Economics of Safe Drinking Water

8/2/2019 Economics of Safe Drinking Water

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The Board of Regents of the University of Wisconsin System

The Economics of Safe Drinking WaterAuthor(s): Robert Innes and Dennis CoryReviewed work(s):Source: Land Economics, Vol. 77, No. 1 (Feb., 2001), pp. 94-117Published by: University of Wisconsin PressStable URL: http://www.jstor.org/stable/3146983 .

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The Economics of Safe DrinkingWaterRobertInnes and Dennis CoryABSTRACT.Thispaperstudiesa drinkingwatermarketin which a water company, aced withrandomcontamination,hoosesa treatmentys-tem,treatmentevels,and whether o notifycon-sumers hattheyshoulddrinkbottledwaterratherthanriskexposure o contaminantsn thetapwa-ter. The paper describesefficientpractices in-cludingprotocolswhichprescribewhena com-pany should notify customersto drink bottledwater, and regulatorystandardson post-treat-mentwaterquality hatdependupon systemsize,the extentof contamination,nd the customerno-tificationdecision.Implicationsor contemporarysafe drinkingwater aw are discussed. JELL51,Q25).

I. INTRODUCTIONTheprovisionof safedrinkingwater s es-sential n maintaininghequalityof life in allcommunities.Unfortunately,roundand sur-face sourcesof drinkingwater can be con-taminated y bacteriarom humanor animalsources,overflowing tormsewers,defectivestorage tanks, leaking hazardous andfills,pesticides and fertilizersfrom agriculturalrun-off,undergroundnjectionof hazardouswastes, decay productsof radon and ura-nium, and industrialsolvents (U.S. EPA1994).Once contaminationasoccurred,heabilityof communities o providesafe andaffordabledrinkingwater is determinedbycost-effective reatment nddeliveryto con-sumers.Treatmentand deliveryare largelythe concernof publicwatersystems, legallydefinedas systemswhich servepipedwaterto atleast15 serviceconnectionsorregularlyserve an averageof at least 25 people eachday at least 60 days per year (U.S. EPA1993).'In the UnitedStates,the Safe Drink-ingWaterAct (SDWA)governspublicwatersystemsby prescribingdrinkingwaterstan-dards orcontaminants,reatmentechniques,sampling regimens, record keeping proce-

dures,andpublicnotification rotocolswhenSDWArequirementsavebeenviolated.The success of the SDWA in preventing

diseaseis a subjectof some debate(NRDC1994). Between 1986 and 1992, the Centersfor Disease ControlandPrevention eporteda total of 102 drinkingwater disease out-breaks inkeddirectlyor indirectly o micro-scopic bacteria,virusesor parasitesstriking34,155 people in 35 states. In 1993, approxi-mately400,000 people in Milwaukeealonebecame ill and over 100 died when cryp-tosporidium lippedthroughwater-filtrationplants.In fact, some expertsbelieve that asmanyas 25 outbreaks o unreportedor ev-ery 1 that is documentedbecausesymptomsare oftenconfusedwith other llnesses.If so,as manyas 1 in 8 Americansarebeing ex-posed to potentiallyharmfulcontaminants(Friedman1996). On the otherside of thiscoin are potentialillnesses avoidedby theSDWA. For example, the EnvironmentalProtectionAgency (EPA)estimatesthat theSurface WaterTreatmentRule alone helpsavoid90,000 cases annuallyof acutegastro-enteritis,and that the Lead andCopperRuleprotects 140 million people, including 18million children,from exposure to unsafelevels of lead (U.S. GAO 1992). Such bene-fits do not come without cost. The GeneralAccountingOffice(U.S. GAO 1992)has es-timated hat ullcompliancewith theSDWA,across all communitywatersystems,wouldcost$1.4 billionannuallywithmany systemshavingto install new equipment.

Theauthors reprofessorsntheDepartmentf Ag-ricultural nd ResourceEconomicsat theUniversityofArizona.Bothareindebted o an anonymous eviewerandProfessorBromleyfor very helpfulcommentsonearlierdrafts,as well as instructive onversationswithRulon Pope, Erik Lichtenberg,Dave Sunding, andBrianWrightat various tagesof this research.The au-thorsarealsograteful or the commentsof seminarpar-ticipantsar the Universityof Arizona, he agriculturalrisk meetings,MonashUniversity,and the AustralianNationalUniversity.As always,responsibility or theviews expressedhere,andfor any remaining laws inthe paper,residessolely with the authors.1 Over85%of Americans eceivetheirdrinkingwa-ter frompublicwatersystems(Friedman 996).Land Economics * February2001 * 77 (1): 94-117


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77(1) Innesand Cory:TheEconomicsof Safe DrinkingWater 95Economiclogic can provideinsightsintoboththeappropriateettings ordrinkingwa-ter standardsand the design of regulatorypolicy. Although economists have exten-sively studied the processandregulationofwaterpollution,relatively ittleattentionhasbeen paid to the process and regulationofwater reatment nddelivery,givencontami-nation hathasalreadyoccurred.2 otableex-ceptionsare recentpapersthat have recog-nized the importance f victimmitigation nthe watercontext.3 n this work, victimsofwater contamination-the water consum-ers-can undertake ostly measures hat re-duce the harm o whichtheyareexposed.Inpractice,however,therearesignificant con-omies of scale in both the processof watertreatmentand in the acquisitionand pro-cessingof information bout he nature f thecontamination,he healthrisksit poses, andtheappropriatendavailablemethodof treat-ment.Due to these economiesof scale,watertreatments conductedby companieswho donot themselves sufferthe harmfromingest-ing anycontaminatedwater hat heydeliver.Of course,mitigationmay also be done by

consumers hemselves,who can switchfromdrinking apwater o drinkingbottledwater.4The multipledecisionsinvolved in this pro-cess-and the regulatoryneed to elicit be-havior romwatercompanies hatreflectsso-cietal interestsin safe drinkingwater-areourcentral ocus in this paper.Specifically, n view of the importance fsafe drinkingwater regulationin practice,ourpurposehere is to presentandanalyzearealistic but tractablemodel of watertreat-ment and use in the presenceof (1) randomcontamination; 2) a water companytreat-mentprocessthat nvolvesbothfixedinvest-ments in treatmentsystems and variabletreatmentnputsthat can be chosen ex-post,afterthelevel of contaminationas beenob-served;and(3) a consumeralternative o thedrinkingof contaminatedap water,bottledwater.We arefirst concernedwith optimality ntreatment nduse (in Section3). For exam-ple, how does the level of watercontamina-tion and the size of a company'scustomerservice populationaffect optimal treatmentactivityandthe optimaldecisionon whether

to substitutebottled waterfor tap waterindrinking?And how does a switchto bottledwater affect optimal tap water treatment?Under an optimal policy, we find thatpost-treatmentwaterquality alls withhigher ev-els of contamination; hencontaminationssufficiently great (and treatmentcosts arecorrespondinglyhigh), consumers are ad-visedto drinkbottledwaterand thetapwateris treated to a lower "non-drinking-use"qualitystandard hatimposes a low cost oftreatment.naddition,we findthat argerwa-ter systems optimally invest more in thetreatmentsystem and treatto higher stan-dardsof quality.InSection4, we turn o theregulatoryideof the problem,how to promptefficient be-havior fromwatersuppliersusingeither ia-bility or regulatory tandards nforced withsufficientlystiff fines.Our mainpolicy con-2 The importance f water reatment, s an alterna-tive topollutionprevention,s widely recognizedn theeconomics iterature.n a generalsetting,PolinskyandShavell (1994) examinethe incentiveeffects of differ-ent liabilityrulesin inducing irmsto employoptimallevels of care and mitigation.Sunding,et al. (1995)study optimaltreatment n the context of CaliforniaDBCPcontaminationsee also Lichtenberg, ilberman,and Bogen 1989). Lichtenberg ndPenn(1996) studythe choicebetweenpreventing ndtreatingnitrate on-taminationof Marylandwaters.Barrettand Segerson(1997) examine the choice between preventionandtreatmentwhen policymakerspursueobjectivesotherthanPareto fficiency.Conceptually,heseanalysesdif-fer fromoursbecausethey do not focus on the treat-mentprocess,and heyabstractrom he consumermiti-gation andregulatory tandard ettingthat arecentralto ouranalysisof drinkingwatermarkets.3 See Segerson 1990), Miceli andSegerson 1993)

and Wetzstein and Centner(1992). Also see Oates(1983) and ShibataandWinrich 1983) for studiesonvictim mitigation in pollution control and Shavell(1983) andGrady 1988)forvictimmitigationn liabil-ity determination.4 An alternative onsumermitigation trategy s toinstallwater reatment evices in one's home.Suchde-vices generallyemploy the same technologiesas docentralized ystems.Due to economiesof scale in thesetechnologies,and in theiroperationand maintenance,watercompany reatment s almostalwaysmore cost-effectiveforall butthetiniestsystems NRC1997).Forexample, n a costcomparison etweenhometreatmentand a companygranular ctivatedcarbontechnology,

Goodrichet al. (1992) find that the home devices areonlycost-effectivewhenthereare ewerthan20 serviceconnections. n thispaper,we assumethatwater reat-ment is done at the company evel.


