Montréal
Série Scientifique
Scientific Series
2001s-43
Fragmentation, Outsourcing
and the Service Sector
Ngo Van Long, Ray Riezman,
Antoine Soubeyran
CIRANO
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© 2001 Ngo Van Long, Ray Riezman et Antoine Soubeyran. Tous droits réservés. All rights reserved.
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Fragmentation, Outsourcing and the Service Sector
*
Ngo Van Long
†
, Ray Riezman
‡
, Antoine Soubeyran
§
Résumé / Abstract
On montre que la croissance du secteur des services facilite la
fragmentation de la production. Les services relient les blocs de production et
permettent la dispersion de la production intégrée. Un pays possédant un grand
nombre de services spécialisés a tendance à exporter les pièces dont la production
utilise intensément les services. Avec la libéralisation de l'échange des services,
les pays possédant un secteur de services avancé tendent à impartir la fabrication
des pièces. Par conséquent, la libéralisation du commerce augmente la
fragmentation. Par contre, si les coûts de transport sont élevés pour les services les
plus complexes, le libre échange des services spécialisés peut réduire la
fragmentation.
We show that the growth of the service sector facilitates outsourcing, or
fragmentation of production. Services link production blocks, and allows the
breaking up of integrated production. The cost of aggregate service decreases as
the number of specialized services increases. A country with a greater number of
specialized services tends to export components that are service-intensive. When
international trade in specialized services are permitted, the country with an
advanced service sector will outsource most of the manufacturing activities. Thus
free trade in specialized services tends to increase fragmentation. On the other
hand, if there are high transport costs with a bias against complex specialized
services, then free trade in specialized services may work against fragmentation.
Mots Clés :
Fragmentation, impartition, secteur des services
Keywords:
Fragmentation, outsourcing, service sector
JEL : L23, F12
*
Corresponding Author: Ngo Van Long, CIRANO, 2020 University Street, 25
th
floor, Montréal, Qc, Canada
H3A 2A5
Tel.: (514) 985-4020
Fax: (514) 985-4039
email: longn@cirano.qc.ca
†
McGill University and CIRANO
There has been a marked increase in the fragmentation of productionin
re-centyears. A given nalgood(forexample,apersonalcomputer,acar)may
include components that are produced atmany di erentparts of the world.
The emergence of contract manufacturers of chips, such as Taiwan's UMC
(United Microelectronics Corporation) and TSMC(Taiwan Semiconductor
Manufacturing Company), and Singapore's CSM (Chartered
Semiconduc-tor Manufacturing) is a spectacular illustration of such fragmentation. It
was Morris Chang,founder and chairman ofTSMC, who pointed out to the
world that the semiconductor industry was in fact not one but two
indus-tries, and that it would be best to separate them out 1
. \One industry is
about designing chips, which requires lots of talent but little capital. The
other is about making chips, which requires more capital than talent"(The
Economist, May 19,2001, p62). Anotherwellknown exampleof
fragmenta-tion concerns the famous camera, Leica, with lenses produced in Germany,
and other parts produced inCanada, Spain,and the FarEast.
To explain the tendency for increased fragmentation, economists have
citedfactorssuchaslowlaborcostsindevelopingcountriesthathaveopened
up and welcome foreign investment, and reduced tranport costs. These
fac-tors alone do not explain why computer chips are made in Taiwan and
Sin-gapore, and car parts are made in Mexico, but these are not made in, say,
Nepal, Vietnam,orBangladesh. Toanswerthis question,onemust takeinto
account the fact that components are not just \manufactured" by
manufac-turinglabor. Theyhavetobemarketed,theirtransportationhavetospeedy,
and insured, deliveries must be timely, communications with head oÆce or
customers must beeÆcient, contracts must be reliable,etc.All these factors
point to the importance of a service industry that supports and facilitates
manufacturing. An important point is that it is not economical to produce
components in a low wage economy that does not have an eÆcient service
sector.
