Delbono, Fla io; Reggiani, Ca lo
Wo king Pape
The degene a ion o wo ke s' coope a i es unde
endogenous membe ship in mixed oligopoly
Quade ni - Wo king Pape DSE, No. 1194
P o ided in Coope a ion wi h:
Uni e si y o Bologna, Depa men o Economics
Sugges ed Ci a ion: Delbono, Fla io; Reggiani, Ca lo (2024) : The degene a ion o wo ke s'
coope a i es unde endogenous membe ship in mixed oligopoly, Quade ni - Wo king Pape DSE,
No. 1194, Alma Ma e S udio um - Uni e si à di Bologna, Dipa imen o di Scienze Economiche
(DSE), Bologna,
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ISSN 2282-6483
The Degene a ion o Wo ke s’ Coope a i es
unde Endogenous Membe ship
in Mixed Oligopoly
Fla io Delbono
Ca lo Reggiani
Quade ni - Wo king Pape DSE N° 1194
The Degene a ion o Wo ke s’ Coope a i es
unde Endogenous Membe ship in Mixed
Oligopoly ∗
Fla io Delbono†Ca lo Reggiani‡
Ma ch 2023
Abs ac
We p opose a new model o mixed oligopoly whe e a wo ke s’ coope a i e
i ms compe es wi h a numbe o p o i maximising companies. Building upon
a la ge empi ical e idence, we inno a e as compa ed o he adi ional li e a-
u e on he objec i e unc ion o he coope a i e; mo eo e , i s membe ship
is ea ed as endogenous in he Cou no -Nash equilib ium. We show which
ac o s may be esponsible o he degene a ion o he wo ke s’ coope a i e
i ms, which occu s when he numbe o membe s sh inks wi h espec o he
o e all employees.
JEL Classi ica ion: L21, L25, P13.
Keywo ds: coope a i es, mixed oligopoly, degene a ion.
∗
We hank Gianni De F aja and John Penca el o insigh ul commen s and sugges ions. The
usual disclaime applies.
†
Depa men o Economics, Uni e si y o Bologna, I aly. Email: la[email p o ec ed]. Co e-
sponding au ho .
‡
Depa men o Economics, Uni e si y o Manches e , Uni ed Kingdom. Email:
ca lo. eggiani@manches e .ac.uk.
1
Non- echnical summa y
In his pape , we ha e p opose a new model o desc ibe he beha io o a wo ke s’
coope a i e ha compe es wi h a numbe o p o i maximising companies. The
main no el ies lie in a e idence-backed o mula ion o he coope a i e objec i e
unc ion and in he endogenei y o membe ship. Building upon a la ge empi ical
e idence, we embed i s s a egic choices wi hin an oligopolis ic indus y popula ed
also by a numbe o p o i seeking companies.
The analysis o he equilib ium o ou model e eals ha membe ship ma e s
in d i ing he p ope ies o he equilib ium i sel . Mo eo e , a ca e ul sc u iny o
he membe ship a e allows one o en isage which ac o s may be esponsible o
a all in he p opo ion o non-membe wo ke s. We in e p e a educ ion o he
membe ship a io as a nea example o ”degene a ion”. We show which ac o s
may be esponsible o he degene a ion o he wo ke s’ coope a i e i ms, which
occu s when he numbe o membe s sh inks wi h espec o he o e all employees.
Beyond hese new heo e ical indings, we also ecommend cau ion when
in e p e ing da a on coope a i e i ms and wo ke s’ coope a i es in pa icula .
We indeed p o ided e idence ha he ac ual weigh o he coope a i e p esence
(unde s ood as he ul ima e decision make ) in an economic sys em is g ea e han
he one ob ained by simply coun ing he o icial di ec weigh . This is because
he ans o ma ion o wo ke s’ coope a i es in o s ock companies con olled by
coope a i es should be conside ed as well o ob ain a mo e accu a e pic u e o
he o e all coope a i e magni ude. The degene a ion issue, i any, could hen be
quan i ied wi hin such a mo e comple e ame.
