Contracts and Technology Adoption By D ARON A CEMOGLU,P OL A NTR`A S,AND E LHANAN H ELPMAN*We develop a tractable framework for the analysis of the relationship between contractual incompleteness,technological complementarities,and technology adop-tion.In our model,afirm chooses its technology and investment levels in contract-ible activities by suppliers of intermediate inputs.Suppliers then choose investments in noncontractible activities,anticipating payoffs from an ex post bargaining game. We show that greater contractual incompleteness leads to the adoption of less advanced technologies,and that the impact of contractual incompleteness is more pronounced when there is greater complementary among the intermediate inputs. We study a number of applications of the main framework and show that the mechanism proposed in the paper can generate sizable productivity differences across countries with different contracting institutions,and that differences in contracting institutions lead to endogenous comparative advantage differences. (JEL D86,O33)There is widespread agreement that differ-ences in technology are a major source of pro-ductivity differences acrossfirms,industries, and nations.1Despite this widespread agree-ment,we are far from an established framework for the analysis of technology choices offirms. In this paper,we take a step in this direction and develop a simple model to study the impact of contracting institutions,which regulate the re-lationship between thefirm and its suppliers,on technology choices.Our model combines two well-established approaches.Thefirst is the representation of technology as the range of intermediate in-puts used byfirms;a greater range of interme-diate inputs increases productivity by allowing greater specialization and thus corresponds to more“advanced”technology.2The second is Sanford J.Grossman and Oliver D.Hart’s*Acemoglu:Department of Economics,Massachusetts In-stitute of Technology,E52-380b,Cambridge,MA02139,Na-tional Bureau of Economic Research,Centre for Economic Policy Research,and Canadian Institute for Advanced Re-search(e-mail:daron@);Antra`s:Department of Eco-nomics,Harvard University,Littauer319,Cambridge,MA 02138,NBER,and CEPR(e-mail:pantras@); Helpman:Department of Economics,Harvard University,Lit-tauer229,Cambridge,MA02138,NBER,CEPR,and CIAR (e-mail:ehelpman@).A previous version of this paper was circulated under the title“Contracts and the Division of Labor.”We thank Gene Grossman,Oliver Hart,Kalina Manova,Damia´n Migueles,Giacomo Ponzetto,Richard Rog-erson,Rani Spiegler,two anonymous referees,participants in the Canadian Institute for Advanced Research and Minnesota Workshop in Macroeconomic Theory conferences,and semi-nar participants at Harvard University,MIT,Tel Aviv Univer-sity,Universitat Pompeu Fabra,University of Houston,University of California,San Diego,Southern Methodist University,Stockholm School of Economics,Stockholm University(IIES),ECARES,University of Colorado–Boul-der,the Kellogg School,New York University,University of British Columbia,Georgetown University,the World Bank,University of Montreal,Brandeis University,Univer-sity of Wisconsin,UC–Berkeley,Haifa University,Syra-cuse University,Universitat Auto`noma de Barcelona,Duke University,Columbia University,and Cornell University for useful comments.We also thank Davin Chor,Alexandre Debs,and Ran Melamed for excellent research assistance. Acemoglu and Helpman thank the National Science Foun-dation forfinancial support.Much of Helpman’s work for this paper was done when he was Sackler Visiting Professor at Tel Aviv University.1Among others,see Peter J.Klenow and Andre´s Rodri-guez-Clare(1997),Robert E.Hall and Charles I.Jones (1999),or Francesco Caselli(2005)for countries,and Tor J. Klette(1996),Zvi Griliches(1998),John Sutton(1998),or Klette and Samuel S.Kortum(2004)forfirms.2See,among others,Wilfred J.Ethier(1982),Paul M. Romer(1990),and Gene M.Grossman and Helpman(1991) for previous uses of this representation.See also the text-book treatment in Robert J.Barro and Xavier Sala-i-Martin (2003).There is a natural relationship between this view of technology and the division of labor within afirm.We investigated this link in the earlier version of the current paper,Acemoglu,Antra`s,and Helpman(2005),and do not elaborate on it here.916(1986)and Hart and John H.Moore’s(1990) approach to incomplete-contracting models of thefirm.We study technology choice offirms under incomplete contracts,and extend Hart and Moore’s framework by allowing contracts to be partially incomplete.This combination enables us to investigate