未来能源研究所-城市水价中的效率、公平和成本回收权衡 Efficiency,Equity,and Cost- Recovery Trade-Offs in Municipal Water Pricing 2024

Efficiency,Equity,andCost-

RecoveryTrade-OffsinMunicipalWaterPricing

CaseyJ.Wichman

WorkingPaper24-18

October2024

AbouttheAuthor

CaseyWichmanisanassociateprofessorintheSchoolofEconomicsattheGeorgiaInstituteofTechnologyandauniversityfellowatResourcesfortheFuture.Heisanappliedmicroeconomistworkingonissuesattheintersectionofenvironmentaland

publiceconomics.Hisresearchfocusesonhowpeopleinteractwiththenaturalandbuiltenvironment,andwhatthatbehaviorrevealsaboutthevalueofenvironmental

amenities.Wichman’sresearchspanswaterandenergydemandmanagement,climatechangeimpactsandpolicy,urbantransportation,publicgoodsprovision,andoutdoorrecreation.

Acknowledgements

IthankDylanBrewer,NathanChan,TeevratGarg,LudovicaGazze,BenGilbert,

JoshGraffZivin,ArikLevinson,SheilaOlmstead,IvanRudik,BlakeShaffer,Steven

Smith,ChrisTimmins,WillWheeler,DerekWietelman,andconferenceandseminar

participantsattheTriangleResourceandEnvironmentalEconomicsseminar,ColoradoSchoolofMines,UniversityofAlabama,UniversityofCalgary,UCSanDiego,

UniversityofHouston,UniversityofWyoming,thePropertyandEnvironmentResearchCenter

(PERC),theYoungScholarsSymposiumonNaturalResourceGovernanceatIndianaUniversity,aswellasthe2023ASSA,AERE,andSEAmeetingsforhelpfulfeedback.ThisresearchwaspartiallysupportedbyagrantfromtheGeorgiaTechStrategicPlanAdvisoryGroupandtheLoneMountainFellowshipatPERC.TurnerStevensprovidedexceptionalresearchassistance.

ResourcesfortheFuturei

AboutRFF

ResourcesfortheFuture(RFF)isanindependent,nonprofitresearchinstitutionin

Washington,DC.Itsmissionistoimproveenvironmental,energy,andnaturalresourcedecisionsthroughimpartialeconomicresearchandpolicyengagement.RFFis

committedtobeingthemostwidelytrustedsourceofresearchinsightsandpolicysolutionsleadingtoahealthyenvironmentandathrivingeconomy.

Workingpapersareresearchmaterialscirculatedbytheirauthorsforpurposesof

informationanddiscussion.Theyhavenotnecessarilyundergoneformalpeerreview.TheviewsexpressedherearethoseoftheindividualauthorsandmaydifferfromthoseofotherRFFexperts,itsofficers,oritsdirectors.

SharingOurWork

OurworkisavailableforsharingandadaptationunderanAttribution-

NonCommercial-NoDerivatives4.0International(CCBY-NC-ND4.0)license.Youcancopyandredistributeourmaterialinanymediumorformat;youmustgive

appropriatecredit,providealinktothelicense,andindicateifchangesweremade,andyoumaynotapplyadditionalrestrictions.Youmaydosoinanyreasonable

manner,butnotinanywaythatsuggeststhelicensorendorsesyouoryouruse.Youmaynotusethematerialforcommercialpurposes.Ifyouremix,transform,orbuilduponthematerial,youmaynotdistributethemodifiedmaterial.Formoreinformation,visit

/licenses/by-nc-nd/4.0/

.