2
1 In oduc ion
Acco ding o a ecen epo o he In e na ional Coope a i e Alliance (see Eu icse
(2020)), a leas a billion people a e membe s o coope a i es. In Eu ope - whe e
I aly, F ance and Spain ank op - coope a i es accoun di ec ly o almos 5 million
employees.
1
Coope a i es a e i ms open o a la ge numbe o ci izens o hey
usually equi e a modes en y ee o become membe . They a e un democ a ically
by membe s (one head-one o e) who a e he ul ima e esidual claiman s o ne
e enue.
Among he a ious ypes o coope a i es (see Ammi a o, 2018 and Zamagni,
2015 o use ul axonomies), we ocus he e on wo ke s’ coope a i es (hence o h,
WCFs) o en named labo -managed i ms in he pas . In such companies he ul ima e
con ol is held by wo ke s because hey own he i m. To p e en misunde s and-
ings, a WCF does no necessa ily mee Se el (1982) de ini ion o wo ke s’ i m,
whe e “all wo ke s a e membe s and all membe a e wo ke s”. In ac , we a e
in e es ed in analyzing he membe ship a io, i.e., he a io be ween he numbe o
wo king membe s and he numbe o wo ke s. Such a a io is ob iously equal o
one in a wo ke s’ i m.
The ounding membe s a e labo supplie s who ad ance he necessa y equi y.
This ea u e es ic s he bi h o WCFs o sec o s wi h ela i ely low capi al/labo
a ios and low isk (as documen ed, o ins ance, by Podi insky and S ewa , 2007
in he B i ish manu ac u ing sec o s). Then, unsu p isingly, WCFs a e mainly
ope a ing in compa a i ely small manu ac u ing business, and hey a e equen ly
ac i e in se ices as anspo a ion, ca e ing, acili y managemen , ou ism, en e -
ainmen .
I is a ma e o ac ha WCFs a e signi ican ly less common han capi al-
managed i ms and “no one a gues ha success ul capi alis i ms end o degene -
a e in o WCFs” (Dow, 2018, p.107).
2
Con e sely, a g oup o schola s
3
ha e claimed
ha WCFs seem o lean owa ds he capi alis ones ( he so-called degene a ion).
In he nex pages we will deal p ecisely wi h such an issue, al hough one may
1
These igu es make i somehow su p ising he subs an ial disappea ance o coope a i es om
economics ex books. See Hill (2000) and Kalmi (2007) o hough ul accoun s and explana ions
o such a endency.
2
As a model o en e p ise al e na i e o he capi alis one, WCFs ha e ecei ed much a en ion
in he li e a u e since John S ua Mill. He seemed exceedingly op imis ic abou he success o he
coope a i e o m. In his P inciples o Poli ical Economy, published in 1848, ou yea s a e he bi h
o he i s (use s’) coope a i e (Rochdale, 1844), he claimed ha wo ke - un o ganiza ions would
e en ually c owd capi alis en e p ises ou o he ma ke because o hei g ea e e iciency and
o he bene i s o he wo king owne s.
3See Dow, 2018, ch. 7, o an excellen discussion o he ele an li e a u e.
3
p e e o e e o i as “ ans o ma ion” o WCFs. The choice would no be a me ely
s ylis ic one o a oid he in insically pejo a i e la o o he e m “degene a ion”,
bu i would also be d i en by he mul iplici y o expe iences ha can be collec ed
when looking a he e olu ion o WCFs in he las decades. We will no ice indeed
ha he ac ual coope a i e magni ude would be signi ican ly unde es ima ed i
summa ized only h ough he numbe and pe o mance o companies egis e ed
as coope a i es. The ich I alian expe ience, o ins ance, p o ides a mo e accu a e
e idence o he di ec and indi ec weigh o coope a i es (including WCFs) wi hin
he economy in e ms o employmen as well as GDP.
