The Welfare Costs of Tied Food
Aid
Abbott, P.C. and McCarthy, F.D.
IIASA Collaborative Paper
March 1981
Abbott, P.C. and McCarthy, F.D. (1981) The Welfare Costs of Tied Food Aid. IIASA Collaborative Paper. IIASA,
Laxenburg, Austria, CP-81-008 Copyright © March 1981 by the author(s). http://pure.iiasa.ac.at/1795/ All rights
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NOT FOR QUOTATION
WITHOUT PERMISSION
OF THE AUTHOR
THE WELFARE COSTS OF
TIED FOOD AID
philip C. Abbott
F. Desmond McCarthy
March, 1981
CP-81-8
C o Z Z a b o r a t i v e P a p e r s report work which has not been
performed solely at the International Institute for
Applied Systems Analysis and which has received only
limited review. Views or opinions expressed herein
do not necessarily represent those of the Institute,
its National Member Organizations, or other organizations supporting the work.
INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS
A-2361 Laxenburg, Austria
PREFACE
The aid given to some developing countries often has
conditions attached. This is particularly true in the case of
food aid. These conditions are often referred to in the literature as tied aid. This paper analyses various tying techniques.
It estimates the type of losses which ensue and some of the
strategies that may be adopted by the recipients.
iii
The Welfare Costs of Tied Food Aid
bs
P h i l i p C. Abbott and F. Desmond McCsrthy
It is now generally understood t h a t aid-tying, whether by
source o r project, imposes an excess cost when t h e t y i n g i s effective.- 1/
However, t h e analysis of such r e s t r i c t i o n s has not been integreted i n t o
a general equilibrium framework i n t h e developmental l i t e r a t u r e .
Hence,
it is i n s u f f i c i e n t l y appreciated t h a t t h e problen of assessing t h e b e n e f i t s
(and possibly l o s s e s ) from t h e r e c e i p t of t i e d a i d i s e s s e n t i a l l y one of
constrained maximization
.-2/
The inadequacy i s p a r t i c u l a r l y evident i n t h e analysis of
P.L.
The c l a s s i c a r t i c l e s by Schultz (1960) and Fisher (1963)
480 aid.
focussed exclusively on t h e impact of P.L.
production.
480 a i d on domestic food
On t h e other hand, even i f such an e f f e c t were present,
the welfare *act
of t h e r e c e i p t of food a i d could be positive.
It i s
the purpose of t h i s note t o develop t h e analysis of t h e l a t t e r question
systematically.
In doing t h i s , we note t h a t P.L. 480 a i d comes t o a country
not e n t i r e l y as a grant.
The c o n s t r a i n t s posed by t h e food a i d (vis-a-vis
Philip C. Abbott is with the Department of Economics, Northeastern University, F. Desmond McCarthy is with the International Institute for Applied
Systems Analysis, Laxenburg, Austria. The authors wish to acknowledge the
helpful suggestions of Professors J.N. Bhagwati and L. Taylor of M.I.T.
1/
For t h e project-tying, s e e Singer (19651, f o r source t y i c g see Haq
(1965) and Bhagwati (1968).
2/
Hovever, t h e general equilibrium approach has e a r l i e r been developed i n t h e trade-tfieoretic, a s d i s t i n c t from t h e developmental
l i t e r a t u r e , by 3hagwati (1968).
cash a i d ) may r e l a t e t o d m e s t i c consumption o r production o r imports
and t h a t t h e l o s s r e s u l t i n g *om
--
meeting such c o n s t r a i n t s nay not be t h e
minimal one, s i n c e second-best p o l i c i e s may be u t i l i z e d t o meet t h e
constraints.
We u t i l i z e t h e usual t r a d e - t h e o r e t i c model, which assumes
two t r s d a b l e s (one being food) and f i x e d i n t e r n a t i o n a l p o l i c i e s , with
t h e food a i d t h e n c o n s t i t u t i n g a " t r a n s f e r " r e c e i p t .
fPcnn standard t r a d e - t h e o r e t i c
The key d i f f e r e n c e
a n a l y s i s i s t h a t t h e p o s t - t r a n s f e r equil-
ibrium must r e r l e c t t h e a d d i t i o n a l c o n s t r a i n t s t h a t P.L.
480 a i d l e g i s -
.-
l a t i o n may r e a u i r e 3/
Vhile each c o n s t r a i n t w i l l be t r e a t e d diagrammatically, we
a l s o analyze it a l g e b r a i c a l l y .
