A C T A U N I V E R S I T A T I S L O D Z I E N S I S
_________________ POLIA OECONOMICA 3 4 , 1986_________
-J a n В . G a jd a * , D o ro ta M isz o z y ň sk a * , M arek M is z o z y ń s k i* , Ł u c ja Tom aszew ioz*, J e r z y S . Z i e l i ń s k i * *
ENERGY CONSTRAINTS
AND OPTIMAL DEVELOPMENT OP THE POLISH ECONOMY1
We b e g an o u r c o n s i d e r a t i o n s c o n c e r n in g t h e f u t u r e o f t h e P o l i s h n a t i o n a l economy I . e . t h e n e x t 20 y e a r s w ith l o o k in g f o r t h e s e e le m e n ts o f t h e eoonomy w hioh seem ed t o c h an g e m ost slow ly end w ere t h e m ost d i f f l o u l t t o m o d ify . N e x t,o n t h e Ъаа1з o f model e t u d i e s t h e c o n c lu s i o n s on t h e im p a c t o f s t r u c t u r a l v a r i a n t s o f th o s e e le m e n te i n t h e f u t u r e on d e v elo p m en t o f t h e economy w ere draw n. B e s id e t h e a r e a o f a g r i c u l t u r a l la n d o r t h e num ber o f P o p u l a ti o n , t h e b a s io e le m e n ts i n o lu d e n a t u r a l r e s o u r c e s fend t h e i r o u t p u t , e s p e c i a l l y pow er r e s o u r c e s and p r o d u c t i o n .
The m odel p r e s e n t e d i n t h i s p a p e r i s c o n s t r u c t e d a s an i n s t r u -ment o f I n f e r e n c e on a p o s s i b l e d e v elo p m en t o f t h e economy, con-d i t i o n e con-d by t h e assum econ-d s c e n a r i o f o r t h e f u t u r e o f f u e l ancon-d pow er p r o d u o tio n . Of c o u r s e su c h a p r o d u o tio n d ep e n d s t o a l a r g e e x to n t on o t h e r e le m e n ts o f t h e f u t u r e econom ic d e v e lo p m e n t, i n o lu d l n g t h e o n es we w ish t o p r e d i c t . We b r e a k t h e v i o io u a c i r c l e o f i n -te rd e p e n d e n c e i n h o p e f u l l y i t e w e a k e st p o i n t w here t h e c o n s t r a i n t s Im posed by n a t u r a l r e s o u r c e s and h ig h c o s t s o f t h e i r p r o d u c tio n ®eke them im pede t h e econom ic d e v e lo p m e n t.
The c o r e o f t h e m odel w hich e n a b le s u s t o tr a n s f o r m t h e s c e -n a r i o s o f f u e l and pow er p r o d u c t i o n up t o 2000 i n t o f o r e c a s t s o f o t h e r eoonom ic c h a r a o t e r i s t i c s , i s a sy ste m o f e q u a ti o n s c a l l e d t h e i n p u t - o u t p u t m o d el. A o r i t e r i o n f u n c t i o n i s th e n a d d e d . The
^ L e c t u r e s , I n s t i t u t e o f E c o n o m e tric s and S t a t i s t i c s , U ni-v e r s i t y o f Łódź.
* * P r o f . D r . , I n s t i t u t e o f E c o n o m e tric s and S t a t i s t i c s , U n i v e r - e i t y o f Łódź and T e c h n ic a l U n i v e r s i t y o f L u b l i n .
1 The s tu d y i s s p o n s o re d by t h e I n s t i t u t e o f E n e r g e t i c s u n d e r t h e G ra n t P R -8.
f u n c t i o n a llo w s f o r a c h o ic e o f auoh a p r o d u c t i o n programme w hioh i s o p tim a l from i t a p o i n t o f v ie w . We a h a l l c o n s i d e r t h r e e m ain g ro u p s o f c r i t e r i a » 2 1 . M a x im iz a tio n o f t h e n e t m a t e r i a l p ro d u c t (NMP) ( f i n a l p r o d u c t )
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1 — - max. T h is i s t h e s im p l e s t f u n o ti o n w hich e n a b le s t o m a in ta in t h e l i n e a r c h a r a c t e r o f t h e w hole and s o lv e i t by means o f l i n e a r program m ing m e th o d s. 2 . M a x im iz a tio n o f NMP u t i l i t y f u n o ti o nZ>iqi
— - m a x , w here t h e w e ig h ts r e f l e o t t h e " u t i l i t y " o f NMP o r i g i n a t i n g i n th e b ra n c h " i " . T h is i s a b e t t e r a p p ro a o h , h o w d v er, i t i a more d i f f i c u l t b e c a u s e o f t h e pro b lem o f p r o p e r w e ig h t s e l e c t i o n i n su c h a way a s t o r e f l e c t e o o i a l p r e f e r e n c e s . 3 . M in im iz a tio n o f t h e f u n o t i o n o f l o s s e s r e s u l t i n g from t h e f a i l u r e i n a c h ie v in g some p r o d u o tio n g o a ls z > i ( q i “ ч * ) 2 * I n t h i s c a s e - b e s id e t h e p ro b lem o f w e ig h t s e l e o t i o n r e -f l e c t i n g s o c i a l p r e f e r e n c e s o r l o s s e s we f a c e t h e p ro b lem o f d e te r m in in g t h e p a t h s qL* o f d e s i r e d g ro w th o f NMP e le m e n ts q ^ . Then o u r m odel i s tr a n s f o r m e d i n t o t h e o p tim a l c o n t r o l m o d el. 'W ritin g down t h e l o s s f u n o t i o n a l t e r n a t i v e l y a sZ / * i k - «1*1 •
we c a n keep t h e s o l u t i o n t e c h n iq u e i n a c l a s s o f l i n e a r programm-i n g m ethods programm-i n t h e programm-i r w programm-ide s e n s e , w h programm-ile programm-i t s o r programm-i g programm-i n a l v e r s programm-i o n makes u s p a s s t o t h e c l a s s o f n o n l i n e a r program m ing t e c h n i q u e s .
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G e n e r a lly s p e a k in g we may t h i n k a b o u t NMP a s o f n a t i o n a l incom e m inus t h e v a lu e o f s e r v i c e s .
