Eco-design of eco-labels with coarse grades Omega

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Omega

journalhomepage:www.elsevier.com/locate/omega

Eco-design of eco-labels with coarse grades ^✩

Emre Nadar

^a,∗

, Mine Su Ertürk

^b

a Department of Industrial Engineering, Bilkent University, Ankara 06800, Turkey

b Graduate School of Business, Stanford University, Stanford, California 94305, United States

a rt i c l e i n f o

Article history:

Received 28 February 2019 Accepted 31 January 2020 Available online 3 February 2020 Keywords:

Sustainability Eco-labels Coarse grading

Quality and quantity competition

a b s t r a c t

Weconsiderathird-partyeco-labelcertifierthataimstoreducethetotalenvironmentalimpactofpro- ductiononnon-targetresourcesandthetotalconsumptionrateoftargetresources.Withtheseobjectives thecertifierdeterminestheenvironmentalstandardsforcoarsegradesofcertification.Eco-labeledpro- ductioninvolvesafixedinvestmentcost, alargermarginal productioncost,and arestricted accessto supply,whileeco-labeled productscommandapricepremium.Inresponsetoagivengradingscheme, weanalyticallycharacterizethesubgameperfectequilibriaforatwo-stagegameofenvironmentalquality investmentandquantitycompetitioninaduopolisticsetting.Wethenconductnumericalexperimentsto gaininsightsintowhetherandwhenmulti-gradeeco-labelsmaybemoreusefulthansingle-gradeeco- labelsbyprovidingbetterenvironmentalprotectioninthedualobjectivesofthecertifier.Whilemultiple gradesofaneco-labelmayappearinamarketwithasymmetricfirms,ourresultsindicatethatmultiple gradescanindeedbeusefulunderadditionalconditions:(i)whentheinvestmentcostsareasymmetric, (ii)whentheinvestmentandproductioncostsareasymmetric,eitherifthefirmwiththecostadvantage hassufficientlylowproductioncostundermildsupplyrestrictionsoriftheproductioncostsareverydif- ferent,or(iii)whenthesupplybasesareonlymoderatelyasymmetricandsufficientlylarge.Ourfindings uncovertherolethecostandsupplycharacteristicsofthemarketplayineco-designofeco-labels,calling intoquestionthecommonpracticeofofferingsingle-gradeeco-labels.

© 2020ElsevierLtd.Allrightsreserved.

1. Introduction

Over the last few decades consumers have been increasingly willing to pay for environmental quality,motivating firms to in- corporate green attributes into their products [12,40,59]. For en- vironmentalproductdifferentiation,sincetheself-claimsmadeby firmsareoftennotconsideredcrediblebyconsumers,third-party- certified eco-labels are attracting widespread interest [5,19,29]. Eco-labels are voluntary certifications that enable consumers to easily perceive differences inenvironmental quality amongprod- ucts. Currently, thereare more than 460eco-labels in 199coun- triesacross 25 industries(ecolabelindex.com). Among the promi- nent eco-labels are the Rainforest Alliance and the Fairtrade for agriculturalproducts,theForestStewardshipCouncil(FSC)forfor- est products, andthe Marine StewardshipCouncil (MSC) forma- rineproducts.Eco-labeledproductsmaycommandsignificantprice premiums (for instance,premiums ofup to75% forbananas;see Pottsetal.[54]).Thus,eco-labeledproductionhasdramaticallyin-

✩ This manuscript was processed by Associate Editor Joe Zhu.

∗ Corresponding author.

E-mail addresses: emre.nadar@bilkent.edu.tr (E. Nadar), mserturk@stanford.edu (M.S. Ertürk).

creased(seeAtkinsonandRosenthal[3],Goldenetal.[31],Howard andAllen[36],andCastkaandCorbett[13],forexamples).

Althougheco-labelsaimtotrulyrevealtheenvironmentalqual- ity of products, the amount of information conveyed via eco- labels isoften limited. The vast majority of eco-labelsonly indi- catewhethera firm surpassesa thresholdlevel ofquality ornot (i.e.,one-tier labelsof the pass/fail form). Asurvey by Harbaugh andRasmusen[35]showsthat,ofthe174eco-labelslistedateco- labelling.org, only five eco-labels report exact grades or grades fromagradingschemewithmultiplelevels(i.e.,multi-tierlabels).

Alloftheaforementionedeco-labelsareone-tierlabels,whilethe Cradle-to-Cradlecertificationisoneofthefeweco-labelswithsev- eraltiers (platinum,gold, silver, andbasic). Despite the popular- ityofeco-labelsinindustry,toour knowledgeno onehasdevel- opeda comprehensivemodelingframeworkthat seeksto address whycertifiersfrequentlypreferone-tier labelsoverthe multi-tier alternatives or how effectivethis practice is.In this research we investigatetheenvironmentalimpactsofvariouseco-labeldesigns (one-tiervs.multi-tier)indifferentduopolisticsituations(symmet- ricfirmsorasymmetricfirmswithrespecttokeyoperationalchar- acteristics)inordertoidentifywhetherandwhenmulti-tierlabels canhelpprovidebetterenvironmentalprotectionthanone-tierla- bels.

https://doi.org/10.1016/j.omega.2020.102209 0305-0483/© 2020 Elsevier Ltd. All rights reserved.

