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Dynamic Relational Contracts for Quality Enforcement inSupply ChainsMariya Bondareva, Edieal Pinker

To cite this article:Mariya Bondareva, Edieal Pinker (2018) Dynamic Relational Contracts for Quality Enforcement in Supply Chains. ManagementScience

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MANAGEMENT SCIENCEArticles in Advance, pp. 1–17

http://pubsonline.informs.org/journal/mnsc/ ISSN 0025-1909 (print), ISSN 1526-5501 (online)

Dynamic Relational Contracts for Quality Enforcement inSupply ChainsMariya Bondareva,a Edieal PinkerbaMotorola Solutions, Inc., Chicago, Illinois 60661; bYale School of Management, New Haven, Connecticut 06520Contact: [email protected] (MB); [email protected], http://orcid.org/0000-0001-7343-9864 (EP)

Received: March 6, 2014Revised: September 17, 2015; August 12, 2016;January 3, 2017; September 6, 2017Accepted: October 2, 2017Published Online in Articles in Advance:June 11, 2018


Copyright: © 2018 INFORMS

Abstract. We model the interaction of a single buyer with a single supplier within a mar-ket in a developing country with homogeneous local suppliers and homogeneous buyersfrom developed nations. The buyer sources a product from a supplier and then inspectsand sells it on the market, subject to quality standards such as regulations about chemicalcontent. Suppliers decide howmuch effort to exert to ensure compliance with quality stan-dards. Buyers are assumed to comply with contracts because they are based in countrieswith strong legal systems. We assume that legal enforcement of the supplier’s contractualobligations is not possible. We model the interaction between buyer and supplier as arepeated game in which the partnership can be terminated by the buyer if the supplierrefuses to pay penalties for quality violations. After termination, the buyer and suppliereach search for a new business partner. We model the interaction between buyer and sup-plier using relational contacts in which penalties for quality failures are set so that thesupplier voluntarily pays them. We show that optimal relational contracts have dynamicform in this setting because the value of the outside option available to the parties, ifthe relationship is terminated, is determined by the contract terms. We characterize theproperties of the optimal dynamic equilibria and analyze the use of third-party qualitycertifications within this framework.

History: Accepted by Martin Lariviere, operations management.Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2017.2990.

Keywords: supply chain • sustainability • quality • relational contracts

1. IntroductionOn November 24, 2012, more than 100 people werekilled in a Tazreen garment factory fire in Bangladesh.Investigations found that conditions in the factorywereunsafe and that the factory was producing garmentsfor a local supplier to several well-known Westernretailers including Walmart and Sears. Both Walmartand Sears denied knowing that this factory was beingused by its suppliers. In fact, Walmart asserts that itdelisted the Tazreen factory because of safety issues.However, one of Walmart’s suppliers placed an orderwith a third party that, facing a capacity shortage, out-sourced some of the order to the company operatingthe Tazreen factory that burned down. Walmart sub-sequently fired its supplier. The above summary ofthe incident is based upon reporting in the Wall StreetJournal and the New York Times (Chiu and Lahiri 2012,Yardley 2012, Zain et al. 2012).This tragic case illustrates the challenges firms face

in maintaining standards in labor practices in theirsupply chains. But the same issues exist, to varyingdegrees, for firms trying to maintain any form of man-ufacturing quality standards. These standards could berelated to the functional performance of the products,to regulatory compliance, or to sustainability goals,

among others. In the following, we refer to firms tryingto maintain quality standards in their supply chains asbuyers, where these could be original equipment man-ufacturers, retailers, or brands.

The example of Walmart and the garments sourcedin Bangladesh shows how complex a firm’s supplychain can be and how difficult it can be to knowwho isproducing the firm’s product and how it is being pro-duced. Both the size and the multitier structure of thesupply chain complicate quality assurance. We see thatdisqualifying a supplier is a tool in a buyer’s arsenal,while at the same time we see that a disqualified sup-plier (e.g., the Tazreen factory) will not necessarily lackfor business. We also see that buyers do inspect theirsuppliers, but this oversight is costly and incomplete.Another dimension to this story is that buyers likeWal-mart know that when sourcing to poor, developingnations they are seeking low costs that are achieved bylower wages and poorer safety conditions. While thebuyers may do more auditing of suppliers and makeinvestments in improving standards, they are not aban-doning Bangladesh. We point this out to indicate thatbuyers do have constraints on their choice of suppliersin the sense that economic factors force them to operatein specific countries.

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Bondareva and Pinker: Dynamic Relational Contracts for Quality Enforcement2 Management Science, Articles in Advance, pp. 1–17, ©2018 INFORMS

For the purposes of this paper, we focus on envi-ronmental standards regarding the chemical contentof products to make the discussion more concrete butalso because it is an especially challenging domain.Environmental regulations vary greatly across coun-tries and are in a state of flux. With chemical content,it can be harder to observe quality failures than in thecase of product function.

When hazardous chemicals are detected in a prod-uct that has reached consumers, the cost to a firmcan be significant. After a melamine contaminationin 2008, Chinese milk products were recalled globally(New York Times 2011). When Yili, a major dairy firmin China, recalled some of its baby formula productsbecause of mercury contamination in 2012, its shareprices immediately fell approximately 10% (BBC News2012). Other examples are the recalls of toxic toys andchildren’s products in 2007 and 2010. In 2007, the U.S.Consumer Product Safety Commission recalled over17 million toys in violation of the lead paint stan-dard, including two million toys of Mattel. Productsafety and health issues contributed to the 2008 finan-cial crisis that caused 4,222 out of 8,610 toy factories inChina to be closed (Macartney 2009). In 2010, McDon-ald’s recalled 12 million Shrek drinking glasses withcadmium contaminated paint. Before the recall, about7.5 million glasses had been sold. McDonald’s paid$3.00 for every returned item, while the price for aglass was $2.49 without a food purchase and only $1.99with one (Neuman 2010). In these cases the buyer borethe direct costs in terms of remediation and reputationeffects.In the electronics industry as of July 2006, the Euro-

pean Union (EU) (Directive 2002/95/EC1) requiresa wide range of products to be Restriction of Haz-ardous Substances (RoHS) compliant. This means thatthe amount of the six substances found in electron-ics products (lead, mercury, cadmium, hexavalentchromium, polybrominated biphenyls, and polybromi-nated diphenyl ethers) is severely restricted. Failure tocomply with RoHS regulations can lead to a productbeing banned from sale in the EU as well as signifi-cant fines. Complying with RoHS is challenging for alarge company like Hewlett-Packard, which operatesin more than 170 countries and has over 600 suppliers(Becker et al. 2010).In 2013, the nonprofit organization, the Center for

Environmental Health (CEH), discovered that majorU.S. retailers were selling personal care products con-taining cocamide diethanolamine (CDEA), a chemicaldeclared as a known carcinogen in California underProposition 65. Among the retailers who did not labeltheir products for hazardous chemical content wereBabies R Us, CVS, J. C. Penney, Kohl’s, Kmart, Macy’s,Marshalls, Rite Aid, Sears, Target, Ulta,Walgreens, andWalmart. The CEH tested 98 shampoos, soaps, and

other personal care products and showed that many ofthe products contained more than 1% of CDEA, whileone shampoo had more than 20%. In August 2013, theenvironmental watchdog filed a lawsuit against fourcompanies including Walgreens, asking the court tofine the companies $2,500 a day per violation. In addi-tion, the CEH sent legal notices to more than 100 othermanufacturers and retailers indicating that theywere inviolation of state law (Environment News Service 2013).

To prevent hazardous chemical content in theirproducts, buyers employ several mechanisms includ-ing financial incentives to encourage better qualityand compliance, financial penalties for quality fail-ures, inspections and testing, and product redesign.For instance, the CEH says that during its 17-year workwith manufacturers and retailers, in 95% of cases, ithas won legally binding agreements requiring productreformulation (Radcliffe 2013).

Some authors advise reducing the cost pressure onsuppliers (Plambeck et al. 2011, Teagarden 2009). Thisapproach has its limitations because instead of stim-ulating quality improvement, higher payments mayencourage a supplier to collect higher profit in the shortrun by reducing its own quality assurance efforts. Buy-ers who use financial penalties for quality failures alsoface challenges because, as Midler (2007) documents,in developing countries such penalties may be difficultto enforce. Reformulating products is not always fea-sible and also can require intensive coordination withthe suppliers. See Becker (2009b, c) for a descriptionof S.C. Johnson and Hewlett-Packard’s efforts in thisregard. Buyers also invest in costly inspection effortsto ensure that products with prohibited and/or haz-ardous chemicals do not reach end consumers. Forexample, after the recalls in 2007, Mattel developedthe redundant four-level inspection system, althoughMattel’s CEO admits this system does not guaranteeabsolute safety (Lyles 2008). See also Becker (2009a) fora description of Nike’s inspection efforts. If a buyerdetects compliance failures at its supplier, it is unclearwhat actions the buyer should take. One option that isalways available is to terminate the relationship withthe supplier; yet the buyer will still need to find a sup-plier, with no guarantee that the new supplier will per-form better.