Efficiency,Equity,andCost-RecoveryTrade-OffsinMunicipalWaterPricing

Efficiency,Equity,andCost-RecoveryTrade-Offs

inMunicipalWaterPricing*

CaseyJ.Wichman†October11,2024

Abstract

Municipalwaterutilitieschooseratestorecovercosts,encourageconservation,andreduceburdensonlow-incomecustomers,whichmaydeviatefromoptimaltwo-parttariffs.Theorysuggeststhatpricesshouldequalmarginalcostwithfixedcostsrecoveredviafixedfeesoralternativetaxrevenues.Usingratestructureandmunicipalfinancedataformorethan700utilities,Ishowthatpricesarediscountedseverelyforlowlevelsofconsumptionwithinnonlinearratestructures,leadingtosuboptimalusageandbudgetdeficits,particularlyinpoorerandsmallercommunities.Marginal-costpricingcorrectsallocativeinefficiencies,andequityandcost-recoverygoalscanbeachievedthroughmoreprogressiveapproachestofixedcosts,whicharebothhighlyregressiveandalargeshareoftotalcosts.

KeyWords:waterpricing;utilitymanagement;naturalmonopolies;two-parttariffs;nonlin-earpricing;affordability;municipalfinance.

JELcodes:D12,H23,L95,Q25

*IthankDylanBrewer,NathanChan,TeevratGarg,LudovicaGazze,BenGilbert,JoshGraffZivin,ArikLevinson,SheilaOlmstead,IvanRudik,BlakeShaffer,StevenSmith,ChrisTimmins,WillWheeler,DerekWietelman,andcon-ferenceandseminarparticipantsattheTriangleResourceandEnvironmentalEconomicsseminar,ColoradoSchoolofMines,UniversityofAlabama,UniversityofCalgary,UCSanDiego,UniversityofHouston,UniversityofWyoming,thePropertyandEnvironmentResearchCenter(PERC),theYoungScholarsSymposiumonNaturalResourceGover-nanceatIndianaUniversity,aswellasthe2023ASSA,AERE,andSEAmeetingsforhelpfulfeedback.ThisresearchwaspartiallysupportedbyagrantfromtheGeorgiaTechStrategicPlanAdvisoryGroupandtheLoneMountainFellowshipatPERC.TurnerStevensprovidedexceptionalresearchassistance.

†Wichman:AssociateProfessor,SchoolofEconomics,GeorgiaInstituteofTechnology,221BobbyDoddWay,Atlanta,GA30332.Email:

wichman@;UniversityFellow,ResourcesfortheFuture

.

1

1Introduction

Municipalwaterandwastewaterutilitiesaretaskedwiththeoperationofcriticalinfrastructureforthewell-beingoftheirresidents:deliveringclean,safe,andreliabledrinkingwaterandre-turningittonaturalwaterbodieswithoutharmingtheenvironment.Duetopoliticalpressure,concernsaboutaffordability,andtheUnitedNations’declarationthataccesstowaterisahu-

manright(UNGeneralAssembly,

2010),waterpricestypicallydonotreflectthetruecostof

service(Hanemann,

1997;

Timmins,

2002b;

Olmstead,

2010)

.Failuretorecovercostscanprevent

utilitiesfrominvestingininfrastructureandmaintainingservicequality(McRae,

2015)

.Evenindevelopedcountries,poorfiscalmanagementcanresultincatastrophicconsequences,suchas

recentservicefailuresinJackson,MS,1

orFlint,MI(Christensenetal.,

2023)

.Efficiencysuggeststhatpricesshouldequallong-runmarginalcostsofprovision,bututilities—–largelyoperatedbyfinanciallyandpoliticallyconstrainedmunicipalgovernments—–needtobalanceequityconsid-erationswithrevenueneedsandclearmarketsignals

.2

Inbalancingthesegoals,utilitiesoften

adoptnonlinearratestructuresthatdiscountmarginalpricesforlowlevelsofconsumption(Olm-

steadetal.,

2007;

Szabo,

2015;

WangandWolak,

2022;

AllaireandDinar,

2022),althoughthese

pricingdecisionsmaygenerateallocativeinefficiencies(Borenstein,

2012,

2016;

Borensteinand

Davis,

2012),requiresubsidizationfromalternativemunicipalrevenuesources(Timmins,

2002a;

Renzetti,

1999),andineffectivelyredistributeincome(LevinsonandSilva,

2022;

Wietelmanetal.,

2024)

.

