T ade, Labo Ma ke s and he O ganiza ion
o P oduc ion wi hin Fi ms
Disse a ion
zu E langung des G ades eines Dok o s de Wi scha swissenscha
de Rech s- und Wi scha swissenscha lichen Fakul ¨
a
de Uni e si ¨
a Bay eu h
Vo geleg
on
Michael Koch
aus
Bambe g
Dekan: P o . D . He be Wo a schek
E s be ich e s a e : P o . D . Ha mu Egge
Zwei be ich e s a e : P o . D . Ca s en Eckel
Tag de m¨undlichen P ¨u ung: 13.11.2013
F¨u meine El e n
i
Acknowledgemen s
I would like o hank all he people ha helped and suppo ed me while
w i ing his heses. In pa icula I would like o hank my i s supe iso
Ha mu Egge o his insigh ul guidance and con inuous encou agemen .
The nume ous discussions and he pleasan a mosphe e a his chai ha e
s ongly con ibu ed o he success o my heses. I would also like o hank
my second supe iso Ca s en Eckel o his use ul ad ice and commen s on
he di e en chap e s in his hesis. My g a e ul hanks a e also ex ended
o my colleges a he depa men o law and economics a he Uni e si y o
Bay eu h, in pa icula Daniel E zel, o inspi ing con e sa ions and help ul
discussions du ing he las yea s.
I would also like o ex end my hanks o he Depa men o Economics
a he Uni e si y o Be gen o hei hospi ali y du ing my esea ch s ay. In
pa icula I would like o hank F ode Meland o in i ing me o Be gen and
his aluable and cons uc i e sugges ions. I would also like o hank Kje il
G ams ad, Inge Somme el E ik, Le oy Ande sland and Hans-Ma in
S aume o he kindly s ay in Be gen.
Fu he mo e, I g a e ully acknowledge he inancial suppo by he Ba a -
ian G adua e P og am in Economics (BGPE).
Finally, I would like o hank my a he Ka l-E ns and my mo he
Ch is a o suppo ing me. Special hanks go o my pa ne Susan o he
encou agemen , he unde s anding and lo e du ing he pas ew yea s.

i
Abs ac
The main esea ch ques ion o his hesis is how globaliza ion shapes he
o ganiza ion o p oduc ion wi hin i ms, wi h a pa icula ocus on he ole
o labo ma ke impe ec ions in open economies. Fo ha eason, I make
use o h ee di e en models o in es iga e he in e ac ion be ween i m o -
ganiza ion and labo ma ke impe ec ions in he p ocess o globaliza ion.
The eby, he o ganiza ion o p oduc ion is discussed om di e en pe spec-
i es: (i) he numbe o p oduc s a i m is willing o p oduce and (ii) he
o ganiza ion o labo wi hin i ms. In each chap e , I use a di e en ap-
p oach o accoun o impe ec ions in ac o ma ke s. This allows a b oad
discussion on how labo ma ke ins i u ions a ec he equilib ium ou come
in closed and open economies, and how hese impe ec ions a ec a i m’s
o ganiza ion choice.
A e a sho in oduc ion in Chap e 1, Chap e 2 se s up a gene al
oligopolis ic equilib ium model wi h mul i-p oduc i ms and union wage
se ing. In his model, wo policy expe imen s a e conduc ed. Fi s , i
is shown ha deunioniza ion induces a gene al decline in i m scale and
scope, wi h he espec i e educ ion being mo e p onounced in non-unionized
indus ies. Second, he consequences o ade libe aliza ion a e s udied, and
i is shown ha access o o eign ma ke s lowe s i m scope in all indus ies
as well as he scope di e en ial be ween unionized and non-unionized i ms.
Adjus men s in i m scale u n ou o be less clea cu and in e alia depend
on he deg ee o p oduc di e en ia ion.
Chap e 3 looks inside he i m and in es iga es how ade al e s he
ma ching o wo ke -speci ic abili ies and ask-speci ic skill equi emen s. The
ou come o his ma ching p ocess depends on how i ms o ganize hei e-
c ui men p ocess and how much hey in es in o he sc eening o applican s.
In he open economy, he mos p oduc i e i ms s a expo ing. They in-
c ease hei ma ke sha e and he e o e ind i a ac i e o inc ease hei
sc eening in es men , which imp o es he ma ching ou come. Things a e
di e en o non-expo e s, whose ma ke sha e sh inks in he open econ-
omy, lowe ing hei incen i e o in es o sc eening applican s. Due o his
asymme ic esponse, access o ade aises he dispe sion o p oduc i i y
be ween he e ogeneous p oduce s, while a he same ime inc easing he
a e age quali y o wo ke - ask ma ches and hus economy-wide labo p o-
duc i i y.
Chap e 4 se s up a he e ogeneous i ms model, whe e p oduc ion consis s
o a con inuum o asks and i ms hi e low-skilled and high-skilled wo ke s o
ii
iii
he pe o mance o asks, which di e in hei complexi y. How i ms assign
wo ke s o asks depends on ac o p ices o he wo skill ypes and he p o-
duc i i y ad an age o high-skilled wo ke s in he pe o mance o complex
asks. A e cha ac e izing he closed economy equilib ium wi h ully lexi-
ble wages, I show how i ms adjus he assignmen o wo ke s op asks in
esponse o he in oduc ion o a binding eal minimum wage o low-skilled
wo ke s and mig a ion o low-skilled o high-skilled wo ke s. Wi h a mini-
mum wage, he opening up o ade educes he ange o asks pe o med
by high-skilled wo ke s. I u he mo e leads o a highe pe -capi a income
o bo h skill ypes, which implies a highe wel a e in he open han in he
closed economy, while inequali y be ween he wo skill ypes inc eases. In
an ex ension, I discuss how he i m-in e nal assignmen o skills o asks is
a ec ed by labo ma ke linkages in open economies.
Con en s
1 In oduc ion 1
2 Labo Unions and Mul i-P oduc Fi ms in Closed and Open Economies 5
2.1 In oduc ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 MPFs and impe ec labo ma ke s: The closed economy . . . . . . . . . . . . . . 7
2.2.1 P e e ences and consume demand . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Technology, p oduc ion, and p o i maximiza ion . . . . . . . . . . . . . . 9
2.2.3 Union wage se ing and he labo ma ke . . . . . . . . . . . . . . . . . . 10
2.2.4 The consequences o deunioniza ion o i m-le el a iables . . . . . . . . 12
2.3 MPFs and labo ma ke impe ec ion in an open economy . . . . . . . . . . . . . 14
2.4 Concluding ema ks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5.1 Ex ension – Linea cos unc ion . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.2 Ex ension – Fi m le el unions . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.3 P og am codes o simula ion exe cises . . . . . . . . . . . . . . . . . . . . 33
3 T ade and he Fi m-In e nal Alloca ion o Wo ke s o Tasks 39
3.1 In oduc ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 The closed economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Model s uc u e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Equilib ium in he closed economy . . . . . . . . . . . . . . . . . . . . . . 44
3.3 The open economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.1 Basic s uc u e and p elimina y insigh s . . . . . . . . . . . . . . . . . . . 46
3.3.2 The open economy equilib ium . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 A model a ian wi h in olun a y unemploymen . . . . . . . . . . . . . . . . . . 51
3.5 A calib a ion exe cise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6 Concluding ema ks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 T ade and he Fi m-in e nal Assignmen o Skills o Tasks 67
4.1 In oduc ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2 The closed economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.1 Model s uc u e and i m-le el analysis . . . . . . . . . . . . . . . . . . . . 71
4.2.2 Gene al equilib ium wi h pe ec labo ma ke s . . . . . . . . . . . . . . . 75
4.2.3 Equilib ium wi h a minimum wage o low-skilled wo ke s . . . . . . . . . 78
4.2.4 Compa a i e-s a ic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 The open economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
ix
2CHAPTER 1. INTRODUCTION
he compa a i e-s a ic expe imen s, he ocus is on wo speci ic esea ch ques ions ha ha e
spa ked conside able in e es in academic ci cles and, a he same ime, a e ele an o policy
make s who aim a in oducing measu es o de egula ion in p oduc and/o labo ma ke s. The
i s ques ion is how i ms abso b changes in labo ma ke ins i u ions, and how ins i u ional
changes in ce ain indus ies spill o e on he es o he economy. F om an empi ical poin o
iew, he p obably mos no able change in labo ma ke ins i u ions is he signi ican decline
in union ele ance. This deunioniza ion p ocess induces an inc ease in he compe i i e as well
as he union wage. In a se ing wi h MPFs he associa ed cos inc ease ende s p oduc ion o
hose a ie ies ha ha e he la ges dis ance o a i m’s co e compe ence una ac i e, so ha
i ms educe he scope o hei p oduc ange and hus sh ink a he ex ensi e ma gin. Bo h
he cos inc ease and he sho ening o he p oduc ange induce a decline in o al i m scale.
Fu he mo e, by ocusing on he p oduc ion o high-compe ence, i.e. low-cos , a ie ies, all i ms
(excep o he newly deunionized ones) can p oduce a highe le el o ou pu wi h a gi en le el
o labo inpu and hus a e mo e p oduc i e on a e age. Finally, i is shown ha deunioniza ion
by lowe ing he union wage p emium makes i ms mo e simila in bo h size dimensions, scale and
scope. In a second pa o his chap e , I in es iga e how i m scale and scope a e a ec ed i a
coun y opens up o ee ade wi h a symme ic pa ne coun y. Access o in e na ional ade
s imula es labo demand and aises he compe i i e as well as he union wage, he eby lowe ing
i m scope in all indus ies. Since he labo ma ke dis o ion becomes less se e e, unionized
and non-unionized i ms become mo e simila in he size o hei p oduc ange. While scope
e ec s a e unambiguous, adjus men s in i m scale u n ou o be less clea cu and in e alia
depend on he deg ee o p oduc di e en ia ion.
S udying he ole o i ms o ma ching wo ke s wi h asks and discussing how access o ade
a ec s he ma ching ou come is he main pu pose o Chap e 3.5S a ing poin o he analysis is
a Meli z (2003) model, in which i ms a e he e ogeneous due o di e ences in hei p oduc i i y
le els. As in Acemoglu and Au o (2011), i is assumed ha p oduc ion consis s o a con inuum
o asks ha di e in hei skill equi emen s. Fo pe o ming hese asks, i ms hi e he e oge-
neous wo ke s. He e ogenei y is ho izon al in he sense ha wo ke s di e in hei abili y o
pe o m speci ic asks because hei human capi al is occupa ion-speci ic, while hey a e equally
p oduc i e o e he whole ange o ac i i ies. This implies ha all wo ke s ha e he same alue
o i ms and, lacking in o ma ion abou abili ies o indi idual wo ke s, i ms andomly d aw hei
employees om he labo supply pool. This lack o in o ma ion gene a es a sou ce o misma ch
be ween ask-speci ic skill equi emen s and wo ke -speci ic abili ies wi hin he bounda ies o a
p oduc ion uni . To educe his misma ch, i ms can in es in o a sc eening echnology o ga h-
e ing some (impe ec ) in o ma ion abou he abili ies o hei wo k o ce. A highe in es men
p o ides be e knowledge abou he abili ies o wo ke s and he e o e leads o a be e ma ch
o hese wo ke s wi h he di e en asks in he p oduc ion p ocess. The incen i es o sc een a e
mo e p onounced in la ge i ms, and hence he e is an addi ional sou ce o he e ogenei y in his
model, which is endogenous and ein o ces he e ogenei y o i ms due o exogenous di e ences
in i m p oduc i i y. This model is used o shed new ligh on he consequences o ade o
labo ma ke ou come, he eby ocussing on adjus men s in he i m-in e nal labo ma ke . To
be mo e speci ic, i is analyzed how ade a ec s unde employmen a ising om a misma ch be-
5This chap e is based on Egge , Koch (2013). When wo king on his chap e , I ha e bene i ed om commen s
by Ca s en Eckel, James Ha igan, F ode Meland, Ma c Muendle , F ank S ¨ahle and pa icipan s a he Eu o-
pean T ade S udy G oup Mee ing in Leu en, he GEP Pos g adua e Con e ence in No ingham, he G¨o ingen
Wo kshop on In e na ional Economics, he Midwes In e na ional Economics Mee ing a he Indiana Uni e si y,
he B own Bag Semina o he Depa men o Economics a he Uni e si y Bay eu h, he Resea ch Wo kshop o
he Ba a ian G adua e P og am in Economics (BGPE) and he Economics Resea ch Semina s a he Uni e si y
o Be gen and he Uni e si y o Tuebingen.

3
ween wo ke -speci ic abili ies and ask-speci ic skill equi emen s. To keep he analysis simple,
he ocus is on ade be ween symme ic coun ies while conside ing he empi ically ele an
case, in which only he mos p oduc i e i ms expo in he open economy. Ha ing access o
he expo ma ke , high-p oduc i i y i ms can expand hei ma ke sha e in he open econ-
omy, which p o ides an incen i e o hese i ms o sc een hei wo k o ce mo e in ensi ely, as
his u he imp o es he ma ching quali y and hus lowe s p oduc ion cos s. Low-p oduc i i y
non-expo e s, on he o he hand, lose ma ke sha e and hus lowe hei in es men in o he
sc eening echnology, which aises hei p oduc ion cos s. By changing he cos s uc u e, his
asymme ic esponse o ade libe aliza ion exe s a eedback e ec on he en y/exi decision
o i ms in bo h he domes ic and he expo ma ke , which is no p esen in o he ade models
wi h he e ogeneous i ms. Fu he mo e, i al e s he p oduc i i y dis ibu ion o ac i e i ms
by d i ing a wedge be ween ma ching e iciency o expo e s and non-expo e s. Finally, ad-
jus men s in he i m-in e nal labo alloca ion p ocess lowe he agg ega e misma ch be ween
wo ke -speci ic abili ies and ask-speci ic skill equi emen s, he eby gene a ing a p oduc i i y
s imulus ha ein o ces he gains om ade in an o he wise iden ical Meli z (2003) model.
Chap e 4 builds upon he amewo k s udied in Chap e 3 and se s up a he e ogeneous
i ms model in which a i m’s ou pu is manu ac u ed using a con inuum o asks.6Fi ms
hi e low-skilled and high-skilled wo ke s o he pe o mance o asks. Tasks di e in hei
complexi y and wo ke s di e in hei abili y o pe o m hese asks, wi h high-skilled wo ke s
ha ing a compa a i e ad an age in pe o ming mo e complex asks. How i ms o ganize he
i m-in e nal p oduc ion p ocess by assigning skills o asks depends on he espec i e ac o
cos s and p oduc i i y ad an age o high-skilled wo ke s in pe o ming mo e complex asks.
This amewo k is used o analyze how impe ec ions in he labo ma ke a ec he i m-in e nal
assignmen o skills o asks in he closed economy. A e cha ac e izing he au a ky equilib ium
ou come wi h ully lexible wages o bo h skill ypes, a ( eal) minimum wage is in oduced,
ha is se by he go e nmen o low-skilled wo ke s and causes in olun a y unemploymen o
ha skill ype. As ela i e ac o p ices a e changed and low-skilled ask p oduc ion becomes
mo e cos ly, i ms assign high-skilled wo ke s o a b oade ange o asks. This i m-in e nal
skill upg ading imp o es a i m’s labo p oduc i i y. Howe e , as mo e high-skilled wo ke s a e
employed o he pe o mance o asks, less o hem a e le o manage i ms and he mass o i ms
he e o e declines. Fi m exi igge s a decline in agg ega e ou pu , income and wel a e. A e
discussing mig a ion o low-skilled and high-skilled wo ke s unde he wo di e en labo ma ke
egimes, he model is used o discuss how ade be ween wo coun ies a ec s he i m-in e nal
p oduc ion p ocess. Only when low-skilled wages a e se by a binding minimum wage, ade
exe s an impac on he i m-in e nal assignmen p ocess. The opening up o ade aises demand
o each i m due o a s anda d di ision o labo e ec . When he ac o p ice o low-skilled
wo ke s is ixed, he skill p emium inc eases implying ha high-skilled ask p oduc ion becomes
ela i ely una ac i e. Fi ms espond in b oadening he ange o asks p oduced wi h low-
skilled wo ke s, which educes labo p oduc i i y o each i m. Beside his nega i e p oduc i i y
e ec , ade inc eases he mass o p oduce s in each coun y and educes he unemploymen
a e o low-skilled wo ke s. This causes an inc ease in he ela i e income o bo h wo ke s wi h
he espec i e inc ease being mo e p onounced o high-skilled wo ke s. Fu he mo e, agg ega e
ou pu , income and wel a e goes up. Mo eo e , high-skilled wo ke s gain in ela i e e ms as
hei skill p emium and ela i e pe -capi a income inc eases. A e discussing he mo emen om
au a ky o ade, i is shown how changes in local endowmen s and labo ma ke ins i u ions
6When wo king on his chap e , I ha e bene i ed om commen s by Ca s en Eckel, Ha mu Egge and
pa icipan s a he Eu opean T ade S udy G oup Mee ing in Bi mingham, he IO and T ade Semina a he
Depa men o Economics a he Uni e si y o Munich and he B own Bag semina a he Uni e si y o Bay eu h.
4CHAPTER 1. INTRODUCTION
spill o e o he pa ne coun y. The eby, i is shown ha an inc ease in he minimum wage
ab oad educes he ange o asks pe o med by low-skilled wo ke s a home, while i inc eases
he p oduc i i y o ac i e p oduce s he e. Bo h skill ypes end up wi h a lowe pe -capi a
income, and hus wel a e is educed a home.
Finally, Chap e 5 concludes wi h a b ie summa y o he mos impo an esul s.
Chap e 2
Labo Unions and Mul i-P oduc
Fi ms in Closed and Open
Economies
2.1 In oduc ion
In his chap e , we analyze how labo ma ke impe ec ion a ec s scale and scope o mul i-
p oduc i ms (MPFs). To add ess his issue, we se up a gene al oligopolis ic equilib ium
(GOLE) model wi h MPFs along he lines o Eckel and Nea y (2010) and en ich his amewo k
by assuming union wage se ing in a subse o indus ies. The asymme y o sec o s wi h
espec o hei labo ma ke ins i u ions is a key aspec o ou analysis. I allows us o s udy
he consequences o union wage se ing on i m scale and scope in unionized indus ies and i
p o ides no el insigh s on how labo ma ke impe ec ions in ce ain indus ies spill o e on i m
o ganiza ion in he es o he economy. Wi hin his amewo k, we unde ake wo compa a i e-
s a ic expe imen s. Fi s , we in es iga e he consequences o deunioniza ion on i m scale and
scope in indus ies ha a e di ec ly exposed o his ins i u ional change as well as in indus ies
whose labo ma ke ins i u ions do no change. Second, we s udy he di e en ial impac o ade
libe aliza ion on i m scale and scope in unionized and non-unionized indus ies.
Relying on he Eckel and Nea y (2010) amewo k, we assume a con inuum o indus ies and a
small (exogenous) numbe o i ms compe ing in quan i ies wi hin each o hese indus ies. Fi ms
employ labo o p oduce a ange o di e en ia ed p oduc a ie ies. They ha e a co e compe ence
in one o hese a ie ies which hey p oduce a he lowes ma ginal cos . By expanding he scope
o hei p oduc ange, i ms s a manu ac u ing a ie ies wi h a la ge dis ance o hei co e
compe ence and hus highe ma ginal p oduc ion cos s.1Se ing a ma kup on he compe i i e
1Abs ac ing om any addi ional cos s o in oducing a new a ie y he model cap u es he idea o lexible
manu ac u ing, which is a widely used concep o ep esen ing MPFs (see Milg om and Robe s, 1990; Ea on and
Schmi , 1994; No man and Thisse, 1999; Eckel, 2009). While he e a e many al e na i e ways o modeling MPFs
(see, o ins ance, Feens a and Ma, 2008; Nocke and Yeaple, 2008; A kolakis and Muendle , 2010; Maye , Meli z,
and O a iano, 2010; Be na d, Redding, and Scho , 2011), he e a e good easons o elying on he Eckel and
Nea y (2010) app oach when accoun ing o union wage se ing. Wi h oligopolis ic compe i ion be ween a small
numbe o compe i o s and linea demand in each indus y, ou model is ela ed o a la ge and well-es ablished
li e a u e on unionized oligopoly. Thus, we can di ec ly compa e ou esul s wi h indings om his li e a u e
o highligh whe he and how p e ious insigh s on he in e play be ween labo ma ke and p oduc ma ke
impe ec ions ha e o be modi ied i one accoun s o mul i- ins ead o single-p oduc i ms.
5
6CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
wage, labo unions en o ce a educ ion in he ou pu and employmen le el o unionized i ms.
While his e ec does also exis in o he models o unionized oligopoly, he e is an addi ional
adjus men ma gin in a se ing wi h MPFs. By aising ma ginal p oduc ion cos s, unions educe
he incen i e o i ms o ope a e a wide p oduc ange and hus lowe i m scope. Fu he mo e,
union wage se ing lowe s agg ega e employmen ce e is pa ibus and hus induces a all in he
ma ke -clea ing compe i i e wage. The decline o he compe i i e wage aises i m scale and
scope in non-unionized indus ies. This poin s o a new ace o spillo e s associa ed wi h
union wage se ing. Unions do no only in luence wage paymen s in o he sec o s (due o labo
ma ke clea ing) bu also a ec he p oduc ange o non-unionized p oduce s – and hus labo
p oduc i i y in ou se ing.
In he compa a i e-s a ic expe imen s, we ocus on wo speci ic esea ch ques ions ha ha e
spa ked conside able in e es in academic ci cles and, a he same ime, a e ele an o policy
make s who aim a in oducing measu es o de egula ion in p oduc and/o labo ma ke s. The
i s ques ion we a e in e es ed in is how i ms abso b changes in labo ma ke ins i u ions, and
how ins i u ional changes in ce ain indus ies spill o e on he es o he economy. F om an
empi ical poin o iew, he p obably mos no able change in labo ma ke ins i u ions is he
signi ican decline in union ele ance. This deunioniza ion p ocess is a wo ldwide phenomenon
which has been obse ed in all indus ialized economies o e he las ou decades (see OECD,
2004). F om Bas os and K eickemeie (2009) we know ha in an o he wise simila amewo k
wi h single p oduc i ms (SPFs), deunioniza ion – cap u ed by a decline in he sha e o unionized
indus ies – aises he compe i i e as well as he union wage and hus lowe s scale o bo h
unionized and non-unionized i ms. Since he union wage inc eases less han p opo ionally,
deunioniza ion lowe s he scale di e en ial be ween he wo ypes o p oduce s.
In his chap e , we show ha i m-le el adjus men s become mo e sophis ica ed when i ms
p oduce mo e han jus a single a ie y and ha he endogenei y o he p oduc ange leads
o u he in e es ing esul s upon how i ms espond o changes in labo ma ke ins i u ions.
To be mo e speci ic, deunioniza ion induces an inc ease in he compe i i e as well as he union
wage, simila o he model wi h SPFs. Howe e , in a se ing wi h MPFs he associa ed cos
inc ease ende s p oduc ion o hose a ie ies ha ha e he la ges dis ance o a i m’s co e
compe ence una ac i e, so ha i ms educe he scope o hei p oduc ange and hus sh ink
a he ex ensi e ma gin. Bo h he cos inc ease and he sho ening o he p oduc ange induce a
decline in o al i m scale. Fu he mo e, by ocusing on he p oduc ion o high-compe ence, i.e.
low-cos , a ie ies, all i ms (excep o he newly deunionized ones) can p oduce a highe le el
o ou pu wi h a gi en le el o labo inpu and hus a e mo e p oduc i e on a e age. Finally,
we show ha deunioniza ion by lowe ing he union wage p emium makes i ms mo e simila in
bo h size dimensions, scale and scope, in ou se ing.
In a second applica ion o ou model, we in es iga e how i m scale and scope a e a ec ed i
a coun y opens up o ee ade wi h a symme ic pa ne coun y. As poin ed ou by B ande
(1981), a mo emen om au a ky o ade aises compe i ion in an oligopolis ic ma ke and
hus p o ides a s imulus o he p oduc ion o all i ms ce e is pa ibus. In a gene al equilib ium
en i onmen wi h ac o ma ke clea ing, his induces an inc ease in he compe i i e wage,
which coun e ac s he pa ial equilib ium p oduc ion s imulus. As ou lined by Nea y (2009), in
a model wi h SPFs, symme ic indus ies, and no labo ma ke dis o ions, he wo e ec s cancel
and hus i m scale emains una ec ed by he ade shock. In an o he wise iden ical model wi h
MPFs, i ms lowe hei scope in esponse o a highe compe i i e wage, he eby lea ing mo e
labo o employmen in ac i i ies ha a e close o he i ms’ co e compe ences. To pu i in
he wo ds o Eckel and Nea y (2010) i ms a e leane and meane in he open economy and
hey expe ience a p oduc i i y su ge as hei o al ou pu inc eases o a gi en le el o labo
2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 7
inpu . This poin s o a new channel h ough which gains om ade can ma e ialize, one ha
is speci ic o models o MPFs.
By ex ending he Eckel and Nea y (2010) amewo k o one wi h labo ma ke impe ec ions,
we u he en ich he pic u e o possible i m-le el adjus men s o globaliza ion. As in ex book
models o unionized oligopoly wi h SPFs, ade exe s a union-disciplining e ec and hus lowe s
union wage claims ce e is pa ibus (Huizinga, 1993; Sø ensen, 1993). Hence, bo h scale and scope
e ec s o ade a e mo e p onounced in unionized indus ies, so ha economic ac i i y shi s
owa ds hese sec o s. All o he hings equal, his lowe s p oduc ion in non-unionized indus ies
and he shi e ec may ac ually be s ong enough o domina e he ou pu s imulus om being
mo e ocused on he p oduc ion o high-compe ence a ie ies. Hence, labo ma ke impe ec ions
ende i m-le el adjus men s o in e na ional ade mo e sophis ica ed and less clea cu han
one migh ha e expec ed om he analysis in Eckel and Nea y (2010).
Aside om looking a pu e le el e ec s, we a e pa icula ly in e es ed in he di e en ial
impac ha ade exe s on unionized and non-unionized i ms. In his espec , we show ha
ade weakens he labo ma ke dis o ion and hus lowe s he union wage p emium. This e ec
is ins umen al o a educ ion in he scope di e en ial be ween he wo ypes o p oduce s.
Simila ly, he decline in he union wage p emium also educes he domes ic ou pu di e en ial
o local p oduce s. Howe e , his e ec is coun e ac ed by a widening o he ou pu gap a
he ex ensi e ma gin as, a e a coun y’s opening up o ade, i ms s a expo ing and he
espec i e expo s a e la ge o non-unionized han o unionized i ms. Which o hese wo
e ec s domina es is no clea cu in gene al and depends on he deg ee o p oduc di e en ia ion.
Smalle deg ees o p oduc di e en ia ion ein o ce he p o-compe i i e e ec o ade and hus
ampli y he union-disciplining e ec o o eign compe i ion. This s eng hens he nega i e im-
pac o ade on he domes ic p oduc ion gap be ween unionized and non-unionized p oduce s,
so ha he scale di e en ial dec eases o small deg ees o p oduc di e en ia ion. On he con-
a y, o high deg ees o p oduc di e en ia ion i is he ou pu expansion e ec in he expo
ma ke ha domina es so ha he i m scale di e en ial inc eases in esponse o ade.
The emainde o he chap e is o ganized as ollows. In Chap e 2.2 we in oduce he main
assump ions, desc ibe he basic model s uc u e, and cha ac e ize he au a ky equilib ium. A e
a b ie discussion on how union wage se ing a ec s i m scale and scope, we s udy how MPFs
espond o deunioniza ion. In Chap e 2.3, we cha ac e ize he equilib ium in an open economy
wi h ee ade be ween wo symme ic coun ies and compa e he ou come in he open economy
wi h he one in he closed economy o shed ligh on how ade a ec s union wage se ing as well
as i m scale and scope in he p esence o labo ma ke impe ec ion. Chap e 2.4 concludes
wi h a b ie summa y o he mos impo an esul s.
2.2 MPFs and impe ec labo ma ke s: The closed econ-
omy
The coun y unde conside a ion hos s a con inuum o indus ies, wi h an oligopolis ic ma ke
s uc u e and a small (exogenous) numbe no i ms in each o hese indus ies. The indus ies
a e iden ical in all espec s excep o he p e ailing labo ma ke ins i u ions. While i ms in a
subse o indus ies a e exposed o union wage-se ing, i ms in he es o he economy pay he
compe i i e wage, which is de e mined by a s anda d labo ma ke clea ing condi ion – p o ided
ha labo is homogeneous and ully mobile ac oss sec o s. Wi h espec o union wage-se ing,
we apply a monopoly union amewo k, in which unions unila e ally se wages p io o he i ms’
choice o employmen , which in ou se ing in ol es he simul aneous decision upon i m scale

8CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
and scope.
2.2.1 P e e ences and consume demand
The e exis s a ep esen a i e consume , whose p e e ences a e ep esen ed by a wo- ie quasi-
homo he ic u ili y unc ion. The uppe ie is an addi i e unc ion o a con inuum o sub-u ili ies,
each o hem co esponding o one indus y z∈[0,1]:
U[u{z}] = Z1
0
u{z}dz. (2.1)
Each sub-u ili y is a quad a ic unc ion o consump ion le els q(i, z), i∈[1, N(z)], whe e N(z)
is he measu e (o , in he in e es o a mo e accessible in e p e a ion, he numbe , hence o h)
o di e en ia ed a ie ies p oduced in indus y z. To be mo e speci ic, we assume
u{z}=aZN(z)
0
q(i, z)di −1
2b
(1 −ρ)ZN(z)
0
q(i, z)2di +ρ ZN(z)
0
q(i, z)di!2
,(2.2)
whe e a,bdeno e non-nega i e p e e ence pa ame e s wi h he usual in e p e a ion and ρis an
in e se measu e o p oduc di e en ia ion, which is assumed o lie be ween 0 and 1.2
Agg ega e demand in his se ing is de e mined by maximizing u ili y o he ep esen a i e
consume subjec o he budge cons ain
Z1
0ZN(z)
0
p(i, z)q(i, z)didz ≤I, (2.3)
whe e p(i, z) deno es p ices o a ie y iin indus y zand Iis agg ega e income o he economy.
This gi es
p(i, z) = 1
λ a−b[(1 −ρ)q(i, z) + ρZN(z)
0
q(i, z)di]!,(2.4)
whe e λis he ep esen a i e consume ’s ma ginal u ili y o income. As i has become s anda d
in he li e a u e, we choose u ili y as he num´e ai e and se λequal o one. Thus, all nominal
a iables a e measu ed ela i e o he ep esen a i e consume ’s ma ginal u ili y o income (see
Nea y, 2009, o u he discussion).
F om Eq. (2.4) we can in e insigh s upon he ole o p e e ence pa ame e ρin ou se ing.
As men ioned abo e, ρis a measu e o p oduc di e en ia ion and lies in in e al [0,1]. I ρ= 1
p oduc s a e homogeneous (pe ec subs i u es), so ha he p ice is linea in o al indus y
consump ion: p(i, z) = a−bRN(z)
0q(i, z)di. In he o he limi ing case wi h ρ= 0, goods a e
pe ec ly di e en ia ed in he pe cep ion o consume s, so ha he p ice o each a ie y only
depends on consump ion o his a ie y bu is independen o he consump ion o all o he
a ie ies in his indus y. In he la e case, indi ec demand is gi en by p(i, z) = a−bq(i, z).
2By o mula ing he espec i e p e e ences o he ep esen a i e consume , we ha e p esumed ha he ollowing
wo condi ions a e ul illed o any indi idual consume : pa icipa ion in he ma ke o any good iand non-
sa ia ion in he consump ion o hese goods. Clea ly, bo h o hese condi ions depend on endogenous a iables.
Howe e , unde he addi ional assump ion o iden ical consume p e e ences, we know om p e ious wo k ha
hese condi ions a e ul illed i a lump-sum ax- ans e sys em edis ibu es a su icien le el o income om ich
o poo agen s. Being no in e es ed in income dis ibu ion o indi idual wel a e le els pe se, we can hus sa ely
assume ha he wo condi ions a e ul illed h oughou ou analysis.
2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 9
2.2.2 Technology, p oduc ion, and p o i maximiza ion
We associa e MPFs wi h he idea o lexible manu ac u ing, and hus assume ha i ms can
expand hei p oduc ange “wi h only a minimum o adap a ion” (Eckel and Nea y, 2010,
p.192). The cos s o adap a ion a e modeled by highe labo equi emen s o p oducing a uni
o ou pu o a i m’s non-co e compe ence p oduc , and he espec i e adap a ion cos s a e
assumed o be mono onically inc easing in he dis ance be ween a speci ic p oduc o he i m’s
co e compe ence a ie y. Howe e , adding a new a ie y o he p oduc ange does no al e
he cos s o p oducing o he a ie ies no does i in ol e any ixed cos s. To pu i o mally, we
deno e ma ginal p oduc ion cos s o i m j= 1, ..., n in indus y z o p oducing a ie y iby
cj(i, z) = γj(i)wj(z), wi h γj(i) being he cons an labo inpu coe icien o p oducing a ie y i
and wj(z) being he wage a e in indus y z. We associa e i m j’s co e compe ence wi h a ie y
i= 0 and cap u e lexible manu ac u ing by assuming ∂cj(i, z)/∂i =∂γj(i)/∂i ×wj(z)>
0. While he main mechanisms o ou analysis do no hinge on a speci ic unc ional o m o
γj(i), we impose he addi ional assump ion γj(i) = eiin he in e es o analy ical ac abili y.
Fu he mo e, we assume ha p oduc anges a e i m-speci ic, implying ha each i m has i s
own co e compe ence and p oduces i s own se o a ie ies.3Finally, as poin ed ou abo e, we
allow o sec o al di e ences in labo ma ke ins i u ions and hus end up wi h indus y-speci ic
wage a es. Hence, in con as o Eckel and Nea y (2010) ma ginal p oduc ion cos s in ou
model comp ise bo h a p oduc -speci ic componen , γj(i), and a sec o -speci ic one, wj(z).
Conside ing he echnology assump ions abo e and deno ing by δj(z) he scope o he p oduc
ange, p o i s o i m jin indus y za e gi en by
Πj(z) = Zδj(z)
0pj(i, z)−cj(i, z)xj(i, z)di, (2.5)
whe e xj(i, z) deno es ou pu o a ie y i. Fi ms simul aneously choose he ou pu le el o all o
hei p oduc s as well as he scope o he p oduc ange. Wages (and hus ma ginal p oduc ion
cos s cj(i, z)) a e exogenous om he pe spec i e o indi idual p oduce s. While he compe i i e
wage is an economy-wide a iable and hus no a ec ed by a single i m’s decision upon i s scale
and scope, he unionized wage is de e mined be o e he i m se s xj(i, z) and δj(z) and hus
also ea ed as exogenous in he ou pu game. Taking accoun o he ma ke clea ing condi ion
xj(i, z) = qj(i, z) and maximizing j’s p o i s in (2.5) wi h espec o xj(i, z) gi es he i s -o de
condi ion
∂Πj(z)
∂xj(i, z)=pj(i, z)−cj(i, z)−b[(1 −ρ)xj(i, z) + ρXj(z)] = 0,
wi h Xj(z)≡Rδj(z)
0xj(i, z)di deno ing i m scale. Subs i u ing (2.4) and deno ing indus y-wide
ou pu o all np oduce s by Y(z) = RN(z)
0x(i, z)di we can sol e o
xj(i, z) = a−cj(i, z)−bρ(Xj(z) + Y(z))
2b(1 −ρ).(2.6)
The nega i e impac o indus y ou pu Y(z) on i m j’s p o i -maximizing ou pu o a ie y
icap u es he ac ha unde Cou no compe i ion (and linea demand) ou pu le els a e
3Adap a ion cos s do no depend on he deg ee o p oduc di e en ia ion in consume demand. This ende s
he analysis simple and allows us o s udy p e e ence and echnology changes as wo independen phenomena.
Howe e , he espec i e esul s om ou analysis may be es ic i e i adap a ion cos s a y sys ema ically wi h
he deg ee o p oduc di e en ia ion, which could be he case in indus ies in which p oduc s a e ailo ed o
speci ic needs o indi idual consume s.
10 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
s a egic subs i u es. Fu he mo e, he addi ional nega i e impac o his i m’s own o al ou pu
Xj(z) e lec s he cannibaliza ion e ec , i.e. unde Cou no compe i ion MPFs in e nalize ha
inc easing ou pu o a ce ain a ie y lowe s p ices o his as well as all o he a ie ies in he
i m’s p oduc ange. Bo h o hese e ec s do exis i and only i ρ > 0, i.e. i p oduc s a e no
pe ec ly di e en ia ed (see abo e).
Fu he mo e, maximizing p o i s (2.5) wi h espec o δj(z) gi es he i s -o de condi ion
∂Πj(z)
∂δj(z)= [pj(δj(z)) −cj(δj(z))] xj(δj(z)) = 0,
which can be sol ed o i m j’s op imal p oduc ange
δj(z) = ln a−bρ(Xj(z) + Y(z))
wj(z).(2.7)
Compa ing Eqs. (2.6) and (2.7), we see ha i ms add new a ie ies o hei p oduc po olio
un il he ma ginal cos s o he las a ie y δj(z) equals he ma ginal e enue o his a ie y a
ze o ou pu . Using he la e insigh in Eq. (2.6), we can de i e a second exp ession o op imal
ou pu o a ie y i, by exp essing he espec i e ou pu le el o his a ie y in e ms o he
di e ence be ween i s own ma ginal cos and ha o he ma ginal a ie y:
xj(i, z) = wj(z)[eδj(z)−ei]
2b(1 −ρ).(2.6′)
In eg a ing ou pu xj(i, z) o e all a ie ies i, inally gi es o al ou pu , i.e. he scale, o i m j:
Xj(z) = wj(z)
2b(1 −ρ)heδj(z)δj(z)−1+ 1i,(2.8)
which, all o he hings equal, inc eases in he i m’s p oduc ange δj(z) and, o a gi en scope,
inc eases in wage a e wj(z). The la e e ec has o be in e p e ed wi h ca e, as i does no
imply ha highe ac o cos s inc ease i m size. Ra he , highe wages lead o ou pu adjus men s
a he in e nal and he ex e nal ma gin. The o me is associa ed wi h a i m’s eloca ion o
p oduc ion om goods wi h a la ge dis ance owa ds goods wi h a small dis ance o i s co e
compe ence, holding he p oduc ange and ou pu o he ma ginal a ie y cons an . The la e
is associa ed wi h a change in he p oduc ange. The posi i e impac o an inc ease in wj(z) on
Xj(z) o a gi en δj(z) only cap u es he i m’s ou pu adjus men a he in ensi e ma gin and
acco dingly should be in e p e ed as a pa ial e ec . As ou lined below, his adjus men a he
in e nal ma gin is coun e ac ed and domina ed by a i m’s ou pu adjus men a he ex e nal
ma gin, so ha o al i m size dec eases in esponse o highe labo cos s, as can be expec ed.
2.2.3 Union wage se ing and he labo ma ke
Rega ding ac o endowmen s, we assume ha he coun y unde conside a ion is popula ed by
Lwo ke s, each o hem supplying one uni o labo . Wo ke s a e mobile ac oss sec o s, wi h
sec o s di e ing in he p e ailing labo ma ke ins i u ions. To be mo e speci ic, we apply he
labo ma ke model o Bas os and K eickemeie (2009) and assume ha a subse o indus ies is
unionized, while in he es o he economy, he labo ma ke is pe ec ly compe i i e. Wi hou
loss o gene ali y, we o de indus ies such ha unions a e ac i e in all sec o s wi h z≤˜z. P o-
ided ha unions a e only ac i e in a subse o indus ies, i.e. ˜z < 1, in olun a y unemploymen
2.2. MPFS AND IMPERFECT LABOR MARKETS: THE CLOSED ECONOMY 11
does no ma e ialize in his se ing, as wo ke s who do no ind a job in unionized indus ies will
mo e o non-unionized indus ies, and he compe i i e wage will all un il all wo ke s can ind
employmen he e. Wi h espec o wage se ing in indus ies z∈[0,˜z], we conside sec o -le el
unions which unila e ally se wages ha a e binding o all wo ke s o he espec i e indus y,
while, a he same ime, lea ing he igh - o-manage employmen o i ms. Since all i ms o an
indus y pay iden ical wages hey a e symme ic, and hence we can combine (2.8) and (2.7) o
ob ain4
eδ(z)=a/w(z)−φ
1 + φδ(z)−φ,(2.9)
whe e φ≡ρ(n+ 1)/[2(1 −ρ)] is a measu e o p oduc ma ke compe i ion, which posi i ely
depends on he numbe o compe i o s, n, and nega i ely depends on he deg ee o p oduc
di e en ia ion, as cap u ed by he in e se o ρ. Eq. (2.9) es ablishes a nega i e ela ionship
be ween wage a e w(z) and i m scope δ(z). Fu he mo e, Eqs. (2.8) and (2.9) de e mine i m
scale X(z) as an implici unc ion o w(z), and i is shown in he Appendix ha dX(z)/dw(z)<
0, as a gued abo e.
The esponse o i m scale and scope o changes in he wage a e is aken in o accoun by
unions. As in o he models o union wage se ing, unions ace a ade-o be ween highe wages
and highe employmen when deciding upon hei wage claims. How unions e alua e his ade-
o depends on hei objec i e unc ion. We impose he common assump ion ha unions a e
u ili a ian and ha e an objec i e unc ion o he o m Ω(z) = [w(z)−wc]nl(z), whe e wcis he
economy-wide compe i i e wage. Subs i u ing l(z) = Rδ(z)
0eix(i, z)di,x(i, z) om (2.6′), and
eδ(z) om (2.9) in o union objec i e Ω, we ob ain5
Ω = n
4b(1 −ρ)(wu−wc)wua/wu−φ
1 + φδu−φ−12
.(2.10)
To ally di e en ia ing he la e wi h espec o wuand se ing he esul ing exp ession equal
o ze o gi es he i s -o de condi ion
dΩ
dwu=n
4b(1 −ρ)a/wu−φ
1 + φδu−φ−1(2wu−wc)a/wu−φ
1 + φδu−φ−1
−2 (wu−wc)eδu(1 + φδu−φ) + φ
1 + φδu= 0.
Rea anging e ms and accoun ing o (2.9) allows us o de i e he union wage claim as an
implici unc ion o he compe i i e wage wc:
wu=1
2wc+a
[1 + φδu][eδu−1] 1−wc
wu.(2.11)
Unions se wages wu> wcand hus end up wi h lowe scale and scope. Fu he mo e, ou model
ep oduces he common esul ha a highe compe i i e wage (and hus a highe al e na i e
income) p o ides a s imulus o he union wage, i.e. dwu/dwc>0.6
4We supp ess i m indices om now on o simpli y no a ion.
5Since sec o s only di e in hei labo ma ke ins i u ions, we in oduce supe sc ip s uand c o e e o
unionized and non-unionized indus ies, espec i ely, and supp ess sec o index z om now on.
6The p oo o his esul is de e ed o he Appendix.
18 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
ca ion. In a u he ex ension, we ha e accoun ed o i m-le el ins ead o sec o -le el unions.17
While in he bo de line case o pe ec p oduc di e en ia ion, his modi ica ion has no impac
on ou analysis, i ende s he o mal analysis much mo e complica ed i one accoun s o pa -
ial p oduc di e en ia ion. Howe e , i is s ill possible o cha ac e ize he au a ky as well as
he ade equilib ium, and esul s om nume ical simula ion exe cises indica e ha he main
insigh s om ou analysis on adjus men s in i m scale and scope a e obus o his modi ica ion.
A u he es ic i e assump ion o ou model is he exogenous and equal numbe o com-
pe i o s wi hin each indus y. This assump ion closes one impo an adjus men ma gin and
es ic s ou analysis o a sho - un pe spec i e. In he long un, i is plausible ha i m own-
e s de-in es hei capi al s ock and sea ch o he bes in es men oppo uni ies in he whole
economy. I he e a e no ex a cos s o mo ing capi al ac oss sec o s, i m owne s will adjus
hei in es men s a egy in he long un un il he e u n o hei in es men is he same in
all indus ies. In compa ison o ou sho - un model wi h an exogenous and equal numbe o
compe i o s in all indus ies, his induces a mo emen o p oduce s owa ds non-unionized in-
dus ies. Since non-unionized i ms a e la ge han unionized ones, his gi es a labo demand
s imulus, he eby aising he compe i i e as well as he union wage. Hence, compa ed o ou
sho - un model i m scale and scope sh ink in bo h unionized and non-unionized indus ies i
capi al is mobile ac oss indus ies (a leas as long as p oduc s a e su icien ly di e en ia ed).
Ano he ex ension o ou model which is wo hwhile o conside is one ha allows o analyzing
he consequences o ma ginal ade libe aliza ion. Since he in oduc ion o ade impedimen s
would signi ican ly complica e ou analysis, such a modi ica ion is beyond he scope o his
chap e . Howe e , we can ollow Eckel and Nea y (2010) and associa e ma ginal s eps o ade
libe aliza ion wi h an inc ease in he numbe o ading pa ne s. In he case o pe ec p oduc
di e en ia ion, opening up o ade wi h an addi ional (symme ic) pa ne coun y ein o ces
he espec i e e ec s iden i ied in he p e ious chap e . While his esul can be ex ended o
su icien ly high deg ees o (pa ial) p oduc di e en ia ion, de e mining he espec i e e ec s
o a bi a y le els o ρis no a i ial ask and, hence, we lea e a mo e de ailed discussion o
his issue open o u u e esea ch.
17De i a ion de ails a e de e ed o he Appendix.

2.5. APPENDIX 19
2.5 Appendix
The link be ween wages and i m scale and scope
Applying he implici unc ion heo em o (2.9) gi es
dδ(z)
dw(z)=−1
w(z)
eδ(z)1 + φδ(z)−φ+φ
eδ(z)(1 + φδ(z)) <0.(2.13)
Fu he mo e, subs i u ing (2.9) in o (2.8) and di e en ia ing he esul ing exp ession wi h e-
spec o w(z) gi es
dX(z)
dw(z)=−eδ(z)−1
2b(1 −ρ)[1 + φδ(z)] <0.(2.14)
This p o es he espec i e s a emen s in he main ex . QED.
The link be ween he compe i i e wage and he union wage
To show ha a highe compe i i e wage p o ides a s imulus o he union wage, i.e. dwu/dwc>
0, we can de ine he implici unc ion
Γ(wc, wu)≡wu−1
2wc−a
(1 + φδu)(eδu−1) 1−wc
wu= 0,(2.15)
acco ding o (2.11). Pa ially di e en ia ing Γ(·) wi h espec o wcand accoun ing o a/wu=
eδu(1 + φδu−φ) + φ, acco ding o (2.9), we ob ain
∂Γ(·)
∂wc=(eδu+ 1)(1 + φδu)−2φ(eδu−1)
2(1 + φδu)(eδu−1) ,(2.16)
which is posi i e.18 Pa ially di e en ia ing Γ(·) wi h espec o wugi es
∂Γ(·)
∂wu= 1 −wc
wu
a/wu
(1 + φδu)(eδu−1) +1−wc
wuaeδu(1 + φδu) + φeδu−1
(1 + φδu)2(eδu−1)2
dδu
dwu.(2.17)
Using (2.13) and subs i u ing a/wu=eδu(1 + φδu−φ) + φ, we can u he calcula e
∂Γ(·)
∂wu=−(α2β−1) −wc
wu(α2β−α),(2.18)
wi h
α≡eδu(1 + φδu)−φeδu−1
(eδu−1)(1 + φδu), β ≡eδu(1 + φδu) + φeδu−1
eδu(1 + φδu)>1.(2.19)
Hence, α > 1, which is equi alen o 1 −φ(eδu−δu−1) >0, is su icien o ∂Γ(·)/∂wu<0.
Using (2.9) oge he wi h (2.11), we can conclude ha 1 −φ(eδu−δu−1) >0 is equi alen o
ω > 1, so ha ∂Γ(·)/∂wu<0 and, by applying he implici unc ion heo em o (2.15), also
dwu/dwc>0 a e immedia e.
18I is immedia e ha he denomina o o his exp ession is posi i e, while he nume a o is s ic ly inc easing
in δuand equals 2 a δu= 0.
20 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
P oo o P oposi ion 1
Le us i s di e en ia e (z)≡w(z)[eδ(z)−1]2wi h espec o w(z). Accoun ing o (2.13), his
gi es19
d (z)
dw(z)=−eδ(z)−1
1 + φδ(z)h(eδ(z)+ 1)(1 + φδ(z)) −2φ(eδ(z)−1)i<0.(2.20)
This implies wu(eδu−1)2< wc(eδc−1)2, so ha he igh -hand side o (2.12) unambigu-
ously alls in ˜z, when holding wages cons an . Fu he mo e, combining d (z)/dw(z)<0 wi h
dwu/dwc>0, we can conclude ha he igh -hand side o (2.12) de e mines a nega i e ela ion-
ship be ween economy-wide labo demand and he compe i i e wage wc. Applying he implici
unc ion heo em o Eq. (2.12), we he e o e ge dwc/d˜z < 0, dwu/d˜z < 0, which, in iew o
dδ(z)/dw(z)<0 and dX(z)/dw(z)<0 (see Eqs. (2.13) and (2.14)), es ablishes a posi i e e-
la ionship be ween ˜zand he scale and scope o MPFs. Finally, subs i u ing x(i, z) om (2.6′)
in o l(z) = Rδ(z)
0eix(i, z)di, gi es l(z) = w(z)eδ(z)−12/[4b(1 −ρ)]. Using he la e oge he
wi h Eq. (2.8) X(z)/l(z) gi es labo p oduc i i y, ξ, as a unc ion o i m scope:
ξ(z) = 2eδ(z)(δ(z)−1) + 1
eδ(z)−12(2.21)
I is s aigh o wa d o show ha dξ(z)/dδ(z)<0, so ha dξ(z)/d˜z < 0 is immedia e. This
comple es he p oo o P oposi ion 1. QED.
Deunioniza ion and he numbe o p oduc a ie ies when ρ= 0
The o al numbe o p oduc a ie ies is gi en by N≡˜zNu+ (1 −˜z)Nc= ˜znδu+ (1 −˜z)nδc.
Di e en ia ing he la e wi h espec o ˜z, we ob ain
dN
d˜z=nln 1
ω−dwc
d˜z˜z1
wu
a+wu
4wu−wc+ (1 −˜z)1
wc,(2.22)
acco ding o (2.7).20 To ally di e en ia ing (2.12) and accoun ing o a/wu= 2ω−1, a/wc=
ω(2ω−1) om (2.11)21, we can calcula e
dwc
d˜z=wc4ω(ω−1)2−[ω(2ω−1) −1]2
8˜zω3(4ω−1)−1(ω−1) + (1 −˜z)[(ω(2ω−1))2−1].(2.23)
Subs i u ing he la e in o (2.22), we ge
dN
d˜z=n(ln 1
ω−4ω(ω−1)2−[ω(2ω−1) −1]22˜zω(4ω−1)−1+ (1 −˜z)
8˜zω3(4ω−1)−1(ω−1) + (1 −˜z)[(ω(2ω−1))2−1] ).(2.24)
E alua ing dN/d˜za ˜z= 0 gi es
dN
d˜z˜z=0
=nln 1
ω−4ω(ω−1)2−[ω(2ω−1) −1]2
[(ω(2ω−1))2−1] ,(2.25)
19Fo a nega i e sign o (2.20) he b acke e m on he igh -hand side o his equa ion mus be posi i e. To
show ha his is he case, we can di e en ia e he b acke e m and ob ain eδ(z)(1 + φδ(z)−φ)+φ=a/wu>0.
Fu he mo e, e alua ing he b acke e m a δ(z) = 0 gi es 2. Hence, we can sa ely conclude ha he b acke
e m is posi i e o any δ(z)>0.
20No e ha wi h ρ= 0 o al i m scope eads δ(z) = ln[a/w(z)].
21Wi h ρ= 0 we ha e wu= 1/2 [wc+a/ω].
2.5. APPENDIX 21
which is nega i e o any ω > 1. E alua ing dN/d˜za ˜z= 1 gi es
dN
d˜z˜z=1
=nln 1
ω−ω−1
ω+[ω(2ω−1) −1]2
4ω2(ω−1) ,(2.26)
which is posi i e o any ω > 1. This p o es he espec i e s a emen in he main ex . QED.
Wel a e e ec s o deunioniza ion when ρ= 0
Se ing ρ= 0 and accoun ing o λ= 1, we can ew i e (2.4) in he ollowing way: q(i, z) =
1
b[a−λp(i, z)]. Subs i u ing he la e in o (2.2), gi es u{z}= [n/(2b)] ha2δ(z)−Rδ(z)
0p(i, z)2i
and, accoun ing o p(i, z) = (1/2)[a+w(z)ei], we can calcula e
u{z}=n
16b6a2ln[ a
w(z)]−4a2+ 4aw(z)−a2+w(z)2.(2.27)
And adding o e all indus ies, we hus ge
U=n
16b˜zh6a2ln[ a
wu]−4a2+ 4awu−a2+ (wu)2i
+n
16b(1 −˜z)h6a2ln[ a
wc]−4a2+ 4awc−a2+ (wc)2i(2.28)
Di e en ia ing he la e wi h espec o ˜z
dU
d˜z=n
16b6(wc)2a
wc2ln 1
ω+ (wc)24a
wcω+ω2−4a
wc−1+
+dwc
d˜z˜zdwu
dwcwu4a
wu+ 2 −6a
wu2+ (1 −˜z)wc4a
wc+ 2 −6a
wc2 (2.29)
Using a/wu= 2ω−1 and a/wc=ω(2ω−1) and dwu/dwc= (a+wu)/4wu−wc) = 2ω2/(4ω−1),
u he implies
dU
d˜z=n
16b(wc)224ω4−24ω3+ 6ω2ln 1
ω+ (wc)28ω3−11ω2+ 4ω−1
+dwc
d˜zwc˜z2ω3
4ω−1−24ω2+ 32ω−8+ (1 −˜z)−24ω4+ 24ω3+ 2ω2−4ω+ 2
And subs i u ing
dwc
d˜z=wc4ω(ω−1)2−[ω(2ω−1) −1]2
8˜zω3(ω−1)(4ω−1)−1+ (1 −˜z)[(ω(2ω−1))2−1] (2.30)
we inally a i e a
dU
d˜z=n
16b(wc)2(24ω4−24ω3+ 6ω2ln 1
ω+ 8ω3−11ω2+ 4ω−1
+˜z2ω3
4ω−1−24ω2+ 32ω−8+ (1 −˜z)−24ω4+ 24ω3+ 2ω2−4ω+ 2ρ(ω)),(2.31)
22 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
wi h ρ(ω)≡dwc/d˜z×(wc)−1.
E alua ing he la e a ˜z= 0, gi es
dU
d˜z˜z=0
=n
16b(wc)2(24ω4−24ω3+ 6ω2ln 1
ω+ 8ω3−11ω2+ 4ω−1
+24ω4−24ω3−2ω2+ 4ω−2(4ω2+ 1)(ω−1)
4ω3+ω+ 1 ),(2.32)
which is nega i e o any ω > 1. Fu he mo e, e alua ing dU/d˜za ˜z= 1, gi es
dU
d˜z˜z=1
=n
16b(wc)2(24ω4−24ω3+ 6ω2ln 1
ω+ 8ω3−11ω2+ 4ω−1
+6ω2−8ω+ 2(4ω2+ 1)(ω−1)),(2.33)
which can shown o be posi i e o any ω > 1. This comple es he p oo . QED.
P oo o P oposi ion 2
Le us i s conside he benchma k case o ρ= 0, which implies φ= 0. Rea anging e ms in
(2.11) and accoun ing o φ= 0, we can calcula e wc= (a/ω) (2ω−1)−1, wi h ω=wu/wcand
dω/dwc<0. No ing dwc/d˜z < 0 om P oposi ion 1, his implies dω/d˜z > 0. Fu he mo e,
subs i u ing δ(z) om (2.9) in o ∆ = δc−δuand e alua ing he esul ing exp ession a ρ= 0,
gi es ∆ = ln(ω), wi h d∆/dω > 0 and, in iew o dω/d˜z > 0, also d∆/d˜z > 0. Finally,
subs i u ing (2.8) in o Ξ = Xc−Xuand e alua ing he esul ing exp ession a ρ= 0, we can
calcula e
Ξ = a
2bln(ω)−ω−1
ω(2ω−1)(2.34)
Di e en ia ing he la e wi h espec o ωand e alua ing he esul ing exp ession a ω > 1,
gi es dΞ/dω > 0.We can hus sa ely conclude ha dΞ/d˜z > 0.
Un o una ely, we a e no able o show ha he insigh s om he benchma k scena io wi h
pe ec p oduc di e en ia ion (ρ= 0) ex end o he mo e gene al case o pa ial p oduc
di e en ia ion, when allowing o a bi a y le els o ρ. Howe e , wi h all a iables o in e es
being con inuously di e en iable in ρ, we can a leas conclude ha he espec i e insigh s om
he benchma k scena io a e obus o small changes in ρ. This comple es he p oo o P oposi ion
2. QED.
P oo o P oposi ion 3
Le us i s conside he benchma k case o ρ= 0. Wi h i ms being a monopolis in all sub-
ma ke s o hei p oduc ion, opening up o ade lea es Eqs. (2.6′), (2.7) and (2.11) una ec ed.
Fu he mo e, wi h i ms se ing wo ins ead o jus a single ma ke o al i m ou pu is gi en
by X(z) = 2D(z) in he open economy, whe e D(z) equals local ou pu in (2.8), when se ing
ρ= 0. As a consequence, labo demand, as de e mined on he igh -hand side o (2.12), dou-
bles o any wage con igu a ion. This implies ha wcand wumus inc ease o es o e labo
ma ke clea ing (see he o mal discussion in he closed economy). Wi h wcand wuinc easing,
2.5. APPENDIX 23
i m scope and domes ic ou pu mus all, acco ding o (2.13) and (2.14). Fu he mo e, labo
p oduc i i y inc eases, acco ding o (2.21).
To de e mine he impac o ade on o al i m scale X(z), we can make use o he ollowing
ac : The impac o ade on X(z) is quali a i ely he same as he impac o ade on Y(z)≡
ˆnX(z), whe e ˆn=nunde au a ky and ˆn= 2nunde ee ade. Di e en ia ing Y(z) wi h
espec o ˆn, accoun ing o (2.8) and se ing ρ= 0, we can calcula e
dY (z)
dˆn=1
2baln a
w(z)−1+w(z)−w(z)a
w(z)−1ˆn
w(z)
dw(z)
dˆn.(2.35)
Dis inguishing be ween non-unionized and unionized indus ies, accoun ing o a/wc=ω(2ω−1)
and a/wu= 2ω−1, acco ding o (2.11), and using dwc/dˆn= (wc/ˆn)β(ω), wi h
β(ω)≡4˜zω(ω−1)2+ (1 −˜z) [ω(2ω−1) −1]2
8˜zω(ω−1)2ω2/[4ω2−5ω+ 1] + (1 −˜z) [ω(2ω−1) −1] [ω(2ω−1) + 1],(2.36)
acco ding o (2.12), he la e can be ew i en as
dY c
dˆn=wc
2bnω(2ω−1) hln ω(2ω−1)−1i+ 1 −hω(2ω−1) −1iβ(ω)o,(2.37)
dY u
dˆn=wc
2bω(2ω−1) hln 2ω−1−1i+ω−4(ω−1)ω2
4ω−1β(ω),(2.38)
espec i ely. I is edious bu s aigh o wa d o show ha he igh -hand sides o (2.37) and
(2.38) a e posi i e, implying ha dY c/dˆn > 0, dY u/dˆn > 0.
No ing om he analysis o he closed economy ha ∆ = ln(ω) i ρ= 0 and ecollec ing
om abo e ha ωsh inks i wcinc eases, i is immedia e ha he scope di e en ial declines in
esponse o a coun y’s mo emen o m au a ky o ee ade wi h a symme ic pa ne economy.
In a u he s ep, we now look a he impac o ade on i m size di e en ial Ξ. No ing ha ,
wi h a cons an numbe o compe i o s in ei he coun y, changes in Ξ a e quali a i ely he same
as changes in Ψ ≡Yc−Yu, we can conclude om Eqs. (2.37) and (2.38) ha dΞ/dˆn >, =, < 0 is
equi alen o [4ω−1] ω(2ω−1) ln(ω)−(ω−1)−(ω−1) 4ω2+ 2ω−1β(ω)>, =, < 0. Fu he -
mo e, aking in o accoun β(ω) is inc easing in ˜zand ha β(ω)|˜z=1 =4ω2−5ω+ 1/(2ω2),
we can u he conclude ha ζ(ω)≡2ω2ω(2ω−1) ln(ω)−(ω−1)−(ω−1)24ω2+ 2ω−1>0
is su icien o dΞ/dˆn > 0.22
No ing inally ha he a iables o in e es a e con inuously di e en iable in ρ, we can
conclude ha he insigh s om abo e a e obus o small changes in ρ. This comple es he
p oo o P oposi ion 3. QED.
Cha ac e iza ion o he open economy equilib ium: he case o ρ > 0
In he open economy, a i m’s domes ic ou pu , D(z), is gi en by Eq. (2.8). Due o symme y
o ading pa ne s, a simila exp ession is ob ained o he o eign economy: D∗(z), whe e he
as e isk is in oduced o indica e o eign a iables. To al sec o ou pu in he open economy is
22Di e en ia ing ζ(ω) h ee imes gi es ζ′′′(ω) = 96ωln(ω)−12 ln(ω) + 8ω+ 2 >0. Toge he wi h ζ′′(1) = 0,
his p o es ha he second de i a i e o ζ(·) is s ic ly posi i e o any ω > 1. No ing u he ha ζ′(1) = 0, we
can also conclude ha he i s de i a i e o ζ(·) is s ic ly posi i e o any ω > 1. No ing inally ha ζ(1) = 0,
he e o e p o es ha ζ(·) has a posi i e sign o any ω > 1.