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96 Land Economics February2001clusionis that economicefficiencyis servedby a regulatory egimethat has two compo-nents:(1) protocols hatprescribeboth whena companyshouldnotifycustomers o drinkbottledwater,and oftenalso when it shouldnot notifyandinstead treat to safe drinkingwaterstandards;nd(2) post-treatmentaterqualitystandardshatrise with the size of theservicepopulation,all with initiallevels ofwater contamination, all when consumersareefficientlynotified o drinkbottledwater,andgive thecompany reereignto designef-ficient treatmentystems.However,if the regulatory egimeis en-tirely "performance-based''-tyingall stan-dardsand notificationprotocols o levels ofpost-treatmentaterquality-then it will of-ten promptan inefficientcompanyaversionto notifyingcustomers hattheyshoulddrinkbottledwater.As a result,customernotifica-tion will occur less frequently han is effi-cient;thecompanywill treatwater o aninef-ficiently high standardof quality (when itinefficientlyails to notify);and hecompanywill overinvestn the treatmentystem n or-der to lower its ex-postcosts of supplyinghighqualitywater.Thereason hat irmsmayinefficientlyail tonotify s asfollows: Whenwater contamination s sufficiently great,therecan be health benefitsassociatedwithconsumers switching from drinking opti-mally treated(but imperfect) tap water todrinkingbottledwater; hese benefitsare off-set by highercosts of bottled water deliver-ies, net of cost savingsfrom lower treatmentstandards hatapplywhen consumersdon'tdrink hetapwater.A publicwatercompanythat s subject o efficientpublicutility regu-lationmustpaythe net costs of switching oa bottledwaterregime,butdoesnotreapthehealth benefitsof the switch. The resultingincentive to undernotify an be curedby ty-ing the notificationprotocol to the initiallevel of watercontamination,atherhanthecompany-controlledhoiceof post-treatmentwaterquality.Theseconclusionssuggestsome tentativeprescriptionsfor the design of the SafeDrinkingWater Act. As we discuss morefully in our concludingSection5, some ofthese prescriptions re heededin the recentreauthorizationf theSDWA;othersare not.

II. THE MODELWe consider a risk neutraleconomy inwhich a watercompanytreatsand deliverstap waterto a homogeneouspopulationofsize N. The companyobtains ts water fromsurfaceor groundsources. Untreatedwaterfromthese sources has a quality evel of X.The company reatsthe water to bring t upto a quality evel of u > X. Higher evels ofwaterquality mprovethe healthand safetyof wateruse in a sense madeprecisebelow.The pre-treatmentincoming)waterqual-ity,X,has theprobability ensityg(X) onthesupport,X,X).Theprobabalisticatureof Xreflects nherent andomnessn the dispersalof contaminantsn the water streamand/ortemporal luctationsn waterqualitydue toseasonalpatternsn the weatherandproduc-tion activities hatcause contamination.

The WaterConsumersThewatercompany'scustomersuse waterfor two purposes:1) drinking; nd(2) otheruses that entail a much reducedexposure o

anycontaminants. he "otheruses" includeboth "residual isk" uses such as showeringandwashinghandsand "no risk" uses suchas flushing oilets andwateringgardens.Consumersare assumed o drinka given(fixed) amountof water,w.5 However, fortheirnon-drinkingses, consumersmayvarytheir waterconsumptionn responseto thepricethattheyarecharged or water.A con-sumer's total water consumption, or bothdrinkingandnon-drinking ses, will be de-noted by w. Excluding any health effectsfrom their water consumption,each con-sumer obtains the gross monetarybenefitB(w),whereB'(w)> 0 andB"(w)< 0 (non-drinkingwaterconsumptionyields positivemarginalbenefits that decline as the con-sumerproceeds o less valuableuses).Fortheirdrinkingwaterneeds,consumershaveanalternativeo tapwater: heycanbuybottledwater.Bottledwater s assumed o betreatedo a fixed andhighlevelof quality,u,with backgroundliability and regulatory5In Arizona, or example,householdsdrinkaboutone half of one percentof theirwateruse (Gelt 1996).


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77(1) Innes and Cory: The Economics of Safe Drinking Water 97

standardsufficient o ensure hatbottledwa-teralwaysmeetsthisqualitystandard.6on-sumerswill wantto drinkbottledwaterwhenthequalityof thetapwater s sufficientlyowand, hence, the health risk associatedwithdrinkingthe tap water is sufficientlyhigh.Forsimplicity,however,we assumethatthecost of using bottled water for "residualrisk" uses exceedsanyexpectedhealthbene-fits fromdoingso, andhence,consumersal-ways use tap water for non-drinkingpur-poses. This assumptionwill be valid whenthe volume of residualrisk wateruse is rela-tively large, he cost of bottled vs. tap)wateris sufficientlyarge,and/orhealthrisksasso-ciated with residualrisk use are sufficientlysmall.7When a consumeruses tapwaterfor bothdrinkingandnon-drinking urposes, he suf-fers an expectedhealth "damage" or costequal oDAu),whereDA'(u)< 0 andDA"(u)> 0 (higher water quality reduces healthcosts ata non-increasingate).If a consumerinsteadbuys bottled waterto drink,she willincur the purchasecost of bottledwater, -,andan expectedhealthcost of DB (u), whereDB'(u) 5 0 (higher apwaterqualitymayre-duce the healthcosts of "residualrisk"use)andDB"(u) = 0 (anormalizationf thewaterqualitymeasureu).8Figure 1 depictsthe relationship etweenthe health damage functions, DA(u) andDB(u).Because the drinkingof wateryieldsa much greaterconsumerexposureto anywatercontaminants,marginalhealthbenefitsof increasedtap water quality are higherwhen consumers drink the tap water:-DB'(u) < -DA'(u). However,if tap waterhas the samehigh quality evel as does bot-tled water,expectedhealthdamagesare thesame to theconsumer,whether hedrinks apwater or bottledwater:DA -) = DB(u).Water Treatment

The local water supply companymakestwo choices in the watertreatmentprocess.First, it chooses a treatment apacityy ex-ante, before observing any realization of X,theincomingwaterquality.Whenmaking tstreatment capacity choice, the companyknows the probability distribution of X.

Higherlevels of treatment apacitylead tolower "variable osts" of treatingwater o agiven quality evel u (foranygivenX). Sec-ond, the watercompanyselects the level oftreatmentu ex-post,afterobservingX.96 In the UnitedStates,approximatelyne in fifteenU.S. householdsbuy bottleddrinkingwater,spending$2.7billionannually n almost700 brands Gelt1996).In our model, and in practice, hefunctionof bottledwater s to providean alternativeo tapwater,albeitathigh cost, that "tastesbetter, s safe andhealthy,or isfree of contaminants" conclusionof the GAO, re-ported n CNI 1991). A suitablyhigh level of bottledwaterquality_is thusanoptimalproperty f thisprod-uctwhich,forsimplicityandwithout oss in generality,we take to be exogenous n thispaper.Ouranalysis snonetheless obust o uncertaintyn bottledwaterqual-ity, with u representingnexogenouscertainty quiva-lent. Althoughbottled waterhas not alwaysbeen freeof contaminantsn practice U.S. WaterNews 1996),the recent reauthorizationf the SDWA strengthensgovernment egulation f bottledwaterqualityby theU.S. Food and DrugAdministration,equiring hatitmeet all contaminant tandards et by the EPA underthe SDWA.7Casualempiricismsupports his conjecture,withbottledwateras much as one thousand imesas expen-sive as tapwater. nCalifornia,orexample,Allen andDarby(1994) report ap waterpricesrangingbetween$.45 and$2.85perthousand allons,comparedwithav-erageU.S. bottledwaterpricesof $.90 persinglegallon(in 1990).8 Implicit n our specification f the healthdamagefunctions s the realisticpremise hat the volume of aconsumer's"residualrisk" wateruse does not affectthe expectedhealthcosts associatedwiththisuse. Notealso that he healthdamage unction,DB(), will dependuponthe qualitystandard or bottledwater;we ignorethis dependenceor notational implicity.9Therearea varietyof technologieshatcanbeusedfor water reatment,ncluding 1) disinfection, 2) cor-rosioncontrol, 3) membraneiltration ystems,(4) re-verse osmosis, (5) electrodialysis electrodialysis e-versal,(6) adsorption,7) lime softening,and(8) ozonesystems.Givenanyof thesetreatment rocesses whichwe call capacity nvestments),watercompaniesmakeavarietyof decisionson the extent to which they treatwaterafterobservingthe level of contaminationourtreatmentevel choice);amongthesedecisions aretheset andextent of chemicaladditives, he schedulingoffilterand membrane leansingand replacement,mea-suresto monitorand removeresidual oncentrations fdisinfectantsand contaminantsincluding esting andrecirculation),elianceonalternativeources,andwastestreamdisposal NRC1997).Inthispaper,we areenvi-sioninga givengroundand/orsurface ource or water

that s subject o random ndexogenouscontamination.In practice,a watercompanymayhavemultiplepossi-ble sources of water.Whenone sourcebecomes con-taminated,one strategyto reducethe impactof the


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98 LandEconomics February2001

D (u)=expectedealthBcostswhenonsumersdrinkottledaterD (u)=expectedealthostsA whenonsumersrinktapwateru=post-treatmentualitylevel f apwater

FIGURECONSUMEREXPECTEDHEALTH COSTSFROMWATER USE

Thecompany'schoices of y and u leadtothe followingex-postcosts of treatment:TreatmentCosts = F(y) + v(u, X, y, W),where W = wNis the total amountof watersupplied.The investment ost functionF(y)has the following properties:F'() > 0 andF"() > 0 (more treatmentcapacity is in-creasingly ostly).The "variable ost" func-tion v() includescosts of watercollection,treatmentnddelivery,and s assumed o sat-isfy: v,, > 0 andvyy, 0 (weakconvexity);v < O0, y < 0, andvwy, 0 (moretreatmentcapacityreducesvariable osts of treatment);v, > 0 andvx < 0 (treatingwater o a higherquality standard s costly, but less costlywhenthe incomingwaterquality s higher);vw> 0 (marginal osts of waterdeliveryarepositive);vx < 0 andvwx - 0 (costs of sup-plyingwaterof a givenquality evel declinewithhigher evels of initialqualityX). Notethat thesecost functionconstructsmplicitlyembed fixedcosts, costs thatare invariant owaterquantitiesdeliveredand that mplythelarge economiesof centralized rather hanhome) treatmentdescribed n the introduc-

tion. Note alsothat,with ahigher evel of ini-tial waterqualityX, it is likely to be at leastas costly to achievea given incrementalm-provementin water quality;the foregoingpropertiesof our cost functionv() arecon-sistent with this property.To convey the intuitive content of ourmodel as simplyas possible,we assume:.?Assumption1: The marginalcost of de-livering treated water is constant,vww =Vuw= 0.