With these observations in mind, in this paper weanalyze quality control and contracting in a supplychain in which there is an asymmetric ability to enforcecontract terms. We assume that the buyers are well-established firms with strong reputations for adher-ing to contracts. We also assume that they trade withsmaller suppliers that operate in countries in which thelegal environment is such that it is difficult to enforcethe suppliers’ compliance with contract terms. Thus,it is necessary to consider supplier termination as anoption in the model. Including termination gives a

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Bondareva and Pinker: Dynamic Relational Contracts for Quality EnforcementManagement Science, Articles in Advance, pp. 1–17, ©2018 INFORMS 3

richer and more realistic framework for understand-ing how a buyer can maintain quality standards in asupply chain.We make the following contributions. First, we for-

mulate a new model of buyer-supplier contracting forquality in an environment in which the buyer can com-mit to contract terms but the supplier cannot; whencontracts are terminated, the parties must engage in acostly search for new partners. Second, we show thatthere are conditions when dynamic contracts are opti-mal even though the problem setting is static. Third, weshow that holding the supplier’s profit low (zero) at thestart of the relationship and postponing the supplier’sopportunity for profit to later periods, while steadilyramping up quality expectations, increases the buyer’sleverage and improves quality. This provides the buyerwith a mechanism for artificially increasing the sup-plier’s termination costs. Fourth, we extend our modelto account for third-party quality-compliance certifica-tion and show that certification can hurt the buyer’sability to design optimal dynamic contracts becausethe certification is inflexible. Certification can essen-tially move the buyer to a more mature state of therelationship prematurely and undermine the buyer’sability to increase the supplier’s termination costs.

In Section 2 we review the related literature. In Sec-tion 3 we present the main model formulation andanalyze enforceable and nonenforceable contracts. InSection 4 we conduct numerical sensitivity analyses toexplore the factors that drive contract performance. InSection 5 we extend our model and analyze situationsin which third-party quality-compliance certification isavailable. We investigate the factors that determine ifsuch certifications have a potential benefit to the buyer.We conclude in Section 6.

2. Literature ReviewOur work belongs to three research areas: qualityenforcement in supply chains, dynamic moral hazard,and relational contracts. The first stream of the relatedliterature studies court enforceable quality control con-tracts and considers different tools to ensure quality.Reyniers and Tapiero (1995) study a contract includ-ing price rebates and after-sales warranty costs. If poorquality is discovered by the buyer, the supplier refundsthe cost of defective units; if poor quality is discoveredby the final consumer, the supplier shares warrantycosts. Sheopuri and Zemel (2008) consider a two-levelsupply chain in which getting redress from the sup-plier for a quality failure is costly to the buyer. Chaoet al. (2009) introduce contracts for sharing the prod-uct recall costs based on root cause analysis. Babichand Tang (2012) offer deferred payments to discour-age product defects. They compare deferred payments,product inspection, and combined mechanisms as thetools of quality support. The combined mechanism is

proved to be redundant. Singer et al. (2003) endogenizethe relationship between consumer demand and qual-ity. They model a contracting game in which the sup-plier is indirectly penalized for poor quality by thereduced demand experienced by the buyer from theend consumer. Baiman et al. (2000) model a one-shotinteraction between a risk-neutral buyer and a risk-neutral supplier. The supplier makes an effort to pro-duce a quality product, and the buyer makes an effortto detect defects. If penalties are enforceable, then thefirst-best is attained even if participants’ efforts are notcontractible, but the event of bad quality detection iscontractible.

Unlike these papers, we assume that the supplier canbreak the contract and refuse to share costs. We alsoassume that the buyer’s cost to get compensation fromthe supplier is prohibitively high. Thus, shared liabilityfor products and warranties are not contractible. Also,unlike these authors, we consider the case of when thesupplier requires advance payment, which is a com-mon practice in China (Midler 2007).

The second stream of literature, dynamic moral haz-ard, has been extensively studied. A detailed reviewon the works in this field is given in Bolton andDewatripont (2005). One of the closest works to ours isthe seminal paper by Holmstrom and Milgrom (1987),which models long-term contracting between a princi-pal and an agent with binary outcomes whose actionset is the choice of a probability of a good outcome.An important result in Holmstrom andMilgrom (1987)is that the optimal incentive contract is stationary andhas memory in the sense that the history of outcomesdetermines the compensation of the agent. In long-term complete contracts, the principal and the suppliercommit to a compensation schedule at the beginningof the relationship. In the dynamic moral hazard lit-erature, it is generally found that optimal contractsmust have memory of past agent performance to createproper incentives. However, such contracts can be com-plex, especially if they are not stationary. Our modeldiffers from Holmstrom and Milgrom (1987) in sev-eral ways. We model an infinite horizon setting withdiscounting in which the agent must be prepaid eachperiod and then can be penalized for poor quality out-put and in which both the agent and principal arerisk neutral. Most importantly, in our model the agentcan deviate from the contract and break the relation-ship. The termination possibility and the limited liabil-ity it entails lead to optimal contracts being dynamic.Dynamic contracts withmemory are complex to opera-tionalize, and therefore in this paper, we limit ourselvesto dynamic but memoryless contracts.

The third stream of related research considers sta-tionary (Levin 2003; Taylor and Plambeck 2007a, b;Belavina and Girotra 2015) and nonstationary (Yang2013, Plambeck and Taylor 2006) relational contracts.

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Relational contracts are agreements made for repeatedbusiness interactions in which some element of theagreement is not enforceable by the court but rather bythe future value of the relationship.Levin (2003) offers a general agency setting in which

repeated interactions between a principal and an agentend if promises of payments are not kept. He assumesexogenous reservation values for both players. If a con-tract is rejected, or if the discretionary payment is notmade, then both sides receive a fixed payment rep-resenting outside opportunities. He shows that sta-tionary contracts are optimal. We differ from Levin(2003) because in his model the only decisions theprincipal makes are the contract terms: the fixed pay-ment and the contingent payment. The principal can-not commit to the contract terms. In our model, thebuyer also chooses inspection effort and can committo the contract terms. Beyond that, we have made spe-cific modeling choices about the way the principal’srevenues are determined, that is, the inspection out-come and internal versus external costs of failures.In Levin (2003), the supplier’s type is chosen ran-domly in every period. Wemodel a market with homo-geneous suppliers and homogeneous buyers and donot consider an adverse selection problem, that is,the cost parameters (which determine the buyer’s andsupplier’s type) are deterministic. More significantlyin our model, the buyer’s and supplier’s reservationvalues are endogenous. The breaking of the contractleads to a search of uncertain length that ends in theestablishment of a new relationship with the sameterms as the previous one. Thus, contract parameterchoices also influence the alternative options. In Levin(2003), exogeniety allows for stationary optimal con-tracts; in our case, with endogenous reservation valuesand one-sided commitment, we get dynamic contracts.Taylor and Plambeck (2007a, b) use Levin’s approachin contracting on supplier capacity investments so theytoo find stationary contracts to be optimal.

Ourworkdiffers fromTaylor andPlambeck (2007a, b)in several ways. We are maximizing profits for oneparty subject to the contract being self-enforcing for theother party. Our external option is not a repeated singleperiod interaction between the same parties but rathera search for another party and then a new contract.They are modeling a capacity and ordering game withuncertain demandwhilewe aremodeling a quality andinspection game. Theirmodel and analysis is leading toa stationary contracting equilibriumwhilewe analyze adynamic equilibrium.

Tunca and Zenios (2006) also model relational con-tracts and quality, but their approach is quite differentfrom our approach and does not directly inform theissues in which we are interested. Tunca and Zenios(2006) are primarily concerned with the way two dif-ferent market mechanisms interact when there is qual-ity heterogeneity. They do not investigate the actions

a buyer takes to account for uncertain quality compli-ance by a supplier. The manufacturer’s quality choiceis binary, as opposed to continuous in our model,and we consider the distinction between internal andexternal failures. They also only consider one possi-ble penalty for supplier failure, which is not to believefuture quality claims, whereas in our paper we canconsider a spectrum of punishment levels and possibletermination.

Belavina and Girotra (2015) study how the topologyof a supply chain influences the opportunity to achievecompliance with the help of stationary relational con-tracts. In their model, suppliers decide on wholesaleprices and whether to comply with sustainability stan-dards. A single buyer decides on quantity, and defectsare discovered by final consumers. All nodes of thesupply chain are known; if all nodes comply, then com-pliance of a final product is certain. In our work, thedecision not to adulterate is not enough to provide aquality product, as unknown upstream suppliers cansecretly deliver bad inputs or unintentional adulter-ation can occur. In Belavina and Girotra (2015), sup-pliers are discouraged from noncompliance and fromsetting higher wholesale prices by the threat of usinga myopic equilibrium, when all players act in self-interest and suppliers do not comply. No other toolsto enforce compliance are used. We model the dynam-ics of compensation, penalties, and inspection effortsto discourage noncompliance as well as certification.

Studying internal wage dynamics, Yang (2013) con-siders a market where homogeneous firms (buy-ers) and high and low type workers (suppliers) arematched. The fired supplier finds another firm andresumes work. In a symmetric perfect public equilib-rium, all firms use the same strategy and all workershave the same strategy. As a result, the outside optionis endogenous and the optimal contract is dynamic.But these dynamics are driven by the fact that thebuyer is learning the supplier’s type so the informa-tion available to the buyer changes over time. Plambeckand Taylor (2006) model a very general supply chainrelationship with both court enforceable and discre-tionary elements. In their setting, the business environ-ment changes stochastically over time, and this natu-rally leads to a dynamic relational contract. In our casethe model parameters are not changing over time, yetthe optimal contracts are dynamic because the termsof the contract are used to affect the cost of the outsideoption.

