contracts sourcing channels - Stanford Universitydaniancu/Papers/Journal/...de Zegher, Iancu, and Lee: Designing Contracts and Sourcing Channels 2 Manufacturing & Service Operations

MANUFACTURING & SERVICE OPERATIONS MANAGEMENTArticles in Advance, pp. 1–19

http://pubsonline.informs.org/journal/msom/ ISSN 1523-4614 (print), ISSN 1526-5498 (online)

Designing Contracts and Sourcing Channels toCreate Shared ValueJoann F. de Zegher,a Dan A. Iancu,b Hau L. Leeb

a Emmett Interdisciplinary Program in Environment and Resources, Stanford University, Stanford, California 94305; b Graduate School ofBusiness, Stanford University, Stanford, California 94305Contact: [email protected] (JFdZ); [email protected] (DAI); [email protected] (HLL)

Received: March 29, 2016

Revised: October 2, 2016

Accepted: December 22, 2016

Published Online in Articles in Advance:October 16, 2017

https://doi.org/10.1287/msom.2017.0627

Copyright: © 2017 INFORMS

Abstract. In complex supply chains, the benefits and costs of technological innovationsdo not always accrue equitably to all parties; thus, their adoption may critically depend onsourcing relationships and incentives. In a setting with uncertain and endogenous processyield, we study the potential of two features—contract design and sourcing channel—tocreate mutual benefit in decentralized value chains, where suppliers bear the costs ofnew technologies while benefits accrue primarily to buyers. Our focus is on agriculturalvalue chains, where parties may transact through a channel that blends farmers’ produce(“commodity-based channel”) or that allows a one-on-one interaction between farmer andprocessor (“direct-sourcing channel”). Our study provides insights to companies seek-ing to incorporate responsible sourcing strategies while also creating economic value—aconcept called “creating shared value.” We identify that the technology’s “cost elasticity”drives whether switching sourcing channel, changing contract structure, or adopting anintegrated change is necessary to create shared value. This highlights that value chaininnovations need to be properly designed—and sometimes combined—to achieve sus-tainable implementation. We also find that certain simple contracts with a linear or bonusstructure are optimal, while other intuitive contracts could be detrimental. Using a data setof farms in Patagonia, Argentina, we estimate that the proposed mechanism could increaseaverage supply chain profit by 6.9% while realizing positive environmental benefits.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2017.0627.

Keywords: supply chain management • value chain innovations in developing economies • sustainable sourcing • incentives and contracting •creating shared value

1. IntroductionMillions of farmers in developing economies supplythe commodity markets that provide the majority ofagricultural raw materials in today’s global supplychains. Low incomes and low bargaining power oftenmean that these farmers make few investments in newmanagement practices and can do little to improvetheir profits. Yet, in many cases, both the supply chainand the farmer could benefit from improved manage-ment practices at the farm level. One example is pre-mature harvesting of produce, which can lead to lossin nutritional and economic value (FAO 2011, APEC2014). Another example is water-efficiency manage-ment by the farmer (e.g., through drip irrigation),which affects water risk in supply chains that are facingdepletion of groundwater resources and rising proba-bilities of droughts (Wilcox 2015, IPCC 2012). A thirdexample is better matching farm practices with rawmaterial end-use. Wheat, for instance, is often grownand traded based on an average quality and variety;yet, synchronizing the breeding and farming of wheatvarieties with their different end-uses would benefit all

parties in the supply chain (Anupindi and Sivakumar2007, Barber 2014). Fourth, farm management prac-tices may have a significant impact on process yieldsdownstream, as is the case with palm fruit picking oncrude palm oil extraction (Jelsma et al. 2009), parch-ment coffee drying on coffee milling (McAuley 2013,NCA 2016), and sheep forage use on wool scouring andcombing (discussed in this paper).

To encourage farmers to adopt improved manage-ment practices, some companies have recently startedswitching from sourcing on commodity markets—which are based on blending farmers’ produce andwhich lose the identity of individual farmers—tosourcing directly from farmers and developing indi-vidual relationships with them (Wal-Mart 2010, BSR2011, Nestlé 2014, Wang et al. 2014). This change insourcing practice is often accompanied by a change inprocurement pricing, from rates based on regionallyset or globally set values to rates that are informedby a farmer’s individual costs (Wal-Mart 2010, BSR2011, Nestlé 2014). Companies claim that such changesbring them closer to their suppliers, enhance their

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de Zegher, Iancu, and Lee: Designing Contracts and Sourcing Channels2 Manufacturing & Service Operations Management, Articles in Advance, pp. 1–19, © 2017 INFORMS

understanding of their suppliers’ operating circum-stances, and help them realize efficiencies, ultimatelygenerating cost advantages and mutual benefit in theform of “shared value” (Porter and Kramer 2011).

However, creating such shared benefit is not straight-forward, even within a single product line. In theMerino wool supply chain, for example, we observedtwo contrasting cases without a clear understandingof what created the discrepancy. In this supply chain,the greasy wool collected by farmers is sold to a top-maker, who then cleans (“scours”) and smooths out(“combs”) the greasy wool, and sells the end prod-uct in the form of wool tops to a spinner. This con-version process from greasy wool to clean woolentops has a particular process yield, which is uncer-tain and is influenced by farmer management prac-tices such as sheep forage use and sheep breeding. InNew Zealand, an innovative manufacturer successfullyused direct sourcing to incentivize farmers to adoptpractices that improved top yields, by offering to sharethe observed benefits. This created mutual benefit forall parties in the supply chain in the form of cross-party production efficiencies.1 However, in the Patago-nia region of Argentina, a consortium has been grap-pling with the use of direct sourcing to incentivize theadoption of new management practices at the farmerlevel. This consortium was led by the internationalenvironmental nongovernmental organization (NGO)the Nature Conservancy, the outdoor apparel companyPatagonia Inc., and the farmer network Ovis XXI inArgentina, as part of a joint project that spanned 2011–2014. The consortium’s attempt was a significant partof a larger effort to combat the regional process ofdesertification—a severe form of land degradation—that was harmful to the entire supply chain (Mazzoniaand Vazquez 2010, Casas 1999). To solve this problem,the consortium championed the use of a new technol-ogy known as “management-intensive grazing” (MIG)and subsidized several farms to implement it. Unfortu-nately, the direct subsidy proved short-lived, as it wasnot economically sustainable for all parties in the sup-ply chain. The reason for the economic challenge, andfor the discrepancy with success stories such as theone in New Zealand, was unclear, making it difficult toresolve the problem.

This prompts several natural research questions. Un-der what conditions is direct sourcing either sufficientor necessary to incentivize new management practicesby the supplier/farmer? What is the structure of theoptimal contract? Does a simple, price-only contractsuffice? And under what conditions can direct sourc-ing indeed help create shared value? Lastly, can theseinsights explain the differences between the two exam-ples in New Zealand and Argentina, as well as providea resolution for the dilemma faced by the consortiumin the latter case?

We use an analytical model and empirical evidenceto help formulate answers to these questions. We mo-del a supply chain with one buyer (topmaker) whocan source through the commodity market or througha direct sourcing relationship. A key feature of thecommodity market is that it is based on blending andthus is always an interaction between multiple sup-pliers (farmers) and the buyer. In contrast, a directsourcing relationship allows for one-on-one interac-tions between a supplier and the buyer. The buyer isthe Stackelberg leader, setting contract parameters. Thesupplier can choose (i) the sourcing channel throughwhich to supply and (ii) whether or not to adopt a new(and more costly) technology. The economic benefit ofthe technology is modeled in the form of an improvedprocess yield downstream.

We first show that if each farmer in the commoditymarket is only responsible for a small fraction of thetotal production, the supply chain will adopt a behav-ior of “growing to meet minimum specs,” which isobserved in most commodity markets including wool.This is a phenomenon where individual farmers havelittle incentive to improve product quality specifica-tions beyond the required minimum, because their(costly) contribution to such value generation is lostin the blending process. As a result, many commod-ity markets do not properly incentivize new technol-ogy adoption by the farmer, even if these technologieswould create value for the supply chain.

To induce benefit through technology adoption, it isthen necessary to introduce the alternative model ofdirect sourcing. However, such an innovation in thesourcing channel may not be sufficient. We find thatswitching the channel to direct sourcing is sufficient tocreate shared value only when the new technology isrelatively cheap, as defined by the cost efficiency rela-tive to process yield improvements. This correspondsto what we observed in New Zealand, where new man-agement practices are relatively cheaper to implementbecause differences in climatological conditions andhistorical farming practices have led to healthier farm-lands compared to those in Argentina (UNCCD 2012).When the new technology is relatively expensive, sim-ply switching the sourcing channel is insufficient toeither incentivize the farmer or create shared value.This corresponds to the case in Patagonia, Argentina,where farmlands are severely degraded. In such cases,direct sourcing contracts with a particular “bonusstructure” are necessary to create shared value. Suchcontracts reward farmers with a per-unit bonus whentheir process yields are larger than a predeterminedthreshold. This requirement of an integrated change inboth sourcing channel and contract structure helpsexplain the puzzle faced by the consortium. Finally,we examine the potential of this approach for creatingshared value in a real-world setting. Using a private

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de Zegher, Iancu, and Lee: Designing Contracts and Sourcing ChannelsManufacturing & Service Operations Management, Articles in Advance, pp. 1–19, © 2017 INFORMS 3

data set of farms in Patagonia, Argentina, we estimatethat the proposed mechanism would increase supplychain profits by 6.9% on average and realize environ-mental co-benefits, even though the new productionmethod is 9% more costly.

