MARS 1 and MARS 2 for the FAP's Study: "Hunger, Growth and Equity"

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W O R K I N G P A P E R

MARS 1 AND IURS 2 FOR THE FAP'S STUDY

"HUNGER GR0WT.H

A W EQUITY'

V. Iakimets

September 1985 WP-85-83

-

I n t e r n a t i o n a l I n s t i t u t e for Applied Systems Analysis

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YOT FOR QLBTATIO?;

WITHOUT PERYISSIOS OF THE AUTHOR

MARS 1 AND X A R S 2 FOR THE FAP'S

STUDY

"HUNGER GROWTH Am EQUITY'

V. Iakimets

September 1 9 8 5 WP-85-83

V o r k i n g Fbpers are interim r e p o r t s on work of t h e International I n s t i t u t e f o r -4pplied Systems Analysis and h a v e r e c e i v e d only lim- i t e d review. Views o r opinions e x p r e s s e d h e r e i n d o 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 o r of i t s Kational Member Organizations.

INTERNATIONAL IX'STITC'TE FOR APPLIED SYSTEYS ANALYSIS 2361 L a x e n b u r g , A u s t r i a

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FOREWORD

Even with globally a d e q u a t e food availability, l a r g e numbers of people remain chronically undernourished today. Evaluation of a l t e r n a t i v e national ant$ international policies t h a t c a n help r e d u c e rapidly h u n g e r in t h e world h a s been a major theme of t h e FAP since i t s inception.

Though national r e d i s t r i b u t i v e policies may b e essential to r e d u c e h u n g e r at a s a t i s f a c t o r y r a t e , t h e r e s o u r c e s available with t h e developing c o u n t r i e s are limited. International c a p i t a l t r a n s f e r s are thus needed.

Among t h e s o u r c e s for such funds can b e reduction in a r m s expenditure.

With t h e help of F.4P1s Basic Linked System (BLS) of national agricul- t u r a l policy models w e h a v e e x p l o r e d consequences f o r economic development and r e d u c t i o n in h u n g e r of mutual a r m s reduction and r e d i s t r i b u t i o n of p a r t s of t h e r e s o u r c e s t h u s saved.

In t h i s p a p e r , Vladimir Iakimets d e s c r i b e s t h e logic a n d specification of mutual arms reduction s c e n a r i o s

-

^{t h a t}^{w e call}^MARS.

Kirit S. P a r i k h P r o g r a m L e a d e r Food and Agriculture Program.

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I am very grateful to Professor Kirit Parikh for fruitful discussions and to CyEthia E ~ z l b e r g e r for editing arrd typing this paper.

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In t h i s p a p e r two v e r s i o n s of t h e MARS f o r t h e

FAP's

s t u d y "Hunger, Growth a ~ d Equity" are elaborated for implementation in t h e

BLS.

-

vii

-

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MARS

₁

7.

MARS

2

7.1 Background

7.2 Distribution of t h e ,UD among "poor" LDC's

7.2.2 Case of unlimited capital absorption capacity of LDC 7.2.3 Case of limited capital absorption capacity of LDC 7.3 Illustrative calcu!atior of values yP(t) m d 7!(t) for 1980 7.4 Implementation of

MARS

2

8. Conclusion References

-

^{i x -}

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MARS 1 and MARS 2 FOR THE FAP'S SRJDY

"HUNGER, GROWTH AND EQUITY"

1. Introduction

In two previous papers of t h e a u t h o r (lakimets 1985a, lakimets 1985b) t h e main ideas for t h e development of t h e MARS (Mutual Arms Reduction S c e n a r i o s ) for t h e Food a n d Agriculture Program's s t u d y "Hunger, Growth a n d Equity" were described. In t h e first p a p e r objectives of t h e MARS, i t s i m p o r t a n c e , assump- t i o n s for i t s c o n s t r u c t i o n , problems t o be solved a s well a s t h e description of i t s s t r u c t u r e were given. The second p a p e r c o n t a i n s t h e formal description of t h e h y p o t h e s e s r e l a t i n g t o desired dynamics of a n n u a l r e d u c t i o n in a c o u n t r y ' s mil- i t a r y e x p e n d i t u r e .

This p a p e r i s devoted t o detailed consideration of two versions of t h e s c e n a r i o ' s implementation with t h e BLS (MARS 1 a n d MARS 2) including m e t h o - dological a n d formalized description of v a r i a n t s for t h e solution of problems of t h e MARS implementation s t a t e d in t h e first p a p e r (lakimets. 1985a).