P roper c h o ic e o f c o n s t r a in t s on p ro d u o tio n c a p a c i t i e s forme th e n ex t problem to be s o lv e d . In th e c a se o f a model w ith th e l o s s fu n c tio n th e demand f o r p ro d u ctio n c a p a c i t i e s i s an elem ent o f th e s o l u t i o n . In th e c a s e o f th e u t i l i t y f u n c tio n and NMP m a x im iza tio n , th e c a p a c i t i e s mu3t be g iv e n a p r i o r i . I t i s th e submodel o f th e developm ent o f p ro d u o tio n c a p a c i t i e s which makes th e system dynam ic. T h is problem r e q u ir e s c a r e f u l i n v e s t i g a t i o n . A c e r t a in group o f s o c i a l l i m i t a t i o n s and p r e f e r e n c e s , ab sen t in th e stan d ard in p u t-o u tp u t m o d e l,is im posed. T hese are th e req u ire- ments co n cern in g th e s tr u c t u r e o f NMP, th e a d m is s ib le im ported part o f th e f i n a l p ro d u ct, o r f i n a l l y th e "minimum e x is te n c e " req u irem en ts i n th e form o f th e minimum consum ption and accumu-l a t i o n . The l a s t e x te r n a l c o n d itio n i s th e "budget c o n s tr a in t" r e q u ir in g some e x c e s s o f e x p o r ts o v er im p o r ts, n e c e ss a r y f o r r e -p aying f o r e ig n d e b t s . The form o f t h e s e l i m i t a t i o n s i s su b je c t t o e v o lu t io n a cco rd in g t o th e a c tu a l s t a t e and c o m p le x ity o f th e m odel. F u rth er d e t a i l s are g iv e n in th e n ex t p a rt o f th e p ap er.
The model c o n s tr u c te d in t h i s way can have a d ou b le u s e . Assuming th e most l i k e l y v a r ia n t o f assu m p tion s o f changes in
p roduct-consum ption l i m i t a t i o n s , s o c i a l p r e fe r e n o e s e t c . we ob-t a i n a f o r e c a s t o f th e n a t io n a l economy developm ent and th e i n -form ation about th e n e c e ss a r y im p orts e t c .
On th e o th e r hand, when we change t h e s e assu m p tion s a ccord -in g t o th e v a r ia n t s o f th e economic p o l i c y , we oan compare th e e f f e c t s o f v a r io u s p o l i c i e s and e v a lu a te t h e i r ad van tages and d isa d v a n ta g es i n com parison w ith o t h e r s , c h o o sin g t h i s one which can b r in g th e most d e s ir a b le r e s u l t s .
The scheme o f i n t e r r e l a t i o n s h i p s betw een th e model elem en ts I s p r e se n te d i n P i g . 1 .
The below p r e sen te d v e r s io n o f th e model i s a subsequent v e r sio n among th o s e which were b e in g v e r i f i e d i n 1982. The v e r s io n s have been e v a lu a te d on th e b a s i s o f d i f f e r e n c e s o f th e s o l u t i o n g e n e r a te d by th e model from th e a o tu a l s t a t e o f th e economy i n 1980,. s in c e th e model i n th e p a rt co n cern in g in p u t - -o u tp u t e q u a tio n s u s e s th e l a s t b a la n ce c o n s tr u c te d f o r 1980. The in p u t-o u tp u t t a b le p u b lish e d i n s t a t i s t i c a l yearbooks oan-not be u sed d i r e c t l y i n our c a lc u l a t io n s m ainly due to th e way i t p r e s e n ts im p o r ts. Im ports are a s s ig n e d to a g iv e n branoh on th e b a s i s o f s i m i l a r i t y o f goods ( e . g . im port o f c o a l - t o th e
Ca poci ty . ( l i m i t a t i o n ) Utility (orli fu n c tio n V- - I n c r e a»e o f г c a p a c i t i e s c a p a c ity submodel P ro d u ctio n ; g lo b a l a n d final, im p o r t, e x p o r t M O D E L ' I1 I ! ! . « : m Investment, A s s u m p t io n Preferences Ü ••
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m in in g i n d u s t r y ,i m p o r t o f f e r t i l i z e r s - t o t h e c h e m ic a l i n d u s t r y ) . T h is d o e s n o t p r o v id e u s w ith any i n f o r m a t io n on t h e volume o f u t i l i z a t i o n o f im p o rte d goods i n t h e p r o d u o tio n p r o c e s s o f a g iv e n b r a n c h . U sin g some e x tr a n e o u s in f o r m a t io n we d i v id e t h e i n p u t - o u t p u t m odel i n t o two p a r t s - flo w s and c o n su m p tio n o f d o m e s tlo g o o d s , an d flo w s and u t i l i z a t i o n o f im p o rte d goods
( P i g . 2 ) . The d i s a g g r e g a t i o n o f t h e m odel i s a s f o l l o w s . P i r s t , e n e rg y l i m i t a t i o n s r e f e r t o t h r e e b r a n c h e s o o n o e rn in g f u e l and pow er i n d u s tr y « 1) c o a l and b r i q u e t t e s (QFW), 2) f u e l s ( e x c lu d in g c o a l and b r i q u e t t e s ) and p r o c e s s e d p r o -d u c ts (Q P P ), 3) e l e o t r i o and ste a m e n e rg y (QFB); o t h e r i n d u s t r i e s a re « 4) m e t a l l u r g i c i n d u s t r y ( b a s i o m e t a ls and n o n - f e r r o u s m e t a l s , QME), 5 ) e l e o t r o - e n g i n e e r i n g i n d u s t r y ( m e t a l , m a c h in e ry , t r a n s p o r t e q u ip m e n t, e l e c t r o n i c and e l e c t r i c a l e n g in e e r i n g - QEM),
6 ) c h e m ic a l and m in e r á l i n d u s t r y (c h e m io a l i n d u s t r y , b u i l d -i n g m a t e r -i a l s and p o t t e r y , o h -in a and e a rth e n w a re - QCH),
7) l i g h t and fo o d i n d u s t r y (wood and p a p e r , t e x t i l e and c l o -t h i n g , f o o -tw e a r , fo o d and o -t h e r s - QPO)j t h e o t h e r b r a n c h e s o f t h e economy« 8) c o n s t r u c t i o n - B, 9) a g r i c u l t u r e - v e g e ta b le p r o d u o tio n - HK, 10) a g r i c u l t u r e a n im a l p r o d u o tio n and s e r v i c e s f o r a g r i c u l -t u r e - RH, 11) f o r e s t r y - L , 12) t r a n s p o r t and co m m u n icatio n - T , 13) t r a d e - H, 14) o t h e r s e c t o r s - PO.
