World Commodity Model for Fertilizers: The alternative long-term prognosis of the world fertilizer production, consumption and trade on the basis of an econometric model

NOT FOR QUOTATION

WITHOUT PERMISSION

OF THE AUTHOR

WORLD COMMODITY MODEL FOK FEHTILIZER

The a1 t e r n a t i v e long-term prognosis of t h e world f e r t i l i z e r production, consumption and t r a d e on t h e b a s i s of an econometric model

January 1980 CP-80-1

C o l l a b o r a t i v e Papers r e p o r t work which h a s n o t been performed s o l e l y a t t h e I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems A n a l y s i s and which h a s r e c e i v e d o n l y

l i m i t e d review. Views o r o p i n i o n s e x p r e s s e d h e r e i n do n o t n e c e s s a r i l y r e p r e s e n t t h o s e of t h e I n s t i t u t e ,

i t s N a t i o n a l Member O r g a n i z a t i o n s , o r o t h e r organi-

z a t i o n s s u p p o r t i n g t h e work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS

A-2361 Laxenburg, A u s t r i a

S. MESZAilOS is head of d e p a r t m e n t 01' 11esearcI1 i n s t i t u t e Tor Agricultural d c o n o n i c s , 1355 Badapest, 55. P f . 5 , Rwlgary

PREFACE

The Food and A g r i c u l t u r e Sieseilrch Program a t I I A S A d e a l s

w i t h t h e w o r l d ' s f o o d problems on two f r o n t s : f i r s t l y i t ana-

l y s e s f u t u r e f o o d problems by b u i l d i n g a system of n a t i o n a l p o l i c y models and s e c o n d l y , i t s t u d i e s p r o d u c t i o n f a c t o r s of a g r i c u l t u r e aimed a t improving t e c h n o l o g i e s and s o l v i n g t h e w o r l d ' s food problems. F e r t i l i z e r s p l a y an i m p o r t a n t r o l e

among t h e p r o d u c t i o n f a c t o r s i n a g r i c u l t u r e , and t h e i r grow- i n g u s e i n t h e f u t u r e w i l l c o n t r i b u t e t o h i g h e r f o o d l e v e l s u p p l i e s b o t h i n d e v e l o p e d and d e v e l o p i n g c o u n t r i e s .

The f e r t i l i z e r model p r e s e n t e d here' w a s c o n s t r u c t e d f o r a l t e r n a t i v e long-range p r o j e c t i o n , consumption, and w o r l d

t r a d e and c a n be l i n k e d t o a g r i c u l t u r a l , i n d u s t r i a l and g l o b a l models. The a u t h o r h e l p e d t o d e v e l o p t h e Hungarian n a t i o n a l p o l i c y model++ on f o o d p r o d u c t i o n a t ILASA and i s t h e r e f o r e a c q u a i n t e d w i t h t h e e f f o r t s , p r i n c i p l e s and m e t h o d o l o g i c a l p r o c e d u r e s u s e d t o d e v e l o p b o t h g l o b a l models. He hopes t h a t t h e p u b l i c a t i o n o f t h i s document on f u t u r e f e r t i l i z e r s prob- lems by IIASA w i l l c o n t r i b u t e t o a b e t t e r u n d e r s t a n d i n g o f w o r l d food problems i n t h e f u t u r e .

+ The model w a s c o n s t r u c t e d as a p a r t of r e s e a r c h work c a r - r i e d o u t by t h e Hungarian N a t i o n a l P l a n n i n g I n s t i t u t e u n d e r c o n t r a c t t o UNIDO.

++ Modelling o f C e n t r a l l y Planned Food and A g r i c u l t u r a l Sys- tems: A Framework f o r a N a t i o n a l P o l i c y Model f o r t h e Hunga- r i a n Food and A g r i c u l t u r e S e c t o r , C. C s a k i , A. J o n a s ,

S, Meszaros. I I A S A , 1978, RM-78-11.

CONTENTS

THE PURPOSE AND C W C T E R I S T I C S OF THE FERTILIZER

COMMODITY MODEL, 1

Tbe purpose of the fertilizer commodity model, 1 The more important determinant factors of fertilizer

consumption and production /the economic sphere modelled/, 3

The mathematical model, the solution and methods of

prognostics, 8

DESCRIPTION OF TBE ECONOMETRIC MODEL, 9

Equations of the sphere of the whole economy, l o

Equations of the food economy, 1 3

! h e equations of fertilizer sphere, 16 The quantification of the model, 20 ALTERNATIVE PROGNOSES

Scenario A /Basic/, 24

Scenario B, 33

Scenario C, 34

Scenario D, 35

Scenario E, 37

Simultaneous s o l u t i o n s , 36 Summary, 40

References, 47

Appendix 1: Simulation models equations, 50

L i s t of variables and partmeters of the model, 54 Besalts o f Scenario A , 57

Results of Scenario B , 64 Results of Scenario C , 71 Results o f Scenario D , 78 Results of Scenario E, 85

Simultaneous solutions, 89

WORLD COMMODITY MODEL FOR FERTILIZERS

S. ~ Q s z G r o s

THE PURPOSE AND CHARACTERISTICS OF THE

FERTILIZE1I COfiPlODITY MODEL

The purpose of t h e f e r t i l i z e r commodity model

The I n t e r n a t i o n a l Centre f o r I n d u s t r i a l S t u d i e s f u n c t i o n - i n g w i t h i n t h e United Nations I n d u s t r i a l Development Organiza- t i o n / f u r t h e r : UNIDO/ worked o u t t h e conception o f a world mo- d e l named UNIDO World I n d u s t r y Co-operation w i t h t h e purpose of a n a l y s i n g t h e problems of t h e r e a l i z a t i o n of L i m a t a r g e t

/UNIDO I n t e r n a t i o n a l Centre f o r I n d u s t r i a l S t a d i e s 1977/.

The world model c o n s i s t s of a s e r i e s of models l i n k e d t o g e t h e r , and w i t h i n t h i s system t h e r e i s a d i f f e r e n c e between an i n n e r l a y e r and an o u t e r l a y e r . The models of t h e i n n e r l a y e r a r e c l o s e l y r e l a t e d , and t h e r e i s a flow of i n f o r m a t i o n i n r a d i a l - d i r e c t i o n among them. The models were p r e p a r e d w i t h i n

UNIDO. The models of t h e o u t e r l a y e r are connected l o o s e l y i n

t u r n w i t h t h e models of t h e i n n e r l a y e r , and t h e r e i s no i n f o r - mation l i n k between t h e models of t h e o u t e r l a y e r t h e r e f o r e

t h e models of t h e o u t e r l a y e r can be s e p a r a t e l y developed as w e l l .

One of t h e i n n e r l a y e r models i s t h e model which d e t e r - mines t h e i n t e r n a t i o n a l Trade Disaggregation. I t s t a s k i s t o d i s a g g r e g a t e i n the p r e v i o u s model i n v a l u e determined f o r e i g n t r a d e matrix at least i n t o 7 p r o d u c t groups. The World Commo- d i t y Models a r e p l a c e d w i t h i n t h e o u t e r l a y e r , deducing t h e expected e x p o r t and import of t h e p r o d u c t s i n q u e s t i o n from

t h e demand and s u p p l y of country-groups and t h e s e r e s u l t s can

be used f o r c o n t r o l l i n g and c o r r e c t i n g t h e d a t a g i v e n by t h e Trade D i s a g g r e g a t i o n Model. The t a s k of t h e World Commodity

Models i s t o g i v e long-range p r o j e c t i o n s / u p t o t d e y e a r 2000/

w i t h r e s p e c t t o t h e demand and supply ^&nd i n t e r n a t i o n a l t r a d e

of t h e products i n q u e s t i o n .

