The Exchange Component of IIASA's Food and Agriculture Model for the European Economic Community

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

THE EXCHANGE COMPONENT OF IIASA'S FDOD

AND

AGRICULTURE

MODEL FOR

THE EUROPEAN ECONOMIC COMMUNITY

Erik Geyskens

June 1 9 8 5

\JP-85-38

Working Papers are interim reports on work of t h e International Institute for Applied Systems Analysis a n d have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute or of its National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 Laxenburg, Austria

Understanding t h e n a t u r e and dimensions of the world food problem a n d t h e policies available to alleviate i t has been the focal point of IIASA's Food a n d Agriculture Program (FAP) since i t began in 1977.

National food systems a r e highly interdependent, and yet t h e major policy options exist a t t h e national level. Therefore, to explore these options, i t is necessary both t o develop policy models for national economies and t o link them together by trade a n d capital transfers. Over t h e y e a r s FAP has, with t h e help of a network of collaborating institu- tions, developed a n d linked national policy models of twenty countries, which t o g e t h e r account for nearly 80 p e r c e n t of important agricultural a t t r i b u t e s such as a r e a , production, population, exports, imports and so on. The remaining countries a r e represented by 14 somewhat simpler models of groups of countries.

The European Community (EC) is a major actor on t h e world market.

An aggregate food a n d agriculture model of the EC, in which t h e EC is t r e a t e d as one nation has been developed by t h e FAP, as p a r t of the IIASA/FAP basic linked sys tem.

In addition, development of a detailed model of the EC, in which t h e member nations of t h e EC a r e represented by separate models which i n t e r a c t among themselves within t h e framework of the common agricul- t u r a l policy (CAP) of t h e EC, was initiated in 1978. This was begun in col- laboration with t h e University of Gottingen, which received a g r a n t from t h e Volkswagen Foundation. The work on model development was t r a n s f e r r e d t o IIASA in 1982, where i t continued until t h e e n d of 1984, u n d e r a g r a n t from t h e Centre for World Food Studies (CWFS) of t h e Neth- erlands.

In t h i s paper, which is one of a series of papers reporting t h e work on t h e development of t h e detailed EC model, Erik Geyskens describes t h e exchange component of t h e model.

Kirit S. Parikh Program Leader Food a n d Agriculture Program.

CONTENTS

1. Introduction

2. Overview of t h e Model

3.

A

Simplified Version of t h e Open Exchange Model 3.1. Supply

-

Gross Domestic Product-Taxes-Trade 3.2. Demand

3.3. Balance of Trade Equation 3.4. Price Formation

4. The Comparative Statics of t h e Simplified Version 5. Countries, Commodities

5.1. Countries 5.2. Commodities 6. The EC-Exchange 6.1. Introduction 6.2. Demand

6.3. Supply

-

Gross Domestic Product-Taxes-Trade 7. EC Policy Setting

8. The EC-Canonical Form References

The Exchange Component of IIASA's Food and Agriculture Model for the European Economic

Community

B i k Geyskens

1. Introduction

The Food a n d Agriculture Model for t h e European Economic Community (EC) describes dynamically supply, demand, income a n d price formation in t h e EC member c o u n t r i e s with special r e f e r e n c e t o t h e a g r i c u l t u r a l s e c t o r a n d t h e food situation. It is a member of a family of linkable models c o n s t r u c t e d t o b e a r e p r e s e n t a t i o n of t h e world food system, a n d h e n c e i t satisfies linkage r e q u i r e - m e n t s with r e s p e c t t o commodity classification, time i n c r e m e n t (one y e a r ) a n d methodology. Within t h e s e linkage r e q u i r e m e n t s t h e r e is e n o u g h scope t o r e p r e s e n t specific issues s u c h a s t h e Common Agricultural Policy (CAP). The work is coordinated by t h e Food a n d Agriculture Program 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 for Applied Systems Analysis (IIASA).

This p a p e r describes t h e e x c h a n g e component of t h e EC-model. The o t h e r c o m p o n e n t s of t h e EC-model, s u c h a s t h e demand component, t h e supply com- p o n e n t a n d t h e policy component, a r e described elsewhere.

The p a p e r i s s t r u c t u r e d a s follows. Section 2 c o n t a i n s an overview of t h e EC-model.* In section 3 a simplified version of t h e open e x c h a n g e model u s e d i n t h e modeling approach of IIASA's Food a n d Agriculture Program is formulated.**

The comparative s t a t i c s of t h e simplified version a r e discussed i n section 4. In section 5 t h e main classifications, i.e. t h e c o u n t r i e s and commodities, of t h e EC-model a r e defined. Section 6 describes t h e exchange component of t h e EC model, a n d i n section 7 t h e EC policy s e t t i n g is discussed.*** The model solution i s p r e s e n t e d in section 8.

2. Overview of the Model

The EC model c a n be logically subdivided i n t o a n e x c h a n g e component a n d a supply component. s e e Figure 1. In t h e supply component, given o n e y e a r ' s p r i c e realizations on t h e national m a r k e t , next year's supply is planned a n d fac- t o r services a s well a s i n t e r m e d i a t e i n p u t s are bought in a c c o r d a n c e with t h e plans. At t h e beginning of t h e n e x t period when t h e production h a s b e e n gen- e r a t e d , e a c h EC c o u n t r y possesses (possibly negative) ownership e n t i t l e m e n t s for commodities.

Then t h e execution of t h e s e c o n d model component, t h e ezchange com- p o n e n t is s t a r t e d . Here for e a c h c o u n t r y income formation a n d demand a r e

*

For a mare detailed overview of the EC-model, see U. Ftirber et a1 (1984).

**

_For an overview of the IIASA/FAP approach see Parikh and Rabar (1 981). The open ex- change m d e l is described in Keyzer ( l 9 8 l a , 1983), and Keyzer and Rebelo (1982).

