DRDI 8

Development Research Center

Discuss icn P a p e r s

No. 18

The A l l o c a t i v e Consequences of Economics of Sca le

Larry E . Westphal and Yung W . Rhee

January 19 7.6 L

KOTE: Discussior, Pap?.. a r c p re l i rn i~ la ry r r a t e r i - l r ; c l r c u i n t e J l o s t i m u l a t e d i s c u s s i o r ~ an(', c r i t i c 2 1 cni- men^. Kcfel-PI rc.s i n yuhl ica t i r \n t o Discuss ion ! 'npcrs s!:ould b c c l ea red w i i 1 , t:;[-. a u t l l a r ( s ) t o p r o t e c t .. . the t c l ~ t a t i v e c h a r a c t e r of t!it:se paper:,. ~ i - c rs ;~>rs rxpr-c3ss t l ~ e viczws of the alltilor a.:d slic:~ld not bc i n c e r l ~ r c t c i ! to I ~ f l c c t r i ~ o s c of the. World B a n k .

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I n t he c o n t e x t of a l l o c a t i n g i n v e s t n e n t r e soLrce s anong projects, t h i s pa?er a d d r e s s e s t h e q u e s t i o n " ~ o e s i n t e rde7endence due rc e:cnoniss of s c a l e ' m a t t e r ' ? " A s t a t i c , z i x e d i n t e g e r prograrrxing :ode1 o f t h e mcchani:al eng inec r i xg s e c t o r i s used. Th i s model was o r i g i n a l l y cons t ruc r ed a s a d e v i c s t o o h t a i a en i n i t i a l comparative advanEage r ank ing of p roduc t i on a c t i v i t i e s p r i o r t3 t h e desi-gn 05 spc- c i f i c p r o j e c t s i n t h e Republ ic of Korea. Here i t is employed, f i rs : , t o n e a s u r e n m e r i c a l l y t h e d e g r e e of i ~ c r e a s i n g r e t u r n s and t h e n a t u r e of i n t e rdependence w i t h i n t h e s e c t o r and, second , t o e s t h t e t h e c o s t of n e g l e c t i n g i n t e rdependence when p l a n n i n g r e s o u r c e a l l o c a t i o n . Tne pape r conc ludes t h a t t h e a l l o c a t i v e con- sequences o f econonies o f s c a l e are f a r l e s s s i g n i f i c a n t t h a n h a s p robab ly been supposed, b u t t h a t t h e y a r e n o n e t h e l e s s g r e a t enough t o w a r r a n t t h e :fie of progran- n i n g methods r a t h e r t h a n c o n v e n t i o n a l b e n e f i t - c o s t p r o j e c t a p p r a i s a l t e c h n i q u e s .

It I s w i d e l y r ecogn i zed t h a c conven t i ona l b e n e f i t - c o s t p r o j e c t q p p r a i s a l

t e chn iques % f a i l t o y i e l d a n e f f i c i e n t a l l o c a t i o n of r e s o u r c e s when a p p l i e d .* .

t o p r a j e c t s c h a r a c t e r i z e d by economies of s c a 1 e . l ' m e t h e r i n f a c t economies of

s c a l e do have such a l l o c a t i v e consequences i s a n m p i r i c a l i s s u e t h a t depends

upon t h e c h a r a c t e r o f t h e i n t e r d e p e n d e n c i e s anong p r o d u c t i o r ~ activities w i t h i n a

p a r t i c u l a r set of c i rcumstances .2 ' Th i s paper e m p i r i c a l l y e s t i m a t e s t h e a l l o c a t i v e

consequences o f e conon i e s of s c a l e u s i n g a n e x p e r i m e n t a l n o d e l developed i n cbn-

n e c t i o n w i t h p l a n n i n g t h e expans ion of t h e of Korea ' s mechanical e n g i n e e r i n g

s e c t o r . / I t i s o rgan i zed as fo l l ows : The model i s d e s c r i b e d i n t h e nex t s e c c i o n ,

a f t e r which pa r ame te r e s t i m a t e s f o r Korea a r e used t o i n v e s t i g a t e t h e d e g r e e o f

i n c r e a s i n g r e t u r n s and t h e c h a r a c t e r of i ~ ~ t e r d e p e n d e n c e w i t h i n t h e s e l c t o r . S o l u t i o n s

t o t h e model a r e used i n t h e t h i r d s e c t i o n t o estimate t h e c o s t of n e g l e c t i n g i n-

t e rdependence , and t h e c o n c l u s i o n c o n s i d e r s t h e r o b u s t n e s s o f t h e e s t i m a t e s o b t a i n e d . , I

L

* The a u t h o r s a r e r c s p e c f i v ~ i y a f f i l i a t e d w i t h t h e Dcvelopnent Economics De;arrxcnt - - and t h e Development Research Cente r of t h e T n t e r n a c i o n a l 5ank f o r R e c o n s t r u c t i o n 2nd

'1 Development, Washington, D C . The views exp re s sed i n t h i s paper a r e t h o s e of ' k c a u t h o r s and n o t n e c e s s a r i l y t h o s e of t h e Bank. 'ITr~is pape r waz presei l ted ai t h e - - Econometr ic S o c i e t y S e s s i o n t i t l e d " ~ o m ~ a r l s o n s of Econes ic S r u c t u r e , " 1 9 7 5 , ASSA

%! X e e t i n ~ s . . - L

1/ See, f o r exan.ple, Chenery (1955) . The s t a t e cf tltc: a r t i n p r o j e c t dpprnis:; t=.:!:~;<~~!?s - i s ap:ly d i s c u s s e d i-n t h e r - c e n t aanr:als by 1 - i r t i c . 2 . ~ ~ e ' . : i r r lces ( lCI65)nxd L";I._L' 11572:.

2 / See V~stphnl. ( 1 9 7 5 ) , p a r ~ ~ c i l l t r - i . y S e c t i c ~ . 5. T(\ c.<::tX there h-i-vc b ~ 0 1 , v e r y f c ~ ; - attemy,:s t c ~ e s s u z - e ea ; l i r i ca l iy chese con:;eque:x\ L,. Ti;,, p r c t r i o u s . > t ~ d i t - s a r c t h o s e by we,ctphal (1971) and ?ianue ( 1 9 7 3 ) .

3 1 -4 f ; ~ ? l r c 2 - r t or, :I:$.; -.,ode1 i s g iven i n Wcstp!?aI r.:?? "n.cc. (19;' I , x h i c ! ~ is ~ . . ~ . i i l - -- rlhle o - : r , . ? q ~ ~ c ~ s t .

I. A Ycdel of t h e r.iechanica1 E n g i n e e r i n g S e c t o r

A tesm of economis t s and e n g i n e e r s des igned and irri3lemented t h e n c d e l , whic5

Tas o ~ i g i n a l l y i n t e n d e d as zn e x p e r i n e n t a l s c r e e n i n g d e v i c e t o o b t a i n an i n i t i a l

c c x p a r a t i v e

p r o j e c t s . A/ a d v a n t a g e rank ing of p r o d u c t i o n a c t i v i t i e s p r i o r t o t h e d e s i g n of s p e c i f i c

The z q ~ d 1 a l s o s e r v e s as a compact d e s c r i p t i o n of t echno-ecmonic

r e l a t i o n s h i p s v i t h i n t h e n e c h a n i c a l e n g i n e e r i n g s e c t o r . Though sector-wid;e i n s c o p e ,

i t i s r a t h e r h i g h l y d i s a g g r e g a t e d , and i t s t e c h n i c a l c o e f f i c i e n t s a r e e n g i h e e r i n g

est imates.T' . te n o d e l is r e s t r i c t e d t o t h e "make-buy" c h o i c e between domest ic p r o d u c t i o n

and i n p o r t s ; however, i t s s t r u c t u r e cou ld e a s i l y b e ex tended t o 2nc lude chb ices among

a l t e r n a t i v e p r o d u c t i o n t e c h n i q u e s f o r i n d i v i d u a l p r o d u c t s . The node1 is s t a t i c and

does no t i n c o r p o r a t e l o c a t i o n a l d e t a i l s . Economies of s c a l e a r e s p e c i f i e d l t h r o u g h t h e

zodel ls f o r n u l a t i o n as a n i x e d i n t e g e r programming (XIP) problem. The o b j e i t i v e f u n c r i o n

i s t o n i n i n i z e t h e c o s t of s a t i s f y i n g a f i x e d b i l l of exogenous demands fo* v a r i o u s

mechan ica l e n g i n e e r i n g p r o d u c t s . The s u p p l y ( p r o d u c t i o n p l u s i n p o r t s ) of each p r o d u c t

must s u f f i c e t o meet t h e exogenous demand p l u s t h e i n t e r m e d i a t e demand t h a e i s due t o

p r o d u c t i o n a c t i v i t y w i t h i n t h e s e c t o r . Inpu t- ou tpu t i n t e r d e p e n d e n c i e s wi th , in t h e

s e c t o r aAde t h u s c a p t u r e d w i t h i n t h e n o d e l .

The f o c a l conce rn of t h e model is t h e i n t e r d e p e n d e n c e among p r o d u c t i o n a c t i v , t i e s

w i t h i n t h e s e c t o r ; t h i s i s i t s advan tage over t r a d i t i o n a l methods o f p r o j e c t e v a l u a t i o n .

S i g n i f i c a n t i n t e r d e p e n d e n c i e s among p r o d u c t i o n a c t i v i t i e s stem from s t r p n g Fconoxies of . f

h

s c a l e i n p r o c e s s i n g a c t i v i t y and a r e t r a n s m i t t e d th rough t h e u s e of ccmnon b a r t s

(components and sub- assembl ies1 i n a l a r g e number of d i f f e r e n t end p r o d u c t s ' a n d t h e u s e i

.a of c o m o n p r o c e s s i n g f a c i l i t i e s by d i f f e r e n t p r o d u c t i o n a c t i v i t i e s . Capac i ty s h a r i n g , - - o u r t e r n f o r t h e u s e of c o n r n o n ~ r o c e s s i n g f a c i l i t i e s , is an e x t r e c e l y impor tan t ?her.o:ner.cr, -

0

t h a c r c s u l t : ~ t ' ron tile inul t i -purpose r ~ n t r l r c o f procc:;sing f a c i l i t i e s w i t h i n $he s e c t o r .

clcpscLt. ; r , . : ~ r i n g can o c c u r d i r e c t l y , a s w h e n t w o o r :;:ore p r o d u c t s a r e produced i:: t;:e

s a c e p l a n t , o r i n d i r e c t l y , a s xhzn d i s s i n l l a r p a r t s used ix d i f f e r e n t end products a r e

I * - he e:. c e r s , from t h e Korean I n s t i t u t e of S c i e n c e and Technology, worked ilnder t h e - d i r e c t i o n of Jcon Xoo :;an. T h e i r l ~ o r k v a s f inanced by the I 3 R D :lid t h e i ' t l ited S t a t e s Agency f o r I n t e r n a t i o n a l Cevelopment '? Xission t o Korea.

I .

d ive r s i t : : ;-ocg 3 i l 0 7 ~ w i t h i n s ~ i ~ ~ e n s?,c? c l a s s t h a n zczcg 2 l a n t s - 2 i t h l n t t e sect::,

- d i s a g g r e ~ ~ r i o r , t o c!-,is Ls- el s i - p l i f i s s ~ 5 e n o a e l ' s s t r T ~ c t h : r e 2s t is rhs

e s c i a a c i o n o f t e c h n i c a l c c e f f i c i c n t s .

S t r u c t u r e sf t h e 'lode1

- 7

~ l l e 2ode. l i s a t a r g e t y e a z z o d e l c o n t a i n i n g f o u r d i s t i n c t s e t s of a c c i v i r i e s .