The t a s k of t h e f i n a l s t u d y was to provide f o r a concep- t i o n of t h e World Commodity Model concerning t h e f e r t i l i z e r s . For t h e consumption of f e r t i l i z e r s a long-range p r o g n o s i s up t o 2000 has a l r e a d y been prepared i n t h e UNIDO I n t e r n a t i o n a l Centre f o r I n d u s t r i a l S t u d i e s , s t a r t i n g from t h e need of f e r - t i l i z e r s presumed on t h e b a s i s of t h e i n c r e a s e of p o p u l a t i o n

/UNIDO I n t e r n a t i o n a l C e n t r e f o r I n d u s t r i a l S t u d i e s 1976/. Only

one prognosis i s provided by t h i s s t u d y f o r t h e t r e n d of Per- t i l i z e r consumption i n t h e developed and d e v e l o p i n g c o u n t r i e s

t i l l t h e y e a r 2000. However, t h e p r e s e n t g e n e r a t i o n of t h e

p r o g n o s i s t s r e f u s e s t h e p r e p a r a t i o n of a s i n g l e long-range prog- n o s i s and a l t e r n a t i v e prognoses a r e prepared i n t h e form of d i f -

f e r e n t s u p p o s i t i o n s , s o c a l l e d s c e n a r i o s concerning t h e f u t u r e /F.H. Sanderson 1977/. I t w a s t h e d e s i r e of t h e p r e p a r a t o r s of t h e UNIDO World Model t h a t t h e F e r t i l i z e r Commodity Model should g i v e a l t e r n a t i v e s c e n a r i o s concerning the p r o d u c t i o n , consump- t i o n and i n t e r n a t i o n a l t r a d e of f e r t i l i z e r s as w e l l .

The r e q u i r e m e n t s concerning t h e f e r t i l i z e r s and meeting t h e World Commodity Model requirements a r e t h e f o l l o w i n g :

-

p r e p a r a t i o n of a l t e r n a t i v e long-range prognoses f o r t h e i n t e r n a t i o n a l t r a d e o f f e r t i l i z e r s should be r e a l i z e d

-

t h e most i m p o r t a n t d e t e r m i n i n g f a c t o r s o f t h e i n t e r n a - t i o n a l t r a d e of f e r t i l i z e r s should be s a t i s f i e d by t h e model /denand, supply, p r i c e e t c . /

-

t h e i n d i v i d u a l prognosis should be c o n s i s t a n t i n t h e l i g h t of e q u i l i b r i u m r e q u i r e m e n t s , and t h e r e l a t i o n among d i f f e r e n t f a c t o r s

-

a l t e r n a t i v e s u p p o s i t i o n s should be made c o n c e r n i n g t h e exogeneous v a r i a b l e s which can o b s c u r e l y be determined i n long term o r have t h e c h a r a c t e r i s t i c s of q u a l i t y from t h e p o i n t of view o f f e r t i l i z e r s

-

t h e model should e l a b o r a t e l y count w i t h t h e world f e r - t i l i z e r p r o d u c t i o n and consumption c o n c e r n i n g a t l e a s t t h e groups of developed and developing c o u n t r i e s

-

t h e model should be r e l a t i v e l y simple, w i t h r e s p e c t t o t h e e a s e of m a n a g e a b i l i t y and p r a c t i c a l a p p l i c a b i l i t y of t h e r e s u l t s .

The most important determinant factors of fertilizer consumption and production

/the economic sphere modelled/

For the formation of the fertilizer product model the de- terminant factors of fertilizer consumption and production, the connection of the fertilizer as a product with its environment must be considered, When forming the model the followings have been taken into consideration:

1. The conditions of the fertilizer production can not be made independent from the situation of other products, from the tendency of environmental factors: the demand on fertilizers basically depends on food production, especially on plant cul- tivation, However, food production is determined by tbe demand on food, the formation of which depends on tbe number of popu- lation and the rate of economic development. The production of fertilizers is determined mainly by the magnitude and utiliza- tion of manufacturing capacity and the availability of raw ma- terials and energy sources. Consequently, for the preparation of alternative and consistant prognoses the modelling of con- catenation can not be avoided even in that case when factors are modelled in a simplified way,

number of population rate of economical

\

development

\

^{demand on}

^u//

^food

food production

L

4 4 - production

I factors

1

I

demand on fertilizers

fertilizer production +production

k

factors

2. I t i s c l e a r t h a t t h e e x p o r t supply and import demand on f e r t i l i z e r s can be deduced only by t h e comparison of t h e domes- t i c f e r t i l i z e r demand and production. Consequently, t h e country- group modelkng of t h e previous c o n c a t e n a t i o n i s needed, i n r e s - p e c t of t h e developed and t h e developing c o u n t r i e s a t l e a s t . A t t h e same time i t i s obvious t h a t i n c a s e of e f f o r t f o r c o n s i s t - a n t prognosis t h e f e r t i l i z e r e x p o r t s u p p l y of t h e developed c o u n t r i e s and t h e f e r t i l i z e r import demand of t h e developing c o u n t r i e s can n o t be c a l c u l a t e d i n d e p e n d e n t l y from one a n o t h e r , b u t an e q u i l i b r i u m must be c r e a t e d between them because t h e im- p o r t demands can be o n l y as much as t h e p r o d u c t i o n f o r e x p o r t s . Not o n l y t h i s one / r e s p e c t i v e l y i n t h e uase of t h r e e a l i m e n t s ,

t h r e e / e q u i l i b r i u m o c c u r s among t h e models of t h e i n d i v i d u a l country-groups. Thinking o v e r , i n t h i s r e s p e c t t h e government of a developing c o u n t r y can choose among t h r e e a l t e r n a t i v e s i n o r d e r t o s o l v e t h e problem of p r o v i s i o n :

-

t o import food

-

t o import f i n i s h e d f e r t i l i z e r

-

t o import c a p i t a l / f a c t o r y f o r f e r t i l i z e r p r o d u c t i o n o r perhaps r a w m a t e r i a l /

The modelling of a l l t b e t h r e e p o s s i b i l i t i e s should be made p o s s i b l e because t h e conversion i n t o each o t h e r of t h e t h r e e p o s s i b i l i t i e s c a n be r e a l i z e d more o r l e s s . Among t h e models of t h e i n d i v i d u a l country-groups w i t h r e g a r d t o t h e

f e r t i l i z e r commodity model a c o n n e c t i o n may be proposed i n t h e f o l l o w i n g t h r e e c a s e s :

Developed countries Developiug countries

economic economic

population population expans ion

demand o n food

I i

I export

b'

food production

iL

demand o n fertilizer

food production

I

demand o n fertilizer

fertilizers

export import

<

^---

I

I

I

fertilizer production fertilizer production V

production factors production factors

capital

/

3. When t h e economic sphere f o r modelling i s c o n s i d e r e d from t h e p o i n t of view of means f o r c o u n t e r b a l a n c i n g , two ones can r e a s o n a b l y be a c c e p t e d f o r being modelled i n t h i s r e s p e c t :