2. General objectives and specific aims for both scenarios

The g e n e r a l objective of t h e MARS1 a n d MARS2 is t o show o n c e m o r e t h a t all c o u n t r i e s will b e g a i n e r s in a social a n d economic s e n s e when t h e r e s o u r c e s u s e d for military purposes a r e r e d i r e c t e d t o development of t h e civil economy.

These s c e n a r i o s a r e devoted t o t h e analysis of t h e possible impact of s u c h a r e d i r e c t i o n of r e s o u r c e s on t h e growth r a t e s of n a t i o n a l economies a n d on alleviating t h e world h u n g e r problem.

The specific aims of t h e s c e n a r i o s a r e t o find t h e most preferable a l t e r n a -

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tives for the utilization of released funds in DC's and LDC's in solving the economic problems in these countries

-

in a case where t h e total released funds of a country are used for only internal purposes (MARS1) and for t h a t and aid by DC's t o LDC's (MARS2).

3. Calculating the annuany released funds of a country

If follow assumption for the MARS elaboration stated in Iakimets 1985a.

then military expenditure M,(t) of j-th country in year t could be determined as the s h a r e ~ , ( t ) of the countryas CDP,(t).

Ir. this case the vaice of XJ(t) could be estimated on the basis of corresponding time series of YJ(t) ard G3PJ(t) taken from national o r international statistical yearbooks. Ther, the estimated value of XJ(t) could be used in the BLS runs exring the simulation perio6 for calcalating annually re!eased fund of j-th country AV,(t) created due to a reduction of military expenditure in the foliowing way:

AM,(^) =

pj(t)

-

~ ~ ( t )

.

⁽²⁾

where p j ( t ) is a coefficient for reducing military expenditures of j-th country in year t. Values of this coefficient should be depended upon hypotheses prescrib- ing the dynamics of a country's behaviour related to its arms reduction (see Iakimets 1985b). However, in the case of the application of the formula (2). the questions about the accuracy of values of the coefficients +(t) could arise.

In order t o eliminate such questions instead of (2) the following way for calculating t h e values of AMj(t) can be used:

AMj(t)

=

Mj(t)

-

^M,-(t) ^, (3)

where M,(t) is determined as in (1) and MP*RS(~) is defined by formula*:

*

^Thisidea w a s suggested by Prof. K. Parikh

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xjNAR"(t) = ( h j ( t )

-

a j ( t ) )

.

GZ)Pj(t) , (4) w h e r e h j ( t ) is t h e same coefficient a s in (1) and a j ( t ) is a reduction coefficient, aj(:) S hj(t) by definition. Substituting (1) and (4) into (3) yields:

&Z j(t)

=

a j ( t )

.

G D P j(t)

Comparing (5) with (2) o n e c a n s e e t h a t :

a J ( t >

=

p j ( t ) . hj(t) (6)

However in c o n t r a s t t o (2) w h e r e values of Xj(t) a r e used explicitly t h o s e a r e exciuded in (5). In o t h e r words we n e e d n ' t know t h e value of h j(t) and according t o (5) t h e value of reieased fund LYj(t) c a n b e calculated on t h e basis of t h e endogenoi;r!y determined G 3 P j ( t ) a n d exogenously given a , ( t ) a e s c r i 5 i n g t h e h y p o t h e t i c a l dynamics of a c o u n t r y ' s military expenditures reduction as i t was done f o r p j ( t ) in Iakimets 1985b.

4. Exogenous calculating values of a ( t )

In o r d e r t o apply formula (5) f o r calculating t h e annual value of r e l e a s e d fund A3!(t) within t h e BLS t h e s c e n a r i o s behaviour of t h e function a ( t ) should b e d e s c r i b e d . This function is used t o r e f l e c t d i f f e r e n t p r e s c r i b e d h y p o t h e s e s of possible c o u n t r i e s ' behaviour c o n c e r n i n g t h e annual r e d u c t i o n in t h e i r military e x p e n d i t u r e . Hypotheses on optimistic, cautious optimistic, cautious g r a d u a l p r o - g r e s s i v e and s t r a i g h t f o r w a r d b e h a v i o u r of c o u n t r i e s w e r e explained in Iakimets 1985b. According t o t h i s d e s c r i p t i o n t h e function a ( t ) in (5) h a s t o possess t h e following p r o p e r t i e s :