In summary, we make the following related contri-butions to the literature:

• First, from a modeling standpoint, we develop aframework that explicitly captures key operating char-acteristics of value chains in developing economies,such as commodity-based sourcing, the use of sim-ple (linear) payment terms, a fragmented supply basewith low bargaining power, and the existence of sim-ple practices/technologies that lead to immediate yieldimprovements. We endogenize process yield improve-ments and identify a technical condition that relatescontract design to the process yield distribution. Thiscondition is based on the harmonic mean residual lifestochastic ordering, which (to the best of our knowl-edge) has not appeared thus far in operations manage-ment (OM) models.

• Second, we find that the required incentives forsustainable technology adoption are driven by (i) a newmeasure of cost efficiency relative to yield improve-ments and (ii) market segmentation. Together, thesedetermine whether it is necessary to only change thecontract design (from a linear contract to a piecewise-constant contract or a bonus contract), only change thechannel design (from commodity sourcing to directsourcing), or make an integrated change in both chan-nel and contract design. We term our new measure ofcost efficiency the “cost elasticity of process yield”: itis intuitive, easy to estimate, and appears novel in thesupply chain literature.

• Third, by combining our normative analyses withempirical data, we test and study the real-life implica-tions of our theoretical results. We are able to retrievethe specifics of two strategies currently employedin practice—one successful and one challenged—andto provide recommendations and practical rules ofthumb to use in the latter case.

The rest of the paper is organized as follows. Weprovide a review of related literature in Section 2. Wepresent the model formulation and preliminaries inSection 3. We then study the sourcing problem andthe contracting problem in Sections 4 and 5. In Sec-tion 6, we use an empirical example to infer practicalimplications of our findings. Our concluding remarksare provided in Section 7. All endnotes are providedafter Section 7, and all proofs are in the online technicalappendix.

2. Related LiteratureThe proposed problem is related to several litera-ture streams in supply chain management, microe-conomics, and strategy. In the literature on socially

responsible operations and value chain innovations indeveloping economies, the concept of creating sharedvalue (CSV) emerged as an umbrella construct for the-ories about the mutual dependence between a com-pany’s competitiveness and the health of environmen-tal and social communities surrounding it, includingits suppliers (Porter and Kramer 2011). However, thereis limited understanding about how to operationalizesuch business models (e.g., London et al. 2010) andhow to design contracts that create value to both par-ties (e.g., Henson et al. 2011, Maertens and Swinnen2009). This paper contributes to filling this gap. Oneemerging topic of study is the business model of directsourcing, which we study here. Wang et al. (2014) pro-vide a review on the topic and conclude that whilethere is strong support for the welfare and produc-tivity impacts of direct sourcing on farms, there is noconsensus on what explains contract participation ornonparticipation. By explaining differences in contractadoption between New Zealand and Argentina, ourstudy contributes to this discussion and helps identifynew contract designs when contract participation mayinitially appear unattractive.

Sodhi and Tang (2014) discuss research opportuni-ties to study operational innovations in supply chainswith the poor as suppliers or distributors in devel-oping economies. Sodhi (2015) and Bessiou and VanWassenhove (2015) identify challenges to studyingsocially responsible operations. They suggest combin-ing different methodologies to tackle these challengesand link socially responsible operations to targeted,analytical models. Our work closely follows these sug-gested approaches.

In supply chain management, there is a large litera-ture on supply uncertainty and contracting. Our workis most closely related to papers that model supplyuncertainty using random yield, i.e., where variabilityin the production process results in an uncertain num-ber of items delivered—see, e.g., Ciarallo et al. (1994),Yano and Lee (1995). The focus in this literature istypically on identifying the optimal procurement strat-egy of a firm in the presence of yield uncertainty, inthe form of exogenous supply disruptions (e.g., Wanget al. 2010, Federgruen and Yang 2008, Tomlin 2006).In contrast, our model focuses on yield uncertainty fora downstream buyer and endogenously incorporatesdecisions made by suppliers that may influence thisprocess yield.

Our focus on incentivizing suppliers to adopt bettermanagement practices relates this paper to the largeliterature on contracting for incentive alignment (seeCachon 2003, Hohn 2010 for recent reviews). Recently,several scholars analyzed such problems in the contextof supply disruption risks (e.g., Hwang et al. 2015).While this literature typically assumes a direct sourc-ing relationship between buyer and supplier, our study

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incorporates the possibility of commodity sourcing,which is pertinent in the context of the agriculturalvalue chains motivating our work. Using stylized mod-els, Tang et al. (2014) and Li (2013) study varioussourcing schemes that the buyer may use to mitigatedelivery risk by suppliers, including direct subsidies,inflated order quantities, and supplier diversification.While these studies typically consider contracts withconstant marginal price, we find that such schemesmay fail to coordinate the supply chain in our setting,and contracts with bonus structures tied to the dis-tribution of the process yields may be required. Thisis consistent with the literature on managerial com-pensation, which argues that such nonlinear output-contingent compensation schemes may be optimal insettings with moral hazard (see, for example, Chunget al. 2014, Bernardo et al. 2001, Basu et al. 1985).

The literature on agricultural operations has consid-ered optimal capacity allocation, production, and pro-curement quantities under uncertain yield and prices(see, e.g., Allen and Schuster 2004, Kazaz and Webster2011, Huh and Lall 2013). The focus of these studieson agricultural yield (also referred to as farm yield) isdistinct from our focus on process yield downstreamin the supply chain. The studies on improving milkquality by Mu et al. (2016) and quality-dependent priceschedules by Ayvaz-Cavdaroglu et al. (2016) are mostclosely related to our setting. Mu et al. (2016) focuson policy interventions to increase the quality of milkin the presence of competition for supply, when farm-ers can deliberately adulterate quality. In contrast, wefocus on buyer interventions to incentivize the adop-tion of a new, costly technology to create mutual benefitin the presence of different sourcing channels. In con-trast to Ayvaz-Cavdaroglu et al. (2016), who focus onfarmer risk aversion, investments in quality, and two-part tariff contracting, we study competition amongfarms of heterogeneous size, and payment schemestied to observed output, with bonus structures.

A related literature stream in agricultural economicsconsiders factors that influence the adoption and effi-cient use of new technologies in developing economies(see Foster and Rosenzweig 2010 for a recent reviewof the topic). This literature has established a strongcorrelation between propensity for technology adop-tion and farm-specific characteristics such as farmerschooling and farm size. The causal pathways forthese correlations vary from access to credit and insur-ance markets (e.g., Karlan et al. 2014) to learningmodels and technology complexity (e.g., Conley andUdry 2010). Our model incorporates features fromthis literature, including uncertainty in benefits fromtechnology adoption and heterogeneity in farm size.Another feature—heterogeneity in the technology’srelative cost—emerges endogenously. Consistent withthis literature, we find that large farms are more likely

to adopt new technologies under the status quo. OurOM perspective allows deriving prescriptive recom-mendations for designing incentive contracts for tech-nology adoption when there is uncertainty in benefitsand the technology is relatively expensive. We find thatsuch uncertainty may require appropriate bonus-basedincentive schemes.

In developmental microeconomics, there is ample lit-erature on the importance of management practices inexplaining productivity. The recent empirical focus onspecific, measurable management practices has yieldeda growing body of literature (Bloom and Van Reenen2011, Lazear and Oyer 2012) that increasingly supportsthe association between management practices andhigher productivity (Bloom et al. 2013, Lazear 2000)and helps explain differences in management qualitybetween developing and developed countries (De Melet al. 2008, Bloom et al. 2010). This literature, however,has largely focused on costs and benefits of productiv-ity gains at the locus of production: farms and facto-ries producing for global buyers. Although this focusostensibly makes sense given that the locus of produc-tion is where the technology has to be implemented,in many cases the benefits of the new managementpractice do not solely lie at the production level butalso in the downstream production process. Such anexpanded view of costs and benefits in the productionnetwork is increasingly recognized as a critical com-ponent of making new management practices work,particularly in the context of socially responsible oper-ations (e.g., Locke 2013).

3. Preliminaries and Model FormulationIn the wool supply chain, a farmer typically sells the“greasy wool” collected from his sheep to a topmaker,who then sells clean “wool tops” to a spinner, after“scouring” (cleaning) and “combing” (smoothing out)the greasy wool. This conversion process from greasywool to clean woolen tops has a particular processyield, known as “top yield” in the industry, which crit-ically depends on the farmer’s practices. Under a graz-ing practice focused on preserving pasture quality andavoiding overgrazing, consistency of greasy wool fiberalso improves, leading to increased top yields. Largertop yields translate into larger revenues for farmers, astopmaker payments are directly tied to the top yields.However, such practices also lead to higher costs for thefarmer, since they are often “management-intensive”rather than letting sheep graze in one place continuallywith a subjectively estimated, fixed number of sheepper unit of land, the new practice requires movingthe sheep in and out of different pastures dependingon the conditions of the grasses (Gunther 2013). Thenew practice, therefore, requires additional planningof sheep grazing, labor to move the sheep around, andmonitoring of grass health. Hence, it has also become

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known as “management-intensive grazing” or “MIG.”(See the online technical appendix for further detailsabout MIG.)