-

t h e p r i c e s

-

t h e investments

The change i n t h e p r i c e s of food p r o d u c t s and f e r t i l i z e r s could be t h e means of c o u n t e r b a l a n c i n g i n t h e s h o r t run. In t h e l o n g run t h e i n v e s t m e n t s have a g r e a t e r r o l e i n c o m t e r - b a l a n c i n g c o n s i d e r i n g t h e investments of b o t h a g r i c u l t u r e and f e r t i l i z e r i n d u s t r y . When t h e v a l u e of t h e s e i n v e s t m e n t s i n t h e g r o s s n a t i o n a l p r o d u c t i o n /GNP/ s h a r e s w i t h a c o n s t a n t r a t e , t h e volume of investment can v a r y depending on t h e al- t e r n a t i v e s of t h e r a t e of economic growth. When t h e r a t i o of investments i n GNP i s c o n s i d e r e d as p o l i c y v a r i a b l e s , a possi- b i l i t y i s given t o c r e a t e and examine a l t e r n a t i v e s i n t h i s r e s p e c t a s w e l l / i n t h e c a s e of developed c o u n t r i e s t h e r e i s a p o s s i b i l i t y t o have t h e investments of f e r t i l i z e r i n d u s t r y i n t h e form of c a p i t a l e x p o r t / .

Only t h e world market p r i c e s can be modelled from a l l t h e p r i c e s because t h e r e i s no p o s s i b i l i t y t o q u a n t i f y t h e domestic p r i c e s i n t h e c a s e of country-groups. Besides, t h e s h o r t term changes i n import demand and e x p o r t supply; on t h e l o n g run o u t e r f a c t o r s a l s o e f f e c t on p r i c e s /e.g. on t h e p r i c e s of f e r - t i l i z e r s , t h e p r i c e s of r a w m a t e r i a l s , energy and c a p i t a l / , on t h e o t h e r hand, p o l i c y v a r i a b l e may a l s o p l a y a r o l e i n t h e form of i n t e r n a t i o n a l p r i c e agreements and p r i c e s u p p o r t s which can be handled as a l t e r n a t i v e exogeneous v a r i a b l e s .

The means of economic p o l i c y on e f f e c t i n g c o u n t e r b a l a n c i n g and t h e i r i n f l u e n c e a r e r e p r e s e n t e d as f o l l o w s :

economic p o l i c y r a t e of economic

growth /GNP/

p r i c e s u p p o r t s

+

₁

I

food p r i c e s 4

-+

^I

investment Jf

f e r t i l i z e r prices<-/ i

a l l o c a t i o n energy p i c e s

< I

/ ' 1

^{,-. '}

a g r i c u l t u r a l f e r t i l i z e r

\

c a p i t a l

investments production e x p o r t

investments /import/

4. The r e l a t i v e l y simple and p r a c t i c a l h a n d l i n g of t h e f e r - t i l i z e r commodity model cannot be r e a l i z e d w i t h o u t c e r t a i n

s , i m p l i f i c a t i o n s , e s p e c i a l l y i n t h e food sphere.

The most i m p o r t a n t s i m p l i f i c a t i o n i s t h a t food production and p l a n t c u l t i v a t i o n w i l l be r e p r e s e n t e d by g r a i n production i n t h e model.

I t h a s more reasons:

-

t h e g r a i n amounts t o 60

5

of d i r e c t c a l o r i e consump- t i o n amounts t o 50 yh,

-

t h e g r a i n amounts t o 50-60 $ of t h e c u l t i v a t e d l a n d of developed c o u n t r i e s as w e l l as i n t h e developing ones,

-

t h e g r a i n r e c e i v e s approximately 50-60 7; of t h e t o t a l f e r t i l i z e r u t i l i z a t i o n i n t h e developed and t h e deve- l o p i n g c o u n t r i e s , t o o /R. h-ell 1976/,

-

^{i t i s a l s o} an important p o i n t of view t h a t we have long term prognoses f o r g r a i n production developed by more o r g a n i z a t i o n s / s e e e.g. F.H. Sanderson 1977/

which can be u t i l i z e d t o c o n t r o l t h e o p e r a t i o n of f e r t i l i z e r commodity model.

I n t h e c a s e of food demand t h e needs i n c e r e a l s , meats, milk and eggs w i l l be taken i n t o account and w i l l be converted i n t o food and f e e d g r a i n demand. This method h a s a l r e a d y been a p p l i e d i n some world food models /e.g. G.F. Framingham 1974/.

Only t h e most important t h i n g , t h e c u l t i v a t i o n of new l a n d s w i l l be taken i n t o c o n s i d e r a t i o n as a g r i c u l t u r a l i n v e s t - ment having t h e e a s e of a v a i l a b i l i t y , e s p e c i a l l y i n t h e deve- l o p i n g c o u n t r i e s . A t t h e same time we do n o t t a k e t h e account of e.g. t h e i r r i g a t i o n a l investments i n t h i s model, though t h e i r r o l e i n c e r t a i n r e g i o n s may be important.

But a t t h e handling of f e r t i l i z e r s t h e t h r e e n u t r i t i v e m a t e r i a l s a r e taken i n t o account s e p a r a t e l y ; t h e y are t h e n i t r o g e n , phosphate and potassium f e r t i l i z e r s . T h i s has more r e a s o n s as w e l l :

-

g e t t i n g on i n time t h e N : P205 : K20 r e l a t i o n s i n f e r t i l i z e r consumption a r e changing,

-

on t h e o t h e r hand, t h e raw m a t e r i a l s o u r c e s of phos- phate and potassium a r e c o n c e n t r a t e d i n d i f f e r e n t c o u n t r i e s , t h e r e f o r e t h e c o n d i t i o n s of export-import a r e v a r y i n g f o r every n u t r i t i v e ,

b e s i d e s , t h e c a p i t a l and energy needs of manufacturing t h e t h r e e n u t r i t i v e s a r e d i f f e r e n t , s o t h e i r world market p r i c e s responded i n d i f f e r e n t way t o t h e changes of energy p r i c e s .

The mathematical model, the solution and methods of prognostics

The satisfaction of requirements set for the model and the modelling of this economic sphere can only be realized with the help of econometric model consisting of more equa-

tions. To provide prognoses for different years an econometric model is being applied as a simulator in that way that the equations of the econometric model will be solved one after another for every prognosticated year /R.C. Meier, W.T. Newell, H.L. Pazer 1969/, but the results will be printed out for

every five years only.

In the case of an econometric model the question arises whether there is some possibility of applying a recursive mo-

del where it is satisfactory to solve the individual equations in turn or a simultaneous model is needed where all the equa- tions concerning the given year should be solved simultaneous- ly. In the case of more country-groups the reason for the ap- plication of a recursive model can be given by the quantifica- tion of the model to be solved, and another reason is the ne- cessity of taking into consideration the non-linear connec- tions /e.g. in regard to the fertilizer portions and yields/.

At the same time the application of prices as endogeneons va- riables and the modelling of their effect on demand and supply as well as the validation of equilibrium requirements would necessitate in a simultaneous solution.