We consider a single third-party certifierwho issues an eco- labelwithtwotiers– regularandpremium– andspecifiestheen- vironmentalstandardsforbothtiers(thatwe refertoasthe‘eco- labeldesign’).Ouruseofasinglecertifiercanbejustifiedbynot- ingthe existenceof themanyeco-labels(especiallyamongthose withasingle-sectorfocus)thatdominatetheirrespectivemarket- places eitherglobally orlocally (see Potts et al.[54] andBowler etal.[10],forexamples).Forexample,Bonsucro– a single-sector initiative forcane sugar – dominates the market with a produc- tion volume ofmore than six timesthat ofFairtrade – the next mostcommon eco-label for cane sugar. In the foodand agricul- ture industry RSPO is very popular in Asia, whereas Organic is very commonin North America. In forestry, FSC is the onlycer- tificationschemeinNewZealand.Onereasonforsuchpracticesis that the presence ofmultiple eco-labels withdifferent standards inthesamemarketmaypotentiallyreducetheinformativenessof labeling, leadingto a ‘non-labeling’ equilibrium [34]. Our use of atwo-tier (ratherthan amulti-tier) eco-label designisbenign in ourduopolistic setting becauseat mosttwo certificate typescan appearinthemarketiftheeco-labelhastwoormoretiers.

The environmentalstandardofan eco-labelholdsthecertified producerresponsible forimprovements in (1)the environmental impactofproductiononnon-targetresourcesand(2)theconsump- tionrateoftarget finiteresources. Forexample,formarine prod- ucts, the MSClabel entailsprotecting by-catch speciesand habi- tats(dimension1) andleavingsustainable fishstocks (dimension 2).See Principles1 and2 oftheMSC labelatwww.msc.org. See alsoAgnewetal.[1],Ward[61],andGulbrandsen[32]fordetailed discussions.Improvementsin(1)maytranslate intoreducingdol- phinby-catchintunafishery,seaturtleby-catchinshrimpfishery, sealion by-catch inrock lobsterfishery, andfur seal by-catch in hokifishery.Onecanachievesuchimprovementsbyadoptingspe- cialfishinggearandmethods.Improvementsin(2)helpensurethe healthandresilienceoffishstocks.Ingeneral, afishstockiscon- sideredsustainablewhenatleast40–60%ofthetotalweightoffish ina particularplace remains afterfishing (oceanhealthindex.org).

Ourclassification ofthe eco-label requirements alsoseems to be validforforestproducts:theFSClabelentailsprotectingrareand threatenedspecies,biodiversity,andwatercourses(dimension1)as well asleaving representative sampleareas of native ecosystems (dimension2).SeePrinciple6oftheFSClabelatic.fsc.org.

Wedevelopatwo-stageduopolymodelofverticalproductdif- ferentiation: In stage one, each firm decides whether or not to makean investment in orderto improveits environmental qual- itylevelandundergothecertificationprocess.Ifafirmdecidesto makeaninvestment,itraisesitsenvironmentalqualitylevelupto theenvironmentalstandard ofeithertheregular orpremiumcer- tificate.Theinvestmentrequiredtoobtainaneco-labeliscostlyin terms of certifier’s auditingand licensing fees aswell as capital outlayfornewadvancedtechnologies(e.g.,theadoptionofspecial fishinggearformarineproducts).Instage two,eachfirm thathas madeaninvestmentinstageone iscertifiedaccordingly.Foreco- labeledproduction,the environmental standardrequires an envi- ronmentallybetterproduction methodindimension (1)(e.g.,the useofselectivefishingmethods)andrestrictedaccesstosupplyin dimension(2)(e.g.,thecatch limit forthe fishstock).Consumers are heterogeneous in their willingness to pay for environmental quality;thiscanonlybeascertainedby certificationstatus(nola- bel,regular, or premium). Ifone firm offers products ofsuperior quality,itdoessobycommandingapricepremium.

For our duopolistic market, in response to any given investment-level(and thus quality) choicesof the firms in stage one,we characterizethesubgame equilibriumproductionquanti- tiesin stage two (Proposition 1). Then, in response toany given grading scheme of the eco-label, we characterize the subgame perfectequilibriuminvestmentlevelsinstageoneandproduction

quantities in stage two (Proposition 2). The third-party certifier has the dual objectives of minimizing the total environmental impact of production on non-targetresources (dimension 1) and the total consumption rate oftarget resources dueto production (dimension 2). From the certifier’s perspective, the eco-label can be deemedusefulifthereexists an eco-labeldesign thatinduces atleast one of the two firmsto exert effortfor certification and leadstoimprovement overthenon-labeling situationinthe dual objectives.Supposethattheeco-labelisuseful.Thentheexistence of a second tier can be justified if, for each particular one-tier eco-label design, there exists an eco-label design that induces the two firms to enhance their quality levels for regular and premiumcertificates, respectively,andleadstoimprovementover thisparticularone-tiereco-labeldesigninthedualobjectives.

We then conduct numerical experiments to gain insights into theusefulnessoftheeco-labelsfromthecertifier’sperspective.We calculatetheParetooptimaleco-labeldesignsinthedualobjective problemofthecertifierineachofalargenumberofinstances.The eco-label is useful ifthe set of Pareto optimal eco-label designs doesnot contain the eco-label designthat setsthe standardsfor both tiersto bethe initialquality levelofthetwo firms(i.e.,the non-labeling situation).The two-tiereco-label is usefulifeach of theParetooptimaleco-labeldesignshasdifferentstandardsforthe two tiers that are both greater than the initial quality level. We have found that the eco-label is usefulin each of our instances, while the two-tier eco-label is useful in a significant number of cases. The latter result is incontrast to the commonpractice of offeringone-tiereco-labels.