24 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
hen gi en by Y(z) = nD(z) + nD∗(z). Subs i u ing he la e oge he wi h (2.8) – sepa a ely
o he home and he o eign coun y – in o (2.7) and no ing ha in he open economy D(z)
assumes he ole ha X(z) had in he closed economy, we can calcula e
eδ(z)=1
w(z)
a−w(z)φ−w∗(z)φ[n/(n+ 1)][eδ∗(z)(δ∗(z)−1) + 1]
1 + φδ(z)−φ,(2.39)
eδ∗(z)=1
w∗(z)
a−w∗(z)φ−w(z)φ[n/(n+ 1)][eδ(z)(δ(z)−1) + 1]
1 + φδ∗(z)−φ(2.40)
o domes ic and o eign i ms’ scope, espec i ely. The eby, φ=ρ(n+ 1)/[2(1 −ρ)] is he same
as in he closed economy. In he case o symme y, wi h δu=δu∗and wu=wu∗, Eq. (2.39)
can be simpli ied o
δ(z) = ln a/w(z)−φ(2n+ 1)/(n+ 1)
1 + φ(δ(z)−1)(2n+ 1)/(n+ 1).(2.41)
Equipped wi h hese insigh s we can now sol e he wage-se ing p oblem o labo unions.
Following he s eps om he analysis in he closed economy and using eδu om (2.39) ins ead
o (2.9), we can calcula e he i s -o de condi ion o he Ω-maximiza ion p oblem as ollows
dΩ
dwu=n(eδu−1
2b(1 −ρ)(2wu−wc)eδu−1+ 2wu(wu−wc)eδudδu
dwu= 0.(2.42)
Applying he implici unc ion heo em o sys em (2.39), (2.40) and e alua ing he esul ing
exp ession a δu=δu∗(symme y), we ge
dδu
dwu=−1
wueδu(1 + φδu−φ) + φ(1 + φδu)−φ2[n/(n+ 1)]2eδu(δu−1) + 1δu
eδuh(1 + φδu)2−(φδu)2[n/(n+ 1)]2i.(2.43)
Subs i u ing (2.43) in o (2.42), we ob ain a e edious bu s aigh o wa d calcula ions:
wu=wc1
2
(eδu−1)
1−eδu+H(δu)+ 1,(2.44)
whe e
H(δu)≡(1 + φδu)eδu(1 + φδu−φ) + φ−φ2δu[n/(n+ 1)]2eδu(δu−1) + 1
(1 + φδu)2−φδu[n/(n+ 1)]2.(2.45)
Finally, we can w i e he ull employmen condi ion as ollows
L=n
2b(1 −ρ)˜zwueδu−12+ (1 −˜z)wceδc−12.(2.46)
Pu ing all elemen s oge he , he open economy equilib ium is cha ac e ized by (2.8), (2.41) –
sepa a ely o uand c–, (2.44), and (2.46). This comple es he cha ac e iza ion o he open
economy.
2.5. APPENDIX 25
2.5.1 Ex ension – Linea cos unc ion
In he main ex , we ep esen adap a ion cos s by an exponen ial uni cos -densi y unc ion. In
his ex ension, we check he obus ness o ou esul s when changing ou assump ion, ega ding
he unc ional o m o adap a ion cos s. To be mo e speci ic, we conside he linea speci ica ion
γj(i) = 1 + i, and in es iga e whe he he main insigh s om ou analysis emain he same in
his modi ied amewo k. To keep he analysis ac able, we ocus on a benchma k scena io wi h
ρ= 0 h oughou he subsequen discussion.
Wi h a linea cos speci ica ion, p oduc -speci ic ou pu and he p oduc ange a e gi en by
xj(i, z) = a−(1 + i)w(z)
2bδj(i, z) = a
w(z)−1 (2.47)
ins ead o (2.6) and (2.7), while p oduc -speci ic ou pu ela i e o he ma ginal good is gi en
by
xj(i, z) = w(z)[δ(z)−i]
2b(2.48)
ins ead o (2.6′). In eg a ing xj(i, z) o e all a ie ies gi es, a e s aigh o wa d calcula ions,
o al i m ou pu Xj(z) = w(z)δ(z)2/(4b). To calcula e i m-le el labo demand lj(z) we use
(2.48) in lj(z) = Rδ(z)
0xj(i, z)γ(i)di and ob ain lj(z) = ah(a/w(z))2−3 + 2w(z)/ai/(12b).
Wi h hese insigh s a hand, we a e now well equipped o calcula e he union wage. Fo
his pu pose, we subs i u e lj(z) in o he union objec i e unc ion Ω = [w(z)−wc]nl(z) (and
supp ess i m indices in he in e es o be e eadabili y). Di e en ia ing Ω wi h espec o wu
and se ing he esul ing exp ession equal o ze o, we can calcula e23
wu= 2wc(δu)2+ 3δu+ 3
(δu)2+ 3δu+ 6.(2.49)
Fu he mo e, accoun ing o δu=a/wu−1, we can ew i e (2.49) as ollows
wu= 2wca2+awu+ (wu)2
a2+awu+ 4(wu)2.(2.50)
Applying he implici unc ion heo em, we can u he mo e calcula e
dwu
dwc= 2 a2+awu+ (wu)2
a2+ 2a(wu−wc) + 4wu(3wu−wc).(2.51)
Hence, (2.50) es ablishes a posi i e ela ionship be ween wcand wu.
Be o e u ning o he gene al equilib ium ou come, i is wo h inspec ing he i m scale and
scope di e en ial be ween non-unionized and unionized i ms. The scope di e en ial is gi en by
∆ = δc−δu=a/wc−a/wu, which, in iew o (2.47), can be ew i en as
∆ = [1 + δc]1−1
ω,(2.52)
which is unambiguously posi i e, as wu> wcand hus ω > 1. The scale di e en ial is gi en by
Ξ = Xc−Xu=wc(δc)2−wu(δu)2/(4b) and, accoun ing o (2.47), we can calcula e
Ξ = wc
4bha
wc(δc−δu) + 1 −ωi,(2.53)
23No ing ha [(δu)2+ 3δu+ 3]/[(δu)2+ 3δu+ 6] ≥1/2, we can easily con i m ha wu≥wc.
26 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
which is posi i e as a > wu> wc.24
The gene al equilib ium ou come is cha ac e ized by he labo ma ke clea ing condi ion
L=R1
0Rδ(z)
0nx(i, z)γ(i)didz =nR1
0l(z)dz. Rea anging e ms, we ge 25
L=an
12b˜za
wu2−3 + 2wu
a+ (1 −˜z)a
wc2−3 + 2wc
a (2.54)
We a e now p epa ed o s udy he implica ions o deunioniza ion in he closed economy.
In analogy o he model a ian in he main ex , a dec ease in ˜z aises economy-wide labo
demand and hence wcmus inc ease in o de o es o e a labo ma ke equilib ium. Fo mally,
his can be shown by applying he implici unc ion heo em o (2.54). Fu he mo e, a highe
compe i i e wage p o ides a s imulus o he union wage, acco ding o (2.51), so ha wualso
inc eases in esponse o a decline in ˜z. Due o hese wage e ec s, i is immedia e ha unionized
as well as non-unionized i ms lowe he scope in esponse o deunioniza ion, i.e. δcand δu
dec ease, acco ding o (2.47). Accoun ing o
X(z) = w(z)
4bδ(z)2=1
4ba2
w(z)−2a+w(z)(2.55)
i is s aigh o wa d o show ha bo h Xcand Xudecline in esponse o deunioniza ion, i.e.
all i ms, excep o he newly deunionized ones, sh ink i ˜z alls.
Aside om hese i m-le el e ec s, we can also analyze he di e en ial impac o deunioniza-
ion on unionized and non-unionized i ms. Fo his pu pose, we can i s analyze he impac o
a decline in ˜zon ω. F om (2.49)
ω= 2(δu)2+ 3δu+ 3
(δu)2+ 3δu+ 6.(2.56)
Since he igh -hand side o he la e inc eases in δu, i ollows om ou insigh s abo e ha a
decline in ˜zinduces a all in ω. Howe e , since wcinc eases while ω alls in esponse o deunion-
iza ion, i ollows om (2.52) ha he scope di e en ial be ween non-unionized and unionized
p oduce s sh inks i ˜zdeclines. Wi h i ms concen a ing mo e on hei co e compe ence p od-
uc s, labo p oduc i i y is s imula ed by deunioniza ion in ou model. Rega ding he impac o
deunioniza ion on he i m scale di e en ial, i is wo h no ing ha (2.55) implies
Ξ = 1
4ba2
wc1−1
ω+wc(1 −ω)(2.57)
Di e en ia ing Ξ wi h espec o ˜z, hen implies
dΞ
d˜z=1
4b−a
wc21−1
ω+ 1 −ωdwc
d˜z+wca
wu2−1dω
d˜z.(2.58)
24To see his, no e ha (1 + δc)(δc−δu) = (1 + δc)2(1 −1/ω), acco ding o (2.52). Hence, Ξ >0 is equi alen
o (1 + δc)2> ω and, in iew o (2.47), equi alen o (a/wc)2> wu/wc. This implies ha a > wu> wcis
su icien o Ξ >0.
25De ining (z)≡a3/w(z)2−3a+ 2w(z) and accoun ing o ∂ (z)/∂w(z) = 2[1 −(a/w(z))3]<0, i is easily
con i med ha he igh -hand side (RHS, in sho ) o (2.54) is s ic ly dec easing in wc. Fu he mo e, no ing
ha limwc→0RHS =∞, while limwc→aRHS = 0, we can sa ely conclude ha he e exis s a unique equilib ium
wi h ac o ma ke clea ing in ou model.
2.5. APPENDIX 27
And no ing dwc/d˜z < 0, dω/d˜z > 0 om abo e, we can conclude ha he i m size di e en ial
sh inks i ˜zdeclines. This comple es ou discussion upon i m-le el adjus men s in esponse o
deunioniza ion. And we can now u n o analyzing he open economy.26
Simila o he scena io wi h an exponen ial cos -dis ance unc ion, ade aises economy-wide
labo demand, so ha wcinc eases. This p o ides a s imulus o wu, while δuand δcsh ink.
As i ms p oduce less a ie ies hei p oduc i i y inc eases. Fu he mo e, simila o he model
a ian in he main ex , we ind ha any i m’s o al domes ic sales, D(z), sh ink, ha ω alls
and ha he scope di e en ial, ∆, dec eases. To analyze he impac on o al i m ou pu we
ollow he analysis in he main ex and no e ha he impac o ade on o al i m ou pu can
be in e ed om dY/dˆn, whe e
Y(z) = ˆnX(z) = ˆn
4bw(z)a
w(z)−12
(2.59)
is indus y-wide ou pu . S aigh o wa d calcula ions gi e
dY (z)
dˆn=1
4bw(z)a
w(z)−12
+ˆn
4b
dw(z)
dˆn"1−a
w(z)2#.(2.60)
And, ollowing he de i a ion in he main ex s ep by s ep, we a i e a
dY c
dˆn=1
4bwcha
wc−1i2+1
4b
g(wc)
g′(wc)a
wc2−1,(2.61)
whe e
g(wc)≡˜za a
wu2−3 + 2wu
a+ (1 −˜z)aa
wc2−3 + 2wc
a>0 (2.62)
and
g′(wc) = 2˜zdwu
dwc1−a
wu3+ 2(1 −˜z)1−a
wc3<0.(2.63)
We can hus conclude ha dY c/dˆn >, =, < 0 is equi alen o
0>, =, < wcha
wc−1i2g′(wc) + g(wc)a
wc2−1(2.64)
Accoun ing o g(wc) and g′(wc) om abo e and subs i u ing κ≡a/wu, we can u he no e
ha dY c/dˆn >, =, < 0 is equi alen o
0>, =, <˜zωκ3−3κ+ 2(κω + 1) −2κ3−1(κω −1) dwu
dwc
+ (1 −˜z)κ3ω3−3κω + 2(κω + 1) −2κ3ω3−1(κω −1) ,(2.65)
26We ha e also analyzed he impac o deunioniza ion on he o al numbe o a ailable p oduc a ie ies
N. While we do no p esen de ails o his analysis he e, i is wo h no ing ha simila o he main ex ,
deunioniza ion does no exe a mono onic impac on N. To be mo e speci ic, ou esul s indica e ha N
inc eases in esponse o deunioniza ion i ˜zhas been small ini ially, while he opposi e is ue i ˜zhas been la ge
p io o he deunioniza ion shock.
34 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
P in ["Scale unionized au a ky: ", Du=(wu1(Exp[δu1](δu1-1)+1))/(2b(1-ρ))];18
P in ["Scale non-unionized au a ky: ", Dc=(wc1(Exp[δc1](δc1-1)+1))/(2b(1-ρ))];19
In a nex s ep we use Equa ions (2.44), (2.41) and (2.46) om he open economy o de ine
Hδu =20
21
((φ+(1+φ*δu -φ)Exp[δu ])(1+φ*δu )-((ρ*n)ˆ2*δu (Exp[δu ](δu -1)+1))/(4(1-ρ)ˆ2))/22
((1+φδu )ˆ2-((ρ*n)ˆ2*δu ˆ2)/(4(1-ρ)ˆ2));23
g10=wc (1+(0.5(Exp[δu ]-1))/(1-Exp[δu ]+Hδu ));24
g20=Log[(a/wu -φ((2n+1)/(n+1)))/(1+((2n+1)/(n+1))(φ*δu -φ))];25
g30=Log[(a/wc -φ((2n+1)/(n+1)))/(1+((2n+1)/(n+1))(φ*δc -φ))];26
g40=(2*b(1-ρ)L/n-z*wu (Exp[δu ]-1)ˆ2)/((1-z)(Exp[δc ]-1)ˆ2);27
whe e he le e added o wu, wc, δu and δc e e s o ade. To sol e he open economy
si ua ion, we use he FindRoo command and p in he a iables o in e es :
B=FindRoo [{wu ==g10,δu ==g20,δc ==g30,wc ==g40},{wc , 75},{wu , 89},{δc ,28
0.15},{δu , 0.1}];29
P in ["Union wage ade: ", wu 1=g10/.B];30
P in ["Scope unionized ade: ", δu 1=g20/.B];31
P in ["Scope non-unionized ade: ", δc 1=g30/.B];32
P in ["Compe i i e wage a e ade: ", wc 1=g40/.B];33
P in ["Scale home unionized ade: ",34
Du =(wu 1(Exp[δu 1](δu 1-1)+1))/(2*b(1-ρ))];35
P in ["Scale home non-unionized ade: ",36
Dc =(wc 1(Exp[δc 1](δc 1-1)+1))/(2*b(1-ρ))];37
P in ["Scale unionized ade: ", Xu =(wu 1(Exp[δu 1](δu 1-1)+1))/(b(1-ρ))];38
P in ["Scale non-unionized ade: ",39
Xc =(wc 1(Exp[δc 1](δc 1-1)+1))/(b(1-ρ))];40
Finally, we compa e he ee ade wi h he closed economy a iables, o de i e he alues as
epo ed in Table 2.1.
P in ["Impac on union wage: ", Round[wu 1-wu1,0.01]];41
P in ["Impac on compe i i e wage: ", Round[wc 1-wc1,0.01]];42
P in ["Impac on scope unionized: ", Round[δu 1-δu1,0.01]];43
P in ["Impac on scope non-unionized: ", Round[δc 1-δc1,0.01]];44
P in ["Impac on scale home unionized: ", Round[Du -Du,0.01]];45
P in ["Impac on scale home non-unionized: ", Round[Dc -Dc1,0.01]];46
P in ["Impac on scale unionized: ", Round[Xu -Du,0.01]];47
P in ["Impac on scale non-unionized: ", Round[Xc -Dc,0.01]];48
P og am code o Table 2.2
In he ollowing we o e he sou ce code o de i e he epo ed alues om Table 2.2. A i s ,
we se he pa ame e alues: a= 100, b= 1, ρ= 0.8, n= 5, L= 20, which de e mines
φ=ρ(n+ 1)/[2(1 −ρ)] and se he sha e o unionized indus y equal o ˜z= 0.1, ˜z= 0.3 o
˜z= 0.5.
Clea ["Global‘*"];1