The question is related to the problem of connecting the individual blocks of the individual country-groups with regard to the counterbalancing of the world market. Three methods of connections are known:

-

wfonnal linkingw

-

^{is a} connection produced by the so called simultaneous solution,

-

wnon-fomal linkingw

-

it does not lead to perfect counterbalancing after a limited number iterative

steps,

-

^{ttloose linkingn}

-

the handling of inconsistencies takes place only after the running of blocks which can only be an emergency solution /M.A. Keyzer 1977/.

According to our opinion the simultaneous one is the best solution in the case of two country-groups; n m e l y , the appli- cation of "formal linking", thus the econometric model will be introduced accordingly. The solution will be carried out by the use of Moris-Normann program package allowing the applica- tion of non-linear equations as well.

Prognoses are carried out by the econometric model as follows :

-

t h e v a l u e s 01' exogeneous v a r i a b 3 . t : ~ siiolild be d e f i n e d e x t e r n a l l y f o r a l l t h e y e a r s of t h e p r o g n o s t i c a t e d pe- r i o d / i n t h e form of a time sequences o r t r e n d s / , and

i n a l t e r n a t i v e way, of c o u r s e ,

-

i n t h e c a s e of lagged endogeneous v a r i a b l e s t h e i r v a l u e s must be g i v e n o n l y f o r t h e s t a r t i n g y e a r ,

-

t h e v a l u e s of endogeneous v a r i a b l e s f o r a l l t h e y e a r s of t h e p r o g n o s t i c a t e d p e r i o d w i l l be c a l c u l a t e d from t h e model i n an a l t e r n a t i v e way.

I n p r i n c i p l e t h e r e i s a p o s s i b i l i t y of c a l c u l a t i n g t h e s o c a l l e d "long-run m u l t i p l i e r s w which show t h e e f f e c t of a s i n g l e change of exogeneous v a r i a b l e s on t h e f i n a l v a l u e s of endogen- ous v a r i a b l e s i n t h e s t a r t i n g p e r i o d of t h e system which con- v e r g e s t o t h e e q u i l i b r i u m / s e e e.g. S. R e u t l i n g e r 1966/.

On one hand t h e forming of a l t e r n a t i v e s can be based on t h e t r e n d a l t e r n a t i v e s of exogeneous v a r i a b l e s /e.g. popula- t i o n GNP/ on t h e o t h e r hand on v a r y i n g some p a r a m e t e r s of t h e model o r some complete e q u a t i o n s of i t s . Each combination of t h e a l t e r n a t i v e s g i v e n f o r t h e parameters and f o r t h e d i f f e r e n t exogeneous v a r i a b l e s means one s c e n a r i o f o r t h e f u t u r e . For t h e a c t u a l forming of s c e n a r i o s s e e more d e t a i l s i n t h e f o l l o w i n g c h a p t e r s .

1IE;SCRIPTION OF THE ECONOMETRIC MODEL

The econometric model i s t o be i n t r o d u c e d i n two d i f f e r e n t ways: w i t h t h e d e s c r i p t i o n of t h e s t r u c t u r e and of t h e equa-

t i o n s of t h e model.

F i g u r e No 1. shows t h e s t r u c t u r e of t h e econometric model.

Three s p h e r e s a r e t o be d i s t i n g u i s h e d h o r i z o n t a l l y w i t h i n t h e system; t h e s p h e r e of t h e whole economy, one s p h e r e f o r food i n d u s t r y and one f o r f e r t i l i z e r s . One p a r t of t h e s p h e r e of t h e whole economic c o n s i s t s of exogeneous v a r i a b l e s . Tbe p e r i o d s t

and t + l a r e s i t u a t e d v e r t i c a l l y , w i t h i n t h e s e p e r i o d s some phases of r e p r o d u c t i o n p e r i o d a r e t o be found. The d i r e c t i o n - s i g n s d e s c r i b e d w i t h continuous l i n e s show t h e c o n n e c t i o n s

w i t h i n a y e a r and t h e ones d e s c r i b e d w i t h d o t t e d l i n e s show t h e lagged e f f e c t s . Thus t h e p r i c e s of g r a i n and f e r t i l i z e r s f o r example have t h e i r i n f l u e n c e on demand i n t h e same y e a r , w h i l e some e f f e c t s on s u p p l y a r e a l r e a d y lagged, and w i l l o n l y be v a l i d i n t h e n e x t year.

I n t h e f o l l o w i n g s t h e e q u a t i o n s of t h e model w i l l be given i n normal form w i t h o u t any numerical d a t a . The numerical equa- t i o n s w i l l be r e p o r t e d i n t h e e n c l o s u r e . The v a r i a b l e s of t h e model a r e i n d i c a t e d by c a p i t a l l e t t e r s , and t h e parameters by

small ones.

The f o l l o w i n g i n d e x e s a r e used i n t h e d e s c r i p t i o n o f t h e model :

t : upper index, i t denotes t h e number o f y e a r s , t = 1, 2 ,

...,

²⁵

i : l o w e r index, i n d i c a t i n g food products

/ c e r e a l , meat, m i l k and egg/

j : lower index i n d i c a t i n g f e r t i l i z e r s / n i t r o g e n , potassium, phophate/

k : lower index i n d i c a t i n g country-groups

/developed and developing ones/

E q u a t i o n s of t h e sphere of t h e whole economy

The number of p o p u l a t i o n , t h e GMP and t h e p r i c e s of energy s o u r c e s used f o r f e r t i l i z e r production a r e exogeneous v a r i a b l e s i n t h e sphere of t h e whole economy. The p r i c e and investment p o l i c i e s a r e exogeneous f a c t o r s , too. These have t o be given f o r t h e model i n e x t e r n a l way; e q u a t i o n s c o n t a i n i n g o n l y endo- geneous v a r i a b l e s w i l l be d e s c r i b e d i n t h e f o l l o w i n g s .

The personal income of p o p u l a t i o n w i l l be deduced from GNP and t h e p e r c a p i t a income w i l l be d e r i v e d from t h e above:

where :

T I N C = t h e t o t a l p e r s o n a l income of t h e

p o p u l a t i o n

GNP = g r o s s n a t i o n a l production /exogeneous v a r i a b l e /

PCINC = personal p e r c a p i t a income

POP = t h e number of p o p u l a t i o n /exogeneous v a r i a b l e /

The a v a i l a b l e funds f o r t h e t o t a l investment w i l l be de- r i v e d from GNP as w e l l . The r a t i o of a v a i l a b l e investment funds

f o r t h e f e r t i l i z e r i n d u s t r i a l investments and f o r t h e i n c r e a s e of c u l t i v a t e d l a n d i s determined by t h e exogeneous investment p o l i c y :

where :

TINV = annual financial funds for investments in the whole economy

L I N W = the available financial funds for the investments in the agriculture, for the increase of cultivated land

a = parameter indicating the ration of

agricultural investments /a parameter of exogeneous economic policy/

F I N W = the annual financial funds for invest- ments in the fertilizer industry

b = parameter indicating the ratio of fertilizer industrial investments /a parameter of exogeneous economic policy/

For simplification reasons agriculture is supposed to utilize the total annual financial funds for investments for

the purpose of expanding, the cultivated land which means that the prices of grain and land have no effect on the ex- pansion of cultivated land. However, in the fertilizer in- dustry the prices and investments are cyclical, BLerefore it is desirable to make it possible to influence the volume of annual investments by the fertilizer prices and accordingly it sbould be permitted to accumulate the annual financial funds for more years. The given financial funds for invest- ments in fertilizer industry which is available in every country-group can be influenced by the capital export or im- port, the volume of which should also be defined as an ex- ogeneous economic parameher.

