Munich Personal RePEc Archive
Dual labor market and strategic efficiency wage
Jellal, Mohamed and wolff, François charles
Al Makrîzî Institut d’Economie
2003
Online at https://mpra.ub.uni-muenchen.de/38395/
Mohamed Jellal
François-Charles Wol y
April2002
Abstrat
Weonsideraduallabormarketsmodelinwhihtheprimarysetorrequiresthe
preseneofeienywage,whiletheseondarysetorisompetitive. Weshowthat
the Solow ondition does not hold in a Stakelberg equilibrium where the primary
setor atsasa leader andthe seondary one asafollower.
JEL lassiation: J41
Keywords: Solow ondition,eieny wage, dual labor markets
ESC Toulouse, 20 bd LasrossesBP 7010, 31068 Toulouse Cedex 7,Frane ; and CES, Université
MohammedV, Rabat,Moroo. E-mail: jellalompuserve.om
y
Correspondingauthor. LEN-CEBS,UniversitédeNantes,hemindelaCensiveduTertreBP52231,
44322NantesCedex 3,Frane. CNAV andINED, Paris,Frane. Tel: 33240141742. Fax: 33240141743.
E-mail: wols-eo.univ-nantes.fr
The literature on eieny wage predits a diret and inreasing relationship between
the wage paid by rms and the level of eort provided by workers (Akerlof and Yellen,
1986, Katz, 1986). In equilibrium, rms may nd it protable to pay wage in exess
of market learing. Eieny wage theories produe several interesting impliations.
In partiular, they explain that permanent involuntary unemployment may exist under
onditions of equilibrium in labor markets. Eieny wage models are also apable of
generatinganumberofotherstylizedlabormarketsfats,inludingrealwagerigidity,dual
labormarkets, wagedistributionsforworkers withidentialprodutiveharateristisand
disrimination amongobservationally distint groups.
Beause of the impat of the wage setting on the workers' eort, prot-maximizing
rms are expeted to set an optimal wage suh that the elastiity of eort with respet
to wage is equalto one. This well-known result of the standard eieny wage modelis
due to Solow(1979)and isknown as the Solowondition. The eieny wage minimizes
the employer'swage ost pereetiveunits ofservie employed and eahrm hireslabor
up to the point where the marginal produt is equal to the eieny wage. However,
it has been suggested that the Solow ondition does not hold in general. In partiular,
Akerlof and Yellen (1986,question 4, pp. 1416) point out that aneort-wage elastiity
of unity is undoubtedly exessive. This is animportantissue, sine it asts doubtonthe
possibility of anequilibrium with unemploymentin aneieny wage model.
Numeroussuggestionshavebeen proposed inthe literaturetoillustrateaneort-wage
elastiity lower than one. Akerlof and Yellen (1986)present a stati modelwith external
osts to aount for the downside risk fromshirking labor. In Shmidt-Sørensen (1990),
sets out a model with spei taxes on labor. Lin and Lai (1994) show that the Solow
ondition does not hold in an intertemporal maximizingframework with turnover osts.
Marti(1997)andFaria(2000)examinemodelsthatombinetheshirkingandtheturnover
models of eieny wage, with the possibility of managerialsupervision. The role of the
qualityofjobmathingoneienywagesisanalyzedby JellalandZenou(1999). When
jobmathingisunobservable,rmsaneithersetwagessuhthattheeort-wageelastiity
islowerorgreaterthanone. Finally,JellalandZenou(2000)onsideradynamieieny
wagemodelwithlearningbydoing,whereworkers aumulateastokofknowledgewhih
allows them toinrease theireort.
Ratherthanrelyingonmiroeonomifoundationsforthe eienywage model,suh
as shirking or labor turnover osts, we followa dierent path inthis paperto show that
the Solow ondition does not hold in general. For our purpose, we analyze the optimal
wagepoliyinadual labormarkets modelwith eieny wage. FollowingDoeringerand
Piore (1971),we onsider two types of setor dierentiated aording to the type of jobs
(see alsoAemoglu,2001). In the primarysetor, jobs are stable and well paid,ontrary
to the seondary setor. Primary jobs are more omplex than seondary jobs, so that it
is more diult to monitor worker performane. This is the explanation of dual labor
markets given by Bulow and Summers (1986), based on the Shapiro and Stiglitz (1987)
laborshirkingeieny wagemodel. Dierentwagelevelsare duetodierentmonitoring
osts aross industries,thusprovidinga supply side explanation of dual labor markets 1
.