***

Sections 6 and 7 are based on the paper of M. Keyzer (1981 b)

d e s c r i b e d taking i n t o consideration g o v e r n m e n t i n t e r v e n t i o n a t t h e national a s well a s a t t h e EC level. In t h e e x c h a n g e c o m p o n e n t commodity b a l a n c e s a n d overall financial balance i n t e r c o n n e c t t h e m a r k e t s of t h e individual commodi- t i e s a n d t h e individual countries according t o a g e n e r a l equilibrium a p p r o a c h . 3. A Simplified Version of the Open Exchange Model

3.1. Supply

-

Gross Domestic Product

-

Taxes

-

Trade

Supply is a s s u m e d t o be d e t e r m i n e d prior t o e x c h a n g e taking place. Supply is defined a s n e t o u t p u t , i.e., gross supply m i n u s i n t e r m e d i a t e demand. Denot- ing t h e supply v e c t o r by y a n d t h e corresponding p r i c e v e c t o r by p, g r o s s domestic p r o d u c t (GDP) Y is given by:

Y

=

p'y (1)

( v a l u e a d d e d d e f i n i t i o n of GDP). We n o t e t h a t in t h i s a n d t h e n e x t s e c t i o n all prices p a r e e x p r e s s e d in t h e same i n t e r n a t i o n a l c u r r e n c y .

The n e t import v e c t o r z is defined a s t h e difference between d e m a n d x a n d supply

Y:

( c o m m o d i t y b a l a n c e e q u a t i o n ) . Defining t h e n e t i m p o r t value a t domestic p r i c e s t o be Z:

z =

p'z, (3)

a n d t o t a l consumption e x p e n d i t u r e s t o be C:

C

=

p'x,

we g e t t h e a g g ~ e g a t e d e m a n d d e f i n i t i o n of GDP:

The i n c o m e d e f i n i t i o n of GDP s t a t e s t h a t GDP e q u a l s disposable income m plus t a x e s f:

In t h e simplified version of t h e model i t is a s s u m e d t h a t consumption C equals disposable income m:

I I t International Exchange

EC Exchange Supply

A + ^Given

-

Supplied quantities

-

Demand behavior

-

EC policies

EC )

-

World prices

Policy

-

EC trade deficit

Solve for

-

Common prices ) SUPP~V _B

+

_-

^-

^{EC demand} EC tax rate

fim

^{behavior behavior}

r - - 1

I Exogenous or linkage to FAP Model System

1 7

^Module

0

Outcome of Module

L - -,

Equations (5), (6) a n d (7) imply t h e

tnz

equation:

Thus t a x e s f is p a r t of GDP u s e d t o finance e x p o r t s -z evaluated a t domestic prices p. Assuming t a x e s proportional t o GDP, denoting t h e t a x r a t e by t a n d defining p

=

( 1 - t), one has:

m

=

pY

=

pp'y. ( 9 )

Suppose, for t h e moment, total consumption C would n o t be equal t o dispos- able income m, b u t be determined by t h e following consumption function:

One t h e n would g e t t h e following t a x equation:

showing t h a t savings perform t h e s a m e role in t h e model a s do taxes. Thus t h e model r e s u l t s will n o t change for different values of a. This is d u e t o t h e f a c t t h a t t h e simplified version of t h e open e x c h a n g e model does n o t distinguish between different income classes.

The income definition of GDP (equation 6) does not s a y how disposable income i s a r r i v e d a t . However, by writing t h i s equation in t h e form:

i t says t h a t disposable income e q u a l s r e v e n u e s from production activities minus taxes. I n s t e a d of value added o r a c t u a l endowments y o n e could work with pseudo-endowments

7

which a r e equal t o a c t u a l endowments plus t r a n s f e r s . Disposable income m is t h e n given by:

a n d t h e t a x equation becomes:

Thus t a x e s now serve t o finance t r a n s f e r s plus exports. Of c o u r s e t h e model solution does n o t c h a n g e by t h e i n t r o d u c t i o n of pseudo-endowments. However, i t s u s e allows o n e t o satisfy t h e m a t h e m a t i c a l conditions for convergence of t h e algorithm.

3.2. Demand

Demand is modeled according t o t h e Linear Expenditure System (LES):

p ' f

=

p'c

+

b(m - p'c), ~ ' b

=

1 , (15)

where:

c

=

committed demand vector b

=

marginal budget s h a r e s

L

=

summation v e c t o r

x

=

diagonal matrix with t h e e l e m e n t s of t h e vector x on i t s diagonal.

Committed demand c is t h e sum of p r i v a t e committed demand, i n v e s t m e n t a n d government demand. Both i n v e s t m e n t a n d government demand a r e exo- genously determined.

Making use of equation (9): m=pp'y a n d defining m a t r i c e s A=yb',

M =

6 - cb', t h e expenditure system above c a n be written as

This system is called t h e canonical form of t h e model. In t h e canonical form t h e m a t r i c e s A a n d

M

a r e predetermined, but only t h e m a t r i x A is affected by t h e t a x variable p.

In t h e algorithm t h e canonical form is solved for p r i c e s p, demand x a n d t a x variable p, taking i n t o a c c o u n t t h e balance of t r a d e equation a n d t h e p r i c e for- mation equation. I t s h o u l d be noted t h a t , s i n c e in t h e algorithm t h e canonical form (16) i s solved, t h e model allows for more g e n e r a l demand systems t h e n t h e LES. One of t h e conditions for t h e convergence of t h e algorithm t o a unique equilibrium solution is:

4, ⁺

^Mij

^>

^{0 ,} for e a c h i a n d e a c h j, s e e Keyzer a n d Rebelo (1982). In t h e c a s e of t h e LES, t h i s implies t h e inequality yi

>

ci, assum- ing bi

>

0 . If t h e inequality does n o t hold, t h e solution is t o work with pseudo- endowments.

