Ownership Structure in Agrifood Chains: The Marketing Cooperative George Hendrikse and Jos Bijman Globalization,technologicaldevelopments,andconsumerconcernspressfarmersandfoodproduc- erstoenhanceproductinnovationandtoseekmoreefficientproductionanddistributionstructures. These changes in agrifood markets shift the relative importance of the investments by different chain partners. It may therefore be necessary to change the allocation of ownership of essential assets to induce agents to make those investments that generate the chain optimum. This article analyzes the impact of ownership structure on investments in a three-tier supply chain from an incompletecontractingperspective.Circumstancesaredeterminedinwhichamarketingcoopera- tiveistheuniquefirst-bestownershipstructure. Keywords:chain,incompletecontracting,marketingcooperative. Globalization, consumer concerns, and needed in R&D and marketing, given their increased competition press farmers and particular characteristics of democratic deci- food producers to enhance product innova- sionmakingandraisingequitycapitalamong tion and to seek more efficient production members? and distribution structures. In recent years, Increasing vertical coordination of produc- agricultureandthefoodindustryhaveshown tion,distribution,andmarketingamongfirms increasing collaboration on issues of prod- in a supply chain may have an impact on the uct development, quality guarantee systems, investment decisions of each firm individu- and improved logistics (Downey; Royer and ally. Investments by a firm in one tier of the Rogers). Spot markets are being replaced chain must be coordinated with investments by contract-production and systems of verti- byfirmsinothertierstoobtainoptimalchain cal coordination (Martinez and Reed). More performance.Astherearecomplementarities coordination and collaboration may lead to amongtheactivitiesofdifferentchainpartic- improved efficiency in production and dis- ipants, the investments are of a relationship- tribution channels and to more product and specific kind. In other words, vertical coor- market innovations (Galizzi and Venturini). dination may increase asset specificity. The These vertical relationships can take many central question of this article is how dif- forms, like strategic alliances, long-term con- ferent ownership structures affect the invest- tracts, licensing, subcontracting, joint ven- ment incentives of firms participating in spe- tures, and franchising (Mahoney and Crank). cificagrifoodsupplychains.Inaddressingthis Marketing cooperatives are a special type question, we apply incomplete contract the- of vertical integration, with farmers owning oryasdevelopedbyGrossmanandHart,and assets in another tier of the agrifood pro- Hart and Moore. duction and distribution system. Changes in We seek to make two contributions to the the market for food products raise the ques- economics of vertical coordination. Where tion whether cooperatives are still efficient incomplete contract models have mainly organizations for processing and marketing been developed on the basis of two agents of agricultural products (Cook). Are coop- engaged in a vertical or lateral relationship, eratives well suited to make the investments in this article we develop a model with three agents. Moreover, the three-agent model is used to analyze the efficiency of ownership Prof.G.W.J.Hendrikse,ErasmusUniversityRotterdam,Rotter- structures in the agrifood sector, particularly damSchoolofManagement,TheNetherlands.Dr.W.J.J.Bijman, Agricultural Economics Research Institute (LEI), The Nether- the farmer-owned marketing cooperative. lands. The rest of this section presents a styl- We thank Frank Bunte and the referees for their valuable comments.Allremainingerrorsareours. ized example for the agrifood industry to Amer.J.Agr.Econ.84(1)(February2002):104–119 Copyright2002AmericanAgriculturalEconomicsAssociation HendrikseandBijman OwnershipStructureinAgrifoodChains 105 introduce the main themes. Consider three Another option for the dairy farmer is to agents, a dairy farmer, a manager of a dairy take over the dairy company or to start his company (the ‘processor’), and a manager ownprocessingcompany.Beingtheownerof of a supermarket store (the ‘retailer’). There the processing plant, the farmer has control are three assets: the farm, the dairy factory, over all activities of the dairy company. The and the store, owned by the farmer, proces- manager of the dairy company is no longer sor, and retailer, respectively. Each agent has also the owner; he is now an employee of investment opportunities. the farmer. This way the farmer can prevent For example, the farmer invests in acquir- opportunisticbehaviorbythemanager.Here, ing knowledge of how to produce organic wehaveoneoftheclassicreasonsforagroup milk. The investment is specific to the farm, of farmers to set up a farmer-owned process- as organic farming requires extensive knowl- ing and marketing cooperative (Schrader). edge of local soil and climatic