With this motivating example in mind, we considera stylized supply chain consisting of one buyer (thetopmaker) and N suppliers (the farmers), indexed byi 2 {1, . . . ,N}. Farmers have fixed production quanti-ties, denoted by wi � 0, correspond to the amount ofgreasy wool collected from each farm. For simplicity,we normalize these quantities so that PN

i⇤1 wi ⇤ 1 andassume that w1 w2 · · · wN , which makes farmer1 (N) the farmer with least (most) weight in the top-maker’s input process. Although production quantitiesare fixed, farmers can influence the process yield oftheir produce by changing their management practice.Specifically, each farmer i chooses whether to adopt thenew MIG practice or maintain the prevailing practice,and this choice is denoted by a variable mi taking avalue of 1 or 0, respectively. We assume that farmersadopting the same practice achieve homogenous (butvariable) response in their yield. We use Ym to denotethe yield associated with management type m 2 {0, 1},and assume that Ym is a random variable taking valuesin (0, 1), with cumulative distribution function Fm , den-sity function fm , and mean µm . Thus, in the wool sup-ply chain, Ym measures the amount of woolen tops (i.e.,output) per unit of greasy wool (i.e., input) achievedunder management type m, with randomness in Ymreflecting inherent yield variability, e.g., due to weatherconditions that impact the quality of pasture grass andfiber fineness. Following the quality control literature,Ym is independent of the quantity produced.

The economic benefit of MIG translates in an im-proved process yield in manufacturing, experienced bythe buyer, i.e., an increase in top yield for the topmaker.To that end, we assume that the yield distributions Y1and Y0 have respective supports [

¯y1 , y1] and [

¯y0 , y0]

satisfying 0 <¯y0

¯y1 and y0 y1 < 1, and that MIG

leads to a higher mean process yield:

µ1 > µ0 , such that �µ :⇤ µ1 � µ0 > 0.

However, the MIG technology is also more costlyto implement for the farmer. A farmer’s productioncost per unit of produce under management prac-tice m 2 {0, 1} is given by cp(m), and—consistent withpractice—we assume that

cp(1) > cp(0), such that �cp :⇤ cp(1)� cp(0) > 0.

Every farmer is able to sell his entire produce (greasywool) to the topmaker, at a per-unit price cg that ischosen by the topmaker, based on the type of sourcingcontract entered (i.e., commodity-based or direct sourc-ing), and the process yield achieved by the topmaker.In turn, the topmaker sells all his output (the woolentops) and is paid a per-unit price ct by the spinner. The

Figure 1. Stylized Illustration of Model Parameters inInteraction Between the Topmaker and a Single Farmer

FarmerTop-

makerSpinner

Greasy wool Wool tops

Ym

cp(m)ct

cg(·)

Notes. The solid lines are financial flows, and the dotted lines arematerial flows. The grey boxes indicate the decision makers, and thegrey circle indicates the optimization variable.

typical material and financial flows are illustrated inFigure 1.

We focus on the interesting case when the adoptionof the more expensive MIG practice would improvethe expected profit of a centrally coordinated supplychain, i.e.,

µ0ct � cp(0) < µ1ct � cp(1) or equivalently �cp < ct�µ,(1)

since otherwise neither the supply chain nor the farmerwould benefit from the practice.

The focal point of our study is the design of con-tractual arrangements (sourcing channels and paymentfunctions cg) that would induce farmers to adopt theMIG technology, in an economically sustainable way.We focus on payment functions cg that are nonnegativeand nondecreasing, i.e.,

cg 2V :⇤ { f : [0, 1]! [0,1), f nondecreasing}, (2)

which we refer to as “valid,” and consider two possibleconfigurations for the sourcing channel. The first is acommodity-based sourcing model, which relies on blend-ing the greasy wool of all farmers. The second is a directsourcing model, characterized by an individual interac-tion between each farmer and the topmaker. We nextdescribe the dynamics of these two different settings inmore detail and formalize the topmaker’s correspond-ing problem under each.

3.1. Commodity-Based SourcingA key feature of commodity markets is that the farm-ers’ produce is blended before processing. Under thissourcing model, a farmer’s greasy wool is thus blendedwith the greasy wool of other farmers in the region,and the topmaker only observes the average yield ofthe blend after processing. Accordingly, the topmakerforms an expectation of the average top yield of theblend prior to processing and compensates each farmerwith a per-unit price that depends on this “forecasted”average top yield.2 Thus, all farmers are paid the sameper-unit price for their output, assuming their producemeets certain baseline specifications (or “specs”) thatcan be verified using simple tests (see Jelsma et al. 2009

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for the description of an analogous process in palm oilextraction).

In our model, with mi 2 {0, 1} denoting the i-thfarmer’s MIG adoption decision, the topmaker wouldachieve an average top yield of Y :⇤PN

i⇤1 wiYmion the

greasy wool blend, and the price cg paid to each farmerwould depend on the expectation of this yield. There-fore, the expected profit achieved by the topmaker andby the i-th farmer would take the following form:

⇡bT ⇤ ⇧[Y]ct � cg(⇧[Y])⇡b

Fi⇤ wi[cg(⇧[Y])� cp(mi)], 8 i 2 {1, . . . ,N}.

Here, superscript b denotes the model of commodity-based or “blending-based” sourcing, and subscripts Fiand T denote the farmer and topmaker, respectively.

The topmaker always offers the farmers a simplecommodity contract, which involves per-unit paymentsthat are directly proportional to the anticipated topyield. In particular, such a commodity contract seeks tomaximize expected topmaker profit under the assump-tion that all farmers use the prevailing technology (i.e.,mi ⇤ 0 for all i), while ensuring that farmers choose todeliver their greasy wool. With a farmer’s opportunitycost normalized to zero, the per-unit payment functionccc

g in a commodity contract thus would be given by anoptimal solution to the problem:

supcg2V

{µ0ct � cg(µ0)}

s.t. cg(µ0)� cp(0) � 0cg(x)⇤ ax , 8 x 2 [0, 1].

(3)

Such simple agreements often constitute the prevail-ing contracts in commodity markets, where buyers donot explicitly incentivize farmers to adopt new man-agement practices, and only maximize profits whileensuring supplier participation. Thus, the commoditycontract becomes a suitable benchmark against whichalternative sourcing channels and incentive mecha-nisms can be compared, and we assume that such acontract is always available for the farmers. Note thatccc

g can be summarized in terms of a single number a,which we refer to as the commodity rate.

In addition to this benchmark commodity contract,a topmaker seeking to induce MIG adoption by (a sub-set of) the farmers may also offer an incentive contract,characterized by a particular valid per-unit paymentfunction cic

g 2V.

Figure 2. Schematic Illustration of Timeline Under Commodity-Based Sourcing.

Topmaker offers

commodity contract cgcc

and incentive contract cgic

Each farmer chooses

contract ki ∈{ic, cc} and

management type mi ∈{0, 1}

Farmers receive payments

from topmaker. Topmaker

processes the greasy wool

and sells the woolen tops.

Topmaker forms

expectation of

average top yield Â[Y ]

The overall sequence of events in the interaction be-tween the parties under commodity-based sourcing isdepicted in Figure 2. The buyer, acting as a Stackelbergleader, offers all farmers the option of a commoditycontract (with payment function ccc

g ) and an alterna-tive incentive contract (with payment function cic

g ). TheN farmers observe the available contracts and engagein a simultaneous-move game, in which each farmerchooses (i) the contract through which to supply, i 2{ic , cc}, and (ii) whether to adopt the new MIG tech-nology, mi 2 {0, 1}. We assume that a farmer acceptsany terms allowing an expected profit greater than orequal to his opportunity cost, which we normalize tozero. Depending on the farmers’ choices, the topmakerthen proceeds to collect all the greasy wool and pay thefarmers based on the expected top yield of the blend.Once the blend is processed, the topmaker then sellsthe entire output to the spinner at a per-unit price ct .All information about costs and yield distributions iscommon knowledge.

Thus, the topmaker’s problem under a commodity-based sourcing model entails optimally choosing thepayment function cic

g to use in the incentive contract,taking into account the farmer’s responses regardingthe technology adoption and contract choice.

3.2. Direct SourcingInstead of relying on contracts based on the commod-ity sourcing model, the topmaker could also innovatein the sourcing channel itself and rely on a direct-sourcing model. A key characteristic of direct sourcingis the individual interaction between the buyer andthe farmer. This makes it possible for the topmaker toobserve the process yield for a specific farmer’s batchof greasy wool, so that the farmer can consequently bepaid based on his individual, realized top yield.

Under this setup, the topmaker (T) and the i-thfarmer (Fi) making a choice of technology mi 2 {0, 1}would face the following expected profit functionsfrom their direct interaction:

⇡dT ⇤ wi[⇧[Ymi

]ct � ⇧[cg(Ymi)]] (4a)

⇡dFi⇤ wi[⇧[cg(Ymi

)]� cp(mi)]. (4b)

It is worth noting that the key distinctive feature hereis the topmaker’s ability to offer a contract based onthe realization of the farmer’s individual yield; thisis in contrast to commodity-based sourcing, where

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Figure 3. Schematic Illustration of Decision Timeline Under Direct Sourcing

Topmaker offers

commodity contract cgcc

and incentive contract cgic

Farmer i chooses

contract ki ∈{ic, cc} and

management type mi ∈{0, 1}

Farmer i receives payment

from topmaker. Topmaker

processes the greasy wool

and sells the woolen tops.