3.3. Balance of Trade Equation

A balance of t r a d e equation is imposed a s a n overall budget equation. I t s t a t e s t h a t n e t imports z, evaluated a t given world m a r k e t prices p,, should be e q u a l t o a prespecified t r a d e deficit k

This equation, t o g e t h e r with t h e t a x equation (8): -p8z

=

f, implies t h e fol- lowing government budget equation:

Trade subsidies a r e t h u s financed by t r a d e deficit plus taxes. If disposable income m is defined in t e r m s of pseudo-endowments i n s t e a d of endowments, t h e n t h e r e l e v a n t tax e q u a t i o n is equation (14) a n d t h e government budget equation becomes:

Thus, t r a d e subsidies a n d t r a n s f e r s a r e financed by t r a d e deficit a n d taxes.

3.4. Price Formation

For e a c h commodity t h e government is t h o u g h t t o p u r s u e a price policy t h r o u g h a tariff. This p r i c e policy is implemented a s follows. Targets a n d bounds for t h e p r i c e a s well a s t h e n e t t r a d e a r e specified, a s i l l u s t r a t e d in Fig- u r e 2. The g o v e r n m e n t would like t h e i-th p r i c e t o h a v e t h e value pi a n d t h e i-th n e t t r a d e t o be

ii.

If p r i c e a n d n e t t r a d e c a n n o t be kept a t t a r g e t simultane- ously, i t wants t h e outcome t o lie on t h e heavy line in Figure 2. This figure illus- t r a t e s t h e policy w h e r e n e t t r a d e should be a t t a r g e t a s long a s t h e price is within bounds ( n e t t r a d e h a s a priority over price), while Figure 3 i l l u s t r a t e s t h e policy where p r i c e s h o u l d be a t t a r g e t a s long a s n e t t r a d e is within bounds (price h a s a priority over n e t trade). The a d j u s t m e n t s c h e m e s may be e x t e n d e d t o a c h a i n of priorities t o include more t h a n two t a r g e t elements (for example, price, n e t t r a d e a n d stocks), o r t o r e p r e s e n t n e s t e d priorities between two vari- ables.

Price

T

2i z . I

-

'i Net trade

Figure 2. Net Trade Has P r i o r i t y Over P r i c e

Ria

-

Pi

bi

Pi

Net trade

3. P r i c e Has P r i o r i t y Over Net Trade

4. The comparative statics of the s-med version

In t h i s s e c t i o n we momentarily d r o p t h e a s s u m p t i o n t h a t supply o r n e t out- p u t is predetermined. The c o m p a r a t i v e s t a t i c ana!ysis can t h e n more con- veniently be c a r r i e d o u t by m e a n s of n e t t r a d e equations i n s t e a d of e x p e n d i t u r e equations.

The c o u n t r y ' s economy i s a s s u m e d t o have a production possibility s e t T which consists of all n e t o u t p u t v e c t o r s y which a r e technically feasible given t h e q u a n t i t i e s of t h e fixed production factors. If t h e n e t o u t p u t s a r e p r e d e t e r - m i n e d a t levels

L.

a s i n t h e simplified version, t h e n T

=

ly ( 0 S y yj.

The t r a d e utility f u n c t i o n g is derived from t h e utility function u a n d t h e production possibility s e t T:

g(z)

=

max tu(x)

I

XET+ZJ

.

x

For e a c h n e t t r a d e v e c t o r z, t h e t r a d e utility function g(z) i n d i c a t e s t h e max- imum level of utility a t t a i n a b l e for t h e c o u n t r y .

The c o u n t r y ' s budget i s d e n o t e d by f , s i n c e in t h e simplified version t h e budget equals taxes. In g e n e r a l , however, t h e budget may consist, for example, of tariff r e v e n u e s o r foreign aid. By analogy with t h e t h e o r y of t h e c o n s u m e r , a n i n d i r e c t t r a d e utility f u n c t i o n h is defined a s

h(p,f)

=

maxtg(z)

1

^p'z

^s

^-fj.

z

For e a c h p r i c e v e c t o r p a n d budget f, t h e i n d i r e c t t r a d e utility f u n c t i o n h indi- c a t e s t h e maximum level of u t i l i t y a t t a i n a b l e for t h e c o u n t r y . The i n d i r e c t t r a d e utility function h is positively homogeneous of degree one in p r i c e s p a n d budget f.

The c o n c e p t of a n i n d i r e c t t r a d e utility f u n c t i o n was i n t r o d u c e d by Wood- l a n d (1980). He showed t h a t , u n d e r c e r t a i n conditions on t h e utility function u a n d t h e production possibility s e t T, t h e derived n e t t r a d e e q u a t i o n s z(p, f) c a n be obtained by applying Roy's Identity t o t h e i n d i r e c t t r a d e utility function h:

According t o t h e simplified version, t h e c o u n t r y will, for given domestic prices p, maximize t h e value of t h e indirect t r a d e u t i l i t y f u n c t i o n h with r e s p e c t t o taxes f s u b j e c t t o t h e balance of t r a d e equation. The equilibrium conditions t h u s consist of t h e derived n e t t r a d e equations a n d of t h e balance of t r a d e equation:

Of c o u r s e , s i n c e t h e price formation equation i s n o t differentiable every- where, t h e comparative s t a t i c r e s u l t s will oniy apply t o equilibrium p r i c e s where t h e price formation equation is differentiable, a n d t h u s , t o (infinitesimal) small c h a n g e s in t h e i n d e p e n d e n t variables which do n o t c a u s e regime switches.