The n o t a t i o n used f o r t h e l a t t e r w i l l
be as follows:
U
Domestic c o n s ~ t i o nof good
Yi :
Domestic productian of good
A
:
Aid received, i n t h e form o f good 1
p
:
World Market P r i c e of good 1 denominated i n terms of
good 2
:
S o c i a l U t i l i t y Function
( c ~ c2)
,
F (Y1,
1
-
i = 1,2
Ci :
y2) :
a :
i'
i'
i = 1,2
Reduction P o s s i b i l i t y R o n t i e r
Grant ccmponent o f a i d .
Hence, t h e r e a r e two goods i n t h i s v o r l d , t h e a i d good 1 (food) and all
3/
The usual t r a n s f e r problem a n a l y s i s , of course, i s a l s o of
i n t e r e s t when t h e terms of t r a d e caD vary. E3y c o n t r a s t , w e a r e
assuming here t h a t t h e terms o f t r a d e a r e f i x e d , s i n c e a i d rec i p i e n t s g e n e r a l l y meet t h e requirements of t h e s m a l l country
assumption.
0th-
goods.
It i s assumed t h a t U
(cl,
C2) and P (Y1,
conditions f o r d i f f e r e n t i a l b i l i t y a s required, and U
p a r t i a l derivatives with respect t o Ci and Yi,
i
Y2) satisf'y
and Fi denote
respectively.
Throughout
t h e analysis non-specialization i n consumption and production w i l l be
assumed, and t r a d e i s allowed, except when s p e c i f i c c o n s t r a i n t s a r e introduced.
I.
We w i l l t h e r e f o r e be concerned only wikh i n t e r i o r maxima.
Consumption Constraint
It is assumed t h a t p r i o r t o receiving aid, t h e r e c i p i e n t country,
a small, open economy;'
maximizes its s o c i a l u t i l i t y U and this r e s u l t s i n
a l e v e l of consumption
q
f o r t h e a i d gwd.
After receiving a i d , t h e
-
consumption l e v e l of good 1 i s constrained t o be C1 = C1
+ A.
(This
1s t h e c o n s t r a i n t of " a d d i t i a a l i t ~which
~
i s o f t e n thought t o be applied
480 donations.)
In US P.L.
I n addition, t h e country now seeks t o max-
imize U subject t o t h i s constraint and a l s o t h e production and foreign
exchange constraints.
The problem faced by t h i s country can, therefore,
be specified a s f o l l m :
Hlu u (C1,
Social U t i l i t y
c2)
Production P o s s i b i l i t y
Frontier
s.t. F (yl, y2) = 0
p.
[cl
- (1-
+ Cp
- Y:,
= 0 Foreign Exchange Constant
Additionality Constraint
A geometric i n t e r p r e t a t i o n of t h e problem i s given i n Fig. 1.
-4/
This implies t h a t i t s behavior does not e f f e c t p, t h e world p r i c e
of good 1.
a
a
Good 2
(all other
Goods)
Good 1
(Food)
Figure 1.
Consumption Constraint o n
Aid Recipient
I n i t i a l production i s a t P and consum-ption a t C , giving maximum u t i l i t y
U1.
A.fter t h e i n f l u x of a i d t h e grant c a g o n e n t moves t h e foreign ex-
change constraint t o albl'yielding t h e primary gain.
-
t h e a d d i t i o n a l i t y c o n s t r a i n t C1 = C1
l i e on t h e l i n e ed.
If one now imboses
+ A then a solution must a l s o
The opthum outcome f o r t h e case i l l u s t r a t e d (with
a ) 0) is a t s where t h e u t i l i t y i s below pre-aid l e v e l U1.
A primary
gcrin moves ab t o a'b"and then t h e concomitant l o s s occurs due t o t h e
binding consumption d i s t o r t i o n .
It i s evident t h a t i f t h e consumption
constraint were not binding a gain would r e s u l t ; a s a'b'passes above
U f o r same portion of t h a t curve.
1
It should a l s o be noted t h a t t h e
outvard s h i f t of t h e budget c o n s t r a i n t a'b'
a = 0, a'b'
transfer.
i s determined by a
s h i f t s by an amount A, and so C:
In t h a t case, no l o s s occurs.
. If
equals Cpprior t o t h e a i d
If a exceeds 0, however, then
a'b' s h i f t s out by an amount l e s s than A, so t h a t C2 i s reduced and a
l o s s i n u t i l i t y may result.
I n t h e extreme case where a = 1, then ab
does not s h i f t , and a l o s s i s obvious.
The optimum s o l u t i o n under t h e consumption a d d i t i o n a l i t y
constraint may a l s o be obtained a n a l y t i c a l l y .