1. i t h a s t o b e a non-decreasing function of time a ( t +l) r a ( t ) ^: t E[O,T]

2. by definition values of a ( t ) h a v e t o meet t h e constrzir,t:

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In a general case values of function a ( t ) in t

=

0 and in t

=

T should be specific ones for each country in the BLS as well as different hypotheses should be used for various countries. However for the sake of simplicity first of all we will use during t h e BLS run t h e same hypothesis for e a c h country. I t means that:

a j ( t )

=

a ( t ) b j

=

I, 2,

...

m. (9)

Behind t h i s an idea about mutually assured efforts in reducing military expenditures in all countries is pursued. The initial value of a ( t ) in t

=

0 as well as t h e value of a ( t ) in t

=

T have t o be accepted to meet requirements (8).

The m a t t e r is if t h e value of a ( t ) is too high t h e n models of countries with real low levels of military expenditures will give inappropriate results. In a n o t h e r c a s e if t h i s value (a(t)) is too low, then t h e impact of released fund utilization c a n be negligible.

In order t o determine the appropriate values a ( 0 ) and a(T) for all countries in t h e BLS, t h e comparison of t h e SIPRI estimates of ratios of each country's military expenditures t o i t s G D P was made (SIPRI, 1984). Because t h e s e d a t a given i n t h i s source contains uncertain information a n d estimates with a high degree of uncertainty (see SIPRI, 1984, pp. 127-130) t h e approximate classification of all countries a n d groupings of countries in t h e BLS i n t o 3 s e t s of countries was made*:

A. countries where military expenditures is less or close t o 1. p e r c e n t of GDP

B.

countries where t h i s value is more than 1 a n d less t h a n 3

C.

c o u n t r i e s where t h i s value is more or close to 3 percent.

Classification of t h e BLS countries into t h e s e 3 s e t s is given in Table 1.

* It should be noted that this classification will be used in the BLS run for only illustrative purposes to show the possibilities of this system

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Table 1.Values of the a(0) and a(T) for three sets of countries in the BLS

C o u n t r i e s ( o r c o u n t r i e s c o d e ) in t h e BLS a (1980) a (2000)

A. Austria, J a p a n , Brazil, Mexico, 911 0.001 0.005

B. Australia, Argentina, Canada, Indonesia,

N e w Zealand, India, 9 0 2 , 906, 908, 916, 9 0 i 0.002 0.01 C. CYEA, EEC, Egypt, Xigeria. P a k i s t a n , T u r k e y ,

Kenya, Thailand, China, US.4, 903, 904, 905, 907,

9 0 9 , 910, 912, 9 1 3 0 . 0 0 3 0.015

Initial value a (1980) f o r a l l t h e s e c o u n t r i e s was d e t e r m i n e d taking i n t o a c c o u n t as a n example t h e S o v i e t p r o p o s a l on t h e r e d u c t i o n of t h e military budgets of states permanent members of t h e U S S e c u r i t y Council by 1 0 p e r c e n t which h a s b e e n s u b r ~ i t t e c ! by t h e USSR in 1 9 7 3 f o r consideration of t h e 27th r S Genera:

Assembly Session. Values of a ( t ) in t = 2000 f o r all BLS c o u n t r i e s were simply t a k e n equal 5 . a(1980). P r e s c r i b e d b e h a v i o u r of a ( t ) f o r d i f f e r e n t h y p o t h e s e s i s shown in F i g u r e 1.

a(')

7

a, (t) optimistic

I /

^az( t ) cautious

optimistic

/ ^/ ^I

gradual progressive

Figure 1. Behaviour of a ( t )

Corresponding formulas f o r caicuiating vzlues of ~ ( t ) a r e :

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a l ( t )

=

o ( 0 ) ( a l l

-

a I 2

-

e*ls") for optimistic hypothesis. (10) a 2 ( t )

=

a ( 0 )

+

azl t2(az2

.

T

-

a23 t)for cautious optimistic (11) a n d cautious gradual progressive hypotheses,

as@)

=

a(T) (12)

P a r a m e t e r s a

. .

(see Table 2) of functions a l ( t ) and a2(t) a r e determined taking into account given duration of considered period T a n d values of a ( 0 ) a n d a(T) from Table 1. Calculated values of a ( t ) for t h r e e s e t s of c o u n t r i e s for two hypotheses a r e given in Table 3.

