The Economics of Traceability for Multi-Ingredient Products: A Network Approach

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1 The Economcs of Traceablty for Mult-Ingredent Products: A Network Approach Dogo M. Souza-Montero and Jule A. Caswell Paper Presented at the Annual Meetng of the Amercan Agrcultural Economcs Assocaton Provdence, Rhode Island July 24-27, 2005 Copyrght 2005 by Dogo M. Souza-Montero and Jule A. Caswell. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on such copes. Dogo M. Souza-Montero s a Ph.D. canddate and Jule A. Caswell s a professor n the Department of Resource Economcs, Unversty of Massachusetts Amherst. The authors thank John K. Stranlund, L. Joe Mofftt, and partcpants n a semnar at the Department of Resource Economcs at Unversty of Massachusetts Amherst for helpful comments. Ths research was supported by a USDA Cooperatve State Research, Educaton, and Extenson Servce (CSREES) Specal Grant to the Food Marketng Polcy Center, Unversty of Connectcut and by subcontract at the Unversty of Massachusetts Amherst. The support of the Portuguese Foundaton for Scence and Technology (FCT) s also gratefully acknowledged. Correspondng author s Dogo M. Souza-Montero (dsm@resecon.umass.edu), 80 Campus Center Way, 404 Stockbrdge Hall, Unversty of Massachusetts, Amherst, MA USA 01003, phone (413) , fax (413)

2 The Economcs of Traceablty for Mult-Ingredent Products: A Network Approach Abstract: The consumpton of mult-ngredent foods s ncreasng across the globe as consumers spend less tme preparng meals. Traceablty s now extensvely used to reduce nformaton mperfectons n food markets and recent EU law suggests t wll be mplemented for manufactured meals as well. We present a model developed to understand how nformaton on dfferent ngredents flows through supply chans for mult-ngredent food products. The network model has three ters lnked by contracts for levels of qualty and nformaton. The model s useful for analyzng tradeoffs and network effects emergng n the choce of traceablty levels. Keywords: Traceablty, mult-ngredent foods, network models

3 The Economcs of Traceablty for Mult-Ingredent Products: A Network Approach Asymmetres n or the absence of nformaton on crtcal attrbutes cause uncertanty n food supply chans. Ths s partcularly true for food safety, ncludng potental boterrorsm rsks, where multple partes have an nterest n tmely access to nformaton. Both publc and prvate authortes have advocated traceablty as the best tool to solve or at least reduce ssues assocated wth nadequate nformaton. Several publc traceablty systems are already n place; they dffer across countres and ndustres, n levels of sophstcaton, and n whether they are mandatory or voluntary. At the same tme, prvate systems are prolferatng. To date studes of the supply of traceablty have focused on sngle ngredent products. These may or not be processed along the supply chan but are not combned wth other products untl they reach the consumer. However, n the Unted States and many other countres consumers are ncreasngly buyng and consumng pre-prepared meals or meal products that mnmze tme spent on preparaton. Many of these products have multple ngredents and nvolve a level of processng where an ndustral cookng faclty prepares and packages the fnal product. In addton, when analyzng the economcs of traceablty the network structure of food supply chans and ts effects must be recognzed and taken nto account. Food supply chans nvolve relatonshps between frms at dfferent stages, whose actons mpact other frms and consumers wth whom they may not have drect contact. When the network structure of supply chans s not consdered, comparson of dfferent traceablty systems and ther effects on compettveness and the lablty exposure of 1

4 frms may be ncomplete. The model developed here focuses on the economcs of traceablty for mult-ngredent products, whle recognzng network effects. Network Approaches to the Economcs of Markets and Traceablty There s a growng body of lterature analyzng the economc mpact of traceablty. However, analyss s lackng that consders the many mportant elements of traceablty systems n a sngle framework. Traceablty nvolves coordnaton of dfferent agents, the sharng of nformaton, close lnks to qualty assurance systems, and the development of new types of organzatons. Economsts have consdered each of these aspects of traceablty extensvely but ndependently. Traceablty s a supply chan ssue as t nvolves coordnaton of product attrbutes and process nformaton among producers, processors, and dstrbutors. Externaltes emergng from mperfect nformaton may be consderably amplfed as the number of agents n the supply chan ncreases. Furthermore, more complex qualty assurance and management systems are requred as the number of partcpants at each level and the number of levels n the supply chan ncrease. The lterature on networks and supply chans provdes a framework for buldng an ntegrated perspectve on markets for qualty and nformaton. Two man streams of ths lterature derve from ndustral organzaton and from operatons research and management scence. From the ndustral organzaton perspectve, the term network relates more to the characterstcs of a good or a commodty than to frms n supply chans. In ther semnal paper, Katz and Shapro (1985) dscuss products whose utlty of consumpton rses wth the number of consumers usng them. They dentfy three postve consumpton 2

5 externaltes: 1) those generated by the physcal effect of the number of purchasers on the qualty of the product; 2) ndrect effects leadng to consumpton externaltes, and 3) effects on the qualty and avalablty of post-sale servce for durable goods due to the experence and sze of the network. These externaltes are common n products such as telephones, computers and assocated software, stereos, cars, and a wde varety of other products. Katz and Shapro develop models of olgopoles where consumpton externaltes are present and analyze the effects on competton and compatblty decsons. They conclude that the expectatons of consumers play an mportant role n markets where network externaltes are present and that publc nterventon may be requred when the source of network externaltes s a compatblty decson. Economdes (1996) suggests that network externaltes mply a need for some sort of coordnaton or compatblty between frms producng goods subject to such effects. He dstngushes the macro approach to network externaltes, whch assumes ther exstence and analyzes the mpact of such effects, from the mcro approach that seeks to explan the orgnal cause of such effects. Economdes proposes a classfcaton of networks and models to analyze cases of compatblty and ncompatblty, effects on ndustry structure, the mportance of sequental games, and markets for adapters and addons. He employs a varety of game theory models to llustrate dfferent problems arsng n network products and markets, usng examples from the telecommuncatons market. The man concluson s that lessons learned n markets where network effects are prevalent apply to other markets structures where vertcal relatons exst. Whle most food products cannot be classfed as network products (Shy 2001), network externaltes arse n several ways. An example of the knd of network 3