T h e r e is a s i x g l e 2 r o d u c t i o n a c t i v i t y (xi) and a s i n g l e i n p o r t a c t i v i t y ( y . ) f o r each 1

p r o 2 u c t , i n d e x e d by i. b p r c d u c t nay be e i t h e r a n end p r o d u c t , s u b - a s s e f u ~ l y , c r I

conpcnen:. F o r e a c h shcp c l a s s ?, t h e r e i s a c o n t i n u o u s a c t i v i t y ( c k ) w h i c h c c r r e s p o n i s

t o t h e t o t a i v o l u n e of precessing w i t h i n s h o p s of z h z t c l a s s and a n i n n e g e r v a l u e d

a c t i - ~ i t y ( :,-) which c o r r s s p o n d s t o t h e number of s h o p s o f t h a t c l a s s <e iEg o ~ e r a z e d . h

The c o s t f u n c t i o n a s s o c i a t e d x i t i e a c h shop i s a f i x e d c h a r g e c o s t functi,n. ?,ere i s

aa u ? p e r bound t o t h e s i z e of a s i n g l e shop w i t h i n e a c h c l a s s , t h u s n o ? e t h a n a s i n g l e

s l o p n a y b e o p e r a t e d w i t h i n a g i v e n shop c l a s s .

T h r e e d i s t i n c t s e t s of c o n s t r a i n t s appear i n t h e n o d e l .

! ! a t e r i a l E a l a n c e C o n s t r a i n t s : There is a n a t e r i a i b ~ l a n c e c o n s t r $ i r , t f o r sash

producc stating t h a t r1;c s u n o f p r o d u c t i u n p l u s i m p o r t s ~ u s t e q u a i t h e ;urn of i , e I

Gxopenous dezitina p l u i :he e n c o g e n o u s l : ~ g e n e r a t e d deaand f o r i t s u s e a s hn ~ n t e c . c d 1 z t c

Di = exugenods demand f o r t h e i ' t h p r o d u c t , i n m e t r i c t o p s ; and,

I = t h e nunber of p r o d u c t s ( p r o d u c t i o n a c t i v i t i e s ) appearir 'g i n t5e mode:.

P;ocessing Requirement C o n s t m i n t s : For each shop c l a s s , a c o n s t r a i n t r e q u i r e s

t h a t t h e t o t a l vo1.une of p r o c e s s i n g be e q u a l t o t h e p r o c e s s i n g requir ,einents g e n e r a t e d 1

by t h e p r o d u c t i o n a c t i v i t i e s :

I

k = 1, ..., K ; where

ck = t h e volume of p r o c e s s i n g i n shops of c l a s s k , i n shop hougs;

B k i = t h e number of shop h o u r s of p r o c e s s i n g r e q u i r e d i n a shop $f c l a s s k p e r

I

metric t o n of p r o d u c t i o n of t h e i ' t h p r o d u c t ; and, I

K = t h e number of shop c l a s s e s a p p e a r i n g i n t h e model.

I n t e g e r i t y C o n s t r a i n t s : F i n a l l y , a n o t h e r se t of c o n s t r a i n t s r e q u i t e s t h a t a

s u f f i c i e n t nunber of s h c p s be o p e r a t e d v i t h i n e a c h shop c l a s s : I

A k = Uk(ck) , k - 1, ..., K; where

bk = t h e number of s h o p s of c l a s s k b e i n g o p e r a t e d ;

Uk(ck) = f u n c t i o n g i v i n g t h e s m a l l e s t i n t e g e r l a r g e r t h a n o r e q u a l ck/Ck, and ,

Ck = t h e maximum p r o c e s s i n g c a p a c i t y of a shop i n c l a s s k , i n shbp h o u r s .

a e c t i v e Func t ion : A s s o c i a t e d w i t h each a c t i v i t y is a c o e f f i c i e n t i n t h e a

I

o b j e c t i v e f u n c t i o n s t a t i n g t h e exogenously g i v e n c o s t of o p e r a t i n g t h a t a c t i v i t y . The I

I

o b j e c t k v e f u n c t i o n i s : - -

minimize F. &:, + V c + F G i xi + L !.Ii Yi, whhre K k k a k= 1 12 i= 1 i= 1 -

I

Fk = t h e f i x e d cha rge a s s o c i a t e d wi th o p e r a t i n g a shop of c l a s s k ;

Vk = t h e v a r i a b l e c h a r g e a s s o c i a t e d w i t h o p e r a t i n g a shop of c i a s s k;

G~ = t h e exogenous c o s t of p roduc ing a m e t r i c t o n of :he i ' t h p r q d u s t ; and

!J = :he zrorld market i x p o r t p r i c e (donesc ic c u r r e n c y equ iva ien t l ) ? e r r?ecri.- i

I

torr of p roduc t i.

c 0 n s : r a i n t s . The ~ c s t s of p r o c e s s l z g i n shc?s a rc a l s o enc!cge-ccsl;; dst2r: ine)i znc

- - 3re c h a r g e d t h r o u g h :he p r o c e s s i n g req1~i rer .e r . t c c n s t r a i n t s . T:?ese c c s h s i n c l ~ d e s - , I

z a p i t 3 1 c o s t s a s -dell a s i n d i r e c t i a b o r and x a t e r i a l s c o s t s i n c v ~ r k e a d czits ( 2 . g . I I

r e p a i r a n d z ~ i n t e n a n c e f a c i l i t i e s , s t e a c g e n e r a t i n g f a c i l i t i e s , and t?e like). Ca; l t z l I

c o s t s a r e b a s e d on :he i nves t zaen t c o s t o f c o n s t r u c t i n g a s h o p and incl lude i n t e r e s t I

as w e l l a s a r e p l a c e ~ e n t c h a r g e c a l c u l a ~ e d u s i n g a c a ? i t a l r e c o v e r y f a l c t a r . Jt3e.r I

i n t e r x e d i a t e i n p u t s , f o r wh ich t h e r e a r e no ?reduction a c t i v i t i e s ix :lie :.ode:, a r e

I i 2 c l u d e d \*<th in t h e exogenous c o s t e l e m e n t G i - ~ i r e c t l a b o r c o s t s a r e a l s o i n c o r F o r a t e d

I i n t h e G i l s a s t h e r e o r e a s s u ~ e d t o b ~ s o n s t z n t r e t c r n s t o t h e u s e o t / a ~ O r a i r e c i l y .-

er .p?ogea i n p r o c e s s i n g . I

I m p l e n e n t a t i o n o f t h e Yodel I I , I I

S e v e r a l i s s u e s must b e c o n f ~ o n t e d i n i m p l e x e n t i n g t h e mode l . ~ i r s k , wh ich

r e c h a n i c a l engf n e e r i n g p r o d u c t s are t o have p r o d u c t i o n a s t i v i t i e ; i n the n o d e l , i . e .

a r e t o be endogenous? A s b r o a d 2 c o v e r a g e a s p o s s i b l e was d e s i r e d i n i h e Korean I

i m p l e m e n t a t i o n , f o r t h e n o d e l was conceive.! a s a neons t o i s o l a t e t ! losj p r o d u c t s i n .'.hizn - I

I

Korea would have t h e g r e a t e s t c o n p a r a t i - r e a d v a n t a q e by 1975, t h e t a r g e f y e a r . T h e r e I 1 .

.vas n o n e t h e l e s s e p r t - s z l e c ~ i o n of p r o d u c t s , f o r i t was d e s i r e d t o c c r . a s ~ t r o : e cr.

I

t h o s e f o r c h i c h t h e r e ..~cls the g r e a t e s t 1Lkelii1cod t h a t Korea cculc! ac':~Seve ?roduct io!: I

c o s t s c o m p e t i t i v e v i t h i m p o r t s . ~ h c i p r e - s e i c c t i o n was p e r f o n e c i . :i:; er:gjirjcers rind :;zs I I

based upon - ~ ~ a r i o u s r u l e s of ~ h u c b and 2 Xnowicdge o f t ' ~ s - t ' ; ~ e : ~ exist in^ c z ; ' ~ b i l l t i e c o i

. . w I

K o r e a ' s nec ! l an icn i e n g i - e e r i r . 3 ir.dus:r:;. .L'?]e iiit cf ~-..:&O~CZC~J.:~ i>ri..cjt:,j:s c c ; ~ : z i ; ~ s I I . . . 120 i te - :5 . T!le f i r a d ~ = : s a p p . : , r i n g cn :!)is :is: r a n g e frcri; s ~ < : i :i::':-:;;~ :1: 2.l;ZS Z??C

. . jolts nl:i, :;in?!t: f a n <;.plt:, ,:i;s ;.I.$ t o .nnai)i;.ic Len:.; ,.;.: '"1~~:j:~'Pi~fs. I:.: ';<is ~i5.5"Z.L:. . '

. - . 1 . . L , 3 c i.:.s c , ;>..c..! . <; :. :':;c :::L:<: t h a t o t l l r r K C : - i ~ a n i c a i e n g i n e e r i r . g prodcc - t s , n o t ,:;~yc:!rii;; C'i: ' - .

d

C o n c l - p t n a l l y , e a c h of t h e i n d i v i d u a l " ? roduc t s " a p p e a r i n g i n t h e c o d e l r e p r e s e c t s

a whole c l a z s of p r o e ~ c t s . F o r e x a n ? l e , t h e p r o d u c t " f r a c t i o n a l horsepower e l 2 c t r i c

c o t o r " r e p r e s e n t s t h e c l a s s of e l e c t r i c n o t o r s o i l e s s t h a n one horsepower . T h i s b e i c g

t h e c a s e , t h e r e i s a s e r i o u s i s s u e r e g a r d i n g how t h e t e c h n i c a l c o e f f i c i e n ~ s d e s c r i b i a g -

t h e p r o d x c t i o n of f r a c t i o n a l horsepower e l e c t r i c m o t o r s s h o u l d b e o b t a i n e d . I n one

v i e w , d e r i v e d f rom t h e p r i n c i p l e s of a g g r e g a t i o n i n i n p u t- o u t p u t a n a l y s i s , t h e s e

c o e f f i c i e n t s s h o u l d be w e i g h t e d a v e r a g e s of t h e c o e f f i c i e n t s p e r t a i n i n g to , i n d i v i d u a l l y

s p e c i f i e d f r a c t i o n a l ho r sepower e l e c t r i c n o t o r s , t h e w e i g h t s b e i n g e q u a l t o ( a n t i c i p a t e d )

- - o u t p u t s h a r e s . I n a n o t h e r v i ew, most c l e a r l y a r r i c u l a t e d Ly V i e t o r i s z (UNF~0,/-1972/),

t h e c o e f f i c i e n t s s h o u l d p e r t a i n t o t h e s i n g l e , most " r e p r e s e n t a t i v e " of t h e i n d i v i d u a l i y

s p e c i f i e d f r a c t i o n a l ho r sepower e l e c t r i c n o t o r s . For a nunber of r e a s o n s , l i n c l u d i n g

t h e e n g i n e e r i n g t r a d i t i o n of employing t h e " r e p r e s e n t a t i v e p r o d u c t" c o n c e p t , t h e

e n g i n e e r s working on t h e m o d e l ' s i a p l e n e n t a t i o n p r e f e r r e d t o have a s i n g l e u n i q u e l y

s p e c i f i e d p r o d u c t s e r v e a s t h e " r e p r e s e n t a t i v e" o f e a c h p r o d u c t c l a s s .