Our paper also differs from much of the literatureon quality management in that besides inspections andpenalties, we also model the use of supplier certifi-cation. Hwang et al. (2006) compare inspection andcertification as approaches to managing quality in asupply chain. However, they assume that penaltiesfor quality failures are set exogenously, that it is an

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either/or choice between the two quality control meth-ods, that penalties are enforceable, and that effort levelsare binary. Our model differs from all of these majorassumptions and thus leads to a very different analysisand set of insights.Our work reveals that, in case of poor legal enforce-

ment, the quality dynamics in the market are deter-mined by the following three factors: first, by the sup-plier’s search costs; second, by the buyer’s ability tohold up the supplier for the value of the initial invest-ment; and third, by the compensation dynamics thatare based on the first two factors. Within such a setting,we show that certification can be helpful but is not apanacea.

3. ModelConsider a market with homogeneous buyers andhomogeneous suppliers. All participants are risk neu-tral. Time is discrete and indexed by t. To simplify theanalysis, we set the coefficient of discounting to α < 1for both parties. A buyer sources a product in fixedbatches from a supplier and then sells it on the marketsubject to quality standards such as regulations aboutchemical content. In period t � 0, the partners agree onthe payment plan for all periods t > 0. At time t � 0, toinitiate work with the buyer, the supplier incurs a one-time fixed cost FS, which represents the cost of estab-lishing the production capacity for the specific prod-uct the buyer wants. Likewise, the buyer incurs fixedstart-up cost FB , which reflects the cost of contractingand training. After that, manufacturing starts; a singlebatch is repeatedly produced, inspected, and sold. Asdiscussed in the introduction, we are considering a set-ting in which the buyer is a well-known internationalbrand with an established reputation, but the supplierdoes not have large capital resources and is local toa country within which there is poor legal enforce-ment. The implications for our modeling approach arethat (a) we formulate the contract optimization prob-lem from the perspective of maximizing the expectedprofit of the buyer; (b) we assume that the buyer cancommit to the terms of the contract; (c) the suppliercannot commit to contract terms and cannot be forcedto pay penalties; and (d) the supplier’s profit in eachperiod of production must be nonnegative.In the next section, we explain how we model the

main decisions made by the supplier and buyer eachperiod, that is, the effort they, respectively, put intoquality and inspection of quality. We then analyze twobenchmark cases: the case when the buyer has central-ized control of the supply chain and the case when thebuyer does not have centralized control but contractterms are enforceable. All notation is listed in Table 1.

3.1. Quality and Inspection EffortsIn period t ≥ 1, the supplier chooses effort pt , the prob-ability the batch violates the quality standards of the

Table 1. Definitions of Notation

Decisions and contract termswt Upfront payment made to the supplier

each periodFI t Fine for defect found internally by buyer

in period tFEt Fine for defect found externally by

market in period tqt Buyer defect detection rate in period tpt Supplier defect rate in period tCt Vector of contract terms (wt , FI t , FEt) in

period tParameters

FS , FB Relationship start-up costs for supplierand buyer

C̃S , C̃B Supplier and Buyer per period newpartner search costs

Π Buyer revenue per product batchP̄S , P̄B Supplier and buyer probabilities of

finding a new partner in a searchperiod

α Discount factor per periodδ Expected discounting factor for duration

of supplier’s searchΘ Random number of periods that it takes

the supplier to find a new partnerL Supplier’s expected discounted search

costsCI Cost to buyer for defect found internallyCE Cost to buyer for defect found externally

by marketCB(q) Cost to buyer of effort to achieve

detection rate qCS(p) Cost to supplier of effort to achieve

defect rate pOutcomes

RBt ,RSt Expected continuation value in period tof the buyer and supplier

rBt , rSt Expected profit in period t of the buyerand supplier

(wFB , qFB , pFB , FFB) First-best contract terms

buyer. We refer to pt as the defect rate in period t. Forevery batch, the supplier incurs a variable quality costCS(pt). Lower pt values reflect greater supplier effortand thus higher costs. For example, consider a buyer(a manufacturer) who outsources the production ofshampoo to China and sells it to large retail chains inthe United States. After the CDEA scandals of 2013, thebuyer sources shampoo that is required to be free fromthis carcinogen. CDEA is freely sold in China and isused as a thickening, wetting, and foam stability agentin the production of detergents, shampoos, and otherproducts. The Chinese supplier itself sources the ingre-dients from a variety of suppliers. In this case the defectrate reflects the effort exerted by the supplier to ensurethat the inputs are CDEA-free. For simplicity we set thevariable production costs of a batch that are unrelatedto quality equal to zero. In this case CS(pt) representsthe additional costs of meeting the environmental stan-dards because CDEA-free shampoo is more expensive.

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This could also include the supplier’s cost to verify thatits suppliers are complying with standards.The buyer chooses effort qt , the probability of detect-

ing a violation in a single batch. We will refer to qt asthe detection rate at period t and to q̄t as the omissionrate at period t. In this paper, for any probability p wedefine p̄ �1−p. The detection rate qt reflects the buyer’sinspection or quality control effort with associatedcost CB(qt). Staying with the chemicals example, inour setting, the effort the buyer exerts to detect defectsshould not be interpreted as the number of items ina batch that he inspects. Rather, it could reflect thenumber of different unwanted chemicals for which thebuyer tests the product. The convexity of CB(qt) impliesthat there are some more likely candidates for chemi-cals that adulterate the product for which one wouldtest first. If the buyer detects a defective batch, he incursan internal remediation cost CI before being able to sellthe products. If a batch is defective but the buyer doesnot detect it, then it is released to the market, and thedefects are detected with certainty by the market. Inthis case, the buyer incurs an external cost CE, whichmay be reputational. We assume that CE > CI, so it isbetter to detect the defect inside the firm.We make the following assumptions about the sup-

plier’s and buyer’s cost curves CS(p) and CB(q):

limp→0

CS(p)�∞, CS(1)�0,

C′S(p)< 0 and C′′S(p)> 0 for p ∈ (0; 1),limp→0

C′S(p)�−∞, C′S(1)�0; (1)

CB(0)�0, limq→1

CB(q)�∞,

C′B(q)> 0 and C′′B(q)> 0 for q ∈ (0; 1),C′B(0)�0, lim

q→1C′B(q)�∞. (2)

The assumptions in (1) and (2) imply that (1) zerodefect rate and absolute detection rate require infinitefunds; (2) a supplier making no effort to comply with

Figure 1. (Color online) Supplier and Buyer Quality Cost Curves

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Supplier’s defect rate (%)

Supplier quality cost

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$$

160,000

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0 20 40 60 80 100

Buyer’s defect detection rate (%)

0 20 40 60 80 100

Buyer detection cost

quality standards or a supplier making no effort toinspect the product both incur zero effort costs; and(3) supplier production costs are decreasing in thedefect rate while buyer inspection costs are increasingin the detection rate. An example of cost functions thatsatisfy these conditions appears in Figure 1.We are alsoassuming that the buyer and supplier efforts are inde-pendent. Therefore the supplier’s quality efforts do notaffect the ability of the buyer to detect a defect whenone occurs.

3.2. Illustrative Numerical ExampleTo illustrate the features of the model and some of ourresults, we construct a numerical example. Consider abuyer who outsources the production of a product toChina and sells it to large retail chains in the UnitedStates. We assume that the buyer can sell the productto retailers for $4.0 per unit and that the supplier’s pro-duction costs are at least $3.0 per unit. Thus, if everymonth 180,000 units are produced, then $180 K is thebuyer’s income and establishes an upper bound onwhat can be spent on quality per batch. Let the dis-count rate be 20% per year corresponding to parameterα � 0.9816. For the purposes of these numerical exper-iments, we use the following functional forms for thequality and inspection costs of the supplier and buyerthat satisfy assumptions (1) and (2):

CS(p)� bS(p−aS − aS p̄ − 1), aS > 0, bS > 0;CB(q)� bB(q̄−aB − aB q − 1), aB > 0, bB > 0.

Given that the compliance failures described in theintroduction are not very frequent, we think it is real-istic to have quality and inspection cost functions suchthat at a low cost, most of the time, defects do notreach the market, but perfect prevention is unattain-able. To that end we set the parameters aS ≈ 0.07, bS �

300,000, aB ≈ 0.9 and bB � 3,000 so that the supplier’sand buyer’s cost curves represent the case shown inFigure 1.

Here, to provide a 99% guarantee that a bad batch iscaught, the buyer spends 100%of his potential revenue.

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To ensure a 60% detection rate, the buyer needs tospend 1% of potential revenue. For the supplier, it costs51% of the potential buyer sales revenue ($180 K) tomake the efforts to ensure a 1% defect rate. We donot claim that these cost curves are representative ofa specific real case; they are purely for illustration. Wehave experimented with a wide range of quality anddetection curve parameter values and observed similarresults for buyer and supplier behavior and outcomes.