III. OPTIMALITYIN WATERTREATMENT AND USEEx-post,afterX has been observedby thewatercompany,the envisionedsequenceofeventsis as follows: (1) thecompanysimul-taneously selects (i) its treatment level(whichdetermines he qualityof the tapwa-

contamination n the qualityof delivered ap water sto drawmore from an uncontaminatedource and lessfrom the contaminated ne. The costs of switchingawayfromthe contaminatedourceareimplicitlyem-bedded n the treatment osts modeledhere.1oAt the cost of complexity,ourexpandedpaperde-rives our resultswithoutAssumption1.


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77(1) Innes and Cory:The Economicsof Safe DrinkingWater 99

ter); (ii) the price that consumerswill bechargedfor the tap water;and (iii) whetheror not to notifyconsumers hatthetapwateris of a lower quality than is suitable fordrinking;and (2) consumers hen decide (i)whether o drink apwaterorbuybottledwa-ter;and(ii) how muchwater to consumeintotal. Because the measurementof waterqualityandthepotential ffects of watercon-taminants n consumerhealth areverycom-plex,we will assume hatconsumersdefertothe advice of theirwatersuppliers andtheexpertregulatorswho overseethem)to buybottled water." Therefore,with the com-pany's waterpricingdecisionisomorphic othe consumer'swaterquantitydecision,it isas if all of the ex-postchoices (of u, w, anddrinkingwater source) are made simulta-neously by the watercompany.At this juncture,we are not concernedwith how these choices are made or elicited(a topic to which we returnn the next sec-tion);rather,we are concernedwith proper-ties of efficientdecisions. To characterizethese properties, t is convenientto beginwith thechoiceof treatmentevel u for eachof the two possiblecases of consumerdrink-ing behavior bottledvs. tapwater).Buildingon thischoice,anefficientrule forthe drink-ing watersourcecan be characterized,ol-lowedbythedeterminationf an efficientex-ante treatment apacity,y.TheChoiceof TreatmentLevelu, and WaterUse w, WhenConsumersDrinkTapWater

In this first case (Case A), net market-wide benefitsof waterconsumption, fterde-ducting costs of treatment and expectedhealthdamages,are:(B(w) - DA(u))N - v(u, X, y, Nw). [1]Optimal evels of u and w will maximize henetbenefits n (1), subject o u - X. Assum-ing interiorsolutions to this problem,12 heywill solve the following first order condi-tions:u: -v.(u, X, y, Nw) - Da'(u) N = 0, [2a]w: B'(w) - Vw(u, X, y, Nw) = 0. [2b]

An optimal reatmentevel equatesmarginalbenefitsof treatmentn reducedhealthdam-ages, -DA'( )N, with the marginalcost oftreatment, ,(7).Similarly,optimalper-capitawateruse equatesmarginalconsumerbene-fits,B'(w), with marginal osts of waterde-livery, vw(). These optimawill be denotedby uA(X, , N) andWA(X,, N).By directly lowering marginalcosts oftreatment(v,), increasesn initialwaterqual-ity (X) and treatmentcapacity (y) prompthigheroptimal evels of post-treatment aterquality(u). Similarly,an increase n the ser-vice populationN increasesthe total healthbenefits of marginal treatment, -DA'N,which also promptsan increase n the opti-mal treatment evel.Proposition1: uA X,y, N) increaseswithX, y, andN.13TheChoice f u andw WhenConsumers rinkBottledWater

In this second case, the net market-widebenefitsof waterconsumption reas follows:(B(w) - DB(u))N- v(u, X, y, N(w - w)) - -N. [1']Theobjective unction n [1']differsfrom tsanalogin [1] in threerespects:First,healthdamages romtapwaterof qualityu are nowlower, DB(u)rather hanDA u). Second,thewatercompanynow supplieswateronly for

"The U.S. Safe DrinkingWaterAct, for example,regulatesover 90 contaminantsoday. Understandingthe healthimplicationsof contaminantmeasurements,andconverting uchmeasurementsntocosts, is argua-bly possibleonly forexpertsonthechemistry, pidemi-ology and economics of drinkingwater.Ouranalysisdoes not relyon consumer ognizanceof this informa-tion,baseduponwhichconsumersouldthemselvesde-cide whether o drinkbottledwateror tapwater.How-ever, in Section4 below, we showthat ourresultsarerobust o a consumer'sability o independentlyest thequalityof hertapwaterand, n turn,decidewhether opurchasebottledwater.12Some positive treatmentwill be optimalso longas marginalhealthbenefits of treatinguntreatedwaterare atleast as highas correspondingmarginalreatmentcosts. This will be true,for example,if the marginalcosts of treatinguntreatedwater s sufficiently mall.13The Appendix providesproofs for all Proposi-tions.


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100 Land Economics February2001consumers' residual needs, after their de-mand for drinking water has been met;hence,total waterdeliveriesare nowN(w -w). Andthird,consumersmust now pay thecosts of bottleddrinkingwater,- per person.Here,optimal evels of u andw will max-imize the net benefits n [1'], subject o u >-. Solutions o this problemwill be denotedby uB(X,y, N) and WB(X,, N). Again as-suminginteriorsolutions,these optimawillsolve the following first orderconditions:u: -vu(u, X, y, N(w - W)) - DB'(u)N = 0, [3a]w: B'(w) -vw(u, X, y, N(w

- -)) = 0. [3b]Comparative taticpropertiesof the opti-maltreatmentevel, uB(), are the same as de-scribedn Propositions forUA( . Moreover,when consumers drink bottled water, thebenefits of treating tap water, in reducinghealthrisks,are lowerthan when consumersdrink the treatedtap water. Therefore,wehave:Proposition 2: When consumers drinkbottled water, optimal levels of tap waterqualityare lower than when they drink thetapwater,uB(X,y, N) < UA(X, , N).

TheDrinkingDecision: Bottledvs. TapWaterConsumers should drink bottled waterwhen theresultingevel of overalleconomicwelfare,given optimaltreatmentand wateruse choices, is higherthan when they drinktapwater:

Economicwelfarewhenconsumersdrink ottledwater- JB(X,y, N)= (B(wB()) - DB(UB( ))N- V(UB(),X, y, N(wB() - W)) - cN> (B(wA()) - DA(uA()))N

- V(UA (), X, y, NWA())SJA (X, y, N)= Economic welfare when consumersdrinkapwater. [4]

To determinewhen [4] holds, we beginwith a compellingpremise:

Assumption 2: Economic Benefit ofDrinkingTap Water.The marginalcost ofdeliveringuntreatedapwater s less thantheperrunit ost of bottledwater.When initial waterqualityX is as highasthe qualityof bottledwater-, Assumption2impliesthat the watercompanycan provideconsumerswithuntreatedapwaterat lowercost than bottled water that has the samequality.Hence,we have:JA(-U, y, N) > JB(--, y, N). [5]As X falls, however,the net economic bene-fits of using tapwater also fall; a declineinX leads to a greaterincreasein treatmentcosts when the watercompanytreatsto thehigher drinkingwater standard,UA(), thanwhen it treats o the lowerstandard, B():14

JA X, y, N)IaX= -Vx(UA(), X, y, NWA()) >-Vx(uB( ), X, y, N(wB() - W)) [6]= dJB(X,y, N)IaX.

Whenincomingwaterquality s sufficientlypoor,X = X, costs of treatingall of the tapwater o levels desirable or "safe drinking"may exceed costs of the relevant alterna-tive-drinking bottledwaterandtreating apwater to a lower standard f qualitythatisappropriateor non-drinkinguses. In suchcases, bottled water will be more econom-ical:JA(X, y, N) < JB(X, y, N). (7)

Condition 7] need notalwayshold,but ismorelikelywhen (1) the two healthdamagefunctionsare "furtherapart" at the mini-mum safe drinkingwaterstandard,UA(X, y,N); and (2) marginalcosts of treatment rerelatively arge(foru - UAX, y, N)). Whenswitchingto bottledwater under these cir-cumstances, he treatment evel can be low-'4 By Assumption1 (v,w() = 0), equation 2b],andequation [3b], we have that WA() = WB(). Inequality[6] thus follows from uA()> > UB() (Proposition ),vxu< 0 andvxw5 0. By the samelogic, we also havethat -v,(uA( ), X, y, NWA()) > -Vy(UB( ), X, y, N(wB()- w)).