Ievaluatetheextenttowhichprevailingwaterpricesdeviatefromeconomicallyoptimalrates,whatdrivesthoseinefficiencies,andwhatimplicationsmispricedwaterserviceshaveonsocialwelfareandutilityrevenue.Ifirstrevisitclassictheoryontwo-partpricinginthespiritof

Coase

(1946),butIrefocusthisframeworkoncontemporaryissuesinmunicipalwaterandwastewater

pricing.Theframeworkdemonstratesthecanonicalefficiencyresultthatpriceshouldequalmarginalcost.However,unlikerecentresearchconcerningincreasing-blockrate(IBR)pricing

forprivate,regulatedelectricutilities(LevinsonandSilva,

2022),municipalmanagerscanrelax

theutility’sbudgetconstraintviaintragovernmentaltransfers.Inpractice,utilitiesoftenrundeficits(subsidizingwaterservicefromgeneralfundrevenue)orsurpluses(fundingotherlocalpublicgoodsthroughwaterrates),soassumingthatthezero-profitconditionholdsisrestrictive.Relaxingthisconstraintallowsmunicipalitiestodrawfromalternativesourcesofrevenuetorecoverfixedcosts.Fixedhouseholdservicefeesforwaterandwastewater—often$250–350peryearorapproximately40–50percentofwaterexpenditures—operateaslump-sumtaxesonhouseholds,whichislikelythemostregressiveformofrevenueraisedbylocalgovernments

.3

1See,forexample,

/news/2023/06/28/timeline-jackson-mississippi-water-problems.

(accessedJune19,2024).

2Approximately150,000USwatersystemsintheUnitedStatesprovidewaterandwastewaterservicesto90

percentoftheUSpopulation;thevastmajorityofthesearepubliclyowned(/dwreginfo/

information-about-public-water-systems)

.

3Fixedaccessfeesdonotvarybyincome.Propertyandsalestaxes,thetwomostlikelysourcesofmunicipalrevenue,arealsoregressive,butconsumptionandpropertyvaluestendtoincrease,albeitlessthanproportionally,withincome.

2

Waterutilitiesthatcareaboutequitycansetthevolumetricrateequaltomarginalcostand,todealwithredistributionandrecoupfixedcosts,theycansetanindividualizedfixedmonthlyservicefeethattargetsdifferencesinincome(e.g.,bysettingservicefeesproportionaltopropertyvalues)orrelyonlessregressivesourcesofmunicipalrevenue.

Empirically,Iexplorewhetherwaterpricesdeviatefromoptimaltwo-parttariffsusingmorethanadecadeofannualdataonutilityratestructuresandmunicipalfinanceinformationformorethan700utilitiesintheSoutheasternUnitedStates

.4

Iprovideevidencethatutilitiesfailtobalancetheirbudgetexactlyand,onaverage,pricewaterbelowaveragecost.Usingvariationinoperatingexpendituresovertimeandacrossutilitiesinsimilarhydrologicregions,Iestimatemarginalcostsforwaterandwastewaterservicesandusetheseestimatestoevaluatehowmuchutilitiesdiscountormarkupwaterrates,accountingfornonlinearitiesintheratestructure.ThepredominantratestructuresareIBRsanduniformratesthatincludeanallocationofwateratzeromarginalprice(“uniform+free”),bothofwhichdiscountvolumetricpricesseverelyforlowlevelsofuse,accountingfornearlyhalfoftheconsumptiondistribution.ThemedianpricediscountforutilitieswithIBRsinthefirsttier(0–3kgal/month)isapproximately34percent,withpricesinhighertiersmarkedupby5–27percentabovemarginalcost.Themedianutilitythatprovidesanallocationoffreewaterinitsuniformratestructurediscountspricesby65percentinthefirsttier,withapproximatelymarginal-costpricinginhighertiers.Utilitieswithpurelyuniformratespricewater,onaverage,closetomarginalcost.