3.3. Centralized Production and OutsourcingUnder Enforceable Contracts

In this subsection, we consider several benchmarkmodels to develop our intuition about the problem set-ting. First, we characterize the first-best solution for acentralized supply chain (Problem 1). Second, we con-struct benchmark models with enforceable defect ratesor fines for outsourcing the production to an externalsupplier (Problems 2 and 3).Suppose both the supplier and the buyer are cen-

trally controlled divisions of the same firm. In the ini-tial period t � 0, both participants incur fixed produc-tion start-up costs FS and FB . Manufacturing starts inperiod t � 1. In every period t ≥ 1, a single batch isrepeatedly produced, inspected, and sold. The buyermakes transfer payments to the supplier for the costof every batch and sells the product, and the firmreceives revenueΠ. In this setup, the first-best outcomeis achieved in every stage. Therefore, the stationarypolicy (pt , qt)� (p , q) for t ≥ 1, is optimal. The firmmax-imizes expected discounted profits by solving for theoptimal stationary quality level p and inspection level qin Problem 1.Problem 1 (Centralized (First Best)).

maxp ,q

α1−α (Π−CS(p)−CB(q)−p(qCI+ q̄CE))−(FS+FB).

From the assumptions (1) and (2), the unconstrainedProblem 1 has an internal optimal solution that satisfiesfirst-order conditions (3) and (4). We assume that thetotal production and noncompliance costs per batch,CS(p) + CB(q) + pS(q CI+q̄ CE), are strictly pseudocon-vex. This assumption guarantees the unique globalmaximum for the expected profit of the centralizedsupply chain. We denote this solution by (pFB , qFB) andassume that it generates nonnegative profit to avoidtrivial cases. For the same reason, we also assume thatthe buyer incurs negative profits if p � 1. The firm’sproblem can be viewed as finding the most cost effec-tive way to prevent defects from reaching the end con-sumer. An interior solution implies that the firm wantssome quality control conducted both on the produc-tion side and on the inspection side:

−C′

S(p)� q CI+q̄ CE, (3)−C

′B(q)� p(CI−CE). (4)

Now suppose that the buyer and supplier are sepa-rate firms. The two parties must then establish a con-tract. If the supplier’s quality choice pt is enforceable,then we can consider a contract in which the buyerspecifies (wt , qt , pt), where wt is an upfront paymentmade to the supplier each period. Consider the station-ary equilibrium (wt , qt , pt) � (w , q , p), t ≥ 1. The buyersolves Problem 2 assuming w.l.o.g. (without loss ofgenerality) that the supplier’s reservation profit is 0.

Problem 2 (Enforceable Defect Rate pt).

maxw , q , p

α1− α (Π−w −CB(q) − p(q CI+q̄ CE)) − FB (5)

s.t. w − 1− αα

FS −CS(p) ≥ 0 w ≥ 0, q and p ∈ [0; 1].(6)

Equation (6) is the supplier’s per-period profit. Prob-lem 2 is reduced to Problem 1 by setting w � ((1−α)/α) ·FS + CS(p), so, the first-best outcome can be achieved,and the solution (wt , qt , pt) � (w , q , p) forms a station-ary equilibrium. The buyer’s payment to the suppliercompensates him for production costs and amortizesthe start-up costs over the lifetime of the relationship,which is infinite here. Problems 1 and 2 are equivalentto multiperiod formulations of the model in Baimanet al. (2000) in the cases when the first-best outcome isachievable with some small modeling differences. Theability to achieve first-best in Problems 1 and 2 corre-sponds to Propositions 1 and 2A in Baiman et al. (2000).

If the defect rate pt is not enforceable, then the buyercan use fines to create an incentive for the supplier toexert quality effort. Let the buyer’s inspection effort qtbe public and verifiable, and let the contract penalizethe supplier FI t for internal failures and FEt for exter-nal failures. We consider three scenarios under a sta-tionary equilibrium (w , q , p , FI , FE)t ≥ 1. Scenario A:both FI and FE are enforceable, and the supplier paysfine FI in case of an internal failure and FE in case of anexternal failure. Scenario B: only FI is enforceable. Sce-nario C: only FE is enforceable. The buyer’s problem isdescribed by Problem 3.

Problem 3 (Unenforceable Defect Rate pt).

maxw , q ,FI,FE

α1− α

(Π− 1− α

αFB −w −CB(q)

− p(q(CI−FI)+ q̄(CE−FE)))

s.t. p � arg maxp̂∈[0; 1]

α1− α

(w − 1− α

αFS −CS(p̂)

− p̂(q FI+q̄ FE)), (7)

w − 1− αα

FS −CS(p) − p(q FI+q̄ FE) ≥ 0,

w , FI, and FE ≥ 0, q ∈ [0; 1]. (8)

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Scenario A has no additional constraints. Con-straint (7) is relevant to Scenario B only. Constraint (8)belongs to Scenario C only.

FE� 0, (9)I � 0. (10)

The first-best is achievable in all three cases. To seethis, note that if the supplier maximizes his goal func-tion then, from (7), −C′S(p) � qFI + q̄FE. It is necessaryto set the fines so that qCI + q̄ CE � q FI+q̄ FE, whichforces the supplier to internalize the cost to the buyerof a defective batch. In Scenario A, where both penal-ties are enforceable, one of the possible ways to achievethe first-best outcome is to set FI � CI and FE � CE.In Scenario B, where FE is not enforceable, from (4),the first-best is achieved by setting FI�CI+(q̄/q)CE. InScenario C, where FI is not enforceable, to achieve firstbest, it is enough to set FE � (q/q̄)CI+CE. Because thebuyer will set w � ((1− α)/α)FS + CS(p)+ p(q FI+q̄ FE)making (6) binding, the buyer’s FOC is simplified to (4).Let (w , q , p ,FI,FE) be the solution to Problem 3.

As the first-best effort is achievable in every period,then the stationary equilibrium (wt , qt , pt ,FIt ,FEt) �(w , q , p ,FI,FE), t ≥ 1, is optimal. We note that whenboth FI and FE are enforceable, it is possible to makethe supplier choose any target defect rate 0< p̂ ≤ 1 withequal fines by setting

F � FI� FE�−C′

S(p̂). (11)

Equation (9) means that the fine is set equal tothe marginal cost of better quality. The first-best isachieved by setting F � FFB � qFB CI+q̄FB CE. Then theoptimal stationary equilibrium can be simplified to(w , q , p , F). In this case, the inspection level q does notaffect the defect rate p, and it is not necessary to haveq verifiable. These two characteristics of the contract,that a single fine can be used for both types of fail-ures and that the supplier’s effort is independent ofthe buyer’s effort, will carry over to our model of con-tracts with unenforceable fines. The analysis of Prob-lem 3 corresponds to Proposition 3 in Baiman et al.(2000), where our enforceable fine is equivalent to their“contractible event” (p. 780). In the rest of the paper wefocus on cases where none of the fines are enforceable.In Baiman et al. (2000) this case is studied (for a singleperiod), but with the buyer given the ability to returnthe product for some compensation in a single periodand with no consideration of the alternative when thesupplier does not comply (i.e., a fine for an internalfailure is enforceable, but the buyer does not need toshow that there was a failure). In this paper we arenot interested in the case of a buyer “pretending” thatthere was a quality failure.

3.4. Analysis of NonenforceableDynamic Contracts

When fines are unenforceable, they become discre-tionary payments by the supplier to the buyer to com-pensate for defects. Thus a relational contract frame-work is appropriate. Expanding upon the benchmarkmodels, we consider the following model of the inter-action between buyer and supplier, which forms adynamic repeated game. In period 0 both sides incurrespective start-up costs, and the buyer commits to acontract Ct � (wt , FI t , FEt) for all periods t ∈ [1;∞]withwt , FI t , FEt ∈ R+. In each production period t ≥ 1 wehave the following sequence of events:

(1) The supplier receives payment wt .(2) The supplier chooses a quality effort pt and pro-

duces a batch, and the buyer simultaneously choosesinspection effort qt .(3) The quality of the batch is revealed. Either it is

good, (yt � 0), defective and discovered internally bythe buyer (yt � 1), or defective and detected externallyby the consumer(yt � 2).(4) The buyer imposes a fine on the supplier, FI t if

yt � 1 and FEt if yt � 2.(5) If the supplier pays any fines imposed by the

buyer then the sequence repeats. If the supplier refusesto pay a fine, the relationship is terminated, and bothparties begin searching for new partners.

As is common in the literature on repeated games,we assume the buyer employs a trigger strategy. If thefines are not paid, the buyer permanently fires the sup-plier and terminates the contract. Termination is theharshest penalty available to the buyer. If the supplieris already refusing to pay a fine, then imposing an addi-tional fine will not achieve anything.

In case of termination, both the supplier and thebuyer must conduct a costly search for new tradingpartners. The search starts in the next period t + 1. Theprobabilities of finding new partners for the supplierand for the buyer in any period are, respectively, P̄Sand P̄B . While the buyer and the supplier search, theydo not generate any profits and incur search costs C̃Sand C̃B every period. Once a new partner is found attime τ, the game starts again, and the partners incurnew fixed costs in period τ + 1. If a contract is termi-nated, let Θ be the random number of periods that ittakes the supplier to find a new partner (i.e., a geomet-ric random variable with mean 1/P̄S); then we define adiscounting factor for the delay in starting a new rela-tionship as δ � E[αΘ]. We define L � C̃SE[∑θ

i�1 αi−1] as

the supplier’s expected discounted search costs.Our solution approach is to search for a symmet-

ric perfect public equilibrium (i.e., all buyers use thesame strategy, and all suppliers use the same strat-egy) in which neither buyer nor supplier knows aboutthe partner’s previous relationships. We focus on thoseequilibria that maximize the buyer’s expected profit.