In he second pa o he pape we will swi ch o heo y. We p opose a new
model o mixed oligopoly whe e a wo ke s’ coope a i e i m compe es wi h a
numbe o p o i maximizing companies. Building upon a la ge empi ical e idence,
we inno a e as compa ed o he adi ional li e a u e on he objec i e unc ion o
he coope a i e; mo eo e , i s membe ship is ea ed as endogenous in he Cou no -
Nash equilib ium. We in es iga e he op imal choice o he membe ship wi hin
a new model o WCF’s beha io and we shall show which ac o s may explain
i s con e gence owa ds a capi alis business o ganiza ion. We will in e p e a
educ ion o he membe ship a io as an ins ance o WCF degene a ion, because as
he p opo ion o membe s dec eases he coope a i e ends o look like he capi alis
ones. To he bes o ou knowledge, we a e i s in ea ing he membe ship wi hin
a WCF as endogenous in a model o oligopoly.4
Among he main indings, we show ha he membe ship a io plays a c ucial
ole. Fi s , i no all wo ke s a e also membe s, hen he wo ypes o i ms beha e
iden ically. I , ins ead, he membe ship a io is uni a y, he equilib ium is asymme -
ic and, in gene al, WCF’s choices di e om hei p o i maximising coun e pa s.
The la e ou come is ypical unde he adi ional objec i e unc ion ha has been
used by mos o he heo e ical li e a u e since Wa d (1958). Second, we in es iga e
which ac o s a e esponsible o he degene a ion o WCF. Fo ins ance, we show
ha an inc ease in ma ke size, which is usually co ela ed o he dimension o he
companies, leads o a all in he membe ship a io.
The es o he pape is o ganized as ollows. Sec ion 2 b ie ly e iews he ela ed
li e a u e wi hin a b oade pe spec i e abou he academic esea ch on WCFs since
he la e ’50s o he las cen u y. In sec ion 3 we cla i y how he ans o ma ion
p ocess o WCFs should be p ope ly add essed on he basis o some a ailable
e idence. In sec ion 4 we p opose a model allowing us o in es iga e he choice o
4
Dow (2018, ch. 9) in es iga es he choice o membe ship unde he assump ions o pe ec
compe i ion in he p oduc ma ke and an objec i e unc ion `
a la Wa d (1958).
4
he membe ship a io wi hin an oligopolis ic ma ke s uc u e. Sec ion 5 p o ides
a ull cha ac e iza ion o he equilib ium o ou mixed ma ke . Sec ion 6 concludes.
2 Rela ed li e a u e
The o e all li e a u e on WCFs is now as : see, o ins ance, he classic su ey
by Bonin e al. (1993) and he mo e ecen con ibu ions by Jones (2018), Dow
(2018), Mi abel (2021) and Mygind and Poulsen (2021). Two phases can be oughly
iden i ied. The i s one, since he pionee ing con ibu ion by Wa d (1958), was
mainly conce ned wi h he analysis o he so-called ma ke socialism, a ma ke -
based economy di e en om he con en ional capi alis ones because o he
p esence o companies own and/o un by wo ke s.
Since Wa d’s a icle, mos o he ea ly heo e ical li e a u e modeled he WCF as
maximizing he ne income pe wo ke (see Doma , 1966 and Vanek, 1970, among
he mos in luen ial essays). Mo e p ecisely, he sho - un WCF’s maximand is
assumed o be e enue, ne o ixed cos , pe membe . Unde p ice- aking beha io ,
i all iden ical wo ke s ( he only a iable inpu ) a e membe s, his is equi alen o
maximize he di e ence be ween e enue and all cos s (named p o i in a capi alis
company) pe membe . Besides no inding signi ican empi ical suppo , such
app oach en ails a dis u bing nega i e esponse o ou pu (and hen labo demand)
o ou pu p ice inc eases: his is known in he li e a u e as he pe e se e ec .