Whydoutilitiessubsidizeasubstantialportionofconsumptionthroughdiscountedmarginalprices?Commonexplanationsarethatthemanagersareinfluencedbypoliticalpressuretokeep

priceslow(Timmins,

2002b)andprovidebasicwaterserviceatlowcostforlow-incomecus

-

tomers(Szabo,

2015),despitemaintainingalump-sumtransferinstrumentonthebillthatcan

addressequityand/oraffordabilityconcernsmoredirectlyandmoreeffectively.Iexplorethefactorsassociatedwithinefficientpricingbycomparingwaterratesandmarkupsacrossutili-tiesinsimilarhydrologicregions.Severalresultsemerge.First,volumetricsubsidiesaremuchmorecommoninsmallerutilities,whichhavehigheraveragecostsofservice;theirinabilitytocapitalizeoneconomiesofscalereducesthelikelihoodofpassingthefullcoststhroughtocus-tomers.Second,volumetricpricesarelowerandmoreheavilydiscountedforutilitieswithlargerlow-incomepopulations,whichisnotablebecauseitrevealsanefficiency–equitytrade-off:theseutilitiesaremorelikelytosubsidizevolumetricpricesratherthanalterthefixedservicefeeorcoverfixedcostsviamunicipalrevenue.Third,waterratesandmarkupsarelargerforcommu-nitieswithnewerhomes,morerenters,andahigherproportionofnon-Whiteresidents.Fourth,greaterhistoricaldroughtintensityincreasesvolumetricpricesbutnotmarkups,indicatingthatscarcityispotentiallypricedintowaterratesviahighermarginalcosts.Furthermore,Ishowthat

4MysampleincludesthevastmajorityofutilitiesinGeorgiaandNorthCarolina,whicharetheeighthandninthmostpopulousstates,respectively.Combined,theirpopulation(~21M)wouldrepresentthefourthlargeststate,afterCalifornia(~39M),Texas(~31M),andFlorida(~23M),comprising6–7percentoftheUSpopulation.Intermsofeconomicoutput,NorthCarolina’sGDPin2023was$626B,andGeorgia’swas$661;combined,theywouldbecomparabletoIndonesia,theNetherlands,Turkey,andSaudiArabiainworldeconomicoutput.

3

thesepricingdecisionsareconsequentialforutilityoperations:decreasesinfixedfeesandinvolumetricpricesinthelowesttierincreasethelikelihoodthatautilityfailstocoveritscosts.

Next,Iestimaterevenueelasticities,whichindirectlyrevealspriceelasticitiesofdemand,leveragingyear-to-yearvariationintheutility-levelpaneldataonrevenuesandratechanges.Iadoptaninstrumental-variable(IV)strategytoaccountfornonlinearratestructuresandpo-tentiallyendogenousratechangesusingratestructurecharacteristicsfromneighboringutilities.Theestimatedrevenueelasticitiessuggestthatforevery10percentincreaseinvolumetricprices,revenuesincreasebyapproximately4–5percent,whichimpliespriceelasticityestimatesof−0.5to−0.6.Usingtheseelasticitiesandtheestimatedmarginalcosts,Isimulaterevenueandsocialwelfareimplicationsofadoptingefficientpricing.Manyutilitiescanincreaserevenuebypricingatmarginalcost,whichislargelyadirectsurplustransferfromconsumers.Inmostcases,thatsurplusdeclinesduetoremovaloftheinframarginalvolumetricsubsidyimplicitinthenonlinearratestructures.Whetherconsumptionincreasesordecreasesdependsonthepresumedmodelofpriceperceptionandthewedgebetweenpricesandmarginalcosts.Marginalpricesaregenerallycloseto,orslightlylargerthan,marginalcost,whichimpliesthatconsumptionincreasesslightly

ifconsumersrespondtomarginalprice(Olmsteadetal.,

2007;

NatarajandHanemann,

2011)

.Forutilitieswithnonlinearratestructures,averagevolumetricpricestendtofallbelowmarginalcostsduetoinframarginaldiscounts,soconsumptiondecreasesifconsumersrespondtoaver-

ageprice(Ito,

2014;

Wichman,

2014;

BrentandWard,

2019;

Shaffer,

2020)

.Regardlessofpriceperception,nonlinearratesgenerateallocativeinefficiencies,whicharealleviatedbymarginal-costpricing.Forthemedianutility,marginal-costpricingeliminatesdeadweightlossandraisesrevenue,whichalmostoffsetsconsumersurpluslosses.Althoughthisispurelyanefficiencyresult,therevenuegainscanbeusedtoadvancedistributionalgoals,byeitheradoptinglower(orprogressive)fixedfeesorleveragingalternative,lessregressivesourcesofmunicipalrevenuetorecoverfixedcosts.

Thispapermakesseveralcontributionstoourunderstandingofinefficienciesinutilitypric-ing.Igeneratenewinsightsonnaturalmonopolypricingthatbalancesequity–efficiencytrade-offsanddocumentwidespreadpricinginefficienciesinthemunicipalwatersector.Thispaperaddstoalong-standinglineofinquiryonoptimalpricingformunicipalutilityservices,someofwhichisfocusedontheredistributionalimplicationsofnonlinearrates(e.g.,

Borenstein,

2012;

BorensteinandDavis,

2012;

LevinsonandSilva,

2022;

BorensteinandBushnell,

2022)

.Mostre-searchonwaterpricingadoptsmodelingframeworksfromenergypricing,butwaterutilitiesaredistinctfromenergyutilitiesinseveralimportantways.First,theytypicallyjointlymanageproduction,distribution,andtreatment,whichisatypicalofenergyutilities.Relatedly,becauseoftheprohibitivecostsofmovingwaterlongdistances,waterutilitiesaresmallerandmanagedmuchmorelocally.Bothofthesefactorslimittheirabilitytobenefitfromscaleeconomies

.5

Asaresult,percapitafixedcostsofwaterservice(and,hence,fixedcharges)arerelativelylarge

5Toemphasizethispoint,Georgiahas52municipallyownedelectricutilities,41electricmembershipcorporations,andoneinvestor-ownedutilitythatoperatesin155ofits159counties(source:

/utilities/

electric/)

.Bycontrast,Ianalyze382municipalwaterutilitiesinGeorgiathatserve,onaverage,5,000customers.

4

anddeservemoreexplicitattentioninwaterpricing.Second,waterutilitiesareoverwhelminglyoperatedbymunicipalgovernments,soratesareregulatedindirectlybyvotersandtypicallynotbyautilitycommission

.6

Thisstructureallowsutilitiestotapintoalternativesourcesofmunicipalrevenue,whicharelessregressivethanafixedlump-sumtaxtorecoverfixedcosts.Third,waterserviceprovidesmanylocalpublicgoods,suchaswaterprovisionforfireprotectionandstormwaterinfrastructureforfloodprotection,thatarefundedthroughutilitybillsandcan

rationalizemunicipalsubsidies(Beecher,

2020)

.

Thispaperalsocontributestoourunderstandingofnonlinearpricingforutilityservices.SeveralstudiesexploretheeffectsofIBRsforelectricity,naturalgas,andwateruseatthehouse-holdlevel(e.g.,

ReissandWhite,

2005;

Olmsteadetal.,

2007;

NatarajandHanemann,

2011;

Ito,

2014;

Wichman,

2014;

Szabo,

2015),butlittleworkhasfocusedonutility-wideconsequences,es

-peciallyforwaterandwastewaterservices

.7

Nonlinearratesarebeingincreasinglyadoptedforwater,largelyunderthebannerofachievingconservationandreducingburdensonlow-incomecustomers.ThisresearchhaslargelyfocusedonIBRs,butIadditionallyhighlightacommonhiddeninefficiencyinutilitypricingdecisions:manyutilitiespossessratestructuresthatembedanallocationoffreeconsumption(onaverage,1–3kgal/monthpercustomer).Thesenonlinearvolumetricratestructuresdonotreflectcosts,oftenrequiresubsidizationfromotherrevenuesources,andcanleadtosuboptimalconsumptionbydrivingawedgebetween(infra-)marginalpricesandmarginalcosts.Ishowthatuniform,marginal-costpricingcaneliminateallocativeinefficienciesandincreaserevenuebyremovingvolumetricsubsidies,whichcouldbeused,inprinciple,tolowerfixedfeesoroffsetthemwithlessregressivesourcesofmunicipalrevenue.

Last,comparativeanalysesofwaterutilitiesarerarebecausenocentralizedrepositoryofdatalinkswaterratestructureswithmunicipalrevenueandcostinformationforthesameutilitiesovertime.Mostresearchonmunicipalwaterpricingevaluatesconsumerresponsestopriceandratestructurechangesusingbillingdata—typicallyfocusingononeorasmallsetofutilities—withthegoalofestimatingpriceelasticitiesofdemand(e.g.,

Olmsteadetal.,

2007;

Olmstead,

2009;

MansurandOlmstead,

2012;

Baerenklauetal.,

2014;

Wichmanetal.,

2016;

El-Khattabietal.,

2021;

Smith,

2022)

.Incontrast,Icharacterizetheefficiencycostsofprevailingwaterpricingpracticesusingadecadeofwaterandwastewaterratestructuresmatchedwithadministrativedataonmunicipalfinancesformorethan700municipalutilities.Tomyknowledge,thedataassembledinthispaperisthemostextensivepaneldatasetofwaterutilityratestructureslinkedwithutilitycostsandrevenues.Thesedataallowmetoestimatemarginalcostsandcompareratestructure

characteristicsacrossutilitiesinvariedgeographicregions(i.e.,coastal,mountainous,urban,

6Privateorfor-profitbutnotmunicipalwaterutilitiesaretypicallyregulatedbystateutilitycommissions.

7ResearchhasaddressedthecomplicationsofIBRsbecausetheygeneratekinksinconsumerbudgetconstraints

(Hanemann,

1984)

.Structuraldiscrete-continuouschoicemodelshavebeenappliedtoestimatepriceelasticitiesofdemandforwaterandelectricity(e.g.,

HewittandHanemann,

1995;

Olmsteadetal.,

2007;

Olmstead,

2009;

Baerenklau

etal.,

2014;

Szabo,

2015;

McRae,

2015)

.However,researchershavealsoquestionedwhetherconsumersunderstandnonlinearratestructuresandprovidedevidence,forbothelectricityandwater,thatconsumersmightrespondto

average,ratherthanmarginal,prices(Ito,

2014;

Wichman,

2014;

BrentandWard,

2019;

Shaffer,

2020)

.Othershave

arguedthatconsumersdorespondtomarginalpriceifthechangesarelargeenough(NatarajandHanemann,

2011)

.

5

rural)andwithheterogeneousservicepopulations.Importantly,thedatasetincludeshundredsofsmall-andmedium-sizedwaterutilitiesthatarerarelyevaluatedineconomicsresearchdespitetheircentralroleindeliveringessentialservicestoresidentsoutsideoflargemetropolitanareas.

Renzetti

(1992),

Renzetti

(1999),and

Timmins

(2002b)areamongthefewpapersthatevaluate

theefficiencyconsequencesofmunicipalwater(andwastewater)prices,buttheyarebasedonnow-outdateddatasetswithlimitedgeographicortemporalscopeanddonotaccountfortherecent,increasingprevalenceofnonlinearratestructuresdespitethetrade-offsinherentinfixedversusvolumetricpricingdecisions.

2Conceptualframework

Inthissection,Ilayoutamodelofrate-settingformunicipalwaterutilities.Myapproachadoptsthegeneralframeworkof

LevinsonandSilva

(2022),whichanalyzestheredistributivepotential

ofnonlinearelectricitypricingbyextendingaformalmodelof

Coase

(1946),butIrefocusiton

theparticularsofmunicipalwaterandwastewaterutilities.

2.1Thehousehold’sproblem

Considerahouseholdthatmaximizesutilityoverwaterconsumption,wi,andanumerairegoodxi,wheresuperscriptsindexhouseholds(i=1,...,n).ThehouseholdearnsincomeMi,whichissubjecttoamarginaltaxrateofτ≥0andalump-sumgovernmenttransfergi(bothofwhichthehouseholdtakesasgiven).Thehouseholdspendsincomeonwater(atmarginalpricepwithafixedservicefeet≥0)andthenumerairegood(withpricenormalizedto1)inthepresentperiod,

leadingtothebudgetconstraintpwi+t+x=(1−τ)Mi+gi.Leti≡(1−τ)Mi+gi−ti

representafter-taxresidualincome.Thehousehold’sproblembecomes

maxui(wi,i−pwi).(1)

wiThehousehold’sfirst-orderconditionis

Thisconditionimplicitlydefinesdemandforwaterandthenumerairegood:wi(p,i)andxi(p,i)=−pwi(p,i).Pluggingthesedemandequationsintotheutilityfunctionresultsinthefollowingindirectutilityfunction:vi(p,i)=u(wi(p,i),xi(p,i))foralli=1,...,n.

2.2Thegovernment’sproblem

Thegovernmentchoosesprices,fixedfees,andmarginaltaxratestomaximizethesumofindirectutilityhouseholdsreceive.Itsroleisthefirstpointofdeparturefrom

LevinsonandSilva

(2022)

6

becausethemajorityofUSwaterutilitiesarepublicentitiesownedandoperatedbymunicipalgovernments;theyarelargelynotprivate,regulatednaturalmonopolies,suchasnaturalgasorelectricutilities.Thisdistinctionhasimportantimplicationsforbudgetbalancingandfixed-costrecoverythatIexploredirectly.

ThegovernmentmanagesawaterutilitythathasfixedcostsFandper-unitcostsc.So,thegovernment’stotalcostofsupplyingW=ΣiwiunitsofwaterisF+cΣiwi.Thegovernmentmustbalanceitsbudgeteachyear,resultinginthefollowingbudgetconstraint:

whereG=Σigiaretotalgovernmentaltransfers.Theleft-handsideofthisequationisgovern-mentalrevenue;theright-handsideisgovernmentalexpenditure.

2.2.1Aself-sufficientwaterutility

First,assumethegovernmentchoosespandtbuttreatsτasfixedandexogenousandthatτΣiMi=G,sothatitfocusesonlyonbalancingrevenueandcosts.ThisresultsinthesimplerbudgetconstraintΣi[t+pwi−cwi]=F,whichreducestothebaselinecasein

Levinsonand

Silva

(2022)

.Thesolution,outlinedindetailin

AppendixA,providesthecanonicalresultthat

priceshouldbesetequaltomarginalcost(p=c).Substitutingthisresultintothegovernment’sbudgetconstraintresultsinsettingfixedfeesequaltoaveragefixedcosts,or,t=F/n.

Ifthegovernmentcaninsteadsetindividualizedprices,pi—whichmightreflectpricediscrim-inationacrosscustomersorheterogeneousmarginalpricesacrosstheconsumptiondistribution(i.e.,IBRs)—theprimaryinsightdoesnotchange.Theoptimalpricingrulewhenindividualizedpricesarefeasibleresultsintheconditionthatpi=cforalli,orthatallunitsofconsumptionshouldbechargedthesamemarginalprice.Thisresult—thatmarginalpriceshouldbeequalacrosscustomersanduses—shouldbeuncontroversialtoeconomistsandsuggeststhatanypric-ingstructurethatdeviatesfrommarginal-costpricingwillbeinefficient.

Borenstein

(2012)claims

thatIBRsforelectricityhavenocostbasis,asIBRsassigndifferentmarginalpricestodifferent

customers,leadingtodifferentincentivestoconsumewater.8

LevinsonandSilva

(2022)additionallyshowthatifthegovernmentcaresaboutequityand

cansetindividualizedfixedservicefeesandmarginalprices,thenmarginalpriceshouldstillbesettoequaltomarginalcost,forallhouseholdsanduses,andthefeeusedtoredistributeincomecompletely(i.e.,ifhouseholdsdifferonlyintheirincomes,thenitwillbeusedtoequalizeincomeacrossallhouseholds).Ofcourse,fullyredistributingincomethroughautilitybillisanimpracti-calresult,althoughmilderversionsofthissolutionmayaidinredistributionwithoutsacrificing

efficiency.9

LevinsonandSilvausethisasapointofdeparturefromoptimaltwo-parttariffsto

8Hanemann

(1997),however,arguesthatIBRscouldbesupportedbyacostargument,inasmuchasblockrate

structures