Topmaker observes

realized yield ymi

payments were based on the expected average pro-cess yield across multiple farmers. In this sense, thecontract can be calibrated under direct sourcing, andthe topmaker can design the payment function cic

g inan incentive contract to induce individual farmers toadopt MIG.

Consistent with our earlier assumption under com-modity sourcing, we assume that even when offereda direct sourcing incentive contract, farmers have thealternative of the benchmark commodity contract. Theoverall sequence of events, illustrated in Figure 3, par-allels the one discussed for commodity-based sourc-ing, with the sole difference in the way payments forgreasy wool are calculated. Table 1 summarizes thecontractual agreements considered in this paper. Toavoid additional notation, we use cic

g to denote theincentive contract under both commodity sourcing anddirect sourcing, with the intended meaning clear fromcontext.

3.3. Discussion of Modeling AssumptionsOur model incorporates several assumptions intendedto either capture practice-based considerations or tomaintain the focus on our core research questions,while retaining analytical tractability.3.3.1. Buyer-driven Supply Chain. We assume the buy-er has all the bargaining power. This is consistent withthe literature on global value chain governance docu-menting the prevalence of buyer-driven supply chainsin the agricultural sector, where producers are boundto buyer decisions (Rodrigue et al. 2013, Gereffi 2001).That said, our model could be readily extended toinclude some bargaining power for the farmer, withoutqualitatively affecting our results (see our discussion inSection 7).3.3.2. Fixed Quantities. We assume that farmers areunable to influence the per-unit prices cg and ct by ad-justing their production quantities, but they can influ-ence the per-unit price cg through the process yield

Table 1. Overview of Contractual Arrangement Considered

Commodity sourcing Direct sourcing

Commodity contract cccg ( · ) ccc

g (⇧[Yield of Blend]) N.A.Incentive contract cic

g ( · ) cicg (⇧[Yield of Blend]) cic

g (Farmer Yield)

Note. The highlighted box is the benchmark contract.

associated with their produce—a variable that has adirect influence on the buyer’s profits. Such a price-setting mechanism was communicated to us duringinterviews with supply chain managers and has beendocumented as a practice by Jelsma et al. (2009) inthe context of palm oil. Furthermore, in agriculturalsettings consistent with our framework, productionquantities involve complex long-term considerationsand large upfront investments. For instance, agricul-tural systems such as livestock, coffee and palm areperennial, so adjusting production quantities requiresenlarging the amount of land available (e.g., throughland purchase or deforestation) and waiting severalyears until the planned-for quantities are reached.Since our focus is on examining the adoption of newmanagement practices, we omit explicitly modelingsuch decisions.3.3.3. Payment Format. We assume that under com-modity-based sourcing, the farmer is paid based onthe expected—rather than realized—regional averageyield. This reflects real-world practice: when buyers setprices based on the expected yields, it allows farmersto know the price and get compensated immediatelyupon the delivery of their produce, without waitingfor these to be processed. Thus, liquidity-constrainedfarmers often perceive such early payments as a bene-fit of supplying through commodity markets (see, e.g.,Gupta et al. 2017, Burke 2014, Sun et al. 2013). In con-trast, under the direct sourcing model, the farmer ispaid a per-unit price that depends on his observedyield. This assumption reflects real-life settings ofdirect sourcing. For instance, companies in the coffeeindustry that use direct sourcing pay farmers contin-gent on coffee quality after tastings or “cuppings” atthe buyers’ facilities.3 Our own interviews with manu-facturers in New Zealand indicated that their paymentto farmers with whom they have a direct sourcing rela-tionship is contingent on top yield. More generally,such contingent payments are also prevalent in certifi-cation schemes, where a premium is paid to the farmeronly after the realization of demand for certified prod-ucts (Potts et al. 2014).3.3.4. Commodity Pricing. We assume that the pricepaid to the farmer, including in commodity-basedsourcing, is only a function of top yield. Clearly, manyother factors may affect pricing in commodity mar-kets, including weather shocks in producing regionsacross the world and other input specs. Our model

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does not purport to capture the complex dynamics ofglobal commodity prices; rather, the commodity con-tract is intended as a normalized benchmark contractthat captures key dynamics of agricultural value chains(blending-based and buyer-driven). Thus, our com-modity contract effectively acts as a numeraire, and thisapproach allows us to relate model results to observa-tions in practice. This is also consistent with the obser-vation that primary processors in agricultural valuechains (i.e., topmaker in wool value chains, or mill inpalm and coffee value chains) sell in global markets butpurchase in local markets. As such, globally set pricesof clean wool primarily affect ct or, in the case of palmvalue chains, the price of crude palm oil (obtained frommilling the fresh fruit bunches of the farmer) and, inthe case of coffee value chains, the price of green cof-fee (obtained from milling parchment coffee from thefarmer). In our model, since buyers capture most ofthe supply chain profit, shocks to global commodityprices are reflected in the buyer’s profit margin, ratherthan price offered to farmers. For our purposes, globalcommodity prices will, thus, primarily affect whetherthe commodity contract is feasible and whether condi-tion (1) is satisfied.

3.3.5. Deterministic Demand. To focus on uncertainprocess yield, we assume that the buyer is able to sellall his output, i.e., he faces deterministic demand. Thisis a common assumption in models with capacity oryield uncertainty (e.g., Ang et al. 2017, Tang et al. 2014,Babich et al. 2012). Furthermore, for many agriculturalproducts used in processed foods and textiles—such aswool, cotton, and palm oil—there is sufficient demandto absorb all outputs. However, this may come at thecost of a lower price ct ; in our model, such shocks todemand are, thus, captured by ct .

3.3.6. Other Considerations. Our model also makesseveral other assumptions, such as lack of MIG adop-tion under status quo, homogenous production costs,and additional costs/benefits of direct sourcing. Wediscuss these in Section 7, where we provide robust-ness checks and outline limitations.

4. Commodity-Based SourcingWe first analyze optimal contracting under commo-dity-based sourcing, and we start by discussing thebenchmark commodity contract.

4.1. Benchmark Commodity ContractThe benchmark commodity contract is given by theoptimal solution to problem (3), i.e., it is character-ized by the optimal linear payment function ccc

g thatmaximizes the expected profits for a topmaker whenno farmers adopt the MIG technology. The followingresult characterizes this simple contract.

Lemma 1. Payments in the commodity contract aregiven by

cccg (x)⇤

cp(0)µ0

x , (5)

where cp(0)/µ0 is the nominal commodity rate.The proof is immediate and is omitted. The nominal

commodity rate cp(0)/µ0 serves as the prevailing rateagainst which alternative contracts and sourcing chan-nels can be compared. The linear structure of the com-modity contract is in line with linear pricing methods inmost commodity markets, including wool and palm oil.Explicitly defining the nominal commodity rate in thissetting, which captures key features of buyer-drivenand blending-based commodity markets, allows us torelate model results to observations about contracts andsourcing channels in practice (see Section 5.1).

4.2. Incentive Contract in Commodity-basedSourcing

When the topmaker offers the incentive contract, farm-ers engage in a simultaneous-move game in whichthey choose the contract through which to supply, andwhether to adopt the MIG technology. Thus, the top-maker’s problem entails optimally choosing the pay-ment function cic

g to use in the incentive contract, tak-ing into account the farmers’ responses. To facilitatea practical interpretation of the results, we focus ouranalysis of this game on pure-strategy Nash equilibria.Mathematically, the topmaker’s problem can thus besummarized as follows:

supcic

g 2V

NXi⇤1

wi

ctµm⇤

i� c

⇤i

g

✓ NXi⇤1

wiµm⇤i

◆�, (6)

where

(m⇤i ,

⇤i)⇤ argmax

mi2{0, 1}i2{ic , cc}

wi

ci

g

✓wiµmi

+Xj,i

w jµm⇤j

◆� cp(mi)

�,

8 i 2 {1, . . . ,N}. (7)

When solving the game, we enforce a unique equi-librium. The reader will observe that if we do notenforce a unique equilibrium for the contract thatsolves (6)–(7), the problem would turn into a coordi-nation game between the farmers. By analyzing thishypothetical coordination game, one can show that twoequilibria would survive, corresponding to no farmersor all farmers adopting MIG. The contractual paymentfunction ensuring this would take an extremal form(compensating with a per-unit price of cp(1) only whenall farmers adopt MIG, and cp(0) otherwise), inducingall farmers to achieve zero profits in both equilibriaand allowing the topmaker to collect all the supplychain profit in the latter (payoff-dominant) equilib-rium. While it is theoretically possible for the payoff-dominant equilibrium to be achieved in coordinationgames (see, e.g., Kim 1996 and references therein),

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recent experimental research has shown that playersgenerally fail to coordinate in such games (see, e.g.,Keser et al. 2012 and Heinemann et al. 2009). Further-more, in the context of the commodity markets andagricultural value chains motivating our work, it seemsill-suited to assume that a large number of farmers inremote areas would coordinate their actions to adoptMIG. Therefore, we focus our analysis on paymentfunctions that induce a unique equilibrium.