The below p r e s e n t e d v e r s i o n o f t h e m odel i s n o t t h e f i n a l one. The m odel h a s n o t r e f l e o t e d t h e i n t e r r e l a t i o n s h i p s b etw e en su b -s e q u e n t p e r i o d -s y e t ( i t i -s a s t a t i c m o d e l). T h is means t h a t t h e in c re m e n t o f p r o d u c t i o n c a p a c i t i e s c a u se d by p r e v io u s i n v e s t -ment o u t l a y s , i s n o t i n c o r p o r a t e d i n t h e m o d el. At p r e s e n t , t h e l i m i t a t i o n s o f p r o d u c t i o n c a p a c i t i e s i n t h e m odel have an exo-g e n o u s c h a r a c t e r . T h is r e q u i r e s c a r e f u l f o r e c a s t i n exo-g o f p r o d u c t i o n c a p a c i t i e s o f s e c t o r s i n p a r t i c u l a r p e r i o d s . Some c h o s e n v a r i a n t s o f s u c h f o r e c a s t s a r e d i s c u s s e d i n t h e f u r t h e r p a r t o f t h e p a p e r . The f o llo w in g n o t a t i o n i s i n tr o d u c e d : - t o t a l d o m e s tic p r o d u c t o f t h e i t h b ra n o h ( o a l o u l a t e d co -lum nw ise) - t h e i - t h ty p e p r o d u c ts f o r d i s t r i b u t i o n ( c a l c u l a t e d row-w ise ) IC^ - im p o r ts o f goods o f k in d p ro d u o ed by t h e i - t h b ra n c h _ t h e flo w o f t h e i - t h ty p e p r o d u c ts t o t h e J - t h b ra n o h qi - f i n a l i - t h ty p e p r o d u c ts q f - f i n a l d o m e s tic i - t h ty p e p r o d u c t s ( I . e . f o r f i n a l u s e r s ) q® - im p o rte d i - t h ty p e p r o d u c ts f o r f i n a l u s e r s z . - im b a la n c e d sum i n t h e i - t h row
Kj - c o r r e c tio n term w hich i n t r o d u c e s c o r r e c t i o n b e c a u s e o f in c lu d in g t o th e t o t a l p r o d u c t i o n o f t h e j - t h s e c t o r t h e p r o d u c ts b elon gin g to another b r a n c h .
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l a o a l l e d t h e i n p u t - o u t p u t c o e f f i c i e n t . I t i e a sum Of d o m e stio i n p u t s o o e f f l o l e n t s I t l e n e c e s s a r y t o d i f f e r e n t i a t e b e tw e e n and I n o u r p a p e r b e c a u s e r e p o r t s d i s t i n g u i s h b e tw e en t o t a l p r o d u c t i o n o a l -T h is i s a l s o t a k e n I n t o a c c o u n t i n l n p u t - o u t p u t b a l a n c e s . -The rows p r e s e n t t o t e d p r o d u c t i o n u s in g t h e p r o d u c t m eth o d , w h ile t h e colum ns t h e p r o d u o tio n c a l c u l a t e d by t h e e n t e r p r i s e metho<?.A c c o rd in g t o t h e above d e f i n i t i o n t h e l n p u t - o u t p u t o o e f f l o i e n t i s a sum o f u n i t d o m e s tio and Im p o rt i n p u t s
The m ain g o a l o f o u r m odel i s t o lo o k f o r su o h v a r i a n t s o f econom io p l a n s w hich a r e c h a r a c t e r i z e d ( u n d e r o e r t a i n assum p-t i o n s ) by a maximum f i n a l p r o d u c p-t .
The c o n d i t i o n s t o b e f u l f i l l e d h a v e t h e f o llo w in g form : A. The b a la n c e o f d o m e s tio oom modity f lo w s .
T h ese a r e t h e b a la n o e e q u a ti o n s o f p r o d u c t i o n . ’We s h o u ld s t r e s s t h a t some u n b a la n c e , w hich r e s u l t s from i n c l u d i n g i n t h e
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c u l a t e d by means o f t h e p r o d u c t m ethod and t h e e n t e r p r i s e me-th o d ql . (4 ) *1;) e a i j + k i j (5 ) 14 1 4 max. (6)
t o t a l p r o d u o tio n o f t h e J - t h a e o t o r - t h e p r o d u c ta b e lo n g in g t o a n o th e r b ra n c h (K ^ ) and c o r r e c t i o n ( * ^ ) » i e i n c o r p o r a t e d I n t o t e c h n l o a l - f i n a a o i a l o o e f f i o i e n t a ^ , i . e . i f 14 Qi m L *13 Q3 + Š + ERROai 1-1 t h e e l i m i n a t i o n o f t h e e r r o r l a re d u c e d t o t h e - f o l l o w i n g e q u a-t i o n s / ERROR. ч r-$ ir f "> ( 1 " Qt “ a l i ) Qi “ “l j 4 ^ " 4i i € { 1 » 2 » **•» l i i
I n t h e b ra n o h e a I n whioh t h e above m e n tio n e d u n b a la n c e doea n o t o c c u r o r i a i n a l g n l f l o a n t , t h e o l a a s l o a l I n p u t - o u t p u t e q u a tio n waa assu m ed , I . e . 14 ( l - a ±1)Q 1 - £ “ i j Q j - ч{ i € | l , 2 , . . . . 1 4 J . ( 7 " ) 3 * i I n g e n e r a l t h i a e q u a tio n c a n b e w r i t t e n a a
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C . P r o p o r t i o n s b e tw e en f i n a l Im p o rte (q™) and f i n a l d o m e stio p ro d u o t ( q k ) .
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t ±1 - 1 , 2, . . . » 14.