The system of derived n e t t r a d e e q u a t i o n s (23) will be examined first without t a h n g i n t o a c c o u n t t h e balance of t r a d e e q u a t i o n . I t is well known t h a t t h e total differential of s u c h a system c a n be m i t t e n a s

dz

= zf

[df - z'dp]

+

Kdp, (25)

where zf is t h e v e c t o r of derivatives of n e t t r a d e

z

with r e s p e c t t o t a x e s f , a n d where

K

i s t h e s u b s t i t u t i o n matrix. Under c e r t a i n r e g u l a r i t y conditions on t h e t r a d e utility function g, t h e substitution m a t r i x K h a s t h e following properties:

K = K ' (symmetry)

p'K

=

0 (adding-up) (26)

Kp

=

0 (homogeneity)

x'Kx <

0, for all x # a p , a a r e a l s c a l a r (negativity)

*

Also, p l z f

=

1 (see B a r t e n , 1977). The negativity condition implies t h a t t h e diag- onal e l e m e n t s of K a r e negative. I t should be n o t e d t h a t t h e m a t r i x K is t h e difference between t h e proper s u b s t i t u t i o n m a t r i x o b t a i n e d from t h e derived

*

^{Barten (1977)} showed t h a t t h e negativity condition i s implied by t h e assumption that t h e (trade) utility function g is strong quasi-concave, i.e .,

x'

-

x

<

0 for all non-zero x s u c h t h a t

-

^{M z ) '} x

=

0.

azazt az

The negativity condition could be relaxed t o the weaker condtion:

x' Kx <

0 for all x # a p , a a r e a l s c a l a r

However, as is clear from t h e discussion in Elarten (1977), t h e (trade) utility function g then cennot be twice different~able. Since we want to interpret t h e infinitesimal changes a s small finite changes, t h e negativity condition as stated s e e m t o be appropriate.

demand equations a n d t h e matrix r e l a t i n g c h a n g e s in n e t o u t p u t s t o c h a n g e s in prices obtained from t h e derived n e t o u t p u t equations. If n e t o u t p u t s a r e p r e d e t e r m i n e d , t h e l a t t e r m a t r i x r e d u c e s t o t h e z e r o matrix.

In t h e simplified model t a x e s a r e n o t p r e d e t e r m i n e d b u t endogenous.

Therefore, t h e c h a n g e s in t a x e s must be c o n s i s t e n t with t h e b a l a n c e of t r a d e equation. Taking t h e t o t a l differential of both sides of t h e balance of t r a d e equation (24) gives

pW1dz

=

dk - z'dp, (28)

Premultiplying of both sides of equation (25) by p,' a n d s u b s t i t u t i o n of t h e r e s u l t i n g expression for p,'dz in (28) gives

df

=

z'dp

+ -

1 ^[dk

-

z'dp, - pw'Kdp].

Pwf=f

In t h i s equation c h a n g e s in t a x e s a r e r e l a t e d t o c h a n g e s in t h e exogenous vari- ables s u c h t h a t t h e balance of t r a d e equation r e m a i n s satisfied. From (29) i t follows t h a t - af

=

1/ pW1zf

.

a k

Substitution of df in (25) by t h e expression for df in (29) leads t o t h e follow- ing system:

dz

=

zk [dk

-

z'dp, - p,' Kdp]

+

^Kdp, (30)

where zk d e n o t e s t h e v e c t o r of p a r t i a l derivatives of n e t t r a d e z with r e s p e c t t o t h e balance of t r a d e k : zk

=

z f / p W 1 z f . In this system c h a n g e s in n e t t r a d e a r e r e l a t e d t o c h a n g e s i n t h e exogenous variables s u c h t h a t t h e b a l a n c e of t r a d e equation r e m a i n s satisfied. For

t h e system above c a n be written a s

dz

=

zk[dk

-

z'dp,]

+

K*dp

.

₍₃₂₎

The matrix K* will be called t h e domestic-price-effect matrix.

From (32) one s e e s t h a t c h a n g e s in domestic prices affect n e t t r a d e only via t h e domestic-price-effect m a t r i x K*. The domestic-price-effect K*dp c a n be split u p i n t o t h e two components: Kdp a n d -zk p,'Kdp. The first c o m p o n e n t , t h e s u b s t i t u t i o n component, r e p r e s e n t s t h e effect of domestic p r i c e c h a n g e s on n e t t r a d e in t h e a b s e n c e of a b a l a n c e of t r a d e r e s t r i c t i o n a n d with t a x e s hold con- s t a n t . The effect on t h e t r a d e deficit situation of t h e c o u n t r y i s pW1Kdp. This a m o u n t c a n , of c o u r s e , be positive, negative or zero. For t h e s a k e of i n t e r p r e t a - tion only, a s s u m e p,'Kdp is negative. The c o u n t r y t h e n h a s a s u r p l u s equal t o -pW1Kdp. This s u r p l u s is s p e n t a s if i t was a n additional i n c r e a s e in t h e t r a d e deficit. The effect on n e t t r a d e is t h e n given by -zk pw'Kdp. Note t h a t t h e

decomposition of t h e r e s t r i c t e d substitution matrix K* i s i n v a r i a n t u n d e r order-preserving t r a n s f o r m a t i o n s of t h e utility function v , s i n c e t h e s u b s t i t u - tion m a t r i x K itself i s i n v a r i a n t u n d e r s u c h transformations. The s e c o n d effect c a n t h e r e f o r e be identified a s t h e balance of t r a d e effect of domestic price c h a n g e s . The t o t a l b a l a n c e of t r a d e effect is given by zk [dk - z'dp, - p,' Kdp]

a s c a n be s e e n from equation (30). I t is made up of t h r e e components: t h e com- p o n e n t zkdk is t h e p r o p e r balance of t r a d e effect, t h e component -zk z'dp, r e p r e s e n t s t h e balance of t r a d e effect of c h a n g e s in world m a r k e t prices, a n d t h e t h i r d component -zk p,' Kdp is t h e balance of t r a d e effect of domestic price c h a n g e s .