The topmaker’s decision problem can then be solvedby considering the optimal profit under the farmers’best response. For simplicity of notation, let us defineµ(S) :⇤µ0+�µ

Pi2S wi , 8S ✓ {1, . . . ,N} as the resulting

expected average yield at the top-making level whena subset of farmers S adopts the MIG technology andthe remaining farmers do not. We also define [k ,N] :⇤{k , . . . ,N}, and the following (potentially empty) setsof farmers:

Scc :⇤⇢

i 2 {1, . . . ,N}: wi ��cp

�µ

µ0

cp(0)

�

⌘{l , l + 1, . . . ,N} (8)

Sic :⇤⇢

i 2 {1, . . . ,N}: wi ��cp

ct�µ

�

⌘{k , k + 1, . . . ,N}. (9)

By construction, it can be checked that Scc ✓ Sic .The following result then completely characterizesthe unique equilibrium of the game, highlighting thedependency on the relative importance of the farmers,as measured through their weights:Theorem 1. In equilibrium,

(i) If w1�(�cp/�µ)(µ0/cp(0)) �so that Scc⇤{1, . . . ,N}�,then the topmaker only offers the commodity contract, andall farmers adopt MIG. The i-th farmer makes an expectedprofit of [(cp(0)/µ0)µ1� cp(1)]wi , and the topmaker makesan expected profit of [ct�cp(0)/µ0]µ1.

(ii) If w1 < (�cp/�µ)(µ0/cp(0)) and wN ��cp/(ct�µ)�so that Scc ⇢{1, . . . ,N} and Sic,ú�, then the topmaker offersthe following piecewise constant incentive contract�

cicg (x) ,

8>>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>>:

cp(0)µ0

· µ(Scc), if x < µ([l ,N])

cp(0)µ0

· µ(Scc)+�cp ,

if µ([l ,N]) x < µ([l � 1,N])...

cp(0)µ0

· µ(Scc)+ (l � k)�cp ,

if µ([k + 1,N]) x < µ([k ,N])cp(0)µ0

· µ(Scc)+ (l � k + 1)�cp , otherwise.

All farmers choose to sell through this contract, and farmersin Sic also adopt the MIG technology. The expected profit forthe i-th farmer is respectively given by

⇢ cp(0)µ0µ(Scc)+ (l � k + 1)�cp

�� cp(1)

�wi , i 2 Sic

⇢ cp(0)µ0µ(Scc)+ (l � k + 1)�cp

�� cp(0)

�wi , i < Sic ,

and the topmaker’s expected profit is given by ctµ([k ,N])�[(cp(0)/µ0)·µ(Scc)+(l�k+1)�cp].

(iii) If wN < �cp/(ct�µ) �so that Scc ⇤ Sic ⇤ ú�, thenthe topmaker only offers the commodity contract, the sup-ply chain does not adopt MIG, and the farmers make zeroexpected profit, while the topmaker makes an expected profitof ctµ0 � cp(0).

For a proof of this result (as well as the succeed-ing ones), please refer to the paper’s online technicalappendix. Before discussing the results in Theorem 1,we point out that the threshold values that determinethe sets of farmers in (8) and (9) have important inter-pretations. The latter is the inverse ratio of per-unitincrease in supply chain revenue to per-unit increase insupply chain cost, and thus is a measure of the supplychain’s profit margin. The threshold value in (8) cor-responds to the inverse ratio of relative yield improve-ments to relative cost increases, which gives it an “elas-ticity” interpretation. This quantity plays a critical rolein the remainder of the paper, and therefore we defineit formally as the “cost elasticity of process yield” inanalogy to the well-known “price elasticity of supply”in microeconomics.

Definition 1 (Cost Elasticity of Process Yield).

" ,cp(0)µ0

�µ

�cp.

When " is high, the relative increase in process yieldfor the supply chain is high compared to the relativeincrease in costs incurred by the farmer. This makes thenew technology relatively cheap compared to the ben-efit it generates. We use this relationship to classify thecost of the new technology into the intuitive categoriesof “cheap” and “expensive” for the remainder of thepaper.

Definition 2 (Relative Cost of New Technology). If " < 1,we say that the new technology is “expensive,” whereasif " � 1 we say that the new technology is “cheap.” Inthe extreme case where " � 1/w1 we say that the newtechnology is “very cheap.”

Theorem 1 indicates that if MIG is very cheap(i.e., " � 1/w1), the topmaker does not need to incen-tivize farmers, since they would automatically adoptMIG through the commodity contract. Equivalently,

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this condition can be interpreted in terms of farmerweights wi , requiring that each farmer be responsiblefor a sufficiently large fraction 1/" of the total produc-tion. Thus, in developing economies where the sup-ply base is typically highly fragmented, the conditionis unlikely to hold. For example, using the empiri-cal data set described in Section 6, the smallest farmin the farmer network supplies w1 ⇤ 1.59% of theblend, whereas 1/" ⇤ 1.10, such that condition (i) isnot met.

As the technology becomes more expensive (or,equivalently, as some farmers become responsible foran increasingly small fraction of the total production),the topmaker prefers to incentivize only the largestsuppliers, who have a significant impact on the processyield of the blend. Interestingly, when these large farmsare incentivized, all farmers choose to supply throughthe incentive contract, since this affords a higher per-unit price than the commodity contract. In this regime,smaller farmers—who do not adopt the MIG technol-ogy in equilibrium—thus essentially free-ride on theyield improvements generated by the larger farmers. Itis worth noting that such an incentive scheme criticallydepends on having sufficiently large farms (i.e., wN ��cp/(ct�µ)). Using the empirical data set described inSection 6, we find that �cp/(ct�µ) ⇤ 0.79. Thus, a farmwould have to contribute at least 79% of the blend forthe topmaker to offer the farmer an incentive contract.However, the largest farm in our data set contributesonly 16% of the blend on average, so that the conditiondoes not hold. Finally, if there are no sufficiently largefarms, i.e., wN < �cp/(ct�µ), the topmaker never offersan alternative contract that incentivizes the adoptionof MIG under commodity sourcing. The supply chainthen never adopts MIG, despite the technology beingbeneficial, by condition (1).

This situation corresponds to the behavior of “grow-ing to meet minimum specs” observed in many com-modity markets, including wool.4 More broadly, theseresults show that while a farmer could sometimes bebetter off by adopting a new technology even under amodel of commodity sourcing, there are many caseswhere the benefits to the farmer alone are too small.The supply chain then ends up in a “commoditydilemma,” which is the equilibrium outcome unlessthe business model is innovated by altering traditionalsourcing channels. It is also worth noting that this situ-ation is likely to be prevalent in cases where the farm-ers are not too different in their production quantities,and the number of farmers is very large, so that a givenfarmer’s share of the total production becomes small.This is a typical case in the developing economies, sug-gesting that MIG adoption in such environments canbe particularly challenging through commodity-basedsourcing models.

5. Direct SourcingWe now focus on the case when there are sufficientlymany farmers and each is only responsible for a smallfraction of the total production (i.e., wN < �cp/(ct�µ)),so that the MIG technology would never be adopted.In this case, the topmaker can engage each farmerthrough a direct sourcing relationship, in which theirrespective profits are characterized by (4a) and (4b).Therefore, the topmaker would solve the followingoptimization problem when designing the paymentfunction cic

g in a direct sourcing contract with any givenfarmer:

maxcg2V

{µ1ct � ⇧[cg(Y1)]}

s.t. ⇧[cg(Y1)]� cp(1) � ⇧[cg(Y0)]� cp(0) (P1)⇧[cg(Y0)]� cp(0). � 0 (P2)

(10)

The first constraint in this formulation ensures thatthe farmer (weakly) prefers MIG to no-MIG undercalibration; the second constraint ensures that thefarmer’s expected profit is at least as good as under thecommodity contract, irrespective of his choice. Con-straint (P1) also justifies the use of Y1 as the relevantyield for the topmaker’s profit from this individualinteraction.

Clearly, at a stylized level, the topmaker’s problemcan be solved by any cic

g satisfying ⇧[cicg (Y0)]⇤ cp(0) and

⇧[cicg (Y1)]⇤ cp(1). However, this solution provides little

insight into the design of the optimal payment scheme.Therefore, we proceed to develop a more detailedunderstanding of the optimal scheme and its structure.Our analysis focuses on continuous payment schemes,considering that these are most often used in practice.Within this class, there exist many different schemeswith various compositions of a fixed bonus, a per-unitbonus, bonus thresholds, and a fixed earnings inter-cept (see, for example, Chung et al. (2014) for differentcompensation schemes used in sales settings). We con-centrate the analysis on two-piece linear payments ofthe following form:

cicg (x)⇤ �1x + �2(x � ✓)+ ,

where x+ ,max(x , 0). Thus, �1 is the nominal rate paidto the farmer, �2 is a bonus rate for higher yields, and✓ is the bonus threshold. This compensation schemeis a more general representation of the linear paymentscheme used in industries with endogenous processyields (see, for example, Jelsma et al. 2009). Becausethe per-unit price is proportional to the realized yieldof the farmer ym 2 (0, 1), this pricing practice is some-times referred to as “ratio pricing” (Boyabatli 2015). Inthe remainder of our analysis, we make the followingassumption about process yields.Assumption 1 (Technology-Adoption Condition).

µ0⇧[(Y1 � ✓)+] � µ1⇧[(Y0 � ✓)+] 8✓ 2 (0, y1).