conditions. Similarly, the farmer could take over the This investment of the farmer will benefit supermarket store if he expects or experi- from all three assets in the chain. Surplus is ences opportunistic behavior from the man- added by the assets at the processing stage ager of the supermarket. Due to scale eco- of production, for instance, the processing nomics this solution cannot easily be chosen, is done in a separate processing line. Sur- although there are small-scale examples of plus is also added in the retailing stage of farmers selling their own specialty products. production, for instance, by putting it on an An example (at least in the Netherlands) attractivelylocatedshelf.Wewillassumethat the total chain surplus, which is generated are the cheese-farms, where milk production, by the investment of the farmer, is (cid:1)2+(cid:2)(cid:3)t. processing milk into cheese, and the sale of The contribution of the assets at the farming cheese are all done on-farm. (processing, retailing) stage of production is The value of vertical coordination among t(cid:1)t(cid:5)(cid:2)t(cid:3). The investment is efficient when the farmer, processor, and retailer increases if costs are not more than (cid:1)2+(cid:2)(cid:3)t. not only the farmer does a chain-specific To secure a net benefit from the invest- investment but the processor and the retailer ment, the farmer may consider signing a as well. The processor may invest in knowl- contract with the processor and the retailer edge of making cheese from organic milk. about the division of the surplus. However, The processor’s investment will generate a a contract is often incomplete, for instance, higher surplus if he receives the organic milk becausedevelopmentsindemandfororganic from the local farm and if his organic cheese dairyproductscannotbeforeseen.Thechain- is sold in the local store. For this reason, the specific nature of the farmer’s investment processor’s investment is also (at least par- means that his investment will yield a sig- tially) chain-specific. Finally, the retailer may nificantly lower return if the local proces- alsomakeaninvestmentinsettingupastore sor and/or the local retailer renege on the identity featuring organic dairy products. As contract. The farmer has become—for a cer- thefocusisonlocallyproducedproducts,the tain part of his investment—dependent on investment is specific to the relationship with the processor and retailer. An opportunis- thefarmerandtheprocessor.Theinvestment tic contract party may take advantage of the by the retailer is also chain-specific. dependency relationship, for instance, when The investment by the processor (retailer) market conditions change. Once the farmer is also vulnerable to contract reneging by the has done his sunk investment, the proces- other chain agents. The processor (retailer) sor or retailer may demand a larger part of also faces the risk that after having made his the total chain surplus under the threat of sunk investment, a larger than contracted for discontinuing the contract altogether. Such part of the surplus will be appropriated by opportunistic behavior is often possible as the other agents. The processor (retailer) has most contracts can hardly cover all relevant futurecontingencies.Particularlyinsituations various options for safeguarding his chain- of great uncertainty and market volatility, specific investment. The option we pursue in opportunities for contract reneging increase. this article is the shift of ownership of essen- Thisuncertaintyaboutthefuturebehaviorof tial assets. Essential assets are those assets his contract partners may lead the farmer to that an investing agent needs to have acces- decide on a lower level of investment. How- sibletogeneratethemaximumsurplus.Thus, ever, this is inefficient from a welfare per- by acquiring essential assets in other stages spective. of the production and distribution chain, the 106 February2002 Amer. J.Agr. Econ. processor (retailer) can safeguard his chain- Moore have developed a property rights the- specificinvestment.Oncehehascontrolover ory of the firm. A firm is identified as a col- those assets, he can fire the managers work- lection of nonhuman assets under common ingwiththeseassetsiftheythreatenhimwith ownership, where ownership means holding contract reneging. residual rights of control. Residual rights are As all three agents can make a chain- all rights to an asset that are not expressly specific investment and all three can acquire assigned to another agent (including the assets in other stages of the chain to safe- state). The allocation of residual rights of guard their investment, the question arises control influences the bargaining position who should own which assets. It entails that of agents to a contract after they have theallocationofownershipoverassetsdeter- maderelationship-specificinvestments.Inthe mines the distribution of the surplus (cid:1)2+(cid:2)(cid:3)t absenceofcomprehensivecontracts,property of the investment of the farmer over the rights largely