Oligopsonis ic Ca s and Dogs
Ge da Dewi De mo Leahy
Na ional Uni e si y o I eland Maynoo h Uni e si y College Dublin
June 2005
Abs ac : We s udy he s a egic in es men beha iou o oligopsonis ic i als in he
labou ma ke . Unde wage compe i ion, i ms play "puppy dog" wi h p oduc i i y-
augmen ing in es men and " a ca " wi h supply-enhancing in es men . Unde
employmen compe i ion, in es ing s a egically always in ol es playing " op dog".
JEL Codes: L13, J42.
Key wo ds: Oligopsony, S a egic beha iou , P oduc i i y-augmen ing in es men ,
Supply-enhancing in es men .
Acknowledgemen s: This esea ch is suppo ed by he In e na ional T ade and In es men
p og amme o he Gea y Ins i u e a UCD.
Co espondence: Ge da Dewi , Na ional Uni e si y o I eland, Maynoo h, Depa men o
Economics, Maynoo h, I eland, el.: (+)353-(0)1-7083776, ax: (+)353-(0)1-7083934, E-
mail: [email p o ec ed]; De mo Leahy, Uni e si y College Dublin, Depa men o
Economics, Bel ield, Dublin 4, I eland, el.: (+)353-(0)1-7168551, ax: (+)353-(0)1-
2830068, E-mail: [email p o ec ed].
1
1. In oduc ion
Since i was i s concei ed, he Fudenbe g-Ti ole "Ca s and Dogs" axonomy o business
s a egies (Fudenbe g and Ti ole, 1984) has become he s anda d amewo k o
cha ac e ising in es men beha iou in an oligopolis ic se -up. Ensuing wo k has
p oduced in e es ing applica ions (Nea y and Leahy (2000)) and e inemen s o he ini ial
axonomy (Lapham and Wa e (1994), Jun and Vi es (2004)). Common o all o hese is
he conce n wi h in es men s a egies ha ein o ce a i m's posi ion in he ou pu
ma ke . Rema kably, he s a egic in es men beha iou o i ms ha wan o s eng hen
hei posi ion in he inpu ma ke has no been o mally analysed. This pape aims o ill
ha gap in he li e a u e.
While ou analysis applies o inpu ma ke s in gene al, we ocus on he labou ma ke in
pa icula . This choice is a na u al one, especially when iewed in ligh o ecen
de elopmen s in labou economics. Con incing a gumen s ha e been p esen ed o
de end he belie ha he labou ma ke −like many o he ma ke s− is essen ially
impe ec ly compe i i e, he eby challenging he old pa adigm o pe ec compe i ion in
he labou ma ke (Manning, 2003). P oponen s o his school o hough a gue ha he
labou supply cu e acing an indi idual i m is ypically no in ini ely elas ic bu upwa d
sloping, he e o e making i ms' beha iou monopsonis ic o oligopsonis ic1.
In his pape , we p esen a axonomy o in es men s a egies o i ms ha ha e
oligopsony powe in he labou ma ke and highligh possible implica ions o labou
ma ke policies on s a egic in es men .
2. The model
Two i ms, i and j, play a wo-pe iod game. In he second pe iod, i ms ac as
duopsonis s in he labou ma ke . They decide simul aneously, ei he se ing wages (we
call his "wage compe i ion") o employmen le els ("employmen compe i ion"). Fo
1 Mo e speci ically, Manning (2003) a gues ha all ha is equi ed o a i m's labou supply cu e o be
upwa d sloping is ha a wage cu o one cen does no cause all wo ke s o lea e he i m immedia ely. He
p esen s empi ical e idence ha suppo s his and explains i by e e ing o he exis ence o "local" labou
2
conciseness, we sol e he model in e ms o gene al "ac ions" ( jihAh, , =) and hen
discuss he implica ions o wage ( hh wA=) and employmen compe i ion ( hh
L
A
=
),
espec i ely. Fi m i aces he labou supply unc ion:
),(jiii wwLL = (1)
Hence o h, pa ial de i a i es wi h espec o ac ions a e subsc ip ed, wi h A, L and w
being supp essed in subsc ip s whe e his canno cause con usion ( o ins ance,
jii
jwLL ∂∂≡/). A ise in i m i’s wage a ac s mo e labou ( 0>
i
i
L); a all in i s i al’s
wage pushes wo ke s owa ds i m i ( 0<
i
j
L). Fo simplici y, we assume pe ec
compe i ion in he goods ma ke , implying ha a i m's p oduc p ice, h
p, is gi en.