The change i n s o c i a l u t i -
Uty, du, obtained i s given by:
(see appendix 1 f o r t h e derivation ; t h e case where t h e additionU t y constraint i s not binding i s a l s o t r e a t e d t h e r e )
If t h e a d d i t i o n a l i t y constraint i s binding, then it follows
t h a t dC1 = dA.
Production i s kept at t h e optimum by maintaining t h e
pre-aid prices t o t h e producer.
A consumption t a x cum subsidy i s reauired
t o insure consmption a t s ( ~ i g .1 , ) .
dU = UldA
-
u1 'pU2
- A3
dU
-
The change i n U i s given by:
a pU2dA
also:
so t h a t :
((1
o ) pU2
-
X 3 ) dA
where X
can be thought of a s t h e shadow p r i c e of t h e a d d i t i o n a l i t y
3
constraint. Since CI is fixed, t h e o t h e r constraints and first order
conditions a l s o f i x C2.
U = U
(q+ A,
c2).
U1 and U2 are evaluated a t t h i s point, where
Note t h a t when t h e a d d i t i o n a l i t y constraint did
not apply, optimality conditions required t h a t t h e country always gain,
The constrained s o l u t i o n , however, allows Up> U1/p which is why t h e country
may lose,
One should note that i n Fig, 1, t h e s o c i a l u t i l i t y function
is no longer tangent t o t h e budget c o n s t r a i n t ( l i n e a%'' )
a t point s ,
t h e constrained outcome,
Some observations a r e relevant a t t h i s juncture,
The above
conditions imply t h a t if a country i s following optimal production policy,
p r i c e t o farmers w i l l not equal p r i c e s to consumers.
of t h e presence of a ire resource
- t h e food aid,
This occurs because
This i s then allocated
between farmers and consumers by appropriate p r i c e s t o each,
!he a i d
inflow w i l l be used t o subsidize lower food p r i c e s t o consumers (and i n
e f f e c t , higher food p r i c e s t o producers than would otherwise obtain).
Hence, t h e c o n s t r a i n t s considered here do not necessarily impose t h e
Schultzian disincentive e f f e c t .
Hence, i f a p p r o p r i a t e p o l i c y i s followed
t h e r e w i l l not b e any change i n domestic production.
By u s e o f an
a p p r o p r i a t e wedge, i n c e n t i v e t o produce i s not reduced, s i n c e t h e producer f a c e s t h e same ( p r e - a i d ) r e l a t i v e p r i c e s .
Thus, a c o n s m t i o n
e x t e r n a l i t y i s b e s t handled by a c o n s u m t i o n p o l i c y o f tax and subsidy.
11.
Production C o n s t r a i n t :
It is assumed h e r e t h a t t h e r e c i p i e n t is r e q u i r e d by t h e
a i d donor t o produce a n a d d i t i o n a l amount of t h e a i d good 1
equal t o 811 above t h e pre-aid
level of
TI.
The problem may be
s t a t e d a s follows:
Max U(C1? C2)
P [cl
Y - 7
-
(1
-
Social U t i l i t y
a)A
- Y1)
+ C2 -
+BA
Y2
-
Production P o s s i b i l i t y
Frontier
0
Foreign Exchange C o n s t r a i n t
Production C o n s t r a i n t
Again a geometric i n t e r p r e t a t i o n i s shown i n Fig. 2.
Before
a i d one i s c o n s t r a i n e d by t h e world market t o ab w i t h a i d good
production a t
5.
I f production of good 1 is now forced t o
t h e r e s u l t i n g f o r e i g n exchange c o n s t r a i n t i s a b.
from t h e a i d w i l l move a'b'nut
by an amount ( 1
!fl
+3A
The primary g a i n
- a)A
tt~
a' b'.
One should a l s o n o t e t h a t a country c o n s t r a i n e d t o produce a t t h e
Same l e v e l a s b e f o r e r e c e i p t of t h e a i d ( i . e . . ,
3 = 0) w i l l always
g a i n from t h e a i d i n f l o w , though t h e v a l u e of t h a t a i d i s reduced by
t h e e f f e c t s of t h e c o n s t r a i n t .
Also, i f t h e a i d is a l l g r a n t , t h e n a c o u n t r y w i l l g a i n once B
is less t h a n u n i t y .
For t h i s c o n s t r a i n t t h e domestic food p r o d u c t i o n
(good 1) i n c r e a s e s .