determine which ex post bar- three parties. In this article, we develop a gaining position will prevail. An agent own- modelforanalyzingtherelationshipbetween ingassetsthatareessentialforvaluecreation ownership structure and efficient investment in the relationship is in a position to reap at decisions. Before we introduce our model, least some of the benefits from the relation- we briefly introduce incomplete contract the- ship that were not explicitly allocated in the ory. The model is elaborated separately for contractbythreateningtowithholdtheassets two agents and for three agents. This is fol- otherwise. Thus, a shift of ownership affects lowed by formulating the comparative statics theexanteinvestmentincentivesofcontract- results, while the final section presents our ing agents.1 conclusions. Thestandardmodelofincompletecontract theory consists of a three-stage noncooper- ative game. The first stage consists of the Incomplete Contract Theory choice of ownership structure, where each ownership structure is associated with a spe- cific distribution of bargaining power. The Incomplete contract theory starts from the second stage holds the specific investment basic idea that it is often difficult to write decision(s). At the third stage, the nonin- enforceable comprehensive contracts. Real- vestor has the choice whether to honor the worldcontractsarealmostalwaysincomplete contract or renegotiate it. in the sense that there are inevitably cir- Thisgameissolvedbybackwardinduction. cumstances or contingencies left out of the Therefore, we start with the third stage. Two contract,becausetheyareunforeseenorsim- agents,forinstance,afarmerandafoodpro- ply because it is too expensive to enumer- cessor, sign a contract before investment by ate them in sufficient detail. As contracts are the farmer takes place. The contract specifies incomplete, actions and payments must often that each agent receives half of the surplus be determined ex post, either unilaterally generated by the investment. The contract is or through negotiation. Consequently, con- incomplete because situations may arise for tracting agents should be concerned ex ante which the contract does not specify anything. with the possibility of opportunistic behav- If, for example, consumer demand turns out ior and the results of possible renegotia- tobelowerthanexpected,theprocessormay tion. This is particularly problematic if ex argue that the quasi-surplus instead of the ante transaction-specific investments must be surplus has to be divided in such situations. made. These investments create the opportu- The specificity of his assets has weakened nityforexpostappropriationofquasi-surplus the farmer’s ex post bargaining position to (surplus plus specific investment costs) by such an extent that he will accept these new the noninvesting agent to the transaction. The anticipation of possible holdup may lead to under-investment in the economic rela- 1The main Grossman/Hart/Moore conclusions on optimal tionship. Klein, Crawford, and Alchian and asset ownership in a two-tier vertical relationship (i.e., buyer– Williamson (1979, 1985) have suggested that sellerrelationship)arethefollowing.(1)Anagentwithanimpor- verticalintegrationmayresolvethisproblem. tantinvestment(inhumancapital)shouldhaveownershiprights overtheassetforwhichtheinvestmentisrequired.(2)Ifinvest- GrossmanandHarthavearguedthatverti- mentsbyagentAbecomerelativelymoreimportantthaninvest- calintegrationbringscostsaswellasbenefits. mentsbyagentB,thenAshouldownmoreassets.(3)Highly To understand what changes when two firms complementaryassetsshouldbeundercommonownership.(4) Independent assets should be separately held. (5) Important merge, Grossman and Hart, and Hart and assetsshouldnotbeownedbyathirdagent. HendrikseandBijman OwnershipStructureinAgrifoodChains 107 contract terms. The subgame perfect equilib- Table 1. Quasi-Surplus for Two Investment rium strategy in the third stage is therefore Decisions and Various Assets Involved to renegotiate the ex ante contract. AssetsInvolved InvestmentDecision q The investment decision in the second stage of the game determines the bargaining A x =1 t 1 1 positions in the third stage. The specificity A A x =1 2t 1 2 1 of the investment places the investor in a A x =1 f 2 2 weak bargaining position regarding the divi- A A x =1 2f 1 2 2 sion of the surplus in the third stage. There- fore, the investor anticipates that the other Notes:xi=1meansthatagentiinvests;q isquasi-surplus;t= surplus generatedbytheinvestmentofagent1atagent1’sstageofproduction; agentmaytakeadvantageoftheincomplete- andf= surplusgeneratedbytheinvestmentofagent2atagent2’sstage ness by claiming a larger share of the ex post ofproduction. surplus than initially agreed upon. This fear of ex post opportunistic behavior results in sharingatT .AscontractsatdateT arenec- 1 0 underinvestment. essarily incomplete, the distribution of value In the first stage of the game, the own- at date T depends on the bargaining power 1 ership structure is chosen. It