Oligopsonistic Cats and Dogs

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. 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