DISCUSSION PAPER

PMILTO INFERIOR TRADE AND OPTIMAL TRADE POLICY

b Y

D a v i d Newbery

J anca ry 1983

1

Development Research Department Economics and Research S t a f f

World Bank

9 e L

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

Pub

lic D

iscl

osur

e A

utho

rized

PARETO INFERIOR TRADE AND OPTIMAL TRADE POLICY*

David M. C. Newbery C h u r c h i l l Co l l ege , Cambridge, and The World Rank

and

5oseph E. S t i g l i t z P r i n c e t o n U n i v e r s i t y

J anua ry 1983

( E a r l i e r v e r s i o n s of t h i s paper appeared a s Economic Theory D i s c u s s i o n P a p e r No. 23, J u l y 1979, Cambridge, England, and Econometr ic Research Program Research Menorandurn

",>%V"..

, May 1981, P r i nce ton . )

* The r e s e a r c h r e p o r t e d h e r e was suppo r t ed i n p a r t by t h e Uni ted S t a t e s Agency f a r I n t e r n a t i o n a l Development and i s a n e x t e n s i o n of Appendix E of Newbery and S t i g l i t z [1977]. We a r e g r a t e f u l t o L. P e r e z and h i s c o l l e a g u e s t o USAID f o r t h e i r comments. We a r e a l s o i ndeb t ed t o t h e e d i t o r , t o p a r t t c i p a n t s a t s e m i n a t s a t Warwick, l J n i v e r s i t y a o f Dubl in , The World Rank, P r i n c e t o n and t o Roy R u f f i n and Robin Ltndsey f o r t h e i r h e l p f u l comments. F i n a n c i a l s u p p o r t from t h e N a t i o n a l Sc i ence Founda t i on , t h e S o c i a l S c i e n c e Research Cor~ncil of r h ~ IJK, and TRM a r p gr;ltefr~llv acknowledeed. Qevisf ons c o c h d w p e r were completed w h t l s t Newbery was on Leave rrom Cambridge un ivers f ; ty a t t h e World Bank. The views p r e s e n t e d a r e t hose of t h e a u t h o ~ r s a l o n e a d do no t n e c e s s a r i l y r e f l e c t t hose of t h e World Bank o r IJSAID. -

i - w *

PARETO INFERIOR TRADE cZND OPTIMAL T2ADE POLICY

by David M. Newbery and Joseph E. S t i g l i t z

One of t h e b a s i c t e n e t s of l i b e r a l economics i s t h a t everyone c o u l d

be made b e t t e r o f f by reduc ing r e s t r i c t i o n s on t r a d e . Even though some g r o u p s

i n t h e popu la t i on may be made i n i t i a l l y worse o f f , t h o s e who g a i n a s a r e s u x k -

of t r a d e l i b e r a l i z a t i o n can more t han a f f o r d t o compensate t h o s e who s u f f e r ,

We show t h a t i n a c o m p e t i t i v e bu t r i s k y economy, f r e e t r a d e may be P a r e t o w

i n f e r i o r t o no t r a d e , and under f a i r l y g e n e r a l c o n d i t i o n s a r e s t r i c t i o n Pn

t r a d e from t h e f r e e- t r a d e p o s i t i o n w i l l c o n s t i t u t e a P a r e t o improvement, &e

r e s u l t c o n s i s t e n t w i th t r a d i t i o n a l b e l i e f s is t h a t t h e r e e x i s t s some f o w o f

l i b e r a l i z a t i o n from t h e no- trade s i t u a t i o n which c o n s t i t u t e s a P a r e t o

improvement . The b a s i c i d e a behind our model is simple. There a r e two c o u n t r i e s

( r e g i o n s ) bo th of which grow'a r i s k y a g r i c u l t u r a l c r o p pqd a s a f e c rop . The

o u t p u t i n t h e two r e g i o n s is n e g a t i v e l y c o r r e l a t e d . (The r e s u l t s can e a s i l y

be extended t o c a s e s where t h e c o r r e l a t i o n i s zero o r even p o s i t i v e , s o Long

a s t h e c o r r e l a t i o n i s n o t p e r f e c t . ) I n t h e absence of t r a d e , p r i c e rises

whenever ou tpu t f a l l s . I f demand f u n c t i o n s have u n i t a r y p r i c e e l a s t i c i t y the

p r i c e v a r i a t i o n s p rov ide p e r f e c t income in su rance f o r t h e farmer. With free

t r a d e t h e v a r i a t i o n s i n t h e ou tpu t of t he r i s k y c r ' o p ' o f f s e t each o t h e r and - c s t a b i l L z e t h e p r i c e , which no longer v a r i e s t o o f f s e t ou tpu t v a r i a t i o n s ,

- Consequently, t h e revenue from t h e ri*y c r o p now v a r i e s and t h e r i s k f a c e d By -

I

w t h e fa rmers is inc reased . TF.is i n d u c e fa rmers t o s h i f t p roduc t ion away f r a m I e I t he r i s k y c r o p , r a i s i n g i ts averaqe p r r c e . S ince consumers have u n i t price

e l a s t i c i t y and t h u s spend a c o n s t a n t amount on both c r o p s , t h e mean income of

t h e fa rmers remains c o n s t a n t wi th t h e opening of t r a d e wh i l e i t s r i s k i n e s s

i n c r e a s e s . Consequently, fanners ' w e l f a r e n e c e s s a r i l y d e c r e a s e s , a s shown i n

F igu re 1.

Whereas b e f o r e ;rade was opened, consumers bore a l l t h e r i s k , w i t h -

f r e e t r a d e they bea r none, and, o t h e r t h i n g s being e q u a l , t h i s would make them

b e t t e r o f f . However, t h e i nc reased r i s k i n e s s of t h e r i s k y c rop induces

fa rmers t o s h i f t t h e i r p roduct ion t o t h e s a f e c rop , and t h e consequent r i s e %a

t h e average p r i c e of t h e r i s k y crop can make consumers worse o f f . Near

au t a rky , t h e r i s k b e n e f i t daminates t h i s a l l o c a t i o n e f f e c t , a s shown i n Fiwre

1, but near f r e e t r a d e t h e o p p o s i t e i s t h e case. I f t h e change i n s u p p l i e s

and p r i c e s i s s u f f i c i e n t l y l a r g e (which i t w i l l be i f p roducers a r e

s u f f i c i e n t l y r i s k a v e r s e ) , and i'f t h e consumer r i s k b e n e f i t s a r e s u f f i c i e n t l y

small (which they w i l l be i f consumers a r e no t very r i s k a v e r s e ) , t h e n

consumers w i l l be made worse o f f by opening t rade . S i n c e producers a r e ,. -

n e c e s s a r i l y worse o f f ( i n t h i s ;nodel), i t fo l lows t h a t f r e e t r a d e i s P a r e t a

i n f e r i o r t o au tarky .

The reconciliation of our r e s u l t s wi th t h e s t a n d a r d theorems of

Welfare Economics i n which f r e e t r a d e is P a r e t o e f f i c i e n t is s t r a i g h t f o r w a r d

10 -- t h e conven t iona l argument r e q u i r e s not on ly t h a t marke ts be c o m p e t i t i v e (a;

we assume), but a l s o complete. In our model t h e r e must be a complete set ~f - i n su rance markets enab l ing fa rmers t o purchase both price and og tpu t - insurance . or-a v a r i e t y of reasons such a s moral haza rd and a & e r s e * *

I w

s e l e c t i o n t h e set of markets is not complete. I n our example autarky p r o v i d e s

farmers wi th income insu rance , and opening a new market ( i n t e r n a t i o n a l trade

i n t h e r i s k y commodity) has t h e same a f f e c t a s c l o s i n g t h e s e i m p l i c i t

- - - 3 -

i n s u r a n c e markets , With a complete s e t of markets each market p rov ides one,

and o n l y one, market ing s e r v i c e , but w i th an incomple te s e t some marke ts may

be p rov id ing s e v e r a l s e r v i c e s , a l l o c a t i n g both goods and r i s k . I n s t i t u t i o n a l

change may change t h e number of s e r v i c e s provided by a p a r t i c u l a r marke t , and

i n our example such changes can make everyone worse o f f . Welfare a n a l y s i s

which assumes t h a t each market s e r v e s o n l y one f u n c t i o n can be s e r i o u s l y

. mis lead ing i n t h e s e cases .

The model w e s h a l l ana lyze h a s been kept s imple t o make t h e main

p o i n t s a s c l e a r l y a s p o s s i b l e . I n p a r t i c u l a r , w e choose very s p e c l a l

f u n c t i o n a l forms -- u n i t p r i c e e l a s t i c i t y -- f o r consumer demand which a l low

UP t o employ t h e concept of mean p re se rv ing changes i n r ' sk , and which t h u s

a l l o w a ' v e r y i n t u i t i v e exp lana t ion of ou r r e s u l t s . It w i l l become c l e a r from

our model t h a t any o t h e r . s p e c i f i c a t i o n would g r e a t l y compl i ca t e t h e a n a l y s i s ,

s i n c e changes i n t r a d e w i l l i n g e n e r a l l e a d t o changes i n both mean income and

i t s r i s k 2 Our r e s u l t s a r e , however, q u i t e g e n e r a l , and r e l y on t h r e e

c r i t i c a l assumptions, F i r s t , t h e r e must be some a g e n t s who, on ave rage , a r e

n e t sellers of t he r i s k y good ( i n our model, t h e fa rmers) and o t h e r s who a r e

n e t buyers (consumers). S ince these i n d i v i d u a l s must engage i n t r a d e , t h e i r

we l f a re is a f f e c t e d by t h e p r i c e d i s t r i b u t i o n Y Second, n e i t h e r p roduce r s

nor consumers ;an buy in su rance f o r t h e r i s k s ( t h e v a r i a b i f i t y of o u t p u t of

t h e r i s k y crop and of i t s p r i c e ) which they f ace . Changes i n t h e l e v e l of

t r a d e change t h e price d i s t r i b u t i o n and t h e r i s k s t h a t ind3viduals f ace . If - they could p e r f e c t l y i n s u r e , then t h e r e w o h d he no change i n r i s k , and hence

8! t

no adve r se consequences. However, w e would a rgue t h a t i t i s more r e a l i s t i c t o

assume t h a t i n d i v i d u a l s cannot p e r f e c t l y i n s u r e themselves, and t h a t t h e r e f o r e

r i s k , and changes i n r i s k , do ma t t e r . Th i rd , ou tpu t i n t he d i f f e r e n t

c o u n t r i e s c anno t be p e r f e c t l y c o r r e l a t e d , f o r t hen (under our a s sumpt ions t h a t

t h e c o u n t r i e s a r e o t h e r w i s e i d e n t i c a l ) opea ing up t r a d e would l e a v e t h e p rPce

d i s t r i b u t i o n u n a f f e c t e d . Thus, a l t h o u g h we assume i n t h e f i r s t s e c t i o n t h a t

o u t p u t s i n t h e two c o u n t r i e s a r e p e r f e c t l y n e g a t i v e l y c o r r e l a t e d , a l l t h a t i s

r e q u i r e d i s t h e absence of p e r f e c t p o s i t i v e c o r r e l a t i o n . L a t e r i n t h e p a p e r

w e show t h a t t h e r e s u l t s c o n t i n u e t o h o l d i f t h e r i s k s i n t h e two c o u n t r i e s

- a r e symmetr ic , a much weaker c o n d i t i o n t han p e r f e c t n e g a t i v e c o r r e l a t i o n .

These t h r e e a s sumpt ions d i s t i n g u i s h ou r paper from e a r l i e r s t u d i e s o f

t r a d e and u n c e r t a i n t y . These o t h e r s t u d i e s have ( f o r t h e most p a r t ) employed

t h e concep t of a r e p r e s e n t a t i v e consumer- producer , assumed t h e p r i c e

d i s t r i b u t i o n w a s g i v e n exogenous ly , r a t h e r t han de te rmined endogenous ly ,

assumed o u t p u t s a r e p e r f e c t l y c o r r e l a t e d a c r o s s c o u n t r i e s , a n d / o r f ocused an

t h e c a s e where t h e r e a r e p e r f e c t r i s k marke t s - s o f a rmer s can d i v e r s i f y o u t o f *

t h e r i s k s t h e y f a c e The c l o s e s t i n s p i r i t t o t h e p r e s e n t s t u d y i s t h e

e x c e l l e n t work of Helpman and Razin (1978) which d e a l t w i th g e n e r a l

e q u i l i b r i u m e f f e c t s . However, t hey assume a p e r f e c t e q u i t i e s market ( a weaker

assumpt ion t han a p e r f e c t r i s k m a r k e t ) , p e r f e c t c o r r e l a t i o n , and t h e y make u s e

4 / of t h e concept of a r e p r e s e n t a t i v e consumer- .producer-

The paper i s d i v i d e d i n t o t h r e e p a r t s . I n P a r t I we deve lop t h e

b a s i c model and d e r i v e t h e c o n d i t i o n s a u n d e r which f r e e t r a d e i s P a r e t o i

i n f e r i o r t o no t r a d e . I n P a r t I1 we u se a more g e n e r a l model t o a n a l y z e t r a d e -

. j policy. i n Par t ii.1 we sllow t n a t cne r e s u l t s a r e more roousc cnall LIle s l1np~12 L

6 C model developed i n P a r t s I and 11. We d i s c u s s t h e c r i t i c a l a s s u a g t i o n s ,

r B p r e s e n t a n a l t e r n a t i v e i n t e r p r e t a t i o n of t h e model, and sugges t e x t e n s i o n s t o

t h e a n a l y s i s .

I. Cornpartson o f Autarky and Free Trade

We cons t ruc t a simple anode1 with two regions which a r e i d e n t i c a l ,

except t h a t t h e i r output of a r%sky a ~ - i c u l t u r a l commcdity is p e r f e c t l y

nega t ive ly c o r r e l a t e d . Each region has n i d e n t i c a l farmers and m

i d e n t i c a l consumers. We f i r s t d e s c r i b e the farmers, then the consumers, and

f i n a l l y the market e q u i l i b r i a d t h and without t rade. We then compare t h e two

. e q u i l i b r i a and e s t a b l i s h condit%ons under which f r e e t r a d e is Pare to i n f e r P o r

t o no t rade .

A. Producers

Each of t h e n i d e n t i c a l producers owns one u n i t of l a n a . A t y p s c a k

farmer a l l o c a t e s a f r a c t i o n x of h i s land t o growing a r i sky crop, which w e

denote by subsc r ip t r , and t h e remainder, 1 - x , t o the s a f e crop, deno ted

by s u b s c r i p t s . Output per a c r e of the r i s k y crop i s 0 , a random

v a r i a b l e , with mean u n i t y and var iance a2 . The output of the s a f e c rop is

always uni ty . (These a r e j u s t norn~a l i za t ions . )

Farmers a r e r i s k averse ; they choose x before they know 8 (the

51 weather) t o maximize the expected u t i l i t y of profi ts :-

where

- * e

a r e the p r o f i t s , p is ?the p r i c e of the r i s k y crop, and q is the p r i c e of

the s a f e crop.

Farmers a r e assumed t o know t h e r e l a t i o n s h i p between t h e p r i c e and

8 , bu t s i n c e each fa rmer is small, he assumes h e h a s no e f f e c t on p r i c e ( i n

any state of n a t u r e ) 2' Our a n a l y s i s t h u s focuses on c o m p e t i t i v e r a t i o n a l

e x p e c t a t i o n s e q u i l i b r i a . The expec ted u t i l i t y maximizing c h o i c e of x i s

g i v e n by t h e s o l u t i o n t o

EU'(n)(p8 - q) = 0 . ( 3 )

B. Consumers

It is convenien t t o r e p r e s e n t t he r e p r e s e n t a t i v e consumer by h i s

i n d i r e c t u t i l i t y f u n c t i o n V = V(1, p, q) where I i s income which i s

c o n s t e n t / For most of t he a n a l y s i s w e s h a l l make u s e of a s p e c i a l

pa rame te r i za t i on o f t h e u t i l i t y f u n c t i o n . We l e t

v---= -

l og I - a l o g p - b l o g q ,

f o r p f 1 ,

f o r p = 1 ,

where p is t h e c o e f f i c i e n t of r e l a t i v e r i s k ave r s ion . These y i e l d agg rega t e

demand funk t ions f o r t h e two commodities which have ur i i t a ry p r i c e and income

e l a s t i c i t i e s :

-

where Qi is agg rega t e demand f o r ccmmodity i ( r i s k y o r s a f e ) , and mI is

a g g r e g a t e consumer inccme.

Thi s s p e c i f i c a t i o n of t h e u t i l i t y f u n c t i o n i s chosen f o r s e v e r a l

reasons : it g r e a t l y simplifies t h e c a l c u l a t i o n s ; i t is t h e c r f l i t y f u n c t i o n

f o r which consumer s u r p l u s c a l c u l a t i o n s employed i n conven t iona l w e l f a r e

a n a l y s i s a r e valid;&/ and i t i m p l i e s t h a t t h e r e w i l l be no income

r e d i s t r i b u t i o n e f f e c t s i n t h e p o l i c y changes which w e s h a l l c o n s i d e r , / and --

t h u s t h i s s p e c i f i c a t i o n enab le s a s imple s e p a r a t i o n of t h e e f f i c i e n c y and

d i s t r i b u t i o n a l consequences of t r a d e pol icy . Moreover, demand f u n c t i o n s wi th

u n i t a r y p r i c e e l a s t i c i t y p lay a c r i t i c a l b o r d e r l i n e r o l e i n t h e a n a l y s i s of

r i s k wi th more than one commodity; i f t h e e l a s t i c i t y of s u i j s t i t u t i o n between

t h e two commodtties is less than u n i t y , t h e induced p r i c e v a r i a b i l i t y r e s u l t s

i n farmers t r e a t i n g t h e s a f e commodity a s i f i t were r i s k i e r than t h e r i s k y

commodity. (See St i g l i t z [I9721 .) F i n a l l y , t h e u t i l i t y f u n c t i o n e x h i b i t s

c o n s t a n t r e l a t i v e (income) r i s k a v e r s i o n , p , and i n t h e s p e c i a l c a s e of

u n i t a r y r i s k a v e r s i o n of equa t ion (5) :

s o changes i n p r i c e do no t a f f e c t t h e m a r g i ~ ~ a l u t i l i t y of income.

C. Markept Equil ibr ium Without Trade &

The s t r u c t u r e of t h e equ i l i b r ium i s simple:

( a ) Prodt-cers d e c l d e on a c r o p a i l o c t i o n , x , g l v e n i n a c t n e ~ r

e x p e c t a t i o n s about t h e r e l a t i o n s h i p between p r i c e and 8 is Ln f a c t t he one

I t h a t emerges. .

(b) A i t e r t h e c rop is h a r v e s t e d , the c r o p s a r e marketed

c o m p e t l t i v s l y . b r k e t p r i c e s e q u a t e demands (g iven by equcrtion ( 6 ) ) t o

s u p p l i e s (which depend on x and 0 ) . I f a l l fa rmers a c t a l i k e then market

c l e a r i n g p r i c e s a r e

where y = mI/n , consumer income per farmer. Equat ion (8) i m p l i e s both c rops

y i e l d p e r f e c t l y s a f e r e t u r n s , which must be i d e n t i c a l i f both c r o p s a r e t o b e

grown:

Equat ions (8) and ( 9 ) imply t h a t

and g ive t h e e q u i l i b r i u m s o l u t i o n

Producer p r o f i t s a r e n = q ( u s i n g (9 ) and ( 2 ) ) s o producer, we l f a re i s simply

~ { ( a + b)y) . The r e p r e s e n t a t i v e consumer's average we l f a re i n t h e

r G g d L L L i l I i 1 ~ ~ C d b C (5). L5 il C - - - s

E v a V n + S l o g 9 , . % = h; I - ( a + b) l o g ((a+b)y) , (12) * - where V,, i s the u t i l i t y wi thout r i sk&/

Note t h a t t h e u n i t e l a s t i c consumer demands t r a n s f e r a l l tne r i s k

from farmers t o consumers. F l u c t u a t i o n s i n t h e supply of t h e r i s k y c r o p

a f f e c t only i t s p r i c e and not t h a t of t h e s a f e crop. Except i n t h i s s p e c i a l

c a s e , p roduct ion r i s k f o r one commodity w i l l s p i l l over t o g e n e r s t e p r i c e r i s k

f o r o t h e r commodities. ( S t i g l i t z [1972]) .

1 D. Harket Equi l ibr ium wi th Free Trade

I Now suppose t h a t , t o t h e e a s t on t h e o t h e r s i d e of s mountain range

I t h e r e is ano the r r eg ion , i d e n t i c a l t o t h e one desc r ibed above i n every r e s p e c t

s ave one -- t h e w e a t h e r x l When i t r a i ~ s i n t h e West i t is d r y i n t he E a s t ,

and v i c e v e r s a . The ou tpu t of t h e r i s k y c rop i s p e r f e c t l y n e g a t i v e l y

E c o r r e l a t e d between t h e two r eg ions . Formally, l e t 0 + 0' = 2. I n i t i a l l y

t h e r e i s no t r a d e between East and Vest, but t h e r e is a pass through the

I mountains which permi ts v i r t u a l l y c o s t l e s s exchange. I f i t is opened, t h e r e

w i l l be compe t i t i ve f r e e t r a d e ; i f n o t , t h e reg ions w i l l remain a u t a r k i c . Is

f r e e t r a d e d e s i r a b l e ?

I n Sec t ion 1 . G below w e show t h a t t h e r e is always a symmetric

equ i l i b r ium, but t h e r e may be a d d i t i o n a l asymmetric e q u i l i b r i a i n which each

coun t ry r e l a t i v e l y s p e c i a l i z e s i n one crop. I f farmers a r e no t too r i s k

ave r se there.wi.11 be a unique symmetric s t a b l e equ i l i b r ium, and f o r moaL o f

t h e paper we s h a l l c o n c e n t r a t e on t h i s .

- .-. $7" A, , L .L a ] : : , , . L L . A L -;?L L.-..L2 ,. - u ., 2 2 - . " - 1 - - , ; , ' > -ii -

'9 i - same f r a c t i o n x of land t o t h e r i s k y crop,, 1 - x t o t h e s a f e croD, *

E a - y i e l d i n g t o t a l s u p p l i e s : -

Qr = nx8 + nx(2 - 0 ) = 2nx, Qs = 2n( l - x) . (13)

F r i c e s w i l l be p e r f e c t l y s t a b i l i z e d a t

and so t o t a l p r o f i t s a r e now

t

r = px0 + (1 - x): = (a0 + b)y ,

and farmers' income i s now r i s k y , thozgh i t

a l l o c a t i o n of land between t h e two crops is

ha.s t h e sarce mean a s before . me

g iven by t h e s o l u t i o n t o equa t ion

aey by EU'{y(ae + b)) (X - l_X? l EM(e ,x) = 0 . (16)

E. Comparison of Free Trz l e and Autarky

Denote t h e equ i l ib r ium va lues of x , p, q , wi th f r e e t r a d e by .h .-. .-.

, , and i n au ta rky by { x , o, q) . P r o p o s i t i o n 1 conpares t h e

a l l o c a t i o n s of t h e e q u i l i b r i a i n the two s i t u a t i o n s :

P ropos i t ion 1 . I f farmers a r e r i s k ave r se , t he s a f e c rop i s cheaper and t h e 4 , e

l and devoted t o the r i s k y crop smal le r wi th f r e e t r a d e than au ta rky .

Proof: With f r e e t r ade and r i s k averse farmers the averaee ref:urn 60 t h e - ---. -

from (14). A comparison wi:h t h e au t a rky equ i l i b r ium (10) i m p l i e s * ; > acd hence < q .

* - - More g e n e r a l l y , i f Ax = x - x is t h e f a l l i n l and a l l o c a t e d t o t h e

r i s k y cro? i n moving from a u t a r k y t o f r e e t r a d e , then P r o p o s i t i o n 2 i d e n t , f i e s -

t w c of t h e c r i t i c a l parameters de te rmining t h e magnitude of Ax . P r o p o s i t i o n 2. (s) The more r i s k a v e r s e a r e farmers t h e g r e a t e r i s Ax . P

(Diamond and S t i g l i t z [1974]) ; (b ) The g r e a t e r t h e riskiness of 0 ( i n t h e

seilse of Rothschi ld-St igLi tz [1970]) , t h e g r e z t e r is Ax , provided

( i ) t h e range of 0 i s not too g r e a t , o r

(ii) t h e r e i s cons t an t c e l a t i v e r i s k ave r s ion R w i th R < 1 . E i t h e r of t h e s e cond i t i ons e n s a r e t h a t t h e exp res s ion M(0,x) is concave i n

8 22/, and ensu res t h e r e s u l t .

F. Welfare Analysis

The next r e s u l t fo l lows immediately from equa t ion (15) :

Propos i t i on 3. Farmers a r e always worse o f f a s a r e s u l t 9f t h e opening o f P

t r ade . I n t h e new equilibric:! mean income i s unchanged b u t r i s k is

131 inc reased - Consume.rs now f a c e no r i s k . This makes them b e t t e n o f f bu t i n r e t u r n

t h e r e is a change i n x , which makes them worse o f f . To s e e t h i s , we a s k

riiCIL Q A A u ~ d ~ ~ ~ ~ i x ncix~inlzes consumer w e i i a r e

w>ere Z(0) > 0 depends on t r a d e pol icy . Thus un. - a u t a r k y Z = e a w h i l s t

i n f r e e t r a d e Z = 1 . However, f o r - any Z(0) > 0 , w e observe t h a t t h e

s o l u t i o n i s

t h e farmers ' cho ice under au t a rky . Any o t h e r cho ice makes t h e consumer worse

o f f . Sence, t h e change i n consumer we l f a re i n moving from a u t a r k y t o f r e e

t r a d e w i l l depend on t h e magnitude of t h e r e sou rce s h i f t , Ax , and on t h e

consumer g a i n from t h e e l i m i n a t i o n of t h e r i s k h e f aces .

From P r o p o s i t i o n 2, Ax depends on t h e s i z e of t h e r i s k and t h e

deg ree of farmers ' r i s k a v e r s i o n , whi le t h e consumers' b e n e f i t from r i s k

r educ t ion depends on t h e s i z e of r i s k , and t h e degree of consumers' r i s k

ave r s ion .

It t h e r e f o r e looks a s though consumers w i l l be worse o f f wi th f r e e

t r a d e provided fa rmers a r e s u f f i c i e n t l y r i s k a v e r s e , and th:s i s indeed t r u e

when comparing t h e symmetric f r e e t r a d e equ i l i b r ium wi th au t a rky . However, '

above a c r i t i c a l l e v e l of farmer r i s k a v e r s i o n , t h e symmetric f r e e t r a d e

equ i l i b r ium i s un:tahle. 2 1 I t i s t h e r e f o r e necessary t o c o n s i d e r t h e

ques t ion of s t a b i l i t y b e f o r e c3ncluding t h a t f r e e t r a d e can be P a r e t o i n f e r i o r

'3 i - - -

G.? Mult ip le E q u i l i b r i a and S t a b i l i t y # . S t a b i l i t y can only be examined i n t he con tex t of a p a r t i c u l a r

adjustment process , which i n t u r n r e q u i r e s a s p e c i f i c a t i o n of t h e way fa rmers

form t h e i r expec ta t ions . We s h z l l assume t h a t fa rmers hold a weaker form of

r a t i o n a l expec ta t ions : g iven t h e i r e x p e c t a t i o n s about t h e l and a l l o c a t e d t o - -- --

t h e r i s k y crop i n each coun t ry , they can deduce t h e p r i c e d i s t r i b u t i o n and

hence de termine t h e i r own land a l l o c a t i o n . 9ut of e q u i l i b r i u m t h e fa rmers

p r e d i c t what t h e i r f e l l o w countrymen w i l l do ( s i n c e they a r e i d e n t i c a l ) b u t

can only observe l a s t yea r ' s c rop a l l o c a t i o n i n t he o t h e r count ry . Suppose

t h a t i n year t coun t ry 2 chose x2t, which fa rmers i n coun t ry 1 c o r r e c t l y

p r e d i c t w i l l be t h e i r cho ice i n year t + 1. Given t h i s , coun t ry 1 fa rmers

choose t h e r a t l o n a l e x p e c t a t i o n s u t i l i t y maximizing cho ice x ~ ~ + ~ which depends

on xzt+l = xzt: x l t+ l = g ( ~ ~ ~ ) , where t h e f u n c t i o n g i s d e r i v e d from t h e

f i r s t o rde r c o n d i t i o n s of t h e farmer 's choice . I n year t + 1 count ry 2

fa rmers r e a l i z e t h a t t h e i r cho ice was i n c o r r e c t , and t h e fo l lowing year ,

having observed x l t+ l and c o r r e c t l y p r e d i c t i n g x l t+2 = x ~ ~ + ~ , they choose

xzt+2 = g(xl t+ l ) , where, by symmetry, t he f u n c t i o n g is t h e same. Thus

farmers a r e c o r r e c t h a l f t h e t ime, and only a d j u s t . a f t e r t hey observe t h a t

they have made a n e r r o r . F igu re 2 i l l u s t r a t e s t h e dynamics a s s o c i a t e d w i t h

these r e a c t i o n f u n c t i o n s , and a fret? t r a d e e q u i l i b r i u m i s any p a i r

* * (x l ,x2) such t h a t

and I s t h u s a flxed m i n t of t h e f u ~ c t 1 . o n ( T t i s c l e a r from s y m m e t r v

' r t h a t t h e r e i s a l ~ a y s a symmetric equ i l i b r ium, but t h e r e may be multiplt:

e q u i l i b r i a , a s i n FiRu& 2, which shows a c a s e i n which t h e r e a r e t h r e e - * e q u i l i b r i a , w-ith t h e symmetric equ i l i b r ium be ing uns t ab le . The c r i t i c a l

c o n d i t i o n f o r ( l o c a l ) s t a b i l i t y is

If farmers are risk neutral, it can be shown that the symmetric equilibrium is

unique and 3table, whilst if farmers are infinitely risk averse there are

/ mulrtple equilibria, and the symmetric equilibrium is unstable (Newbery and

I Stiglitz [1981b]. It is thus reasonable to conjecture that there is some.

1 critical value of (relative) risk aversion, R* say, (which will depend on

the parameters a, b, and the distribution of 8 ) below which the symmetric

equilibrium is unique and stible, and above which there are multiple

equilibria, with the symmetric equilibrium unstable, and this can be

demonstrated for constant absolute or relative risk aversion utility functions

15/ . and a two point distribution for 8 - Since farmers are always worse off in a free trade equilibrium, free

trade will be Pareto inferior to autarky if consumers are worse off under free

trade, i.e., if

a . I

In the symmetric equilibrium, substituting for prices, this is equivalent to

The RHS i s a monotonical ly d e c r e a s i n g func t fon of consumer's r e l a t i v e r i s k

a v e r s i o n p whi le t h e LHS is a monotonica l ly d e c r e a s i n g f u n c t i o n of fa rmers '

r e l a t i v e r i s k a v e r s i o n R . It fo l lows t h a t t h e r e is a montonica l ly

i n c r e a s i n g c r f t i c a l f u n c t i o n R = f ( p ) f o r which consumers a r e i n d i f f e r e n t

between au ta rky and t h e symmetric f r e e t r a d e equ i l i b r fum, and i t can he shown

t h a t f ( 0 ) Ro > 0 , where the v a l u e of &, depends on ?he form o f t h e

u t i l i t y func t ion , t h e na tu re of r i s k , and o t h e r parameters . The c r u c i a l

q u e s t i o n is whether Ro < R* , t h e c r i t i c a l v a l u e a t which t h e symmetric

e q u i l i b r i u m becomzs uns tab le .

For t h e two po in t d i s t r i b u t i o n , 8 = 1 a , and v a l u e s of

a = 9.9 t h e r e Ls a wide range of va lues of a and b f o r which

Ro < R* : 0.2 P< a J - 0.8 ; a + b 5 0.9 , f o r both cons t an t a b s o l u t e and

r e l a t i v e r i s k a v e r s i o n u t i l i t y func t ions . Ro i n c r e a s e s w i th b , dec reases

w i th a , an:: i s l e s s than 3.0 f o r a 2 0.4 . However, f o r a < - 0.8 t h e r e a r e

v e r y few such c o n f i g u r a t i o n s , and hence f o r f r e e t r a d e t o be P a r e t o i n f e r i o r

t o au t a rky , the degree o f r i s k must be q u i t e extreme.

When t h e symmetric equ i l i b r ium is u n s t a b l e , t h e r e w i l l i n g e n e r a l

ex is t s t a b l e e q u i l i b r i a , and i t is a l s o p o s s i b l e t h a t t h e s e e q u i l i b r i a a r e

P a r e t o i n f e r f o r t o au tarky . For our two po in t d i s t r i b u t i o n example, computer 0 . t

s imu la t ion confirmed t h a t t h e r e i s a l s o a set of va lues of .R above R* For

w\fch the asymmetric e q u i l i b r i a a r e s t a b l e and Pa re to i n f e r i o r t o f r e e t r a d e ,

bounded by a curve R = F(p) which near R* i s dec reas ing in p and 'Shich - i n t e r s e c t s R - f ( p ) a& R*.

1

These computer s o l u t i o n s a l l ow 3s t o a s s e r t

P ropos i t i on 4. There e x i s t

t r a d e equ i l i b r ium is Pa re to

sets of parameter va lues f o r which t h e s t a b l e f r e e

i n f e r f o r t o au tarky .

The simulations suggest that the range of values of (R,p) for which

this is true increases with a , a, and b. There is a larger range of values

of (R, p) for which free trade is potentially Pareto inferior to autarky in

the sense that though consumers would be better off with free trade, they

would not be willing to pay the fixed sum needtd to compensate producers for -

accepting free trade.

In the remainder of the paper we shall confine attention to the

symmetric free trade equilibrium and hence restrict attention to cases where

11. TRADE POLICY

The preceding section demostrated that the opening up of trade could,

fn the absence of perfect risk markets, result in all individuals in both

countries being worse off. Whilst the example is dramatic, and has the merit

of simplicity, it is clearly a special case, and needs considerable extension

if it is to provide any practical insights. It is special in a number of

ways, many of which have already been mentioned, but here we wish to draw

attention to, and relax, two of these special features. First, the assumptien

that production is perfectly negatively correlated allowed us to use a single

, I 9 risk parameter, 8, to describe the itate of the world, whi?at avoiding the

degenerate case of perfectly positively correlated risk. Yowever, this is an.

extreme assumption which we shall replace by the much weaker assumption that

risk is symmetric. That is, to every state s there correspond: a state Z #

I

s' such that country 1 in state s is indistinguishable from country 2 in

state s', and vice versa (in the symmetric equilibrium). Second, the absence

of a complete set of insurance markets constitutes a market failure, and hence

r a i s e s t he q u e s t i o n of what is t h e b e s t f e a s i b l e i n t e r v e n t i o n -- i n t h i s ca se ; k r b

what is the b e s t t r a d e pol icy? Whi ls t t h e r e is a presumption t h a t f r e e t r a d e

is not op t imal ( s i n c e i t may be dominated by a u t a r k y ) , i t w i l l be shown below

t h a t au t a rky is a l s o not op t imal . A model which only compares t h z s e two

extremes does l i t t l e t o shed l i g h t on the more important q u e s t i o n of t h e b e s t

c h o i c e of t r a d e pol icy .

This q u e s t i o n t u r n s o u t t o be very complicated t o answer i n g e n e r a l ,

f o r t h e fo l lowing reason. I n t h e absence of r i s k , t r a d e p o l i c y is concerzed

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

compe t i t i ve world ( a s i d e f r o 3 r e a l l o c a t i o n s of r e n t ) whether t h i s i s achieved

by t a r i f f s o r quotas . I n t he presence of r i s k , however, t a r i f f s and quotas

have a q u i t e d i f f e r e n t e f f e c t on t h e d i s t r i b u t i o n o f t r a d e , p r i c e s , and hence

t h e r i s k s borne by consumers and producers - a r e s u l t a l r e a d y noted i n a

p a r t i a l e q u i l i b r i u m c o n t e x t by F i she l son and F l a t t e r s (1975) and Dasgupta and

S t i g l i t z (1977) . In s h o r t , i t i s no longer enough t o choose t h e l e v e l of

t r a d e , but r a t h e r , t h e l e v e l of t r a d e i n each s t a t e of t he world, o r t h e t r a d e

i n t e r v e n t i o n p o l i c y a s a f u n c t i o n of the s t a t e of the world.

Whilst i t is p o s s i b l e t o c h a r a c t e r i s e t h i s op t imal mode o f

i n t e r v e n t i o n , i t is not c l e a r t h a t t h i s i s the r t g h t way t o formula te t h e , e

p o l i c y ques t ion . ~ f the government can , ex p o s t , i d e n t i f y (he s t a t e of t h e

world and make p o l i c y con t ingen t on t h i s s t a t e , then i t might j u s t a s w e l l . -

o f f e r i n su rance , i n '4hich c a s e t h e problem d i sappea r s . Presumably, t h e - - r ea sons t h a t m i l i t a t ' a a i n s t complet ing t h e market s t r u c t r l r e a l s o g rave ly Or

II 'C l i m i t t he cho ice of t r a d e pol fcy . I n p r a c t i c e , t r a d e p o l i c y appea r s t o be

l a r g e l y a q u e s t i o n of choosing between r e l a t i v e l y simply in s t rumen t s such a s a

uniform t a r i f f o r quo ta and i t t h e r e f o r e s e e n s s e n s i b l e t o a s k of t h e

I

uncons t r a i ced optimum t r a d e p o l i c y whether i t looks more l i k e a t a r i f f o r a

quota. A l t e r n a t i v e l y , one can a s k d i r e c t l y which of t h e s e two a l t e r n a t i v e s is

p r e f e r a b l e , and when.

I n t h i s s e c t i o n , we prove two g e n e r a l p r o p o s i t i o n s concern ing t h e

e f f e c t s of small d e v i a t i o n s from t h e f r e e t r a d e and au ta rky p o s i t i o n ; provide

a gene ra l c h a r a c t e r i z a t i o n of t h e r i s k e f f e c t s of quo ta s ve r sus t a r i f f s w i t h i n

ou r gene ra l e q u i l i b r i u m model; pose t h e q u e s t i o n of choosing t h e opt imal s e t

o f b a r r i e r s t o t r a d e ; and provide some p a r t i a l answers t o t h e e v a l u a t i o n of

a l t e r n a t i v e t r a d e r e s t r i c t i o n s . For s i m p l i c i t y , we assume each c o u n t r y

p u r s u e s -i d e n t i c a l t r a d e p o l i c i e s , so t h a t symmetry is not d i s t u r b e d . We a l s o

assume throughout t h a t any revenues from t r a d e p o l i c y a r e d i s t r i b u t e d a s lump

sum payments t o producers. Symmetry r e q u i r e s t h a t s t a t e s of t h e world occur

i n e q u a l l y prdbahle p a i r s , s, s ' , s o t h a t when t h e ou tpu t o f t h e r i s k y c rop

i n c o u n ~ r y i i s xi Bi (s ) , then ,

Symmetry of t r a d e po l i cy mean:; t h a t when a po l i cy ins t rument is set a t l e v e l

z , i n s t a t e s , and t h e l e v e l of imports i n coun t ry i i s x , t { e i ( s ) , z ) , t h e n , - . -

. I i n t h e symme&ic equ i l i b r ium when xl = x2 = x

-

- - ! t

I f i n c r e a s e s i n z correspond t o l i b e r a l i z i n z t r a d e p o l i c y , and i f t h e e f f e c t

of t h e l i b e r a l i z a t i o n i s t o i n c r e a s e t r a d e i n every s t a t e of t h e world (o r n o t

j * i , and

d t{e , (s ) , z) dt{e,(s ' ) , z) a - > o f o r e i < s ) < B L ( s 8 ) - (25)

d z d z

Symmetry a l s o impl i e s t h a t

The corresponding d i s t r i b u t i o n of domestic p r i c e s i s

Trade po l i cy has two e f f e c t s - i t changes the r i s k f a c i n g producers

and consumers, and hence changes t h e a l l o c a t i o n of land between t h e two

crops . S t a r t i n g from autarky ( z = O), i n c r e a s i n g t r a d e i n c r e a s e s the r l s k

f a c i n g farmers, and t h i s w i l l , i n g e n e r a l , cause them t o swi t ch land from t h e

r i s k y t o the s a f e c r o p 1 6 1 Rather than s p e c i f y r e s t r i c t i o n s on the u t i l q t y

f u n c t i o n s , r i s k , and t r a d e p o l i c y which guarantee t h i s , i t i s more d i r e c t t o

s p e c i f y the a l l o c a t i v e consequences bf t r ade pol icy . We s h a l l say t h a t t r a d e *

po l i cy has a monotonic a l l o c a t i v e e f f e c t i f t h e s h a r e of land a l l o c a t e d t o t h e

r i s k y crop dec reases monotaa ica l ly wi th t r a d e l i b e r a l i z a t i o n . ' i L

We a r e now a p o s i t i o n t o s t a t e and prove two rcbz rkab le a s u l t s : B n

Propos i t ion 5: Any & a l l symmetric t r a d e l i b e r a l i z a t i o n from autarkyR is

~ a r e t d improving.

I I I

I

P r o p o s i t i o n 6: Any smal l symmetric t r a d e r e s t r i c t i o n a t t h e symmetric f r e e - t r a d e e q u i l i b r i u m is Pa re to improving provided t h e a l l c c a t i v e e f f e c t i s

monotonic.

Thus, whi le t h e p r e v i o u s s e c t i o n e s t a b l i s h e d t h a t no t r a d e may be - Pare to s u p e r i o r t o f r e e t r a d e , t h i s s e c t i o n e s t a b l i s h e s t h a t n e i t h e r p o l i c y i s

i t s e l f , i n g e n e r a l , P a r e t o e f f i c i e n t , and hence t h e r e e x i s t a l t e r n a t i v e t r a d e

p o l i c i e s which make some i n d i v i d u a l s b e t t e r o f f wi thout making any i n d i v i d u a l

worse off=/ To e s t a b l i s h t h i s r e s u l t , we need t o ana lyze t h e e f f e c t s of

t r a d e p o l i c y on producers and consumers.

A. E f f e c t of Trade Po l i cy on Producers

I n equ i l i b r ium producers must r e c e i v e the amount s p e n t by consumers

on t h e s a f e and r i s k y c rops , less t h e v a l u e of consuners ' pu rchases of t h e

r i s k y crop from t h e o t h e r c o u n t r y , s o producer p r o f i t s w i l l be

whete D { ~ ( s ) , z ) is the t r a d e d e f i c i t ; i t s va lue w i l l depend on che world

p t i c e , which i n t u r n w i l l depend on t h e s p e c i f i c a t i o n of t r a d e pol icy . For

example, wit6 quo ta s i t w l l l depend on how t h e r e n t s gen8ra ted by t h e quo ta s

a r e a l l o c a t e d between e x p o r t i n g and import ing c o u n t r i e s . F o r t u n a t e l y , i t i s .

not necessary t o be s p e c i f i c about t h e de t e rmina t ion of . D(8, z ) s i n c e we c a n

u s e the symnle t r y assumption: - I

d w c u w m c u L l d 2 P. e -

m

I f t h e count ry i s impor t ing i n s t a t e s (0 ( s ) < B ( s ' ) ) , so t h a t t and . L.-

d t / d z a r e p o s i t i v e , then p wi l l be high, w h i l s t i n s t a t e s' , wi th t h e

count ry expor t ing , d t / d z i s n e g a t i v e , and p w i l l be low. The whole

expres s ion w i l l be p o s i t i v e i f pV i s p o s i t i v e l y c o r r e l a t e d wi th p , which I

i t i s from (4) f o r

The e f f e c t of t r a d e l i b e r a l i z a t i o n from t h e consumer's po in t of view

is t h a t of a mean q u a n t i t y p rese rv ing dec rease i n t h e r i s k i n e s s o f

consumption, which, i f consumers a r e r i s k a v e r s e , t h a t is, i f u t i l i t y is

concave i n t h e r i s k y good, i s b e n e f i c i a l .

2. Free Trade. A t f r e e t r a d e p r i c e s a r e t h e same i n both coun t r i e s .

Consider t h e e f f e c t on consumer we l fa re of r e s t r i c t i o u s i n s t a t e s s and

s' taken t o g e t h e r , i n which p r i c e s a r e t h e same land henc5 so ix -.onsumer

wel fare) . From (32)

The f i r s t t e r m c a n c e l s hy ( 2 6 ) , w h i l s t i f x i s m o n o t o n i c a l l y d e c r e a s i n g L

i n z , s i n c e a t au@rky pO = ay/x = q = b y / ( l - x) , t h e second term i s "

JI N nega t ive , and hence z t f r e e t r a d e

Consequent ly, both producers and consumers b e n e f i t from t r a d e r e s t r i c t i o n s a t

f r e e t r a d e , and, a s shotm i n Figure 1 t h e r e i s an i n t e r m e d i a t e l e v e l of t r a d e ,

between no t r a d e and f r e e t r a d e , a t which consumers' w e l f a r e is wximized .

Any r e s t r i c t i o n s up t o t h i s l e v e l w i l l make both producers and consumers

b e t t e r o f f . -

C. Gptimal Trade p o l i c y

R e s t r i c t i o n s on t r a d e obv ious ly i n t r o d u c e an inefficiency: t h e

marginal r a t e of s u b s t i t u t i o n betweea t h e r i s k y c r o p and o t h e r commodities

w i l l d i f f e r i n t h e two c o u n t r i e s . A t t he same time, r e s t r i c t i o n s on t r a d e

s e r v e a s a p a r t i a l s u b s t i t u t e f o r t h e in su rance ( r i s k ) markets which a r e

absent . There i s thus a s t a n d a r d , second b e s t w e l f a r e problem, ba lanc ing t h e

d i r e c t a l l o c a t i v e i n e f f i c i e n c i e s with t h e g a i n s from ,.he improved d i s t r i b u t i o n

of r i s k .

A s s u m e , f o r i n s t a n c e , t h a t t a r i f f s o r quotas could be made s t a t e

cont ingent ( i n t h a t c a s e , t a r i f f s and quotas would be eqa l iva len t ) . Le t

~ { B ~ ( s ) ) x be t h e q u a n t i t y of impor t s i n t o count ry i i n s t a t e s. Civen

symmetry, it i s on ly necessary t o lo.>k a t one count:y i n choos ing p ~ l i c y , and

sc the s e t of P a r e t o e f f i c i e n t symmetric t r a d e pol icier* a r e t i ts s o l u t i o n s t o

s u c n cna!.

20/ EU(m) > 8 and -

where p ( s ) is g iven by (27) and q by (8). Consider 2 p a i r of s t a t e s s , s ' ,

such t h a t t h e count ry imports i n Eca te s and hence e x p o r t s i n s t a t e s' ,

and suppose t h a t t h e impor t ing coun t ry imposes s t a t e c o n t i n y q n t t a r i f f s ,

bu t t h e e x p o r t i n g coun t ry i s always pas s ive . The t a r i f f revev.lue w i l l b e

{ ~ ( s ) - p ( s ' ) } t ( s ) x i n s t a t e s , and z e r o i n s' , and s o producer incone

i n c l u d i n g t h e lumpsum payment f r o n t h e government i s

whi le when t h e coun t ry e x p o r t s

Equat ion (38) and i c s s)xlmetrir. c o c n t e r p a r t (39) can be i n s e r t e d i n t o

t h e c o n s t r a i n t s (37) and , i n p r i n c i p l t , t h e optimum t r a d e p o l i c y can be

solved. The f i r s t o r d e r c o n d i t i o n s demons t ra te , a s expec t ed , t h a t t h e e f f e ~ t s L

of a change i n t h e l e v e l of t r a d e have t h r e e e f f e c t s . F i r s t , i n c r e a s i n g t r a d e .

1 P f -

.a i

lowers producers ' expected u t i l i t y . Second, t h i s causes a n a l l o c a t i v e e f f e c t - - - a s producers *educe t h e a r e t of land a l l o c a t e d t o t h e r i s k y c rop (under t h e

monoton!city hypo thes i s ) . Th i s a l l o c a t i v e e f f e c t r educes consumer we l f a r e a s

shown i n 1.F abosa. Th i rd , t h e r educ t ion i n p r i c e v a r i a b i l i t y reduces

. .

consumer r i s k which b e n e f i t s consumers. The opt imal l e v e l o f t r a d e r e p r e s e n t s I

l

a balanc ing of t h e s e t h r e e e f f e c t s . S ince pruducer; a r e unambi&uously worse

o f f a s t r a d e i n c r e a s e s , i t must be t h e c a s e t h a t a t t h e optimum, consumers a r e I

b e t t e r o f f , i . e . t h e g a i n s from r i s k r e d r ~ c t i o n exceed :he l o s s e s fror. t h e -

a l l o c a t i v e e f f e c t . Although t h e d e t a i l e d form of t h e optimum t r a d e p o l i c y

depends on t h e n a t u r e of r i s k , a t t i t u d e s t o r i s k , and o t h e r parameters , t h e r e

is one s t r o n g r e s u l t t h a t fo l lows d i r e c t l y from OUA e a r l i e r a n a l y s i s :

P ropos i t i on 7: It i s never desirable t o prevent t r a d e i n any s t a t e .

The importance of t h i s r e s u l t i s t h a t t a r i f f s n e c e s s a r i l y prevent

crade i n ttlc,k;e s t a t e s where t h e p r i c e d i f f e r e n c e between t h e c o u n t r i e s i s l e s s

than the he fgh t of tk.2 t a r i f f w a l l , w h i l ~ t quotas never competely prevent

t r a d e . I n t h i s s ense , then , quo ta s a r e p r e f e r a b l e t o t a r i f f s , o r , more

p r e c i s e l y , t h e s t a t e c o n t i n g e n t op t imal t r a d e po l i cy works more l i k e 3 quota

than a t a r i f f f o r t hose s t a t e where p r i c e d i f f e r e n c e s a r e small . The proof

fo l lows e x a c t l y t h e same s t e p s a s P r o p o s i t i o n 5, except i t i s confined t o

t hose s t a t e s where t r a d e h a s been prevented. L i b e r a l i z a t i o n i s then P a r s t o

improving . D. R e s t r i c t e d Trade P o l i c y

The previous s u b s e c t i o n demonstrated t h a t theechoice of cp t ima l t r a d e

po l i cy invo lves a second b e s t compromise between the a l l o c e t i v e b e n e f i t s o f -

tree t rade ana c n e rlsk consequences . iyhe second oesc na tu re o r Lne p r o o l e m . -3 L

p e r s i s t s even though w e have imposed ne c o n s t r a i n t s on t r a d e pol icy . i - - $?

We argued i n t h e i n t r o d u c t i o n - t c r h i s p a r t t h a t t h e informat ion ;I

r equ i r ed t o implement t h e uncons t ra ined opt imal p o l i c y were e s s e n t L a l l y t h e

same a s t h a t r equ i r ed t o complete t h e market s t r u c t u r e and hence e l i m i n a t e t h e

secksd b e s t a s p e c t s of t h e problem. Arguably, t h e reasons which prevent t h e

c r e a t i o n of t h e miss ing i n s u r a n c e markets w i l l a l s o l i m i t t h e f l e x i b i l i t y of

t r a d e pol icy. I n p r a c t i c e governments u s u a l l y l i m i t t h e n s e l v e s t o choosing

s imple t r a d e p o l i c i e s such a s s p e c i f i c o r ad valorem t a r i f f s and/or quota;.

This choice r a i s e s two n a t u r a l ques t ion: (a ) which of t h e two po la r p o l i c i e s , -

t a r i f f s o r quotas , both s e t a t t h e i r op t ima l l e v e l , g e n e r a t e s t h e h i g h e s t

l e v e l of wel fare? and (b) j f it i s p o s s i b l e t o combine t h e tm p o l i c i e s ,

e.g. , impose a quota i n a d d i t i o n t o ad valorem t a r i f f , i s i t d e s i r a b l e t o do

so?

The key d i f f e r e n c e between quotas and t a r i f f s i s cha t quotas o f f e r

b e t t e r insurance t o farmers than t a r i f f s , w h i l s t t a r i f f s o f f e r b e t t e r

insurance t o consumers than quotas . This is most e a s i l y seen f o r t h e case of

p e r f e c t negat ive c o r r e l a t i o n between output r i s k s . Figures 3, 4 and 5 g i v e

t h e d i s t r i b u t i o n of p r i c e s , consumption and p r o f i t s f o r t h e two p o l i c i e s i n

t h i s case. Thus t a r i f f s r e s t r i c t t r a d e most f o r va lues of O n e a r u n i t y , when

t h e r i s k s f a c i n g t h e farmers wi th f r e e t r a d e would be sma l l , w h i l s t quotas

r e s t c t t r a d e f o r extreme v a l u e s of 8 f o r which f r e e t r a d e i s most r i s k y .

Conversely, t a r i f f s a r e b e t t e r a t t r u n c a t i n g t h e t a i l s of t h e p r i c e

d i s t r i b u t i o n , which ccuse most consumer r i s k . This sugges t s t h a t n e a r

a u t a r k y i where producer r i s k i s n e g l i g t b l e , t a r i f f s a r e s u p e r i o r t o quotas , . w h i l s t near f r e e t rade,where producers bear n o s t of rhe r i s k , quo tas w i l l be

- - The second ques t ion posed above can a l s o be answered fbr t h e c a s e of pr - p e r f e c t negat ive c o r r e l a t i o n , where i t can be shown t h a t even a y t e r t h e

opt imal t a r i f f is imposed, i t w i l l be d e s i r a b l e t o impose a quo ta , while wi th

the opt imal quo ta , i t i s i n g e n e r a l not d e s i r a b l e t o impose a sma l l t a r i f f

which would on ly o p e r a t e nea t f r e e t r a d e , where w e showed t h a t no i n t e r v e n t s o n

i s opt imal . (The d e t n i l s a r e g iven i n Newbery and S t i g l i t z , 1 9 5 2 ~ ) .

111. Extens ions and L i m i t a t i o n s

The previous s e c t i r m s of t h e paper used an extremely s imple model t o

e s t a b l i s h a nuiuber of q u i t e s t r o n g r e s u l t s : n o t o n l y may f r e e t r a d e be P a r e t o

i n f e r i o r t o no t r a d e , some t r a d e r e s t r i c t i o n s w i l l always be d e s i r a b l e , and

t h e r e i s a s e n s e i n which quo ta s a r e superior - t o t a r i f f s . To what e x t e n t a r e

t h e r e s u l t s dependent on t h e s p e c i a l pa rame te r i za t ions we have employed? And

t o aiiot e x t e n t do they depend on the p a r t i c u l a r i n s t i t u t i o n a i assumptions we

have made? The c r i t i c a l assumption i n our a n a l y s i s , we contend , is t h e

absence of p e r f e c t r i s k marke ts , an assumption which, though n o t j u s t i f i e d

w i t h i n t h e con tex t of t h e model, seems e m p i r i c a l l y more p l a u s i b l e ( a t l e a s t i n

t h e con tex t i n v e s t i g a t e d h e r e ) than the o t h e r po la r assumption c o n v e n t i o n a l l y

211 ' employed, t h a t r i s k markets a r e p e r f e c t .- rn

To s e e why t h i s i s impor tan t , l e t us cons ide r b r i e f l y t h e n a t u r e 02

e q u i i i b t i n ~ under a l t e t n a t i v e assumptions, and concen t r a t e on t h e r e s u l t s of

t he f i r s t p a r t of t h e paper , which assume p e r f e c t nega t ive o u t p u t c o r r e l a t i o n .

A. F i n s n c i a l Yarke ts

F i r s t , w e no te t h a t i n t h e c e n t r a l c a s e of consumers having

Ll)gdLlclriIlsC \ l c ~ ~ ~ & y ' L U I ~ C L L U I I S , ~ t ~ t ! i r l a i i i l L c . u ~ < L U L L U L C ~ ~ L ~ I d L h c ~ a i . 1 L..L L-C - .i

t r a d e s i t u a t i o n ; f o r then VIP = 0, t he margina l u t i l i t y oE income is t h e same - - s'

independent of t h e s t a t e of n a t u r e , and hence market e q u i l i b r i u m r e q u i r e s t h a t * . i f a smal l f u t u r e s market were in t roduced , i t be a c t u a r i a l l y f a i r . Eut f o r

producers , p r o f i t s a r e c o z s t a n t , and they t o o would r e q u i r e a n a c t u a r i a l l y

f a i r f u t u r e s market. Hence t h e only equ i l i b r ium i s one where t h e r e i s no

t r a d e on t h e f u t u r e s market. With p e r f e c t nega t ive ou tpu t c o r r e l a t i o n , t h e r e

would be no scope f o r a f u t u r e s market i n t h e f r e e t r a d e s i t u a t i o n e i t h e r ,

s i n c e p r i c e s would not vary.

The coilsequ, -es of opening up a market f o r ownership s h a r e s i n farms

is -more s e r i o u s . (We ignore a l l t h e problems of moral haza rd , which a r e

fundamental t o an unde r s t and ing of why such markets might n o t e x i s t . ) I f

f anne r s could purchase s h a r e s i n each o t h e r s ' farms, then income of fa rmers

would be c o n s t a n t ; they would t h u s be i n d i f f e r e n t between t h e opening of t r a d e

and au ta rky , bu t consumers would be unambiguously b e t t e r o f f . Thus, t h e

s t a n d a r d r e s u l t t h a t f r e e t r a d e i s p r e f e r a b l e t o no t r a d e i s r e s t o r e d , i f

t h e r e is a complete set of s e c u r i t i e s markets .

B u t . a n e s s e n t i a l p a r t of t h e argument s o f a r is t h a t t r a d e i s

c o s t l e s s . With c o s t l y t r a d e , t h e p o s s i b i l i t y t h a t opening t r a d e w i l l a t l e a s t

lower t he w e l f a r e of producers is r e s t o r e d . With f r e e t r a d e i n s e c u r i t i e s ,

farmers ' income is smoothed, bu t t h e opening of t r a d e l e a d s t o fa rmers ' n e t

income being lowered by t h e e ~ p e n d i t u ~ e on t r a n s p o r t c o s t s . Thus fa rmers a r e

worse o f f a s a r e s u l t of t h e opening of t r a d e .

The major reason t h a t t h e u n i t p r i c e e l a s t i c i t y assumption is

employed i s i t h a t i t avo ids t b e confus ion between t r a n s f e r ,and r i s k e f f e c t s .

I f t h e e l a s t i c i t y of demand is n o t u n i t y , a mean q u a n t i t y p r e s e r v i n g change i n

- - 7 - - 3 , . . . . . * . - . . - - - -

I - A - *,- - i .-- - - >

> 1 1 - , - L a * , - , L A ,

-r 5

a n d s t i g l i t z [198 l ] . ) I n p a r t i c u l a r , i f dern=nd cu rves have c o n s t a n t e l a s t i c i t y - = g r e a t e r than u n i t y , farmers ' revenue is a capvex f u n c t i o n of consumption, s o ,

a t each va lue of x, mean income is h ighe r under au t a rky than wi th f r e e

t r a d e . Although i n a u t a r k y , producers ' income is v a r i a b l e , i t i s l e s s

v a r i a b l e than o u t p u t , and hence less v a r i a b l e than income under f r e e t r ade .

\

It can thus be shown t h a t ( i ) a s l i g h t i n c r e a s e i n t r a d e from t h e no t r a d e

p o s i t i o n always i n c r e a s e s producers ' we l f a re ; ( i i ] provided t h e e l a s t i c i t y i s

1 n o t too l a r g e , a s l i g h t r e s t r i c t i o n on t r a d e from t h e f r e e t r a d e p o s i t i o n a l s o I i n c r e a s e s producers ' wel fa re . I

I Ths e f f e c t on consumers is more d i f f i c u l t t o ana lyze . There a r e now I t h r e e e f f e c t s : ( i ) t h e r i s k e f f e c t ; a s b e f o r e , opening t r a d e reduces consumer

r i s k ; ( i i ) t h e t r a n s f e r e f f e c t ; because of t h e change I n t h e d i s t r i b u t i o n of 1 I

p r i c e s , mean expend i tu re of consumers i s i n c r e a s e d , which makes them worse 1 o f f ; ( i i i ) t h e a l l o c a t i o n e f f e c t ; because of t h e t r a n s f e r e f f e c t , t he

i

a l l o c a t i o n e f f e c t w i l l be s m a l l e r , and may a c t u a l l y be p o s i t i v e r a t h e r t h a n

n e g a t i v e . S i m i l a r l y , i f t he e l a s t i c i t y of demand is less than u n i t y t h e

I r educ t ion i s p r i c e v a r i a b i l i t y reduces producers ' mean income, and, i f t h e

e l a s t i c i t y is g r e a t e r than 0.5, opening t r a d e i n c r e a s e s t h e v a r i a b i l i t y of

t h e i r income. Thus, producers a r e unambiguously worse o f f . Again, t h e

e f f e c t s on consumers a r e more complicated: now t h e t r a n s f e r e f f e c t is

p o s i t i v e , bu t t h e a l l o c a t i o n e f f e c t i s l a r g e r . Thus t h e r e a r e a l a r g e v a r i e t y

of p o s s i b l e p a t t e r n s .

I f t h e p r i c e e l a s t t c i t y is very sma l l (less than 0 .5) , then pre- t rade e I r

income v a r i a b i l i t y is g r e a t e r than pos t- t rade Income v a r i a b i l i t y , i n which

r - c n Fl-n n - n - l r v n F +rq?a -?v hn D + ~ y r ~ t r , c ~ : ~ ~ r f q ~ OVP- q* t h r , - ~ + d i r e c t

'3 C compensation schemes. - - C

For e l a a i c i t i e s of demand near u n i t y , however, t h e q u a r n t a t i v e I R

p r o p e r t i e s remain unaf fec ted : f r e e t r a d e may be Pa re to i n f e r i o r t o no t r a d e ,

provided fa rmers a r e s u f f i c i e n t l y r i s k a v e r s e ; i f t he e l a s t i c i t y i s g r e a t e r

than u n i t y , a s l i g h t l i b e r a l i z a t i o n of t r a d e from the no t r a d e p o s i t i o n i s

P a r e t o improving; i f t he e l a s t i c i t y i s l e s s than u n i t y , prqducers a r e s t r i c t l y

worse o f f ; a s l i g h t r e s t r i c t i o n on t r a d e from t h e f r e e t r a d e p o s i t i o n i s

P a r e t o improving provided producers a r e s u f f i c i e n t l y r i s k ave r se .

C. The Theory of Coioparative Advantage

S p e c i a l i s t s i n t r a d i t i o n a l t r a d e theory have, on a number of

occas ions , expressed a n uneas iness with our a n a l y s i s , on t h e grounds t h a t i t 1 appea r s t o ignore t h e p r i n c i p l e of ccmparat ive advantage which u n d e r l i e s

convent ional t r a d e theory. Note t h a t t h i s i s n o t q u i t e c o r r e c t . Although

t h e r e i s no long run comparative advantage, each of t he c o u n t r i e s having I

p r e c i s e l y the same endowments and t a s t e s , every per iod t h e r e i s a s i g n i f i c a n t

comparative advantage, depending simply on the vea ther . I

This , i n f a c t , we would c l a im is one of the a t t r a c t i v e f e a t u r e s of l

o u r a n a l y s i s : There i s cons ide rab le evidence t h a t much t r a d e cannot be

expla ined s o l e l y on t h e b a s i s of f a c t o r endowments o r t a s t e s . It seems,

according:;, d e s i r a b l e t o exp lo re models i n which t h e r e i s t r a d e without long

22/ run comparative advantage. - We can, none the le s s , e a s i l y inco rpora t e elements of t r a d i t i o n a l

comparative advantage theory w i t h i n our framework. Although we l e a v e t h e

formal development of such s y n t h e s i s t o another occas ion , b r i e f l y

show how i t may be done. Assume, f o r s i m p l i c i t y , t h a t t h e r e a r e two f a c t o r s ,

sav c a n i t 2 1 a n d I z h o r , 44s71me, t h a t t h o s ~ f e r t -nn !g 1 l h n r f n t ~ - $ ? . r o ?r

s i m p l i c i t y , l e t us assume t h a t t h e two c o u n t r i e s have the same f a c t o r - endowments. Clear ly , t h e r e is a g a i n no ion@ run comparative advantage. We

I

can ask , however, what happens a s a r e s u l t of t h e opening up t o t r a d e . Our

previous a n a l y s i s a p p l i e s almost i d e n t i c a l l y , except now farmers do not f ace a

s t r a i g h t l i n e product ion p o s s i b i l i t i e s schedule , but f a c e a concave product ion

- 3 1 - ,

? o s s i b i l i t i e s schedule . It i s s t i l l t r u e , however, t h a t t h e opening up of

t r a d e w i l l l e ad t o an i n c r e a s e i n t h e product ion o f t h e s a f e c r o p ( i n t h i s

I I case labor)*

Pssume, now, t h a t t h e two c o u n t r i e s have s l i g h t l y d i f f e r e n t

f a c t o r endowments. There w i l l now be two e f f e c t s : i n t h e absence of r i s k ,

t h e opening up of t r a d e w i l l l e a d t o t h e e q u a l i z a t i o n of f a c t o r p r i c e s , a. I

d e c r e a s e i n t h e p r i c e of l a b o r i n one coun t ry , and an i n c r e a s e i n i t s p r i c e i n

1 t h e o the r . Now, however, t h e r e i s an a d d i t i o n a l r i s k e f f e c t , which w i l l tend

t o s h i f t p roduct ion toward t h e s a f e c r o p (more, presumably, i n t h e coun t ry

which has a comparative advantage i n i t s product ion) . This e f f e c t may

I outweigh t h e f i r s t e f f e c t , so t h a t , s t i l l , t h e p r i c e of l a b o r i n bo th 1. c o u n t r i e s rises; it i s even p o s s i b l e t h a t f a c t o r p r i c e d i f f ~ i e n t i a l s widen.

-. IV. Concluding Remarks

T h e r e is an argument, popular w i th economists , t h a t i f n a r k e t s a r e

compet i t ive and a g e n t s we l l informed, then government i n t e r v e n t i o n w i l l l e a d

t o i n e f f i c i e n c y . Th i s argument h a s been used both t o a rgue a g a i n s t

r e s t r i c t i o n s on t r a d e and a g a i n s t t h e e s t ab l i shmen t of i n t e r n a t i o n a l b u f f e r

Our a n a l y s i s q u e s t i o n s t h e premises of t h i s reasoning. W e show t h a t I e &

t h e r e i s no presumption t h a t f r e e markets w i l l be P a r c t o opt imal . But o u r

- a n a l v s i s i s no t s i m ~ l v nceatfve. W e ~ r o v i d e a framewotk which e n a b l e s , i n Eny

" s f t u a t i o n , a d e t a i l e d e v a l u a t i o n t o be made of whether t r a d e l i b e r a l i z a t i o n * * - !,(or a commodity b u f f e r s tock ) w i l l be a Pa re to improvement. Our m a l y s i s - .

sugges t s t h a t , under some q u i t e ~ l a u s i b l e c o n d i t i o n s , i t i s d e s i r a b l e f o r t h e

government not on ly n o t t o i n t r o d u c e a b u f f e r s t o c k , but a c t u a l l y t o r e s t r i c t

t h e a r b i t r a g e a c t i v i t i e s of s p e c u l a t o r s . Our a n a l y s i s a l s o shows t h a t some

trade restrictions may 5e desirable in the presence qf+&m~erfectly correlated

risk.

Our analysis has, quite obviously, left out all considerations of the

political processes by which trade policy becomes determined. Though the

greater effectiveness of quotas in reducing producer uncertainty, which we

established in Section 11, may provide part of the explanation of the seeming

preference of many trade associations for quotas over tariffs, there is little

to suggest W a t present trade barriers are chosen with the considerations we

have raised in mind. What our analysis does explain, however, is why the

simplistic arguments for free trade, making use of tkz competitive paradigm,

with all of its assumptions, inchding that of a complete set of risk markets,

are often far from persuasive.

FOOTNOTES

11 Elsewhere (Newbery and S t i g l i t z [1982a]) we have demonstrated t h e - i n e f f i c i e n c y (except under ve ry s t r i n g e n t c o n d i t i o n s ) o f c o m p e t i t i v e

- ( i . e . , f r e e t r a d e ) e q u i l i b r i a f o r a more g e n e r a l model. The r e s u l t t h a t

t h e r e e x i s t s some i n t e r v e n t i o n t o t h e f r e e t r a d e e q u i l i b r i u m d e r i v e d i n

t h e p re sen t paper is r o b u s t , and would con t inue t o apply i n more g e n e r a l

models.

2 1 Thus, i f i n d i v i d u a l s a r e a l l i d e n t i c a l , t h e changes i n p r i c e d i s t r i b u t i o n - which a r e c e n t r a l t o ou r a n a l y s i s have no we l f a re consequences.

31 For a n e x t e n s i v e survey of t h e recenc l i t e r a t u r e on t r a d e and u n c e r t a i n t y , - see Pomery (1979). .bong t h e s t u d i e s focus ing on t h e sma l l coun t ry c a s e

wi th t h e p r i c e d i s t r i b u t i o n g iven exogenously a r e t hose of Bat ra and

Russe l l (1975) and Ruff in (1974). The Bat ra and R u s s e l l and RuZfin papers I

a l s o assumed producers had no o u t p u t v a r i a b r l i t y whereas t h e t e l a t i o n s h i p

between t h e v a r i a b i l i t y of ou tpu t and p r i c e s plays a c r u c i a l r o l e i n ou r

a n a l y s i s .

41 Even when t h e r e a r e p e r f e c t e q u i t i e s markets , t he assumption of i d e n t i c a l - consumers i s c r u c i a l . S t i g l i t z (1982) has shown, f o r i n s t a n c e , t h a t w h i l e

m . Q

t h e s tock market equ?.librium wi th m u l t i p l i c a t i v e u n c e r t a i n t y and two

comrnbdities is always a c o n s t r a i n e d Pa re to optimum wi th I d e n t i c a l

consumers, i t e s s e n t i a l l v never is i f co%sumers d i f f e r , e i t h e r i n t h e i r - iC pre fe rences f o r goods o r t h e i r a t t i tudes ' towards r i s k .

Jr I m

5 1 An i n e s s e n t i a l s i m p l i f i c a t i o n of t h i s a n a l y s i s is t h a t producers do no t - - consume what they produce; t h e i r we l f a re depends on ly on what t hey o h t a r n

from s e l l i n g t h e i r c rops .

6 / I n ou r s imple model, s i n c e t h e on ly sou rce ?f p r i c e v a r i a b i l i t y is supply - v a r i a b i l i t y , p r i c e w i l l b e a d e t e r m i n i s t i c f u n c t i o n of 0 ; i n more g e n e r a l

models, i t would be a s t o c h a s t i c func t ion .

7-1 I i s t h e consumer's endowment o f a t h i r d good (o r a Yicks ian composi te - commodity, r e p r e s e n t i n g a l l o t h e r goods) , which is taken t o be t h e

numeraire.

8/ See Samuelson (19421. - 1 - 9 / For o@$g::uEEttO%ty -....T_ - -- f u n c t i o n s ~ 7 & , ~ ~ m c o _ m e QS. f anne r s "M1.1 f n c r e a s e o r

dec rease a s a r e s u l t of t h e opening of t r a d e . See S e c t i o n I I 1 . B below.

10/ The d o l l a r va lue of t h e loss from t h e randomness i n 8 is apoproximately - a 2 - a . I n t h e cae of c o n s t a n t r e l a t i v e r i s k ave r s ion n o t e q u a l l i n g u n i t y 2

""5

The d o l l a r va lue of t h e l o s s from r i s k i s then approximate ly

1 I a ( 1 - a ( 1 - p ) } a2 which ag rees w i th t h e l o g a r i t h m i c case f o t p = I .

11/ This r u l e s o u t t h e conven t iona l reasons f o r t r a d e and a l l o w s u s t o - concen t r a t e o n ' t h e r i s k a s p e c t a lone , Regions have a compara t ive

advantange i n weather a lone i n t h i s model. Obviously, t h i s heav i ly

4 . I

q u a l i f i e s any po l i cy conc lus ions which might be drawn from the s tudy . See

a l s o 1 I I . C below.

121 Since by and R E - n ~ " ( n ) / U ' ( n ) , - M E U'[aO + b ) y l ( $ ~ --I, 1-x

X 1-x a 2 ~ < 0 . w i l l t ~ e smal l , s o- I f t h e range of 0 ts sma l l , - - - ao

can be weakened.

131 A q u a n t i t a t i v e e s t i m a t e of t h e i r w e l f a r e l o s s expressed a s a percentage of - mean income i s provided by Taylor S e r i e s approximation:

1 4 / S t a b i l i t y must be de f ined r e l a t i v e t o a p a r t i c u l a r ad jus tment p roces s , - which is d i scussed i n s e c t i o n 1 . G below.

151 D e t a i l s a v a i l a b l e from Newbery on r e q u e s t . - *

161 The c o n d i t i d n s r equ i r ed f o r t h i s t o be t r u e a r e d i scussed i n Newbery and - S t i g l i t z (1981). -

1 7 / There may, of cou r se , e x i s t a l t e r n a t i v e p o l i c i e s whi'ch c o n s t i t u t e a P a r e t o J - B - 9

iaprovement, t h e most obvious of wh$h is t h e opening of a d d i t i o n a l C

I rr .I i n su rance markets.

-

18/ The e f f e c t of a smal l change i n po l f cy can be found by d i f f e r e n t i a t i n g - t o t a l l y w i th r e s p e c t t o z. where z = 0 corresponds t o a u t a r k y ( t = 0) and

z = 1 corresponds t o f r e e t r a d e . The e f f e c t on producer 's w e l f a r e i s , .

from (28)

~ E U = acu ax - EU, ~ D { Q ( s ) , 21 dz F E d z

The f i r s t term is z e r o by t h e envelope theorem, w h i l s t t h e second i s b e s t

cons idered by t a k i n g sums of paLrs of s t a t e s , s, s': ?

us ing symmetry, which, by t h e mean va lue theorem i s , f o r some l e v e l o f

, I

p r o f i t s n* ,

A t t - 0, D = 0, and t h e r e i s ( l o c a l l y ) no e f f e c t on producers ' w e l f a r e ,

o the rwi se t r a d e liberalization is harmful.

19/ From ('31) o -

20/ We could have formulated t h e problem l e t t i n g x be a f u n c t i o n of t ; i t i s - s i m p l e r , however, i f we l e t x be a c o n t r o l v a r i a b l e and a d j o i n t h e

c o n s t r a i n t .

21/ B r a z i l i a n c o f f e e growers do n o t a s a r u l e own s h a r e s i n Kenyan c o f f e e - farms, o r converse ly . Although we have n o t expla ined t h i s ebsence o f

p e r f e c t r i s k markets , i t would no t be d i f f i c u l t t o c o n s t r u c t a model which

i s c o n s i s t e n t with our a n a l y s i s and which would st t h e same time have t h e

p rope r ty t h a t t h e r e i s imper fec t r i s k s t lar ing. See, f o r i n s t a n c e , k n o t t

and S t i g l i t z (1951 ).

22/ Of course , t h e r e a r e a t h e r p o s s i b l e models, emphasizing economies of s c a l e - and monopo l i s t i c compet f t ion ; aga in , i n such models, opening t r a d e need

> . no t be P a r e t o improving.

23 / The p a r a l l e l between t h e opening of t r a d e b e t ~ e e n two c o u n t r i e s and t h e - opening of t r a d e between two d a t e s should be obvious. Our a n a l y s i s

imp l i e s t h a t a b u f f e r s t o c k t h a t p e r f e c t l y s t a b i l i z e s p r i c e s (correspond-

i n g t o f r e e t r a d e ) may be P a r e t o i n f e r i o r t o having no b u f f e r s tock . Oclr

a n a l y s i s s u g g e s t s t h a t , i n t h e absence of a complete set of s e c u r i t i e s

markets, che market may g e n e r a t e an e x c e s s i v e amount of i n t e r t e m p o r a l

REFERENCES

Ba t ra , R. N. and R u s s e l l , W. R. (1974) "Gains from Trade TJnder Uncer ta in ty ," American Economic Review, - 64, (6) 1040-45.

Bat ra , R. N. (1975) "Product ion Unce r t a in ty and t h e Heckscher-Ohlin Tineorem," Review of Economic S t u d i e s , - 62, 259-2158.

i Dasgupta, P. and S t i g l i t z , J. E. (1977) " T a r i f f s vs. Quotas a s Revenue- Raising Devices under Urrcertainty," American Economic Review, - 67, 975-951,

Diamond, P. A. and S t i g l i t z , .!. E. (1974) " Increases i n Qisk and Risk version," J o u r n a l of Economic Theory, - 5 , 337-3613.

F ishe lson , G. and F l a t t e r s , F. (1975) "The (Non-) Equivalence of Optimal T a r i f f s and Quotas under TJncertainty," Jou rna l of I n t e r n a t i o n a l Economics, 5 , 385-3930 -

Helpman, E. and k z i n , A. (1978) "Uncertainty and I n t e r n a t i o n a l Trade i n t h e Presence of S t

. , - - " L - - "*A< ~ 4 , ~ " A ~ ~ z ~ , " * - - a - \ ~ -

Helpman, E. and R a Goods. and Secu

tielpman, E. and Razin, A. (1978) A Theory of I n t e r n a t i o n a l Trade Under Uncertafnty. - -

Helpman, E. and Razin, A. (1980) "P ro tec t ion and Uncer ta in ty ," 4mekican Economic Revizw, - 7 J , 4 , 716-731.

Newbery, D. M. G. and S t i g l i t z , J. E. (1977) The Economic Impact of Commodity P r i c e S t a b i l i z a t i o n -9 USAID, Washington, D.C.

Newbery, D. M. G. and S t i g l i t z , J. E. (1981) The Economic Impact of Commodity - P r t c e S t a b i l i z a t i o n , Oxford Un ive r s i ty P res s .

,,& *<., *-.c ..- +s!* -: p+-$?p&yc-'+i,; --&;;,2~L +g+5.L*~&*k+e~ees i: &id , .; - - . . . - . . . Newbery,-D. M. G. and ~ t i @ W z , * ~ . -. ... a''

t h e 8 p t i m a l i t y of Market Equil ibr ium wi th Rat ional Expecta t ions ," J o u r n a l of P o l i t i c a l Economy, 90 (2) , 222-246.

I - \ T ' . - 7 - - - - 1 7 : -, - - , - - . - . - - . :* . * -

, -: ? - ,- --- -. - I '7 - 1 I

Response, and t h e Op t ima l i ty of Randdm Pr i ces : A Diag~ammat ic Ar,alysis," - Q u a r t e r l y Journa l of Eco.--.-mics, X C V I I (11, 1-26.

11

r Newbery, D. d. G. and S t i g l i t z , J. E. ( 1 B 2 c ) "Pare to I n f e r i o r Trade and

I Optimal Trade Pol icy ," Econometric Re-search Program Memorandum No. 281, I P r ince ton .

b P e l c o v i t s , M. G. (1976) "Quotas vs. T a r i f f s , " J o u r n a l of I n t e r n a t i o n a l Economics, - 6 , 363-370.

.plL

porner:., J. (1979) " Unce r t a in ty and I n t e r n a t ioni l l Trade," Chapter 4 of ~o;nbusch and Frankel , I n t e r n a t i o n a l Economic Pol icy .

Ro thsch i ld , M. and S t f g l i t z , J. 3. (1970) " Inc reas ing Risk I: A D e f i n i t i o n , " J o u r n a l o f Economic Theory, - 2, 225-43.

Ruf f in , R. J. (1974) " I n t e r n a t i o n a l Trade under Uncer ta in ty ," Journa l -. of I n t e r n a t i o n a l Econcmics, - 4 , 243-259. .

Ruf f in , R. J. (1974) "Comparati.ve Advantage under Uncer ta in ty ," J o u r n a l of I n t e r n a t i o n a l Economics, - 4 , 261-273.

Samuelson, P, A. (1942) "Constancy of t h e ?farginas U t i l i t y of Income," r e p r i n t e d i n Col lec ted S c i e n t i f i c Paper.!, Vol. 1, 37-53.

S t i g l i t z , J . E, (1969) "Behavior Towards Risk wi th Many Commodities," Econometrica, 660-667.

S t i g l . i t z , .J. E. (1972) "Taxat ion, Risk Taking and t h e A l l o c a t i o n of Investment i n a Risky Zconomy," M, C. Jensen (ed.) - S t u d i e s i n t h e Theory of C a p t t a l Xarke ts , New York.

S t i g l i t z , .T. E, (1992), "The I n e f f i c i e n c y of t h e Stock Market Equil;.brium," Review of Economic S t u d i e s , - XLIX(2), 241-

Turnovsky, S . 5. (1974) "Technological and P r i c e Unce r t a in ty i n a R i c a r d i a n Model of I n t e r n a t i o n a l Trade," Review of Economic S t u d i e s , 4 0 , 201-217. -

Young, 5. (1979) "Optimal Revenue-Raising Trade R e s t r i c t i o n s under Uncer ta ln ty ," J o u r n a l of I n t e r n a t i o n a l Economics.

Young, L. (1980) " T a r i f f s vs. Quotas under Uncer ta in ty : An Extension," American Economic Review, 70 - -

Young, L. and Arderson, J. E. (1980) "The Optimal P o l i c i e s f o r Restricting Trade Under Unce r t a in ty , " Review of Economic S t u d i e s , XLVI, 927-932.

C

Wellarc

-

. .

Autarky Level or trade Free trade

Fi4ure 1: Welfare Consequences of Opening Trade