6 externaltes Katz and Shapro (1985), Economdes (1996), and Shy (2001) focus on s the effect of mcrowave technology on the market for ready to eat frozen meals: there was not much ncentve for the food ndustry to produce mcrowave meals untl a suffcent number of households adopted the technology. Informaton on the characterstcs of food producton and processng, whch consttute the base of traceablty, can be analyzed as a network product. Agents n the supply chan may have to engage n or avod actons dependng on what they know about what other agents n the supply chan are dong. In addton, many agrcultural commodtes are complementary, as n the case of bread and butter, and therefore presumably subject to postve network externaltes. Though these examples llustrate stuatons where network approaches would be welcome n analyzng food markets, to date there s not much research on food as a network product. The ndustral organzaton approach to network economcs emphaszes the need to analyze coordnaton and the mpacts of each frm s actons on other agents n the supply chan. From an operatons research and management scence perspectve, network economcs addresses many dfferent ssues from decsons on optmal flows of products or producton, to storage and dstrbuton locatons and the strategc behavor of frms and regulatng authortes at dfferent levels of supply chans. Fearne (1998), for example, uses an operatons research perspectve to descrbe the evoluton of the Brtsh beef supply chan. He focuses on motvatons for horzontal and vertcal relatonshps, developng the concept of a learnng chan, where competton s ncreasng between food chans, rather than between partners wthn a supply chan. Supply chans that 4

7 establsh strong bonds among partners, and that are able and commtted to learnng from ther mstakes, wll have a better chance of succeedng. The management scence approach uses mathematcal network models to obtan quanttatve solutons to hghly complex problems nvolvng several dfferent agents who are lnked by dfferent paths n multple tered supply chans. Most problems are addressed usng computatonal algorthms, such as those based n varaton nequalty. Nagurney (1999) presents ths methodology and llustrates ts applcaton to transportaton, nformaton, fnancal, energy, and communcaton networks. Ths lterature provdes mportant nsghts nto how network externaltes nfluence product flows and provdes solutons to problems n whch dfferent crtera of optmzaton can be smultaneously consdered. For example, Dong, Zhang, Yan, and Nagurney (2005) develop an applcaton of networks models, based on the varaton nequalty methodology, to mult-tered supply chans where agents have multple and dfferent crtera and there s uncertanty. They consder a supply chan composed of manufacturers, dstrbutors, and retalers who compete wthn a ter but cooperate between ters. Ther conclusons provde equlbrum condtons for all agents n the network. The result s an ntegrated vew of the supply chan that optmzes the flows for the entre system rather than for ndvdual components. The management scence approach provdes a powerful mathematcal framework wth whch to analyze the supply chan as an ntegrated system of ndependent agents. In addton, contract theory provdes a convenent framework to analyze the flow of nformaton among partcpants n a supply chan. The relatonshps between partes at dfferent stages of a food supply chan are often modeled as contracts, where one of the 5

8 partes, the prncpal, needs the other party, an agent, to engage n a costly actvty that benefts the prncpal. The prncpal-agent model s partcularly suted for the analyss of cases where nformaton s costly. In such cases dfferent organzatonal forms may be more economcal than the prce system n obtanng effcent outcomes (Slberberg and Suen 2001). Moral hazard and adverse selecton are also ssues successfully tackled usng a prncpal-agent model. Typcally the prncpal decdes what unobservable level of effort e, n an nterval lmted by mnmum and maxmum levels, wll be nduced from an agent. A contract s desgned to obtan such an effort level, wth the compensaton scheme lnked to effort levels (Trole 1988). Prncpal-agent models are wdely used to analyze mperfect nformaton ssues n agrcultural and food markets from analyss of poultry contracts to qualty assurance system applcatons. Starbrd (2005), for example, uses such a model to examne how nspecton polces affect food safety. A prncpal decdes what prce w to pay for hgher or lower levels of technology and methods used to mprove food safety. Hs man concluson s that the samplng nspecton polcy has a sgnfcant mpact on the producton of safer food. The challenge n ths paper s to merge the prncpal agent model nto a network economcs framework. Ths goal s accomplshed by modelng the prncpal as usng a prce scheme to obtan approprate levels of qualty and nformaton from agents at dfferent levels n the supply chan network. 6

9 The Demand for and Supply of Traceablty Several dfferent approaches to traceablty systems for agrcultural and food products are already n place. They dffer across countres and products, and have been motvated by a wde varety of scentfc, socal, and economc factors. Publc and prvate decsons to adopt traceablty systems have mportant economc mplcatons (Hobbs 2003, Golan et al. 2003). In addton to ther mpact on food safety, traceablty systems can affect anmal health and producton management decsons (see Dsney et al. 2001; Pett 2001; Vtello and Thaler 2001). Traceablty also affects the structure of supply chans because t requres coordnaton and allocaton of costs and benefts among partcpants n order to work effcently (Kola and Latvala 2002). The economc mpacts of traceablty have only recently started to be played out. Meuwssen, Velthus, Hogeveen, and Hurne (2003) dentfy three gaps n the lterature: 1) what s the break even pont for levels of traceablty, 2) what are the mpacts on current lablty and recall nsurance schemes, 3) how can regulatory ncentves be created to avod free-rdng? They offer an overvew of potental costs and benefts of traceablty and certfcaton n meat supply chans. Traceablty costs are assocated wth system mplementaton (e.g., changes n procedures, decreased flexblty, and ncreased automaton, nventory, personnel, and documentaton) and mantenance (through audtng). The benefts nclude ncreased transparency, reduced rsk of lablty clams, more effectve recalls, enhanced logstcs, mproved control of lvestock epdemcs, possble postve effects on trade, easer product lcensng, and possble prce prema. Hobbs (2002) focuses on the role of traceablty n the food system and dstngushes between ex post trace back systems and ex-ante qualty verfcaton 7