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Assumption 1 corresponds to requiring that Y1 islarger than Y0 in the harmonic mean residual life order.This stochastic ordering has been studied in reliabilityanalysis and actuarial science (Heilmann and Schroter1991) and is known to be slightly stronger than sec-ond order stochastic dominance. For particular classesof distributions, the condition is not very restrictive.For example, for the uniform and exponential dis-tributions, it is equivalent to requiring ⇧[Y1] � ⇧[Y0](Heilmann and Schroter 1991), which is already sat-isfied in our basic model. This order also has conve-nient closure properties, including order preservationunder the convolution operation and mixing (Shakedand Shanthikumar 2007). Lastly, we can also confirmthat this condition is satisfied in our data set for thecase of MIG in Argentina (see Section 6 for details).

Under two-piece linear contracts, the topmaker’sproblem is then given by

max✓�0, �1 , �2

⇧[ctY1 � �1Y1 � �2(Y1 � ✓)+]

s.t.�µ ⇧[(Y1 � ✓)+]� ⇧[(Y0 � ✓)+]µ0 ⇧[(Y0 � ✓)+]

� �1�2

�

��cp

cp(0).

�(P1)(P2)

(11)

For a fixed ✓, the problem of finding the nominalrate �1(✓) and the bonus rate �2(✓) reduces to solv-ing a linear program (LP). Note that while we refer to�2(✓) as a bonus rate, it only acts as a genuine bonusfor the farmer when it is positive; otherwise, when�2(✓) < 0, the payment function effectively includes adiscount on the per-unit purchase price for high yields.We first solve this LP and subsequently return to thefull problem to find the optimal contract by optimiz-ing over ✓. Theorem 2 states the finite optimal solutionunder Assumption 1.

Theorem 2. Under Assumption �, the LP in (11) is solved by

�1(✓)⇤cp(0)⇧[(Y1 � ✓)+]� cp(1)⇧[(Y0 � ✓)+]µ0⇧[(Y1 � ✓)+]� µ1⇧[(Y0 � ✓)+]

, and

�2(✓)⇤cp(1)µ0 � cp(0)µ1

µ0⇧[(Y1 � ✓)+]� µ1⇧[(Y0 � ✓)+].

Furthermore, �2(✓) � (>)0 if and only if " (<)1.

Thus, it is always feasible to design an incentive con-tract under direct sourcing that incentivizes MIG adop-tion. However, Theorem 2 indicates that the cost elas-ticity of the new technology (") has a critical impacton the structure of the optimal contract. When MIGis expensive (" < 1), the optimal contract is convex(�2 > 0), such that the topmaker has to offer a per-unitbonus for higher yields. In contrast, when MIG is cheap(" � 1), the optimal contract is either concave or linear.Note that the contract offers a larger bonus �2(✓) and

reduces the nominal rate �1(✓) as the MIG technologybecomes more expensive relative to the prevailing one,i.e., as cp(1)/cp(0) increases.

To find the overall optimal contract and develop fur-ther insight into the dynamics of the optimal contract,we divide the analysis into two cases, depending onwhether MIG is cheap or expensive.

5.1. MIG Is Cheap (" � 1)If MIG is cheap, Theorem 2 indicates that the opti-mal contract is concave, and the bonus rate is nega-tive. Furthermore, we find that the per-unit price forlarge yields (�⇤1 + �⇤2) when MIG is cheap in the strictsense (i.e., " > 1) becomes even lower than the nom-inal commodity rate cp(0)/µ0 (see Theorem 3 in theonline technical appendix for details). This is a featurethat may make the contract more difficult to implementand sustain in practice. However, as formalized in ournext result, if the topmaker’s main goal were to incen-tivize the adoption of the new technology, then simplychanging the sourcing channel while maintaining thenominal commodity rate would be sufficient when thetechnology is cheap. In fact, such a simple linear con-tract would also create “shared value” when MIG ischeap in the strict sense (i.e., " > 1), meaning that boththe topmaker and the farmer would be strictly betteroff by interacting through this contract than by inter-acting through the existing commodity market.

Theorem 4 (Shared Value Contract). If " � 1, a contractbased on direct sourcing that pays the nominal commodityrate (cp(0)/µ0) incentivizes farmers to adopt MIG. Further-more, if " > 1, such a contract would create strictly sharedvalue.

Effectively, this “shared value contract” means thatthe topmaker pays back the top yield differential tothe farmer at a rate that equals the nominal com-modity rate. Because of its simple structure, this con-tract is robust and relatively easy to implement, andcalibrating it does not require any additional informa-tion about farmer-specific yield distributions. The top-maker only needs to estimate whether the new tech-nology is cheap or not.

This contract is used successfully by an innova-tive manufacturer who sources directly from farm-ers in New Zealand.5 This is plausible and con-sistent with our model predictions; the equivalentof MIG in New Zealand appears to be relatively“cheap,” especially when compared with Argentina.Two main reasons for this difference were conveyedduring a personal communication. First, the grass-lands in New Zealand are considerably less degradedcompared to those in Argentina, implying that �µ/µ0is expected to be larger (this is also consistent withour empirical findings in Argentina alone, where wedocument a negative relationship between �µ/µ0 and

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the degree of desertification—see the paper’s onlinetechnical appendix). Second, management practices inNew Zealand are also more sophisticated and efficientthan in Argentina, implying that cp(0) is likely largerand�cp/cp(0) smaller. The compounding effect of thesetwo forces is that " ⇤ (cp(0)/�cp)(�µ/µ0) is likely to behigher in New Zealand than in Argentina, making thecorresponding MIG “cheap.”

5.2. MIG Is Expensive (" < 1)We first observe that if MIG is expensive and the top-maker desires to incentivize adoption, it is no longersufficient to only change the sourcing channel whilepaying according to the nominal commodity rate, asformalized in our next result.

Corollary 1. If " < 1, a contract based on direct sourcingthat pays the nominal commodity rate (cp(0)/µ0) cannotincentivize farmers to adopt MIG.

To incentivize the farmer, it is then necessary to alsoinnovate the contract structure. Our next result char-acterizes the optimal contract when the process yieldscan be ordered in the mean residual life order (denotedby Y1 �mrl Y0). This stochastic ordering is known to beslightly stronger than Assumption 1, but for particularclasses of distributions such as the uniform and expo-nential, the two orderings are equivalent (Heilmannand Schroter 1991). We can also confirm that this con-dition is satisfied in our data set for the case of MIG inArgentina (see Section 6 for details).

Theorem 5 (Optimal Contract). When " < 1, if Y1 �mrl Y0,then there exists a ⇠ > 0 such that the optimal contract isgiven by any bonus threshold ✓⇤ 2 [⇠, y1) with correspond-ing nominal rate �1(✓⇤) and bonus rate �2(✓⇤) given byTheorem �. The nominal rate and bonus rate satisfy

0 < �1(✓⇤) <cp(0)µ0< [�1(✓⇤)+ �2(✓⇤)],

and the threshold ⇠ ⇤¯y0 if (cp(1)µ0 � cp(0)µ1)/�cp

¯y0,

and ⇠ >¯y0 otherwise. The topmaker captures all the supply

chain profit, and adopting direct sourcing increases his per-unit expected profit by ct�µ��cp .

Several comments concerning this result are in order.There is substantial degeneracy in the optimal bonusthreshold. This degeneracy can be useful in prac-tice for addressing additional considerations such asprofit variability and parameter estimation error. UsingMonte Carlo simulations parameterized by the empiri-cal data described in Section 6, we find that increasingthe bonus threshold ✓ monotonically increases profitvariability for both the topmaker and the farmer (seeFigure 4). Furthermore, when the topmaker has lim-ited data on yield distributions, he may prefer settingcontract parameters that are less prone to estimation

error. Because �1(✓) and �2(✓) depend on the quan-tiles of the yield distribution (see Theorem 2), settinga lower bonus threshold ✓ allows using more obser-vations in parameter estimation. Figure 5 indicates theimpact of estimation error on the topmaker’s expectedprofit, using Monte Carlo simulations parameterizedby the empirical data in Section 6. (The impact on thefarmer’s expected profit mirrors Figure 5 and is omit-ted for space considerations.) We find that the top-maker risks eroding his profits when setting ✓ rela-tively high. When ✓ is set relatively low, the estimationerror is negligible. In summary, concerns about profitvariability and estimation error suggest that it wouldbe recommended to set ✓ quite low. The lower boundof ⇠ (always positive when MIG is expensive) thusbecomes critical.

When MIG is expensive, the topmaker can alwaysextract all the supply chain profit in optimality. How-ever, the topmaker may wish to ensure shared value,i.e., that both the topmaker and the farmer are strictlybetter off. Theorem 6 identifies conditions under whichthis can be ensured, establishing that it can be diffi-cult to strictly create shared value when the contract islinear.Theorem 6 (Shared Value Contract). There always existsa bonus contract �✓ > 0, �2 > 0� that results in shared value.However, a linear contract (✓⇤ 0) creates shared value if andonly if

ct�µ��cp

ctµ0 � cp(0)>�µ

µ1. (12)

The left-hand side of (12) is the relative increase inexpected supply chain profit from adopting MIG; thus,for a linear contract to create shared value, the relativeincrease must be large enough. This condition impliesthat the buyer could be worse off under a linear con-tract that incorporates a per-unit price premium. Suchcontracts are common in practice; e.g., some certifica-tion schemes have a linear structure that incorporatesa nominal per-unit price premium to compensate forcost increases of a new management practice (Pottset al. 2014). This may unnecessarily undermine the eco-nomic sustainability of the scheme or would requirepassing a price premium to the final consumer. Usingthe empirical data described in Section 6 for the caseof MIG in Argentina, we find that (12) was not satis-fied during the project. In such cases, only a convexcontract that embeds a bonus structure would strictlycreate shared value. To create such a bonus contract,one could simply increase the value of the nominal rate�1(✓) or the bonus rate �2(✓) in the feasible direction.