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J (X,y,N)=economic elfareA whenconsumers rinktapwaterJ (X,y,N)=economic elfareB whenconsumers rink* bottledwater

drinkbottledI drinkapwater-,!water% -X X*(y,N) u

FIGUREECONOMICWELFAREAND THE OPTIMALDRINKING DECISION

ered dramatically-yielding large cost sav-ings-without causing healthdamages anyhigher hanthoseexperiencedwhendrinkingtap water. Greatermaximal levels of watercontaminationlowerX), lower treatmenta-pacity investments, and smaller customerservicepopulations ll favor condition 7]byraisingtreatmentcosts, lowering the mini-mal safe drinking tandard A (X, y, N), andthereby widening the disparity betweenhealthdamagesunder the alternativedrink-ing sourcestrategies.As illustratedn Figure2, equations[5]-[7] will implythatthere s a criticalvalue ofinitial waterquality,X = X*(y, N), belowwhich bottledwatershouldbe used fordrink-ing and above which tap water should beused for drinking.Whenthis criticalqualitylevel is aboveX (because 7]holds),it can beshown to decline with increases n treatmentcapacityy and the servicepopulationN. Ahigher evel of treatmentapacity educes hecost of raisingthe treatment evel from thelower "drinkbottledwater" standard, B( ),to the higherdrinkingwaterstandard, A);as a result,the "drink apwater"alternativebecomes relativelymore economicaland isoptimally invoked more frequently.Simi-

larly, a largerN reducesthe per-capita ostof switchingto the higher drinkingwaterstandard,again implying that the "safedrinkingwater"regime s optimally nvokedmore often.Formally,let us define the switch-pointqualitylevel X*(y, N) min X e [XY,):JA(X,y, N) > JB(X,y, N). If condition(7)does nothold,thenX*(y, N) = X. If condi-tion [7] holds,thenX*(y, N) is aboveX anduniquelysolves:1"JA(X,y,N)= JB(X, ,N) atX= X*(y.N). [8]Thisconstruct ives us thefollowing "drink-ing waterrule":Proposition3: The optimalrule for theconsumers'choicebetweendrinking apwa-ter and bottled water is either:(a) alwaysdrink apwater,regardless f theinitialwaterqualityX;or (b)drink apwaterwhen thein-

'~ If condition [7] does not hold, then X*(y, N) =Xby the definition of X*( ) and equation [6]. If [7] holds,the existence of X*(y, N) > X as defined in equation[8] follows from equation [5] (Assumption 2) and theIntermediate alueTheorem.Uniquenessof X*( ) fol-lows fromequation 6].


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uu (X,y,N)optimal treatment Alevel

u (N) ------------------------S N u (X, y,N)drinkbottled

w a t e r d r i n k t p w a t e r

X*(y,N) XFIGUREEx-POSTOPTIMALOLICY: HETREATMENTNDDRINKING ECISIONS

comingwaterquality,X, is at or above a crit-ical value,X*(y, N) e (X, X), and drinkbot-tled waterwhenXis below this criticalvalue.The optimal frequencywith which bottledwateris consumedfalls when treatment a-pacity (y) or system size (N) is higher,aX*(y, N)/ly < 0 andaX*(y, N)/IN < 0.16Propositions1 to 3 together mplytheop-timal water reatment olicy depicted n Fig-ure 3. Whenthe incomingwaterqualityX ishigh, the cost of treatingwater to make itsuitable for drinkingare sufficientlysmallthat the watercompanyshould do so. As Xfalls, the post-treatmentquality of watershould also be lowered.Below some criticalX level, consumersshould often be advisedto drinkbottledwater,nottapwater,and thetapwatershouldbe treated o a substantiallylower standard f qualitythatis appropriatefornon-drinkingses andthat mposesa cor-respondinglyow cost of treatment.The TreatmentCapacityDecision,y

Because the treatment apacity s chosenbeforeX is observed,optimality equires x-pected economic welfareto be maximized,

given efficient choices that result from thechoseny level ex-post:X*(y,N)max - F(y) + JB(X,y, N) g(X) dX

yx+ JA(X,y, N) g(X)dX. [10]x*(y, M

The correspondingnecessaryconditionforan optimal y, y*(N), is:-F'(y)

-- x* Vy(UB( ), X,y, N(wB() - w))g(X)dX- Vy,(uA(), X, y, NWA())g(X)dX = 0.[11]

'6A higherlevel of bottledwatercost c will alsolead to a reducedoptimalfrequencyof bottled waterconsumption. orexample, f logisticalrigidities ead toa relativelyhighcost of respondingo a hightemporarydemand or bottledwater,thenc will reflectthis highcost of switchingcustomers o bottledwater andwillreducethe economicdesirability f the switch.


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Equation(11) equatesthe ex-antemarginalcost of y with the expectedvariablecost re-ductionsachievedwithmarginalnvestmentsin treatment apacity.Withv, < 0, investmentsn treatmenta-pacity yield higher cost-reductionbenefitswhen ex-post treatment evels are higher.Therefore,a largercustomer ervicepopula-tion, N, will lead to a higher optimal y ifhigher levels of N are also associatedwithhigheroptimal reatmentevels ex-post.Nowrecall thata higherN leads to a higher evelof treatment,given a consumerdecision todrinkeithertapwaterorbottledwater(fromProposition1). Moreover,a higherN leadsto a higheroptimal frequencyof the highertreatmentCase A) consumer. rinkingdeci-sion (recallingPropositions2 and 3). Thus,for allpossibleincomingwaterquality evelsX, a higherN yields a higheroptimaltreat-ment level andtherebypromptsa higherop-timalinvestmentn treatmentcapacity.17Proposition4: The optimaltreatment a-pacity level, y*(N), increases with the cus-tomerservicepopulation,N.In sum, we find thatlargerwatersystemsshould(all else equal)makelarger reatmentcapacity investments,meet higher ex-posttreatment tandardsby Proposition1), andinvoke the bottled water option less fre-quently(by Proposition3).

IV. OPTIMAL REGULATION:HOWTO ACHIEVE EFFICIENCYDrinkingwatermarketsmay fail becausethe health costs of contaminatedwater areexternal o thewatercompany'soptimizationcalculus.Policy measuresto controlhealthrisksmayapplybefore(orindependently f)theoccurrence f harm,or they mayonly betriggeredby theoccurrence f harm Shavell1987).Using tort law to impose liabilityforharmdone is an exampleof the latterap-proach,whereasregulatory egimes such asbest managementpractices, njunctions,andcorrective axes areexamplesof the former.In this section,we explorepossible avenuesto controlhealthrisksfromwatercontamina-

tion, beginningwith a strictliabilitybench-mark, then turningto "negligence rules"thatmaybe implementedwitheither iability

or regulatorystandards,and finishingwithregimesof fixed standards nd variable ines.We will be interested n how theserules canbe designed o elicit the efficient watercom-panypracticesdescribedn Section3 above.Althoughour initial analysispresumesthatconsumersonly buy bottled water when ad-visedto do so by the watercompany,we willlater show(in Section4D below) thatourre-sults are robust o a consumerability o inde-pendently est the tapwaterand,baseduponthis test,to choose betweendrinking apandbottled water.Whenmaking ts decisions,a watercom-pany maybe subject o public utilityregula-tion.Forconceptual larity,we do not wantto motivatewatertreatmentaw by any pre-sumed nefficiencies n thepublicutilityreg-ulator'srestraints n the company'sexerciseof monopoly power. We thereforeassumethat, in the absenceof fines or liabilityas-sessments, the companyobtains profitsor"rents" that include all non-health-relatedcosts andbenefitsof watertreatment, eliv-eryanduse, less a per-capitaonsumer"res-ervationbenefit"(beforehealthcosts) of B.Thisspecifications consistentwith a varietyof actualregulatory ettings, ncludingwhen:(1) the company s a privateprice-discrimi-natingmonopolywhich is subject o eitheraregulatoryconstraintthat consumerseachobtainnetbenefitsof B oramarket onstraintthatconsumersobtainat least the net benefitavailable from an alternativewater source

17 We assume here that the distributionof waterqualityXis invariant o the servicepopulationN. How-ever, if a higherN requires he watercompany o seekout less pristinewatersourcesand/oryields morepol-luted downstream ources,then the distribution f Xwill be worsened.This would increasethe frequencywithwhichcustomers renotified o drinkbottledwater(ceterisparibus),whichwould tendto lower marginalbenefitsof treatmentapacity.However, t mayalso in-crease hefrequencywith which ncomingwaterqualityis ratherpoor,but not sufficientlypoorto require heswitchto bottledwater.In thesecircumstances,he ad-ditional reatment hat is calledfor (i.e., u-X) tendstobe greater-and hence, the cost-reducingbenefitsoftreatment apacity endto be higher-than whenX ishigher.Overall, t seemsunlikely hat henetimpactofa worsenedXdistribution ncapacitynvestment ncen-tives wouldbe so stronglynegative hat t woulddomi-nate the effects thatunderpinProposition .