The domestic-price-effect matrix K* h a s t h e following properties:

p,'K*

=

0 (adding-up)

K*p

=

0 (homogeneity)

Also, pW1zk

=

1. The adding-up property, which reflects t h e balance of t r a d e r e s - t r i c t i o n , follows from t h e definition of K* itself (equation 31). The homogeneity p r o p e r t y , which shows t h a t t h e decisions of t h e c o n s u m e r a n d p r o d u c e r a r e b a s e d on domestic p r i c e s , follows from t h e homogeneity property of t h e substi- t u t i o n matrix K. The homogeneity property says t h a t a proportional change in all domestic p i i c e s will leave n e t t r a d e unchanged. Of c o u r s e , t a x e s will i n c r e a s e by t h e same proportion, a s c a n be seen from equation (29). Because of t h e homogeneity property, domestic prices c a n be normalized by r e s t r i c t i n g t h e p r i c e of a base commodity, t h e l a s t commodity for example, to be equal t o t h e world m a r k e t price. This approach also implies t h a t tariffs a r e normalized by s e t t i n g t h e tariff of t h e l a s t commodity equal t o zero.

We t u r n now t o t h e discussion of t h e welfare effects of c h a n g e s in t h e exo- g e n o u s variables. The t o t a l differential of t h e indirect t r a d e utility function h is given by:

Making use of equation (22) a n d equation (29), o n e g e t s d h

= -

h [dk - z'dp,

-

p,'Kdp],

p i Zf

with h t h e marginal utility of t h e budget: h

=

a h ( ~ . f )

_a

_f

,

^o.

The marginal utility of t h e t r a d e deficit i s given by

I t is e q u a l t o t h e marginal utility of t h e budget multiplied by 1/ pW1zf, which is t h e derivative of t h e budget with r e s p e c t t o t h e t r a d e deficit.

The effect o n utility of a n i n c r e a s e in t h e world m a r k e t p r i c e of a single commodity i is equal to:

The effect is positive if t h e c o u n t r y is a n e x p o r t e r of t h e commo&ty, negative if i t is a n importer of t h e commodity. If all world m a r k e t p r i c e s c h a n g e , t h e change in utility is e q u a l t o

--

A z'dp,, a n d t h u s of t h e s a m e sign a s t h e mag-

Pw'zf

nitude -z'dp,. This magnitude c a n be i n t e r p r e t e d a s c h a n g e s in t h e t e r m s of t r a d e ( s e e Woodland, 1980, pp. 912-913). Thus small c h a n g e s in world m a r k e t prices p, will c a u s e a n i n c r e a s e in utility if, a n d only if, t h e t e r m s of t r a d e improve.

The effect of domestic price changes on t h e level of utility is given by

In general, nothing c a n be said a priori on t h e sign of t h i s effect. However, if t h e c h a n g e in domestic p r i c e s is positively (negatively) proportional t o t h e world m a r k e t prices t r a n s l a t e d by any s c a l a r multiple of t h e domestic prices, t h e n t h e level of utility does increase ( d e c r e a s e ) . To s e e t h i s , let:

d p

=

(pw

-

^Bp)da

,B

a r e a l s c a l a r , a

>

⁰

.

⁽³⁸⁾

Because of t h e homogeneity property a n d t h e negativity p r o p e r t y of t h e substi- tution m a t r i x K, one t h e n h a s

I t should be s t r e s s e d t h a t in g e n e r a l nothing c a n be said about t h e effect on t h e level of utility of a c h a n g e in one domestic price. Since p'K

=

0, equation (37) c a n be written a s

Thus, even in t h e c a s e t h a t all domestic p r i c e s e x c e p t two a r e equal to t h e world m a r k e t p r i c e s and t h a t one of these two domestic p r i c e s moves i n t o t h e direc- tion of t h e world m a r k e t price, c a n t h e level of utility d e c r e a s e .

In t h i s section t h e comparative s t a t i c r e s u l t s of t h e simplified version of t h e open exchange model have been presented. One s h o u l d k e e p i n mind t h a t t h e s e r e s u l t s a r e derived u n d e r t h e assumption of t h e existence of one (social) utility function. Therefore t h e r e s u l t s may differ if t h e r e a r e many socio- economic groups with different utility functions.

5. Countries, Commodities 5.1. Countries

The EC model comprises 8 national models for:

1. Federal Republic of Germany 2. F r a n c e

3. Italy

4. The Netherlands 5. Belgium - Luxemburg 6. United Kingdom 7. I r e l a n d

8 Denmark

Development of a model for Greece is being considered.

5.2. Commodities

I n t e r EC supply a n d d e m a n d a r e expressed a t raw material level according t o a 15 commodity classification. The EC commodity list is somewhat more disaggregated t h a n t h e so-called IIASA commodity list.

EC Commodity List IIASA Commodity List

1. wheat

2. c o a r s e g r a i n 3. r i c e

4. bovine

+

ovine m e a t 5. dairy

6. pork,poultry, eggs

7. fish

I

8. p r o t e i n feed 9. oilseeds 10. s u g a r 11. f r u i t 12. vegetables

13. beverages

+

resid. o t h e r foods 14. nonfood a g r i c u l t u r e

15. n o n a g r i c u l t u r e

1. wheat

2. c o a r s e g r a i n 3. r i c e

4. bovine

+

ovine m e a t 5. dairy

6. o t h e r animals 7. protein feed

8. o t h e r food

+

beverages

9. nonfood a g r i c u l t u r e 10. n o n a g r i c u l t u r e 6. The EC-exchange

6.1. Introduction

This section describes t h e e x c h a n g e component of t h e EC model. Here sup- ply a n d demand of t h e individual EC c o u n t r i e s a r e i n t e r c o n n e c t e d t h r o u g h m a r k e t clearing a n d policy s e t t i n g . The exchange r a t e s a r e supposed t o be exo- genously given. At a l a t e r s t a g e a version with endogenous e x c h a n g e r a t e s i n t e r l i n k e d t h r o u g h a "snake" a g r e e m e n t u n d e r t h e European Monetary System may be implemented (see M. Keyzer, 1981b). A variable now may have two s u b - scripts. The first subscript r e f e r s t o commodities, t h e second s u b s c r i p t r e f e r s t o c o u n t r i e s o r t h e world market. The commodity index is i, t h e index for coun- t r i e s is j a n d t h e index for t h e world m a r k e t is w

.

