integration versus outsourcing in industry …erossi/courses_files/intout.pdf · integration versus...

INTEGRATION VERSUS OUTSOURCINGIN INDUSTRY EQUILIBRIUM*

GENE M. GROSSMAN AND ELHANAN HELPMAN

We develop an equilibrium model of industrial structure in which the orga-nization of rms is endogenous. Differentiated consumer products can be pro-duced either by vertically integrated rms or by pairs of specialized companies.Production of each variety of consumer good requires a specialized component.Vertically integrated rms can manufacture the components they need, but theyface a relatively high cost of governance. Specialized rms can produce at lowercost, but search for partners is costly, and input suppliers face a potential holdupproblem. We study the determinants of the equilibrium mode of organizationwhen inputs are fully or partially specialized.

I. INTRODUCTION

The make-or-buy decision is fundamental to industrial or-ganization. Hundreds of activities go into the sale of a nishedproduct, from basic research to product design, from preparationand installation of machinery and the production of components,to assembly, packing, marketing, and shipping. For each suchactivity, a producer must decide whether to undertake the activ-ity in-house or to purchase the input or service from the outside.As Coase [1937] emphasized long ago, the cumulation of thesedecisions denes the boundaries of the rm.

Outsourcing is more prevalent in some industries than oth-ers. Helper [1991], for example, has documented the pervasiveoutsourcing of parts by U. S. automobile producers. Even in agiven industry, the mode of organization may vary from oneregion or country to another. Chinitz [1961] found that rms inPittsburgh typically engage in a wider range of activities thansimilar rms located in New York City, while many have notedthe relatively greater prevalence of vertical integration in theJapanese and Korean consumer electronics industries as com-pared with the United States. Industrial organization alsoevolves over time. Several researchers have observed that out-sourcing seems to be on the rise in recent years; for example,Abraham and Taylor [1996] substantiate an increase in the out-

* A previous version of this paper was titled Imperfect Contracts and Indus-trial Organization. We thank Patrick Bolton, Eddie Dekel, Drew Fudenberg,Edward Glaeser, Oliver Hart, Giovanni Maggi, Ariel Rubinstein, Steven Tadelis,and Manuel Trajtenberg for helpful comments and the National Science Founda-tion and the US-Israel Binational Science Foundation for nancial support.

2002 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnology.The Quarterly Journal of Economics, February 2002

85

sourcing of business services in thirteen U. S. industries, whileCampa and Goldberg [1997] and Hummels, Rapoport, and Yi[1998] report evidence of growth in international outsourcing.1

Economists who have studied the make-or-buy decision havefocused on the bilateral relationship between a single producerand a potential supplier. Beginning with Williamson [1975, 1985]and Grossman and Hart [1986], a body of literature has developedthat claries the role of transactions costs, asset specicity, andincomplete contracts in guiding a rms choice of whether toundertake an activity in-house or to seek to ll the need from theoutside. Yet, inuential as this work has been, it can provide onlya starting point for understanding cross-sectional or cross-re-gional differences in outsourcing behavior, or for evaluating ex-planations for recent trends. This is because a decision-theoreticapproach treats the industry environment as given, and therebyneglects the interdependence among the choices facing the vari-ous rms in an industry. For example, the attractiveness ofoutsourcing to a certain producer may well depend on how manyrms potentially can provide the inputs it needs, which in turnmay depend on whether other rms in the industry have chosento be vertically integrated or to buy their inputs from others.

In this paper we offer a framework for examining industrialstructure in which integration and outsourcing are treated asequilibrium phenomena. In modeling the determinants of themode of organization, we emphasize a trade-off between the costsof running a larger and less specialized organization and coststhat arise from search frictions and imperfect contracting. Avertically integrated rm may face a higher cost of producingcomponents and services, because such a rm has many divisionsto manage, and because the organization does not benet fromthe learning that comes with specializing in a single activity. Buta rm that opts to outsource its components must search for asuitable partner, and if successful, must try to provide its partnerwith incentives to produce inputs to its specications and in thequantity it demands. Search is costly and does not always end insuccess. And contracting may be imperfect, if some attributes ofthe input are not veriable by third parties.

Our model incorporates a rudimentary treatment of searchfrictions and contractual incompleteness, based on the early

1. See McMillan [1995], who surveys the evidence on increased outsourcingand discusses possible explanations for these trends.

86 QUARTERLY JOURNAL OF ECONOMICS

works in these areas by Diamond [1982], Williamson [1975, 1985]and others. At the same time, we require that all rms entry,contracting, and pricing decisions are optimal given the choicesmade by others. By so doing, we are able to identify the feedbackmechanisms by which a rms choices affect market conditions,which in turn inuence other rms decisions about organiza-tional form.2

In the next section we develop a simple, multi-industry modelin which differentiated consumer products can be produced eitherby vertically integrated rms or by pairs of specialized compa-nies. In the latter case, one rm manufactures an intermediateinput while the other designs and assembles a variety of the nalproduct. The production of each variety of consumer good requiresa unique, specialized component. Vertically integrated rmsmanufacture their own components in the quantity and designthat maximizes prots. However, such rms face relatively highxed and variable production costs, due to their lack of completespecialization and the extra governance costs associated withtheir extensive organizations. Specialized rms may be able toproduce at lower cost, but they suffer from two potential disad-vantages. First, a specialized nal good producer must nd asuitable supplier of inputs, while a specialized component pro-ducer must nd a potential customer. We model search as amatching process, in which some rms are successful in locatingpartners and others are not. Second, the specialized rms maysuffer from an inability to prove the quality and other attributesof an input to outside parties. This limits contracting possibilitiesand creates a potential holdup problem.

In Section III we characterize the equilibrium modes of or-ganization under the assumption that the search technology ex-hibits constant returns to scale. With constant returns in search,a doubling of the number of specialized rms of each type resultsin a doubling of the number of partnerships that are formed. Weshow that, except in a knife-edge case, there are no equilibria inwhich an industry is populated by both specialized and verticallyintegrated rms. We then discuss the conditions for the existenceof an equilibrium with pervasive vertical integration and theconditions for the existence of one with pervasive outsourcing. Wealso discuss the stability of each type of industry equilibrium.

2. See McLaren [2000] for an interesting predecessor to this paper, which,however, was constructed to make a more narrow point.

87INTEGRATION VERSUS OUTSOURCING

In Section IV we identify the industry conditions that sup-port vertical integration or outsourcing as the equilibrium modeof organization. We focus especially on how the efciency of thesearch technology, the degree of substitutability between an in-dustrys consumer products, and the distribution of bargainingpower between intermediate and nal-good producers affect theviability of each organizational form. Improvements in thematching of buyers and suppliers of specialized inputs and busi-ness serviceswhich may have resulted from the IT revolutioncan give rise to an increase in outsourcing activity. A more subtlerole is played by the elasticity of demand for consumer goods. Amore elastic demand for nal goods may favor either outsourcingor integration, depending on the size of the cost advantage ofspecialized producers and the distribution of bargaining powerbetween intermediate-good and nal-good producers. Thus, thegreater prevalence of outsourcing in the United States comparedwith Japan or Korea might be explained by the relatively greaterdegree of competition in the U. S. market, but only if the costadvantage of specialized producers is relatively large or the shareof the surplus in a bilateral relationship that accrues to the nalproducer is relatively small.

With constant returns to matching, neither the size of anindustry nor the size of the aggregate economy favors one mode ofindustrial organization over the other. But size can matter whenthere are increasing returns to scale in matching, as we show inSection V. When the chances of nding a suitable partner im-prove for a given rm as the number of rms on each side of themarket grows, there can be two stable equilibria for an industry,one with vertical integration and the other with pervasive out-sourcing. Outsourcing is more likely to be viable in large indus-tries and in large economies, due to the benets of having athicker market. This might help to explain the greater special-ization of rms in New York City compared with Pittsburgh, andperhaps in the United States compared with elsewhere in theworld.

In Section VI we extend our model to allow for a secondarymarket in intermediate inputs. The simple model overstates theholdup problem for many industries, because we assume thatinput producers have no option to sell their wares to any rmother than the one for whom the components were designed. Inreality, specialization typically occurs in stages, and it is oftenpossible to recoup some of the investment if it becomes necessary


to nd a new business partner. To capture this idea, we introducecomponents that differ in their degree of specialization. We asso-ciate with each nal good an ideal component, which is the onemost suitable for producing that good. But nal producers can useinputs of different specications at an additional cost. Now thebargaining between supplier and nal producer takes placeagainst a backdrop in which each side has an outside option.