In pe iod one, i m i chooses an in es men le el, K. Fo cla i y and simplici y, we
assume only one i m in es s (as do Fudenbe g and Ti ole (1984))2. Fi s , we conside
he case in which K has a posi i e e ec on he in es ing i m’s ma ginal labou
p oduc i i y. We call his o m o in es men “p oduc i i y-augmen ing” (PA).
Al e na i ely, in es men may cause an ou wa d shi in he labou supply cu e acing a
i m (examples include job ad e ising as well as wi hin- i m c èche acili ies, a
commu e shu le se ice o i m employees, ec ea ional a eas su ounding o ices –a
nice dining hall, a spacious co ee oom, a g een zone). This al e na i e o m o
in es men will be labelled as “supply-enhancing” (SE). In bo h cases, i ms’ p o i s (
π
)
a e gi en by exp essions (2) and (3):
)(KCLwqp iiiiii −−=
π
(2)
jjjjj Lwqp −=
π
(3)
Fi m ou pu is deno ed by h
q. i
C ep esen s i m i's cos o in es men , wi h ma ginal
cos 0>
i
K
C and second de i a i e 0≥
i
KK
C.
ma ke s (which occu , o ins ance, because o a desi e o a oid conges ion and/o cu commu ing ime o
mee he demands o amily li e).
2 Ex ending he model o allow in es men by bo h i ms is s aigh o wa d.
3
Wi h PA in es men , i m i’s ou pu unc ion is gi en by ),(KLqq iii = wi h pa ial
de i a i es 0>
i
Li
q, 0≤
i
LL ii
q and 0>
i
K
q. Because in es men aises labou p oduc i i y,
0>
i
iK
q. Since we assume ha i m j does no in es , i s ou pu unc ion simply is
)( jjj Lqq = wi h 0>
j
Lj
q and 0≤
j
LL jj
q. I i ms se wages, we use he di ec labou
supply unc ion in exp ession (1). Wi h employmen -se ing i ms, we use he in e se
labou supply ),(jiii LLww =, wi h 0>
i
i
w and 0>
i
j
w.
Wi h SE in es men we assume ha , unlike wi h PA in es men , K does no en e i m i's
p oduc ion unc ion di ec ly, which allows us o dis inguish clea ly he e ec s o each
ype o in es men ; hus, )( iii Lqq =. Impo an ly, in es men now shi s he labou
supply cu e. Hence, we ha e ),,(KwwLL jiii =, wi h 0>
i
K
L, and ),(jijj wwLL =
when i ms choose wages. When i ms se employmen le els, ),,(KLLww jiii = wi h
0<
i
K
w and ),(jijj LLww =.
3. The in es men axonomy unde oligopsony
We now de i e op imal in es men s a egies unde oligopsony. In compac no a ion, we
ha e ),,(KAA jiii
ππ
= and ),(jijj AA
ππ
=. Using backwa d induc ion, we i s u n
o he second pe iod. Fi m i chooses i s p o i -maximising ac ion gi en i s i al’s ac ion,
implying
0)( =+−= i
A
ii
A
ii
A
i
iiii wLLwpq
π
(4)
Fo b e i y, we de ine i
A
i
L
i
Aiii Lqq ≡. Unde wage compe i ion, i
w
i
Aii LL = and 1=
i
Ai
w,
while 1=
i
Ai
L and i
L
i
Aii ww = unde employmen compe i ion.