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Let h t � (w1, FI1, FE1, q1, y1; . . .wt−1, FI t−1, FEt−1,qt−1 , yt−1) be the public history for a current relation-ship up to time t ∈ [1;∞]. We include the buyer’s effortsqt in the public history because the kind of detectionefforts in which he engages are publicized and can beobserved by suppliers (e.g., inspections of facilities orrequirements to send samples to third-party labs). Theknowledge of whether or not the supplier pays a fineis not included in the history because once he failsto pay the fine, the relationship is terminated and anew history begins. Let H t be the set of possible pub-lic histories up to time t. We define a relational con-tract as a complete plan for a relationship. For eachperiod t and all public histories h t ∈ H t , a relationalcontract describes the following actions as functions ofpublic history: (1) the contract the buyer offers Ct �

(wt , FI t , FEt) and (2) the effort level the buyer and sup-plier choose (pt , qt).

Let RBt and RSt be the respective continuation valuesof the game in period t ≥ 0 on the equilibrium pathwhen both the buyer and the supplier are complyingwith the contract terms. Let rBt and rSt be the corre-sponding expected stage profits. In any one period t ≥ 1the supplier has three ways to potentially deviate fromthe contract. He can refuse to pay any fines, refuse topay external fines, and refuse to pay internal fines. Wedenote the continuation values if the supplier makesa single period deviation of any of these three typesas RX

St (X ∈ {A,E, I} “any,” “external,” “internal”). Wedenote the corresponding defect rate chosen by thesupplier as pX

t ,X ∈ {A,E, I}. The following equationsestablish the relationships between the actions takenby the buyer and the supplier and their payoffs forall t ≥ 0.

For t � 0, RB0 �−FB + αRB1 and RS0 �−FS + αRS1.(12)

For all t ≥ 1

RBt � maxqt∈[0; 1]

{Π−wt −CB(qt) − pt(qt(CI−FIt)

+ q̄t(CE−FEt))+ αRB(t+1)}, (13)RSt � max

pt∈[0; 1]{wt −CS(pt) − pt(qt FIt +q̄t FEt)

+ αRS(t+1)}, (14)RA

St � maxpA

t ∈[0; 1]{wt −CS(pA

t )+ α(pAt (δRS0 − L)

+ p̄At RS(t+1))}, (15a)

RISt � max

pIt∈[0; 1]{wt −CS(pI

t) − pIt q̄t FEt + α(pI

t qt(δRS0 − L)

+ (p̄It + pI

t q̄t)RS(t+1))}, (15b)RE

St � maxpE

t ∈[0; 1]{wt −CS(pE

t ) − pEt qt FI t + α(pE

t q̄t(δRS0 − L)

+ (p̄Et + pE

t qt)RS(t+1))}. (15c)

Equation (12) defines the total value of the relationshipfor each party and captures the start-up costs. There

are no actions taken in period 0. Equation (10) showshow given contract terms Ct , the buyer’s action, qt ,affects the payoff in period t in a relational equilibrium.Equation (11) shows the same for the supplier. Equa-tions ((15a)–(15c)) define the expected continuationprofit for the supplier if he intends to deviate inperiod t. In Equation (12) the supplier does not pay“Any” fine if there is a defect, hence the super-script “A.” The first two terms give the current periodprofit, while the third term shows the expected profitfrom future periods. If there is no defect then there isno need to deviate, and the supplier receives the con-tinuation profit from the current contract, RS(t+1), whichis defined by Equation (11). If there is a defect, then thecurrent contract will be terminated because the defectwill be discovered internally or externally, a fine willbe levied on the supplier by the buyer, and the supplierwill refuse to pay. When the contract is terminated, thesupplier receives the future expected profit of a newcontract, RS0 (defined in (12)), discounted by δ, theexpected discounting factor for the time to find a newpartner. The supplier also incurs the expected searchcost L. Equations ((15b) and (15c)) show what happensif the supplier deviates by not paying the internal orexternal fine, respectively, (superscripts “I” and “E”).In the case when the internal fine is ignored (13), thecontract is terminated when there is a defect that isdetected internally by the buyer (with probability pI

t qt).In the case when the external fine is ignored (14), thecontract is terminated when there is a defect that is notdetected by the buyer (with probability pE

t q̄t).A solution of the following program (DRE) is a

dynamic relational equilibrium optimal for the buyer:

DRE: maxct , qt , t∈[1;∞]

RB0

s.t. RSt ≥ maxX∈{A,E, I}

RXSt for all t ∈ [1; ∞], (16)

RB0 ≥ 0 and RS0 ≥ 0, (17a)RSt − αRS(t+1) ≥ 0 for all t ∈ [1;∞]. (17b)

In the DRE the buyer is committing to a payment to thesupplier, fine (internal and external), and inspectioneffort for each period to maximize his own expectedprofit from the relationship, RB0. Equation (15) is anincentive compatibility constraint for the supplier toprefer to adhere to the contract terms and not to deviatein any period. Equation (16) gives participation con-straints for the supplier and the buyer. Equation (17a)is the requirement that the supplier is not producing ata loss in any production period.

We note that because the DRE is formulated as max-imizing the buyer’s expected profit and because wehave assumed that the buyer can commit to the termsof the contract, we do not need incentive compatibil-ity constraints for the buyer. This means that the buyeris better off because the problem is less constrained

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(i.e., the reputation of the buyer gives credibility to hiscontract commitment and thus gives the buyer a largerprofit than if he were not able to commit). Also, as aresult, the buyer-related search parameters C̃B and P̄Bare irrelevant to the formulation. Similarly, the param-eter FB is not important as long as the buyer participa-tion constraint RB0 ≥ 0 can be satisfied.

Lemma 3.1. The DRE can be simplified as follows:

DRE : maxwt , Ft , qt

RB0

s.t. RB0 ≥ 0, RS0 ≥ 0, rSt ≥ 0; (18)−C′S(pt)� Ft ; (19)α(RS(t+1) − (δRS0 − L)) ≥ Ft t ≥ 1; (20)wt ≥ 0, qt ∈ [0; 1], Ft ≥ 0.

Proof. See the online appendix.In this reformulation we have that, w.l.o.g., the inter-

nal and external fines can be set equal to each other sothat there is only one fine to determine for each period.As a result qt drops out of Equation (11). Equation (18)indicates that the supplier’s defect rate is completelydetermined by the fine. Equation (19) is a new incen-tive compatibility constraint for the supplier (replacingEquation (16)), which can be interpreted as follows: thesupplier does not deviate if the expected discountedloss from contract termination is greater than the fine.The fact that RS0 is in the incentive compatibility con-straint indicates that the value of the supplier’s out-side option is endogenous to the contracting problem.Proposition 3.1 gives conditions for the DRE to achievethe first-best outcome.

Proposition 3.1. (a) The necessary and sufficient conditionfor a stationary solution to DRE to achieve the first-best isFS + αL ≥ FFB . (b) The necessary and sufficient conditionfor a dynamic solution to DRE to achieve the first-best isα−1FS + αL ≥ FFB .

Proposition 3.1 shows that if the supplier’s ini-tial investment into a relationship and expected dis-counted search costs for a new partner are high (i.e.,if the switching/termination costs for a supplier arehigh), then the feasible parameter space for the first-best solution is larger. It also shows that a dynamicequilibrium achieves the first-best outcome for a widerrange of parameters. The difference is in the addi-tional discounting factor on the supplier start-up cost.Since the supplier is not paid the same in each periodin the DRE, it is possible to delay compensating himfor the start-up costs; that is reflected in the α−1 factorin condition (b) of the proposition. If the supplier mustbe immediately compensated for his start-up costs, itis equivalent to setting FS � 0. From Proposition 3.1we can see that this would reduce one advantage thata dynamic solution to the DRE has over a stationarysolution.

Proposition 3.2. Assuming DRE is feasible, (a) if FS � 0,and the first-best solution is achieved, then this equilibriumis unique. (b) Otherwise, if Ft � FFB for some t ≥ 1, thenDRE has infinitely many optima.

Proposition 3.2 shows that when FS � 0, if the first-best is achievable, there is no difference between a sta-tionary and a dynamic solution to the DRE.Wewill seein the following that when the first best is unachiev-able, then even with FS �0, a nonstationary contract isoptimal. The nonstationary contract gives the buyer amechanism to inflate the termination costs of the sup-plier, thus gaining additional leverage and improvingsupplier compliance with quality standards. Propo-sition 3.3 shows that when the first best cannot beachieved, there is an optimal equilibrium characterizedby a particular period T at which point the fine, Ft ,is set to the same fine as in the first-best case andis constant after that point. In periods before T thefine will be increasing. The fine determines the defectrate selected by the supplier and the inspection levelselected by the buyer, so the dynamics of penalty Ftdrive the dynamics of these decisions as well. (Note:there can be cases in which T � 1 and T �∞.) Thesedynamics lead to a situation in which, in the initialperiods of a contract, the supplier makes less moneythan in later periods.