In this paper, we develop a general equilibrium model with a
manufac-turing sector, and a service sector. We show how the growth of the service
sector enables the economy to manufacture and export components. The
1
In1987,MrChangfoundedTSMC,theworld's rst\fab",orfabricationplan. Many
\fabless" designers(among which are university-basedresearchcenters) havebought
ca-pacity fromTSMC.Integrateddesignmanufacturers(IDMS) such asIntelstillmaintain
price of service. Wealsoshow howinternationaltrade inservices may a ect
the tradein components,and the degreeof fragmentation.
Our story may be summarised as follows. There are two countries, and
advanced country, and a developing country. There are two nal goods, say
bananas and cars. Bananas are produced by labor, and no fragmentation
is possible in banana production. Cars are produced by assembling
compo-nents, such as spark plugs, seat belts, tyres, gear box, transmission, engine,
and soon. Toproducethesecomponentsand connectthem withother
\pro-duction blocks", an economy needs both manufacturinglabor, and services.
A manufacturer of a given component hires manufacturing labor and buys
and combines services from\service providers", such as an accounting rm,
a marketing rm, a security rm, a bank, a delivery rm, a cleaning
con-tractor, and so on. These service rms have a constant variable cost, and
a xed cost. Thus their average cost falls as their volume of service output
rises. Decreasing average cost isnot compatible with price-taking behavior.
Therefore we assume that the service industry is characterized by
monopo-listiccompetition: eachservice rmfacesadownwardslopingdemandcurve,
and sets its price, taking as given the prices of imperfect substitutes set by
other service rms.
Thenumberofdi erentservicesthataneconomycano erdependsonits
stage of development and the size of the economy. Forexample, a matured
economysuchastheUShasmorespecializedservicesthanlessmaturedones,
suchasIndonesia. Alargeeconomy,suchasGermany,cano ermoreservices
than asmalleconomy,such asNew Zealand,even if the two economieshave
the samelevelof human capitalper person.
Wearguethatthe greateristherangeofservices,the moreeÆcientisthe
productionof components. On the other hand, acountry that has a greater
range of services may have a more expensive service price, perhaps due to
higher labor cost. For example, a computer programmer in the US earns
more than his couterpart working in India. The trade-o between range of
services andcostsofindividualservicesdeterminewhattypesofcomponents
will be producedin whichcountry. We expect that a component that has a
high ratio of service tomanufacturinglaborwillbe producedinthe country
that has agreater range of services.
Inwritingourpaper,wehavebene tedfromthetheinsightfuldiscussions
onfragmentation,containedinJonesandKierzkowski. (1990,2001a,b).Jones
frag-agoodtakesplacewithinasingleproductionblock,andtheroleofservicesis
ratherlimited. Fragmentedtechnologyrequiresthatservice linksconnect
in-dividualproductionblocks. \Theselinkscanbebestthoughtofasconsisting
ofbundlesofactivities-coordination,transportation,telecommunication,
ad-ministration, insurance, nancialservices, and soon." (2001a,p368).
How-ever, Jones and Kierzkowski (2001a)did not modelthe service sector. They
focussed attention on the case in which one integrated production activity
gets segmentedintotwocomponentsasaresultofanexogenousreductionin
thecost ofinternationalservicelinks.Jonesand Kierzkowski(2001b)devoted
a shortsection totherole of services infragmentation. They mentionedtwo
stylized facts about the costs of service links: \First, purely domestic
ser-vice links are less costly than those required to connect production blocks
located in more than one country...Second, production of services displays
strong increasing returns to scale." The second stylized fact seems to call
for a departure from a model based on perfect competition. Our paper is
attempt tomovein that direction.
Various aspects of fragmentation have been studied by a number of
au-thors. Arndt (1997)showed thatintra-productspecializationcanbeasource
of gains from trade. harris (1993, 1995) focussed on the role of
telecommu-nications. Hanson (1996) mentioned fragmentation in the context of trade
between Mexico and the United States. Feenstra (1998) linked the
integra-tion of trade with the disintegrationof production.Ra (2001) discussed the
role ofdirect foreigninvestment inservices. Deardor (1998,2001) provided
insightfuldiscussions of the role of services in coordinating the fragments.
This paper is organized as follows. In section 2, we develop a simple
modelofaclosedeconomywithaservicesector. Insection3,wecharacterize
the autarkic equilibrium. Section 4 considers two economies with di erent
numbers of specialized service rms, and shows how the pattern of trade in
componentsis determined,given thatthere isnotradeinservices. Section5
allowstradeinservices. Section6discusses some generalisationsofthe basic
sector
2.1 The service sector
An aggregate service is produced usingspecialisedservices as inputs. There
aren specialisedservices(e.g.,accounting,marketing,legalservice,auditing,
security...). We let S denote the number of units of aggregate service
pro-duced, and m i
denotethe units of specialised service i, used as input in the
production of the aggregate. We assume the following productionfunction:
S =[m 1 +::::+m n ] 1= (1)
where 0 < < 1. For example, if = 1=2 and n = 2, then using 4 units
of specializedservice 1 and zero unit of specializedservice 2 willresult in 4
units ofaggregate service, while using2units of each specializedservice will
result in8 units of aggregateservice. (This idea of gains fromspecialization
wasforcefullyputforwardsbyAdamSmith: 4bricklayerscanbuild4houses
in one year, but two brick layers and two carpenters can build 8 houses in
one year.)
Letp i
bethepriceofaunitofspecialisedservicei. Thecost ofproducing
oneunitof aggregateservice isthe solutionofthecostminimizationproblem
P S =min m i n X i=1 p i m i subjectto " X i m i # 1= =1
The solution yields
P S = " n X i=1 p =( 1) i # ( 1)= (2)
From Shephard's lemma, the conditional factor demand function (here,
m d i (p;S=1)= @P S @p i =Ap 1=( 1) i where A " n X j=1 p =( 1) j # 1=
If S units of the aggregate service is to be produced, the conditional factor
demand is m d i (p;S)=ASp 1=( 1) i (3)
Itdoesnot matterinour modelwhetheraggregate services areproduced
by \aggregate service rms" that buy specialializedservices, and sell
aggre-gate services in the market, or whether aggregate services are produced by
users of the aggregate service (such as a manufacturer of a car component.)
Inthe lattercase, P S
isthecost(ratherthantheprice)ofaunitofaggregate
service.
Concerningthe industry that produces the n specialisedservices, we
as-sume it consists of service rms that operate under monopolistic
competi-tion.Weassumethat service rm iproduces thespecialisedservice i:Service
rm i takes the function (3) as the demand function that it faces. It takes
S as given, and even though it can in uence p i
, we assume it takes A as a
constant. (Thisisthethe assumptionmadebyDixitand Stiglitz). Inverting
(3), weget the inverse demand function
p i = h m i AS i 1 =p i (m i )
The marginal revenue is
MR i =p i 1 1 = p i
where is the elasticity of demand
dlnm i dlnp i = 1 1 >1
toproducem i
unitsofspecialisedservicei,theservice rmimustincur xed
costandvariablecost. Assumethe xedcostisF =wf andthevariablecost
is cwm i
, where c is a positive constant representing the amount of units of
labor required perunit of service output, and w isthe wage rate, which the
rm takes as given.Since the rm equates marginal revenue with marginal
cost, we have
p i
=cw
Non-negative pro trequires
p i F m i cw (4) and pro t is r i =pm i cwm i wf = 1 cm i f w (5) In asymmetric equilibrium,p i =p j =p, so(2) gives P S =n ( 1)= p=n ( 1)= cw (6)
This equationsays thatthe greateristhe number ofspecialisedservices, the
loweris the price (=cost)of a unit of aggregate service.