Equations of the food economy

The per capita food demand can be expressed as the func- tion of per capita income for grain, meat, milk and eggs sepa- rately:

where :

PCFDi = the quantity of per capita food demand on food product i.

I n t h e f o l l o w i n g e q u a t i o n a l l t h e food demand w i l l be con- v e r t e d i n t o g r a i n demand and a t t h e same time t h e g r a i n demand w i l l be made dependent on t h e world market p r i c e of g r a i n :

where :

PCGD = p e r c a p i t a g r a i n demand /consumption/

TGD = t o t a l g r a i n demand /consumption/

GPR = world market p r i c e of g r a i n

c = a m u l t i p l i e r t o c o n v e r t t h e food-demand i i n t o g r a i n demand on food product ⁱ

d = t h e p r i c e - e l a s t i c i t y f o r g r a i n demand

e - = m u l t i p l i e r f o r c a l c u l a t i n g t h e need of seed-grain

The l a n d y e a r l y taken i n t o c u l t i v a t i o n i s c a l c u l a t e d as t h e q u o t i e n t of investment funds a v a i l a b l e f o r t h i s purpose and of c o s t s of t a k i n g l a n d i n t o c u l t i v a t i o n pro h e c t a r e . The a n n u a l l y c u l t i v a t e d a r e a i s reduced f o r u r b a n i s t i c purposes b u t a t t h e same time t h e y a r e expanded by t h e new l a n d s taken i n t o c u l t i v a t i o n :

where:

LINC = new l a n d taken i n t o c u l t i v a t i o n L = e u l t f v a t e d l a n d

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

e = t h e r a t e of annual reducement of c u l t i v a t e d l a n d f o r t h e purpose of u r b a n i z a t i o n .

The q u a n t i t y of g r a i n p r o d u c t i o n i s c a l c u l a t e d on t h e

basis o f c u l t i v a t e d l a n d , t h e t e r r i t o r i a l r a t i o o f g r a i n and

g r a i n y i e l d . The t e r r i t o r i a l r a t e o f g r a i n depends on t h e ra- t i o of t h e p r e c e d i n g y e a r and on t h e p r i c e o f g r a i n i n t h e p r e c e d i n g y e a r . But t h e g r a i n y i e l d depends on t h e f e r t i l i z e r demand and y i e l d - t r e n d i n t h e p r e c e d i n g y e a r .

dt/

_{= f}

_/

_{Yk / t o /}

_,

_t

_,

_{FEDH /t-I/}

_/

k jk

where :

G P = t h e q u a n t i t y of g r a i n p r o d u c t i o n

A = t h e r a t i o of g r a i n w i t h i n t h e c u l t i v a t e d l a n d s

Y = t h e y i e l d of g r a i n pro h e c t a r e FEDH = f e r t i l i z e r demand f o r 1 h e c t a r e on

j n u t r i t i v e j

.

The q u a n t i t y of g r a i n s u p p l y i s deduced from t h e produc- t i o n and from t h e change i n s t o c k s . The forming o f s t o c k s i s determined by t h e p r e v i o u s y e a r s t o c k s , s t o r a g e l o s s and change i n s t o c k s . But t h e change i n s t o c k s depends on t h e volume of s t o c k o f t h e p r e v i o u s y e a r , on t h e g i v e n annual p r i c e of g r a i n as w e l l as on t h e exogeneous v a r i a b l e s e x p r e s s i n g economic pur- p o s e s i n c o n n e c t i o n w i t h t h e forming of s t o c k s / e . g . e n s u r i n g t h e s a f e t y of w o r l d - p r o v i s i o n i n g may r e q u i r e t h e i n c r e a s e of g r a i n s t o r e s i n t h e developed c o u n t r i e s :

where :

GSP = t h e q u a n t i t y of :rain s u p p l y GST = t h e volume of g r a i n s t o c k s

GSTM = changes i n the g r a i n s t o c k / t h e r e a c t i o n of s t o c k / , which can have a p l u s s i g n as w e l l as a minus one /stock i n c r e a s e o r

stock decrease/

h = a parameter t o express t h e l o s s i n s t o r a g e

m = parameter t o express t h e economic

purposes i n connection w i t h t h e volume of g r a i n s t o c k s /exogeneous parameter/

The q u a n t i t y of g r a i n g e t t i n g i n t o foreign-trade i s c a l - c u l a t e d from t h e d i f f e r e n c e between t h e supply and demand. It means n e t export o r import depending on t h e sign. The e q u i l i b - rium of t h e q u a n t i t y t o be exported o r imported i s c r e a t e d by t h e equilibrium c o n d i t i o n through t h e g r a i n p r i c e s :

where :

GTR = t h e q u a n t i t y of g r a i n export / o r import/.

The equations of f e r t i l i z e r sphere

The l e v e l of f e r t i l i z e r demand / f e r t i l i z e r consumption/

on 1 hectare c u l t i v a t e d land i s expressed i n the form of a f u n c t i o n of g r a i n y i e l d s o t h e fertilizer-consumption i s de- termined b a s i c a l l y by t h e g r a i n y i e l d , b u t t h e a c t u a l degree of consumption depends on the p r i c e s of f e r t i l i z e r and g r a i n , as w e l l as on t h e i r r a t i o . The f e r t i l i z e r consumption may be c a l c u l a t e d f o r n u t r i t i v e s s e p a r a t e l y o r a l l t o g e t h e r start- i n g from the c o n s t a n t r e l a t i o n N : P205 : K20.

/ t /

= FEDH

k nk

where :

FEPRj = t h e world market p r i c e of f e r t i l i z e r

f o r n u t r i t i v e j

T F U = the total fertilizer demand /consumption/

j from nutritive j

n = multiplier rate for fertilizer consumption for non agricultural purposes.

The available investment funds for fertilizer industry are defined by the rest from previous year, by the annually forming funds and by the capital export-import. The capital export and import should counterbalance.

where :

FINVA = the available financial investment funds for the fertilizer industry

FINVli = the rest of financial funds from the previous year

CAPTR = the quantity of capital export /or import/

for fertilizer purposes

0 = coefficient to determine the ratio of capital export /only for the developed countries, exogeneous economic parameter/

The given annual actual volume of fertilizer industrial investments are calculated by functions. It is possible to give the minimum volume of investments pro nutritives and the maximum volume defined by the available Fnnds in the function.