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Baoh o f t h e ab ove i n e q u a l i t i e s s h o u ld be I n t e r p r e t e d a s f o l l o w s . P o r e a ch z ł o t y o f f i n a l d o m e stio p ro d u o t o f t h e i - t h ty p e no more th a n t^ z l o t y s o f t h e i - t h ty p e p r o d u c t o a n be Im p o rte d f o r f i n a l u s e . I t s h o u ld be added t h a t q™ o o n t a l n s n o t o n ly t h e oo n su m p tlo n o f Im p o rte d goods b u t a l s o im p o r ts f o r i n -v e stm e n t p u r p o s e s , in c re m e n t o f stoolc and t h e s o o a l l e d r e - e x p o r t . T h u s, t h e p a ra m e te r s h o u ld b e d e te rm in e d on t h e l e v e l n o t lo w e r t h a n t h i s one r e s u l t i n g from p la n n e d v a lu e s o f t h e s e c a t e -g o r i e s i n r e l a t i o n t o p la n n e d volum e o f f i n a l d o m e s tic p r o d u c tio n i n t h i s s e o t o r .D. The "minimum e x i s t e n c e " r e q u ir e m e n t.
C o n d itio n s (11) r e s u l t from t h e o l a s s i c a l b a la n c e o f f i n a l p r o d u o t, i . e . from t h e e q u a tio n qj^ ■ C.^ + o r , q^ - E^ ■
q^ — Ajl 1 — 1, 2 , • • . , 14. ( 1 1 )
The aim o f t h e above s y s te m o f i n e q u a l i t i e s i s t h e p r o t e c t i o n a g a i n s t g e n e r a t i n g an u n a c c e p ta b le v a r i a n t o f t h e econom ic p l a n . I t i e an open q u e s t i o n w hat u s e c a n be made o f t h e e x c e s s o f t h e l e f t hand s i d e (11) o v e r t h e assum ed r i g h t hand s i d e . T h is oan b e u s e d b o th f o r a d d i t i o n a l e x p o r t s and f o r t h e a d d i t i o n a l ( I n r e l a t i o n t o t h e assum ed l e v e l ) c o n su m p tio n o r /a n d accum ula-t i o n .
E . R e q u ire m e n ts o o n c e rn ln g t h e s t r u o t u r e o f f i n a l p r o d u o ts . The sy ste m o f i n e q u a l i t i e s (12) was d e r i v e d f i r s t o f a l l t o P r o t e c t t h e s o l u t i o n g e n e r a te d by t h e m odel a g a i n s t s o c i a l l y I n a c o e p ta b l e s t r u c t u r e o f t h e f i n a l p r o d u o t. E ach i n e q u a l i t y (1 2 ) oan be t r e a t e d a s a k in d o f c o m p le tio n o f t h e c o r r e s p o n d in g i n -e q u a l i t y ( 1 1 ) . I t m -e a n s ,i f I n -e q u a l i t y (11) I s t h -e so o a l l -e d lo w -e r bound f o r t h e f i n a l p ro d u o t q ^ , i n e q u a l i t y (12) i s t h e so c a l l e d " l i q u i d a t e d " u p p e r bound f o r t h i s p r o d u c t . I t s h o u ld be ex-p e c te d t h a t t h e r o l e o f c o n s t r a i n t s (1 2 ) w i l l be t h e l a r g e r , t h e
180 J a n В. Ciajda <?t u l .
l a r g e r w i l l be th o e x c e s s , m entioned above in p o in t D, o v er th e minimum consum ption and a ccu m u la tio n .
14
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q^ ^
1 « 1, 2, . . . ,
14*
(12)
The param eter ß ^ ( 6 ( 0 , D ) d e n o te s a maximum a d m i s s ib l e sh are o f f i n a l p ro d u o tio n o f t h e i - t h b r a n c h i n t h e t o t a l f i n a l n r o d u c tio n . L et u s n o te t h a t s h o u ld be o h o se n a s 14 L p i
*
1* i = i The s t r u c t u r e o f t h e f i n a l p ro d u o t w i l l be o f o o u r s e c l o s e r t o th e s t r u c t u r e o f t h e c l o s e r w i l l b e t o u n ity .H o w e v e r, 12 ^ > 1 s h o u ld be l e f t a s a m a rg in n o t o n ly f o r n u m e ric a l r e a s o n s . I t a l s o r e f l e c t s t h e f a o t t h a t we oan be p r e t t y s u r e what i n d i v i d u a l s h a r e p^ oan s t i l l be a c o e p te d , b u t o u r c o n -f id e n c e d e c r e a s e s when t h e e n t i r e s e t o f t h e e h a r e s ( t h e s t r u c -tu r e o f f i n a l p r o d u c t) I s c o n c e r n e d . I t s h o u ld be m e n tio n e d th a t r e s t r i c t i o n s (1 2 ) a r e v e r y t r i c k y . A c t u a l l y , i n any a c c e p t -a b le s o lu t i o n t h e sum o f t h e s e s h a r e s e q u a ls t o o n e . Has any p a r t ic u l a r p ro d u o t had t h i s s h a r e to o h ig h - some o f t h e o t h e r s sh o u ld have t h i s s h a r e v e r y lo w . T h is may a o t i v a t e o t h e r g ro u p s o f r e s t r i c t i o n s (1 0 , 1 1 , 13" )• As a r e s u l t o n ly few r e s t r i c -t i o n s (1 2 ) work aa -th e b i n d in g c o n s -t r a i n -t s .P. P ro d u ctio n o a p a c ity o f p a r t io u la r s e c t o r s .
T hese c a p a c i t i e s can be in tr o d u ce d i n two ways: e i t h e r i n th e form o f a t y p i c a l upper bound 0 3 ') o r i n th e form o f c o n s t r a in t s im posed on t o t a l p r o d u c tio n s t r u o t u r e , i . e . (1 3 " )- However, In th e l a t t e r c a s e th e l i m i t i n g s e c t o r s sh o u ld s t i l l have o a p a c ity c o n s t r a in t s o f th e ty p e (1 3 ') . In s p e c i a l c a s e s ( 1 3 ') and ( 1 3 " ) can be t r e a t e d as s u b s t i t u t i o n s , e . g . i n th e c a s e when a sen -s i b l e r e l i a b l e f o r e c a s t o f p ro d u ctio n c a p a c i t i e s i n a g iv e n s e c -t o r i s m is s in g , o r i n th e c a s e o f s e c t o r s i n whioh p ro d u ctio n volum es a re d e r i v a t i v e s o f th e p r o d u c tio n volum es o f o th e r s e c -t o r s , a s i t i s th e c a s e i n su ch s e c t o r s as tr a d e and t r a n s p o r ta -t i o n and com m unica-tion.