Exp ession (4) de e mines i m i’s bes esponse unc ion, )( jii AA
ψ
=, o a gi en le el
o in es men . Simila ly, i m j’s bes esponse unc ion, )( ijj AA
ψ
=, is ob ained om
0=
j
j
π
. I will p o e use ul o sign he slope o )( ij A
ψ
. To al di e en ia ion o 0=
j
j
π
gi es j
jj
j
ji
ijij dAdAA
ππψ
//)('−=≡ . No e ha 0>
j
ji
π
unde wage compe i ion,
4
assuming ha j
ji
L, i nega i e, is su icien ly small in absolu e alue (which is in line
wi h he no mal s anda d assump ion); unde employmen compe i ion 0<
j
ji
π
, assuming
ha j
ji
w, i nega i e, is su icien ly small in absolu e alue3. Thus, since 0<
j
jj
π
om he
second-o de condi ions, 0)('>
ij A
ψ
unde wage compe i ion and 0)('<
ij A
ψ
unde
employmen compe i ion. Using e minology in oduced by Bulow, Geanokopolos and
Klempe e (1985) in he oligopoly li e a u e, wages a e s a egic complemen s whe eas
employmen le els a e s a egic subs i u es.
Tu ning o pe iod one, i m i maximises p o i s wi h espec o K, aking in o accoun he
e ec o in es men on p o i s h ough i s i al’s second-pe iod ac ion ( )/(dKdAji
j
π
):
0=+= dK
dA
dK
dj
i
j
i
K
i
ππ
π
(5)
The second e m in exp ession (5) is he s a egic e m. In he absence o s a egic
beha iou , i m i would choose K such ha 0=
i
K
π
. I , howe e , he s a egic e m is
posi i e o nega i e, he i m will − ela i e o he non-s a egic benchma k− o e in es
(0<
i
K
π
) o unde in es ( 0>
i
K
π
), espec i ely. Cha ac e ising s a egic in es men
beha iou equi es signing he s a egic e m. Assuming ha he sign o j
i
π
is he same
as he sign o i
j
π
(see also Ti ole (1988), p.326), and since dK
dA
A
dK
dA i
ij
j)('
ψ
=, we ha e
( )
)('ij
i
j
i
j
i
jAsign
dK
dA
sign
dK
dA
sign
ψππ
×








=







(6)
F om ou ea lie discussion, we know he sign o )('ij A
ψ
. The o he e m on he igh
hand side in exp ession (6) comp ises o he e ec o a i m's ac ion on i al p o i abili y
( he " iendliness" e m4), j
i
π
, and he e ec o in es men on he i m's own ac ion,
dKdAi/. Since j
i
jj
L
j
iLwpq j)( −=
π
unde wage compe i ion and j
i
jj
iwL−=
π
unde
3 Mo e speci ically, jji
jj
L
jj
i
jj
j
LL
jj
ji LwqpLLqp jjj )()1(−+−=
π
when hh wA= and )( j
ji
jj
L
j
ji wLwi+−=
π
when hh LA=. Wi h linea labou supplies, bo h jji
L and j
ji
w a e ze o.
4 This e m was i s in oduced by B ande (1995, p.1415).

5
employmen compe i ion, ac ions in oligopsony a e always "un iendly" ( 0<
j
i
π
). An
exp ession o dKdAi/ is ob ained by o al di e en ia ion o second-pe iod i s -o de
condi ions wi h espec o K:
i
ij
j
ji
j
jj
i
ii
j
jj
i
iK
i
dK
dA
ππππ
ππ
−
−= (7)
wi h s abili y equi emen 0>− i
ij
j
ji
j
jj
i
ii
ππππ
and 0<
j
jj
π
om he second-o de
condi ions.
The sign o dKdAi/ is he same as he sign o i
iK
π
and hinges on he ype o in es men
conside ed. We now discuss he in es men axonomy o PA and SE in es men ,
espec i ely.
3.1. P oduc i i y-augmen ing in es men
Unde PA in es men , 0>= i
KA
ii
iK i
qp
π
since 0>
i
KAi
q. Hence, 0/>dKdAi bo h unde
wage and employmen compe i ion. This, combined wi h he ac ha ac ions a e
"un iendly", implies ha PA in es men always makes he in es ing i m " ough"
(0<
dK
dAi
j
i
π
). When i ms se wages −bea ing in mind ha 0)('>
ij A
ψ
−, he s a egic
e m is nega i e ( 0<
dK
dAj
i
j
π
). The e o e, 0>
i
K
π
( om exp ession (5)), which indica es
ha s a egic beha iou in ol es unde in es men . In he Fudenbe g-Ti ole (1984)
e minology, he i m plays "puppy dog" unde wage compe i ion, ha is, i chooses o be
small and ino ensi e. In ui i ely, because he in es ing i m knows a high i al wage
educes i s own p o i s, i wan s o supp ess i . Gi en he s a egic complemen a i y
be ween wages, his necessi a es a commi men by i m i o a low wage ( ela i e o he
non-s a egic benchma k). Unde in es men ensu es a low u u e wage since i keeps a
i m's labou p oduc i i y low.