2.5. APPENDIX 35
a=100;2
b=1;3
ρ=0.8;4
n=5;5
L=20;6
φ=(ρ(n+1))/(2(1-ρ));7
z=0.1; (* z=0.3 ; z=0.5 *)8
In a nex s ep we use Equa ions (2.9), (2.85) and (2.12) o de ine
Gδu=9
(((ρ(n+1))(Exp[δu]δu+1)-(3*ρ*n-2*ρ*n)Exp[δu])(4(ρ-1)-ρ(n+1)δu)+10
4(1-ρ)ˆ2(n-1)Exp[δu])/ ((2*n(ρ-1)-ρ(n+1)δu)(4(ρ-1)-(ρ(n+1)δu))-4(1-ρ)ˆ2(n-1));11
g1=wc(1-0.5(Exp[δu]-1)/(Exp[δu]-1+Gδu));12
g2=Log[(a/wu-φ)/(1+φδu-φ)];13
g3=Log[(a/wc-φ)/(1+φδc-φ)];14
g4=(4*b(1-ρ)L/n-z*wu(Exp[δu]-1)ˆ2)/((1-z)(Exp[δc]-1)ˆ2);15
To sol e he au a ky si ua ion, we use he FindRoo command and p in he a iables o in e es ,
ha a e lis ed in Table 2.2:
B=FindRoo [{wu==g1,δu==g2,δc==g3,wc==g4},{wc, 40},{wu, 50},{δc, 0.15},{δu,16
0.1}];17
P in ["Compe i i e wage: ", wc1=g4/.B];18
P in ["Union wage: ", wu1=g1/.B];19
P in ["Scope non-unionized: ", δc1=g3/.B];20
P in ["Scope unionized: ", δu1=g2/.B];21
P in ["Scale non-unionized: ", Xc=(wc1(Exp[δc1](δc1-1)+1))/(2*b(1-ρ))];22
P in ["Scale unionized: ", Xu=(wu1(Exp[δu1](δu1-1)+1))/(2*b(1-ρ))];23
P in ["Union wage p emium: ", ω=wu1/wc1];24
P in ["Scope Di e en ial: ", Δ=δc1-δu1];25
P in ["Scale Di e en ial: ", Ξ=Xc-Xu];26
P in ["Numbe o a ie ies: ", N =z*n*δu1+(1-z)n*δc1];27
P og am code o Table 2.3
In he ollowing we o e he sou ce code o de i e he epo ed alues om Table 2.3. A i s ,
we se he pa ame e alues: a= 100, b= 1, ρ= 0.8, n= 5, L= 20, which de e mines
φ=ρ(n+ 1)/[2(1 −ρ)] and se he sha e o unionized indus y equal o ˜z= 0.1, ˜z= 0.3 o
˜z= 0.5.
Clea ["Global‘*"];1
a=100;2
b=1;3
ρ=0.8;4
n=5;5
L=20;6
φ=(ρ(n+1))/(2(1-ρ));7
z=0.1; (* z=0.3 ; z=0.5 *)8
In a nex s ep we use Equa ions (2.9), (2.85) and (2.12) o de ine
36 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
Gδu=9
(((ρ(n+1))(Exp[δu]δu+1)-(3*ρ*n-2*ρ*n)Exp[δu])(4(ρ-1)-ρ(n+1)δu)+10
4(1-ρ)ˆ2(n-1)Exp[δu])/ ((2*n(ρ-1)-ρ(n+1)δu)(4(ρ-1)-(ρ(n+1)δu))-4(1-ρ)ˆ2(n-1));11
g1=wc(1-0.5(Exp[δu]-1)/(Exp[δu]-1+Gδu));12
g2=Log[(a/wu-φ)/(1+φδu-φ)];13
g3=Log[(a/wc-φ)/(1+φδc-φ)];14
g4=(4*b(1-ρ)L/n-z*wu(Exp[δu]-1)ˆ2)/((1-z)(Exp[δc]-1)ˆ2);15
To sol e he au a ky si ua ion, we use he FindRoo command and p in he a iables o in e es :
B=FindRoo [{wu==g1,δu==g2,δc==g3,wc==g4},{wc, 40},{wu, 50},{δc, 0.15},{δu,16
0.1}];17
P in ["Union wage au a ky: ", wu1=g1/.B];18
P in ["Scope unionized: ", δu1=g2/.B];19
P in ["Scope non-unionized: ", δc1=g3/.B];20
P in ["Compe i i e wage au a ky: ", wc1=g4/.B];21
P in ["Scale unionized au a ky: ", Du=(wu1(Exp[δu1](δu1-1)+1))/(2*b(1-ρ))];22
P in ["Scale non-unionized au a ky: ",23
Dc=(wc1(Exp[δc1](δc1-1)+1))/(2*b(1-ρ))];24
In a nex s ep we use Equa ions (2.41), (2.46) and (2.85) o de ine
Gδu =25
(((ρ(2n+1))(Exp[δu ]δu +1)-(6*ρ*n-4*ρ*n)Exp[δu ])(4(ρ-1)-ρ(2*n+1)δu )26
+4(1-ρ)ˆ2(2*n-1)Exp[δu ])/27
((4*n(ρ-1)-ρ(2*n+1)δu )(4(ρ-1)-(ρ(2*n+1)δu ))-4(1-ρ)ˆ2(2*n-1));28
g10=wc (1-0.5(Exp[δu ]-1))/(Exp[δu ]-1+Gδu );29
g20=Log[(a/wu -φ((2*n+1)/(n+1)))/(1+((2n+1)/(n+1))φδu -φ)];30
g30=Log[(a/wc -φ((2*n+1)/(n+1)))/(1+((2n+1)/(n+1))φδc -φ)];31
g40=(2*b(1-ρ)L/n-z*wu (Exp[δu ]-1)ˆ2)/((1-z)(Exp[δc ]-1)ˆ2);32
To sol e he open economy si ua ion, we use he FindRoo command and p in he a iables o
in e es :
B=FindRoo [{wu ==g10,δu ==g20,δc ==g30,wc ==g40},{wc , 40},{wu , 50},{δc ,33
0.15},{δu , 0.1}];34
P in ["Union wage ade: ", wu 1=g10/.B];35
P in ["Scope unionized ade: ", δu 1=g20/.B];36
P in ["Scope non-unionized ade: ", δc 1=g30/.B];37
P in ["Compe i i e wage a e ade: ", wc 1=g40/.B];38
P in ["Scale home unionized ade: ",39
Du =(wu 1(Exp[δu 1](δu 1-1)+1))/(2*b(1-ρ))];40
P in ["Scale home non-unionized ade: ",41
Dc =(wc 1(Exp[δc 1](δc 1-1)+1))/(2*b(1-ρ))];42
P in ["Scale unionized ade: ", Xu =(wu 1(Exp[δu 1](δu 1-1)+1))/(b(1-ρ))];43
P in ["Scale non-unionized ade: ",44
Xc =(wc 1(Exp[δc 1](δc 1-1)+1))/(b(1-ρ))];45
Finally, we compa e he ee ade wi h he closed economy a iables, o de i e he alues as
epo ed in Table 2.1.
2.5. APPENDIX 37
P in ["Impac on union wage: ", Round[wu 1-wu1,0.01]];46
P in ["Impac on compe i i e wage: ", Round[wc 1-wc1,0.01]];47
P in ["Impac on scope unionized: ", Round[δu 1-δu1,0.01]];48
P in ["Impac on scope non-unionized: ", Round[δc 1-δc1,0.01]];49
P in ["Impac on scale home unionized: ", Round[Du -Du,0.01]];50
P in ["Impac on scale home non-unionized: ", Round[Dc -Dc1,0.01]];51
P in ["Impac on scale unionized: ", Round[Xu -Du,0.01]];52
P in ["Impac on scale non-unionized: ", Round[Xc -Dc,0.01]];53
38 CHAPTER 2. LABOR UNIONS AND MULTI-PRODUCT FIRMS
Chap e 3
T ade and he Fi m-In e nal
Alloca ion o Wo ke s o Tasks
3.1 In oduc ion
In any indus ialized economy, labo ma ke s ha e o sol e he complex p oblem o ma ching
ask-speci ic skill equi emen s and wo ke -speci ic abili ies. The ou come o his ma ching
p ocess is ypically no e icien . This is no only because some wo ke s do no ind a job a
all. Ra he , a signi ican sha e o wo ke s canno exploi ull p oduc i i y because hey a e no
ma ched wi h he bes occupa ion (see Leg os and Newman, 2002; Eeckhou and Ki che , 2011).
In ecen yea s, his sou ce o ine iciency has also spa ked conside able a en ion in he ade
li e a u e. Wi h an inc easing gene al in e es in he consequences o ade o unde employmen ,
se e al au ho s ha e highligh ed imp o emen s in ma ching quali y as a key aspec o gains
om ade in e ms o bo h wel a e and employmen (Ami i and Pissa ides, 2005; Da idson,
Ma usz, and She chenko, 2008; La ch and Lech hale , 2011). The eby, he ypical app oach is
o associa e he quali y o he ma ching p ocess wi h i s abili y o ma ch he e ogeneous wo ke s
wi h he e ogeneous i ms in an e icien way, assuming implici ly ha he p oduc ion p ocess
co e s jus a single ask wi h a ce ain skill equi emen . Howe e , his igno es he sophis ica ed
s uc u e o mode n p oduc ion p ocesses and hus misses an impo an ole o i ms in educing
he equi emen -abili y misma ch by imp o ing he assignmen o wo ke s o speci ic asks wi hin
he bounda ies o a single p oduc ion en i y.1
S udying he ole o i ms o ma ching wo ke s wi h asks and discussing how access o
ade a ec s he ma ching ou come is he main pu pose o his chap e . S a ing poin o ou
analysis is a Meli z (2003) model, in which i ms a e he e ogeneous due o di e ences in hei
p oduc i i y le els. As in Acemoglu and Au o (2011), we assume ha p oduc ion consis s
o a con inuum o asks ha di e in hei skill equi emen s. Fo pe o ming hese asks,
i ms hi e he e ogeneous wo ke s. He e ogenei y is ho izon al in he sense ha wo ke s di e
in hei abili y o pe o m speci ic asks because hei human capi al is occupa ion-speci ic (see
1The idea ha he quali y o wo ke - ask ma ches a e impo an o i m pe o mance a leas da es back o
wo k by Ba on and Loewens ein (1985) and Ba on, Black, and Loewens ein (1989). Meye (1994) poin s o
he ele ance o op imal ask assignmen in he con ex o eam p oduc ion. Bu gess, P oppe , Ra o, on Hinke
Kessle Scholde , and Tominey (2010) show ha p oduc i i y losses om a misma ch o wo ke s and asks in
eams can indeed be signi ican and ha one impo an channel h ough which incen i e paymen s o manage s
can imp o e he ou come o p oduc ion uni s is he be e assignmen o wo ke s o asks.
39

40 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
Kambou o and Mano skii, 2009; Sulli an, 2010, o empi ical e idence), while hey a e equally
p oduc i e o e he whole ange o ac i i ies. This implies ha all wo ke s ha e he same alue
o i ms and, lacking in o ma ion abou abili ies o indi idual wo ke s, i ms andomly d aw hei
employees om he labo supply pool. This lack o in o ma ion gene a es a sou ce o misma ch
be ween ask-speci ic skill equi emen s and wo ke -speci ic abili ies wi hin he bounda ies o
a p oduc ion uni . To educe his misma ch, i ms can in es in o a sc eening echnology o
ga he ing some (impe ec ) in o ma ion abou he abili ies o hei wo k o ce. We model he
sc eening in es men in a udimen a y way, allowing o wo possible in e p e a ions ha a e
common in he li e a u e. On he one hand, sc eening may be pa o he ec ui men p ocess as
in Helpman, I skhoki, and Redding (2010) and can help na owing he pool o sui able applican s.
On he o he hand, sc eening may ake place a e he ec ui men o wo ke s, o ins ance, in
he o m o job o a ion (see Li and Tian, 2013).2In bo h in e p e a ions, a highe in es men
p o ides be e knowledge abou he abili ies o wo ke s and he e o e leads o a be e ma ch
o hese wo ke s wi h he di e en asks in he p oduc ion p ocess (c . Pellizza i, 2011). The
incen i es o sc een a e mo e p onounced in la ge i ms, and hence he e is an addi ional sou ce
o he e ogenei y in ou model, which is endogenous and ein o ces he e ogenei y o i ms due o
exogenous di e ences in i m p oduc i i y.
We use his model o shed new ligh on he consequences o ade o labo ma ke ou come,
he eby ocussing on adjus men s in he i m-in e nal labo ma ke .3To be mo e speci ic, we
a e in e es ed in how ade a ec s unde employmen a ising om a misma ch be ween wo ke -
speci ic abili ies and ask-speci ic skill equi emen s. To keep he analysis simple, we ocus on
ade be ween symme ic coun ies and conside he empi ically ele an case, in which only he
mos p oduc i e i ms expo in he open economy (see, o ins ance, Be na d and Jensen, 1995,
1999). Ha ing access o he expo ma ke , high-p oduc i i y i ms can expand hei ma ke
sha e in he open economy, which p o ides an incen i e o hese i ms o sc een hei wo k o ce
mo e in ensi ely, as his u he imp o es he ma ching quali y and hus lowe s p oduc ion
cos s. Low-p oduc i i y non-expo e s, on he o he hand, lose ma ke sha e and hus lowe
hei in es men in o he sc eening echnology, which aises hei p oduc ion cos s. By changing
he cos s uc u e, his asymme ic esponse o ade libe aliza ion exe s a eedback e ec
on he en y/exi decision o i ms in bo h he domes ic and he expo ma ke , which is no
p esen in o he ade models wi h he e ogeneous i ms. Fu he mo e, i al e s he p oduc i i y
dis ibu ion o ac i e i ms by d i ing a wedge be ween ma ching e iciency o expo e s and non-
expo e s. This p o ides an al e na i e o he ‘lea ning-by-expo ing’ hypo hesis o explaining
he empi ical inding ha i ms become mo e p oduc i e when en e ing he expo ma ke
(see F yges and Wagne , 2008).4Finally, adjus men s in he i m-in e nal labo alloca ion
p ocess lowe he agg ega e misma ch be ween wo ke -speci ic abili ies and ask-speci ic skill
equi emen s, he eby gene a ing a p oduc i i y s imulus ha ein o ces he gains om ade in
an o he wise iden ical Meli z (2003) model. The i m-le el adjus men s o ade libe aliza ion
2The li e a u e dis inguishes h ee mo i es o job o a ion: employee lea ning (job o a ion as a aining
de ice); employee mo i a ion (job o a ion makes wo k mo e in e es ing) and employe lea ning (job o a ion as
a way o disco e in which jobs di e en employees a e bes a ). Ou model is in line wi h he ‘employe lea ning’
iew, which was i s discussed by O ega (2001). Empi ical suppo o his mo i e is p o ided by E iksson and
O ega (2006).
3Acco ding o Doe inge and Pio e (1971) an in e nal labo ma ke is “an adminis a i e uni , such as a
manu ac u ing plan , wi hin which he p icing and alloca ion o labo is go e ned by a se o adminis a i e ules
and p ocedu es. [... This ma ke ] is o be dis inguished om he ex e nal labo ma ke o con en ional economic
heo y whe e p icing, alloca ing and aining decisions a e con olled di ec ly by economic a iables” (pp. 1 ).
4G eenaway and Knelle (2007) and Wagne (2007) summa ize exis ing empi ical e idence ega ding he
eedback e ec s o expo ing on i m p oduc i i y. Ou eading o he li e a u e is ha he e is some suppo o
such a posi i e eedback e ec , bu no all exis ing s udies can iden i y a signi ican impac .
3.1. INTRODUCTION 41
a e no so di e en , in p inciple, om he adjus men s in Helpman, I skhoki, and Redding
(2010). In hei model, i ms can in es in o a sc eening echnology in o de o ecei e a mo e
p ecise signal abou he quali y o applican s. Mo e speci ically, sc eening allows he i m o
de ec (and ejec ) applican s below a ce ain abili y h eshold. The highe he in es men , he
mo e e ec i e is sc eening and he highe is he a e age abili y o wo ke s employed by he i m.
The sc eening in es men is endogenous and esponds o ade in a simila way as he sc eening
in es men does in ou model. I inc eases in expo ing i ms and sh inks in non-expo ing ones.
Aside om hese simila i ies, he e is a c ucial di e ence be ween he ocus o Helpman, I skhoki,
and Redding (2010) and he ocus o his chap e . Whe eas Helpman, I skhoki, and Redding
(2010) s udy impe ec ions in he ex e nal labo ma ke , we a e in e es ed in he i m-in e nal
alloca ion o wo ke s. To be mo e explici , in ou se ing all wo ke s a e equally aluable o
i ms and only di e in hei abili y o pe o m speci ic asks, whe eas wo ke s in Helpman,
I skhoki, and Redding (2010) di e in he p oduc i i y hey can elici in a i m o a speci ic
ype. Hence, he e is an e iciency loss in he Helpman, I skhoki, and Redding (2010) model,
because i ms a e no ma ched wi h he ideal wo ke , while he e is an e iciency loss in ou
se ing, because wo ke s do no pe ec ly i he skill equi emen s o asks hey a e pe o ming
wi hin he bounda ies o a i m.
By opening up he black box o p oduc ion and modeling explici ly he i m-in e nal labo
alloca ion p ocess, ou model no only iden i ies a new channel h ough which posi i e ade
e ec s can ma e ialize, bu also con ibu es o a g owing li e a u e on he ole o globaliza ion o
i m o ganiza ion. A i s line o esea ch in his li e a u e has poin ed o he ole o openness o
he bounda ies o i ms (see G ossman and Helpman, 2002; An ´as, 2003; An ´as and Helpman,
2004; Conconi, Leg os, and Newman, 2012). In con as o hese s udies, we ocus on he
ques ion how ade changes he o ganiza ion o labo wi hin hese bounda ies. This ende s
ou analysis akin o Ma in and Ve die (2008a, 2012) who in es iga e he impac o ade on
he hie a chy s uc u e in i ms and he incen i es o empowe human capi al. The hie a chy
s uc u e o i ms is also add essed by Caliendo and Rossi-Hansbe g (2012) who analyze how
access o expo ing changes he numbe o laye s o managemen .5In con as o all o hese
s udies, we do no look on changes in he hie a chy s uc u e bu on ma ching quali y, so ha
ou indings a e complemen a y o he esul s in his li e a u e. Finally, he key mechanism
discussed in his chap e di e s om a pu e di ision o labo e ec , which a ises i he e is a
change in he numbe o asks pe o med by a single wo ke (Becke and Mu phy, 1992) o a
eam o wo ke s (Chaney and Ossa, 2013). In ou se ing, i is no he numbe o asks pe o med
by a single wo ke bu a he he ma ching o wo ke s wi h hese asks ha ma e s.
The emainde o he chap e is o ganized as ollows. In Chap e 3.2, we se up a baseline
model wi h a pe ec labo ma ke and cha ac e ize he equilib ium in he closed economy. In
Chap e 3.3, we conside ade be ween wo symme ic coun ies, cha ac e ize he open economy
equilib ium, and in es iga e how a mo emen om au a ky o ade a ec s he alloca ion o
labo ‘inside’ he i m as well as pe capi a income. We also shed ligh on he consequences o
ma ginal ade libe aliza ion. In Chap e 3.4, we ex end he baseline model o one wi h sea ch
ic ions in he hi ing p ocess and analyze how impe ec ions in he ou side labo ma ke al e
ou insigh s ega ding he impac o ade on he i m-in e nal o ganiza ion o wo ke s. Chap e
3.5 p o ides a calib a ion exe cise ha allows us o quan i y he impac o ade on wel a e and
unde employmen . Chap e 3.6 concludes wi h a b ie summa y o he mos impo an esul s.
5In a ecen s udy, Sly (2012) in es iga es he composi ion o managemen eams and shows ha ade can
al e his composi ion signi ican ly.
42 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
3.2 The closed economy
3.2.1 Model s uc u e
We conside an economy ha is popula ed by an exogenous mass o wo ke s L, who supply
one uni o labo in a pe ec ly compe i i e labo ma ke . The e a e wo sec o s o p oduc-
ion: a pe ec ly compe i i e inal goods indus y ha p oduces a homogeneous ou pu good by
assembling di e en ia ed in e media e goods; and a monopolis ically compe i i e in e media e
goods indus y ha hi es labo o i s p oduc ion o di e en ia ed goods. Simila o Egge and
K eickemeie (2009, 2012), we ep esen he inal goods echnology by a cons an -elas ici y-o -
subs i u ion (CES) p oduc ion unc ion wi hou ex e nal scale economies. To be mo e speci ic,
we assume ha he echnology o p oducing inal ou pu Yis gi en by
Y=M−1
σZω∈Ω
x(ω)σ−1
σdωσ
σ−1
,(3.1)
whe e x(ω) deno es he quan i y o in e media e good ωused in he inal goods p oduc ion, Mis
he Lebesgue measu e o se Ω and ep esen s he mass o a ailable in e media e goods, and σ > 1
deno es he (cons an ) elas ici y o subs i u ion be ween di e en p oduc a ie ies. Yse es as
num´e ai e in ou analysis, implying ha he p ice index co esponding o he p oduc ion unc ion
in Eq. (3.1) is equal o one, by assump ion. Deno ing by p(ω) he p ice o in e media e good ω,
we can w i e o al cos s o p oducing ou pu Yas ollows: Rω∈Ωp(ω)x(ω)dω. Maximizing inal
goods p o i s wi h espec o x(ω), hen gi es in e media e goods demand
x(ω) = Y
Mp(ω)−σ.(3.2)
A he in e media e goods le el, he e is a con inuum o i ms, each o hem supplying
a unique a ie y unde monopolis ic compe i ion. Following Acemoglu and Au o (2011), we
assume ha in e media e goods p oduc ion is a composi e o di e en asks. To be mo e speci ic,
he e is a con inuum o asks ha is ep esen ed by he uni in e al. The p oduc ion echnology
is o he Cobb-Douglas ype and gi en by
x(ω) = φ(ω) exp Z1
0
ln x(ω, i)di,(3.3)
whe e x(ω, i) is he p oduc ion le el o ask iin i m ωand φ(ω) is his i m’s baseline p oduc i -
i y. Task x(ω, i) is pe o med (p oduced) by wo ke s who a e employed in a linea -homogenous
p oduc ion echnology, which is he same o all asks. To keep hings simple, we assume ha
ask-le el ou pu is equal o he e ec i e labo inpu : he mass o wo ke s pe o ming he ask
mul iplied by hese wo ke s’ a e age p oduc i i y. The p oduc i i y o wo ke s in pe o ming
a speci ic ask di e s, because wo ke s di e in hei abili ies, whe eas asks di e in hei skill
equi emen s. To cap u e his in a ac able way, we assume ha bo h wo ke s and asks a e
uni o mly dis ibu ed along he uni in e al, and he gap be ween abili y and skill equi emen
is measu ed by he dis ance o a wo ke o he ask in he uni in e al.
In he hi ing p ocess i ms ha e o sol e he p oblem o ma ching speci ic wo ke s wi h
speci ic asks, and his is essen ial because i ms ace an e iciency loss om misma ch i wo ke s
do no end up in hose occupa ions, in which hey ha e he highes compe ence. The deg ee
o misma ch depends on he a e age dis ance be ween wo ke s and asks in a i m’s p oduc ion
p ocess. To de e mine his a e age dis ance, we can i s no e ha he expec ed dis ance when
3.2. THE CLOSED ECONOMY 43
andomly assigning wo ke s om in e al [0, b] o a ask loca ed a ∈[0, b] is gi en by
dis ( ) = 1
b"Z
0
( −j)dj +Zb
(j− )dj#=1
b 2− b +b2
2,(3.4)
whe e jgi es he loca ion o wo ke s in he conside ed in e al. Acco dingly, he expec ed
dis ance when d awing andomly om in e al [0, b] amoun s o
d
dis =1
b2Zb
0 2− b +b2
2d =b
3.(3.5)
F om (3.5) i ollows ha he ex en o misma ch c ucially depends on he leng h o he in e al,
b. We in e p e bas he amoun o in o ma ion i ms ha e abou he loca ion o wo ke s in
he uni in e al. Wi hou sc eening, i ms a e unin o med abou he speci ic abili ies o hei
applican s. Hence, hey hi e wo ke s by andomly selec ing hem om he labo supply pool a
he common ma ke -clea ing wage a e w.6This gi es b= 1 and d
dis = 1/3.
Howe e , i ms do no ha e o accep his ou come. They can educe he e iciency loss om
misma ch by sc eening hei applican s. Simila o Helpman, I skhoki, and Redding (2010),
we associa e he implemen a ion o a sc eening echnology wi h a ixed cos expendi u e µ=
[1+µ(ω)]γand assume ha sc eening p o ides an imp ecise signal abou wo ke abili y, wi h he
quali y o he signal inc easing in sc eening e o µ(ω). To be mo e speci ic, by sc eening wi h
e o µ(ω), a i m can di ide he abili y in e al in o 1+µ(ω) segmen s o equal leng h. Fi ms can
hen hi e wo ke s a he ma ke -clea ing wage a e, w, o a speci ic ask by andomly selec ing
hem om he espec i e abili y segmen , so ha he a e age dis ance be ween wo ke -speci ic
abili ies and ask-speci ic skill equi emen s educes o d
dis (ω) = (1/3) [1 + µ(ω)]−1.7
A he i m le el, e iciency o wo ke s in he pe o mance o asks is in e sely ela ed o
d
dis (ω) and deno ed by κ(ω). In he in e es o analy ical ac abili y, we choose a speci ic unc-
ional o m and cap u e he ela ionship be ween κ(ω) and d
dis (ω) by κ(ω)≡(1/3)d
dis (ω)−1.
This gi es κ(ω) = 1 + µ(ω). E ec i e labo inpu a he ask le el is he e o e gi en by
[1 + µ(ω)]l(ω) and, since asks en e p oduc ion unc ion (3.3) symme ically, o al ou pu o
i m ωcan be w i en in he ollowing way:
x(ω) = φ(ω) [1 + µ(ω)] l(ω).(3.6)
Acco ding o (3.6), i m p oduc i i y consis s o wo pa s: an exogenous baseline p oduc i i y
φ(ω), which cap u es he e iciency o coo dina ing he bundle o di e en asks wi hin he
bounda ies o he i m, and an endogenous p oduc i i y e m κ(ω) = 1 + µ(ω), which cap u es
how e ec i ely he he e ogeneous abili ies o wo ke s a e used o pe o ming he di e en asks
in he p oduc ion p ocess. C ucially, i ms can inc ease hei p oduc i i y by in es ing in o a
sc eening echnology which imp o es he ma ching quali y in he i m-in e nal labo alloca ion
p ocess and hus aises κ(ω).8
The baseline p oduc i i y is d awn by i ms in a lo e y om he common Pa e o dis ibu ion,
G(φ) = 1−φ−ν. To pa icipa e in his lo e y, i ms ha e o pay a ee ein uni s o inal ou pu
Y. This in es men allows jus a single d aw and is immedia ely sunk. A e p oduc i i y le els
6Due o symme y, all wo ke s ecei e he same wage in equilib ium, i espec i e o hei loca ion in he abili y
in e al.
7We igno e in ege p oblems and, due o symme y, supp ess ask indices.
8This mechanism is no oo di e en , in p inciple, om an R&Din es men ha lowe s a iable p oduc ion
cos s (see, o ins ance, Eckel, 2009).
50 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
P oo . Analysis in he ex .
Due o asymme ic i m-le el consequences, i is clea ha access o ade exe s coun e ac ing
e ec s on he gene al equilib ium a iables o in e es : wage a e (wel a e) wand unde employ-
men u. Simila o he au a ky scena io, he wage a e in he open economy, can be de i ed by
combining (φ∗) = p(φ∗)x(φ∗) wi h he adding up condi ion Y=M(1 + χ x/ ) (φ∗)ν/(ν−ξ).
Subs i u ing (3.2) and (3.10) – wi h M(1 + χ) p esuming he ole o Min he open economy –
and accoun ing o (3.14), (3.16), and (3.24), we can calcula e
w=1 + χ x/
1 + χ1
σ−11 + χ x
1
ν
wa.(3.27)
Hence, gains om ade a e gua an eed i x/ ≥1, while losses om ade canno be uled
ou i x/ < 1.13 T ade can be wel a e-de e io a ing in ou se ing, because unde p oduc ion
echnology (3.1) he ou come o decen alized i m en y is no socially op imal. To he ex en
ha ade agg a a es he dis o ion o i m en y, he esul ing wel a e loss may ou weigh he
wel a e s imulus om ma ke in eg a ion (c . Shy, 1988). In ou se ing, he exis ence o ne
gains om ade depends on he ela i e s eng h o wo selec ion e ec s. On he one hand, he e
is selec ion o he bes p oduce s in o expo ing, which aises labo demand ce e is pa ibus. On
he o he hand, he e is selec ion o he leas p oduc i e i ms ou o he ma ke , which lowe s
labo demand. The wo selec ion e ec s a e in e dependen and hei ela i e s eng h depends
on ixed cos a io x/ . I his ixed cos s a io is su icien ly high, i is he selec ion in o
expo ing ha domina es ende ing he o e all e ec o ade on labo demand and hus wel a e
posi i e.
As ou lined in P oposi ion 4, he e a e asymme ic i m-le el e ec s o ade on he misma ch
be ween abili ies and skill equi emen s. Expo ing i ms inc ease hei sc eening expendi u es,
and hence hei ma ching ou come is imp o ed. The opposi e is ue o non-expo ing i ms.
Howe e , he e is an addi ional posi i e e ec on economy-wide unde employmen because labo
is eloca ed owa ds expo ing i ms in he open economy and, due o his change in labo
composi ion, he o e all impac o ade on he a e age quali y o wo ke - ask ma ches is posi i e.
To see his, we can explici ly sol e o ou measu e o unde employmen in he open economy.
As o mally shown in he appendix, we ge :
u=1 + a(τ)χ1+ξ/(νγ) x/
1 + χ x/ ua,wi h a(τ)≡1 + τ1−σ(γ−1)ξ
γ(σ−1) −1
(1 + τ1−σ)ξ
σ−1−1
.(3.28)
No ing ha a(τ)<1, i is immedia e ha u < ua, which p o es ha ade educes he a e age
misma ch be ween ask-speci ic skill equi emen s and wo ke -speci ic abili ies, he eby lowe ing
unde employmen .
We can summa ize he main insigh s om ou analysis as ollows.
P oposi ion 5 Opening up o ade imp o es he a e age quali y o wo ke - ask ma ches, he eby
educing economy-wide unde employmen due o a misalloca ion o wo ke s o asks. The im-
pac o ade on wel a e is no clea -cu in gene al. Only i ixed cos s o expo ing ela i e o
p oduc ion ixed cos s, x/ , a e su icien ly high, he e a e gains om ade in ou se ing.
13Fo ins ance, wi h a pa ame iza ion o ν= 8, σ= 3, τ= 1.5, and γ= 10, he e a e losses om ade i
x/ ≤0.77 – wi h x/ ≥0.58 es ablishing selec ion o only he mos p oduc i e i ms in o expo s a us, i.e.
χ∈(0,1).