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^ ac^ i £ ^ l , 2 , . . « , 14•>
( 1 3 " )The p a r a m e te r s h o u ld s a t i s f y s i m i l a r c o n d i t i o n s a s ^ i n ( 1 2 ) . I n t h e f u t u r e , w ith p r o p e r l y s p e c i f i e d subm odel g e n e r a t i n g th e dynam ics o f c a p a c i t y , v e r s i o n ( 13') w i l l b e p r e f e r a b l e . G. F o r e ig n t r a d e b a la n c e (b u d g e ta ry c o n s t r a i n t ) . The c o n s t r a i n t r e p r e s e n t s t h e p o s t u l a t e o f a c h ie v in g a t l e a s t a g iv e n s u r p l u s o f e x p o r ts o v e r im p o r ts : 14 14 L h - L a r > ( u ' i - 1 i - 1 I f t h e e x c e s s i s n e g a t i v e , th e n (1 4 ) can be r e w r i t t e n as 14 14 L
Mi -
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i - 1 i - 1 H, P i n a l p r o d u o tio n b a la n c e .The f i n a l p r o d u o tio n b a la n c e i n t h e f o llo w in g c a t e g o r i e s : °o n s u m p tio n , a c c u m u la tio n and e x p o r t s , i s ta k e n i n t o a c c o u n t i n
(•11). I n t h e c a t e g o r i e s o f f i n a l im p o r ts and f i n a l d o m e s tic p r o -d u c tio n t h i s b a la n o e i s p r e s e n t e d i n t h e form o f e q u a ti o n s - d e f l n i t i o n s (1 5 )«
» 4 i + q” i ■ 1» 2 , . . . , 14 (1 5 )
The sy ste m o f e q u a tio n s and i n e q u a l i t i e s ( 8 ) - ( 1 5 ) c o m p le te d w ith n o n - n e g a t i v i t y c o n d i t i o n s (16) and c r i t e r i o n f u n o ti o n ( 6 )
182 J a n В. Gajdą e t a l . 14 ( Wi * a i i ) Qi - Tj a i j Qj “ > 1 № 14 L ki 3 « i * * i • “ i 1™/ 4j[ ^ qi “ E1 > 5 i + - 1 14 ' h / L
’ 1 5 S1
« 1 « 5 l 14Qi
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14 14 T j Bi " L Mi > a * i« 1 1-1 1 » 1 f 2 , • • • ! 14# 1 6 ^ 1 , 2 , • • • i к , m q± - q± + > O, ^ O, q^ ^ Of q j > O, E± ž O, Mt > O, 1 - 1 , 2 , . . . , 14. (1 6 ) I n I t s p r e s e n t v e r s i o n I t h a s 99 c o n s t r a i n t s and 84 d e c i s i o n v a r i a b l e s . I n i t i a l f o r e c a s t s g e n e r a te d by t h e m odel We s h a l l s t a r t w ith t h e a s s u m p tio n s ab o u t t h e p a r a m e te r s o f ( 6 ) 0 6 > T h ese a s s u m p tio n s w i l l be d i s c u s s e d s u b s e q u e n tly a c c o r d -i n g t o c o n s t r a -i n t s o f t h e above p r e s e n t e d m o d el.A. B a la n c e o f flo w s o f d o m e s tic c o m m o d ities
The b a s i s f o r c o n s t r u c t i n g t h o s e e q u a ti o n s a r e t h e u n i t i n p u t c o e f f i c i e n t s a ^ . F o r t h e y e a r 1980 t h e m a t r ix [ а ^ ] k a s b een u s e d . T h e re a r e s l i g h t d i f f e r e n c e s o n ly i n pow er i n d u s t r y and o t h e r f o u r b r a n c h e s w here t h e c o e f f i c i e n t s a i;L h av e b een c o r r e c -t e d due t o u n b a la n c e e r r o r s ( o f . ( ? ' ) ) . The m ost s i g n i f i c a n t p ro v ed t o b e t h e c o r r e c t i o n made f o r m e t a ll u r g y w here t h e c o e f -f i c i e n t a ^ c a l c u l a t e d a c c o r d in g t o t h e c l a s s i c a l d e -f i n i t i o n ( o -f . ( 2 ) ) was o v e r e s tim a te d by a b o u t 7056. The c o r r e o t e d v e r s i o n o f c o e f f i c i e n t m a t r ix [ a ^ j ] was u s e d t o g e n e r a t e t h e s o l u t i o n s f o r 1990 and 2000.
I n o r d e r t o i l l u s t r a t e t h e p o s s i b i l i t y o f e x t e r n a l dynom iza- t i o n i t was assum ed t h a t e n e rg y c o n su m p tio n o f t h e economy t i l l 1985 would be k e p t on t h e 1980 l e v e l and t h e n i t would d e-c r e a s e by 1.7% a n n u a ll y ( m a in ly due t o t e c h n i c a l im provem ents I n e n e rg y u t i l i s a t i o n , s i n c e we s h o u ld n o t e x p e c t a s i g n i f i c a n t d e c r e a s e o f e n e rg y c o n su m p tio n by r e p l a c i n g t h e e n e rg y -c o n su m in g - t e c h n o l o g i c a l p r o o e s s by l e s s e n e rg y -c o n su m in g p r o c e s s e s ) . T h is c a u s e s a ohange i n t h e c o e f f i c i e n t s a ^ j f o r t h e rows o f pow er s e c t o r s ( i . e . rows QPW, OFP, QFE) a c c o r d in g t o t h e f o llo w in g scheme j a ’ ’ 50 - < 0 .9 8 3 )5. ’ f ° and a ™ 00 . < 0 .9 8 3 > 15a ’ f 0 Of c o u r s e t h e c h a n g e s o f u n i t I n p u t c o e f f i c i e n t s a ^ need n o t I n c lu d e a l l s e c t o r s t o t h e same d e g r e e . I t i s a l s o p o s s i b l e t o ta k e i n t o a c c o u n t s i n g l e ohanges o f c o e f f i c i e n t s f o r a c h o se n P e r io d o o n n e o te d e . g . w ith t h e e x p e o te d ch an g e o f te c h n o lo g y . po r i n s t a n c e , t r a n s i t i o n from t h e wet te c h n o lo g y o f cem ent p r o -d u c ti o n t o d r y p r o d u o tio n te c h n o lo g y d i m i n i s h e s , among o t h e r s , e l e c t r i c e n e rg y c o n su m p tio n w hich i s r e f l e c t e d by d im in is h in g t h e c o e f f i c i e n t a ^ ^ .