The sum of pro ts inthe service industryis
R=nr i =n 1 cm i f w (7)
2.2 The goods sector
The goods sector is perfectly competitive. The economy produces two nal
goods, denoted by X and Y. To produce one unit of good Y, the input
requirement is a Y
units of labor. Thus
P Y
=wa Y
To produce one unit of good X (say a car), k components must be
k components. We assume that assembling a car requires g units of labor
and X
units of services. Then the price of a car is the sum of the prices
(denoted by j
) of the k componentsand the cost of assembling:
P X = 1 + 2 +:::+ k +gw+P S X
Toproduceoneunit ofcomponentj,twoinputs arerequired: one unitof
laborand j
unitsofaggregateservice. Thepriceofcomponentj istherefore
j =w+ j P S
The price of goodX is then
P X =(k+g)w+P S =(k+g)w+n ( 1)= cw where X + X i
denotes the number of units of aggregate service required per unit of good
X.
It follows that, for given n, the economy has the following property of a
Ricardian model: the prices P X
, P S
, and P Y
are determined only by
tech-nology.
2.3 Consumers
In this economy, the pro ts of the service rms are in general positive in
equilibrium. So nationalincomeis the sum of laborincomeand pro t
M =wL+n 1 cm i f w (8)
Assume thatthelaborsupplyLis xed. The representativeconsumersolves
max X ;Y U(X;Y) subjectto P X X+P Y Y =M
Y
Then the demand functionstakesthe form
X d = X (P X ;P Y )M (9) and Y d = Y (P X ;P Y )M (10)
where, inview of the budget constraint,
P X X (P X ;P Y )+P Y Y (P X ;P Y )=1 (11) 3 Autarkic equilibrium 3.1 Equilibrium conditions In equilibrium, m i =n 1= S =n 1= X d =n 1= X (P X ;P Y )M (12)
Substituting (12) into(8), we get
M =wL+w 1 cn ( 1)= X (P X ;P Y )M wfn hence M = (L fn)w 1 w 1 cn ( 1)= X (P X ;P Y )
The equilibrium outputof X is then
b X = (L fn)w X (P X ;P Y ) 1 w 1 cn ( 1)= X (P X ;P Y ) (13)
Remark: Notethat, in viewof (11),
w 1 cn ( 1)= X (P X ;P Y )=(1 )P S X (P X ;P Y )
X X X Y
Example: WithCobb-Douglas utility,U =X Y 1 P X X d = M that is P X X (P X ;P Y )M = M or X (P X ;P Y )= P X (14)
Substituting (14) into(13), we get
b X = w (L fn) P X w 1 cn ( 1)= b X = (L fn) (k+g)w+n ( 1)= cw [1 (1 ) ] >0
3.2 A modi ed version of the model
From this point onwards, for convenience, we assumethat thereis a
contin-uum ofcomponents,represented bythe interval[0;k]. Let betheindex for
the component. The priceofcomponent is( ),and theprice ofthe caris
P X = X P S + Z k 0 ( )d where ( )=w+( )P S
Assume for simplicitythat
( )=b
Then we can draw the graph of ( )as afunction of
( )=w+ bP S
This graph is astraightlinewith slopebP S . In autarkicequilibrium, ( )=w+ bn ( 1)= cw
4.1 Assumptions
Nowconsider atwocountryworld. The homecountryis the US,the foreign
country is Mexico. All consumers have identical preferences. The
endow-ments of labor are L and L
: There are n service rms in the US, and n
service rms in Mexico, where n
< n. We assume, in this section, that
SERVICESARENOT INTERNATIONALLY TRADED,whilecomponents
can betraded. Mexicohas the component pricecurve
( )=w + b (n ) ( 1)= c w We assume a Y >a Y
. Then Mexico's wage islowerthan US wage:
w <w: Ifthe slopeb b P S >b b P S
,then thetwocurves
( )and ( )willintersectat
a point I
. Mexicowill exportthose components with index < I
and the
US willexport (if Mexicoalsoassembles cars atthe new equillibrium)those
components with > I
.
One may assumethat
g
>g
and g
g is sogreat that Mexico does not 2
assemblecars when it can buy
cars from the US.
4.2 Free-trade equilibrium (without trade in services)
Assume that services are not internationally traded. To nd a free-trade
equilibrium, let us at rst consider the simple case where the assembling of
components doesnot require services,that is, X = X =0. Assumethat g
is much greater than g, so that car assembling takes place only in the US.