Intuitively,the two-tier eco-label seemsto be bettersuited to duopolisticmarketswithasymmetricfirms.Ournumericalresults, however,suggest that offering a two-tier (rather thana one-tier) eco-labelinsuch marketswithoutcloselyexaminingthecostand supplystructuresofthefirmsmayprovidenoadditionalenviron- mentalbenefitinthedualobjectives.Specifically,ourresultsimply thatthetwo-tiereco-labelisusefulwhen:

(i) Thefirmsareasymmetricwithrespecttoinvestmentcosts;

(ii) The firms are asymmetric with respect to investment and productioncosts eitherifthe firm withthecost advantage has a sufficiently low production cost under mild supply constraints or if the firms have very different production costs;or

(iii) The firmsare only moderately asymmetric withrespect to supply constraints and their supply bases are sufficiently large.

Wehavealsoextendedourexperimentsbytakingtheperspec- tive of a certifier that has the objectives ofnot only minimizing thetotalenvironmentalimpactandthetotalconsumptionratebut alsomaximizing the total profitofthe firms.Thisextension may berealisticforeco-labelssponsoredbyindustrytradeassociations that seekto maximize theaggregate profits of theindustry. One sucheco-labelistheSustainableForestryInitiativeforforestprod- ucts[28].Wehavefoundthatthetwo-tiereco-labelmaybeuseful onlywhenthefirmshaveverydifferentandsufficientlylargesup- plybases.

Therestofthepaperisorganizedasfollows:Section2reviews the relatedliterature. Section 3 describes ourduopolistic setting, characterizes the subgame perfect equilibria, and formulates the eco-labelcertifier’sproblem. Section4presentsournumericalre- sultsforthecertifier’sproblemandSection5concludes.

2. Relatedliterature

Ourworkisrelatedtotheliteratureonstrategicqualitychoice models. In this literature, many papers consider vertical product

differentiation: Motta [53] compares the equilibrium quality lev- elsunderpricevs. quantitycompetition,andthoseunderfixedvs.

variablecostsofquality.Lehmann-Grube[45]revealstheeconomic benefits ofoffering high-qualityproducts in a two-stagegameof quality andpricecompetitionunderfixed costsofquality.Banker et al.[4] consider vertical differentiation in oligopolistic markets and analyze the impact of competition intensity on equilibrium qualitylevels.Chambersetal.[15]examinetheimpactofvariable productioncostsinatwo-stagegameofquality andpricecompe- tition.Matsubayashi[51]studiesqualityandpricecompetitionby allowing fordifferentiationviafactors otherthanquality andver- ticalintegrationamongfirms.BoccardandWauthy[7]formulatea three-stagegameofquality,capacitycommitment,andpricecom- petition,andanalyzetheimpactofquality costsonqualitylevels.

LaugaandOfek[44]developatwo-dimensionalverticaldifferenti- ationmodelandexaminetheroleofqualitycostsonproductpo- sitioning.Yayla-Küllü etal.[62]considerverticaldifferentiationfor multi-productfirmsinanoligopolisticmarketandanalyzetheim- pactsofresourceconstraintsandcompetitionintensityonproduct- mix decisions.Wedepartfromallofthesepapersby focusingon verticaldifferentiationviaacredenceattributeoftheproduct– the environmentalqualitylevel– thatcanbediscernedbyconsumers onlythrougheco-labels.

Several other papers investigate the effect of imposing min- imum quality standards (MQSs) to producers on social welfare:

Ronnen [56] considers a duopolistic setting in which the firms compete in quality andprice under fixed costs of quality and a mandatoryMQS.CrampesandHollander[18]extendthemodelof Ronnen[56] by allowing forvariablecosts ofquality,andValletti [60] considers qualityandquantity competitionunderfixed costs of quality.Ronnen [56] and Crampesand Hollander[18] demon- strate that the existence of an MQS improves the social welfare, whereas Valletti [60] shows that this result need not extend to quantitycompetition.JinjiandToshimitsu[38]generalizetheanal- yses ofRonnen[56] andValletti[60] byallowing the firmstobe asymmetric withrespect to quality costs. Kuhn [43] considers a verticallydifferentiatedduopolyundervariablecostsofqualityby allowingconsumerstoderivenotonlyaquality-relatedbenefitbut alsoaquality-independentbaseline benefit.Kuhn[43]showsthat anMQScanenhancethewelfareonlyifthebaselinebenefitissuf- ficiently low.Garella andPetrakis[30] analyze theimpacts of an MQS on quality levels andwelfare in oligopolistic markets when consumershaveimperfect informationaboutthequalityofgoods.

Inourstudy,unlikeallthesepapers,theeco-labelcertifiermakes acontinuouschoicefortheMQSforeachcertificatetype,andthe firmshavediscretechoicesinthelevelsofquality.

Our work is also related to the literature on eco-labeling schemes. In this literature, several papers highlight the potential benefitsofeco-labels:Inathree-stagegameofinvestment,quality provision, and pricecompetition, Amacher et al.[2]demonstrate that eco-labelsmayenablebetter environmentalqualitylevels by curbingexcessiveinvestmentundercertaincoststructures.Hamil- tonandZilberman[33]findthateco-labelsmayreducethesalesof fraudulently-labeledproductsundermonopolisticcompetition.Ina three-stagegameofproductiontechnology,signal,andpricecom- petition, Ibanez and Grolleau[37] show that eco-labels may im- provetheeconomicandenvironmentalperformancesofduopolis- tic markets. Bleda and Valente [6] assert that graded eco-labels mayinducefirmstoadoptcleanertechnologiesundercompetition.