The actual investment volume as well as its combination pro nutritives may vary between the minimum and maximum values, making also possible the formation of the rest of funds. The investment volume between the minimum and maximum values de- pends on fertilizer prices of the previous year:

FCIMI /t/ = P . FEC /t/

jk ~k jk

FECI jt/ = f

/

FCIMI / t /

/

j k _{j k} t/

'

FEPH; FINW% ^/27/

F I N V ~ ~ / = F I N V F ~ ~ I

-

^{FECI j k}

^/

^{t/ r j k}

j where :

FCIMIj = t h e minimum investment volume from n u t r i t i v e j

FEC = f e r t i l i z e r p r o d u c t i o n c a p a c i t y from j n u t r i t i v e j

FECI = minirmun of volume from n u t r i t i v e j P = c o e f f i c i e n t t o determine t h e minimum

j r a t i o f o r a u n i t of investment /exogeneous parameter/

r j = c o e f f i c i e n t d e f i n i n g t h e c o s t f o r a u n i t of investment

/exogeneous parameter/

~ e r t i l i z e r p r o d u c t i o n c a p a c i t i e s a r e a n n u a l l y updated by t h e s e l e c t i o n s because of a m o r t i z a t i o n and by t h e i n v e s t m e n t s from t h e p r e v i o u s year. The u t i l i z a t i o n of c a p a c i t i e s depends on t h e s t a r t i n g v a l u e and t h e t r e n d of u t i l i z a t i o n and i t i s a l s o i n f l u e n c e d by t h e f e r t i l i z e r p r i c e s . So t h e f e r t i l i z e r p r o d u c t i o n i s c a l c u l a t e d from t h e c a p a c i t i e s and from t h e i r u t i l i z a t i o n , t h e c a l c u l a t i o n does n o t depend on r a w material

/ t h e r a w m a t e r i a l s w i l l n o t be l i m i t i n g f a o t o r s up t o t h e

y e a r 2000, s e e UNIDO I n t e r n a t i o n a l Centre f o r I n d u s t r i a l S t u d i e s 1977/. The f e r t i l i z e r s u p p l y i s r e c e i v e d from t h e q u a n t i t y , t h e l o s s e s a r e discounted:

FEC jt/ = s FEC/~-'/

+

FECI /t-I/

j k j k j k

FECU

It'

^{= f}

/

FECU jto/, t

,

FEPR / t /

/

j k j k j

FEP

It/

^{= FEC}

It'.

FECU / t / + uk FEP /t-l/

j k j k j k j k

where :

FECU = capacity utilization by the production

j of nutritive j

FEP = fertilizer production from nutritive j j

FESP = fertilizer supply from nutritive j

S

S j = amortization rate at the production capacity of nutritive j

/exogeneous variable/

u = coefficient defining the ratio of other /not producted/ phosphates

/exogeneous parameter/

v j = coefficient defining the losses by transport and storage of nutritive j /exogeneous parameter/

The net export as well as the import of fertilizers are calculated from the difference of supply and demand. The quan- tity of net export and import will be equal in consequence of the counterbalance condition. The counterbalance will be real- ized through the fertilizer prices, though they are influenoed by the exogeneous energy prices and by price supports. In

order to receive the gross export-import data in the statis- tics and in UNIDO world model, the export within the indivi- dual country-groups should be added to the net export:

FENTR

It/

= FEsp /t

/

jk _3k

It/ -

^TFEDjk

FEPR/~/ = f /FEPR /to/, FESUP~, BPR /t/

j j

FEBTR /t/ = wjkFENTR /t/

jk jk

where :

FENTR = the net export /or import/ of j fertilizer from nutritive j FESUP = fertilizer price supports by

j nutritive j

/exogeneous economic variable/

EPR = price index of energy sources for fertilizer industry

/exogeneous variable/

FEBTR = g r o s s export / o r import/ of f e r t i l i z e r j from n u t r i t i v e j

W jk = c o e f f i c i e n t d e f i n i n g t h e r a t i o of export /import/ w i t h i n country-groups /exogeneous parameter/

The model d e s c r i b e d here i n a general form c o n s i s t s of 36 eqaations. The block of a country-group c o n t a i n s 65 equa- t i o n s t a k i n g i n t o c o n s i d e r a t i o n t h e 4 food products and t h e 3 f e r t i l i z e r products. The model c o n s i s t s of 124 equations i n t h e case of 2 country-groups /developed and developing ones/

because t h e equilibrium requirements and p r i c e equations oc- c u r only once.

23 out of 65 equations of a country-group should be given i n the form of a f u n c t i o n t h e o t h e r 42 express only e i t h e r c e r t a i n o p e r a t i o n s between t h e v a r i a b l e s o r 1-2 c o e f f i c i e n t s should be given only t o t h e equation.

There a r e 63 v a r i a b l e s i n t h e equations of a country- group from which 57 a r e endogeneous v a r i a b l e s and 6 exogeneous v a r i a b l e s /population, GNP, energy-price index, f e r t i l i z e r p r i c e support/. There a r e y e t 30 c o n s t a n t c o e f f i c i e n t s i n a country-group block which a r e n o t changing i n time, they a r e parameters expressed in exogeneous way, but t h e r e a r e 4 between them which a r e economic p o l i c y parameters, t h a t i s why they should be d e f i n e d i n an a l t e r n a t i v e way / t h e r e l a t i o n s of in- vestments i n GNP, t h e r a t i o of c a p i t a l e x p o r t , t h e o b j e c t i v e s i n connection w i t h g r a i n stocks/.

The q u a n t i f i c a t i o n of t h e model

The f i r s t phase of our q u a n t i f i c a t i o n work w a s t h e col- l e c t i o n of s t a t i s t i c a l time s e r i e s f o r t h e y e a r s 1960-1975 con- c e r n i n g t h e endogeneous and exogeneous v a r i a b l e s of t h e model w i t h r e s p e c t t o t h e developed and developing c o u n t r i e s and t h e world t o t a l s e p a r a t e l y . D a t a were c o l l e c t e d f o r i n d i v i d u a l

c o u n t r i e s i n t h e f i e l d s of t h e consumption of f e r t i l i z e r s , t h e y i e l d of g r a i n , t h e personal p e r c a p i t a income and food con-

sumption as w e l l ; we d i d i t f o r 2-3 occasions w i t h i n t h e period of 15 years.

The second phase w a s t h e e s t i m a t i n g of f u n c t i o n s needed by t h e model on t h e b a s i s of time s e r i e s of t h e p e r i o d 1964-1974, i . e . i t w a s based upon 11 y e a r s time sequences. I n t h e experi- mental period we had t o c o n s i d e r s e v e r a l types of a l t e r n a t i v e

f u n c t i o n s and v a r i a b l e s . Data from i n d i v i d u a l c o u n t r i e s were a p p l i e d f o r t h e c a l c u l a t i o n of f u n c t i o n s expressing t h e r e l a - t i o n between t h e consumption of f e r t i l i z e r s and t h e y i e l d of g r a i n as w e l l a s t h e r e l a t i o n between t h e per c a p i t a income and t h e food consumption. Two c r i t e r i a were taken i n t o conside- r a t i o n when making our choice among d i f f e r e n t a l t e r n a t i v e func- t i o n s :

1. the function must reflect appropriately the factual values of the base period 1964-1974

2. the function should result in a reasonable prognosis for the forecast period /by the substitution of data from advanced countries/. Accordingly, for example, the consumption of cereals, meat, milk and eggs were described by different types of functions in a proper way with regard to the developed or developing coun-

tries.

The third phase was the creation of simultaneous equa- tions on the ground of the functions previously described.

The individual equations were grouped according to their blocks as well, i.e. whether they were contained by a recur- sive, a simultaneous or postsimultaneous ones.