LetP X
(=P X
)denotethe worldprice ofgood1(cars)underfree trade,and
P Y =P Y =1. 2
Alternatively, one may assume that thecost of assembly is zero, and service is not
neededforassembly. Thenconsumersdonotbuycars,theybuycomponentsandassemble
Z wL+w L +n 1 cm f w+n 1 cm f w (15) where w= 1 a Y
if good2 is producein the home country, otherwise
w> 1 a Y similarly, w = 1 a Y
if good2 is producein the foreign country, otherwise
w > 1 a Y
World demands for good1 and good 2are
X ! = X (P X ;1)Z = X (P X ;1)Z (16) Y ! = Y (P X ;1)Z =[1 P X X (P X ;1)]Z (17)
Suppose that in equilibrium, the foreign country exports components with
index inthe range [0; I
] and the home country exports components with
index in the range [ I
;k]. Then the total quantity of aggregate services
supplied by the foreign country is
S = Z I 0 b d X ! = 1 2 b 2 I X ! (18)
Similarly,for the home country,
S= Z k I b d X ! = 1 2 b k 2 2 I X ! (19)
m =n 1= S m =(n ) 1= S Since I
istheintersectionofthe twocomponent-pricecurves, itmust bethe
case thatfor component I
the productioncosts inboth countries are equal:
w +b P S I =w+bP S I (20) That is, w + I b (n ) ( 1)= c w = w+ I bn ( 1)= cw (21) Equation(21)determines I asafunctionofn,n ,wandw :Weassume n >n . Then I = I (n;n ;w;w )= w w >0 (22) where b (n ) ( 1)= c w bn ( 1)= cw >0
provided thatn issuÆciently great relative ton : Lemma: I (n;n ;w;w
) is anncreasing function of with wand n , and is a decreasing functionof w and n. Proposition 1
(i)The foreigncountryexports componentsinthe range[0, I
](i.e.,
com-ponentthat areless service-intensive)and thehomecountryexports
compo-nents that are more service-intensive).
(ii)An increase inn
or adecrease in c
will result ina greater range of
componentsexportedbythe foreigncountry. (Inotherwords,itwillincrease
(iii)Anincrease inw willresultinadecreaseintherangeofcomponents
exportedby the foreign country.
Proof: obvious
Now, since the price of good 1 must equal the cost of production, in a
free trade equilibrium,we must have
P X =P X = b P X = Z I 0 (w +b P S )d + Z k I (w+b P S )d (23) More precisely P X =P X = b P X = Z I 0 (w +b P S (n ;w ))d + Z k I (w+b P S (n;w))d Observation 1: Since b P X
is the area underthe kinked curve de ned by
the lowerboundof the two curves
( )and ( ),we may write this as
b P X = Z k 0 min[ ( );( )]d b P X (w;w ;n;n ) (24)
(An explicit expression for b P X
is given in the Appendix.) Notice that, if we
assume that good Y are produced in both countries, then w = 1=a Y and w =1=a Y
,and the equilibriumprice b P X
is independentof demand.
UsingObservation 1, wecan state
Proposition 2: b P X
is an increasing function of w and w
and is a
decreasing function of n and n
:
Proof: obvious from Observation 1.For a more formal proof, see
Ap-pendix 2
Letus now compute the equilibriumoutput of cars. First, we must
cal-culate world's income, Z. From (15),
Z =wL+w L wnf w n f+ where 1 [cwnm+c w n m ]
m =n 1= S =n 1= b[k 2 2 I ]X ! and m =(n ) 1= S =(n ) 1= b 2 I X ! we get =qX ! where q (1 ) (w w ) 2 + 1 bcwk 2 n ( 1= ) b Thus (16) gives X ! = X ( b P X ;1)[wL+w L wnf w n f +qX ! ] (25) Since b P X
has been deternined in (24), equation (24) determines the
equilib-rium X ! : b X ! = X ( b P X ;1)[wL+w L wnf w n f] 1 q X ( b P X ;1) >0
Notethat since 1 P X (P X ;1)= Y (P X ;1)>0 andsince P X >q,wehave 1 q X ( b P X ;1)>0. (qX ! <P X X !
because the value of output of X must
exceed thevalueofpro ts tothe serviceindustry,by theaccounting identity
that revenue equals the sum of paymentsto inputs.)