how the degree of contractual incompleteness and the extent of technological complementarities between inter-mediate inputs affect the choice of technology. In our baseline model,afirm decides on technology(on the range of specialized inter-mediate goods),recognizing that a more ad-vanced technology is more productive,but also entails a variety of costs.In addition to the direct pecuniary costs of engaging more suppli-ers(corresponding to the greater range of inter-mediate inputs),a more advanced technology necessitates contracting with more suppliers. All of the activities that suppliers undertake are relationship-specific,and a fraction of those is ex ante contractible,while the rest,as in the work by Grossman-Hart-Moore,are nonverifi-able and noncontractible.The fraction of con-tractible activities is our measure of the quality of contracting institutions.3Suppliers are con-tractually obliged to perform their duties in the contractible activities,but they are free to choose their investments in noncontractible ac-tivities and to withhold their services in these activities from thefirm.This combination of noncontractible investments and relationship-specificity leads to an ex post multilateral bar-gaining problem.As in Hart and Moore(1990), we use the Shapley value to determine the di-vision of ex post surplus between thefirm and its suppliers.We derive an explicit solution for this division of surplus,which enables us to develop a simple characterization of the equilibrium.A supplier’s expected payoff in the bargain-ing game determines her willingness to invest in the noncontractible activities.Since she is not the full residual claimant of the output gains derived from her investments,she tends to un-derinvest.Greater contractual incompleteness thus reduces supplier investments,making more advanced technologies less profitable.Further-more,a greater degree of technological comple-mentarity reduces the incentive to choose more advanced technologies.Although greater tech-nological complementarity increases equilib-rium ex post payoffs to every supplier,it also makes their payoffs less sensitive to their non-contractible investments,discouraging invest-ments and,via this channel,depressing the profitability of more advanced technologies. An advantage of our framework is its relative tractability.The equilibrium of our model can be represented by a reduced-form profit func-tion forfirms given by(1)AZF͑N͒ϪC͑N͒Ϫw0N,where N represents the technology level,C(N) is the cost of technology N,A is a measure of aggregate demand or the scale of the market, and w0N corresponds to the value of the N suppliers’outside options.F(N)is an increasing function that captures the positive effect of choosing more advanced technologies on reve-nue.The effects of contractual incompleteness and technological complementarity are summa-rized by the variable Z.This variable affects productivity and is decreasing in the degree of contract incompleteness and technological complementarity.Moreover,the elasticity of Z with respect to the quality of contracting insti-tutions is higher when there is greater comple-mentarity between intermediate inputs.This last result has important implications for equilib-rium industry structure and the patterns of com-parative advantage,because it implies that sectors(firms)with greater complementarities between inputs are more“contract dependent.”We use this framework to show that the combination of contractual imperfections and technology choice(or adoption)may have im-portant implications for cross-country income differences,equilibrium organizational forms, and patterns of international specialization and trade.First,we show that our baseline model can generate sizable differences in productivity from3Eric S.Maskin and Jean Tirole(1999)question whether the presence of nonverifiable actions and unfore-seen contingencies necessarily leads to incomplete con-tracts.Their argument is not central to our analysis because it assumes the presence of“strong”contracting institutions(which,for example,allow contracts to spec-ify sophisticated mechanisms),while in our model a fraction of activities may be noncontractible,not because of“technological”reasons but because of weak contract-ing institutions.917VOL.97NO.3ACEMOGLU ET AL.:CONTRACTS AND TECHNOLOGY ADOPTIONdifferences in the quality of contracting institu-tions.In particular,using a range of reasonable values for the key parameters of the model,we find that when the degree of technological complementarity is sufficiently high,relatively modest changes in the fraction of activities that are contractible can lead to large changes in productivity.Second,we derive a range of implications about the equilibrium organizational form. Our results here show that the combination of weak contracting institutions and credit mar-ket imperfections may encourage greater ver-tical integration.Third,we present a number of general equi-librium applications of this framework.The general equilibrium interactions result from the fact that an improvement in contracting institu-tions does not increase the choice of technology in all sectors(firms).Instead,more advanced technologies are chosen in the more contract-dependent sectors.We show that in the context of an open economy,this feature leads to an endogenous structure of comparative advan-tage.In particular,among countries with iden-tical technological opportunities(production possibility sets),those with better contracting institutions specialize in sectors with greater complementarities among inputs.These predic-tions are consistent with the recent empirical results presented in Nathan Nunn(2006)and Andrei A.Levchenko(2003).As mentioned above,our work is related to two strands of the literature.Thefirst investi-gates the determinants offirm-level technology (including the division of labor)and includes, among others,Gary S.Becker and Kevin M. Murphy(1992)and Xiaokai Yang and Jeff Bor-land(1991)on the impact of the extent of the market on the division of labor,and Romer (1990)and Grossman and Helpman(1991) on endogenous technological change.None of these studies investigates the effects of con-tracting institutions on technology choice.The second literature deals with the internal organi-zation of thefirm.It includes the papers by Grossman-Hart-Moore discussed above,as well as those of Benjamin Klein,Robert G.Craw-ford,and Armen A.Alchian(1978)and Oliver E.Williamson(1975,1985),who emphasize incomplete contracts and hold-up problems. Here,the papers by Lars A.Stole and Jeffrey Zwiebel(1996a,b)and Yannis Bakos and Erik Brynjolfsson(1993)are most closely related to ours.Stole and Zwiebel consider a relationship between afirm and a number of workers whose wages are determined by ex post bargaining according to the Shapley value.They show how thefirm may overemploy in order to reduce the bargaining power of the workers,and discuss the implications of this framework for a number of organizational design issues. Stole and Zwiebel’s framework does not have relationship-specific investments,however, which is at the core of our approach,and they do not discuss the effects of the degree of contractual incompleteness and the degree of complementarity between inputs on the equi-librium technology choice.4Finally,our paper is also related to the liter-ature on the macroeconomic implications of contractual imperfections.A number of papers, most notably Erwan Quintin(2001),Pedro S. Amaral and Quintin(2005),Andre´s Erosa and Ana Hidalgo(2005),and Rui Castro,Gian Luca Clementi,and Glenn MacDonald(2004),inves-tigate the quantitative impact of contractual and capital market imperfections on aggregate pro-ductivity.5Our approach differs from these pa-pers since we focus on technology choice and relationship-specific investments,and because we develop a tractable framework that can be applied in a range of problems.Although we do not undertake a detailed calibration exercise as in these papers,the results in Section IVA sug-gest that the economic mechanism developed in this paper can lead to quantitatively large ef-fects.Finally,Levchenko(2003),Arnaud Costi-not(2004),Nunn(2006),and Antra`s(2005) also generate endogenous comparative advan-tage across countries from differences in con-tractual environments.Among these papers, Costinot(2004)is most closely related,since he also develops a model of endogenous compar-4Another related paper is Olivier J.Blanchard and Mi-chael Kremer(1997),which studies the impact of inefficient sequential contracting between afirm and its suppliers in a model where output is a Leontief aggregate of the inputs of the suppliers.5Acemoglu and Fabrizio Zilibotti(1999),David Marti-mort and Thierry Verdier(2000,2004),and Patrick Fran-cois and Joanne K.Roberts(2003)study the qualitative impact of changes in the internal organization offirms on economic growth.918THE AMERICAN ECONOMIC REVIEW JUNE2007ative advantage based on specialization,though his approach is more reduced-form than our model.The rest of the paper is organized as fol-lows.Section I introduces the basic environ-ment.Section II characterizes the equilibrium with complete contracts.Section III introduces incomplete contracts into the framework of Sec-tion I,characterizes the equilibrium,and derives the major comparative static results.Section IV considers a number of applications of our basic framework.Section V concludes.Proofs of the main results are provided in the Appendix.I.Technology and Payoffs Consider a profit-maximizingfirm facing a demand function qϭApϪ1/(1Ϫ)for itsfinal product,where q denotes quantity and p denotes price.The parameterʦ(0,1)determines the elasticity of demand,while AϾ0determines the level of demand or the“market size.”The firm treats the demand level A as exogenous. This form of demand can be derived from a constant elasticity of substitution preference structure for differentiated products(see Sec-tion IVC)and it generates a revenue function (2)RϭA1Ϫq.Production depends on the technology choice of thefirm.More advanced(more productive) technologies involve a greater range of interme-diate goods and thus a higher degree of special-ization.The technology level of thefirm is denoted by Nʦޒϩ,and for each jʦ[0,N], X(j)is the quantity of intermediate input j. Given technology N,the production function of thefirm is(3)qϭNϩ1Ϫ1/␣ͫ͵0N X(j)␣djͬ1/␣,0Ͻ␣Ͻ1,Ͼ0.A number of features of this production func-tion are worth noting.First,␣determines the degree of complementarity between inputs; since␣ʦ(0,1),the elasticity of substitution between them,1/(1Ϫ␣),is always greater than one.Second,we follow Jean-Pascal Benassy (1998)in introducing the term Nϩ1Ϫ1/␣in front of the integral,which allows us to sepa-rately control the elasticity of substitution be-tween inputs and the elasticity of output with respect to the level of the technology.To see this,consider the case where X(j)ϭX for all j. Then the output of technology N is qϭNϩ1X. Consequently,both output and productivity(de-fined as either q/(NX)or q/N)are independent of ␣and depend positively on N,with elasticity determined by the parameter.6There is a large number of profit-maximizing suppliers that can produce the necessary inter-mediate goods,each with the same outside op-tion w0.For now,w0is taken as given,but it will be endogenized in Section IVC.We assume that each intermediate input needs to be produced by a different supplier with whom thefirm needs to contract.7A supplier assigned to the production of an intermediate input needs to undertake relation-ship-specific investments in a unit measure of (symmetric)activities.There is a constant mar-ginal cost of investment c x for each activity.8 The production function of intermediate inputs is Cobb-Douglas and symmetric in the activi-ties:(4)X͑j͒ϭexpͫ͵01ln x(i,j)diͬ,where x(i,j)is the level of investment in activity i performed by the supplier of input j.This formulation will allow a tractable parameteriza-tion of contractual incompleteness in Section III,whereby a subset of the investments neces-sary for production will be nonverifiable and thus noncontractible.Finally,we assume that adopting(and using) a technology N involves costs C(N),and im-pose:6In contrast,with the standard specification of the CES production function,without the term Nϩ1Ϫ1/␣in front (i.e.,ϭ1/␣Ϫ1),total output is qϭN1/␣X,and the two elasticities are governed by the same parameter,␣.7A previous version of the paper,Acemoglu,Antra`s, and Helpman(2005),also endogenized the allocation of inputs to suppliers using an augmented model with addi-tional diseconomies of scope.8One can think of cxas the marginal cost of effort;see the formulation of this effort in utility terms in Section IVC.919VOL.97NO.3ACEMOGLU ET AL.:CONTRACTS AND TECHNOLOGY ADOPTIONASSUMPTION1:(a)For all NϾ0,C(N)is twice continuouslydifferentiable,with CЈ(N)Ͼ0and CЉ(N)Ն0.(b)For all NϾ0,NCЉ(N)/[CЈ(N)ϩw0]Ͼ[(ϩ1)Ϫ1]/(1Ϫ).Thefirst part of this assumption is standard; costs are increasing and convex.The second part will ensure afinite and positive choice of N. Let the payment to supplier j consist of two parts:an ex ante payment(j)ʦޒbefore the investment levels x(i,j)take place,and a pay-ment s(j)after the investments.Then,the payoff to supplier j,also taking account of her outside option,is(5)x͑j͒ϭmaxͭ(j)ϩs(j)Ϫ͵01c x x(i,j)di,w0ͮ. Similarly,the payoff to thefirm is (6)ϭRϪ͵0N͓͑j͒ϩs͑j͔͒djϪC͑N͒,where R is revenue and the other two terms on the right-hand side represent costs.Substituting (3)and(4)into(2),revenue can be expressed as(7)RϭA1ϪN͑ϩ1Ϫ1/␣͒ϫͫ͵0Nͩexpͩ͵01ln x(i,j)diͪͪ␣djͬ/␣.II.Equilibrium under Complete ContractsAs a benchmark,consider the case of complete contracts(the“first best”from the viewpoint of thefirm).With complete contracts,thefirm has full control over all investments and pays each supplier her outside option.In analogy to our treatment below of technology adoption under incomplete contracts,consider a game form where thefirm chooses a technology level N and makes a contract offer[{x(i,j)}iʦ[0,1],{s(j),(j)}]for every input jʦ[0,N].If a supplieraccepts this contract for input j,she is obliged to supply{x(i,j)}iʦ[0,1]as stipulated in the con-tract in exchange for the payments{s(j),(j)}.A subgame perfect equilibrium of this game is a strategy combination for thefirm and the sup-pliers such that suppliers maximize(5)and the firm maximizes(6).An equilibrium can be al-ternatively represented as a solution to the fol-lowing maximization problem:(8)maxN,͕x͑i,j͖͒i,j,͕s͑j͒,͑j͖͒jRϪ͵0N͓͑j͒ϩs͑j͔͒djϪC͑N͒subject to(7)and the suppliers’participation constraint,(9)s͑j͒ϩ͑j͒Ϫc x͵01x͑i,j͒diՆw0for all jʦ͓0,N͔.Since thefirm has no reason to provide rents to the suppliers,it chooses payments s(j)and(j)that satisfy(9)with equality.9Moreover,since the firm’s objective function,(8),is(jointly)concave in the investment levels x(i,j),and these invest-ments are all equally costly,thefirm chooses the same investment level x for all activities in all intermediate inputs.Now,substituting for(9)in (8),we obtain the following simpler unconstrained maximization problem for thefirm:(10)maxN,xA1ϪN͑ϩ1͒xϪc x NxϪC͑N͒Ϫw0N.From thefirst-order conditions of this problem, we obtain9With complete contracts,(j)and s(j)are perfect sub-stitutes,so that only the sum s(j)ϩ(j)matters.This will not be the case when contracts are incomplete.920THE AMERICAN ECONOMIC REVIEW JUNE2007(11)͑N*͒͑͑ϩ1͒Ϫ1͒/͑1Ϫ͒A1/͑1Ϫ͒c xϪ/͑1Ϫ͒ϭCЈ͑N*͒ϩw0,(12)x*ϭCЈ͑N*͒ϩw0c x.Equations(11)and(12)can be solved recur-sively.Given Assumption1,equation(11) yields a unique solution for N*,which,together with(12),yields a unique solution for x*.10 When all the investment levels are identical and equal to x,output equals qϭNϩ1x. Since NXϭNx inputs are used in the pro-duction process,we can define productivity as output divided by total input use,PϭN.In the case of complete contracts,this produc-tivity level is(13)P*ϭ͑N*͒,which is increasing in the level of technology. In the next section we compare this to equilib-rium productivity under incomplete contracts.11 The next proposition describes the key properties of the equilibrium(proof in the Appendix).PROPOSITION1:Suppose that Assumption1 holds.Then with complete contracts there exists a unique equilibrium with technology and in-vestment levels N*Ͼ0and x*Ͼ0given by (11)and(12).Furthermore,this equilibrium satisfiesѨN*ѨAϾ0,Ѩx*ѨAՆ0,ѨN*Ѩ␣ϭѨx*Ѩ␣ϭ0.In the case of complete contracts,the size ofthe market(as parameterized by the demandlevel A)has a positive effect on investments bysuppliers of intermediate inputs and productiv-ity.The other noteworthy implication of thisproposition is that,under complete contracts,the level of technology and thus productivitydoes not depend on the elasticity of substitutionbetween intermediate inputs,1/(1Ϫ␣).III.Equilibrium under Incomplete ContractsA.Incomplete ContractsWe now consider the same environment un-der incomplete contracts.We model the imper-fection of the contracting institutions byassuming that there exists aʦ[0,1]suchthat,for every intermediate input j,investmentsin activities0ՅiՅare observable andverifiable and therefore contractible,while in-vestments in activitiesϽiՅ1are not con-tractible.Consequently,a contract stipulatesinvestment levels x(i,j)for thecontractibleactivities,but does not specify the investmentlevels in the remaining1Ϫnoncontractibleactivities.Instead,suppliers choose their invest-ments in noncontractible activities in anticipa-tion of the ex post distribution of revenue,andmay decide to withhold their services in theseactivities from thefirm.We follow the incom-plete contracts literature and assume that the expost distribution of revenue is governed by mul-tilateral bargaining,and,as in Hart and Moore(1990),we adopt the Shapley value as the so-lution concept for this multilateral bargaininggame(more on this below).12The timing of events is as follows:●Thefirm adopts a technology N and offers acontract[{x c(i,j)}iϭ0,(j)]for every inter-mediate input jʦ[0,N],where x c(i,j)is aninvestment level in a contractible activity and10We show in the Appendix that the second-order con-ditions are satisfied under Assumption1.11This measure of productivity implicitly assumes that all the investments x(i,j)are measured accurately.Theremay be some tension between this assumption and the assumption that the cost of these investments is not pecu-niary.For this reason,in the previous version we considered another definition of productivity:output divided by the number of suppliers,Pϭq/Nϭ(N)x.The ranking of productivity levels between complete and incomplete con-tracts is the same under both definitions,and the quantitative effects of changes in contractibility on productivity are smaller with the definition used here.12The incomplete contracts literature also assumes that revenues are noncontractible.As is well known,with bilat-eral contracting or with multilateral contracting and a bud-get breaker(e.g.,Bengt R.Holmstro¨m1982),contracting on revenues would improve incentives.In our setting,we do not need this assumption,since eachfirm has a continuum of suppliers,and contracts on total revenues would not provide additional investment incentives to suppliers.921VOL.97NO.3ACEMOGLU ET AL.:CONTRACTS AND TECHNOLOGY ADOPTION(j)is an upfront payment to supplier j.The payment(j)can be positive or negative.●Potential suppliers decide whether to apply for the contracts.Then thefirm chooses N suppliers,one for each intermediate input j.●All suppliers jʦ[0,N]simultaneously choose investment levels x(i,j)for all iʦ[0, 1].In the contractible activities iʦ[0,] they invest x(i,j)ϭx c(i,j).●The suppliers and thefirm bargain over the division of revenue,and at this stage,suppli-ers can withhold their services in noncon-tractible activities.●Output is produced and sold,and the revenue R is distributed according to the bargaining agreement.We will characterize a symmetric subgame perfect equilibrium(SSPE for short)of this game,where bargaining outcomes in all sub-games are determined by Shapley values.B.Definition of Equilibrium andPreliminariesBehavior along the SSPE can be described by a tuple{N˜,x˜c,x˜n,˜}in which N˜represents the level of technology,x˜c the investment in con-tractible activities,x˜n the investment in noncon-tractible activities,and˜the upfront payment to every supplier.That is,for every jʦ[0,N˜],the upfront payment is(j)ϭ˜,and the investment levels are x(i,j)ϭx˜c for iʦ[0,]and x(i,j)ϭx˜n for iʦ(,1].With a slight abuse of termi-nology,we will denote the SSPE by{N˜,x˜c,x˜n}. The SSPE can be characterized by backward induction.First,consider the penultimate stage of the game,with N as the level of technology and x c as the level of investment in contractible activities.Suppose also that each supplier other than j has chosen a level of investment in non-contractible activities equal to x n(Ϫj)(these are all the same,because we are constructing a symmetric equilibrium),while the investment level in every noncontractible activity by sup-plier j is x n(j).13Given these investments,the suppliers and thefirm will engage in multilat-eral Shapley bargaining.Denote the Shapley value of supplier j under these circumstances by sx[N,x c,x n(Ϫj),x n(j)].We derive an explicit formula for this value in the next subsection. For now,note that optimal investment by sup-plier j implies that x n(j)is chosen to maximize sx[N,x c,x n(Ϫj),x n(j)]minus the cost of invest-ment in noncontractible activities,(1Ϫ)c x x n(j). In a symmetric equilibrium,we need x n(j)ϭx n(Ϫj)or,in other words,x n needs to be a fixed-point given by14(14)x nϭarg maxx n͑j͒sx͓N,x c,x n,x n͑j͔͒Ϫ͑1Ϫ͒c x x n͑j͒.Equation(14)can be thought of as an“incentive compatibility constraint,”with the additional symmetry requirement.In a symmetric equilibrium with technology N,with investment in contractible activities given by x c and with investment in noncontract-ible activities equal to x n,the revenue of the firm is given by RϭA1Ϫ(Nϩ1x cx n1Ϫ). Moreover,let s x(N,x c,x n)ϭsx(N,x c,x n,x n); then the Shapley value of thefirm is obtained as a residual:s q͑N,x c,x n͒ϭA1Ϫ͑Nϩ1x cx n1Ϫ͒ϪNs x͑N,x c,x n͒.Now consider the stage in which thefirm chooses N suppliers from a pool of applicants.If sup-pliers expect to receive less than their outside option,w0,this pool is empty.Therefore,for production to take place,thefinal-good pro-ducer has to offer a contract that satisfies the participation constraint of suppliers under in-complete contracts,i.e.,13More generally,we would need to consider a distri-bution of investment levels,{xn (i,j)}iʦ(,1]for supplier j,where some of the activities may receive more investment than others.It is straightforward to show,however,that the best deviation for a supplier is to choose the same level of investment in all noncontractible activities.For this reason we save on notation and restrict attention to only such deviations.14This equation should be written with“ʦ”instead of“ϭ.”However,we show below that thefixed point xnin (14)is unique,justifying our use of“ϭ.”922THE AMERICAN ECONOMIC REVIEW JUNE2007。