is assumed in of the agents. incomplete contracting theory that an own- We assume complementarities in asset ership structure is efficiently chosen. Every use.2 An investment by agent 1 generates a ownership structure is associated with a higher value if not only asset A , but also A 1 2 particular distribution of bargaining power. is used. Similarly, for an investment by agent For capturing bargaining power, we adopt 2: it generates a higher value if more assets the game theoretic solution concept Shapley are used. As the generation of maximum value (Shapley), just like the seminal article value depends on the use of assets belonging by Hart and Moore. to another tier of the chain, the investments are chain-specific. Because chain-specificity refers to assets and not to agents, not always all agents are needed to generate the total The Model: Two Agents chain value. The total chain value of an investment will be established by coalitions There are two agents (1 and 2), two assets consisting of at least the investing agent and (A and A ), and two investment decisions the agents owning assets. For example, if 1 2 (x and x ). For simplicity, x can only take agent1istheinvestorandownsassetsA and 1 2 i 1 the value 0 or 1. The investment is in A ,thenagent2isnotneededforgenerating 2 human capital; that is, it is person-specific. the maximum chain value of the investment The investment pays off in the future only of agent 1. if the agent has access to a particular asset; The value generated by a specific invest- thatis,theacquiredskillisasset-specific.This ment is the quasi-surplus (q), being the sur- impliesthattheinvestmentdoesnotgenerate plus plus that part of the investment that is surplus if the investing agent is denied access sunk in the relationship. The actual value of to the asset. q depends on who invests and which assets Themodelconsistsofthreestages:anown- are used. We assume that agent 1 generates ership structure stage, an investment stage, a quasi-surplus of t when A is used and 1 and a bargaining stage. We make the follow- 2t when both assets are used. Similarly, we ingassumptionsaboutinvestment(x).Invest- assumethatagent2generatesaquasi-surplus ments are made simultaneously and nonco- of f when A is used and 2f when both 2 operatively (i.e., each agent invests without assetsareused. Thequasi-surplusforvarious taking into account the choice of the other investment decisions and various assets used agent). Investments are observable, but not are shown in table 1. The full quasi-surplus verifiable. This means that no contract can ofeachinvestmentisgeneratedonlywhenall be written about the precise investments, assets are used. but that agents can observe each other’s investments once they have been made. The 2Complementarity among a group of activities means that observability implies that bargaining at T 1 if the levels of any subset of activities is increased, then the takes place under symmetric information marginalreturntoincreasesinanyoralloftheremainingactiv- about the T investments. No contracts are ities rises (Milgrom and Roberts). Notice that our model has 0 complementarityinassetuse,whereasHartandMooreprovide possible about cost sharing at T0 or benefit anexampleofcomplementarityininvestment. 108 February2002 Amer. J.Agr. Econ. Table 2. Shapley Values for Two Agents, Two Investment Decisions, and Three Own- ership Structures X=(x (cid:5)x ) G SV SV 1 2 1 2 (1, 0) I 1.5t 0.5t (1, 0) II 2t 0 (1, 0) III t t (0, 1) I 0.5f 1.5f (0, 1) II f f Figure 1. Three ownership structures (0, 1) III 0 2f Notes:xi=1meansthatagentiinvests;G= governancestructure;and SVi= Shapleyvalueofagenti. Various distributions of asset ownership arepossible.Wehavedistinguishedthreedif- The characteristic function and the compu- ferent ownership structures. Figure 1 shows tation of the Shapley values are provided the assets that each agent owns for each of in Appendix A. Table 2 presents the result- the three ownership structures. Ownership ing Shapley values (SV) for each investment structure I represents market exchange. For- decision and all ownership structures. This ward integration, where both A and A are 1 2 entails six cases. owned by agent 1, is captured by ownership The Shapley value is a measure of power structure II. This ownership structure is asso- in the ex post bargaining process.5 It spec- ciated with the agricultural marketing coop- ifies for each agent the size of the quasi- erative, where farmers own the processing or trading company at the second tier of the surplusthatthisagentwillreceiveinthebar- chain. Finally, ownership structure III repre- gainingprocess.Therefore,theShapleyvalue sents backward integration. determines the maximum costs of invest- The bargaining power of each agent in the ment the agent is willing to make. If we supply chain under the various ownership denote the sunk cost (or specific) part of structures is captured by its Shapley value.3 the investment as ‘k,’ then the (investment) TheShapleyvalueiscomputedforeachown- ershipstructureandeachinvestmentbyusing the characteristic function. A characteristic todistributechainbenefitsinthedifferentgovernancestructures. function v assigns a number to every coali- Thecaseofnondistinguishablemarginalcontributionscanalso tionS,givenaparticularownershipstructure beanalyzedinourmodel.Themotivationfornondistinguishable G and given an investment choice x and is marginalcontributionscanbemadebypointingtothenonverifi- abilityofmarginalcontributions.ThecalculationoftheShapley denoted v(cid:1)S(cid:3)G(cid:5)x(cid:3). This number is the total valuehastobedoneinadifferentway.Itcannotbebasedany- valuegeneratedbytheagentsinthecoalition more on marginal contributions, but it can be based on which S withoutanyhelpfromtheagentsoutsideof partiesareessential.Essentialpartiesaretheinvestorandthe partieswhoownassets.Thisprovidessufficientvariabilityinthe S.4 G gives the allocation of asset ownership. Shapleyvaluetodistinguishthevariousgovernancestructures. Theresultsaresimilar. 5In our model, we have assumed that a specific agent 1 is tradingwithaspecificagent2,andthateachinvestmentisspe- 3TheShapleyvalueisanallocationofpayoffstoeachplayer. cific to this trade relationship, in the sense that it generates a Thepayoffofaplayerisbasedonthemarginalcontributionof highersurplusinthisparticularrelationshipthanintradewitha aplayertoasurplusthatiscreatedjointly.Shapleyrecognized thirdagent.However,substitutabilityofagent1andagent2can thatthesequenceinwhichthevariousplayersparticipateina be easily incorporated in the model, both for the noninvestor coalitionhasaneffectonthevalueofthemarginalcontribution and the investor. Substitutability of a particular agent reduces ofeachplayer.Thenthequestionariseswhichsequencetocon- itsShapleyvalueintwowayswhentheagentisanoninvestor. sider?Heresolvedthisissuebytakingallpossiblesequencesinto First,anincreasingnumberofsubstitutesforaparticularagent accountandtogivethemequalweight.Thepayoffassignedtoa reducestheShapleyvalueofallthesesubstitutesjointly.Therea- playerisequaltotheaveragemarginalcontributionhemakesto sonisthattheprobabilityincreasesthataparticularorderofthe eachcoalitiontowhichhecouldbelong,whereallcoalitionsare grandcoalitionhasthefeaturethatoneofthesenoninvestorsis regardedasequallylikely.Thiswayofdetermininganddisentan- earlierthantheinvestor.Thevalueaddedbyanoninvestorin glingindividualcontributionstoajointprojectwasanimportant suchanorderiszero,whereasthevalueaddedbytheinvestor reasonforchoosingtheShapleyvalueinourmodel.Anempir- andthenoninvestortogetherisassignedtotheinvestor.Second, ical reason for choosing the Shapley value is that the “perfor- one of the four axioms underlying the Shapley value requires manceoftheShapleyvalueforpredictionoranalysisturnsout thatidenticalplayershavetohaveidenticalShapleyvalues.So, ratherwell”(DixitandSkeath,p.572). thedecreasingshareofthesurplusgoingtothenoninvestorhas 4Wemaketheassumptionthatmarginalcontributionsaredis- tobesplitequallybetweenanincreasingnumberofsubstitutes. tinguishable.ThisisinlinewiththeseminalarticlesofGrossman Iftheagentisaninvestor,thenitisobviousthatitsincentives andHart(1986)andHartandMoore(1990).Itcanbetracedto toinvestarediminishedwhenidenticalrivalsbenefitfromthe theassumptionthattheinvestmentsareobservableforthepar- positiveexternalityoftheinvestment.Thisistheclassicpublic tiesinvolved.ThisisusedinthecalculationoftheShapleyvalue goodproblem. HendrikseandBijman OwnershipStructureinAgrifoodChains 109 participation constraint6 for agent 1 under ownership structure I is (1) k ≤1(cid:16)5t(cid:16) 1 Efficient Ownership Structures (with Two Agents) An ownership structure is first-best efficient when it implements all and only surplus gen- erating investments. To determine whether Figure 2. First-best efficient ownership a particular combination of investments will structures yield the first-best, we use the participation constraints of the two agents, i.e., k ≤SV , The choice of governance structure does not 1 1 and k ≤SV . matter in these circumstances. However, the 2 2 Table 2 implies a ranking regarding the choiceofownershipstructuremattersforeffi- suitability of the various ownership struc- ciency when the value of at least one of the tureswithrespecttothespecificinvestments.7 k’s exceeds a certain level. With higher lev- i Therankingofmaximumpossibleinvestment elsofinvestment,fewerownershipstructures outlays by agent 1 for the various ownership are efficient. For instance, if f < k ≤ 1(cid:16)5f 2 structures is: and t<k ≤1(cid:16)5t, then only I is first-best effi- 1 cient. The general result is that a first-best (2) III<I<II(cid:16) ownershipstructureassignsmorepowertoan agent when its sunk costs/quasi-surplus ratio Ownership structure II is always first-best increases, ceteris paribus.8 efficient regarding the specific investment of There is no first-best efficient combination agent 1. In other words, every surplus gen- ofinvestmentspossibleintheareasA,B,and erating investment by agent 1 will be imple- C in figure 2. If investments of 1 and 2 fall mentedunderownershipstructureII,regard- in the area A, B, or C, then only second- less of the value of k . The reason is that all 1 best efficient ownership structures are pos- benefits of the investment accrue to agent 1. sible. This means that only one of the two The ranking of maximum possible outlays agents will invest. The second-best owner- regarding the investment k by agent 2 for 2 ship structure choice in region A is III when the various ownership structures is: 2f −k ≥2t−k and I or II, otherwise. Sim- 2 1 ilarly, the second-best ownership structure (3) II<I<III(cid:16) choiceinregionCisIIwhen2t−k ≥2f−k 1 2 Figure 2 shows which ownership structures and I or III, otherwise. Finally, the second- are first-best efficient as a function of the best ownership structure choice in region B sunk costs of each agent. The smaller the is II when 2t−k ≥2f −k and III, other- 1 2 specific part of the investment, the more wise. The general result is that the second- the ownership structures yield the first-best best ownership structure assigns more power efficient outcome. If k as well as k have to an agent when the surplus of its invest- 1 2 a low value, then the invariance and effi- ment increases, ceteris paribus. ciency result of the Coase theorem holds. The Model: Three Agents 6The participation constraint formulates the circumstances underwhichtheinvestorinvests.Itisaninequalitywhichstates Now we will present the model for the three that the revenues of the investment for the investor are not smaller than the costs of investment (k). The revenues of the agents (1, 2, and 3), three assets (A , A , 1 2 investmentfortheinvestorareequaltotheShapleyvalueofthe and A ), and three investment decisions (x , investorinourmodel. 3 1 x , and x ). For simplicity, x can only take 7Theordinalrankingoftheownershipstructurescanbeinter- 2 3 i pretedasa‘reducedform’ofanunderlyingmodel(Williamson, 1991).Thereducedformisanearlystageofthedevelopmentof thetheoryofthefirm(cf.HolmstromandRoberts).Theempir- icalimportanceofordinalrankingsisthattheyformulatesome 8Thechoiceofownershipstructureisinourmodeldrivenby constraintswithrespecttothedata.Tobemorespecific,various efficiencyconsiderationsonly.However,considerationsofequity changesinthechoiceofownershipstructureasafunctionofthe maypreventthatthefirst-bestownershipstructurewillbecho- levelofassetspecificityarepredictednottohappen.Iftheydo sen.Apossiblesolutionistoaccompanythechoiceofownership occurinreality,therelevanceofthemodelmustbedoubted. structurewithalumpsumtransferscheme. 110 February2002 Amer. J.Agr. Econ. the value 0 or 1. The three agents repre- Table 3. Quasi-Surplus for Three Invest- sent a specific tier in this agrifood chain: ment Decisions and Various Assets Involved agent 1 is a farmer, agent 2 is a manager AssetsInvolved InvestmentDecision q in a processing firm (hereafter called a pro- cessor), and agent 3 is a manager in a retail A x =1 t 1 1 firm(hereaftercalledtheretailer).Theassets A A x =1 2t 1 2 1 are land, factory, and shop. The investments A A x =1 (1+(cid:2))t 1 3 1 are in human capital (e.g., skills) and are A1 A2 A3 x1=1 (2+(cid:2))t A x =1 f asset-specific.Forinstance,thefarmerinvests 2 2 A A x =1 2f in skills to improve the productivity of his 1 2 2 A A x =1 2f fields, the processor invests in knowledge to 2 3 2 A A A x =1 3f increase the efficiency of processing in his A1 2 3 x2=1 h 3 3 factory, and the retailer invests in particu- A A x =1 (1+(cid:18))h 1 3 3 lar knowledge of the consumers that visit A A x =1 2h 2 3 3 his shop. The asset-specificity of the invest- A A A x =1 (2+(cid:18))h 1 2 3 3 ment implies that if the agent does not have access to the asset, the investment will not Notes:q isquasi-surplus;xi=1meansthatagentiinvests;t=surplus generatedbytheinvestmentofagent1atagent1’sstageofproduction; pay off. f= surplusgeneratedbytheinvestmentofagent2atagent2’sstageof Once again, we assume complementari- production;and,h= surplusgeneratedbytheinvestmentofagent3at agent3’sstageofproduction. ties in asset use. The whole quasi-surplus of an investment will be generated when cooperative, agent 1 owns A and A , while all assets in the chain are used. The notion 1 2 agent 3 owns A . of a chain entails that there is a difference 3 Also for the three agent supply chain, we between being in the middle or at the end can find the bargaining power of each agent of the chain. We capture this by assuming by computing the Shapley values for each that the value generated by the investment investmentandeachownershipstructure(see will be higher if two adjacent assets are used Appendix A for an example). The Shapley than if two nonadjacent assets are used. In value determines the appropriation rate; that the three-tier agrifood chain, this means that is, it allocates the surplus which the invest- the positive externalities of the investment ment of an investor generates between the of the farmer (agent 1) are higher for the parties. processing company (agent 2) than for the OnceweknowtheShapleyvalue,weknow retailer (agent 3). The quasi-surplus for var- the maximum investment each agent is will- ious investment decisions and assets used ingtodoundereachownershipstructure.As is shown in table 3, where the difference we have assumed noncooperative investment between adjacent and nonadjacent assets is decisions,eachagentwillbasehisinvestment captured by (cid:2)<1 and (cid:18)<1. only on its own Shapley value. The (invest- Figure 3 distinguishes ten ownership struc- ment) participation constraint for agent 1 tures. It shows the assets that each agent under ownership structure I is owns for each ownership structure. For instance, ownership structure V entails that (4) k ≤(cid:1)9+3(cid:2)(cid:3)t/6=(cid:1)1(cid:16)5+0(cid:16)5(cid:2)(cid:3)t(cid:16) the assets A and A are owned by agent 3 1 2 3 andassetA isownedbyagent1.Ownership Table 4 gives the maximum cost of invest- 1 structureIIrepresentsthecooperative,where ment for each investing agent under the farmers own the processing company at the ten different ownership structures. It follows second stage of the chain. In a marketing immediately from table A-5 in appendix A. Figure 3. The ten possible ownership structure choices HendrikseandBijman OwnershipStructureinAgrifoodChains 111 Table 4. Maximum Investment Levels Under Various Ownership Structures Ownership Max.Investment Max.Investment Max.Investment Structure byAgent1 byAgent2 byAgent3 I (1(cid:16)5+0(cid:16)5(cid:2))t 2f (1(cid:16)5+0(cid:16)5(cid:18))h II (2+0(cid:16)5(cid:2))t 4f/3 (1(cid:16)5+0(cid:16)5(cid:18))h III (1+(cid:2)/3)t 2(cid:16)5f (1(cid:16)5+0(cid:16)5(cid:18))h IV (1(cid:16)5+0(cid:16)5(cid:2))t 2(cid:16)5f (1+(cid:18)/3)h V (1(cid:16)5+0(cid:16)5(cid:2))t 4f/3 (2+0(cid:16)5(cid:18))h VI (1(cid:16)5+(cid:2))t 2f (5/6+0(cid:16)5(cid:18))h VII (5/6+0(cid:16)5(cid:2))t 2f (1(cid:16)5+(cid:18))h VIII (2+(cid:2))t 1(cid:16)5f (1+0(cid:16)5(cid:18))h IX (1+0(cid:16)5(cid:2))t 3f (1+0(cid:16)5(cid:18))h X (1+0(cid:16)5(cid:2))t 1(cid:16)5f (2+(cid:18))h Efficient Ownership Structures in a From the perspective of an investment by Three-Tier Chain agent 1, ownership structure VI is less effi- cient than ownership structure II. Under II Just as for the two-agent model, in the three- agent 1 owns the assets at tiers 1 and 2 (see agent agrifood chain, an ownership structure figure3)andunderVIheownsassetsattiers is first-best efficient when it implements all 1 and 3, while his investment generates more (and only) surplus generating investments. valueintier2thanintier3.Ownershipstruc- The participation constraints of the three tures I, IV, and V are identical and domi- agentsdeterminewhetheraparticularcombi- nated by ownership structure VI because in nation of investments will yield the first-best. I, IV, and V, agent 1 only owns the asset at The constraints are k ≤SV , k ≤SV , and the first tier of the chain. Ownership struc- 1 1 2 2 k ≤SV . tures IX and X are identical with respect to 3 3 Table 4 implies a ranking with respect to investment incentives for agent 1: he is indis- the incentives that each ownership structure pensable because he makes the investment, holds for various investment decisions. The while the other agent (i.e., agent 2 in IX and ranking of ownership structures according to agent 3 in X) is indispensable because he themaximumlevelofinvestmentundereach ownsallassets.OwnershipstructureIIIisless structure is: efficient than IX and X because agent 1 has to negotiate with two other agents instead of (5) VII<III<IX/X<I/IV/V only one. Finally, ownership structure VII is the least efficient with respect to the invest- <VI<II<VIII(cid:16) ment incentives for agent 1. It is even less efficientthanownershipstructureIIIbecause Ownership structure VIII is always first- the combination of agents 1 and 2 in III gen- best efficient regarding the specific invest- eratemoresurplusthanthecombinationof1 ment of agent 1. In other words, every sur- and 3 in VII. plus generating investment by agent 1 will Therankingofownershipstructureaccord- be implemented under ownership structure ing to the maximum possible investment k VIII, because all benefits of the investment 2 by agent 2 is: accrue to agent 1. Becausethepositiveexternalitiesofinvest- (6) II/V<VIII/X<I/VI/VII ment are not fully taken into account when <III/IV<IX(cid:16) theinvestingagentmakesitsinvestmentdeci- sion, underinvestment may result. For exam- Similarly,therankingofownershipstructures ple,agent1willinvestunderownershipstruc- for the maximum possible investment k by ture II when k ∈ (cid:21)0(cid:5)(cid:1)2+0(cid:16)5(cid:2)(cid:3)t(cid:22), but not agent 3 is: 3 1 when k ∈(cid:1)(cid:1)2+0(cid:16)5(cid:2)(cid:3)t(cid:5)(cid:8)(cid:3). Ownership struc- 1 tureIIisinefficientforhighlevelsofk ,when (7) VI<IV<VIII/IX 1 k ∈(cid:1)(cid:1)2+0(cid:16)5(cid:2)(cid:3)t(cid:5)(cid:1)2+(cid:2)(cid:3)t(cid:3), because agent 1 1 <I/II/III<VII<V<X(cid:16) does not take the full positive externality of investment for agent 3 into account in its The explanation of these rankings is similar investment decision. to that of agent 1. 