The fourth phase was meant by the estimation of factual values of the base period of 1965-1974 years with the help of all simultaneaus equations effecting as a simulator. It was carried out in the following way: first, the annual ones were calculated independently /started with the factual values of the previous year/ and this was followed by the calculation of the se uence of years /started with the factual values of 1964 year?. The model was not applied for the purpose of prog- nostics until it has resulted in satisfactory estimation for the base period.

The fifth phase was the application of the simulation model for prognostics of the years 1975-2000.

Our greatest intention was to solve the model in simul- taneous way. At first we didn't succeed in the formation of price-equations being capable of providing dynamic counter- balance within the system for a long period of 25 years where conditions seem to vary too often. That was why the price- equations were neglected and simultaneous equations were

solved in recursive way and the counterbalance was established by the final calculation of variants where some role was as- signed to the counterbalancing effect of grain and fertilizer stocks as well. The prognosis-alternatives A-E of the follow- ing chapter were based on recursive solutions of this type.

Some simplifications were allowed compared with the pri- mary description of the model. As the program available for us was not able to operate with inequalities, limitations on

the financial funds of investments in fertilizer industry as well as the capital export were disregarded. Because of the imperfectness of price equations the price support of ferti- lizers was not considered either. The lack of data concerning fertilizer production capacities made it impossible for us to define the degree of utilization as a function of price, thus the production capacity was handled in an exogeneous way. The forming export surplus /the quantity above import/ was con-

s i d e r e d t o i n c r e a s e stock i n t h e c a s e s of g r a i n and f e r t i l i - z e r and t h a t ' s why g r a i n s t o c k s in t h e c a s e of increase d i f - f e r from t h e ones i n t h e computer o u t p u t l i s t .

The a n a l y s i s of t h e f i v e scenarious r e s u l t e d i n t h e si- multaneous s o l u t i o n as w e l l , where t h e p r i c e s of f e r t i l i z e r s and g r a i n a r e d e f i n e d by t h e model. A s r e s p e e t s t h e r e s u l t s of t h e s c e n a r i o s

-

except t h e p r i c e s , they do n o t d i f f e r es- s e n t i a l l y from t h e ones of t h e r e c u r s i v e s o l u t i o n s and con- sequently, they w i l l be r e p r e s e n t e d only i n t h e folla of ex- aaples.

ALTERNATIVE PROGNOSES

The r e s u l t s of our prognostic a c t i v i t y w i l l be presented i n t h e following c h a p t e r s i n t h e form of w r i t t e n e v a l u a t i o n and t a b l e s enclosared. I n o r d e r t o i n t e r p r e t e t h e r e s u l t s pro- p e r l y some i n f o n a t i o n i s needed:

1. The Grouping of Countries: The following c o u n t r i e s and t e r r i t o r i e s were e n l i s t e d i n t o t h e group of developed coan- t r i e s : USA, Canada, Western-Enrope, Eastern-Europe, t h e Sow- j e t u n i o n , Japan, t h e South Sea I s l a n d s / A u s t r a l i a , New-Zealand e t c . / . The following c o n t i n e n t s belong t o t h e cafegory of de- veloping c o u n t r i e s : A s i a /except ~apan/, A f r i c a , Lafia-Bnerica.

'PBus our grouping somewhat d i f f e r s from f h e s t a n d a r d r e g i o n a l groups of UNO but i t seems t o be more reasonable f o r t h e per- pose of f e r t i l i z e r s . The same c a t e g o r i e s were used in Hr.

well's study /R. Ewe11 1976/ ae well.

2. The Concept of Grain: A l l k i n d s of g r a i n c r o p s a r e un- d e r s t o o d by t h e concept of g r a i n , a l l e n e e r e g i s t e r e d and ac- cumulated by t h e s t a t i s t i c a l year-books of FAO. !Werefore food g r a i n i n c l u d e s r i c e as w e l l , while feed g r a i n c o n t a i n s maize;

aad t h e c a t e g o r y of g r a i n i n c l u d e s both food and f e e d g r a i n . 3. The Concept of F e r t i l i z e r s : F e r t i l i z e r s ^{a r e} n e a t by t h e i r e f f e c t i v e snbstanoe, according t o t h i s BT i s fhe e f f e c - t i v e substance f o r n i t r o g e n , P 0 f o r phosphate mil K20 f o r

potassium. ² 5

4. The Character of Prognoses: our i n t e n t i o n w a s t o pro- v i d e a c o n s i s t a n t , s o c a l l e d "counterbalancingn prognosis i n each case. They a r e i n accordance w i t h each o t h e r from t h r e e p o i n t s of view / i t i s only p a r t i a l l y trvle i n t h e c a s e of s c e n a r i o E/. They a r e as _follows:

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an accordance i n time: t h e prognosis s t a r t e d w i t h d a t a from 1974-1975 y e a r s and i s a n n u a l l y calcu- l a t e d u p t o 2000 year /however, r e s u l t s a r e pub- l i s h e d f o r every f i v e y e a s only/,

-

^an accordance i n place: prognoses c o n s i d e r i n g the groups of developed and developing c o u n t r i e s a r e i n accordance w i t h r e g a r d t o t h e g r a i n and f e r t i - l i z e r s e x p o r t and import,

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an accordance i n economic spheres: t h e growth of population and t h e d e v e l o p e n t of economy, t h e g r a i n production and consumption, t h e f e r t i l i z e r production and coasumption a r e accorded w i t h one another w i t h i n t h e country-groups.

5 . The A l t e r n a t i v e s of Prognoses: t h e c a l c u l a t i o n of prognoses w a s c a r r i e d out in some versions. The a l t e r n a t i v e s a r e connected w i t h d i f f e r e n t presumptions f o r t h e f u t u r e ; one group of a1 t e r n a t i v e presumptions i s considered t o f o w one n s c e n a r i o n , o r one f u t u r e nimagen. The r e s u l t s of prognoses

w i t h t h e f u r t h e r s c e n a r i o s a r e d e s c r i b e d i n t h e followings:

Scenario A: a moderate growth r a t e of population and economy and t h e presumption of unchanged / f o r t h e y e a r 1976/ world market p r i c e s of g r a i n and f e r t i l i - z e r s .

Scenario B: a more i n t e n s i v e growth r a t e of population and economy, a moderate r i s e i n world market p r i c e s of g r a i n /1 % per year/.

Scenario C: a more i n t e n s i v e growth r a t e of population and economy, and t h e developing c o u n t r i e s i n c r e a s e

t h e i r c u l t i v a t e d area.

Scenario D: a more i n t e n s i v e growth r a t e of population and economy, t h e developed c o u n t r i e s have i n c r e a s e d t h e g r a i n y i e l d i n s t e a d of i n o r e a s i n g t h e cul- t i v a t e d a r e a , t h e r e i s a r i s e i n world market p r i c e s of f e r t i l i z e r s /2 $ per y e a r / , t h e u t i l i - z a t i o n of productive c a p a c i t y i s i n c r e a s e d t o some e x t e n t as well.

Scenario E: a more i n t e n s i v e growth r a t e of population and economy: higher g r a i n y i e l d than i n t h e deve- loped c o u n t r i e s , though t h e e f f i c i e n c y of t h e u t i l i z a t i o n of f e r t i l i z e r s i s reduced.