3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 51
P oo . Analysis in he ex .
We comple e he analysis in his chap e by shedding ligh on he consequences o a ma ginal
educ ion in anspo cos pa ame e τ. Such a decline inc eases expec ed income om ex-
po ing, and hus aises χ, acco ding o (3.23), as well as a e age p o i income ¯π, acco ding
o (3.24). On he o he hand, he e is a s imulus on labo demand, which en o ces addi ional
ma ke exi a he lowe bound o he p oduc i i y dis ibu ion and he e o e leads o an upwa d
shi in cu o p oduc i i y φ∗. Fu he mo e, a ma ginal decline in he icebe g anspo cos
pa ame e augmen s he he e ogenei y in sc eening e o be ween non-expo ing and expo ing
p oduce s, acco ding o (3.20). Wi h espec o adjus men s in he wage a e, we can in e om
(3.27) ha dw/dτ < 0 i x/ > 1. In his case, a g adual educ ion in he icebe g anspo
cos pa ame e exe s a posi i e mono onic impac on wel a e. In con as , i x/ < 1, changes
in τneed no exe a mono onic impac on w. Finally, om he analysis abo e we know ha a
coun y’s mo emen om au a ky o ade wi h an a bi a y anspo cos le el unambiguously
imp o es he a e age quali y o wo ke - ask ma ches. We can he e o e sa ely conclude ha a
ma ginal decline in τmus lowe ui anspo cos s ha e been la ge ini ially. In he appendix
we show ha his e ec ex ends o he case whe e τhas al eady been low p io o he all in
he icebe g anspo cos pa ame e , so ha a g adual decline in τ educes unde employmen
umono onically.
3.4 A model a ian wi h in olun a y unemploymen
In his chap e , we in oduce sea ch ic ions as an addi ional sou ce o ine iciency in he alloca-
ion o labo o show how misma ch be ween he abili ies o wo ke s and he skill equi emen s
o asks in e ac wi h adi ional o ms o unde employmen . Fo his pu pose, we conside a
compe i i e sea ch model along he lines o Roge son, Shime , and W igh (2005), in which i ms
pos wages and wo ke s di ec hei sea ch o he mos a ac i e employe o queue o a job,
he e.14 The mass o ma ches be ween wo ke s and jobs, m, depends posi i ely on he numbe
o applican s, s, and he numbe o open acancies, . In he in e es o analy ical ac abili y,
we choose a Cobb-Douglas speci ica ion and w i e m(s, ) = As1−ζ ζ, whe e ζ, A ∈(0,1) a e
he same o all p oduce s.15 Measu ing by q≡s/ he queue leng h o wo ke s applying o
jobs, he p obabili y o he i m o ill a speci ic acancy is gi en by αe(q)≡m(s, )/ =Aq1−ζ.
In ou s a ic model, his equals he sha e o acancies illed in he espec i e i m. The p oba-
bili y o a wo ke o be hi ed, when queuing o a job, is gi en by αw(q)≡m(s, )/s =Aq−ζ.
In he subsequen analysis we ocus on in e io solu ions wi h αe(q), αw(q)∈(0,1). Fo which
pa ame e domain such an in e io solu ion is ealized will be discussed below.
Se ing unemploymen compensa ion equal o ze o and deno ing by V he highes income a
wo ke can expec when applying o a job a a di e en i m, queuing o acancies in a i m
wi h p oduc i i y φis only a ac i e o he wo ke i V≤αw[q(φ)]w(φ). Since i ms se he
same wage o all wo ke s in ou se ing (see abo e), addi ional wo ke s apply o jobs in his
14Roge son, Shime , and W igh (2005) p o ide an excellen o e iew o di e en sea ch- heo e ic app oaches,
hei main ad an ages and disad an ages. In he con ex o he e ogeneous i ms, a compe i i e sea ch model has
also been conside ed by Ri e (2011) and Felbe may , Impulli i, and P a (2012).
15In a compe i i e sea ch model i is no necessa y o choose an ad hoc speci ica ion o he ma ching unc ion.
Ins ead, one can as well ake he coo dina ion p oblem o di ec ed sea ch se iously and p o ide a clean mic o-
ounda ion o his p oblem by choosing an u n-ball ma ching unc ion (see Pe e s, 1991, o an ea ly con ibu ion
and King and S ¨ahle , 2010, o an applica ion in he con ex o ade). A disad an age o his mo e ad anced
app oach is i s lowe analy ical ac abili y, and we he e o e p e e ea ing he ma ching unc ion as a black
box as i is s ill common in he li e a u e.
52 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
i m as long as he inequali y is s ic . This lowe s he p obabili y o being hi ed by he i m,
αw[q(φ)], and he adjus men p ocess con inues un il he expec ed e u n o wo ke s is he same
in all ac i e i ms. Hence, V=Aq(φ)−ζw(φ) mus hold in equilib ium, and he di ec ed sea ch
mechanism he e o e es ablishes a posi i e link be ween queue leng h q(φ) and he pos ed wage
w(φ):
w(φ) = q(φ)ζV
A.(3.29)
The mass o acancies se up by a i m wi h p oduc i i y φ, (φ), is linked o his i m’s employ-
men le el, l(φ), acco ding o (φ) = l(φ)/[Aq(φ)1−ζ]. The cos s o ins alling and ad e ising a
acancy a e measu ed in uni s o inal ou pu and a e gi en by k > 0.
Wi h hese insigh s a hand, we can w i e i m-le el p o i s in he closed economy as ollows:
π(φ) = p(φ)x(φ)−q(φ)ζV
Al(φ)−[1 + µ(φ)]γ− −kl(φ)
Aq(φ)1−ζ.(3.30)
The i m se s l(φ), q(φ), and µ(φ) simul aneously o maximize p o i s (3.30) subjec o (3.2),
(3.6), and a se o non-nega i i y cons ain s. The (in e io ) solu ion o his maximiza ion
p oblem is cha ac e ized by he ollowing h ee i s -o de condi ions:
πl(φ) = σ−1
σp(φ)φ[1 + µ(φ)] −w(φ)−k
Aq(φ)1−ζ= 0,(3.31)
πq(φ) = −l(φ)ζq(φ)ζ−1V
A+ (1 −ζ)l(φ)k
Aq(φ)2−ζ= 0,(3.32)
πµ(φ) = σ−1
σp(φ)l(φ)φ−γ[1 + µ(φ)]γ−1= 0.(3.33)
Equa ions (3.29) and (3.32) join ly de e mine
q(φ) = (1 −ζ)k
ζV ≡q, w(φ) = (1 −ζ)k
ζAq1−ζ≡w, (3.34)
implying ha all i ms pay he same wage, i espec i e o he p e ailing p oduc i i y di e ences.
This ou come is in line wi h models o andom ma ching be ween wo ke s and he e ogenous
i ms, in which wages a e de e mined by indi idual Nash ba gaining. Fo ins ance, Felbe may
and P a (2011, p. 286) poin ou ha in hei se ing all i ms pay he same wage, because
“mul iple-wo ke i ms exploi hei monopsony powe un il employees a e paid hei ou side
op ion [ ha ] is cons an ac oss i ms because i depends solely on agg ega e ou comes.” This
gi es a p ominen ole o o e -hi ing in models wi h indi idual wage ba gaining, which, howe e ,
is no p esen unde wage pos ing. Ins ead, in ou model he inding o a uni o m wage le el is a
consequence o h ee model ing edien s: linea hi ing cos s, he same ou side op ion o wo ke s
wi h di e ing abili ies, and he isoelas ic demand s uc u e.16
16The e a e di e en possibili ies o modi y he model such ha i gi es ise o he empi ically well-documen ed
pa e n ha la ge , mo e p oduc i e i ms pay highe wages. Fo ins ance, one could conside con ex ins ead
o linea ec ui men cos s, as sugges ed by Helpman and I skhoki (2010). Al e na i ely, one could modi y he
wage se ing p ocess and assume ha i ms pos ai wages, as in Egge and K eickemeie (2009, 2012) and Ami i
and Da is (2012). Finally, one could also gi e up he symme y o i m-wo ke ma ches and ins ead assume ha
abili y is i m-speci ic and employe s can lea n abou his abili y du ing he ec ui men p ocess by ins alling a
sc eening echnology, as sugges ed by Helpman, I skhoki, and Redding (2010). While all o hese modi ica ions
would allow o i m-speci ic wage paymen s, he cos s o hese ex ensions in e ms o analy ical ac abili y
would be eno mous, and we he e o e decided o s ick o he mo e pa simonious model a ian wi hou wage
di e en ia ion.
3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 53
Combining (3.31) and (3.34) gi es he modi ied p ice-ma kup ule
p(φ) = σ
(σ−1)φ[1 + µ(φ)]
k
ζAq1−ζ,(3.35)
whe e ma ginal labo cos s a e augmen ed by ec ui men expendi u es. Con as ing (3.9) and
(3.33), we see ha he exis ence o sea ch ic ions does no change he p o i -maximizing choice
o sc eening. Since sea ch ic ions do also no a ec i m en y decisions, cu o p oduc i i y
φ∗and e enues o he ma ginal i m (φ∗) emain o be gi en by (3.14). Simila ly, he ze o-
cu o p o i condi ion and he ee en y condi ion emain o be gi en by (3.15) and (3.16),
espec i ely, and hence nei he ¯πno φ∗depend on he p e ailing sea ch ic ions o he cos s
o es ablishing and pos ing acancies, k.
Wi h he i m-le el a iables a hand, we can now sol e o he gene al equilib ium ou come
in he closed economy. Fo his pu pose, we i s look a queue leng h q. Subs i u ing (3.2)
in o (φ∗) = p(φ∗)x(φ∗) and accoun ing o Y=M (φ∗)ν/(ν−ξ) gi es p(φ∗)σ−1=ν/(ν−ξ).
Using (3.35) and no ing ha φ∗[1 + µ(φ∗)] = [( ξ)/γ]1/γ {( ξ)/[ e(ν−ξ)]}1/ν ollows om
(3.14)-(3.16), we can de i e
q=(kσ
Aζ(σ−1) ν−ξ
ν1
σ−1 e
ν−ξ
ξ1
νγ
ξ 1
γ)1
1−ζ
.(3.36)
To sol e o economy-wide unemploymen ˆu, we can subs i u e V= (1 −ˆu)win o (3.29).
Rea anging e ms, yields 1 −ˆu=Aq−ζ, which es ablishes he in ui i e esul ha a la ge
queue leng h a indi idual i ms leads o highe economy-wide unemploymen . Accoun ing o
q om (3.36), we can compu e
1−ˆu=(ζ(σ−1)
kσ ν
ν−ξ1
σ−1
e
ξ
ν−ξ1
ν ξ
γ1
γ)ζ
1−ζ
A1
1−ζ.(3.37)
Eq. (3.37) cha ac e izes in olun a y unemploymen as one impo an aspec o unde employmen
and measu es he e iciency loss due o sea ch ic ions. Howe e , i does no cap u e he e i-
ciency loss, a ising om a misma ch be ween wo ke s and asks in he i m-in e nal alloca ion
o labo . This o m o unde employmen can be measu ed by he a e age dis ance be ween
ask-speci ic skill equi emen s and wo ke -speci ic abili ies and is ep esen ed by u. C ucially,
he exis ence o sea ch ic ions does no impac i m-le el sc eening (see abo e), and hence i
does no al e i m-in e nal labo alloca ion. Due o his, u emains o be gi en by (3.18) in he
closed economy.17
Finally, wel a e in he closed economy is gi en by (1 −ˆu)w, which, in iew o (3.34), (3.36),
and (3.37), can be exp essed as
(1 −ˆu)w=1−ζ
ζ
k
q= (1 −ζ)A1
1−ζζ
kζ
1−ζ
˜w1
1−ζ= (1 −ζ)(1 −ˆu) ˜w, (3.38)
17Eqs. (3.36) and (3.37) can be used o cha ac e izing he pa ame e domain ha es ablishes an in e io
solu ion wi h αe(q), αw(q)∈(0,1). Mo e speci ically, we can conclude ha αe(q) = Aq1−ζ<1 and αw(q) =
Aq−ζ<1 simul aneously hold i
A1
ζ<kσ
ζ(σ−1) ν−ξ
ν1
σ−1 e
ν−ξ
ξ1
νγ
ξ 1
γ<1,
while he wo p obabili ies a e posi i e i ζ, k, A > 0 (and ν > ξ as p e iously assumed).
54 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
whe e ˜wequals he wage a e in he benchma k model wi h a pe ec labo ma ke , gi en by
(3.17). F om (3.38) i is ob ious ha he exis ence o sea ch ic ions educes pe capi a labo
income and hus wel a e in ou se ing. This comple es he discussion o he closed economy.
We now u n o he open economy and shed ligh on he e ec s o ade o he wo sou ces
o unde employmen . The eby, we impose he same assump ions as in he baseline model and
conside wo symme ic coun ies, icebe g anspo cos s o shipping in e media e goods ac oss
bo de s and ixed expo ing cos s o gene a e selec ion o only he bes i ms in o expo s a us.
Wi h hese assump ions a hand, we can now epea he analysis o he closed economy s ep
by s ep in o de o de i e he main a iables o in e es o he open economy. Howe e , since
he espec i e calcula ions a e s aigh o wa d, we lea e hem o he in e es ed eade and only
summa ize he main esul s om his analysis, he e. F om he closed economy, we know ha
he exis ence o labo ma ke impe ec ion does no a ec he alloca ion o wo ke s o asks, and
hence ou insigh s ega ding he consequences o ade o he i m-in e nal misma ch emains
una ec ed by adding a sea ch ic ion. This implies ha he open economy le el o u emains
o be gi en by (3.28).
Fu he mo e, i is easily con i med ha he exis ence o a sea ch ic ion does no al e Eqs.
(3.19)-(3.21), he e o e lea ing he expo ing decision una ec ed. As a consequence, he sha e o
expo ing i ms emains o be gi en by (3.23). No ing om (3.38) ha pe capi a labo income
in he mo e sophis ica ed model a ian wi h sea ch ic ions is a con ex unc ion o he wage
a e in he benchma k model wi h a pe ec labo ma ke , we can in e he wel a e e ec s o
ade by conside ing Eq. (3.27). To mo e speci ic, we can w i e
(1 −ˆu)w
(1 −ˆua)wa=˜w
˜wa1
1−ζ
="1 + χ x/
1 + χ1
σ−11 + χ x
1
ν#1
1−ζ
.(3.39)
Hence, he exis ence o sea ch ic ions does no change he wel a e e ec s o ade in a quali a i e
way, bu i magni ies he (posi i e o nega i e) wel a e implica ions iden i ied in Chap e 3.3.
To unde s and, whe e he addi ional wel a e e ec comes om, i is wo h no ing ha we can
w i e
w
wa=q
qaζ−1
=1 + χ x/
1 + χ1
σ−11 + χ x
1
ν
,(3.40)
acco ding o (3.34) and (3.39). F om (3.27) and (3.40) i ollows ha in he p esence o sea ch
ic ions he wage adjus men s igge ed by ade a e o equal magni ude as in he benchma k
model wi h a pe ec ly compe i i e labo ma ke . The e o e, any addi ional wel a e e ec mus
come om adjus men s in he employmen a e. Looking a
1−ˆu
1−ˆua=q
qa−ζ
=(1 −ˆu)w
(1 −ˆua)waζ
="1 + χ x/
1 + χ1
σ−11 + χ x
1
ν#ζ
1−ζ
(3.41)
p o ides suppo o his conclusion. Eqs. (3.39)-(3.41) show ha he e is a di ec link be ween
employmen , wage, and wel a e e ec s o ade in ou se ing. F om Chap e 3.3 we know ha
lacking an ex e nal scale e ec in he p oduc ion o inal goods, selec ion o expo e s mus be
su icien ly s ong in o de o ade o p o ide a s imulus on agg ega e labo demand and equi-
lib ium wages. In his case, he p ice o he inal good alls ela i e o he wage a e. This lowe s
he cos s o ins alling and ad e ising acancies ela i e o he cos s o compensa ing wo ke s,
and hus alle ia es he sea ch ic ion wi h posi i e consequences o agg ega e employmen .
3.4. A MODEL VARIANT WITH INVOLUNTARY UNEMPLOYMENT 55
Bo h o hese e ec s con ibu e o a wel a e gain i sea ch ic ions exis . Things a e di e en
i selec ion e ec s a e weak. In his case, i is possible ha labo demand is dampened in he
open economy, so ha wages decline. Howe e , i wages decline ela i e o he p ice o he inal
good, he es ablishmen o new acancies becomes less a ac i e, ende ing he sea ch ic ion
mo e se e e han unde au a ky, wi h ad e se e ec s on economy-wide employmen .
The ollowing p oposi ion summa izes he main insigh s om he analysis in his chap e .
P oposi ion 6 The exis ence o sea ch ic ions does no al e ou insigh s om he benchma k
model ega ding he impac o ade on he misma ch be ween wo ke s and ask in he i m-
in e nal labo ma ke . Fu he mo e, wi h sea ch ic ions, ade igge s wage and employmen
e ec s ha go in o he same di ec ion. As a consequence, he wel a e implica ions o ade, while
no al e ed quali a i ely, a e ein o ced in he model a ian wi h sea ch ic ions.
P oo . Analysis in he ex .
We comple e he discussion in his chap e by ha ing a close look on he speci ic ole played
by adjus men s in he i m-in e nal alloca ion o wo ke s o he impac o ade on wel a e and
economy-wide unemploymen . In pa icula , we wan o shed ligh on whe he one o e -es ima es
o unde -es ima es he e ec s o ade, when dis ega ding he i ms’ abili y o endogenously
adjus he quali y o wo ke - ask ma ches. Fo his pu pose, i is wo h no ing ha ou model
degene a es o one wi hou sc eening i γ→ ∞. We can he e o e in e insigh s upon he ole
played by he i m-in e nal labo alloca ion om di e en ia ing (3.39)-(3.41) wi h espec o γ.
Mo e speci ically, we can de e mine how changes in γal e he employmen and wel a e e ec s
o ade, by s udying he sign o
d(w/wa)
dγ =d(w/wa)
dχ
dχ
dγ .(3.42)
Di e en ia ing (3.23) wi h espec o γgi es
dχ
dγ =−νχ
γ


1
γ−σ+ 1 1 + τ1−σξ
σ−1
(1 + τ1−σ)ξ
σ−1−1
ln 1 + τ1−σ−1
γln χξ
ν

<0.(3.43)
A highe γimplies ha ixed cos s a e mo e esponsi e o changes in he sc eening e o .
Acco dingly, i ms will adjus hei sc eening e o less s ongly when acing he oppo uni y o
expo ing, so ha he ixed cos inc ease due o expo ing is less p onounced (see Eq. (3.20)),
and hence he sha e o expo e s inc eases ce e is pa ibus i γgoes up. On he o he hand,
he now lowe wedge o sc eening e o ea s up pa o he p oduc i i y ad an age o expo e s
ela i e o non-expo e s, he eby lowe ing he incen i es o i ms o sell ab oad. In ou model,
i is he second e ec ha domina es, so ha a highe γ ein o ces sel -selec ion in o expo ing,
and he e o e implies a smalle sha e o expo ing i ms χ.
Fu he mo e, di e en ia ing (3.40) wi h espec o χyields
d(w/wa)
dχ =w/wa
ν(1 + χ x/ ) (1 + χ)ν
σ−1 x
−1+ (1 + χ) x
.(3.44)
I is easily con i med ha he b acke e m on he igh -hand side o (3.44) is inc easing in
x/ , and hence wages inc ease mono onically in he sha e o expo ing i ms i x/ (and hus
he selec ion e ec ) is su icien ly la ge. In line wi h ou insigh s om Chap e 3.3, x/ ≥1
is su icien (no necessa y) o a mono onically posi i e impac o an inc ease in χon w/wa.