Figu e 1 shows second-pe iod eac ion unc ions when i ms se wages. N deno es he
equilib ium when i ms in es non-s a egically. Fi ms i's p o i s inc ease as j
w
6
dec eases. S a egic in es men shi s i m i's eac ion unc ion o he le , esul ing in he
equilib ium deno ed by S. A ),(jSiS ww , wages a e lowe han in he non-s a egic
benchma k.
No e ha , unde employmen compe i ion, he s a egic e m is posi i e ( 0>
dK
dAj
i
j
π
)
because PA in es men makes he in es ing i m " ough" ( 0<
dK
dAi
j
i
π
) and he i al's
bes esponse unc ion is nega i ely sloped ( 0)('<
ij A
ψ
). Hence, 0<
i
K
π
and i m i
plays " op dog", o , o e in es s, he eby educing i al employmen , o look big and
agg essi e.
3.2. Supply-enhancing in es men
Ou discussion now u ns o s a egic beha iou unde SE in es men . Unde wage
compe i ion, 0)()1(<−+−= i
iK
ii
L
ii
K
i
i
i
LL
ii
iK LwqpLLqp iii
π
(assuming i
iK
L is no oo
posi i e) and hence 0/<dKdAi, implying ha SE in es men makes he in es ing i m
"so ". S a egic in es men hus in ol es adop ing a " a ca " a i ude: o e in es o look
big and ino ensi e. SE in es men shi s down he labou supply cu e acing he i m,
lowe ing he ese a ion wage as non-wage bene i s o wo ke s inc ease. Apa om
lowe ing he i m's own wage, his also educes he i al's wage. Finally, unde
employmen compe i ion, 0)( >+−= i
iK
ii
K
i
iK wLw
π
(assuming i
iK
w is no oo posi i e) and
hence 0/>dKdAi. So, like wi h PA in es men , a s a egically in es ing i m adop s a
" op dog" s ance unde employmen compe i ion.
Table 1 summa ises ou discussion o s a egic in es men beha iou unde oligopsony5.
4. Concluding ema ks
5 S a egic in es men o de e i m en y in he labou ma ke seems less plausible. I is, howe e ,
s aigh o wa d o expand he axonomy o inco po a e his case.
7
I is wo hwhile poin ing ou ha exis ing labou ma ke policies may ha e implica ions
o s a egic in es men beha iou . We ocus on he e ec s o a minimum wage, w, using
igu e 1 in ou explana ion. Assume w > ),min( jSiS ww (in igu e 1, w > wiS). A w,
i ms' eac ion unc ions exhibi a kink. Fi m i's incen i e o s a egic beha iou is now
mi iga ed as i s own wage (and indeed he i al’s wage) canno be pushed below w. In
igu e 1, i m i shi s i s eac ion unc ion only o poin M. In he case o PA in es men ,
i m i −al hough s ill unde in es ing− now in es s mo e han in he case wi hou he
minimum wage. Wi h SE in es men , i m i o e in es s less, which implies ha wo ke s
−al hough paid mo e− ecei e ewe non-wage bene i s on he job.
8
Re e ences
B ande , J. (1995), “S a egic ade policy”, in G ossman, G. and K. Rogo (eds.),
Handbook o In e na ional Economics, Volume III, Ams e dam: No h-Holland,
1395-1455.
Bulow, J., J. Geanokopolos and P. Klempe e (1985), “Mul ima ke oligopoly: s a egic
subs i u es and complemen s”, Jou nal o Poli ical Economy, 93, 488-511.
Fudenbe g, D. and J. Ti ole (1984), "The a ca e ec , he puppy dog ploy and he mean
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368.
Jun, B. and X. Vi es (2004), "S a egic incen i es in dynamic duopoly", Jou nal o
Economic Theo y, 116, 249-281.
Lapham, B. and R. Wa e (1994), "Ma ko puppy dogs and ela ed animals",
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oligopolies", Economic Jou nal, 110, 484-508.
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