4

Outsourcing, Contracts,
and Innovation Networks
Alireza Naghavi and
Gianmarco Ottaviano

4.1

Introduction

A substantial growth in the outsourcing of activities in industrial countries is the most recent form of a greater division of labor (Feenstra
1998). When corporations began selling their factories and relocating
manufacturing in the 1980s and 1990s to boost efﬁciency and focus on
specialization, most insisted that important R&D would remain
in-house. Today leading multinationals are turning toward a new
approach to innovation, one that employs global networks of partners.
Dell, Hewlett-Packard, Motorola, and Philips, among others, havestarted buying complete designs of some digital devices from Asiandevelopers, modifying them to their own speciﬁcations, and using
their own brand names. Dell, for example, does little of its own designfor notebook PCs, digital TVs, or other products. Hewlett-Packard contributes key technology and some design to all its products but relies
on outside partners to codevelop everything from servers to printers.
Motorola buys complete designs for its cheapest phones but controls
all of the development of high-end handsets. Asian contract manufacturers and independent design houses have become key players innearly every technological device, from laptops and high-deﬁnition
TVs to MP3 music players and digital cameras. While the electronics
sector is the most signiﬁcant example of search for offshore help with
innovation, the concept is spreading to nearly every sector of the economy. Boeing, for instance, is working with India’s HCL Technologies
to codevelop software for everything from navigation systems andlanding gear to the cockpit controls. Pharmaceuticals as GlaxoSmithKline and Eli Lilly are teaming up with Asian biotech research companies in a bid to cut the average $500 million cost of bringing a new
drug to market. Procter & Gamble also wants half of its new product68

Alireza Naghavi and Gianmarco Ottaviano

ideas to be generated from outside by 2010, compared with 20 percent
now (Engardio and Einhorn 2005).
The growing importance of outsourcing has generated an intense debate on the costs and beneﬁts of industrial fragmentation. Within theinternational trade literature, a recent strand of research tries to investigate the phenomenon of outsourcing as the result of a trade-off between the governance costs of complex vertical organizations and thecontractual costs of networks of independent specialized upstream
and downstream producers. Such networks are tainted by problems ofcontractual incompleteness stemming from the lack of ex post veriﬁability by third parties as the quality of deliverables is too costly to observe by courts. Related models can be classiﬁed in terms of theirrelative focus on two decisions: the ‘‘ownership decision’’ on whether
production should be in-house or outsourced and the ‘‘location decision’’ on where to place production. The ownership decision is thefocus of, for example, McLaren (2000) and Grossman and Helpman(2002) for a closed economy and Antras (2003), Grossman and Helpman (2003), and Feenstra and Hanson (2003, 2004) for an open economy. The location decision is analyzed by Grossman and Helpman(2005). Both decisions appear in Antras and Helpman (2004) as determinants of ﬁrm organizational form.1
While all these studies focus on the static effects of outsourcing, weinvestigate instead its dynamic effects. Our aim is to shed light on thedriving forces behind the new approach to innovation based on global
networks of partners. In so doing, we model an industry in which
R&D is performed by independent research labs and outsourcing production requires complementary upstream and downstream inventions. In the presence of search friction and incomplete outsourcing
contracts, we show that the ex post bargaining power of upstream anddownstream parties at the production stage feeds back to R&D incentives, thus affecting the emergence and the performance of networks oflabs specialized in complementary inventions.
In our model, R&D is always outsourced, and independent labs
choose whether to invent integrated upstream and downstream production processes or to focus on specialized upstream or downstream
innovation. Lai, Riezman, and Wang (2005) endogenize the decision to
outsource R&D rather than perform it in-house by emphasizing thetrade-off between the costs of information leakage and the beneﬁts ofspecialization. In Acemoglu, Aghion, and Zilibotti (2005), R&D is al-

Outsourcing, Contracts, and Innovation Networks

69

ways performed in-house, and ﬁrms closer to the technology frontier
have a stronger incentive to outsource production in order to concentrate on more valuable R&D. Our model thus complements both contributions. This is achieved by introducing innovation and growth in
the static outsourcing model of Grossman and Helpman (2002), whostudy the industrial organization of a sector in which the varieties of ahorizontally differentiated good are produced by monopolisticallycompetitive ﬁrms. Production has two stages: intermediate supply andﬁnal assembly. Firms choose whether to enter as intermediate suppliers, ﬁnal assemblers, or vertically integrated ﬁrms by paying thecorresponding organization-speciﬁc ﬁxed costs. Vertical integration
bears additional costs due to more complex governance and limited
specialization. Specialized suppliers face, instead, additional costs ofsearching and contracting with complementary partners. Contracts
themselves are incomplete due to input characteristics that are unveriﬁable by third parties, which leads to bargaining between intermediate
suppliers and ﬁnal assemblers after the former have produced their
inputs. In Grossman and Helpman (2002) unobservable intermediate
input quality is an issue insofar as only high-quality inputs can be processed, whereas low-quality inputs are useless even though supplied atzero cost.2 The fear of being held up during the bargaining processcauses the intermediate suppliers to underproduce, and this reduces
the joint surplus of specialized ﬁrms with respect to vertically integrated ones. Accordingly, the choices of ﬁrms in terms of organizational modes depend on the balance between the costs of the two
types of industrial structure.
Grossman and Helpman (2002) show that the bargaining power ofpartners plays a key role in the fragmentation of production. Outsourcing is preferred when specialized ﬁnal assemblers have a good chanceof ﬁnding specialized intermediate suppliers; when product differentiation is weak so that the proﬁt portion of the revenues of verticallyintegrated ﬁrms is small relative to the share appropriated by ﬁnal
assemblers through bargaining in an outsourcing deal; when verticalrevenues are relatively small due to large gains from specializationand mild intermediate underproduction thanks to strong supplier bargaining power; and when the entry costs for specialized assembly are
relatively small compared with those for vertically integrated production. The matching probability of ﬁrms entering as specialized assemblers itself depends negatively on their relative costs of entry and70

Alireza Naghavi and Gianmarco Ottaviano

positively on their relative proﬁt margin with respect to intermediate
suppliers. The result is a relationship between the incentives to outsource and supplier bargaining power that has an inverted-U shape.
Intuitively, when their bargaining power is very weak, intermediate
suppliers have little incentive to produce, so intermediates are very
costly. When intermediate bargaining power is very strong, few ﬁnal
assemblers are attracted to the industry, so intermediate suppliers
have little chance of ﬁnding partners.
To the static setup of Grossman and Helpman (2002) we add dynamic product innovation. Whatever their organizational choice, ﬁrms
need blueprints for production to enter the market. These are invented
by perfectly competitive labs. They are protected by inﬁnitely lived
patents and come in three organization-speciﬁc types depending onwhether they are designed for vertical integration, intermediate supply, or ﬁnal assembly. We show that for speciﬁc parameter values, thesteady state of the dynamic model is isomorphic to the static equilibrium of Grossman and Helpman (2002) once their ﬁxed entry costs
are interpreted as the marginal costs of innovation.3 Our analysis
therefore complements their work by providing microfounded transitionary dynamics. This has three interesting implications. First, explicit
dynamics allow a formal stability analysis and qualify the conditions
for the existence of multiple equilibria.4 Second, they introduce new
microeconomic parameters that are shown to affect the steady-stateoutcomes. Third, they allow characterizing the path and speed of convergence to steady state after the economy is hit by some shock.5
Some parameters have the same impact independent of the industrial organization of ﬁrms. Weaker product differentiation reduces
product development due to thinner proﬁt margins. Also, faster depreciation has a negative impact on product development. Both discourage innovation and divert labor away from the latter. Stronger time
preference slows product development by biasing intertemporal decisions toward consumption. Higher costs of innovation have a negative
impact on product development, whereas a larger economy supports
the creation of a proportionately larger number of product varieties.
The relationship between the incentives to outsource and the bargaining power of intermediate suppliers has the same inverted-U
shape as in Grossman and Helpman (2002), and for the same reasons.
Accordingly, outsourcing is sustainable in an industry equilibrium
only if supplier bargaining power is neither too weak nor too strong.
When the outsourcing mode is selected, supplier bargaining powerOutsourcing, Contracts, and Innovation Networks

71

plays a crucial role for innovation. In particular, product development
is maximized when supplier bargaining power does not take extreme
values.
The rest of the chapter is organized as follows. Section 4.2 presents
the model. Section 4.3 determines the equilibrium of the dynamic
model. Section 4.4 concludes.
4.2

A Model of Product Innovation

To study the organizational choice between vertical integration andoutsourcing in a dynamic environment, we merge the organization
model with incomplete contracts by Grossman and Helpman (2002)
and the innovation model with horizontal product differentiation by
Grossman and Helpman (1991).
4.2.1 Demand
There are L inﬁnitely lived households that share the same preferencesdeﬁned over the consumption of a horizontally differentiated good C.
The utility function is assumed to be instantaneously Cobb-Douglas
and intertemporally constant elasticity of substitution (CES) with unit
elasticity of intertemporal substitution:
U¼

ðyert ln CðtÞ dt;

0

where r > 0 is the rate of time preference andCðtÞ ¼

"ð

nðtÞ

#1=a
a

cði; tÞ di0

is a CES quantity index in which cði; tÞ is the consumption of variety i,nðtÞ is the mass (‘‘number’’) of varieties produced, and a is an inverse
measure of the degree of product differentiation between varieties. In
particular, if s is deﬁned as the constant own- and cross-price elasticity
of demand, then a ¼ 1  1=s. Households have perfect foresight, andthey can borrow and lend freely in a perfect capital market at instantaneous interest rate RðtÞ.
Given the chosen functional forms, multistage budgeting can be used
to solve the utility maximization problem. This allows the households’
decisions to be modeled as a two-stage sequence. In the ﬁrst stage, they

72

Alireza Naghavi and Gianmarco Ottaviano

allocate their income ﬂow in each period between savings and expenditures. This yields a time path of total expenditures EðtÞ that obeys
the Euler equation of a standard Ramsey problem:
E_ ðtÞ
¼ RðtÞ  r;
EðtÞ

ð4:1Þ

where we have used the fact that the intertemporal elasticity of substitution equals unity. By deﬁnition, EðtÞ ¼ PðtÞCðtÞ where PðtÞ is theexact price index associated with the quantity index CðtÞ:"ð#ð1aÞ=anðtÞPðtÞ 1

pði; tÞ

a=ð1aÞ

di

:

ð4:2Þ

0

In the second stage, households allocate their expenditures acrossall varieties, which yields instantaneous demand functions for eachvariety:cði; tÞ ¼ AðtÞ pði; tÞ1=ð1aÞ ;i A ½0; nðtÞ;ð4:3Þ

where pði; tÞ is the price of variety i andAðtÞ ¼EðtÞPðtÞa=ð1aÞð4:4Þ

is aggregate demand. To simplify notation, from now on we leave thetime dependence of variables implicit when this does not generate
confusion.
4.2.2 Supply
The economy is endowed with two factors. Labor is inelastically supplied by households. Each household supplies one unit of labor, andwe call L the number of households as well as the total endowment oflabor. Labor is chosen as numeraire. The other factor is knowledge
capital in the form of blueprints required for the production of differentiated varieties. These blueprints are protected by inﬁnitely lived patents that depreciate at the constant rate d.
There are two sectors: production and innovation (R&D). Innovationis performed by perfectly competitive labs that invent different types of
blueprints for vertically integrated processes and fragmented ones.
Each of the former processes requires a blueprint with marginal cost of

Outsourcing, Contracts, and Innovation Networks

73

invention equal to k v . Each of the latter requires two blueprints: one for
an intermediate component and one for ﬁnal assembly with marginal
R&D costs equal to k m and ks , respectively, where ks þ k m a k v .6 We
call v, m, and s the numbers of the three types of blueprints available
at time t.
As to production, varieties are supplied by monopolistically competitive ﬁrms that buy the corresponding patents from R&D labs and hire
an amount of labor proportionate to output. Therefore, each ﬁrm produces under increasing returns to scale as the price of its patent generates a ﬁxed cost and the wage bill a variable cost. Depending on thepatent it has chosen to buy, a ﬁrm can enter in three alternative modes:
as a vertically integrated ﬁrm, as an intermediate supplier, or as a ﬁnal
assembler. The ﬁrst needs l units of labor per unit of ﬁnal output; thesecond needs 1 a l units of labor per unit of intermediate component;
the third needs one unit of intermediate component per unit of ﬁnal
output. Accordingly, fragmented production is cheaper in terms ofboth ﬁxed and marginal costs. The reason is lower R&D costs and productivity gains from specialization.
Fragmented production (henceforth referred to as outsourcing) faces
additional costs that result from search frictions and incomplete contracting. After buying their patents, specialized entrants of each typemust ﬁnd a suitable partner in a matching process that may not always
end in success. Moreover, intermediate suppliers also suffer hold-up
problems due to contractual incompleteness. In particular, after matching, each intermediate supplier produces a relation-speciﬁc input. This
input has no value outside the relation, and its quality is unveriﬁable
by third parties.7 This implies that the ﬁnal assembler can refuse payment after the intermediate has been produced and the parties have tobargain on the division of the joint surplus that will materialize after
ﬁnal assembly. This gives rise to a holdup problem insofar as the production cost of the variety-speciﬁc input, which has no alternative useat the bargaining stage, is sunk. The transaction costs involved in expost bargaining may then cause both parties to underinvest in theircontractual relation, thus reducing their joint surplus.
Speciﬁcally, deﬁne s_ ¼ ds=dt and m_ ¼ dm=dt as the ﬂows of new
entrants as ﬁnal assemblers and suppliers, respectively, that is, thenumbers of new assembler and supplier blueprints invented at time t.
Let nðs_ ; m_ Þ a minðs_ ; m_ Þ be a constant-return-to-scale matching functionthat at time t determines the number of new supplier-assembler

74

Alireza Naghavi and Gianmarco Ottaviano

matches given the number of entrants of each type s_ and m_ . Then if
we deﬁne r 1 m_ =s_ , hðrÞ 1 nðs_ ; m_ Þ=s_ is the matching probability of anassembler entrant, while hðrÞ=r is the matching probability of a supplier entrant. Accordingly, the relative abundance of the two types ofentrants determines their probabilities of being matched.
After a match is formed, each pair of ﬁrms bargains on the divisionof their joint surplus, given by the prospective revenues of the corresponding variety. Since both parties cannot ﬁnd a replacement, there
is bilateral monopoly so that they will eventually agree on a share thatmakes both better off than if they had not met. We denote the bargaining weight of the intermediate input producer by o.
To summarize, in each period t, the sequence of actions is the following. First, R&D takes place, and ﬁrms choose their mode of entry bybuying the corresponding patents. Second, prospective parties of an
outsourcing agreement search for partners, which could end in a successful or an unsuccessful match. Unmatched entrants exit, and their
blueprints are destroyed. Third, each matched intermediate producer
manufactures the input needed by its partner. Fourth, parties bargain
over the division of total revenues from ﬁnal sales, and inputs arehanded over to assemblers. Fifth, ﬁnal assembly takes place, and theﬁnal goods are sold to households, together with those supplied byvertically integrated ﬁrms.
4.3

Organization and Product Variety

At time t the instantaneous equilibrium is found by solving the model
backward from ﬁnal production to R&D for given numbers of eachtype of blueprints: vertically integrated ﬁrms v, intermediate suppliersm, and ﬁnal assemblers s. For production and innovation to take placeat time 0, we assume that the economy is initially endowed with positive stocks of both vertically integrated and matched pairs of specialized blueprints: v0 > 0 and f0 > 0.8
4.3.1 Production
Varieties can be sold to ﬁnal customers by two types of ﬁrms: verticallyintegrated ﬁrms and ﬁnal assemblers. A typical vertically integrated
ﬁrm faces a demand curve derived from equation 4.3 and a marginal
cost equal to l. It chooses its scale by maximizing its operating proﬁt,
pv ¼ pv yv  lxv ;ð4:5Þ

Outsourcing, Contracts, and Innovation Networks

75

where xv is the amount of the intermediate input produced and yv ¼ xv
is ﬁnal output. Optimal ﬁnal output and price are then given by 1=ð1aÞa
xv ¼ yv ¼ A
l

ð4:6Þ

and
l
pv ¼ :að4:7Þ

Replacing these values in equation 4.5 results in operating proﬁt equalto a=ð1aÞa
pv ¼ ð1  aÞA
;
l

ð4:8Þ

which is a decreasing function of the elasticity of substitution 1=ð1  aÞand of the marginal cost l.
Turning to outsourcing, there is a one-to-one equilibrium relationship between the number of matched assemblers, the number ofmatched intermediate suppliers, and the number of outsourced varieties, which are all equal to f . The joint surplus of a matched pair ofentrants is given by the revenues from the ﬁnal sales of the corresponding variety ps ys . This is divided according to the bargaining weights ofthe parties. Accordingly, a share ð1  oÞ goes to the ﬁnal assembler:
ps ¼ ð1  oÞps ys :

ð4:9ÞThe remaining ops ys goes to the intermediate supplier.
Moving one step backward, the intermediate producer must decide
how much input xm to produce, anticipating a share of revenues ops ys
while bearing a cost of xm units of labor. Therefore, the intermediate
supplier maximizes
pm ¼ ops ys  xm ;

ð4:10Þ

which implies intermediate and ﬁnal outputs equal toxm ¼ ys ¼ AðaoÞ 1=ð1aÞð4:11Þ

with associated prices
pm ¼

1
;
o

ps ¼

1
:
ao

ð4:12Þ

76

Alireza Naghavi and Gianmarco Ottaviano

Note that pv =ps ¼ lo, which is the ratio of the efﬁciency loss of vertical
integration to that of outsourcing. The former stems from the lack of
specialization, the latter from intermediate underproduction due toholdup fears. Using these results in equations 4.9 and 4.10 gives
the operating proﬁts of matched ﬁnal assemblers and intermediate
suppliers:
ps ¼ ð1  oÞAðaoÞ a=ð1aÞð4:13Þ

andpm ¼ ð1  aÞoAðaoÞa=ð1aÞ :ð4:14Þ

Finally, when both vertically integrated ﬁrms and ﬁnal assemblers
are active, substituting equations 4.7 and 4.12 into 4.2 and 4.4 allows
us to write aggregate demand as
E
A¼ 
;
a a=ð1aÞþ f ðaoÞ a=ð1aÞv l

ð4:15Þ

where v is the number of vertically integrated ﬁrms and f is the number of matched pairs of specialized producers that are active at time t.
4.3.2 Innovation
Going backward, we reach the entry stage. Here labs invent new blueprints at marginal costs k v , k m , and ks depending on the organizationalmodes. Their output determines the laws of motion of v and f . For vertically integrated ﬁrms, we have
v_ ¼

LvI
 dv;
kv

ð4:16Þ

where v_ 1 dv=dt, LvI is labor employed in inventing new blueprints forvertically integrated production, 1=k v is its productivity, and d is thedepreciation rate. For specialized pairs, we havef_ ¼ hðrÞs_  df

with

r1

m_
LI
LI
; s_ ¼ s ; m_ ¼ m ;
s_
ks
km

ð4:17Þ

where f_ 1 df =dt, LsI , and LmI are labor employed in inventing new ﬁnal
assembler and intermediate supplier blueprints, while 1=ks and 1=k m
are their respective productivities.

Outsourcing, Contracts, and Innovation Networks

77

Labs pay their researchers by borrowing at the interest rate R whileknowing that the resulting patents will generate instantaneous dividends equal to the expected proﬁts of the corresponding ﬁrms. Since
specialized entrants are not sure of being matched, equations 4.13 and4.14 imply that the expected dividends of intermediate and ﬁnal assembly patents are, respectively,
pme ¼ ð1  aÞhðrÞoAðaoÞ a=ð1aÞr

ð4:18Þ

andpse ¼ hðrÞð1  oÞAðaoÞa=ð1aÞ :ð4:19Þ

Then if we call Jj the asset value of a patent for j ¼ v; s; m, arbitrage inthe capital market implies
R¼

pje
Jj

þ

J_j
Jj

 d;

ð4:20Þ

where J_j 1 dJj =dt is the capital gain.
Due to perfect competition in R&D, patents are priced at marginal
cost, which requires
J j ¼ kj :The value of a patent is therefore constant through time so that J_j ¼ 0.
When substituted into equation 4.20, these results giveRþd¼

pv pse pme¼ ¼;
k v ks k m

ð4:21Þ

which pins down the interest rate in the Euler, equation 4.1.
Finally, the aggregate resource constraint (or full employment condition) closes the characterization of the instantaneous equilibrium.
Since labor is used in innovation and in intermediate production byboth vertically integrated and specialized producers, we have L ¼
LvI þ LsI þ LmI þ vlxv þ fxm . By equations 4.6, 4.11, 4.16, and 4.17, thecondition can be rewritten as 1=ð1aÞa
L ¼ k v ðv_ þ dvÞ þ ks s_ þ k m m_ þ vlA
þ fAðaoÞ 1=ð1aÞ :lð4:22Þ

78

Alireza Naghavi and Gianmarco Ottaviano

4.3.3 Equilibrium
The ﬁrst thing to notice is that in any instant t, there is never simultaneous invention of both vertically integrated and specialized blueprints. This would be the case if all equalities in equation 4.21 held at
the same time. This is generally impossible. To see this, consider ﬁrst
that new outsourcing agreements are signed only if there is new creation of both intermediate supplier and ﬁnal assembler blueprints,
which requirespmepeks ð1  aÞo;¼ s , r ¼ r1
k m kskm 1  oð4:23Þ

where we have used equations 4.18 and 4.19. Thus, the two types of
specialized blueprints have to be invented in ﬁxed proportion. Second,
if vertically integrated patents are simultaneously invented, it must be
pv pseð1  aÞla=ð1aÞ hðrÞð1  oÞo a=ð1aÞ¼,¼:
k v kskv
ks
Since both sides are constant, this equality is satisﬁed only for a zeromeasure set of parameter values. Hence, in general, vertically integrated and specialized blueprints are not invented together in
equilibrium. In particular, only the former are created when
ð1  aÞla=ð1aÞ hðrÞð1  oÞo a=ð1aÞ
>
;
kv
ks

ð4:24Þ

and only the latter when the reverse is true.
Vertical Integration
When condition 4.24 holds, LsI ¼ LmI ¼ 0, so no new specialized blueprints are ever created: s_ ¼ m_ ¼ 0. As a result, the initial stocks of specialized blueprints are eroded by depreciation:
f_ ¼ df :ð4:25Þ

Then, using equations 4.6, 4.8, 4.15, and 4.21, the full employment condition, equation 4.22, and the Euler condition, equation 4.1, can be respectively rewritten as  1=ð1aÞvl al
þ f ðaoÞ 1=ð1aÞ
L ¼ k v ðv_ þ dvÞ þ E   a=ð1aÞ
v al
þ f ðaoÞ a=ð1aÞð4:26Þ

Outsourcing, Contracts, and Innovation Networks

79

anda a=ð1aÞE_ ð1  aÞEl¼
 r  d:a a=ð1aÞkv
Ev
þ f ðaoÞ a=ð1aÞð4:27Þ

l

Equations 4.25, 4.26, and 4.27 form a three-dimensional dynamic system that has a unique steady state in E, v, f , and is saddle-path stable(see the appendix). The steady-state values can be obtained by solving
the system after setting E_ ¼ v_ ¼ f_ ¼ 0:
Ev ¼

rþd
L;
d þ ar

vv ¼

1a L
;
d þ ar k v

fv ¼ 0:

ð4:28Þ

Due to depreciation, the steady-state mass of vertically integrated
ﬁrms is maintained through ongoing innovation. When all ﬁrms aredestroyed instantaneously ðd ¼ 1Þ, these results are the same as in the
dynamic model of Grossman and Helpman (1991). In addition, when
there is no time discounting ðr ¼ 0Þ, they are the same as in the static
model by Grossman and Helpman (2002).
Outsourcing
When condition 4.24 does not hold, LvI ¼ 0, so no vertically integrated
blueprints are ever created, implying that their initial stock is depleted
by depreciation:v_ ¼ dv:

ð4:29Þ

Using equations 4.13, 4.14, 4.15, 4.17, 4.21, and 4.23, the full employment condition, 4.22, and the Euler condition, 4.1, can be respectively
rewritten as  1=ð1aÞvl al
þ f ðaoÞ 1=ð1aÞ
ks þ k m r _L¼
ð f þ df Þ þ E   a=ð1aÞhðrÞ
v a
þ f ðaoÞ a=ð1aÞð4:30Þlanda a=ð1aÞE_ hðrÞð1  oÞEl¼
 r  d:  a=ð1aÞks
Ev a
þ f ðaoÞ a=ð1aÞð4:31Þ

lThis dynamic system 4.29-4.30-4.31 has a unique steady state, and
it is saddle-path stable (see the appendix).9 The associated level of80

Alireza Naghavi and Gianmarco Ottaviano

expenditures and numbers of ﬁrms can be obtained by solving thesystem after setting E_ ¼ f_ ¼ v_ ¼ 0:
E ¼

rþd
L;
d þ oarf  ¼ hðrÞ1o L;d þ oar ks

v  ¼ 0:

ð4:32Þ

Note that the number of active outsourcing pairs fs depends on thematching probability of assembler entrants hðrÞ. Again, due to depreciation, the steady-state masses of ﬁrms are maintained through ongoing
innovation. Given equation 4.23, imposing f_ ¼ 0 and r ¼ r in equation
4.17 allows us to determine the ﬂows of assembler and intermediate
entrants in each period:s_  ¼

dð1  oÞ L;d þ oar ks

m_  ¼

doð1  aÞ L:d þ oar k m

ð4:33Þ

Note that the static equilibrium in Grossman Helpman (2002) corresponds to the steady state of our model when r ¼ 0 (no time discounting) and d ¼ 1 (all ﬁrms die every period).
4.3.4 Comparative Statics
Economic intuition on the driving forces behind the choice of the organizational mode is boosted by remembering that a ¼ ð1  1=sÞ and rewriting equation 4.24 as
1
hðrÞ
|{z}

1=s
1
o
|ﬄﬄ{zﬄﬄ}

probability v=s proﬁt share v=s


l 1s
>
1=o
|ﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄ}
revenues v=s

kv
ks
|{z}

ð4:34Þ

R&D cost v=s

withdhðrÞ > 0;
dr r¼ r

r¼

ks
km
|{z}

1=s
:
1=o  1
|ﬄﬄﬄﬄ{zﬄﬄﬄﬄ}

ð4:35Þ

R&D cost s=m margin s=m
r k m 1=o  1 1=s
l 1s k v>hðrÞ ks 1=s 1  o 1=oksoðloÞ s1 hðrÞ=r < k m =k v :If condition 4.34 holds, all entrants choose vertical integration. Of
course, this is the case when the relative beneﬁts of vertical integration
dominate the relative costs. The left-hand side of equation 4.34 shows

Outsourcing, Contracts, and Innovation Networks

81

that the former come from three sources: the fact that specialized ﬁnal
assemblers face matching uncertainty whereas vertically integrated
ﬁrms do not ð1=hðrÞÞ, the relative proﬁt margin ðð1=sÞ=ð1  oÞÞ, andthe relative total revenues ððloÞ 1s Þ. The right-hand side shows instead that the relative costs of vertical integration derive from the costs
of innovation ðk v =ks Þ. Then vertical integration is chosen when specialized ﬁnal assemblers have low chances of ﬁnding specialized intermediate suppliers (small hðrÞ); when product differentiation is strong,so that the proﬁt share of revenues of vertically integrated ﬁrms islarge (large 1=s) relative to the share appropriated by ﬁnal assemblers
through bargaining (small 1  o); when vertically integrated revenues
are relatively large due to small gains from specialization (small l) andsevere intermediate underproduction caused by weak supplier bargaining power (small o); and when the blueprints for vertically integrated production are relatively cheap compared with those for
specialized assembly (small k v =ks ). Expressions 4.35 highlight the factthat the matching probability of specialized assemblers itself depends
on the relative R&D costs ðks =k m Þ and the relative proﬁt margin of ﬁnal
assemblers and intermediate suppliers ðð1=sÞ=ð1=o  1ÞÞ. When their
R&D costs are relatively small and the proﬁt margin is relatively large,
the entrants are mostly ﬁnal assemblers, reducing their probability hðrÞof being matched. This makes condition 4.34 easier to fulﬁll.
All parameters have unambiguous impacts on the propensity to vertical integration except s and o. Larger s unambiguously fosters outsourcing provided that lo > 1. Otherwise that happens only if s issmall enough. This can be understood by plugging r from equation
4.35 in 4.34 and rewriting the resulting condition as oðloÞ s1 hðrÞ=r <k m =k v . As larger s decreases r, it always raises the matching probabilityof intermediate suppliers hðrÞ=r. On the other hand, larger s ampliﬁes
the revenue advantage of ﬁnal assemblers ðloÞ s1 if their relative marginal costs are lower ðlo > 1Þ and their revenue disadvantage if theirrelative marginal costs are higher ðlo < 1Þ. This is because larger s
makes demand more sensitive to small price differences. In the former
case, both effects work in the direction of fostering outsourcing. In thelatter, the relative revenue effect favors vertical integration, the moreso the larger is s.
As to o, stronger supplier bargaining power also has two opposite
effects: it promotes intermediate production but at the same time
reduces the matching probability of intermediate suppliers. While the82

Alireza Naghavi and Gianmarco Ottaviano

former effect fosters outsourcing, the latter hampers it. Favorable scenarios for outsourcing strike a balance between the two effects. This
happens for values of o that are neither too small nor too large. Too
see this, use equation 4.24 to derive the following condition for outsourcing to dominate vertical integration:
g1

hðrÞð1  oÞk vðolÞ a=ð1aÞ > 1:
ð1  aÞks

Then, recalling the value of r from equation 4.23, g is an increasing
function of o if and only if
eh >

oa
;
1a

where e h is the elasticity of hðrÞ with respect to r. Given our assumptions of the matching function, we have 0 < e h < 1, and therefore g
is increasing (decreasing) in o when this is very small (large).
This implies a relationship between the incentives to outsource and thebargaining power of intermediate suppliers that has an inverted-U
shape.
All results so far mirror those in Grossman and Helpman (2002).
Parameters speciﬁc to our dynamic setting play a role when we turn tosteady-state outcomes. Most parameters have the same impact underboth vertical integration and outsourcing. Larger elasticity of substitution (larger s, i.e., larger a) reduces both expenditures and variety. The
reason is thinner proﬁt margins, which discourage innovation andforce ﬁrms to employ more workers to cover their ﬁxed R&D costs
through large-scale production. Faster depreciation (larger d) also negatively affects both expenditures and variety as it reduces the incentives to innovate and diverts labor from alternative use. Differently,
stronger time preference (larger r) has a negative impact on productvariety but a positive one on expenditures since it biases intertemporaldecisions toward consumption and away from saving. Finally, higher
costs of innovation (larger k v , ks , or k m ) have no impact on expenditures and a negative impact on product variety, whereas a larger economy (larger L) supports both higher expenditures and more productvarieties.
The bargaining weight o is, of course, peculiar to outsourcing.
Larger o is associated with smaller expenditures. Its impact on productvariety is instead ambiguous depending on the speciﬁc functional form

Outsourcing, Contracts, and Innovation Networks

83of hð:Þ. Given equation 4.32, f  is an increasing function of o if andonly ifeh >do þ oar:d þ oarSince 0 < e h < 1, this condition holds for o ¼ 0 and is violated foro ¼ 1. Hence, product development is higher for values of o that areneither too small nor too large. This is because larger o encourages
more intermediate entry (larger r) and thus increases the matchingprobability of assemblers (larger hðrÞ). On the other hand, it reduces
their share of surplus once matched. Finally, larger o always leads tofaster convergence to steady state (see the appendix).
4.4

Conclusion

We have proposed a theoretical framework to shed light on some
aspects of the new approach to innovation that relies on increasingly
global networks of partners. In particular, conditional on the outsourcing of innovation occurring, we have studied how alternative organizational forms in production arise and how these affect the incentives
to innovate.
The underlying idea is that the outsourcing of production brings
about gains in terms of both lower costs of R&D and higher beneﬁts ofspecialization in upstream and downstream production. It is, however,associated with larger transaction costs due to incomplete contracts
and holdup problems. We have shown that the bargaining power of
upstream and downstream parties at the production stage feeds backto R&D incentives, thus affecting innovation. The reason is that specialized production also requires specialized R&D, whose returns dependon the bargaining outcomes. Product development is best served bycontracts in which the bargaining power of upstream suppliers is neither too weak nor too strong.
The proposed framework combines the new features of outsourcing
contracts as in Grossman and Helpman (2002) with the well-known
model of growth under horizontal differentiation as in Grossman andHelpman (1991). While one might have guessed that the combination
would be too complex to analyze, we have shown that this is not thecase. Indeed, as discussed by Naghavi and Ottaviano (2005a, 2005b),
the framework is simple enough to be extended to model endogenous

84

Alireza Naghavi and Gianmarco Ottaviano

growth and study how the organizational choices of ﬁrms affect thelong-run growth rate of the economy even in the presence of heterogenous ﬁrms. These are interesting directions for future research.
Appendix: Stability of Steady States
We show that in section 4.3.3 the steady states with vertical integrationand outsourcing are both saddle-path stable. Consider the former case.
The corresponding dynamic system is formed by equations 4.27, 4.26,
and 4.25. The Jacobian matrix evaluated at equation 4.28 is
2

dþr

6
6
Dv 1 6  a
4 kv



3

ðdþrÞ 2 k v
1a



d

ðdþrÞað1oÞðloÞ a=ð1aÞ 7
5
1a

0

d

0

ðdþrÞ 2 k v
a=ð1aÞ
1a ðloÞ
7

7

with eigenvaluessﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃrrðd þ rÞðd þ arÞ1þ4;
l1;v 2 ¼ G
22r 2 ð1  aÞl3v ¼ d:

Consider now the outsourcing case. The associated dynamic system
is formed by equations 4.31, 4.29, and 4.30. The Jacobian matrix evaluated at steady state in equation 4.32 is given by
2
6
6
D 16
6
4

ðdþrÞ 2 k sðdþrÞ 2 khðrÞð1oÞðloÞ a=ð1aÞ hðrÞð1oÞs

0

d

0

hðrÞaoð1oÞ ks ð1aoÞðdþrÞað1oÞ

d

dþr





ð1aoÞðloÞ a=ð1aÞ

3
7
7
7:
7
5

The associated eigenvalues are independent from hðrÞ:sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃrrðd þ rÞðd þ oarÞ1þ4
l1; 2 ¼ G
; l3 ¼ d:2
2r 2 ð1  aoÞ
Then, all the rest given, the speed of convergence to steady state isincreasing in o.
Notes
We are indebted to Elhanan Helpman, two anonymous referees, and seminar participants at the PSE-CEPR workshop, ‘‘Globalization and Contracts,’’ in Paris as well as at

Outsourcing, Contracts, and Innovation Networks

85

the CESIFO workshop, ‘‘Globalization and the Multinational Enterprise,’’ in Venice for
helpful comments.
1. See Helpman (2006) for an overview of recent models of ﬁrm involvement in foreign
activities and Gattai (2005) for a survey of additional applications of the theory of theﬁrm to international trade issues.
2. Marin and Verdier (2003) as well as Antras (2003) argue that within a vertically integrated ﬁrm, the agreements among stakeholders are also incomplete. This approach differs from the transaction-cost approach adopted by Grossman and Helpman (2002, 2003,
2005) in the wake of Williamson (1985). It is, instead in line with the property rights
theory proposed by Grossman and Hart (1986) and further developed by Hart andMoore (1990), according to which holdup problems arise also within integrated ﬁrms
with their relevance depending on the allocation of property rights between stakeholders.
3. Speciﬁcally, when all ﬁrms are destroyed instantaneously, our results are the same asin the dynamic model by Grossman and Helpman (1991). In addition, when there is notime discounting, they are the same as in the static model by Grossman and Helpman(2002).
4. Our analysis is performed under the assumption of constant-returns-to-scale matching. Grossman and Helpman (2002) also consider the case of increasing returns to scaleand show how matching externalities may generate multiple stable steady states. We do
not cover this case but note that with explicit transitionary dynamics and multiple stablesteady states, history (‘‘initial conditions’’) or expectations (‘‘initial beliefs’’) would determine the steady state that is eventually reached, depending on the speed of adjustment
and the strength of the externalities (Ottaviano 2001).
5. The stability analysis is presented in the appendix, which reports the eigenvalues of the
dynamic systems. Together with the steady-state values in the main text, the eigenvalues
allow one to derive the (unreported) adjustment paths following standard techniques.
6. This assumption captures the idea that the coordination of research teams is more
complex when their aim is to create vertically integrated blueprints. In other words, thegovernance costs of R&D labs are higher for vertically integrated than for specialized
blueprints. In equilibrium, such assumption will prevent vertically integrated ﬁrms frombuying inputs from specialized suppliers.
7. As in Grossman and Helpman (2002, 2003, 2005), unobservable input quality is an
issue to the extent that only high-quality inputs can be processed, whereas low-quality
inputs are useless even though freely supplied.
8. The zero-measure case with v0 > 0 and f0 ¼ 0 is discussed in section 4.3.3 for comparison with the static setup.
9. In the static model by Grossman and Helpman (2002), the outcome such that all ﬁrms
are vertically integrated remains an equilibrium even when condition 4.24 is violated. In
particular, it is a self-fulﬁlling expectation equilibrium supported by the common belief
that no specialized ﬁrm will ever enter the market. As this implies zero matching probability, no specialized ﬁrm will indeed enter, thus making the common belief selffulﬁlling. This equilibrium is, however, unstable: any specialized entry would make allﬁrms abandon vertical integration. In our dynamic model, the positive initial stockf0 > 0 rules out the possibility of such a self-fulﬁlling equilibrium. This would be viable
only in the zero-measure case where f0 ¼ 0 and v0 > 0.

86

Alireza Naghavi and Gianmarco Ottaviano

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