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104 Land Economics February 2001

(suchas deliveredwater);"182) the companyis municipal,with managerswho maximizethe economic rents available to them andtheir employerssubjectto a political con-straint hatconsumers ach obtainthe B netnon-healthbenefit;or (3) the company issubject to "price cap" regulation whichspecifiesa maximumpricethat heutilitycancharge.19StrictLiability

Undera strict iabilityrule,the watercom-pany pays for realized healthdamages,andthereby aces the trueexpectedhealthcosts,DB(u) when it "notifies"andDA(u) when itdoes not notify.Strict iabilityconfronts hecompanywith all of the societal costs andbenefits of its choices and, therefore,elicitsefficientbehavior.However, or a varietyofreasons, this rule is difficult,and perhapsimpossible, to implement.Particularly orhealthdamagesthat are realizedonly aftermany years,both causationanddamage ev-els are difficult to prove.20Moreover,regu-lated watercompaniesoften have "shallowpockets"thatprevent he assessmentof fullhealth damages, even when such damagescan be established.Criticsof the tortsystemarguethat toxic tortlitigation s very costly,andthatcourts ack the technicalcompetenceto deal effectivelywith healthandsafetyis-sues whendesignated egulatory genciesarebetterpositioned o performwell.21

NegligenceUndera negligenceliabilityrule,the wa-tercompany s subject o liabilityfor healthdamages,or another ighpenalty, f andonlyif it behaves"negligently"by notexercisingsufficient"care."Similarly, egulatorytan-dardsof "due care" can be enforcedwithsufficientlyhigh fines for non-compliance.As is well known,suchnegligencerules canelicit efficient decisions with prospectivepenalties for inefficient / negligent behaviorthat are smaller than true expected damages.The judgment proof problem (for firms withshallow pockets) can thereby be mitigated.

Using regulatory pproacheso enforcenon-negligent behavior has added advantages,economizingon the damageassessmentpro-cess; exploitingregulatory conomiesin ac-quiringthe specializedexpertiseneeded toevaluate hetoxicproperties f contaminantsand theirhealth mpacts;and furthermitigat-ing thejudgement-proof roblem hat ariseswhen realizeddamagesare high relative to

18 nthiscontext, might lsobethoughtf astheminimumustomer enefit eeded o forstall oter n-actmentfprice egulation.neitherase, hecompanycanmaximizerofits sing wo-partriceshat xtractall non-health-relatedconomicents. or xample,hecompanyancharge highpriceon a first raunchfa consumer's ater onsumptionthe"essential se"belowwhich onsumptionever alls)anda marginalcostpriceonadditionalse.Thehighprice anbe setto extract ither heper-capitaetrevenue (w)- B(whenconsumersrinkapwater) rB(w)- - - B(when onsumersuybottledwater).

19Solongastheprice ap s set abovehemarginalconsumeralueof optimalwateruse (forallX), themonopolist ill maximize rofits y (i) chargingheprice aponan nitial raunchf water se(i.e.,uptoa w* atwhichB'(w*) qualsheprice ap); nd ii)onfurtherse, evyinghemaximumfmarginalostanddiscriminatoryricesB'(w), rslightlyess).20Inpractice,efendantsavebroughtuitagainstwater ompaniesordeliveringontaminatedrinkingwater nder othbreach f warrantynd trict roductliability heories f liability.See, forexample, altRiver Project AgriculturalImprovement nd PowerDistrictv. Westinghouse lectricCorp.,143 Ariz.368,694 P. 2d 198, 1984;Zeppv. Mayor& CouncilofAth-ens,180 Ga.App.72,348S.E.2d673, 1986;Moodyv. City of Galveston,524 S.W. 2d 583, Tex. Ct. App.1975).)Onceheld iable, amagesncludeoss of earn-

ings and earningcapacity,pain and suffering, oss ofconsortium,medicalexpenses,fearof disease,medicalmonitoring, nd diminutionn qualityof life (Froder-man,Karnas, nd Lucia1996).Obtainingull recoveryfor thiswide arrayof damages s onerous orplaintiffs.In addition,claimantsmustdemonstrate hat the con-ductof the defendanthas been a substantialactor nbringingabout he harm uffered,andovercomea vari-ety of defensesto productiability,defensesthat hem-selves present omplexefficiency ssues (BoydandIn-gberman 1997). For further discussion of theseproblems, ee Kaplowand Shavell(1999).21 The strengths ndlimitations f usingtort aw asa meansto controlenvironmentalnd otherriskshavebeendiscussedextensively n the literaturee.g., Rose-Ackerman1991; Shavell 1984; Viscusi 1984), as haslimited iability(e.g., Innes 1999;Kaplowand Shavell1999).


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77(1) Innes and Cory:The Economicsof SafeDrinkingWater 105averagedamages.22For all of these reasons,a negligence rule enforcedwith regulatoryfines is less subjectto the economic draw-backs of strict iability.In this section,we focus on regulatory e-gimes that elicit non-negligent(compliant)behavior.23ines or liabilityforviolationsof"due care" standardsare assumed to belargeenough o deterviolations.Therelevantquestion s: How mustnegligencestandardsbe defined n order for the company's opti-mal non-negligentchoices to be efficient?Forexample,musttreatmentapacitybe reg-ulated with a minimumstandard?Must ex-post treatment evels be regulatedwith vari-able standards hatdependupon the extentof initial contamination X) and the size ofthe customer ervicepopoulationN), or canfixed standards uffice? Can negligence bedefinedusing standards hat areonly tied topost-treatmentwater quality u? How mustcustomernotification bout hequalityof thetap water be regulated?To address thesequestions, three alternativedefinitions ofnegligencewill be examined:24

Rule 1: Due care non-negligence)equires:(i) u - UA X, y*(N), N) - USA(X, N) when hecompanyoesnotnotifyconsumers,(ii) u - uB(X,y*(N),N) USB(X, ) whenthecompany otifies onsumershat heyshoulddrink ottledwater,(iii) notifyingwhen X < X*(y*(N),N)X**(N),and(iv)notnotifyingwhenX - X**(N).Rule2: Duecare equiresnly i), (ii),and iii)of Rule1 (not(iv)).Rule3: Due carerequiresi) and(ii)of Rule1,and(iii') notifyingwhenu < uA(X**(N), y*(N),N) us(N).None of these rulesregulatesreatment a-pacityat all. Unlike Rule 1, Rule 2 does notpenalizea companywhen it inefficientlynoti-fies consumers n order o lowerthe standardof treatment o which it is held. However,both rules set a consumernotification tan-dard hatdependsupon incomingwaterqual-ity X, rather hanpost-treatmentwaterqual-ity u. Rule 3 requiresnotificationwhenever

the watercompany's reatmentevelfalls be-low theminimumreatmentevel that s effi-cient when a no-notificationtrategy s also

efficient(see Figure3). Rule 3 thus ties allstandards opost-treatmentwaterquality,asdoes contemporaryU.S. policy. Unlike re-cent safe drinkingwater aw (see Section5),all threerulesdefinetreatment tandardshatare variable,notfixed. We turn now to theeffects of the threenegligenceruleson com-pany incentivesto treat water,notify con-sumersand invest in treatment apacity.Treatmentevels.Given(X,y) anda notifi-cationdecision,thecompany owers its costsby lowering hetreatmentevel u. Therefore,the companywill exactlymeetits treatmentstandards, nd will not "over-comply." Bythe same token, becauseefficienttreatmentlevels are variable dependinguponX andNby Proposition1), the treatment tandardsmust also be variable n order o promptef-ficient behavior.Consumernotification. n the optimum de-scribedin Section 2 above, consumersarenotifiedthatthey should drinkbottledwater

22 Historically,damages in privately-initiatedortactionsmustbe set equalto the actualdamagesvisiteduponthe defendantdueto the plaintiffs negligentact,not baseduponthe expected,average, ypical,or rea-sonablyanticipateddamagesresulting romthe act (apracticeknownas the "thin skull"doctrine n tort he-ory). For a discussionof the advantagesof liabilitybasedon expecteddamages n the natural esource on-text, see Phillipsand Zeckhauser1995).23 Negligence rulesdesignedin this way may alsobe advantageous ecausethey neverrequire he actualassessmentof liabilityorfines;as a result, headminis-trativeand legal costs of such assessmentsare neverborne.Generallyspeaking,an offsettingdisadvantageof such negligencerules is that,by confronting irmswith no liability orharm aused, heylead to excessiveentry(Polinsky1980;Shavell 1980). However, n thepresent ontext,one watercompany fficientlyserves agiven customerpopulation ndentry s not an issue.24 The questionposed here-how alternative egli-gence rules perform n eliciting desiredconduct-issimilar o thatposed by Shavell(1992) in a somewhatdifferentcontext.In Shavell (1992), potential njurerschooseboth their evel of care(accidentprevention f-fort)andwhether o obtain nformation bout heirriskof a harmful ccident beforecare s undertaken).f thenegligencerule stipulatesstandardsor both efficientcare and the efficientacquisitionof information, ffi-cient conduct s elicited;however,Shavell(1992) alsoshows thatefficientconductresultsfroman appropri-atly designednegligencerule thatonly regulatescare.

Similarly, n the presentanalysis,we areinterested nwhetherand how negligencerules can elicit efficientwater companybehaviorwithoutregulatingall deci-sions.