The optimum (second b e s t ) p o l i c y r e q u i r e s a
ducer t a x
cum s u b s i d y .
pro-
Such changes i n p r o d u c t i o n r e q u i r e advance
n o t i c e of t h e a i d a v a i l a b i l i t y , however.
Good 2
(all other
Goods)
1(Food)
Figure 2.
Production Constraint
111.
Import Constraint
I n t h i s instance t h e country i s required t o lmport some given
amount of food.
This may a r i s e where business i n t e r e s t s i n t h e donor
country seek t o i n s i s t on t h e r e c i p i e n t s of t h e i r c m e r c i a l i m ~ o r t s
continuing those commercial imports o r a t l e a s t some s p e c i f i e d f r a c t i o n
of t h e pre-aid l e v e l of comrmercial inqorts.
The problem may be stated:
Social U t i l i t y
Production P o s s i b i l i t y
Frontier
Foreign Exchange Constraint
Import Constraint
The mathematical s o l u t i o n obtained f o l l a r s along similar l i n e s t o I and
11.
( s e e appendix 3 f o r d e t a i l s . )
Results again i n d i c a t e t h a t constraints
came with a c o s t , and a severe enough constraint may induce a l o s s from
t h e r e c e i p t of t i e d a i d .
A similar problem has been analyzed by Bhagwati (1968) f o r t h e
case y = 1. This i s shown in Fig. 3 and it i l l u s t r a t e s t h e points outl i n e d i n Appendix 3.
I n f t i a l production and consumption a r e a t Y1 and
C1 giving u t i l i t y
$.
a t C1 ~ i v i n gu2.
I f t h e recipient i s n m constrained t o imports a t t h e
For food a i d A and no c o n s t r a i n t s consumption i s
pre-aid l e v e l ( y = 1) i n addition
t o t h e a i d A then one possible solution
is t o consume a t C1 y i e l d i n g u t i l i t y
sumption t a x cum subsidy.
$.
This nay be r e a l i z e d by a con-
This would, however, be an i n e f f i c i e n t policy.
The r e c i p i e n t could a l s o s a t i s f y t h e c o n s t r a i n t and do b e t t e r i f consump-
*
t i o n were a t Cl y i e l d i n g U
.
TO achieve t h i s l e v e l , U
*
(higher than $)
*
requires producing a t Y1.
Thus, t o achieve t h e optimum solution (under t h e imaosed pattern
of t r a d e ) , t h e r e c i p i e n t i s obliged t o i n t e r f e r e i n both consumption and
production markets.
*
t o Y1,
production
This requires a production t a x cum subsidy t o drive
lowering t h e r e l a t i v e food p r i c e t o t h e producer to-
*
gether with a consumption t a x cum subsidy t o d r i v e consumption t o Cl
1)
(assuming t h a t t h e associated U i s t h e maximum t h a t can be achieved).
The two taxes should be eaual f o r a lowest cost solution.
point iras not highlighted by Bhagwati.
Appendix 3.
This
Analytical d e t a i l s a r e given i n
It is noted i n this instance t h a t t h e Import constraint
r e s u l t s i n t h e r e c i p i e n t producing less food domestically than i n t h e
pre-aid s i t u a t i o n by making food production l e s s a t t r a c t i v e .
t h e Schultzian, disincentive e f f e c t i s operating i n . t h i s case.
Hence,
Good 2
(all other
Goods)
Good 1,( Food)
Fiqure 3.
I m p o r t C o n s t r a i n t on Aid
Recipient
IV.
Distributional Effects
I n t h i s s e c t i o n t h e model is modified t o a n a l y z e t h e e f f e c t s
on a c o u n t r y ' s w e l f a r e when a l l i n d i v i d u a l s { w i t h i n t h e c o u n t r y a r e
n o t t h e same.
I n o r d e r t o f o c u s on t h i s a s p e c t of t h e problem i t
is assumed t h a t t h e c o u n t r y consumes a l l t h e o u t p u t and a l s o any
aid.
The u s u a l c a v e a t s a b o u t normative u t i l i t y f u n c t i o n s a p p l y .
The a n a l y s i s o f t h e e f f e c t s i s based on a model of a c o u n t r y
w i t h two c l a s s e s of w r k e r .
The L1 members of t h e f i r s t produce
o n l y food (Goodl) w h i l e t h e L2 members of t h e o t h e r produce o n l y
machines (Good 2).
lations.