An in e es ing o mula ion a oiding backwa d-bending supply cu e o he
WCF is in Kahana and Ni zan (1989). Unde p ice- aking beha io and a uni a y
membe ship a io, a WCF chooses he le els o inpu s and ou pu o maximize he
income pe wo ke /membe subjec o an employmen cons ain o , al e na i ely,
he le el o employmen subjec o a p o i pe wo ke /membe cons ain . By
duali y a gumen s, one p o es he equi alence be ween wo app oaches which aim
a cap u ing he conce n o employmen ha should shape he decisions o i ms
owned and un by wo ke s-membe s acco ding o a democ a ic go e nance. This
conce n has been o en de ec ed in empi ical esea ch ( u he e iewed below).
The heo e ical li e a u e made li le p og ess un il he ea ly ‘90s when, e aining
he same objec i e unc ion as in Wa d (1958), he beha io o a WCF has been
s udied wi hin models o mixed oligopoly, i.e., concen a ed ma ke s hos ing i ms
pu suing di e en goals (De F aja and Delbono, 1990). Howe e , while hese
models emo e he ex eme assump ion o p ice- aking beha io in he p oduc
ma ke , hey e ain Wa d (1958)’s o mula ion abou he WCF objec i e unc ion
5
(see, e.g., Delbono and Rossini, 1992 and Delbono e al., 2023 o he ele an
e e ences).
Likely also because o he s alema e in modeling WCF’s beha io , he las hi y
yea s ha e wi nessed a massi e inc ease in empi ical s udies. S a ing om a g oup
o seminal pape s in es iga ing he plywood indus y in he US Paci ic No hwes ,
C aig and Penca el (1992, 1993) and C aig e al. (1995) d ew he conclusion ha a
WCF ends o adjus ea nings mo e han employmen when eac ing o changes
in ma ke condi ion. The same conclusion is eached by Bu d
´
ın and Dean (2009,
2012) ega ding he U uguayan economy. Bo h se s o pape s sha e he inding
ha employmen seems o occupy a mo e p ominen ole han ea nings in he
objec i e unc ion o WCFs . This empi ical e idence has been con i med, in e alia,
in a g oup o s udies on I alian WCFs, e.g., Delbono and Reggiani (2013), Eu icse
(2013), Na a a (2016), and Caselli e al. (2022).
As o he so-called degene a ion p oblem, se e al schola s ha e a gued ha
- unde impe ec (o no) membe ship ma ke s - membe s o success ul WCFs
would ind i p e e able o hi e employees and o pay hem he ma ke wage
when depa ing membe s ha e o be eplaced.
5
The e idence collec ed in se e al
coun ies is a om being conclusi e and also shows ha some ins i u ional
mechanisms may es ain he ac ual easibili y o he “degene a ion”. Fo ins ance,
in F ance, also non-membe s a e eligible o pa icipa ing in he dis ibu ion o
di idends; iscal incen i es, as in I aly, may discou age WCFs om sh inking he
membe ship a io o he con e sion in o a capi al-managed company.6
Mo eo e , i is wo h no icing ha some imes he ans o ma ion goes he o he
way a ound, when unsuccess ul capi alis companies some imes “degene a e” in o
WCFs. This is he case o wo ke s buy-ou by means o which employees in a capi al-
con olled i m ake o e he company o p e en i s bank up cy. Fo ins ance, be-
ween 2011 and 2021, he I alian coope a i e und CFI (h ps://www.c i.i /wo ke s-
buyou .php) has suppo ed 88 such acquisi ions o i ms which accoun o a o al
u no e o 365 million eu o and employ 2,286 pe sons. A simila con e sion has
been obse ed in F ance: be ween 1997 and 2001, abou 7% o WCF’s en y in
F ench indus ies esul ed om escues o capi al-con olled companies (P
´
e o in,
2006).
Fu he mo e, “a ela ed p ocess may in ol e he o ma ion o non-coope a i e
5
Se el (1991) shows ha unde impe ec compe i ion in he p oduc ma ke , he equilib ium is
no al e ed by eplacing a p o i maximise by a Wa d (1958)-like WCF i (i) he e is a ma ke o
coope a i e membe ships and (ii) he membe ship a io is uni a y. Unde condi ions (i) and (ii),
Mikami (2018) inds ha a WCF is as e icien and iable as a capi alis i m.