In t h i s s e c t i o n a n d t h e n e x t sections national prices a r e expressed in n a t i o n a l c u r r e n c i e s , EC prices in European C u r r e n c y Units (ECU), a n d world m a r k e t prices in US dollars.

6-2. Demand

Private demand, qi,, follows a Linear E x p e n d t u r e System, e x p r e s s e d a t raw m a t e r i a l level:

p . . ₁₁ q.. ₁₁

=

p.. ₁₁ v . . ₁₁

+

b..(C. _{11 1}

-z

^ph. _J ^V. n1 ^.) ,

z

^bij

⁼

^{1. (4 1)}

h i

where:

v . . = private committed demand

11

bij

=

marginal budget s h a r e C.

=

t o t a l private consumption

J

Government demand, gij, is d e t e r m i n e d exogenously t o t h e -model. The v a l u e of government demand

Gj

is:

G .

=

p . . ..

1J g l J -

i

Gross investment, iij, is also exogenously determined. The i n v e s t m e n t v a l u e I. is:

J

1.

=z

p.. i . . i ^{11 11 '}

Total demand %j is t h e s u m of private demand, government d e m a n d a n d g r o s s investment.

%.

=

q..

+

g . .

+

i..

J ^{11 11} '1 ' (44)

Total demand c a n be written i n t h e form of a Linear Expenditure System:

w h e r e

6.3. Supply - Gross Domestic Product

-

^Taxes

-

Trade Gross domestic product a t m a r k e t p r i c e s Yj is given by

P r i v a t e consumption Cj is t a k e n a s a l i n e a r function of disposable income mj a n d commodity prices pi,:

This c a n be looked at a s a specification with r e a l consumption a s a l i n e a r func- tion of r e a l income. Disposable income mj is defined a s g r o s s domestic p r o d u c t Y,. plus private t r a n s f e r from a b r o a d

F,

m i n u s t r a n s f e r t o EC budget T,, m i n u s g o v e r n m e n t consumption:

Clearly, (47) a n d (48) imply:

Y j

=

C,

+

^S,

+

(T,

-

^F,)

+

G,

.

where Sj s t a n d s for savings.

Tax contribution t o t h e EC is, in a c c o r d a n c e with EC r e g u l a t i o n , t a k e n t o be proportional t o t h e "tax base", i.e. t h e GDP a t m a r k e t prices:

Observe t h a t t i s t h e s a m e for all c o u n t r i e s in t h e EC. Transfer from a b r o a d i s t r e a t e d a s a given commodity bundle:

The commodity balance e q u a t i o n now becomes:

A t EC level n e t import zi obviously i s

a n d t h e n e t import value at domestic market prices, Zj, is given by

The a g g r e g a t e demand definition of GDP becomes:

The t r a d e deficit k, in i n t e r n a t i o n a l c u r r e n c y i s given by

w h e r e pi, is t h e given i n t e r n a t i o n a l price of commodity i.

7 .

EC

Policy Setting

We first describe t h e modeling of t h e price policy for t h e CAP commodities, i.e. t h e commodities s u b j e c t t o t h e CAP.

For t h e CAP commodities, t h e EC s e t s a n import price ( t h r e s h o l d prices)

p,

and a n export price ( i n t e r v e n t i o n price )

&,

s u c h t h a t

<pi,

expressed in t e r m s of ECU's.

Let

ns

be t h e exogenously prescribed exchange r a t e between US$ a n d t h e ECU ($ p e r ECU) a n d l e t world m a r k e t p r i c e s pi, be m e a s u r e d in US$. The levy on i m p o r t t h e n is

1;

= A -

pi^

n,,

and t h e r e f u n d on e x p o r t is:

The levy c h a r g e d (i.e. r e s t i t u t e d ) becomes prohibitive a s soon a s t h e intra-EC p r i c e pi drops below

pi.

Thus import is z e r o if pi

< pi.

Analogously, e x p o r t out- side EC c a n n o t be performed without a loss u n l e s s pi

=

^pj. In t e r m s of com- p l e m e n t a r i t y conditions t h i s c a n b e specified as:

pi S pi S

pi

p r i c e within bounds

Gi -

^Pi)zi+

=

0 n o imports unless price is a t u p p e r bound

(pi

-

p j ) z ~

=

0 n o export unless price is a t lower bound (57)

z. =

2.+

- -

1 1 'i

zi+

,

zi- r

0

where z+ r e f e r s t o imports a n d

z ;

t o exports.

Figure 4 i l l u s t r a t e s t h e i n t e r n a l effect of t h e CAP. The n e t t r a d e of t h e EC with t h e world is indicated on t h e horizontal axis. Exports a r e m e a s u r e d nega- tively t o t h e left of t h e z e r o point, a n d imports positively to t h e r i g h t of t h i s point. P r i c e s a r e m e a s u r e d vertically. Instead of using s e p a r a t e l y a total EC demand a n d a t o t a l (fixed) EC supply curve, a n EC n e t demand c u r v e i s u s e d which gives for every price t h e difference between total EC demand a n d t o t a l (fixed) EC supply. The EC n e t demand c u r v e c a n vary because of shifts in t h e demand c u r v e s of individual c o u n t r i e s (due t o a higher income, for example).