These may b e t y p i c a l l y r u r a l and u r b a n popu-
Each c l a s s , i, consumes b o t h goods,
u t i l i t y functions U
i
(clip
CZi),
i
-
I n d i v i d u a l s have
1 , 2 where C
of food j consumed by a member o f c l a s s i and C
1,2.
ji
-
is t h e q u a n t i t y
Cjl C j 2 '
The p r o d u c t i o n f u n c t i o n s are assumed t o have t h e form:
with the usual properties.
j
I =
+
A s o c i a l u t i l i t y function U f o r t h e
c o u n t r y is assumed of t h e form:
Before f o o d a i d a r r i v e s i t is assumed t h a t a g e n e r a l e q u i l i brium exists w i t h a l l markets i n e q u i l i b r i u m and a l l income consumed.
Let a q u a n t i t y dA of food a i d a r r i v e i n t h e c o u n t r y ; t h e quest i o n of how i t is d i s t r i b u t e d is d i s c u s s e d l a t e r . It is assumed t h a t
s t r u c t u r a l r i g i d i t y of t h e economy i s s u c h t h a t workers c a n n o t change
from prdoucing o n e good t o a n o t h e r s o t h a t t h e p h y s i c a l o u t p u t of
goods remains t h e same. (This d i s t o r t i o n is n e c e s s a r y t o make commodity t y i n g of t h e a i d i m p o r t a n t .
Otherwise, s h i f t s of l a b o r between
o c c u p a t i o n s w i l l m i t i g a t e t h e r e d i s t r i b u t i v e e f f e c t s of t h e a i d t r a n s -
fer).
However, t h e money wage of workers i n food w i l l t y p i c a l l y
f a l l , i n e f f e c t reducing t h e i r a b i l i t y t o t r a d e f o r o t h e r goods.
It is assumed t h a t a l l f a c e t h e same p r i c e f o r food p, w i t h t h e
p r i c e f o r machines being 1.
The change i n u t i l i t y f o r a member of c l a s s i i s given by
The change i n u t i l i t y f o r t h e country is given by:
It is of i n t e r e s t t o examine when du may be n e g a t i v e ( i . e . ,
aid induces a n e t l o s s i n s o c i a l u t i l i t y ) .
the
(The d e t a i l s a r e given
i n Appendlx 4 . )
The a n a l y s i s s u g g e s t s t h a t s u f f i c i e n t c o n d i t i o n s t o produce a
net l o s s i n
(a)
social u t i l i t y are:
The d i s t r i b u t i o n of food a i d t o t h e food producing
c l a s s does n o t outweigh
(b)
i t s l o s s i n marketed s u r p l u s .
The marginal u t i l i t y of food (machines) of t h e food
producers is s u f f i c i e n t l y h i g h e r than t h a t of t h e
machine producers.
(c)
F a c t o r markets a r e r i g i d s o t h a t food producers w i l l
n o t s h i f t t o producing machines.
The t y p i c a l s i t u a t i o n where one might a n t i c i p a t e such a r e s u l t
would be a country receiving food a i d when a l a r g e segment of i t s popu l a t i o n i s involved i n agriculture.
The optimum (second b e s t ) policy i n t h i s instance n e c e s s i t a t e s
a r e d i s t r i b u t i v e mechanism.
This would require d i f f e r e n t consumption
and production t a x cum subsidy f o r each class.
V.
Conclusions
The analyses of c o n s t r a i n t s placed on US P.L.
480 food a i d pre-
8ented here have shown t h a t t h e value of t h a t a i d t o a r e c i p i e n t country
can be sharply reduced and may i n f a c t r e s u l t i n a net l o s s i f t h a t a i d
is accompanied by s u f f i c i e n t l y severe constraints.
The results are summn-rized i n Table 1 f o r t h e p a r t i c u l a r models
discussed.
I n addition, if t h e a i d causes sharp r e d i s t r i b u t i o n a l e f f e c t s ,
then t h e net s o c i a l u t i l i t y of an aid receiving country may a l s o decrease.
These r e s u l t s follow from t h e e f f e c t s of d i s t o r t i o n s i n a l l o c a t i o n s of
renources i n t h e receiving country a s a r e s u l t of t h e c o n s t r a i n t which
accmpanies t h e aid.
Further, it i s a l s o important t o r e a l i z e t h a t a r e c i p i e n t may
meet t h e s e c o n s t r a i n t s i n a number of ways, and f o r each s i t u a t i o n t h e r e
i s an optimum (second b e s t ) policy.
The departure from unified exchagge
r a t e s requires a c t i v e government p a r t i c i p a t i o n t o minimize t h e loss.
The lessons from US food aid, which was considered e x p l i c i t l y
here, can be e a s i l y extended t o o t h e r forms of a i d which come with s t r i n g s
attached.
Hence, one should not assume t h a t a i d with conditions attached
w i l l benefit a recipient, and even i f there i s b e n e f i t , t h e r e a l value
of the aid t o a recipient
rnw
well be less than i t s nominal value.
Table 1.
SUMMARY OF EFFECTS OR RECIPIENT
AID KITH CO~JSTRAINTSA ' T ' T A o OR WHEN MA~DISTRIBUTIORMISTS
Cause o f Loss
1.
Consumption
additional it^
2.
Domestic
Production
Incre~se
I
I
(&j
Optimum
(second best)
Policy
Can net loss
occur if aid
is all grant!
Post Aid
Domestic
food production
Consumption
Tax cum subsidy
ti0
Unchanged
Production
YES If
Increase
NO
Decrease
YES
Unchanged
( short-run )
Tax cum subsidy
T1 = Y i + ' B A
3-
Import Level
Maintenance
Equal
Consumption and
Production tax
cum subsidy
C1
b.
Maldistribution
o f purchasing
pover
*Note:
Different
Consumption and
Production tax
cum subsidy
for each
class
for 1,2 and 3 it is assumed that no distribution problems exist,
Bhagwati, J., " l i m e r i s e r i z i n g Growth: A Geometrical mote,"
Economic Studies, Vol. 25, 1958, pp. 201-205.
Review of
"The Tying of Aid, " UmCTAD S e c r e t a r i a t , TD/7/Supp. 4, United Nations,
1967, pp. 1-57.
"The Theory and P r a c t i c e of Commercial Policy: Departures from
Unified Exchange Rates," Special papers i n I S t e r n a t i o n a l Economics,
No. 8, Princeton University, 1968.
,
..
Eckaus R S , "Economic C r i t e r i a f o r Foreign Aid f o r Economic Develoment ,"
i n Foreipn Aid, e d i t e d by J. Ehepwati and R.S. Eckaus, Penguin
Books, Baltimore, MD., 1970, pp. 142-164.
Fisher, F.M., "A T h e o r e t i c a l Analysis of t h e Impact of Food S q l u s
Disposal on A g r i c u l t u r a l Production i n Recipient countries," Journal
of Farm Economics, Vol. 45, 1963, pp. 863-875.
Haq, M. U1,"Tied C r e d i t s : A Q u a n t i t a t i v e ~ n a l y s i s , " i n J. Adler (ed.)
~ a ~ i t Movements
a l
and Economic Develooment, I n t e r n a t i o n a l Economic
Association, M a d i l l a n and St. Martin1s Press, 1965.
I s e m , P.J., and H.W. Singer, "Food Aid: Disincentive E f f e c t s and
Econonic Develoment and C u l t u r a l Change,
t h e i r Policy Implications."
Vol. 25, Number 2, January, 1977, pp. 205-237.
Keynes, J .M. , "The Geman T r a n s f e r Problem,"
XXXIV, 1929, pp. 1-70
M-,
Economic J o u r n a l , Vol.
J.S., "The Impact of P.L. 480 Imports on P r i c e s and D m e s t i c Supply
of Cereals i n India," Journal of F m Economics, Vol. 49, 1963,
pp. 131-146.
Metzler, L. A,,
Economy,
"The Transfer Problem ~ e c o n s i d e r e d , " Journal of P o l i t i c a l
Vol. V, 1942, pp. 397-414.
Papanek, G., "The E f f e c t of Aid and Other Resource Transfers on Savings
and Growth i n LDC's," Economic Journal, Vol. 82, 1972, pp. 934-950.
Pincus, J.A.,
istics,
"The Cost of F o r e i m Aid,"
V O ~ . 45, 1963, pp. 360-367.
Review of Economics and S t a t -
Rosenstein-Rodan, P.N.,
" I n t e r n a t i o n d Aid f o r Underdeveloped Countries ,"
Review of Economics and S t a t i s t i c s , Vol. 43, 1961, pp. 107-138.
Rogers K.P., U.K. S r i v a s t a v a , and E.O. Heady, "Modified P r i c e ,
P r o d u c t i o n , and Income I m p a c t s of Food Aid Under Market
iff e r e n t i a t e d ~ i s t r i b u t i b n , " American J o u r n a l of A g r i c u l t u r a l
Economics, Vol. 54, 1972, pp. 201-
--
--
S c h u l t z . T.W.. "Value of U.S. Farm S u r p l u s e s t o Underdeveloped
1019~ o ; n t r i e s , " J o u r n a l of Farm ~ c o n b -9m i c s Vol. 4 , 1960,
1030.
bp.
S i n g e r , H.W. " ~ x t e r n a lAid: For Plows o r P r o j e c t s ? "
J o u r n a l , 75, September 1965, pp. 539-45,
The Economic
Appendix 1
Optimum p o l i c y f o r a n a i d r e c i p i e n t u n d e r a consumption
addition
Consider
constraint
Lagfangian m u l t i p l i e r s X
i
i =1 , 2 , 3 f o r t h e s e c o n s t r a i n t s ,
t h e problem becomest
MZUC
u(cl,
c2) +
) . l ~ ( ~ l y
-
Y2) + A ~ [ P ( c ~ (1
+
3(C1
- -C 1 - A)
- a ) A - Y1)
+ C2
- Y2] ,
F i r s t o r d e r c o n d i t i o n s f o r t h i s problem a r e :
plus the original constraints
Using t h e s e f o u r c o n d i t i o n s t o g e t h e r w i t h t h e t h r e e c o n s t r a i n t
c o n d i t i o n s , one may e v a l u a t e t h e s e v e n unknowns:
X l
Y
x,
a3
C1, C2, Y1, Y 2 ,
The change of U
Note a l s o t h a t :
dU = UldC1 +
u
L -pdC1
+ ( 1
-
a
1 w]
It i s now of i n t e r e s t t o analyze t h e various p o s s i b l i t i e s .
I f the
"additionality" c o n s t r a i n t i s not binding then f o r a maximum U one has
3
= 0 and so U1 = U2.
Thie yields:
In t h i s instance a country always
gains by accepting a i d
(0 1_ a < 1). Hence, t h e requirement t h a t some of an a i d good be paid
f o r cannot, by itself, induce a l o s s i n this instance.
Appendix 2.
Optimum Policy for an a i d recipient under a production
Constraint.
For t h i s instance the problem is:
U(C1.
Cp)
+
+
?,
AIF(Y1. Y2) + A2(p(c1
y1
- (1 -
a )A
- Y1
- (Tl + B A ) )
F i r s t order conditions f'rm t h e analgtic formulation are:
plus the o r i g i n a l constraints.
+
C2)
Change i n u t i l i t y i s g i v e n by;
dU
U l dCl
+ U2dC2
Noting t h a t :
dC2 = -pdC1
+
(1
- a)
pdA
+
pdYl
+ dY2
one may e v a l u a t e t h e v a r i o u s subcases.
If t h e c o n s t r a i n t on p r o d u c t i o n i s n o t binding, t h e n
A3
=
0,
F 1 = pF2 and U 1 = pU2
This yields:
a s before.
That is, p r o d u c t i o n is allowed t o remain a t p o i n t D i n
F i g u r e 2, which is t h e optimum p o i n t , s o t h a t t h e primary g a i n
from a i d w i l l be a l l t h a t o c c u r s .
If c o n s t r a i n t is b i n d i n g , however, t h e n p =
becomes
also
and
1% and dU
This y i e l d s
dU = U 1 [ ( I
- ),
pdA - 6 3 d A
Note t h a t f o r a = 1 ( a l l ' a i d '
paid f o r ) dU< 0. T h i s i s
s i m p l y t h a t a b i n d i n g p r o d u c t i o n c o n s t r a i n t w i l l produce a l o s s ,
s i n c e i t moves t h e r e c i p i e n t from t h e o p t i m a l p r o d c u t i o n p o i n t D.
For a = 0 , (no payment f o r a i d ) g a i n ( l o s s ) r e q u i r e s p
t o be positive (negative),
- 68
T h i s says t h a t a r e c i p i e n t of c o m p l e t e l y
"free" a i d may i n c u r a l o s s i f t h a t a i d i s t i e d t o a s u f f i c i e n t l y
r e s t r i c t i v e production constraint,
Optimum P o l i c y f o r a n a i d R e c i p i e n t under
Appendix 3
an Import Cons t r a i n t
I n t h i s i n s t a n c e , the problem f a c e d by t h e r e c i p i e n t c o u n t r y is:
Max U(C1, C 2 ) + %IF( Y 1 , Y2) + A2(p(C1
+
Y1
(Cl
-
- (1-
7 (El - T I )
a)A-Y1) + C 2
- Y2)
+ A)
F i r s t order conditions f o r t h i s problan are:
uy + A ~ P+
u2
plus
%
=o
A2
+
A1
F,
-
A2P
1
2
-
A2
= 0
- A3
- 0
= 0
the original constraints,
e v a l u a t e t h e s e v e n unknowns;
Using t h e s e c o n d i t i o n s , one may
C 1, C2, Y 1, Y2,
S i n c e t h e change i n u t i l i t y i s g i v e n by
A1, X2,
and X3.
aa&
from the above conditions:
?l&e
t h a t f o r an optimum (lowest c o s t ) soll:tion production and world
p r i c e s shoald be s e p a r a t e d by an amount
p r i c e s should be s e p a r a t e d by
-.