Weassumethat wage dierenes between setorsstem fromthe presene of eieny
1
Additional referenesonerning dual labormarkets in theeld of eieny wagesinlude Agénor
andSantaella(1998),AlbrehtandVroman(1992),Jones(1987)andSaint-Paul(1996,hapter5)foran
empirialsurvey.
eort-wageelastiityisexpetedtobelowerthanunityinaStakelberg equilibrium. The
primary setor ats as a leader in setting the wage poliy and the seondary setor as
a follower, thus leading to a strategi eieny wage. The remainder of the paper is
organized asfollows. In setion 2,we present a dual labormarkets modelwith eieny
wage. In setion3, wedetermine the strategieieny wage and examine the relevane
of the Solowondition. Conluding ommentsare in setion4.
2 A dual labor markets model
Weonsideraneonomyinwhihtherearetwosetors. Duallabormarketsanarisewhen
monitoring diulties vary aross rms. The wage-produtivity nexus is thus important
only in one setor of the eonomy, the primary setor. We assume that there exists one
representative rm persetor.
That eah rm ats as a monopsonist within its setor may seem unrealisti. An
interpretationistoonsider thatthere areinfatseveral rms persetor,butthese rms
olludetoat asamonopsonist(seeWauthy andZenou, 2000,2001). Anotherargument,
whih ismore relevant inour ontext, isto relyonloallabormarkets (see Topel,1986).
For instane, let us assume the presene of a two-setors labor market, with a high-
tehnology setorand alow-tehnologysetor. Workers deidetoworkby omparingnet
wages aross setors. In eah setor, the same level of qualiation is required by rms.
So, workers are haraterized by low mobility within eah setor and even if rms are
numerous, amonopsony marketpowerprevailsineah setor. Clearly,monopsony power
is bounded bymobilityosts (duetohangesof industry, ofity,of qualiation),sothat
monopsonistirmsareredibleasoneonsiderssuientlyimportantmobilityosts(see
the disussion in Thisseand Zenou, 1997) .
The output of the primary rm is a funtion of the workers' level of eort, whih is
variable due to imperfet monitoring. The eieny wage hypothesis is relevant in the
primary setor and there are job rationingand voluntary payments by rms of wages in
exess of market-learing. Thus, the output in the primary setor is a funtion of labor
eieny units, i.e. the produt of eort and employment. The prot funtion of the
primary rm is :
=F
e
w
w
0
N
wN (1)
where e(:)isthe aggregatedeortfuntionforthe primaryworkers, wisthe levelofwage
in the primary rm, w
0
is the level of wage in the seondary rm, N is the number of
workers inthe primaryrm, andF(:)isthe produtionfuntionof theprimary rm. We
makethe standard assumption of onavity (F 0
>0, F 00
<0).
Conversely, for the seondary rm, the wage-produtivity relationshipis supposed to
be nonexistent. Therefore, a fully neolassialbehavior is expeted for that rm. Owing
to perfet monitoring, the output in the seondary setor is supposed to depend on a
onstant level of eort. In the model, there is no unemployment. As laimed by Akerlof
and Yellen (1986, p. 3), the market for seondary jobs lears, and anyone an obtain a
job inthis setor, althoughitmightbe atalowerpay. LetG(L N) bethe prodution
funtion of the seondary rm, where L is the total labor fore in the eonomy. Thus,
the wageintheompetitiveseondarysetorisgivenby themarginalprodutivityinthis
setor, whih isgiven by G 0
(L N). Again, wesuppose that G 0
>0 and G 00
<0.
Wemakethe following assumption onerning how dual loal labormarkets operate.
We fous on a Stakelberg equilibrium whih leads to a strategi eieny wage. The
2
Forempirialevideneonmonopsonypowerinthelabormarket,see BoalandRamson(1997).
deisions, while the seondary rm ats as a follower. Hene, the rm operating in the
primary setor faes the followingmaximizationprogram:
max
w;N
=F
e
w
w
0
N
wN s.t. w
0
=G 0
(L N) (2)
whih an alsobe expressed as:
max
w;N
=F e
w
G 0
(L N)
!