Proposition 3.3. If a solution to the DRE exists then wehave the following:

(1) If the first-best is achieved, then one of the possibleoptimal equilibria has Ft , pt , and qt at their first-best levelsfor all t; the per-period payment wt is set so that in thefirst period the supplier has zero profit (rS1 � 0); and insubsequent periods, the supplier’s profit is at a level that onlyrecoups the start-up cost (rSt � ((1− α)/α2)FS, t ≥ 2).

(2) If the first-best cannot be achieved, then there existsan optimal equilibrium defined by a critical time period Tthat determines when the fine is set at the first-best level forthe first time and stays at that level for all t ≥ T.

(a) If T � 1, then the fine is set at the first-best levelin each period, the inspection and quality efforts are at thefirst-best levels. The supplier has a positive surplus.

(b) If 1 < T < ∞ then the fine increases each perioduntil T, at which point it stays constant at the first-best level.As a result, the inspection effort and the defect rate are bothdecreasing until T and then stay at the first-best levels. Thesupplier has no profit until time T and a positive profit fromtime T onward.

(c) If T � ∞, then in all periods the fine is set at aconstant less than the first-best value and the supplier makesno profit. This can only occur if FS � 0.

The structure of the equilibrium in Proposition 3.3when first-best is not achieved is such that all the con-tract parameters can be derived from the fine in thefirst production period, F1. Corollary 3.1 provides thespecific relationships.

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Corollary 3.1. Suppose there exists a relational equilib-rium. If the first-best outcome cannot be achieved, then theoptimal equilibrium described in Proposition 3.3 has the fol-lowing properties.(a) The supplier’s total expected discounted profit is RS0 �

α(F1 − α−1FS − αL)/(1− δα2).(b) The fine in period t � 1, F1 will fall in the range:[α−1FS + αL; FFB].

(c) The fine in all other periods 1 < t < T will be deter-mined recursively by the following equation: Ft � Ft−1/α +

((1− α)(δαF1 − δFS − L))/(1− δα2).(d) For 1≤ t ≤ T, Ft+1 > Ft , pt > pt+1, qt > qt+1.(e) The supplier’s profit in each period t ≥ 1 is

rSt �

0 1 ≤ t < T,Ft−1

α− FFB

+(1− α)(δαF1 − δFS − L)

1− δα2 t � T,

1− αα

FFB+(1− α)(δαF1 − δFS − L)

1− δα2 t > T.

(f) The supplier’s profit after period T is always greaterthan his profit in period T.

(g) The per-period payment from buyer to supplier, wt , isincreasing for 1 ≤ t ≤ T and is constant for t ≥ T + 1.(h) The buyer’s profit in each period, rBt , is increasing

until period T − 1. After period T the buyer’s profit remainsconstant at a level below that in period T. rBT itself may belarger or smaller than rB(T−1).

The challenge for the buyer is that if the quality tar-get is initially high then the cost of production will behigh for the supplier. Therefore the upfront paymentthe buyer must make to the supplier will be large andat risk of loss if the supplier deviates from the contract.Deviation may be attractive to the supplier if the termi-nation costs are not too high. This is why it is optimalfor the buyer to gradually increase the fine and his pay-ment to the supplier over time. The buyer also createsan incentive for the supplier to stay in the contract bydeferring payment of the start-up cost FS until afterperiod T and giving the supplier a profit in these laterperiods. Once the partners get past period T, the qual-ity level is at the first-best level and the fines for defectsare high. High fines create an incentive for the supplierto deviate by refusing to pay. However, the deferral ofpositive profits and compensation for FS until period Tis the incentive for the supplier to pay higher fineswhen they are assessed. In every further period, as thefuture rewards are closer and discounted less, the sup-plier becomes less willing to deviate and the buyer isable to charge higher fines.The special cases of T � 1 and T �∞ are caused by

particular parameter combinations. If the terminationcosts are large enough, then it is possible that from thefirst period the buyer can set the fines at the first-bestlevel. If FS � 0 and the search costs are relatively low,

Table 2. Parameter Values for NumericalExample—Base Case

Parameter Base case value

FS , FB $180,000, $0C̃S $3,000Π $180,000P̄S 0.6667α 0.9816Θ Three monthsL $8,680CI $180,000CE $360,000

the supplier has more power; and if αL is close enoughto FFB , then we get the third equilibrium in which thefine is constant but below FFB and the supplier makesno profit. This could be optimal if the additional profitthe buyer would have to provide the supplier to boostquality does not gain himmuch in terms of fewer defectcosts. Corollary 3.1 also shows that finding the profitfor the optimal DRE just involves a one-dimensionalsearch for F1 on the feasible interval [α−1FS + αL; FFB]and calculating RB0.

Continuing the base case numerical example fromSection 3.2, we set CI � $180K to replace the batch andset CE� 2 CI�$360 K. We assume that it takes the sup-plier three months on average to find a new buyer,meaning that the supplier’s probability of finding anew partner in any given month 1− P̄S is 33%, and weset the supplier’s cost per search period C̃S to $3,000.We set FS �Π�$180 K, that is, equivalent to one monthof sales profit. As the buyer’s decisions are enforceable,and we are restricting ourselves to relational contracts,the buyer’s corresponding parameters—C̃B , P̄B , andFB—are not relevant. The parameters for this exampleare summarized in Table 2.

To find the optimal dynamic equilibrium for the basecase, we use the procedure described in Corollary 3.1.To determine wt , Ft , qt , and pt for t ≥ 1, we vary thefine for the first production period F1 in the inter-val [α−1FS + αL; FFB]; that is, we tabulate the interval[$191,900; $243,700]. The optimal relational dynamicequilibrium for the base case has the following char-acteristics: F1 � $191,900, T � 15, RS0 � $11, and RB0 ≈$6,206,000; that is, the DRE does not quite achieve firstbest. The dynamics of the relationship in the base caseare displayed in Figure 2 and can be seen to have theproperties described in Proposition 3.3 (part 2) andCorollary 3.1.

4. Sensitivity AnalysisHere we use sensitivity analysis to identify the fac-tors that influence the efficiency of the DRE relative tofirst best. We vary the external failure cost from CI to50 × CI, the supplier’s initial investment FS from 0%

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Figure 2. (Color online) Optimal Dynamic Equilibrium in the Base Case

0.640

0.645

0.650

0.655

0.660

0.665

0.670

0.675

0.680

0

0.02

0.04

0.06

0.08

0.10

0.12

1 3 5 7 9 11 13 15

Det

ectio

n ra

te q

Def

ect r

ate

p

Period

Defect and detection rates

Defect rate pDetection rate q

50,000

52,000

54,000

56,000

58,000$

60,000

62,000

64,000

1 3 5 7 9 11 13 15

Period

Buyer payment w

-

50,000

100,000

150,000

200,000

250,000

300,000

1 3 5 7 9 11 13 15

Period

Fine level in each period

115,000115,500116,000116,500117,000117,500118,000118,500119,000119,500120,000120,500

-500

1,0001,5002,0002,5003,0003,5004,0004,5005,000

1 3 5 7 9 11 13 15

Buy

er p

rofit

($)

Sup

plie

r pr

ofit

($)

Period

Supplier and buyer per period profits

Supplier profit

Buyer profit$

Note. See Table 2 for parameters.

to 100% of a month’s revenue, and the expected searchlength between one and six months. In Table 3, weshow the efficiency of the DRE for the buyer and forthe entire supply chain. We see that higher externalfailure costs CE and shorter new partner search timesfor the supplier both undermine contract efficiency.Higher CE values put pressure on the buyer to pre-vent defects from getting to the market, but becauseof agency issues during the earlier stages of the con-tract, the buyer must exert more effort on this thanhe would in the first-best case. The expected time ittakes for the supplier to find a new partner reflects the

Table 3. Efficiency of DRE Contract Relative to First-Best for Buyer (RDREB0 /RFB

B0) and Entire Supply Chain((RDRE

S0 +RDREB0 )/(RFB

S0 +RFBB0))

Buyer efficiency (%) Supply chain efficiency (%)

FS FS

CE Expected search 50% monthly 100% monthly 50% monthly 100% monthlylength (months) 0 revenue revenue 0 revenue revenue

CI ≤1 92 99 100 97 99 1003 94 100 100 98 100 1006 95 100 100 98 100 100

2 CI ≤1 90 98 100 95 98 1003 92 98 100 97 98 1006 93 99 100 97 99 100

25 CI ≤1 74 86 94 88 91 943 77 87 94 91 91 946 81 88 95 92 93 95

50 CI ≤1 61 75 85 81 84 893 65 76 85 84 85 886 70 79 86 88 88 90

Note. Base case in bold.

relative power of the two parties in the relationship.If the expected time is long, then the buyer has moreleverage over the supplier and can structure the con-tract in a more efficient manner.