5 Trade in services
Now suppose that services are internationally tradable. We consider two
cases: (i) complete free trade in services, which equalizes the prices of
ser-vices, and(iii)tradeinservices withtransportcosts(e.g. the\iceberg
trans-portationcost" model.)
We assume that, before the opening of trade in services, the n
services
produced in the foreign country have their exact counterparts in the home
country. (The home country has n n
services that are not produced
in the foreign country. We number services so that the rst n
services are
produceableinbothcountries,andthelastn n
function of aggregate services in the home country is S = " X i (m i +m i ) # 1=
and thus the price is
P S = " n X i=1 [min(p i; p i )] =( 1) # ( 1)=
if there is no transportation cost. If the transport cost is positive, and is of
the iceberg type, then
P S = " n X i=1 [min(p i ;Æ i p i )] =( 1) # ( 1)= where Æ i > 1:Here, 1=Æ i
is the fraction of one unit of service i that remains
afterbeingtransported. Byconvention,iftheforeigncountrycannotproduce
service n j, then p n j
isany numbergreater than p n j
(j n n
):
5.1 Complete free trade in services
Recall that the autarkic price of the aggregate service in the foreign
coun-try is P S = (n ) ( 1)= (c w
= ) and that of the home country is P S = (n) ( 1)= (cw= ). By assumption P S >P S
(because n is much greater than
n
), complete free trade in services will result in the export of specialised
services( indexed n) from the home country to the foreign country, and
theequalizationofserviceprices. Thehomecountrywillstopproducing
spe-cialized services n. The equalizationof the price of aggregage services
means that, under free trade inservices, the costs of producingcomponents
are lower in the foreign country. The home country willtherefore stop
pro-ducing allcomponents: allthe car components are producedin Mexico, and
the cars are assembled in the US (recall our assumption that g
is much
greater than g.)
Proposition3: Freetradeinservices resultsincomplete outsourcingof
This occurs whenthereisan\icebergtransportationcost"ofservices. Then
service pricesare not equalized. Still,the e ect of the incompletefree trade
in services is the narrowing of the gap between P S
and P S
. The foreign
country imports the last n n
services from the home country, and the
home country may import the rst n
services fromthe foreign country, but
the price ofaggregate servicein theforeign countrymay remainhigherthan
in the home country. In this case, the curve
( ) is rotated downwards,
leading toan increase in I
.
Proposition 4: Incomplete free trade in services may result in an
in-crease inthe range of componentsexported by the foreign country.
6 Generalisation: services withincreasing
com-plexity
We now relaxthe assumption that all services cost the same. We introduce
the idea that some services are more complex than others. It is convenient
to have a continuum of services, indexed by in [0;n]:The greater is , the
higher is the variable cost c():
6.1 Assumptions for a closed economy
The production functionof the aggregate service is
S = Z n 0 [m( )] d 1=
Let p() be the price of the specialisedservice . Then
P S = Z n 0 [p()] =( 1) d ( 1)= (26)
The conditionaldemand for service is
m()=AS[p( )] =( 1) where A= Z n 0 [p()] =( 1) d 1=
This gives
p()= wc()
(27)
Substituting (27) into(26), we get
P S = w Z n 0 [c()] =( 1) d ( 1)= For concreteness, let c()=c 0 where 0; then Z n 0 [c( )] =( 1) d ( 1)= = c 0 K [n] ( + 1)=
where we assumethat
K = + 1 1 >0 Then P S = wc 0 K [n] ( + 1)=
(If =0, we have the result in the main text)
6.2 The two-country case
With two countries, the range [0;n] overlaps with the range [0;n
] where
n
<n. The cost of producingspecialised service inthe homecountry is
p()= wc 0
and that ofthe foreign country is
p ( )= w c 0
> >0
De ne the cost ratio
v()= p() p () Assumew c 0 <wc 0 . Thenv(0)=.(wc 0 =w c 0
)>1,andthereexistsaunique
e
such that
v(e)=1 and v()<1for all >e
We assume that e < n
< n: Then the home country has comparative
ad-vantage inproducing complexservices.