Table 2. Valuesdparametersa..

a , ( t ) optimistic a2(t) cautious optimistic

Table 3. Values of a(t) for groups of countries

A B

and C

optimistic hypothesis cautious optimistic hypothesis

Year A B C A B C

1980 0.001 0.002 0.0 03 0.00 1 0.002 0.003 1985 0.0035 0.007 0.011 0.0016 0.00325 0.00487 1990 0.0044 0.009 0.0 13 0.003 0.006 0.009 1995 0.0048 0.0096 0.0 144 0.0044 0.00875 0.0131 2000 0.005 0.0 1 0.0 15 0.005 0.01 0.015

5. Adjustment. needed for the BLS models

A t the present time t h e BLS of t h e FAP consists of 34 models. Eighteen of these models are national a g r i c u l t u r a l policy models with s t a n d a r d s t r u c t u r e (Australia, Austria. Canada, Japan, Argentina. Brazil, Egypt. Indonesia. Mexico, Nigeria, Pakistan, Turkey, Kenya. New Zealand. Thailand) and individual

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country-specific s t r u c t u r e (China, India, USA). 2 models a r e c o u n t r y groups models (CMEA and EEC) a n d 14 a r e simplified c o u n t r y groupings models including 13 groupings of developing countries a n d 1 mixed grouping. An allocation of countries among the 14 groupings is described in FAP, 1985.

For t h e purpose of t h e

MARS

implementation within the BLS, mainly t h e adjustment of the last 14 models was found necessary, because t h e approach taken for t h e s e countries is t h a t t h e i r supply is exogenously calculated on t h e basis of t h e results of t h e FA0 study (FAO, 1981) a n d holds a t c o n s t a n t prices.

In order t o have opportunities for reflection of t h e s e countries' supply in depen- dence on additional capital resources, t h e corresponding correcting term AYjj(t) for i-th commodity output function of j-th c o u n t r y was introduced.

where AMj(t) and CDPj(t) a r e determined as early, AYji(t) is a n increment of i-th commodity output in a year t in comparison to t h e previous year determined on the basis of t h e results of t h e FA0 study (FAO, 1981) a n d coefficient Kj(t) for all c o u n t r y groupings is calculated as follows:

where v is index of v-th country in j-th grouping. Initial values of ~ ? ( t ) for t

=

0 a r e taken from Yearbooks of National Accounts Statistics. Calculated values of Kj(t) for 1980 for all country groupings in t h e BLS a r e given in Table 4.

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Table 4. Calculated v d u e s or K,(t)

Country groupings code 9 0 1

90 2 90 3 904 905 90 6 907 908 909 91 0 91 1 912 91 3

8.1. Background

The main objective of this s c e n a r i o i s t o analyze t h e impact of different v a r i a n t s f o r utilizing a c o u n t r y ' s released f u n d s for i t s own economic development. We c a n call MARS 1 t h e s c e n a r i o for autonomous self-supporting develop- m e n t . Because for e a c h c o u n t r y in t h e BLS a n u m b e r of balances have to be m e t for e a c h y e a r during t h e simulation period in o r d e r t o exclude t h e possible violation of balances, we need t o consider t h e opportunity for r e d i r e c t i n g p a r t of t h e military expenditure for civil purposes. One i m p o r t a n t f a c t o r for t h e implementation of MARS is t h e balance of national income distribution.

Let us consider t h e following balance equation for a c o u n t r y ' s GDP (or n e t national product) by type of expenditures (all indexes a r e omitted)

GDP =

gov

+

priv

+

c a p

+

bal , where

gov i s governmental final consumption expenditure, priv is private final consunlption expenditure, c a p i s g r o s s fixed capital formation, a n d

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bal

=

e x p

-

^impis t r a d e balance with e x p and imp c o r r e s p o n d i n g i y e x p o r t and import values.

Let u s consider t h a t a l l military e x p e n d i t u r e s are inc!uded into governmental final consumption e x p e n d i t u r e s .

In o r d e r t o e x t r a c t t h e value of r e l e a s e d fund l e t u s r e w r i t e (16) as follows:

go\?

=

^[I

-

(A

-

^B)]gov^{+ [A}

^-

^81gov.

Because by definition:

gov

=

v

.

G3P

t h e n t h e su5stitutior. cf ( 1 S j i n t c (17) rni reerrer.gernenL yieldz

go\.

=

( 2

-

A)

.