Looking across the columns of Table 3, the negativeeffects of a large external failure cost or short new part-ner search time are counteracted by relatively smallsupplier initial investment costs FS.We can also see thata large part of the efficiency loss to the buyer is a shiftin profit to the supplier, not a loss to the supply chainas a whole. For example, looking at Table 3, if CE � CI,the expected new partner search time is three months,

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Table 4. q1 ,w1, and p1 for Different Values of External Failure Cost, Supplier Expected Search Time, and SupplierStart-up Cost

q1 (DRE) (%) w1 (DRE) ($) p1 (DRE) (%)

FS (% of monthly rev) FS (% of monthly rev) FS (% of monthly rev)CE Expected search

length (months) 0 50% 100% 0 50% 100% 0 50% 100%

CI ≤1 0 0 0 14,638 37,552 50,566 52 20 123 0 0 0 20,141 38,643 50,566 41 19 126 0 0 0 25,021 40,067 50,566 34 18 12

2 CI ≤1 85 76 68 15,437 37,552 51,308 51 20 123 82 75 68 21,818 38,643 51,946 38 19 116 80 74 67 27,236 40,067 52,796 31 18 11

25 CI ≤1 97 95 94 21,735 39,770 51,308 39 18 123 96 95 94 29,903 41,740 51,946 27 17 116 96 94 93 34,887 44,725 52,796 22 15 11

50 CI ≤2 98 96 96 24,501 41,047 52,270 34 17 119 97 96 96 32,041 43,493 52,878 25 16 1112 97 96 95 40,030 47,277 54,554 18 14 10

Note. Base case in bold.

and the start-up cost FS is 0, then the efficiency of thecontract for the buyer is 94%. If the external cost ismuch higher (e.g., CE� 25 CI), then the efficiency of thecontract drops to 77%, a drop of approximately 17%.However, in this scenario the drop in the total sup-ply chain profit is from 98% to 91%, or about 7%. Thismeans that almost one-half of the change in the effi-ciency of the contract for the buyer is a shift of profitsto the supplier.In Table 4 we report the first period values of q, w,

and p for the DRE in monthly operations. From ourresults in Section 3 we know that qt is decreasing in t,wt is increasing in t, and pt is decreasing in t, so look-ing at the first period values gives us an indication ofhow the contract terms reflect the business conditions.We can see that when CE � CI, the buyer can afford toput all of the burden on the supplier to prevent defectsfrom reaching the consumer, but ifCE is large the buyermust exert a large inspection effort. As the supplier’snew partner search time increases, the buyer can forcehim to increase quality (reduce the defect rate) and thebuyer can spend less on inspections. This requires thebuyer to increase the payment to the supplier, and w1increases as well. When FS increases, the buyer’s lever-age over the supplier also increases, and we see thatthe defect rate decreases; but the payment to the sup-plier increases both because of the increased supplierquality cost and the increase in FS.Even though we saw that increasing FS increases

contract efficiency, it does not mean that the buyeralways prefers high FS. Table 5 shows buyer profitwhen CE � CI. As FS grows, the buyer can chargehigher fines because of the hold-up problem, but thebuyer needs to compensate the supplier’s initial invest-ment. As a result, the buyer profit is maximal when FSis equal to the revenue from 15 days of operations.

Table 5. Buyer Profit with CE�CI

Buyer profit ($)

Fs

Expected search 50% monthly 100% monthlylength (months) 0 revenue revenue

<� 1 6,363,075 6,764,360 6,716,0753 6,466,078 6,772,836 6,716,0756 6,556,767 6,782,228 6,716,075

The lower values of FS do not discipline the supplierenough; the higher values are too costly for the buyer.At the same time, as Table 3 shows, the relative effi-ciency of the DRE grows in FS. When FS is sufficientlyhigh that the conditions in Proposition 3.1 hold, theDRE achieves the first-best outcome.

In summary, our memoryless contract performs bet-ter the higher the discounting coefficient is and thelower the expected failure cost is compared to revenue.The efficiency increases in the supplier’s expected timeof search for another buyer and in the supplier’sinitial investment. One of the drivers of the magni-tude of the discounting coefficient is the frequencyof transactions between the trading partners. Higherfrequency improves efficiency. The DRE contract per-formed very well relative to first best for a wide rangeof parameter values, and it is not clear whether con-tracts with memory can significantly outperform.

5. Dynamic Relational Contracts withCertification

As we discussed in the introduction, one tool for man-aging compliance is for suppliers to get certification oftheir production process compliance to industry norms

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through a third party that may or may not be act-ing as an agent for the buyer. This third party woulddo upfront work with the supplier before productionstarts to establish the certification and possibly doperiodic monitoring as part of maintaining the certifi-cation. Certification helps establish some transparencyabout the supplier’s quality assurance efforts. Theupfront work to establish the certification is intendedto make monitoring adherence to the norms easy forthe third party. In our framework, we can representsuch certification as setting an upper bound p̃ on thesupplier’s defect rate pt in any period t. Certificationhas a cost, and our approach is to model it as a one-time start-up cost that we assume w.l.o.g. is completelyborne by the buyer as part of his start-up costs FB . Inthe following, we focus on studying how certificationstructurally changes the outcomes of the relationshipbetween buyer and supplier, and thus we set the cer-tification costs to zero. Once we know the potentialbenefits of certification we can always compare that toits cost.Herewe consider amodification of the dynamic rela-

tional contract from Section 3 incorporating certifica-tion, denoted CDRE, in which the supplier’s choice ofdefect rate in any period is constrained from aboveby p̃.

Lemma 5.1. CDRE can be formulated as follows:

maxwT , Ft , qt

RB0

s.t. RB0≥0, RS0≥0, rSt ≥0, (21)pt �argmax

p(0; p̃]{wt−CS(p)−pFt}, (22)

α(RS(t+1)−(δRS0−L))≥ Ipt<p̃Ft + Ipt�p̃CS(p̃),t≥1. (23)

The main difference between CDRE and DRE canbe seen in Equation (22) and in the formulation of thenondeviation constraints (23). In any period t ≥ 1, thesupplier may choose a defect rate from the followingsubinterval only pt ∈ (0; p̃]. So one effect of certificationis to put a limit on how far the supplier can deviatefrom the effort expected by the buyer. In (23), Ipt<p̃ isan indicator variable that is equal to 1 when the sup-plier chooses a lower defect rate (better quality) thanrequired by certification and 0 otherwise. We defineIpt�p̃ as an indicator for when the defect rate chosen isequal to the requirement of certification. Comparing itwith Equation (19), we see that the fine is only a fac-tor in the supplier’s incentive compatibility constraintwhen a quality level better than the certification level isselected by the buyer. When the defect rate target is thecertification rate, which is by definition verifiable, thereare no fines when defects occur. Equation (23) revealsone of the potential benefits of certification: it can limitthe supplier’s benefits from deviating, which relaxes

the constraint (20) of DRE, making the buyer better off.Without certification, the right-hand side (r.h.s.) of (21)would be Ft . If certification is used, then sometimes ther.h.s. of (21) is CS(p̃). Define F̃ � −C′S(p̃), if CS(p̃) < F̃;then certificationmakes it possible for the buyer to givea smaller incentive to the supplier not to deviate. How-ever, Proposition 5.1 shows that certification does notalways give a benefit to the buyer.

Proposition 5.1. Necessary conditions for implementinga certification mechanism are α−1FS + αL < FFB andCS(p̃) < F̃. Otherwise DRE dominates CDRE.

Proposition 5.1 is established by two observations.First, the buyer does not need certified suppliers ifthe first best can be achieved in the dynamic rela-tional equilibrium without certification. Therefore,from Proposition 3.1, certification is used only ifα−1FS + αL < FFB . Second, if CS(p̃) > F̃, there will be noimprovement in constraint (23). Therefore, the certifi-cation mechanism is used only if CS(p̃) < F̃.A third way in which certification can fail to add

value over DRE is when p̃ ≤ pFB . This situation impliesthat certification sets a quality standard that is optimalor higher than optimal for the supply chain. This canhappen when a generic standard for multiple indus-tries is all that is available for certification purposesand it meets or exceeds the specific needs of a partic-ular industry. It is possible that p̃ is so expensive toachieve, that is, CS(p̃) is so high, that the buyer wouldprefer that the supplier remain uncertified. High pro-duction costs cut into the buyer’s profits. On the otherhand, it is also possible for there to be p̃ < pFBfor whichit is more profitable for the buyer to take the betterquality that certification is providing, even if it exceedsthe first-best quality level. Proposition 5.2 characterizesthe optimal contracts when the equilibrium is one inwhich pt � p̃.

Proposition 5.2. Let pt � p̃ for all t ≥ 1 then. (1) If thecost, to the supplier, of termination is high enough, α−1FS +

αL ≥ CS(p̃) and the supplier’s total expected profit is zero.(2) Otherwise (when α−1FS + αL < CS(p̃)), the supplier’stotal expected profit is RS0 � α((CS(p̃) − α−1FS − αL)/(1− δα2)) > 0. In both cases the payment to the supplier inperiod 1 is CS(p̃) and is constant in all periods t > 1.