10 systems (p.1). Traceablty has three man functons: 1) reduce costs assocated wth rsks of food safety occurrences; 2) strengthen lablty ncentves, and 3) allow for ex ante verfcaton of credence qualty attrbutes. The man problem yet to be solved s how to make sure that the nformaton flow s credble. Golan et al. (2003) suggest that traceablty s a record-keepng system prmarly used to help keep foods wth dfferent attrbutes separate from one another (p. 27). They address the queston of the usefulness of mandatory traceablty as a polcy choce. They suggest that mandatory traceablty for product dfferentaton, when t does not target specfc attrbutes of value to consumers, wll be too costly and unnecessary. Also mandatory traceablty may be neffcent for the purpose of ncreasng food system safety, as t would reduce the ncentves for frms to nnovate n order to mprove safety levels. Accordng to Golan et al. (2004), whle n Europe traceablty has been manly motvated by regulatons, n the US t tends to be motvated by economc ncentves. They surveyed several dfferent systems of traceablty n agro-food ndustres and characterzed them usng three dmensons: depth (how far up and downstream the system goes), breadth (how many attrbutes are traced), and precson (to what extent the orgn s correctly dentfed). They found that there s no sngle best way to ntroduce traceablty and there s a large varablty n the characterstcs of system wthn and across ndustres, dependng on specfc attrbutes of products or motvatons to ntroduce traceablty. Souza-Montero and Caswell (2004) descrbe and compare mandatory and voluntary traceablty systems for beef supply chans found n seven countres n terms of ther depth, breadth, and precson. They show there are consderable dfferences among 8

11 countres and that the European Unon and Japan have the most sophstcated systems. Dfferent motvatons, specfc product characterstcs, and even soco-cultural patterns may determne what levels of traceablty are acceptable and to what extent traceablty should be adopted. The Demand for Traceablty Dcknson and Baley (2002) analyze the exstence of a market for meat traceablty n the US. Snce there s no publcly avalable data to measure the market for traceablty n the US, the authors turned to a laboratory experment to estmate the wllngness to pay for traceablty. Ther expermental desgn follows the one proposed by Shogren, Shn, Hayes, and Klebensten (1994), n whch partcpants make bds to upgrade a beef or pork sandwch. The results suggest that consumers from all groups were wllng to pay more for food safety assurance, a guarantee of humane anmal treatment, or no growth hormones than for traceablty. Ths study also revealed that traceablty was more valued when combned wth the other attrbutes tested. The man concluson s that, f the results obtaned n the expermental desgn can be verfed wth other trals, a proftable market for traceablty and other assurance systems may exst n the Unted States. Smlar experments conducted by Hobbs (2002, 2003) n Saskatchewan and Ontaro, showed that Canadans would be wllng to pay a premum of less than 10% for traceablty on a beef sandwch worth C$2.50. However most consumers assocated other meat characterstcs (such as safety and natural producton) wth traceablty, whch may have nflated the bd values reported. Based on these results, Hobbs concluded that 9

12 consumers are not wllng to pay for traceablty alone. Hence, to have appeal to consumers traceablty systems should be lnked wth qualty assurance for credence goods and provde nformaton before consumpton. A further concluson s that the credblty of the source of nformaton matters. Canadan consumers vew government agences and ndependent qualty assurance frms as more credble sources of nformaton. Overall, the results of research n Canada and the Unted States suggest that traceablty alone does not appeal to consumers. Rather t has value to consumers when t s assocated wth a desrable qualty assurance system or other product attrbutes. The Supply of Traceablty To date the analyss of the supply of traceablty has manly focused on the meat and gran sectors. For example, Buhr (2003) analyzed the adopton of traceablty n the European meat and poultry sectors. Hs fndngs suggest that nformaton asymmetry between fnal product handler and consumer s one of the reasons to ntroduce traceablty. However a stronger motvaton s to reduce nformaton ssues among partcpants n the supply chan. Incentves to adopt traceablty are larger when there s: 1) hgh producton uncertanty, 2) more doubt assocated wth moral hazard and opportunstc behavor, 3) ncreasng montorng costs, and 4) ncapacty to dentfy trats. Starbrd and Amanor-Boadu (2004) analyze the mplcatons of ntroducng traceablty n a food supply chan where there s an nspecton protocol. They model the relatonshp between a producer and processor, usng prncpal agent theory. The producer s the agent and knows how safe the product s, whle the processor (the prncpal) does not know the qualty and safety of the product. The processor wants to 10

13 offer a prce that maxmzes hs proft whle forcng the producer to delver nformaton and a safe product. The model developed here departs from the current analyss on the economcs of traceablty n two key ways. Frst, t embeds the nformatonal and qualty assurance aspects of traceablty n a network model. The lnkng of nformaton and qualty assurance s mportant because research on demand for traceablty suggests there may be lttle value to consumers for traceablty alone. Furthermore, a network approach s necessary to capture nterrelatonshps between members of a supply chan. The second pont of departure n the model s the consderaton of mult-ngredent foods. These products are becomng an ncreasng share of food purchases and can pose complex challenges for traceablty, ncludng how much traceablty to apply to dfferent ngredents and the benefts and costs of traceablty throughout the supply chan. Modelng Traceablty n Mult-Ingredent Supply Chans Traceablty s a flow of hgher or lower levels of nformaton on nput and product characterstcs, ncludng orgn and process attrbutes, across agents n the supply chan. In the model developed here, nformaton and qualty levels are choce varables n an optmzaton problem nvolvng agents n a food supply chan. We use the three-tered network structure presented n fgure 1 to model traceablty n supply chans for mult-ngredent products. Ths s a herarchcal and drected network. Accordng to Jackson (2005), a herarchcal network s one where a sngle actor chooses flows; the decsons depend on a sngle agent. He defnes drected 11