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106 LandEconomics February2001if andonly if incomingwaterquality s suf-ficientlylow, X < X**(N). For the sake ofexposition,et us suppose hat suchcustomernotification is sometimes efficient, X nB*(N) (- DA(USAX**(N), N))> DB(usB(X**(N),)). [14]Equation[14] requiresthat, underoptimaltreatment oliciesat thecriticalwaterqualitylevel, X**(), health damages are higherwhen consumersdrinktapwater thanwhenthey drinkbottledwater. This conditionre-flects the intuitivenotionthatswitching romtap water to bottled water (at the X**()switch point) has the benefit of reducedhealthrisk and the cost of increasedwaterexpenditures.However, f a switch to bottledwater is instead motivatedby cost savingsthat it permitsby loweringthe standard owhichtapwatermust be treated, hencondi-tion [13] will hold (not(14]) and Rule2 willbe inefficient.UnderRule3, the company'spayoffsun-der no-notification nd notification trategiesare exactly the same as under Rule 2 (i.e.,7TA() and7lB() in (12)) whenX is above theefficient notification threshold X**(N).Therefore, f condition[13] holds, Rule 3will also be inefficient,providing ncentivesfor over-notification.

Let us suppose nstead hat nequality 14]holds, as depicted n Figure5. In this case,the companywill sometimeswantnot to no-tify when notification is efficient, X


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77(1) Innes and Cory:The Economicsof SafeDrinkingWater 107

RA(X,y,N)=waterompanypayoffwhenconsumersrenotnotifiedto drinkottledwater

RB(XYN)=waterompany ayoffwnenconsumersrenotd that heyshould rinkottledwater

company companyprefers prefers ottonotify tonotifyX*(y,N)X**(N)

FIGURE4WATER COMPANY PAYOFFS UNDER A NEGLIGENCE RULE AND ALTERNATIVE NOTIFICATION

DECISIONS

rA(X,y'(N),N)A

B(X,y*(N),N)K *(N) S (Xy* =waterompanypayoffS A hN*e treatso"notheaonstandard, and oesnotnotifycompany company refersotprefersonbtifytonX+ X++ X**(N) XFIGURE5WATER COMPANY PAYOFFS UNDER "TREATMENT NEGLIGENCE" (RULE 3) AND ALTERNATIVE

TREATMENT AND NOTIFICATION POLICIES


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108 Land Economics February2001

xAt(X, , N)= companyprofitwhen u is setequalto UsN(N)_= max {(B(w) - B)N - F(y)- v(usN(N), X, y*(N), wN)}for X 5 X**(N). [15]

WhenX is less thanX**(N), ItA() differsfrom A (), theno-notificationrofit unctionin equation(12a), because the notificationstandard indsthecompany o a higher reat-mentlevel, USN(N) uSAX,N), andtherebylowerscompanyprofits: x (X,y, N) < A (X,y, N) for X < X**(N). However,becauseusN(N) equals uSA(X,N) at the switchpointX**(N), t(X, y, N) =- A(X,y, N) at X =X**(N).In view of these properties, Figure 5shows thatthere s a rangeof X levels belowthe switchpoint,X**(), wherein nAf() isgreaterhannB( so that hecompanyprefersto set its treatmentevel to usN(N) and notnotify,rather hannotifyandsetits treatmentlevel to the lowerstandard,USB(). ince noti-fication s efficient or these X values,Rule 3yields inefficientunder-notification.n intu-itive terms,condition[14] implies that thecompanystrictlyprefersnot to notifyat theoptimalswitchpoint,X**(), because t doesnot obtain he nethealthbenefitsproduced ythe shift to bottledwater.Hence, as X fallsbelow X**(), the companywill still prefernot to notify even though,under Rule 3, itcannot ower its treatmentevel.To developa positive efficiencypropertyof Rule2, it is instructive o consider he fol-lowing simplifyingrestriction:Assumption3: When zero, the net com-panybenefitof customernotification,ltB() - lA ( ), is non-increasingn X:

a(nA() - 7B(O))/~X0 if Aa) = 7B().

Assumption3 is generallyrealistic be-causea higherincomingwaterquality evelX reduces reatmentosts in thehigher reat-ment(CaseA) regimemorethan n the lowertreatment(Case B) regime.28Given thispremise,companyprofit unctionsareas de-pictedin Figures4 and5, witha switchpointbelow which notification is preferredandabove which it is not, X+(y, N) min X:

nA(X,y, N) -2TB(X,y, N). Withan efficienttreatmentapacitychoice,Rule2 thusyieldsefficient notificationdecisions so long ascondition 13) is violated(see Figure4).Table 1 summarizesheefficiencyproper-ties of the alternativerules, includingthetreatment apacityeffects to which we nowturn.TreatmentCapacity

Withanyof thethreenegligencerulesde-scribedabove, societalcosts andbenefitsoftreatment apacitydecisions are exactlythesame as those whichconfront hewatercom-pany,viz, marginal osts of capacity nvest-mentsF'(y) andbenefitsof attendant educ-tions in variablecosts of treatment, ,()


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77(1) InnesandCory:TheEconomicsf SafeDrinkingWater 109TABLE

FEATURES ND EFFICIENCYROPERTIESFTHREENEGLIGENCEULESRule 1 Rule 2 Rule 3

RuleFeaturesEx-Post EfficientVariableTreatment tandards x x xStandardRequiringConsumerNotificationWhen X Is Small x xStandardRequiringNo NotificationWhen X Is Large x -StandardRequiringConsumerNotificationWhen u is Small - - xEfficiencyPropertiesof AlternativeRules Rule 1 Rule 2 Rule 3

WithAssumption3 Efficient Over-notify Over-notifytA*(N) < RB*(N), Y< y*(N) y < y*(N)pereqn. [13]a WithoutAssumption3

Efficient Over-notify Inefficienty < y*(N) (some over-notification)WithAssumption3 Efficient Efficient Under-notify*tA*(N)>7RB*(N), y > y*(N)pereqn. [14],b andX**(N) > X WithoutAssumption3 Efficient May Be Efficient Inefficient(some un-der notifi-cation)

a If notifications sometimesefficient,X**(N) > X, condition 13] will hold if the optimalswitchto bottledwater s motivatedby treatmentost savingsthatoffset higherhealthrisks,DA usA(X**(N),N)) < DB(use(X**(N), N)).bWithX**(N) > X, condition 14] will hold if the optimal witch to bottledwater owers healthrisks,DA(usA(X**(N), N)) >DB(usB(X**(N),))

panyinefficiently efrains rom customerno-tificationandsets treatmento thehigh noti-fication standard,uSN(N) > USA(X,N) >USB(X,N) for X < X**(N). Becausehigherex-post treatment evels yield higher cost-savingbenefits rom investmentn treatmentcapacity, the company's privately optimalpolicy of under-notification-andovertreat-ment-will also promptit to invest morein treatment apacitythan would otherwisebe efficient,y > y*(N).29 Hence,ourRule3,the negligencerule that most closely resem-bles contemporary olicy, can onlyelicit ef-ficient firm choices if either notification sneveroptimal(X**(N) = X) or,by happen-stance,healthdamagesareexactlythe sameat the optimal switch point, regardlessofwhether onsumersdrink apwateror bottledwater:DA(USA(X**(),N)) = DB(UsB(X**(),N). If, instead,notifications sometimesopti-mal (X**() > X), and theoptimalswitch tobottledwateris motivatedby the lowering

of health costs, DA USA X**(), N)) >DB(UsB(X**(), N), then Rule 3 generallyprompts hecompany o: (a) notify oo infre-quently; b) treatwater to a higherstandardthan is efficientwhenit inefficiently ails tonotify; and (c) overinvest in treatmentca-pacity.In contrast,when treatment nd notifica-tion decisions are first-best-as they are un-der Rule 1 and sometimes under Rule 2(when condition [14] and Assumption 3hold)-expected company profitsare max-imized with a first-besttreatment apacitychoice,thuspromptingullyefficient ompanybehavior.n sum(referringgain o Table1):Proposition5: In order for a negligencerule to prompt fficientnon-negligent ehav-ior, it need not definea "due care" standard29Theeffectsof Rules 1-3 on thewatercompany'streatment capacity choice, as stated here, are derivedformally in our expanded paper.