In the extended model, component producers choose the de-gree to which they specialize their inputs for their prospectivecustomers. A more specialized input offers greater prot oppor-tunities in its intended use. But a more generic input enhancesoutside options and so improves the input producers bargainingpower. In equilibrium the producer strikes a balance between theopposing forces, and manufactures a component that is partiallyspecialized. We describe the determinants of the equilibriumdegree of specialization and the mode of organization. Here weconsider a new factor, which is the sensitivity of manufacturingcosts of nal goods to the specications of the component. Weshow that, contrary to what one might have expected, a greatersensitivity of manufacturing costs of nal goods to the specica-tions of the components does not necessarily favor vertical inte-gration as an equilibrium mode of organization. When sensitivityof production costs to input specications rises, this strengthensthe bargaining position of potential input providers, which mayenhance their protability despite the direct effect of a decline inthe efciency of arms-length dealing.

Section VII provides a brief summary and some concludingremarks.

II. A SIMPLE MODEL

We begin with a simple version of our model. In the simpli-ed model, intermediate inputs must be fully tailored to a par-ticular product or else they are worthless to the nal producer.With this assumption, an input producer has no choice but to sellits output to the rm for whom it was designed. Later, we willallow nal producers to use components that are not built exactlyto their specications. Then we will treat the degree of special-ization as a choice variable for the input providers.

The economy has J industries. In each industry, rms pro-duce a continuum of different varieties. The representative con-sumer maximizes a utility function of the form,


(1) u 5 Oj 5 1

J

m j log F E0

Nj

yj ~ i !a j di G 1/ a j,

where yj(i) is consumption of variety i in industry j and Nj is thenumber (measure) of differentiated varieties produced by thatindustry. We assume that S j m j 5 1, so that the parameter m jgives the share of spending that a consumer devotes to productsof industry j. The parameter a j [ (0,1) measures the degree ofproduct differentiation in industry j; the greater is a j, the lessdifferentiated are the outputs of the industry. There is a unitmeasure of consumers.

As is well-known, these preferences yield demand functions,

(2) y j ~ i ! 5 A jp j ~ i ! 2 1 / ~ 1 2 a j ! ,

where pj(i) is the price of good i in industry j,

Aj 5m jE

* 0Nj p j ~ i ! 2 a j / ~ 1 2 a j ! di

,

and E is aggregate spending. The unique supplier of variety i inindustry j treats A j as a constant, and so perceives a constantelasticity of demand 1/(1 2 a j). Aggregate spending equals na-tional income in the general equilibrium.

The production of a unit of any nal good requires one unit ofa specialized component. For now, the component must be exactin its specications, and the different nal goods require distinctcomponents. An input must also be of suitably high quality, orelse it is useless for producing nal output. Besides the interme-diate goods, there are no other variable inputs into nal produc-tion. However, there are xed costs associated with entering themarket and searching for a potential supplier.

Final goods may be produced by vertically integrated rms orby specialized producers that purchase their inputs at armslength. A rm that specializes in manufacturing intermediatescan produce a high quality input with one unit of labor per unit ofoutput. Alternatively, it can produce a low quality (and thereforeuseless) input at some lower cost. An integrated rm in industryj requires l j $ 1 units of labor to produce a unit of the (highquality) intermediate. The possibility that production may bemore costly for an integrated rm reects the fact that its activ-


ities are not so highly specialized and that the bureaucratic costof managing a larger operation may be higher.3

As for the xed costs, these may vary by type of rm andmode of organization. The total xed input required of a verticallyintegrated rm in industry j is k jv units of labor. This includes theresources needed to enter the market (e.g., researching the mar-ket opportunities and setting up an organization), those needed todesign a product, and those necessary for corporate governance.The xed input requirement for a specialized producer of inter-mediates in industry j is kjm units of labor. This includes ele-ments that are analogous to those for a vertically integrated rm,and also the resources required to search for a potential partner.A specialized producer of nal goods in industry j has a xedinput requirement of kj s units of labor, which similarly includes asearch component. We assume that the xed costs for an inte-grated rm are no lower than those for a pair of specializedproducers; i.e., kjs 1 kjm # k jv.

Our setting is one with incomplete contracting. We supposethat the quality of an intermediate input can be observed by thecollaborating partners, but cannot be veried by a court of law.The lack of veriability precludes contracts between input sup-pliers and potential customers that stipulate a given price for anagreed quantity. If such a contract were signed, an intermediateproducer could lower its costs by shaving quality. The buyerwould be obliged to buy the inferior products without recourse.Much has been written about possible alternatives to quality-contingent contracts in contexts such as ours. For example,Aghion, Dewatripont, and Rey [1994] argue that specic-perfor-mance contracts coupled with certain renegotiation schemessometimes can be used to promote efcient relationship-specicinvestments. Maskin and Tirole [1999] suggest alternative con-tract contingencies; in our economy, for example, a nal-goodproducer might agree to compensate its component supplier

3. Williamson [1985] emphasized that production by a vertically integratedrm may entail greater governance costs due to attenuated incentives and bu-reaucratic distortions. Holmstrom and Tirole [1991] provide an early analysis oftransfer-pricing incentives within rms, which affect their organizational forms.McAfee and McMillan [1995] have developed a model in which employees withprivate information are organized in a hierarchical structure. The employeescapture informational rents, which cumulate along the hierarchy. They nd thatproduction costs are increasing in the length of a rms hierarchical structure.More generally, there may be some diseconomies of scope that are independent ofthe volume of output and others that affect per unit costs. We allow for both typesof extra costs here.


based on the revenues received from sales of the nal product.Since the nal producer has no moral hazard in choosing itsassembly or marketing efforts, the intermediate producer can begiven the appropriate incentive to invest in quality. In response,Hart [1995], Segal [1999], and Hart and Moore [1999] have ar-gued that there are settings in which these various xes forincomplete contracts fail. We have nothing new to add to thedebate about the foundations of incomplete contracts; we simplyassume that they are a fact of commercial life.

The absence of ex ante contracts creates a potential holdupproblem, as is well known from the writings of Williamson [1985],Klein, Crawford, and Alchian [1978], Hart [1995], and others.Once a component producer specializes its production for a par-ticular nal good, these inputs have no value to other rms. Thenal producer can threaten to refuse delivery of the componentsunless the price is sufciently low. But an ex post negotiation ofthe price leaves the intermediate producer in a relatively weakbargaining position, because the manufacturing costs are by-gones by that time. Foreseeing this prospect, the intermediateproducer has insufcient incentive to produce the efcient quan-tity. The inefciency that results from the holdup problem givesa reason for vertical integration, which must be weighed againstany excess production and governance costs that such an organi-zational structure might entail.4

Having described the technology for production and the lim-itations on contracting, we detail the sequence of events in theeconomy. First, rms enter as either intermediate producers,nal-good producers, or vertically integrated entities. In eachcase, an entrant pays the relevant entry cost. Next, the special-ized rms search for partners. A rm that has entered as aspecialized component producer seeks a producer of nal-goods toserve with inputs. A manufacturer of nished goods seeks aninput provider. Matches occur randomly. We assume that everyspecialized producer of nal goods has the same probability ofnding a supplier. Similarly, every potential producer of compo-

4. As is well-known, the possibility of repeat business can mitigate theholdup problem to some degree. An input supplier might produce high-qualitycomponents even if it is not bound to do so by an enforceable contact, in order toestablish a good reputation with the buyer. Similarly, the buyer might pay a fairprice for the inputs, even when it could capture short-term gains by behavingopportunistically. In many situations, however, the prospect of repeated interac-tion will not fully solve the holdup problem. We choose to keep our model simpleand stark by focusing on a one-shot game.


nents has the same probability of nding a customer. The twoprobabilities are not equal, however; rms on the short end ofthe market have a greater chance of achieving a match.5 Thesearch frictions and associated uncertainties give a second ad-vantage to vertical integration.

When specialized rms are paired in a match, the nal-goodproducer describes its input requirements. Then all integratedrms and component producers manufacture their specializedinputs. These may be of high quality or of low quality, and theymay be produced in any quantity. Firms that have failed in theirsearch efforts have no choice but to exit the market. Next, thespecialized input producers bring their components to their po-tential customers, and the partners negotiate over the terms oftrade. Bargaining results in the input producer in industry jcapturing a fraction v j of the surplus in its relationship with thenal producer. We take the bargaining weights to be exogenous.After the negotiations have been concluded and the inputs turnedover to the nal-goods producers, these producers and the verti-cally integrated rms assemble their differentiated varieties. Fi-nally, the goods are sold to consumers.

To summarize, rms play a game with the following vestages: (1) entry, at which time a portion of the xed costs areincurred; (2) search, at which time the remaining xed costs areincurred and rms that do not nd partners exit the market; (3)production of intermediate inputs; (4) bargaining; and (5) produc-tion and sale of nal goods. In this setting, we seek a generalequilibrium in which the aggregate labor market and all productmarkets clear. Free entry ensures zero expected prots for eachtype of rm that enters a market.6 If some type of rm does notenter in equilibrium, then its expected prots must be zero ornegative. The supply of labor is xed and equal to L. We chooselabor as the numeraire, so that the wage rate is equal to one.

Now we consider the protability of the different types ofrms that might enter in industry j. Since we will focus for the

5. In principle, a rm might enter as vertically integrated and nonethelessseek a potential partner. Then, if it fails to achieve a match, it can produce its owninputs. Even if it nds a partner, it might produce some inputs itself, in order tostrengthen its bargaining position. However, these strategies will not be prot-able if the search costs and the manufacturing costs are sufciently high. Weassume a cost structure such that vertically integrated rms will not wish tosearch for suppliers, without dwelling on the implied parameter restrictions.

6. The matching process creates risk for specialized producers. But thehouseholds hold diversied portfolios of equities, so the rms maximize expectedprots.


time being on this single industry, we omit the index j from theindustry-specic variables.

Let v be the number of rms that enter as vertically inte-grated enterprises, s, the number that enter as specialized pro-ducers of nal goods, and m, the number that enter as specializedsuppliers of intermediate products. The specialized producers ofnal goods seek partners among the potential input producersand vice versa. Not all rms are successful in their searches. Weassume that n(s,m) pairings are formed, where n(s,m) #min{s,m} and n[ is increasing in both of its arguments. For themost part, we will assume constant-returns-to-scale in matching;i.e., a doubling in the number of rms on each side of the marketresults in a doubling in the number of partnerships. But the caseof increasing returns is also of interest, so we will consider itseparately in Section V.7

Since all specialized producers of nal goods have the samechance of nding a partner, the probability of being matched isn(s,m)/s for each one. Assuming that matching has constantreturns to scale, we can rewrite this probability as h (r) [ n(1,r),where r 5 m/s is the ratio of specialized component producers tospecialized nal producers. Similarly, since all intermediate-goodproducers have the same chance of nding a partner, each has aprobability n(s,m)/m 5 h (r)/r of realizing a match. Note that theelasticity of h [ must be smaller than one, in view of the linearhomogeneity of n[. Thus, the probability h (r) increases with r,while the probability h (r)/r declines with r.

Consider what happens after a match takes place between acertain intermediate-good producer and a rm that has developeda certain differentiated product, say good i. If the input providerproduces x(i) units of the specied component, its partner willhave the ability to produce y(i) 5 x(i) units of variety i. Thepotential revenue from sales of these goods is p(i) x(i). Once thex(i) units of the intermediate good have been manufactured, thetwo rms meet to negotiate an exchange. At this point, all costsare sunk. If the exchange takes place, the nal producer stands to

7. Matching functions are commonly used in the analysis of job search; see,for example, Pissarides [2000]. Blanchard and Diamond [1989] nd that thematching of workers and vacancies exhibits constant returns to scale in macrodata. Coles and Smith [1996] corroborate the Blanchard-Diamond ndings usingmicro data. Lagos [2000] develops a spatial model of matching between buyersand sellers, which also implies constant returns to scale in matching. But increas-ing returns can arise if a concentration of searchers in a given geographic areamakes nding a match easier for all parties.


realize revenues of p(i) x(i). If, instead, the rms go their sepa-rate ways, revenues for each side are zero. This is because thenal producer has no alternative source for components, whilethe intermediate producer has a quantity of specialized inputsthat is of no value to any other producer. It follows that theexchange generates a joint surplus of p(i) x(i). In the bargain, therms divide this surplus, with a share v going to the producer ofintermediates and the rest to the nal producer.

Now roll back the clock to the time when the intermediaterm must decide how much to produce and of what quality. Therm foresees a potential reward of v p(i) x(i) from producing x(i)units of a high-quality component. This it could do at a variablecost of x(i). If, instead, it produces low-quality components, notransaction will occur, and all manufacturing costs will be lost.The intermediate rm maximizes prots by choosing to producehigh quality and, in view of the demand function (2), by settingy(i) 5 x(i) 5 A( a v )1 /(1 2 a ). All prices are the same in a symmetricequilibrium. Therefore, the price of a nal good sold by a special-ized producer is

(3) ps 5 1/ a v ,

and the resulting sales are

(4) ys 5 A ~ a v ! 1/ ~ 1 2 a ! .

The price ultimately charged for goods assembled by rms thatoutsource their components is 1/ v times as much as what aunitary actor with a unit cost of one would charge. The dimin-ished output and higher price reect the distortionary impact ofthe imperfect contract.8

A nal-good producer realizes operating prots equal to afraction 1 2 v of its revenues of ps ys . An entrant obtains theseprots if and only if it nds a partner, which happens withprobability h (r). Therefore, the expected prots of a specializedproducer of nal goods are

(5) p s 5 h ~ r ! ~ 1 2 v ! A ~ a v ! a / ~ 1 2 a ! 2 ks,

after taking account of the xed costs of entry and search.

8. This distortion is analogous to the double marginalization that ariseswhen an input supplier with market power prices above marginal cost and thenthe nal producer, also with market power, introduces an additional markup.Double marginalization provides an incentive for vertical integration in marketswith perfect contracts; see, for example, Perry [1989].


An intermediate-good producer captures operating protsequal to a fraction v of the revenue from sales of the nal goodless production costs, or v ps ys 2 ys . An entrant obtains theseprots with probability h (r)/r. Therefore, expected prots for aspecialized producer of intermediate inputs are

(6) p m 5 ~ 1 2 a !h ~ r !

rv A ~ a v ! a / ~ 1 2 a ! 2 km,

again after accounting for xed costs.Notice the positive relationship between the number of one

type of specialized producer and the potential prots of the other.Given an industry demand level A, the expected prots of aspecialized nal-good producer are greater the larger is the num-ber of specialized input suppliers, because an increase in thenumber of potential suppliers improves the prospects for a givennal-goods producer to nd a partner. The expected prots of aspecialized input supplier increase with the number of specializedproducers of nal goods for the same reason. But the expectedprots of each type of producer decline with entry of other rmslike it, because additional rms on the same side of the marketreduce the likelihood of a match for each one. This, of course, is astabilizing force. A second stabilizing inuence comes throughadjustments in the demand factor A, which reects competitionamong the nal-good producers.

A vertically integrated rm faces a marginal production costof l and a demand curve given by (2). The constant demandelasticity dictates markup pricing, with a prot-maximizingprice of

(7) pv 5 l / a .

The resulting sales of a vertically integrated rm are

(8) yv 5 A S a l D 1 / ~ 1 2 a ! .Operating prots of such a rm, which equal revenue less inputproduction costs, are pvyv 2 l yv. Therefore, at the entry stage,the rms expected prots are given by

(9) p v 5 ~ 1 2 a ! A S a l D a / ~ 1 2 a ! 2 kv.In equilibrium, no rm has positive expected prots; i.e., p l #


0 for l 5 v, s, m. Moreover, expected prots are zero for any typeof rm that enters in positive number. With aggregate protsequal to zero, aggregate income and aggregate spending are equalto the aggregate wage bill, L. It follows from the denition of A jin (2) and our pricing equations (3) and (7) that the industrydemand level is given by

(10) A 5m L

v ~ a / l ! a / ~ 1 2 a ! 1 s h ~ r ! ~ a v ! a / ~ 1 2 a !.

This completes our discussion of the prot opportunities in indus-try j.

There are two channels through which rms interact in ourmodel. First, the nal-good producers compete in the productmarket. This affects not only the protability of nal production,but also of specialized input producers, who share in the revenuesfrom downstream sales. Second, specialized rms on each side ofthe market compete for partners, while rms on opposite sides ofthe market provide complementary services. These sorts of inter-actions are the focus of our equilibrium analysis. These consid-erations would be absent, of course, from an analysis that ad-dressed only the incentives facing a pair of rms.

III. TYPES OF EQUILIBRIA

Three types of outcomes may characterize the organization ofrms in our model: the rms in an industry may all be verticallyintegrated; the rms in an industry may all be specialized pro-ducers; or vertically integrated rms and specialized producersmay compete in the same industry. We argue in this section thatan industry is unlikely to be populated by rms with differentorganizational forms. Then we identify conditions under whichthere is a stable industry equilibrium with pervasive verticalintegration or with pervasive outsourcing of intermediates.

III.1. Mixed Equilibria

We rst examine conditions for the existence of an industryequilibrium in which both vertically integrated rms and special-ized rms are active in the marketplace. For this outcome tomaterialize, there must be positive values of v, s, and m for whichthe expected prots of all three types of rms are equal to zero.

If both p s 5 0 and p m 5 0, we have two equations that


provide a unique solution for the industry demand level A and therelative number of rms r 5 m/s. Using (5) and (6), we see thatboth specialized intermediate producers and specialized nal-goods producers will expect to break even if and only if

(11) rO 5v ~ 1 2 a !

1 2 vkskm

and

(12) AO 5~ a v ! 2 a / ~ 1 2 a ! km

v ~ 1 2 a !rO

h ~ rO!,

where the subscript O indicates a variable relating to an equilib-rium in which rms engage in outsourcing.

Meanwhile, using (9), we see that a vertically integrated rmearns zero prots if and only if the industry demand level is

(13) AI 5~ l / a ! a / ~ 1 2 a !

1 2 a.

The two demand levelsAO (required for the viability of out-sourcing) and AI (required for the viability of vertical integra-tion)are incompatible with one another, except in a knife-edgecase. Unless the industry parameters happen to produce AO 5AI , at least one type of rm will face conditions that are adverseto entry. We have thus shown that

PROPOSITION 1. Generically, no industry has both vertically inte-grated and specialized producers.

This nding reects our assumption that all potential en-trants of a given type are identical. If we had assumed that somevertically integrated rms can produce components at lower costthan others, it might be possible for these especially efcientrms to enter protably alongside rms that are specialized inproducing components or nal goods. Our result also relies on theassumption of constant returns to scale in matching. With de-creasing returns to matching, specialized rms might be prot-able if relatively few of them enter, but unprotable if many ofthem choose to enter. Then the industry might be populated by amoderate number of specialized rms and some rms that arevertically integrated. But the empirical evidence suggests thatmatching has constant or slightly increasing returns to scale, and


so does not support an assumption that would lead to organiza-tional diversity.

There is another way to understand Proposition 1. In FigureI we show the combinations of numbers of specialized nal-goodproducers and vertically integrated rms that are consistent withzero expected prots for a typical one of each of these rms, whenspecialized intermediate and nal-good producers enter in theratio rO . The line OO depicts combinations of s and v that implyp s 5 0. These combinations satisfy

9

(14) v S a l D a / ~ 1 2 a ! 1 s h ~ rO! ~ a v ! a / ~ 1 2 a ! 5 m LAO .Similarly, the line VV depicts combinations of s and v that implyp v 5 0. The equation for this line is given by

(15) v S a l D a / ~ 1 2 a ! 1 s h ~ rO! ~ a v ! a / ~ 1 2 a ! 5 m LA I .Figure I depicts the case where AI . AO ; then, OO lies outside ofVV. In any case, the two lines are parallel. This means that nocombination of s and v yields zero prots for both types of rms,unless the lines happen to coincide. Entry by one type of rm innumbers that ensure zero expected prots guarantees losses forthe other.

The question that remains is when will an industry organize

9. Given an entry ratio rO , the specialized nal-good producers will earn zeroexpected prots if and only if the industry demand level is AO . Equation (14) givesthe combinations of s and v that yield the required level of industry demand, inview of (10).

FIGURE IEquilibrium Curves: AI . AO


with vertically integrated rms and when with specialized pro-ducers that outsource their components. A response to this ques-tion will help us to predict the cross-sectoral variation in modes oforganization. Intuitively, competition at the entry stage favorsthe mode of organization that is viable with a lower level ofindustry demand. We develop this intuition in the next twosections.

III.2. Vertical Integration

We now consider equilibria in which all rms that enter someindustry j are vertically integrated. We argue that economywideequilibria with this property always exist. However, an equilib-rium with vertically integrated rms in industry j will be stableif and only if AI , AO in that industry.

When all rms are vertically integrated, we have a standardsituation of monopolistic competition. The conditions for equilib-ria of this sort are familiar from the work of Dixit and Stiglitz[1977] and others. Prices and output levels are given by (7) and(8). Free entry implies zero prots, which means that A 5 AI.Then, with s 5 m 5 0, (13) and (10) imply that the equilibriumnumber of integrated rms is

(16) vI 5 @ ~ 1 2 a ! m L # /kv .

For this to be an industry equilibrium, it must be that no rmwishes to enter as a specialized producer of intermediate goods oras a specialized producer of nal goods. But given that s 5 m 50, if a single rm were to enter as a specialized producer, it wouldnd no counterpart on the other side of the market with which tointeract. Such a rm would search in vain for a partner andultimately forfeit its entry fee. Thus, an industry equilibriumwith v 5 vI and s 5 m 5 0 can always be sustained.

Although equilibria with vertically integrated rms in indus-try j exist for all parameter values, such equilibria may not bestable. To discuss stability, we need to specify out-of-equilibriumdynamics. In our context, the most natural process to consider isone in which rms of a particular type enter the industry whenthey expect to earn positive prots and exit when they foreseeexpected losses.

Recall that Figure I depicts a setting with AI . AO . With theindicated dynamics, specialized producers enter at all points be-low the OO line and exit at all points above this line, whilevertically integrated rms enter at all points below the VV line


and exit at all points above this line. Thus, the arrows in thegure describe the evolution in the number of rms.10 It is clearthat point EV in Figure Iwhich represents an outcome with s 50 and v 5 vI is not stable. Any perturbation of the equilibriumtriggers dynamics that lead the industry to diverge from thispoint.

Figure II depicts a situation with AI , AO . Now the VV lineis above the OO line, and the industry equilibrium with pervasiveintegration is at point EV . This equilibrium is stable. We havetherefore established11

PROPOSITION 2. There always exists an equilibrium with verticalintegration in industry j. The industry equilibrium is stableif and only if AI , A0 for industry j.

III.3. Pervasive Outsourcing

Pervasive outsourcing requires that r 5 rO and A 5 AO , withv 5 0. It follows from (10), (11), (12), and (14) that

(17) sO 5 @ ~ 1 2 v ! m L # /ks

10. Since the industry potentially has three different types of rms, thedynamic analysis ought to be conducted in a three-dimensional space. Our dis-cussion in the text is limited to situations in which entry and exit of specializedproducers of intermediate and nal goods occur in the xed proportions rO . We dothis for expositional convenience only, because the two-dimensional analysisprovides a simpler (and correct) intuition. We have carried out the three-dimen-sional stability analysis and nd that it yields the same conclusions. This analysisis contained in our working paper, [Grossman and Helpman 2001].

11. Note that, in the knife-edge case of AI 5 AO , the coincidence of OO andVV implies the existence of a continuum of equilibria. In this case, the assumeddynamics dictate that the outcome will vary with the initial conditions.

FIGURE IIEquilibrium Curves: AI , AO


and

(18) mO 5 @ ~ 1 2 a ! v m L # /km

Evidently, the larger is the industry (as measured by m ) or theeconomy (as measured by L), the greater is the number of spe-cialized rms of each type that enters the industry. The larger arethe xed costs, the smaller is the number of rms. The division ofbargaining power affects the incentives for entry in oppositeways; the greater is the share of the surplus that goes to inter-mediate-good producers, the greater is entry by this type of rmand the smaller is the entry of specialized nal-good producers.Finally, the greater is the substitutability between an industrysproducts, the smaller is the number of rms that enter to producespecialized components. Variation in a has no effect on the num-ber of rms that enter as specialized producers of the nal goods.The reason for this asymmetry is that, due to the imperfectcontracting, the component producers bear all of the cost of manu-facturing the intermediate inputs. As a result, the nal-goodproducers earn as prots a fraction of revenues, which, in equi-librium, are invariant to the elasticity of demand. But the inter-mediate producers capture the remaining fraction of revenuesless the variable costs, an amount that does depend on the elas-ticity of substitution between nal goods. If contracting were nota problem (i.e., if the quality of inputs were veriable and there-fore contractible ex ante), then the substitutability of nal goodswould affect the protability of both types of producers and there-fore the numbers of each type of entrant.

For the existence of an equilibrium with s 5 sO , m 5 mO ,and v 5 0, it must be the case that potential entry is not attractiveto any vertically integrated producer. Such an entrant wouldanticipate an industry demand level AO . Its expected prots arenegative if and only if AO , AI, since AI is the minimum levelrequired for these rms to break even. It follows that there existequilibria with pervasive outsourcing in industry j if and only ifAI $ AO . Such an industry equilibrium is represented by thepoint EO in Figure I. From the gure, we can see that theequilibrium with pervasive outsourcing is stable, whenever AI .AO . We have thus proved

12

12. Formally, we must also check that a rm would not wish to enter as anintegrated rm, search for an entrant, produce a quantity of its own intermedi-


PROPOSITION 3. There exist equilibria with pervasive outsourcingin industry j if and only if AI $ AO for industry j. Theindustry equilibrium is stable if AI . AO .

IV. EQUILIBRIUM MODE OF ORGANIZATION

We now examine in detail the factors that determine theequilibrium mode of organization in an industry. As we haveseen, this amounts to a comparison of AI and AO . Factors thatfavor outsourcing are those that increase the ratio AI/AO , where

(19)A IAO

5 v ~ l v ! a / ~ 1 2 a !h ~ rO !

rO

kvkm

and

rO 5v ~ 1 2 a !~ 1 2 v !

kskm

as given by (11).Not surprisingly, pervasive outsourcing is a more likely out-

come in an industry the greater is l , the cost advantage ofspecialized component producers relative to vertically integratedrms. Similarly, the greater are the xed costs for verticallyintegrated rms and the smaller are the xed costs for the twotypes of specialized producers, the more likely is outsourcing to bean equilibrium outcome. An efcient search technology also fa-vors outsourcing; the larger is n[ for given values of s and m, thegreater is h (rO )/rO and thus the greater is AI/AO . In equilibrium,an improvement in the search technology does not affect sO ,mO ,or the ratio of the two. But it does raise the probability that anygiven entrant will nd a partner. This reduces the level of indus-try demand necessary for a typical specialized rm to break even.

With constant returns to scale in matching, neither the shareof spending devoted to an industrys output nor the overall size ofthe economy has any effect on the likelihood that outsourcing willbe the equilibrium mode of organization. As we will see in thenext section, this conclusion is dependent on the properties of thesearch technology; with increasing returns to matching, largerindustries are more likely to be organized into specialized rms.

ates, and then purchase additional intermediates from its partner. It is straight-forward to show that, with kv $ ks 1 km , this strategy never is protable.


The interesting part of Proposition 3 concerns the roles of theparameters a and v in determining the equilibrium mode oforganization. Let us begin with a , the parameter that describesthe degree of substitutability between an industrys nal goods. Ifa is close to one, the industrys goods are nearly perfect substi-tutes and the industry is highly competitive. If a is close to zero,consumers regard the industrys goods as distinct products andeach producer enjoys substantial monopoly power.

As can be seen in equation (19), there are two distinct chan-nels by which the substitution parameter affects the relativeprotability of the alternative modes of organization. For a givenratio rO , an increase in a increases AI/AO if and only if l v . 1. Tounderstand this effect, recall that pv 5 l / a and ps 5 1/ v a , sothat pv /ps 5 l v . If l v . 1, specialized nal producers would selltheir output at a lower price than would their vertically inte-grated counterparts. Then the potential operating prots of thespecialized rms would be relatively greater, the greater is theelasticity of demand. If l v , 1, it is the vertically integratedproducers who would sell their output at a lower price, and thenthe relative operating prot of the specialized producers falls withthe elasticity of demand. The comparison of l with 1/ v is acomparison of the cost disadvantage that reects the disecono-mies of scope with the distortion that results from the imperfectcontracting. With an imperfect contract, the specialized compo-nent producer receives only a fraction v of the operating prots,but bears the full cost of producing the inputs. Therefore, thisrm produces less than the joint-prot-maximizing volume ofoutput, causing an elevated price of the nal good.

The degree of substitutability between nal products alsoaffects AI and AO through its inuence on the fraction of revenuesthat producers are able to capture as operating prots. Withvertical integration, operating prots are a fraction 1 2 a ofrevenues, so potential prots fall (given revenues) as a rises. Withoutsourcing, the operating prots of a component producer are afraction v (1 2 a ) of revenues, so these producers too face lowerpotential earnings the greater is a . Since the potential protabil-ity of each type of rm is reduced in the same proportion, there isno net effect on the ratio AI/AO on this account.

But there is one more channel by which the degree of substi-tutability affects the relative viability of the alternative modes oforganization. Recall that a plays a role in determining the num-ber of specialized intermediate producers that enters the industry


in an equilibrium with outsourcing; the more substitutable arethe nal products, the smaller is mO . With less entry by inter-mediate producers (and an unchanged sO ), the probability thatany such entrant will nd a partner increases. This reduces thelevel of industry demand needed for a specialized componentproducer to have zero expected prots, given the operating protsit can anticipate if it is successful in its search for a partner. Interms of equation (19), an increase in a reduces rO , therebyincreasing h (rO )/rO and AI/AO .

Figure III shows the relationship between the elasticity ofsubstitution and the ratio AI/AO for the case where l v . 1. As wehave indicated, when ps , pv, an increase in a raises the relativeoperating prots of specialized producers. It also increases theprobability that a given intermediate producer will nd a partner.For both reasons, AI/AO rises with a , which means that an in-crease in the elasticity of substitution increases the relative via-bility of outsourcing. A stable equilibrium with pervasive out-sourcing exists if and only if AI/AO . 1; in the gure, this is truefor a . a 1. For a , a 1, there is a stable industry equilibrium inwhich all rms are vertically integrated.

Now consider an industry in which l v , 1. In such anindustry, the relative operating prots of an integrated rm arehigher, the greater is the elasticity of demand for a typical nalgood. But an increase in a also reduces the ratio of the number ofspecialized intermediate producers to the number of specializednal producers, thereby raising the likelihood that a typical com-

FIGURE IIIIndustry Organization for l v . 1: The Role of the Elasticity of Substitution


ponent producer will nd a partner. As we have seen, this booststhe likelihood that outsourcing will emerge as the equilibriummode of organization.

Since these two forces pull in opposite directions, the neteffect of a change in a depends upon which is stronger. Figure IVdepicts two possibilities. In panel a the ratio AI/AO is a monoton-ically decreasing function of a . This case arises when the proba-bility that a given component producer will nd a match does notchange very much with changes in the ratio of specialized inter-mediate producers to specialized nal producers. Then the directeffect of a on the protability of integrated versus specializednal-good producers will dominate the effect of the change inh (r)/r, and vertical integration is more attractive in industrieswith a high degree of substitution. Note that, in the circum-stances depicted in panel a, outsourcing can emerge in equilib-rium only when a , a 2.

Panel b depicts an industry in which the probability of amatch for a typical component producer responds more sensi-tively to changes in r. Here, the ratio AI/AO increases with a fora range of low values of a , and falls with a when a is large.Thendepending on the height of the curvevertical integrationmay be an equilibrium outcome for a range of low and high valuesof the a , while pervasive outsourcing is a stable outcome when afalls in an intermediate range. The gure illustrates an exampleof this; specialized production is viable if and only if a fallsbetween a 3 and a 4.

To better understand these different possibilities, we calcu-

FIGURE IVIndustry Organization for l v , 1: The Role of the Elasticity of Substitution


late how the right-hand side of (19) varies with a . We nd thatAI/AO increases with a if and only if

(20) 1 2 e h . 2 @ log ~ l v ! # / @ 1 2 a # ,where e h is the elasticity of h (r) with respect to r.

13 When l v .1, the right-hand side of (20) is negative, and thus the inequalitymust be satised. This is the case depicted in Figure III. Whenl v , 1, the right-hand side of (20) is positive and tends to innityas a approaches one. Since, with constant returns in matching,the elasticity e h must fall between zero and one, the curve must bedownward sloping when a is close to one, and it will be downwardsloping for all values of a if 1 2 e h is small enough.

14

Next we discuss how the distribution of bargaining poweraffects the likelihood that outsourcing will be viable as an equi-librium organizational form. We nd that changes in the divisionof surplus affect the ratio AI/AO in three ways. First, an increasein v directly increases the prot share of specialized componentproducers, which tends to reduce the industry demand levelneeded for these rms to break even. Second, an increase in vshrinks the distortion caused by imperfect contracting. This tooincreases the protability of specialized input producers. But anincrease in the bargaining power of intermediate-good producerscauses the relative number of these rms to increase, whichmeans that the typical such producer would have lower odds ofnding a partner. This effect of an increase in v tends to increaseAI/AO .

Using (19), we calculate that AI/AO increases with v if andonly if

e h . ~ v 2 a ! / ~ 1 2 a ! .

At v 5 0, the condition is satised, because e h . 0. At v 5 1, thecondition is violated, because e h , 1. Therefore, the relationshipbetween AI/AO and v has an inverted-U shape, such as the onedepicted in Figure V. A very low or a very high value of v pointsto vertical integration as the equilibrium mode of organization,

13. Note that the probability of a match for a component producer is given byh (r)/r, which has an elasticity of e h 2 1. Thus, the probability of a match for acomponent producer will be unresponsive to changes in r when e h is close to one.

14. As an example, consider the matching function n(s,m) 5 sm/(s 1 m).For this technology, h (r) 5 r/(1 1 r), and e h 5 1/(1 1 r). Then, for l v , 1, theAI /AO curve is everywhere downward sloping as in panel a when log ( l v ) ,2 v ks/(1 2 v )(ks 1 km ), and it has an inverted-U shape as in panel b when log( l v ) . 2 v ks/(1 2 v )(ks 1 km ).


whereas pervasive outsourcing is the unique stable outcomewhen v falls in an intermediate range.

Intuitively, if v is very small, the component producers wouldhave little incentive to produce intermediates, and the cost of thenal goods produced by specialized rms would be very high. If vis very large, there would be many more component producersattracted to the industry than specialized producers of nalgoods, and each component producer would have little chance ofnding a partner. Thus, outsourcing is sustainable in an industryequilibrium only if the bargaining power of the intermediateproducers is neither too high nor too low.

V. INCREASING RETURNS TO MATCHING

Empirical studies of search have focused primarily on labormarkets and the matching of workers and rms. This researchsuggests a search technology with constant or slightly increasingreturns to scale. In business-to-business (B2B) matching that isour concern here, the evidence is more indirect and anecdotal. Wenotice that rms in a given line of business often locate in thesame small neighborhood of a big city. One will nd in New YorkCity, for example, a textile district, a diamond district, a furnituredistrict, etc. It might seem surprising at rst that rms wouldwant to be near their rivals, in view of the intense competitionthat could result. But increasing returns in search could readily

FIGURE VIndustry Organization: The Role of Bargaining Power


explain this phenomenon. Similarly, an increasing-returnssearch technology might explain why rms in markets of differ-ent sizes opt for different modes of organization. Indeed, whenChinitz [1961] compared the industrial structure in New YorkCity and Pittsburgh, he found that rms in the former city weremuch more specialized than those in the latter. He attributed thisdifference to agglomeration economies such as could arise fromincreasing returns to matching.15

In this section we revisit the determination of the equilib-rium mode of organization in a setting where the search technol-ogy has increasing returns. Recall that n(s,m) gives the numberof partnerships that are formed when s specialized nal produc-ers search for potential input providers and m component pro-ducers search for potential customers. We now assume that n[ ischaracterized by increasing returns in its two arguments, whilecontinuing to take the probability of a match to be the same for allrms on a given side of the market.

With increasing returns to matching, we must rewrite theexpressions for the potential prots of specialized rms. Analo-gous to (5) and (6), specialized nal-good producers see expectedprots of

(5 9 ) p s 5n ~ s,m !

s~ 1 2 v ! A ~ a v ! a / ~ 1 2 a ! 2 ks,

while specialized component producers perceive expected protsof

(6 9 ) p m 5n ~ s,m !

m ~ 1 2 a ! v A ~ a v !a / ~ 1 2 a ! 2 km.

Industry demand now is given by

(10 9 ) A 5m L

v ~ a / l ! a / ~ 1 2 a ! 1 n ~ s,m ! ~ a v ! a / ~ 1 2 a !.

Using (5 9 ) and (6 9 ), we nd that for both types of specializedproducers to earn zero expected prots, we still require the ratioof intermediate to nal producers to be rO 5 v (1 2 a )ks/(1 2v )km . However, the level of industry demand needed for theviability of these types of rms must be expressed differently, as

15. We thank Edward Glaeser for drawing our attention to Chinitzs ndings.


(12 9 ) AO 5~ a v ! 2 a / ~ 1 2 a ! km

v ~ 1 2 a !rOs

n ~ s,rOs !.

Notice that the required demand level now depends not only onthe composition of entry, but also on the absolute number of rmsthat enter the market; for given rO , the greater is s, the smalleris the demand level AO needed for the two types of specializedrms to break even. This, of course, reects the increasing re-turns to matchingwhen more rms enter on each side of themarket, every rm has a better chance of nding a partner.

Recall Figures I and II, in which the line OO gives combina-tions of s and v consistent with zero expected prots for special-ized nal-good producers, conditional on the entry of specializedrms being in the proportions dictated by rO . With increasingreturns to matching, the modied equation for this curve (whichno longer is linear) is given by

(14 9 ) v S a l D a / ~ 1 2 a ! 1 n ~ s, rOs ! ~ a v ! a / ~ 1 2 a ! 5 m LB n ~ s,rOs !rOs ,where B 5 ( a v ) 2 a / (1 2 a )km / v (1 2 a ). The line VV in Figures Iand II similarly gives combinations of s and v for which verticallyintegrated rms break even. With increasing returns to match-ing, the equation for this curve becomes

(15 9 ) v S a l D a / ~ 1 2 a ! 1 n ~ s,rOs ! ~ a v ! a / ~ 1 2 a ! 5 m LA I .Figure VI shows the new VV curve and two possible shapes

of the new OO curve. The VV curve is downward sloping, becausethe more crowded is the market with vertically integrated rms,

FIGURE VIIncreasing Returns to Matching: Multiple Equilibria


the smaller must be the number of competing specialized produc-ers for an integrated rm to break even. The OO curve might alsoslope downwardas depicted in panel a or it might slope up-ward and then downwardas depicted in panel b.16 The curvewill slope downward if the increasing returns to scale are slight.With stronger increasing returns, a rise in the number s ofspecialized nal producers (together with the associated rise inthe number of specialized component producers) may so improvethe prospects for a given rm to nd a match that its expectedprots will grow, even considering the implied crowding of theproduct market. Then an increase in v would be needed to restoreexpected prots to zero.

In both panels of the gure, there is a mixed equilibrium inwhich vertically integrated rms and specialized rms coexist inthe market. This equilibrium is found at the point of intersectionof the OO curve and the VV curve. However, if the OO curveslopes downward, it must have a less negative slope than the VVcurve at any point of intersection. This means that any mixedequilibrium will be unstable, as can be seen from the dynamicsindicated in the gure.

In each panel of Figure VI, there are two additional equilibriathat are denoted by EV and EO . EV is an equilibrium in which allrms are vertically integrated. At EO , all rms are specialized. Ineach case, both of these equilibria are locally stable. There arealso some possibilities that are not shown in the gure. If indus-try conditions happen to be such that the VV curve lies every-where above the OO curve, then there is a unique industryequilibrium in which all rms are vertically integrated. Alterna-tively, if conditions are such that the OO curve lies everywhereabove the VV curve, then the only stable equilibrium is one withpervasive outsourcing.

We can now see how the size of an industry or the size of theeconomy can be a determinant of the equilibrium organizationalform. As m L increases, the point of intersection of the VV curveand the horizontal axis shifts to the right in the same proportion,while the point of intersection of the OO curve and the horizontalaxis shifts to the right less than proportionately. Therefore, anindustry equilibrium with pervasive outsourcing is more likely toexist, the larger is the industry and the larger is the aggregate

16. Equation (14 9 ) always has a solution with v 5 0 and s 5 (1 2 v ) m L/ks.The OO curve must slope downward in the neighborhood of this solution.


economy. Our model thus provides a possible explanation for theChinitz [1961] nding; outsourcing may have been viable in NewYork City but not in Pittsburgh, because the scale of the formereconomy admitted a sufcient number of entrants for productiveB2B search, whereas the scale of the latter economy did not. Themodel also is consistent with another possible explanation for theChinitz ndings. If conditions in each city were like those de-picted in either panel of Figure VI, the difference in industrialstructure might have been a historical accident. When eithermode of organization is viable, the equilibrium structure willdepend on initial conditions and the vagaries of how potentialentrants form their expectations about the intentions of others.

VI. PARTIAL SPECIALIZATION

So far, we have assumed that an input must be tailoredexactly to the specications of a particular nal good or else it isuseless to the nal producer. By making this assumption, wehave eliminated all outside opportunities for producers on bothsides of the market. An input supplier that has specialized acomponent for a particular end use has no threat to sell its outputto another rm if its negotiation with the intended customer fails.Similarly, a nal producer cannot threaten to turn to alternativesuppliers, if it is not happy with the price it is asked to pay. Whileour assumption proved useful for keeping the model simple, it isundoubtedly too extreme. In this section we outline an extensionof our model that gives an outside option to both parties to therelationship. After describing the extension, we discuss the de-terminants of the mode of organization in this more generalsetting. The details of the analysis are similar to what has comebefore (albeit more tedious), so we relegate them to our workingpaper [Grossman and Helpman 2001].

Our goal is to extend the model so that input suppliers havean opportunity to sell their components to producers other thanthose for whom they were intended. When this is true, the sup-pliers face an important trade-off that is absent from the simplemodel. On the one hand, an input that is highly specialized will beof maximal value to the prospective customer for whom it isdesigned. On the other hand, a more standardized and exibleinput may be more valuable in alternative uses. The componentproducer may be able to choose the degree of specicity of itsproduct, trading off value within the intended relationship and


value outside. Riordan and Williamson [1985] allowed the degreeof specialization to be a choice variable in their analysis of thebilateral holdup problem. We do likewise here, although in amanner that is rather different from theirs.

To capture input specicity, we associate each nal good witha different ideal component. As before, the production of a unit ofany nal good requires one unit of an intermediate input. If theintermediate is perfect for that variety, then no further inputs arerequired. However, if the intermediate is not fully specialized tothe needs of the nal producer, the rm must add labor to makethe input t its purposes. The additional labor costs are greater,the more different is the input from the producers idealspecication.

Specically, we adopt a two-dimensional representation ofthe space of input characteristics.17 The ideal components for thevarious nal products are arrayed along the circumference of aunit circle, as shown in Figure VII. The point labeled i representsthe characteristics of an intermediate input that is fully special-ized to the needs of the producer of nal good i. If this produceruses an input with characteristics different from these, it mustemploy extra resources to make the component t. We take thelabor requirements per unit of intermediate to be an increasing

17. Our discussion in this section applies to a particular industry. We omitthe industry subscripts that implicitly are attached to all parameters and vari-ables to make the text easier to read.

FIGURE VIIInput Characteristics


and convex function of the distance between the intermediateactually used and the products ideal component. Consider, forexample, the input with characteristics represented by the points i in the gure. This input has been designed with the needs ofproducer i in mind. However, it does not fully meet the producersspecications. If the rm were to employ this input in producinggood i, it would also need to employ labor per unit of output thatreects the distance isi. If the producer of product h instead wereto use the component with characteristics described by point s i,its labor costs per unit output would reect the distancehsi between the intermediate and this other producers ideal.

For simplicity, we take the labor cost to be proportional to thesquare of the distance between an input and a producers ideal,although other functions would do as well. We measure the de-gree of specialization of an input toward product i by r i, thedistance of the input from the center of the circle along the radiusleading to point i. The angle u ih measures the similarity of theideal components for goods i and h.18 With these measures, wecan write the labor cost to producer i of using the input si asb (1 2 r i)

2 and the cost to producer h of using the input s i asb (1 1 r i

2 2 2 r i cos u ih), where b reects the importance of inputspecicity in the industry under consideration. The input at thecenter of the circle is a standardized or generic input; it is notparticularly well suited for any of the nal producers, but isequally productive in all uses.

The rest of the model is basically as before. Firms in eachindustry incur xed costs to enter as vertically integrated orspecialized producers. Upon entry, specialized rms search forpotential partners. Matching occurs randomly and, as in SectionII, with constant returns to scale. When a supplier and a nalproducer meet, the latter provides the specications for its idealcomponent, as well as technological information needed to pro-duce any intermediate good. A potential input producer that failsto nd a partner does not receive this information and has nochoice but to exit the industry.19 Those component producers whond partners choose the quantity, quality, and specication of

18. We take the smaller angle between i and h, so that u ih # p .19. Alternatively, we could assume that unmatched input producers can

manufacture certain types of components (e.g., standardized inputs) withoutguidance from nal producers. Then entrants who fail to nd a partner in the rstround might produce some components in the hope of nding a customer later.This case is a bit more complicated, but not essentially different.


their products. They may choose to manufacture their inputsprecisely to the specications of their intended customer or todesign their inputs more exibly so that they can readily be soldto other producers.

After the components have been produced, the partners meetto negotiate a sale. It is at this stage that the outside options canmake a difference. If a supplier rejects a buyers offer, it has thepossibility of searching for another customer. Similarly, if thebuyer refuses the suppliers demands, it might turn elsewhere forits components. However, a exible technology is not enough tomake for a secondary market. There must also be some sellerswho are looking for buyers, and vice versa, at this later stage.Otherwise, a failed negotiation will leave each party searching invain for a new partner.

To ensure the existence of a secondary market, we assumethat a fraction d of relationships dissolve exogenously. When abreakdown occurs, the input producer has no choice but to seekout a new customer for its (already produced) components, whilethe nal producer must locate a new supplier. The remainingnegotiations take place against the backdrop of these exogenousseparations. That is, when a component producer and nal pro-ducer engage in bargaining, the threat for each is to leave thepartnership and enter the secondary market where those whohave been separated are searching for matches. We take d to bevery small.20 Still, the fact that it is not zero makes a difference,for it gives each of the rms in every partnership an outsideoption that otherwise would be lacking.

Matching in the second stage is random, much like in therst. Firms with components to sell have an equal chance ofmeeting any of the nal producers that are seeking inputs, andsimilarly, each nal producer might be matched with any of theinput rms. At this stage, there are the same number of inputproviders searching for customers as there are nal producerssearching for suppliers. Thus, each rm in the secondary marketnds a new partner with probability h [ h (1). In principle, theremight be further separations and further rounds of matchingafter the second, but for simplicity we take the outside optionsafter the second stage to be nil.

We now describe an equilibrium with pervasive outsourcing;

20. Technically speaking, we derive the limit equilibrium as d approacheszero.


details of the analysis can be found in Grossman and Helpman[2001]. As before, specialized intermediate and nal-good produc-ers enter in numbers that ensure zero expected prots for bothtypes of rms. The input suppliers produce a smaller quantity ofcomponents than that which maximizes the joint prots of thetwo partners; this is a consequence of the imperfect contracting.The new element here is the endogenous degree of specialization.An input provider chooses r i to maximize expected prots. On theone hand, an increase in the degree of specialization enhancespotential prots from sales of nal good i. Since the componentproducer shares in these prots, it has an incentive to specializethe good for its partners use. On the other hand, an increase in r i(beyond a point) reduces the potential value of the input in thesecondary market. The component producer seeks to avoid suchreductions in outside value, because they weaken its bargainingposition vis-a-vis its partner. In choosing the degree of specicity,the supplier strikes a balance between these two opposing forces.

In a symmetric equilibrium, all rms in an industry special-ize their inputs to the same extent. And all inputs are sold to thecustomers for whom they were designed, except for the smallfraction d of relationships that break up exogenously. We ndthat, in equilibrium,

r O 5 1/ @ 1 1 ~ 1 2 v ! h # .

The greater is h , the better is the prospect for a componentproducer to nd a new customer, if the negotiation with its initialpartner should fail. This means that there is a greater return toproducing an input that the average nal producer nds attrac-tive. The greater is v , the greater is the share of the surpluscaptured by the intermediate producer, and the less the outsideoption gures in its expected prots. Therefore, a componentproducer with greater bargaining power produces a more special-ized input.

Notice that b does not enter into the determination of theequilibrium degree of specialization. It might seem that compo-nent producers will have more of an incentive to specialize theirinputs, the more sensitive are manufacturing costs to the degreeof specialization. But there are offsetting forces at work here. It istrue that the greater is b , the greater is the marginal benet ofspecializing the input for the intended user. However, a highervalue of b also means that the marginal cost of specialization willbe higher, because a more specialized product is less valuable in


outside uses when b is large. An increase in per unit adjustmentcosts has the same proportionate effect on the suppliers outsideoption as it has on the rms stake in prots inside the relation-ship. Thus, there is no effect of b on its choice of design.

We can also examine the determinants of the equilibriummode of organization. As in the discussion of Section III, a givenindustry is quite likely to be characterized either by pervasiveintegration or by pervasive outsourcing. Most of the parametershave a similar effect on AI/AO in the extended model as they do inthe simple model. But an interesting new question arises con-cerning the relationship between the importance of input speci-city in an industry and the viability of outsourcing as an orga-nizational form.

The adjustment cost parameter affects the demand levelrequired for specialized rms to break even in three ways.First, the greater is b , the greater is marginal cost for aspecialized producer, and so the smaller are the revenues inwhich the component producers share. Second, the greater is b ,the smaller is rO , because nal producers bear the adjustmentcosts and so enter in relatively small numbers when the costsof imperfect specialization are especially large. A small rOmakes it more difcult for a typical component producer to nda partner. Both of these effects point to a positive associationbetween b and AO. But also, the greater is b , the smaller is theoutput of intermediate goods. Since component producerschoose their outputs to maximize prots, there is no rst-ordereffect of a change in xi on the producers earnings. But when allcomponent producers reduce their output together, collectivelythey damage the outside option for nal producers. This im-proves the bargaining position of the component producersand, all else equal, enhances their protability. Although itmight seem that outsourcing would be less viable when inputspecialization is more important, in fact outsourcing may bethe unique stable outcome in an industry with a moderatelylarge b where specialized producers could not survive in anotherwise similar industry in which the specicity of the com-ponent is less important.

VII. CONCLUSIONS

This paper incorporates familiar ideas from organizationtheory in a setting of industry and general equilibrium. We


have modeled a rms make or buy decision as a trade-offbetween the transaction costs that stem from search and in-complete contracts on the one hand and the extra governancecosts associated with vertical integration on the other. Ourcontribution has been to cast these decisions in an environ-ment where a rms market opportunities depend on the orga-nizational choices of others.

Our model allows us to pose questions that were outside thepurview of the previous literature focusing on bilateral relation-ships. For example, we examined how the intensity of competitionin a market affects the prospect for arms-length dealing betweeninput suppliers and nal producers. We found that when marketsare highly competitivebecause consumer products are highlysubstitutable for each otherthe occurrence of outsourcing re-quires a large per-unit cost advantage for specialized input pro-ducers relative to integrated rms. This advantage must be largeenough to overcome search frictions and the pricing disadvantagethat stems from the holdup problem. In contrast, when marketsare not highly competitive, the viability of outsourcing hingesmostly on a comparison of the xed costs that must be borne by anintegrated rm and those that are paid by specialized producers.We also examined how the specicity of inputs affects the possi-bilities for arms-length dealing. The more sensitive are manu-facturing costs to the detailed characteristics of the intermedi-ates, the more costly will be the inefciency arising from partialspecialization of components under incomplete contracting. Thistends to reduce the viability of outsourcing. At the same time, anincrease in specicity reduces the equilibrium volume of inputsand enhances the bargaining power of each input supplier in itsbilateral relationship with a nal producer. This makes entry byspecialized input producers more protable, and may allow out-sourcing to occur in cases where costs are highly sensitive toinput specications, where it would not be possible if they wereless so.

The main contribution of this paper has been to provide asimple general equilibrium framework for studying the equilib-rium mode of organization, the resulting degree of input special-ization, and other variables of interest, such as prices and varietychoice. Our model is simple enough to allow modications andextensions, for example to a richer menu of contractual options, todifferent matching technologies and to alternative types of corpo-rate partnerships. We are condent that it can be used to shed


light on important issues, such as the increasing extent of spe-cialization and especially the causes and consequences of therapid growth of international outsourcing.

PRINCETON UNIVERSITYHARVARD UNIVERSITY, TEL AVIV UNIVERSITY, AND CIAR

REFERENCESAbraham, Katharine G., and Susan K. Taylor, Firms Use of Outside Contractors:

Theory and Evidence, Journal of Labor Economics, XIV (1996), 394424.Aghion, Philippe, Mathias Dewatripont, and Patrick Rey, Renegotiation Design

with Unveriable Information, Econometrica, LXII (1994), 257282.Blanchard, Olivier J., and Peter A. Diamond, The Beveridge Curve, Brookings

Papers on Economic Activity, 1 (1989), 160.Campa, Jose, and Linda Goldberg, The Evolving External Orientation of Manu-

facturing Industries: Evidence from Four Countries, Federal Reserve Bank ofNew York Economic Policy Review, III (1997), 5381.

Chinitz, Benjamin, Contrasts in Agglomeration: New York and Pittsburgh,American Economic Review (Papers and Proceedings), LI (1961), 279289.

Coase, Ronald, The Nature of the Firm, Economica, IV (1937), 386 405.Coles, Melvin G., and Eric Smith, Cross-Section Estimation of the Matching

Function: Evidence from England and Wales, Economica, LXIII (1996),589597.

Diamond, Peter A., Wage Determination and Efciency in Search Equilibrium,Review of Economic Studies, XLIX (1982), 217227.

Dixit, Avinash K., and Joseph E. Stiglitz, Monopolistic Competition and Opti-mum Product Diversity, American Economic Review, LXXXVII (1997),297308.

Grossman, Gene M., and Elhanan Helpman, Integration vs. Outsourcing inIndustry Equilibrium, Discussion Paper in Economics No. 212, WoodrowWilson School of Public and International Affairs, Princeton University, 2001.

Grossman, Sanford J., and Oliver Hart, The Costs and Benets of Ownership: ATheory of Vertical and Lateral Integration, Journal of Political Economy,XCIV (1986), 691719.

Hart, Oliver, Firms, Contracts, and Financial Structure (Oxford: Oxford Univer-sity Press, 1995).

Hart, Oliver, and John Moore, Foundations of Incomplete Contracts, Review ofEconomic Studies, LXVI (1999), 115138.

Helper, Susan, Strategy and Irreversibility in Supplier Relations: The Case of theU. S. Automobile Industry, Business History Review, LXV (1991), 781824.

Holmstrom, Bengt, and Jean Tirole, Transfer Pricing and Organizational Form,Journal of Law, Economics, and Organization, VII (1991), 201228.

Hummels, David, Dana Rapoport, and Kei-Mu Yi, Vertical Specialization and theChanging Nature of World Trade, Federal Reserve Bank of New York Eco-nomic Policy Review, IV (1998), 7999.

Klein, Benjamin, Robert G. Crawford, and Armen A. Alchian, Vertical Integra-tion, Appropriable Rents, and the Competitive Contracting Process, Journalof Law and Economics, XXI (1978), 297326.

Lagos, Ricardo, An Alternative Approach to Search Frictions, Journal of Politi-cal Economy, CVIII (2000), 851873.

Maskin, Eric, and Jean Tirole, Unforeseen Contingencies and Incomplete Con-tracts, Review of Economic Studies, LXVI (1999), 83114.

McAfee, R. Preston, and John McMillan, Organizational Diseconomies of Scale,Journal of Economics and Management Strategy, IV (1995), 399 426.

McLaren, John, Globalization and Vertical Structure, American EconomicReview, XC (2000), 12391254.

McMillan, John, Reorganizing Vertical Supply Relationships, in H. Siebert, ed.,


http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0734-306X^281996^2914L.394[aid=1926686]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0022-3808^281986^2994L.691[aid=115109]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0022-3808^282000^29108L.851[aid=1926694]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0034-6527^281999^2966L.83[aid=1926695]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0002-8282^282000^2990L.1239[aid=1926697]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0022-3808^281986^2994L.691[aid=115109]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0022-3808^282000^29108L.851[aid=1926694]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0002-8282^282000^2990L.1239[aid=1926697]

Trends in Business Organization: Do Participation and Cooperation IncreaseCompetitiveness (Tubingen: J.C.B. Mohr, 1995).

Perry, Martin K., Vertical Integration: Determinants and Effects, in R.Schmalansee and R. D. Willig, eds., Handbook of Industrial Organization(Amsterdam: North-Holland, 1989).

Pissarides, Christopher A., Equilibrium Unemployment Theory, second edition(Cambridge, MA: MIT Press, 2000).

Riordan, Michael H., and Oliver E. Williamson, Asset Specicity and EconomicOrganization, International Journal of Industrial Organization, III (1985),365378.

Segal, Ilya, Complexity and Renegotiation: A Foundation for Incomplete Con-tracts, Review of Economic Studies, LXVI (1999), 5782.

Williamson, Oliver E., Markets and Hierarchies: Analysis and Antitrust Implica-tions (New York, NY: Free Press, 1975).

, The Economic Institutions of Capitalism (New York, NY: Free Press, 1985).

http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0167-7187^281985^293L.365[aid=1403707]http://thesius.ingentaselect.com/nw=1/rpsv/cgi-bin/linker?ext=a&reqidx=/0167-7187^281985^293L.365[aid=1403707]

integration versus outsourcing in industry …erossi/courses_files/intout.pdf · integration versus...

Documents