56 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
I such a mono onic e ec exis s, an inc ease in γunambiguously lowe s he posi i e wage,
employmen , and wel a e e ec s o ade, and hence posi i e economy-wide e ec s would be
unde es ima ed i one igno es endogenous adjus men s in he i m-in e nal alloca ion o wo ke s
o asks. Howe e , i he impac o a highe χon w/wais non-mono onic, hings a e e en mo e
wo ying, because in his case igno ing endogenous adjus men s in he way wo ke s a e assigned
o asks may gi e w ong p edic ions ega ding he exis ence o posi i e wage, employmen , and
wel a e e ec s o ade. The ollowing p oposi ion summa izes hese esul s.
P oposi ion 7 The abili y o i ms o adjus he quali y o wo ke - ask ma ches leads o weake
selec ion o i ms in o expo ing, and hus a la ge sha e o expo ing i ms. P o ided ha an
inc ease in he sha e o expo ing i ms exhibi s a posi i e mono onic impac on wages, adjus -
men s in he i m-in e nal alloca ion o wo ke s o asks he e o e s eng hen he employmen and
wel a e s imulus ela i e o a model whe e such adjus men s do no exis . I he ela ionship be-
ween he sha e o expo ing i ms and wages is non-mono onic, adjus men s in he i m-in e nal
alloca ion o labo may e e se he employmen and wel a e e ec s o ade.
P oo . Analysis in he ex .
3.5 A calib a ion exe cise
In his chap e , we aim a quan i ying he e ec s o ade in ou se ing. Fo his pu pose, we
calib a e ou model, using pa ame e es ima es om he li e a u e. A i s se o use ul pa ame e
es ima es is p o ided by Egge , Egge , and K eickemeie (2011). Egge , Egge , and K eickemeie
(2011) s uc u ally es ima e he main pa ame e s o a ade model wi h he e ogeneous i ms
and labo ma ke impe ec ions due o a ai -wage e o mechanism, using i m-le el da a om
i e Eu opean coun ies – Bosnia and He zego ina, C oa ia, F ance, Se bia, and Slo enia – o
he pe iod 2000 o 2008. Fo ou calib a ion exe cise, we conside he pa ame e es ima es
o F ance, which hos s he majo i y o i ms in he espec i e da a-se . A i s pa ame e
a ailable om he empi ical applica ion in Egge , Egge , and K eickemeie (2011) is he elas ici y
o subs i u ion, o which hey epo a alue o σ= 6.7. This es ima e is simila o o he
indings in he li e a u e (see, o ins ance, B oda and Weins ein, 2006). Fu he mo e, using
he s uc u al ela ionship be ween e enues o expo ing i ms, Egge , Egge , and K eickemeie
(2011) es ima e an analogon o ξ/ν, o which hey epo a alue o 0.87, when elying on
in o ma ion o F ench i ms. This is ai ly close o he es ima e o 0.83 epo ed by A kolakis
and Muendle (2010) o B azilian i ms.
Un o una ely, he e a e no di ec es ima es a ailable o γ, and we a e he e o e no able o
calcula e he pa ame e alues o γand νsepa a ely. Howe e , om he o mal discussion in
Chap e 3.2 we can in e ha exis ence o an in e io solu ion equi es a su icien ly high le el
o ν. Wi h ξ/ν = 0.87, νmus be la ge han 6.5 in ou calib a ion exe cise. Since we canno
u he con ine he possible pa ame e alues, we conside h ee pa ame e alues ha a e in
line wi h his cons ain and choose ν= 7, ν= 9 and ν= 11 o ou calib a ion exe cise.18
Taking accoun o σ= 6.7 and ξ/ν = 0.87, we can hen calcula e he co esponding γ-le els:
γ= 89.01 o ν= 7, γ= 20.95 o ν= 9 and γ= 14.10 o ν= 11.
An addi ional a iable o in e es is he sha e o expo e s, χ. Ea on, Ko um, and K ama z
(2011) epo om o icial adminis a i e s a is ics ha 15 pe cen o F ench manu ac u ing
i ms we e expo e s in 1986. Egge , Egge , and K eickemeie (2011) ind a signi ican ly la ge
18These ν- alues a e well in line wi h shape pa ame e s o he p oduc i i y dis ibu ion applied in o he
nume ical applica ions o he Meli z (2003) model. Fo ins ance, A kolakis and Muendle (2010) conside 5 and
8 as low and high alues o he shape pa ame e , whe eas Felbe may and P a (2011) conside a alue o 9.23.
3.5. A CALIBRATION EXERCISE 57
sha e o expo e s, using he Amadeus da a-se . Acco ding o hei da a-base, 45 pe cen o
F ench i ms did expo in he a e age yea be ween 2000 and 2008. Since i is well known ha
he Amadeus da a is biased owa ds la ge, inco po a ed i ms, we conside he e idence p o ided
by Ea on, Ko um, and K ama z (2011) o be mo e eliable and acco dingly se χ= 0.15 in
ou calib a ion exe cise. Recen empi ical esea ch aims a es ima ing compulso y measu es o
he icebe g ade cos pa ame e τby employing in o ma ion on obse ed in e na ional ade
lows in o a s uc u al g a i y equa ion. Exis ing esul s om his li e a u e sugges se ing
τ= 1.5 (see, o ins ance, McGowan and Milne , 2013; No y, 2013). Wi h he icebe g ade
cos pa ame e and he sha e o expo e s a hand, we can hen compu e a heo y-consis en
alue o ixed cos a io x/ . Using he pa ame e alues om abo e, we ob ain x/ = 0.93
i ν= 7, x/ = 0.96 i ν= 9, and x/ = 0.98 i ν= 11. Finally, we ollow common p ac ice
in he sea ch li e a u e and se ζ= 0.5 (see Pe ongolo and Pissa ides, 2001, o suppo i e
empi ical e idence).
Table 3.1: Quan i ying he impac o ade on wel a e and unde -
employmen
Pa ame e alues Changes in pe cen
ν γ x/ ∆(1 −ˆu)w∆(1 −ˆu) ∆u
7 89.01 0.93 3.45 1.71 −0.37
9 20.95 0.96 2.81 1.39 −1.54
11 14.10 0.98 2.45 1.22 −2.29
No es: An expo e sha e o χ= 0.15, an icebe g ade cos pa ame e o
τ= 1.5, a σ- alue o 6.7, a ζ- alue o 0.5, and a pa ame e a io ξ/ν = 0.87
ha e been conside ed o compu ing he igu es in his able.
Table 3.1 summa izes he main insigh s om ou calib a ion exe cise and epo s employmen
and wel a e e ec s associa ed wi h a mo emen o F ance om au a ky o i s obse ed deg ee
o openness: χ= 0.15. F om Column 4 we see ha gains om ade seem o be a he small in
ou se ing, which a leas pa ly may be explained by he absence o ex e nal scale economies
in he p oduc ion o inal goods. Howe e , he wel a e gains documen ed in Table 3.1 a e in
he ange o wel a e e ec s epo ed by Ea on and Ko um (2002), who se up a mul i-coun y
Rica dian model o 19 OECD economies and in es iga e how much coun ies in hei da a-se
would lose i ade we e en i ely abolished. They compu e losses anging om 0.2 pe cen o
Japan and 10.3 pe cen o Belgium, and o F ance hey epo a wel a e loss o 2.5 pe cen .
This is ai ly close o he wel a e loss om abolishing ade en i ely when se ing ν= 11 in ou
model, which amoun s o 2.4 pe cen .
The e ec s o ade on economy-wide employmen a e epo ed in Column 5. A a i s
glance, he employmen e ec s may seem no sizable. Howe e , i is no ewo hy ha e alua ed
a a cu en unemploymen a e o abou 10 pe cen , an employmen e ec o ∆(1 −ˆu) = 1.22
( o ν= 11) implies ha he obse ed deg ee o openness has lowe ed he F ench unemploymen
a e by 1.1 pe cen age poin s ela i e o au a ky. Column 6 epo s ou calib a ion esul s o he
impac o ade on he a e age misma ch in he i m-in e nal alloca ion o wo ke s o asks. In
line wi h ou heo e ical esul , his misma ch is educed in he open economy and he mo e so,
he la ge is ν. This is in ui i e, as we see om Column 2 ha highe le els o νa e associa ed
wi h smalle le els o γand hus a smalle elas ici y o sc eening cos s in sc eening e o . As a
consequence, o highe alues o ν i ms will adjus hei sc eening e o mo e s ongly o new
58 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS
expo ing oppo uni ies, leading o a mo e p onounced educ ion in he economy-wide misma ch
o wo ke s and asks in esponse o ade.
Fo p o iding insigh s on he ex en o which adjus men s in he i m-in e nal alloca ion o
wo ke s go e n he employmen and wel a e implica ions o ade in ou se ing, we can con as
he indings in Table 3.1 wi h hose om an o he wise iden ical model a ian in which such
adjus men s a e no easible. Fo his pu pose, we look a he limi ing case o γ→ ∞, which,
as ou lined in he p e ious chap e , implies ha p oduce s do no sc een hei applican s, so
ha µ(φ) = 0 o all φ. Conside ing ν= 11 as he p e e ed alue o he shape pa ame e o
he Pa e o p oduc i i y dis ibu ion and hus se ing x/ = 0.98 acco ding o Table 3.1, we
can compu e a heo y-consis en sha e o expo e s ha co esponds o he pa ame e alues a
hand. We compu e χ= 0.02, which con i ms ou insigh om he o mal analysis ha highe
le els o γlowe he sha e o expo e s mono onically (see Eq. (3.43)). F om he analysis in
Chap e 3.4, we a e wa ned ha changes in he sha e o expo ing i ms need no exhibi a
mono onic e ec on employmen and wel a e i x/ < 1, which is he case in ou exe cise. I is
he e o e a p io i no clea whe he he mo emen o F ance om au a ky o he obse ed deg ee
o openness would ha e been bene icial in he absence o sc eening. In he nume ical applica ion,
we can e alua e he wel a e and employmen e ec s o ade o he limi ing case o γ→ ∞. Fo
he p e e ed pa ame iza ion, his gi es ∆(1 −ˆu)w= 0.28 and ∆(1 −ˆu) = 0.14, espec i ely.
The e o e, elimina ing he abili y o i ms o sc een hei wo k o ce and endogenously adjus
he quali y o wo ke - ask ma ches would no al e he wel a e and employmen e ec s o ade
quali a i ely, bu i would lead o a signi ican decline o i s bene icial consequences. Finally,
ecollec ing om Chap e 3.4 ha gains om ade in ou model a e a composi e o posi i e
employmen and posi i e wage e ec s, we can ask which o hese wo pa ial e ec s is he mo e
impo an sou ce o wel a e s imulus. The answe o his ques ion is simple. Se ing ζ= 0.5,
we ob ain ∆(1 −ˆu) = ∆w, acco ding o (3.40) and (3.41). Since ∆wco esponds o he wel a e
e ec o ade in he absence o sea ch ic ions, we can he e o e conclude ha dis ega ding
labo ma ke impe ec ions leads o a signi ican downwa d bias in he calib a ed wel a e e ec s
o ade.
3.6 Concluding ema ks
This chap e se s up a model o he e ogeneous i ms along he lines o Meli z (2003) and en iches
his wo kho se o mode n ade heo y by associa ing p oduc ion wi h a con inuum o asks ha
di e in hei skill equi emen s. Fu he mo e, we assume ha wo ke s di e in hei abili ies o
pe o m hese asks, and i ms he e o e ace he complex p oblem o ma ching he e ogeneous
wo ke s wi h he e ogeneous asks. To sol e his alloca ion p oblem in a sa is ac o y way, i ms
equi e in o ma ion abou wo ke abili y and hey can ge his in o ma ion by sc eening hei
applican s. Sc eening in ol es ixed cos s and p o ides an imp ecise signal abou he abili y o
wo ke s. The highe he in es men in o he sc eening echnology, he be e is he signal and
he be e is he e o e he ma ch be ween abili ies o wo ke s and skill equi emen s o asks.
In ui i ely, i ms ha ha e a highe ex an e p oduc i i y ins all a be e sc eening echnology,
so ha he e ogenei y o i ms is ein o ced by he endogenous in es men in o sc eening.
We use his amewo k o s udy he consequences o ade o wel a e and unde employmen ,
a ising om he misma ch be ween wo ke s and asks. I only he bes (mos p oduc i e) i ms
sel -selec in o expo ing, ade exe s an asymme ic e ec on he sc eening incen i es o high-
and low-p oduc i i y i ms. High-p oduc i i y i ms expand p oduc ion due o expo ing, and
he e o e ind i a ac i e o ins all a be e (mo e expensi e) sc eening echnology han in he
closed economy. In con as , low-p oduc i i y i ms do no expo and lose ma ke sha e a
3.6. CONCLUDING REMARKS 59
home. In esponse, hey lowe hei sc eening expendi u es. Despi e his asymme y in i m-
le el adjus men s o ade, we show ha he a e age misma ch be ween wo ke -speci ic abili ies
and ask-speci ic skill equi emen s unambiguously sh inks in he open economy. This poin s o
a so a unexplo ed channel h ough which ade can imp o e he labo ma ke ou come and
s imula e wel a e.
In an ex ension o ou baseline model, we conside impe ec ions in he ex e nal labo ma -
ke due o sea ch ic ions. Relying on a compe i i e sea ch model wi h wage pos ing, we
show ha his modi ica ion does no al e ou insigh s ega ding he consequences o ade o
he i m-in e nal alloca ion o wo ke s o asks. Howe e , due o adjus men s in in olun a y
unemploymen , he e is now a second channel h ough which ade a ec s economy-wide unde -
employmen . Whe he mo e o less wo ke s ind a job in he open economy is in gene al no
clea and depends on he s eng h o selec ion o i ms in o expo ing. I ixed cos s o expo ing
a e high ela i e o domes ic ixed cos s, selec ion in o expo ing is s ong and in his case ade
inc eases wel a e and lowe s unde employmen due o a highe ma ching e iciency inside and
ou side he i m. In a calib a ion exe cise, we ely on pa ame e es ima es o F ench i ms o
quan i y he ela i e impo ance o adjus men s in he i m-in e nal and he i m-ex e nal labo
ma ke . We ind ha bo h adjus men s a e impo an channels o gains om ade o ma e i-
alize. Fo ins ance, elimina ing he abili y o i ms o sc een hei applican s and o adjus he
quali y o wo ke - ask ma ches endogenously would lowe gains om ade by almos 90 pe cen ,
whe eas dis ega ding imp o emen s in he ou side labo ma ke would lowe gains om ade
by 50 pe cen when elying on he p e e ed pa ame iza ion o ou model.
To pu i in b oade pe spec i e, one can in e p e ou analysis as an a emp o widen he
pic u e o unde employmen and o show ha posi i e labo ma ke consequences o ade need
no only ma e ialize due o a educ ion in in olun a y unemploymen . Ra he e iciency gains
may be igge ed by adjus men s in he i m-in e nal o ganiza ion o labo and acco ding o ou
esul s hese gains may indeed be sizable. O cou se, mo e esea ch is needed be o e one can
d aw a de ini e conclusion abou how ade a ec s he way labo is used in mode n p oduc ion.
We hope ha he insigh s om ou analysis encou age such esea ch.
66 CHAPTER 3. TRADE AND THE ALLOCATION OF WORKERS TO TASKS

Chap e 4
T ade and he Fi m-in e nal
Assignmen o Skills o Tasks
4.1 In oduc ion
The o ganiza ion o p oduc ion wi hin i ms is a key de e minan o i m pe o mance. The
abili y o alloca e sca ce esou ces wi hin he bounda ies o i ms e icien ly, is essen ial o
i ms o compe e in mode n economic li e.1When i comes o he o ganiza ion o labo wi hin
i ms, his opic is discussed in he li e a u e on pe sonnel economics. Howe e , in he ade
li e a u e, i ms we e ea ed as a black box o e cen u ies. This pe spec i e has changed o e
he las ew yea s, whe e ecen con ibu ions ha e p o ided new insigh s, how ade shapes
he in e nal o ganiza ion o na ional and mul ina ional i ms. The eby, he ocus has been on
co po a e hie a chies. Fo ins ance, Caliendo and Rossi-Hansbe g (2012) highligh ha a i m’s
p oduc i i y depends on how p oduc ion is o ganized, and his o ganiza ion changes in he
p ocess o globaliza ion.2This chap e akes a di e en app oach and in oduces he idea o
a ask-based p oduc ion p ocess in o a amewo k o in e na ional ade. O cou se, wi h he
p oduc ion p ocess consis ing o di e en asks, i ms ace new p oblems ha a e igno ed in
he exis ing li e a u e. I he se o asks in a i m di e in complexi y and wo ke s di e in
hei abili ies o pe o m hese asks, he o ganiza ion o wo ke s o speci ic asks inside he i m
becomes ele an .3Modeling he assignmen o wo ke s o asks and a discussion on how his
assignmen changes in an open economy is in he cen e o his chap e ’s in e es .
Fo his pu pose, I in oduce a ask based p oduc ion p ocess along he lines o Acemoglu and
Au o (2011) in o a s anda d ade model wi h monopolis ic compe i ion among he e ogeneous
i ms, as in Meli z (2003). In his amewo k, i m ou pu is assembled om a con inuum o
asks ha di e in complexi y. Fo he pe o mance o asks, i ms can hi e low-skilled o high-
skilled wo ke s, while a highe skill le el causes a compa a i e ad an age in he pe o mance o
mo e complex asks. How i ms assign skills o asks depends on he compa a i e ad an age
o high-skilled wo ke s and hei skill p emium. By al e ing he ange o asks pe o med by
1In a ecen pape by Gi oud and Muelle (2012), i is shown ha i m-le el p oduc i i y inc ease, due o he
e icien esou ce ealloca ion wi hin i ms.
2See also Ma in and Ve die (2008b, 2012).
3Clea ly, he e exis s a la ge heo e ical li e a u e, ha discusses how he e ogeneous wo ke s so o di e en
indus ies, how hey ma ch wi h o he wo ke s, i ms, and wi h o he ac o s o p oduc ion and how ade a ec s
his ma ching and he wage dis ibu ion (see G ossman, 2013, o a ecen su ey o his li e a u e).
67
68 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
high-skilled wo ke s, i ms do no only a ec hei labo cos s bu also hei p oduc i i y. To
de e mine he op imal skill ange and o manage he i m and o ganize he complex p oduc ion
p ocess, i ms need a ixed inpu o high-skilled wo ke s. In a benchma k model, I assume
ha labo ma ke s a e pe ec ly compe i i e. A e sol ing o he gene al equilib ium in a
closed economy, I analyze changes in ac o endowmen s, which can be in e p e ed as mig a ion
p oblem. The main insigh s om his analysis a e ha an inc ease in he supply o low-skilled
wo ke s aises he ange o asks pe o med by his skill ype, which igge s a decline in he
p oduc i i y o i ms. While low-skilled wo ke s lose due o a educ ion in hei eal wage, high-
skilled wo ke s gain in absolu e and ela i e e ms, as hey see hei eal wage and skill p emium
ising. E en hough he mass o i ms inc eases, o e all wel a e e ec s a e ambiguous due o he
decline in p oduc i i y. In he case o high-skilled mig a ion, i m p oduc i i y inc eases as i ms
use his skill ype o he pe o mance o a b oade ange o asks. While low-skilled wo ke s
expe ience an inc ease in hei income, he impac on high-skilled wages a e less clea -cu and
depend on model pa ame e s. As i m numbe and p oduc i i y inc eases, o e all wel a e e ec s
a e posi i e.
In a second s ep, I conside a minimum wage o he g oup o low-skilled wo ke s, o accoun
o he empi ical ac ha unemploymen is pe sis en especially among his g oup o wo ke s.
This educes wel a e ela i e o a benchma k wi h ully lexible wages and gene a es unemploy-
men o low-skilled wo ke s. Mo eo e , he in oduc ion o a minimum wage lowe s pe -capi a
income o high-skilled and low-skilled wo ke s and inc ease he ela i e income o high-skilled
wo ke s. Simila o B eche (1974), in such an economy mig a ion o low-skilled wo ke s is ully
abso bed by a pa i passu inc ease in unemploymen and a educ ion in wel a e bu lea es all
o he a iables una ec ed. In con as o a si ua ion wi h ully lexible wages, mig a ion o
high-skilled wo ke s educes he ange o asks pe o med by his g oup o wo ke s, and hus
i m-le el p oduc i i y, due o a magni ica ion e ec a he en ance o i ms. Mo eo e , high-
skilled wo ke s gain in absolu e and ela i e e ms, and he unemploymen a e o low-skilled
wo ke s goes down, implying ha wel a e mus inc ease.
To shed ligh on he assignmen o skills o asks and a i m’s p oduc ion p ocess i he coun-
y unde conside a ion opens up o ade, I discuss ade be ween wo ully symme ic coun ies.
Simila o K ugman (1979), in a si ua ion wi h ully lexible wages, ade only inc eases he eal
wage o each skill ype and agg ega e wel a e, while lea ing all o he a iables una ec ed. How-
e e , when low-skilled wages a e ixed by he go e nmen , ade also a ec s a i m’s p oduc ion
p ocess. Due o a s anda d di ision o labo e ec , demand o i ms in each coun y is highe in
he open economy. This s imula es agg ega e labo demand, and, as low-skilled wages a e ixed,
he skill p emium in each coun y. Fi ms espond o his change in ela i e ac o p ices and
assign low-skilled wo ke s o a b oade ange o asks. This skill downg ading educes p oduc-
i i y o i ms and accoun s o a so a unexplo ed channel, h ough which ade a ec s local
p oduc ion p ac ices. Howe e , as ade educes high-skilled ask p oduc ion, mo e i ms can
en e he ma ke , implying ha wel a e e ec s a e posi i e.
A e shedding ligh on how ade be ween wo coun ies a ec s he ask based p oduc ion
p ocess, I use he amewo k o discuss how changes in a coun ies labo ma ke ins i u ions spill
o e o he pa ne coun y. S a ing om an equilib ium wi h ade be ween wo minimum
wage economies, an inc ease in one coun y’s minimum wage also a ec s he assignmen o
skills o asks in he pa ne coun y. Due o a educ ion in agg ega e labo demand which
educes he skill p emium, i ms p oduce a b oade sha e o asks wi h high-skilled wo ke s and
he e o e become mo e p oduc i e. Howe e , beside hese posi i e p oduc i i y spillo e s, i m
numbe and pe -capi a income o high-skilled wo ke s a e educed, while low-skilled wo ke s
ace a highe unemploymen a e, which, in sum, a e ins umen al o a decline in wel a e.
4.1. INTRODUCTION 69
Accoun ing o di e ences in ac o endowmen s has no impac on he insigh s om an open
economy scena io wi h ully lexible wages. Howe e , i bo h coun ies se a minimum wage
o he g oup o low-skilled wo ke s, high-skilled mig a ion in one coun y inc eases he mass o
i ms and he ange o asks pe o med by low-skilled wo ke s in he pa ne coun y, and educes
i m-le el p oduc i i y, he e. Low-skilled wo ke s ace a lowe unemploymen a e, while high-
skilled wo ke s ace an inc ease in he eal wage, bu see hei ela i e income sh inking, and
wel a e in he pa ne coun y ises.
By shedding ligh how ade a ec s he i m-in e nal labo ma ke , his chap e is ela ed o
a g owing li e a u e ha analyzes how globaliza ion shapes he o ganiza ion o p oduc ion. In
his chap e , changes in he assignmen o wo ke s wi h di e en skills o asks wi h di e ing
complexi y a ec s a i m’s p oduc i i y le el. This is a no el mechanism ha di e en ia es his
model om o he ade models wi h a ask-based p oduc ion unc ion. Fo ins ance, ecen
con ibu ions o he li e a u e on o sho ing builds upon G ossman and Rossi-Hansbe g (2008).4
In he G ossman and Rossi-Hansbe g (2008) amewo k, p oduc ion also consis s o a con inuum
o low-skilled and high-skilled asks. Howe e , hei model p o ides a pe ec mapping be ween
skills and asks, as he se o asks o each skill ype is exogenous: low-skilled wo ke s a e
es ic ed o wo k in low-skill asks and high-skilled wo ke s a e only assigned o high-skill asks.
In my amewo k, hings a e mo e sophis ica ed, because each skill ype can in p inciple pe o m
he whole ange o asks wi hin a i m and he assignmen decision depends on he ela i e
pe o mance o low-skilled and high-skilled wo ke s in ask p oduc ion and on he espec i e
ac o cos s. The endogenous assignmen o wo ke s wi h di e ing abili ies o asks wi h di e ing
skill equi emen s is also discussed in a ecen pape by Egge and Koch (2013). While he
p oduc ion side is simila o my amewo k, hey di e wi h espec o he e ogenei y in he
wo k o ce. In he Egge and Koch (2013) amewo k, wo ke s a e ho izon ally di e en ia ed,
implying ha wo ke s di e in hei abili y o pe o m ce ain asks because hei human capi al
is occupa ion-speci ic. Mo eo e , i ms ha e o in es in o a sc eening mechanism o ge some
in o ma ion abou he hidden ask-speci ic abili ies o wo ke s. By inc easing he sc eening
in ensi y, i ms can imp o e he ma ching o wo ke s o asks and he eby i m p oduc i i y. In
he p esen model, i ms ha e pe ec in o ma ion abou he abili ies o wo ke s and he ocus
is on how i ms assign low-skilled and high-skilled wo ke s o asks wi h di e ing complexi y.
The eby, high-skilled wo ke s ha e an absolu e p oduc i i y ad an age in he pe o mance o
all asks. Howe e , hey a e also mo e expensi e, and hence i ms ind i a ac i e o assign
high-skilled wo ke s only o asks wi h high complexi y, since hei compa a i e ad an age is
declining wi h less complexi y. The ange o asks pe o med by high-skilled wo ke s de e mines
i m-p oduc i i y, and hence i ms wi h highe skill in ensi y end up being mo e p oduc i e.
An al e na i e mechanism, ha ela es i m p oduc i i y o he o ganiza ion o wo ke s in he
p oduc ion p ocess is discussed by Caliendo and Rossi-Hansbe g (2012). In hei model i is he
hie a chy s uc u e wi hin i ms, i.e. he numbe o laye s o managemen and he knowledge
and span o con ol o each agen ha is ins umen al o i m pe o mance.
By allowing o changes in he i m-in e nal assignmen o wo ke s o asks, he chap e also
con ibu es o a i id discussion on how ade a ec s p oduc i i y. The seminal pape by Meli z
(2003) p oposes an inc ease in agg ega e p oduc i i y due o a change in he composi ion o
ac i e p oduce s, while lea ing i m-le el p oduc i i y una ec ed. Bus os (2011) ex ends he
Meli z- amewo k by allowing i ms o in es in o hei echnology. Since expo e s gain ma ke
size in he open economy, hey ind i mo e a ac i e o in es in o hei echnology, and hence
end up ha ing a highe p oduc i i y. In Helpman, I skhoki, and Redding (2010), expo e s
ex end hei sc eening in es men s and hus ha e a be e wo k o ce composi ion and he e o e
4See, o ins ance, Kohle and W ona (2011), Benz (2012) o G ossman and Rossi-Hansbe g (2012).
70 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
highe p oduc i i y han in he closed economy. In Egge and Koch (2013) he expansion o
sc eening lea es he wo k o ce composi ion una ec ed bu imp o es he assignmen o wo ke s o
asks wi h posi i e p oduc i i y e ec s. In e es ingly, empi ical e idence a he i m-le el is no
conclusi e.5My model p o ides a easoning o his. Because ade expand demand o high-
skilled wo ke s as a ixed inpu in he p oduc ion p ocess, i lea es less high-skilled esou ces
o ask p oduc ion. This wo sens he skill composi ion wi h co esponden consequences o
i m-le el p oduc i i y.6This e ec , howe e , does only exis i labo ma ke s a e no pe ec ly
compe i i e, wi h labo ma ke impe ec ion being modeled by means o a binding minimum
wage.
By in oducing a minimum wage o low-skilled wo ke s, his chap e is ela ed o a sizable
li e a u e ha accoun s o di e en o ms o labo ma ke impe ec ions in he Meli z (2003)-
amewo k.7One ea u e in hese s udies is ha he labo ma ke impe ec ion has no impac
on he p oduc i i y o a speci ic i m bu a ec s he a e age p oduc i i y o all ac i e p oduce s
due o changes in he composi ion o i ms. Fo ins ance, in Egge and K eickemeie (2009),
a mo e impo an en sha ing mo i e in wo ke s’ ai wage p e e ences educes labo cos s o
low p oduc i e i ms ela i e o hei mo e p oduc i e compe i o s, because wages in high p o-
duc i e i ms inc ease disp opo iona ely wi h he en sha ing mo i e. This implies, somewha
coun e in ui i e, ha p o i s o he cu o i m inc ease. Wi h mo e unp oduc i e i ms being
able o su i e in he ma ke , he a e age p oduc i i y alls. A di e en mechanism is s udied
in Egge , Egge , and Ma kusen (2012). In hei pape , a mo e se e e labo ma ke impe ec-
ion inc eases he common wage and he ma ginal p oduc ion cos s p opo ionally. This o ces
he leas p oduc i e i ms o exi and hus inc eases a e age p oduc i i y, because he compo-
si ion o i ms imp o es. In my model, p oduc i i y e ec s a ise om di e en wage se ing
ins i u ions o low-skilled and high-skilled wo ke s which a ec he i m-in e nal assignmen o
skills o asks and hus a i m’s p oduc i i y. Hence, he labo ma ke impe ec ion leads o a
ealloca ion o wo ke s wi hin i ms, while in exis ing s udies on he e ogeneous i ms, labo is
ealloca ed be ween i ms.
Allowing o di e ences in he p e ailing labo ma ke ins i u ions be ween wo ading
pa ne s, he chap e is also ela ed o a li e a u e ha discusses labo ma ke linkages in open
economies. S a ing wi h he seminal wo k by Da is (1998), se e al au ho s ha e discussed
how labo ma ke impe ec ions in one coun y spill o e o o eign ma ke s.8In a ecen pa-
pe , Egge , Egge , and Ma kusen (2012) build upon a simila amewo k as he one conside ed
in his chap e . In pa icula , hey also conside monopolis ic compe i ion be ween he e oge-
neous i ms. Howe e , in con as o he app oach aken he e, p oduc ion in Egge , Egge , and
Ma kusen (2012) only consis s o a single ask. They u he mo e di e in he unde lying en y
mechanism, by assuming an exogenous mass o po en ial en an s. This modi ica ion u ns ou
o be ins umen al o hei esul s. In pa icula , he exogenous pool o po en ial en an s
es ablishes a link be ween he minimum wage and he cu o p oduc i i y o he ma ginal i m
and implies ha i wo coun ies wi h di e ing minimum wages engage in ade, hey end up
5Wagne (2007) p o ides a su ey on he link be ween expo e s and p oduc i i y on he e idence om i m
le el da a. A e s udding 45 mic oeconome ic s udies he concludes ha ”expo ing does no necessa ily imp o e
p oduc i i y” (p.1).
6This e ec is well in line wi h empi ical e idence. Fo ins ance, Ha igan and Reshe (2011) a gue he
”empi ical s udies ha e ailed o ind la ge e ec s o ade libe aliza ion on i m-le el o plan -le el skill upg ading”
(p.3).
7P ominen examples a e Da idson, Ma usz, and She chenko (2008); Da is and Ha igan (2011); Egge and
K eickemeie (2009, 2012); Egge , Egge , and Ma kusen (2012); Felbe may , P a , and Schme e (2011); Helpman
and I skhoki (2010); Helpman, I skhoki, and Redding (2010).
8P ominen examples a e Osling on (2002), K eickemeie and Nelson (2006), Meckl (2006) o Felbe may ,
La ch, and Lech hale (2013).
4.2. THE CLOSED ECONOMY 71
wi h di e ing composi ions o local p oduce s. In he p esen chap e , i m en y is modeled
along he line o Meli z (2003), and his ende s he cu o p oduc i i y le el independen o he
p e ailing minimum wage. None heless, despi e di e ences in he le el, minimum wages can be
binding in bo h coun ies, because he endogenous assignmen o skills o asks allows o abso b
o di e ences in local labo ma ke ins i u ions. Taking s ock, he model p esen ed in his
chap e sugges s ha di e ences in labo ma ke ins i u ions lead o di e en skill in ensi ies
and i m p oduc i i ies, bu lea e he composi ion o p oduce s una ec ed.9
The emainde o he chap e is o ganized as ollows. In Chap e 4.2, I in oduce he model
and cha ac e ize he equilib ium ou come in he closed economy. I s a wi h a benchma k
model, in which wages a e ully lexible and hen conside a model a ian wi h a binding
minimum wage. Fu he mo e, I conduc wo compa a i e s a ic expe imen s and analyze how
changes in he endowmen wi h low-skilled and high-skilled wo ke s a ec he equilib ium ou -
come in he closed economy unde he wo labo ma ke egimes. In Chap e 4.3, I p o ide
insigh s in o he impac o ade on he i m-in e nal assignmen o skills o asks when labo
ma ke s a e pe ec ly compe i i e o low-skilled wages a e se by he go e nmen . In Chap e
4.4, I discuss how labo ma ke s a e linked in open economies and analyze o wha ex en p e-
ious insigh s om my analysis depend on he assump ion o symme ic coun ies. Chap e 4.5
concludes wi h a b ie summa y o he mos impo an esul s.
4.2 The closed economy
4.2.1 Model s uc u e and i m-le el analysis
Conside an economy ha is popula ed by an exogenous mass o Llow-skilled and Hhigh-skilled
wo ke s and hos s wo sec o s o p oduc ion: a inal goods indus y ha assembles in e media es,
and an in e media es goods indus y, which employs labo o pe o ming di e en asks. The
inal good Yis homogeneous and p oduced unde pe ec compe i ion, acco ding o a cons an -
elas ici y-o -subs i u ion (CES) p oduc ion unc ion (see Ma usz, 1996):
Y=Zω∈Ω
x(ω)σ−1
σdωσ
σ−1
,(4.1)
whe e x(ω) deno es he quan i y o in e media e a ian ωused in he p oduc ion o Y, se
Ω ep esen s he mass o a ailable in e media e goods wi h Lebesgue measu e M, and σ > 1
deno es he (cons an ) elas ici y o subs i u ion be ween a ian s o he in e media e.
Choosing he inal good as num´e ai e, p o i s in he inal goods indus y a e Y−Rω∈Ωp(ω)x(ω)dω,
whe e p(ω) deno es he p ice o a ie y ω. Maximizing hese p o i s wi h espec o x(ω) gi es
in e media e goods demand10
x(ω) = Y p(ω)−σ.(4.2)
In e media e goods p oduce s compe e wi h i al i ms in a monopolis ically compe i i e
en i onmen . Each i m p oduces a unique a ie y, by combining a con inuum o asks ep e-
sen ed by he uni in e al. I ollow Acemoglu and Au o (2011) and use a simple Cobb-Douglas
9This mechanism would also be e ec i e in a K ugman (1979)- ype model wi h homogeneous p oduce s.
Howe e , in line wi h he ecen li e a u e in in e na ional economics and o con as my esul s wi h Egge ,
Egge , and Ma kusen (2012), I p e e a se ing wi h he e ogeneous i ms along he lines o Meli z (2003), whe e
i ms di e in e ms o hei (exogenous) p oduc i i y.
10Due o he choice o he num´e ai e, he CES p ice index co esponding o Y,P= [Rω∈Ωp(ω)1−σdω]1/(1−σ),
is equal o one.