For t h e n o s t p a r t , w e c h o s e as r e p r e s e n t a t i v e t h o s e p r o d u c t s t h a t would have ':he

I

l a r g e s t s h a r e s e i t h e r of t h e a n t i c i p a t e d a b s o l u t e o u t p u t o r t h e a n t i c i p a t e d , growth of

c s t p u t v i t h i n t h e i r r e s p e c t i v e p r o d u c t c l a s s e s . The b o u n d a r i e s demarca t ing ! i n d i v i d u a l

p r o d u c t c l a s s e s were drawn on t h e b a s i s of s i m i l a r i t i e s among i n d i v i d u a l p r o d u c t s w i r h

r e s p e c t t o i n t e m e d i a t e i n p u t and p r o c e s s i n g r e q u i r e m e n t s . Thus t h e r e p r e s k n t $ I t i v e . I

p r o d u c t s a r e i n t e n d e d t o b e " r e p r e s e n t a t i v e " of t h e i n t e m e d i a t e i n p u t and p r o c e s s i n g

r e q u i r e m e n t s of a l l t h e i n d i v i d u a l p r o d u c t s f a l l i n g w i t n i n each p r o d u c t c l n g s . The - - d e g r e e t o which tI$zy a r e t r u l y r e p r e s e n t a t i v e i s of c o u r s e dependen t upon Ildw na r rowly

t h e b o l ~ n d a r i c s begdcen p r o d u c t c l a s s e s a r e drawn. 8 e . I

One l o o s e end remains t o b e t i d i e d up, and t h a t i s i n r e g a r d t o t h e ccnversion

of indi:ridual, n o n- r e p r e s e n t a t i v e p r o d u c t s i n c l u d e d w i t h i n a p a r t i c u l a r prcduc: ciass

FnEo u n i t s of t h e r e p r e s e n t a t i v e p r o d u c t . T h i s c o n v e r s i o n i s r e q u i r e d i n o r d e r to c:;iz

tb.e d c ~ a n d f o r t h e p r o d u c t c l a s s i n u n i t s of r h e r e p r e s e n t a t i v e ~ r o d u c : . The 2 c c z n d

I , -

su;ply and denand i s p'n;isical xe ighc ( i 2 : 3 e r r t c c a n s ) . 3; I s q~rr.p-:.- the ? s f az?c - I I - - - -

v o l u n e :n ~ s t r i c t o n s of t h e exogencus ?urc:?ases o r a,: of c:?e i n d i v i $ u a ; z ~ ' Z ; i : t s I

f a l l i n g y i i t h i n t h e p a r t i c u l a r ? r o d u c t c i a s s . I

The s e c c n d n a j o r i s s u e 2190 c o n c e z p s a n a g g r e g a t i o n p r o ' c l m , t h i S Z ize ;llt'n I

r e c p s c r t o t t i e i d e n t i f i c a t i o n of shop c l a s s e s . i n o u r i z p ? e ~ . e n t a t i c n i two r,r::ents I

d e s c r i b e a snop c l a s s : (1) t h e t y p e o f p r o c e s s i c e a c r i v i c y ; and , ( 7 ) +he c o l l e c t i z n I I

of p r o d u c t s c h a t c a n be p r o c e s s e d together t r i t h i n a s i s g l e shop . To '$orrow z n a n a l c g y I

P r o r b i o l o s y , t h e f o r n e r i d e n t i f i e s t h e g e n u s and t h e l a t t e r :he s p e c i e s . !.!e r a v e

distinguished anong 37 shop t:J?es, o r g e n e r a , a c c o r d i n g t o t h e k i n d 08 p r c c e s s L n ~ I

a c ; l v i r y c o n d u c t s d ( f o r g i n g , c a s t i n g , x a c n i n i n g , f a b r i c a t i o n , e t c . ) , <he ~ a j o r

p i e c e s cf equ ipmen t i n c l u d e d v i t h i n t h e s h o p , t h e maxinun w e i g h t of thle p a r t s -.:LC

can b e worked , t h e rnaxinunz f o r c e d e v e l o p e d by p r i x e equipment i n - t h e sihop, and s o c n . I

A l l s h o p s b e i o n g i n g t o t h e s a x e genus a r e assurried t o nave i d 2 n t i c a l fii:<ed c h a r g e I

c o s t f u n c t i o n s , which s o n s i d e r a b L y reduce ; t h e s z o u n t o f p a r a m e t e r e s t i h a t i o n

I . . r e q ~ i r c d t o 1rr.plemenr t h e model . W i t h i n a p a r t i c u l a r qeni l s , t h e r e e d i s : i n rc>.:;:-J l

a ~ i d e ; ~ z r i e t y of p a r t i c u l a r i z e d s h o p s , t h e d c s i g x o i each d e p e n d i c g ubcn :he L

. t I

I . . p a r t i c u i a r p r o d u c t x i - : b e i n g p roduced . !;e g i v e s x a r e s s j oi; t o thiy f a 2 k >y ais:ir?;;u:s!iing

I I

among s p e c i e s on t h e basis of the p r o d \ i z t s t h a t c c n b e ?roccs.cec! 1:eget;ler ~ L i ! ? i r , a - 3 I

s i n g l e s h o p . T h e d e s i g n a z i o n cf i n d i v i d d a l shop c : a s s - ~ v i t i i i n n g e n c k ;~:;:-es a * * I

r e a s c n a b i e l i z i t o n t h e e:<cer.r tc .~ilic:h #e i20de l car: ~ : . . p i o i .:2pL:ci:y i s ! ~ r % r z ct: m I . .

? - - . l o ~ . e r at:crage prudi!:: t i o n cos;; . In a l l , the >(oren 3 ~ 2 2 2 .I<. s i - i n ~ i i.r,ilcs L - c . 2 ~ .t..:> ::::I I -

- '. - , ,.: ,< . - . - - . . . .lc ne:<': ;?;;jar j 5.535 : ~ T . c ~ T : : s : : ! .e i r e a : - z c r ? l . - . - . ~ -.,. ,. : :!,,I: :?,; .L:--- c,. :. I:;:, :.:-.L

- 8 -

t h e f o l l o w i n g : I n r i i v i d u a l p i e c e s of e q u i p n e n t w i t h i n a shop a r e i n d i v i s i b l e . The re - is a l s o e v i d e n c e t h a t a s lx i l a r p i e c e of equipment of g r e a t e r c a p a c i t y c o s t s l e s s

p e r u n i t of c a p a c f t y t h a n d o e s one w i t h l ess c a p a c i t y . F i n a l l y , t h e r e a r e economies

of s c a l e w i t h r e s p e c t t o l o t s i z e because o f t h e f i x e d tine r e q u i r e d t o s e t - u p a

machine f o r a p a r t i c u l a r p r o d u c t i o n s e e p . Our i m p l e m e n t a t i o n i s focusLd on t h e I

i n d i v i s i b i l i t y of p r o c e s s i n g f a c i l i t i e s and a n economies o f s c a l e i n t h e i r c a 7 i t a l

c o s t s ; t h e s e would a p p e a r t o b e t h e i f i o ~ t s i g n i f i c a n t s o u r c e s o f d e c r e a b i n g a v e r a g e I

c o s t s i n t h e p r e s e n t Korean c o n t e x t . The p r o c e s s i n g i n p u t r e q u i r e m e n t c o e f f i c i + n t s

a p p e a r i n g i n t h e mod21 i n c l u d e t h e a v e r a g e ( w i t h r e s p e c t t o t h e a n t i c i b a t e d s c a l e I

o f uu ;pu t ) t ine s p e n t on s e t t i n g- u p t h e equ ipmen t . I I I I

To e s t i m z t e t h e p r o c e s s i n g i n p u t r e q u i r e m e n t s and c o s t s , a " r e f e r i n c e shop" I

was d e s i g n e d f o r e a c h genus o f s h o p . c l a s s e s . E n a i n e e r i n g e s t i m a t e s o f t h e p r o c e s s i n g I I

i n p u t c o e f f i c i e n t s , Bki, were o b t a i n e d i n r e l a t i o n t o t h e s e r e f e r e n c e qhops. Shop 1 I

p r g c e s s i n g a c t i v i t y and c a p a c i t y v e r e i n i t i a l l y measured i n a a c h i n e ho(rs w i t h

r e s ? e c t t o t h e r e f e r e n c e s h o p . Thus t h e B c o e f f i c i e n t s i n i t i a l l y s t i t e d t h e t o t a l I

k i I I I

t i m e , summed o v e r t h e machines used w i t h i n t h e r e f e r e n c e s h o p , r e q u i r e d \ i n a c t u a i I

p r o c e s s i n g . &/ The machine t i n e c a p a c i t y of a p a r t i c u l a r shop e q u a l s t e numker of b mach ines i t c o n t a i n s m u l t i p l i e d by t h e number of h o u r s w i t h i n a y e a r t h b t t h e shop

I

may b e o p e r a t e d . I n t h e c a s e of shop g e n e r a i n which t h e c a p a c i t y of c i r c a i n p r i n e I

machines c o n r r o l s t h e p r o c e s s i n g f low, pr ime machine h o u r s s u b s t i t u t e f)r t o t a l I e

C I I

machine h o u r s as t h e measure of b o t h p r o c e s s i n g a c t i v i t y and c 9 p a c i t y . f o r c o n v e n i e n c e , I I

b o t h i n computa t ion and r e p o r t i n g s o l u t i o n r e s u l t s , machine t i r e was =or /ver ted t o

"shop t i n e " a f t e r t h e e s t i m a t e s were o b t a i n e d . T h i s c o n v e r s i o n s i m p 3 e q u i r e s C 1 - C I

d i v i d i n g p a r a m e t e r . measured i n a a c h i n e t i n e u n i t s by t h e number of - cq ines ( o r =a - I I I

p r i n e a a c h i n e s ) c o n t a i n e d i n t h e r e f e r e n c e shop . I I I

6 / Nr,'ce t h a t t h i s is n o t t h e s a c : h i n g 3 s t h e t o t s 1 " r c o l " t i n e a pa r t l i c i l l a r i:rx - spends w i t h i n a s h o p , which .*.culd i n c l u d e t h e "...iaitingU tLze d u r i n g ' : < h i ~ i ~ i t 1s b e i n g s t o r e d o r h e l d f o r f u r t h e r precessing. I

I I I I

I

I I I , !

of ? i e c e s p r c d u c e d , t h e o ~ h e r i zpc r : an r 2e:eni:;zn:s ?i tkle t o c a l 2 r c k z s z i n - 6

I

r e c u i r e l e r . E s a s s o c i a t e d w i t h a p a r c i c - l a r i:en inc:ude the g e c g e t r i c coc f igu ra r i c . : l

o f t h e p i e c e t o be worked , t h e bi-,e;..siori and ; leigi l t of t h e ? i e c e t o be worked, ~ k s I

l e g r e e of ? r e c i s i o n r e q u i r e d , t h e l e n g t h cf t h e p r o d u c t i o n r u n , and t$e h a r d n e s s of I I - ,:,e - p i e c e t o b e v o r k e d . L/ However, n e a s u r e ~ e n t i n u n i t s o f t i m e i s Brckward wkeil i t I

cotes t o r r a s u r i n g c a p a c i t y , s i z c e any s h c p h a s t h e same c a p a c i t y i n isms of t h e I

t i z e i t nay be o p e r a t e d , r s g a r i i e s s of i c s s i r e i n t2L-35 of t h e n a a i r 4 n p o s s i b l e I I ~

v o l u ~ e of p r o d u c t i o n d u r i n g t h a t t i c e p e r i o d . I I

I

To o b c a i n e s t i n a t e s of t h e c o s t s of c o n s t r u c t i n g and o p e r a t i n g s q o p s of I I

d i f f e r e n t p h y s i c a l o u t ~ u t c a p a c i t i e s and f a l l i n g w i t h i n t h e s a o e % e c u g , t h e f o l l o u i n g I ~ I

p r o c e d u r e was employed. F i r s t , e s t i a a t s s o f t h e c o s t s of c o n s t r u c t i c $ and operating I l

e a c h r e f e r e n c e shop were o b t a i n e d . Then a shop w i t h i n each genus was d e s i g n e d t h a t - . I

had c ; i c e t h e 2 h y s i c a l o u t p u t c a p a c i t y cf t h e r e f e r e n c e s h o p , ; . hys i ca i o u t p u t c a p a c i t y I

b e i n s measu red i n soEe way t h a t was m e a n i n g f u l t o t h e e n g i n e e r s . :<e niay r e f e r to I

I

t h e s e s l ~ o p s a s t h e " d o u b l e - r e f e r e n c e - c z p a c i t y " s h o p s . C iven t h e e c c n o n ~ i e s of s c a l e I I

p r e v a l e n t i n t h e s e c t o r , t h e s e s h o p s do n o t mere ly r e p r e s e n t p r o ? o r t i o b a i b l o w - u ~ s

* o f t h e r e f e r e n c e ' s 2 o p s . Thus , i n d i v i d u a l p i e c e s of z a c h i n e r y f o u z d i n a g i v e n I

r e f e r e n c e shop n i g h t nc: e v e n be p r c s e n t ir, t h e a s s ~ 7 c i a t e d doub l c - r e f e ence-ca;>; lci : y k sllop. R e g a r d l e s s c f i t s ~ i t u a l x a c h i n e t ize capacit::, t i e s! lup tiae ;Gpa:i;y cf . i i ; i l

I

i - doubie- re lerence- l :ap:~ci ty sho; i s p r e c i s e l y twice I::s a s s c c i a c e d rc ferkr !cc shop's

8 I I

cap:acit:r. : ; ieasured iri shop tirne. Si:cp t i y e I S t ! :e refore a c : a " r e s l " t!::.~. : o ? i c p t I . . I

1 . a s e:n;;oyei in t ;?e ~ c ~ i e l ; i t is 1 r e l a t L - : ~ ,once?: -- <,:on c t r . 2 !:as se:r::..;z - o;,l-: -1:

rc1.q ?:i(~;l tc. tj:e ~ i : ~ p ~i:::f ,:3-; . i . . i a [ t::e c . . - ; s o ~ i a ; ~ . . .-;r: ;.reg:? si:::;!. .:,: : refer2r . : t .

- .. -.. .. , . ,,,,- ;:2?n:-:~: o f 2 , . : . ; , ; _ : LC!.?;; i;.:):rs :;; s;.zgAL ,-:!::: ::,. t ,> ;-ere ;?;cczed t o ';:;i..;e 3:i n - - , - I

o;.er:e:zI::. - - . ~ ~ ~ f ~ ~ ~ . f - r i j s:l:F ? f 1 , ,)(?;- 2..>4,2 ;lL,.,.: :::;,~:: Y . ~ : is ci 5fl:j;3 ; : ; : y ; : : . , :

I

- - . - - --. .- - - - I

I 7 , .- ( . -, v . . P .; i T.., , . , - . . . I .- .'c.. . . c . L , . . . -, a n d !<GI:.~ , . - . ; . ! I .

I I

one h a l f the p h y s i c a l o u t p u t c a p a c i t y of t h e r e f e r e n c e shop ; a shop hav ing 5,OCO -

she? !,curs c a p a c i t y h a s t x o znd one h a l f t i x e s t h e p h y s i c s 1 outpu; c a p a c l t y of t h e ,

r e f e r e n c e shop.

E s t i u a t e s of t h e c o s t s of c o n s t r u c t i n g and o p e r a t i n g e a c h of t h e doub le- re fe rence- ,

capacity s h o p s were a l s o o b t a i n e d . C a p i t a l c o s t s were a n n u a l i z e d a{d a f i x e d cha rge

c a p a c i t v c o s t f u n c t i o n f o r e a c h genus was e s t i m a t e d by f i t t i n g a s t n a i g h r l i n e t o I

t h e p o i n t a n n u a l c o s t e s t i m a t e s f o r the r e f e r e n c e and double-referen)ce-shcps. F i n a l l y , I

t h e r e i s a n llpper l i m i t t o t h e p e r n i s s i b l e shop ttme c a p a c i t y of a s j n g l e shop w i t h i n

a g i v e n shop c l a s s . T h i s l i m i t r e f l e c t s two f a c t o r s : o u r i n t e r p o l a t e d f j s e d cha rge

c o s t f u n c t i o n f o r p r o c e s s i n g i n p u t s i s r e a s o n a b l y v a l i d o v e r o n l y a p a r t i c u l a r range;

and, t h e r e a r e sometimes p h y s i c a l l i m i t s t o t h e c a p a c i t y of a s i n g l e shop. I I

A 1 1 s h o p s a r e assumed t o o p e r a t e a t f u l l c a p a c i t y . T h a t i s , t h g volume of I

p r o c e s s i n g by a chop i s t h e s a n e a s i t s c a p a c i t y . 3/ Thus, shops had ing a vo lunc

I

of p r o c e s s i n g l e s s than 2 ,000 shop hours do n o t have e x c e s s c a p a c i t y l a s c a p a c i t y I I

measured i n shop t i n e i s a r e l a t i v e r a t h e r t h a n an a b s o l u t e c o n c e p t . Converse ly , a

volume o f p r o c e s s i n g i n e x c e s s of 2,000 h o u r s i s no t t o b e i n t e r p r e t e d i n t e r n s of

0 3 e r a t i o n i n e x c e s s of " d e s i r e d" o u t p u t o, m u l t i p l e s h i f t o p e r a t i o n . : F i n a l l y , i t

shou ld a l s o be c l e a r t h a t t h e d i f f e r e n c e between a p a r t i c u l a r s h 3 p 1 s ! c a p a c i t y and the I

maximum c a p a c i t y f o r a shop i n i t s r e s p e c t i v e c l a s s dogs n o t r e p r e s e n k e x c e s s c a p a c i t y . I

IIowever, i t does r,ef;ect t h e d e g r e e t o which p o t e n t i a l economies of s k a l c have n o t L - I

been e x p l o i t e d , s i n c e econocnes cf s c a l e f o r a p a r t i c u l a r shop a r e e i b a u s r e d a t a

c a p a c k t y e q u a l t o , where t h e a v e r a g e c o s t of an hour of p r o c e s s i n g ! i s a t i t s Lo.*-er

'9 I

bound. - - a / T h i s is t h e a p p r o p r i a t e a s s u n p t i o n i n a s t a t i c node l focused cn d o t e m i n i n g -

c o m ~ a r a t i v e advan tage i n Lhe z e d i u n t e r n . Bowevcr, i n a dy1:anic a n a l v s i s , t!x p o s s i b l i t y of ex:ess c a p a c i t y x u s t be a d a i t t e d . See C h e n e r ~ (1952) and Hanne ( 1067 ) .

-, t a k e s :p :h is t a s k . r ; r s t , a cunber 3f r e ; * ~ i r e l conce? rc m u s t b e C e v - z l 2 p e d .

E s c i z a t e s of c o s ~ f o r individual ? r o d u c t i s n activities can onL;~ b e o b t s i z e c

if i n t e r d e p e n d e n c e t h r o u g h c a p a c i t y s h a r i n g i s r . eg lec t=d . Thus, i n what f3115;~5,

w e te rnporar i l j r n e g l e c t c a 7 a c i t y s h a r i n g . The a v e r a g e p r o c e s s i n g c o s t of a .:ieLris

t o n of p r o d u c t i i s g i v e n by:

Average P r o c e s s i n g COSC = : - 17 vk (Bki x i17 /K, + 1 irk Bki . " 'n

The x a r g l n a l c o s t of p r o c e s s i n g a n e t r i c t o n of p r o d u c t i i s s i x p l y Z V 3 . The k k k i

p o i n t s c a l e a l a s t i ~ i t y of r h e p r o c e s s i n g c o s t of p roduc ing a E e t r i c t o n ai p r c d u c t I

i s t h e x a r g i n a l c o s t d i v i d e d by t h e a v e r a g e c o s t : ,- -

E v 5, k t t i

?recessing Cos t P o i n t S c a l e E l a s t i c i t y = k - TiFk - Ck (aki xi)-? /xi +- L vk 3, ti i k li

The p o i n t s c a l e e l a s t i c i t y is n o t d e f i n e d f o r v a l u e s of x i t h a t a r e i n f i n i t e s i ~ a l l y less

I t h a n i n t e g e r i ; i u l t i p l e s of Ck/aki, f o r k such t h a t Ski > 0 , f o r t h e s e a r e t h e s c a l e s of

o u t p u t a t whish a a a r g i n a l e x p a n s i o n of o u t p u t r e q u i r e s t h a t a n a d d i t i c n a i f i x e d cha rge

be i n c u r r e d . Were one t o ?lo& t h e p o i n t s c a l e a l a s t l c i t : ~ a s a f u n c t i o n of E U C F C Z , i t

~ - o l ~ l d be found t o h a - ~ e a d t s c o n t i n u o u s downward "juzipl ' s: eocil I n t e g e r m u l t i ~ l e ~f

* c ~ / B ~ ~ , f o r k such chat H k i 0; between t h e s e p o i n t s , t h e e1aS i : i t . y i s a con:iz:~cus,

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i n c r e a s i n z i u n c t i c n of output. - - - I r is p o F s i b i s :o d e c e m i n c a x z s ; ~ ~ ~ p t o t i ~ s s a i e el;scizit>T i ~ h i : ! ~ is the 17--er - i f

I boned ox t h e p o i n t scale c i r ? s ~ l c l t : : . Ccns!iirr tile a v r , i c t l ccc,t - f ;'roc : . s : i i . ~ 2: ,:

h s y - r p t o t i c P r o c e s s i n g Cost = 7 (Fk/ck) %i + Vk alii X

Averagd c o s t i s minimized a t t h o s e o u t p c t l e v e l s where e v e r y shop employed i n producing

t h e p r o d u c t i s o p e r a t e d a t a c a p a c i t y e q u a l t o i t s naxinu.. p o s s i b l e c a p a c i t y , i . e . wherz I

e c o n o a i e s of s c a l e have been f u - l y e x p l o i t e d . Using t h e ninirnum;value of ave rage cost

t o d a t e r n i n e t h e p o i n t s c a l e e l a s t i c i t y y i e l d s the a s y u p t o t i c sc41e e l a s l i c i t y :

Precessing Cost Asymptotic Sca le kl . E l a s t i c i t y =

Depending upon t h e p a r t i c u l a r c o s t components i n c l u d e d i n thb f i x e d and v a r i a b l e I

I c o s t p a r a m e t e r s , t h e d e f i x i t i o n s above y i e l d the p o i n t and a s p p t b t i c s c a l e e l a s t i - i t i e s

I

of c a p l t a l c o s t and v a l u e added. The d e f i n i t i o n of t h e s c a l e e l a p t i c i t y of t o t a l

2 I

p r o d u c t i o n c o s t depends npon t h ~ way i n w h i c i ~ endogenous i n t e r m e d i a t e i n p u t c o s t s a r e I

measured. Endogenous i n t e r n e d i a t e i n p u t s g i v e r i se t o i n d i r e c t e ionomies o f s c a l e , I

w5ereas o u r d e f i n i t i o n s of t h e c a p i t a l c o s t and v a l u e added s c a 1 e ) e l a s t i c i t i e s ~ e r t a i n I

Before t a k i n g up t h i s i s s u e , hoyever , we f r s t g i v e t h e g e n e r a l h_ - I

e x p r e s s i o n s f o r t h e n z r g i n a l and average ( t o t a l ) c o s t s of p roduc i Jg a m e t r i c t o n of I

2 r o d u c t i , as w e l l a s t h o s e f o r t h e p o i n t and a s y m p t o t i c s c a l e e l d s t i c i t i e s . The f o m e r

f o l l o w from t h e s t a t e m e n t of tt.e model: I I I

>!arginzl P r o d u c t i o n Cost a MCi =

- I

Avera'ge' P r o d u c t i o n Cost = ACi =' i ok uk(Bki xi)-7/xi + v Bki + Gi + 5 ' ' k C I

j j i jj 1

u h e r e p j and p ' a r e (shadow) p r i c e s of t h e j ' t i , p r o d u c t p e r me t r ik t o n . The f i r s t t e r n - j I i

i n t h e e x p r e s s i o n f o r m a r g i n a l c o s t g i v e s the marg ina l c o s t of d i r b c t p r o c e s s i n g i n s t l o p s I - - t h e second , the d i r e c t n a r g i n a l exogencus c o s t ; and, t h c t h i r d , thk n a r g i n a l c o s t o f * I 8

1 C

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i n s h o p s ; the second and t h i r d t e r n s r e s p e c t i v e l y cor respond t o the fLrs: and second I I

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of e n d a g e n o ~ ~ s i n t e m e d i z t e i n p u t s , if the measure a v e r a g e s u p p l y i o s c s . ~ I v e r s g e I I

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An a s p p t o t i c s c a l e e l a s t i c i t y f o r t o t a l c o s t nay a l s o be d e f i n e ~ d . S i n c e che oct:cr

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c o s t of p r o d u c t i o n i s x i n i n i z e d a t t h e l e v e l of o u t 2 u ~ f o r w h i c h p r o c e s s i n g c c s t is I I

n i n i ~ i z e d . The p r z c e d i n g d i s c u s s i o n of a s l m p t o t i c 7 r o c e s s i n g c o $ t is t h u s r e l e v a n t ,

and vie O D t a i n : I 1

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where p? g i v e s t h e a s y n p t o t i c a v e r a g e s u p p l y c o s t of t h e j' t h p l o d u c t . J

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c o s t s cf t h e endogenous i n t e m e d i a t e i n p u t s a r e t o be d e r e r n i n e d l C o n s i d e r t h e F o i l c w i r I

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1 p r i m a l . The two c o n s t r a i n t sets of t h e d u a l may 3e r e p l a c e d by a s n g l e c o n s t r a i n t : 1