6
See Dean (2019) o an empi ical s udy on he p esence o degene a ion in U uguayan WCFs.
6
subsidia ies by wo ke coope a i es o ou sou cing o some ac i i ies o con en-
ional i ms” (Dow, 2018, p.108). This aspec seems impo an in gene al and in
I aly in pa icula ; hence, we b ie ly u n ou a en ion o his addi ional e idence.
3 The coope a i e magni ude
To assess he o e all coope a i e magni ude, we need a se o da a which anscend
he numbe o coope a i es, hei di usion, sizes and di ec impac on he economy
(e.g., employmen , GDP). A p elimina y ques ion, indeed, deals wi h he coope a-
i e con ol o e i ms: a con ol which o en ex ends ou side he bounda ies o
coope a i e i ms. In o he wo ds, while s ock companies can ha dly ake coop-
e a i es o e , gi en he dissemina ion o (no mally un adable) p ope y igh s,
coope a i es can acqui e con ol o e s ock companies as his o en occu s. Fo
ins ance, Unipol-Sai, one o he leading companies in he I alian insu ance ma ke ,
is a i m lis ed on he na ional s ock ma ke , bu i is con olled h oughou an
ag eemen among a g oup o coope a i e companies.
To pu sue he goal o summa izing he o e all coope a i e con ol o e i ms,
we need o ely upon he ca ego y o business g oup, de ined by Eu os a as: “an
associa ion o en e p ises bound oge he by legal and/o inancial links. (...) I
cons i u es an economic en i y which is empowe ed o make choices, pa icula ly
conce ning he uni i comp ises” (Eu opean Regula ion 696/93). O cou se, we
a e in e es ed in business g oups con olled by WCFs.
To begin wi h, we ocus on he I alian expe ience as i anks op wo ldwide o
he mac oeconomic impac o coope a i es (7% o o al employmen and abou
4% o he GDP o he p i a e sec o , acco ding o Is a ). In 2015 in I aly 29,414
coope a i es ou o 59,027 ac i e coope a i es we e o he wo ke s’ ype and we e
esponsible o abou 45% and 42% o o e all coope a i e added alue and employ-
men , espec i ely. Mo eo e , as ca e ully epo ed in Bo zaga e al. (2019), 812
business g oups we e con olled by a coope a i e i m and 1971 is he numbe o
con olled non-coope a i e en e p ises. I we conside WCFs, hey a e 389 ou o
812.
We may conclude ha , conside ing subsidia ies and coope a i e g oups, he
o e all mac oeconomic impac o I alian coope a i es ( he coope a i e magni ude)
goes up o 4.4% o GDP and 7.4 % o employmen o he p i a e sec o . Mos o
his upli can be a ibu ed o he con ol o non-coope a i e companies by WCFs,
as hey accoun o abou a hal o he business g oups led in 2015 by coope a i e
companies.
7
Compa a i e s a ics. We now pe o m a compa a i e s a ics analysis on he
equilib ium alue o he membe ship a io o he case o
<
, i.e.,
m∗<1
. To do
so, we di e en ia e
m∗
wi h espec o he pa ame e s o ou model ( ea ing
n
as
a con inuous a iable). By simple inspec ion o he equilib ium membe ship a io
(13)
, he de i a i e wi h espec o
and
τ
is clea ly posi i e. In bo h cases, p o i s
a e una ec ed, bu he inc ease in he alue o asse s domina es he addi ional cos
o ex a membe s. On he con a y, an inc ease in
c
only wo sens he o e all payo
and, as a eac ion, membe ship is educed.
I he maximum size o he ma ke ,
a
, inc eases, ins ead, he model p edic s a
degene a ion o he WCF as he membe ship a io dec eases. Fo mally, his happens
because
LM
does no a y, whe eas
LW
inc eases: hence,
m∗
sh inks. In ui i ely,
cu en membe s ace a ade-o . Indeed, he p o i s o be dis ibu ed a e highe i
he demand inc eases. Howe e , on he one hand, he cu en membe s would no
like o sha e hem wi h mo e membe s; on he o he hand, mo e membe s would
s eng hen he inancial posi ion o he i m. The i s e ec domina es he second.
I he ma ke size is co ela ed wi h i m size, ou esul a ionalizes some
e idence abou he membe ship a io. Indeed, his seems dec easing in he size
o he WCF. Fo a sample o WCFs adhe ing o Legacoop, such a a io is cu en ly
a ound 60% o small and medium i ms, bu i alls o abou 36% in la ge WCFs.
10
The e ec s o changes in he ma ginal cos o labo ,
ω
, and in he numbe o
capi alis i ms,
n
, ha e he same in ui i e explana ion. In ei he case, as a esponse
o he all in p o i s, he WCF inc eases i s membe ship o expand he alue o i s
asse s.
As long as
Γ<Γ
, he WCF is ac i e and i s alue does no impac he equilib ium
membe ship. Simila ly, also he alue o he weigh o p o i s
ϕ
does no a ec he
equilib ium membe ship a io.
The nex p oposi ion summa izes he p e ious esul s abou degene a ion:
P oposi ion 3 (Degene a ion).The membe ship a io m∗is dec easing in aand c.
10
These pe cen ages a e epo ed in a p i a e communica ion (e-mail, No embe 14 h, 2023)
by F ancesco Lingui i, o he Resea ch A ea o Legacoop (Rome, I aly). His es ima es come om
he analysis o a sample o 146 I alian WCFs, accoun ing o 12,722 wo ke s and 6,223 wo king
membe s, whe e he a e age membe ship a io is a ound 49%.
14
6 Concluding ema ks
In his pape , we ha e p oposed a new model o desc ibe he beha io o a wo k-
e s’ coope a i e. The main no el ies lie in a e idence-backed o mula ion o he
coope a i e objec i e unc ion and in he endogenei y o membe ship. We embed
i s s a egic choices wi hin an oligopolis ic indus y popula ed also by a numbe
o p o i seeking companies.
The analysis o he Cou no -Nash equilib ium o ou model e eals ha mem-
be ship ma e s in d i ing he p ope ies o he equilib ium i sel . Mo eo e , a
ca e ul sc u iny o he membe ship a e allows one o en isage which ac o s may
be esponsible o a all in he p opo ion o non-membe wo ke s. We in e p e a
educ ion o he membe ship a io as a nea example o ”degene a ion”.
Beyond hese new heo e ical indings, we also ecommend cau ion when
in e p e ing da a on coope a i e i ms and wo ke s’ coope a i es in pa icula .
We indeed p o ided e idence ha he ac ual weigh o he coope a i e p esence
(unde s ood as he ul ima e decision make ) in an economic sys em is g ea e han
he one ob ained by simply coun ing he o icial di ec weigh . This is because
he ans o ma ion o wo ke s’ coope a i es in o s ock companies con olled by
coope a i es should be conside ed as well o ob ain a mo e accu a e pic u e o
he o e all coope a i e magni ude. The degene a ion issue, i any, could hen be
quan i ied wi hin such a mo e comple e ame.
Ou app oach can be ex ended in many di ec ion; we ske ch h ee o hem. Fi s ,
he s a ic na u e o he model could be elaxed in o de o s udy he dynamics o
he membe ship and he ole o undis ibu ed p o i s on i s e olu ion. Second, he
weigh o dis ibu ed p o i s in he objec i e unc ion o he wo ke s’ coope a i e
i m could also be conside ed as endogenous. Las ly, ou analysis is inhe en ly
sho - un in na u e and i could be o some in e es o make also non-labo inpu s
s a egically chosen by he companies. These po en ially ui ul ex ensions a e
le o u u e esea ch.
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18
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