112 February2002 Amer. J.Agr. Econ. Thesethreerankingscanbepresentedina efficient. The ordering of efficient ownership three-dimensionaldiagramwithk ,k ,andk structuresforeachinvestingagentshowsthat 1 2 3 ontheaxes.Thisdiagramrepresentsfirst-best achangeinownershipstructureincreasesthe efficient ownership structures. For reasons of incentive to invest for one agent as well as simplicityitisslicedintosixtwo-dimensional decreases the incentive to invest for other figures, with each figure representing a range agents. While a shift in ownership structure ofvaluesofk .Figure4presentsthefirst-best strengthens agent i’s bargaining position, it 2 ownership structure for k ≤1(cid:16)33f. Agent 2 weakens agent j’s bargaining position. 2 will always invest when the specific level of An interesting case is ownership structure investment is not above 1(cid:16)33f. II:thefarmerownsboththelandandthefac- The next step is finding first-best effi- tory, and the retailer owns the shop. This is cientownershipstructuresforahigherinvest- the typical farmer-owned marketing cooper- ment by agent 2: 1(cid:16)33f <k ≤1(cid:16)5f. Figure 5 ative (MC). If the three agents—the farmer, 2 presents this slice. Ownership structures II themanager/processorofthefactory,andthe andVarenolongerfirst-bestefficient.Addi- retailer—all make chain-specific investments, tional figures, shown in Appendix B, show it is the relative size of the investment that that: determineswhetherthisparticularownership structure is efficient. Figures 4 and 5 show • if 1(cid:16)5f <k ≤2f, then VIII and X are no 2 that ownership structure II is the unique longer first-best efficient; first-best efficient structure if and only if • if 2f <k ≤2(cid:16)5f, then I, VI, and VII are 2 (cid:1)1(cid:16)5+0(cid:16)5(cid:2)(cid:3)t<k ≤(cid:1)2+0(cid:16)5(cid:2)(cid:3)t, 0<k ≤1(cid:16)33f, no longer first-best efficient; 1 2 and(cid:1)1+0(cid:16)5(cid:18)(cid:3)h<k ≤(cid:1)1(cid:16)5+0(cid:16)5(cid:18)(cid:3)h.Herethe • if 2(cid:16)5f <k ≤3f, then III and IV are no 3 2 farmer’sspecificinvestmentisrelativelylarge longer first-best efficient. compared to the investments by the proces- It follows from figures 4 and 5 (and the sor and the retailer (i.e., k /q >k /q and 1 1 2 2 ones in Appendix B) that each possible own- k /q >k /q ). If the farmer’s investment is 1 1 3 3 ership structure can be uniquely first-best smaller, then also I and V are first-best effi- Figure 4. First-best efficient ownership structures when agent 2 always invests, i.e., k ≤ 2 1.33 f HendrikseandBijman OwnershipStructureinAgrifoodChains 113 Figure5. First-bestefficientownershipstructureswhenthecostsofinvestmentofagent2are 1(cid:16)33f <k ≤1(cid:16)5f 2 cient. With ownership structure I each agent MC to another ownership structure may be owns an asset, and with ownership structure necessary. For instance, if the manager owns Vtheprocessingplantandtheshopareboth the processing firm, he has a much stronger owned by the retailer. If the investment by bargaining position and therefore a better the retailer is smaller (if k ≤ (cid:1)1+0(cid:16)5(cid:18)(cid:3)h(cid:3), incentive to invest. 3 then also VIII becomes first-best efficient. Ownership structure VIII means that the farmer owns all three assets. This situation of full chain integration will only yield the Comparative Statics Results social optimum if the specific investments by the processor and the retailer are much A number of comparative statics results can smaller than the investment by the farmer. be derived from this model. First, the set of Ownership structure II does not show efficient ownership structures shrinks when up anymore in figure 5, indicating that an the specific costs of investment increases rel- increaseink willreducetheattractivenessof 2 ative to the surplus it generates. When k/q an MC in inducing investments by all agents increases, the ownership structure has to be inthechain.Whenthespecificinvestmentby more fine-tuned to prevent holdup problems. agent 2 increases in proportion to the invest- Anotherwayofformulatingthisresultisthat ments by agents 1 and 3, an MC is no longer an increase in the value of q, given the level the best solution to the various holdup prob- of k, will increase the set of efficient own- lems. Because an MC is geared toward the ership structures. The increase in the ratio interests of the farmer (agent 1), expressed surplus/quasi-surplus provides more leeway by farmer-ownership of the processing firm, investments by agent 2 face the threat of inthechoiceofownershipstructuresuchthat holdupbythefarmers.Theconclusionisthat bothagentsfeelsecurethattheirinvestments if the manager of a farmer-owned process- will be recouped. In the cells in the upper ing firm needs relatively high chain-specific right corners of figures 4 and 5, there is no investments, for instance, in product innova- first-best ownership structure; that is, there is tion or marketing innovation, a shift from no ownership structure that is able to obtain