B . B a la n o e o f im p o rte d comm odity f lo w s .
F o r t h e y e a r s 1990 and 2000 t h r e e f i r s t rows o f m a t r ix k ^ ( i . e . f o r QFW, QPP and QPE) w ere changed a c c o r d in g t o t h e assum p-t i o n o f an a n n u a l d e c r e a s e o f e n e rg y c o n su m p tio n i n t h e w hole economy by 1.756 b e g in n in g from t h e y e a r 1985.
Suoh an approaoh i a tr u e when we t r e a t th e w hole su p p ly im-p o r t s a s com im-plem entary and im-p r o im-p o r tio n a l t o th e dom eetic^'.produc-t i o n .
N a t u r a lly , i f a d om estio s u b s t i t u t e i s fou n d , th e s i z e o f a p a r t ic u l a r flo w (o r a group o f flo w s ) may d e c r e a s e o r even d isa p p e a r whioh sh ou ld be r e f l e c t e d by an a p p r o p r ia te d e c r e a se o f th e c o e f f i c i e n t (o r a group o f o o e f f i o i e n t e ) k ^ . I n th e v a r ia n t s f o r th e y e a r s 1990 and 2000 th e c o e f f i c i e n t s k ^ f o r power s e o t o r s a r e determ ined on th e b a s i s o f th e dependenoet
* ’ f ° - <0.98J>5*’ f O
. CO.Sejl’ M
f 0
C. P r o p o r tio n s betw een f i n a l im p orts ( q j ) and f i n a l d om estic p ro d u ct.
Por b o th v a r ia n t s ( i . e . f o r th e y e a r s 1990 and 2 0 0 0 ) th e assumed l e v e l o f th e maximum sh a re o f f i n a l im p orts i n f i n a l d o m estic produot was by about 50% h ig h e r th an t h a t rep o rted i n 19 80.
The param eter was d eterm in ed on th e b a s i s o f th e form ula!
= q j / q f 1.5,
where q™ and q ^ .a re th e v a lu e s o f f i n a l im p orts and f i n a l domes-t i c produodomes-t i n domes-th e i - domes-t h branoh re p o r domes-te d f o r 1 980, r e s p e c domes-t i v e l y .
D, The mini mum e x is t e n o e l e v e l s o f consum ption and accumula-t i o n .
We assumed th a t th e l e v e l o f consum ption and a ccu m u la tio n , s t a r t i n g from 1980, would r e v e a l , f i r s t , a downward tre n d (up t o 1983-1 9 8 4 ) and th e n i t would in c r e a s e t o a c h ie v e i n 1990 th e 1980 l e v e l . In subsequent y e a r s 1990-2000 a 1% annu el grow th r a t e o f consum ption and accu m u la tio n was assumed, i . e .
- i " - i 2000 “ 1,01 Ci + Ai 1980*
The f o llo w in g v a r ia n t s f o r th e miniaum l e v e l o f consum ption end a ccu m u lation were ta k en (T a b . 1 ) .
T a b' 1 e 1 The minimum assum ed f o r a c c u m u la tio n and c o n su m p tio n
Y ear QFVf QFP QPE QME QEM QCH QPO
• 19.90 2000 3 557 3 929 31 618 34 925 22 344 24 681 6 670 7 368 441 667 487 875 102 336 113 043 750 370 828 875 Y ear В BR RH L T H PO 1990 2000 422 015 466 167 6 815 7 528 53 962 59 608 1 229 1 358 92 444 91 069 259 012 286 110 39 075 43 163 I n b i l l , z ł , 1980 p r i c e s . E . R e q u ire m e n ts r e f e r r i n g t o t h e f i n a l p r o d u c t s t r u c t u r e . I n a l l v a r i a n t s o f 1990 and 2000 a " lo o s e n e ď 'b y 50Í& s t r u c t u r e r e p o r t e d f o r 1980 was assum ed, i . e .
T a b l e 2 The s h a r e s o f f i n a l p r o d u c t i n 1980
S e c to r QFiY QFP QFE QME QEM .QCH QPO
^ ßi 0 .0 4 0 .0 4 0 .0 2 0 .0 3 5 0 .3 0.1 0 .3 5
S e c to r В BR RH L T H PO
Pi 0 .2 5 0 .0 5 0 .0 5 0.01 0 .1 0 .1 5 0 .0 2 5
F . P r o d u c tio n c a p a c i t y o f p a r t i c u l a r s e c t o r s .
F o r t h e s e c t o r s QME, QEM, QCH, QPO, B, T , H, PO we had n o t g o t s a t i s f a c t o r y f o r e c a s t s foi* t h e y e a r s 1990 and 2 0 0 0. T h e r e f o r e , I n o r d e r t o l i m i t t h e p r o d u c t i o n c a p a c i t y o f t h e s e s e c t o r s i n -e q u a l i t i -e s ( 1 3 " ) w -er-e u s -e d . Th-e p a r a m -e t-e r was assum ed a t t h e l e v e l r e a l i z e d f o r 1 9 80, i . e .
14
o 8 0 , У q 80 * i я Qi 1 L Qi
The s h a r e s o f s e l e o t e d p r o d u c t i o n c a p a c i t i e s i n 1980
S e c t o r QME QEM QCH QPO В T H PO
* i 0 .0595 0 .185 0.0 7 5 6 0.2401 0 .0927 0 .0 6 8 9 0.0 5 6 2 0 .0 1 6 3 P o r o t h e r s e c t o r s i n e q u a l i t y ( 1 3 ') was u s e d . T h i s r e q u i r e d t h a t f o r e c a s t s o f p r o d u c t i o n c a p a c i t i e s o f t h r p e s e c t o r s heul t o be g e n e r a t e d .
For s e c t o r s RR, RH, and L a 2% a n n u a l r a t e o f g ro w th s t a r t i n g from 1985 was a ssum ed. P o r b o t h a g r i c u l t u r a l s e c t o r s , t h e y e a r 1985 was assumed a t t h e l e v e l o f t h e b e s t y e a r o f 1 9 76-1980, i . e . R R ^ y g and R H ^ ^ g , w h i l e f o r L - t h e 1980 l e v e l , i . e . T a b l e 4 p r e s e n t s p r o d u c t i o n c a p a c i t y e s t i m a t e d i n t h i s way. T a b l e 4 P r o d u c t i o n c a p a c i t i e s assumed f o r a g r i -c u l t u r e and f o r r e s t r y Y ear RR RH L 1985 1990 2000 446 593 493 075 601 055 409 588 452 218 551 252 31 266 34 520 42 079 I n b i l l , z ł , 1980 p r i c e s .
The b a s i s f o r f o r e c a s t s f o r t h e s e c t o r s QFY/, QPP and QPE were t h e d a t a p r e s e n t e d by K. Kopeclci i ń " J u t r o e n e r g e t y c z n e P o l s k i ” ("Tomorrow o f t h e P o l i s h E n e r g e t i c s " ) , Wiedza P o w szechna, Warsaw 1981. Prom t h e s e d a t a t h e s o c a l l e d " s t r o n g " v a r i a n t o f t h e n a t i o -n a l eco-nomy developm e-nt was s e l e c t e d . Such a-n a p p r o a c h -n e e d s some j u s t i f i c a t i o n i n t h e c a s e o f h eavy economic c r i s e s . We s h a l l p r e -s e n t i t b e lo w .
E s t i m a t e s a c c o r d i n g t o t h e s t r o n g v a r i a n t f o r 1990 a r e g e n e -r a l l y t h e same a s t h o s e made by J . D a n i e le w s k i ( " Ż y c i e G ospoda-r- ospodar-c z e " , Но. 35, v o l . XXXVII, 19 S e p t . 1982, p . 4) e x ospodar-c e p t f o r brown c o a l ( t h e t a b l e p r e s e n t e d i n t h e a r t i c l e shows a d i f f e r e n t ap-p r o a c h t o s o u r c e s and c o n s u m ap-p tio n o f e n e r g y ) . The summary o f t h e a s s u m p t io n s i 3 shown i n T ab . 5 .
T а b Д e 5 P e r o e a t i n o r e a s e o f e n e r g y r e s o u r c e s ( i n 5») S o u r c e o f e n e r g y 1980-1985 1985-1990 1990-1995 1995-2000 Coal and b r i q u e t t e s • (QPW) 83*3 13*6 2 0 .4 6 . 4 L i g u i d and g a s f u e l s (QPP) 2 9 . 3 1 8 .8 1 9 .0 1 7 .3 E l e c t r i c and h e a t power (QPE) • 1 2 .5 31.5 3 0 .9 3 4 .4 On t h e b a s i s o f T a b . 5 t h e f o r e c a s t s o f p r o d u o t i o n c a p a c i t i e s i n s e c t o r s QPW, QPP and QPE ha v e b e e n made ( T a b . 6 ) .
T a b l e 6 P r o d u c t i o n c a p a c i t i e s assumed f o r o o a l , f u e l s and e l e c t r i c e n e r g y Y ear QPW QPP QPE ' 1990 2000 280 424 359 240 205 932 287 454 134 013 235 770 I n b i l l , z ł , 1980 p r i c e s . C. P o r e i g n t r a d e b a l a n o e . I t i s assumed f o r t h e y e a r s 1985-2000 t h a t t h e a n n u a l b a l a n c e * i l l be p o s i t i v e and e q u a l t o US jS 3 .5 b i l l . i . e . a b o u t 210 000 b i l l , z ł o t y s ( i n t h e b a s e y e a r 1980 US jS 1 « 60 z ł ) . T h u s, i n a u b e eq u e n t v a r i a n t s ft в 210 ООО ( i n b i l l , z ł o t y s , 1980 p r i o e s ) . b o t h 1990 and 2000 v a r i a n t s c o n d i t i o n (1 4) was u s e d . As a n i l l u s t r a t i o n o f t h e p i l o t model e x p e r i m e n t s we s h a l l P r e s e n t a c o m p a r is o n o f f o u r v a r i a n t s o f s o l u t i o n (A, B , C ,a n d D, Tab. 7 ) . E x c e p t f o r t h e p a r a m e t e r s a ^ ( b a l a n c e o f d o m e s t ic commodity How s ( 8 ) ) and k ^ j ( b a l a n c e o f i m p o r t e d commodity f l o w s ( 9 ) ) a l l t h e r e m a i n i n g p a r a m e t e r s o f t h e model a r e o o n e t a n t f o r t h e V a r i a n t s А, В , C, and D. The p r e s e n t e d v a r i a n t s a r e c h a r a c t e r i z e d
d i f f e r e n t a s s u m p t i o n s c o n c e r n i n g t h e p r e s e n c e o r a b s e n c e o f a downward t r e n d i n e n e r g y c o n s u m p tio n i n o u r economy and p o s s i -b l e r e a s o n s f o r t h i s d e c r e a s e . T h e r e f o r e ,
C om parison o f f o r e c a s t s f o r g l o b a l p r o d u c t s o f b r a n c h e s o f t h e n a t i o n a l economy a t v a r i o u s a s s u m p t io n s o f e n e r g y c o n s u m p tio n (.1980 - 100) V a r i a n t P r o d u o t i o n S e o- A В С D c a p a c i t i e s t o r 1990 2000 1990 2000 1990 2000 1990 2000 1990 2000 QPW 192x 232x 197х 262х 197х 262х 192х 232х 208 267 QFP 154 214 154 214 154 214 154 214 154 214 QPE 148 215x 148 250х 148 250х 148 215Х 148 260 QME 139 172 139 175 139 175 139 172 - -QEM 141 176 142 178 142 178 141 176 - -QCH 139 172 139 175 139 175 139 172 - -QPO 129* 157x 129х 157х 129х 157х 129х 157х - -В 137 170 138 173 138 173 137 170 - -RR 124 151 124 151 124 151 124 151 124 151 RH 122 149 122 149 122 149 122 149 122 149 L 110 135 110 135 110 135 110 135 110 135 T 138 171 138 174 138 174 138 171 -H 140 174 140 177 14 0 177 140 174 - -PO 137 170 138 173 138 173 137 170 Qi 136 169 