14 networks as those where three or more agents do not necessarly need to be connected n order for flows to occur between them. a 111 a 11m a 11 a 1m a 1n1 a 1nm 1 st ter producers a 21 a 2 a 2n 2 nd ter processors 3 rd ter processor (a 3 ) Fgure 1. Network Structure of a Mult-Ingredent Product Supply Chan The structure of fgure 1 reflects agrcultural and food supply chans. Upstream, the 1 st ter nvolves a large number of producton agents as s seen at the farm level n many food supply chans. The other two ters n the model nvolve processng. The 2 nd ter processors produce ntermedate products or ngredents. The 3 rd ter processor produces the fnal output, whch s sold to consumers. In ths network, a flow of products wth chosen qualty levels and assocated nformaton moves downstream. An example of ths network structure s a supply chan for frozen pzza manufacturng. In the 1 st ter are the producers of commodtes (tomatoes, wheat, mlk, 12

15 etc.). The agents n the 2 nd ter are processors of tomato paste, flour, and cheese. Fnally, the 3 rd ter processor s the pzza manufacturer sellng to consumers. Ths paper focuses on transactons wthn the network. In realty, any of the agents consdered may be, and often are, nvolved n other markets. These markets wll be consdered through the presence of an outsde opton. The model assumes that the 3 rd ter processor only sells one product; agan ths s a smplfcaton of the realty. The network represented n fgure 1 can be thought of as a two-stage vertcal coordnaton game, where each player has full nformaton about other agent s strategy sets. In the frst stage, each of a fnte number (n) of 2 nd ter processors chooses levels of qualty and nformaton to pass downstream, whle usng prces to nduce the qualty and nformaton levels of the nputs purchased from a pool of m farms n the 1 st ter. In the 2 nd stage the 3 rd ter processor decdes what levels of nformaton and qualty wll be requred from n dfferent ngredent producers. The 3 rd ter processor s assumed to be the prncpal, and the other partcpants are agents, hence the desgnaton as a herarchcal network. Note however that there are really two levels of herarchy because each 2 nd ter frm acts as prncpal wth respect to ts 1 st ter producers. Furthermore n ths network we assume that there are no drect transactons between the 3 rd ter processor and the 1 st ter agents. Ths herarchy does not necessarly mply the exstence of market power, whch s an ssue not dscussed n ths paper. Here the prncpal maxmzes ts profts, choosng the levels of nformaton and qualty from ts supplers. These levels of nformaton and qualty are mportant because they nfluence the probablty of ncurrng a loss, mposed by an external party that 13

16 montors the fnal output of the supply chan. The total loss mposed on the 3 rd ter processor s related to the probablty of occurrence of a food safety hazard and to the levels of nformaton and qualty acqured. If the 3 rd ter processor has hgh levels of nformaton and qualty, then not only does t have a better chance of preventng any hazard but t s also possble that these levels wll create goodwll wth the external party resultng s a lower loss beng mposed. Therefore acqurng hgh levels of qualty and nformaton has advantages both n preventon and mtgaton of losses. Another beneft of havng more nformaton and qualty may be that the technologcal process of the 3 rd ter can be more effcent. Studes on demand for traceablty have not clearly establshed the exstence of a premum prce for traceablty (Dcknson and Baley 2002; Hobbs, Baley, Dcknson, and Haghr 2005). Here we assume that the prce s not nfluenced by the nformaton. The model s complex because the qualty and nformaton levels change vertcally and horzontally at dfferent stages of the supply chan. Another complexty emerges n the assumpton of heterogenety between agents n the 2 nd ter that produce dfferent products. In addton, ther products have asymmetrc (wth respect to the 3 rd ter processor) qualty and nformaton levels. Fnally, there are dfferent agents at both the 1 st and 2 nd ter of the network, whch prevents the smplfcaton of the analyss based on representatve frms. Each ngredent used to produce the fnal product may present dfferent food safety hazards, whch have to be taken nto account by a ratonal 3 rd ter processor. Rsks of food safety hazards can be sgnfcantly mtgated usng approprate producton processes and technologes. These are constantly changng and n real markets 14

17 at any level of the supply chan there s a dstrbuton of frms operatng wth dfferent technologes. To smplfy the problem we assume that there are no dfferences n rsks assocated wth processng technologes between producers of the same product n the 1 st ter. We also wll not consder processng costs throughout, as we assume they do not affect decsons over qualty and nformaton levels, and assume agents n the 1 st ter producng the same nput have the same levels of nformaton and qualty. The level of nformaton s the quantty of nformaton on orgn, product attrbutes, or processng technologes; these levels are bounded by a mnmum and maxmum amount of nformaton that agents have avalable. The flow of product and nformaton along the supply chan s governed by the objectve functon of the 3 rd ter processor and by partcpaton and ncentve compatblty constrants for the other ters of the supply chan. The partcpaton constrants are condtons that have to be met n order for product to flow between 1 st ter producers and 2 nd ter processors and between the 2 nd ter and the 3 rd ter processor. Incentve compatblty constrants guarantee that agents share hgher levels of nformaton. Table 1 shows the varables, parameters, and agents used n the model. The qualty and nformaton varables are treated as ndexes. A crtcal assumpton s that the nformaton exchanged s truthful. The ndex of qualty contans all the relevant qualty attrbutes and the nformaton ndex comprses all peces of nformaton that are relevant for the agents of the supply chan. We use the symbols θ, γ, Θ and Γ to denote lower levels of qualty and nformaton respectvely at the 1 st and 2 nd ters. Ths means that all qualty attrbutes are lower and the relevant peces of nformaton are fewer. The 15