Case (1) in Proposition 5.2 is when the cost of con-tract termination is high relative to the cost of produc-ing at the required quality level. As a result, the buyerhas a lot of leverage over the supplier and can set theterms so that the supplier makes no profit, that is, thereare no agency issues. In case (2) the cost of contracttermination is not as high for the supplier, so there isthe risk that he will take the payment wt and breakthe contract. The buyer must pay the supplier more tocreate an incentive for him to stay with the contract.This enables the supplier to collect rents and achieve

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a positive expected profit. Even though the suppliercollects rents in this case, they may still be lower thanwhat the supplier would get in the DRE, and thus thebuyer could in theory be better off with the certifica-tion.When Proposition 5.2 holds, the fine does not playa role because the certification is a binding constraint.To illustrate, consider a case in which the optimal

DRE contract leads to pt � pFB and Ft � FFB for all t,but the first-best outcome is not achieved. Then wehave that RS0 � α((FFB − α−1FS − αL)/(1− δα2)) for theDRE and RS0 � α((CS(p̃)−α−1FS−αL)/(1− δα2)) for theCDRE (from part 2 of Proposition 5.2). If CS(p̃) < FFB ,then CDRE might yet have an advantage over DREeven though it yields a higher quality than wanted bythe buyer. The comparison of these two cases illus-trates that the question of whether or not the buyercan be better off with certification depends upon theinterplay between the cost of producing at the qualitylevel of the certification and upon the differences inagency costs that are driven by the cost of contract ter-mination. The situation described in Proposition 5.2 isjust the simplest of three possible equilibrium types inthe CDRE. Though more complicated to characterize,the same factors are at work in determining if CDREdominates DRE. Proposition 5.3 describes three scenar-ios for the CDRE with p̃ > pFB . To the contrary, in thethird scenario, the supplier’s compensation is designedto prevent deviation when fines are implemented; thecertification is tailored accordingly.

Proposition 5.3. Suppose there exists a dynamic relationalequilibrium with certification for some p̃ > pFB . Then theoptimal equilibrium belongs to one of the following threecases.(1) CDRE1: The certification defect rate is used in every

period, that is, pt � p̃ for all t ≥ 1, and thus there are no finesas in Proposition 5.2.(2) CDRE2: The relationship has three distinct stages. In

the initial stage the certification defect rate is used and nofines are imposed. During the second stage, fines are usedto drive the defect rate down to levels below that of the cer-tification, and in the third stage the first-best defect rate isachieved. The three stages are defined by two time periods,τ ≥ 1 and T ≥ τ + 1, such that pt � p̃ for 1 ≤ t ≤ τ, pFB <pt < p̃ for τ < t < T, and pt � pFB for t ≥ T.

(a) If the cost to the supplier of meeting the certificationquality level is low enough, that is, CS(p̃) ≤ α−1FS + αL,then the buyer does not have to provide excess compensationto the supplier to maintain the relationship and RS0 � 0.

(b) If the cost to the supplier of meeting the certificationquality level is high enough, that is,CS(p̃)> α−1FS+αL, thenthe buyer must provide excess compensation to the supplierto maintain the relationship, and the supplier has a positivesurplus RS0 � α((CS(p̃) − α−1FS − αL)/(1− δα2)) > 0.

(3) CDRE3: There exists τ ≥ 1 and T ≥ τ+ 1 such that

pt �

p̃ 1 ≤ t ≤ τ,p ∈ (pFB ; p̃) τ < t < T,pFB t ≥ T,

and RS0 � ατ+2((α−1Fτ+1 − α−(τ+2)FS − L)/(1− δατ+2)).

Details on how to construct this equilibrium and existenceconditions appear in the online appendix.

It follows that when CDRE2 exists, it dominatesCDRE1 because for the same total profit provided tothe supplier, it is achieving lower defect rates. Whencertification of quality is possible at some defect rate p̃,one might think that the buyer will be automaticallybetter off (ignoring the cost of the certification process)because the supplier is forced to deliver at least thecertification quality level without the buyer having toprovide any incentives. The flaw in this thinking is thatthe certified defect rate p̃ is not free for the buyer. Thebuyer must compensate the supplier for productioncosts. If these costs are high relative to contract termi-nation costs, there is a threat that the supplier will takethe upfront payment and abandon the buyer. So whilein the DRE the buyer can gradually decrease pt , withcertification he may have to start at an initially higherlevel of quality and thus provide stronger incentivesto the supplier not to renege early on. These strongerincentives in the form of higher payments later in thecontract may make the buyer worse off with certifica-tion even if the certification itself is free.

The supply chain expected stage profit for a givendefect rate p isΠ−CS(p)−CB(q)− p(q CI+q̄ CE), wherefrom the buyer’s FOC we have C′B(q) � p(CE−CI).We denote the value of the certification for a given p̃ asV(p̃)�max{Vi(p̃)}, where and Vi(p̃)�RCDREi

B0 (p̃)−RDREB0 ,

i ∈ {1, 2, 3} and CDREi feasible.In Figure 3, we plot the value of certification as

a function of the certification defect rate, p̃, for thethree equilibria, CDRE1, CDRE2, and CDRE3, for anillustrative example. We use the same parameter val-ues as the base case except set the cost of externaldetection of a defect, CE, to be 50 CI, so that there isroom for improvement over the DRE solution. We seethat for each equilibrium, there is a range of defect ratesfor which there is some potential benefit to the buyerif the supplier can be certified. For CDRE2 and CDRE3the feasible range begins close to the peak of CDRE1and CDRE2 dominates CDRE3. Looking at CDRE1, tothe left of the peak, the value of certification is decreas-ing because it is requiring a quality level that is toocostly for the buyer. To the right of the peak, the qual-ity level being certified is not high enough to give alarge benefit to the buyer. Generally, the ranges overwhich each equilibrium adds value over the DRE donot necessarily overlap, which means that there is notnecessarily a contiguous range of defect rates for whichcertification adds value.

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Figure 3. (Color online) Value of Certification as a Function of the Maximum Defect Rate Established by Certification, forIllustrative Example

–1.00E+06

–8.00E+05

–6.00E+05

–4.00E+05

–2.00E+05

0.00E+00

2.00E+05

4.00E+05

6.00E+05

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11

Val

ue o

f cer

tific

atio

n

Certification defect rate

CDRE1 value

CDRE2 value

CDRE3 value

6. ConclusionConsumers and regulators in developed countriesexpect products and the processes used to producethese products to meet high standards for safety, chem-ical content, pollution, and labor conditions. At thesame time buyers (brands) are seeking the lowest costsuppliers in developing countries in which regulationand legal enforcement is weak. Supply chains are com-plex, and buyers rely on first tier suppliers tomake suretheir own suppliers are complying with standards, allthe while working with razor thin margins. The lowprofit margins require the buyers to provide upfrontworking capital to suppliers, thus exposing themselvesto some financial risk.In this paper, we model how financial penalties can

be used to create incentives for suppliers to exert effortto achieve compliance, even when these penalties arenot legally enforceable. To do this, we use the frame-work of relational contracts where the supplier’s self-enforcement of penalties is motivated by the threatof contract termination. The potential cost to the sup-plier of lost revenues while searching for a new part-ner and the cost of setting up a new relationship deterthe supplier from violating the contract terms. How-ever, unless the termination costs are very high, thethreat of termination is limited in its ability to motivatethe supplier to achieve high levels of compliance. Weshow that a dynamic contract can artificially increasethe termination cost and strengthen the buyer’s handvis-à-vis the supplier. The dynamic contract appears asif it has a probationary period during which the sup-plier “proves” itself to the buyer, but this is not what

is going on at all. There are multiple ways the suppliercan cheat. The dynamic contract structure is workingto reduce the supplier’s incentive to cheat in differentways in different stages of the relationship.

We have assumed that the buyer is a well-knownbrand with commitment credibility. If this were notthe case, the formulation of the DRE would requireadditional constraints to prevent the buyer from devi-ating from the contract. We found such a formula-tion intractable but conjecture the following outcomes.Additional constraints on the buyer will of coursemake him worse off. We expect that the resulting con-tract would have to have RBt nondecreasing to providethe buyer an incentive to continue in the relationship.At the same time, the supplier faces less certainty, sowe expect him to require higher compensation for anyparticular level of quality. The net effect will be a reduc-tion in the optimal quality level.

We also model how third-party certification fitsinto this framework by setting a floor on compli-ance effort. We show that this can be beneficial tothe buyer because it limits the ability of the sup-plier to deviate from the desired quality levels. At thesame time, certification can hurt the buyer’s ability todesign optimal dynamic contracts because the certifi-cation is inflexible. In a sense, it moves the buyer toa more mature state of the relationship prematurelyand undermines the buyer’s ability to increase the sup-plier’s termination costs.

Greater supplier effort to comply with sustainabilitygoals is not simply a question of increasing payments.The buyer will have to pay for whatever compliance

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effort he wants the supplier to exert so that the supplieris not losing money. The challenge for the buyer is tomake sure that as much of the payment he makes tothe supplier is used on the compliance effort as possi-ble, as opposed to being taken as a rent by the supplier.This is where the contract structure is important. Whatwe have shown is that holding the supplier’s profitlow (zero) at the start of the relationship and postpon-ing the supplier’s opportunity for profit to later peri-ods, while steadily ramping up quality expectations,increases the buyer’s leverage and improves quality.

AcknowledgmentsThe authors acknowledge the thoughtful and constructivecomments of the associate editor and the rest of the reviewteam.

Endnote1http://eur-lex.europa.eu/legal-content/EN/TXT/?uri�CELEX:32002L0095 (last accessed May 24, 2018).

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