We depart from all of these papers by analyzing andcomparing the implications of various eco-label designs (one-tier vs. multi- tier).

There are also papers that reveal the potentially adverse im- pactsofeco-labels:MattooandSingh[52]showthattheelevated pricesofeco-labeledproductsmaycauseincreasedproductionvol- umes.Dosi andMoretto[25] outlinethe situationsinwhicheco-

labels may raise investment for conventional technologies. Sedjo andSwallow[57]demonstratethateco-labelsmaydraintheprof- itsoffirmsundercertainconditions.Conrad[17]findsthattheen- vironmental quality choices of firms in a duopolistic setting de- viatefromthechoicesofawelfare-maximizingauthority. Bottega andDe Freitas [8]show that a compulsory MQSreduces the av- erageenvironmental quality if a public certifier(regulator) coex- ists with a private certifier (for-profit or non-profit institution).

Deltasetal.[23] revealthat anMQSmayreduce theaverageen- vironmentalqualityinahorizontallydifferentiatedduopolywhere the firmsmay differ intheir ‘greenness’levels. Fischerand Lyon [27]find thatthe environmental benefits may be smallerif a non- governmentalorganization (NGO)labelcoexistswithanindustry- sponsored label. Unlike these papers, we examine the impacts of various eco-label designs from the perspective of a certifier with dual environmental objectives in a vertically differentiated duopoly.Ourfindingssuggest thateco-labelscanhelp reduceen- vironmentalimpact and that multi-tier designs can enhance this benefitundercertainconditions.

Intheliteratureoneco-labelingschemes,theclosest papersto oursarethoseofLiandvan’tVeld[47]andFischerandLyon[28]. Li and van’t Veld [47] compare the implications of single-grade single-label,multi-gradesingle-label,andsingle-grade multi-label scenariosforeachofthreedifferentsponsortypes:industryspon- sorsareindifferentamongthesescenarios,environmentalistspon- sors may prefer multiple labels, and government sponsors may prefer multiplegrades. Fischerand Lyon[28] assess the environ- mental impacts of grading schemes and competition of the eco- labelssponsored by NGOs andindustry tradeassociations. When thetwosponsortypescompeteusingsingle-gradeeco-labels,com- petitionmayprovideeithermoreorlessenvironmentalprotection dependingonindustrystructure.Whentheycompeteusingmulti- gradeeco-labels,competition always provides less environmental protectionthanwouldtheNGOalone.Unlikethesetwopapers,we take into account not only environmental quality levels but also productionquantities– a legitimateconcernincasesof finitere- sources– inourassessmentofenvironmentalimpact.Wealsoin- corporatethesupplyconstraintsforproductionintoourduopolis- tic setting with possibly asymmetric firms. We are thus able to provide novel insights into the eco-design of eco-labels that are notavailableintheabovetwopapers.

3. Problemformulation

Weconsideramarketwithtwocompetingfirms(i=AandB).

The firms are initially capable of offering perfectly substitutable products sothat consumers areindifferent betweentheproducts thatthe firmsofferforthesameprice. Wedenote by

α

L theini- tialenvironmentalqualitylevelofbothfirms.Eachfirmmaymake aninvestmenttoimprovetheenvironmentalqualityofitsproduct.

Wedenotebye_ithepost-investmentqualityleveloftheproductof firm i. Establishingcredible information aboutthe environmental qualityof theproductis crucialforproduct differentiationin the market,andthird-partycertificationsareofteneffectiveindeliver- ingsuchinformation[20,55].Inourmodelthereisasinglethird- partyeco-labelcertifierwhoseproductlabelaccuratelyrevealsthe environmentalbenefitsofthe product.Consumersrespondto the credibleinformationthatisestablishedonlythroughtheeco-label issuedbythiscertifier.

Theeco-label certifiercan issueone ofthefollowing two cer- tificates:regularorpremium. Itdetermines theminimumquality levels requiredto obtainregular andpremium certificates, which we denote by

α

M and

α

H, respectively. Thus

α

L ≤

α

M ≤

α

H. If a firm chooses to improveits environmental quality,it must ob- tainaneco-labelinordertoreapthepotentialbenefitsoftheim- provedquality,strivingforeitheraregularorpremiumcertificate.

Anyinvestmentthatfailstomeettherequirementsoftheregular certification,anyinvestmentthat exceedstherequirementsofthe regularcertification withoutmeeting thoseofthepremiumcerti- fication,andanyinvestmentthatexceedstherequirementsofthe premiumcertificationhavenopositivereturntothefirm.Thus

α

L,

α

M,and

α

H are the only possiblequality levels that can exist in themarket.