-133
-' while c o n s u m ~ t i o nand world
U2
This t a x package t o g e t h e r with an
u2
appropriate subsidy y i e l d s t h e optimum (second b e s t ) s o l u t i o n .
Once again, i f t h e c o n s t r a i n t is n o t binding,
reduces t o
dU
dA
= U2(1 - a ) p
=
dU
i3 = 0 an11 dA
(1 - a ) U 1
However, with t h e c o n s t r a i n t , changes i n production (dY ) a r e
induced,
and t h i s can counteract t h e primary gain from t h e a i d
I n t h a t caset
Again, h 3 i s i n t e r p r e t e d a s t h e c o s t of t h e c o n s t r a i n t , and i t s
v a l u e can be c a l c u l a t e d from t h e f i r s t order conditions discussed
earlier.
Those conditions and, hence, t h e c o n s t r a i n t , a l s o t m p l y
r e l a t i o n s h i p between dA ( t h e a i d inflow) and dY
i n production.
, the
a
induced change
The d i s t r i b u t i o n e f f e c t f o r a n a i d r e c i p i e n t
Appendix 4
I n t h e t e x t i t i s shown t h a t t h e change i n u t i l i t y f o r
a two c l a s s s o c i e t y a f t e r r e c e i v i n g a i d i s g i v e n by dU where
dU
a
LldU1
+
L2dU2
It i s of i n t e r e s t t o c o n s i d e r a number of c a s e s .
Egalitarian Society
If one makes a common assumption t h a t a l l members of t h e
s o c i e t y have s i m i l a r m a r g i n a l u t i l i t y ( f o r each good) i.e.,
then i t follows that:
s i n c e t h e n e t i n c r e a s e i n food consumption i s dA w h i l e t h e
n e t i n c r e a s e i n machine consumption i s z e r o one o b t a i n s :
dU
=
lJipd~ > 0
Accordingly one c o n c l u d e s t h a t a n e g a l i t a r i a n s o c i e t y w i l l
i n c r e a s e i t s w e l f a r e by a c q u i r i n g a i d .
I n many c o u n t r i e s t h e r e is a s h a r p d i f f e r e n c e between v a r i o u s
c l a s s e s t h i s may b e viewed a s a d i f f e r e n c e i n m a r g i n a l u t i l i t y
between, s a y , a r u r a l food producing and a n urban machine producing
class.
Consider t h i s somewhat more g e n e r a l s i t u a t i o n .
i n t h e c o u n t r y ' s u t i l i t y dU i s g i v e n by
The change
Noting t h a t :
one o b t a i n s :
The q u e s t i o n i s t h e n whether dU can b e n e g a t i v e .
The second term
I t remains t o a n a l y z e t h e f i r s t term.
w i l l be p o s i t i v e .
1
typical situation Ul
-
can be
<
For a
T h i s o c c u r s when c l a s s e s
0.
have d i f f e r e n t t a s t e b u t s i m i l a r endowments, o r s i m i l a r t a s t e s
w i t h d i f f e r e n t endowments, o r both.
, is
f o r members of Class 1, dU
The changes i n wages (money)
g i v e n by:
where f i s t h e f r a c t i o n of food a i d g i v e n t o c l a s s 1 and da is
1
a i d / c a p i t a i n c l a s s 1.
S i n c e each consumes t o t a l income one a l s o
o b t a i n s ( i g n o r i n g 2nd o r d e r e f f e c t s ) ;
Hence ,
PldCll
+ dCZ1
-
Ap
(
C1
L1
-
CllAp
-Cll)
Ap
+
+
pda
pda
This l a s t term I s t h e d i f f e r e n c e between t h e marketed s u r p l u s
o f a c l a s s one member ( a l o s s ) and t h e v a l u e of t h e food a i d
received (gain).
Thus t h e n e t e f f e c t can b e n e g a t i v e
n e t w e l f a r e l o s s c a n r e s u l t t o c l a s s 1.
- and
If i n addition
lJ1
1
is s u f f i c i e n t l y n e g a t i v e t h e n o n e o b t a i n s t h e r e s u l t t h a t dU
can be n e g a t i v e , i.e.,
t h e c o u n t r y a s a whole l o s e s by aid.
so a
-
U: