!Jorld Bank

D e v e l o p ~ t n t Research Cen t e r

D i scus s ion Tapers

No. 32

COMMODITY PRICE STALBILIZATION

I N IMPERFECTLY COMPETITIVE N E T S

David 11. Nevbery k'orld Bank

Note: D i scus s ion Papers are p r e l im ina ry m a t e r i a l s c i r c b l a t e a t o s t f d a t e - d i s c u s s i o n and c r i t i c a l comrent. g e f e r e n c e s i n pub l i c ap ion t o Discussfcm Papers shou ld be c l e a r e d w i t h t h e a u t h o r s t o p r o t e c t t h b tentative c h a r a c t e r of t h e s e pape r s . The papers e x p r e s s t h e v i e v s of t h e a u t h a x s a d should n o t be f n t e r p r e t e d t o ref l e c t t h o s e af che world Bank.

Paper p repared f o r t h e December z \ g r i c u l t u r a l Trade c o n s i r t i u s Xee t i ng , Claremont Resor t Ho te l , Berke ley , C a l i f o r n i a , Dec. 12-18, 1981

I

Sess ion L: Xarket S t r u c t u r e and S t a b i l i z a t i o n P o l i c i e s ~ I I

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

CG!-EODI'iY PRICE STA3ILIZXTION I N IYPEwECTLY

David X. Sewbery

I , -

1. Int roduct ion I

I

I n Sewbery 2nd S t i g l i t z (1981a), we developed a r easona i ly compre-ive

a n a l y s i s of commodity p r i c e s t a b i l i z a t i o n on t h e assumption t h a t both p r o h c e z s l

and consumers were p r i c e t ake r s . W e recognized t h a t t r a d e i n G n y commodirles I

e c t t o a v a r i e t y of d i s t o r t i o n a r y i n t e r v e n t i o n s , such a s : t a r i f f s , I

quotas , domestic s u b s i d i e s , acreage r e s t r i c t i o n s and t h e l i k e , qnd a n a l y s d I I

t h e impact of i n t e r n a t i o n a l commodity p r i c e - s t a b i l i z a t i o n i n a d i s t o r t e d worLd I

economy (Newbery and S t i g l i t z , 1981a. Ch. 19, pp 272-83). I!owe\ier, our ,

a n a l p i s of d i s t o r t e d markets assuned t h a t the s t r u c t u r e of prodect ion and- , I

d i s t o r t i o n would not be a f f e c t e d by i n t e r n a t i o n a l p r i c e s t a b i l i z i a t i o n , v h L l s t I

i n d i v i d u a l producers and consumers remained p r i c e t a k e r s wi th in ! t h i s d i s t o r t e d

I framework. In s h o r t , governments were not assuned t o be in t e rvep ing t o

I

e x e r c i s e i n t r r n a t i o n a l market power, and hence would have no reaeon t o chapge I

t he p a t t e r n of interventj .on i n response t o changes i n t h e world h r k e t . I

Clear ly i t wouid be d e s i r a b l e t o t r y and extend the ana$ys is of e tY , . @ I

p r x e s t a b i l i z a t i o n t o d e a l with imperfec t ly compet i t ive comodi$y markets, I

- A t l e a s t some c o u n t r i e s have a s u f f i c i e n t l y high s h a r e of world drade i n s p e s z t f f c - - I

I 'f commodities t o g ive then some market power. I 1 -

Table 1: Shares of i n d i v i d u a l c o r n t r i e s i n world t r a d e o f commodities, Averages 1977-79

Country Product Percentage

Sangladesh

Yalays ia

Coconut O i l

J u t e

Palm O i l

Argentina Linseed O i l 62 I 1

>-us t r a l i a Fool (greasy)

Yalays ia Copra I I 55 I Va1ay.s ia Rubber 5 1 1 I

USA A l l Cerea ls

Sf sal B r a z i l I I L'2 I

USA \ h e a t I I 39 I

?!al~jrs ia T in I 3 6

Vfrocco Phosphate Rock i 34

Senegal I

Ground n u t O i l ~ 29 I

USA Cotton I 29

Tanzania S i s a l 28

I n d i a Tea 27

O i l 1

Saudi Arabia I 26 I

Guinea Bauxite 1 25

Canada Barley I . e . I 2 5

Ciiba Sugar 2 5

- - .* I I

Sources: Conmodit? Trade and P r i c e Trends. World Bank 1981 ~ FA0 Tra* Yearbook 1979 I 1

s I I .. I I I

I

I

I

I

I I I ' I

The ~ o p u l a r example today would no doubt he OPEC o i l , though i t i s

d i f f i c u l t t o d e t e r d n e how f a r OPEC's market power i s exerc ised by a w e l l

coordina ted c a r t e l , o r s u b c o a l i t i o n , o r how f a r it depends on t h e a c t i o n s of

t h e l a r g e s t zenber , Saudia Arabia. Before 1973, t h e examples which 3 i g h t have

sprung t o mind were B r a z i l i a n c o f f e e o r Indian t e a . Table 1 l is ts c o u n t r i e s

wnicn had Eore than 252 of world t r a d e i n a given corrmodity on average over

1973-79. I n t e r e s t i n g l y , B r a z i l i a n c o f f e e does no t appear (only 472), w h i l s t

Saudi o i l is 262, nea r t h e cut- off po in t on t h e l i s t . Of courseq t r z d e s h a r e s I

i n s p e c i f i c commodities a r e an imperfec t measure of market power; which depends I I

on e l a s t i c i t i e s of demand and r e s t of world supply, as w e l l a s tde e x t e n t of I

d o n e s t i c product ion and t r a n s p o r t c o s t s , bo th of which d e f i n e the/ s i t e of t h e rc!evant

n a r k e t . Amongst t h e vege tab le o i l s s u b s t i t u t i o n p o s s i l r i l i t i e s w q l l c l e a r l y I

l i m i t t h e e x e r c i s e of m r k e t power, w h i l s t s:.nthetic s c b s t i t u t e s i l ikewise I I

c o n s t r a i n t h e f i b r e and rubber markets. On t h e o t h e r hand, t r a d s p o r t c o s t s

zay mke r eg iona l m r k e t s =ore r e l e v a n t than t h e vho le uo r ld oarket f o r some I I

commodities w h i l s t a given coun t ry ' s comnodity may b e suf f i c i e n t l b d i f f e r e n t i a t e d I I

from grades suppl ied by o t h e r c o u n t r i e s t h a t t h e coun t ry czn e x e r k i s e sorce I

market power d e s p i t e i t s low o v e r a l l market sha re , S e x e r t h e l e s s , ~ d e s p i t e I

a l l t h e s e q u a l i f i c a t i o n s , i t seems reasonable t o conclude t h a t soke c o u n t r i e s I

(o r c a r t e l s of c o u n t r i e s ) have some market power i n some c o m o d i t ~ markets , l

and t h a t it is &herefore worth enqui r ing how t h i s market power IafFects t h e

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

The paper i s organised a s fo l lows. s e c t i o n 2 ' ?

of t h e case f o r i n t e r n a t i o n a l p r i c e s t a b i l i z a t i ~ n i n - - m 1, . m

*

I I

I

summarises f he a n a l y s i s

d i s t o r t e d n h r k e t s

I

I "

r e f e r r e d t o above i n t h e f i rs t 2aragraph. Xost d i s t o r t i o n s a r e probably

2 o t designed t o e x e r c i s e z a r k e t power, y e t c l e a r l y have an Imyact on t h e

= rZe t , and hence on c5e case f o r s t a b i l i z a t i o n . The remainder of t h e I

paper s t u d i e s t h e c a s e i n which a producer e x e r c i s e s d e l i b e r a r e m r k e t

?over . In s e c t i o n 3 t h e va r ious ques t ions t h i s r a i s e s a r e posed, ,

2nd then answered i n t h e remaining s e c t i o n s . S e c t i o n 4 conpuies t h e I ,

. .

o p t i n m s tock ing r u l e f o r a nonopo l i s t and compares i t wi th t l ie . . . '. I

I

c o o p e t i t i v e r u l e , a s k i n g wnether he w i l l under take more o r l e s l s I

. -

agency on an imper fec t ly compet i t ive market.

2 . Do Yarket Imperfect ions Strengthen the Case For Comnodity ? r i c e S:cbi l izat ion?

I n solce cocnod i t i e s , -;,c,bLy r 'oodstuffs, i n t e r ~ a t i o n a l t r a d e i s I

s u b j e c t t o a v a r i e i y of d i s t 0 r t i . c ~ a r y i n t e r ~ e n t i o n s . (See, e.g. 3 a l e and I

I

Lurz, 1981; Lutz and S c a n d i z ~ o , 1980.) These t y p i c a l l y emerge h e n l o c a l I

producers f ind thease lves i n competition wi th i a p o r t s , and a r e $ u a n t i t i v e l y ,

i s p o r t a n t f o r sugar , c e r e a l s , r i c e , and, t o a l e s s e r e x t e n t , n e a t and Ca i ry I I

products . In most cases , i t is d i f f i c u l t t o argue t h a t these & l i c i e s I

b e n e f i t t h e importing country a s a whole, f o r , wi th t h e no tab le : exceptfon of t h e

U. S . , t h e c o u n t r i e s imposing the r e s t r i c t i o n s a r e small r e l a t i v k t o world I

t r a d e i n the commodity. (Arguably, t h e EEC i s t h e o t h e r main eSception,

thoug* i t seeas u n l i k e l y t h a t t h e main motive f o r t h e Comwn ~ ~ i i c u l t u r a l

Pol icy was t o inprove t h e E X ' S t e r n of t.rade, thought t h i s ma4 w e l l be one I I

of i t s consequences.) I f t h f s a n a l y s i s i s accepted ( f o r sone ~ { m n o d i t i e s , and , I

some c o m t r i e s ) then t h e market d i s t o r t i o n s a r e not evidence of b r k e t power.

l

and i t i s poss ib le t o r e t a i n the s impl i fy ing assumption t h a t proiducers and I

consumers a r e p r i c e t a k e r s , though t h e p r i c e s they f a c e w i l l no (longer b e I

uniform throughout t h e market. Xuch of t h e convent ional a n a l y t G s of p r i c e I

s t a b i l i z a t i o n theory w i l l s t i l l apply , though t h e d i s t o r t i o n s inkroduce I I

a d d i t i o n a l complicat ions, e s p e c i a l l y f o r t h e we l fa re a n a l y s i s . Zn, t h i s . I I

s e c t i o n w e a s k whether t h e presence of t r a d e d i s t o r t i o n s increashs o r I

reduces the amount of p r i c e s t a b i l i z a t i o n which is d e s i r a b l e ccm&xed t o 1 .

t h a t d e s i r a b l e i n an undis tor ted raarket. I - I I

To t h e e x t e n t t h a t domestic p r i c e support Programmes a n d ) s l i d i n g - . I

s c a l e tariffs a r e designed t o s t a b l i z e dones t i c p r i c e s , d i s t o r t i d n s m y

a l r eady have reaped many of the p o t e n t i a l b e n e f i t s of p r i c e s t s b i l i z a t i o n ,

2nd 3ence wezken t h e case f o r a d d i t i o n a l b u f f e r s t o c k schemes. Howevsr, t h e r e .-

a r e s e v e r a l , a d n i t t e d l y c a s u a l , arguments which sugges t t h a t d i s t o r t i o n s ray

s t r eng then t h e case f o r ? r i c e s t a b i l i z a t i o n , though l i t t l e t h e d r e t i c a l work

has been done t o zake these arguments p rec i se . I I 1

P r i c e s t a b i l i z a t i o n usy genera te l a r g e r b e n e f i t s i n t h 4 presence o f I

I

t r a d e d i s t o r t i o n s than in t h e i r cbsence f o r four q u i t e d i f f e r e n t r easons :

( i ) It is o f t e n argued t h a t world and d o n e s t i c p r i c e s Ars rcore v o l a t i l e

i n t h e presence of t r a d e r e s t r i c t i o n s than i n t h e i r absence, add less u s e is oade I I

cF t h e r i sk- sha r ing a s p e c t s of i n t e r n a t i o n a l t rade . If s t a b i l i i r a t i o n is I

denirabl ; under f r e e t r a d e then t h e g r e a t e r i n s t a b i l i t y under + s t r i c t a d I

t r a d e makes i t even mre d e s i r a b l e . Between 1972 m d 1974 t h e IS wholesa le I

g r a i n p r i c e ;nore than t r i p l e d , whi le i n t h e EEC i t r o s e by 20 pbr c e n t , and i n I

t h e USSR i t appa ren t ly remained unchanged. Johnson (1975) argubs t h a t t h e inter- I I

n a t i o n a l market could have absorbed t h e m d e s t world p r o d u c t i o n s h o r t f z l l s with

only modest p r i c e i n c r e a s e s , bu t because t h e s h o r t f a l l s were on y shared by

p a r t of t h e world a a r k e t t h e p r i c e i n s t a b i l i t y w a s s eve re .

1 1

A t t h i s p o i n t , it should be s t r e s s e d t h a t t h e l i n k berwden t r a d e I

r e s t r i c t i o n s , market fragmentat ion, and p r i c e v o l a t i l i t y is no t i s imple , and I

many types of t r a d e po l i cy may a c t u a l l y reduce p r i c e v o l a t i l i t y / a s w e show

below. Another apparent source of market fragmentat ion is vhen m c h of t h e . a I

t r a d e is so ld on long- term f ixed- pr ice c o n t r a c t s , w i th a srnalled f r a c t i o n sold

on t h e spo t market. The c r u c i a l determinant o f t h e v o l a t i l i t y df t h e s p o t - .a I

ca rkee is then t h e e x t e n t t o which consumption d e c i s i o n s a r e gudded by the_

w s p o t &=her o r t h e long-tern c o n t r a c t p r i ce . I f c o n s m e r s a r e i , i l l i n g t o . m

r e s e l l on the spo t m r k e t vhen t h e spo t p r i c e is h igh , and buy wben t h e p r i c e

is low, then t h e long- t t? rs c o n t r a c t i s equiva lent t o hedging on a f u t u r e s

r ia rks t , wi th a l l t r a d e e f f e c t i v e l y passing through t h e s p o t market. I n

such cases t h e a c t u a l volume of s p o t t r a d e is a poor guide t o t h e e f f e c t i v e

volurie which d e t e d n e s t h e p r i c e and i t s v o l a t i l i t y . While perhaps n o t so I

i z p o r t a n t f o r a g r i c u l t u r a l c o m o d i t i e s (except f o r b i l a t e r a l t i a d e ) , scch

c o n t r a c t s are pervas ive f o r many n i n e r a l s . 1 I

I

( i i ) ? t has been argued t h a t p r i v a t e s p e c u l a t o r s a r e lgss w i l l i n g to

s t o c k p i l e and reduce p r i c e f l u c t u a t i o n s i n t h e presence of p a r i e t d i s t o r t i o n s

I

(FAO, 1975; Gray, 1960). The argument is' t h a t i n such markets ! s p e c u l a t o r s have I

t o f o r e c a s t t h e a c t i o n s of governments who have taken r e s p o n s i t / i l i t y f o r I I

r e g u l a t i n g t h e markets. m e r e is an important and unresolved ques t ion a s t o I I

how specu la to r s would r e a c t t o t h e presence of a g e n t s wi th conSiderable market I I

power, such a s governments f i x i n g t a r i f f s o r exchange r a t e s t o b e n e f i t t h e

d o a e s t i c economy. A s i m i l a r i s s u e a r i s e s i n f o r e i g n exchange G r k e t s when I

Cent ra l Banks engage i n ' p n a g e d ' o r 'dirty f&a.cing. ~ ~ e c ~ l d f ~ r s may. b e l i e v e . - - ----- , f--,-. ?.,-----. - 7--

> . - - - , < - - ? - ? - 7 " . . - . - . - I

t h a t t h i s market power w i l l be used t o nan ipu la t e t h e market i n ( such a way I

a s t o genera te p r o f i t s f o r t h e in t e rven ing a u t h o r i t y a t t h e exp(ense of t h e I

s p e c u l a t o r s ( c f . Hart, 1977). I f s o , t h e s p e c u l a t o r s w i l l be lLso w i l l i n g t o I

undertake s t a b i l i z i n g s p e c u l a t i o n , and t h e r e w i l l be i n s u f f i c i e b t s t a b i l i z a - I I t i o n , and a d d i t i o n a l p r i c e s t a b i l i ~ a t i o n is needed, which wouldlnot be r e q u i r e d I

i n a conipetit ive market. This second aigubent is mainly about Gho G i l l have 1

t o do t h e s t a b i l i z a t i o n , o r how nuch s t a b i l i n t i o n is needed, r h t h e r than I - I

about t h e b e n e f i t s of t h e s g b i l i z a t i o n . * I

I

( i i i ) I f t h e t o t a l ypr ld consumption of commodities s u b j e c t t o

* I I

d i s t o r t i o n is increased, then t h e r e is zn a d d i t i o n a l ga in (equa: t o a r e d u c t i o n I

i n t h e excess burden of the d i s t o r t i o n ) equal (roughly) t o t h e i n c r e a s e i n

supply m u l t i p l i e d Sy t h e d i f f e r e n c e 3etveen consumer and producer p r i c e . T h i s

j e n e f i t i s an i a p o r t a n t conponint i n cos t- bene f i t s n a l y s i s ( s e e e.g. Boadway,

1974, o r Earberger , 1971). m e argunent is then t h a t p r i c e s t a b ~ i l i z a t i o n I I

induces a ~ o s i t h e supply respcnse which then g e n e r z t e s e x t r a e4ficienc); g a i n s I

(over and above t h o s e r e a l i z e d on compet i t ive r a r k e t s ) . !,%ether! i n f a c t p r i c e I

s t a b i l i z a t i o s l w i l l l e a d t o i nc reased supply is d i scussed i n 3ewbLry and S t i g l i t z I

(1981a, P a r t V) where i t w i l l be s een t h a t t h e znswer i s by no means obvious. I

( i v ) It has been c o s e n t l y a r p e d 0 1975) t h a r i f prike s t a b i l i z a - I

t i o n is achieved by c r e a t i n g b u f f e r stoc: I , then t h i s w i l l p rovibe an impetus

t o h igh ly d e s i r a b l e t r a d e l i b e r a l i z a t i o n . The argunent h e r e is Lhat r e s t r i c t e d I . I

t r a d e =d t h e r e s u l t i n g p r i c e v o l a t i l i t y make both t h e a v a i l a b i l k t y and c o s t 1

of s u p p l i e s so uncertain t o impor t ing c o u n t r i e s t h a t they c r e a t e farm s u p p o r t I

programmes t o ensu re s u p p l i e s , and impose f u r t h e r r e s t r i c t i o n s tb make t h e n I

viab.&e, I f t h e v o r l d p r i c e were s t a b i l i z e d and s u p p l i e s p a r a n t b e d , t h e n these

r e s t r i c t i v e measures would be unnecessary and n i g h t be dismantle+. Even where

t h e o r i g i n a l i n t e r v e n t i o n was i n e f f i c i e n t i t s t r u e c o s t may rema 1 n obscure

u n t i l t h e p r i c e i s s t a D i l i z c d . Once t h e c o s t is e v i d e n t , t h e s o i r c e of t h e I I

i n e f f i c i e n c y might be reaoved. I I

I

This l a s t argument may w e l l be t h e most impor t an t , b u t i d r e q u i r e s

i I . I

a theory of t h e cho ice of t r a d e p o l i c y before i t is p o s s i b l e t o ?ay how . I

i n s t i t u t i o n a l change may a f f e c t t h e s t r u c t u r e of t r a d e d i s t o r t iod. - ::ew'Jery and S t l g l i t z (1981a. Chapter 24), goes soee way'sowards 4, theory of

I .)

t h e ch6 ice of t r a d e p o l i c y under r i s k , and sugges t s tha&countr i{s oay a c t u a l l y s - I

0 I

i nc reace p r o t e c t i o n if world p r i c e s a r e s u c c e s s f u l l y s t a b i l i z e d , (bu t t h i s

i g z o r e s t h e o t h e r reasons f o r t r a d e po l i cy , s p e c i f i c a l l y market power. B u f f e r

s t o c k s by making world d e x n d n o r e e l a s t i c m y r educe o a r k e t pqver and hence

lower rhd upt inun t a r i f f . These i s s u e s ue d i s c u s s f u r t h e r beldw. I

On t h e f a c e of it these arglments s e e n q u i t e persuas ivd , b u t i n t h e I I

zbsence of any f o r a a l model i t is d i f f i c u l t t o see whether t h e iareuoents a r e -

g e n e r a l l y t r u e , t r u e under r e s t r i c t i v e assumptions, o r , i

indeed ,I f a l s e .

Sewbery and S t i g l i t r (1981a, Ch. 19, pp. 276-82) c o n s t r b t a s imp le I

m d e l t o ana lyse t h e f i r s t argument, and . the s ane node l could r)eadi ly be I

extended t o ana lyse t h e t h i r d a r g w e n t . The model h a s l i n e a r dbmand s c h e d u l e s I I

t o p e r n i t c r o s s c o u n t r y aggrega t ion and an a n a l y t i c a l s o l u t i o n lor t h e world I

market c l e a r i n g p r i c e . It ignores supply responses (though l i n k a r supply I

, - " , L-L J+ A " A

I ----.%la$'. - -3

--=fiedules could e a s i v b e inc luded) , d i s t r i b u t i o n a l i s s u e s , a t t b t u d e s t o r i s k ,

and concen t r a t e s on t h e aggrega te e f f i c i e n c y ga ins of s t a b i l i z a I I

presence of d i s t o r t i o n s . I I -- - I I

We f i n d t h a t l i n e a r t r a d e p o l i c i e s ( i n which t h e r e is a i l i n e a r rela- I

I

t i o n s h i p te tween domest ic anL world p r i c e s , a s w i t h t a r i f f s ) do ino t a f f e c t I I

t h e b e n e f i t s o f p r i c e s t a b i l i z a t i o n s i g n i f i c a n t l y , b u t non- l inesr p o l i c i e s - 1

I

do. I n p a r t i c u l a r , i f c o u n t r i e s u s e quotas r a t h e r than t a r i f f s 1 &en even i f I

i they do not change wi th p r i c e s t a b i l i z a t i o n , t h e r e may b e a d d i t o n a l b e n e f i t s

over and above t h e b e n e f i t s conven t iona l ly c a l c u l a r e h (assuming n o d i s t o r t i o n s ) . I

The reason i s t h a t w i th l i n e a r p o l i c i e s t h e average degree of d d s t o r t i o n does - I i

n o t change a s t h e v a r i a b i l i t y of p r i c e s chari;e, b u t w i t h non-l iqear p o l i c i e s '9 a

i t cay be reduced. The l a t t e r r e s u k i s s u f f i c i e n t l y i r l t e r e s t i d g t o bear - I I i

r e p e a t i n g t h e argument contained i n 'Newbery and S t i g l i t z (1981a, Ch. 19, i I

p p . 280-2). I I I i I

I ,

I

I

Suppose that i n every cocn t ry i, demand i s l i n e a r and non- stochas t ic , I

v h i l e s ~ p p l y expe r i ences a d d i t i v e r i s k : I

S e r e pi is t h e d o e e s t i c p r i c e in country 1 and Et is t h e randonness i n supply ,

assllmed uncor re l a t ed wi th o t h e r count r ies 1 randonness , y. . I !

J I ! I

R e s t r i c t i o n s on t r a d e are nodel led a s fo l lows . ~ o ~ e s t f c excess I !

demand f o r imports I I

, . * ~*J.*-&+5a<* .A, . ~ . :.?%.=I- .....;*-.;.. : ,*;..-.,- - .; ..= ... i.-...r%^.-.^.-..,"- . . .. .,

where p is t h e world p r i c e , and ai measurzs t h e deg ree t o whic4 domest ic I

re t ranrmif ted A=-- abroad. Equating (3) and (4) g i v i s t h e r e l a - I I

t i o n between t h e domest ic and world p r i c e I I

I

I A pure tar i f f- cum- export subsidy has i i / a i = 1 + t i , ci = ci , p i = I, bu t I

most d i s t o r t i o n s do n o t f i t e a s i l y i c t o t h i s framework s i n c e thby a r e t y p i c a l 9 . * I

non- l inear . Thus an import quota which always b inds has ii = 01, a i = 0, but i f . . l

i t only binds some of t h e time p i w i l l be a n3n- l inear func t ion of p and gi. . - i

- 4 '3 L Thus a quota set a t a f i x e d l e v e l qi impl ies t h e fo l lowing impo t demand

Ir I - equa t ion (compare equa t ions (3) and ( 4 ) : * L

. I I !

C i - sip - ei if ei 5 ki(p) I

x. = I I

1 , ( 6 ) + - 1

e, ,<.ki(?) :q i I

I I I

I

I I

I I I I I

- ki(p) = ci - q i - aip ( 7 )

is the l e v e l of domestic supply r i s k below sihich the inpoe t quota b inds . The I

domestic p r i c e is tken

} I

Pi ' ) (8) i

I

I

which is a non- linear f u n c t i o n of p. I I

I !

It is obvious ly d i f f i c u l t t o s o l v e f o r t h e i n t e r n a ion31 p r i c e when f a l a r g e number of c o u n t r i e s have s t o c h a s t i c nun-l inear e x c l s s dercand f u n c t i o n s ,

1 bu t we can ga in some q u a l i t a t i v e i n s i g h t by examining t h e $ f f e c t of a quota

I N

on a s i n g l e small country. h count ry is s m a l l i n t h i s con tex t i t Cov(7, €Ii) i s I

s u f f i c i e n t l y s n a l l t o be ignored , s o t h a t t h e a c t i o n s of t i e coun t ry are

asaimed n o t t o a f f e c t t h e world p r i c e .

CI Y K ~ r r o v e r , s i n c e B t is uncor re l a t ed w i t h e j , ai w i l t h e r e f o r e be r

m a r r e l a t e d wi th t h e worJ.ri p r i c e i;. I n t h e absence of i n d e r n a t i m a l p r i c e I

s t a b i l i z a t i o n , ki(;) is a random v a r i a b l e , and t h e p r o b a b i i i r y of t h e quo:a I !

r e s t r i c t i n g t r a d e is I I

I I

ni(;) = P r {Tigi.%(?) 1 = ~ i k ~ ( ; ) 1 , I i I i

I where G(el) is t h e d i s t r i b u t i o n func t ion of Si, whil , ,=+' i f th/e warld p r i c e is

p e r f e c t l y s t a b i l i z e d a t 'i;, then t h e p r o b a b i l i t y becones I I - .. Cr

nit;) = Pr{gi <ki(F) l . I

'2 I I

If the p r o b a a l i t y d e n s i t y func t ion of e i i s g(ei) = dG/dBi, symmetric about 1 * I m

i t s me.m o i ze ro , and unimodal, as shown i n Fig. 1, then nit?) is t h e shaded I

area. I !

I Fig 1 P r o b a b i l i t y of quota b inding , We wish t o know whether t h e p ropor t ion o f t h e t i m e i h a t t h e q c o t a

I I

Sinds i n c r e a s e s wi th p r i c e s t a b i l i z a t i o n ; i.e. i f I I I

vhich w i l l be t h e c s e i f n is a concave func t ion of p. ~ 4 n c e p is a linear i I

func t ion of ki from equat ion (7), t h i s is equ iva len t t o I

I I l

o r g must be i n c r e a s i n g over a range of va lues n e a r ki(F). h i s i s e q u i v a l e n t

t o requiring ki@) < 0, a s i n Fig. 1, o r t h e quota must b i n less than half d t h e t i m e . I f k i@)> 0 , and t h e quota binds more than h a l f t h e t ime, t h e n i

Obviously, t h e m r e o f t e n t h e quota b i n d s , t h e greatkr w i l l be the - p r i c e s t a b i l i z a t i o n w f l l reduce t h e propor t ion o f t h e time

- I

d i s p a r i t y between the -domest ic and world p r i c e , and hesce thb g r e a t e r vill

. t

it binds .

be t h e degree o f d i s t o r t i o n and t h e t o t a l c o s t of d i s t ~ r t i o n : ( ignor ing , as * I I

mentidned b e f o r e , t h e d i s t r i b u t i o n of t h e c o s t and t h e c o s t s ! of r i s k ave r s ion ) . I I

Sururnarizing, w e can say t h a t p r i c e s t a b i l i z a t i o n which does n o t

I I I I

I

change t h e zean world ?rice l e a d s t o a r educ t ion i n t h e degree of d i s t o r t i o n

caused by a qso's, 3rovfde5 t h a t t h e quota b inds less than hql f t h e t i n e a f t e r I

s c z b i l i z a c i o n . I T , :A:- ever, t h e quota then b inds r o r e than h a l f t h e t ime, I

? r i c e s t a b i l i z a t i o n w i l l have inc reased t h e degree of d i s t o r d i o n . i n q u i t e I I

p l a u s i b l e c i r c ~ m s t a n c e s , then, p r i c e s t a b i l i z a t i o n w i l l geii=date sorre addi- I

c i o n a l e f i i c i a c y ga ins by r educ ing t h e average l e v e l of d i s d o r t i o n i n t h e v o r l d

economy. I

Y s r e o ~ e ~ . t h e change i n average d i s t o r t i o n has o t h e r l e f f ec t s as we l l .

The average d o n e s t i c p r i c e is a n i n c r e a s i n g f u n c t i o n of t h e d 1 g r e e of d i s t o r t i o n I

a s measured by t h e p r o b a b i l i t y ni , b e c a ~ s e t h e quota raises kbe domest ic I

p r i c e r e l a t i v e t o t h e no-quota c a s e . For a s m a l l count ry whobe supply r i s k

is independent of world r i s k , p r i c e s t a b i l i z a t i o n has no e f f e t qn ave rage I p r o f i t s i n t h e absence of a quo ta (assuming as be fo re no chan e i n t h e mean 1 world p r i c e ) b u t w i th a quota average p r o f i t s f a l l , s i n c e the l ave rage domest ic

I

p r i c e w i l l f a l l w i th s t a b i l i z a t i o n . (We con t inue t o assume that tt;e quota I

j i n d s less than h a l f t h e t i m e a f t e r s t a b i l i z a t i o n . ) This fa14 i n average I I

p r o f i t s m y l e a d producers t o reduce supply. S ince t!~e q u o t a ~ e n c o u r a g e s I

i n e f f i c i e n t l y h igh domestic supp ly , t h i s f a l l i n supply w i l l improve world I

? .

e f f i c i e n c y , and gene ra t e a ' w o r l d we l f a re ga in equa l , roughly , ! t o t h e f a l l i n I

supp ly times t h e averags excess o f domestic over w&ld p r i c e . ) This f a c t o r I I

w i l l augment t h e e f f i c i e n c y g a i n s due t o t he f a l l i n average d i s t o r t i o n . I f - I -

w e cont inue t o t r a c e through t h e e f f e c t s of t h e quo ta , w e n o t i t h a t t h e ave rage '1 I

4

demand f o r i r ipor t s r i s e s with s t a b f l i z a t i o n , s i n c e t h e quota iestricts impor ts - I

I r . less of t e n , conpared wi th t h e no-qbota s i t u a t i o n . This w i l l dlend t o r a i s e t h e

I

v o r l d p r i c e , and t o o f f s e t t h e f a l l i n supply. Given assumptions about t h e I

I

d i s t r i b u t i o n of t., p, and t h e 2roduct ion func t ion i t would be! p o s s i b l e t o i d e n t i f y I

I

each o f t hese e f f e c t s and f i n d t h e i r o v e r a l l s i z e and d i r e c t i o p . I I

I

3 . P r i c e S t a b i l i z a t i o n i n a Xonopolized Comodi ty Xarket

I

I n a c o ~ p e t i t i v e m r k e t economy wi th a complete set o~f f u t u r e s and I I

i n surance ~ a r k z t s t h e m;trket equ i l i b r ium is P a r e t o e f f i c i e c t hnd n a r k e t

i n t e r ~ e n t i o n by, f o r example, 2x1 I n t e r n a t i o n a l Buffer Stock .ilgency, t o I -

f u r t h e r s t a b i l i s e comoc!it;r p r i c e s , would 5 e i n e f f i c i e n t . In1 such a market ,

j a r k e t s a r e c o n p e t i t i v e , it is clear t h a t . t h e market s t r u c t x r L i s n o t complete , I I

l a c k i n g insur2nce markets a.qd mst f u t u r e s markets . I n such l a s e s Xexbery and ~

~ r i v a t e agents would provide t h e e f f i c i e n t l e v e l of s t o r a g e a b t i v i t y and

S t i g l i t z (1982) show t h a t i n g e n e r a l a corcpet i r ive m r k e t i l i b r i u m is n o t

even cons t r a ined Pa re to e f f i c i e n t , so t h a t . i n p r i n c i p l e a

could make everyone b e t t e r o f f by market i n t e r v e n t i o n

? r i c e s t a b i l i z a t i o n . !low, w h i l s t i t can f r e q u e n t l y b e argued

s u b s i d i s i n g s t o r a g e a c t i v i t i e s ) .

t h a t commodity

However, they a l s o show t h a t i f agen t s a r e r i s k - n e u t r l l and h o l d

r a t i o n a l e x p e c t a t i o n s , then t h e compet i t ive equ i l i b r ium w i l l I/e e f f i c i e n t . n e reason is obvious. ~f a g e n t s a r e r i s k- n e u t r a l , and hold dommon ( o b j e c t i v e )

I

b e l i e f s about t h e economy, then they would n o t wish t o t r a d e {n r i s k marke ts

even i f they e x i s t e d . S i m i l a r l y , i f they hold common (ob jec t ve) b e l i e f s i about f u t u r e s p r i c e s , they would ,not wish t o t r a d e on fu tu re4 marke ts , and .

r l I

i n both cases such market3 c;ould be redundant. The i r absence i t h e r e f o r e makes I - - no d i f f e r ence t o t h e market equ i l i b r ium, which w i l l remain padeta e f f i e i e n t .

I _ It w i l l g r e a t l y s i m p l i f y t h e a n a l y s i s i f we cont inue do nake t h e s e

?

r assumptions of r i s k - n e u t r t l i t y and r a t i o n a l e x p e c t a t i o n s , thou(#h a f u l l L I

a n a l y s i s would c l e a r l y r e l a x t h e s e ossunptions. (See, i n ? a r t l i c u l a r , Bewbery

S t i g l i t z , 1981a, Chapters 13 , 14.1, 15 and 30; and NeW:bery 2nd S t i g l i t z

1981b). I n m k i n g these assumptions we a r e fo l lowing t r a d i t 4 o n (e .g. Gus tafson , I

1958; Samuelson 1971). :bough most w r i t e r s appear unaware of t h e s t r e n g t h of I

t h e s e o f t e n h p l i c i t assunpt ions . L'nder c e r t a i n a d d i t i c n a l d s sunp t ions

( s t a b l e l i n e a r demand, s t a t i o n a r y s t o c h a s t i c supply , and son4 r e s t r i c t i o n s I

on va r ious parameters) i t is p o s s i b l e t o s o l v e a n a l y t i c a l l y dhe compe t i r ive I

(and thus e f f i c i e n t ) s t o c k p i l i n g r u l e ( sez Newbery and s t i g 1 4 t z 1981a, Ch. 30; I

1981b). A t t h i s s t a g e t h e main poin t t o n o t i c e i s t h a t t h e d u l e is v e r y I

d i f f e r e n t f r o n t h e favored i n t e r v e n t i o n r u l e proposed f o r I n e r n a t i o n a l

Buffer Stock Schemes, vhich would at tempt t o keep p r i c e s w i t 4 i n a s p e c f f i e l

band width; The e f f i c i e n t r u l e would s t o r e a f r a c t i o n (som what g r e a t e r el than one h a l f ) of t h e excess of ha rves t p lus l a s t y e a r f s ~ a r 4 ~ o v e r above

I

some c r i t i c a l arcount. (See below.) >is r u l e remains a approximat ion

(and a n a t u r a l - s t a r t i n g - po in t f o r i n t e r a t i v e numerical s o l u t i Q n ) when the I " I I

s impl i fy ing assumptions do no t hold. (See Newbery and S t i g l i l t z , 1981a, Ch. 30; ' Gustafson, 1958). 1 !

I Given t h i s benchmark of t h e compet i t ive s tock ing rulle f o r t h e e f f i c i e n t

"+ 1

l e v e l of p r i c e s t a b i l i z a t i o n , a number of i n t e r e s t i n g ques t io& can now be I

asked of an imper fec t ly compet i t ive conmodity market. ~ ~ a . l - ,i i n t h e i n t e r e s t s I

I I

of s i m p l i c i p j , we s h a l l conf ine a t t e n t i o n t o a monopolist kabinp a l a r g e

number of competfve consumers. F i r s t , on t h e assumption t h a t t h e p roduce r d o e s - - t h e s to rage and prk!e a r b i t r a g e , how does the &mount of s t o r a e and h e n c e price f

I

s t a b i l i z a t i o n cornpaGe under monopoly with t h e e f f i c i e n t l e v e l ? Do m o n o ~ o l i s c s r I

perform more o r less ' p r i c e s t a b i l i z a t i o n ? The answer t o t h i s q u e s t i o n

i m e d i a t e l y r a i s e s r e l a t e d ques t ions - under what

20 less stabilization, and whic3 a g e n t s , consumers o r producers , w i l l c a r r y

;he s tocks? Again,, t h e answer w i l l a f f e c t t h e 2 e x t ques t ion , which i s , i f

c o n s m e r s have a c o ~ p a r a t i v e zdvantage i n c a r r y i n g t h e s t o c k s , how does t h e

1. change i n t h e i r l e s a n d s ( f o r c?osunption and s t o r a g e ) a f f e c t tpe n a r i e c poGer I

of :he ~ o n o p o l i s c ? I I I

- The n e x t s e c of ques t ions concern t h e consequences of b s t a b l i s h i n g

I

an International 3 u f f e r Stock t o s t a b i l i z e p r i c e s . Cne n igh t First a s k

what e f f e c t t h i s would have on t h e s a r k e t i f t h e Buffer Stock lol lowed

convent iona l r u l e s , and d id not a t t empt t o u se i ts p o t e n t i a l r k e t power. 4 Do d i f f e r e n t b u f f e r s t o c k r u l e s (e.g. band width r u l e s o r comp t i t i v e r u l e s ) C I

d i f f e r i n t h e i r robus tnes s t o nonopoly manipula t ion? I

I

F i n a l l y , w*at might happen i f t h e Buffer S tock Agency &ere a b l e t o

u s e i t s na rke t power t o c o u n t e r v a i l t h e monopolist? (The more I p l a u s i b l e

s c e n a r i o , i n which t h e Agency a c t s a s a c a r t e l l i z i n g i n f l u e n c e on t h e

a s s tockholder . )

4 . The Opt-imal s t o c k r u l e f o r a monopolist

primary producers is s.rbsuned i n t h e a n a l y s i s which t r e a t s t h e

The s i m p l e s t model which a l lows an a n a l y t i c a l s o l u t i o n i n t h e

monopolis t

I

compe t i t i ve c a s e (see Aewbery and S t i g l i r r 1981b) c o n t a i n s the1 fo l lowing

elements: . . @

L

( i ) There is a s t o c k c a r r i e d forward from t h e prevkous year . I

( i i ) ,To t h i s i s added a random harveec, L t , s o t h a t a t d b t e t t h e .* .L I

amount a v a i l a b l e f c r consumption, C t , and f o r s t o r a g e , S is the t o t a l - - - t ' I

supply 9 +: (Ir r I I

.I I I

K e a s s m e t h a t t h e r e a r e no l o s s e s i n s t o r a g e (though t h e s e a r e

ea sy t o handle - s e e Sanuelson, 1971), and t h a t planned product ion dces n o t

change each year (e .g . , f o r a t r e e crop l i k e c o f f e e ) . I f weath+r and o t h e r

I

randcn f a c t o r s a r e s e r i a l l y u n c o r r e l a t e d , t h i s i m p l i e s t h a t t h e h a v e s t i s ~

a l s o 2 s e r i a l l y un -o r r e l a t ed , s t a t i o n a r y random v a r i a b l e . V e cqoose - n i t s I I

s o t h a t t h e average ha rves t is one u n i t : I ~ d J 2 ~ Eht = 1, Var ht = u , Cwv(ht , htt ) = 0, t # t' . (10)

F i n a l l y , w e assume t h a t demand i s . s t a t i o n a r y and non-st Dl c h a s t i c ,

s o t h a t t h e marker c l e a r i n g p r i c e p t , depends on ly on c u r r e n t cdlnsumption, I

s o t h a t s tocks neither c o n t i n u a l l y i n c r e a s e nor d e c r e a s e , t h e ( i v e r s e ) b I

demand schedule w i l l be I

I

Pt = P K t ) (1~1)

I . * n e u t r a l i t y and i g n o r e income d i s t r i b u t f o n , a s I

- 1 ~ 1 U(C) - p{ l + ; ) C - -- c2]

2 E (1p) - i I

s o cha t '9 I - *

C

p (C) = I

# I e m

d C

When i t comes t o so lv ing e x p l i c i t l y f o r t h e s t o r a g e r u l e w e s h a l l

assume t h a t t h e demaci schedule i s l i n e a r , w i t h e l a s t i c i t y E a t t h e pre- I

s t a b i l i ~ ~ a t i o n mean p r i c e , 7. I f , on average, consumption equalis h a r v e s t ,

The c c n p e t i t l v e s t o r a s e r u l e can Ee focnd by n a x i n i s i n g expected s o c i a l

x e l f a r e ( t h e approach taken by Gustafson, 1958, and Samuelson, 1971) o r

der ived d i r e c t l y from t h e c m p e t l t i v e a r b i t r a g e cond i t ions . I t l i s easy t o I

<enons t r a t e t h e equivalence of t h e s e two approaches ( s e e ~ e v b e r d and I

S t i g l i t z , 1981a) s o we s h a l l fo l low t h e second, =ore t ransparen zpproach. 4 I f t h e a r ~ l u a l s t o r a g e c o s t s excluding i n t e r e s t is Ic per u n i t st

-

!

t h e c a r g i n , then a specu la to r who buys a f t e r t h e h a r v e s t a t pride pt and I

sells a f t e r t h e nex t h a r v e s t ar pri:+ pt+l rill have uiade a mardinal

p r o f i t ( i n zoney term a t d a t e t i 1 ) of i i

i n v e s t i g a t e the form of t h e compet i t ive s t o r a g e

per u n i t , where r is t h e r a t e of i n t e r e s t . I f s p e c u l a t o r s a r e

n e u t r a l then they w i l l s t o r e noth ing i f

r u l e , and t h i s a i p e a r s I I I

I I ! I I I I

I

r i s k

I

E pt+l < (pt + k) ( 1 + r ) i

1 bu t w i l l o t h e r r i s e cont inue t o s t o r e u n t i l they have d r iven up t h e c u r r e n t

I

p r i c e and d r iven down t h e expected f u t u r e p r i c e t o t h e poin t whtre !

(p t + k ) ( l + r ) E pt+l I i

These two cases can be combined i n the fundamental compet i t ive a r b i t r a g e I

equat ion ~ I , I

L I

I

I - I pt + k 2 a E P ~ + ~

i

I I complimentari ly 114) ' f

I - > I C

* St = 0 1

e # I

I 0

where 9 = 11 ( 1 + r ) is t h e d iscount f a c t o r . Our f i r s t o b j e c t i v e lis t o

be d i f f i c u l t Secanse t h e expected p r i c e nexrr year d e ~ e n d s on ? l a m e d ca r ry -

ove r s next yea r , vn ich in turn d e ~ e n d cn t h e planned car ryovers i n t h e

f c l l o v i n g year . To f i n d t h e s t o r a g e r u l e now w e need t o know tde s t o r a g e !

r u l s s t o be fo l loued h e r e a f t e r . To so lve t h e p rob lea w e csed rzd, s t a r t I I

x i t h a t e r n i n a l d a t e a t which t h e carryforward is s p e c i f i e d , and hence !

X ~ o m , and work backwards. This is the s tandard cethod of s o l v i g s t o c h a s t i c r p r o g r a d n g p r o b l e m , but w i th a long time horizon is coinputatio&lly demand-

ing . I f , however, t h e t i m e hor izon is a l loyed t o lengthen and ii t h e

expected present d isccunted va lue of terminal s t o c k s , 3T ST EP 1 , t ends t o T 1

I i t fol lows t h a t w e a r e looking f o r a s t o c k r u l e which is a

zero , then t h e i n f l u e n c e of t h e f u t u r e on t h e p resen t a l s o tends

I I ! ; Cont ra s t t h e f o m of t h i s r u l e w i t h t h e bandwidth r u l e , where i f Ithe 'demand

t o ze ro ,

1 is

1

- - c = D(P) i

- 1 and t h e p r i c e band has upper j n d lower i n t e r v e n t i o n p o i n t s pU, , then t h e

m 1

and w e can insrread of looking f o r a p a r t i c u l a r s o l u t i o n (which d pends on ST), t look f o r a s t a t i o n a r y s tock r u l e which is independent of termina s t o c k s , and hence

independent of t ime. Since p r i c e only depends on consumption f r n ( l l ) , and

s i n c e from (9) 1 i

s t o c k r u l e i s I I 1

I

, I ! I . I

~ ~ I

I

~ I

0 , o therwise I

1 I I I

Re bandwidth r u l e has s t o r a g e depending 'on both supply - and ha est over t h e 3 I

c e n t r a l range, and thus is not a competi t ive a r b i t r a g e r u l e . ~ 4 r e impor t an t ly ,

it fol lows t h a t i t is not a n e f f i c i e n t method of s t a b i l i s i n g co sumntion i n t a c o n p e t i t i v e n a r k e t , which, given our assumptions about r i s k n u t r a l l t y , is

t h e b a s i c reason f o r s t a b i l i s i n g p r i c e s . e

To'return t o t h e problem of f ind ing t h e c o n p e t i t i v e s t o

seek a funct ion f ( x ) which s o l v e s equat ion (14) , which, given ( l ) , (15) and i (16) , can be w r i t t e n

The prcblem i n so lv iZg t h i s a r i s e s from the r ig3thand s i d e , i n he t e r n 4 ' ' f { h + f ( x ) 1. One key f e a t u r e of t h e r u l e is , however, immediate/. -

' Jt I

The optimum i t o r a g e r u l e is non- linear . T h i s ~ f o l l o v s belcause s t o c k s - .ustobe n o n - n e g a t i v ~ , so f ( x ) = 0 below some c r i t i c a G a l u e of

8 - . -

In t h e Appendix w e show how t o so lve equa t ion (18) f o r t h e s p e c i a l

c a s e of a two p o i n t d i s t r i b u t i o n :

l + u ?rob 3 h =

1 - yu Prob 1 - p

so t h a t

I n t h i s case t h e c o n p e t i t i v e s tock ing r u l e is l i n e a r beyond q,: I

where r a = 1 + E - N ( 1 + 0)' - 4Bo

and a = 1 + c ( 1 - B + k /F) ,

provided t h e parameters l i e i n a c e r t a i n range:

1 Given s p e c i f i c va lues of 0 , s , kfi, u, and P , a and xo can be £0 nd and

equat ion (22) checked t o ensure t h e v a l i d i t y of (21) . I

So f a r w e have der ived t h e c o n p e t i t i v e r u l e , bu t f o r t u n t e l y t h e L a

mnop ly s tock ing r u l e now fo l lows i m e d i 2 ly , f o r t h e m o n o p o l i ~ t is i n t e r e s t e d

i n a r b i t r a g i n g marginal revenue, r a t h e r than pr.ice. S ince f o r b l i n e a r - i I I

demand schedule t h e marginal revenue is a l s o l i n e a r , t h e nonoPo l i s t s ' pro Uem 3

- i s isomorphic t o t h e c o r n p e t i t i s problem. Ins t ead of t h e a r b i t r a g e r u l e o f s

w 0

vhere nt i s t h e m r g i a a l revenue, and i n t h i s c a s e , .Ailst

Ins t ead of t h e s t o r a g e r u l e having t h e form ( s e e Appendix) I I

i t t akes t h e form

1

1 I

I where x; now s a t i s f i e s ( 2 2 ) , r e p l a c i n g a by 2 (a +B ) . I

It is i n t e r e s t i n g t o n o t e thai. t h e e lope a of t h e s tock ing r u l e lis unchanged, I

b u t t h e amount o f s t o c k i n g i s unambiguously inc reased , s i n c e 64 a. Fig. 2

i l l u s t r a t e s .

Stock

r u l e I

Fig. 2 Monoply and Competit ive r u l e s compared

p = 0.75 (3ad h a r v e s t s once every fou r yea r s )

u = 0.20 (Ifarvests 1 .2 o r 0.6, c o e f f i c i e n t of v a r i a t i n (CV) of o u t p u t .i

k / p = 3% ( s t o r a g e c o s t s )

35%) I I

E = 2.5 ( e l a s t i c i t y , u n s t a b i l i z e d C? of p r i c e = 13.94)

then a = 1.2

6 = 0.95 (5% i n t e r e s t r a t e ) I

I

compe t i t i ve case, and p r i c e s would not be , s t a b i l i z e d any fu r the f .) I

> Competit ive s t o r a g e r u l e : f C(x ) = 0.6835 (x - 1 . 2 ) , x = 1.2

> >!anopoly s t o r a g e r u l e : f m (x) = 0.6835 (x - 0.9563), x = 0.9513

1

(?taximum supply x = 1.7263, nlaximum s t o c k p i l e 0.5263) i m

(Thus, s i n c e h a r v e s t s never exceed 1.2, t h e r e is never any s tokage i n t h e

This s t o c k i n g r u l e i a p l i e s average s t o c k s of 25.6% of average h which

i s s u b s t a n t i a l . Moreover, i t reduces the CV of consumption f r o

and lowers t h e CV of p r i c e s from 14% t o 9%. I

The effect of s t o c k p i l i n g i n t h i s example i s t o subs tan . fi

inprove monoply p r o f i t s and reduce average consumer s u r p l u s re1 a t i v e t o I

t h e no s t a b i l i s a t i o n monoply equi i ibr ium, The e x t r a l o s s of co sumer s u r p l u s - - averages about of ( r i s k l e s s ) consumer expend i tu re on t h e c r o -

The r e sa t s of t h i s s e c t i o n can now be summarized i n a r b

e

.I monopolist f a c l n q a s t a b l e l i n e a r denand schedu le w i l l under r ike nore

p r i c e s t a b i l i z a t i o n through s t o r a g e a c t i v i t i e s than a compet i t ive na rke t

?reducing t h e s a e e averiige supply, and w i l l thereby be a b l e t o e x p l o i t t he

consucer =ore e f f e c t i v e l y . , I

This i m e d i a t e l y r a i s e s t h e next ques t ion .

$.1 :%!en do -,onopolists s t a b i l i z e =ore than t h e compe t i t i ve &rke t? I

- Consider a s i t u a t i o n i n vhich , wi th a given l e v e l of c q r r e n t supply ,

i t i s j u s t no t worth a compet i t ive market s t o r i n g , s o t h a t

p(Q o + k = BEp(Q1) (25)

I where period 0 is today, and pe r iod 1 is t h e n e x t per iod . In uch c a s e s i t

w i l l pay a monopolist t o s t o r e i f

~ d R ( B + k < BE dR (Q1)

dQ0 1 (26)

dQ1 I I ~ where R(Q) is revenue from the s a l e of Q. This c m be r ewr i t r4n a s

I where ei= &(Qi) is t h e e l a s t i c i t y of deinand when s a l e s a r e Q S u b s t i t u t i n g i'l

I from ( 25 ) , t h e monopolist w i l l s t o r e more i f I

I I I

< 1 - ( 1 + r )k / - I

€ r P . @

' (27)

where r is the r a t e of i n t e r e s t and is an a\ %rage p r i c e e l a s t c i t y :

- - EP -s 1

Ep / e - * 0

• The accumulated p ropor t iona l s t o r e c o s t , (It-r)k/- , t kes va lues I P I I

between 1.3% and 5.12 f o r t he s i x co re commodities con:l"-~d bb Ntv.rhery and

I

I

I

I

S t i g l i t z (1981a, Table 20.7 , p 2 9 5 ) . Equation (27) derncnstrates i r m e d i a t e l y

t h a t i f t h e demand s c h e d ~ l e has cons t an t e l a s t i c i t y t h e monopolist w i l l do

l e s s s t a b i l i z a t i o n than a compet i t ive market, bu t t h i s r e s u l t is very s e n s i t i v e - I

t o t h e shape of t h e eeland schedule. A s l i g h t f a l l i n Fried e l a s t i c i t y at I

lower p r i c e s (by, s . p. 5-10%) w i l l induce t h e ronopoli-st t d under take n o r e I

s t a b i l i z a t i o n . Vi th a l i n e a r demand s c h e d i ~ l e ( f o r whcch the; e l a s t i c i t y f a l l s

r a p i d l y ) t h i s tendency can be q u i t e pronounced, a s t h e previious s e c t i o n

demonstrated.

Of cou r se , t h e r e mav be q u i t e d i f f e r e n t reasons why monopolis t 1 might p r e f e r p r i c e s t a b i l i t y . H e might f e a r t h a t t empora r i l k h igh p r i c e s

would induce aew e n t r a n t s i n t o t h e i n d u s t r y and reduce h i s f t u r e p r o f i t s , L and hence might l i m i t p r i c e ( o r , more t o t h e p o i n t , m i n t a i n l t h e e q u i v a l e n t

I

of excess c a p a c i t y i n t h e form of b u f f e r s t o c k s t o d e t e r e n t f y . See Spence,

1977). Ignor ing such s t r a t e g i c i s s u e s , t h u g h , we can sunma

r e s u l t s a s fo l lows . I i

Propos i t i on 2 . A monopolist f a c i n g a s t a b l e cons t an t e l a s t i h i i y of demand I

schedule o r a schedule whose p r i c e e l a s t i c i t y f a l l s a s p r i c e ) rises w i l l I I

undertake - less p r i c e s t a b i l i z a t i o n than a compe t i t i ve r n r k e t (producing the

same average supply. Whether o r not t h e monopolist does mord o r less s c a b i l i r a -

t i o n depends s e n s i t i v e l y on t h e shape of t h e demand schedule . . I f m o n o p ~ l i s t s u n t z r t a k e less s t a b i l i z a t i o n than t h e

I

market, then w e have t o cons ide r t h e p o s s i b i l i t y t h a t o t h e r dgenfa (consumers, I -

' J o r , more probably, independent s t o c k ho lde r s ) w i l l perform fuu the r . i r b i t r a g e .

f o r a d d i t i o n s t o s to rage ) f a c i n g t h e monopolist . This nay l e&d t h e monopol i s t I I

t o change h i s behavio:. Thus i t i s important t o ask: I I I I

I

I I

! I

4 . 1 :+lo . e r fo r r~s the s t o r a g e a c t i v i t i e s i n an i n p e r f e z t l y compet i t ive z a r k c t ?

h l a r g e nunber of f a c t o r s a r e r e l e v a n t even i n the s impler compe t i t i ve

c a s e , and soEe of then a r e reviewed i n Newbery a ~ d S r - i g l i t z (!1981a, Ch. i 4 , I I

pp. 195-6). I f agents a r e n o t r i s k n e u t r a l , then s tocks *rov~ide a convenience 1 I

v i e l d i n t h e f o r s of i n s ~ r a n c e , and the agent whose-net c o s t b f s t o r a g e I

( ca r ry ing c o s t s l e s s convenience y i e l d ) a r e lowest w i l l have ccmparat ive I. sdvantage i n s to rage . Thus, i f t h e aggregate demand f a c i n g p oducers is

e l a s t i c , and p r i c e s a r e nega t ive ly c o r r e l a t e d wi th output (e . . i f supply I shocks genera te p r i c e i n s t a b i l i t y ) then producers d e r i v e a po i t i v e convenience

I

y i e l d £0; s t o c k s . I f , on t h e o the r hand, demand f l u c t u a t i o n s a r e t h e source

of t h e p r i c e i n s t a b i l i t y , consumers w i l l enjoy a p o s i t i v e con en ience y i e l d

, - 1

un les s p r i c e s vary wirh t h e i r incomes. In t e rmed ia t e producer ( i . e . a g r i c u l - I t u r a l processors ) enjoy a p o s i t i v e convenience y i e l d s i n c e t h i r p r o f i t s w i l l h be nega t ive ly c o r r e l a t e d wi th input p r i ces .

On t h e o the r hand, t tar .sport and handl ing c ~ t s w i l l onvey a c o s t C I

advantage on producers , s i n c e downstream u s e r s w i l l have t3 i$cur a d d i t i o n a l I

i n t e r e s t c o s t s oil t h e m r k e t i n g margin. However, economies 04 s c a l e i n

s t o r a g e , a c c e s s t o cheaper f i n a n c e , hedging f a c i l i t i e s , b e t t e market i n f o m a - t t i o n , and r i s k pooling advantages may o f f s e t t h e s e c o s ~ d i s a d an tages and 4

r

confer t he comparative advantage on middle rcen. The s e c t i o n assumes I

t h a t a l l t h e s e va r ious f a c t o r s cance l o u t , s o t h a t producers ,. consumers and I

middle men f a c e equal n e t s t o r a g e c o s t s . ~ I I

Consider t h e case i n which t h e consu+tion demand schAdule is s t a b l e - I

and has cons tan t e l a s t i c i t y of demand. The argument of t h e pr/evious s e c t i o n I

then shows t h a t , i f only producers s t o c k p i l e , the? a aonopol id t would p e r f o r n

l e s s s t a b i l i z i n g a c t i o n than a compet i t ive m r k e t . Consequently, t h e r e would . - .- be enough r e z a i n i n g p r i c e v a r i a b i l i t y t o j u s t i f y f u r t h e r p r i d e s t a b i l i z a t i o n

I

by c o c p e t i t i r e a g e n t s , assuming they f ace no c o s t d isadvantdge . khat ~ ~ o u l d I

hzppen i f such agents in te rvened and c o l l e c t i v e l ~ y achieved a lcompetitive

degree of p r i c e s t a b i l i z a t i o n ?

The a n a l y s i s of Newbsry and S t i g l i t z (1991a, Ch. 30) nd Gustafson I. (1958) shows t h a t t h e q u a l i t a t i v e form of t h e s tock ing r u l e r m i n s unchanged I. a s t h e shape of t h e denand schedule -2nd t h e form of t h e prcba i l i t y d e n s i t y b of h a r v e s t s v a r i e s . The l e v e l of supply below which t h e r e i no s t o c k i n g b

I (xo) dces depend on two f e a t u r e s , bu t can be found r e l a t i v e l y e a s i l y . The

s tock ing r u l e w i l l t y p i c a l l y be a convex f u n c t i o n of supply whose gene ra l I shape is r e a d i l y approx imtpd by a piecewise l i n e a r form. ( ~ b w b e r y and

I

S t i g l i t z , 1981a, pp. 435-438.) I f compet i t ive consumers unde

s t o r a g e a c t i v i t y , tnen t h e producer w i l l f a c e a d isp laced gro

schedule ( f o r consumption p l u s s t o r a g e a d d i t i o n s ) a s shown

I rY

A car ryover from l a s t y e a r , S i I

p r i c e

I ' wi th s t a b i l i z a ion i

- without s t a b i l i z t i o n

2 I - 1 , . 4 I - * CI * % - S ha rves t I L

I I

F i g . 3 E f f e c t i v e I

The form of t h e denand schedule i s approximately

- ~ ( 2 3 ) c = ax, 4- ( 1 - 3) (q + S) = P - ~ q Z x , - s

~ .. where S i s t h e (raniom) c a r r j o v e r from l a s t y e a r , and a , xo, d f ined by (21) ,

r e p r s s e n t t h e l i n e a r a?proxina t ion t o the compet i t ive s tocking) r u l e . The ~ n e t + f f e c t of t h e consumer s t o c k p i l i n g is t o make t h e e l a s t i c i t y of demand

I i n c r e a s e a s t h e ;upply i n c r e a s e s and p r i c e f a l l s , and hence t o f u r t h e r d i s -

I I

co-xage t h e ~ o n o p o l i = t from underta-:ing any s t o r a g e . Thus, p rov id ing t h e r e

is no co.st d isadvantage f ac ing t h e consumers, they w i l l p r e s u 4 b l y d i s p l a c e

t h e m n ~ p ~ l i s t and a l l s t o r a g e xi11 be undertaken by

Sucmarising t h i s argcment w e have, depending

I s t a b i l i z a t i o n :

* 1 Propo. i t i o n 3 . I f consumzrs f a c e t h e same o r l o v e r n e t s t o r a g b c o s t s

I

( inc lud ing i n t e r e s t charges) than producers , then p r i c e s shoul be e i t h e r t more s t a b l e , o r a t wors t , no l e s s s t a b l e , than i n compet i t ive r k e t s t handling t h e sane average product ion. '

I f , on the o t h e r hand, consumers f a c e c o s t d isadvantages , t h e s e I

p r i c e s :nay r e n a i n l e s s s t a b l e under monoply. 0 r t

5 . The E f f e c t of I n t e r n a t i o n a l a u f f e r Stocks on Imperfec t ly O m p e t i t i v e Markets I ~ -

So f a r we have r e s p i c t e d a t t e n t i o n t o e i t h e r t he prod c e r o r t h e L y

competi t ive consumers, e i t h e r of yihich might c a r r y s tocks and t e n c e s t a b i l i z e *

I

s p r i c e s . I f , however, an In t ie rna t ional S t a b i l i z a t i o n Author i ty ( i s s e t up,

then i t w i l l presumably be given r u l e s f o r o p e r a t i n g i t s t n t e r j e n t i o i i

activities, and t h e s e r u l e s m y a f f e c t t h e n a r k e t f a c i n g t h e n o n o p o l i s t . It

i s i c t e r e s t i n g t o cons ide r t h r e e c a s e s . The f i r s t would e n q u i r e i n t o t h e

l i k e l y consequences of i n t r o d u c i n g t h e favored Band With r u l e n t o t h e in- t ? e r f e c t l y conpet i : ive s a r k e t . The second c a s e womlld examine t h e consequences

of i n t r o d u c i n g t h e b u f f e r s t o c k r u i ? i ~ h i c h would be o p t h l in a cornpe t L ~ i - ~ e

market, 5 u t which would n o t n e c e s s a r i l y be b e s t f o r an ic lperfe t l y c o m p e t i t i v e + market. F i n a l l y , t h e n o s t d i f f i c u l t bur n o s t i n t e r e s t i n g ques i on i s ta ask

. .ha t r u l e would be opt imal i n an imper f ec t ly compe t i t i ve mark

~ 5 .1 Bandwith Rule

I

This rule is s p e c i f i e d i n squa t ion (17) and gene ra t e s an e f f e c t i v e

demand f a c i n g t h e producer as shown i n Fig. 4 below (assuming u f f i c i e n f

s t o c k s a r e on hand, i .e . a t least hl). I

/ ~ I I

I ~ s2 ~

~ @

'~

0 . h l h2 t '4 h , ha est

- -. - 4

rig. 4. E f f e c t i v e demand under t h e a n d w i d t h Rulq -

The sane f i g u r e shovs tks z a r g i n a l revenue f a c i n g t h e - ,onopolis t , and i t is

t h i s s ckedc l s whlch is r s l s v a n t f o r h i s product ion and s t o r a g e d e c i s i o n s . I

F i r s t , no t2 :hat i f t h e m n o p o l i s t r e r a i n s any s n o r t run suppl: d i s c r e t i o n r once t h e s t o c n a s t i c u n c e r t a i n t y has been r e s o l v e d , then t h e Sa dwidth r u l e 4 can a c t . a l l y Z e s t a b i l i s e 7 r i c e s . F o r suppose t h a t i n bad y e z r l t h e supply

1 ' I scheduie is S v h i l s t i n 3ood yea r s it is S2. Gi thout s t a b i l ~ z a t i o n t h e I

p r i c e would be e i t h e r ?I, o r p2, b u t w i th s t a b i l i z a t i o n t h e no o ~ o l i s t would 1 choose t o supply hl, o r h2 ( s i g n i f i c a n t l y .nore v a r i a b l e ) a t p r i

It i s q u i t e 1ikel.y i n t h i s c a s e t h a t t h e b u f f e r agency w i l l ov$raccurculate I

s tocks s i n c e t h e f l o o r p r i c e pf may genera te a ve ry a t t r a c t i v e iaarg ina l

revenue f o r t h e monopolist .

I f t h e producer 52s n e g l i g i b l e s h o r t run supply d i s c r e t i o n ( i . e . I t h e case considered i n :he previous s e c t i o n ) then t h e appropr ia l te q u e s t i o n

t o a s k of t h e i n t e r n a t i o n a l b u f f e r scheme is whether i t is s u s t h i n a b l e , o r I I

whether i t w i l l induce s p e c u l a t i v e a t t a c k s which render i t non-jTiable. I

The i s s u e of v u l n e r a b i l i t y t~ s p e c u l a t i v e a t t a c k has been addre

Sa l an t (1979) and Newbery and S t i g l i t z (1981a, p 413-4). I n a a

m r k e t i n which t h e upper and lower p r i c e bands a r e set a t p ( l+b ) , i ( 1 - b ) ,

i t w i l l pay producers o r s p e c u l a t o r s t o s p e c u l a t e an a p r i c e r i le whenever

* ' t h e p r i c e f a l l s t o t h e f l o o r p r i c e un le s s

I I

I f t he bandwidth is set f u r t h e r a p a r t than t h i s , then p r i v a t e a e n t s w i l l i specu la t e a g a i n s t t he s t o c k p i l e . Noreover, even i f t h e b u f f e r agency sets

I

t h e bandwidth a p p r o p r i a t e l y , t5en i f i t s ohm s t o c k s a r e i n s u f f i c i e n t t o

s u s t z i n t h e c e i l i n g p r i c e , t h e r i g h t hand s.-de c f (29) w i l l be; i nc reased , I I

s i n c e t h e e x ~ e c t e d next per iod ? r i c e w i l l be b i a s sed up by t h e p r o b a b i l i t y

of a s h o r t f a l l too l a r g e t o be n e t by the 9gency1s b u f f e r s -oc

i n a p r i c e zbove 5 ( 1 -!- 5 ) and hence r a i s i n g 29 above 5.

I n a non-competitive n a r k e t t he ngency i s s u b j e c t - t o a h d i t i o n a l

s p e c u l a t i v e p res su res from t h e monopolist , f o r i t is c l e a r i n

t h e expected a r g i n a l revenue next per iod is s u b s t a n t i a l l y r a i

i n t e r v e n t i o n ?rites. Even i f i t would no t pay a compet i t ive s e c u l a t o r P t o buy now i n t h e expec ta t ion of f u t u r e ; = o f i t , i t might w e l l pay a

monopolist. As an example, cons ide r t h e l i n e a r demand schaduli

of equa- - e

cion (12), and suppose t h e d i s t r i b u t i o n of h a r v e s t h is symmetkic

about h = 1. Let ~

Prob [l - ~b < h < 1 + ~ b ) = il

then , wi th no producer c a r r y forward expected marginal revrnu

- 1 - 1 Em = p i 2 ( 1 - E ) ( 1 - b + 1 + b) + ll ( 1 - €1)

- = p ( 1 - n / € )

becones

I e 1 a

i n s t e a d of p ( 1 - E) . The monopolist w i l l thus s t o r e i f h i

h a r v e s t , h , s a t i s f i e s

( i . e . t h e r e is no b u f f e r s t o c k i n t e r v e n t i o n ) , and I I

1 a . 1 + r - E C k l ? < $Em - = ~ ( 1 - -

P I I I I I I

I

I

uhici; i s a ve r , z e a t cond i t ion in l eed (!tote 7 depends on b ) . T$us if 3 = 0.95, I

c = 32, h is roughly a o r ~ l wirh CV of 242 , E = 3, then a coripe i t f v e band t width r u l e wouid r e q u i r e b SI, but i f b is s e t a t 8%, (so t h a Z = 3-57)> i then t h e nonopol i s t w i l l s t o r e on h i s own behal f whenever 0.94 { h < 1.24 ,

i . e . 35% of t h e time.

It is c l e a r t h a t t he same problem w i l l a r i s e even when he conslimer 1 demand schedule i s non- linear . Thus i f an i n t e r n a t i o n a l b u f f e r agency is

s e t up i n d i n s t r u c t e d t o m i n t a i n p r i c e s wi th in a bandwidth, then any aonopo l i s t

w i l l probably (depending on t h e va r ious parameters) be a b l e t o s p e c u l a t e

a g a i n s t t h e :.gency, buying whenever the p r i c e f a l l s n e a r , bu t n

f a r a s , t h e f l o o r p r i c e i n o r d e r t o s e l l t h e fol lowing per iod (

5 _Abi_ .. . .-->. ..,...-A.-.. ;.. ,;.:>:.: .<.:.. , . ~

---4-%a3.k,*<7L.7 -...? "=:....z ~..: . , .. . . , , ~ ..,* -.=<r. .-.

f f e r agency i s i n s t r u c

: compet i t ive s t o r a g e r u l e ( i . e . , t he r u l e r e l a t i n g s t o r a g e ,

vould p r e v a i l i n a competi t ive market). Such a r u l e would have (two obvious

r a t i o n a l a s - i t would break even i f t h e r e were cons tan t s t o r a g e ' c o s t s (or

makn a p r o f i t w i th inc reas ing marginal c o s t s ) , and i t would be q f f i c i e n t

given t h e a l r eady rcenfiqned assumptions of r i s k n e u t r a l i t y e t c .

s t o c h a s t i 5 supply shocks of be ing non-manipulable. There a r e t a t

It would

have t h e a d d i t i o n a l advantage when confront ing a monopolist s u b j e c t t o

s t a b i l i r a g o n than a compet i t ive producer. I f he would undertade inore (e .g. . - *

c a s e s , d e ~ e n d i n g whether t h e monopolist would undertake nore o r t

t he

l e s s

demand schedule is l i n e a r ) then the b u f f e r agency w i l l never in t e rvene , I

a i a c e th2 r e m i n i n g p r i c e v a r i a b i l i t y wouLd be inadequate t o j p s t i f y compe t i t i ve

i ~ z e r v e n t i o n . I f h e woulO cnde r t ake l e s s , (e.g. i f h e faced a : c o n s t a n t I

e l a s t i c i t y 6ez;;nd schedule) then t h e agency would have a conpa a t i v e advantage f i3 s t o r a g e , as d iscussed zbove i n s e c t i o n 4 , and would unde r t a e a l l s t o r a g e , 1. 1 x i t h t h e nonopo l i s t perforzing no s to rage .

-

There r e n a i n s one curiosum, which is a consequence of he k ink I induced i n t h e e f f e c t i v e denand schedule a t t h e po in t a t which t h e agency

f i r s t adds t o s t o r a g e (xo - S i n Fig. 3 ) . Sewbery (1978) demo s t r a t e d 4 t h a t it vould i n gene ra l pzy a monopolist f a c i n g a kinked demadd schedule 1 (one which becones no re e l a s t i c j u s t below t h e kink) t o i n t r o d ce randomness Y i n t o an o the rwi se non-random market. The r eason is t h a t t h e n o p o l i s t can

e x p l o i t t h e d i s c o n t i n u i t y in t h e n a r g i n a l revenue f a c i n s h i s .

- an In t eg ra t ed Programne f o r ~ o m o d i t i e $ (by LMCTAD i n Nai robi ,

.L

t h e kinked denand theory of o l igopo ly , i n which t h e demnd s c h

becomes - less e l a s t i c be iov che k ink , which provides an explana

p r i c e s t a b i l i t y .)

6. Counterva i l ing I n t e r n a t i o n a l P r i c e S t a b i l i z a t i o n I I

was more i n t e r e s t e d i n c o u n t e r v a i l i n g t h e imperfec t ions on t h e uying s i d e . 0

I IF w by c r e a t i n g producer c a r t e l s , r a t h e r t h i n defending t h e consume s a g a i n s t I

monopol i s t ic producers , and i t would be i n t e r e s t i n g t o extend the a n a l y s i s

I f some commodity m r k e t s a r e recognized t o be monopolised

c a r t e l l i s e d , then i n s t e a d of fol lowing a p a s s i v e r o l e , no re s u i t e d

compet i t ive market , t h e i n t e r n a t i o n a l s t a b i l i z a t i o n agency might

up t o & r y and m i t i g a t e t h e monopol i s t ic d i s t o r t i ~ n b . A t t h i s

i t should be poin ted o u t t h a t t h e p o l i t i c a l impetus behind t h e

o r

t o a

be set

s t a g e

c a l l f o r

t o c o n s i d e r x c o p s o n y i r q c r t e r s faci r ig c o n p e t i t i v e ~ r o d u c e r s , b u t t h a t

w i l l have t o z v a i t a c o t 3 e r occa s ion . Sose of t h e l c s i g h t s obyained by

s ccdy ing t h e :ore t r a c t a b l e z~oonoopoly p roducer c a s e mdy, howevdr, be u s e f u l . I

%is c a s e ha s a l r e a d y been t h e s1:bjact of a most i n t s i e s t i n g s t x d y I

3y S i c h o l s azc! Zzckhauser ( 1 9 7 7 ) . They cons ide r ed t h e c a s e 01 a l a r g e

consuming n a t i o n (such a s r h e U.S.), c o n t a i n i n g many compet i t v e f i n a l i consumers, f z c i n g a c a r t e l (obv ious ly OPEC prov ided t h e n o t i v f o r a d d r e s s-

i n g t h e q u e s t i o n , b u t t hey drew a t t e n t i o n t o c a r t e l s i n banan s, b a u x i t e , ! c o f f e e , coppe r , i r o n o r e , mercury, phospha te , 2nd t i n ) . They d e m o n s t r a t e d

I

t h a t und'er c e r c a i n c i r cums t ances i t would pay t h e conr :~ming n a t i o n t o

b u i l d up a s t r a t e g i c s t o c k p i l e , whose p r e s e n c e would s u p p r e s s p r i c e s i n

f u t u r e ? e r i o d s , even when t h e supply c o n d i t i o n s of t h e produc ng c a r t e l i were non-random and s t a t i c n a r y , s o t h a t on c o m p e t i t i v e p r i c e r b i t r a g e

grounds t h e r e would be no c a s e f o r s t o c k p i l i n p . i

The r e f e r e n c e =ode1 had t h e f o l l o w i n g f e a t u r e s . The d a r t e l maximizes

t h e p r e s e n t d i s coun t ed revenues n e t of p roduc t i on c o s t s by s e t i n g t h e 4 supply p r i c e e ach pe r i od . The consuming n a t i o n maximizes t h e Ip resen t v a l u e

of n e t ccnsumers ' s u r p l u s (consumers ' s u r p l u s l e s s s t o r a g e a n i n t e r e s t c h a r g e s d on t h e s t o c k p i l e ) , by choos ing i t s s t o c k p i l e l e v e l each Consumers

-. dec ide on c u r r e n t consusp t i on g i v e n t h e c u r r e n t p r i c e . I n t h s i m p l e s t s model t h e world lasts two p e r i o d s , i n t h e f i r s t of which t h e onsumer 1 government buys s t o c k s f o r resale nex t p e r i o d . The game is o

i n f o m a t i o n i n vh i ch t h e s u p p l i e r p l a y s f i r s t (announcing a p - ~ * consumer ,gove+ent p l a y s second (choos ing a s t o c k p i l e l e v e l ) .f ?'he game is

so lved r o c u r s i v e l , , and can be sclveci nurcer ica l ly f o r any f i n i t e nunbe r

o f 7e r iods . Yi th zero product ion and s t o r a g e c o s t s t h e e f f e c t of t h e s tock-

p i l e vas t o mice f u t c r e demnd nore e l a s t i c and hence reduce che deadweight

l o s s of t h e nonopoly. Consumers b e n e f i t f ro= t h i s , w h i l s t wit$ l i n e a r decand

and two pe r iods , producers a l s o gain because of t he h ighe r f i r t period I cim:,nd and ? r i c e . I n s h o r t , boch p a r c i e s ga in from t h e counte v a i l i z g .i m r k e t power which reduces deadweight i n e f f i c i e n c y l o s s e s , tho gh a s t h e i number of t i n e periods i n c r e a s e , s o t h e consumers ga in r e l a t i v

iiroducers . Tiese r e s u l t s a r e q u i t e s t r ik ing , . bu t need c a r e f u l i n t d r p r e t a t i o n .

I

F i r s t , t.he b e n e f i t s a r e measured by comparing an i n t e r v e n t i o n i t s t o c k p i l i n g 1 s t r a t e g y by t h e s o l e consuming country wi th no i n t e r v e n t i o n a t a l l . The I f a c t t h a t t h e country is t h e s o l e consumer means t h a t t h e mark t s t r u c t u r e 4

I is one of p o t e n t i a l b i l a t e r a l monopoly, r a t h e r than pure monopo/ly, end

i t s i z h t have been nore l o g i c a l t o compare s t o c k p i l i n g v i t h o t ' e r counter- n v a i l i n g a c t i o n s such a s import t a r i f f s .