WedenotebyI_i(e_i) thenecessarylevelofinvestmentforfirmi toachievethequalitylevele_i≥

α

L.Specifically,weassumethat

I_i

(

^ei

)

=

β

i

(

^ei−

α

^L

)

², (1)

where

β

i≥ 0.Forfirmi,atanygivenqualitylevel,asmallervalue oftheparameter

β

iindicatesabetterproductioncapabilityanda lowerinvestmentcost.Therearemanyexamplesofsimilarformu- lationsintherelatedliterature(see,forinstance,Banker etal.[4], Economides[26],Lehmann-Grube[45],Motta[53],andFischerand Lyon[28]).Wealsodenotebyc_i(e_i)theunitproductioncostoffirm iatqualitylevele_i.Becausetheenvironmentalstandardindimen- sion(1)oftenrequiresmorecarefulandselectiveproductiontech- niques that help reduce the environmental impact on non-target resources,itisnaturaltoassumethatc_i(e_i)isnon-decreasingine_i. We denote by q_i the production quantity of firm i. The pro- duction quantity of each firm is subject to limited supply. Sup- ply scarcity is a legitimate concern for manyproducts that ben- efitfromthedevelopmentofeco-labels.Examplesinclude,butare notlimitedto,eco-garments,seafood,ediblenuts,driedfruits,and wood (CBI Ministry of Foreign Affairs [14], Connell [16], Delmas etal.[21], Jonell etal.[39],and Boukherroubet al.[9]). Wede- noteby Q_i(e_i) themaximum possibleproductionquantity offirm iwithquality levele_i. Becausethe environmentalstandard indi- mension(2)oftenimposesarestrictedaccesstosupplyinorderto mitigatethedepletion oftarget resources,itis naturaltoassume thatQ_i(e_i)isnon-increasingine_i.

Asafirm increasesitsenvironmentalqualityandbecomescer- tified accordingly, consumers’ willingness to pay for its product alsoincreases. Consumers are heterogeneous intheir willingness topayforincrementalenvironmentalquality,whichwedenoteby

θ

^{.Weassume that}

θ

^isuniformlydistributedover[0,1].Thisas- sumptionisstandardintheliterature(see,forinstance,Motta[53], andKalraetal.[41]).Aconsumerlocatedat

θ

experiencesautility ofU(^e,p

| θ

)=

θ

^e− p ifshepurchasesaproductwithquality level eatpricep,andautilityof0ifnopurchaseismade.Aconsumer doesnot purchaseanyproductifher utilityfromthepurchaseof eachproductisnegative,andshepurchasestheproductmaximiz- ing her utility function otherwise. The competition between the twofirmscanbemodeledasatwo-stagegame:

Stage One: Eachfirm i ∈{A, B} is fullyinformed by thecost structure(i.e.,I_j(e_j) andc_j(e_j))andsupplyconstraint(i.e.,Q_j(e_j))of firmj=iaswellasitsown.The firmssimultaneously determine thequalitylevelsthattheywillofferinstagetwo:Eachfirmimay make no investment (i.e., e_i=

α

^{L); may make an investment of}

I_i(

α

M)toimproveitsqualityforaregularcertificate(i.e.,e_i=

α

M);

ormaymake an investmentofI_i(

α

H) toimproveits quality fora premiumcertificate(i.e.,e_i=

α

H).

Stage Two: Based on their quality level choices in stage one, the firms obtain their certificates at the beginning of stage two.

Thefirms andconsumers observethe certification status ofeach firmatthebeginningofstagetwo.Thefirmsthensimultaneously determinetheirproductionquantities.

We denote by p_i(e_A, e_B, q_A, q_B) the inverse demand function forfirm i ∈ {A, B} when the quality levels of firms A and B are e_A and e_B, and the production quantities of firms A and B are q_A and q_B, respectively. If e_A=e_B, the firms sell their products atthe same price(in equilibrium).If eA = eB, thefirm withsu- periorquality has the advantage ofhaving a higher selling price (inequilibrium).Section 3.1formulatestheinversedemandfunc-

tion and characterizes the Nash equilibria in the second stage subgame. Section 3.2 establishes the subgame perfect equilibria.

Section3.3describestheeco-labelcertifier’sproblem.

3.1. Thesecondstage

Inordertofindthesubgameperfectequilibria(inSection3.2), weneedtodeterminetheNashequilibriainthesecondstagesub- game.Tothisend, weformulate thepriceandprofitfunctionsof bothfirmsinstagetwo,characterizethebestresponseofeachfirm toevery possibleactionofits competitorinstagetwo, andinter- sectthebestresponsefunctionsofthetwofirms.

Supposethat firmsAandBofferqualitylevels e_A ande_B with pricesp_A andp_B,respectively.Alsosupposethat e_A > e_B.Forfirm B to have a nonzero market share, the price of firm B must be lower than that of firm A, but the quality per dollar of firm B mustbehigherthanthat offirmA(i.e., ^e_p^B

B > ^ep^A_A).Thisisbecause when the quality per dollar is lower for firm B anda consumer located at

θ

^{can derive a} nonnegative surplus from the product of firm B (i.e., ^e_p^A

A ≥^ep^B_B and

θ

^eB− pB≥ 0), it can be shown that this consumer always prefers to buy the product of firm A. The consumerlocated at

θ

^{buys the product offirm A ifand onlyif}

θ

^eA− pA≥ 0 and

θ

^eA− pA≥

θ

^eB− pB. Thus the set ofconsumers who buy the product of firm A is [

θ

¯,1] where

θ

¯=min

{ θ

^:0≤

θ

≤ 1,

θ

^eA− pA≥ 0,

θ

^eA− pA≥

θ

^eB− pB

}

^{.Since e}p^B_B > ^e_p^A_A,note that

θ

¯=min

{ θ

^:0≤

θ

≤ 1,

θ

^eA− pA≥

θ

^eB− pB

}

^{.Theconsumerlocated}

at

θ

^{buys the product of firm B if andonly if}

θ

^eB− pB≥ 0 and

θ

^eB− pB≥

θ

^eA− pA.Thusthesetofconsumerswhobuytheprod- uct offirm Bis[

θ

,

θ

¯^]where

θ

=min

{ θ

^:0≤

θ

≤ 1,

θ

^eB− pB≥ 0

}

^.

Finally,theconsumerlocatedat

θ

∈[0,

θ

^{]doesnotbuyanyprod-}

uct.HencedemandfortheproductoffirmAisgivenby DA

(

^eA,eB,pA,pB

)

^=1−p_e^{A− pB}

A− eB,

anddemandfortheproductoffirmBisgivenby DB

(

^eA,eB,pA,pB

)

^{= p}_e^{A− pB}

A− eB − pB

eB =eBpA− eApB

eB

(

^{eA− eB}

)

^.

Now suppose that e_A=e_B.Because theproducts areperfect sub- stitutes in this case, the firms must choose the same price (i.e., p_A=p_B).Thus:

DA

(

^eA,eB,pA,pB

)

^+DB

(

^eA,eB,pA,pB

)

^{=1− p}_e^A

A =1−pB

eB. Noticethat thetotaldemandinthemarketisnolargerthanone.

(SeeMotta[53] andKalraetal.[41]forsimilardemandformula- tions.)

Aswewanttoincorporatethesupplyconstraintintotheopti- mizationproblemofeachfirmi∈{A,B}bylimitingtheproduction quantityq_i,wewillcalculatetheinversedemandfunctionforeach firm i, whichisa mapping fromtheproductionquantities ofthe firmstothesellingpriceoffirmi.Solvingtheabovedemandequa- tions forprices p_A andp_B,andsubstituting q_A andq_B forD_A( · ) andD_B( · ),respectively,we obtainthe followinginversedemand functionsforfirmsAandBwhene_A ≥ eB:

pA

(

^eA,eB,qA,qB

)

^{=eA− eAqA− eBqB}

and

pB

(

^eA,eB,qA,qB

)

^{=eB− eBqA− eBqB.}

Theinversedemandfunctionswhene_A ≤ eBcanbeeasilyobtained by interchanging the subscripts A and B in the above equations.

(SeeDixit[24],SinghandVives[58],andBankeretal.[4]forsim- ilarpriceformulations.)Intheremainderofthepaper,forbrevity, we restrict our analysis to settings in which (i) the production quantitiesinequilibriumareguaranteedtobenonnegativeand(ii)

thetotalproductionquantityinequilibriumisguaranteedtobeno largerthanone.Withtheabovepricefunctions,wearenowready toformulatetheprofitofeachfirmiinstagetwoasafunctionof theenvironmentalqualitylevelsandproductionquantitiesofboth firms:



i2

(

^eA,eB,qA,qB

)

=pi

(

^eA,eB,qA,qB

)

^qi− ci

(

^ei

)

^qi

subjecttoq_i≤ Qi(e_i).Bycharacterizingthebestresponsefunctions of thetwo firmsandintersecting thesefunctions, we are ableto findtheNashequilibriainstagetwo:

Proposition1. SupposethatfirmsAandBofferqualitylevelse_Aand e_B, respectively, in stage two. Then the Nash equilibrium quantities whene_A≥ eBcanbespecifiedasfollows:

(^q∗A(^eA,eB),q^∗_B(^eA,eB))

=

⎧⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎨

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎩

_{2eA−eB−2cA (eA )+cB (eB )}

4e_A−eB ,^{eA+cA (eA )} 4⁻²e_A⁽−e^eAB^{/eB ) cB (eB )}

 if ^2eA−eB−2_4e^{cA (eA )+cB (eB )}

A−eB ≤ QA(^eA)^{and eA+cA (eA )} 4⁻²e_A⁽−e^eAB^{/eB ) cB (eB )} ≤ QB(^eB),

Q_A(^eA),^{eB−eBQA (}₂^e_e^A_B ^{) −cB (eB )}  if ^2eA−eB−2_4e^{cA (eA )+cB (eB )}

A−eB >Q_A(^eA)^{and eB−eBQA (}2^ee^AB ^{) −cB (eB )} ≤ QB(^eB),

_{eA−eBQB (eB ) −cA (eA )}

2eA ,Q_B(^eB) if ^{eA−eBQB (}₂^e_e^{B ) −cA (eA )}

A ≤ QA(^eA)^{and eA+cA (eA )} 4⁻²e_A⁽−e^eAB^{/eB ) cB (eB )} > QB(^eB), (^QA(^eA),Q_B(^eB))

if ^{eA−eBQB (}₂^e_e^{B ) −cA (eA )}

A >Q_A(^eA)^{and eB−eBQA (}2^ee^AB ^{) −cB (eB )} > QB(^eB). Proof of Proposition 1. We first characterize the best response of firm A to action q_B of firm B when e_A ≥ eB: BR_A(e_A, e_B, q_B) denotes the action that maximizes A2(e_A, e_B,q_A, q_B) subjectto q_A ≤ QA(e_A).Notethat ^∂A2(e_∂^A,e_q^B,qA,qB)

A =e_A− 2e_Aq_A− eBq_B− cA(^eA) and ^{∂2A2(eA,eB,qA,qB)}

∂^q2_A =−2e_A<0. Thus, from the first order con- dition, the unconstrained maximizer of A2(e_A, e_B, q_A, q_B) is

e_A−eBq_B−cA(e_A)

2e_A . But ifQ_A(^eA)< ^eA−eBq2^Be^−c_A^A(eA), it is optimal to pro- ducethequantityQ_A(e_A).Hence,

BRA

(

^eA,eB,qB

)

=min



eA− eBqB− cA

(

^eA

)

2eA ,QA

(

^eA

)

.