18 symbols θ, γ, Θ and Γ represent hgher levels of qualty and nformaton respectvely for the 1 st and 2 nd ters of the supply chan. Table 1. Lst of Varables, Parameters, and Agents Symbol P ρ p g[ α. f ( mq. ), ΘΓ, ] f (m.q ) q Π Ψ Γ Θ Γ γ Θ θ m n c 1 c 2 c 3 c 4 L U O α Defnton Prce of fnal output Prce pad to 2 nd ter processor, by the 3 rd ter processor Prce pad by 2 nd ter processor to ts 1 st ter supplers Quantty of fnal output obtaned at the 3 rd ter level and sold to consumers Quantty of ntermedary product sold by 2 nd ter processor Quantty of commodty suppled by each of m 1 st ter producers Profts of 3 rd ter processor Probablty of fnal output hazards faced by 3 rd ter processor Vector of nformaton levels Vector of qualty levels Level of nformaton at each of the 2 nd ter processors Level of nformaton at the each of 1 st ter producers Qualty level at each of the 2 nd ter processors Qualty level at the each of 1 st ter producers Number of agents supplyng to each 2 nd d ter processor Number of 2 nd ter agents and of ngredents used on fnal output Cost of qualty borne by each of the 1 st ter producers Cost of nformaton borne by each of the 1 st ter producers Cost of qualty borne by each of the 2 nd ter processors Cost of nformaton borne by each of the 2 nd ter processors Loss ncurred by the 3 rd ter processor Outsde optons of the 2 nd ter processors Outsde optons of the 1 st ter agents Proporton of ngredent used n the fnal output 16

19 We assume that agents n the 1 st ter are endowed wth a quantty (q ) of nput to sell, whch has levels of qualty ( θ [ θ, θ ]) and nformaton ( γ [ γ, γ ]) that may or not be passed down. Each unt of nput s sold at a prce ( p ( θ, γ ) ). The margnal costs of qualty and nformaton are assumed to be constant. Agents n the 1 st ter make decsons on the levels of qualty and nformaton to pass down based on the followng: (1) Max θ, γ p ( θ, γ ). q c. θ c. γ 1 2 st.. θ [ θ, θ ], γ [ γ, γ ] The Kuhn-Tucker condtons for ths problem are as follows: p 0, θ = θ (1a). q c 1 θ < 0, θ = θ and p 0, γ = γ (1b). q c 2 γ 0, γ < = γ The agents n the 1 st ter may decde not to sell to the 2 nd ter processor; they have an outsde opton n a market where they can sell wth a reservaton proft level (O ). The partcpaton constrant for the 1 st ter agents s derved as: (2) p( θ, γ). q c1θ c2γ O Assumng agents are ndfferent between acceptng a contract or not, we have: 1 (3) p( θ, γ) [ O + c1. θ + c2. γ ] q The ncentve compatblty constrant must take nto account that the 2 nd ter processor may nduce lower or hgher levels of qualty and nformaton through varyng 17

20 prces. Usng the Kuhn-Tucker condtons (1a) and (1b) above, each agent n the 1 st ter wll provde hgh levels of nformaton and qualty f and only f: p c θ q 1 p c2 and γ q If lower levels of nformaton and qualty are enough, a fxed prce that satsfes condton (3) s suffcent. The prce schedule for the 1 st ter agents s then defned as: (4) 1 [ O + c1. θ + c2. γ ] f ( θ, γ ) = ( θ, γ ) q p( θ, γ) = 1 [ O + c1. θ + c2. γ ] otherwse q The 2 nd ter processor plays a crtcal role n the establshment of a farm to fork traceablty system because t acqures nformaton from 1 st ter producers, whch t may or not pass downstream. When nformaton obtaned from 1 st ter producers s not passed down, the traceablty system s called one up-one down (.e., nformaton s mantaned between adjacent members of the supply chan but not passed to non-adjacent parts of the supply chan). Agan, agents n the 2 nd ter may choose to nduce hgher or lower levels of nformaton dependng on the prce they offer to 1 st ter agents, as shown n equaton 4. At the 2 nd ter stage of the supply chan, the producton process changes the characterstcs of the ntal product and generates new qualty and nformaton levels. In the model there s the same fnte number (m) of agents n the 1 st ter supplyng each of the 2 nd ter processors; the total cost of acqurng nformaton rses over the number of supplers. However the hgher the levels of qualty and nformaton obtaned, the lower s the cost of acqurng new qualty and nformaton levels by processors on the 2 nd ter. The objectve functon of the 2 nd ter processor s smlar to that of 1 st ter agents: t chooses qualty and nformaton levels to maxmze profts. However, each agent on the 18

21 2 nd ter has a dfferent producton functon and produces a dfferent product. They each have dfferent levels of qualty and nformaton. The prncpal at the 3 rd ter knows the mplcatons of the dfferent levels of qualty and nformaton on ts objectve functon. Hence the objectve functon for each 2 nd ter processor s: (5) Max 2 Θ, Γ ρ ( Θ, Γ ). f ( mq. ) c ( θ ). Θ c ( γ ). Γ m( O + c. θ + c. γ ) st.. Θ Θ [, Θ] and Γ Γ [, Γ] c3 ( θ ) c4( γ ) c3( θ) = and c4( γ) = c3 ( θ ) c4( γ ) The fourth term n the objectve functon s the cost of acqurng nput from the 1 st ter (equaton (4) s substtuted here). As wth agents n the 1 st ter, the nformaton and qualty levels are bounded by lower and hgher levels. We assume that all producton (f ), cost of qualty, and cost of nformaton levels are contnuous functons. The costs of obtanng more nformaton or qualty are lower, the hgher are the levels obtaned from 1 st ter producers. However, these costs are stll lnear over the new levels of qualty and nformaton. Ths hghlghts a tradeoff between the prce pad for nputs and costs of nformaton that may be passed down. The Kuhn-Tucker condtons for the problem of each 2 nd ter frm are gven by: (5a) ρ 0, Θ =Θ. f( mq. ) c3( θ) Θ < 0, Θ =Θ and ρ 0, Γ = Γ (5b). f( mq. ) c4( γ ) Γ < 0, Γ =Γ 19