^?I GDP

+

0 ^.?I

-

CDP

+

(A

-

0)

-

7X;DP. (19) The t h i r d term in (19) is t h e vaiue of governmental e x p e n d i t u r e s f o r military p u r - p o s e s a f t e r Its reduction, t h e second term i s t h e value of r e l e a s e d fund and t h e f i r s t t e r m i s t h e "oid" value of governmental e x p e n d i t u r e s f o r civil p u r p o s e s . Both first and second terms in (19) give u s t h e current vaiue of governmental expen&- tures f o r civii p u r p o s e s .

In a c c o r d a n c e with our p r e v i o u s notations t h e v a l u e of r e l e a s e d fun6 is:

AV = a - C D P = $ . v - G D P (25)

In o r d e r t o utilize r e l e a s e d fun6 d u e t o i t s r e d i r e c t i o n f o r civil p u r p o s e s we need t o t a k e i n t o account b a l a n c e equation (15). F o r t h e s a k e of simplicity w e decided t o s u p p o s e t h a t p r i v a t e final consumption e x p e n d i t u r e s ( p r i v ) f o r t h e who!e p e r i o d u n d e r simlilation wi!i b e c o n r t z ~ t s h a r e of GDP. T h e r e f o r e we c a n u s e r e i ~ n s e c i , fund f o r i n c r e a s i n g g r o s s fixed c a p i t a l formation anZ f o r improvement of t h e t r a t e b a l a n c e .

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6.2. Versions for utilization of released fund

We have a t least t h r e e versions of t h e released fund utilization:

Version A. (total released fund i s u s e d for domestic investment)

In t h i s version balance equation (15) taking into a c c o u n t ⁽¹⁷⁾a n d (20) c a n b e written as follows:

GDP

=

(1-8)

-

^vGDP

+

priv

+

(cap

+

0 v GDP)

+

bal Actually (21) means t h a t

GDP = [gov

-AM] +

priv

+

[cap

+

AM]

+

bal (22)

In o t h e r words such a r e d r e c t i o n of a p a r t of military e x p e n d i t u r e s for civil purposes provides for meeting national income balance.

Version B: (total released f u n d is used for t r a d e balance improvement)

For t h i s version balance equation (15) taking into a c c o u n t (19) a n d (20) c a n be rewritten as follows:

GDP

=

( 1

-

0)

-

^v

.

GDP

+

priv

+

c a p

+

(bal

+

8

.

v GDP) (23)

GDP = [gov

-AM] +

priv

+

c a p

+

[bal

+

AM] ₍₂₄₎ Version C: (total released fund i s used both for increasing domestic i n v e s t m e n t a n d t r a d e balance improvement)

For thi.s version we have:

GDP = ( 1 - 0 ) . v G ~ ~ + ~ r i v + ( c a ~ + ~ . 0 . v . G D P ) + [ b a l + ( l - ~ ) . @ . v . G D P ] (25) o r in o t h e r notation

GDP

=

[gov

- A M ] +

priv

+

[ c a p

+ B .

AM]

+

[bal

+

(1 - p) AM] (26) The last equation means t h a t total reieased fund A!! is divided i n two p a r k with r a t i o

- '

and x e d both f o r domestic investment an6 t r a d e balance improvement.

1-8

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I t should be noted t h a t utilization of released f u n d in accordance with Ver- sion A means actually t h a t in each model in equation for calculation of value of capital stocks one additional term ( AMt(t)) is added:

where

K ( t ) is capital stocks in year t.

d (t-1) is depreciation rate, I ( t ) is investment.

In Version C apart from (27) t h e equation for t r a d e balance calculation has t o be substituted by:

6.3. Implementation ^of 1

1. In order to implement MARSl r u n s within t h e BLS a t first corresponding adjustments of country models have to be made. These a r e related to those mentioned in section 5 and in section 6.2 (equations (27) and (28)).

2. Subroutines for exogenous calculating values of a ( t ) in accordance to ( l o ) , (11) and (12) have to be programmed.

3. Main steps For MARSl implementation are:

1. Equilibrium for one year is calculated, and all indicators a r e generated.

2. Values of a ( t ) a r e calculated

3. Values of K,(t) for country groupings a r e calculated 4. Values of M j ( t ) a r e calculated

5. Released Fund AMj(t) is allocated in accordance t o one of t h e versions (A,

B,

o r C) of t h i s Fund utilization in MARSl

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6. Step 1 for next year is repeated

7.1. Background

General idea of the

MARS

2 is to use some share of each country's (LDC and DC) released fund for domestic purposes a s i t was described in section 6 for

MARS

1 and t h e r e s t of these resources a r e used for creating AID (Aid Interna- tional Donation) which has t o be distributed among "poor" LDC's.