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Thus :he shadow p r i c e o f t h e i ' t h p r o d u c t , pi , i s e q u a l t o t h e r i n i n u n o f t h e impor t I I

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produc ing and i m p o r t i n g e a c h p r o d u c t o r t h e v a l u e s of t h e p r o d u c t dhadow p r i c e s . The

s o l u t i o n t o t h e d u a l n o d e l i s t h u s u n i q u e l y de te rmined by t h e va ludls o f t h e iii p a r a n e t e r s . I

T h r e e p a r t i c u l a r c a s e s of t h i s l i n e a r programming problem are r e l e v a n t , e a c h d i f f e r i n g I i n t h e p r e c i s e d e f i n i t i o n of t h e T~ p a r a m e t e r s . 1

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l i n e a r program:-ng ndrdel t h e n c o r r e s p o n d s t o t h e HIP model when t h f i x e d c h a r g e s and l-' t h e c o r r e s p o v d i n g i n t e g e r i t y c o n s t r a i n t s a r e t o t a l l y n e g l e c t e d . ~ h k d u a l v a r i a b l e s , c

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gave-:er, t h e a v e r a g e c o s t o f s u p p l y f o r p r o d u c t i depends upon t h e a s s u r e d l e v e l s of I o u r p r : o f - a l l t h e p r o d u c t s , u n l e s s t h e X x a t r i x i s cec:ornposable.( Thus t h e ? r c d u c t i a n ~

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c o s t ? o i n t s c a l e e l a s t i c i t y i s a l s o a f u n c t i o n o; t h e assumed ou~ tpuc l e v e i s af a l l I

t h e d i r e c t and i n d i r e c t endosenous i n t e r n e d i a t e i n p u t s . - 10 /

E s t i z a t e s of S c a l e E l a s t i s i t i e s

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a t t h e e x ~ e c t e d o u t p u t l e v e l s f o r e a c h o f t h e p r o d u c t s a s *dell a a s p p t o t i c s c a i e

e l a s t i c i t i e s o f c a p i t a l c o s t , ~ a l u e added , and ( t o t a l ) p r o a u c t i o c o s t . ( ~ i 1 f i g u r e s '2nd

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, p r o d u c t i s t h e c : , ~ i ; ; e e r s ' e s t i n a t e of t h e a o s l i : : e lv .:olume of $ ro t iucc lon i n 1975 , r_ivc

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l a r g e r t h a n t h o s e a t expec ted o u t p u t l e v e l s . The f o l l o w i n g t a b l e s u ~ x a r i z e s t h e s e

f requency d i s t r i b u t i o n s i n t e r n s of the averages and s t a n d a i d d e v i a i t i o n s over t!le 120

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o u t p u t l e v e l s a t v h i c h econoxics of s c a l e a r e f u l l y e x p l o i t e d a r e exltremeiy l a r g e 1

r e l a t i v e t o t h e expec ted o u t p u t l e v e l s , xe. Below a r e g iven statistics frcx t k e i I

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e r y e c t e d o u t p u t l e v e l s (E ) and f r o n t h e e x p e c t 2 d o u t p u t l a v e i s ( E l ) . !%ere t h 2 . 5

c u m u l a t i v e f r e q u e n c y d i s t r i b u t i o n s o f c o r r e s p o n c ~ i n g ~ c i n t and i n r e n r a l e l a s t i c i t i e s

d i v e r g e , t h e l a t t e r i s shown by a d a s h e d c u r v e .

D i s t r i ' o u t i o n s o f c o r r e s p o n d i n g p o i n t and i n t e r v a l e l a s t i c i t i e s 20 d i v e r g e , h u t

w i t h monor e x c e p t i o n s o n l y a t e l a s t i c i t 1 1 v a l u e s g r e a t e r t h a n 0 .7 . S w m a r y statistics

f r o n t h e s e d i s t r i b u t i o n s a r e g i v e n be low:

Va lue Added P o i n t S c a i e Elasticities -

Simple Ave rage 0 .655 0 .751 0 .82A

S t a n d a r d D e v i a t i o n 0 .250

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f i r s t two of t h e s e a r e h i g h l y significant, u h i l e t h e l a t t e r i s s i g n i f i c a n t

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f o u r t h p h a s e , ;he p r c d u c t ' s x k e - b u g c h o i c e i s agc?in n o t c r i i c a i l ; , a f f e c t ~ 6 'zv i - - - j - . . L C

l e p e n d e n c e , b u t i t s h c u l c b e p roduced . I -. ~ n e se-cnd q u e s t i o n h a s t o do w i t h t h e c o n s e ? u e c c e s of ? I n t e r d a p 2 r . d e r r i re;-

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be tween p r c d u c t i o n c o s t and i m p o r t p r i c e , t h e y w i l l va,? w i t p a r a n e t e r changes i n t:

sarie d i r e c t i o n a s d c z s t h e a e a s u r e of I0 I n t e r d e p e n d e n c e . F r r h e n o r e , c h i s i s r r u ~ Ij whe::ter one i s s p e c i f i c a l l y conce rned v i t h t h e consequer .ces cf I0 i n t c r d e ~ e ~ . 2 e n c e OL-

o f c a ? > i c i t y i n t e r d e p e n d e n c e . Wi:h r e g a r d t o a s l n g l e p r c d w c t , a r i s e i- t':e ;:cc?sn$

r a t e zakes. i t n o r e c c s t l y t o n e g l e c t i n t e r d e p e n d e n c e ~ h l : ~ - z n i n c r e a s e ir. * ~ c : : e r r k e

r4 t t . , or =he i n t e r e s t r a t e nakeg i t l e s s c o s t l y . ';:len a! i o t h e r ; ~ r o d u ~ t s ' i ' ~ t ; ) x t L.zv

a re t:nchnnqed, t h e c c n s c q t ~ e n c c s of e i t ! l e r t y p e of i n t e r d c ? e n d o n c e genera;?:: : n c r c , . s e

a r i s e i r ? ie::nnd f o r the p r c d c c r s i n c e r?verage Air&?(.!: '%xed c o s t s n , enpra ' i : : , i l l A;;

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c o n s e q u e 3 c e s of i n t e r d e ~ e n d e n c z v:r:: n o n o t ~ n i c a l l y w i t h changes i n a p a r t i c u l a r ?araF.e=er,

b e i n g i r , c r e a s e d vhex t h e pars l r .e te r change r e s u i t s i n a r e d u c t i o n of d o n e s t i c ?reduction

c o s t s r e l a t i v z t o i n p o r t p r i c e s and reduced i n t h e o ? ? o s i t e Ho;~ever , tilis r.eecj

n o t b e t h e c a s e b e c h u s e p a r a s c t e r changes a l s o i n f l u e n c e u c t s a r e c r i t i c a l i v

a f f e c t e d b y i n t e r d e p e n d e n c e . I n a d d i t i o n , by a f f e c t i n g t h e compos t i o n a n d / o r c a p a c i t y 't e c t i l i z a t i o r , of t h e s e t of p r o d u c t s ::hich s h o u l d be p roduced i r r e s p c t i v e of i n t e r -

d e p e n d e n c i a s , p a r a n e t e r changes a l s o a f f e c t t h e magn i tude o f t h e g i n s due t o c a p a c i t y

s h a r i n g . Thus t h e s e c t o r- w i d e consequences of i n t e r d e p e n d e n r ? n z e

a o n o t ~ r ~ i c a l l y t o p a r t i c u l a r p a r a m e t e r changes . And t h i s i s t r u e w e t h e r t h e s e 4 c o c s e q c e n c e s are a e a s u r e d i n a b s o l u t e terms o r r e l a t i v e t o t h e s u p l y c c ; t of t h e

c r i t i c a l l y a f f e c t e d p r o d u c t s t h a t s h o u l d b e produced o r t o t o t a l v

The r e s p o n s e o f t h e consequences of i n t e r d e p e n d e n c e t o c h a n g e s i n s e c t o r- w i d e

demand p r o v i d e s t h e c l e a r e s c examples t o i l l u s t r a t e t h e f o r e g o i n g a a l y c i s . D i e s e l b e n g i n e s of 200 t o 500 horsepower ( i - 51) a r e c r i t i c a l l y I0 i n t e r d e e n d e n t unde r t h e S l , b b a s i c , a n d 5 3 s p e c i f i c a t i o n s ; i n c l u d i n g t h e a d d i t i o n a l s a v i n g s due t c a p a c i t y s h a r i n g ,

t h e c o s t s a v i n g s due t o p r o d u c i n g t h e s e d i e s e l e n g i n e s i s 3 . 4 4 , 3 . 6 , and 3.S0 p e r c e n t

of t h e i r i m p o r t c o s t unde r each of t h e s p e c i f i c a t i o n s r e s p e c t i v e l y s e e F i g u r e 9 ) . These k e s t i m a t e s i l l u s t r a t e t h e monotonic i n c r e a s e i n t h e consequences of n terdepender lce a t

t h e l e v e l of a s i n g l e p r o d u c t a s domes t i c p r o d u c t i o n c o s t f a l l s r e 1 t i v e t o t h e c o s t of

i m p o r t s ; :?is i s :he p r c l c t i c a l l y un,exceptiona! r e s p o n s e w i t h , r e spec t o e i t h e r t y p e I o f i n t e r d e p e n d e n c e where c * ~ r d a t a p e n n i t compar i sons a c r o s s s p e c i f i a t i o n s , r e g a r d l e s s 4 of t h e ; a r t i c u l a r p 3 g a n c t e r ttlar: is v a r i e d . An e x c e p t i o n (one of o r l y two t h r o u g h o u t

-* t h e s p e c i f i c a t i o n s ) ? s p r o v i d e d by b a l l mi l ls (i = 69) which a r e c r ' t i c a l l y c a p a c i t g - - - i n t e r d e p e n d e n t u n d e r x h e S 1 and b a s i c s p e c i f i c n e i o n s and c r i t i c a l l y I0 i n t e r d e p r n b ~ n t I .

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u n d e r t h e S 3 s p e c i f i c ; l t i o r i . The c o s t s a v i n g s ice t o ?reducing ball -:ills i s 3 . 5 0 , !G.i5,

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I S:c and i 5 . 1 3 p c r c e i ~ e zf i z p o r t c c c t L ~ I , C ~ C T t d i i i CI t ! ;cse s ? c c ~ f i i ~ L > c ~ ; ~ Iro~;xc~c:l..3c::7 '

. . . F i g u r p s 1 and S), s o ':h,.it ~ i ~ o ;;cns.cjue;:c:is 0 5 . < r : : . ~ y ~ p ? e ~ ; d ~ ~ : i i . in

r a t h e r :L>,:r r i s e v+-i;pr, +!.n -n.>-~.,--, , .

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I . . . I . - ,- CiL ;rzducts, t h e n v - ~ k e r o f v i c h :>sn-~s ~;C!ll-~inotC!.7.;.;cJi~-: '.;It? l::.re&sc:? '- .- . - ' - - - . - . . .- - . . . , . -. ~ . , . , r - - -> , .rLL a r ? 2 CIL ? r c c u c : ~ unde r ~ p e c i f l c a t i o r ~ S i , 4 ~ r 2 e r r'::e j a s f - ~ r , e c ; i : c ~ : i ~ ~ , . L - - . - - .

3 =ricer s ; : e c i f i c a z i ? n S 3 ( see F i g c r e 3 ) . X o n e t h e l e s s , o n l t t i n g ..2 a c l i t i c n a l 2iF.1 ;::Y lL - -Gpa:ity shar- ,ng, t:;e lcss t h a t would be i n ~ a r r e d L-re zhsse p r o k c c t l ~ . p . ; r ~ ; d Escs

i n c r e a s e 1 ~ i t ; l ds;r.arid: i n r c i 2 t i o ; i EC t h e i r aggrega te i!;pcrt c o s t 4 t k e Loss is 3 .1 , 3 . 5 .