Second, t h e c a r t e l ' s supply s t r a t e g i e s a r e r a t h e r s p e c ' a l , and 1 correspond more c l o s e l y t o OPEC's s t r a t e g i e s than those of a n d g r i c u l t u r a l

I

c o m o d i t y c a r t e l (though t h e r e a r e a d d i t i o n a l complicat ing f a c t b r s i n t h e

case of exhaus t ib l e resources which s u b s t a n t i a l l y modify t h e co c l u s i o n s ,

a s the au thor s recognise) . Only i f s h o r t run supply is .h ighly e l a s t i c

w i l l i t be f e a s i b l e f o r a c a r t e l t o announce a supply p r i c e and I a l low

consumers then t o d i c t a t e demand and hence supply. I f t h i s e l a t i c i t y of b I

supply is t o be achieved by producer s t o c k p i l i n g then t h e same bomplicat ing

i n t e r t e n p o r a l i s s u e s a r i s e a s with exhauf t ib l e r e sources , and t 0

n u s t be s u b s t a n t i a l l y modif ied. It is c l e a r chat t h i s assumpti n a f f e c t s b

t h e r e l a t i y e z larket povers o f t h e two p a r t i e s s u b s t a n t i a l l y . I f , f o r

e s a p l e , t h e prodricer al.--ays h a s t h e f i r s t s a y , and s p e c i f i e d a s u p p l y

p r i c e , t h e n t h e i m p o r t e r c a never u s e f u l l y i s p o s e a n i n p o r t t a

t h i s , 5y zssumpt ion , w i l l n o t a Z f e c t t h e s u p p l y p r i c e . C l e a r l y

i q o r t e r p l a y s f i r s t , and ansourices a t a r i f f , t h e n t h e r o l e s a r r e v e r s e d i and t h e p r o d u c e r f a c e s a d i f f e r e a t demand c u r v e a g a i n s t which h 4

I o p t i d s e s , and t h e r e s u l t h g m r k e t e q u i l i b r i u m is q u i t e T h i s

is d r a m a t i c a l l y i l l u s r r a t e d i n t h e f o l l o w i n g n u m e r i c a l example,

u s e s t h e sane s o d e l as S i c h o l s and Zeckhauser (19777, pp 70-74).

T a r i f f s v s . S t o c k p i l e s i n t h e Nichols- Zeckhauser model

t h e d i s c o u n t f a c t o r i s 6, aod t h e r e a r e no p r o d u c t i o n o r s t o r a g e ( c o s t s .

which

We e n p l o y t h e same o o t a t i o n and fo rmat a s t h e two p e r i o d

C o n s u m ~ t i o n , C , and p r i c e , p , a r e r e l a t e d by

C = K - CIp,

With no consumer a c t i o n , t h e p r i c e is set a t t h e monopoly l e v e l " = i(/2a, b

model.

and consumers e n j o y a p r e s e n t v a l u e of conscrner s u r p l u s IF' = K~

I f t h e sequence of e v e n t s is (1) c a r t e l selects p l , ( 2 ) consumer

(4) consumers s e l e c t C2(p2) and import C2 - S , t h e n Nicho ls and I e c k h a u s e r

C1(pl) and t h e i r government chooses s t o c k , S , (3 ) c a r t e l s e l e c t s

4 compute the top t imum p l , p2 and 5. w i t h B = 0.9524 ( r a t e of i n t e l e s t = 5X)

p2

t h e y show t h a t t h e o p t i m a l s t o c k p i l i n g s t r a t e g y raises t h c n e t - i

v a l u e o f consumer s u r p l u s by 7.7% and t h e c a r t e l ' s r evenue r i s e s 3 Ir C I f , i n c o n t r a s t , t h e sequence is (1) c a r t e l s e l e c t s p l , I - choose C1(pl), ( 3 ) t h e government s e t s a n ad va lo rem t a r i f f r f o r

p e r i o d ( 4 ) t h e c a r t e l s e l e c t s p2 , and (5) consumers demand C2{p2

p r e s e n t

12.

(3) consumers m . t h e second

(1 + T) 1,

Appendix Characterising the Optimm Stock 3ule

The Following results are defended in Sewbery and Stiglitz (1985). I

(i) The competitive stock function f (x) is continuous and nonotonically

increasing.

(ii) Its derivative f ' (x) is less from unity.

(iiij In a stationary xorld with bounded harvests stocks ar also boenled.

If the oaxinum possible harvest is h then there is unique number x m ' in

such that t

If by soEe un fo re seen even t supp ly e v e r rises above some l e v e l xn, s a y

t o x*, t h e s t o c k l e v e l nusc s t e a d i l y d e c r e a s e , f o r even a sequence o f 1 Scriper h a r v e s t s h w i l l l e a d t o a s ~ c c e s s i v e d e c r e a s e ib supp ly and hence

P I

s t o c k s , a s shown by t h e a r roved Line i n F i g u r e A:.

For t h e two p o i c t d i s t r i b u t i o n cons ide r ed i n Se : t i0 3 , and f o r thf: C I -

l i n e a r demand s c h e l u l e of equa t i on (12) , t h e s t o c k i n g r u e can b e s o l v e d

ss f o l l o w s . Equa t ion (18) can b e r e k i r i t t e n as f o l l o w s .

g i v e I

> = IXo ,

I

= 0 ,

- - 1 > D ( 1 - B 1 + + k = {X - £(XI - BE [ h + f ( x )

> X = X . o

v h e r e x is d e f i n e d by equa t i on (19)'. Equa t ion -42 can 0

(A?

. - f{h + f(x:)]:r

ment ar i n q u a l t ie,s

m b e r e a r r a n g e d t o

I where a i s a c o n s t a n t : 1 1

r I I -

a = 1 + ~ ( 1 - 0 + k/i) 2 1 + E ( C + r ) I c 5 k/p' (A4 1

- - and c is t h e t o t a l annua l s t o r a g e t o s t exc lud ing i n t e r e t , a s a f r d t i o n

t o show t h a t f o r c e r t a i n pararne:..r v a l u e s t h e s o l u t i o n t o (X2) is a p i ece- I

- - of t h e average p r i c 2 , p .

8

- - * w

Provided t h e haGvest rakes e d i s c r e t e d i s t r i b u t i o n , t hen it i s p o s s i b l e ~

I

vhere x is =he z.xxi,?un p o t e n t i a l s c p p l y d e f i c e d 5 y equ m

Subs i s c - l t e (A5) i n t o (A31 :

- Tke problem l i e s i n t h e benaviour cf t h e t e rm h + a ( x - ) , which may be

g r e a t e r o r l e s s t h a n xo, t h e p o i n t a t which f ( x ) is non- i n e a r . P Def ine

t h e n

I

The s t o c k r u l e can o n l y be l i n e a r o v e r [xo, xm] i f a ( 4 ) is independent I

of x o v e r this range ; and H(x) is c o n s t a n t o r - l i n e a r i n 8

e q u i v a l e n t t o r e q u i r i n g

x. T h i s is

I For example, i f t h e h a r v e s t h a s a LWO p o i n t d i s t r i b u t i o n i

I l + u Prob p

s o t h a t

2 - 2 . E h = 1, V a r h = y u = a .

To erlsure a l i n e a r s t o c k r u l e we r e q u i r e t h a t i f t h e c u r r e t h a r v e s t is low t (h = 1 - y u ) , then no ma t t e r how l a r g e was t h e ca r ryove r , c u r r e n t s t o r a g e

:,. must be ze ro , and i f *he c u r r e n t h a r v e s t is high (h = 1 + ) , then even w i t h

zero ca r ryove r , some s tock ing must occur . I n t h a t c a s e 1 Equation (A81 can be so lved f o r x :

0 1 r

(A l l ) I

The maxima stock is found from equation ( A l ) :

The condizion of p o s i t i v e ciirryovers i f and only i f the c lrrent harvest is I

good is equivalent t o

which is ident i ca l t o equa.@on ( A 9 ) . Given s p e c i f i c v a l u l s of 13, E . L I

c , u , and p , a and r can be found and checked t o $ee i f they s a t i s f y is 4 I

the constraints of equat i o h (Al5) . I I I I I

I

Zale , ?.I., and L~rz, 3 . (198i), ' ? r i c e D i s t c r t f o n s i n A g r i c u l t u r e 2nd T5e l r - E C ;,,ects: A-n I n t e r n a t f o c a l Conpar i son ' , . U e r i c a n J c u r n a l o f X q r i c c l i u r a l - r conon l :~ , g, (1) 'eb. pp 8-22

3oaduay. R.:s7. (1975) 'The Ye l f a re "ucdat icns of Cos t- Seapi i t . 4 c a l y s i s 1 , - =coccnic J o u r n a l , z h (Cec.) ?p 925-39 I

, v -

'10 - - (1975) :ccd Xeser-;e P c l i c i e s f o r World Fccd Secur i ty ; : X C a n s u l t s n t Stcdy o f 2 - l re rzas ive X?praaches l , E J c : ~ S ? / 7 5 / 2 , Xcme, Food znd -1-sricalcure Q r ~ a o i z a t i o n ,

Gray, ?..X. (1960) 'The C h a r a c t e r i s t i c S i a s on Scme T5in FGtcre : J a r k e r s l , ?cod Research I n s t i t u t e S t u d i e s (J!ov.)

Gus tafson , R.L. (1958) C a r ~ ~ o v e r Leve l s f o r G r a i n s , U.S. Oepar tzent of A g r i c u l t u r e , Tec5n ica l B u l l e t i n Yo. 1178

I

EarSe rge r , X.C. (1971) 'Three 3 e s i c P o s t u l a t e s f o r App l i ed lXe l f a re Ecoccnies: An I n t e r p r e t i v e Essay ' J o u r n a l of Ecoocmic ~ i t e r a t u r a , 9 (Sept . ) pp 785-97

Xart, O.D. (1977) 'On One P r o f i t a b i l i t y of S p e c u l a t i o n ' , Q d a r t e r l y J o u r n a l of Economics, 91 , ?p 579-97

I I I

I

Johnson, D. Gale (1975) Korld Food Problems and P rospec t s , ; ;Jashington D . C . , American E n t e r p r i s e I n s t i t u t e f o r P u b l i c 7 o l c i y ~ e s e a r i c h

Lutz , E. and Scandizzo, P .L. (1980) , ' P r i c e D i s t o r t i o n s i n beve loping Coun t r i e s : X 3 i a s a g a i n s t ~ g r i c u l t c r e ' , European Review of ~ e r j c u b t u r a l Economics, 7 ( I ) , pp 5-27

Xewber], D.E.G. (1973) ' S t o c h a s t i c L h i t P r i c i n g ' , Bell Jou fna l of Economics, 9 , pp 260-9

I

Xewbev, D . 3 . G . and S t i g l i t z , J . E . (1981a1, T h e Theory of ~ b m o d i t v P r i c e S t a b i l i z a t i o n , Oxford C n i v e r s i t y P r e s s

I - (1981b) ' O p t p a l Comodi ty S t o c k p i l i n g S u l e s ' , 1 Zconomic '73'eor-j Discuss ion Paper So. 4 0 , (Yarch) Cambridge , I

I

- 1 Xewbery, D.X.G. and S t i g l i t z , J . E . (1982). 'The Choice of.?ebhniques and

t h e Op t ima l i t p of Harket E q u i l i b r i m wi th R a t i o n a l E q e k t a t i o n s ' , J o u r n a l o f P o l i t i c a l Economy, A p r i l a , - - I

B r l Z

Nichols , X.L. and Zeckhauser, 2.J. (1977) ' S t o c k p i l i n g s t r a t i e g i a s and C a r r e l ?rlcesl, 3 e l l J c q ~ r n a l of Eccnomics, 3 , pp 66-36 I I

S a l a n t , 5.:;. (1979) 'The V u l n e r a b i l i t y of ? r i s e S t a b i l i z a t i o h Drogrsrns t o S p e c u l a t i v e A t t a c k , ' mimeo.

Sanuelson, ? . A . (1971) ' S t o c h a s t i c S p e c u l a t i v e P r i c e ' , ? roc . S a t . .\cad. S c i . 68 ( T e b . ) pp 335-7

Spence, A . (1977) ' E n t r y , Capaci ty I n v e s t = e n ~ , &nd O l i g o p o ~ i ~ t i c P r i c i n g ' , 3 e l l Jou rnz l of Econonics 9 ( 2 ) , pp 534-44 I

I I