Definition: "Poor" LDC's a r e those with annual GDP per capita less t h a n US $ 1000.

Let us denote

barjMo(t)

= # . AM^(^)

(29)

s h a r e of e a c h country's released fund used for domestic purposes, where

#,

0

< # <

1 is exogenously given coefficient. The total aid fund (AID) c r e a t e d by all countries for allocation among "poor" LDC's is defined a s follows:

where m is t h e number of all countries.

Let u s define

6Mj(t)

=

y,(t)

-

^AID(t) ^.j

⁼

^{1. 2.}

^....

^m_PI^mp

^<

^rn

s h a r e of j-th "poor" LDC in total AID(t) with

$0 5 y j ( t ) < l

j-1

(32) We postpone explanation how yj(t) is determined till subsection 7.2. Now l e t u s discuss how t h e balance of national income of each country will be met.

For all countries with GDP per capita higher t h a n U.S. $ 1000 share of t h e i r released fund available for domestic purposes is calculated as in (29). And now

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in order t o meet balance of national income for t h r e e versions of utilization of

~ % ~ ( t ) t h e value of AMj(t) in corresponding balance equations (22). (24) and (26) h a s to be substituted by dA4Fm(t). It is also t r u e for equations (27) and (28).

After s u c h a substitution we have For all j E 11, 2

,....

mj \ [ 1,2

,....

_mpj

for version A:

GDP

=

(gov

-

^AMm)

+

^priv

+

^(cap

+

^{AM^)}

+

bal ;

for version B:

GDP

=

(gov

-

^AMm)

⁺

^priv

⁺

^{c a p}

⁺

^(bal

⁺

^{AM^)}^;

and for version C

GDP

=

(gov

-

^AMAD)

+

priv

+

(cap

+ fl - ^AMAm) +

^(bal

+

⁽¹

- **@)AM*),**

₍₃₅₎

as well a s

K, = K,-, .

(1

-4-,) +

I,

+

d q r n and

What is concerning to all "poor" countries (j

=

^1.2 ,

....

m a , m p

<

m corresponding baiance equations f o r t h r e e versions of allocating their own reieased 13x22 ~ ! ? t ' ~ ( t ) and t h e i r s h a r e of dY,(t) in AID(t) will be written a s follows (indexes a r e omitted):

for version k

GDP

+ ^dM =

(gov

-

A M ~ I ~ )

+

^priv

+

^(cap

+

AMm

+

^bM)

+

bal ^; (38) for version B:

GDP

+

6M

=

(gov

AM^) +

priv

+

^{c a p}

+

(bal

+

AMAm

+

616) ; (39) for version C:

GDP

+

6M

=

(gov

-AMAU>) +

^priv

+

(40)

[cap

+

fl(mAU>

+

6M)]

+

[bal

+

(1

-

@ ) ( A M ~ ' ~

+

bM)]

(20)

For these c o u n t r i e s equations (38) and (37) have t o be r e w r i t t e n as follows:

K(t)

=

K(t-1) ( 1

-

^d(t-1)) ^t^I(t)^t^(AMrn(t)^t^dM(t)⁾

a n d

ball(t)

=

bal(t)

+ AM^(^) +

6M(t) )

7.2. Distribution of the

AID

among "pooi' L S C s

In t h i s section t h e problem of calculating t h e s h a r e dMj(t) of "poor" coun- t r i e s i n AID(t) is discussed (see equation (31)). Two definitions of yj(t) j

=

1. 2 . . . 5 a r e suggested: first when yj(t) is d e t e r m i n e d without taking i n t o a c c o u n t t h e bounds on t h e capital absorption c a p a c i t y of "poor" LDC's in t h e BLS a n d second when yj(t) i s determined with t a k n g i n t o account such bounds.

7.2.1. Case of unlimited capital absorption capacity of LDC

In t h i s c a s e y r ( t ) i s s u g g e s t e d t o be determined a s t h e weighted mean for all "poor" c o u n t r i e s value inversely proportional t o GDP p e r c a p i t a of j-th country:

where

In o t h e r words AJD(t) will be distributed among "poor" LDC's according t o weighted mean value proportional to population of j-th c o u n t r y a n d inversely proportional to i t s GDP:

(21)

7.2.2. Case of limited capital absorption capacity ^ofLDC

Using (41) for calculation of value bMJ(t) we c a n g e t such value of bMj(t) for poorest c o u n t r i e s (with GDP

<< U.S.