22 As wth agents n the 1 st ter, the 2 nd ter processors have an outsde opton for sellng ther product n whch they earn a reservaton proft (U ). Takng ths nto account from the expresson (5) above, the partcpaton constrant for the 2 nd ter processors s: (6) ρ( Θ, Γ) f( mq. ) c3( θ). Θ c4( γ). Γ m( O + c1. θ + c4. γ) U If each frm s ndfferent between acceptng a contract from the 3 rd ter processor and gettng the reservaton proft, the followng prce schedule follows from the partcpaton constrant: 1 ρ ( Θ, Γ ) = { U + c ( θ ). Θ + c ( γ ). Γ + m( O + c. θ + c. γ )} (7) f( mq. ) The prce schedule faced by 2 nd ter processors has more cases than that of the 1 st ter producers. We wll assume that a hgh level of qualty and nformaton passed down by each 2 nd ter processor (that s Θ, Γ ) to the 3 rd ter mples that nformaton and qualty obtaned from the 1 st ter s passed to the 3 rd ter prncpal. However ths does not necessarly mean that hgher values are contracted wth 1 st ter producers. When lower levels of nformaton are contracted there s no oblgaton of passng down nformaton on the 1 st ter to the 3 rd ter processor. In a sense the 2 nd ter processors are less constraned than agents at the 1 st ter. If they accept a prce for levels of qualty and nformaton, they can offer a prce to nduce levels of qualty and nformaton from the 1 st ter that have a drect mpact n reducng costs. There s a tradeoff between the cost of nformaton and qualty nduced on the 1 st ter and the cost of these levels for the 2 nd ter processors. Ths leads to opportuntes for rent seekng condtoned on what contract s offered by the 3 rd ter processor and the rato of costs of nformaton n the 2 nd ter to nformaton and qualty prces n the 1 st ter. 20

23 Furthermore the prce offered to 2 nd ter frms may ndrectly affect the decson on what prce to offer 1 st ter agents. An mportant network effect emerges through the costs of qualty and nformaton faced by 2 nd ter processors. The objectve functon of the 3 rd ter processor has three terms: total revenues, whch depend on prce and quantty sold; a cost assocated wth purchase of nputs; and a loss functon. The objectve functon of the prncpal s defned as: (8) Max Π= Pg.{ α. f ( mq. ), ΘΓ,} { U + c ( θ). Θ + c ( γ ). Γ + mo ( + c. θ + c. )} ΘΓ, = 1 Ψ. L( ΘΓ, ) s.t. ( ΘΓ, ) Χ n γ where Χ s a compact set and g s a contnuous functon. As before all other costs are assumed to be zero. Also let Θ= [ Θ1,..., Θn] and Γ =Γ [ 1,..., Γ n ], P s the prce pad by consumers, Q= g { α. f ( mq. ), Θ, Γ} s the total output sold, and α s the fxed but not necessarly equal proporton wth whch each of the ngredents s used n the producton of fnal output ( n = 1 α = 1). The maxmzaton occurs over a vector of qualty (Θ) and nformaton (Γ) levels nduced on each of the supplers of ngredents. The remanng varables are as defned n table 1. For the frst term of equaton (8), the total revenue term, we assume that the prce pad by consumers s exogenous and ndependent of qualty and nformaton levels. Ths s a restrctve assumpton n the case of qualty where there s emprcal evdence that consumers are wllng to pay a premum for qualty but s much less restrctve n the case of nformaton where there s no clear evdence that consumers are wllng to pay a premum for traceablty. Ths assumpton does not mean that nformaton and qualty 21

24 levels for ngredents have no mpact on the revenues of the 3 rd ter processor. In the model they do a have postve mpact on the processng of the fnal output, as more nformaton on and qualty levels n the ngredents mprove productvty and effcency through the mpact on the producton functon g. The second term n the objectve functon, the costs assocated wth acqurng ngredents, depends on the levels of qualty and nformaton that the prncpal wants for each ngredent. The prce schedule offered to each 2 nd ter processor nduces these levels of qualty and nformaton. Fnally the thrd term of the objectve functon s a loss functon that captures the probablty of a loss due to safety hazards emergng n the fnal output. For ths model, these hazards are assumed to be due only to the ngredents used n the producton of the fnal output. A hazard occurs wth probablty ( Ψ [0,1] ), whch s assocated wth a loss. We assume that when a hazard occurs an external party observes t perfectly and mposes a penalty (the loss). When the 3 rd ter processor has hgh levels of qualty n and nformaton on the ngredents t uses, the external party takes ths nto account and reduces the total value of the loss when a hazard occurs. Ths s another ncentve for the 3 rd ter processor to demand hgh levels of qualty and nformaton for purchased ngredents. The model developed here has a broad range of applcatons. Frst t can be seen as an nsttuton and then be compared wth other nsttutonal settngs for traceablty. Ths model proposes an nsttutonal arrangement where traceablty s voluntary; t s entrely up to the 3 rd ter processor to decde on whch ngredents traceablty wll be mposed. Also all other partes n the supply chan may choose to sell on ther reserve, 22

25 outsde opton market where nformaton and qualty are not as mportant. Second one may derve the condtons for full traceablty,.e., the case where all ngredents carry full traceablty nformaton. Another applcaton s to analyze tradeoffs between qualty and nformaton levels. Fourth, the model can llustrate tradeoffs between the costs of traceablty and opportuntes for reducton n food safety losses. Fnally ths model may be used to analyze how decsons taken by one element of a mult-tered supply chan mpact other frms. The model has applcatons beyond the food ndustry (for example n the producton of personal computers); wth approprate adjustments t can be used to llustrate stuatons emergng n operatons research or to obtan quanttatve results. The model s formulated as a network n order to enable the analyss of network effects. A frst network effect emerges wth postve and negatve externaltes related to complementartes between ngredents. For example, these complementartes exst between the ngredents suppled by the 2 nd ter processors because f any of the ngredents underperforms then the fnal product wll be affected. A second network effect emerges due to the ndrect nfluence of a party at one ter of the network on the transactons between partes on the other two ters. An example s the decson of a 2 nd ter processor when choosng whch level of nformaton and qualty t demands from 1 st ter producers. Note that the 3 rd ter frm does not trade wth 1 st ter frms, nevertheless the objectve functon of the 3 rd ter frm ncludes the levels of nformaton and qualty nduced from the 1 st ter, whch denotes a network effect. 23