6.3 Free trade in services without transport costs
Withfreetradeinservices,the foreigncountrywillimportallservicesinthe
range[e;n],(and export thelesscomplexservices. ifassemblyneedsservices
andcanonlybedoneinthehomecountry). Allcomponentswillbeproduced
inthe foreigncountry(becausetheprices ofaggregateservice P S
and P S
are
equalised, andcomponent productionrequiresdirectlabor,whichischeaper
in the foreign country)as wellas aggregate services).
6.4 Free trade in services with transport costs
Assume insteadthat trade inservices involvestransportcost (of the iceberg
type), and that the transport cost of specialised services from the foreign
country to the home country is low (say zero), while the transport cost of
complexspecialisedservices(thosewithindexgreaterthane)isprohibitively
expensive. Furthermore, weassume itis not possible totransportaggregate
services. Then free trade willresult inthe foreign country exporting all the
services withe:Thee ectsonthepricesof aggregateserviceare: P S
be-comessmaller,whileP S
isunchanged. Under thesecircumstances, therange
of componentsproduced in the foreign country will contract. Thus trade in
services can lead to less fragmentation when there are transportation costs
that are biasedagainst complexed services produced by the home country.
Proposition5: Trade inservicesinthe presenceof transportationcosts
thatare biasedagainstthemorecomplexspecialisedservicessuppliedby the
We have showed that the fragmentation of manufacturing depends on the
level of development of the service industry in each country. Advanced
economies have higher cost of supplying simple services, but they have a
greater variety of services, so that their price of \aggregate service" tends
to be lower than those of less developed economies. As a result, advanced
economies tend to produce components that are service-intensive, and
out-source the manufacturing of components that are less service-intensive to
developing countries that have abasic servicesector. Complete freetradein
service will lead to complete outsourcing of components. Trade in services
under non-negligible transport costs will result in partial fragmentation of
manufacturing. If transport costs are biased against complex services, then
a reduction in transport costs for less complexed services can reduce
frag-mentation.
We have assumed that the numberof specialized services that acountry
can produce is given. This is a simpli cation that should eventually be
relaxed. As countries grow, the number of services also tends to grow. It
is tempting to endogenize n, the number of services, by allowing free entry
and letting the \zero pro t condition" determine the equilibriumn. In our
model, we assumethat eachservice rmmust incura xed cost, interms of
labor. We should interpret \labor" in the sense of human capital. Then a
countrythatinvests inhumancapitalwillincrease its\labor" force,and will
Appendix 1: An explicit expression for b P X
.
Denote the equilibriumvalue by b P X :Then b P X :=w I (n;n ;w;w )+w[k I (n;n ;w;w )]+ 1 2 b P S (n ;w )[ I (n;n ;w;w )] 2 + 1 2 bP S (n;w) k 2 [ I (n;n ;w;w )] 2 (28)
IF BOTH COUNTRIES PRODUCE GOOD 2 (bananas) THEN w and w
are determined by w = 1=a Y and w = 1=a Y
. IN THAT CASE, equation
(28) adeterminesthe relativepriceofgood1interms ofgood2asfunctions
of (a Y ,a Y ,;L,L ). (recall that P X = P X =P Y because P Y = 1).Then, after
substituting (22) and (6) into(28) we get
b P X = 3 2 (w w ) 2 +wk+ 1 2 bn ( 1)= cw k 2 2k(w w ) (29) Appendix 2 Proof of Proposition 1 From (23), @ b P X @w = Z I 0 @ ( ) @w d + ( I ) @ I @w ( I ) @ I @w = Z I 0 (1+b @P S @w )d >0
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