. . . . . . (9)

14

- i i i

4

s

4- x

‘-“*.(I)

5 ’

3- -

2

4

5

4r x. . . . . . . (II)

UIH

x a 4 4

- = ‘jXwio xp=-XI

5L

xI 4 4m = -

X 5uia x3=-x,

5I

ikia XL a x

alx3 = 5 a 4 : 4

uau

x =axiJ i.l J(i,J=1,‘2,3)

x =xi f iia t=j

I II III

0 2 3

3 0 1

2 2 0

5 4 4

k&l

wa

bU#wl

13

290 “ivlMl7wnlwbl:u

ALMON, C. %aCrir Methods in Economics. Reading, Mass.! Addison-

Wesley Publishing Company, Inc., 1967.

ARCHIBALD, G. C., AND RICHARD G. LIPSEY. An Introduction to a Ilathe-

maticaf Treatment of Economics. 2d ed., London: Cox and Wyman

Ltd., 1973.

BAUMOL, W. J. Economic Theory and O p e r a t i o n A n a l y s i s . 2d ed.,

Englewood Cliffs, N.J.1 Prentice-Hall, Inc., 1965.

CHIANG, A.C. Fundamenta

New York: McGraw-Hi

I Methods of Mathematical Economics. 3d ed.,

11 Book Company, Inc., 1984.

CHU, K. Princip/e of Econometrics. 2d ed., Scranton: Intext Educa-

tion Publishers, 1972.

CHENERY, H. B., AND P. G. CLARK. Interindustry Economics* New York:

John Wily & Sons, Inc., 1959.

LEONTIEF, W.W. 7'he Structure of American Economy 1919-1939, 2d ed.,

Fair Lawn, N. J.: Oxford University Press, 1951.

ROWEROFT, J. E. NathematicaI Economics : An Integrated Approach.

London: Paul Chapman Publishing, 1994.

.

i

0.2 0.3 0.2

A = 0.4 0.1 0.2

0.1 .0.3 0.2

.

i

I 300 200 t30 1 420 1000I

II 200 0 200 I 100 500I

III 100 150 40 I 110 400

_ _ _ _ _ _ _ _ _ _ - - - - - - t- - - - - - - - - - - - -

J4mJw1u 4 0 0 150 80 .I GOP = 630ue

iGaiwnI

1000 500 400 I

I

mn57u-b:

II II 111 I ihA17ih 1 sdayl

I100 400 200 I 300

0 300 1 0 0 0 600

0 0 200 I 800

II 2 1 2 : 5

II 1 2 3 i 6

III 1 2 5 I 8