We also characterize the best response of firm B to action q_A of firm A when e_A ≥ eB: BR_B(e_A, e_B, q_A) denotes the action that maximizes B2(e_A, e_B, q_A, q_B) subject to q_B ≤ QB(e_B). Note that

∂B2(^eA,eB,qA,qB)

∂^qB =e_B− eBq_A− 2e_Bq_B− cB(^eB)^{and ∂2B2(e}_∂^A_q^,e2^B,qA,qB)

B =

−2e_B<0.ThustheunconstrainedmaximizerofB2(e_A,e_B,q_A,q_B) is ^eB−eBq₂^A_e^−cB(eB)

B .ButifQ_B(^eB)< ^eB−eBq2^Ae^−c_B ^B(eB),itisoptimaltopro- ducethequantityQ_B(e_B).Hence,

BRB

(

^eA,eB,qB

)

=min



eB− eBqA− cB

(

^eB

)

2eB ,QB

(

^eB

)

.

Intersectingthebestresponsefunctions,weobtainthefourdiffer- entNashequilibriumsolutionsinProposition1andtheconditions ensuringeachoftheseNashequilibriumsolutions. 

3.2. Thefirststage

We denote by ^∗i2(^eA,e_B) ^{the second stage} equilibrium profit offirmi asa functionoftheenvironmentalqualitylevelsofboth firms.Onecaneasily calculate^∗_i2(^eA,e_B)^{by pluggingthesecond} stageequilibriumquantitiesofthefirmsassociatedwiththequal- ity levels e_A and e_B (available from Proposition 1) into the sec- ondstageprofitfunctionoffirmi.Recallourdefinitionsof

α

L,

α

M, and

α

H.We labelthepair(

α

M,

α

H) asthetwo-tier eco-label de- signspecified by thecertifier. Notice that ourequilibriumresults

(below)fortwo-tier designs canbe extendedtoone-tier designs:

If

α

M=

α

H, theregular andpremium certificates are identical.If

α

M=

α

L,theregular certificatereducesto thenon-labelingsitua- tion.Thesetwo specialcasescorrespond toone-tier eco-labelsin whichacertificateiseitherawardedornotawarded.Wenextfor- mulatethetotalprofitofeachfirmi∈{A,B}instagesoneandtwo asafunctionofthequalitylevelse_A,e_B∈{

α

L,

α

M,

α

H}:



i1

(

^eA,e_B

)

⁼



^∗i2

(

^eA,e_B

)

^{− I}i

(

^ei

)

^.

Wenowestablishthesubgameperfectequilibriaforourtwo-stage game:

Proposition 2. Suppose that (a) ^∗A2(^eA,e_B)− IA(^eA)≥ max_e∈{α

L,αM,αH},e=e_A

^∗_A2(^e,e_B)− IA(^e)



and (b) ^∗_B2(^eA,e_B)− IB(^eB)≥ maxe∈{αL,αM,αH},e=e_B

^∗B2(^eA,e)− IB(^e)



. Then the equilib- riumqualitylevelsof firmsAand Baree_A ande_B,respectively,and theirequilibriumquantitiesareasdescribedbyProposition1. ProofofProposition2. GiventhatfirmBchoosesqualitylevele_B instageone,point(a)impliesthatthebestresponseoffirm Ain stageone isto choosequalitylevel e_A.Giventhatfirm Achooses quality level e_A in stage one, point (b) implies that the best re- sponseoffirmBinstage oneistochoosequalitylevele_B.Hence, theequilibriumquality levels offirmsA andBare eA andeB,re- spectively.Theequilibriumquantitiesinstagetwoarethesameas those describedby Proposition 1under the condition setthat is satisfied. 

3.3.Thecertifier’sproblem

Wedenoteby e^∗_i(

α

M,

α

H)^the equilibriumquality leveloffirm i (available from Proposition 2) in response to the eco-label de- sign(

α

M,

α

H).Weassumethattheenvironmentalimpactperunit of production is linearly and inversely proportional to the envi- ronmentalquality of the product, andthe environmental impact iszeroatthehighestpossiblequalitylevel.(SeeFischerandLyon [28]forasimilarenvironmentalimpactcalculation.)Theeco-label certifierhasthedualobjectivesofminimizingthetotalproduction quantityinequilibrium,whichcanbewrittenas

Q

( α

M,

α

H

)

=q^∗_A

(

^e∗A

( α

M,

α

H

)

,e^∗_B

( α

M,

α

H

) )

+q^∗_B

(

^e∗A

( α

^M,

α

^H

)

,e^∗_B

( α

^M,

α

^H

) )

^,

andthetotal environmentalimpact inequilibrium, which canbe writtenas

E

( α

M,

α

H

)

=

( α

− e^∗A

( α

M,

α

H

) )

^q∗A

(

^e∗A

( α

M,

α

H

)

,e^∗_B

( α

M,

α

H

) )

+

( α

− e^∗B

( α

M,

α

H

) )

^q∗B

(

^e∗A

( α

M,

α

H

)

,e^∗_B

( α

M,

α

H

) )

where

α

^{isthehighestpossiblequality level.Aneco-label design}

(

α

M,

α

H)isParetooptimalifandonlyifthereisnoother feasible eco-label design (

α

M,

α

H) ^{such that Q}(

α

M,

α

H)≤ Q(

α

M,

α

H) ^and E(

α

M,

α

H)<E(

α

M,

α

H), orsuch that Q(

α

M,

α

H)<Q(

α

M,

α

H)^and E(

α

M,

α

H)≤ E(

α

M,

α

H)^.WedenotebyP thesetofParetooptimal eco-labeldesigns.