26 Model Interpretaton The model presented above can be analyzed n dverse ways. Here we derve three results based on dfferent combnatons of levels of nformaton to llustrate tradeoffs and network effects emergng n the model. The frst model nterpretaton focuses on the choce on whch ngredents wll have traceablty. Ths mples a tradeoff between the cost of nformaton and the reducton of the probablty of losses assocated wth dfferent levels of nformaton. The other two model nterpretatons focus on the network effects assocated wth complementartes between ngredents used by the 3 rd ter processor and wth the levels of nformaton demanded from the 1 st ter producers when the prce pad to the 2 nd ter processor s fxed and a low level of nformaton s elcted. For the frst nterpretaton, we assume a one-to-one relatonshp between the qualty and nformaton levels, e.g., a low qualty level corresponds to a low level of nformaton and the same for hgh levels. We further assume that for the ngredent under consderaton, the mpact of hgher levels of nformaton on revenues s neglgble, n other words the margnal effect of nformaton n the producton functon (g) of the 3 rd ter processor s small. Ths allows a focus on the tradeoff between the prces assocated wth hgher levels of nformaton and ther mpact on reducng the expected loss due to food safety hazards. Dependng on the magntude of ths prce relatve to the reducton of losses, the prncpal wll demand a hgher or lower level of nformaton flow or traceablty from 2 nd ter processors. Ths result s obtaned by rewrtng the objectve functon of the 3 rd ter processor (equaton (8)), substtutng the second term wth the prce as defned by equaton 7: 24

27 (9) n Pg. { α. f( mq. ), ΘΓ, } ρ ( Θ, Γ). f( mq. ) Ψ. L( ΘΓ, ) = 1 When decdng what level of nformaton to nduce from the producer of ngredent 1, the 3 rd ter processor uses the followng margnal condton derved from the equaton above: L() ρ1() (10). Ψ+. f 1( ) = 0 Γ Γ 1 1 The margnal effect of nformaton n the frst term of equaton 9 s not ncluded n ths equaton because, as noted above, the effect of levels of nformaton for ngredent 1 on the total output produced s assumed to be very small. To nterpret equaton 10, note that we assumed that the losses are decreasng wth the nformaton levels, whle the prces pad are ncreasng n such levels. Also note that the loss s a bad and the frm wants ths term to have the smallest possble value. Ths expresson says that the margnal effect of nformaton levels on the probable loss must be equal to the margnal ncrease n the cost of acqurng ngredents due to more nformaton. If the prce pad for hgher levels of nformaton s larger than the reducton n the probable loss, the 3 rd ter processor wll only pay for lower levels of nformaton, offerng a fxed prce. Otherwse hgher levels of nformaton are demanded. One of man reasons for formulatng ths model as a network s to account for network effects. Two nterpretatons of the model llustrate why t s mportant to account for these effects. The frst relates to the effect of complementartes. In ths model, all ngredents enter the fnal product on fxed but not equal proportons. Thus the 3 rd ter producer s forced to use all ngredents and all ngredents are complements n the producton of the fnal product. However, because the ngredents have dfferent mpacts on the probable loss, through ther qualty and nformaton levels, t s possble that 25

28 dfferent prces wll be pad to dfferent ngredents, dependng (among other factors) on whch respectve levels of qualty and nformaton the 3 rd ter processor requres. Furthermore, f a lower level of nformaton for a gven ngredent s contracted, and t s later found that a food safety hazard emerges due to ths ngredent, the 3 rd ter processor and possbly all ts supplers may face the maxmum loss. Regardless of the prces offered to nduce levels of nformaton from the 2 nd ter processors, there s always a chance that losses wll emerge due to an ngredent that was thought to be less rsky. A second network effect s assocated wth the choces of the 2 nd ter processors. Suppose a fxed prce s offered to a frm at ths ter by the 3 rd ter processor, meanng that only low levels of nformaton and qualty are requred. Wll the 2 nd ter processor necessarly contract a lower level of qualty and nformaton from ts 1 st ter supplers? The answer s not clear-cut. On the one hand, hgher levels of nformaton wll requre a hgher prce. On the other hand, the costs of obtanng nformaton n the 2 nd ter (even f at lower levels) wll be smaller f hgher levels of nformaton are obtaned from the 1 st ter processors. A network effect emerges because the levels of nformaton and qualty of the 1 st ter agents enter the objectve functon of the 3 rd ter processor. The sgn and magntude of ths network effect depend on how the costs of nformaton compare n the 1 st and 2 nd ters. Let us now turn to the crcumstances n whch a 2 nd ter processor would demand hgher levels of nformaton from 1 st ter producers, even f t s only requred to offer lower nformaton levels to the 3 rd ter processor. The partcpaton constrant of the 2 nd ter processor gven by equaton 7 can be rewrtten substtutng equaton 4 (the partcpaton constrant for frms n the 1 st ter) for the fourth term nsde the curled 26