6. A Puzzle RevisitedThe analyses in Sections 4 and 5 help to explain whatmay cause the discrepancy in the sufficiency of directsourcing to incentivize new management practices by

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Figure 4. Profit Variability for Various Choices of ✓⇤ 2 [⇠, y1), Under the Optimal Contract

Std

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rofit

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(a) Truncated normal yield distribution (b) Uniform yield distribution

Notes. The standard deviation of the topmaker’s (T) profit and of the farmer’s (F) profit are displayed in the top row and middle row,respectively. Each row displays this for two distinct distributions that were parameterized using the empirical data described in Section 6 andare shown in the bottom row.

Figure 5. Impact of Estimation Error on Expected Topmaker (T) Profit for ✓⇤ 2 [⇠, y1)

Ratio (

T p

rofit)

à

–0.5

0.3

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distribution

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T p

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(b) Uniform yield distribution

Notes. Each panel displays the ratio of ⇧[c100g (Y1)] over ⇧[c1,000

g (Y1)], where ckg(Y1) is the contract price when �1 and �2 are estimated based on

k observations. For each simulation, the distribution with 100 observations is bootstrapped from the distribution with 1,000 observations,considered the “true” yield distribution. This procedure was repeated 10,000 times. The solid line is the average of 10,000 simulations; thedotted line is one standard deviation from the average. Y1 and Y0 are drawn from the truncated normal distribution in Figure 4(a) and uniformdistribution in Figure 4(b), parameterized by the data set in Section 6.

farmers, for the observed cases of New Zealand andArgentina. These two countries differ in the currentstate of their farmlands—due to distinct climatologicalconditions and historical practices—as well as in the

current state of farming practices (UNCCD 2012). Asa result, in New Zealand the equivalent of MIG is rel-atively “cheap,” and a linear direct sourcing contractwith a rate that equals the nominal commodity rate

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is sufficient to incentivize the adoption of MIG andcreate shared value. But when MIG is “expensive,” asin Argentina, such a simple mechanism is insufficient.Equipped with the insights from our theoretical model,we can revisit the puzzle faced by the consortium.

To apply our analytical results, we perform the fol-lowing steps. First, we empirically estimate key param-eters of the model, i.e., the yield differences (�µ) andcost differences (�cp) associated with the adoption ofMIG. (We use the hat-symbol ˆ to refer to an estimateof a population parameter.) Second, we verify whetherkey assumptions of the model are satisfied, such as thetechnology-adoption condition and the mean residuallife order. We then combine this information to identifywhich model results and which insights are applicable.Finally, we use the data to infer the magnitude of thebenefits to the supply chain if our proposed strategywere followed.

We draw on two data sets created as part of the con-sortium’s project. The first is a farm-level data set withinformation about top yields and management typesof farmers who participated in the project, which wasbased on a direct subsidy. The data include yields fromfarms supplying through a direct sourcing channel,and both farms implementing and not implementingMIG are included. The second is a low-resolution dataset with variable costs and mark-ups at each stage ofthe wool supply chain in the outdoor apparel market,averaged at the industry level. To estimate �cp andcp(0), the Nature Conservancy and Ovis XXI directlytracked farm revenues and additional costs incurredby farmers for MIG during the project’s third year (i.e.,2013). In the absence of more granular information onbaseline costs, we imputed cp(0) from farm revenuesper unit of greasy wool. Consistent with our model-ing assumption that the farmer’s opportunity cost isnormalized to zero, we set the average per-unit cost ofgreasy wool equal to its average per-unit revenue.6

Before presenting our results, it is necessary to pointout the limitations of these data sets and to clarifythat this empirical section is not intended as a stand-alone empirical study, but is rather intended to comple-ment and test our theoretical results in practice. First,from the perspective of a rigorous program evalua-tion, the data set on top yields has important short-comings. Specifically, the strict method of a controlledexperimental design with a control group and a ran-dom assignment was not applied at the time of projectimplementation in 2011. Consequently, the estimate ofMIG’s impact on top yields may be caused by con-founding variables (Imbens and Rubin 2015). We cor-rect for such issues as best as we can, by using a strat-ified experimental design in which we compare topyields of farms within stratified categories based onecological regions (see the online technical appendix).As a result of this process, the total number of farms

included in the analysis is reduced from 142 to 63.Due to the shortcomings of the experimental designand the small sample size, our quantitative results haveto be interpreted with caution; while these are thebest estimates currently available in such data poorregions as the world’s drylands, they remain roughestimates. Second, the information on costs and mar-gins at each stage of the supply chain has been aver-aged at the industry level to protect company-specificpricing negotiations.

6.1. Estimation of Key Parameters and Verificationof Key Assumptions

Using the farm-level data set described previously ontop yields and management types, we estimate that theaverage yield increase is �µ ⇤ 5.21%, with correspond-ing µ0 ⇤ 61.81% such that µ1 ⇤ 67.03%. Table 2 providessummary statistics for each year; the online technicalappendix provides a more detailed analysis by strati-fied categories. This estimate is based on a weightedaverage of top yields, where the relative weight is deter-mined by the number of kilograms (kgs) of greasywool, to ensure that our estimate is representative of themean difference observed by the topmaker. Figures 6(a)and 6(b) show the empirical cumulative distributionfunction (CDF) and probability density function (PDF)of top yields under the two management types. Wethen used the costs associated with implementing MIGduring the project to arrive at an estimate of the costincrease �cp , using a weighted average across farms,where the relative weight is determined by the numberof kgs of greasy wool. Combining�cp with our estimateof cp(0), we estimate that, on average, the adoption ofMIG increases farmer costs by�cp/(cp(0))⇤ 9%. Puttingtogether our estimates for average yields and produc-tion costs, we find that MIG is “expensive”:

" :⇤2014X

h⇤2011wh ⇥

cp(0)µ0,h

�µh

�cp⇤ 0.91,

where h refers to the harvest year, and wh 2 [0, 1] isthe relative weight of greasy wool in kgs in harvest

Table 2. Number of Farms Included in the Analyses, byYear, When Management Type is MIG (m ⇤ 1) or No-MIG(m ⇤ 0), and Estimates of Yield Increases �µ

2011 2012 2013 2014 Total

m 1 0 1 0 1 0 1 0 1 0

# of farms 5 15 5 14 5 12 3 4 18 45�µ (%) 5.76⇤⇤⇤ 4.50⇤⇤ 4.96⇤⇤⇤ 5.82† 5.21⇤⇤⇤

Notes. Estimates of �µ are computed based on the weighted averageof top yields Ym , by year, with the relative weight determined by thefarmer’s share of the total production. For the difference in means, ⇤⇤⇤,⇤⇤, and † denote significance at 1%, 5%, and 20% level, for a two-tailedWelch t-test. The significance level was computed at the farm levelusing clustered standard errors.

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Figure 6. Empirical CDF and PDF of Top Yields

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Positive part means ratio

Average yields ratio

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(a) Empirical CDF of top yields (b) Empirical PDF of top yields (c) Technology-adoption condition

Notes. The left and middle panel show the empirical CDF and PDF of top yields under two different management types, using data from 2011–2014. The PDF is estimated using kernel density estimates with a Gaussian smoothing kernel. The right panel shows empirical verificationof the technology-adoption condition. The solid line shows the ratio of positive part means ( ú⇧[(Y1 � ✓)+]/ ú⇧[(Y0 � ✓)+]) as a function of ✓; thedashed line shows µ1/µ0.

year h. As a result, switching to direct sourcing onlyis insufficient to incentivize the farmer to adopt MIG(Corollary 1), and offering a simple linear contract thatincentivizes the farmer was not economically sustain-able for the topmaker (Theorem 6). This may helpexplain the challenges that the consortium faced. Toincentivize farmers and to create shared value, thetopmaker needs to offer a direct sourcing contractwith a bonus structure. Finally, we argued that thetechnology-adoption condition (Assumption 1) is asensible assumption for new technologies to be worth-while, and therefore we adopted this key assumptionin the remainder of our analyses. Using the farm-level data set, we can verify whether this assumptionis indeed met. Figure 6(c) plots the ratio of positivepart means ( ú⇧[(Y1 � ✓)+]/ ú⇧[(Y0 � ✓)+]), and the ratioof average yields (µ1/µ0) as a function of the bonusthreshold. As the former always exceeds the latter, thetechnology-adoption condition is indeed satisfied. Fur-thermore, because the ratio of positive part means isincreasing in ✓, we also have that Y1 �mrl Y0 is satisfied(Shaked and Shanthikumar 2007).

6.2. Hypothesized Benefit to the Supply ChainSince our key assumptions are satisfied, we can use es-timates of the model parameters to infer what the ben-efit of direct sourcing and MIG would be to the supplychain. For this, we also use the data set that containsinformation about variable costs and markups at eachstage of the wool supply chain. We then estimate that,using our proposed mechanism, average supply chainprofits would increase by 6.9% even though the newproduction method is more costly. Specifically,

2014Xh⇤2011

wh ⇥ct ,h�µh ��cp

ct , h µ0, h � cp(0)⇤ 6.9%. (13)

In the case of Patagonia, Argentina, our proposed me-chanism also incentivizes a production method withimportant environmental benefits, since MIG helpscombat regional desertification.