3 . 9 percent r e s ? e c t i - ~ e l y under t h e S 1 , b a s i c , znd 5 3 s p e c i f i c a ~ i n s ; ;n r 2 i a t i c n :(: i a g g r e p i t e v a l u e a l l e c , t h e c o r r e s p o n d i n g fLgures a r e . 6 7 i , .732 , arc2 ,821 p e r c c n t

r e s p a c t i v e l : ? . (These and t h e e s E i c a ~ e s g i v e n below a r e taken fr x T a b l e 2 , ) ? o . i ~ v e r , r i f tiye a d d i t i o n a l g a i n f r o n c a p a c i t y s h a r i n g i s i n c l y ~ c e d , :he? t t ; c - l o s s c h a n g s s nor.- 1 a u n o t c n i c n l l y ? ~ i t S i n c r e a s e s i n denand : i n r e l a t i o n t o t h e i r agg egdLe i ~ p o r ~ c c s t ,

t h e t o t a l 135s i s 3 . ? , 3 . 6 , and 4 . 1 p e r c e n t r e s p e c t i v e l y ; i~ r e 1 t i o n t o t o t a l v a l u e i a d d e d , t h e c o r r e s p o n d i n g f i g u r e s a r e 0 . 7 7 5 , 0.756,and 0.860 p e r c d n t .

l Tur2 ing t o t h e C C I p r o d u c t s , we fLnd t h a t t h e i n p a c t of d e a nd c h a n g e s on t h e s e : t c i

wide consequences of c a p a c i t y interdependence i s just :he o p p o s i i e of t h a t on ti:c s r c :u r .

v i d e c o n s e q u e n c e s of I C i n t e r d e p e n d e n c e . Tliat i s , An i n c r e a s e i{ d r z a r d r a a - . - ~ - -ic3 th.2 :CS

i n c u r r e d by i ~ y s r t i z ; ; Chc CCI p r o d u c t s which o u g h t te be produced i s 1 7 . 7 , !3.7: a x - - z e r 3 p e r c c n : r e s 2 e c t i v e l y of ::?cse ; r o d u c t d zggrcE;a tc inpcrr c o s ~ c u:;Jor t?:e C : , '3;151c,

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as 5e t-zecr: ri:t s e t :,-.r-.~ii.e ~ , . ; S ? ~ U E T . C ~ : ~ ', r.ap.lc<try I:.- : - . : 1,- z C . . 7. 5 : ; . ..: :- . . I

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t h a t t he sectsr-vi ide cocse:Lences of i r i t e rdspen lence need no t vary u n i i o r x i i y l.,~iti-~

changes i n the k e y ?arazc.:ers, :..l?ereas :he cor~sequences f o r s i n g l e ?ro<uc ts geze r z l l - r I

d o . We cou-J g s cn t o f u r c k e r i l l g s r r a t e t h i s p o i x t wi th r e s p & c t t o v a r i a t i o n s iz I

the o t h e r p a r a e t a r s . Esz2ver, .<e s h a l l l e a v e t h i s f o r t h e r e i d e r t o pursue if s o I

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who le . On t h e o t > . e r hanr',, Scc t io r .

F i r s t , t h e n u z b e r 05 p r o d u c t s a i f s c t e l i iy i a r e r d e p e r d o n c e i s d a i e r p ' l l ? : l i re 5:rall ~3:;:: ;

- i. :o :he n u a b e r of p r ~ d x c : s :h2: s a t i s f y t 5 e z e c e s s a r y c o n d i c i o z 13r r c i u e t i o z . 5ac~:.c,

t i e 20s t 3f n e g l e c t i n g i n t e r d e p e n l e n c e , w h i l e s o e e t i z e s su5s t a x i l a l , --, :- Zei-s n f t h e

? r o d u c t ' s orm s u p p l y c o s t , i s g e r e r a l y v e r y s~.:.ali r e l a t i v e :o t ~ t z l adddd L ~ - : T ' - -..-.. zkr:

s e c c o r . I n no c a s e v o u l d t h e c o n ? l e t e n e g l e c t or' i n t e r i e p e n d e z c e c h c o s i n ~ b e t ~ e ~ r ,

p r ~ d u c t i o n and i n p o r z s i n c r e a s e s e c t o r - : ~ % d e t o t 2 1 s u p p i y c o s t b:; e :ban 3 .0 ;erz:rt s:

t o t a l v a l u e added . Tc! p l a c e t h i s e s t i r : a t e i n p e r s p e c t i v e , L t -. ; : e a l :,-;thix :'st. rar.c,e of :- t

e m p i r i c a l e s c l n a t e s f o r t h e e f i i c i e x c y l o s s Ooa t o t h e c!e~-i:ore frbn P z i 2 t e c p t i z n l l r .

:a!? be c r a c e d t o t z r i f f s , t a x e s , xonopo iy , and tk.e l i l i ? ix t h e sbs? ce of ec2r.-- 'es cf 2 2 2 t. . - ,,e a r e t h u s l e d t o c o n c l u d e t h a t rhe i n t e r d e p e x d e x e co v h i c h i e s of s c a l e g l v e r i s e

d c e s n ' t "nat:er: ' v e r y much.

O f c o u r s e , a c o n c l u s i o n drak-n f r cm the e s t i a a t e s p r e s e n t e d i n e c c i c n liI r . uc t Se

: e n t a t i - ~ e , and i s b e s t r e g a r d e d a s a n h y p o t h e s i s s u b j e c t t o f u r c h e r ies: i : i~ r,r.r', rcf::.ez.ent

w i t 5 c t h e r , n i a i l a r S o d i e s o f p r a d u c t i c n i n f o r x a t i o n zsr c z h e r coun r L e s 2nd scc tc rs .

. , . -.:e ?;;i;-c VC\,.<EL :.:- :' T h e r e a r e s e . ~ e r a l r e a s c c s f o r c h i s . F i r s t , t h e " ~ 2 ~ 3 l e s i ze"

o n l y one s e t of u s d e r l y i n g p r ~ d a c t i , c n d a t a and x i t n %?n',y r ~ i - c se t ; f ;;ra;r.cte

. I . . s p e c i f i c a t i c n s . Second, a l l o w a n c e n u s t be n a d c f o r ;cssiL:c errors o f 2 5 k n ~ ~ ~ n c ~ r ~ ~ p ; -,cn

- - . _ .I 29,' C : l r sc~j:;t:.or. ;.ro:edcre - . - . - . , . . , , . - , . , .. .. . - .

- I n e r r e :: lez,.is .JS !I(: 2.c : . L . _ ... . . . . . . . .. .: . < . L & . :..-., . . 1 .

!:.:fr.r,:i:r_r?decrc. .-,-r~..b,ez,zr~.. . c h p fz i ; :yyc :- :;.& ;ri ,I..;;..a.,- ,..-I t c I : - . . . . .-.. . - i;: '.:: r:. - ..--:-:.:: . . . - . > f - ; -. ,

1 ; L 5 . = . [ ! : - , - . - : - : Y . . .-..: <- .- ' . -- .. . . ' . ?, . . -. ,- 0 7- . . - ,. . ..L -,. ;.f SCT -;.r-,c!:~ct:s .-.::2 : , i q ; r :a tc:l :r.c .?; t L . %.. . . .

a r e c o n s i s t e n t v i t h t h e n e z r l y u r . i ve r sa1 f i r -d i n g t 5 a t t h e s u r f a c e of t h e c b j e c t i v e fxcctls

i n a n i n c r e a s i n g r e t u r n s ~ o d e l i s c u i t ~ f l a r o v e r a r e l a t i v e l y l a r g e n e i g h j o r h c o 5 of E ~ S

g l o b a l o p t i x u r ~ . z/ F i n a l l y , t h e x c d e l o x i t s s e v e r a l f e a t u r e s whiqh have been ky;oc>.ssiz:.~ I

t o i n c r e a s e t h e consequences of i ~ c e r d e p e n d s n c e : =/ t h e model i s s t a t i c r a t h e r t h a n I d y n z i c ; i t n e g l e c t s s p a t i a l allocation and t r a n s p o r t c o s t s ; and , irt does n o t incor?ora:e

I -

There a p p e a r s t o be a q u i t e s ic rp le e x p l a n a t i o n f o r o u r which we F;elLZv= -

s u b s t i t u t i o n ariong p r o d u c t i o n a c t i v i t i e s , e i t h e r i n t h e p r o d u c t i o n

o r chrough r e s o u r c e b u d g e t c o n s t r a i n t s .

n a k e s i t n o r e p l a u s i b l e . The consequences of i n t e r d e p e a d e n c e a r e a f u n c t i o n of t h e n c x t e r

of i n d i v i d u a l p r o d u c t s

of c r i t i c a l l y i n t e r d e ~ e n d e n t p r o d u c t s and , f o r e a c h cf t h e s e t h a t o g h t t o 11e ?reduced, t k ~ C c o s t s a v i n g s a s s o c i a t e d w i t h rhe r e c o g n i t i o n of i n t e r d e p e n d e n c e . ~ { e s e c t o r - v i d e

I

consequences of i n t e r d e p e n d e n c e i n t h e Korea4 model a r e i n i n i a a l l a r e l y because 0:: t h t 4 m a l l nunber of c r i t i c a l l y i n t e r d e p e n d e n t p r o d u c t s . R e c a l l t h a t a r o d u c t i s cr2t l :al l : : 4 i n t e r d e p e n d e n t i f i t s i m p o r t p r i c e l i e s be tween i t s a v e r i g d p roduc tdon c o s t a t wor ld p r i c e 3

Wi > c On 2 p r i o r ; and i t s z i n i n u n m a r g i n a l p r o d u c t i o n c o s t , i . e . i f >ICY + f i - - g r o u n d s , t h e r e i s no more r e a s o n t o e x p e c t a l a r g e nunber of s u c h p r d u c t s w i t h i n a s e c t o r b t h a n t h e r e i s t o e x p e c t a s m a i l number; i f a n y t h i n g , a m a l l nunber o u l d g e n e r a l l y be

expected. F i g u r e 9 g i v e s . t h e cumula t i \ re f r equency d i s t r i b u t i o n of t e r a t i o s of average?

p r o d u c r i o n c o s t a t t h e e x p e c t e d o u t p u ~ l e v e l s t o i n p o r t p r i c e ( i . e . , Ci/K.) i n t h e b a s i c ? s p e c i f i c a t i o n of t h e Korean model. The d i s t r i b u t i o n of a v e r a g e prod c t i o n c o s t t o i n p o r t ,

. I

p r i c e r a t i o s i s w i d e l y d i s p e r s e d ; 98 p r o d u c t s have r a t i o s between .1 and 1 .70, rci t ! l a r r o u g h l y u n i f o r m d i s t r i b u t i o n o v e r t h i s i c t e r v a l . Hore t o t h e p o i n t , o n l y a r e l a t i - ~ e i y f~7:; - 'I - - p r o d u c t s have r a t i o s c l o s e t o i . 0 , and t h e s e a r e t h e p r o d u c t s ~ o s t b e crl:;:s--:: -

i n t e r k p e n d e n t . G/ The e?c;rlanation is tb.us fcund i n t h e v i d e I

30/ S e e , f o r exampie , :!snne : 1 9 6 7 ) , p . i 5 f f . and :;ss:~i~al - ? l / See :!anne ( 1 9 7 3 ) and :.;es:?!?ai ( i 5 7 5 ) .

I I -- I

. . 32,' A t :his point; i t i s rele\;an'; to r ,cte : i 1 - ; ~ ::'Ji\_ : . : cZ? C ' G ~ C ~ G : ~ . ; - : c Y - - . . . t h e i 2 0 p rcduc ts . T h e !~;:..est c:>rrsizt lcr , is :cur,d .:;C; : :;.;c. :s::..: ::. 2

c o r r e i a t i o n i s i 9 3 6 , while t h e raak c o r r e l a t i c n i s . 9 7 2 .

.- -< , - -..c7 - . .. ,- . , - ,. ;-,, . ,_ ,:ect - a p ? r a i s e l cri tert-7. f c r ~ r c d c c 1 5 3 1 states t h a t a ? r o c : ,:c c!:z::::. . - - \ - . - : -

-

. I - ., - c s 2: ; ;or lc ~ r i c c s der i - jes f r r , tr,e 7 c r f e c t l y c z ~ y e r i : ' c . ~ . - -2:e wl::n :;o:.-Lx:-e~z:n:

rs:;rns to s c a l p zr.2 f r e e inter ; ls :Far .al t r z d e . L'zi'er t h i s :;rd&, - ~ - ~ o i l i ~ t , - ~ L-.~,:;. ..- - tntc-.- - - -

- . . s 3: :*.s Le:.ci,-pz.t:n: 7 . : ; * r % 3 - . . a o r . T h e r e is a x p l c . . . . . ,. . . . ,

, . - - . zc: ::.ec::ar.~ca- ,~2gi :< :e r ing ? . r s d l ~ c t s a cour1cr;l ~ u s " ~ s ; r s t

J ,- ,. ' . . . . -A,, iL<,L:;.); :-52 : l : f i + , , i S t ~ : ~ y , : , i g : < : - ! - : l j . 2 P".?

- . 3 - ; 1 - . , , - 7 . ~ --<.A ....- ,-.- iin ~ c ~ c i u ; r . : ~ - ::;isc? .:5 ..- . . - - -. , . . I ,. - , -5 -,??or r s r i c y C 0 5 i o l i t i ~ p l l ~ 5 i ! 1 ~ 5 S?.CU?I 9 ~ t 5.2 ~ a l y j x 2.5 2 <.:-.:::- ?:,

C . r

I T o c r g i : ! u < z i : \:?.,i;e i::cy:l:;.ci;dcnce da($ t-2 r+.-<-r. . - -

. I

3 , -- ,- ..u,.:l.c.s (.I +,(.a,~? ~:t.::s L C ~ : ; : , ~ L : C Y 5:- I - . .-

Coat Saving Resulting from Capacity Sharing

Cumulal~ve

Fpmuencv: Number ol Process Elements

0 20 4 0 60 80 (00 ' Percenregd at C o y Seved under C a ~ d f % t y S h s r ~ n q

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I World bnk-9912

1

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T o d Cmt S r r i n ~ k 1rnpa-t C a t for Gibdlv to I n a d . p r d . R t Roductr

?. k n l u - & r r c Lrw.1 L* 7 ~ ' 0 . 3 d + >. r . ~ h . ~ ~ . 1 . c . (von per U.I. dal :*r ) ~------I50----$ $50 300 4 3, I rmrrb . b u r l , Gag. b e (wnn) t 15; > I , . ~.t.r..r r.cr c p . r = . o c ) L I e--- 20

K* + - >O ----------4 215 3 73 t i ?5 ------t

1 3 >D

I - I ' . I. g 4 . r o f r r o d u c t l o n A c r l r l t l ~ ' :

1. Ior w i ~ i c h rC 5 2 ' Y 58 >S 5 1 , 72 ( 6 1 2, l a cb* S o l u r i o n r i C l w t S l a r l r B :

2 1 6 9 I. rrodurrd r r ? r % L = u D ~ t p u t Ltrrl >9 6 0 & 9 66 62 6 9 6 1 5 2 b. Impor ted . o r l o p o r t e d r s d Produc.6 I I I

I, troduc-4 v l t h S h r i n g . . 61 61 57 6 7 & 6 5 3 5 3

:. * o c a ~ v. ~ u c ~ ~ 8 . 4 <-!l!ion ran$' - . I . ~ l c b v l Shoring 81516.7 1 6 S . 7 9?215.1 42517.6 9 0 . I . 71117.6 1 9;112.'1 1. w i t h Sharing W731.8 1b017t.: - 5 . e 3 ; c i . r 606oL.7 7 . 101-I:.$ 76175.1 i E;i;6.:

>. roinc Lrl lz - l r . a 1 C t c t o r - v { d e V a l r a Led14 S c a l e : I r a : l r l r *

1. F l t h o ~ r S h r l n g 0.661 0 . ~ 6 1 5 .115 0 . 7 0.802 1.872 3 . 6 7 1 I O.E:5 1 0.5% 2. Y l t h S h r l r g 0 . W 0.905 C . j i 3 ' 0.891 O.SL3 , 1.901 0 ' 0.WZ . ( 1 . 8 3 j

. Cosr Zavl: ,rr d u e . .I.pbtltv S ? a L n $

1. D l a r r r d u c t s ? r a d . ~ ~ t J ~ 1 t . L S : Y ~ ~ ~ : ' a . Saving. i n F ixed Cost /p . r r tnc l . lL.B ' 20.1 ' 12.L 16.6 22.9 :&.I lL.7 27.C 11.2 b, Savlnsa i n ' l * ! c . ~C2.d r:mrr.nc) .. 3.1 1.L 3.8 4.1 1.1 3.2 1 . 2

2 . W e r F r o d u c : ~ tk.nr a r e C r l t ~ r . 1 : ~ C a p a c i t y :?rr:!c:e:t.?t a. Shauld t. 7roddc.d r i r l l i t a r l c ~ : i o l a l CaaI i r v ~ = ( s

I . Ar r*rren: of t ~ 3 I : ? ~ r c ' < o s ~ L , 13.7 0.0 1 5 . 1 . 26.7 11.0 10. 2 11. A s P e r t e c c of Icc.1 :.lie ~ d 4 . d - .0.069 . I 1 9

b. Should ::or tr Pra3:c.a v::h Skar lng: I o t a ! C a a : !rcrersm i . A s I.r<.ar of h. I=-orc Co.: 61.6 0.7 6.7 . A.6 6.5 5 . 1 I..> l . 1 : c . ?

' 1 1 . A. ?.rc.nc o f I~: . I i . : ~ t A d d . d i l 0.011 0 . 0 ~ 5 I 0 . i c 9 0.0'6 0.0:s c.::: 0.01: I C . k 2

. Frat 5,v!ng&q I > 7ccos?1:L? o f ! O i,:rrtr~r-ts:rr

1. A r ? c r c c n t o f AT l c p ~ r c Core . .. L' t rhrur Sh. r l , ( 3.5 3.9 . 3 . : . ' 8 . 3 1.0 0.0 i . 7 2.1 C.i

b . u l t h S D s r t ~ c b I , .

1.6 c-1 ~ J.5 7 ' 1.1 0 . 0 2. ' ( . I , r . A,- P*.?:*.*t of : r t , t .:a Sde A&,td -

a . Y l t h o u c S h a r l n ~ 0.712 0.171 1.:?1 2.757 0.115 0 .3 b. P!ch PharL~.& 0.756 0 . 4 5 0 , . 1.$10 0.116 3 .0

I

TO ~ o t i - ~ a t e t k e f o l l s v i n g d i s c u s s - L A C , ce s h a l l EL::? t C G C 5 r < r : r 1 a ? a r t i c n l a :

f o m of t k e !.iIT r o l c l . Suppose =b.zt t::sre vr:e TAG ca>;cily :~c'-ricig ( I e , f o r wc?,

k~ 3ki > '? Ear o d j r a s i c g l e i ) a d :hzt t h e r e vtre no er.6?&en.cs 5 t t e r r . r - ? f ? t e I

i c p t c o s r ( i e , Aij = 0.0 , all i ztd j ) . ?'be f u l i ~ o d e l slculd t k e b k c 4ec~--?o,ccblc I

F 2 t o a set o f models, a c e f o r ecch p r o d u c t , of :he Zoi lcwing f c r z : ~

. I where R d e n c t e s t h e s e t of p r o c e s s e l e n e r t s !n which ~ r c c e s s i n g ils r e q u i r e d r o

i

prcduce product i . This i s .I very si:pla earif1 t o s o l v e . iJse eccdt- icn 1 2 ) to I

s u b s ~ i t u t e i n t o t h e objrcr:ve f c n c r i o n F o r yi; (31, fcr c , ; and, !b), f o r 2,. . 7Yi.e A K

I ' .

o b j ec t i v c f u n q t i o n t h e n becones : i I r

. . I

I .I I - I

- l a s t t c r n on t h e r l g h c $3 a cons tanc tern e q u a l :o ;kc ccsr a f i m p 8 r t i r . g a:: * I

I t h a t i s exoeenor!sly derranded: it m2.y be ~ e g l e c t e d . 3 e r.Fra {I; pkr:inck:escs t h a t

I

c u l t - l p l i e s x; i s t h e ~ a r g i n a ; s a v i n g s of c i c ~ e s t i c prcl1:cticn cver I:r.yc.r: c o s t : *

i s the u n i t i r . ao r t c ~ s t anti Gi i s t b ~ - - r ~ i 2 a l 6:csc of t:.-,cc?.stlc i

. . 2 y p r o d u c t i o n . Let I!S d e n o t e u n i t marg1z;il s a v i n g s . :+I? t~pi.:;:.;,t eql ln t ion ( 5 ) '

i

n i n u s one n l t l droc;) iny, :i:e c o n s t a n t t e r n , w o b t a i n :

In equa t i on ( 6 ) , (i(xi) i s t he "breakeven func t i on" f o r ~ r o q u c t i: it

s t a t e s thc! t o t a l s av ings (of domest ic p r cduc t i on over import c o s t ) when t h e

q u a n t i t y x i s produced. Cne may e a s i l y v e r i f y t h a t marginal s a d i n g s must be i

p o s i t i v e i f i t i s t o be op t imal t o produce any of t h e product . Vhen MS > 0, i

one need on ly e v a l u a t e ( f o r va lue s of xi equa l t o z e ro and tho& marg ina l l y i

I

l e s s than m u l t i p l e s of C k / q i , kaKi, t o f i n d t h e op t imal s o l u t i o n . Th is is

because t h e f u n c t i o n 3 i s upward s l o p i n g excep t a t those p o i n t s &here a f i x e d i

cha rge is i n c u r r e d , where t h e r e i s a d i s con t i noub downward "jump"d The op t ima l

s o l u t i o n might b e t o produce some of t h e product and import t h e re(mainder, even

thosgh t h e t o t a l c o s t of domes t i c a l l y producing a s u f f i c i e n t v o l d e t o meet t h e

exogenous demand is l e s s than t h e c o s t of impor t ing a l l t h a t i s d e p n d e d . This

I

Under c a p a c i t y s h s r i n g , t h e f u l l MTP model is no longer decomposable i n t o

i n d i v i d u a l "produr:t models". Nonetheless , s t i l l assuming t h e r e a r + no endogenous

i n t e r m e d i a t e i n p u t s , one can o b t a i n a "reasonably good" s o l u t i o n by f i r s t ne-

. g l e c t i n g c a p a c i t y s h a r i n g and s o l v i n g each' s i n g l e product model coddensed i n I

q u a t i o n ( 6 ) . Let x* denote t h e va lue of xi t h a t m i m i r e s t h e brsakeven func t i on . i

C a l c u l a t e e* Ck q ( B k i X$ k i - Bki x;, kaKI, wf th r e s p e c t t o 'each product

independent ly and - C

wi th r e s p e c t t o a l l t h e p roduc ts j o i n t l y . The e and e,i v a r i a b l e s a r e measures k

of unexplo i ted i n c r e a s i n g r e t u r n s ; they s t a t e t h e amount by which t h e c a p a c i t y

con s t ruc t ed i n shops of a p a r t i c u l a r p roce s s e lement f a l l s s h o r t of t h e nzaxizum

amount t h a t could be cons t ruc t ed ~ i v e n t h e f i xed c o s t s t h a t have been i ncu r r ed .

I f : (Condi t ion 1 ) x* = D, f o r a l l i such t h a t XSi > 0 ; and (Condj t i cn 2 ) - i 1

- i -.

. ' ,-!.Lr + : 7 . ye 5!-cL-:a 0" < e* , K - 1 ,..., K , acd i s u c h :hat r k > 3 2 x 5 :, , z , - 1 j. .' - - . A

8. - k i . & I

-

z26el s o l ~ i t i c a s Iz715es g l o > a l o p t l r ~ 1 i ; y i f cer:aFz ~ e s t r ~ c t i z r - s 1 / - . -

ZTE 21.50 CEE. 3 r c o f s of t 5ese a s s e r t i c n s &re gF-:~n La : + e s t ~ l . a l

ar,d z l r e a d y ' ' i n existe: lceV by 7 . - t r tue of iEs use t o PrccGss

., ;-kith ,:f 0. 1-1 t h i s case, expans icn 3 prcrduct i t s

2 : ~ l r . g t3ose f i x e d c!iar&es ::':st have a l r e a d y been m e t

o:?,er products.

- 7 c n ? e z a n ~ .e i3eIs

7 - ,--- ~r .1 Y-:F-C .-; ;:-,

- * LX C c n d i z i c n I Is 'riolzted, t:?erl f: ;ray reduce systen c c s t s

s r o d u c t i o n of a ? r o l v c t f o r vh ich x: < 3 i such ;ha: XS > 0 , if * i'

to ~::pznd t h e c6paci:j. o f a s t o p ( o r s ~ v e r a l s h o p s ) r equ i red i n it..s

If Cond i t i r n 2 i s -riola:ed, then it m y reduce s j 7 s t e x roses :

:kc ~ r c d u c t i o n cf ~t l e a s ; cre of those p ~ c b u c t s r c a u i z i c g Flrciess

* k z e x 2, ;he=a ir Ls also s i :~ i -n :hat x > 12 i a s x f f i c i e n ; c c n t i l i c n 2 7 I:r.lf i

I 1.' - tka t c l e o p t k a i value of x, ~ n C e r c a 7 z c l t y starirg acsc be pcs i tkve.

I

!:o Z r . c r ~ a c e

. - i t is ?c.:s:b~e

prz2ccticn

c e a s e i e r e n t v h i c 5 e: > e-~cr some 1. i i t is l o t necraaviilp t ~ k : T L < s c + ( ~ : r~ P. i

* P f o r xhich e* > e that shsu lZ e s r e r i e n c e a rcducticr, i n 7rcdlJc:io .> :-cs5der, k k i . . I

* f z r example, a case :n uh'eh production at l e v e l r 4 r e q u L ~ e s !C, , ' [ 2 j A 5 u i t s A 1 " 1 + of capacit:; i n p r c c e s s elrrent 4, and ; ; r ~ d u c t i o n a t l e _ v e l :. . a l s r 1ret;uircs t h e

I .9

17 L

s a x nueber *>f u r . i t s c f caFzc::y L n p r o c e s s e lement k r , t ! - , ~ ~ r S e i n co ~ t k e z a - i * " T O ~ C t~ rc .q1; l r i r .g p r c c c ~ s i - ; : i? ..;is 1:rccess P . ~ F L ~ C ; ; " , ) ' ; I I F J ~ . E t h e . m

I

l/ Tne conciitior, i s s u f f i c i . x i t 5 a t n o t nc.cess?.iy. . T: .'- - .,., i t I:: ; : c : k:e,:c..:s;y :a:- :,p clc.-.,-..%L .-,., : - a tr.: I.? z ' n p i e e..:m-?l.es.. I

I

!

and P l a r g e e>oocgh, t h i s can no t be o p t i n z l s i n c e t h e a s soc i a t ed i n c r e n e n t a l kl

t o t a l n a r g i n a l s av ings would n o t be s u f f i c i e n t t o o f f s e t t h e a d d i t i o n a l f i x e d

charge .

To su-riz~e, by t a k i n g t h e va lue s x* a s r e f e r e n c e p o i n t s and cons ide r i ng i

p c j s i b l e s av ings i n system c o s t s 1 ) through i n c r e a s i n g produc t ion by e x p l o i t i r g

c a p a c i t y s h a r i n g p o s s i b i l i t i e s where t h e r e a r e shops of l e s s t h a n maximum c a p a c i t y

and 2 ) through reduc ing produc t ion i n shops where economies of scale are n o t

s u f f i c i e n t l y e x p l o i t e d , one can o b t a i n a " reasonably good" solut ion. . The pro-

cedure is f u l l y s p e l l e d o u t i n Westphal and Rhee [1975]. However, t h e r e i s no

g c a r a n t e e t h a t t h e r e s u l t i n g s o l u t i o n i s t h e op t ima l s o l u t i o n ; no r i s i t p o s s i b l e

t o s t a t e how f a r i t i s from t h e g l o b a l optimum.

Breakeven a n a l y s i s c an a l s o be used when endogenous i n t e rn i ed i a t e i n p u t c o s t s

and demands must b e taken in:o account . A s no ted i n s e c t i o n 11, t h e Korean d a t a

e x h i b i t no c i r c u l a r in te rdependence among i n t e r m e d i a t e i npu t f lows. The o r d e r i n g

of p roduc t ion a c t i v i t i e s and produc ts i n such a way t h a t A = 0.0 f o r i > j i j

makes i t a s imple uatter t o c a l c u l a t e t h e lower bound, MCi, on t h e marg ina l c o s t

o f p roduc t i ng t h e i ' t h i tem: 2- 1

MCi = C V B + G + Z

A ~ i P~ , where p = min (MC , v . ) ,

k k i 1-1 1 j J ( 7 )

K, e A

and one c a l c u l a t e s n a r g i n a l c o s t s s t a r t i n g w i th t h e f i r s t product and proceeds

- i n o r d e r . Observe t h a t p i n equa t ion (7 ) is t h e same as t h a t i n t h e Marginal

1 '3 L

Cost Model. The f i r s t s t e p of ou r procedure t o o b t z i n a s o l u t i o n is t o s e t xi -,O - f o r i such t h a t ?iCi Wi. ObsZrve t h a t IIC 2 W i s a s u f f i c i e n t c o n d i t i c n t h a t x - 0 i n t h e op t ima l s o l u t i o n P i i i

- . J u s t a s lower bounds on n a r g i n a l c o s t may b e c a l c u l a t e d , upper bocnds on o u t -

put l e v e l s may be c a l c u l a t e d . And a g a i n , t h e t r i a n g u l a r i t y of t h e A mat r ix s i m -

p l i f i e s the p:ocess. Let X denote t h e upper bound on t h e p roduc t ion of t h e i ' t h i

p roduc t , then:

I

Xi Di + Z A X , f o r icI : j=i+l ij j x

Furthermore, t h e r e i s no vap t o a d j u s t t h e s i n g l e p roduc t models, f o r ex&mple by

i n c l u d i n g i n d i r e c t f i x e d charges (which l e a d s t o double- counting c o s t s ) o r va lu ing

i n t e r n e d i a t e inpucs a t world p r i c e s (which l e a d s t o n e g l e c t i n g I0 in te rdependence) ,

t o g a i n a c l e a r advan tage fn r h e s o l u t i o n s ob t a ined u s ing them.

The d i s c u s s i o n has s o f a r preceeded a s i f one had e s t i m a t e s of t h e exogenous

derand l e v e l s , D However, -ae v e r e unab le t o o b t a i n such e s t i m a t e s , a s t h e i '

sample survey work which would have been r equ i r ed was beyond t he lirnits of our

r e sou rce s . I n s t e a d , t h e e n g i a e e r s provided t h e set of expected o u t p u t l e v e l s , xz.

The s o l u t i o n procedure rook t h e s e a s t h e upper bounds f o r t h e permiasab le p roduc t ion

l e v e l s i n t h e s i n g l e p rcduc t c o d e l s s t a t e d i n equa t i on (8). The s i n g l e product

model s o l u t i o n s , xo g i v e t h e s o l u t i o n wi thout c a p a c i t y sha r i ng . These va lue s i'

were then taken as r e f e r e n c e p o i n t s and a d j u s t e d accord ing t o t h e method ske tched

o u t above t o i n c r e a s e t h e p roduc t ion of product i, i.1 i f xy was l e s s than xe X' i

and i f i t was p r o f i t a b l e t o e x p l o i t c a p a c i t y s h a r i n g i n " ex i s t i ng" shops of l e s s - t h an maximum c a p a c i t y . In =king t h e adjustment t o e x p l o i t c a p a c i t y s h a r i n g pos-

s i b i l i t i e s , we were a t t emp t ing t o o b t a i n a reasonably good s o l u t i o n t o equa t i on

(9 ) , s u b j e c t t o t h e c o n s t r a i n t s t h a t x < xe i.1 i - i' x'

0 The v a l u e s of x were not a d j u s t e d t o dec r ea se t h e p rcduc t ion of sorce p roduc ts i

i if xi - x0 wi th c a p a c i t y . s h a r i n g vould r e s u l t i n such a small shop t h a t t h e a s - i

s o c i a t e d incrementa l s av ings vould n o t cover t h e f i x e d c o s t of i ts c n n s t r u c t i o n .

That is, we d i a n o t a d j u s t t he s i n g l e product model s o l u t i o n s f o r v i o l a t i o n s of 'I -

.%

Ccndi t ion 2 . Such ad jus tments v e r e i n gene ra l n o t r equ i r ed . Furthermore, by - - - B n o t making s u c p ad ju s tmen t s , b-e can s t a t e t h a t our s o l u t i o n s gove t h e upper bound * - t o t h e g l o b a l l y op t imal va lue of xi i n t h e f u l l MIF model. This is n o t a n a n a l y t -

i c a l r e s u l t , bu t r a t h e r depends upon t h e c h a r a c t e r i s t i c s of t h e s o l i t u o n s ob-

t a i n e d .

The procedure we employed n e g l e c t s t h e m a t e r i a l ba l ance c o n s t r a i n t s . I n

t e rms of simply a s s u r i n g t h e c o n s i s t e n t c y of q u a n t i t i e s , t h i s does not c o n s t i t u t e

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. . Cherer;,, :o::is 3 . , 1952, f f0. .~rc2=zcl t ; r acd t>.e ?Lcce ler2 t lon ?rir.cis?.e, I'

E c c z c ~ . e ~ r i c z , SO, 1-22.

7 . 7 . - Cherer;r, :?g:::s 5., 1559, I I T k L-.terdeyerfence of I zves tncn t z e c l s i c n s , " Lq I!. - . - A3pLnc.,rizz, e s . 2:. , T;".? .:-llcc?:isn cl" =ccr.cr.:c: :? zcurces , Stri-2or.l: StarYcrd - Uci-,-ersity rre ss.

I n s t i h t e f o r &search i.. k c l a l Sc iecce , Vz2re r s l t y of !:orth C e r o l k e , 1953, -. "hcu t -&t - ,u t i'Lr.zlysis Sc-riet ::az-.;T Xrc:?i?rq; ( k - ~ i e t 131zrLyLyg Study :Io. 6 ) , I f .. . Chapel n~ll. (n ixeo . )

I n s t i t u t e f o r ?*search 3 Scclzl Sclezce, Cnl=-e=.si',y of !:crth Carol:,-..a, 1959, m nFroduct ion CocfYicle2ts zcd i e c h o l o g f c ~ l 'i'ren2s L? Sovie t I ~ < u s t ; - ~ : 1.n

In~ut-Cutnu' , -2-mlgsis of )iac:.lberj- C c ~ s t r c c t i o n ( Sc-r let P l a r x i z g Study 20. 7): "

]4zpxe, S, , 1973, u.3. 'IJ,.ced I x t e g e r Alge r i tF -7 Tor P r o j e c t 2 - . d - ~ r t i c n : ~ ' L? L. !-!. Goreux snd $. , 5. :!??~le, &. , :.!i11%F-i.evel ?! 3n22?z : C Z SP St7:dfe s 55 I ' ! ~ : ~ c c , A ~ s t e r d a x : ::cr"vh-!!ollar,d ?:blishLig Co .

- l!zr::o!jits, s a r y ~ :.!. , 2nd k l z n J . ncm, 1963, "J- !lachin.e - ? c c ~ - .- -- T. C a "opnans, e d . , S h d i 2 3 i n y o c e ss . : .zal~sis , .re:.~ lark : zokd? Yi ley a::& - Sons, Inc .

- V i e t o r i s z , Thcnas, 1973, 1 ' 2 2 ~ ~ 5 x 3 zt the :.!icro Lcvel : The Fez-s; ~ l e c t r i c a l - E ~ u i p ~ e n t ~ q d u s t r ; 5n :Iexico, I t iijashir.r,:on. ( 3 ~ i e o . ) - -

9 Westphrl, L o F r j 3., 1975, I1?la-ni lg ;. th ~ c o n o z l e s of ~ c z l e , "37 C . 3. 2lit=c:., m 7 - ,.. * 7. 3. Clark, 2nd L. l a y l o r , cd.;. , :-concr.-,--;;:cc : ' c d c l ~ zn.! ?~v~ !c r - ,?n% ?:-.r.ntr.c - -- - 9

London: @Lord Unlverp;+-r 3 - V J Press ( f o r t>.c Ylcrld x ~ : c ) .

n .. . . -. ;-Jest?l'lal, L.7.r~"r L., i-nd L~LYG ii. ?see, 1975, Iri. Frccezs .\;;zlysis l.!cdel c f t he - P!cchcnical ; r . g lEec rL i~ k c t c r , " h'ss'r.i?~-~n. (ni-.eo . )