According t o t h e p r i c e policy of t h e EC, t h e u p p e r price ( t h r e s h o l d p r i c e )

pi

i s valid when t h e EC is a n importer of t h e a g r i c u l t u r a l product, while t h e lower p r i c e ( i n t e r v e n t i o n price)

B

is valid when t h e EC is an e x p o r t e r of t h e product.

Only if t h e t r a d e of t h e EC with t h e world is z e r o may t h e price lie between t h e two bounds. The a c t u a l price (equilibrium price) will t h e n d e p e n d on t h e posi- tion of t h e EC n e t demand curve. Clearly, t h e g r e a t e r t h e difference between t h e u p p e r p r i c e

pi

a n d t h e lower price

&,

t h e h i g h e r t h e probability of self- sufficiency of t h e EC.

EC net demand curve

Exports

-

Zero EC

-

trade l mports

Figure 4. The Variable Import/Export Levy a n d Refund Policy.

I m p o r t e r s a n d e x p o r t e r s in t h e EC do n o t t r a d e in t e r m s of European Units of Account, b u t in national c u r r e n c i e s . Therefore, t h e p r i c e s (E, , pi) have t o be converted i n t o national c u r r e n c i e s . A very special f e a t u r e of t h e CAP is t h a t t h e e x c h a n g e r a t e s which a r e u s e d t o convert Units of Account i n t o n a t i o n a l c u r r e n c i e s , t h e so-called "green" r a t e s , may (temporarily) lag b e h i n d t h e official r a t e a n d deviate from t h e m a r k e t r a t e .

Thus m a r k e t p r i c e s pij of CAP commodities i n c o u n t r y j a r e d e t e r m i n e d as:

where

nf

i s t h e g r e e n exchange r a t e . Obviously t h e p r i c e s between two EC c o u n t r i e s , s a y j a n d k, will differ a t m a r k e t e x c h a n g e r a t e s . The difference is c o m p e n s a t e d by a kind of tariff r a t e , t h e so-called Monetary Compensatory Amount (MCA),

hk.

where

nj

i s t h e m a r k e t exchange r a t e . The price relation t h e n is:

We observe t h a t t h e system e n s u r e s t h a t whenever

hj <

pij

< piJ.

i t does n o t pay for a n y c o u n t r y t o t r a d e with non-EC members, b u t t h a t intra-EC t r a d e is possi- ble a t all prices pj

<

pi

<

p i . *

For commodities n o t subject t o t h e CAP, a s t r a i g h t common import tariff is imposed:

Although (57) shows t h e main principles of t h e CAP, t h e i m p o r t a n d e x p o r t prices ( b ,

pi)

a r e , for s e v e r a l commodities, d e t e r m i n e d a s f u n c t i o n s of i n t e r n a - tional p r i c e s a n d a r e n o t fixed within a year. Moreover, buffer s t o c k s also play a role of t h e i r own, especially in commodities for which t h e EC h a s a l a r g e s h a r e of t h e i n t e r n a t i o n a l m a r k e t ( s u c h a s dairy).

Let s t o c k s of commodity i be d e n o t e d by t h e variable wi. The EC defines a lower bound

.

^- IV~, a n u p p e r bound Fi, a n d a t a r g e t q u a n t i t y wi, s u c h t h a t w. ^-I

<

wi

<

wi. T h e price bounds a t which t h e s t o c k policy becomes active a r e denoted by pi a n d pi. These price bounds may differ from t h e p r i c e bounds W pj

111

a n d

pi

a t which t h e variable import/export Levy a n d r e f u n d policy becomes active. Since t h e s t o c k policy (if a n y ) becomes a c t i v e first, o n e h a s

B <

^pi

<

^pi 111

<

Pi. The s t o c k policy c a n be r e p r e s e n t e d i n t e r m s of t h e following a

complementarity conditions:

* We must assume that this relation also holds for specifying price bounds at the national level. Otherwise the relations (57) would not hold, since a levy might be prohibitive in Coun- try A without being prohibitive in Coun B. In actual fact the bounds at the national level are specified ^as

6 = nfFi

^and

^{Bj =}

^{f i b .} Ths. however, is an inconsistency in the CAP which cannot be represented in this mode\. 11

pi s p. c m

1 - pi price within bounds

RI

vvi s w: s Wi stock within bounds

(wi

-

wi)

=

wi+

-

w r stock deviation from t a r g e t (62) w: (pi - pi)

=

0 n o buying of stock unless price is a t lower bound

Y

m

w i (pi

-

pi)

=

⁰ n o selling of stock unless price is a t upper bound.

wi+ , w; ² 0

where wi+ refers t o increase of stocks and w i t o decrease of stocks.

Clearly, commodity balance with stocks is:

zi

= C

zij

+

wi

j

The stock policy is illustrated in Figure 5.

Figure 5. Stock policy

The combination of t h e two s e t s of complementarity conditions (57) and (62) defines t h e complementarity conditions representing t h e combination of t h e stock policy with t h e variable import/export levy and refund policy.

8.

The

EC-canonical form

S t a r t i n g from t h e total demand system (45) a n d substituting back t o exo- genous variables leads t o t h e following system:

Define matrices A, and Mj with typical elements

where bhi

=

1 if h=i a n d zero otherwise. The expenditure system (64) c a n t h e n in matrix notation be written as

where fj is a diagonal matrix with t h e elements of t h e vector x, on its diagonal.

This system is t h e canonical form for country j expressed in national prices pj.