7. Concluding Remarks, Limitations, andFuture Research Directions

We study situations where suppliers have an opportu-nity to create economic (and, possibly, environmental)value by adopting a new technology, but the economicbenefit is either too small for the suppliers or accruesprimarily to other parties in the value chain. Our prin-cipal goal was to provide insights about contract andchannel design to companies seeking to innovate theirsourcing model, to create economic value while pre-serving responsible sourcing. We identify that the costelasticity of the technology’s economic benefit (in thiscase process yields) drives whether the buyer needsto change only its sourcing channel, only its contractstructure, or both to incentivize farmers to adopt thenew technology and to create shared value. To inducethe intended supply chain benefit, it may thus be nec-essary to adopt an integrated change. We also find thatcertain simple contracts with either a linear or a “bonusstructure” are optimal, while other intuitive contractscould be detrimental. This highlights that value chaininnovations need to be properly designed—and some-times combined—to achieve a sustainable implemen-tation. Table 3 summarizes these findings.

This research was positioned in the context of incen-tivizing new management practices by farmers inArgentine Patagonia to combat the process of deserti-fication. Although our findings have implications fordirect sourcing as a sustainable sourcing strategy inagricultural value chains, we note that direct sourcing

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Table 3. Summary of Findings in This Paper

Relative cost Suggested Suggested Change in Change in Suggested innovationof MIG channel contract ⇡T ⇡F for topmaker

Very cheap (" � 1/w1) Commodity Linear Increase Increase No innovation necessaryCheap (" � 1) Direct Linear Increase Increase Change sourcing channel,

maintain contract structureExpensive (" < 1) Direct Strictly convex Increase None/Increase Change sourcing channel

and contract structure

alone may not be sufficient. To ensure sustainable pro-duction, companies may also need to invest in capacity-building initiatives, compliance audits, and collabora-tions with government and other agencies (see, e.g.,Locke 2013). There are also limits to what companiescan achieve with a for-profit motive alone, particularlywhen accounting for implementation constraints. Ouranalyses show that the complexity of the coordinatingcontract increases as MIG becomes expensive. Devel-oping such an understanding is a first step; e.g., whenthe technology is “cheap,” a small change in procure-ment contract suffices to induce MIG adoption. Gov-ernments, NGOs, or donors could subsidize farmersup to where MIG becomes “cheap” (" � 1) to avoid theneed for complex contracts. This would allow resource-constrained agencies to cost effectively facilitate thecreation of shared value. Alternatively, to catalyze theimplementation of direct sourcing and contract cali-bration, these agencies could invest in tracking devicesand data collection.

In our modeling efforts, we abstracted away fromcultural or behavioral aspects of decision making bymanagers and farmers. However, such variation incontexts highlights the complexity of making innova-tions work in developing economies. Furthermore, themodel assumes that decision makers have visibility ofdata such as yields and costs. We recognize that inmany cases, there is limited data to inform decisionmaking, and we encourage researchers to explore howthis impacts our results. As best as we could, we incor-porated a modus operandi in our analyses. As a result,we were able to retrieve the specifics of a current strat-egy used in practice, giving confidence that our resultsindeed provide insights that can be applied.

7.1. ExtensionsOur analyses incorporated three assumptions that maybe changed without altering the qualitative insights.First, we assumed that all bargaining power underdirect sourcing lies with the topmaker. This assump-tion could be relaxed in several ways. For instance,we could assume that the i-th farmer has a per-unitopportunity cost �i � 0, reflective of some bargain-ing power. By suitably altering the incentives (P2)in the topmaker’s problem, it can be seen that thischange is equivalent to increasing the farmer’s pro-duction cost to cp(0) + �i . Our qualitative findings in

Section 5 persist under these modified costs, with thesole difference that the i-th farmer now makes a profitwi�

i , and the topmaker collects the remainder of thetotal profit. Interestingly, since the nominal rate �1(✓)offered under direct sourcing is increasing in cp(0),this change has nontrivial implications for contractdesign, as farmers with lower opportunity costs areoffered lower nominal rates. In such cases, the topmakercould use the degeneracy in the optimal contract choiceto ensure that all farmers receive the same nominalrate �1, with potentially different thresholds and bonusrates.

Alternatively, we could consider the direct sourc-ing contract as a solution to a Nash bargaining gamebetween the topmaker and the farmer. In this case, itcan be shown that the equilibrium solution would be toadopt MIG by using any payment function satisfying⇧[cg(Y1)] ⇤ cp(1) + (ct�µ � �cp)/2, which would resultin an equal split of profits between the farmer andthe topmaker (details are available from the authorsupon request). Since examples of such payment func-tions also include the bonus contracts that we study,our insights again remain robust.

Second, we assumed that all farmers use the pre-vailing technology when deriving the benchmark com-modity contract ccc

g . This is consistent with our focuson the introduction of a new, costly technology notpreviously adopted by farmers in the commoditymarket. Our qualitative insights would not change ifwe assumed instead that a set of farmers T alreadyadopted MIG under the status quo. In fact, the nominalcommodity rate would decrease in the latter case com-pared to our current analysis (becoming cp(0)/µ(T)),which would imply that even fewer farmers (not inthe set T) would adopt the MIG technology throughthe commodity contract. Interestingly, the set of farm-ers adopting MIG through an incentive contract basedon commodity sourcing would remain the same (S ic),and so would the condition under which the topmakerwould find it optimal to offer such a contract (wN >�cp/(ct�µ)). Thus, under a highly fragmented supply,the MIG technology would only be adopted by a sub-set of farmers under commodity sourcing, motivatingthe need for direct sourcing.

Finally, we assumed that farmers incurred the samemarginal cost for adopting MIG, independent of theirproduction quantities. In practice, larger farms may

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incur smaller adoption costs, e.g., due to economiesof scale. In this case, the set of farmers adopting MIGunder the commodity contract would become Scc

⇤

{i: wi � (�cip/�µ)(µ0/cp(0))}, where �ci

p ⇤ cip(1)� cp(0).

Thus, the adoption of MIG would depend on eachfarmer’s individual cost elasticity of process yield. How-ever, our other qualitative results for commodity-basedsourcing remain unaltered: the topmaker would onlyoffer an incentive contract when the market is nottoo fragmented (i.e., wN > �cN

p /(ct�µ)), and only thelargest farmers (with wi � �ci

p/(ct�µ)) would adoptMIG through such a contract. Note that the topmaker’spreference for incentivizing only the largest farmersbecomes even stronger, since this can now be done atlower cost. Interestingly, under direct sourcing, costheterogeneity may have subtle effects similar to bar-gaining power: farmers with higher adoption costsmight be offered lower nominal rates �1, so that degen-eracy may once again prove useful (as per our briefdiscussion in the previous section).

7.2. Future Research DirectionsThere are multiple avenues for further research thatwould relax limitations of the current paper. One suchdirection would be a multiperiod stochastic modelcapturing long-term costs and gains of sustainability-related concerns. This would also allow explicitly mod-eling certain long-term decisions made by farmers,with direct economic and environmental implications.Production quantities are one such example, oftenrequiring large upfront investments (e.g., purchasingland) or practices with severe repercussions for theenvironment (such as deforestation in the case of palmoil crops). Such an extension would also allow cap-turing liquidity constraints impacting various supplychain parties, or other costs and benefits of directsourcing, with fixed or variable components.

Additionally, one could extend the model to capturecompetition among the topmakers, or the interactionamong other parties downstream in the supply chain.Lastly, one could also explore different contract designsthat could improve upon our commodity incentivecontract, eliminating the need to change the sourcingchannel. One example of the latter could be a com-modity sourcing contract that pays farmers based onthe realized average yield of the blend, instead of theexpected average yield. Although preliminary analysiswith this model suggests that it may not always dom-inate our current incentive contract, determining theexact conditions when this holds and characterizingthe power of such contracts would be an interestingdirection of future research.

AcknowledgmentsThe authors acknowledge constructive and thoughtful feed-back from two anonymous referees, the senior editor, and the

editor-in-chief, Chris Tang. Joann F. de Zegher acknowledgesDeborah Froeb at the Nature Conservancy for her early sup-port of this research, anonymous stakeholders in the Merinowool supply chain for inspiring this research, and Ovis XXIfor providing the data. Joann F. de Zegher was supportedby a Ph.D. fellowship from the Stanford Institute for Innova-tion and Entrepreneurship in Developing Economies (SEED)at the Stanford Graduate School of Business, and the SykesFamily Fellowship in E-IPER.

Endnotes1 This was conveyed during a personal communication with oneof the authors in January 2015. Due to the private nature of thesourcing strategies, the manufacturer preferred to not have theirname revealed.2 Our model effectively assumes that the topmaker’s forecast is con-sistent with the actual expectation of the average top yield; while thismay not hold in a given (single-period) interaction, it is reasonablefor it to hold on average, over several repeated, identical interactions.3 We obtained this information from a 2013 site visit of SustainableHarvest, located in Lima, Peru.4 This term frequently came up in several interviews by one of theauthors between May 2014 and January 2015.5 This was conveyed during a personal communication with one ofthe authors in 2015. Due to the private nature of the sourcing strate-gies, the manufacturer preferred to not have their name revealed.6 Our main results do not change when incorporating a representa-tive profit margin for farmers (profit margin not further disclosed, toprotect confidentiality).

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