$ 1000 ) which can essentially exceed their capital absorptive capacity. In order t o take i n t o a c c o u n t upper bounds for such capacities of LDC's t h e other formula for calculating value of yj(t)=y:(t) is suggested:

L j GDPf ( t ) where

capj(t) is t h e value of gross Bxed capital formation of j-th c o u n t r y and GDP;(t) is i t s GDP p e r capita. Equation (43) can be written as follows:

In o t h e r words in this case AID(t) will be distributed among "poor" countries according t o weighted mean value proportional t o product of j-th country's population and value of gross fixed capital formation a n d inversely proportional to i t s GDP.

Note:

I t should be noted t h a t upper bounds for capital absorption capacity of LDCBs would be changed during the simulation period. Dr. J. Hrabovszky suggested in t h e FAP internal memo t o fix values of t h e s e bounds for 1980 and 2000.

We c a n use t h i s information also and calculate:

cap,(t)

=

capj(0) . ( I

+

pj(t))

.

where

(22)

w h e r e

Pj(0)

a n d Dj(T) a r e c o r r e s p o n d i n g l y u p p e r b o u n d s f o r 1980 a n d 2 0 0 0 a n d T

=

20.

7.3. Illustrative calculation of values y f a n d yf (t) for 1980

F o r a l l c o u n t r i e s in t h e BLS with value of a n n u a l GDPJC(t)

<

^U.S. ^$1 0 0 0 f o r 1 9 8 0 c a l c u l a t i o n s of 7 f ( t ) a n d y f ( t ) as w e l l as 6 K f ( t ) a n d 6 ~ f ( t ) were made f o r i l l u s t r a t i v e p u r p o s e s . The list of t h e s e c o u n t r i e s includes: Egypt, Indonesia.

N i g e r i a , P a k i s t a n , Kenya, Thailand, China, India a n d 1 0 c o u n t r y groupings. Values of GDP, p o p , c a p , GDPC f o r 1980 f o r a l l 18 c o u n t r i e s w e r e t a k e n from Y e a r b o o k s of National Accounts S t a t i s t i c s . U p p e r bounds o n t h e c a p i t a l a b s o r p t i o n c a p a c i t y of t h e s e c o r n t r i e s were a c c e p t e d f o r 1980 as t h e s e were determined by D r . J. H r a - bovszky. Values of 7 j ( t ) a n d y f ( t ) were c a l c u l a t e d using equations (41) a n d (43) c o r r e s p o n d i n g l y , valiies of i ! f m ( t ) a n d 6 K f ( t ) a n d

mf(t)

^were c a l c u l a t e d in a c c o r d a n c e with (29) a n d (31). Results of i l l u s t r a t i v e calculations a r e summarized in Table 5. F o r t h e s e calculations t h e value of #

=

0.9 a n d a(:)

=

^a,

=

0.02. The value of AID (1980) was M e n as 0 . 1

.

~ ~ ~ ~ ~ ' ~ ~ ( 1 9 8 0 )

=

25660

-

10' U . S . $ 1975.

Columns 1 4 a n d 1 9 r e p r e s e n t r e s u l t s of by what e x t e n t u p p e r bounds f o r c a p i t a l a b s o r p t i o n c a p a c i t y of a c o u n t r y would b e e x c e e d e d (values with sign (+)) o r n o t ( v a l u e s with sign (-)). When comparing v a l u e s in t h e s e columns w e c a n s a y t h a t t h e s e c o n d a p p r o a c h f o r calculation of 7f(t) i s t h e most a p p r o p r i a t e o n e , b e c a u s e e x c e e d i n g u p p e r bounds i s o b s e r v e d in 6 c a s e s with v e r y low value of it.

7.4. Implementation or 2

1. A s in t h e c a s e of MARS 1, i m p l e m e n t a t i o n r u n s of MARS 2 w i t h i n t h e BLS r e q u i r e a d j u s t m e n t s of c o u n t r y m o d e l s , m e n t i o n e d i n s e c t i o n 5 a n d 7 . 1 ( e q u a t i o n s (36). (37) a n d (29) f o r DC's).