One p a r t of t h e i n d i v i d u a l scenario-elements / l i k e t h e growth of economy and population f o m s a v e r s i o n of d i f f e r e n t prognoses from t h e p o i n t of view of demand on g r a i n /an in- d i r e c t demand on f e r t i l i z e r s / while t h e o t h e r ones l i k e t h e r a t e of growth of c u l t i v a t e d land and g r a i n y i e l d s do t h e same from t h e p o i n t of view of g r a i n production /a d i r e c t de- mand on f e r t i l i z e r s / , and t h e r e s t / t h e world market p r i c e s of f e r t i l i z e r s , t h e percentage of t h e u t i l i z a t i o n of produc- t i v e c a p a c i t y / o p e r a t e s from t h e p o i n t of view of f e r t i l i z e r production.

The above s c e n a r i o s r e s u l t i n an e v e r i n c r e a s i n g f e r t i - l i z e r consumption and according t o t h i s i n an e v e r i n c r e a s i n g f e r t i l i z e r production ^as well. The f e r t i l i z e r c o n ~ u m p t i o n and production of S c e n a r i o s E and D have resohed t h e l e v e l fore- c a s t i n t h e study of UNIDO /UNIDO I n t e r n a t i o n a l Centre f o r In- d u s t r i a l S t u d i e s 1976/. The t r a d e of f e r t i l i z e r between deve- l o p i n g and developed c o u n t r i e s d s e s n o t how an i n o r e a s e ac- cordingly t o t h e l e t t e r s of t h e alphabet f o r a g r e a t e r e x t e n t of e q u a l i z a t i o n can be observed w i t h i n t h e country-groups be- tween f e r t i l i z e r consumption and prsduction.

The r e s u l t s of prognoses belonging t e t h e f i r s t s c e n a r i o , Scenario A w i l l be discussed i n d e t a i l s so t h a t t h e way of c a l c u l a t i o n s , t h e reasons f o r t h e r e s u l t s could e a s i l y be understood. When p r e s e n t i n g t h e r e s u l t s of t h e r e s t o f scena- r i o s we s t r e e s e d t h e essence, t h e d i f f e r e n a e among them,

t h e r e f o r e they a r e d i s c u s s e d i n a s h o r t e r w a y . By t h e end of e v a l u a t i o n a table w i l l be given i n c l u d i n g t h e most charac- t e r i s t i c f e a t u r e s of prognoses belonging t o t h e i n d i v i d u a l scenarios.

Scenario A / ~ a s i c /

I t i s c h a r a c t e r i z e d by a moderate growth of population and economy, unchanged world market p r i c e s .

The F a c t o r s of Grain Consumption

Taking i n t o c o n s i d e r a t i o n t h e number of population t h e b a s i c s c e n a r i o had t h e lowest v a r i a n t . T h i s prognosis cor- responds t o t h e wmediuaH v a r i a n t defined by Population Divi- s i o n of UNO i n 1975, and a t t h e same time i t i s considered t o be t h e more reasonable one beeaolee t h e l a t e s t prognosis published i n Monthly B u l l e t i n of FA0 i n March, 1978 contained a v a r i a n t c l o s e t o t h e above one. By t h i s v e r s i o n , t h e annual development r a t e i n developed c o u n t r i e s

-

^{0,8 %} i n t h e y e a r s 1970-1975

-

^{w i l l} be redxaced t o 0 , 6

5

By t h e y e a r s 1995-2000, and t h e same i n developing c o u n t r i e s w i l l be reduced from 2 , 3

5

t o 1 , 9

5.

Accordingly, t h e t o t a l population of t h e world w i l l i n c r e a s e from 4 m i l l i a r d I n 1975 u p t o 6,25 m i l -

l i a r d by t h e y e a r 2000.

I n t h e f i e l d of t h e economic growth w e had t h e lowest v a r i a n t again i n t h e b a s i c scenario. Thie v a r i a n t t a k e s i n t o account t h e moderate r a t e of growth of g r o s s o u t p u t /GNP/

f o r each year. The annual r a t e of growth i n developed corn- t r i e s

-

^{5 , 3 %} i n t h e y e a r s 1970-1975

-

w i l l be reduced t o 3 , 8 % by t h e y e a r s 1995-2000, while i n developing c o u n t r i e s i t w i l l be reduced from 6 , 1

%

t o 4 , 4

5.

Accordingly, t h e g r o s s output of t h e world

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i n t h e value of 3886 m i l l i a r d d o l l a r s i n 1975

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^{w i l l} be e x a c t l y three-times more by t h e y e a r 2000 /based upon t h e value of d o l l a r i n 1970/.

" I n d i v i d u a l consunption expensesn were considered t o be t h e per a a p i t a income of t h e population. This name oecurs i n

FA0 Commodity P r o j e c t i o n as w e l l . I t s r e l a t i o n w i t h i n GNP had a f a i r l y a o n s t a n t value, 59 per c e n t s i n developed a o u n t r i e s and 70 per c e n t s i n developing c o u n t r i e s w i t h i n t h e period 1965-1975. Theref o r e t h e p e r c a p i t a inaeme w a s e a l e u l r t e d from t h e s e r e l a t i o n s f r o n t h e a c t u a l value of 6NP. The p e r c a p i t a personal inoome w a s deduoed by simple d i v i s i o n n o t con-

s i d e r i n g t h e i n t e r r e l a t i o n s of t h e growth rate between t h e population and economy. Aacordingly, t h e per c a p i t a personal income w i l l i n c r e a s e from 1749 $ of t h e y e a r 1975 t o 4274 $ by t h e y e a r 2000 i n developed u o t a n t r i e ~ , w h i l e i n developing c o u n t r i e s from 155 $ up t o 319 $. With r e g a r d t o t h e great importanae of t h e s e index-numbers some a e r p a r i a o n s were made w i t h o t h e r a u t h o r s p prognoses as well. Blakeslee-Heady-

Framingham i n t h e i r p b l i c a t i o n e n t i t l e d : "World Food Prodtao- t i o n , Denaad and Traden /Iowa S t a t e Univ., d r e s 1973/ provided t h e i r prognoses f o r 96 o o u n t r i e s i n d i v i d u a l l y . On t h e b a s i s of

t h i s work t h e index-numbers of personal income i n t h e a m e d i ~ w

v e r s i o n r e l a t e d t o t h e year 1960 a r e r e p r e s e n t e d by t h e f o l -

lowing data i n peroentage /with t h e exception of china/:

1985 2000

developed c o u n t r i e s 235 345

developing c o u n t r i e s 165 213

world t o t a l 186 249

In t h e case of our prognosis t h e s e index-numbers

-

^re-

l a t e d t o t h e year 1960

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^{a r e as follows:}

1985 2000

developed c o u n t r i e s 273 452

developing c o u n t r i e s

world t o t a l 216 311

According t o our prognosis, t h e growth r a t e of personal income i s more i n t e n s i v e , b u t t h e two kinds of prognoses do n o t d i f f e r e s s e n t i a l l y , b o t h a r e acceptable.

With t h e h e l p of t h e f o r e o a s t values of personal income

t h e per c a p i t a consumption of c e r e a l s , meat, milk, and eggs were c a l c u l a t e d i n t h e r e c e n t paper, We made use of t h e con- sumption by q u a n t i f i e d f u n c t i o n s f o r both oountry-groups and time s e r i e s ,