N
!
wN (3)
The orrespondingrst-order onditions are :
N e
0
w
w
0
w
0 F
0
e
w
w
0
N
N =0 (4)
"
e
w
w
0
+e 0
w
w
0
wN G
00
(L N)
G 0
(L N) 2
#
F 0
e
w
w
0
N
w=0 (5)
Aording to (4), the marginal benet of adjusting wages is equalized with its marginal
ost, whih is the optimal ondition for wage setting. Aording to (5), the rm hires
laborup to the point where the marginalost of laboris equal to itsmarginalrevenue.
3 Strategi eieny wage and the Solow ondition
Giventhe ompetitivebehaviorfortheseondary rm,weannowdeterminetheoptimal
valuefor theeieny wage. Sine theondition G 0
(L N)=w
0
holds, equation(5)an
also be expressed as :
"
e
w
w
0
+e 0
w
w
0
w
w
0 N
L N
G 00
(L N)
G 0
(L N)
(L N)
#
F 0
e
w
w
0
N
w=0 (6)
Using (4), the marginalprodutivity of the primary rm is suh that :
F 0
e
w
w
0
N
= w
0
e 0
w
w0
(7)
Let ( w
w0 )=
e 0
e w
w0
be the eort-wage elastiity ; =
G (L N)
G 0
(L N)
(L N) is the elastiity of
the marginalprodutivity (wage)inthe seondary setor; N
L N
indiatesthe relativesize
of theprimary rminomparisonwiththe seondary rm. Hene, weobtaintheoptimal
strategi eieny wage given inthe following proposition.
Proposition 1 The eort-wage elastiity in a dual labor markets model is :
w
w
0
=
L N
L N+N
(8)
Proof : Using (6) and (7), and by rearranging some terms, we arrive at the following
expression for the eort-wage elastiity :
e 0
w
w
0
e
w
w0
w
w
0
=
1
1 G
00
(L N)
G 0
(L N)
(L N) N
L N
From the denitions of and ,we dedue that ( w
w
0
)=(L N)=(L N +N). QED
Corollary 1 The eort-wage elastiity in a Stakelberg equilibrium is less than one.
Thus, in this framework, we provide formal proof that the Solowondition does not
holdwithduallabormarkets. Indeed,theprodutionfuntionisharaterizedbydereas-
ingreturnstosale,sothatwehave = G
00
(L N)
G 0
(L N)
(L N)>0. Hene,L N+ N >L N
and learly ( w
w
0
)<1. Therefore, our result an be treatedas theoretial support forthe
argument developed inAkerlof and Yellen (1986),who argue that aneort-wage elasti-
ity of unity is quitehigh. Given the prodution tehnologies, the eort-wage elastiity is
less than one when one aounts for strategi interations between the primary and the
seondary setors 3
.
3
With aprodution funtion of thesort F(e;N), there is notneessarilya lowerequilibrium eort-
wageelastiity. Thisresultisstandardin theeienywageliterature(seeRamaswamyandRowthorn,
of two levels of tehnology, high and low. An eieny wage is implemented for the
high-tehnology rm beause of imperfet monitoring. Hene, high wages are paid in
exhange of high amounts of eort. Workers partiipateonly inone of the tworms (no
unemployment). ByplayingaStakelbergequilibrium,theprimaryrm anthreatenthe
workers not to nd a job in the high-tehnology setor, thereby leading to a lower wage
fortheminthermwithlow-tehnology. Thelessonofourpaperisthatinsuhasetting,
theeort-wageelastiityislowerthanone. Thereisaninentiveforamanagertoinrease
the wage levelinthe primaryrm. Forahigh value ofw, the levelof employmentinthis
setor islowand thereis ashiftoflaborfromthe primarytothe seondary setor,whih
dereases the value of w
0
(sine L N is higher).
4 Conlusion
In this paper, we have presented adual labormarkets model with eieny wage. Con-
sidering a Stakelberg equilibrium in whih the primary setor ats as a leader and the
seondary setor asafollower,we showthatthe Solowonditiondoesnot holdingeneral
and an eort-wage elastiity lower than one is expeted. This theoretial result puts in
perspetive the intuition presented in Akerlof and Yellen (1986) and indiates that it is
importantto aount for the strategiaspets between setors in the labormarket when
1991). Inthedual labormarketase,thestrategieienywageis:
w
w
0
=
N
e 1
1+ N
L N
whereF
e
=F=eandF
N
=F=Nareelastiitiesofprodutionwithrespettoeortandemployment
in the primarysetor. Thus,
w
w
0
is greater(respetivelylower)than onewhenthe inequality
N
e
>
1+ N
L N
holds(respetively
N
e
<1+ N
L N ).
In addition, the dual labor markets model with eieny wage provides a new ex-
planation onerning the presene of a minimum wage in the labor market. While the
low-tehnology rm isharaterizedby awage whihdepends onitsmarginalprodutiv-
ity, the minimum wage is not aeted by the struture of employment. Thus, by setting
a minimum wage, the publi authority prevents the rm haraterized by leadership to
inuene the wage levelinthe low-tehnologyrm. It follows that theSolowondition is
restored inthe ase of dual labormarkets whena minimum wage exists.
Aemoglu D., (2001), Good jobs versus bad jobs, Journal of Labor Eonomis 19, pp.
121.
Akerlof G.A.,YellenJ.L., (1986),Eieny wage models of the labor market, Cambridge
University Press, Cambridge.
Agénor P.R., Santaella J.A., (1998), Eieny wages, disination and labor mobility,
Journal of Eonomi Dynamis and Control 22,pp. 267291.
Albreht J.W., Vroman S.B., (1992), Dual labor markets, eieny wages, and searh,
Journal of Labor Eonomis10, pp. 438461.
Boal W., Ransom M., (1997), Monopsony in the labor market, Journal of Eonomi
Literature 35,pp. XXXX.
BulowJ.,SummersL.,(1986),Atheoryof duallabormarketswithappliationtoindus-
trial poliy, and Keynesian unemployment,Journal of Labor eonomis4, pp. 376414.
Doeringer P.B., Piore M.J., (1971), Internal labor markets and manpower analysis, Lex-
ington, Heath.
FariaJ.R.,(2000),Supervisionandeortinanintertemporaleieny wagemodel: the
role of the Solowondition, Eonomis Letters 67, pp. 9398.
Katz L.,(1986),Eienywagetheories: Apartialevaluation,NBER Maroeonomis
Annual,pp. 235275.
Jellal M., Zenou Y., (1999), Eieny wages and the quality of job mathing, Journal
of Eonomi Behavior and Organization39,pp. 201217.
Jellal M., Zenou Y., (2000), A dynami eieny wage model with learning by doing,
Eonomis Letters 66,pp. 99105.
Lin C., LaiC., (1994), Theturnover osts and the Solowondition inaneieny wage
model with intertemporaloptimization,Eonomis Letters, 45, pp. 501505.
Marti C., (1997), Eieny wages : ombining the shirking and turnover ost models,
Eonomis Letters 57,pp. 327330.
Pisauro G., (1991), The eets of taxes on labour in eieny wage model, Journal of
Publi Eonomis 46,pp. 329345.
ia 58,pp. 501514.
Saint-Paul G., (1996), Dual Labor Markets : A Maroeonomi Perspetive, MIT Press,
Cambridge.
Shmidt-Sørensen J.B., (1990), The equilibrium eort-wage elastiity in eieny-wage
models,Eonomis Letters 32, pp. 365369.
Shapiro C., Stiglitz J.E., (1984), Equilibrium unemployment as a worker disipline de-
vie, Amerian Eonomi Review 74,pp. 433444.
SolowR.,(1981),Anotherpossiblesoureofwagestikiness,Journalof Maroeonomis
1, pp. 7982.
Thisse J.F., Zenou Y.,(1997), Segmentationet marhés loaux du travail,Eonomie et
Prévision 131, pp. 6576.
Topel R.H., (1986), Loal labor markets, Journal of Politial Eonomy 94, pp. S111-
S143.
Wauthy X., Zenou Y., (2000),How the adoption of a new tehnology is aeted by the
interationbetweenlabourandprodutmarkets,inG.Norman,J.F.Thisse,eds.,Market
Struture and Competition Poliy. Game-theoreti Approahes, Cambridge University
Press, Cambridge.
WauthyX.,ZenouY.,(2001),Howdoesimperfetompetitioninthelabormarketaet
unemployment poliies ?, Journal of Publi Eonomi Theory, forthoming.