(23)

2. Subroutines for exogenous calculating values of a ( t ) in accordance with ( l o ) , (11) a n d (12) have t o be programmed.

3. Subroutines for endogenous annual calculating values of y?(t) and l:(t) dMP(t) a n d 6 ~ ; ( t ) for "poor" countries should be prepared in accordance t o (41). (43), (30) and (31).

4. Steps for MARS 2 implementation are:

Equilibrium for 1 year is calculated and all indicators a r e generated Values of a ( t ) a r e generated and value of [ is fixed

Values of K,(t) for country groupings a r e calculated Values of AMjm(t) a r e calculated

AID(t) is created

Values of yF(t) (or y)(t)) a r e calculated Values of dMP(t) (or 61dL(t)) a r e calculated

Released funds AMjm(t) (for DC's ) and [dldjm(t)

+

6M,(t)) ] (for "poor"

LDC's) a r e allocated in accordance with one of the versions (A, B. o r C) Step 1 i s repeated a n d all indicators a r e generated. GDPf(t) for "poor"

LDC a r e compared with U.S. $ 1000 a n d y:(t) ( o r y;(t)) a r e adjusted.

Step 2

(24)

8. C a n c h i o n

First e f o r t s t o develop m c r e o r less reasonable versions of t h e

MARS

for t h e FAP's s t u d y "Hunger, growth a n d equity" were described in t h i s paper. D ~ r i c g t h i s stage a n u m b e r of assumptions simplifying a n d even over-simplifying t h e real problem were accepted. However, from o u r point of view t h e v a r i a n t s of t h e MARS elaborated in t h e paper a r e q u i t e appropriate ones for t h e simulation purposes for t h e BLS. There is n o doubt t h a t t h e analysis of simulation resuls will give oppprtunity for f ~ r t h e r improvement of both variants.

REFERENCES

Iakimets V. (198%) Mutual Arms Reduction Scenarios (MARS) for t h e FAP's study "Hunger, Growth a n d Equity". IIASA, L a x e ~ b c r g , ( f c r t h c o m i ~ g ) . Iakimets V. (19E5b) MARS: Describing dynamics of military expenditures reduc-

tion. IIASA, Laxerbcrg, ( f o r t h c o m i ~ g ) .

SIPRI (1984) World Armamerts a n d D i s a r m a m e ~ t s . SIPRI yearbook 1984. Taylor a n d Francis Ltd. London a n d Philadelphia.

FA0 (1981) Agriculture: Towards 2C00. FAO, R o n e

F A . (1985) Free Trade in Agriculture. IIASA, L a x e ~ b u r g , (forthcomir-g).

(25)

Table 5. Two caaes of distributing AID

No. Country Country code

GDP POP GDPC

CAP CAP

CAP

(m' ^(-1

108US $ mill. US $

loe

US $ actual upper

AMm

bounds

3 ₄ 5 6 7 8 9

Indonesia Nigeria Pakistan Kenya Thailand Oil exporters med. income/

food exports med. income/

food imports low income/

food exports low income/

food im@orts med. income High-med.income/

food exports High-medincome/

food imports Low income hied.-low income China India

(26)

Table 5. Two cases of distributing AID

Case of unlimited absorption capacity Case of limited capital absorption capacities

yU 6MU A M ~ ~ + ~ M ~ *Mm+6MU (13+7)-8 TI 6M1 A M * ~ + ~ M ~

3

17 (7+ 18)-8 GDP

10 1 1 12 13 14 15 16 17 18 19

MARS 1 and MARS 2 for the FAP's Study: "Hunger, Growth and Equity"

W O R K I N G P A P E R

A W EQUITY'

-

STUDY

-

FAP's

BLS.

-

-

CONTENTS

MARS

MARS

MARS

-

MARS 1 and MARS 2 FOR THE FAP'S SRJDY

"HUNGER, GROWTH AND EQUITY"

-

AM,(^) =

-

.

=

-

*

-

.

=

.

=

=

=

=

=

...

=

=

B.

C.

7

I /

/ / I

=

-

-

=

+

.

-

=

. .

A B

MARS

=

GDP =

+

+

+

=

-

=

-

-

-

=

.

=

-

.

+

-

+

-

-

=

-

+

+

+

+

-AM] +

/ ^/ ^I

^-

⁼

^....

^<

⁺

⁺

⁺

⁺

+ fl - ^AMAm) +

- **@)AM*),**

+ ^dM =