Definition1. Fromthecertifier’sperspective,theeco-labelisdeemed useful if and onlyif (

α

L,

α

L)∈/P, whereasthe two-tier eco-labelis deemed useful if and only if

α

^M =

α

^L,

α

^H =

α

^{L, and}

α

^M =

α

^H,

∀

(

α

M,

α

H)∈P.

Iftheeco-labelisusefulaccordingtoDefinition1,thecertifier isabletospecifyenvironmentalstandardsforitseco-labelthatnot onlyinduceatleastoneofthetwofirmstogetcertifiedbutalso providebetterenvironmentalprotectionthanthenon-labelingsit- uationinthedualobjectives.Ifthetwo-tiereco-labelisuseful,the certifieris able to specifyenvironmental standardsthat not only inducethe twofirmsto getregular andpremiumcertificates, re- spectively, butalso provide better environmental protectionthan anyspecificone-tiereco-labeldesigninthedualobjectives.

Fig. 1. 2D projections of 3D graphs for the subgame perfect equilibria. αL = 1 , I A(e ) = ^(e₃₀⁻¹₀⁾₀² , I ^B(e ) = ^(e₁₀⁻¹₀₀⁾² , c ^A(e ) = c B(e ) = ₂₀^e2₀₀ , Q ^A( e ) = Q B( e ) = 0 . 5  1 −₁₅₀₀^e−1

. Darker color indicates lower value. The equilibrium solution with the highest total profit appears in case of multiple equilibria.

AswecouldnotanalyticallycharacterizethesetofParetoopti- maleco-labeldesigns,wecalculatethissetwiththecompleteenu- merationmethod inour numericalexperiments inSection 4.We demonstratebelowourstepsincalculatingtheParetooptimalset inanumericalexample,providingexplanations ofourkey obser- vations.Weconsideraduopolisticsettingwhere

α

L=1,

α

=1000, e_A,e_B∈

{

¹,...,1000

}

,I_A(^e)= ^(e₃₀⁻¹₀₀⁾², I_B(^e)=^(e₁₀⁻¹₀₀⁾², c_A(^e)=c_B(^e)=

e²

2000,andQ_A(^e)=Q_B(^e)=0.5



1−₁₅₀₀^e−1



.Notice thatthefirmsare asymmetric with respect to only investment costs: firm A can achievethesame qualitylevelasfirm Bwithalower investment cost.Figs. 1–2 exhibit the subgame perfect equilibria conditional ontheeco-labeldesign(

α

M,

α

H)inourexample.

The firms are not certified if

α

M is large (the top right triangular-likeregions inFig.1aandb).Thisisbecauseveryhigh standards involve high investment/production costs and severe supply restrictions. Firm A gets certified if

α

M is low: it prefers thepremiumcertificateif

α

H issmall(the bottomleft triangular- like region in Fig. 1a), and the regular certificate otherwise. But firmBgetscertifiedif

α

Mistoolow: itprefersthepremiumcer- tificate if

α

H is too small (the bottom left triangular-like region inFig. 1b), and the regular certificate otherwise. Hence, because firm A ismore advantageous thanfirm Bin termsof investment cost,thequality leveloffirm A isno lessthanthat offirm Bfor each specific eco-label design. The firms offerthe same quantity

if no firm is certified (the top righttriangular regions in Fig.1c andd), orif both firms get the premium certificate (the bottom left triangular-like regions in Fig.1c and d), or ifboth firms get the regular certificate (the bottom right trapezoid-like regions in Fig.1candd).Whenthefirmshavethesamecertificate,thequan- tityofeach firm slightlygrowsasthestandard forthecertificate drops: thefirms focusmore onimproving their quantitiesby of- fering lower prices for their products withlower standards. The quantity offirm A isalways nolessthan that offirm Biffirm A hassuperiorquality(theregionsinFig.1canddotherthanthose depictedabove): Thefirms refrainfromhigh-standardlabels that requirelargeinvestment costs.Thus only low-standardlabels can ariseinequilibrium.Alow-standardlabelinducesfirmAtooffera smallpricepremium.Sincethelow-standardlabelonlyslightlyin- creasestheproductioncost,firmAcanaffordapricepremiumthat issmallenoughtoraiseitsdemand.Theincreaseddemandcanbe metthanks tothemildsupplyrestrictionsofthelow-standardla- bel.

The Pareto optimal set in our example is P=

{

(¹,101), (101,101), (85, 370)}∪{(101, 356), (101,357), ..., (101, 1000)}. For (

α

M,

α

H)∈P

\ {

(⁸⁵,370)

}

,bothfirmschoosethequalitylevel101, which is the highest possible level that can arise in equilib- rium when the firms have the same certificate. Fig. 2 indicates that the totalproduction quantity islowest when (

α

M,

α

H)∈P

\

{

(⁸⁵,370)

}

^{. For} (

α

M,

α

H)=(⁸⁵,370), firms A and B choose the