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110 LandEconomics February2001fortheinvestmentn (ordesignof) thetreat-ment system, but must (i) define standardsfor minimumpost-treatmentwater qualitythat are tied to the incomingwaterqualitylevelX, the size of the customer ervicepop-ulationN, andthe decisionon whetheror nottonotifyconsumers hat heir apwater s un-safe todrink; ii) almostalwaysdefinea stan-dard or consumernotification hat is tied tothe incomingwaterquality evel X, and notthe post-treatmentwaterqualityu; and (iii)sometimesrequirea companynot to notifyconsumerswhen notification andtreatmentto a lower standard) re inefficient.FixedStandards

Withnegligencerulesdesigned o promptnon-negligent compliantbehavior,variablestandards reneeded o achieve efficientout-comes. However,fixed standards,ombinedwith a regimenof fines for non-complianceand "bonuses" for over-compliance,canbe designedto elicit efficientnon-compliantand over-compliantbehavior. Consider thefollowing notification-contingentreatmentstandards:I) usAwithoutnotification nd(II)a lowerstandardwithnotification,UsB< USA,whereDB(USB) DA(USA) Dexpected ealth ostswithoptimal ehavior,3and a violationor exceedanceof a standardpromptsa net fine thatcharges(orrewards)the firmfor the differencebetween trueex-pected damages and damages with exactcompliance:Net Fine = DA u) - DA USA)when there s no notificationNet Fine= DB(u) - DB(UsB)whenthere s notificationHere, when damages are greaterthan D(which will occur, for example, when thecompany sets u below usAand does not no-tify), the companywill pay a fine;however,when damagesare less thanD (which willoccur,for example,when the companysets

u above USAnd does not notify), the com-pany gets a bonus(a negativefine).Becausethisrule s equivalent o strict ia-bility (with a fine equal to healthdamagesless the constant D), it elicits efficientchoices.However, he fines are based on ex-pectations not realizations)of damagesandare zero on average, husavoidingmany pit-falls of strict iability.Bilateral Care:ConsumerWaterTesting

Despitecosts andcomplexitiesassociatedwith testingfor watercontaminants, con-sumermightbe able to test hertapwater norder to determine ts quality;based uponsuch a test,a consumer ould make an inde-pendentjudgementabout whether to drinktaporbottledwater.Intheprioranalysis,weassume hatconsumersdo nottesttheirwaterand insteaddeferto the watercompany'sad-vice about whether to buy bottled water.However, hispremise s not essential or ourresults.Specifically,we have:Proposition 6: If regulatory policypromptsefficient water companytreatmentand notificationdecisions,then:(i) anycon-sumerwho tests her tap waterqualitywillmakethe same(tapvs. bottledwater)drink-ing decision as is recommended y the com-pany;and (ii) consumerswill not test theirtapwater f the test involves a positivecost.Consider a consumer's incentive to"switch" away fromcompanyadvice-forexample, drinkingbottled water when thecompanyrecommendsdrinking he tap wa-ter.The consumergainsless from the unilat-eralpurchaseof bottledwater hanwould begained, per-capita,rom a full blown "soci-etal switch"to bottledwater.Witha "soci-etal switch,"the companyoptimally owersits post-treatmentwater quality level andlowers its marginalcost price in tandem;both of these actionsraisethepotentialbene-fit to be enjoyed romthe bottledwateralter-

30 Formally,D -- DaB(uB(X,*(N), N)g(X)dX

+ J)DA(uA(X, y*(N), N)g(X)dX.*()


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77(1) Innesand Cory:The Economicsof Safe DrinkingWater 111native. These optimal adjustmentsare notmade when a consumer unilaterallypur-chases bottled water;hence, the consumerhas less incentive to make the switch thandoes societyas a whole.31 ecausesocietyasa whole loses with a "switch" away fromefficientcompanyadvice, a consumermustalso lose if she unilaterally ejectsthis ad-vice. Hence, an independentwater qualitytestreveals nformationhat a consumerwillneveruse;clearly,consumerswill notpayforsuchworthless nformation.Now supposethat the watercompany snot behavingefficiently,butrather s ineffi-ciently notifyingconsumers o drinkbottledwater-or inefficiently ailingto notify-aswe arguedcould occur under he negligenceRules 2 and 3. Then will a consumersome-times have an incentive to "switch"?And,if so, will this behavioraffect thecompany'snotification incentives?Because the watercompanychargesa marginalprice equal tomarginal cost, a consumer's decision to"switch" does not affect either the watercompany'sprofitsor, therefore,ts incentivesto notify(or not). However,when the com-pany is not notifying efficiently-and soci-etal gains from a full blown "societalswitch" are thereforepositive-consumersmay conceivablyhave an incentive to rejectthecompany'sadvice,giventheinformationneeded orthem o do so. Ofcourse,any pos-itive consumer benefits from "switching"must be highenoughandfrequent noughtojustify the consumer'scost of waterqualitytesting.Moreover, f a consumercan raiseherwelfareby testinghertapwater,societalwelfare will also be raised (with producerwelfareunaffected),whichwill mitigate butnot eliminate) the efficiency costs of overandunder-notification.32Insum,a consumer'sability o testhertapwater-and use the test results to decidewhetheror not to purchasebottledwater-does not alterany of ourqualitative onclu-sions. If an efficientregulatory egimeis inplace, consumerswill have no incentivetoengage in independentwatertesting.How-ever,under heinefficient egulatoryegimesdiscussed in this paper, independentcon-sumertestingandswitchingcould occur,inprinciple; nd f it did,suchtestingwouldre-duce the extent of inefficiency.

V. CONCLUSION: IMPLICATIONSFOR SAFE DRINKING WATER LAWIn this paper,we presenta simplemodelof drinkingwatermarkets n whicha watercompany,faced with randomcontaminationof its source, chooses a treatmentsystem,treatmentevels, and whether o notify con-sumersthatthey shoulddrinkbottledwaterrather han riskexposure o contaminantsnthe tap water. In closing, we considerwhatimplications his theorymayhave for recentexperienceandpracticewith the Safe Drink-ing WaterAct (SDWA).Under he SDWA,watersuppliersarere-sponsible for ensuringthat drinkingwatermeetsEPA standardsnd forcomplyingwithestablishedmonitoring, peration, ndmain-tenance protocols.Each supplierof watermustcollect samples romthe watersystem,take them to a certified aboratoryor analy-sis, and sendtheresults o theregulatory u-thority.Any time there s a violationof a re-quirement, he public must be notified. Ingeneral,publicnoticesmust ncludea discus-sion of theviolation; hepotentialoradverse

effects; the populationat risk such as chil-dren or pregnantwomen;the stepstakento31Implicit n thisarguments thefollowingobserva-tion:Whenpost-treatmentaterqualityu andwaterusew remainunchanged,a consumer's"switch" (to bot-tled water, orexample)yieldsthe samenetbenefits othe individual onsumer s it does to society.Withcon-stantu andw, therearethreeeffects of a "switch" onboth societal and individualbenefits:(1) health dam-ages change(forexample, romDAto DB);(2) the bot-tled watercost, -, is borne(or saved);and(3) the costof drinking apwater,wvO(),is saved(orborne).32Inprinciple,hewatercompany ouldbe requiredtonotifycustomers bout hepost-treatmentaterqual-ity u, essentiallymakingconsumerwater estingunnec-essary.If such notificationswere costless, they couldpotentially educeprospectivenefficiencies f over andunder-notificationor the reasonsdescribedabove. Inpractice,however,we believe that such waterqualityinformations unlikely o be of practical se to consum-ers,absent hespecificrecommendationso drink aporbottledwater hatwe model nthispaper.Therearetworeaons.First,translatinghe multitudeof contaminantmeasurementsntohealth-based rescriptionsor action(see note 11) requiresexpertisethat most consumerslack. Second, prospectiveconsumergains from re-jectingthecompany's tapvs. bottledwater)advicearesubstantiallyess thancorresponding er-capitagainsfroma "societalswitch";hence,even withinefficientregulations, hese gainscan be smallandinfrequentfthey areeverpositiveat all.


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112 LandEconomics February2001TABLE 2

DISTRIBUTIONOF SYSTEM SIZE (N) AND CONTAMINATIONX) IN ARIZONAA) SystemSize (1994)'

Numberof Systems Percentof PercentServicePopulation in Arizona Population erved of Systems>50,000 9 59% .5%>3,300 & 1,000 &


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77(1) Innes and Cory:TheEconomicsof Safe DrinkingWater 113morecomplex, small systemshave founditincreasinglydifficult to comply. The 1996reauthorization f the SDWA attemptstoaddress cost and compliance issues facingsmall systems.33A principalhrustof thereauthorizationsrisk assessmentandbenefit-costanalysis inregulatory ecisionmaking Clark1997;Tie-man1996).Under he reformedaw,theEPAmay consideroverall riskreductionbenefitsin settingnew drinkingwaterstandards, ndmust determine whether the benefits of astandardustify its costs. The SDWA reau-thorization lso revokestherequirementhatthe EPA regulatean additional25 contami-nants every three years, and establishes aprocessfor EPA to select contaminants orregulatoryconsiderationbased on occur-rence,healtheffects, andmeaningfuloppor-tunity for health risk reduction. Theseamendments reconsistentwith the implicitprescriptionf thispaper'sanalysis hatstan-dards of post-treatmentwater quality-asmeasuredby both the level of contaminantstandards nd the set of contaminantshatareregulated-reflect tradeoffs between costsand healthbenefits.The reauthorizationlso adds some flexi-bility to the enforcementof standards.Forsmall systems, the reauthorizationnablesstates o grant echnologyandtreatment ari-ances,withEPAapproval,based on cost andhealth-riskreductionconsiderations,an ex-plicitrecognition hatoptimal reatmentev-els mustvarywith the size of the customerpopulation.n addition,he new law requiresStates to establishprograms or watersys-tems to attain the technical,financial,andmanagerial capacity to comply with theSDWA. These capacity developmentprovi-sionsattempto avoiddetailed ommand-and-controlregulationsby enablingsmall watersystems and their state regulators o tailortreatmentpractices to individual circum-stances(Shanaghan 996).Ouranalysissug-geststhatthesechangesare ikelyto enhanceeconomic welfare. Under plausible condi-tions in ourmodel, argerwatersystemsopti-mally invest more in the treatment ystem,treatto higherstandards f quality(becausehealthbenefitsof treatment rehigher),andresort ess frequentlyo bottledwater "warn-

ings" (Proposition ). Elicitingsuchoptimalbehavior requiresregulatorystandardsonpost-treatmentwater quality that dependupon the size of the system, the extent ofcontamination, nd whetheror not consum-ersare notified o drinkbottledwater Propo-sitions 1 and5).Despite its addedflexibility,the reautho-rizedSDWA retains woregulatory igiditiesthat this analysis suggests may impedeeco-nomic efficiency.The first concerns notifi-cation.The SDWA amendments larifypub-lic notificationrequirementsor violationsof maximumcontaminantevels, treatmenttechniques, testing procedures,monitoringrequirements,ndviolationsof a varianceorexemption.If violations have the potentialfor "seriousadverseeffect," consumersandthe state must be notified within 24 hoursof the violation. However, notably absentfromthe notificationeforms s arecognition,combinedwith efforts to informwater com-paniesandthe public they serve, that therecan sometimes be efficiency advantagesofnotifyingcustomers to drinkbottledwater.When contamination s sufficiently great(and treatment costs are correspondinglyhigh), we find thatconsumersareoptimallyadvised o drinkbottledwater,nottapwater,and the tap wateris optimallytreatedto asubstantiallyowerstandard f quality hat sappropriateor non-drinkinguses and thatimposesa correspondinglyow cost of treat-ment. Efficient notificationprotocols pre-scribe both when a companyshould notifycustomersto drinkbottledwater and oftenalso when it should not notify and instead

33Accordingto the National Research Council(NRC 1997), the numberof small communitywatersystemshasincreased ubstantiallyn the UnitedStatesin the last threedecades, rom 16,700in 1963 to morethantriple hatnumber, 4,200,by 1993,withapproxi-mately1,000new systems ormed achyear.The smallwatersystemswill incurnearly70%of thetotalcost ofcomplyingwith drinkingwaterrequirementsRaucher1994).Beyondotherreformsdescribed bove, he 1996SDWAamendmentswill promote omplianceof smallsystemsby (i) requiring perator ertification rogramsto be in place by the year2001; and(ii) creatinga re-volving fundfor statesto makedirectgrantsand low-interest oans to publicwatersystems.The loans maybe used to upgradewatersystemfacilities,equipment,andpiping,or for complianceactivities,operator erti-ficationprograms, nd sourcewaterprotection.


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114 LandEconomics February2001treatto safe drinkingwater standards.Con-trary o contemporary ractice, his analysissuggeststhatefficiency gainscanbe securedby explicitly recognizing that notificationshouldsometimesoccurandbasingnotifica-tionprotocolson thelevel of initialcontami-nation,not the post-treatmentwaterquality(Proposition 5).34Secondly, the reauthorizedSDWA pre-serves a regulatorypreoccupationwith thedesignof a company's reatmentystem,re-quiringgovernmentapprovalof the treat-menttechnology hat s used,approvalhat sinformedby governmentechnologicalbulle-tins andothersourcesof regulatory uidance.Although he government anexploitecono-mies of scale in providing information ocompaniesabout reatmentechnologies, hisanalysis suggests that it need not regulatetreatmentdesign decisions either indirectly(withdesign-contingenttandards,or exam-ple)ordirectly Proposition ). Rather,t canrely uponwaterqualitystandardshatdo notspecify(orchangewith)a company'schoiceof treatmentystem,andthatprovidecompa-nies withan unfettered bilityto adoptcost-savingdesign innovations.By doing so, thegovernment an also free up regulatory e-sourcesfrom treatment ystemoversighttoimproveboth SDWA enforcement35nd theinformationused to design drinkingwaterregulationsthat efficiently tradeoff healthdamagesavertedandcosts incurred.

APPENDIXProof ofProposition1:Differentiatinghefirstorderonditions2a]and 2b],and xploitingec-ond order conditions, yields:

JUA( /IX = {vux(B" - vww )}+ { (vwxN) vuw), [Ala]auA( )/y s{Vu (B" - vwwN)+ {(vw,N) vuw}, [Alb]

)UA( /)N s (vuww + DA)(B" - vwwN)+ vwwwN vuw(first form)= (B"/N)(vwW - vu)vwwv (second form). [Alc]

where "=" denotes "equals in sign," and thesecond equality n [Alc] follows from substitu-tion for DA = -v,/N from condition[2a]. Thefirst bracketed erm in [Ala] is positive (withvux< 0 and,fromsecondorderconditions,B" -vwwN < 0) andthe secondbracketed erm s zero(by Assumption 1). Identical logic applies to[Alb].Turning o [Alc], note thatconstantreturns oscale (vww()= 0 fromAssumption1) implythefollowingvariablecost function:v = a(u, X, y) + P(u, X, y) W [A2]Furthermore,ithvu> 0 everywhere, umustbepositive.Differentiating () to evaluatethe sec-ond form forauA(O/N aboveyields:JuA/JN = -(B"/N) au > 0,where the inequalityresults from B" < 0 andacu 0. QED.Proofof Proposition2: Appealing o Assump-tion 1 (vuw()= 0), we can evaluateour firstordercondition oruB(), [3a],at u = UA(),as follows:

-V() - D' (u) N = (D'(u)) - D'(u)) N < 0,where heinequalityollows fromD (u) < D'(u)< 0 and(byconvexityof v( ) in u) establishesheProposition.QED.Proof of Proposition3: The firstpartof theProposition ollows from equation[5], equation[6] andthe definitionof X*(). To establishthe

34 n this paper,we assume that the populationofconsumerss homogeneous. f instead hereare "highrisk" and "low risk" consumers(with consumersknowingwhattheyare), herewill be addedbenefitsofmore complicatednotification-and attendant reat-ment-regimens. When nitial evels of watercontami-nationareneither oo greatnortoo small,optimalcus-tomernotificationswill need only to warnhigh riskgroupsthatbottled watershould be substituted;withsuchnotices ssued(andhighriskconsumerspresumedto respond), optimal tap water treatmentmay fallslightlyornot atall. Forcasesof greaterwater ontami-nation,optimalnoticeswill warnall consumers, s de-scribed n the foregoinganalysis.Thispaper'squalita-tive conclusionsabout he natureof optimalregulationwill extend o suchanenvironment,lthoughhe formalanalysiswouldclearlybecomemorecomplicated.

35 Resourceso supportmonitoring ndenforcementactivitiesareseverely imited n moststates.The GAOconcluded n 1993: "Severeresourceconstraints avemade it increasinglydifficult or manystatesto effec-tivelycarryoutthemonitoring, nforcement, ndothermandatorylementsof EPA'sdrinkingwaterprogram.... The situationpromises o deteriorateurther" U.S.GAO 1993).


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77(1) Innesand Cory:TheEconomicsof SafeDrinkingWater 115derivativepropertiesof X*(y, N), differentiateequation[8] withrespectto y:aX*(y, N)lay

[-[vB(X*(),) - vA(X*(),)]/[v' x(X*( ), ) - v(X*( ),)]} < 0, [A3]wherevB() = V(UB(), X, y, N(wB() - w)) andvA( ) = V(UA( ), X, y, NWA()) denotecost functionvalues with optimal treatment and water usechoicesfor CasesB andA, respectively; (X,) =V(UB(), X, y, N(wB() - w)) and vA(X,) =Vz(UA( ), X, y, NwA() denotecorrespondingeriv-atives forz = y, X. Theinequalityn (A3)followsfromequation 6) and its counterpart, vA >vB(see note 14).

Differentiating8] withrespectto N gives:3X*(y,N)aN

= [a JB(X*(), y, N)/IaN- aJA(X*(), y, N)/IN]= N-`I[vB(X*, )- V(X* ) N(wB() - w)]- [A(X*,) - vIA(X*,WA()N], [A4]where the second equalityis obtainedby per-formingthe indicateddifferentiation nd substi-tutingfrom equation[8]. By Assumption1, v(X*,) = vA(X*,), WA() = WB() andvB() =v(uB( , X, y, NwB()) - v4(X*,). Substitutinginto [A4], we thus have:aX*(y, N)aN

SN' {V(UB(), X, y, NWA())- V(UA(), X, y, NWA())}

< 0, [A4']wheretheinequalitys due o uA) > UB() (Prop-osition2) andvu() > 0. QED.Proof of Proposition4: Differentiating qua-tion(11) andappealingo the secondorderneces-sarycondition or anoptimum,we have:

wherevAandvBare as defined n [A3].With wA/DN = DwB/BN 0 (by Assumption1, equation[2b], and [3b]), vy < 0, v,w- 0, and vB(X*())- vA(X*()) > 0 (note14),we see that hefollow-ing conditions are sufficientfor dy*(N)/dN in[A4] to be positive:(1) JuA/lN> 0 for all X -*(y*(N), N), (2) auBIaN > 0 for all X


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CA- CA -O, [A7a]CA- CB < 0 when JA -JB 0, [A7b]whereJk (fork e {A,B)) is the maximal ocietalbenefit n casek, as defined n equation 4). Nownote:(I) withJ?(u, w) definedas the societal ob-jective functiongiven in (1) (fork = A) and(1')(for k = B), we have Jk = maxlu,,, I(u,w); and(II)from[A6] and the definitionsof J () andJk,C B- CA = JO(UA, WA JA < JB JA, [A8a]CB - CB = JO(UB, WB) - JB < JA- JB, [A8b]where the inequalities follow from (UA,WA) ? (UB,WB) andobservationI). [A8] implies[A7]. QED.

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Economics of Safe Drinking Water

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