29 brackets, and assumng that a lower level of nformaton from the 2 nd ter s enough for the 3 rd ter: 1 (7a) ρ( Θ, Γ ) = { U + c3( θ). Θ + c4( γ). Γ + p( θ, γ )} f ( mq. ) Ths expresson can be used to derve another comparng the tradeoff between the costs of qualty and nformaton on the 2 nd ter and prces pad to 1 st ter producers. Frst create two expressons for the partcpaton constrant of the 2 nd ter processor: one where hgher levels of nformaton are requred from the 1 st ter and the other wth lower levels of nformaton. Subtractng these two equatons and collectng and elmnatng common terms gves: (11) c4( γ ). Γ+ p( θ, γ) = c4( γ). Γ+ p( θ, γ) If ths equalty holds, the 2 nd ter processor s ndfferent between demandng hgher or lower levels of nformaton from the 1 st ter. Note however that the cost of nformaton generated by the 2 nd ter s decreasng wth the levels of nformaton from the 1 st ter so that: (12) c4( γ ). Γ > c4( γ ). Γ Hence there are opportuntes for cost savngs for the 2 nd ter processor when obtanng more nformaton from ts 1 st ter supplers. Ths occurs when the dfferences n prces pad to frms n the 1 st ter for hgher or lower levels of nformaton are smaller than the respectve dfference n cost savngs. In other words, f the expresson (13) below holds, 2 nd ter processors wll demand hgh levels of nformaton from 1 st ter producers. Ths n turn mpacts the profts of the 3 rd ter processor, generatng a network effect: (13) c4( γ ). Γ c4( γ). Γ> p( θ, γ) p( θ, γ ) 27

30 Ths secton develops three examples of the nsghts provded by the model. Frst, nterpretaton of the model ndcates that the level of nformaton (traceablty) produced by the supply chan crtcally depends on the relatve magntude of the costs of nformaton relatve to opportuntes for savngs due to reductons n the probable losses. Imposng hgh traceablty levels on the most rsky ngredents does not necessarly prevent the occurrence of losses, showng the mportance of takng complementartes nto account. Fnally, a network effect emerges from the model n whch low levels of nformaton nduced from a 2 nd ter processor by the 3 rd ter processor do not necessarly mean lower levels of nformaton demanded by a 2 nd ter processors from ts 1 st ter supplers. Conclusons Ths paper proposes a new model for analyzng the adopton of traceablty n supply chans for mult-ngredent products. Traceablty s defned as a flow of an ndex of nformaton between stages of a food supply chan. The am s to understand how nformaton flows occur n a supply chan wth three ters and heterogenety among partcpants. The model draws on the network economcs and contract theory lterature to develop a drected and herarchcal network structure. Ths paper contrbutes to the lterature n two mportant ways. The frst s n hghlghtng the mportance of consderng the exstence of network effects n analyzng traceablty. These effects have not been taken nto account n research on traceablty thus far. The second s n consderng the case of mult-ngredent products, whle accountng for heterogenety n supply chan relatonshps. Here a producer of a mult- 28

31 ngredent product chooses levels of nformaton or traceablty and qualty to reduce exposure to losses assocated wth food safety hazards and to mprove productvty. However, hgher levels of nformaton and qualty are more costly. In our formulaton, network effects are made explct n the objectve functon of the 3 rd ter processor, for when ths party chooses the prce to pay for each ngredent, t nfluences the choces of nformaton and qualty levels offered by the remanng partcpants of the supply chan. The model can be extended n several ways. Frst the assumpton that the nformaton revealed s true can be relaxed, whch means that some sort of certfcaton mechansm would need to be added. Second the nformaton level of the 2 nd ter processor may be a functon of the nformaton obtaned at the 1 st ter level. The model could be extended to account for full traceablty n a more explct way. Thrd the objectve functon of the prncpal (the 3 rd ter processor) could be formulated so that the probablty of a loss s drectly assocated wth the qualty and nformaton levels of the ngredents. Fnally a loss functon could be added to the objectve functon of the 2 nd ter processor, to express the possblty of a transfer of losses from the 3 rd ter processor to ts supplers. Ths model addresses an nsttutonal settng where frms have total lberty to decde whether and to what extent traceablty s adopted. An extenson to the model would adapt t to a context where traceablty s mandatory; n such a case a governmental authorty steps n and mposes a certan level of requred nformaton. Comparng the voluntary and mandatory nsttutonal settngs for the model can provde nsghts nto why we already observe dfferences n traceablty systems worldwde. The present model assumes full nformaton about other agents strategy sets n the supply 29

32 chan. If ths assumpton were relaxed, the market would requre revelaton and montorng mechansms. Fnally a crtcal aspect of the model s the defnton of the loss functon. We assume there s a known probablty of falures due to safety hazards and that the probablty s assocated wth the fnal product. Ths probablty could be expanded so that t becomes a functon of the qualty of the ngredents, producton technologes, and securty polces. 30

33 References Amanor-Boadu, V. and Starbrd, S. A "The Value of Anonymty n Supply Chan Relatonshps." Selected paper for AAEA Annual Meetng, Montreal, Quebec, Canada, July. Buhr, B. L Traceablty and Informaton Technology n the Meat Supply Chan: Implcatons for Frm Organzaton and Market Structure. Journal of Food Dstrbuton Research 34(3): Dcknson, D. L. and D. Baley Meat Traceablty: Are U.S. Consumers Wllng to Pay for It? J. Agr. Res. Econ. 27(2): Dsney, W.T., J. W. Green, K.W. Forsythe, J.F. Wemers, and S. Weber Beneft- Cost Analyss of Anmal Identfcaton for Dsease Preventon and Control. Rev. Sc. et Techque de l Offce Internaconal des Epzootes 20(2): Dong, J., Zhang, D., Yan, H. and Nagurney, A Multtered Supply Chans Networks: Multcrtera Decson-Makng under Uncertanty. Annals of Operatons Research 135(1): Economdes, N "The Economcs of Networks." Internatonal Journal of Industral Organzaton 14(6): Fearne, A The Evoluton of Partnershps n the Meat Supply Chan: Insghts from the Brtsh Beef Industry. Supply Chan Management: An Internatonal Journal 3(4): Golan, E, B. Krssoff, F. Kuchler, K. Nelson, G. Prce, and L. Calvn Traceablty for Food Safety and Qualty Assurance: Mandatory Systems Often Mss the Mark. Current Agr., Food, & Resource Issues 4: