Fringe size and cartel stability

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EUROPEAN UNIVERSITY INSTITUTE, FLORENCE

i h :UU*

5 ECONOMICS DEPARTMENT

EUI Working Paper ECO No. 90/16

Fringe Size and Cartel Stability

St e p h e n Ma r tin

BADIA FIESOLANA, SAN DOMENICO (FI)

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All rights reserved.

No part of this paper may be reproduced in any form

without permission of the author.

© Stephen Martin

Printed in Italy in September 1990

European University Institute

Badia Fiesolana

1-50016 San Domenico (FI)

Italy

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FRINGE SIZE AND CARTEL STABILITY S te p h e n Martin

D epartm ent of Economics European Universi ty I n s t i t u t e

J u ly 1 9 9 0

ABSTRACT: S t a ti c c a r t e l s t a b i l i t y w i t h a p r i c e - t a k i n g fringe is sh ow n t o be perilous: if fringe firms a c t a s Cournot o l ig o p o l i s t s , th e p r e s e n c e of a fringe is n e c e s s a r y for s t a t i c s t a b il i ty . Conditions for c a r t e l s t a b i l i t y in s u p e rg am e s enforced by a t r i g g e r s t r a t e g y and by a s t i c k - a n d - c a r r o t s t r a t e g y are examined.

JEL Code: 611

I th an k Ron H a r s ta d , P e t e r Hammond, and Louis P hlips for comments. R esponsibili ty for e r r o r s is my own.

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I. I n t r o d u c t i o n

Two di fferent n o t i o n s of c a r te l s t a b i l i t y a p p e a r in t h e l i t e r a t u r e . One is s t a t i c , and mig ht be called h o rizo n tal s t a b i l i t y td'A sp rem ont, Jacquemin, Gabsewicz, and Weymark [1 9 8 3 ]). A c a r t e l is h o r i z o n t a l l y s t a b l e if firms in th e c a r t e l p r e fe r t o s t a y in th e c a r t e l and firms o u ts id e t h e c a r t e l prefer t o remain o u t s i d e the c a r t e l , whe n firms are able t o c o r r e c tl y c a l c u l a te t h e c o n s e q u en c es of a s h i f t in p o s itio n . The o t h e r n o tio n of c a r t e l s t a b i l i t y is dynamic. In a r e p e a t e d game, a c a r t e l is s t a b le if t h e r e is a subgam e p e rfe c t equilibrium s t r a t e g y t h a t induces c a r t e l members t o adhere t o t h e ir c a r t e l o u t p u ts .

I examine h ere t h e im pact of fringe s iz e on c a r t e l s t a b i l i t y in b o t h t h e s e s e n s e s . The p re s en c e of a fringe is much more d e s t r u c t i v e fo r h o r iz o n ta l s t a b i l i t y t h a n a p p e a r s from t h e l it e r a t u r e , b u t a

re fo rm u latio n of t h e h o r i z o n t a l s t a b i l i t y problem a l t e r s t h i s r esu lt. I conclud e b y examining t h e c o n d it io n s for dynamic c a r t e l s t a b i l i t y in t h e p r e s e n c e of a fringe if collu sion is e n forc ed by a t r i g g e r

s t r a t e g y [Friedman [ 1 9 7 1 ] ) o r by a s t i c k - a n d - c a r r o t s t r a t e g y (Abreu [1 9 8 6 ]).

II. S t a t i c Models - Horizonta l Cartel S ta b ility A. Carte l S t a b ility W it h a P ric e-T ak in g Fringe

The Model

N firms prod uc e a hom ogen eous product. F of t h e s e firms are p r i c e - t a k e r s , forming a c o m p e titiv e fringe. The remaining K firms a c t a s a c a r t e l and maximize pro fit, tak in g fringe b e havior into acco u n t.

The in verse demand curve is linear:

(1) p - a - bO . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Each firm o p e r a t e s w i t h a c o s t func tio n c(q) = cq + dq2 ,

w here d is a p a r a m e t e r t h a t in d ex e s t h e e x t e n t of d ise co n o m ies of scale.

Since fringe firms are assu m e d t o be price t a k e r s , d m u s t be p o s itiv e if t h e r e is t o be any p o s s ib i l it y of c a r t e l s t a b i l i t y . If fringe firms a c t as price t a k e r s and r e tu r n s to s c a le are c o n s t a n t , fringe firms will su p p ly t h e e n ti r e m arket a t a price equal t o a v erag e c o s t . This lim its t h e a p p lic ab ility of t h e model, sin ce empirical s t u d i e s m o s t o f te n find a s u b s t a n t i a l range of o u t p u t over w hich r e tu r n s t o scale are a p p r o x im a t e ly c o n s t a n t.1 As will be sh o w n p r e s e n tly , th e requ ire ment t h a t d be g r e a t e r t h a n zero can be elim inated b y re s p e c if y in g fringe behavior.

E ac h fringe firm, a c t i n g a s a p r i c e - t a k e r , picks an o u t p u t t h a t e q u a t e s marginal c o s t and price. The fringe firm and fringe su p p ly fu n cti o n s are t h e r e f o r e

(3) P - c _{2 d} _{°F ' ^}

S u b s ti t u ti n g for 0 F from (3) in to (1) and c o ll e c t in g term s, t h e c a r t e l residual demand curve, w r i t t e n in inverse form, is

(4 ] p - c + p + 2g(S - Qk) .

6 = g is th e dise conomies of s c a le pa ram ete r m easured in p r o p o rtio n t o t h e slo p e of t h e demand curve. S = ^ T - - is t h e u p p e r limit of t h e q u a n tity demanded as price a p p r o a c h e s c, t h e minimum value of av era g e/m arg in al c o s t . I t can be t h o u g h t of a s a m ea s u re of m arket size.

1. See Martin [ 1 9 8 8 , p. 24] for referen ces.

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J o i n t p r o f it m ax im iz atio n implies t h a t e a c h firm in t h e c arte! will p ro d u c e a t t h e same marginal c o s t . Since c o s t f u n c tio n s are id en tica l a c r o s s firms, e a c h firm in t h e c a r t e l will produce t h e same o u t p u t . The c a r t e l c o s t fu n cti o n for o u t p u t QK is th en

(5 ) C(Qk ) = K c ( x ) * c 0 K * dX •

S e t t i n g marginal revenue from (4) equal t o marginal c o s t from (5), p r o fit-m ax im iz in g o u t p u t p e r c a r t e l member is

(6J \ = R- T ' 2 6 - T -k '

S u b s t i t u t i n g (6) into (4), t h e price which maximizes c a r te l profit is

(7) (N ♦ 26)

(N * 2 6 )2 - K22b6S

From (3), (6), and (7), profit per c a r te l firm and fringe firm are (8a) and n k(KJ4) b6S (N h- 26)2 - K2 (8b) 7i,(KJ4) b6S'

[

26 (N 25 )2 - K'

J

r e s p e c t i v e l y.2

Following d'A sprem on t, Jacquemin, Gabszewicz and Weymark [1 9 8 3 ] , a c a r t e l is in te rn ally s t a b le if a firm which is a member of th e c a r t e l e a r n s a t l e a s t a s g r e a t a pro fit by remaining w i t h t h e c a r te l a s it would by joining t h e fringe,

(9 ) 7ik(KJsl) 2 7r,(K - 1.N) .

Similarly, a c a r t e l is e x te r n a l l y s t a b le if a fringe firm e a r n s a t l e a s t a s g r e a t a p r o f it by s t a y i n g in t h e fringe a s it would by joining t h e c a r t e l . The c a r t e l is e x te r n a l l y s t a b le if F > 1 ( o t h e r w i s e , t h e r e are no firms in t h e fringe) and

2. 7Tk and 3rf are pro p o rtio n a l t o th e square of m arket siz e S. C hanges in m ark e t siz e have n o effe c t on h o r i z o n t a l s t a b i l i t y , since t h e y do n o t affe c t t h e r a t i o of c a r t e l firm and fringe firm

p r o f i ts . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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4

( 1 0 ) 71,(KM 2 7ik(K - 1 ,N) .

Firms have d e ta ile d informatio n a b o u t th e e f fe c t of c h a n g e s in t h e i r own o u t p u t on price (Dorisimoni e t al [ 1 9 8 6 , pp. 3 1 9 - 3 2 0 ] ) :

...firms are assum ed t o have e x a c t knowledge of t h e dependence of p r o f i t s a t equilibrium on t h e s i z e of t h e c artel: i.e., t h e y know t h e fu n cti o n s [nk(K,N)] and [7if(KJd)]... This l a t t e r knowledge is indispens able , si nce a move b y firms a f f e c t s t h e s i z e of t h e c a r t e l and hence t h e re s u l ti n g level and d i s t r ib u t i o n of pro fits . S t a b il i ty of t h e Cartel of t h e Whole

If all firms join t h e c artel, e x te r n a l s t a b i l i t y is n o t an issu e. Fo r th e c a r t e l of t h e whole, we n e ed only examine t h e c o n d itio n for in te rn al s t a b il i ty . The c a r t e l of t h e who le is in te rn ally s t a b l e if

The second r i g h t - h a n d - s i d e term in (1 2 ) is n eg ativ e, and in equalit y (1 2 ) is s a tis f ie d , for all valu es of 6 if N - 1, 2, or 3. The c a r t e l of th e who le is t h u s in te rn ally s t a b le for N = 1, 2, and 3.

If N 2 4, t h e second r i g h t - h a n d - s i d e term in (12) is positive. By division, if N 2 4, th e c a r te l of th e whole will be st a b le if

The term on t h e rig h t is an u p per bound for values of 6 t h a t are c o n s i s t e n t w i t h in te rnal s t a b i l i t y for t h e c a r te l of t h e w hole when t h e r e a re 4 or more firms.

The u p per bound co n v erg es t o z e r o a s N rises. Fo r 4 or more firms, t h e c a r t e l of t h e whole will be u n s ta b le if d ise co n o m ies of s c a le are t o o g r e a t . If 6 is sufficie ntly small, t h e c a r t e l of th e (1 1) 7ik (N >l) 2 71,(N - 1 Jsl)

or. using (8a) and (8b), if

(1 2) (N - l ) ‘t 2 (N » 26)2[2(N - l )2 - N2)

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whole will be st able .

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H o riz o n ta l S t a b i l i t y W it h a P ric e-T ak in g Fringe

Now s u p p o s e t h e fringe is n o n - e m p ty . Consider f i r s t in te rn al s t a b i l i t y . When t h e r e is a t l e a s t one firm in t h e fringe, th e in te rn al s t a b i l i t y c o n d itio n (9) b eco m es

(1 4 ) (K - l)4 2 (N ♦ 26)2[2(K - l )2 - K2] . For K = 1, 2, and 3, (1 4 ) is s a t i s f i e d for all N and 6. Combined w i t h t h e r e s u l t s of t h e p re v io u s s e c ti o n , it follows t h a t a o n e - , t w o - or t h r e e - f i r m c a r t e l is in te r n a lly s t a b l e for all v alu es of 6 and for all v a lu e s of F.

For K 2 4, t h e second term on t h e r ight in (14) is positive. By division, t h e c a r t e l will be in te r n a lly s ta b le if

(1 5 ) F ♦ 28 < f t l)2 . K .

«J2(K - l ) 2 - K2

The t e r m on t h e left is an u p p e r bound on t h e size of t h e fringe t h a t is c o n s i s t e n t w i t h in te rn al c a r t e l s ta b ility .

Fo r K - 4, a c a r t e l will be inte rnally s t a b le for F ♦ 26 s 2.36. The maximum number of fringe members c o n s i s t e n t w i t h in te rnal s t a b i l i t y of a fou r-m em b er c a r t e l is 2; th e e x a c t u p p e r bound on F dep en d s on 8. If t h e r e are 3 or more firms in t h e fringe, t h e n t h e p r o f it s p l i t by a 4 - f i r m c a r t e l is s o small t h a t a c a r t e l member will find it p ro fita b le t o join t h e fringe.

Fo r K = 5, a c a r t e l will be in te rn ally s t a b le for F + 26 s 1.05. The maximum number of fringe firms c o n s i s t e n t w ith in te rn al s t a b i l i t y of a fiv e-firm c a r t e l is 1 . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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6

For K = 6, th e upper limit on F + 26 is 0.68, which is le s s than one. F u rth e r, t h e u p p e r limit on F * 26 falls as K rises. I t follo w s t h a t c a r t e l s of 6 or more firms are internally unstable if t h e r e are any firms in t h e fringe.

The d is c u s s io n to t h i s poi nt h a s e s t a b l i s h e d th e following; P rop osition X; A c a r t e l of 1, 2 or 3 firms is inte rnal ly s t a b le , r e g a r d l e s s of t h e size of t h e p r i c e - t a k i n g fringe; c a r t e l s of 4 and 5 firms may be inte rnally s t a b le w ith fringes of no more t h a n 2 or 1 fringe firms, r e s p e c tiv e ly , if 6 is sufficiently small; c a r t e l s of 6 or more firms are in te rn ally u n s ta b le if t h e r e are any fringe firms; th e c a r t e l of th e whole is in te rn ally s t a b le , provided 5 is s u ffic ie n tly small.

Now turn t o e x te r n a l s t a b il i ty . Using (8a) and (8b), th e e x te r n a l s t a b i l i t y condit ion (10 ) is

(16 ) 0 s (N + 26)2[(K *■ l)2 - 2K2) * K4 .

In eq u alit y (16 ) is v io la ted for all values of N and 6 if K = 1 or 2. A fringe firm will alw ays w ant t o join a o n e - or t w o - f i r m c a r te l, and s u c h c a r t e l s are e x te r n a l l y u n s ta b le unles s t h e fringe is empty.

For K a 3, t h e e x te rn al s t a b i l i t y c ondit ion (16) is s a t i s f i e d for values of F s u fficie ntl y large;

(17 ) F * 26 > ■ ... . ... - K N2K2 - (K ♦ l )2

The more firms t h e r e are in t h e fringe, t h e smaller t h e p ro fit c o ll e c t e d by e ac h c a r t e l member. If t h e number of firms in t h e fringe is large enough, fringe firms will n o t be t e m p t e d t o join t h e c artel.

For K = 3, a c a r t e l will be e x t e r n a l l y s t a b le provided F + 26 a 3 .36. I t h as been sh ow n above t h a t a 3 -firm c a r t e l Is In ternall y s t a b l e for all values of F and 6. Thus a 3 -flrm cartel t h a t d o e s not

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include all firms will be h o ri z o n t a l l y s t a b l e - i n te r n a lly s t a b l e and e x te r n a l l y s t a b l e - if t h e r e are a t l e a s t 4 firms in t h e fringe, and p o s s ib l y w i t h few er fringe firms, depending on t h e value of 6.

Fo r K - 4, a c a r t e l will be e x te r n a l l y s t a b le if F + 26 2 2.05. Combined w i t h t h e c o n d itio n for i n te r n a l s t a b i l i t y , a 4 - f i r m c a r t e l t h a t d o e s n o t include all firms will be h o ri z o n t a l l y s t a b l e provided 2 .3 6 2 F ♦ 25 2 2.05. If F * 2, t h e r e is a n a rro w range

for 6 (0.1 8 2 6 2 0.05) over which t h i s c ondition is met. If F - 1, t h e r e is an implausib le range for 6 (0.6 8 2 6 2 0.53) over which t h is c o n d itio n is m et . But for F 2 3, a 4 -firm c a r t e l is n o t h o r i z o n t a l l y sta b le .

A 5 - f i r m c a r t e l will be e x t e r n a l l y s t a b l e provided F + 26 2 1.68. But for K - 5, in te r n a l s t a b i l i t y r e q u ir e s F ♦ 26 s 1.05. I t follows t h a t t h e p r e s e n c e of any fringe a t all will d e s ta b iliz e a c a r t e l of 5 o r more firms. If t h e number of fringe firms is t o o small, firms in t h e fringe will w a n t t o join t h e c a r t e l . If t h e number of firms in t h e c a r t e l is t o o g r e a t , t h e n c a r t e l mem be rs will w a n t t o jo in t h e fringe. The same r e s u l t holds for all K 2 5. This d is c u s s io n e s t a b l i s h e s t h e follow ing for c a s e s whe n t h e number of firms in t h e fringe is p o sitiv e:

P ro p o s itio n 2: If t h e number of fringe firms is p o s itiv e , a 3 -firm c a r t e l is h o r i z o n t a l l y s t a b l e if t h e r e a r e 4 o r more fringe firms (and may be h o r i z o n t a l l y s t a b le for a sm all er fringe, depending on the value of 6)i a four-firm c a r te l may be horizo n tally st a b le for a fringe of 1 o r 2 firms (depending on t h e value of 6); c a r t e l s of 1 firm, 2 firms, o r 5 or more firms a re h o r i z o n t a l l y u n sta b le .

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8

Taking P r o p o s it i o n s 1 and 2 t o g e t h e r , it a p p e a r s t h a t a n y th in g l e s s t h a n c o m p le te coll usi on is unlikely t o be h o rizo n tally s t a b le , if fringe firms a c t a s p r i c e - t a k e r s . But is it reaso n ab le t o r e g a r d e x te r n a l s t a b i l i t y a s a n e c e s s a r y co n d it io n for c a r t e l s t a b i l i t y when fringe firms a c t a s p rice ta k e r s ?

On t h e one hand, fringe firms are assum ed t o a c t a s price ta k e r s . P r i c e - t a k i n g b e h av io r is usu ally th o u g h t of as a re aso nable

s p e c if i c a t io n if fringe firms ignore t h e e f fe c t of ch an g es in t h e i r own o u t p u t on price. But in t h is model, firms are assum ed t o know en ough about t h e w ay th e i r o u t p u t a f f e c t s price t o be able to c a lc u la te t h e w ay t h e i r profit would c hange if t h e y were t o s w it c h from one gr oup t o a n o th e r.

In models of c o m p e titiv e m ark e ts , it is o f t e n argued t h a t it is re aso n a b le t o e x p e c t firms t o ignore t h e e ffe c t of c h an g e s in t h e i r own o u t p u t on price if e a c h firm is small re la tiv e t o t h e m ark e t. In t h is model, fringe firms free ride on th e c a r te l, and in equilibrium fringe firms prod uc e more t h a n c a r t e l firms.

The model p r e s e n t e d here (which follows t h e l i t e r a t u r e ) as s u m e s t h a t fringe firms have spe cific and d e ta ile d informatio n a b o u t t h e way th e i r o u t p u t a f f e c t s m ark e t equilibrium, t h a t t h e y make d e cis io n s on w hich role t o play b a s e d on t h is information, and t h a t t h e y ignore t h is informatio n whe n t h e y make o u t p u t decisions . Each e le m ent of t h i s s p e c if i c a t io n can be plausible, for some p u rp o se s. The

combina tio n is u n s a t i s f a c t o r y . © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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B. Carte l S t a b il i ty W i t h a Cournot Fringe

In t h i s s e c ti o n , I e x p lo re t h e im p lica tio n s of an a l t e r n a t i v e s p e c if ic a tio n of fringe firm b e havior for h o r i z o n t a l c a r t e l s t a b i l i t y . As in t h e p re v io u s s e c ti o n , I assu m e t h a t fringe firms have en o u g h infor matio n t o c a l c u l a te t h e effe c t on p r o f it if th e y jo in t h e c a r t e l . But in t h is s e c ti o n , I assum e t h a t e a c h fringe firm picks an o u t p u t t h a t maxim izes i t s ow n p ro fit, t a k i n g th e o u t p u t of o t h e r firms as given. O utput d e c is io n s and t h e decisio n on w h e t h e r o r n o t t o remain w ith t h e fringe are made usi ng t h e same d e g ree and t y p e of

information.

Since firms in a Cournot fringe will v o lu n ta rily limit o u t p u t , th is s p e c if i c a t io n p e r m i t s me t o d is p e n s e w i t h t h e a s s u m p t io n t h a t t h e r e are d e c r e a s in g r e t u r n s t o s c a le . For s im pli cit y, t h e r e f o r e , in w h a t follows I s e t 6 » 0.3

Eac h fringe firm will s e l e c t o u t p u t a lo ng a r e a c t i o n curve

w here QK is c a r t e l o u t p u t and 0F_j is the combined o u t p u t of all fringe firms e x c e p t firm j. But in equilibrium, all fringe firms will prod uc e th e same o u t p u t. Equilibrium fringe firm and fringe o u t p u t are t h e r e f o r e (18) - è ® - °K ' ° F - j ) ' 3. I f 6 > 0, 7ikCFJt) (N * 1 * 26 - KHK * 6(N * 1 <■ 26 * K)] bCI * 26)2

The c o r re s p o n d in g s t a b i l i t y c o n d itio n s have defied t r a c t a b l e a n aly sis.

tv J|C 0 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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10

S - Q, S - 0 ,

0 9 ) ^ - T - r f Or ■ f t -t t •

From (19), t h e residual demand curve facing t h e c a r t e l is

(2 0 ) p - c - p - r r ( S - 0 K) .

Using t h e c a r t e l c o s t functio n (5), p ro fit- m ax im iz in g c a r t e l firm arid c a r t e l o u t p u t are

C2i>

\ - H

I )

- 1

A c tin g a s a S ta c k e lb e r g q u a n ti t y leader a g a i n s t Cournot firms, th e c a r t e l pro d u ces t h e m onop oly o u t p u t.

S u b s ti t u ti n g (2 1 ) in to (19 ) and (20) gives fringe firm o u t p u t

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■

f

-

t t

( I )

and t h e c a r t e l price (23)

P rofit per c a r t e l firm and fringe firm profit are p = c * f-t t ¥ • (2 4a) n k(FJt) _KlF

‘H r C f ]

and (24 b) h,(F) - -— ^ f f l 2 ' (F * l ) 2*' 2 J

F ir s t co n sid er t h e s t a b i l i t y of t h e c a r t e l of t h e whole. If all firms are in t h e c artel, we need only co n sid er t h e c ondit ion for in te rn al s t a b il i ty . The c a r t e l of t h e w ho le is sta b le if

(2 5 a ) nk(0J4) 2 ti((1) ,

or if

(25 b) 4 2 N .

If t h e r e are four or few er firms su pplying t h e market, t h e c a r te l of t h e whole is sta b le . If t h e r e are five o r more firms in t h e c artel, e a c h c a r t e l member's s h a r e of c a r t e l pro fit is so small t h a t it is p ro fita b le t o d efect, and t h e c a r t e l of t h e whole is inte rnally u nstable . © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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If t h e nu mber of fringe firms is p o s itiv e , c o n d itio n s for in te rn al and e x te r n a l s t a b i l i t y yield t h e h o r i z o n t a l s t a b i l i t y c ondit ion

a K a

_ ,

F + 1 F F » 3 + p - J —j- > K 2 F * 1 - t p-

w h e re t h e f i r s t in eq u alit y is n e c e s s a r y and su ffic ie n t for inte rnal s t a b i l i t y and t h e s e c o n d in eq u alit y is n e c e s s a r y and s u f f ic ie n t for e x te r n a l s t a b ility .

Since K and F are i n te g e rs , (26 b) implies t h a t if t h e r e are F firms in t h e fringe, only c a r t e l s o f K = F * 2 or K ■ F * 3 firms will be stable .

We have now e s t a b l i s h e d

P rop osition 3: If fringe firms a c t a s Cournot q u a n t i t y - s e t t e r s , t h e c a r t e l of t h e w ho le is inte rnally s t a b le fo r up t o 4 firms; o t h e r w is e , a c a r t e l of K firms is s t a b l e if and only if t h e r e are K - 2 o r K - 3 firms in t h e fringe.

When firms in t h e fringe a c t a s price t a k e r s , t h e p r e s e n c e of a fringe ba sica ll y a c t s t o d e s ta b iliz e a c a r t e l , u n les s t h e c a r t e l is formed by a small number of firms. The p r o g n o s i s fo r m a r k e t pe rform ance is o p t im i s t ic : if fringe firms a c t as price t a k e r s , a c a r t e l is likely t o be u n s ta b le u n les s it includes all firms. But it will be difficult t o form c a r t e l s of t h e who le u n le s s t h e number of firms is small.

When firms in t h e fringe a c t a s Cournot o l ig o p o l i s t s , t h e ro le of t h e fringe is q u ite different, and s o is t h e implied p r e d ic ti o n for t h e impact of a fringe on m ark e t performance . If fringe firms a c t as o l ig o p o l i s t s , a c a r t e l will be s t a b le if t h e r e a re eno u g h firms in t h e

(2 6a) or (26b) © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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12

fringe s o t h a t fringe firm pro fit is n o t t o o gre at; o t h e r w is e c a r te l members will be t e m p t e d t o d efect t o t h e fringe. At t h e same time, t h e r e m u st be eno u g h firms in t h e c a r te l s o t h a t fringe firms are n ot t e m p t e d t o join t h e c a r t e l .

If fringe firms t a k e a cc o u n t of th e e ffe ct t h e i r o u t p u t deci si ons have on price, t h e n p a r ti a l s t a b le c a r t e l s are a p o s s ib ilit y . In such c a s e s , th e p r e s e n c e of a fringe does n o t s u g g e s t t h a t t h e c a r te l will e ventually break down. Indeed, t h e p re s en c e of a Cournot fringe only s l i g h tl y smaller t h a n t h e c a r t e l s e r v e s t o s ta b ilize p arti al

collusion.

III. Fringe Size and Ca rte l S t a b il i ty in Su pe rgames

Ho rizonta l s t a b i l i t y is a s t a t i c c o n cep t. In a r e p e a t e d game, collusive be hav ior is s t a b le if it is s u p p o r t e d by a subgame p erfect equilibrium s t r a t e g y . This is t h e a p p r o p r i a te n o t io n of s t a b il i ty for n o n c o o p e r a tiv e co ll u sio n by a pa rti al c artel, and I examine here t h e im pa ct of fringe siz e on t h e s t a b i l i t y of collusion in su pergam es w he n collu sio n is s u p p o r t e d by a t r i g g e r s t r a t e g y (Friedman [1985;

1 986, pp. 9 4 - 1 0 3 ) ) o r by a t w o - p h a s e s t i c k - a n d - c a r r o t s t r a t e g y (Abreu [1 9 8 6 ]). Subgame p e r fe c ti o n t h e r e f o r e t a k e s t h e place of t h e internal s t a b i l i t y c ondit ion ap pli ed in a s t a t i c model.

Even in a r e p e a t e d game, however, e x te rn al s t a b i l i t y is th e a p p r o p r i a te c o n d itio n for firms in a Cournot fringe. Such firms maximize th e i r own r e tu rn , given t h e o u t p u t of o t h e r firms. If subgame p e r fe c tio n indu ce s c a r t e l firms t o maintain t h e i r t a c i t l y collusive o u t p u ts , and firms in t h e fringe find it p rofita ble to remain in t h e fringe, t h e n no firm will wish t o d efect from i t s role, and t h e c a r t e l will p e r s i s t . © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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A. Trigge r S t r a t e g y

Consider a su p erg am e v e rsio n of t h e c o n s t a n t r e t u r n s t o s cale model ou tli ned above. K firms form a p a r tia l c a r t e l in a m ark e t w ith an F-firm Cournot fringe. The m ark e t o p e r a t e s for an infinite number of periods. Each firm in t h e c a r t e l s e e k s t o maximize t h e p r e s e n t d i s c o u n te d value of i t s p ro fit. A t r ig g e r s t r a t e g y for c a r t e l members is t o

(a) produce Tk = } in t h e f i r s t period; a f t e r t h e first period, play qk if all c a r t e l members play ed qk in t h e previo us period;

C

(b) r e v e r t t o 9Cournol “ -■ —p in any p e rio d following d efecti o n from q . , and c o n ti n u e t o play q t h e r e a f t e r .

k r ^Cournot

Fringe firms a c t a s Cournot q u a n t i t y - s e t t e r s . A fringe firm

c a s e , a fringe firm is maximizing i t s own payoff, given t h e o u t p u t s of o t h e r firms.

Following Friedman ( 1 9 7 1 ; 1986 ), a t r i g g e r s t r a t e g y will s u p p o r t n o n c o o p e r a tiv e coll usi on if t h e p r e s e n t d isc o u n te d value of t h e income s t r e a m from adhering t o t h e s t r a t e g y Is a t l e a s t a s g r e a t a s t h e p r e s e n t disco u n te d value of t h e income s t r e a m from d e fec tio n . Fo r t h e c a s e a t hand, c a r t e l mem bers will p r e fe r to ad h ere t o t h e t r i g g e r s t r a t e g y if

collusion h as n o t brok en down and q

Cournot if c a r te l members have r e v e r t e d to C ournot behavior. In e a c h

(27) _1_ s " d e f e c t " k r 7Tk "coumot w h e r e r is t h e i n t e r e s t r a t e u s e d to disco u n t f u tu re income. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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14

n. is given by (24a). If all firms play q , e a c h firm

K Cournot

e a r n s a profit

71 Cournot '

bC

K * F * f j

I t re main s t o dete rm ine a c a r t e l member's o n e - p e r i o d pro fit if it d e f e c t s from t h e t r ig g e r s t r a t e g y . If K - 1 c a r t e l mem bers play qk and F fringe firms prod uc e qf, a sin gle c a r t e l member fa ce s th e resid ual demand curve

fo o l „ * K ♦ F O r bS 1 .

( 2 9 ) P - c K(F ♦ 1) l 2 ) ' bqi ■

The d e f e c tin g firm's p ro fit-m ax im iz in g o u t p u t and maximum p ro fit are

t 3 0 ) q d e f« c t “ K K ( F F- l / [ I ]

and

( 3 1 ) " d e f e c t ' b [ K K ( F F* 1 ) ' 4 ] '

S u b s t i t u t i n g t h e v a rio u s e x p r e s s i o n s for pro fit in (2 7 ) and sim plifying, t h e t r i g g e r s t r a t e g y o u tli ned above will s u s t a i n n o n c o o p e r a ti v e j o in t p r o f it maxim iz at ion by t h e c a r t e l i f4

(32 ) i (K ♦ F + 1 ) ₄ _{K(F - 1)}

For n o t a t i o n a l sim pli cit y, let z - ^ Then

(3 3 a ) (33 b) (3 3 c )

U

. . ?2 - - - r ....»- 2i )2 < 0 3F K(F * l ) 2 3z _ K2 - (F + I )2 3K _K2(F

₁₎

> 0 3zj (K F •*' P [K2 - (F ♦ l ) 2] e 3F N-R K2(F ♦ l ) '

w h e re t h e s i g n s of t h e d e riv a tiv e s depend on t h e a s s u m p t io n t h a t th e c o n d itio n for e x te r n a l s t a b i l i t y condition , (26b), is met.

4. If (32 ) is v io la ted , u s e of a t r i g g e r s t r a t e g y will allow a c a r t e l t o in c r e a s e p r o f it com pared w i t h Cournot behavior, b ut t h e c a r t e l will n o t be able t o maximize j o in t profit.

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The d e riv a tiv e s (33 ) e s t a b l i s h

P r o p o s i t i o n 4: If fringe firms a c t a s Cournot q u a n t i t y - s e t t e r s and t h e e x te r n a l s t a b i l i t y c o n d itio n is met, an in c r e a s e in fringe siz e and an i n cre as e in fringe siz e, holding th e number of firms in t h e i n d u s tr y c o n s t a n t , r a is e t h e u p p e r limit of t h e ra n g e of i n t e r e s t r a t e s ov er w hich t h e t r ig g e r s t r a t e g y is a subgame p e r f e c t equilibrium for c a r t e l j o in t pro fit maximization; an increas e in t h e number of c a r t e l mem be rs and an i n cre as e in t h e number of c a r t e l members, holding t h e number of firms c o n s t a n t , h as t h e o p p o s i t e effe c t. B. S t l c k - a n d - C a r r o t S t r a t e g y

A t r i g g e r s t r a t e g y s u s t a i n s c o o p e r a tiv e be h av io r b y a s e v e re t h r e a t ; if any play e r d e f e c t s from t h e c o o p e r a ti v e p a th , all p l a y e r s fo reg o collusive r e tu r n s fo rev e r t o pun ish t h e d e f e c to r . The r e s u l ti n g s t r a t e g y v e c t o r is a subgame p erfect equilibrium. But it is n a tu r a l t o i n v e s ti g a te t h e s t r u c t u r e of s t r a t e g i e s t h a t a re l e s s grim t h a n t r ig g e r s t r a t e g i e s .

Abreu ( 1 9 8 6 ) o u tlin e s a sym m etric, t w o - p h a s e o u t p u t p a t h t h a t s u s t a i n s collusive o u tc o m e s for an n -firm oligopoly of identica l q u a n t i t y - s e t t i n g firms. An o u t p u t p a t h is sy m m etric if all firms pr oduce t h e same o u t p u t in any one period. An o u t p u t p a t h h a s tw o p h a s e s if in any period firms produce one or t h e o t h e r of tw o sp ecific values.

The o u t p u t p a t h c o n sid ere d by Abreu h a s a s t i c k and c a r r o t p a t t e r n . The o u t p u t p a t h beg in s w i t h a single p e rio d of high p e r -f ir m o u t p u t (qh ) and low p e r-firm p ro fit, followed by a s w i t c h t o low p e r - firm o u t p u t (q() and high p e r -f ir m p ro fit. qh and q > a re d ete rm in ed by c o n d itio n s t h a t make t h e t w o - p h a s e o u t p u t p a t h a subgam e p e r fe c t equilibrium s t r a t e g y . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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16

The equilibrium s t r a t e g y c o n s id ere d by Abreu begin s w i t h all firms produ cing qh, follow ed by q^ The s t r a t e g y calls for all firms t o c o n ti n u e t o p roduce q^ u n l e s s an ep is o d e of d e f ec tio n o c cu rs. If some firm d e f e c t s ( e i t h e r whe n it is s u p p o s e d t o p roduce q or whe n it is s u p p o s e d t o p roduce q ^ , t h e s t i c k - c a r r o t o u t p u t p a t h defined by t h e o u t p u t pair Cq^. q ^ is r e s t a r t e d from t h e beginning.

L et 7t(q) be per firm p ro fit if all firms produce q, and let n ‘(q) be b e s t - r e s p o n s e firm p r o f it if all o t h e r firms produce q.

The c o n d itio n s fo r s t a b i l i t y a re t h a t adherence is a t l e a s t as p ro fita b le a s d e f e c ti o n w he n q = qh and when q - q (. If o u t p u t is qh> t h i s co n d it io n be com es

(34) "*(qh) - " ( V

“ 2 * ( q , ~ * ( q hl

w h e re a = -j- -7 — is t h e disc ount fa ctor. Abreu [19 8 6 ] s h o w s t h a t t h i s co n d it io n will hold w i t h equality . If all firms produ ce q (, th e s t a b i l i t y c o n d itio n is

**n*(q,) - n(q|)**

a 2 [n(q ) - rr(qj)

I n

If (3 5 ) is s a t i s f i e d w hen all firms in t h e c a r te l pro duce t h e (35)

j o in t p r o f it maximizing o u t p u t q, , t h e n qt is determined by solving

J TTTQ h

(34 ) w i t h q - q If (35 ) is v io la te d when q • q , t h e n q

M Jum M ’ jum l

qh a re d ete rm in ed by solving (34 ) and (35), when (35) holds w i t h e q u ality , a s a s y s t e m of sim u lta n eo u s equations.

Begin w i t h t h e c a s e In w hich q > q, . If (34) and I jum (35 ) hold w i t h e q u ality , t h e n n '( q h) ' 71 n*(qt) - ^(q,) and (36) ___________ V ____— M' b b

In t h e model c o n sid ere d h ere, t h i s is

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(37) _K _{- r - T - ^ T ] 2 =} _h _{- r - H} _{^ r ) 2 .}

w h ic h h a s t w o r o o t s . This fi r s t is qh - q ^ w hich can be ruled o u t here. The se c o n d i s5

(38)

(39)

1. + \ ' 2K" + F + 1 '

The o t h e r e q u a t i o n needed t o solve for q ] and q^, a ls o from (34), is

an l q ^ - 7i(qh) 7i*(qh) “ n(qh )

b ' b

E v alu atin g t h e v a r io u s e x p r e s s i o n s for profit, t h i s b eco m es

™

- v k

* « . , - ! ] ■

~ r

^

r

) 2

S u b s t i t u t i n g (38) in to (40) g i v e s6 ( 4 1 a ) _{q> =}

f

1 ♦ 8 a lK - (F * 1 ) U F / l (K + F + l ) 2 ( 4 1 b ) r i - 8 a t* - g - - 1) l (K » F + ♦ 1 )2

T h es e s o l u t i o n s are valid s o long as q

2

q =

^r,

and

M unm 2K

from (4 1a), t h i s c o n d itio n is met if

(42) (K * F ♦ l ) 2 s _{K(F ♦ 1)} _{2 1 6 a}

5. A ltern a tiv e ly , w r i t e

S _ S

n * 1 " n + 1

qft is a s far above t h e Cournot equilibrium o u t p u t level a s q ) is below t h e C ournot equilibrium o u t p u t level.

6. If (42 ) Is v io la ted , a p a r tia l c a r t e l will be able t o maximize Jo int p ro fit. In t h i s c as e, q^ is determined by solving (39) w ith

q,

= q,

.

The r e s u l t is a _ r 1 + 2(F - l)«fcK K - (F + 1) I S

h

L

N + 1 - 2(F ♦ 1 ) 4oK 2K J N ♦ 1 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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18

I t follows t h a t a s t i c k - a n d - c a r r o t s t r a t e g y will be a subgame p e r fe c t equilibrium s t r a t e g y for t h e m ax im iz atio n of j o in t p r o f it if

(43) _{01 2 Ï 6}r. . 1 (K ♦ F •* 1 )2_{K ( F ”}_{1 )}

Comparing (32 ) and ( 4 3),7 it is evident t h a t ch an g e s in K and F will affe c t t h e rang e of i n t e r e s t r a t e s over w hich a p a r tia l c a r t e l will be able t o s u s t a i n p a r ti a l j o i n t pro fit m ax im iz atio n u sin g a c a r r o t - a n d - s t i c k s t r a t e g y in t h e same w ay t h a t s u c h c h a n g e s affe c t t h e range of i n t e r e s t r a t e s over w hich a pa rti al c a r t e l will be able t o s u s t a i n p a r ti a l jo in t pro fit maxim iz at ion using a t r i g g e r s t r a t e g y .

T he r e s u l t s of t h i s s e c t i o n are t h e r e f o r e

P ro p o s itio n 5; If fringe firms a c t a s Cournot q u a n t i t y - s e t t e r s and t h e e x te r n a l s t a b i l i t y condit ion is met, an in cre as e in fringe siz e and an increas e in fringe size, holding t h e number of firms in t h e i n d u s t r y c o n s t a n t , r a is e t h e u p p e r limit on t h e range of i n t e r e s t r a t e s o v e r which a s t i c k - a n d - c a r r o t s t r a t e g y is a subgame p e r f e c t equilibrium for c a r t e l jo in t pro fit maximization: an in cre as e in t h e number of c a r t e l members and an in cre as e in th e number of c a r t e l members, holding th e number of firms c o n s t a n t , h as t h e o p p o s i t e effe ct.

7. And reca lling t h a t a - ^ * If (4 3 ) is viola ted , u s e of a s t i c k and c a r r o t s t r a t e g y will allow a a c a r t e l t o i n cre as e pro fit co mpared w i t h Cournot behavior, b u t will n o t be able t o maximize jo in t pr ofit. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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IV. Summary

If fringe firms a c t a s price ta k e r s , a n y th i n g le s s t h a n a c o m p le te c a r t e l is likely t o be u n s ta b le . If fringe firms b e h av e a s Cournot o l ig o p o l i s t s , t h e p re s en c e of a fringe of t h e a p p r o p r i a t e size s e r v e s t o s t a b il i z e t h e c artel.

E it h e r a t r i g g e r s t r a t e g y o r a s t i c k - a n d - c a r r o t s t r a t e g y will s u s t a i n c a r t e l j o in t p r o f it m axim iz ation in t h e p r e s e n c e of a fringe, if t h e d is c o u n t f a c t o r is su ffic ie n tl y c lo s e t o one. If th e s t a t i c e x te r n a l s t a b i l i t y c o n d itio n is met, c h a n g e s in fringe siz e and c a r t e l siz e affe c t t h e ra n g e o v e r which s u c h s t r a t e g i e s will s u p p o r t c a r t e l j o i n t p r o f it m ax im iz atio n in t h e same ( q u ali tativ e) way. A d e c r e a s e in c a r t e l s i z e or an i n cre as e in fringe size i n c r e a s e s t h e range of i n t e r e s t r a t e s ov er w h ic h t h e s t r a t e g y will s u p p o r t n o n c o o p e r a ti v e collusion. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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20

REFERENCES

Abreu, Dilip "Extremal equilibria of o lig o p o lis tic s u p e rg am e s ," J o urnal of Economic T h eo ry Volume 39, Number 1, J u n e 1 9 8 6 , pp. 1 9 1 - 2 2 5 .

d'A sp remon t, Claude, Jacquemin, Alexis, Gabszewlcz, J e a n J a sk o ld , and Weymark, J o h n A. "On t h e S t a b il i ty of Collusive Price Lea dership," Canadian J o urnal of Econ omics Volume 16, Number 1, F ebruary

1 9 8 3 , pp. 1 7 - 2 5 .

Donsimoni, Marie-Paule "S ta b le H etero g e n eo u s C a rte ls," I n t e r n a tio n a l J o urnal of In d u s tr ia l Org aniza ti on Volume 3, Number 4, December 1 9 8 5 , pp. 4 5 1 - 4 6 7 .

Donsimoni, Marie-Paule, Economides, N. S., and Po lem archakis, H. M. "S ta b le C arte ls," I n t e r n a ti o n a l Economic Review Volume 27, Number 2, J u n e 1 9 8 6 , pp. 3 1 7 - 3 2 7 .

Friedman. Ja m e s W. "A n o n - c o o p e r a ti v e equilibrium for su pergam es, " Review of Economic S tu d ies Volume 38, Number 1, J a n u a r y 1 9 7 1 , pp. 1 - 1 2 , r e p ri n t e d in Daughety, Andrew F. C ournot oligopoly: c h a r a c t e r i z a t i o n and ap p lic atio n s . Cambridge; Cambridge Universi ty P r e s s , 1 9 8 8 , pp. 1 4 2 - 1 5 7 .

--- Game T h eo ry W it h App licatio ns t o E co n o m ics. Oxford: Oxford U niversi ty P r e s s , 1 9 8 6 .

Martin, S t e p h e n In d u s trial Econ omics. New York; Macmillan, 1 988.

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Renzo DAVIDDI

Rouble Convertibility: A Realistic Target 8 9 /3 7 7

Elettra AGLIARDI

On the Robustness of Contestability Theory 8 9 /3 7 8

Stephen MARTIN

The Welfare Consequences of Transaction Costs in Financial Markets

8 9 /3 8 1

Susan SENIOR NELLO

Recent Developments in Relations Between the EC and Eastern Europe

8 9 /3 8 2

Jean GABSZEWICZ/ Paolo GARELLA/ Charles NOLLET

Spatial Price Competition With Uninformed Buyeis

8 9 /3 8 3 Benedetto GUI

B e n eficiary and D om inant R oles in Organizations: The Case of Nonprofits 8 9 /3 8 4

Agustfn MARAVALL/ Daniel PENA Missing Observations, Additive Outliers and Inverse Autocorrelation Function

8 9 /3 8 5 Stephen MARTIN

Product Differentiation and Market Performance in Oligopoly

8 9 /3 8 6 Dalia MARIN

Is the Export-Led Growth Hypothesis Valid for Industrialized Countries?

8 9 /3 8 7 Stephen MARTIN

Modeling Oligopolistic Interaction 8 9 /3 8 8

Jean-Claude CHOURAQUI

The Conduct of Monetary Policy: What have we Learned From Recent Experience

8 9 /3 9 0 Corrado BENASSI

Imperfect Information and Financial Markets: A General Equilibrium Model

8 9 /3 9 4

Serge-Christophe KOLM

Adequacy, Equity and Fundamental Dominance: Unanimous and Comparable Allocations in Rational Social Choice, with Applications to Marriage and Wages

8 9 /3 9 5

Daniel HEYMANN/ Axel LEUONHUFVUD On the Use of Currency Reform in Inflation Stabilization

8 9 /4 0 0

Robert J. GARY-BOBO

On the Existence of Equilibrium Configurations in a Class of Asymmetric Market Entry Games* 8 9 /4 0 2

Stephen MARTIN

Direct Foreign Investment in The United States 8 9 /4 1 3

Francisco S. TORRES

Portugal, the EMS and 1992: Stabilization and Liberalization

8 9 /4 1 6 JOrg MAYER

Reserve Switches and Exchange-Rate Variability: The Presumed Inherent Instability of the Multiple Reserve-Currency System

8 9 /4 1 7

José P. ESPERANÇA/ Neil KAY

Foreign Direct Investment and Competition in the Advertising Sector: The Italian Case 8 9 /4 1 8

Luigi BRIGHI/ Mario FORNI

Aggregation Across Agents in Demand Systems

(30)

8 9 /4 2 0 Corrado BENASSI

A Competitive Model of Credit Intermediation 8 9 /4 2 2

Marcus MILLER/ Mark SALMON When does Coordination pay? 8 9 /4 2 3

Marcus MILLER/ Mark SALMON/ Alan SUTHERLAND

Time Consistency, Discounting and the Returns to Cooperation

8 9 /4 2 4

Frank CRITCHLEY/ Paul MARRIOTT/ Mark SALMON

On the Differential Geometry of the Wald Test with Nonlinear Restrictions

8 9 /4 2 5

Peter J. HAMMOND

On the Impossibility of Perfect Capital Markets 8 9 /4 2 6

Peter J. HAMMOND

Perfected Option Markets in Economies with Adverse Selection

8 9 /4 2 7

Peter J. HAMMOND

Ineducibility, Resource Relatedness, and Survival with Individual Non-Convexities

ECO No. 9 0 / r

Tamer BA^AR and Matk SALMON Credibility and the Value of Information Transmission in a Model of Monetary Policy and Inflation

ECO No. 90/2 Horst UNGERER

The EMS - The First Ten Years Policies - Developments - Evolution

ECO No. 90/3 Peter J. HAMMOND

Interpersonal Comparisons of Utility: Why and how they are and should be made

A Revelation Principle for (Boundedly) Bayesian Rationalizable Strategies

Independence of Irrelevant Interpersonal Comparisons

ECO No. 90/6 Hal R. VARIAN

A Solution to the Problem of Externalities and Public Goods when Agents are Well-Informed ECO No. 90/7

Hal R. VARIAN

Sequential Provision of Public Goods ECO No. 90/8

T. BRIANZA, L. PHLIPS and J.F. RICHARD Futures Markets, Speculation and Monopoly Pricing

ECO No. 90/9

Anthony B. ATKINSON/ John MICKLEWRIGHT

Unemployment Compensation and Labour Market Transition: A Critical Review ECO No. 90/10

Peter J. HAMMOND

The Role of Information in Economics ECO No. 90/11

Nicos M. CHRISTODOULAKIS Debt Dynamics in a Small Open Economy ECO No. 90/12

Stephen C. SMITH

On the Economic Rationale for Codetermination Law

ECO No. 90/13 Elettra AGLIARDI

Learning by Doing and Market Structures ECO No. 90/14

Peter J. HAMMOND Intertemporal Objectives ECO No. 90/15

Andrew EVANS/Stephen MARTIN

Socially Acceptable Distortion of Competition: EC Policy on State Aid

ECO No. 90/16 Stephen MARTIN

Fringe Size and Cartel Stability

’ Please note: As from January 1990, the EUI Working Papers Series is divided into six sub series, each series will be numbered individually (e.g. EUI Working Paper LAW No. 90/1).

Fringe size and cartel stability

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EUROPEAN UNIVERSITY INSTITUTE, FLORENCE

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ECONOMICS DEPARTMENT

EUI Working Paper ECO No. 90/16

Fringe Size and Cartel Stability

BADIA FIESOLANA, SAN DOMENICO (FI)

All rights reserved.

No part of this paper may be reproduced in any form

without permission of the author.

© Stephen Martin

Printed in Italy in September 1990

European University Institute

Badia Fiesolana

1-50016 San Domenico (FI)

Italy

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