72 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
unc ion o o malize he assembly o asks in he p oduc ion o in e media es:
x(ω) = φ(ω) exp Z1
0
ln x(ω, i)di,(4.3)
whe e φ(ω) is a i m’s baseline p oduc i i y ha measu es he e iciency o coo dina e and
bundle asks and x(ω, i) is he p oduc ion le el o ask iin i m ω. Tasks a e pe o med by
low-skilled and high-skilled wo ke s, l(ω, i) and h(ω, i) espec i ely, who a e employed in a
linea -homogeneous p oduc ion unc ion o he o m11
x(ω, i) = αl(i)l(ω, i) + αh(i)h(ω, i),(4.4)
whe e αl(i) and αh(i) a e he labo p oduc i i ies o he wo skill ypes, when pe o ming ask
i. The ask le el p oduc ion unc ion in (4.4) implies ha low-skilled and high-skilled wo ke s
a e subs i u es in he pe o mance o asks. Howe e , he p oduc i i y o wo ke s in pe o ming
a speci ic ask di e s, because wo ke s di e in hei abili ies, while asks di e in hei skill
equi emen s. To cap u e pe o mance (i.e. p oduc i i y) di e ences ac oss asks be ween he
wo skill g oups in a simple way, I impose he ollowing assump ion on absolu e and compa a i e
ad an ages in he pe o mance o asks:
Assump ion 1 Deno ing he labo p oduc i i y a io be ween high- and low-skilled wo ke s in
asks i by α(i)≡αh(i)/αl(i), i is assumed ha α(i)is a con inuously di e en iable, s ic ly
inc easing and con ex unc ion o i, i.e. α′(i)>0,α′′(i)≥0, wi h α(0) = 1. To implemen hese
p ope ies in a ac able way, I conside αl(i) = 1 and αh(i) = α(i) = exp[i] o all i∈[0,1].
This assump ion cap u es he idea ha asks can be o de ed acco ding o hei complexi y,
wi h a highe index e e ing o highe complexi y. A high-skilled wo ke ha is assigned o he
leas complex ask, is as p oduc i e as he low-skilled cowo ke , since he speci ic skills a e no
equi ed o pe o ming he espec i e ask. Things a e di e en in he case o a mo e complex
ask, whe e he highe skill le el causes an absolu e p oduc i i y ad an age o e low-skilled
cowo ke s. Changes in he assignmen o wo ke s o di e en skill le els o he di e en asks
a ec a i m’s p oduc i i y le el. This is a no el mechanism ha plays a c ucial ole in he
subsequen analysis and di e en ia es his model om o he ade models wi h a ask-based
p oduc ion unc ion.
In e media e goods p oduce s maximize hei p o i s acco ding o a wo-s age op imiza ion
p oblem. In a i s s ep, i ms assign skills o asks and he eby de e mine he ange o asks
pe o med by low-skilled and high-skilled wo ke s, espec i ely. In a second s ep, hey choose
ask-le el ou pu , which is equi alen o de e mining he ask-le el employmen o a gi en
skill assignmen . In he subsequen analysis, I sol e his wo-s age p oblem h ough backwa d
induc ion.
Fo a gi en assignmen o wo ke s o asks, in e media e goods p oduce s se ask-le el ou pu
x(ω, i), o maximize hei p o i s
π(ω) = p(ω)x(ω)−Z1
0
x(ω, i)ck(ω, i)di − wh,(4.5)
subjec o (4.2) and (4.3), whe e ck(ω, i) deno es he uni cos s o a i m ωpe o ming ask i
wi h he p eassigned skill ype k=l, h and measu es he ixed inpu o high-skilled labo
11Acemoglu and Au o (2011) addi ionally accoun o medium-skilled wo ke s in hei model, since hei main
mo i a ion is o analyze he obse ed inc ease o employmen in high-skilled and low-skilled occupa ions ela i e
o middle skilled occupa ions, which hey call ”job pola iza ion”. To keep he model ac able, I abs ac om
his hi d skill ype, he e.
4.2. THE CLOSED ECONOMY 73
ha is equi ed o manage he i m and o ganize he p oduc ion p ocess.12 Wi h a Cobb-
Douglas p oduc ion unc ion, his gi es he s anda d esul o a cons an cos sha e o each ask.
Fu he mo e, in he special case o each ask en e ing he p oduc ion unc ion symme ically,
cos sha es o all asks a e he same. To be mo e speci ic, subs i u ion o (4.2) in o he i s -o de
condi ion ∂π(ω)/∂x(ω, i) = 0 gi es
σ−1
σp(ω)x(ω) = x(ω, i)ck(ω, i).(4.6)
In eg a ing o e he uni in e al, shows ha p ices a e se as a cons an ma kup σ/(σ−1) o e
a iable uni cos s C(ω)/x(ω): p(ω) = [σC(ω)]/[(σ−1)x(ω)], whe e C(ω)≡R1
0x(ω, i)ck(ω, i)di
a e a i m’s o al a iable labo cos s.
Wi h hese insigh s a hand, I am now equipped o de e mine he op imal ange o asks
pe o med by a speci ic skill ype. Fo his pu pose, I ocus on he case o in e io solu ions and
assume ha bo h skill g oups a e used o he p oduc ion o in e media es.13 Since asks a e
o de ed acco ding o hei complexi y, I can hen de ine a unique h eshold ask z(ω)∈(0,1),
o which he i m is indi e en be ween hi ing low-skilled o high-skilled wo ke s, a p e ailing
ela i e wages s≡wh/wl. To pu i o mally, he uni cos s ck(ω, z(ω)) o a i m ωpe o ming
ask z(ω) a e he same i espec i e o he assigned skill ype k=l, h. This implies cl(ω, z(ω)) =
ch(ω, z(ω)) o , equi alen ly
wl=wh
αh(z(ω)) (4.7)
and es ablishes s≡wh/wl=α(z). Due o he absolu e ad an age o high-skilled wo ke s in
he pe o mance o all asks, he exis ence o an in e io solu ion, z(ω)∈(0,1), equi es a
skill p emium, i.e. s > 1. Fu he mo e, due o ela i e ad an age o high-skilled wo ke s in
pe o ming mo e complex asks, i ollows ha low-skilled wo ke s will be assigned o all asks
i < z(ω), while high-skilled wo ke s will be assigned o all asks i≥z(ω).14 No ably, since all
i ms a e p ice ake s in he labo ma ke and pay he same wh,wl, he h eshold ask z(ω) is
he same o all in e media e goods p oduce s, and hence I can w i e z(ω)≡z o all ω. Wi h
he h eshold ask a hand, I can combine Eqs. (4.3) and (4.4) o ew i e i m ou pu as
x(ω) = φ(ω)ϕ(z) exp Zz
0
ln l(ω, i)di +Z1
z
ln h(ω, i)di(4.8)
whe e ϕ(z)≡exp hRz
0ln αl(i)di +R1
zln αh(i)dii= exp[(1 −z2)/2]. Acco ding o (4.8), i m
p oduc i i y consis s o wo pa s: an exogenous baseline p oduc i i y φ(ω) and he endogenous
p oduc i i y e m ϕ(z), which a ies wi h he assignmen o skills o asks, and hus is a unc ion
o h eshold ask z. F om ϕ′(z) = −ϕ(z) ln α(z) = −zϕ(z) i ollows ha i ms can aise hei
p oduc i i y when pe o ming a la ge sha e o asks wi h high-skilled wo ke s. Howe e , i
s > 1, his comes a he cos o highe wages and is he e o e no necessa ily bene icial.
A di ec implica ion o he iden ical cos sha e (see abo e) is ha he amoun o wo ke s
o a speci ic skill ype employed o pe o ming asks is he same o all asks pe o med by
12The assump ion ha high-skilled wo ke s a e needed o manage he i m and o ganize he p oduc ion p ocess
is in line wi h he li e a u e ocusing on he in e nal o ganiza ion o i ms in economies wi h he e ogeneous wo ke s
(see, o ins ance, Ma in and Ve die , 2008b, 2012).
13Below, I will discuss a pa ame e cons ain ha needs o be ul illed in o de o such an in e io solu ion
o ma e ialize.
14Fo con enience, i is assumed ha i ms hi e high-skilled wo ke s o pe o ming ask z(ω).
74 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
wo ke s o his skill ype. This can be seen om subs i u ion o (4.4) and ck(ω, i) = wk/αk(i),
wi h k=li i < z and k=hi i≥z, in o (4.6), which gi es wll(ω, i) = wll(ω) o all i < z
and whh(ω, i) = whh(ω) o all i≥z. Simila ly, i ollows om (4.4), (4.6) and (4.7) ha
wll(ω) = whh(ω). This implies
s=l(ω)
h(ω)=1−z
z
L(ω)
H(ω),(4.9)
whe e L(ω) = Rz
0l(ω, i)di =zl(ω) and H(ω) = R1
zh(ω, i)di = (1 −z)h(ω) a e i m ω’s o al low-
skilled and high-skilled a iable labo inpu , espec i ely. Acco dingly, a i m’s skill in ensi y is
gi en by H(ω)/L(ω) = (1 −z)/[zα(z)] and hus dec easing in z. Pu ing oge he , I can hus
w i e a i m’s o al a iable labo cos s as C(ω) = [wL(ω)/H(ω) + wh]H(ω), while his i m’s
ou pu is gi en by x(ω) = φ(ω)ϕ(z){[(1 −z)/z]L(ω)/H(ω)}zh(ω). Subs i u ion o (4.9), hen
gi es me o he a iable uni cos o his i m: C(ω)/x(ω) = wz
lw1−z
h/[φ(ω)ϕ(z)], which is equal
o he ma ginal cos o he espec i e p oduce . Cons an ma kup p icing he e o e implies
p(ω) = σ
σ−1
wz
lw1−z
h
φ(ω)ϕ(z).(4.10)
No ing ha e enues o i m ωa e gi en by (ω) = p(ω)x(ω) and aking in o accoun ha wl,
whand ϕ(z) a e he same o all p oduce s, i ollows om (4.2) and (4.10) ha he e enue
a io o wo i ms 1 and 2 wi h p oduc i i y le els φ(ω1), φ(ω2) is gi en by (ω1)/ (ω2) =
[φ(ω1)/φ(ω2)]σ−1. Hence, ela i e i m pe o mance is ully cha ac e ized by he baseline p o-
duc i i y a io. I can hus skip i m index ω om now on, and ins ead e e o i ms by hei
p oduc i i y le els.
Rega ding i m en y, I ollow he li e a u e on he e ogeneous i ms along he lines o Meli z
(2003) – wi h he me e di e ence ha I conside a s a ic model a ian along he lines o
Helpman and I skhoki (2010) and Helpman, I skhoki, and Redding (2010) – and assume ha
he baseline p oduc i i y is d awn by i ms in a lo e y om he common Pa e o dis ibu ion,
G(φ) = 1 −φ−k.15 The pa icipa ion ee o he lo e y is ewhand his ee gi es a i m a
single p oduc i i y d aw. Ha ing e ealed hei p oduc i i y, p oduce s decide upon se ing up
a plan and s a ing p oduc ion by making he addi ional in es men o uni s o high-skilled
labo (see abo e). Wi h e enues (and hus p o i s) inc easing in baseline p oduc i i y, I can
iden i y a cu o p oduc i i y le el, φ∗, which sepa a es ac i e i ms wi h φ≥φ∗ om inac i e
ones wi h φ < φ∗. The p o i s om p oduc ion o a i m wi h cu o p oduc i i y φ∗a e equal
o ze o by de ini ion and I can hus cha ac e ize he ma ginal i m wi h cu o p oduc i i y
le el φ∗by means o a ze o p o i condi ion π(φ∗) = 0. This ze o p o i condi ion is usually
e e ed o by he e m ze o-cu o p o i condi ion. In iew o a Pa e o dis ibu ion o baseline
p oduc i i y le els, he e is a p opo ional link be ween e enues o he ma ginal p oduce and
a e age e enues o all ac i e p oduce s. As ou lined in he appendix, his link can be used o
es ablish he modi ied ze o-cu o -p o i condi ion
¯π= wh(σ−1)
k−σ+ 1 ,(4.11)
whe e k > σ −1 is equi ed o a posi i e, ini e alue o ¯π. In equilib ium he cos s o en e ing
he p oduc i i y lo e y, ewh, mus be equal o he expec ed p o i o doing so, ¯π(1 −G(φ∗)).
15Co cos, Del Ga o, Mion, and O a iano (2012) p o ide e idence o he Pa e o dis ibu ion, using i m le el
da a o Eu opean coun ies.
4.2. THE CLOSED ECONOMY 75
This es ablishes he ee en y condi ion
¯π= ewh(φ∗)k.(4.12)
Combining (4.11) and (4.12), I can explici ly sol e o cu o p oduc i i y le el φ∗:
φ∗=
e
σ−1
k−σ+ 11/k
.(4.13)
Eqs. (4.11) and (4.13) a e he key i m-le el a iables, which a e also in o ma i e o economy-
wide a iables. In pa icula , wi h φ∗a hand, I can calcula e he p oduc i i y a e age ˜
φ≡
[k/(k−σ+ 1)]1/(σ−1)φ∗,16 which is use ul because key agg ega e a iables in his model o
he e ogeneous i ms a e he same as hey would be in an o he wise iden ical model o homo-
geneous i ms wi h p oduc i i y ˜
φ:R=M (˜
φ), Π = Mπ(˜
φ), and, Y=Mσ/(σ−1)x(˜
φ) and
P=M1/(1−σ)p(˜
φ). Wi h hese insigh s a hand, I can now u n o s udy he gene al equilib-
ium ou come in my model.
4.2.2 Gene al equilib ium wi h pe ec labo ma ke s
To sol e o he gene al equilib ium ou come in he closed economy, I ha e o speci y how
wages a e de e mined. I s a wi h a benchma k scena io, in which wages o low-skilled and
high-skilled wo ke s a e lexible and de e mined in pe ec ly compe i i e ma ke s. Using he
adding up condi ion, which simply says ha adding up employmen o a gi en skill ype o e
all p oduce s mus gi e o al employmen o he espec i e skill g oup, ma ke clea ing o
low-skilled wo ke s es ablishes17:
L=MZ∞
φ∗
L(φ)dG(φ)
1−G(φ∗)=zMs k(σ−1)
k−σ+ 1 ,(4.14)
whe eas o high-skilled wo ke s, I ob ain
H=MZ∞
φ∗
H(φ)dG(φ)
1−G(φ∗)+M +Me e=M k
k−σ+ 1[(1 −z)(σ−1) + 1].(4.15)
Fu he mo e, he e exis s a hi d condi ion, which I ha e o conside o cha ac e izing he
gene al equilib ium ou come in he closed economy: I ha e o make su e ha p o i -maximizing
p ice-se ing is in acco dance wi h i m en y. Following Egge , Egge , and Ma kusen (2012)
I call he espec i e condi ion p o i maximiza ion condi ion and combine he solu ion o he
CES p ice index, P=M1/(1−σ)p(˜
φ), wi h he choice o num´e ai e, P= 1, and he p ice ma kup
condi ion in (4.10), applied o he i m wi h p oduc i i y ˜
φ. Using (4.13) and he de ini ion o
˜
φ, I can sol e o
M=wz
lw1−z
hζ
ϕ(z)σ−1
,(4.16)
16As discussed in Meli z (2003), he a e age p oduc i i y ˜
φequals he weigh ed ha monic mean o he φ’s o
ac i e p oduce s, wi h ela i e ou pu le els x(φ)/x(˜
φ) se ing as weigh s.
17In iew o cons an ma kup p icing, labo cos s a e a cons an sha e (σ−1)/σ o a i m’s e enues: wlL(φ)+
whH(φ) = (φ)(σ−1)/σ. Using L(φ) = zl(φ), H(φ) = (1 −z)h(φ) and accoun ing o wll(φ) = whh(φ), u he
implies L(φ) = z[(σ−1)/σ] (φ)/wland H(φ) = (1 −z)[(σ−1)/σ] (φ)/wh, espec i ely. Finally, combining
wh=α(z)wland MR∞
φ∗ (φ)dG(φ)/[1 −G(φ∗)] = Mσk wh/(k−σ+ 1) om he appendix and Me=M(φ∗)k,
allows me o compu e (4.14) and (4.15).
82 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
his issue, I can subs i u e (˜
φ) = σk wh/(k−σ+ 1) oge he wi h (4.7) and he wo labo
ma ke clea ing condi ions (4.14) and (4.15) in o W= (Lwl+Hwh)/(L+H) = M (˜
φ)/(L+H)
o calcula e
W=σwh
z(σ−1)(exp[z]−1) + σ.(4.28)
F om inspec ion o (4.28), he inc ease in wh igge ed by he highe supply o low-skilled wo ke s
s imula es pe -capi a income, while he implied inc ease in z educes wel a e due o he nega i e
p oduc i i y e ec , as all p oduce s pe o m less asks wi h high-skilled wo ke s. Accoun ing o
(4.26) I can u he mo e calcula e
W= exp 1
2(1 + z2)[(1 −z)(σ−1) + 1]−1
σ−1
zexp[z](σ−1) + (1 −z)(σ−1) + 1 ˆ
ζ, (4.29)
whe e ˆ
ζ≡[H(k−σ+ 1)/ k]1/(σ−1)σζ−1and
dW
dz =W(exp[z]−1)(z2−z−1)(σ−1) + z
z(σ−1)(exp[z]−1) + σ+1
(1 −z)(σ−1) + 1.(4.30)
Eq. (4.29) es ablishes a non- i ial ela ionship be ween zand W, wi h he sign o (4.30)
depending on σand he ini ial alue o z. Clea ly, i zis close o ze o, dW/dz > 0 holds o
all σ, while hings a e di e en o z > 0. In pa icula o la ge σ- alues i canno be uled
ou ha dW/dz < 0 o su icien la ge z. To see his, one can e alua e (4.30) o ins ance a
σ= 2 and σ= 8, wi h co esponding ˆz- alues o ˆz|σ=2 = 0.382 and ˆz|σ=8 = 0.69, espec i ely.
This gi es dW/dz|σ=2
z=0 = 0.5, dW/dz|σ=2
z=0.3= 0.53, dW/dz|σ=2
z=ˆz= 0.53 and dW/dz|σ=8
z=0 = 0.125,
dW/dz|σ=8
z=0.3=−0.14 and dW/dz|σ=8
z=ˆz=−0.29.
Le us now u n o he minimum wage economy, o which he e ec o changes in La e
depic ed by Figu e 4.4. Since in his case a highe Ldoes nei he a ec he posi ion o locus
(4.15) no he posi ion o locus (4.16′), i lea es he mass o p oduce s Mas well as he h eshold
ask zuna ec ed. Fu he mo e, since a change in Ldoes no a ec he posi ion o locus (4.7)
in he lowe igh panel o Figu e 4.4 ei he , he skill p emium also emains una ec ed by an
expansion o low-skilled labo supply. O cou se, an inc ease in Lshi s locus (4.17) ou wa ds
in he lowe igh panel o Figu e 4.4 and hus igge s a clockwise o a ion o locus (4.25) in
he lowe le panel o he igu e. This implies an inc ease in unemploymen a e u. Simila
o B eche (1974), labo supply o unskilled wo ke s in he minimum wage economy is no
a binding cons ain , and hence an inc ease in he espec i e supply is ully abso bed by a
pa i passu inc ease in unemploymen . As a consequence, an inc ease in labo supply Llea es
high-skilled wo ke s una ec ed and lowe s pe -capi a income o low-skilled wo ke s, which is
ins umen al o a decline in wel a e.
P oposi ion 9 Wi h compe i i e labo ma ke s, an inc ease in L aises he ange o asks pe -
o med by low-skilled wo ke s. This igge s a decline in he p oduc i i y o in e media e goods
p oduce s and leads o addi ional i m en y. The highe supply o L educes pe -capi a income
o low-skilled wo ke s and inc eases wel a e o high-skilled wo ke s while o e all wel a e e ec s
a e ambiguous. Wi h a binding minimum wage, an inc ease in he supply o low-skilled wo ke s
is ully abso bed by a pa i passu inc ease in unemploymen . This lowe s wel a e and lea es all
o he a iables una ec ed.
P oo . Analysis in he ex
The implica ions o an inc ease in he supply o high-skilled wo ke s when wages a e ully lexible

4.2. THE CLOSED ECONOMY 83
z
M
s
(4.16′)
(4.15)
(4.7)
(4.17)
zc
Mc
sc
L↑
L↑
sc
L↑
Mc
L↑
zc
L↑
H↑
H↑
H↑
sc
H↑
Mc
H↑
zc
H↑
Figu e 4.3: Equilib ium wi h ully lexible wages in he closed economy
a e indica ed by he dashed lines in Figu e 4.3. A highe Hshi s locus (4.17) inwa ds and he e-
o e lowe s he h eshold ask (and he skill p emium). As a consequence, i ms become mo e
p oduc i e, because high-skilled wo ke s a e now used o a b oade ange o asks. Howe e ,
in an economy wi h compe i i e labo ma ke s he addi ional supply o high-skilled wo ke s is
only pa ly abso bed by his i m-in e nal adjus men . Since low-skilled wo ke s a e eplaced by
high-skilled ones, addi ional i ms mus en e o es o e ma ke clea ing o low-skilled wo ke s,
acco ding o (4.14). This is cap u ed by an upwa d shi o locus (4.15) in he uppe panel o
Figu e 4.3. And he upwa d shi o (4.15) pai ed wi h he decline in zcimplies ha (4.16′) mus
shi le wa ds, which equi es an inc ease in he low-skilled wage wc
l. In con as , he impac
o an inc ease in Hon he eal wage o high-skilled wo ke s is less clea cu . On he one hand,
an inc ease in he supply o a skill ype ende s his ac o less sca e and hus lowe s i s e u n
ce e is pa ibus. On he o he hand, he inc ease in he skilled labo supply leads o addi ional
i m en y and hus s imula es demand o high-skilled wo ke s as a iable p oduc ion inpu as
well as demand o high-skilled wo ke s as a ixed inpu o manage he i m and o ganize he
p oduc ion p ocess. To shed u he ligh on his issue, I can combine (4.14) and (4.16′) and
84 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
accoun o wh=wlα(z) om (4.7) o compu e
wh=L(k−σ+ 1)
k(σ−1) 1
σ−1
ζ−1exp 1 + z2
2 1
zexp[z]1
σ−1
.(4.31)
Di e en ia ing (4.31) wi h espec o zgi es
dwh
dz =whz−1 + z
z
1
σ−1(4.32)
which is nega i e as long as z < (1 + √4σ−3)/2(σ−1) ≡˜z. No ing om he de ini ion o
ˆzin (4.22), ha ˜z > ˆzas long as σ≤3 + √5, I can u he mo e conclude ha dwh/dz < 0
and hus dwh/dH > 0 holds in he ele an pa ame e domain i he elas ici y o subs i u ion
is low. Howe e , i σ > 3 + √5, I canno ule ou ha dwh/dH < 0 o la ge ini ial alues o
z. Finally, as a la ge supply o high-skilled wo ke s aises he mass o ac i e i ms, o al labo
income inc eases. To discuss he impac on a coun y’s wel a e le el, I can in e om (4.28), ha
gi en he inc ease in whand he educ ion in z, which leads o a posi i e p oduc i i y e ec , a
coun y’s pe -capi a income is inc easing in i s endowmen wi h high-skilled wo ke s.24
Again, an inc ease in he supply o high-skilled wo ke s exe s a di e en impac on he
gene al equilib ium a iables o in e es , when he wage a e o low-skilled wo ke s is ixed by
a binding minimum wage. In a minimum wage economy, an inc ease in Hshi s locus (4.15)
upwa ds, as indica ed by he do ed cu e in Figu e 4.4. Hence, simila o he benchma k
scena io wi h compe i i e labo ma ke s, he addi ional supply o high-skilled wo ke s allows o
addi ional i m en y, so ha Minc eases. Howe e , wi h low-skilled labo supply being no a
binding cons ain in he minimum wage economy, he addi ional demand o low-skilled labo a
he ex ensi e ma gin – igge ed by he addi ional i m en y – does no inc ease he ac o e u n
o low-skilled wo ke s implying ha in e media e goods p oduce s ha e no incen i e o educe
he ange o asks pe o med by low-skilled wo ke s. Mo eo e , since he new in e sec ion poin
be ween locus (4.15) and locus (4.16′) mo es no h-eas in Figu e 4.4, he e is a magni ica ion
e ec in he sense o dM/dH > 0, so ha he ange o asks pe o med by low-skilled wo ke s
inc eases. Hence, wi h a binding eal minimum wage an inc ease in H educes he ange o
asks pe o med by high-skilled wo ke s and, as can be seen in he lowe igh panel o Figu e
4.4, i aises he skill p emium. Mo eo e , he inc ease in zimplies a all in p oduc i i y o
in e media e goods p oduce s. The implica ions o he wage a e o high-skilled wo ke s can
be seen when ew i ing Eq. (4.7) as wh=wexp[z]. Since z ises in H, a highe supply o high-
skilled wo ke s inc eases wh. Hence, high-skilled wo ke s gain in ela i e25 and absolu e e ms,
which is in con as o he benchma k si ua ion wi h compe i i e wages. Howe e , also low-
skilled wo ke s gain om he addi ional supply o H, due o addi ional employmen o his skill
ype. This can be seen om Figu e 4.4, when no ing ha a highe supply o high-skilled wo ke s
shi s locus (4.17) inwa ds, and he e o e o a es locus (4.25) coun e -clockwise in he lowe le
panel o ha igu e. As a consequence, a highe skill p emium mus he e o e be associa ed wi h
lowe unemploymen o low-skilled wo ke s, implying a highe pe -capi a income (1−u)wo his
skill g oup. This is in ui i e as he demand o low-skilled wo ke s is s imula ed by a inc ease in
zand M. Finally, he inc ease in he mass o in e media e p oduce s also leads o highe o al
labo income and, since bo h skill g oups bene i , o highe pe -capi a income and hus wel a e.
24As shown in he appendix, he posi i e impac is also p esen i σis la ge and dwh/dH < 0 ma e ializes.
25This can bee seen om (4.27). Accoun ing o dz/dH > 0 and dM/dH > 0, he ela i e pe -capi a income
o high-skilled wo ke s wh/[(1 −u)w] clea ly inc eases.
4.2. THE CLOSED ECONOMY 85
z
M
s
u
(4.16′)
(4.15)
(4.7)
(4.17)
(4.25) z
M=ML↑
s=sL↑
u
L↑
L↑
uL↑
H↑
H↑
H↑
uH↑
sH↑
MH↑
zH↑
Figu e 4.4: Endowmen changes wi h a binding minimum wage
P oposi ion 10 Wi h ully lexible wages, an inc ease in he supply o high-skilled wo ke s
educes he ange asks pe o med by low-skilled wo ke s, he eby inc easing he p oduc i i y o
ac i e p oduce s and he mass o ac i e i ms. Low-skilled wo ke s ecei e a highe income and
he skill p emium o high-skilled wo ke s is educed. The impac on high-skilled wages a e
ambiguous and depend on he elas ici y o subs i u ion be ween a ian s o he in e media e.
Only i σ≤3+ √5wages will inc ease, while o σ > 3 + √5 he impac on wages is ambiguous.
I espec i e o he change in wh, wel a e is posi i ely a ec ed by he expansion o H. Wi h a
binding minimum wage, an inc ease in H aises he mass o i ms and he h eshold ask, he eby
educing he p oduc i i y o ac i e p oduce s. High-skilled wo ke s gain in absolu e and ela i e
e ms, and he unemploymen a e o low-skilled wo ke s goes down, implying ha wel a e mus
inc ease.
P oo . Analysis in he ex .
This comple es he discussion o he closed economy.
86 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
4.3 The open economy
4.3.1 Basic s uc u e
I is he pu pose o his chap e o shed ligh on he assignmen o skills o asks and a i m’s
p oduc ion p ocess i he coun y unde conside a ion opens up o ade. I he eby discuss he
di e en ial consequences o ade be ween wo coun ies indexed by j= 1,2, whose economies
a e cha ac e ized as in he p e ious chap e , when labo ma ke s a e pe ec ly compe i i e o
when he e is a binding minimum wage o low-skilled wo ke s. To keep he analysis ac able,
I he eby abs ac om any ade impedimen s and assume ha all i ms expo . This simpli-
ica ion seems o be jus i ied, because in my model he e enue a io o any wo i ms and hus
he expo decision is ully cha ac e ized by baseline p oduc i i y le els, and hence my model
is no equipped o shed new ligh on he expo ing decision o i ms (see, o ins ance, Meli z,
2003; Be na d, Redding, and Scho , 2007; Meli z and O a iano, 2008). The e o e, I p e e he
mo e pa simonious s uc u e wi hou sel -selec ion o i ms in o expo ing in o de o ocus on
hose aspec s o he model ha a e new in he li e a u e.
When he coun y opens up o ade, in e media e goods p oduce s can aise hei p o i s by
selling hei a ie y o he o eign ma ke . Abs ac ing om any ade impedimen s, Yand P
a e iden ical o all i ms i espec i e o hei home coun y. Fu he mo e, wi hou selec ion in o
expo ing, ade does no al e he i m en y mechanism, so ha (4.11)-(4.13) s ill hold a e
a coun y’s mo emen om au a ky o ade. As discussed in he p e ious chap e , he cu o
p oduc i i y is independen o he labo ma ke egime, hence φ∗
1=φ∗
2≡φ∗and ˜
φ1=˜
φ2≡˜
φ∗
hold in he benchma k scena io o compe i i e labo ma ke s as well as he minimum wage
economy. Cons an ma kup p icing in bo h economies implies πj(φ∗) = j(φ∗)/σ − whj = 0,
and he e o e 1(φ∗)/σ = wh1and 2(φ∗)/σ = wh2. Accoun ing o (4.2), (4.7) which is he
same as in he closed economy, (4.10) and he de ini ion o β(z) I can compu e
wl1
wl2
=α(z2)
α(z1)1
σβ(z1)
β(z2)σ−1
σ
= exp z2−z1
22−σ−1
σ(z1+z2),(4.33)
which de e mines z1 ela i e o z2in he open economy and implies z1< z2i wl1> wl2. To
compa e p ices o he ma ginal i ms in he wo coun ies, i s subs i u e (4.7) in o (4.10), which
en ails pj(φ∗) = σwlj/[(σ−1)φ∗β(zj)]. As he cu o p oduc i i y is he same in bo h economies,
I ge p1(φ∗)/p2(φ∗) = wl1β(z2)/[wl2β(z1)]. Accoun ing o (4.33) and he de ini ion o β(z) hen
gi es
p1(φ∗)
p2(φ∗)=α(z2)β(z2)
α(z1)β(z1)1
σ
= exp z2
2−z2
1
2σ.(4.34)
To analyze he impac o in e media es ade on he gene al equilib ium a iables o in e es ,
no e i s ha bo h adding up condi ions o low-skilled and high-skilled wo ke s a e he same
as in he closed economy. Howe e , as he inal good is now assembled wi h in e media e
a ie ies om bo h coun ies, he co esponding p ice index and he e o e (4.16′) need o be
adjus ed. In he open economy he mass o a ailable in e media e a ie ies has changed o
M =M1+M2, implying ha he p ice index in he open economy is gi en by P= [M1p1(˜
φ)1−σ+
M2p2(˜
φ)1−σ]1/(1−σ). Accoun ing o (4.7) and (4.10) oge he wi h P= 1 his can be w i en
as (see he appendix)
Mj=wljζ
β(zj)σ−1"1 + M−j
Mjpj(φ∗)
p−j(φ∗)σ−1#−1
.(4.35)
4.3. THE OPEN ECONOMY 87
This equa ion s ill es ablishes a posi i e ela ionship be ween he mass o p oduce s and he
h eshold ask in he home coun y j, o gi en alues o zand Min he o eign coun y −j.
Wi h hese insigh s, I am now equipped o s udy he impac o ade on he a iables o in e es .
I he eby s a wi h a si ua ion, in which bo h coun ies a e ully symme ic and pos pone a
discussion o coun y asymme ies o he ex ensions in Chap e 4.4. In Chap e 4.3.2, I he eby
analyze he implica ions o ade when labo ma ke s a e pe ec ly compe i i e, whe eas in
Chap e 4.3.3, I shed ligh on he consequences o ade in a minimum wage economy.
4.3.2 T ade wi h pe ec labo ma ke s
Wi h ully lexible wages, he eigh endogenous a iables in he open economy, wlj,whj,zj
and Mj, o j= 1,2 a e de e mined by condi ion (4.7) and he labo ma ke clea ing condi ions
(4.14) and (4.15) – applied o he wo economies – Eq. (4.33) and inally he p o i maximiza ion
condi ion in he open economy, Eq. (4.35), applied o coun y j.26 To illus a e he equilib ium
in he open economy, I can use he same g aphical ool, as in he p e ious chap e . I wages a e
se in pe ec ly compe i i e ma ke s, he equilib ium h eshold ask and he skill p emium a e
join ly de e mined by (4.7) and (4.17), which a e plo ed in he lowe panel in Figu e 4.5. As
bo h loci emain una ec ed by an opening up o ade, he skill p emium and he h eshold ask
a e he same as in he closed economy, i.e. sc
a=sc
jand zc
a=zc
j, whe e index a e e s o au a ky
a iables. Mo eo e , since he labo ma ke clea ing condi ion o high-skilled wo ke s and hus
locus (4.15) emains una ec ed as well, also he mass o i ms in coun y js ays cons an , i.e.
Mc
a=Mc
j. These indings indica e, ha he in e sec ion poin be ween loci (4.15) and (4.35)
in he uppe panel o Figu e 4.5 is he same as in he closed economy equilib ium. Acco ding
o (4.33) and (4.34), p ices o he cu o i m in each ma ke a e iden ical when bo h coun ies
a e ully symme ic, implying ha (4.35) eads Mj= [wljζ/β(zj)]σ−1(1/2). Hence, compa ed
o i s closed economy coun e pa in (4.16′), he p o i maximiza ion condi ion (4.35) is shi ed
igh wa ds o any gi en wage a e o low-skilled wo ke s wa
lj. Opening up o ade aises
he mass o a ailable in e media e a ie ies o M =M1+M2. This inc eases coun y-speci ic
ou pu Yand s imula es demand o each i m, acco ding o (4.2). The e o e, agg ega e labo
demand o each skill ype is s imula ed. Wi h ully lexible wages, wlmus inc ease, o b ing
he economy back o zc
j=zc
aand Mc
j=Mc
a. Acco ding o wh=wlα(z) he wage a e o high-
skilled wo ke s inc eases by he same ex end, so ha he skill p emium emains a he au a ky
le el. Simila o K ugman (1979), ade be ween wo ully symme ic coun ies he e o e leads o
a posi i e income and hus wel a e e ec , while lea ing all o he a iables o in e es una ec ed.
These indings a e summa ized in he ollowing p oposi ion.
P oposi ion 11 I wages a e ully lexible, a coun y’s opening up o ade wi h a symme ic
pa ne coun y has no impac on he skill p emium, he i m in e nal assignmen o skills o
asks and he mass o ac i e i ms. Howe e , ade inc eases he eal wage o bo h skill ypes
and hus wel a e.
P oo . Analysis in he ex .
The indings om P oposi ion 11 do no hinge on he assump ion ha bo h coun ies a e
symme ic in hei ela i e endowmen s wi h high-skilled and low-skilled wo ke s. This can be
easily in e ed om he discussion abo e. As any change in he supply o Lo Hin Fo eign,
lea es he posi ion o loci (4.7), (4.15) and (4.17) in Home una ec ed, i does no a ec zj,sj
and Mj. Thus, when wages a e ully lexible, ade be ween wo coun ies ha di e in hei
26No e ha (4.35) can only be applied o one coun y. Applying i o he o he coun y simply con i ms ha
P1=P2= 1.

88 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
z
M
s
(4.16′)wa
lj =(4.35)wlj
(4.15)
(4.7)
(4.17)
zc
a=zj
Mc
a=Mj
sc
a=sj
(4.35)wa
lj
Figu e 4.5: T ade wi h ully lexible wages
ela i e endowmen s s ill exe s only a posi i e income and wel a e e ec , bu does no change
he o he a iables o in e es . Mo eo e , he s eng h o hese e ec s depends on he s imulus
in labo demand o he wo skill ypes. The highe he mass o in e media e p oduce s in
he o eign coun y, he la ge is he posi i e demand shock by opening up o ade om a
domes ic coun y’s pe spec i e. As M−jis inc easing in L−jand H−j, wel a e e ec s a Home
a e he e o e inc easing in he size o he o eign ac o ma ke s.
4.3.3 T ade wi h a minimum wage o low-skilled wo ke s
In his chap e , I again s udy ade be ween wo ully symme ic coun ies, wi h he me e
di e ence, ha go e nmen s in each coun y now se a binding minimum wage, w1=w2. To
de e mine he eigh endogenous a iables sj,zj,Mjand uj, o j= 1,2 I can make use o
(4.7), (4.15) and (4.24) – applied o bo h economies – (4.33) and (4.35). As discussed in he
closed economy, he labo ma ke clea ing condi ion o high-skilled wo ke s and he p o i
maximiza ion condi ion now join ly de e mine he mass o i ms and he h eshold ask. Wi h
pe ec symme y be ween he wo economies, (4.35) eads Mj= [wjζ/β(zj)]σ−1(1/2) and is
shi ed igh wa ds ela i e o i s closed economy coun e pa in Figu e 4.6, implying ha M
and za e inc eased compa ed o he au a ky scena io. Since all o he hings equal, inal goods
4.3. THE OPEN ECONOMY 89
p oduce s ha e access o mo e di e en ia ed in e media e goods, inal ou pu inc eases due o
a s anda d di ision o labo e ec . This s imula es demand o in e media e goods, acco ding
o (4.2), and he e o e agg ega e labo demand o each skill ype. While he ac o p ice o
low-skilled wo ke s is ixed and emains una ec ed, he wage a e o high-skilled wo ke s will
inc ease.27 Thus, he ela i e ac o cos s ha e changed in a o o low-skilled wo ke s and i ms
espond o he cos inc ease by aising he h eshold ask o z > za. A lowe skill in ensi y
implies ha mo e high-skilled wo ke s a e le o en e ing he lo e y and o manage he i m
and o ganize he p oduc ion p ocess, so ha he mass o local in e media e goods p oduce s
inc eases in bo h coun ies ela i e o he closed economy. The highe z u he mo e implies an
inc ease in he skill p emium, as can be seen in he lowe igh panel o Figu e 4.6. Finally, he
adjus men in zand Mcon ibu e o an inc ease in low-skilled labo employmen and a decline
in unemploymen a e uas depic ed in he lowe le panel o Figu e 4.6.28 F om inspec ion
o Eq. (4.27) he e a e coun e ac ing e ec s on he ela i e pe -capi a income o high-skilled
wo ke s. Howe e , sol ing (4.15) o Mand subs i u ing he espec i e exp ession in o (4.27), I
can compu e
wh
(1 −u)w=L k[(1 −z)(σ−1) + 1]
Hz(k−σ+ 1) (4.36)
which, acco ding o z < za, implies ha ade unambiguously inc eases he ela i e pe -capi a
income o high-skilled wo ke s. Finally, he inc ease in he wage a e o high-skilled wo ke s
and he educ ion in he unemploymen a e igge s an inc ease in wel a e. These indings a e
summa ized in he ollowing p oposi ion:
P oposi ion 12 Wi h a binding minimum wage o low-skilled wo ke s, a coun y’s opening up
o ade wi h a symme ic pa ne coun y educes he unemploymen a e o low-skilled wo ke s
and inc eases he eal wage, he skill p emium and he ela i e pe -capi a income o high-skilled
wo ke s. Wel a e is unambiguously highe in he open economy han in he closed economy and
all ac i e i ms p oduce a b oade ange o asks wi h low-skilled wo ke s, which educes obse ed
labo p oduc i i y.
P oo . Analysis in he ex .
The esul s in P oposi ion 12 demand u he discussion. Fi s , he e is a c ucial di e ence
o he indings in he li e a u e on he e ogeneous i ms. Usually, he claim in he li e a u e is
ha ade libe aliza ion has a posi i e impac on economy-wide labo p oduc i i y by eloca ing
p oduc i e ac o s owa ds high-p oduc i e i ms, which ha e excess o expo ma ke s and hus
bene i disp opo iona ely om ade libe aliza ion (see Meli z, 2003). The eby, he i m-le el
p oduc i i y s ays cons an , bu selec ion o mo e p oduc i e i ms inc eases he economy-wide
p oduc i i y. In my model, his channel is closed, as ade is cos less and all i ms pa icipa e in
expo ing. This lea es he ela i e pe o mance o any wo i ms una ec ed, and hence he e is no
eloca ion o p oduc i e ac o s owa ds high-p oduc i e i ms. He e, p oduc i i y e ec s a ise
a he i m-le el due o adjus men s in he assignmen o wo ke s o asks. The eby, i ollows
om P oposi ion 11 and 12 ha he exis ence o labo ma ke impe ec ions a e ins umen al
o he impac o ade on i m p oduc i i y. Wi h di e ences in he wage se ing ins i u ions
among low-skilled and high-skilled wo ke s, a highe labo demand in he open economy changes
27To see his, emembe om (4.26), ha dwh/dz > 0.
28The educ ion in he unemploymen a e is also p esen in he Egge , Egge , and Ma kusen (2012) amewo k,
whe e p oduc ion consis s o a single ask pe o med by one ype o wo ke s. Simila o his chap e , he posi i e
impac is a consequence o ex e nal scale economies in he p oduc ion o he inal good.
90 CHAPTER 4. TRADE AND THE ASSIGNMENT OF SKILLS TO TASKS
z
M
s
u
(4.16′)w1
(4.35)
(4.15)
(4.7)
(4.17)
(4.25)
sc
1
za
1
Ma
1
sa
1
ua
1z1
M1
s1
u1
Figu e 4.6: T ade be ween wo ully symme ic minimum wage economies
he ela i e ac o e u n and he e o e leads o adjus men s in he assignmen o skills o asks
wi h consequences o a i m’s labo p oduc i i y.29
4.4 Ex ensions
So a I ha e es ic ed he analysis o he compa ison o open and closed economy equilib ia.
The aim o his Chap e is o shed ligh on how labo ma ke s a e linked in he open economy, i.e.
how a ia ions in na ional labo ma ke ins i u ions and endowmen s spill o e o he pa ne
coun y. I he eby ocus on ade be ween wo minimum wage economies as discussed in he
p e ious chap e . S a ing om a scena io wi h ully symme ic coun ies, I discuss how (i) an
inc ease in Fo eign’s minimum wage o low-skilled wo ke s and (ii) mig a ion o high-skilled
wo ke s in o he o eign economy, spill o e o he domes ic coun y.30
29I do no discuss endowmen asymme ies he e, as hey a e in he con ex o open minimum wage economies
a he agenda o Chap e 4.4.2.
30F om he discussion in he closed economy, I know ha adjus men s in zand Ma e only p esen i he e is a
change in he supply o high-skilled wo ke s, while any change in Lis ully abso bed in he unemploymen a e.
4.4. EXTENSIONS 91
4.4.1 Minimum wage a ia ions in he open economy
I s a wi h a si ua ion, in which he o eign coun y j= 2 adjus s i s labo ma ke ins i u ions
by inc easing he minimum wage, such ha w1< w2holds.31 While he implica ions o coun y
j= 2 a e simila o hese o he closed economy, he inc ease in w2implies p1(φ∗)< p2(φ∗)
acco ding o (4.34) and a lowe mass o i ms in coun y j= 2. This educ ion in he mass o
in e media e goods p oduce s now exe s an impac on he domes ic coun y j= 1 acco ding
o (4.35). A smalle mass o p oduce s in coun y j= 2, shi s locus (4.35) o coun y j= 1
le wa ds in Figu e 4.6, whe eas i lea es loci (4.7), (4.15) and (4.17) and hus (4.25) una ec ed.
As a consequence, he ange o asks pe o med by low-skilled wo ke s in coun y j= 1 mus
all.32 While he minimum wage o low-skilled wo ke s is ixed in coun y j= 1, he ac o
e u n o high-skilled wo ke s alls acco ding o wh=wα(z). Fu he mo e, since i ms b oaden
he ange o asks pe o med by high-skilled wo ke s, all ac i e i ms become mo e p oduc i e.
Howe e , inc easing a iable labo demand o high-skilled wo ke s in he p oduc ion p ocess
lea es less esou ces as a ixed inpu o i m en y. As a consequence, he mass o in e media e
goods p oduce s mus all in coun y j= 1. The adjus men s in M1and z1imply a all in
he labo demand o low-skilled wo ke s and he unemploymen a e inc eases. Looking a he
skill p emium, high-skilled wo ke s lose, bu , acco ding o (4.36), he educ ion in zinc eases
ela i e pe -capi a income o high-skilled wo ke s, due o an expansion o L-unemploymen .
The nega i e impac on he wage o high-skilled wo ke s and he inc ease in he unemploymen
a e u he mo e imply a educ ion in wel a e. These indings a e summa ized in he ollowing
p oposi ion.
P oposi ion 13 S a ing om an open economy equilib ium wi h minimum wages, an inc ease
in he minimum wage in one coun y educes he mass o i ms and he ange o asks pe o med
by low-skilled wo ke s in he pa ne coun y, while i inc eases he p oduc i i y o ac i e p oduc-
e s he e. Low-skilled wo ke s ace a highe unemploymen a e while high-skilled wo ke s ace
a educ ion in he eal wage. The ela i e pe -capi a income o high-skilled wo ke s inc eases,
whe eas wel a e is educed in he pa ne coun y.
P oo . Analysis in he ex and he o mal p oo in he appendix.
In e es ingly, an implica ion o (4.33) and (4.34) is ha minimum wages emain binding
a e opening up o ade and unemploymen is pe sis en in bo h economies. In his seminal
a icle, Da is (1998) concludes, ha ”in e na ional ade equalizes ac o p ices” (p.482), im-
plying ha only one minimum wage emains binding. This has been c i icized by Egge , Egge ,
and Ma kusen (2012), using a model o he e ogeneous i ms whe e ”p oduc i i y di e ences o
ma ginal i ms compensa e o he p e ailing wage di e ences” (p.774) such ha minimum wages
emain binding in bo h coun ies. In he Egge , Egge , and Ma kusen (2012) amewo k, ade
changes he composi ion o ac i e i ms due o adjus men s in he cu o p oduc i i y. Mo eo e ,
i coun ies di e in hei minimum wage, adjus men s in he en y decisions o i ms lead o
φ∗
16=φ∗
2and es ablish p1(φ∗
1) = p2(φ∗
2). In my model, any adjus men in he cu o p oduc i i y
is closed since φ∗ emains una ec ed om changes in he minimum wage. In con as , he i m-
in e nal adjus men in he ask-based p oduc ion p ocess allows i ms o espond o changes in
labo ma ke ins i u ions and he e o e ac o p ices. The endogenous assignmen o skills o
asks gi es mo e lexibili y o abso b di e ences in e enues, ope a ing p o i s and ixed cos s
Thus, I es ic he discussion o he in e es ing case whe e coun ies di e wi h espec o Hand he e o e z,s
and Min he closed economy.
31Compa ing au a ky wi h ee ade be ween wo coun ies ha di e wi h espec o he minimum wage hen
ollows om adding he insigh s om his chap e o he discussion in he p e ious one.
32In he appendix, I p o ide a o mal p o e o dz1/dw2<0 and dz2/dw2<0.
98 CHAPTER 5. CONCLUSIONS
he misma ch be ween wo ke s and asks. I only he bes (mos p oduc i e) i ms sel -selec
in o expo ing, ade exe s an asymme ic e ec on he sc eening incen i es o high- and low-
p oduc i i y i ms. High-p oduc i i y i ms expand p oduc ion due o expo ing, and he e o e
ind i a ac i e o ins all a be e (mo e expensi e) sc eening echnology. In con as , low-
p oduc i i y i ms do no expo and lose ma ke sha e a home. In esponse, hey lowe hei
sc eening expendi u es. Despi e his asymme y in i m-le el adjus men s o ade, he a e age
misma ch be ween wo ke -speci ic abili ies and ask-speci ic skill equi emen s unambiguously
sh inks in he open economy. This poin s o a so a unexplo ed channel h ough which ade
can imp o e he labo ma ke ou come and s imula e wel a e.
Chap e 4 has p esen ed a he e ogeneous i ms model along he lines o Meli z (2003). How-
e e , he model accoun s o a mo e sophis ica ed p oduc ion p ocess, in which a i m’s ou pu
is manu ac u ed using a con inuum o asks simila o he amewo k in he p e ious chap e .
Fi ms hi e low-skilled and high-skilled wo ke s o he pe o mance o asks. Tasks di e in hei
complexi y and wo ke s di e in hei abili y o pe o m hese asks, wi h high-skilled wo ke s
ha ing a compa a i e ad an age in pe o ming mo e complex asks. How i ms o ganize he
i m-in e nal p oduc ion p ocess by assigning skills o asks depends on he espec i e ac o
cos s and p oduc i i y ad an age o high-skilled wo ke s in pe o ming mo e complex asks.
This amewo k has been used o analyze how impe ec ions in he labo ma ke a ec he
i m-in e nal assignmen o skills o asks in he closed economy. A e cha ac e izing he au-
a ky equilib ium ou come wi h ully lexible wages o bo h skill ypes, a ( eal) minimum wage
has been in oduced. The minimum wage is se by he go e nmen o low-skilled wo ke s and
causes in olun a y unemploymen o ha skill ype. As ela i e ac o p ices a e changed and
low-skilled ask p oduc ion becomes mo e cos ly, i ms assign high-skilled wo ke s o a b oade
ange o asks. This i m-in e nal skill upg ading imp o es a i m’s labo p oduc i i y. Howe e ,
as mo e high-skilled wo ke s a e employed o he pe o mance o asks, less o hem a e le o
manage i ms and he mass o i ms he e o e declines. Fi m exi igge s a decline in agg ega e
ou pu , income and wel a e. A e discussing mig a ion o low-skilled and high-skilled wo ke s
unde he wo di e en labo ma ke egimes, he model has been used o discuss how ade
be ween wo coun ies a ec s he i m-in e nal p oduc ion p ocess. Only when low-skilled wages
a e se by a binding minimum wage, ade exe s an impac on he i m-in e nal assignmen p o-
cess. The opening up o ade aises demand o each i m due o a s anda d di ision o labo
e ec . When he ac o p ice o low-skilled wo ke s is ixed, he skill p emium inc eases implying
ha high-skilled ask p oduc ion becomes ela i ely una ac i e. Fi ms espond in b oadening
he ange o ask p oduc ion wi h low-skilled wo ke s, which educes labo p oduc i i y o each
i m. Aside om his nega i e p oduc i i y e ec , ade inc eases he mass o p oduce s in each
coun y and educes he unemploymen a e o low-skilled wo ke s. This causes an inc ease in
agg ega e ou pu , income and wel a e and widens he gap o high-skilled and low-skilled labo
income. A e discussing he mo emen om au a ky o ade i has been shown how changes
in local endowmen s and labo ma ke ins i u ions spill o e o he pa ne coun y. The eby,
an inc ease in he minimum wage ab oad educes he ange o asks pe o med by low-skilled
wo ke s a home, while i inc eases he p oduc i i y o ac i e p oduce s he e. Bo h skill ypes
end up wi h a lowe pe -capi a income, and hus wel a e is educed a home.
O cou se, he o ganiza ion o p oduc ion has many di e en dimensions and his hesis
canno p o ide a comp ehensi e pic u e o all possible channels h ough which globaliza ion
and labo ma ke impe ec ions may a ec he o ganiza ion o p oduc ion. Mo eo e , o keep
he analysis ac able, he di e en amewo ks ely on se e al simpli ying assump ions, which
help o concen a e on he main issues ha a e ocus o his hesis, such as adjus men s in he
p oduc ange o he assignmen o wo ke s o asks in esponse o ade libe aliza ion. By

99
shedding ligh on hese new, so a unexplo ed i m-in e nal adjus men ma gins, I hope ha
my indings encou age u he esea ch on he o ganiza ion o i ms.
100 CHAPTER 5. CONCLUSIONS
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