Since t h e levels of prices within t h e EC a r e determined by t h e demand of all countries, t h e c o u n t r y specific canonical forms have t o be added up. To do this, t h e y first have t o be expressed in the same base price vector. Let lCaP be t h e s e t of commodities subject t o t h e

CAP.

Define t h e base price vector pg a s

and d e h e t h e matrix D a s

The matrix D is determined exogenously. The price equations (58) and (61) c a n t h e n be expressed as

p..

= 4.

p. , for each i ,

11 J ' b (70)

or in t h e usual vector notation as

Making use of t h e l a t t e r e q u a t k n , t h e expenditure system (67) can, after post- multiplication of both sides by d;', be written as

Defining

one c a n write

which i s t h e canonical form for c o u n t r y j e x p r e s s e d in t h e base price v e c t o r pb.

The EC-canonical form is obtained by adding up all c o u n t r y canonical forms expressed in base p r i c e vector pb:

The EC-canonical form is solved for base price pb. t o t a l EC demand

C

xj a n d EC- tax r a t e t , s u b j e c t t o t h e r u l e s of t h e common p r i c e policy, t h e s t o c k policy a n d J

t h e following EC t r a d e deficit equation:

where k is t h e prespecified t r a d e deficit a t EC level evaluated a t world m a r k e t prices. One n o t e s t h a t t h e EC t a x r a t e is endogenously d e t e r m i n e d

The approach described above is not fully c o n s i s t e n t . First, t h e r e is a n inconsistency i n t h e calculation of taxes. Because of t h e e x i s t e n c e of MCA's.

t h e a m o u n t of t a x e s c o u n t r y j pays according t o t h e solution of t h e model may differ from t h e t a x e s t Yj t h e c o u n t r y h a s t o pay according t o t h e EC-rule. In fact, from equation (72) one derives t h a t t a x e s Tj c a l c u l a t e d by t h e model a r e given by:

(one makes use of equation 65 a n d 71) where L i s t h e summation vector, a n d where

4, = n,/ nf

^{if i E IcaP} a n d one otherwise. If C b i j

4)

# l

.

^{t h e n Tj # t}

^Yj.

i

The i n c o n s i s t e n c y c a n be solved by working with pseudo-endowments

y. =

Y./

C

^{b.. . .}

J J i 11

41 .

A s e c o n d i n c o n s i s t e n c y may a r i s e s i n c e t h e c o s t of t h e MCA's is n o t included i n t h e model. The model solution does n o t e n s u r e t h a t t h e computed cost of t h e price s u p p o r t for a CAP-commodity equals i t s r e a l cost. Hence, t h e model solution does n o t e n s u r e t h a t t h e EC-budget is in equilibrium. The calcu- l a t e d cost i n ECU's of t h e p r i c e s u p p o r t for CAP-commodity i i s

while t h e r e a l c o s t i s Piw Z i

- - &

^{. .}

ns C n,

^z1J

j

Making use of the relations: pij

= n!

^pi

.

^{i E} ICaP (equation 5 0 ) and pi

=

pib, i Z Icap (equation 68), one sees t h a t both cost amounts are equal if, and only if

If t h e equality above does not h o l d the EC-tax rate is corrected ex post so as to ensure t h a t t h e EC-budget is in equilibrium. This method is.also used to correct for t h e omission of t h e cost of stocks. Ex post correction of t h e EC-tax r a t e almost does not affect the net-trade figures of t h e CAP-commodities, since the consumption of these commodities largely exists of committed consumption.

The trade deficit now becomes t h e final adapting variable.

I t might be t h a t the difference between t h e computed cost and t h e real cost of the EC budget is considered too high t o apply the ex post correction of the EC tax rate. In t h a t case t h e expected difference between computed cost and real cost is added to the prespecified trade deficit figure before running t h e . model. The trade deficit Q u r e obtained after t h e correction of the EC-tax r a t e will then be equal t o the .prespecified trade deficit. The expected difference between computed cost and real cost is calculated, e i t h e r by using last year's n e t trade figures, or the net trade figures corresponding to expected or average prices, or t h e n e t trade figures obtained by a first r u n of the model.

B a r t e n , AP. (1977). "The Systems of Consumer Demand Function Approach: A Review", E c o n o m e t r i c a , 45, pp. 23-51.

Farber, U. e t al.. "The IIASA Food a n d Agriculture Model for t h e EC. An Over- view", WP-84-50, Laxenburg, Austria: 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.

Keyzer, M.A. (1981a). The m t e r n a t i o n a l Linkage of Open &change E c o n o m i e s , Ph.D. Thesis. Amsterdam: Vrije Universiteit.

Keyzer. M.A. (1981b), "The Exchange Component of t h e EC Model", WP-81-3, Amsterdam: Centre for World Food Studies.

Keyzer, M.A (1983), "Policy Adjustment Rules in a n Open Exchange Model with Money a n d Endogenous Balance of Trade Deficit", in Kelley,

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Sanderson a n d J.G. Williamson (eds.), Modeling Growing E c o n o m i e s in E q u i l i b r i u m a n d h e g u i l i b r i u m . Durham: Duke P r e s s Policy Studies.

Keyzer. M.A a n d Y. Rebelo (1982). "The Open Exchange Model: Modelling Approach, Formulation and Solution", WP-82-15, Amsterdam: Centre for World Food Studies.

P a r i k h , K. a n d F. Rabar (1981), "Food Problems and Policies: P r e s e n t and F u t u r e , Local a n d Global", in P a r i k h , K. a n d F. Rabar (eds.) Food f o r All in a .9ustainuble World, SR-81-2, Laxenburg, Austria: International I n s t i t u t e for Applied Systems Analysis.

Woodland, A.P. (1980), "Direct and Indirect Trade Utility Functions", Rewiew of E c o n o m i c S t u d i e s , 4 7 , pp. 907-926.