136 172 136 172 136 169 x X qi 138 174 138 174 138 174 138 174 x X x - d e n o t e s p r o d u c t i o n c a p a c i t i e s n o t f u l l y u t i l i z e d . - t h e v a r i a n t A assum es t h e e n e r g y c o n s u m p tio n d e c r e a s e by 1.7% p e r y e a r , s t a r t i n g from 1985, b o t h i n d o m e s t ic ( a ^ j ) *m” p o r t e d e n e r g y s o u r c e s , - t h e v a r i a n t В ( p e s s i m i s t i c ) d o e s n o t a l l o w f o r ohanges i n e n e r g y c o n s u m p tio n ( a ^ and re m a in a t t h e 1980 l e v e l ) , - t h e v a r i a n t С a s su m e s 1.7% a v e r a g e a n n u a l d e c r e a s e of e n e r g y '.onsumption o n l y i n i m p o r te d e n e rg y s o u r c e s ( j )* a i j r e m a in s a t t h e 1980 l e v e l , - t h e v a r i a n t D assum es 1.7% a v e r a g e a n n u a l d e c r e a s e of e n e rg y c o .isu m p tio n o n l y i n d o m e s t ic e n e r g y s o u r c e s ( a i j ) í r e m a in s a t t h e 1930 l e v e l ,
- x - d e n o t e s p r o d u o t i o n c a p a c i t i e s n o t f u l l y u t i l i z e d ( s e e Qj o r жŁ o f . ( 1 3 ') and ( 1 3 " )
-Prom t h e above c o m p a ris o n i t i s a p p a r e n t t h a t u n d e r o u r a s s u m p t io n s a b o u t 70& i n o r e a s e of g r o s s p r o d u o t i o n c a n be e x p e c t e d . I t
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an o p i n i o n t h a t up t o 1990 t h e m ain g o a l o f t h e economy w i l l be t o r e s t o r e e q u i l i b r i u m , t o overoome b o t t l e - n e c k s and t o a c h i e v e a f i n a n c i a l s u r p l u s i n f o r e i g n t r a d e . I n power i n d u s t r y , t h e m ain l i m i t i n g r o l e i s p l a y e d by l i q u i d f u e l i n d u s t r y w i t h c o a l b e i n g t h e n e x t. I n o t h e r a e c t o r 3 a s i g n i f i c a n t c o n s t r a i n t i s t h e assumed l e v e l o f a g r i c u l t u r a l p r o d u c t i o n and t h e s h a r e o f p a r t i c u l a r i n d u s t r i a l b r a n c h e s i n t h e e r o a s o u t p u t . I f t h e p r o d u c t i o n t e c h n o l o g y o f t h e n a t i o n a l econo-my i n 2000 i s t o rem ind t h e 1980 t e c h n o l o g y (b y t e c h n o l o g y we mean u n i t a r y raw m a t e r i a l c o n s u m p tio n ) t h e n t h e c o m p a ris o n o f V a r i a n t s A, C, D w i t h В p o i n t s out t h a t t h e d e c r e a s e o f e n e rg y o onsum ptlon by 1«7% a n n u a l l y d o e s n o t p r o v i d e a s u f f i c i e n t p r e -r e q u i s i t e f o -r a s i g n i f i c a n t g ro w th o f t h e eoonomy. T h u s , i n t h e f u t u r e i n v e s t i g a t i o n s more a t t e n t i o n s h o u l d b e p a i d t o t h e assump-t i o n s c o n c e r n i n g assump-t e c h n o l o g i c a l c h a n g e s . The problem o f model d y - f te m iz a tio n s h o u ld a l s o be s o l v e d t h r o u g h p r o p e r t r a n s f o r m a t i o n o f c u r r e n t a n n u a l i n v e s t m e n t o u t l a y s i n t o t h e f u t u r e c a p a c i t y i n -o r e a s e .J a n B . G a j d a , D o r o t a M ls z c z y ń s k a , Marek M is z o z y ń s k i, Ł u c ja T om aszew icz, J e r z y S . Z i e l i ń s k i
OGRANICZENIE ENERGETYCZNE A OPTYMALNY ROZWÓJ GOSPODARKI POLSKI
P r z y k o n s t r u k c j i p r e z e n to w a n e g o modelu z a główne o g r a n i c z e n i e rozw oju g o s p o d a rc z e g o p r z y j m u j e s i ę z a s o b y p a l i w o w o - e n e r g e t y c z n e . 0&l s z y m i o g r a n i c z e n i a m i s ą m o ż liw o ś c i p r o d u k c y j n e , im portow e, a t a k ż e z n a c z n a s z ty w n o ść s t r u k t u r y p r o d u k c j i uwarunkowana s t r u k -t u r ą k a p i -t a ł u . O pis pow ią z ań pomiędzy d z i a ł a m i g o s p o d a r k i . ^ a r o d o - ^ ej ma p o s t a ć modelu i n p u t - o u t p u t w y r ó ż n i a j ą c e g o 14 d z i a ł ó w , ym 3 e n e r g e t y c z n e . , „ , C e n t r a l n ą c z ę ś ć m odelu s ta n o w i u k ł a d warunków 8 k l a s y o z n e g o s y s te m u równań i n p u t - o u t p u t Q e AQ + Я* U z u p e łn io n y j e s t warunkami d o ty c z ą c y m i s t r u k t u r y doohodu n a r o d o -w®go b r u t t o qi / ^ q 1 < fł± , z d o l n o ś c i p r o d u k c y j n y c h wybranych wychodzący Układ t e n
działów, dochodu narodowego tworzonego
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( w y p ł a c a ln o ś ć w i e r z y c ie l o m z a g r a-nicznym) .
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model Q - AQ + q z o e t a ł zmodyfikowany do p o s t a o iQ + M * ocQ + q z powodu o h a r a k t e r u d o s t ę p n e j i n f o r m a c j i e t a t y
-styczn ej
(M - i m p o r t ) .Model s ta n o w i p u n k t w y j ś c i a d l a a n a l i z y s t a n u i m o ż liw o ś c i g o s p o d a r k i w o k r e s i e b ież ą c y m i . o k r e s a c h p r z y s z ł y o h .
